-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '193426863523529205827188716495,439494015200559894639143278553,545953404415572843696792945240,802480990601106978280541897092,1123377577896619335956716516087,1172501321415742493442344177052,1246199920243221362470633723014,1478333037524889129713394922538,1484004269274988131109145730022,1507491914519545665937449600801,1553568910763570360456978195876,1596545965614742990109085064173,1729302209692817691796898479554,1860173680510249316601594616932,2241241661353087129236355270974,2650815637450856802693415901074', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -4, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2494.0212030618445, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[3, [1]], [11, [1]]], 'bad_primes': [3, 11], 'central_character': '3267.1', 'coefficient_field': '1.1.1.1', 'conductor': 168417087089595893335914666294701590604740371451720604481, 'conductor_radical': 33, 'degree': 32, 'euler_factors': [[1, 0, 4, 0, 10, 0, 20, 0, 35, 0, 52, 0, 68, 0, 80, 0, 85, 0, 80, 0, 68, 0, 52, 0, 35, 0, 20, 0, 10, 0, 4, 0, 1], [1], [1, 0, -4, 0, 10, 0, -20, 0, 35, 0, -52, 0, 68, 0, -80, 0, 85, 0, -80, 0, 68, 0, -52, 0, 35, 0, -20, 0, 10, 0, -4, 0, 1], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], [1], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], [1, 0, 4, 0, 10, 0, 20, 0, 35, 0, 52, 0, 68, 0, 80, 0, 85, 0, 80, 0, 68, 0, 52, 0, 35, 0, 20, 0, 10, 0, 4, 0, 1], [1, 0, 0, 0, -2, 0, 0, 0, 3, 0, 0, 0, -4, 0, 0, 0, 5, 0, 0, 0, -4, 0, 0, 0, 3, 0, 0, 0, -2, 0, 0, 0, 1], [1, 0, 16, 0, 120, 0, 560, 0, 1820, 0, 4368, 0, 8008, 0, 11440, 0, 12870, 0, 11440, 0, 8008, 0, 4368, 0, 1820, 0, 560, 0, 120, 0, 16, 0, 1], [1, 0, 4, 0, 10, 0, 20, 0, 35, 0, 52, 0, 68, 0, 80, 0, 85, 0, 80, 0, 68, 0, 52, 0, 35, 0, 20, 0, 10, 0, 4, 0, 1], [1, 0, 2, 0, 1, 0, -2, 0, -4, 0, -4, 0, -1, 0, 4, 0, 7, 0, 4, 0, -1, 0, -4, 0, -4, 0, -2, 0, 1, 0, 2, 0, 1], [1, 0, -4, 0, 10, 0, -20, 0, 35, 0, -52, 0, 68, 0, -80, 0, 85, 0, -80, 0, 68, 0, -52, 0, 35, 0, -20, 0, 10, 0, -4, 0, 1], [1, 0, 4, 0, 10, 0, 20, 0, 35, 0, 52, 0, 68, 0, 80, 0, 85, 0, 80, 0, 68, 0, 52, 0, 35, 0, 20, 0, 10, 0, 4, 0, 1], [1, 0, 0, 0, 8, 0, 0, 0, 28, 0, 0, 0, 56, 0, 0, 0, 70, 0, 0, 0, 56, 0, 0, 0, 28, 0, 0, 0, 8, 0, 0, 0, 1], [1, 0, -4, 0, 10, 0, -20, 0, 35, 0, -52, 0, 68, 0, -80, 0, 85, 0, -80, 0, 68, 0, -52, 0, 35, 0, -20, 0, 10, 0, -4, 0, 1], [1, 0, -4, 0, 10, 0, -20, 0, 35, 0, -52, 0, 68, 0, -80, 0, 85, 0, -80, 0, 68, 0, -52, 0, 35, 0, -20, 0, 10, 0, -4, 0, 1], [1, 0, -4, 0, 10, 0, -20, 0, 35, 0, -52, 0, 68, 0, -80, 0, 85, 0, -80, 0, 68, 0, -52, 0, 35, 0, -20, 0, 10, 0, -4, 0, 1], [1, 0, 0, 0, -2, 0, 0, 0, 3, 0, 0, 0, -4, 0, 0, 0, 5, 0, 0, 0, -4, 0, 0, 0, 3, 0, 0, 0, -2, 0, 0, 0, 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, -4, 0, 10, 0, -20, 0, 35, 0, -52, 0, 68, 0, -80, 0, 85, 0, -80, 0, 68, 0, -52, 0, 35, 0, -20, 0, 10, 0, -4, 0, 1], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], [1, 0, 4, 0, 10, 0, 20, 0, 35, 0, 52, 0, 68, 0, 80, 0, 85, 0, 80, 0, 68, 0, 52, 0, 35, 0, 20, 0, 10, 0, 4, 0, 1], [1, 0, 16, 0, 120, 0, 560, 0, 1820, 0, 4368, 0, 8008, 0, 11440, 0, 12870, 0, 11440, 0, 8008, 0, 4368, 0, 1820, 0, 560, 0, 120, 0, 16, 0, 1], [1, 4, 6, 0, -15, -28, -22, 12, 60, 80, 36, -56, -129, -120, -20, 108, 167, 108, -20, -120, -129, -56, 36, 80, 60, 12, -22, -28, -15, 0, 6, 4, 1], [1, 0, 4, 0, 10, 0, 20, 0, 35, 0, 52, 0, 68, 0, 80, 0, 85, 0, 80, 0, 68, 0, 52, 0, 35, 0, 20, 0, 10, 0, 4, 0, 1], [1, 4, 6, 0, -15, -28, -22, 12, 60, 80, 36, -56, -129, -120, -20, 108, 167, 108, -20, -120, -129, -56, 36, 80, 60, 12, -22, -28, -15, 0, 6, 4, 1], [1, 0, 4, 0, 10, 0, 20, 0, 35, 0, 52, 0, 68, 0, 80, 0, 85, 0, 80, 0, 68, 0, 52, 0, 35, 0, 20, 0, 10, 0, 4, 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, 10, 0, -20, 0, 35, 0, -52, 0, 68, 0, -80, 0, 85, 0, -80, 0, 68, 0, -52, 0, 35, 0, -20, 0, 10, 0, -4, 0, 1]], 'euler_factors_factorization': [[[[1, -1, 1, -1, 1], 4], [[1, 1, 1, 1, 1], 4]], [1], [[[1, 0, -1, 0, 1, 0, -1, 0, 1], 4]], [[[1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], 1]], [1], [[[1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], 1]], [[[1, -1, 1, -1, 1], 4], [[1, 1, 1, 1, 1], 4]], [[[1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], 2]], [[[1, 0, 1], 16]], [[[1, -1, 1, -1, 1], 4], [[1, 1, 1, 1, 1], 4]], [[[1, 0, 1, 0, 0, 0, -1, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1], 2]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1], 4]], [[[1, -1, 1, -1, 1], 4], [[1, 1, 1, 1, 1], 4]], [[[1, 0, 0, 0, 1], 8]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1], 4]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1], 4]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1], 4]], [[[1, 0, 0, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, 0, 0, 1], 2]], [[[1, 0, -1, 0, 1], 8]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1], 4]], [[[1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], 1]], [[[1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], 1]], [[[1, -1, 1, -1, 1], 4], [[1, 1, 1, 1, 1], 4]], [[[1, 0, 1], 16]], [[[1, 1, 0, -1, -1, -1, 0, 1, 1], 4]], [[[1, -1, 1, -1, 1], 4], [[1, 1, 1, 1, 1], 4]], [[[1, 1, 0, -1, -1, -1, 0, 1, 1], 4]], [[[1, -1, 1, -1, 1], 4], [[1, 1, 1, 1, 1], 4]], [[[1, 0, 0, 0, -1, 0, 0, 0, 1], 4]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1], 4]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 0, 'label': '32-3267e16-1.1-c0e16-0-0', 'leading_term': '0.11085646026352822421162732890677286839833540430234281130707864802299876304979832543584156', '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/3267/1/l/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.003662109375', 'prec': 47}, 'plot_values': [0.11085646026352818, 0.11098558822907904, 0.11095143609829208, 0.11075786237004091, 0.1104088476665901, 0.10990845168827672, 0.10926077188103696, 0.10846990388097932, 0.10753990377226726, 0.10647475216870259, 0.10527832010562845, 0.10395433670710309, 0.10250635857370974, 0.10093774081882662, 0.09925160783555836, 0.09744972159475104, 0.09553064347755408, 0.09349214776192992, 0.09133130730802377, 0.08904507342295043, 0.0866304708144802, 0.08408462231183547, 0.08140477500301184, 0.07858832782679567, 0.0756328606486194, 0.07253616483923984, 0.06929627536384855, 0.0659115043765551, 0.062380479297849886, 0.0587024794351456, 0.05487769684524208, 0.05090673000229902, 0.046790549134083474, 0.04253053029601132, 0.03812849499262099, 0.033586721482774425, 0.02890797174364554, 0.024095524568723773, 0.019153209338956707, 0.014085440366969813, 0.008897251698227202, 0.003594332235633672, -0.0018169387965370964, -0.0073294420685019596, -0.012935239212195975, -0.018625522902310145, -0.024390580678731084, -0.03021976045628049, -0.03610143805945122, -0.042022975752760774, -0.04797064866783891, -0.05392963495987153, -0.05988400607731593, -0.06581671367144754, -0.07170958218094464, -0.07754330777822754, -0.08329746051016082, -0.08895042845862447, -0.09447946055685172, -0.09986077424886303, -0.105069603467012, -0.11008025496086503, -0.1148661764875598, -0.11940003768758027, -0.12365382446877712, -0.12759893044540885, -0.13120622612426683, -0.13444624693663246, -0.1372893694375203, -0.1397059887501411, -0.14166671332300898, -0.14314257666895555, -0.14410529948800252, -0.14452755932956562, -0.14438326568059187, -0.14364785415929615, -0.14229859982206672, -0.14031494923892038, -0.1376788708009272, -0.1343752225135368, -0.13039213630254623, -0.12572140310757846, -0.12035884853052035, -0.11430481374193548, -0.10756463007436876, -0.10014919546480083, -0.09207535706357167, -0.0833662933593425, -0.0740519521844263, -0.06416948130198308, -0.053763647039822254, -0.042887236382368604, -0.03160143758801799, -0.01997619406182176, -0.008090525887175449, 0.003967186890722164, 0.016098965427771075, 0.0281970420091886, 0.04014368922060173, 0.051811067326351684, 0.06306137898263622, 0.07374702441931896, 0.08371079692868205, 0.09278617226448808, 0.10079769866174118, 0.10756149396133183, 0.1128858560268535, 0.11657199225712148, 0.1184148735221555, 0.11820421727781866, 0.11572560394069155, 0.11076172983817001, 0.1030938559053014, 0.09250352807153256, 0.07877419193648164, 0.06169300590590381, 0.041052799319226, 0.01665415259275591, -0.011692400946014708, -0.044164059221985054, -0.08092333096765884, -0.12211552183623058, -0.1678661400676372, -0.21827823657495266, -0.2734296962195502, -0.33337049795520235, -0.3981197518611039, -0.4676626885880248, -0.5419483982879232, -0.6208873053099216, -0.7043486227606174, -0.7921580340244709, -0.8840955220521955, -0.9798933756834486, -1.0792344197895345, -1.1817505019449508, -1.2870212686202263, -1.3945732638764872, -1.5038793832098227, -1.6143587136726252, -1.725376787376879, -1.836246535495526, -1.946229769040481, -2.054538975108119, -2.160339621466164, -2.2627529640273876, -2.360859326630865, -2.4537021418100333, -2.5402925055350294, -2.619614265984128, -2.690629672504246, -2.7522855736535434, -2.803520147308019, -2.8432701803401357, -2.87047996432397, -2.8841100927488297, -2.8831451318633747, -2.866602468064339, -2.833541478562556, -2.783072905446411, -2.7143683624223787, -2.626669893094641, -2.519299497323051, -2.3916685767610084, -2.2432871642135734, -2.0737728503093384, -1.8828593157540414, -1.6704045533142378, -1.4364009394756698, -1.1809815378727566, -0.9044239024254636, -0.6071548575314099, -0.28975432150784597, 0.047041966390989634, 0.4023408958199158, 0.7750916851239019, 1.1640868955809396, 1.5679648311927736, 1.9852134196647118, 2.414175472263803, 2.8530553917917407, 3.299927116101788, 3.7527420457466376, 4.20934197285993, 4.667473174722256, 5.124800487201975, 5.578922604371463, 6.027388520628631, 6.467715003213568, 6.897404967469673, 7.313966612338303, 7.714933159600938, 8.097883027499394, 8.46046044639277, 8.800396578436741, 9.115529782758623, 9.403827908344354, 9.66340759898067, 9.892552303008339, 10.089729814440753, 10.253608559868583, 10.383072426488107, 10.477233936721095, 10.535445586457087, 10.557309178077347, 10.54268299604952, 10.491686691911362, 10.404703766757333, 10.282381562731743, 10.125630804030394, 9.935626984703864, 9.713796492597345, 9.46180377088407, 9.181537968016537, 8.875097147374872, 8.544770181933801, 8.193016489580563, 7.822443794001661, 7.4357841239039875, 7.035868289335175, 6.62559909761953, 6.207923592544415, 5.78580462252854, 5.36219438163623, 4.940008935165501, 4.522093692278227, 4.111194674313396, 3.709930536303275, 3.320766653607245, 2.9459911842523967, 2.5876931556926435, 2.247742860962081, 1.9277748236927912, 1.6291735619188652, 1.3530623473037984, 1.1002951197780542, 0.8714516890469108, 0.6668372549984746, 0.48648435797465794, 0.3301558234063649, 0.197353376488003, 0.08732978037334456, -0.0008959614928569534, -0.06852054164699534, -0.11693552333374059, -0.14770414164254567, -0.1625360765112249, -0.163260553533487, -0.1517981551334048, -0.13013174593558854, -0.10027693647020446, -0.06425271247512346, -0.024052374725891414, 0.018385182951222885, 0.061202821898386134, 0.10265081122914073, 0.14111041632098875, 0.1751150874270265, 0.20336897013266597, 0.22476232921224232, 0.23838372794932025, 0.24352881359354964, 0.2397055870701376, 0.22663610118608915, 0.20425459927217351, 0.1727023542750635, 0.13231908565072448, 0.08363086316006635, 0.02733507100373591, -0.035717330472297, -0.10454191137949193, -0.1780428676471645, -0.25503669100707504, -0.33427700974235514, -0.414480253883979, -0.49435135896220556, -0.5726091533371929, -0.6480110060275196, -0.7193762411554824, -0.7856077548975511, -0.8457120228035778, -0.898816699032951, -0.9441853000866344, -0.9812289055854069, -1.009514684657124, -1.0287711180919157, -1.038889853865088, -1.0399242026221422, -1.032084348884172, -1.0157295842076857, -0.9913579306635317, -0.9595920929300417, -0.9211634257652584, -0.8768944134490932, -0.8276790387391045, -0.7744620467425007, -0.718217770861054, -0.6599288476849008, -0.6005653104394977, -0.5410645404981891, -0.482312534412396, -0.42512691102474703, -0.37024204008868383, -0.3182966212367096, -0.2698239811683818, -0.225245352354397, -0.1848662977513304, -0.14887588003844363, -0.11734877585406031, -0.0902506237474813, -0.06744622800222806, -0.04871025905613109, -0.03374010738312583, -0.022170485880605384, -0.013589323645740052, -0.007554453157043886, -0.003610564699285992, -0.00130588751637262, -0.00020805748677065044, 8.135340103034137e-05, -8.58602234795852e-05, -0.00041495282374473373, -0.0006759805427931421, -0.0007085803892370346, -0.0004235284867280695, 0.00019905584340904436, 0.001114881229166854, 0.002223940334688211, 0.0033820461928813906, 0.0044151299382548664, 0.00513587033287639, 0.005362121323453931, 0.00493650954185813, 0.0037464923196705805, 0.0017441018401464351, -0.001035450996360629, -0.004457167405464068, -0.008272480011062604, -0.012109112048018865, -0.015465435823947557, -0.017709973211038333, -0.01808662994982894, -0.015726135749569065, -0.009664002005437376, 0.001134865446265179, 0.01774495379939676, 0.04124259349463763, 0.07266255033785507, 0.1129494142899215, 0.16290480317250236, 0.22313164062390597, 0.2939766792016285, 0.3754728554690435, 0.46728311308472875, 0.5686473718817425, 0.6783351377138834, 0.7946053810193943, 0.9151756471629153, 1.0372023928417617, 1.1572743986626215, 1.2714209582392932, 1.375136367038525, 1.4634227443447398, 1.5308511343278386, 1.5716404609178822, 1.5797560329155031, 1.5490268386829618, 1.4732808126223251, 1.346496795966297, 1.1629713412638865, 0.9174981340270325, 0.6055578030238558, 0.2235140202172679, -0.23118765683216766, -0.7598222149674201, -1.3621932236199317, -2.036450201821486, -2.7789241094424586, -3.5839838796329264, -4.443916849365567, -5.348839198395587, -6.286640962393878, -7.242969792929053, -8.201257163763636, -9.142790137421935, -10.046830934005083, -10.890785737425736, -11.650424999437263, -12.300153633452604, -12.813330800518845, -13.162643505658249, -13.32051380386845, -13.259541016099144, -12.95297967148627, -12.375243095791252, -11.50242496641533, -10.312830331002726, -8.787506840391748, -6.910766337676323, -4.6706864938467, -2.059581905274784, 0.925566020605189, 4.282731133449973, 8.004527511259871, 12.07797417800357, 16.484344205551242, 21.19909598059657, 26.19189845612323, 31.426756085053697, 36.86223680380659, 42.45180468571238, 48.14425701262468, 53.88426354859237, 59.61300377604427, 65.26889580936349, 70.78840867201993, 76.10694765219189, 81.159828106128, 85.88336674139512, 90.21584901038723, 94.09853992432676, 97.47671300091739, 100.30065525519903, 102.52662932147051, 104.1177737664909, 105.04492298594047, 105.28732877625902, 104.83326674455357, 103.68051215510755, 101.83667159955945, 99.31935910406125, 96.15627066382665, 92.38512469780834, 88.0531711341572, 83.21664723331997, 77.94007265961602, 72.29538739956075, 66.36093912018347, 60.22033015969602, 53.96114053223358, 47.673546175978714, 41.448854251628056, 35.377979546508804, 29.54988790377545, 24.050034408370138, 18.95885710182015, 14.350285901527815, 10.290248689261528, 6.835368955785024, 4.031810682515636, 1.9142855257120168, 0.5052441148834734, -0.18572628361317364, -0.16228343017184563, 0.558520627228521, 1.9463307285612526, 3.95782389703704, 6.537287905816618, 9.617437235482443, 13.12044133432557, 16.95917758943438, 21.03871060137954, 25.257926368730583, 29.511306149958816, 33.69081043734965, 37.687840741944086, 41.39524583488923, 44.709325257294324, 47.53179951334703, 49.771709431635216, 51.34720683044077, 52.18720105518797, 52.23282901896792, 51.4387348166296, 49.77410141556608, 47.22339906105757, 43.78686558057663, 39.48069779045589, 34.33694701995509, 28.403117971414375, 21.741475935737725, 14.4280688823448, 6.5514730651710815, -1.7886810573428635, -10.483401822662561, -19.416216970933576, -28.465205710529492, -37.50517715723569, -46.40991469983186, -55.054413468207045, -63.31710304981233, -71.08200694154006, -78.24079636155035, -84.69469828419436, -90.35622044079997, -95.15065968829119, -99.01736451372766, -101.91074097779432, -103.80099421231066, -104.67448303882249, -104.53381848148395, -103.39779655750463, -101.30078868047217, -98.29183899574547, -94.4335610696709, -89.8007885956113, -84.47900969748113, -78.56261908779456, -72.15302590671993, -65.35665780247339, -58.2829036524869, -51.04203822991009, -43.74317207273158, -36.49227294169439, -29.390318342742837, -22.53160683505819, -16.002088098321636, -9.877986491335555, -4.224702103297681, 0.904031672136532, 5.4667216335764195, 9.434413190152329, 12.790713885465061, 15.531548463827871, 17.66465794085769, 19.20886079874741, 20.193099586574718, 20.65530075031129, 20.64108619341721, 20.202382613556782, 19.395914737030555, 18.281636398719954, 16.92116372118675, 15.37624379953757, 13.707293018648667, 11.972038726695619, 10.22429454407672, 8.512895435058287, 6.880813923625941, 5.364473622295761, 3.9932707013867983, 2.7893082313284916, 1.7673474785566952, 0.9349594725729279, 0.2928542267831588, -0.16459650296445485, -0.4486779998331861, -0.575520037203231, -0.5651813453948883, -0.44066265707797064, -0.22688051422463543, 0.05036572767402557, 0.3654018467476603, 0.6936312873933504, 1.012404250473732, 1.3017784026986143, 1.545148584752767, 1.7297319118245933, 1.846898394108945, 1.8923337334829093, 1.866034878612925, 1.7721425667931767, 1.6186198713039237, 1.416790631792153, 1.1807569062675987, 0.9267175825619801, 0.6722134568495286, 0.4353264239724101, 0.23386182981872314, 0.0845435229332616, 0.002250682220064646, -0.0006756994348179028, 0.08496874613750427, 0.26477084402040324, 0.5403551159909709, 0.909189181443588, 1.3645483120959219, 1.8956435336842863, 2.4879132350883895, 3.123464473078738, 3.781654402091145, 4.439794358482283, 5.073953591886707, 5.659836446937527, 6.173706683785467, 6.593320218935301, 6.8988330350180975, 7.0736558949376445, 7.105221319984737, 6.985632106778083, 6.712163646680094, 6.287596195994649, 5.720357994833248, 5.024466817636199, 4.219261962265259, 3.3289162272357733, 2.3817472814605285, 1.409338297052735, 0.44548343537218, -0.4750150903953648, -1.3176623252572806, -2.0496643671689783, -2.641361029380542, -3.0676543306492765, -3.3093880501342707, -3.354633114337767, -3.1998344173330198, -2.850776826224494, -2.323331568100019, -1.6439492385867092, -0.8498700664080292, 0.010973154596996292, 0.8803706853170922, 1.6905760407115902, 2.3653575102389715, 2.821351527069731, 2.9696971737659887, 2.7179215913787615, 1.9720381611863536, 0.6388122207383542, -1.371857030510683, -4.144494696883835, -7.755608249500576, -12.271307398762422, -17.745048204602778, -24.215567038802536, -31.705092352674928, -40.21786203064095, -49.7389743740581, -60.23362586207984, -71.64676694987618, -83.90319712653329, -96.9081101439779, -110.54808953983017, -124.69254358209989, -139.19555784212932, -153.89813303601258, -168.6307658401894, -183.2163214707713, -197.47322032368047, -211.2188913492949, -224.27306206766653, -236.4612930684633, -247.61817412831175, -257.59044558108656, -266.2399555712404, -273.4463386681398, -279.10935448986197, -283.1508326600289, -285.5161794460736, -286.1754115783822, -285.1236937735364, -282.38137008489514, -277.99368474800485, -272.02995784807047, -264.5817640182173, -255.76097706500244, -245.69753560204217, -234.53699560398928, -222.4373875248997, -209.56602085924226, -196.09623177531432, -182.20407834161264, -168.06505835541498, -153.85092310196018, -139.72665688023392, -125.8476903952515, -112.35751497666092, -99.38548527549868, -87.04484304872193, -75.43134536171895, -64.62233793668867, -54.67626800958612, -45.632649980966974, -37.51246758979762, -30.318860230901336, -24.03823983900727, -18.64175135455425, -14.087005014897846, -10.320025648523, -7.277360995211109, -4.888293698663669, -3.077070825819263, -1.765119395962235, -0.8731971369242169, -0.32340825814727203, -0.04103733588992719, 0.04383804689895319, -0.005012629622637207, -0.13105678579996155, -0.285792301600633, -0.4292489760454458, -0.5301986766619394, -0.5660849069716839, -0.52269184017599, -0.39357989852079867, -0.17931711639669085, 0.11345501642705287, 0.4730788138714553, 0.8840186500330144, 1.3280371771369623, 1.7853674620489215, 2.2358412965049053, 2.659937413814898, 3.039717853622291, 3.3596259833736624, 3.607125837361514, 3.773169644445757, 3.8524865004627737, 3.8436980904014253, 3.7492453051035994, 3.575150769763904, 3.3306401020535725, 3.027640238360469, 2.6801806579505514, 2.303725919606178, 1.9144693841032054, 1.5286183302030145, 1.1616999015146037, 0.8279155035068739, 0.5395684954522211, 0.3065864367414542, 0.13615506352561013, 0.032475418265007, -0.0033509227804339728, 0.026699459876288623, 0.11772299142014275, 0.2621603160419324, 0.4501741925180388, 0.6701167589632209, 0.9090656460507992, 1.1534060524250918, 1.389434445624459, 1.6039590557816799, 1.7848727919844438, 1.9216756022374464, 2.005926003814789, 2.031604993484702, 1.9953751206819994, 1.8967249591246897, 1.7379957850433, 1.5242898198102242, 1.2632641581796007, 0.9648191791977376, 0.6406943460165279, 0.3039878855618598, -0.031380232529845495, -0.3512404329148397, -0.641757878518852, -0.8900056740325571, -1.084503524359671, -1.215700125216943, -1.2763813722368347, -1.261986353153731, -1.1708191305292595, -1.004146740655013, -0.766180378405774, -0.46394019984149587, -0.10700863807769866, 0.29281838780266617, 0.7219689800751837, 1.165604593231763, 1.6081814368801617, 2.034042213723257, 2.428022440653504, 2.776039484735719, 3.065625378614464, 3.286405177601917, 3.4304955121120244, 3.492806643057062, 3.4712358379477424, 3.3667424850825665, 3.183303120347225, 2.9277474836303465, 2.6094813822349945, 2.2401068298941005, 1.8329540670857551, 1.4025439285397505, 0.9640066146105459, 0.5324648813044288, 0.12241176179934668, -0.25287783466387387, -0.5818859975730849, -0.8553191895135178, -1.0664843025909956, -1.2115567976948514, -1.289728056679779, -1.3032257881660028, -1.2572042970249242, -1.1595068913984867, -1.020308161352068, -0.8516488509252225, -0.666881697379629, -0.4800445109250163, -0.30518769887333197, -0.15568613405247267, -0.04356193550468475, 0.021153551106812322, 0.030991107817497178, -0.01847719559910123, -0.12827360698375434, -0.29578402361957234, -0.5146762766186981, -0.7749732748851741, -1.0632835387164723, -1.3631868095016666, -1.6557661518579263, -1.9202715884134403, -2.1348919952922896, -2.2776098914798024, -2.3271097399110783, -2.2637071634202903, -2.0702646530080275, -1.7330587288062989, -1.2425641531242344, -0.594122694978905, 0.21153293291695244, 1.1679280212551326, 2.2626949963333667, 3.477613013741443, 4.788864697132416, 6.1675012771978475, 7.5801040847818015, 8.98963099793638, 10.356424820616374, 11.639355064601986, 12.797059246703995, 13.789245489677445, 14.578015096517452, 15.129161982068469, 15.413405477930814, 15.40751411449433, 15.095280516892167, 14.468329081671449, 13.526736219350388, 12.279292311651886, 10.74354507030605, 8.94559743207331, 6.919641951025755, 4.707240650693882, 2.3563675691375945, -0.07976095560214903, -2.5440361152472764, -4.976948291942555, -7.318177292695433, -9.508234267548053, -11.490106265845748, -13.21085980113244, -14.623162424751625, -15.686645556230035, -16.369094550809944, -16.647368343136108, -16.50807321044168, -15.947969472075998, -14.974092294988106, -13.603583074972864, -11.863236785632898, -9.788779419053666, -7.423897901985775, -4.819052392869478, -2.0301074299871327, 0.8831767820504575, 3.858763197001718, 6.834003368843178, 9.747282669073206, 12.539614193694856, 15.156151035849206, 17.547522918932284, 19.670983321652404, 21.491344412434085, 22.981673456085925, 24.123735462385607, 24.908175133268546, 25.334439525057544, 25.410452053517794, 25.152093319506903, 24.582444854227045, 23.730786340052834, 22.631494514894204, 21.322843019218645, 19.845741131904028, 18.24246204755371, 16.555404403326325, 14.825859169623868, 13.092900857070479, 11.392419352834285, 9.756307915894597, 8.211826484311915, 6.781153660867381, 5.481146067041165, 4.32326051102076, 3.3136539037388935, 2.453474924534656, 1.739306239265177, 1.163731930707701, 0.7160021421184545, 0.3827646842297342, 0.1488323878788598, -0.002045443695351154, -0.08643683558537513, -0.1205319982690435, -0.11952525586101687, -0.09709406335338852, -0.06499005394696727, -0.032751541049391195, -0.007540750727319042, 0.005894596100678352, 0.005141568953151263, -0.010064562076190277, -0.03811849202397003, -0.07589607506846373, -0.11915765135538788, -0.16298123393466551, -0.20220301990983613, -0.23184345513585947, -0.24749722277407057, -0.24566941999082237, -0.2240429062435685, -0.18166600912927655, -0.11905366120769871, -0.03819921859128256, 0.057501208543375294, 0.16340595977404251, 0.273856809340301, 0.3824667091883399, 0.4824506624375937, 0.5669822639800774, 0.6295574482243418, 0.664346858752526, 0.6665195607101098, 0.6325228654686347, 0.5602993040593925, 0.4494303832441049, 0.3012033367115164, 0.11859664072809566, -0.09381578821612484, -0.33003739766854245, -0.5828908060006281, -0.8443173179429946, -1.1057200991604408, -1.3583348679934917, -1.5936106295905856, -1.8035824655473298, -1.9812187259594491, -2.120727280359956, -2.217808128668766, -2.2698350236283384, -2.2759536232154116, -2.2370985939184087, -2.1559284503008285, -2.0366803095864667, -1.884951641763778, -1.7074196806230344, -1.5115122696570837, -1.3050463979352596, -1.0958524105008332, -0.891402763521933, -0.6984641830030428, -0.5227914143042216, -0.3688779121936754, -0.23977691558975292, -0.13700539449038954, -0.06053538677936224, -0.008870963291227541, 0.020785930590867616, 0.03228981102296782, 0.030238550289949262, 0.019608354567998226, 0.005355582900309804, -0.007993403955861103, -0.016741689076004096, -0.0183874241620297, -0.011933209998630703, 0.0018816691104822786, 0.02044380276811977, 0.039236420658257526, 0.05192752368531875, 0.050579050505094765, 0.025974993044567813, -0.0319392171166486, -0.13352045159650838, -0.2888147053293145, -0.5068919934667182, -0.7951586455699863, -1.1586795598051969, -1.5995450619919744, -2.1163203699353974, -2.7036095909391973, -3.3517608873714693, -4.0467448981251755, -4.770227451976413, -5.499851934284688, -6.209739152777407, -6.8712047983610125, -7.453685697855649, -7.925850896600582, -8.256875335373538, -8.4178399376988, -8.383214248532044, -8.132371698603992, -7.651073714769445, -6.932867287636782, -5.980355100570288, -4.80627405873832, -3.4343290787059617, -1.8997346237749142, -0.24942359757696372, 1.4581078519769315, 3.1533406097893106, 4.756668170143131, 6.179727109577682, 7.327096940796594, 8.09834197792597, 8.39036277065189, 8.100037205996243, 7.126928184323873, 5.376087865130264, 2.760923798141049, -0.793990725793092, -5.35024554408511, -10.953143663049206, -17.62955071661309, -25.386115878759284, -34.20792768858742, -44.05765752472562, -54.875244145136236, -66.57817931699658, -79.06236501613304, -92.20389628696475, -105.86092529325909, -119.87595482454921, -134.0786675785617, -148.28911668491364, -162.32120055042748, -175.9863368641384, -189.09724455833353, -201.47173907858755, -212.9364455761585, -223.33033662215723, -232.50800569249571, -240.34259484176746, -246.72867784133445, -251.58545947825002, -254.8571870556147, -256.51361214326454, -256.55023090237677, -254.98795150683958, -251.87220759700182, -247.27155100541634, -241.27577006736303, -233.99359131077415, -225.5500319062704, -216.0834777083565, -205.74256686416456, -194.68296230202102, -183.0644354125965, -171.04810844264847, -158.79247262334067, -146.4504445041355, -134.166557331271, -122.0746337833193, -110.29589005104285, -98.93744102616257, -88.09122090605625, -77.8333213665484, -68.22373785349285, -59.30650382516763, -51.11018322863271, -43.648684578597845, -36.92245752054563, -30.91981157934065, -25.618158677064457, -20.9856390038636, -16.98284605817842, -13.564565294735853, -10.681439501959446, -8.28158258742967, -6.312081215567212, -4.720345242216289, -3.4552839423903747, -2.468292628698524, -1.7140417252244136, -1.1510676345975572, -0.7421753697047587, -0.4546482828735025, -0.2602929807215437, -0.13535171499232174, -0.06028994200318793, -0.019483320973329662, -0.0008298420071525778, 0.004687696005828734, 0.003464917980536626, -0.00025686936153753196, -0.003938290703341236, -0.006320246324586769, -0.007045346674722268, -0.00633117384071177, -0.004700532544619066, -0.0027706432406128184, -0.0010998983199067564, -8.840771989680967e-05, 7.340633328234937e-05, -0.0005844156368754834, -0.0018327872054324855, -0.0032882921917823955, -0.0044723799688861365, -0.004876757899907117, -0.004027595147172172, -0.001542407791360755, 0.0028250574319199184, 0.009155080395442267, 0.017348976850086184, 0.02713290132728445, 0.03807719486867272, 0.049628949323987176, 0.06115455406810306, 0.07198843886059791, 0.08148396602579856, 0.0890624604005317, 0.09425667353469962, 0.09674552221512536, 0.09637771354701798, 0.0931827229163823, 0.08736813051824664, 0.07930400034209502, 0.06949558492274475, 0.05854591395509242, 0.0471112190204717, 0.035852346537532484, 0.02538540904312009, 0.016235033261385253, 0.00879337789504499, 0.003287712131261871, -0.00024120505606236087, -0.0019483885002056728, -0.002180750786182257, -0.00146012066553389, -0.0004540012740467679, 6.433052417842116e-05, -0.0007359135131397936, -0.0036892500990233688, -0.009577747935467737, -0.019075798158237203, -0.03269914070957319, -0.05076123911776229, -0.07333970694451307, -0.10025494604218016, -0.13106249079979732, -0.16505980126058348, -0.20130745321876564, -0.2386638790410347, -0.2758320625901345, -0.31141608872611576, -0.3439850444250475, -0.3721404393219599, -0.3945828693127125, -0.41017559951843086, -0.4180017252155788, -0.4174117747326106, -0.40805927242767265, -0.3899223955397499, -0.3633105710151215, -0.32885562925810125, -0.28748792019666064, -0.24039856147578098, -0.18898968921225312, -0.13481521884811862, -0.07951489914180442, -0.02474500047221363, 0.027890414466891975, 0.07690453065853933, 0.12098776014758342, 0.15905772482515151, 0.19029740120977062, 0.21418007156699428, 0.23048016468977778, 0.23926980443187346, 0.24090161726011547, 0.2359790429192527, 0.2253160039678438, 0.20988801199935497, 0.1907777603583718, 0.1691189020679421, 0.1460401099560039, 0.12261247791370676, 0.09980292487906915, 0.07843580489310091, 0.05916419431832944, 0.04245224965502935, 0.028569060568761052, 0.017593768209260018, 0.009431118987664135, 0.003836053098159808, 0.0004454465414380762, -0.0011852148440355877, -0.0015425754365073362, -0.0011164849101356258, -0.0003638302786587148, 0.0003228372044991447, 0.0006400530363716103, 0.0003901981691078447, -0.0005105621521165045, -0.0020333948625010814, -0.004046672966375315, -0.006333689668405933, -0.008616784370431927, -0.010586044700936688, -0.01193046518437504, -0.012369490601466157, -0.01168195139510273, -0.009730230775076329, -0.0064782737284745685, -0.002001846088732611, 0.0035098843060836454, 0.00976178426545684, 0.016368932888446475, 0.022880650389513632, 0.028810909969042786, 0.033673164206006606, 0.03701732181999566, 0.03846626291084595, 0.037749359583280434, 0.0347314386685204, 0.029432143494243893, 0.02203467751976345, 0.012883769404443666, 0.002471790097047585, -0.008586771184018443, -0.019591456320143183, -0.029800809890037867, -0.03848364583400792, -0.044973467657155826, -0.04872243835623067, -0.04935097933983048, -0.04668897803783439, -0.040805154883479126, -0.032021032365373764, -0.020907661021585842, -0.00826170005400979, 0.004939631833960271, 0.017604105914122276, 0.0286089603596273, 0.03690150277218106, 0.0416118639579354, 0.04217287771346916, 0.03844119409898104, 0.03081310598512137, 0.020328227533050695, 0.008754143944780298, -0.0013545680889299335, -0.006628569259789607, -0.002891210179297275, 0.01479463468946304, 0.052038557914239864, 0.11499342482280252, 0.21018678266392535, 0.344316564814802, 0.5240166331515332, 0.7555994150491694, 1.0447843827942453, 1.3964223152469577, 1.8142261075280681, 2.300519307117282, 2.856017828947136, 3.479659684462563, 4.168474543490639, 4.917526037007202, 5.719897452438438, 6.566745712137167, 7.447425612745549, 8.349679885299542, 9.259891157606152, 10.163389417178777, 11.044806273225323, 11.888465298628722, 12.67879608640102, 13.400758710922945, 14.040291433728482, 14.584743302374617, 15.023201591052867, 15.346804282371139, 15.549012816063307, 15.625843699009968, 15.575942099296102, 15.400601992796602, 15.103720283769539, 14.691673456307585, 14.173121399448062, 13.558745643825882, 12.86093154866915, 12.093406735366749, 11.270876946358767, 10.408613410480234, 9.521990532998549, 8.626076460193229, 7.735252044593044, 6.862867321614097, 6.020951457185685, 5.219984189517097, 4.468692184356418, 3.773932189906435, 3.140647664328113, 2.571889525792531, 2.068896511342462, 1.6312288878728187, 1.256951308165088, 0.942840355444194, 0.6846167726944906, 0.4771996499870616, 0.31496360137148527, 0.19198843063173068, 0.10229208930326605, 0.04003910929999045, -0.0002816630653900104, -0.023714627488713943, -0.03473226862775391, -0.03716748136057631, -0.034182973561706825, -0.028274890863717397, -0.021306345677995123, -0.014565347657934864, -0.008841078430134082, -0.0045122103145558414, -0.0016408221288569534, -6.58382221142514e-05, 0.0005093964548958415, 0.0004398604396658807, 7.526313563208132e-05, -0.0002877573078727401, -0.0004367689047462413, -0.0002583551275737597, 0.000262033195726839, 0.0010528741036008758, 0.00197896255397246, 0.002869897000094252, 0.003550996944177495, 0.003873089957694652, 0.003737966784292716, 0.003116881129142791, 0.002060220489593288, 0.000697339055813683, -0.000773539595965256, -0.0021045386078662447, -0.003024823825416377, -0.003272446900828138, -0.0026284910739264983, -0.0009503753360043573, 0.001798940703461028, 0.005528826359142759, 0.010008432040973736, 0.014865640990197455, 0.019598603701324494, 0.02360001030080041, 0.026193277951378706, 0.026678867935777614, 0.02438806722613775, 0.018740835092889607, 0.009303781915835096, -0.00415594126462255, -0.0216250782431134, -0.042811066446324736, -0.06712481354183517, -0.09368135765150212, -0.12132084491899679, -0.1486494916848178, -0.1740995326648295, -0.19600595491358033, -0.21269649291320103, -0.222590284692108, -0.22429974006638956, -0.21672961352385345, -0.19916705467022516, -0.17135655891535287, -0.13355427174674983, -0.08655733773352439, -0.031704003740937715, 0.029158445630282085, 0.0937355219082674, 0.15937624227949443, 0.22318957218244576, 0.28218145099917147, 0.33340567439190616, 0.3741208242420441, 0.4019446736738413, 0.4149971870280643, 0.4120234281552638, 0.3924883986827252, 0.35663705453093913, 0.3055154500093855, 0.2409481435172604, 0.16546935960764408, 0.08221371608944258, -0.005230397087382989, -0.09299826481435809, -0.17714848701570887, -0.2538742491334155, -0.3197143261459725, -0.37175160076386143, -0.40778692559786456, -0.42647696386075207, -0.4274261579489549, -0.41122514013078243, -0.37943056153958205, -0.3344845609147957, -0.2795758283335937, -0.21844752425268812, -0.1551607064060376, -0.09382500691424217, -0.03831091553971821, 0.008039950894898912, 0.04268913790483592, 0.06414308037997651, 0.072144582182874, 0.06779896502544329, 0.05362251387582127, 0.033504349231557144, 0.012577084187454866, -0.003001043500812379, -0.00634709307449038, 0.009772356817331353, 0.05250972143056127, 0.12846767202281753, 0.24321669986538844, 0.4008250686657157, 0.6034285610885572, 0.8508674645636456, 1.140416939281057, 1.4666330559307406, 1.8213332673113538, 2.193727360746029, 2.570728513818063, 2.9373854825471333, 3.277441974070649, 3.574028868157784, 3.810453405334125, 3.971053749002297, 4.042081925838079, 4.012574047147176, 3.8751643229934563, 3.626798914768046, 3.269307265236637, 2.8097927537884564, 2.2608094155979983, 1.6402973008809918, 0.9712588249206947, 0.2811402757634437, -0.39901085245355744, -1.0356050222922437, -1.5937649160219405, -2.0387332925962682, -2.3373837823341037, -2.4597765777666765, -2.380695750001073, -2.0811021714947624, -1.549435987105822, -0.7827053652147318, 0.21269611927923165, 1.420488368484134, 2.8143859289044917, 4.35843318131973, 6.007695473655346, 7.709321385433018, 9.403961693562703, 11.027505256600536, 12.513078008839026, 13.79323899697727, 14.802297452727235, 15.478667742020622, 15.76717502688834, 15.621223857550333, 15.004744948695304, 13.893948924771081, 12.278818110725332, 10.163732331820176, 7.567752093109858, 4.5244256202674915, 1.0811086610765845, -2.7021909223122482, -6.754410994241928, -10.995422172919822, -15.338335881168899, -19.69205295711193, -23.9639631775368, -28.062700352032444, -31.90085486402795, -35.39748131497226, -38.48046692378892, -41.0887670813473, -43.17407660695285, -44.70204870774661, -45.65305991626514, -46.0224038184001, -45.82000877942544, -45.069696112630034, -43.808007037382055, -42.08265320713476, -39.95065830375794, -37.476267882950616, -34.72871234793383, -31.77995903074389, -28.702449040364748, -25.56684247118377, -22.44000118718153, -19.38322697530787, -16.450802313279517, -13.688874572130235, -11.134703187919976, -8.816248022473706, -6.752133505686035, -4.9519521739862, -3.4168658829601557, -2.140458425129113, -1.1097862940918997, -0.30657292669697733, 0.2915332113821093, 0.7096737871105178, 0.9745180588143711, 1.1130855286821644, 1.1516962102956958, 1.1150810408265432, 1.0256746116532456, 0.9031020147250964, 0.7638609370341611, 0.6211886277823843, 0.4850998970040082, 0.362572039612131, 0.2578477895304334, 0.1728250277143603, 0.10749816041255537, 0.0604223428247543, 0.02917134104369968, 0.010762491487596459, 0.0020284438412365847, -7.87606008215829e-05, 0.0017404117380049363, 0.005282814380985475, 0.008917412124221286, 0.011593007188357889, 0.0127905605511731, 0.012434207509273836, 0.010776334431798045, 0.008272042409888398, 0.005456864928541853, 0.0028397606420772414, 0.0008203431248218092, -0.00036421156058952703, -0.0006606926831078912, -0.0001913662445157923, 0.0007799747619210899, 0.0019005194919845736, 0.002791091823615804, 0.003109947233228217, 0.0026090820802466084, 0.001175680087013908, -0.0011466880129890533, -0.004159971082159736, -0.007536428305374985, -0.010863436026534655, -0.013702777024598937, -0.01565681203595188, -0.01643269830668028, -0.015895522163692423, -0.01410195946452628, -0.011307869198380277, -0.007945965108331704, -0.00457320669066409, -0.0017915265945022045, -0.0001496177917795207, -3.734353929541791e-05, -0.0015874921848844075, -0.0046018201164006, -0.00851867342875975, -0.012438175533756281, -0.015218033074571995, -0.015647965811570855, -0.012703930777357646, -0.005874942793270126, 0.004454166665904181, 0.01659067137777143, 0.027128917357179115, 0.030597419220589235, 0.019210007814483527, -0.017222659594307493, -0.09116460840122667, -0.2169580896572767, -0.41011432008186555, -0.6862608643205887, -1.0597339331086248, -1.5418256705176345, -2.138723125215152, -2.8492050249207073, -3.6621932755115907, -4.55428685710303, -5.487434668482912, -6.406928933590593, -7.239920258538692, -7.894682624496752, -8.260834048514008, -8.2106757652595, -7.601872438465136, -6.28161330396727, -4.092355520052796, -0.8791866683934901, 3.5012364468296306, 9.170255865938113, 16.21547963163389, 24.6780263272249, 34.53911017803728, 45.70641259814163, 58.00076056219998, 71.14370222192305, 84.74658012699109, 98.30169245615235, 111.17619764504018, 122.6093716143184, 131.7137699576478, 137.4807669670433, 138.79087979079597, 134.42914254219457, 123.1052030448904, 103.47839015691586, 74.1874502714279, 33.88444049657712, -18.72798037540971, -84.8583603665384, -165.5863528715576, -261.8208386886192, -374.25948464406144, -503.350420454375, -649.2573260465674, -811.8292295765473, -990.5762560374253, -1184.652460425436, -1392.8471685790703, -1613.5866233529139, -1844.9429476872378, -2084.6529424482173, -2330.148413277764, -2578.608741236626, -2827.005826745784, -3072.1520702078446, -3310.760912994382, -3539.512267268347, -3755.121146246837, -3954.407728609392, -4134.366995917995, -4292.236043495026, -4425.55718593742, -4532.235059068935, -4610.587421847207, -4659.389735275785, -4677.905816626218, -4665.92784548097, -4623.763468850362, -4552.217293607809, -4452.570847062322, -4326.551287515109, -4176.289754807726, -4004.2705676224036, -3813.272734922944, -3606.305461902554, -3386.5394892147247, -3157.236203096055, -2921.6764903272347, -2683.091285092955, -2444.600067109096, -2209.1602353079634, -1979.4946787529398, -1758.0414607698333, -1546.918142792505, -1347.8961276774442, -1162.3852769147848, -991.4287281665838, -835.7075256736093, -695.5543867690185, -570.9756723419943, -461.68041544696024, -367.1150964542702, -286.5027404775946, -218.88537939389366, -163.1673801295932, -118.15675081425407, -82.60726774995274, -55.25822506294581, -34.87030488607444, -20.256709109961392, -10.308969332378277, -4.017085653947915, -0.4838804982450941, 1.0663231580142483, 1.2843869151884433, 0.6979175539398121, -0.2829278852914555, -1.3561354346106427, -2.315846726181234, -3.0384831762132647, -3.4678030114040874, -3.599705064969589, -3.4675060057662233, -3.1282860461400888, -2.650830557315138, -2.1055309619452407, -1.5564655987361522, -1.0557473297412385, -0.6400966532067933, -0.3294852537885628, -0.12759978090070503, -0.023802765501750367, 0.003785421894619296, -0.015527715744570679, -0.04915262084107662, -0.0653113546780248, -0.036745204538349834, 0.0562377812295655, 0.22357825233035977, 0.46426880816154986, 0.7661891892068088, 1.1069406249008205, 1.4555767982264676, 1.7750699234121528, 2.0253055561839455, 2.16637806697878, 2.1619258162080452, 1.9822476852464772, 1.6069881019799195, 1.0271965431258434, 0.2466161342137672, -0.7178897425463381, -1.8368052975228546, -3.069298193706397, -4.3653415248688665, -5.668482344269378, -6.919082581622824, -8.057829585647491, -9.029297984056855, -9.78536915656275, -10.288236932229813, -10.512803369713657, -10.448349443723806, -10.099362219452853, -9.485462247730933, -8.640429650706515, -7.610381727419449, -6.451205966790141, -5.22539714651406, -3.9984826268703584, -2.8352453813021925, -1.795972646265615, -0.9329483807948235, -0.28739723455695243, 0.11297232175823448, 0.25562380659969786, 0.14395297156035344, -0.20288549708205794, -0.7510810340830504, -1.4541428316956286, -2.2556405994287734, -3.092558679556008, -3.899075886814545, -4.610558024384314, -5.167536480873088, -5.519435430104671, -5.627805594730717, -5.468958707296205, -5.035787795670883, -4.338668790920149, -3.405393058810242, -2.28012199729474, -1.0214103017275096, 0.30060461677732536, 1.6077039061719023, 2.8175980772218074, 3.848237842032434, 4.622198342784276, 5.070905053150128, 5.138476893407262, 4.78498523611046, 3.988961805681566, 2.7489632802812274, 1.0840348545178529, -0.9667710987576908, -3.3458454281386922, -5.979389867687459, -8.780582977669754, -11.653385302255769, -14.496793151561132, -17.209328975168322, -19.693545956845746, -21.86032564605376, -23.632760189004124, -24.949482192262604, -25.76725969235139, -26.06255360375127, -25.832244384118585, -25.093497113206034, -23.88239789154409, -22.251839377249294, -20.268737437576828, -18.010686619869535, -15.562233119892865, -13.010958290778111, -10.44356981642373, -7.942191495630347, -5.581027080304125, -3.423564256443209, -1.5203896433351527, 0.09229094898832915, 1.3933145253029475, 2.376451730430974, 3.049577488695072, 3.433211591679211, 3.5584811663703744, 3.464667501240207, 3.1965037966678875, 2.801379036551682, 2.326603226245502, 1.81687852715125, 1.3121025607679493, 0.8456037515497986, 0.4428824198583713, 0.12090636693966918, -0.11203628393463597, -0.25595433363908776, -0.3182960807081073, -0.31269712833404656, -0.25743335533339806, -0.17368999505394778, -0.0837521270253693, -0.009244255587502751, 0.030472306575259376, 0.019652599362278072, -0.052801089063305585, -0.1926812203622942, -0.40021674564284543, -0.6702093770844094, -0.9925350262792648, -1.3529606249668937, -1.734208561766872, -2.1171880978303266, -2.4823058387772217, -2.8107658872424994, -3.0857724615187796, -3.2935586786547515, -3.424197150317434, -3.472127708665306, -3.436382792545994, -3.3205233486593118, -3.132252784824057, -2.8827733664277244, -2.585952819861565, -2.257353590029724, -1.9131949933762031, -1.5693205652807665, -1.2402399341936383, -0.9383070127381585, -0.6730848043665851, -0.45093255430181906, -0.27483441760465044, -0.14447124694591987, -0.05652015670122926, -0.0051512938402067466, 0.017324575531178516, 0.01970670003913153, 0.011115464027552613, 0.00022569555642586785, -0.0054207439567337075, 2.645253087370967e-05, 0.02033479526718606, 0.056989975380748265, 0.10919867292250007, 0.1740870442846893, 0.2470736298717067, 0.3223820687970818, 0.3936492250902924, 0.45457819401131994, 0.4995730687181465, 0.5243052168504154, 0.5261633108766947, 0.504547764547756, 0.4609834411216373, 0.3990393295469311, 0.3240597846931423, 0.24272769623147822, 0.1624943742711663, 0.09092287790030983, 0.034999981096439155, 0.0004762153812079925, -0.008707143502157252, 0.009149156362557743, 0.0532561457366124, 0.12030764234944558, 0.20467880598333188, 0.2988446802749322, 0.3939932018391023, 0.4807886632380107, 0.5502260496326487, 0.5945051015293706, 0.6078465030056702, 0.5871721015944371, 0.5325769934062513, 0.44753369070021437, 0.33878811755154564, 0.215925867853945, 0.09061567765799795, -0.024422851626439934, -0.11666094728724825, -0.17511751986050586, -0.19171488236750392, -0.1624982683939042, -0.08858109679085409, 0.023319971979620484, 0.16088316106271866, 0.30681187555126643, 0.4401620207412414, 0.5383880973681118, 0.5800805727558345, 0.5483141628021101, 0.43445939757116775, 0.24226056801068724, -0.008061165637125344, -0.2759613591046504, -0.49729069339298115, -0.5818969214888614, -0.4124154979482119, 0.15547056881517832, 1.2910655777820708, 3.1848209501558715, 6.042532495060463, 10.077581313832637, 15.50126938993312, 22.51152837405399, 31.280407138677884, 41.94069375269183, 54.57222872984894, 69.1885213763817, 85.72433232286609, 104.0249106134106, 123.83763783850294, 144.8068801577143, 166.4720463867108, 188.2696624654702, 209.53980832204718, 229.5369632195491, 247.4444445925592, 262.39353052058215, 273.4868580995655, 279.8246867639456, 280.533600790545, 274.79675238473135, 261.8846187454287, 241.18516182674347, 212.2322364496675, 174.73109480287533, 128.57996107384426, 73.8864869185979, 10.977564668578271, -59.59775989716055, -137.07727420474103, -220.4948835965928, -308.6958678675356, -400.3607380103304, -494.03500695432575, -588.1640166920059, -681.1317702622977, -771.3025486456844, -857.0639682726882, -936.8700603027407, -1009.2829318390179, -1073.0116033573963, -1126.9473932397048, -1170.197856242044, -1202.1168736369916, -1222.311359607652, -1230.644817692603, -1227.2365165063707, -1212.453069414277, -1186.8928249755343, -1151.3637276409893, -1106.855531078483, -1054.5074318244262, -995.5723317894374, -931.3790294966841, -863.2936789696139, -792.6818417476017, -720.8739677416957, -649.1351895472382, -578.6313725062574, -510.4020192502133, -445.3413762230922, -384.18593748856887, -327.507911038554, -275.71447826610915, -229.05246411608985, -187.6178489980335, -151.36940065053665, -120.14558984772178, -93.68388127551029, -71.64146206820536, -53.616615892262345, -39.16954460686649, -27.841705327322067, -19.173866429686893, -12.721800453843171, -8.069104348921499, -4.837095649950226, -2.6916353364555508, -1.3469506745226347, -0.5666888185032004, -0.16254107731149564, 0.009140078007576994, 0.05225619994563362, 0.03691197861717024, 0.0059060722028749435, -0.018699484234761015, -0.02933512767980367, -0.027337080857833287, -0.018271177447541816, -0.00832514584916833, -0.0018339347359895535, 8.520565902842123e-05, -0.00011101327570616209, 0.003120920747046122, 0.017292208115587668, 0.05036916063249692, 0.10911301634146435, 0.19750652313344197, 0.3154744281674379, 0.45806158677684083, 0.6151762017609803, 0.7719500522178346, 0.909705963518768, 1.0074653098551993, 1.043877735094551, 0.9994157837780676, 0.8586491562587881, 0.6123918129988776, 0.2595334343772602, -0.19162123089905572, -0.7226502150844989, -1.3050505596432216, -1.9010693884499532, -2.465314979046025, -2.947066690112362, -3.293172802556509, -3.4513701851363905, -3.373823489508015, -3.020658291948558, -2.36325372319457, -1.3870665117109147, -0.0937851456501876, 1.497352219152033, 3.3492470226609763, 5.407661277755784, 7.602980482187177, 9.85300782013551, 12.066588256857344, 14.147863951645418, 16.00098001388725, 17.534974476325196, 18.668579073033868, 19.334656856191625, 19.484018264890807, 19.08838838518694, 18.142343131218293, 16.664088407602872, 14.695021104387266, 12.298074542479306, 9.554929983020367, 6.562249270467508, 3.426993179265859, 0.26127069661925684, -2.823023263812952, -5.719521319418569, -8.33235791964581, -10.58053415409529, -12.401438501708068, -13.7533383873158, -14.6167176197276, -14.994402233743253, -14.910487965873202, -14.408152363989183, -13.546528435566026, -12.396851182163969, -11.037886013783462, -9.55120392864986, -8.016550027821683, -6.507550102598588, -5.088007555761366, -3.8090020368190265, -2.7069473272270925, -1.8027024624813242, -1.1017606889019715, -0.59546987343438, -0.26316980337615203, -0.07507070027884424, 0.004352882516176794, 0.012714563247516608, -0.013905209969627448, -0.04426933265640831, -0.05471690845522239, -0.03109149889883221, 0.030306684663573107, 0.1228517561706772, 0.23084005439085176, 0.3318108213744821, 0.39981796267132763, 0.4094587663463372, 0.3404027412020441, 0.18211490977504674, -0.06155771289531456, -0.3682903846259676, -0.6940308736787517, -0.9708752537689121, -1.1063257205680486, -0.9841125426584467, -0.466664517689856, 0.600765213553188, 2.38441046055335, 5.05493055461894, 8.77925526352963, 13.711693053492475, 19.984721500530767, 27.69992457732535, 36.91975091354095, 47.660478130231276, 59.88644365889063, 73.50628596674315, 88.37140522118861, 104.27682728912232, 120.96464367091836, 138.13016932409457, 155.42993575965303, 172.49174357650418, 188.92641607519894, 204.34072776096116, 218.3509818290959, 230.5967339213226, 240.75524760016793, 248.5537046577235, 253.7784567294631, 256.28311330502834, 255.99418989329993, 252.914021859848, 247.1208120342604, 238.76580761959207, 228.06789906730165, 215.30596945521455, 200.80798521796146, 184.93883894505663, 168.0872294376367, 150.65204661581794, 133.02948682201742, 115.59911358349291, 98.71102777963536, 82.67544641681597, 67.75431440955509, 54.155217752269564, 42.02776564548216, 31.46249124774221, 22.492203839799025, 15.09561497483705, 9.202969960905783, 4.703306269482548, 1.452895616786989, -0.7154722950142646, -1.9829248758039515, -2.5351815379705442, -2.553775757002977, -2.2082801825769165, -1.649877745144102, -1.0065025502005185, -0.37968122573490376, 0.15689001247123127, 0.5570900622712458, 0.8005822702326248, 0.8897051111171945, 0.8453197996634254, 0.7019323779069885, 0.5024301153587443, 0.2927697133466169, 0.11693814387693213, 0.012497463337175184, 0.006956808499581188, 0.11515102022430576, 0.33773826599718504, 0.6608566099094647, 1.0569079917935893, 1.4863714750406116, 1.9004894358005975, 2.2446235314060514, 2.4620440070743874, 2.497897552832354, 2.3030887910889155, 1.837819253728573, 1.0746053395778656, 0.0005441633470821748, -1.3812801303644482, -3.0513236997179316, -4.974064797317363, -7.099402296035678, -9.364880818140334, -11.698606710040927, -14.022682619552148, -16.25696285147019, -18.322918087253527, -20.147397091219897, -21.666138968389202, -22.826813128390846, -23.591233110985712, -23.93693481041074, -23.858025315058594, -23.365039538846826, -22.484030919958258, -21.254958871645933, -19.729457355213377, -17.96812238314653, -16.037476706893322, -14.006780830691644, -11.944860598797092, -9.917113622021539, -7.982854152450728, -6.1930713958789605, -4.588706434165626, -3.1995712549230912, -2.043886132313364, -1.1284229197379576, -0.44920331997438123, 0.007357588071918683, 0.26288941629159723, 0.3452197120280087, 0.28637048196311066, 0.12051826588018695, -0.11796824853943394, -0.3963117645926274, -0.6848538180452169, -0.9582543875292426, -1.1963134343366169, -1.3844148556352578, -1.5136003742556265, -1.580304637380912, -1.5858007917755021, -1.5354195206056291, -1.4376136097637822, -1.302939659454565, -1.1430313350992276, -0.9696324912974009, -0.7937476971084195, -0.6249549950170401, -0.470911757566628, -0.3370615205566608, -0.22654695399085836, -0.1403139817213105, -0.07737532756378418, -0.03519590592307061, -0.010156860124418524, 0.0019471008375839729, 0.005421107178710124, 0.0042338438245562385, 0.0016640346799212046, 5.2991238567552135e-05, 0.0006762049233911263, 0.0037363342317457177, 0.008469578704913867, 0.013347987040597396, 0.016352770701370617, 0.015289045705593902, 0.008110075909355391, -0.006780553602806135, -0.030277492856348277, -0.06239641528475277, -0.10218759526209727, -0.14774867772269762, -0.19633633219001795, -0.244567976079114, -0.28869703807552377, -0.3249386242861136, -0.3498208105088215, -0.36052217410822, -0.355171243193853, -0.3330822340485767, -0.2949032692634105, -0.24266095668032586, -0.17969295193934962, -0.11046862677420119, -0.040306608394092135, 0.024993883612069775, 0.07958389121540503, 0.11802826295061061, 0.13576891208363787, 0.12955307506177471, 0.09779300935826969, 0.040832166925548, -0.03890887271114129, -0.13692105223219075, -0.24673620898070167, -0.36019466788480936, -0.46783933012929835, -0.5594159077725366, -0.6244514967133977, -0.652877886831849, -0.6356622709026523, -0.5654065953083964, -0.43687779856328673, -0.24742466449419678, 0.0027607559918201192, 0.310505136956369, 0.6696818360568426, 1.0714050497586345, 1.5043772412032792, 1.9553728881454913, 2.4098328887574034, 2.852537364023273, 3.2683200313506835, 3.6427849514945776, 3.962986398480514, 4.218034856863416, 4.39959704211004, 4.502311844026368, 4.524043889090712, 4.465840487184014, 4.331797326045439, 4.128786510578249, 3.8660562343279046, 3.5547152312254426, 3.2071471719383067, 2.8363869161753064, 2.455492017614946, 2.0769436114692916, 1.7121078992038101, 1.3707847994071205, 1.0608646658149823, 0.7881164430261283, 0.5560803273002441, 0.36607888991810533, 0.21737250112991913, 0.10741648128598555, 0.032196534551667606, -0.013382786495054809, -0.03508342388646723, -0.03891984705727729, -0.030771206816442128, -0.01604147497863085, 0.0006150837166914161, 0.015491069938723435, 0.025939519656584586, 0.030404326982113074, 0.028371789791128497, 0.020251159124131595, 0.007199994081149863, -0.009088170080906502, -0.026615044717121363, -0.043308925397824764, -0.0572387128930938, -0.06679574749930373, -0.0708320044277531, -0.06874649389244326, -0.060517270368336394, -0.046680415406046935, -0.028261302940823668, -0.0066675808301755145, 0.016447223724283203, 0.03933614854836315, 0.060312343146471624, 0.07789115177001223, 0.0909093173935029, 0.09861227189147975, 0.10070347640754256, 0.09735312899685382, 0.08916699253571302, 0.07711940543733768, 0.062457260864172415, 0.04658348969742607, 0.030931256779339087, 0.016839906732949526, 0.005441983861887854, -0.0024286613617020662, -0.006300014955993631, -0.006091699800232605, -0.0021095709810739255, 0.0049937599650231625, 0.014288484230358006, 0.02466076757471037, 0.03492114616216483, 0.04391855270074434, 0.050649977166839125, 0.054356232580738996, 0.05459555925994962, 0.051288346667158986, 0.04472879863663763, 0.035562719378040626, 0.024733113710297724, 0.01339802312580069, 0.0028274789977201157, -0.005711702076042285, -0.011073420388251319, -0.012341902726748583, -0.008923740532605275, -0.0006139981647874553, 0.012369932441236336, 0.029390458061130182, 0.049428651486974486, 0.07115748936330174, 0.09304436553007091, 0.11347464057607634, 0.13088628989465256, 0.14390451072071592, 0.15146467718175105, 0.1529125933534014, 0.14807244482144846, 0.13727512309538017, 0.12134254301972819, 0.1015269845065822, 0.07940811870108092, 0.056753951717651505, 0.03535483402395209, 0.016843203198388303, 0.002514195500376301, -0.0068402826028129, -0.011069207126193921, -0.01075855941694938, -0.007275314556691916, -0.0027521669021671772, -9.761270137115295e-06, -0.0024176053111471052, -0.013699382719847653, -0.03769273837534307, -0.07807744944269764, -0.13808896727374084, -0.22023857245722359, -0.32606099775710745, -0.4559019566539617, -0.608765893713467, -0.7822372609170528, -0.9724852251619681, -1.1743579785342002, -1.3815608223134646, -1.5869135894323279, -1.7826757256291756, -1.9609218475893297, -2.1139471549846123, -2.2346794722898213, -2.317074138015857, -2.3564827399811783, -2.349940524176169, -2.2963483447243993, -2.1965742517476845, -2.0534515740457624, -1.8716707684816714, -1.6575695935276267, -1.418833062264909, -1.1641192771817341, -0.9026261190036806, -0.6436313932220035, -0.3960313204222794, -0.16790306934149637, 0.03388373376000135, 0.20398924199288446, 0.3388316299981518, 0.43670478313454353, 0.4977896787055642, 0.5240593576970435, 0.5190850514093562, 0.48775701115277004, 0.4359386104599718, 0.37007610816044273, 0.29678885860577225, 0.22246547936409578, 0.15289065613829467, 0.09292530218925997, 0.04625856090030367, 0.015245025541090754, 0.0008344886451616805, 0.0025994065694325925, 0.01885279762961286, 0.04684448638122089, 0.08301988128397228, 0.12332179931945333, 0.16351353643871877, 0.19950056442940256, 0.22762894415404158, 0.24494071214327612, 0.24937001357174177, 0.23986783539779621, 0.21644875547002118, 0.18016093323165394, 0.13297616289549927, 0.07761740000411753, 0.017338786732218645, -0.04432553382705771, -0.10382451512705353, -0.1578455881732928, -0.2035437814036165, -0.23872842973954186, -0.26199484044958327, -0.2727926576755757, -0.2714275751345732, -0.25899812873348915, -0.23727563099108542, -0.20853836655108707, -0.17536261477377468, -0.14040239614461217, -0.10617398818812807, -0.07486091224792427, -0.04815484560034932, -0.027144841868689755, -0.012263229162840074, -0.003291901722937763, 0.0005722243290723208, 0.0005986864210492591, -0.001637602990648518, -0.0044458383100023854, -0.006220612995751754, -0.005637355828565809, -0.0018229395855380102, 0.005515276968889562, 0.016015258596590563, 0.028649880249673236, 0.041784296531686374, 0.05329967845341501, 0.06077641430378061, 0.061724749466157164, 0.05384646303087918, 0.03530788710277343, 0.0050026375452690165, -0.037217970449935266, -0.090366873525807, -0.1522146117318608, -0.21927110222332996, -0.2868608262136519, -0.349293845002903, -0.4001283959948157, -0.4325096443177208, -0.4395683356345893, -0.4148567018790992, -0.3527947830776485, -0.24909860912471882, -0.10116156016896467, 0.09163800996059879, 0.3277261269364273, 0.6032344236291923, 0.9120311435322681, 1.245890628647053, 1.5947868366685505, 1.9473013019938061, 2.2911259002601008, 2.613636971101117, 2.9025148577049626, 3.1463504595291947, 3.3352204406004082, 3.461198681341524, 3.518772090233719, 3.5051363463152447, 3.420354291228482, 3.2673728278163177, 3.0518860008557738, 2.782049337782924, 2.4680727682002286, 2.1217119940336855, 1.7556873869407184, 1.3830636201506137, 1.0166251330102063, 0.6682830051379928, 0.3485435710857058, 0.06606272746902266, -0.1726789778468665, -0.3635709665265216, -0.5049323900204271, -0.5974412170101253, -0.6439366986760886, -0.6491128208634828, -0.6191291987786632, -0.5611654420369606, -0.48294841858753945, -0.39228222233499, -0.2966090768217634, -0.20262607401927513, -0.1159778297392136, -0.04103925510161352, 0.019204564176506903, 0.06318041839097494, 0.09065499887627301, 0.10258247055296542, 0.10088760785362912, 0.0882042502221339, 0.06759188499142998, 0.042252385262714985, 0.01526734189196653, -0.01062649837473532, -0.03321022994572048, -0.05089559339822707, -0.06277417709719883, -0.06860479484372457, -0.06874559023710697, -0.06404152473827544, -0.055680799553542715, -0.04503451838730361, -0.03349604992839615, -0.022334928287536346, -0.012577744831184713, -0.004925319164615479, 0.0002883809743848591, 0.0030942530375271836, 0.003845796187788868, 0.0031430738295642265, 0.0017324112197773182, 0.0003933897052660321, -0.00017436550620770832, 0.0005476445927320072, 0.0028185291438667798, 0.006591103259701535, 0.011501402695876893, 0.016896268970254757, 0.02189665445410793, 0.025490594918773066, 0.026646744043002508, 0.02443709897507405, 0.018156335269078647, 0.0074251392829820925, -0.007733897579646353, -0.0268569562732847, -0.049042127446603405, -0.0729969825186972, -0.09712878193485848, -0.11967049434616865, -0.13883023169867253, -0.15295332304661038, -0.16068198878387147, -0.16109639377677268, -0.1538230495531191, -0.13909856372171223, -0.11778020592525776, -0.0912993738076062, -0.061559216621099255, -0.030783025268581624, -0.0013250494680677942, 0.024540339764329858, 0.04483315844221355, 0.05806364901235325, 0.06338715978279774, 0.06070449986519212, 0.05069335656633104, 0.03476279970185089, 0.014929644750500175, -0.006377407140292516, -0.026571549763616538, -0.04319902519939584, -0.05424161209497317, -0.05840076111173769, -0.055332469936253986, -0.045803503183854656, -0.03174414973406099, -0.016178042629199484, -0.003022178276739838, 0.0032379385162602794, -0.0020165354075761216, -0.02301955800432637, -0.06305726007175316, -0.12390746730868843, -0.2053346471065924, -0.3046978188902942, -0.4167245923394558, -0.5334984989028272, -0.6446957660521146, -0.7380925852608922, -0.8003524488370198, -0.8180535098420502, -0.7789083711753941, -0.6731245846869689, -0.49481693560545853, -0.24337182889656475, 0.07534535191907434, 0.4480519464957474, 0.8534861271333395, 1.2623184952630524, 1.6376141330294613, 1.935868479444575, 2.108645280779791, 2.1047948378934307, 1.8732235046523118, 1.3659881949602706, 0.5415897353196126, -0.6316675596223539, -2.172471185046943, -4.0836639898448555, -6.34998827748124, -8.936608820742709, -11.788585840134298, -14.831428910339127, -17.97281129041604, -21.10548376995405, -24.111377483264807, -26.86664172941939, -29.247737542059042, -31.137851282423604, -32.43347337871962, -33.050914431900324, -32.932341431291206, -32.05097228666606, -30.415087566422038, -28.070559174027284, -25.101655699489644, -21.629961090325704, -17.81133376597367, -13.830933083041215, -9.89644413756744, -6.229805001421904, -3.057707287718804, -0.6007461867079316, 0.9374127207672363, 1.380521839468186, 0.5894592033191881, -1.52936245705003, -5.0173575103767085, -9.8593003488944, -15.981334168868118, -23.25164560893821, -31.483866823550866, -40.443130846870474, -49.85456994095742, -59.41384364163893, -68.79928844410944, -77.68558729563203, -85.75799579017128, -92.7258716469215, -98.33534360397071, -102.38051002471735, -104.71255123026303, -105.24629911413628, -103.96393108015583, -100.91559710150601, -96.21694141053396, -90.04363601807944, -82.62319319138268, -74.22440595209477, -65.1449843233624, -55.69815038392987, -46.19866312219012, -36.94906979482894, -28.22683711827336, -20.27270143144285, -13.281295032442005, -7.394325885339725, -2.696533127367383, 0.7854474140546442, 3.0813278976480354, 4.2726944287538755, 4.486125911300264, 3.884364580844355, 2.655923248887309, 1.0038157346517884, -0.8658276012750723, -2.7547488746277926, -4.482591007660582, -5.895472239800096, -6.872721511353782, -7.331405098177051, -7.22851370943599, -6.560810603662578, -5.362454774239535, -3.700638323029045, -1.6695811865765828, 0.6167075440550174, 3.032474334475454, 5.448455706962482, 7.739807126868363, 9.793309122240561, 11.513465155234956, 12.82718914548629, 13.68687935303835, 14.071809945206798, 13.987892275020572, 13.465679751915129, 12.55701458586336, 11.330607586877296, 9.866876534396413, 8.25245178613779, 6.574546864412932, 4.915710143569578, 3.3493215501027507, 1.9360184542819707, 0.7212201548507384, -0.2661620033560514, -1.0138268413214888, -1.525076800090075, -1.8168531516890287, -1.9170177440953762, -1.8611349713882235, -1.6890431944016886, -1.4414408326690518, -1.1567628929683675, -0.8685501335062619, -0.6035022149468509, -0.3803157947545199, -0.20933328781678703, -0.09296624727075893, -0.0267957024787437, -0.0012001573811598215, -0.003323993750967497, -0.01917734316764883, -0.03565445460495755, -0.04227123509256267, -0.032452736395917996, -0.004245226003471457, 0.039619810504043076, 0.0923209227368536, 0.14414417307250946, 0.1841715351863534, 0.20230056183757147, 0.1913995599628981, 0.1493824850979403, 0.08098536603340376, -0.0009581840971312823, -0.07491175231519967, -0.11082234583098699, -0.07115907152979256, 0.08720243354391966, 0.41032782444545346, 0.9439593825015384, 1.7298468200253865, 2.801924012970846, 4.182614436794904, 5.879552946274261, 7.8830011430482685, 10.164200514190062, 12.67485542446468, 15.347869775152075, 18.099380903643905, 20.832047238685007, 23.439458114066912, 25.811451550979015, 27.84018050507503, 29.426540560675104, 30.48605913604216, 30.9544038499281, 30.7920453740795, 29.987676135349474, 28.56015431256159, 26.558792682492125, 24.061906826332226, 21.173646931820866, 18.019244693657313, 14.738908737370288, 11.480691930298265, 8.39272697132214, 5.615316700255395, 3.273189664994715, 1.4684447467217496, 0.2748357900603998, -0.2663867433455806, -0.14882388707184005, 0.5986940070309852, 1.9137453566765381, 3.7038849833331198, 5.851938740514201, 8.222719886931342, 10.670774141844136, 13.048695993460163, 15.215524392656588, 17.04478394622944, 18.431614437507964, 19.298450880248318, 19.59905038212885, 19.320610209939503, 18.483863373955494, 17.141165586793846, 15.372716639149324, 13.281167588628804, 10.984920287604536, 8.610607084684634, 6.28521702719409, 4.128355958391638, 2.2451243259887277, 0.7200705586983609, -0.3875017872145737, -1.0464981201282162, -1.2550852654207678, -1.0398464504738436, -0.45312813010158537, 0.4312184172719129, 1.523397413130831, 2.724147682153455, 3.9317038929184553, 5.04877891418707, 5.989099314363445, 6.683072717773589, 7.082236249335516, 7.162263054121771, 6.924171277126594, 6.393763307045677, 5.619421055365543, 4.668392433042088, 3.6218377698136157, 2.568983552970718, 1.6007853208899883, 0.8035289700455125, 0.25279864977618194, 0.008210215257203477, 0.10925504472726082, 0.5725326971839528, 1.3905391017556845, 2.532066657366858, 3.9442000858646784, 5.5557379674009555, 7.281786367238407, 9.029206684289498, 10.702547295529582, 12.210062131461676, 13.469419490997328, 14.41273077238599, 14.990579235378979, 15.174799746018486, 14.95984672829075, 14.362683346538137, 13.421261159685212, 12.19172787442385, 10.744268622296772, 9.15823380789758, 7.516842448763835, 5.9017798297964426, 4.388049088245992, 3.039411446253011, 1.9047031131769738, 1.0152519427174371, 0.38353844711828927, 0.0031592520712826313, -0.14993753563962564, -0.11506030648603119, 0.05658346855686571, 0.30596226542271876, 0.5707254410197485, 0.789809406526558, 0.9078105185343247, 0.8788325997877605, 0.6695665162946195, 0.261413967637391, -0.34846163463177676, -1.1471977448883448, -2.107372048681151, -3.189109401233641, -4.342984100797914, -5.513495989478676, -6.642884557894128, -7.67500923028865, -8.558962460686562, -9.252228708850776, -9.723201032183564, -9.952929893146568, -9.935867968311207, -9.679716467357297, -9.20441947767509, -8.54039852684973, -7.7261835863056465, -6.805632721931196, -5.824953385692092, -4.82974342561701, -3.8622713303523923, -2.959133879546023, -2.149448175237456, -1.4537221052028357, -0.8834130481825931, -0.4411590608425457, -0.12162073208521566, 0.08717749283656454, 0.202156522622237, 0.24327169703652832, 0.2315649546327668, 0.18734550619820337, 0.12864008706663405, 0.07002295697743126, 0.021896928331682834, -0.009747067722737118, -0.0231069021630095, -0.019941334910004174, -0.004631581770840884, 0.0169483292754122, 0.038618918689952486, 0.05500501286706083, 0.062443092968111624, 0.05958351461615805, 0.047616875107837756, 0.030090500950119288, 0.01232369056563992, 0.0004722345247777202, 0.0003303917600633024, 0.01599054961073284, 0.0484994539162483, 0.09465680166976081, 0.14609778491726025, 0.1887832277279956, 0.20299145425025594, 0.16386700454827166, 0.04253572425932259, -0.19225285777071266, -0.5720427616356665, -1.1262788550545517, -1.8797691142643698, -2.8501956844823106, -4.045922469911751, -5.464210661588805, -7.090008983440795, -8.895478760395482, -10.840324804352594, -12.872959153969267, -14.932465936189935, -16.951277007764837, -18.858414031026776, -20.583107367542127, -22.05856920591962, -23.22568041164846, -24.036356893516476, -24.456446108502245, -24.46801993689843, -24.070263761240223, -23.279488554157695, -22.128245687288963, -20.66350184328215, -18.943991153885968, -17.036917433398166, -15.014223085400914, -12.94866971943992, -10.909986581666814, -8.961335703557568, -7.156317674479391, -5.536700947408462, -4.131022705637037, -2.9540973460128788, -2.007348239432506, -1.2800869324674546, -0.7515374201042538, -0.3933932603131199, -0.1726874620150921, -0.05474099829909409, -0.005958205818672299, 0.003742029626691828, -0.0009667034380069199, -0.002049614162235233, 0.011383474168317607, 0.043297436459068445, 0.09161179337011491, 0.14962132277171067, 0.20779679196303177, 0.2557633173453885, 0.28424559498931995, 0.2867755942588608, 0.2609854945714054, 0.2093510223806109, 0.1393055281905265, 0.06270856342456842, -0.0052815161882806515, -0.04781918610440668, -0.0483030678777068, 0.00757590416117341, 0.1298940880587712, 0.32288921999765396, 0.5838779352602564, 0.9028457977769089, 1.2627986935087872, 1.6408886892549557, 2.0102478598424396, 2.342380193709695, 2.6098971804612634, 2.7893296816281596, 2.8637190812012436, 2.8246899525180797, 2.673736146954411, 2.4225136087516765, 2.09204064571246, 1.7107403794426883, 1.3114559790647586, 0.9277523896572645, 0.5898513282142765, 0.32067396314335495, 0.13253763771694627, 0.02508174998296974, -0.015021955850864646, -0.012096352970535348, 0.0031225230626812477, 0.0008447332710166635, -0.037693395334116205, -0.10774242228527034, -0.16673326031105581, -0.11901256679709678, 0.1992836535386615, 1.0339382303328528, 2.7235362427514413, 5.706077633478457, 10.519930554296577, 17.79789984625763, 28.253454959592336, 42.65857644633941, 61.813269009241665, 86.50686579931532, 117.47218709692147, 155.33424257535833, 200.5566189199891, 253.38688237191124, 313.803764627991, 381.470077401472, 455.69437184190184, 535.4044987591535, 619.1359347564094, 705.0372558081289, 790.8944781900067, 874.1751691594425, 952.0922891391183, 1021.687575564761, 1079.9334509132477, 1123.84462703304, 1150.607642298319, 1157.7015922173168, 1143.0173452546717, 1104.972385635962, 1042.6123781784677, 955.6939472931357, 844.7437194296119, 711.0895074449214, 556.8605941642825, 384.95535819352415, 198.97592246139322, 3.1310292390381274, -197.89011862715634, -399.06851183346333, -595.2282842368331, -781.2267258520008, -952.1422761130299, -1103.4571771984595, -1231.2280401590724, -1332.2367008423691, -1404.1144702968334, -1445.4339566527017, -1455.7640070099565, -1435.6849271691976, -1386.7629094592344, -1311.4844501593714, -1213.1533817810794, -1095.7567932266975, -963.8036581860102, -822.1354664038001, -675.7305869611309, -529.5028876718749, -388.1096993609103, -255.77596030413918, -136.14134105320827, -32.13683055623225, 54.10420065677946, 121.29714033558875, 169.01799860934784, 197.67641119107182, 208.45205977124385, 203.19968110628292, 184.3266035820319, 154.64631044942738, 117.22095751384957, 75.19965767133705, 31.66012656261216, -10.539033439792043, -48.8874075778281, -81.32779313614945, -106.33298419482844, -122.95158669645225, -130.82180304907848, -130.1538013481451, -121.68285953987525, -106.59616049495654, -86.43924487109047, -63.00898870223584, -38.237477384280844, -14.074007099047668, 7.628365194986801, 25.215878589085946, 37.32174594437569, 42.934113722375855, 41.44139382407944, 32.65363998476766, 16.799857835074913, -5.497566274965577, -33.26899363786853, -65.26217622080782, -100.02022974375164, -135.9655368351845, -171.4865869012864, -205.0228539157185, -235.14319392514105, -260.61383547405796, -280.4527961167022, -293.9686703711922, -300.7827892384473, -300.83261275516736, -294.3585686645353, -281.8759323022194, -264.1342418884844, -242.0694363876347, -216.74377523107978, -189.28264516794644, -160.81485999419112, -132.4170862012716, -105.0651178285713, -79.59420077662621, -56.66995089355767, -36.770706433576834, -20.181447473593295, -6.998749632634636, 2.854423097157882, 9.605694602097058, 13.603854220081065, 15.28561790342306, 15.140196895872956, 13.674122143950253, 11.37882227998483, 8.702630512436064, 6.028521238835131, 3.6584169126462602, 1.8044282271067815, 0.5869270247229174, 0.038929232684792675, 0.11590792578079062, 0.7098821530181629, 1.66644528422298, 2.8032928251986178, 3.9287955526597833, 4.859538384419547, 5.4355941332972, 5.532603662554928, 5.070105302716252, 4.015845707189076, 2.3861031654299283, 0.24232742414440664, -2.315368990488222, -5.157156438441866, -8.134045067920525, -11.089178393287835, -13.86900419667941, -16.333674545379598, -18.366052720840905, -19.877923905150578, -20.81401722650339, -21.15360669931199, -20.909677658936168, -20.125899226806467, -18.871780768596352, -17.236489071396473, -15.321860068344485, -13.235153474257167, -11.082072839331918, -8.960512173777538, -6.955400730108979, -5.134935682302132, -3.5482472413190864, -2.224525878901416, -1.1737433217075828, -0.38862758562136335, 0.15239641332793016, 0.4816289285386763, 0.6382118338688403, 0.6642631277491644, 0.6013202533729178, 0.48732965135664597, 0.35435293464607925, 0.22708570997164032, 0.12220988694156142, 0.04853207503709784, 0.007786242231790555, -0.004037047041120343, 0.00499252969639634, 0.024569072508630368, 0.04392533253106817, 0.0533939405699184, 0.04562550895706147, 0.0163824214675206, -0.03512465596816223, -0.10634409414619539, -0.19187892998380213, -0.2842818091736314, -0.3750376042470441, -0.45560861103892386, -0.5184310114788646, -0.5577581120526935, -0.5702566971217874, -0.5553067827662972, -0.5149866182539761, -0.45375883731975486, -0.37790429848644264, -0.29477448003946227, -0.21195332320075128, -0.1364218782817595, -0.07381589179936363, -0.027854642196610675, 1.0209608795095449e-06, 0.0106290105312361, 0.007060694815772784, -0.005944787511433251, -0.022516772126407875, -0.03640995526327508, -0.041779396344928776, -0.03390744103356418, -0.009801734287929005, 0.03140267762448232, 0.08828340923939627, 0.15723408128704752, 0.23282145179283445, 0.3083595407155569, 0.37664145243100305, 0.4307520562958684, 0.46486988428023, 0.47496837906075384, 0.45933658422544615, 0.41885469126273644, 0.35698482332637155, 0.2794671420674055, 0.19374337432760502, 0.10816102203841492, 0.031038638642190797, -0.030307325551955682, -0.07046340080633771, -0.08663668138502481, -0.07908571538053476, -0.05119477674205814, -0.009150302166342094, 0.038781072963180285, 0.08333062349452243, 0.11557667350242079, 0.12844148002453937, 0.11818300220019459, 0.08571120918134588, 0.0375558451845213, -0.013673853082708404, -0.04946685418945053, -0.04630928689549466, 0.022669827742357644, 0.18534925106379152, 0.4676891039902431, 0.890411906181668, 1.4655251483075895, 2.192972109549475, 3.057721801744123, 4.027611869465565, 5.052236306920757, 6.063122460687058, 6.975370381530497, 7.6908355084641125, 8.102828061794444, 8.102186084233402, 7.5844617582917015, 6.457917320067967, 4.651858319881143, 2.124422328837294, -1.130418123637768, -5.077299585874858, -9.635800103256216, -14.67911525682701, -20.03540423710113, -25.49197801241338, -30.802334483319637, -35.695866034110544, -39.8898840639328, -43.10343456144338, -45.07223055378818, -45.56394755801023, -44.392954389694964, -41.43344101583624, -36.630270570311936, -30.006815288175932, -21.669106262833676, -11.805525054368731, -0.6823030725608743, 11.365212450620247, 23.94529407206929, 36.62604940232122, 48.95437630806498, 60.47673605743444, 70.76069855279036, 79.41654596822872, 86.11714317533333, 90.61434214246142, 92.75212990934767, 92.47540945847327, 89.83383336839107, 84.98050490801049, 78.16560395378065, 69.72439494856799, 60.06106513829713, 49.62913326519695, 38.90935270815847, 28.386276983637533, 18.524735842042222, 9.747468060506051, 2.4149180822384815, -3.191343406276851, -6.880731358257031, -8.560862763948867, -8.23957033456078, -6.0216941013542895, -2.1009213301762344, 3.2527712762411265, 9.709295023197065, 16.897396589991658, 24.425141942094434, 31.900774242028056, 38.952827752268114, 45.24873459133324, 50.51029119390802, 54.52519368879434, 57.15455712159233, 58.336036785955926, 58.08256302097535, 56.47696029955486, 53.66295366516756, 49.83326024321876, 45.21560985685235, 40.05762582747492, 34.61152037080494, 29.11957571774657, 23.801284135326878, 18.84292347762679, 14.389530003460171, 10.540264883872664, 7.347254469553287, 4.817622364221409, 2.918387746851256, 1.5837322798571913, 0.7240039127928993, 0.2357379205210232, 0.011937806533508464, -0.04812784778867604, -0.030294287048748487, 0.0013889853037911228, 0.009369431531827024, -0.015145727577043374, -0.05245255898564977, -0.05704761669980488, 0.037506173665220265, 0.3119553817513061, 0.8534964408698885, 1.7472777543677966, 3.067893483758153, 4.871488875564503, 7.189045856486215, 10.021329794467064, 13.335860360884046, 17.066129675577518, 21.11314234988899, 25.349268982187677, 29.62428161380343, 33.772610386973945, 37.62177473510492, 41.00147620599804, 43.752741814360945, 45.73656623543206, 46.841540219376924, 46.99002238005628, 46.14250675448223, 44.299952595738475, 41.50396816039367, 37.83486821475092, 33.40761871534736, 28.36590665925253, 22.87524383923317, 17.115091151160787, 11.270461574938778, 5.523271729988475, 0.044386032124543146, -5.013402128778141, -9.521181154759965, -13.378278890551783, -16.51501537904695, -18.893796027349957, -20.5085854103134, -21.38289377795455, -21.56672217802164, -21.132257836692887, -20.168319844336917, -18.774827518648294, -17.057252424154882, -15.121336219629194, -13.068330830493885, -10.990797399389788, -8.969365202613975, -7.07048480271354, -5.345167378461862, -3.8286725504554213, -2.5410560686449495, -1.4884485816944688, -0.6649140664591755, -0.054668849379960076, 0.3654592086218505, 0.6234934133983709, 0.7498894457493769, 0.7753648047806238, 0.7290728559954924, 0.6371837449446792, 0.5218992802735414, 0.4008967772495936, 0.2871741198586674, 0.18923980888772968, 0.11157684422348946, 0.05530135965802285, 0.018935358715101998, -0.0007849887172964645, -0.008129481287361883, -0.007678119829418961, -0.0037507977872703775, 1.4113181979700078e-05, 0.0009246605326255757, -0.0026498810774415677, -0.011296420769594378, -0.02468166903114081, -0.04175184280170985, -0.060974595651158404, -0.08059106027909532, -0.09885172520956921, -0.11421603745200493, -0.12549915273025739, -0.13195960669667375, -0.13332905167036624, -0.12978939934473602, -0.12190738149759058, -0.1105392427666845, -0.096719366007337, -0.08154622818262351, -0.06607743467189199, -0.051243007903851, -0.03778315714644846, -0.026213032675783003, -0.01681325060701675, -0.009645501235925598, -0.004584923514759336, -0.0013664104356150373, 0.0003626391295514687, 0.0009903464458108867, 0.0008946652550963618, 0.00040793009995236006, -0.00020620937527132408, -0.0007631170660306274, -0.0011559934147625664, -0.0013456245242896847, -0.0013442066610952394, -0.001196601039447438, -0.0009621987381399053, -0.0006996349960159115, -0.0004555446143267273, -0.00025931677401801396, -0.00012261495408584007, -4.236722509793e-05, -5.839375068290516e-06, 3.6376425236396737e-06, 1.542622858898863e-06, -1.432852741128815e-06, -9.535672545603896e-07, 1.4629164177195532e-06, 6.466288751418987e-07], 'positive_zeros': ['0.15258689065323235842523057925581', '0.34669964667033080075886463479769', '0.43068129681576193715264096458533', '0.63304588066824351742954666002519', '0.886188653004514832453301012964760', '0.924940453784855138517614883580289', '0.983078397169420318390823652211802', '1.16619913820001205251355152874883', '1.17067295121211329376219747123417', '1.18920143630124494389179214402906', '1.22554977726817142538065734546973', '1.25945269566180054280318475513118', '1.36417890653897213981761366211123', '1.46741829347561648117891561707153', '1.65383512614875707759921920345836', '1.66014619884992120719471127831771', '1.76802792579404070325287092039778', '1.89995998755732687185511280733306', '1.99435865501308734993850452317026', '2.01720155902631622372864514192317', '2.08759716635764155310524896208339', '2.09112482333349634024479048525924', '2.19168363399318001586107407331904', '2.23750292159158818923295133690228', '2.26815971663040867106034850828978', '2.51323951846356027015164846668980', '2.51933629844779239433390031451702', '2.55117617851007652666873958086115', '2.65032457991358590505413557978087', '2.65267263624233295962240111953487', '2.73158617323826797637217215701542', '2.77689284013895541461487162776246', '2.85759782762158150729223672888088', '2.91714526215407673227707678162107', '2.92508562816897517109392922132136', '2.98738465729378153963531781143106', '3.07971541992418771274754003250094', '3.15197777062040201778723862840532', '3.28850976420990516536381320701610', '3.31581641547828152460305261833983', '3.32318865814808563111796291151672', '3.37066188118227708094761357023249', '3.42251186699316920350359868858487', '3.52747787912402605060295333949564', '3.54630121080593589671291324978170', '3.56281480999043333341723487878160', '3.58348915984394351229030868609261', '3.68462016643140450619198518861867', '3.72729047365320498732631439076850', '3.98833281026919273058005822233207', '3.99878968579795002560419198530738', '4.02893505616840435110266225466660', '4.03273756133781538159435564944508', '4.05910810440658591429789221393364', '4.14883819720093513771396099830947', '4.16629354733893665600468378208200', '4.16858829870369060677789181889453', '4.27904039296474071752662941925371', '4.36961790662430934089483371881748', '4.38532399028027712552371183486147', '4.39645062846893636768718656376038', '4.43987910172009155018175336988960', '4.49058098561877458183449576552524', '4.53598131170721908770322959431812', '4.57340288780439488799194435188201', '4.58220999494675065451734370454300', '4.80831694470678973350776581739004', '4.84887751292469121028238542199640', '4.86030043943429285393228253724178', '4.87269908046222981157458928013264', '4.90896047274438158454242020588894', '4.93063230822298460842323990550040', '4.97212523801421561005704019331452', '5.03734489667721323162576234370320', '5.09743961299624291393947322844265', '5.15921035436385732826333329337392', '5.18830002093268639229146036758460', '5.19495858522531893981043954340109', '5.29324493533744418782176899166862', '5.33131276202724699023675114036100', '5.40635447902892503915551444763965', '5.54250119422698290627006493039241', '5.61301910866459448418082226057958', '5.61454609782385332099476287105933', '5.65650055307991812059617099623932', '5.66612911225605233875556011169191', '5.68926862580309376658556635019842', '5.73923556404982947143949327324322', '5.74198513557267096752641050780875', '5.77369127872901694884807182199133', '5.79209469452651247114826755125281', '5.86752371143551787277716215239560', '5.94239978384049176612817710446941', '6.18244061513063455055842729298909', '6.19530651296143474492933288811715', '6.25339330649354929453520665190084', '6.25632512553464191221870340413152', '6.27133000468208695667130827155505', '6.32180314362712704775376814863227', '6.40739113875133326004097908021809', '6.41782736838824107089606649835020', '6.47743853029988811298947408804006', '6.51690755325409044029723532081298', '6.61353958824165358962593857295021', '6.66676201213035514869613039975189', '6.69492827332307969169185530593124', '6.70304414427207437864487071741193', '6.81208981858364561726121642537185', '6.82625993105732086858842380188937', '6.83348811615590779726675734284363', '6.90681732541223864727579472436446', '6.91281092020145091713910841683360', '6.97182912173584667892716283588844', '6.99394491256407438496958343241127', '7.02747784360579723588534146420915', '7.04515517372000576502886756315098', '7.16001962700275869855861589361933', '7.35683961957015230975891221852639', '7.36890440183870921641968434092624', '7.39307124777618580017454041052786', '7.39534717613930537514239017694894', '7.39805918383502590889406739924031', '7.45824956389277756248743175799353', '7.50389787019201477383881240553281', '7.58087061093774244561794553613105', '7.67173441000587862871541294112297', '7.67782804496646100838645389234030', '7.69254626215024327712184032929974', '7.72256321691022467921170622069677', '7.74723202868378783724316144783512', '7.923399406818103638840591730882818', '7.952941532957029686974848945024628', '7.988096721370573416170426353330815', '7.990087919011386982709375293522547', '8.038330664443173014179896660808776', '8.155441970492068531937367948537723', '8.172122468793051809769186250228315', '8.257182242482379676395163267012986', '8.273103022521806797360665315061730', '8.274175481943559679583579421570117', '8.300577029821686795597087425656910', '8.366465428727734270716279903429775', '8.391885694492574606477852346425180', '8.437462614021968044226496234105967', '8.557028932020514747988458097692036', '8.576521189996604884775192467179508', '8.600318455223118400348272185968077', '8.639985437574688295331768699888131', '8.696172754021391535641798082821197', '8.709741581406830751127542904934827', '8.760863659997982818502349970740994', '8.778283416708278123001854072352347', '8.848465226937882216976576090272637', '8.869676825760762830205283667504743', '8.870609657124705274573867854667780', '8.989823672051613544856246502109409', '9.049721564052550452092542956763031', '9.051231326211761942788019023430312', '9.108693262732714004245426640441491', '9.179963402800902264464744338324841'], 'prelabel': '32-3267e16-1.1-c0e16-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.276888952208459, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c0e16-0', 'trace_hash': 981285227265663419, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.15258689065323235842523057926', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.34669964667033080075886463480', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.43068129681576193715264096459', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2494.0212030618445, 'bad_primes': [3, 11], 'central_character': '1.1', 'conductor': 168417087089595893335914666294701590604740371451720604481, 'conductor_radical': 33, 'degree': 32, 'dirichlet_coefficients': [1, 0, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 4, 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, -4, 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, -4, 0, 0, -16], 'euler11': [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], 'euler13': [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], 'euler17': [1, 0, 4, 0, 10, 0, 20, 0, 35, 0, 52, 0, 68, 0, 80, 0, 85, 0, 80, 0, 68, 0, 52, 0, 35, 0, 20, 0, 10, 0, 4, 0, 1], 'euler19': [1, 0, 0, 0, -2, 0, 0, 0, 3, 0, 0, 0, -4, 0, 0, 0, 5, 0, 0, 0, -4, 0, 0, 0, 3, 0, 0, 0, -2, 0, 0, 0, 1], 'euler2': [1, 0, 4, 0, 10, 0, 20, 0, 35, 0, 52, 0, 68, 0, 80, 0, 85, 0, 80, 0, 68, 0, 52, 0, 35, 0, 20, 0, 10, 0, 4, 0, 1], 'euler23': [1, 0, 16, 0, 120, 0, 560, 0, 1820, 0, 4368, 0, 8008, 0, 11440, 0, 12870, 0, 11440, 0, 8008, 0, 4368, 0, 1820, 0, 560, 0, 120, 0, 16, 0, 1], 'euler29': [1, 0, 4, 0, 10, 0, 20, 0, 35, 0, 52, 0, 68, 0, 80, 0, 85, 0, 80, 0, 68, 0, 52, 0, 35, 0, 20, 0, 10, 0, 4, 0, 1], 'euler3': [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], 'euler31': [1, 0, 2, 0, 1, 0, -2, 0, -4, 0, -4, 0, -1, 0, 4, 0, 7, 0, 4, 0, -1, 0, -4, 0, -4, 0, -2, 0, 1, 0, 2, 0, 1], 'euler37': [1, 0, -4, 0, 10, 0, -20, 0, 35, 0, -52, 0, 68, 0, -80, 0, 85, 0, -80, 0, 68, 0, -52, 0, 35, 0, -20, 0, 10, 0, -4, 0, 1], 'euler41': [1, 0, 4, 0, 10, 0, 20, 0, 35, 0, 52, 0, 68, 0, 80, 0, 85, 0, 80, 0, 68, 0, 52, 0, 35, 0, 20, 0, 10, 0, 4, 0, 1], 'euler43': [1, 0, 0, 0, 8, 0, 0, 0, 28, 0, 0, 0, 56, 0, 0, 0, 70, 0, 0, 0, 56, 0, 0, 0, 28, 0, 0, 0, 8, 0, 0, 0, 1], 'euler47': [1, 0, -4, 0, 10, 0, -20, 0, 35, 0, -52, 0, 68, 0, -80, 0, 85, 0, -80, 0, 68, 0, -52, 0, 35, 0, -20, 0, 10, 0, -4, 0, 1], 'euler5': [1, 0, -4, 0, 10, 0, -20, 0, 35, 0, -52, 0, 68, 0, -80, 0, 85, 0, -80, 0, 68, 0, -52, 0, 35, 0, -20, 0, 10, 0, -4, 0, 1], 'euler53': [1, 0, -4, 0, 10, 0, -20, 0, 35, 0, -52, 0, 68, 0, -80, 0, 85, 0, -80, 0, 68, 0, -52, 0, 35, 0, -20, 0, 10, 0, -4, 0, 1], 'euler59': [1, 0, -4, 0, 10, 0, -20, 0, 35, 0, -52, 0, 68, 0, -80, 0, 85, 0, -80, 0, 68, 0, -52, 0, 35, 0, -20, 0, 10, 0, -4, 0, 1], 'euler61': [1, 0, 0, 0, -2, 0, 0, 0, 3, 0, 0, 0, -4, 0, 0, 0, 5, 0, 0, 0, -4, 0, 0, 0, 3, 0, 0, 0, -2, 0, 0, 0, 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, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], 'euler71': [1, 0, -4, 0, 10, 0, -20, 0, 35, 0, -52, 0, 68, 0, -80, 0, 85, 0, -80, 0, 68, 0, -52, 0, 35, 0, -20, 0, 10, 0, -4, 0, 1], 'euler73': [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], 'euler79': [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], 'euler83': [1, 0, 4, 0, 10, 0, 20, 0, 35, 0, 52, 0, 68, 0, 80, 0, 85, 0, 80, 0, 68, 0, 52, 0, 35, 0, 20, 0, 10, 0, 4, 0, 1], 'euler89': [1, 0, 16, 0, 120, 0, 560, 0, 1820, 0, 4368, 0, 8008, 0, 11440, 0, 12870, 0, 11440, 0, 8008, 0, 4368, 0, 1820, 0, 560, 0, 120, 0, 16, 0, 1], 'euler97': [1, 4, 6, 0, -15, -28, -22, 12, 60, 80, 36, -56, -129, -120, -20, 108, 167, 108, -20, -120, -129, -56, 36, 80, 60, 12, -22, -28, -15, 0, 6, 4, 1], 'euler_factors': [[1, 0, 4, 0, 10, 0, 20, 0, 35, 0, 52, 0, 68, 0, 80, 0, 85, 0, 80, 0, 68, 0, 52, 0, 35, 0, 20, 0, 10, 0, 4, 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, -4, 0, 10, 0, -20, 0, 35, 0, -52, 0, 68, 0, -80, 0, 85, 0, -80, 0, 68, 0, -52, 0, 35, 0, -20, 0, 10, 0, -4, 0, 1], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 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, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], [1, 0, 4, 0, 10, 0, 20, 0, 35, 0, 52, 0, 68, 0, 80, 0, 85, 0, 80, 0, 68, 0, 52, 0, 35, 0, 20, 0, 10, 0, 4, 0, 1], [1, 0, 0, 0, -2, 0, 0, 0, 3, 0, 0, 0, -4, 0, 0, 0, 5, 0, 0, 0, -4, 0, 0, 0, 3, 0, 0, 0, -2, 0, 0, 0, 1], [1, 0, 16, 0, 120, 0, 560, 0, 1820, 0, 4368, 0, 8008, 0, 11440, 0, 12870, 0, 11440, 0, 8008, 0, 4368, 0, 1820, 0, 560, 0, 120, 0, 16, 0, 1], [1, 0, 4, 0, 10, 0, 20, 0, 35, 0, 52, 0, 68, 0, 80, 0, 85, 0, 80, 0, 68, 0, 52, 0, 35, 0, 20, 0, 10, 0, 4, 0, 1], [1, 0, 2, 0, 1, 0, -2, 0, -4, 0, -4, 0, -1, 0, 4, 0, 7, 0, 4, 0, -1, 0, -4, 0, -4, 0, -2, 0, 1, 0, 2, 0, 1], [1, 0, -4, 0, 10, 0, -20, 0, 35, 0, -52, 0, 68, 0, -80, 0, 85, 0, -80, 0, 68, 0, -52, 0, 35, 0, -20, 0, 10, 0, -4, 0, 1], [1, 0, 4, 0, 10, 0, 20, 0, 35, 0, 52, 0, 68, 0, 80, 0, 85, 0, 80, 0, 68, 0, 52, 0, 35, 0, 20, 0, 10, 0, 4, 0, 1], [1, 0, 0, 0, 8, 0, 0, 0, 28, 0, 0, 0, 56, 0, 0, 0, 70, 0, 0, 0, 56, 0, 0, 0, 28, 0, 0, 0, 8, 0, 0, 0, 1], [1, 0, -4, 0, 10, 0, -20, 0, 35, 0, -52, 0, 68, 0, -80, 0, 85, 0, -80, 0, 68, 0, -52, 0, 35, 0, -20, 0, 10, 0, -4, 0, 1], [1, 0, -4, 0, 10, 0, -20, 0, 35, 0, -52, 0, 68, 0, -80, 0, 85, 0, -80, 0, 68, 0, -52, 0, 35, 0, -20, 0, 10, 0, -4, 0, 1], [1, 0, -4, 0, 10, 0, -20, 0, 35, 0, -52, 0, 68, 0, -80, 0, 85, 0, -80, 0, 68, 0, -52, 0, 35, 0, -20, 0, 10, 0, -4, 0, 1], [1, 0, 0, 0, -2, 0, 0, 0, 3, 0, 0, 0, -4, 0, 0, 0, 5, 0, 0, 0, -4, 0, 0, 0, 3, 0, 0, 0, -2, 0, 0, 0, 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, -4, 0, 10, 0, -20, 0, 35, 0, -52, 0, 68, 0, -80, 0, 85, 0, -80, 0, 68, 0, -52, 0, 35, 0, -20, 0, 10, 0, -4, 0, 1], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], [1, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, -1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 1], [1, 0, 4, 0, 10, 0, 20, 0, 35, 0, 52, 0, 68, 0, 80, 0, 85, 0, 80, 0, 68, 0, 52, 0, 35, 0, 20, 0, 10, 0, 4, 0, 1], [1, 0, 16, 0, 120, 0, 560, 0, 1820, 0, 4368, 0, 8008, 0, 11440, 0, 12870, 0, 11440, 0, 8008, 0, 4368, 0, 1820, 0, 560, 0, 120, 0, 16, 0, 1], [1, 4, 6, 0, -15, -28, -22, 12, 60, 80, 36, -56, -129, -120, -20, 108, 167, 108, -20, -120, -129, -56, 36, 80, 60, 12, -22, -28, -15, 0, 6, 4, 1]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3267/1/l/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': '32-3267e16-1.1-c0e16-0-0', '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': '32-3267e16-1.1-c0e16-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.276888952208459, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e16-0', 'trace_hash': 981285227265663419, 'z1': {'__RealLiteral__': 0, 'data': '0.15258689065323235842523057926', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '193426863523529205827188716495,439494015200559894639143278553,545953404415572843696792945240,802480990601106978280541897092,1123377577896619335956716516087,1172501321415742493442344177052,1246199920243221362470633723014,1478333037524889129713394922538,1484004269274988131109145730022,1507491914519545665937449600801,1553568910763570360456978195876,1596545965614742990109085064173,1729302209692817691796898479554,1860173680510249316601594616932,2241241661353087129236355270974,2650815637450856802693415901074', 'Lhash_array': ['193426863523529205827188716495', '439494015200559894639143278553', '545953404415572843696792945240', '802480990601106978280541897092', '1123377577896619335956716516087', '1172501321415742493442344177052', '1246199920243221362470633723014', '1478333037524889129713394922538', '1484004269274988131109145730022', '1507491914519545665937449600801', '1553568910763570360456978195876', '1596545965614742990109085064173', '1729302209692817691796898479554', '1860173680510249316601594616932', '2241241661353087129236355270974', '2650815637450856802693415901074'], 'label': '32-3267e16-1.1-c0e16-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3267/1/l/a'}