Lfunction data - 24-3380e12-1.1-c0e12-0-2

Formats: - HTML - YAML - JSON - 2026-01-14T15:47:13.509600

• lfunc_lfunctions •

  Column	Type
  A10	numeric
  A2	numeric
  A3	numeric
  A4	numeric
  A5	numeric
  A6	numeric
  A7	numeric
  A8	numeric
  A9	numeric
  Lhash	text
  a10	jsonb
  a2	jsonb
  a3	jsonb
  a4	jsonb
  a5	jsonb
  a6	jsonb
  a7	jsonb
  a8	jsonb
  a9	jsonb
  accuracy	smallint
  algebraic	boolean
  analytic_conductor	double precision
  analytic_normalization	numeric
  bad_lfactors	jsonb
  bad_primes	bigint[]
  central_character	text
  coeff_info	jsonb
  coefficient_field	text
  conductor	numeric
  conductor_radical	integer
  conjugate	text
  credit	text
  degree	smallint
  dirichlet_coefficients	jsonb
  euler_factors	jsonb
  euler_factors_factorization	jsonb
  gamma_factors	jsonb
  group	text
  index	smallint
  label	text
  leading_term	text
  load_key	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  origin	text
  plot_delta	numeric
  plot_values	jsonb
  positive_zeros	jsonb
  precision	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  root_number	text
  self_dual	boolean
  sign_arg	numeric
  spectral_label	text
  st_group	text
  symmetry_type	text
  trace_hash	bigint
  types	jsonb
  values	jsonb
  z1	numeric
  z2	numeric
  z3	numeric

  
  {'Lhash': '520115774389156586278672981953,722765930816619848051145614207,892077891831292194257989985889,1035882074544800704701564868554,1199046823644490003011689832958,1302552108441503826859898959436,1512851749860466898582814070716,1542224275963170204639493785470,2240700405843963017609802552381,2349037400331036082022387816404,2522202050671437172892289350886,3147681933424124456112146712469', 'a10': 0, 'a2': 0, 'a3': -2, 'a4': 3, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 530.7449806163954, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, -3, 0, 6, 0, -7, 0, 6, 0, -3, 0, 1]], [5, [1, 0, 6, 0, 15, 0, 20, 0, 15, 0, 6, 0, 1]], [13, [1]]], 'bad_primes': [2, 5, 13], 'central_character': '3380.1', 'coefficient_field': '1.1.1.1', 'conductor': 2223311955453421620312454598656000000000000, 'conductor_radical': 130, 'degree': 24, 'euler_factors': [[1, 0, -3, 0, 6, 0, -7, 0, 6, 0, -3, 0, 1], [1, 2, 1, -2, -4, -2, 3, 4, -1, -6, -4, 4, 9, 4, -4, -6, -1, 4, 3, -2, -4, -2, 1, 2, 1], [1, 0, 6, 0, 15, 0, 20, 0, 15, 0, 6, 0, 1], [1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1], [1, 0, -6, 0, 21, 0, -50, 0, 90, 0, -126, 0, 141, 0, -126, 0, 90, 0, -50, 0, 21, 0, -6, 0, 1], [1], [1, 0, 6, 0, 21, 0, 50, 0, 90, 0, 126, 0, 141, 0, 126, 0, 90, 0, 50, 0, 21, 0, 6, 0, 1], [1, 0, -6, 0, 21, 0, -50, 0, 90, 0, -126, 0, 141, 0, -126, 0, 90, 0, -50, 0, 21, 0, -6, 0, 1], [1, -2, 1, 2, -4, 2, 3, -4, -1, 6, -4, -4, 9, -4, -4, 6, -1, -4, 3, 2, -4, 2, 1, -2, 1], [1, -2, 1, 2, -4, 2, 3, -4, -1, 6, -4, -4, 9, -4, -4, 6, -1, -4, 3, 2, -4, 2, 1, -2, 1], [1, 0, 12, 0, 66, 0, 220, 0, 495, 0, 792, 0, 924, 0, 792, 0, 495, 0, 220, 0, 66, 0, 12, 0, 1], [1, 0, -6, 0, 21, 0, -50, 0, 90, 0, -126, 0, 141, 0, -126, 0, 90, 0, -50, 0, 21, 0, -6, 0, 1], [1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1], [1, -2, 1, 2, -4, 2, 3, -4, -1, 6, -4, -4, 9, -4, -4, 6, -1, -4, 3, 2, -4, 2, 1, -2, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -6, 0, 7, 0, -6, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, -12, 0, 66, 0, -220, 0, 495, 0, -792, 0, 924, 0, -792, 0, 495, 0, -220, 0, 66, 0, -12, 0, 1], [1, 0, -6, 0, 21, 0, -50, 0, 90, 0, -126, 0, 141, 0, -126, 0, 90, 0, -50, 0, 21, 0, -6, 0, 1], [1, -2, 1, 2, -4, 2, 3, -4, -1, 6, -4, -4, 9, -4, -4, 6, -1, -4, 3, 2, -4, 2, 1, -2, 1], [1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1], [1, 0, -6, 0, 21, 0, -50, 0, 90, 0, -126, 0, 141, 0, -126, 0, 90, 0, -50, 0, 21, 0, -6, 0, 1], [1, 0, 12, 0, 66, 0, 220, 0, 495, 0, 792, 0, 924, 0, 792, 0, 495, 0, 220, 0, 66, 0, 12, 0, 1], [1, 0, -12, 0, 66, 0, -220, 0, 495, 0, -792, 0, 924, 0, -792, 0, 495, 0, -220, 0, 66, 0, -12, 0, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -6, 0, 7, 0, -6, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1], [1, 0, -6, 0, 21, 0, -50, 0, 90, 0, -126, 0, 141, 0, -126, 0, 90, 0, -50, 0, 21, 0, -6, 0, 1], [1, 2, 1, -2, -4, -2, 3, 4, -1, -6, -4, 4, 9, 4, -4, -6, -1, 4, 3, -2, -4, -2, 1, 2, 1], [1, 4, 10, 20, 35, 56, 84, 116, 149, 180, 206, 224, 231, 224, 206, 180, 149, 116, 84, 56, 35, 20, 10, 4, 1], [1, -12, 78, -352, 1221, -3432, 8074, -16236, 28314, -43252, 58278, -69576, 73789, -69576, 58278, -43252, 28314, -16236, 8074, -3432, 1221, -352, 78, -12, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -6, 0, 7, 0, -6, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, 6, 0, 21, 0, 50, 0, 90, 0, 126, 0, 141, 0, 126, 0, 90, 0, 50, 0, 21, 0, 6, 0, 1]], 'euler_factors_factorization': [[[[1, 0, -1, 0, 1], 3]], [[[1, 1, 0, -1, -1, 0, 1, 0, -1, -1, 0, 1, 1], 2]], [[[1, 0, 1], 6]], [[[1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1], 1]], [[[1, 0, -1, 0, 1], 6]], [1], [[[1, -1, 1], 6], [[1, 1, 1], 6]], [[[1, 0, -1, 0, 1], 6]], [[[1, -1, 0, 1, -1, 0, 1, 0, -1, 1, 0, -1, 1], 2]], [[[1, -1, 0, 1, -1, 0, 1, 0, -1, 1, 0, -1, 1], 2]], [[[1, 0, 1], 12]], [[[1, 0, -1, 0, 1], 6]], [[[1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1], 1]], [[[1, -1, 0, 1, -1, 0, 1, 0, -1, 1, 0, -1, 1], 2]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], 2]], [[[1, -1], 12], [[1, 1], 12]], [[[1, 0, -1, 0, 1], 6]], [[[1, -1, 0, 1, -1, 0, 1, 0, -1, 1, 0, -1, 1], 2]], [[[1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1], 1]], [[[1, 0, -1, 0, 1], 6]], [[[1, 0, 1], 12]], [[[1, -1], 12], [[1, 1], 12]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], 2]], [[[1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1], 1]], [[[1, 0, -1, 0, 1], 6]], [[[1, 1, 0, -1, -1, 0, 1, 0, -1, -1, 0, 1, 1], 2]], [[[1, 1, 1, 1, 1, 1, 1], 4]], [[[1, -1, 1], 12]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], 2]], [[[1, -1, 1], 6], [[1, 1, 1], 6]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 2, 'label': '24-3380e12-1.1-c0e12-0-2', 'leading_term': '3.6520816118340808275552102296435902911094382025077164668704691524910143248108763980814747', '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}], 'nu_real_doubled': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3380/1/w/e', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0048828125', 'prec': 40}, 'plot_values': [3.6520816118340824, 3.6593689988969307, 3.665055586301902, 3.669419587739403, 3.67274008742455, 3.675296352108995, 3.677367331815484, 3.6792313475259015, 3.6811659634940037, 3.6834480415856268, 3.6863539750613357, 3.690150546862521, 3.694961304271573, 3.7007742278498985, 3.7074802270369016, 3.714945012321819, 3.723031638068178, 3.731600160885315, 3.7405073339890147, 3.7496063398437305, 3.7587465637120454, 3.7677734936044924, 3.7765461275339267, 3.7849593454273776, 3.792910749991398, 3.800299816092811, 3.8070410550360863, 3.8130505184338745, 3.818241320706012, 3.822523628585966, 3.825804663315724, 3.8279887168138256, 3.8289750840739116, 3.82864467606821, 3.826868622466523, 3.8235153439980865, 3.8184507915056187, 3.8115364694103904, 3.802623192523248, 3.791558345538507, 3.7781885781745097, 3.762360303592166, 3.7439203259922254, 3.722719204509547, 3.6986129602082163, 3.6714605195913608, 3.6411242310027747, 3.6074706732398054, 3.5703715179702016, 3.5297043495130627, 3.4853533784330826, 3.4372108026483574, 3.3851779741106327, 3.3291672314554286, 3.2691053219328676, 3.2049325477632675, 3.1366032251806995, 3.0640868580991665, 2.9873693175117695, 2.9064540181360474, 2.821363082983763, 2.73213829696772, 2.6388417252874725, 2.541557782373349, 2.440398660283846, 2.3355039767532033, 2.2270380036460775, 2.1151901754550377, 2.0001755648276247, 1.8822352193459335, 1.761636344929863, 1.6386723212488785, 1.5136625346870523, 1.3869520518636143, 1.2589132367251714, 1.1299470151666968, 1.0004770670737544, 0.870947703810559, 0.741822182956259, 0.6135807711374748, 0.48671855202988573, 0.36174297875075756, 0.23917117222047693, 0.11952696962905852, 0.0033381285522886234, -0.10886495069632879, -0.21655558085343535, -0.31921630188426636, -0.41634295898840157, -0.5074488958903707, -0.5920692473640882, -0.669765298751584, -0.7401288771216091, -0.8027867357151612, -0.8574048820097517, -0.9036926815313069, -0.9414077595853563, -0.9703607928713582, -0.9904193976170471, -1.0015111242982513, -1.0036261966939133, -0.9968199065655821, -0.9812145354735985, -0.9570007568341268, -0.9244384736607363, -0.8838574317473041, -0.8356582048789737, -0.7803102978175153, -0.7183497999511926, -0.6503766858411364, -0.5770514609778331, -0.49909050470076605, -0.4172609000841702, -0.33237463076547696, -0.24528207618396466, -0.15686492601896637, -0.068029546558791, 0.020301918527738234, 0.10720163566387336, 0.1917456041371742, 0.2730234761639579, 0.35014865996305744, 0.42226875866947494, 0.4885757450686849, 0.5483159636522512, 0.6007999133328186, 0.645411636067446, 0.6816179716851157, 0.7089773137768778, 0.7271471435826913, 0.7358905896780992, 0.7350819336898866, 0.724710947986478, 0.7048861092705121, 0.675836718826795, 0.6379126085123736, 0.5915827918460823, 0.5374338281827618, 0.476164716446104, 0.40858002137651755, 0.3355819396924447, 0.2581608065247782, 0.1773841043210491, 0.09438406259671149, 0.010343960288568188, -0.07351675638742605, -0.15595858683850544, -0.2357379961919895, -0.3116247290839777, -0.3824210685222774, -0.4469799372468953, -0.5042227657058286, -0.5531569581112895, -0.5928926869829291, -0.6226587445216831, -0.6418171809498194, -0.6498764657718035, -0.646503090562536, -0.6315318978219538, -0.6049733437702535, -0.5670180394134797, -0.5180387422572488, -0.4585895916253915, -0.3894024932218676, -0.31138059849875616, -0.22558886698335381, -0.1332417444547816, -0.0356880359138097, 0.06560689298724247, 0.16908110654034664, 0.2730980267456059, 0.3759725936400355, 0.47599825408432417, 0.5714748808312735, 0.6607375793240606, 0.7421859447844592, 0.8143133062130973, 0.875735474791814, 0.9252186249485702, 0.9617058195188362, 0.9843411396672124, 0.9924915775138758, 0.9857667522248201, 0.9640342569819373, 0.9274309471907038, 0.876370099140933, 0.811544041063498, 0.7339220265489087, 0.6447432343773366, 0.545504943628226, 0.4379451201200527, 0.3240201691051312, 0.20587813122805432, 0.0858280324169757, -0.03369362659175204, -0.15016373920000395, -0.26101556573072215, -0.3636836207352285, -0.45565036337989334, -0.5344940692317709, -0.5979369039609196, -0.6438920413805455, -0.6705093023798022, -0.6762183718522886, -0.6597687036954585, -0.6202649737487641, -0.5571973658669133, -0.47046809539170725, -0.3604103291171146, -0.227799238343152, -0.07385417848622386, 0.0997658233653937, 0.29097501532663284, 0.49728259109432565, 0.7158228531176902, 0.9433937017080218, 1.1765031272584547, 1.4114229686031738, 1.6442488182926045, 1.8709678329385777, 2.0875363406988328, 2.2899565671483892, 2.474352596850492, 2.637050909123573, 2.7746610920038774, 2.8841551918633073, 2.9629442091888873, 3.0089502372109984, 3.0206727521893164, 2.997247380314388, 2.938499479259957, 2.8449898151473136, 2.718035554939285, 2.5597252267741415, 2.3729218632932803, 2.161252512337401, 1.929083711700796, 1.6814827547546292, 1.4241648159066436, 1.1634262552748662, 0.9060652935132325, 0.6592927084869679, 0.43062350339698513, 0.2277610978055332, 0.05847579931391192, -0.06952310172301544, -0.14871965337046023, -0.1719258891553901, -0.1324165963526591, -0.024061920710194876, 0.15854455206327842, 0.4199660003244145, 0.7638126037569741, 1.1926420022181228, 1.707874554044676, 2.309724122198585, 2.997145939750336, 3.7678029831768343, 4.61805196374845, 5.542949754066506, 6.536280742440472, 7.59061089897399, 8.697379609378077, 9.84698305324038, 11.028880380205486, 12.231722358455904, 13.443497721416119, 14.651689638289918, 15.84344411203106, 17.00574776265295, 18.125611721208443, 19.190262254868376, 20.187380511135125, 21.105286194952992, 21.933078329525017, 22.66080014507132, 23.27959232538669, 23.781832965069967, 24.161264123682216, 24.413086452490113, 24.534035283861694, 24.522435551183175, 24.37827375239579, 24.103254298318006, 23.700695111553305, 23.17546400163018, 22.533903301236595, 21.783731509892494, 20.93392359325834, 19.994574146855996, 18.976747149542383, 17.89229750500919, 16.753697550672253, 15.573910437666285, 14.366134441651475, 13.143564770246467, 11.919197318220613, 10.705639044880504, 9.514928022864229, 8.358366183459667, 7.246367526034822, 6.188325066236151, 5.1924990407793885, 4.265940950667558, 3.414415112844767, 2.6423188950706527, 1.9526637397357292, 1.3470833777120994, 0.8258661250344896, 0.3880100583978181, 0.031299444574017406, -0.2475995840633779, -0.4530264532971036, -0.5901997227901893, -0.6650836944558958, -0.6842445722897422, -0.65469458346965, -0.5837338402962234, -0.47879395117394186, -0.3472865208159681, -0.19645948659124612, -0.03326398595519474, 0.1357658544278678, 0.3046177956315089, 0.46788544567840673, 0.6208426132275426, 0.7595015906398664, 0.8806467465710972, 0.9818482644264552, 1.0614569251279342, 1.1185809101227058, 1.1530460363963275, 1.1653411758480245, 1.1565509013826838, 1.128277996064208, 1.0825590925119113, 1.0217732932869754, 0.9485469914675573, 0.8656586058907259, 0.7759443951976924, 0.6822094072876996, 0.587145503556368, 0.4932581687529972, 0.4028036963486697, 0.317738283576368, 0.23968092491458834, 0.1698857125451716, 0.1092279068888649, 0.058204091892298075, 0.016944683462670584, -0.01476226132089019, -0.03743721346027685, -0.051866745953799136, -0.059054387165063615, -0.060166683465982675, -0.056476350736320194, -0.04930504256610941, -0.03996726124874991, -0.02971688950723324, -0.01969857247284509, -0.010905516849298053, -0.004144990607214616, -1.2513338084236234e-05, 0.0011245704786532265, -0.0008662022499582332, -0.0058853911767805765, -0.013613896366058467, -0.02353399736626243, -0.03495823772658111, -0.04706488869646418, -0.05893855386633824, -0.0696143047813198, -0.07812362732768464, -0.08354043239831896, -0.08502539006317984, -0.08186665750484767, -0.07351555315949751, -0.059616058222410874, -0.04002682204193516, -0.014834637796094164, 0.015641090363124218, 0.05085313525031932, 0.09004040305742456, 0.1322506370995739, 0.17637112554881196, 0.221166436698726, 0.2653221715130401, 0.30749261961189833, 0.3463503567914054, 0.38063654577246886, 0.4092099193324131, 0.4310925561249504, 0.4455106752088954, 0.45192882070315715, 0.45007601244046264, 0.4399626960527551, 0.42188770826832717, 0.3964351307439882, 0.36445955063771074, 0.3270600790236472, 0.28554511254108983, 0.24138838019075692, 0.19617747139193184, 0.151556478554316, 0.10916463740900775, 0.07057303988722094, 0.03722161594915844, 0.010358453220720466, -0.009016147389002641, -0.02019818683882157, -0.022819573344983954, -0.016876993252652784, -0.002748695382130035, 0.018801721957848225, 0.04663508618550039, 0.0792601110803862, 0.1148702051553192, 0.15139296841305722, 0.186551752417728, 0.21793647748205375, 0.24308163184653125, 0.2595494617232138, 0.26501580185657364, 0.25735492842600527, 0.23472118384435603, 0.19562457077886616, 0.13899754912004625, 0.06425071961417095, -0.028682783767900656, -0.1393209462555144, -0.26662495619035, -0.4090071642917008, -0.5643566751972612, -0.7300825356417162, -0.9031744085938962, -1.0802770857327162, -1.2577776856390221, -1.4319033035146738, -1.598826003916926, -1.7547731699338216, -1.8961390975408148, -2.0195923411288623, -2.1221764541166497, -2.2014009090807263, -2.255319113221449, -2.282591730650237, -2.282534218634944, -2.255139192721322, -2.2010799667912204, -2.121697044777198, -2.018957512199052, -1.8953944915280057, -1.7540304512774536, -1.5982850232033332, -1.4318702949222277, -1.2586770176441675, -1.0826555216895681, -0.907695882985473, -0.7375116528030441, -0.5755282590761233, -0.42478130291179766, -0.28782842505763023, -0.16668163653830634, -0.06276000986837936, 0.02313573311576091, 0.09082581801768116, 0.14073111492311263, 0.1738307053155063, 0.19159893167937922, 0.1959246375965181, 0.189016190319471, 0.17329326031605552, 0.15127170794231498, 0.12544666391188314, 0.09817847127838723, 0.07158633697102919, 0.04745432946839628, 0.027153960307850326, 0.011587008994141702, 0.001151519742160585, -0.0042670038310813055, -0.005278628072358102, -0.0029453282437512424, 0.0012880526185927161, 0.005685462964295253, 0.00833040210431574, 0.007251252475502488, 0.0005557772608888355, -0.013431335639012831, -0.036034509748413775, -0.06810364278517694, -0.10990746973137931, -0.16105146684327276, -0.2204264543657061, -0.28619351666304216, -0.3558079416560629, -0.42608591254057976, -0.49331538847537737, -0.5534107373305182, -0.6021090381431067, -0.6352040553406056, -0.6488118751195385, -0.6396625349798144, -0.6054070153260469, -0.544928927539071, -0.45864966346704256, -0.34881357076401015, -0.21974125685641233, -0.07803996510185165, 0.0672416574933006, 0.2045255566787887, 0.31969278095791065, 0.39615653699111397, 0.41502536095995585, 0.3553594323865842, 0.19452039504570268, -0.0913879002291611, -0.5269915586938183, -1.1370389599743433, -1.945741079364627, -2.9760596474674865, -4.248961932091918, -5.7826667657975825, -7.591897382258721, -9.687164086452741, -12.07409997615235, -14.752871476670103, -17.717684959634823, -20.956409203349438, -24.450339244329516, -28.174135497120144, -32.09588689579402, -36.17737500867885, -40.37449361438498, -44.63780774490076, -48.91328842081604, -53.14319618997191, -57.26709713812014, -61.22299133872528, -64.94852987464567, -68.38229325472496, -71.46513394303824, -74.1416375712137, -76.36138337572174, -78.0800351788421, -79.26041681500996, -79.87346733747673, -79.89903631236456, -79.32649548816241, -78.1551473905187, -76.39441629018872, -74.06381240298582, -71.19268010768457, -67.81982501651842, -63.99281586536473, -59.766875025063435, -55.203723804581536, -50.37031283083484, -45.33743054226633, -40.17822399593024, -34.96666877197935, -29.776026351322574, -24.6773284099939, -19.737941815053425, -15.020207991307787, -10.580203984571156, -6.466697190281127, -2.720253580680245, 0.6273959098890018, 3.553749519356128, 6.04569299511349, 8.099421803532765, 9.720133458842726, 10.921503885324867, 11.724964611185685, 12.158793779883192, 12.257067896241388, 12.058511054928307, 11.605280316002027, 10.941666000794617, 10.112805105993518, 9.163439960795767, 8.136750138117131, 7.07328834161685, 6.0100328103529215, 4.979616993395019, 4.009749422333625, 3.122808093174581, 2.3356250355448, 1.659461176681252, 1.1001624192699881, 0.6584779405033706, 0.33053713931392587, 0.10845566693487937, -0.018962997760075557, -0.0654474126162557, -0.04642339276434427, 0.02180842921113462, 0.1228670800769002, 0.24103138125321039, 0.36189993144491556, 0.4729492271275983, 0.5639733317409196, 0.6273890760045663, 0.658402134585782, 0.6550392518162786, 0.6180247316055759, 0.5505288941399105, 0.45781069049819967, 0.346769605367705, 0.22542970568853196, 0.10238110574453783, -0.013794501926165468, -0.11508742629066253, -0.19458767695801815, -0.24695314399766996, -0.26879264360431887, -0.2589376083925695, -0.21859602005356168, -0.15138176339409748, -0.06321713869194126, 0.03788812478076735, 0.14217261171207485, 0.23855991190464365, 0.31517791737661954, 0.35994209582685355, 0.36119099971031154, 0.30831720477766783, 0.19236973726637602, 0.006606116511971879, -0.2530335900423959, -0.5875541468945084, -0.9946535711241035, -1.4686074961277524, -2.000298991066121, -2.577394517354231, -3.1846272359840166, -3.8042703774694333, -4.416765158404477, -5.001424942265482, -5.537214894780392, -6.003578177657679, -6.381276453213844, -6.6532106349803986, -6.805187715070212, -6.826600691805973, -6.710978798662771, -6.45640372413593, -6.065803342491014, -5.547028795790114, -4.912734692821498, -4.18006806891846, -3.3701705994968543, -2.507509146334896, -1.6190566342870674, -0.7333515155679855, 0.12052986887290622, 0.9140451172744952, 1.6202686962362634, 2.2149479379288786, 2.6774816590677784, 2.9917793911198327, 3.146962975309163, 3.1378833153569707, 2.965424119833325, 2.636574486795512, 2.1642615217111008, 1.5669374974499959, 0.8679405522357674, 0.09465471101123625, -0.7225188613256217, -1.551337530962946, -2.358996114304684, -3.113458529141738, -3.784783054733105, -4.346404536958345, -4.776316676462534, -5.058105060938823, -5.181788574560522, -5.144397708395591, -4.950293332829064, -4.611200710998492, -4.145944442763881, -3.5798856198859297, -2.94407426362695, -2.274133459049472, -1.6089091229120156, -0.9890040587411915, -0.45517100700271557, -0.04662822808131674, 0.20061785322777564, 0.2553772379316841, 0.0927469561092311, -0.3046143261154954, -0.9454641980493217, -1.8292554821105929, -2.9457548618938656, -4.275050007556294, -5.788017505594351, -7.447071151895827, -9.207247898629246, -11.017631910481372, -12.823058168662572, -14.566038798840239, -16.18884626845442, -17.635679578679202, -18.854834056422845, -19.800792611563104, -20.436165289284766, -20.733488366357253, -20.67670497297113, -20.261946674494084, -19.498017097845803, -18.406471590222758, -17.02122570630936, -15.387692324548173, -13.56146441749535, -11.606577604631815, -9.593403587085932, -7.596257012729727, -5.690742433971185, -3.95095361265396, -2.4466736643090217, -1.2405807926649035, -0.38569791619471644, 0.0768667729929389, 0.11981726206748682, -0.2688723691840165, -1.0850035381005831, -2.307750833835409, -3.8998507402883242, -5.8083914763567295, -7.966179092652339, -10.293657667167722, -12.701363138797722, -15.092748689205134, -17.3673215838568, -19.424000292903493, -21.164574954279566, -22.497158653614022, -23.33956945735944, -23.622398953564787, -23.291661252566996, -22.311017261141945, -20.6634538078579, -18.35237214439869, -15.402033741455238, -11.857152578672693, -7.781871204788126, -3.258111278973897, 1.6166642762815366, 6.732252659249546, 11.969018731309152, 17.20148343470959, 22.30212140648377, 27.145250082808303, 31.6108815348709, 35.58845217047793, 38.98038615750066, 41.705005512641236, 43.69895588157699, 44.919141565728545, 45.34387646065816, 44.97332716005917, 43.82928682861801, 41.95425864687683, 39.40988533194301, 36.27478349997942, 32.64186155664436, 28.615252338710718, 24.30696674977806, 19.83310747936451, 15.31009445001372, 10.851013287520386, 6.562206536187978, 2.540184350914557, -1.1310475923161578, -4.382159906628759, -7.160107298240772, -9.429129980586568, -11.171128876044474, -12.385459887541186, -13.088225434496204, -13.310744464535741, -13.097581051743214, -12.504216081059905, -11.594425225398583, -10.43747143469762, -9.105224294593148, -7.669318400420638, -6.198458405682213, -4.75597258375987, -3.39772574727782, -2.170373105679447, -1.1100721752522, -0.24170683922727973, 0.42135151329199555, 0.8769748204162205, 1.1335378628992157, 1.2087557154949344, 1.1281646231547051, 0.923325020152625, 0.6298351376099748, 0.2852499442442756, -0.07300114671391257, -0.4096015429093481, -0.6931508824908633, -0.8977072244505906, -1.0039964746294534, -1.000243144631754, -0.882592836324296, -0.6551151599579738, -0.32939508364144804, 0.07626135267854794, 0.5379652506331253, 1.027663158731756, 1.5147629806276173, 1.9678880839794635, 2.356675954416729, 2.653519667599289, 2.8351732046056313, 2.884143815215613, 2.7898016531352035, 2.5491492484429563, 2.1672074839563025, 1.657001087509154, 1.039140489036042, 0.3410142786869767, -0.4043743750202552, -1.1598784416300627, -1.8859271500885033, -2.54240418132266, -3.0905931500325274, -3.4951121868869626, -3.725747428320199, -3.7590591713352848, -3.5797242193673418, -3.181541865083727, -2.5680447635398935, -1.7526772722477444, -0.758522235563599, 0.3824237437909514, 1.6304184091148324, 2.9395429042227077, 4.2596297640062115, 5.538410481802017, 6.723781231540804, 7.766154280972044, 8.62077610607546, 9.249911378225498, 9.624796168973154, 9.727271205563293, 9.551017274813429, 9.102340897697477, 8.400503025452737, 7.4774239868876915, 6.376757134020303, 5.152539199003817, 3.867389360939581, 2.590305994570416, 1.394139035264242, 0.3528299245594432, -0.4614782638623107, -0.9813511141724853, -1.146881320743114, -0.9083062107537073, -0.22829739355379547, 0.9162015703735453, 2.5326305834339884, 4.61201197259424, 7.128729921637866, 10.040905419013226, 13.29135981472819, 16.809138341803283, 20.51154574577808, 24.306692690205658, 28.096413269037257, 31.77939381461512, 35.254691109465355, 38.42486693385099, 41.19906730167345, 43.49594306615145, 45.246252281342635, 46.395055908234056, 46.903433824919546, 46.749726903056235, 45.93032464996191, 44.45947457868521, 42.36861932014442, 39.705385735553534, 36.53233844562663, 32.92442099594918, 28.96632309771541, 24.749737444937757, 20.37046596259595, 15.925483382007151, 11.510092359460788, 7.215086150011634, 3.12417744303386, -0.6881626487888298, -4.158473451130274, -7.235572092635611, -9.881286309962915, -12.071149864068923, -13.794396262165565, -15.053423679391255, -15.862894650371222, -16.248507015652233, -16.245341220330747, -15.896038212448921, -15.248858499603429, -14.355691339039844, -13.270090230095631, -12.045400594363315, -10.733049822170107, -9.381076153190266, -8.032880704991921, -6.726283289710752, -5.4927924575508555, -4.357202983207185, -3.3375151185752148, -2.4451245268281245, -1.6852498220376848, -1.0575573652813965, -0.5569378722871658, -0.1743867342956392, 0.10206122265011518, 0.28638808851965253, 0.39368568760964945, 0.43931764184740296, 0.438179520539302, 0.4040859310829484, 0.349299399029808, 0.28420705031482246, 0.2171429894040028, 0.15434696339970164, 0.10004372804010304, 0.056622706079185035, 0.024893922372676992, 0.004395396118232126, -0.0062728868251519495, -0.009113432238784035, -0.006415964708674755, -0.00048040886702936203, 0.006608414855479664, 0.01314587896633774, 0.01790898277014551, 0.020195530209565233, 0.0198067641530841, 0.016982932580267746, 0.012303449907436512, 0.006565164139396458, 0.000652964467991417, -0.004583932804427373, -0.008438347849037645, -0.010424965666667655, -0.010327550702598644, -0.00821093151363977, -0.004398681854989613, 0.0005792389326653311, 0.006061728253089468, 0.011345320431729861, 0.015775959029777974, 0.018832888182107172, 0.02019430480759699, 0.01977653303845329, 0.01774115340447946, 0.014467969278156328, 0.01049566725932174, 0.0064362228149506895, 0.0028733564152642103, 0.0002586757367780774, -0.00117794224360944, -0.0014853178643505502, -0.000996401320566732, -0.0002642526798004315, 8.656421371451727e-05, -0.0003959639733543575, -0.001646667973445913, -0.002639992987059351, -0.0008579142068831368, 0.008313461104103019, 0.03223202850818529, 0.08165788520491138, 0.17137963865246125, 0.3207605610173263, 0.554151336717719, 0.9011192574681748, 1.39644078791828, 2.0798168829870587, 2.995301517848622, 4.1903680046027505, 5.714614171450567, 7.618112426574958, 9.949417626354215, 12.753267393645254, 16.0680281968429, 19.922964532420984, 24.3354387055734, 29.3081237640837, 34.82666931119388, 40.85747904796359, 47.34560927234163, 54.21330926150062, 61.35917379238089, 68.6580023108387, 75.96144710214811, 83.09951106415284, 89.88292979975563, 96.10650350373149, 101.55402116051032, 106.00403934480445, 109.23454221937037, 111.02883696242631, 111.1819577941825, 109.50724636076362, 105.84291149935018, 100.05835965003232, 92.06008199279569, 81.79688627974707, 69.26450121921971, 54.51035461249219, 37.63450115251322, 18.788996034241585, -1.8231834476322897, -23.950590783071945, -47.29718837907143, -71.52759078040532, -96.27356836199797, -121.14166452572391, -145.7217344060988, -169.5960933054723, -192.34984128856104, -213.5816133235875, -232.9140892663583, -250.0029619669285, -264.5452759889165, -276.2869077136128, -285.0288193513483, -290.63190264647545, -293.0202699532325, -292.18326636374826, -288.1766887315052, -281.120099322829, -271.1928616609043, -258.6292153812598, -243.71239074796608, -226.76592650914202, -208.1446837814508, -188.22551419595464, -167.3975955063995, -146.05279215811387, -124.5770872647213, -103.34106360444248, -82.69072820367322, -62.940199209957115, -44.36560542424646, -27.20033920255899, -11.631645094511613, 2.201581097086932, 14.20924241288594, 24.349027137753477, 32.62401139026016, 39.07923110701097, 43.797547547437624, 46.89438498513544, 48.51185559689718, 48.81254065251487, 47.97315096145677, 46.178337696855, 43.614894893380125, 40.466046730420366, 36.906476283257064, 33.09820798248807, 29.187181617339693, 25.300706666540403, 21.54584244688832, 18.008642375521557, 14.754206251211464, 11.827458801988577, 9.254552038697797, 7.044785964499896, 5.192913895070248, 3.6816255821137442, 2.484195267769089, 1.5671453361730414, 0.8928204276752504, 0.42175361010297674, 0.11474696245472074, -0.06538895895743072, -0.1524709166171308, -0.1759672274220755, -0.1604039872285296, -0.12512966257376815, -0.08439932407339841, -0.04772543706999073, -0.020441637563258664, -0.004417140214670527, 0.0011423973027684961, -0.001131463624937453, -0.007566674715389713, -0.01417107176551137, -0.01723973590906454, -0.01382387844407143, -0.002046963419999619, 0.018734170287934403, 0.047914615454907, 0.08375656980696006, 0.12361005947048158, 0.16420964827256068, 0.2020149221183829, 0.2335621466269721, 0.2557962887944615, 0.2663563372425619, 0.26379307303188587, 0.24770322290188238, 0.21876866406374293, 0.17870478857406416, 0.13012352367068727, 0.07632320767046794, 0.021024176218374796, -0.03192816054177291, -0.07886889300425735, -0.11660361681482055, -0.14266015656270367, -0.15548272207094124, -0.15455219197233006, -0.14042307836510604, -0.11467427565582852, -0.0797765838026923, -0.03888631738412586, 0.004420025196331272, 0.04644953681724452, 0.08371173326520968, 0.11322701872140714, 0.13279841420159988, 0.1412228784278252, 0.13842246698710864, 0.12547781454704746, 0.10455398890502572, 0.07871521962914861, 0.051632321956481195, 0.027194167855893275, 0.009041864205123524, 5.032287344886548e-05, 0.001787308323585288, 0.013984997720898692, 0.0340583125759378, 0.05670222944771365, 0.07360157468558284, 0.07328210558359867, 0.04112579981894075, -0.04043397456154275, -0.1915323004099146, -0.4343181775543959, -0.7922249048888542, -1.2891064913514887, -1.9482696356670286, -2.7914185325780028, -3.837566943684818, -5.101962217988049, -6.595069325424789, -8.3216628108498, -10.28007210754418, -12.46162104371014, -14.850330288948644, -17.423064224514548, -20.14986633836746, -22.99432480161692, -25.91428788849478, -28.862830506207032, -31.789422460813896, -34.64126057522682, -37.36471965832231, -39.90687196541312, -42.217021423828854, -44.24825982168314, -45.959375138390186, -47.31616707221113, -48.29200544078215, -48.868482474895465, -49.035890130243196, -48.793423861442, -48.14910933365779, -47.11945880268811, -45.72887370210022, -44.00882650562758, -41.99711267623359, -39.736685609804255, -37.27402255742764, -34.657894622291316, -31.93771126714434, -29.16210807529195, -26.377708889103754, -23.628020857721758, -20.95249271443557, -18.385758958594227, -15.957130205724097, -13.690336117589883, -11.603174368426806, -9.707527976920435, -8.009637969672015, -6.5105424968206655, -5.20654755951939, -4.089868771036265, -3.149358742914672, -2.371265256640537, -1.7399902770504234, -1.2388322136854262, -0.8506383528864365, -0.5583957049769357, -0.34575613253076243, -0.19746086130708115, -0.09965999076873584, -0.040127434240906555, -0.008377139339028115, 0.004307973121257052, 0.004925174299439957, -0.0011348781234265862, -0.009926300409709196, -0.018754178383729017, -0.02596352800243315, -0.03072388470388638, -0.0328215104891441, -0.03246889229899051, -0.030138741795957755, -0.026426986109970456, -0.021945657418662064, -0.017246747331270816, -0.012774770695911479, -0.00884430180307623, -0.005637759589556709, -0.003218367734765684, -0.0015531057852067025, -0.0005407607110923896, -4.082989896672399e-05, 0.00010010568458759191, 2.6928279109672356e-05, -0.00013918147288647373, -0.0003092665933507803, -0.00042886690538589454, -0.00047510049112754814, -0.0004500663149915952, -0.0003722623432137703, -0.0002676715451448563, -0.0001619307744239243, -7.461176814770105e-05, -1.6167796553467134e-05, 1.2402415455894834e-05, 1.7586981812634046e-05, 9.873275330169708e-06, -2.4260878439818326e-07, -5.667143961383363e-06, -4.582963993540657e-06, -1.1583137887398233e-07, 2.437876378258219e-06, 5.187117809218194e-07, 4.621507433807785e-07, 2.346622071799818e-05, 0.00010946568049299977, 0.00031671579223488936, 0.0007148137471325591, 0.0013690435043153828, 0.002314395445259464, 0.003518340688521739, 0.0048324198858242275, 0.00593388988554737, 0.00625998018150611, 0.00493865271634375, 0.0007210260216320633, -0.00807821072297866, -0.023625599901625192, -0.04859217843247815, -0.08614757439130642, -0.13991867454305978, -0.2139075802147649, -0.31236539523961515, -0.4396207132620256, -0.599864354851036, -0.7968949282367981, -1.0338337185719402, -1.3128251290959243, -1.6347258662074249, -1.9988003733572133, -2.4024435104234443, -2.84094929212234, -3.307348501273925, -3.7923166018608367, -4.284177299774859, -4.769014517269332, -5.230899837604688, -5.652245285395424, -6.014255438644563, -6.297467144629144, -6.482391218884704, -6.55022614173382, -6.483618761239091, -6.2674495504261944, -5.889613647644138, -5.3417127352207565, -4.619677244712262, -3.7242517251957525, -2.6612350356331818, -1.4416794156254977, -0.08190338581300545, 1.3967077765812672, 2.9680986686838557, 4.602132679957463, 6.265360115264763, 7.921953642490587, 9.534807105356736, 11.066701799326689, 12.481788103216257, 13.746767615464023, 14.831811351258748, 15.711568750904862, 16.366044618227683, 16.781302434776265, 16.949964220593994, 16.871484713395084, 16.552186311012253, 16.00507435426857, 15.249606048499215, 14.311070178406453, 13.2193059466691, 12.007584170456362, 10.711432223283602, 9.367398738742889, 8.01180646721211, 6.679541680688894, 5.4029265009603495, 4.210716577734219, 3.1272745860333004, 2.171984180332492, 1.3586952720421035, 0.6954507632538659, 0.18454079281858413, -0.17721388687178768, -0.3979781937163816, -0.49024734361892824, -0.470054803789363, -0.3560831176063889, -0.16871981622339385, 0.07089868613592676, 0.3418165804676379, 0.6241258231117396, 0.8997303202778753, 1.152979792679033, 1.3711399667264619, 1.544691126657749, 1.6674539494174425, 1.7365486369025476, 1.7522009929704958, 1.7174197038902936, 1.6375751507704692, 1.5198735639590197, 1.37278823153714, 1.2054829794664272, 1.0272568153152324, 0.8470152040054574, 0.6728180460298456, 0.5115197844395555, 0.3685110576970333, 0.24756806895122604, 0.15081079802451025, 0.07875492406753641, 0.030454660962112273, 0.003723284205519943, -0.004592195405093777, 0.0016964066727492065, 0.018436189811638814, 0.041441496012525066, 0.06677548628686744, 0.0909873823677857, 0.11129259025833672, 0.1256888366265339, 0.13300842855736061, 0.1329050049888844, 0.1257814231257534, 0.11266863102494905, 0.09506793666004935, 0.07477082735323869, 0.05367134247601548, 0.033585749960470035, 0.016092219039389958, 0.0024017941148045834, -0.006729195339732781, -0.011042573581237777, -0.010776233178484123, -0.006618182755968275, 0.00037788798661870024, 0.008907373041101011, 0.01754958592468244, 0.02491110076523535, 0.029765599324331808, 0.03117820982464674, 0.028603795839501924, 0.0219523735414284, 0.011616043208879772, -0.0015450816709174971, -0.016257276291305696, -0.030924208635223802, -0.04374801917712102, -0.05287161429184904, -0.05653160301778049, -0.05321042083414256, -0.0417742165888969, -0.021584253951892084, 0.007422627135801282, 0.04469231325674111, 0.08905495056495052, 0.1387707881491105, 0.1916182956094524, 0.24501949460994113, 0.2961947185002814, 0.34233749450331685, 0.38080706738195, 0.40930414383405483, 0.42602090761258554, 0.42976686910160833, 0.42005710488341846, 0.3971561648754406, 0.3620736275050345, 0.31651075553715224, 0.2627609984876026, 0.20357027179865053, 0.14196749286426158, 0.08107031799678974, 0.023877985614302034, -0.026919648284723614, -0.06911128422921194, -0.10110318234684797, -0.12201558897640152, -0.13173021600394555, -0.13088541704864648, -0.1208188697315007, -0.10346154819608265, -0.08119062373837158, -0.0566440165170012, -0.03251738418526115, -0.011358891110669303, 0.004625262295139524, 0.013740361599480746, 0.0149352216933565, 0.007886765905177808, -0.006970144674121681, -0.028471198099086138, -0.05481028899966512, -0.083683593808937, -0.11247694875163441, -0.138484018404726, -0.1591405984699704, -0.17225848227839707, -0.17624207839947276, -0.17027145367634197, -0.1544354929028929, -0.12980548292455857, -0.09844310183423645, -0.0633388573838754, -0.028261356108142812, 0.0024536811476308183, 0.02416529402200846, 0.03222715910682177, 0.02230704978506201, -0.009294486249700187, -0.06534734106299367, -0.14743797833425737, -0.2557761672664265, -0.38906725732052605, -0.5444791171812542, -0.7177143041045668, -0.9031713912175598, -1.094192559803209, -1.2833850223413055, -1.462998664159298, -1.6253382723444703, -1.7631859796197462, -1.8702099312609544, -1.9413347744649387, -1.9730427246399116, -1.9635965589540296, -1.9131555903137916, -1.8237807666224166, -1.699328024128512, -1.5452352812828276, -1.368215340886126, -1.1758731792469679, -0.9762712283939913, -0.7774709690994825, -0.5870843413108229, -0.41184608335460515, -0.25724559327613716, -0.1272527934646745, -0.02415038750111028, 0.05151711794206094, 0.10087426231307824, 0.12653028827617077, 0.13229270843515872, 0.12279935577799432, 0.10309561545388447, 0.07818941174323592, 0.0526166772854424, 0.030051134700608603, 0.012991802919062396, 0.0025569875148588037, -0.0015945155542578247, -0.001202618016798917, 0.0007972013765622691, 0.0006117265756301874, -0.005955584174508006, -0.022962199283160078, -0.05373236407480707, -0.10025264099484656, -0.1626033839815194, -0.23847361916842405, -0.3228027813853996, -0.40758794473115056, -0.4818869810087327, -0.5320370006809044, -0.5420952173626519, -0.4945014098017045, -0.37092166910937985, -0.1532384232131919, 0.17534927432279646, 0.629178028510523, 1.2189912649723926, 1.9509040706277367, 2.82552412526819, 3.83728972676034, 4.974081226517113, 6.2171740112832925, 7.541571633059346, 8.916611077254135, 10.30691015750682, 11.673617428490655, 12.975909427126526, 14.172669159009017, 15.224279251170811, 16.094462102996527, 16.75196898186436, 17.172133279130794, 17.338322904939453, 17.242752719730937, 16.886899094709552, 16.28156977964342, 15.44652958744821, 14.409691767056888, 13.205908951584806, 11.875419908005854, 10.462036954429143, 9.011171885307872, 7.567795178519741, 6.174347277673015, 4.868729865781575, 3.6826892144888785, 2.6405586776601435, 1.758419736691396, 1.0437263985669403, 0.49541206170705443, 0.10447083072331936, -0.14502182410343328, -0.2745094695473269, -0.30926178271207877, -0.2764819714717113, -0.20332608131031338, -0.11497128545357613, -0.03285295299430022, 0.02682145675228519, 0.054189522224146004, 0.046411290957725226, 0.007862112343803124, -0.050175230713259286, -0.11030716647895016, -0.1502783229009468, -0.14459033187187695, -0.06638161609522734, 0.11054467788148523, 0.40966958213850546, 0.8498135852685577, 1.4434229294591279, 2.195199371863503, 3.101166777068757, 4.148238363084579, 5.314343411999729, 6.569137280468127, 7.875229102575344, 9.18989529953685, 10.467110563882466, 11.659831641123322, 12.722406286002087, 13.612961157175066, 14.295628834377942, 14.742493869512577, 14.935204143505125, 14.865963806746016, 14.53793124835086, 13.96504748049163, 13.171283267157692, 12.189351593619735, 11.058888702726707, 9.824303354765167, 8.532406357834406, 7.229951966994733, 5.961268572455916, 4.766036533102412, 3.677354403050736, 2.7203139341142952, 1.9111069557116431, 1.2567048301084267, 0.7551179776437108, 0.3962060955958738, 0.1629742777894957, 0.03325396936873896, -0.01835325598813656, -0.0184071016617952, 0.007420473805665417, 0.036226594502045774, 0.04945537358959456, 0.03406252578560218, -0.016812951502949543, -0.10371394749048865, -0.2212742756341017, -0.35914162664600446, -0.5033197902683797, -0.637841944484698, -0.7466317683855559, -0.8153866280286551, -0.8333364918496406, -0.7947240425086898, -0.6998704900283461, -0.5557190763451236, -0.3757845538858995, -0.17947995403865172, 0.009160979159095558, 0.1632997737794846, 0.25554486778611274, 0.2604756290725674, 0.1572260709893868, -0.06805832609739941, -0.4200938299273368, -0.8928563428699207, -1.4686735956856407, -2.118142724664004, -2.800954016829149, -3.467642665465351, -4.062246670082988, -4.525783414032902, -4.800251254701845, -4.832972784216887, -4.58101131274384, -4.015350899166863, -3.1245285976878705, -1.917419594686639, -0.4249084456950961, 1.2997673670398846, 3.1821248313142965, 5.1291131635495795, 7.033352323395257, 8.778753080456077, 10.247176044607135, 11.325832800225927, 11.915044832428554, 11.935892188245813, 11.337260656301469, 10.101794769640518, 8.250314129933678, 5.844309441745411, 2.986012006139511, -0.1839944950578398, -3.4917008117677626, -6.7371336710886425, -9.704049829811495, -12.171392748592911, -13.9260282607838, -14.776122282276697, -14.56443445491707, -13.18076271453659, -10.572713446464242, -6.754050219990721, -1.810001145241998, 4.101012780871163, 10.749629589821268, 17.842080799720495, 25.030746718500623, 31.92845539299136, 38.12608286496441, 43.212751751414345, 46.79763854995796, 48.5322592808842, 48.13227551526214, 45.397632148116486, 40.2298790061343, 32.64561357254242, 22.785167679386255, 10.915648413595122, -2.5726320830729885, -17.17583323194653, -32.29322161323238, -47.248382139893245, -61.314905248376064, -73.7461588407636, -83.80760704863131, -90.81026122011424, -94.14373773174334, -93.30735442420352, -87.93801938771726, -77.83391095782022, -62.97073331988452, -43.50961291646267, -19.796229727457344, 7.646966278947774, 38.136384259215106, 70.85033318088131, 104.85860729746248, 139.15742673554863, 172.70826987614078, 204.47892383942437, 233.48590140922516, 258.838281048212, 279.7728126049682, 295.6838710395282, 306.147358145613, 310.93676865496525, 310.03067645736667, 303.6112907089935, 292.0541443807937, 275.9093899476255, 255.87578784893017, 232.77095502874357, 207.49238171094208, 180.97434826295188, 154.14496373030013, 127.8852866090927, 102.99182407269693, 80.14381799430073, 59.876785500338826, 42.5634685115558, 28.402981980485535, 17.418748183808706, 9.464590686816335, 4.2385121491649125, 1.30478763503834, 0.12219018552344174, 0.07672981456170162, 0.5172208922564793, 0.7917578689337952, 0.2832576009083759, -1.5576749999560278, -5.184140509757785, -10.929985952169144, -18.993491099436095, -29.428442948688787, -42.14287799873793, -56.90539670008067, -73.35872340818771, -91.03918603752628, -109.4011258384222, -127.84491750385652, -145.7470768283352, -162.49178502595043, -177.50113590693823, -190.2611680600819, -200.34469771280965, -207.42928587266698, -211.30954204995547, -211.90358316373207, -209.2537546573216, -203.5199326165897, -194.96789009365642, -183.9538804313265, -170.9064771087013, -156.30251808558089, -140.6433079098127, -124.43160563762495, -108.14998074769825, -92.24156848595761, -77.0940714022196, -63.02769862707243, -50.28737903529984, -39.0389385435887, -29.370105967874842, -21.29480087824098, -14.760988053119936, -9.661616682487516, -5.847325741169727, -3.1400200653282813, -1.3464466795630308, -0.27096711459788486, 0.27316755643693363, 0.45458594203684527, 0.4169931470435687, 0.2749568710210962, 0.11227646734870389, -0.017154390968583514, -0.08634709481483101, -0.09055152457419875, -0.04147302057137394, 0.03904030118610236, 0.1252596660939395, 0.19325493864681445, 0.2255439702525425, 0.21438454755622122, 0.16348904935277622, 0.08809132960158667, 0.013464261070935993, -0.0278898234311453, -4.398911130316317e-05, 0.13196461309463386, 0.3976178433414877, 0.8167332186038927, 1.3960437966679304, 2.1268885479318693, 2.984292380312127, 3.927630230089403, 4.90286257617895, 5.846200205473914, 6.688951234524125, 7.363187461032019, 7.80778006824072, 7.974306567504466, 7.832319755076947, 7.37349675575777, 6.614263409646485, 5.596596777701269, 4.386791912351281, 3.072178527903987, 1.7559237901966305, 0.5502077595777075, -0.43178202138498273, -1.0844918074853236, -1.318651936852783, -1.0692686529084918, -0.3022614030650645, 0.9807938903204503, 2.7402670601521506, 4.898802958175759, 7.344510861655689, 9.936951555957073, 12.515633119706322, 14.910587153990862, 16.954362368190537, 18.494624433584455, 19.406538195940378, 19.603889857165726, 19.047700990132206, 17.75192511193334, 15.785432955424742, 13.269775892008195, 10.37249835784125, 7.296042529117724, 4.262679870702871, 1.4963156170644336, -0.7982352533322965, -2.457277992759863, -3.38012643366752, -3.5492734448688315, -3.0474106027651464, -2.0698731863102138, -0.9312181571069353, -0.06487940737964666, -0.015161525414885116, -1.4212851094471053, -4.994167096066712, -11.486382979316227, -21.655982566849545, -36.22567007016323, -55.83908979503366, -81.01624636417864, -112.11027839625595, -149.2678986122696, -192.395794293246, -241.1351456035987, -294.84616620655595, -352.60726251378634, -413.23618229973215, -475.308410339589, -537.1893279211363, -597.0799318993153, -653.0724652239996, -703.214077930299, -745.5761968378478, -778.3269313793786, -799.8036009167687, -808.5828233498038, -803.5510347625358, -783.961350678308, -749.4788006544213, -700.1942789654046, -636.630985216579, -559.7387163732379, -470.87246604420574, -371.75595725772376, -264.43136007384015, -151.19702881616655, -34.536881764892826, 82.95916639214344, 198.6834401698319, 310.0956725980407, 414.8096248531878, 510.66859099359255, 595.8086175175278, 668.710199142231, 728.2364609442662, 773.6567143828516, 804.6555913729408, 821.3313281982183, 824.172596548562, 814.0214327912837, 792.0270620144421, 759.5933571743715, 718.3241422339834, 669.9495877485446, 616.2572423246105, 559.0279089776033, 499.97639238949847, 440.70127899097497, 382.64042269670585, 327.03311456783155, 274.8964913488242, 227.01304010216163, 183.92860583922177, 145.96054571547168, 113.2146430392426, 85.60620019967122, 62.88864291372588, 44.68641232129419, 30.529516779153884, 19.887323673133828, 12.201320005276385, 6.914842680714965, 3.498487171067895, 1.4704197867991027, 0.4111615110490077, -0.027252503859549627, -0.11752898716536025, -0.05827723880695596, 0.020642590509075794, 0.049427843401135686, 0.007271438735429884, -0.09004957476159646, -0.20293647419704208, -0.28017317877777304, -0.26980000849984614, -0.1280562648160445, 0.17401513262352084, 0.6465066899989669, 1.2791401009576855, 2.0421263675471426, 2.889069332572168, 3.7614461334287856, 4.594140364628277, 5.321466599427067, 5.883130652637782, 6.229615263850364, 6.326559084291829, 6.157800745923909, 5.726876076167863, 5.056864967905893, 4.188702800833747, 3.1780826076739634, 2.091275140180447, 1.0001979968848553, -0.02288840799168407, -0.9106567348032695, -1.6055726781567177, -2.0639914494933675, -2.2592074585045987, -2.1832811836613137, -1.8474425438349915, -1.2810554045662919, -0.5292909067700027, 0.350185000767323, 1.2913352867358658, 2.224407493747206, 3.0807830893896413, 3.7976886672143415, 4.322453668344769, 4.616049932676506, 4.655698249911351, 4.436256807327394, 3.970435640442267, 3.287866919468722, 2.4330748986561455, 1.462337463222936, 0.4399412570852326, -0.5659782954343848, -1.487768714555572, -2.2624885197642834, -2.8357995521644446, -3.16521807406709, -3.222519702207887, -2.995232387628984, -2.487140692523182, -1.7178067106038792, -0.7211383025642464, 0.4569430768084574, 1.761426326973737, 3.1315490728825215, 4.504368653926103, 5.818367562021538, 7.016755583812903, 8.05033714149453, 8.87980651383293, 9.477362107724161, 9.827580958382727, 9.927595819024035, 9.786656125088628, 9.424702428426134, 8.870523464775317, 8.159652914806195, 7.331889957817495, 6.428791222713925, 5.491318518251834, 4.557729011845783, 3.6618156223921026, 2.8315748262448084, 2.088345608944855, 1.4464383815040294, 0.9132163889936955, 0.489532154195155, 0.17055795502244692, -0.053115845203452916, -0.1942212667000638, -0.26751022849754913, -0.2885035894675298, -0.27237156565335796, -0.23300721011575395, -0.18233376470822663, -0.1298648600700518, -0.08251675196574527, -0.04464956374016902, -0.01829315822372596, -0.0035296685402528647, 0.0010281903801077359, -0.002278476777911182, -0.010655604930958018, -0.02129855090377232, -0.03174349036807461, -0.040108252329871905, -0.04521637453111681, -0.04661090866710174, -0.04447416039721354, -0.0394782209883833, -0.03259615513853992, -0.024903454531150275, -0.01739807727870063, -0.010861592797501946, -0.005776064818836613, -0.0023022354374234335, -0.00031530137639376493, 0.0005138392067087686, 0.0006106084063165028, 0.0003848085194464983, 0.00013840447936725285, 1.4403275109685882e-05, 2.7950445942435606e-06, 1.1509899495965889e-05, 4.209497527287148e-07, 0.00016581115332302306, 0.0011525231410163869, 0.004262431220050459, 0.011622301724088046, 0.026272121479737023, 0.05213689794348577, 0.09385170041577459, 0.15642074063026362, 0.24470659843928502, 0.3627638998742541, 0.5130503460311157, 0.6955676266285873, 0.9070025265591514, 1.1399623103290664, 1.3823892797763826, 1.6172273987233203, 1.822449790257131, 1.9715171599468684, 2.0343205493575196, 1.9786384529525525, 1.7721025291896044, 1.3845870388916002, 0.7909653452788401, -0.0258963170144393, -1.0721045126944062, -2.3398186860698473, -3.8046164940969955, -5.4233645445843415, -7.132793705913393, -8.848958996914696, -10.46773317016117, -11.86648542542043, -12.907116946930644, -13.440092105257357, -13.309709785342864, -12.360071666202002, -10.44160122666074, -7.418109797473796, -3.173985808100779, 2.378829419734992, 9.294425682780135, 17.587410155317606, 27.22861664787158, 38.14223475126079, 50.20484352856704, 63.247462048265575, 77.05854742532804, 91.38882530307185, 105.95788459089022, 120.46226854932677, 134.58477186445785, 148.00459073713884, 160.40792562444355, 171.4986067269678, 181.00862443130634, 188.70985877821266, 194.42168087310992, 198.01572874966536, 199.4198556529381, 198.6201371571494, 195.66073090463837, 190.64161833358045, 183.71434925537886, 175.07599492621003, 164.96162459839204, 153.6368134997289, 141.38800769744077, 128.51079264729887, 115.3002567729042, 102.04076387642881, 88.99723447143987, 76.40788294697911, 64.47841598443951, 53.37784471301817, 43.23598278097657, 34.14273021092778, 26.148975046714792, 19.268233512376362, 13.480124327506006, 8.735005624685169, 4.9592808070297965, 2.060999989123388, -0.06429137186492016, -1.5278641190876723, -2.44255221711143, -2.9181325893069596, -3.0575146161759026, -2.9537387892217626, -2.687838764558852, -2.327630276578564, -1.9273421107745101, -1.5279886422642281, -1.158350276500967, -0.836389736169285, -0.5709924887438098, -0.3638664085034151, -0.2114566228662555, -0.10674830842981325, -0.040861129165135714, -0.004383258805229796, 0.011603904341384254, 0.014821161471458035, 0.011391329555236154, 0.005707221925369299, 0.0005165703339773486, -0.002835979211164943, -0.004071614720845178, -0.0036047552080907567, -0.002186664995105776, -0.0006065690416504236, 0.000523145271341258, 0.0008857496096012106, 0.00048496428416528814, -0.0004102166662301239, -0.0013773455359597847, -0.0019799526109293523, -0.0019037039370172926, -0.0010603420889393974, 0.0003640479443874791, 0.0019318105129545184, 0.0030530826498100794, 0.0031564949713331937, 0.001915778535558953, -0.0004919373247386824, -0.0031268019217757037, -0.004059990183296071, -0.00021460883825109116, 0.012695902541457514, 0.04011041601842663, 0.08843109592639276, 0.16469989918992345, 0.2761517221486195, 0.4296674381109873, 0.6311612463916838, 0.8849457883145044, 1.1931244885525671, 1.5550629097793074, 1.9669915388634187, 2.421820273547699, 2.909143782306859, 3.4154471514854294, 3.924544587413641, 4.418234052782794, 4.877140145044062, 5.281700377798842, 5.613239120964298, 5.855064245137793, 5.993516642630225, 6.0189484418973, 5.926519563924358, 5.716588088776879, 5.394892862280881, 4.97244239415841, 4.46508866992253, 3.892813661917665, 3.278759587531478, 2.6480536893447355, 2.026493747200912, 1.4391740740148846, 0.90913477639745, 0.45606619204219273, 0.09523653500643557, -0.16330775220358573, -0.3152429853933429, -0.3621360181370972, -0.31123747462691004, -0.17496027593844835, 0.029935127800899904, 0.2834043595408516, 0.5633725806587363, 0.8471079923320642, 1.1126052936635875, 1.339895856540997, 1.5122087083487006, 1.616913228708281, 1.6461947044910676, 1.597427597895766, 1.4731779214238985, 1.2808958045244294, 1.0323248100652598, 0.7426658825526142, 0.4294987233939811, 0.11159702731864493, -0.19229333180680397, -0.4646426961060738, -0.6902186358192606, -0.8569940393181079, -0.9568318456566747, -0.9859117049828502, -0.9448510316152471, -0.8385375053465218, -0.6756920824362502, -0.4682018366895863, -0.23027299587495365, 0.022536042939695067, 0.27433647599289496, 0.5099190048141418, 0.7156881188898911, 0.8804637644172173, 0.9961060499059543, 1.0579451006821017, 1.0649634756114095, 1.019695548506119, 0.927923685886034, 0.7981842443279914, 0.6411190321975679, 0.46871973313267057, 0.29351760972780017, 0.1277720990488696, -0.01729026042590617, -0.1321400250704816, -0.20947482028057784, -0.2445918444697531, -0.2355679615820584, -0.18325279449835866, -0.09108968982973686, 0.03521476927736779, 0.18814351311168356, 0.35890864856751, 0.5380391474049746, 0.7159769649258699, 0.8836494286745502, 1.0329796748832345, 1.1573005547030517, 1.2516729638010102, 1.3130336035338785, 1.3402262826812117, 1.333921209056429, 1.2964300643505746, 1.2314370553439529, 1.1436700422030615, 1.0385409808582677, 0.9217824766098333, 0.7990799888196894, 0.675752559354324, 0.5564966198688279, 0.445198674398936, 0.34480134704670434, 0.2572581229839818, 0.18356080796225452, 0.12382532004519667, 0.07742279750443253, 0.043141464615429836, 0.019362072586548835, 0.004234848207215632, -0.004155310801600692, -0.007647062030404504, -0.007891576468918542, -0.006276087917991306, -0.0038820881336965184, -0.0014766463004937296, 0.0004678265672134348, 0.0017321748275263417, 0.0022950890023918816, 0.0022713601989390324, 0.0018511454365270788, 0.0012462195947551722, 0.0006475443295634741, 0.00019663720594974702, -2.864014447533446e-05, -1.4961605103743194e-05, 0.00019651036080229687, 0.0005277247741279519, 0.0008849520497735395, 0.0011797254176948392, 0.001346145735337954, 0.001352099024985304, 0.0012030515346285989, 0.0009382851560824209, 0.0006205710996720828, 0.0003212205890542165, 0.0001030996244534085, 4.439007420004964e-06, 2.6168600022290365e-05, 0.00012521146668390275, 0.00021517692885435408, 0.00017486493190045933, -0.0001360969505310057, -0.0008562122946069134, -0.002098268544186173, -0.003925858051970786, -0.006333644809781765, -0.009234544131912442, -0.012456297700351594, -0.015748830348049307, -0.01880327189070205, -0.021281358606720965, -0.022852765580863865, -0.023236829063315135, -0.022244206047833483, -0.01981357729019935, -0.016038569921195626, -0.011180687449315385, -0.005665116937809697, -5.7370851201302214e-05, 0.0049770646264531105, 0.0087279705540182, 0.010507493370953924, 0.009722849549093379, 0.005947609923842643, -0.0010159454514124392, -0.011090727515404668, -0.023901378500076547, -0.03877816603512677, -0.05479201416822803, -0.07082044661409809, -0.08563436835288636, -0.09800416640144459, -0.10681605742221023, -0.11118729864740193, -0.11056880766479306, -0.10482356351299882, -0.09427024132156271, -0.07968383513504607, -0.062248485815811355, -0.04346131680661005, -0.024988529798546506, -0.008488989469325808, 0.004582121457834391, 0.013173741417968895, 0.016824000940106908, 0.015809045693613088, 0.01123562561365007, 0.00506004126426562, 2.0053715235554223e-05, -0.0005280373787972576, 0.007132690643749887, 0.026738541518795688, 0.06163745480763022, 0.11433801847636835, 0.18604569708658197, 0.2762220102098639, 0.3822063819075439, 0.4989358622982431, 0.6187981373049861, 0.7316569315972477, 0.8250973904850906, 0.8848269001602073, 0.8952608937818933, 0.8402824664542612, 0.7041395850289344, 0.4724372608867626, 0.13317194401435015, -0.322252681693412, -0.8981023311691096, -1.593541031614484, -2.4019997913111117, -3.3109132994831385, -4.301812306745493, -5.350682930641321, -6.428648506092968, -7.502957893104135, -8.538243675115718, -9.497996063923603, -10.346183153541656, -11.048964647382268, -11.576478786313272, -11.90439160304904, -12.0151874259161, -11.899172241304525, -11.555116774151239, -10.990494490685823, -10.221294106616883, -9.271409767445137, -8.171635805605266, -6.958315452791901, -5.671719757501802, -4.354285696709234, -3.048699061620973, -1.7958282583741982, -0.6328902958946024, 0.4081272331737591, 1.3017394580094381, 2.029870406744775, 2.582351860960462, 2.9569989795868326, 3.1592721320422474, 3.201576896076968, 3.1022216410506793, 2.8840745679451576, 2.573072593474211, 2.196671470623451, 1.7823026869003042, 1.3559404633823413, 0.9408610855639523, 0.5566570240710811, 0.21854900803502533, -0.06298467442641378, -0.282266889335569, -0.43816377723583544, -0.5335642169942002, -0.5746573451935516, -0.5700732121736393, -0.529953327383618, -0.4650254684371621, -0.38574906425668976, -0.30158648090024986, -0.2204424671325973, -0.1482988657332968, -0.08904676892036774, -0.04451802531546115, -0.014693226953768294, 0.0019541504557571733, 0.00802231886784231, 0.006703661235769481, 0.0013141120432409012, -0.005125241093987285, -0.010217083367620236, -0.01240151514333679, -0.011041662540815426, -0.006381583013574931, 0.0006090843302948459, 0.008477596562603586, 0.01558334698233134, 0.020406505482327857, 0.0218296783182336, 0.01935516038153506, 0.013226419062681927, 0.004433367919465085, -0.005407377884382776, -0.01429008534335041, -0.020155428980113285, -0.02129339807570558, -0.016772950462491946, -0.006851969021845721, 0.006680710226110406, 0.020276770974783382, 0.02855173043905411, 0.024387918285177352, -0.0007663364244447409, -0.05641063346322311, -0.15234720242943625, -0.29791027571445966, -0.5011227910611173, -0.7678432038555449, -1.1009710503753882, -1.499780664321731, -1.9594476829670917, -2.47082277170625, -3.020503051529667, -3.591252746310336, -4.162678595418441, -4.712173768284062, -5.216089499989451, -5.651059676004113, -5.995395564945668, -6.230458603153377, -6.341916132545678, -6.32078875268642, -6.164216476588994, -5.8759724731127765, -5.4664164162782605, -4.951950527150958, -4.354215939180267, -3.6989327169649218, -3.014456075906553, -2.3301451416040786, -1.6746485710482826, -1.0742192084559756, -0.5511702405511192, -0.12259216481517715, 0.20061822860464926, 0.41436304015600406, 0.5214336293265813, 0.5311252756276978, 0.4584435896164976, 0.32295246796766747, 0.1473345183357424, -0.04423488227309234, -0.22778677315150136, -0.3812133519351348, -0.48576689994150585, -0.5272931697449561, -0.49710818063072265, -0.3924637825945563, -0.2165701289316919, 0.02184189529761913, 0.30932396892309244, 0.6288190536735626, 0.9610016302176329, 1.2857447408434963, 1.5836147664793045, 1.8372770841836714, 2.0326812697290326, 2.1599640536812927, 2.214007243787006, 2.194618167683624, 2.106346477320823, 1.957968983134017, 1.7615716177577703, 1.5314616554338802, 1.2829842580989124, 1.031324065456746, 0.7903556626757245, 0.5716815563212277, 0.38392162903454197, 0.23229780008430145, 0.11853627979968911, 0.041081526495893056, -0.00441085297358852, -0.024361146753405345, -0.026408992434138318, -0.018494714925252793, -0.007976338636160495, -0.0008705119667301962, -0.0012918002643413208, -0.011142158015217727, -0.030076670158068076, -0.05574325635478655, -0.08426549856071608, -0.11091171918897313, -0.13087271758147978, -0.1400572735452411, -0.13580529978302247, -0.11742619078483243, -0.08648597836489609, -0.04678860381701802, -0.004026527304862956, 0.03488998671564305, 0.06278011862967017, 0.07333784246302014, 0.0623683151167934, 0.0289865363598579, -0.023365395917591816, -0.08619858165411999, -0.14567663736955683, -0.18282484025860693, -0.17429693033693433, -0.09370346107680584, 0.08654525822322956, 0.39297991285024997, 0.8485426073431008, 1.4699741382272817, 2.265402074614589, 3.2323371555295988, 4.356145316288982, 5.609352339484962, 6.951809395635857, 8.331830112462493, 9.688326177604162, 10.953873273937244, 12.058568384630696, 12.9344663503007, 13.520435392028762, 13.767216260965153, 13.641346616074998, 13.128528407718637, 12.236116055105173, 10.994400310031292, 9.456136207596602, 7.694575343748752, 5.800003602606495, 3.8748798536862274, 2.02782549560409, 0.36679693097305244, -1.0082959389270214, -2.0126469079976808, -2.582806478225692, -2.681786139370778, -2.3026194644114404, -1.4700809594389803, -0.24020850344510358, 1.3023461174082795, 3.049060833745286, 4.874244752227452, 6.643472821104133, 8.222839841209538, 9.488475904379152, 10.335706309900132, 10.687174930544467, 10.499296428439564, 9.766513675326653, 8.522933246641374, 6.840899419665894, 4.826800641079404, 2.6144420663644157, 0.35510840273548594, -1.7940085962467212, -3.682104934089517, -5.177203787631879, -6.177856972031241, -6.623235777836104, -6.50080774111248, -5.850940751093117, -4.767917731697257, -3.3969371847536367, -1.9274535576606733, -0.5823430948599981, 0.39675219181692084, 0.76689332178013, 0.30306590192021066, -1.1821204956390345, -3.8196820681579746, -7.667948547028838, -12.700136418759593, -18.799776039231354, -25.77335998091278, -33.35897566715005, -41.238057490631974, -49.051562679101764, -56.41786164277697, -62.951053909596205, -68.27848729671626, -72.05640338390674, -73.9828361211033], 'positive_zeros': ['0.41029900060435761315937134187377', '0.57016178644690592563445887185713', '0.70372537327768501312331637760889', '0.817166871027631114444307414589566', '0.945881162702571285306121609482644', '1.02753243536270224154717360985264', '1.19342960086011963789553649312590', '1.21660043839012596588136241528393', '1.51415988002894388174364802078342', '1.56835154410693863282321618764404', '1.70653180766348117051954374236954', '1.76760095048315719694056695654447', '1.77598558590967914869263832689211', '1.85306377002315342007867076375123', '1.98966659284296221469051126806307', '2.01244266418160247925440200170870', '2.08843404143042881270283718405832', '2.26420305282857945330390063955357', '2.33961915151079165590267788064948', '2.35702418820719239043730764157368', '2.37819317041807503626218672984958', '2.48308321934877943424920698009632', '2.51820558738696211067371205816207', '2.77247460420880530447858801874441', '2.89939325284227409844063259615526', '2.91375413890107180596661138637137', '2.98767398242980822801988721272390', '3.03044170371257812946220361148569', '3.07143685917097775504318720981314', '3.20241817007525704282275361347662', '3.26717684446622485151568242156919', '3.36496412211232152366631603809110', '3.38035240969221438299654970409631', '3.53882211625115991536429072201423', '3.54709859381052730583812569165670', '3.66052207779540427052490956159187', '3.78750105785122941924589594219830', '3.88344692642747756920085506729792', '3.92477737387531372304437657685046', '3.96886677605457110447487823063956', '4.04034369338598203710583361173501', '4.10486748618041303312243638100541', '4.20603142907028183589621921382266', '4.22967061806138260523686716145142', '4.38873640725518369716860938170048', '4.51946982499993589330588766097205', '4.58652228879179247648336010569754', '4.60483445165325459883733553130007', '4.64899961197908974998430039287407', '4.68208550517152644313435500019531', '4.74185442783175110068801951448252', '4.76325453745815276361147225480524', '4.76764973664758085161829698644421', '4.78597425931589919852203514486381', '4.99958447345048057146528038566180', '5.17007727693803576070613451599811', '5.31524893277317446342593760751662', '5.35933508326913723387066209777684', '5.36496721485964395945794058847738', '5.39121856989038499576712635089394', '5.47064396036378585018059263998334', '5.52196320670823811594297938178284', '5.58600430358398782739462158488951', '5.58920693459498926954262760951461', '5.62301049518186736211696972087330', '5.93510965372880464082354525973536', '5.94655165922615375481497930500019', '6.03101655938672694540602499370749', '6.04094550293886930895688259155403', '6.09104201359579846948192507705160', '6.10826047141591979196388284878517', '6.12317866578448815587374717146290', '6.13366127638711768436287369708832', '6.13729235154775748345393095207990', '6.19683518656975567997159569558816', '6.36746516441942851814892056758259', '6.52568533544690427915511095797806', '6.55625486146963072293829105842150', '6.67604840758029486624224351810482', '6.68384708706789745122728736488769', '6.76376202265842098534768606646056', '6.78687742521922887813933187331506', '6.83051655141373293102803577779514', '6.87387664586204859894028121567888', '6.97486137313162398978862986290038', '7.03450880959758736925235523726139', '7.05366350535171270884187937669577', '7.12847204189656003154473898022040', '7.14732338312574174819934471658624', '7.29142011989877076191377474270775', '7.34593083004363090964738243027696', '7.35637007287794768827321693540753', '7.36418953476780200231737744718769', '7.43413836324804252257436944170683', '7.61405118205600771669953088113329', '7.64887821816758990760557362043534', '7.66675150900230254535254658009446', '7.69264214509033680396615529625330', '7.87347227691849934111732361990079', '7.88454536810201912637032837520149', '7.904000965319235057048693672424021', '7.973379907254560412124200869141423', '7.996829532980341195621254162112920', '8.072547506738839756110238355321061', '8.144256571343769364385501600882092', '8.199816701282001699880707728841698', '8.275471983484790574524365525892291', '8.348308209917263750995728405181641', '8.508020735638030079269566530370783', '8.508810752169691237740382640950988', '8.526499973232757855777133291028972', '8.727534629422236332735674267447383', '8.754098495767390559968645451118328', '8.772184911705222712704307267183823', '8.818361980018682301061709504770680', '8.946654328087353085732927394078164', '9.041127581202077932785062683409540', '9.077777365914010566898616490427147', '9.081895342275751436479535881560468', '9.622138568555005166744702573901392'], 'prelabel': '24-3380e12-1.1-c0e12-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.2987839476600973, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c0e12-0', 'trace_hash': 1544554089887280105, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.41029900060435761315937134187', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.57016178644690592563445887186', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.70372537327768501312331637761', 'prec': 103}}
• lfunc_search •

  Column	Type
  algebraic	boolean
  analytic_conductor	double precision
  bad_primes	bigint[]
  central_character	text
  conductor	numeric
  conductor_radical	bigint
  degree	smallint
  dirichlet_coefficients	numeric[]
  euler11	numeric[]
  euler13	numeric[]
  euler17	numeric[]
  euler19	numeric[]
  euler2	numeric[]
  euler23	numeric[]
  euler29	numeric[]
  euler3	numeric[]
  euler31	numeric[]
  euler37	numeric[]
  euler41	numeric[]
  euler43	numeric[]
  euler47	numeric[]
  euler5	numeric[]
  euler53	numeric[]
  euler59	numeric[]
  euler61	numeric[]
  euler67	numeric[]
  euler7	numeric[]
  euler71	numeric[]
  euler73	numeric[]
  euler79	numeric[]
  euler83	numeric[]
  euler89	numeric[]
  euler97	numeric[]
  euler_factors	numeric[]
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  is_instance_Artin	boolean
  is_instance_BMF	boolean
  is_instance_CMF	boolean
  is_instance_DIR	boolean
  is_instance_ECNF	boolean
  is_instance_ECQ	boolean
  is_instance_G2Q	boolean
  is_instance_HMF	boolean
  is_instance_MaassGL3	boolean
  is_instance_MaassGL4	boolean
  is_instance_MaassGSp4	boolean
  is_instance_NF	boolean
  label	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  self_dual	boolean
  spectral_label	text
  trace_hash	bigint
  z1	numeric

  
  {'algebraic': True, 'analytic_conductor': 530.7449806163954, 'bad_primes': [2, 5, 13], 'central_character': '1.1', 'conductor': 2223311955453421620312454598656000000000000, 'conductor_radical': 130, 'degree': 24, 'dirichlet_coefficients': [1, 0, -2, 3, 0, 0, 0, 0, 3, 0, 0, -6, 0, 0, 0, 3, 0, 0, 0, 0, 0, 0, 2, 0, -6, 0, -2, 0, 2, 0, 0, 0, 0, 0, 0, 9, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, -6, -1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, -2, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 12, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 6, 0, 0, 0, 0, 0, 0, 0, -18], 'euler11': [1, 0, -6, 0, 21, 0, -50, 0, 90, 0, -126, 0, 141, 0, -126, 0, 90, 0, -50, 0, 21, 0, -6, 0, 1], 'euler13': [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], 'euler17': [1, 0, 6, 0, 21, 0, 50, 0, 90, 0, 126, 0, 141, 0, 126, 0, 90, 0, 50, 0, 21, 0, 6, 0, 1], 'euler19': [1, 0, -6, 0, 21, 0, -50, 0, 90, 0, -126, 0, 141, 0, -126, 0, 90, 0, -50, 0, 21, 0, -6, 0, 1], 'euler2': [1, 0, -3, 0, 6, 0, -7, 0, 6, 0, -3, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, -2, 1, 2, -4, 2, 3, -4, -1, 6, -4, -4, 9, -4, -4, 6, -1, -4, 3, 2, -4, 2, 1, -2, 1], 'euler29': [1, -2, 1, 2, -4, 2, 3, -4, -1, 6, -4, -4, 9, -4, -4, 6, -1, -4, 3, 2, -4, 2, 1, -2, 1], 'euler3': [1, 2, 1, -2, -4, -2, 3, 4, -1, -6, -4, 4, 9, 4, -4, -6, -1, 4, 3, -2, -4, -2, 1, 2, 1], 'euler31': [1, 0, 12, 0, 66, 0, 220, 0, 495, 0, 792, 0, 924, 0, 792, 0, 495, 0, 220, 0, 66, 0, 12, 0, 1], 'euler37': [1, 0, -6, 0, 21, 0, -50, 0, 90, 0, -126, 0, 141, 0, -126, 0, 90, 0, -50, 0, 21, 0, -6, 0, 1], 'euler41': [1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1], 'euler43': [1, -2, 1, 2, -4, 2, 3, -4, -1, 6, -4, -4, 9, -4, -4, 6, -1, -4, 3, 2, -4, 2, 1, -2, 1], 'euler47': [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -6, 0, 7, 0, -6, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], 'euler5': [1, 0, 6, 0, 15, 0, 20, 0, 15, 0, 6, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler53': [1, 0, -12, 0, 66, 0, -220, 0, 495, 0, -792, 0, 924, 0, -792, 0, 495, 0, -220, 0, 66, 0, -12, 0, 1], 'euler59': [1, 0, -6, 0, 21, 0, -50, 0, 90, 0, -126, 0, 141, 0, -126, 0, 90, 0, -50, 0, 21, 0, -6, 0, 1], 'euler61': [1, -2, 1, 2, -4, 2, 3, -4, -1, 6, -4, -4, 9, -4, -4, 6, -1, -4, 3, 2, -4, 2, 1, -2, 1], 'euler67': [1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1], 'euler7': [1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1], 'euler71': [1, 0, -6, 0, 21, 0, -50, 0, 90, 0, -126, 0, 141, 0, -126, 0, 90, 0, -50, 0, 21, 0, -6, 0, 1], 'euler73': [1, 0, 12, 0, 66, 0, 220, 0, 495, 0, 792, 0, 924, 0, 792, 0, 495, 0, 220, 0, 66, 0, 12, 0, 1], 'euler79': [1, 0, -12, 0, 66, 0, -220, 0, 495, 0, -792, 0, 924, 0, -792, 0, 495, 0, -220, 0, 66, 0, -12, 0, 1], 'euler83': [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -6, 0, 7, 0, -6, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], 'euler89': [1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1], 'euler97': [1, 0, -6, 0, 21, 0, -50, 0, 90, 0, -126, 0, 141, 0, -126, 0, 90, 0, -50, 0, 21, 0, -6, 0, 1], 'euler_factors': [[1, 0, -3, 0, 6, 0, -7, 0, 6, 0, -3, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 2, 1, -2, -4, -2, 3, 4, -1, -6, -4, 4, 9, 4, -4, -6, -1, 4, 3, -2, -4, -2, 1, 2, 1], [1, 0, 6, 0, 15, 0, 20, 0, 15, 0, 6, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1], [1, 0, -6, 0, 21, 0, -50, 0, 90, 0, -126, 0, 141, 0, -126, 0, 90, 0, -50, 0, 21, 0, -6, 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], [1, 0, 6, 0, 21, 0, 50, 0, 90, 0, 126, 0, 141, 0, 126, 0, 90, 0, 50, 0, 21, 0, 6, 0, 1], [1, 0, -6, 0, 21, 0, -50, 0, 90, 0, -126, 0, 141, 0, -126, 0, 90, 0, -50, 0, 21, 0, -6, 0, 1], [1, -2, 1, 2, -4, 2, 3, -4, -1, 6, -4, -4, 9, -4, -4, 6, -1, -4, 3, 2, -4, 2, 1, -2, 1], [1, -2, 1, 2, -4, 2, 3, -4, -1, 6, -4, -4, 9, -4, -4, 6, -1, -4, 3, 2, -4, 2, 1, -2, 1], [1, 0, 12, 0, 66, 0, 220, 0, 495, 0, 792, 0, 924, 0, 792, 0, 495, 0, 220, 0, 66, 0, 12, 0, 1], [1, 0, -6, 0, 21, 0, -50, 0, 90, 0, -126, 0, 141, 0, -126, 0, 90, 0, -50, 0, 21, 0, -6, 0, 1], [1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1], [1, -2, 1, 2, -4, 2, 3, -4, -1, 6, -4, -4, 9, -4, -4, 6, -1, -4, 3, 2, -4, 2, 1, -2, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -6, 0, 7, 0, -6, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, -12, 0, 66, 0, -220, 0, 495, 0, -792, 0, 924, 0, -792, 0, 495, 0, -220, 0, 66, 0, -12, 0, 1], [1, 0, -6, 0, 21, 0, -50, 0, 90, 0, -126, 0, 141, 0, -126, 0, 90, 0, -50, 0, 21, 0, -6, 0, 1], [1, -2, 1, 2, -4, 2, 3, -4, -1, 6, -4, -4, 9, -4, -4, 6, -1, -4, 3, 2, -4, 2, 1, -2, 1], [1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1], [1, 0, -6, 0, 21, 0, -50, 0, 90, 0, -126, 0, 141, 0, -126, 0, 90, 0, -50, 0, 21, 0, -6, 0, 1], [1, 0, 12, 0, 66, 0, 220, 0, 495, 0, 792, 0, 924, 0, 792, 0, 495, 0, 220, 0, 66, 0, 12, 0, 1], [1, 0, -12, 0, 66, 0, -220, 0, 495, 0, -792, 0, 924, 0, -792, 0, 495, 0, -220, 0, 66, 0, -12, 0, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -6, 0, 7, 0, -6, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 0, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1], [1, 0, -6, 0, 21, 0, -50, 0, 90, 0, -126, 0, 141, 0, -126, 0, 90, 0, -50, 0, 21, 0, -6, 0, 1]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3380/1/w/e'], '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': '24-3380e12-1.1-c0e12-0-2', '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}], 'nu_real_doubled': [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'order_of_vanishing': 0, 'prelabel': '24-3380e12-1.1-c0e12-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.2987839476600973, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e12-0', 'trace_hash': 1544554089887280105, 'z1': {'__RealLiteral__': 0, 'data': '0.41029900060435761315937134187', 'prec': 103}}
• lfunc_instances •

  Column	Type
  Lhash	text
  Lhash_array	text[]
  factors	text[]
  label	text
  type	text
  url	text

  
  {'Lhash': '520115774389156586278672981953,722765930816619848051145614207,892077891831292194257989985889,1035882074544800704701564868554,1199046823644490003011689832958,1302552108441503826859898959436,1512851749860466898582814070716,1542224275963170204639493785470,2240700405843963017609802552381,2349037400331036082022387816404,2522202050671437172892289350886,3147681933424124456112146712469', 'Lhash_array': ['520115774389156586278672981953', '722765930816619848051145614207', '892077891831292194257989985889', '1035882074544800704701564868554', '1199046823644490003011689832958', '1302552108441503826859898959436', '1512851749860466898582814070716', '1542224275963170204639493785470', '2240700405843963017609802552381', '2349037400331036082022387816404', '2522202050671437172892289350886', '3147681933424124456112146712469'], 'factors': ['2-3380-260.179-c0-0-0', '2-3380-260.199-c0-0-3', '2-3380-260.199-c0-0-5', '2-3380-260.199-c0-0-7', '2-3380-260.179-c0-0-2', '2-3380-260.179-c0-0-3', '2-3380-260.199-c0-0-9', '2-3380-260.199-c0-0-10', '2-3380-260.199-c0-0-14', '2-3380-260.179-c0-0-12', '2-3380-260.179-c0-0-13', '2-3380-260.179-c0-0-15'], 'label': '24-3380e12-1.1-c0e12-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3380/1/w/e'}