Lfunction data - 40-1380e20-1.1-c0e20-0-1

Formats: - HTML - YAML - JSON - 2024-05-05T22:04:05.024140

• 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
  instance_types	text[]
  instance_urls	text[]
  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': '317653429759773821019169805829,950501207312577819595839471574,984652246130357690478794125225,988941046999112670746821176763,1057564054830624731375147040374,1341602899664838285181400202071,1526367778903334566095908292136,1658702454069810717404193951369,1661292240368185707045612529969,1700316610493054258511042752826,1732064094728668502055199344273,1855477092893915339256686352263,1984892483805664439744800859331,2162628616155045753209873057576,2178802016855051960849554408820,2396288002082484940271272321933,2414517020915590790586200344768,2573214987109603609664660932134,2859401267031288376621177363319,3073008291095205881415193721261', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 1, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.0005764003225726267, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1]], [3, [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1]], [5, [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1]], [23, [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1]]], 'bad_primes': [2, 3, 5, 23], 'central_character': '1380.1', 'coefficient_field': '1.1.1.1', 'conductor': 627453762719724095122406062634362166417817600000000000000000000, 'conductor_radical': 690, 'degree': 40, 'euler_factors': [[1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 10, 0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 10, 0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 10, 0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, 0, 9, 0, 36, 0, 84, 0, 126, 0, 126, 0, 84, 0, 36, 0, 9, 0, 1, 0, 0, 0, 1, 0, 9, 0, 36, 0, 84, 0, 126, 0, 126, 0, 84, 0, 36, 0, 9, 0, 1], [1, 4, 10, 20, 35, 56, 84, 120, 165, 220, 286, 360, 439, 520, 600, 676, 745, 804, 850, 880, 891, 880, 850, 804, 745, 676, 600, 520, 439, 360, 286, 220, 165, 120, 84, 56, 35, 20, 10, 4, 1], [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 10, 0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 10, 0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -6, 0, 7, 0, -8, 0, 9, 0, -10, 0, 11, 0, -10, 0, 9, 0, -8, 0, 7, 0, -6, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 10, 0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 10, 0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -6, 0, 7, 0, -8, 0, 9, 0, -10, 0, 11, 0, -10, 0, 9, 0, -8, 0, 7, 0, -6, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -6, 0, 7, 0, -8, 0, 9, 0, -10, 0, 11, 0, -10, 0, 9, 0, -8, 0, 7, 0, -6, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -6, 0, 7, 0, -8, 0, 9, 0, -10, 0, 11, 0, -10, 0, 9, 0, -8, 0, 7, 0, -6, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 10, 0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 10, 0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -6, 0, 7, 0, -8, 0, 9, 0, -10, 0, 11, 0, -10, 0, 9, 0, -8, 0, 7, 0, -6, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 10, 0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, -4, 10, -20, 35, -56, 84, -120, 165, -220, 286, -360, 439, -520, 600, -676, 745, -804, 850, -880, 891, -880, 850, -804, 745, -676, 600, -520, 439, -360, 286, -220, 165, -120, 84, -56, 35, -20, 10, -4, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -6, 0, 7, 0, -8, 0, 9, 0, -10, 0, 11, 0, -10, 0, 9, 0, -8, 0, 7, 0, -6, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -6, 0, 7, 0, -8, 0, 9, 0, -10, 0, 11, 0, -10, 0, 9, 0, -8, 0, 7, 0, -6, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -6, 0, 7, 0, -8, 0, 9, 0, -10, 0, 11, 0, -10, 0, 9, 0, -8, 0, 7, 0, -6, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 10, 0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 10, 0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -6, 0, 7, 0, -8, 0, 9, 0, -10, 0, 11, 0, -10, 0, 9, 0, -8, 0, 7, 0, -6, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 10, 0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -6, 0, 7, 0, -8, 0, 9, 0, -10, 0, 11, 0, -10, 0, 9, 0, -8, 0, 7, 0, -6, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1]], 'euler_factors_factorization': [[[[1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], 1]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], 1]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], 1]], [[[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 2], [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 2]], [[[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 2], [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 2]], [[[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 2], [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 2]], [[[1, 0, 1], 10], [[1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], 1]], [[[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 4]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], 1]], [[[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 2], [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 2]], [[[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 2], [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 2]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], 2]], [[[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 2], [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 2]], [[[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 2], [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 2]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], 2]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], 2]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], 2]], [[[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 2], [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 2]], [[[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 2], [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 2]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], 2]], [[[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 2], [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 2]], [[[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 4]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], 2]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], 2]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], 2]], [[[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 2], [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 2]], [[[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 2], [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 2]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], 2]], [[[1, -1, 1, -1, 1, -1, 1, -1, 1, -1, 1], 2], [[1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 2]], [[[1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1], 2]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 1, 'label': '40-1380e20-1.1-c0e20-0-1', 'leading_term': '0.43817695430114036130744166641477078239994612835358236615883529309502943753865748288787486', '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}, {'__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, 0, 0, 0, 0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1380/1/bn/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.003125', 'prec': 27}, 'plot_values': [0.43817695430114034, 0.4394820350221338, 0.4406365717836458, 0.44165550775261414, 0.44255387997688056, 0.44334677761838037, 0.444049305131741, 0.44467655035534315, 0.44524355745262384, 0.4457653046163032, 0.44625668642711586, 0.4467325007413049, 0.4472074399673972, 0.4476960865823123, 0.4482129127294149, 0.44877228373640826, 0.44938846538863575, 0.4500756347931308, 0.4508478946702695, 0.45171924485715065, 0.45269805357569953, 0.4537807751338003, 0.45495874344937454, 0.45622208295987365, 0.4575605678318181, 0.4589635828072123, 0.46042008364888226, 0.46191855717564406, 0.4634469808889051, 0.4649927822035502, 0.46654279730779213, 0.46808322968920535, 0.4695996083773261, 0.4710767459671374, 0.47249869650244436, 0.4738487133136305, 0.47510920692056774, 0.4762617031285974, 0.4772868961715161, 0.4781667062313891, 0.4788843012034523, 0.4794221548907588, 0.47976238216945494, 0.4798861971323485, 0.47977369455601915, 0.4794037903531162, 0.4787541593551881, 0.4778011703376274, 0.4765198181978863, 0.47488365319796627, 0.472864707182371, 0.4704334166831839, 0.4675585428248158, 0.46420708794224225, 0.46034420882827076, 0.4559331265275829, 0.45093503259804607, 0.44530889696367937, 0.4390106544940288, 0.4319935574712182, 0.4242085219844834, 0.4156039598007694, 0.40612545468204275, 0.39571596663079484, 0.38431584368162813, 0.3718627458021875, 0.3582915704637539, 0.3435343803059411, 0.327520333353657, 0.3101756162794885, 0.29142338124076805, 0.2711836868577939, 0.24937344393785216, 0.2259063665887636, 0.20069292940547492, 0.17364033145363178, 0.1446526096423024, 0.11363105300033137, 0.08047377946006475, 0.045075589856786426, 0.007327971249458823, -0.03288088767129659, -0.07566605389644948, -0.12114579034136633, -0.16944149678278628, -0.2206776375370797, -0.27498165308462, -0.3324838545760979, -0.39331730013557664, -0.4576176518576861, -0.525523012383035, -0.5971737399272015, -0.6727122406350664, -0.752282737134299, -0.8360310096110365, -0.9241037993980851, -1.0166481614148026, -1.1138116280240329, -1.215741910096711, -1.322586501099658, -1.4344922509835742, -1.5516048298069904, -1.6740679546515425, -1.8020230195435238, -1.9356085970929162, -2.074959838406431, -2.2202078394387246, -2.371478973770376, -2.5288941919679497, -2.692568287862768, -2.8626091322808196, -3.0391168749669104, -3.2221831156716196, -3.411890046402063, -3.6083096208473253, -3.811502816466934, -4.021518784049656, -4.238393931165274, -4.462150987672752, -4.6927980566555005, -4.930327653894604, -5.174715595156238, -5.425919541551522, -5.683878369342256, -5.948511326344947, -6.219717065557133, -6.497372693312718, -6.781332837423255, -7.071428741082969, -7.3674673886285404, -7.669230669546931, -7.976474587412996, -8.28892871629999, -8.606297187704964, -8.928257711955737, -9.254460331229614, -9.584527006089862, -9.91805129646266, -10.25459813764773, -10.593703718762802, -10.934875470994626, -11.277591943173437, -11.621302296074802, -11.965427273626544, -12.309359923892266, -12.652466247766485, -12.994085999703653, -13.333533646203408, -13.670099487271441, -14.003050945502459, -14.331634026785222, -14.65507632626593, -14.972593319644782, -15.283386887448405, -15.586646204055327, -15.881550074190121, -16.167269435779552, -16.442970025910817, -16.70781520547284, -16.960968936852314, -17.20159890780096, -17.42887955595912, -17.641994734076427, -17.840141912957858, -18.022536041824548, -18.18841326778887, -18.337034732760316, -18.467690431279042, -18.57970311140367, -18.672432234292454, -18.745282145090226, -18.797710337068008, -18.829224242810554, -18.839383976077478, -18.827805897821143, -18.79416605418432, -18.7382034608432, -18.659723207639747, -18.558599357181947, -18.434777610994143, -18.288277716884394, -18.119195423985015, -17.927703813588675, -17.71405532022138, -17.478583031561186, -17.221701433220296, -16.943906749035268, -16.64577685688643, -16.32797107115466, -15.991235884328871, -15.636403135384782, -15.264380967273532, -14.87615089607048, -14.472764701841413, -14.055340830068895, -13.62506030758882, -13.183162180609068, -12.730938486138509, -12.269728772027673, -11.800914184783359, -11.325911148344483, -10.846164602156545, -10.363140794645611, -9.878320132093094, -9.393189597049487, -8.909234868285905, -8.427932254090074, -7.950741172355054, -7.479100756899684, -7.014417627203108, -6.558054285083744, -6.111320901631479, -5.675467317887534, -5.251675298696851, -4.841051106266208, -4.444618460196093, -4.063311950444704, -3.6979709688023816, -3.349334222981182, -3.018034895338689, -2.704596505542894, -2.4094295288176713, -2.1328288217549565, -1.8749719352940022, -1.6359183125857792, -1.4156094189884036, -1.2138702496616354, -1.030412263827704, -0.8648346536573043, -0.7166281130263588, -0.5851801380672395, -0.4697813306373605, -0.36963268081181644, -0.28385379487254936, -0.21149202550293472, -0.15153245108711694, -0.10290864124613812, -0.06451413611027033, -0.035214557424915534, -0.013860260514663632, 0.000700572512701111, 0.009608506071181938, 0.013979206210068585, 0.014889699118618448, 0.013364661113611688, 0.010362890465484048, 0.006764070456036059, 0.0033558878678676797, 0.0008217595290076973, -0.00027068476285425507, 0.0005197755016005397, 0.003498362255533655, 0.008825876183823862, 0.016511568326078037, 0.026407426141607963, 0.03820398527029209, 0.05142776781145396, 0.0654404361090672, 0.0794397378284333, 0.09246230360573653, 0.1033883428325111, 0.1109482669987654, 0.11373125233964936, 0.1101957294062918, 0.09868186288596328, 0.07742601798428905, 0.044576934929703, -0.0017864145698197156, -0.06363538825454366, -0.14297078757486809, -0.24180068037574584, -0.3621171061813655, -0.5058718563460478, -0.6749515381997041, -0.8711521477313483, -1.096153389106237, -1.3514929911937867, -1.6385412810976123, -1.9584762822424007, -2.312259609717211, -2.700613438151675, -3.123998851741919, -3.582595717389561, -4.076282762773742, -4.604622104150444, -5.166846598191378, -5.76184904887366, -6.388174281824589, -7.044014282738892, -7.7272065648220645, -8.43523590322783, -9.165239545093034, -9.914015972254301, -10.678037260316017, -11.453465042713999, -12.236170052100208, -13.021755174100141, -13.80558191062944, -14.582800111881829, -15.348380798216022, -16.097151855883414, -16.823836530582575, -17.523095252399628, -18.18956901843942, -18.81792393277385, -19.402897011600015, -19.939342811401456, -20.422280446824974, -20.846940548364138, -21.208811697627826, -21.503685870229116, -21.727702413378587, -21.877390087279817, -21.949706706525852, -21.94207592995343, -21.852420764840137, -21.679193373881805, -21.421400800961248, -21.07862626414854, -20.65104572775388, -20.13944273869903, -19.545219113853825, -18.87039197884771, -18.117586421618736, -17.29002415601233, -16.39150697918334, -15.426394606716904, -14.399577002364575, -13.31644137977448, -12.182834113390864, -11.005017854103768, -9.789624201544331, -8.54360233844548, -7.274164082546103, -5.988725857451482, -4.694848125054902, -3.4001728579943755, -2.112359660636271, -0.8390214104636087, 0.4123353774427359, 1.634375749266448, 2.8200052275440726, 3.9624318270241075, 5.055224860213284, 6.092370183216384, 7.068321578246401, 7.978047697957396, 8.817074053818807, 9.581519581693316, 10.268127374835334, 10.874289237088567, 11.398063776443507, 11.83818783056268, 12.194081090567071, 12.46584386642646, 12.6542480157817, 12.760721136993102, 12.787324196335877, 12.736723203884445, 12.612155645790128, 12.41739031613871, 12.156682177473543, 11.834723598453953, 11.456588361037888, 11.027673402850024, 10.553638448822802, 10.040343722790368, 9.493786481305102, 8.920037124715316, 8.325175643614289, 7.7152291520265, 7.096111242151435, 6.473563869287458, 5.8531024399917, 5.239964732012456, 4.639064221603783, 4.05494873337529, 3.4917650559091022, 2.9532266951385466, 2.4425887434189377, 1.9626294932926038, 1.5156385704121549, 1.1034115196068377, 0.7272501260596298, 0.3879695349712424, 0.08591156631005636, -0.17903623670128113, -0.40741621728044375, -0.6001713364481677, -0.7586115540169263, -0.8843764435536754, -0.9793946731057415, -1.0458410212296094, -1.086091625322954, -1.1026781772978786, -1.0982419544405153, -1.0754882736417735, -1.0371415021979669, -0.9859019830472234, -0.9244053892819487, -0.8551850637632232, -0.7806379628872675, -0.7029947145222525, -0.6242934589813391, -0.5463586025285141, -0.4707845867012882, -0.39892471083826453, -0.33188505281301084, -0.2705234422062384, -0.2154533505619658, -0.1670524764987757, -0.12547572078203625, -0.09067216944838856, -0.06240563510804814, -0.04027826844584572, -0.023756563771394363, -0.012199250755002576, -0.004886490426893695, -0.0010496404938233994, 9.908028390963822e-05, -0.0006623101917168251, -0.0025930528002744784, -0.005015118757038523, -0.007336120872695384, -0.009069136234687403, -0.009848977780508101, -0.009444541195420516, -0.007766935711082829, -0.004873196498302154, -0.0009654703862633796, 0.0036143361041766054, 0.008394358746574094, 0.012786840098669455, 0.016106171164952825, 0.0175905776387923, 0.016426954059318117, 0.011778295980468133, 0.0028131298654305273, -0.011263725979597688, -0.03117978133278609, -0.05756361841243398, -0.09091451745018839, -0.13157371183188737, -0.17969805723305468, -0.235236830418111, -0.29791232930639555, -0.3672048948263603, -0.4423429002294326, -0.5222981673540837, -0.6057871714919452, -0.6912782885944256, -0.7770052421968046, -0.8609868309652062, -0.9410526676726412, -1.0148747397321798, -1.0800044412161915, -1.133914570005808, -1.1740456749952697, -1.1978560277129924, -1.2028743926310506, -1.1867546830052451, -1.1473315154687829, -1.0826756309851044, -0.991148099478112, -0.8714521716176212, -0.7226816955141084, -0.5443650259453455, -0.33650339323978584, -0.0996027631259388, 0.16530169703675224, 0.4566294080883215, 0.7722473328230535, 1.1094721963590124, 1.4650822937473083, 1.8353392090927596, 2.2160194743689074, 2.6024560147062483, 2.989589045994542, 3.372025910239002, 3.7441091575419927, 4.099992014155549, 4.433720308677146, 4.739319864464702, 5.01088730352755, 5.24268339393121, 5.429227454415688, 5.565391188036886, 5.64649035084696, 5.668372785814783, 5.627504019527518, 5.521043256192561, 5.346907583876498, 5.103828996396975, 4.791400560633285, 4.410110537280973, 3.961363570824608, 3.4474882623096077, 2.8717306527980897, 2.2382333727464507, 1.552000449189209, 0.8188480045552663, 0.045341325785358044, -0.761281237514705, -1.593196618647427, -2.4420958495643386, -3.2992922106328333, -4.155837204927187, -5.0026425129916445, -5.830605983941514, -6.630742288249274, -7.39431258150656, -8.112951286211322, -8.778788828861234, -9.38456830547129, -9.923754116987961, -10.39063072538457, -10.78038982409012, -11.089204390758255, -11.314288293553783, -11.453940350892909, -11.507571995181854, -11.47571872929361, -11.360035993121, -11.163273114493304, -10.88923143121944, -10.542706688563802, -10.129417006583164, -9.65591840941255, -9.129499975206585, -8.55807010561813, -7.950034512232526, -7.3141667433227004, -6.659473400693595, -5.995056292493478, -5.329973824455297, -4.673103947823369, -4.033010956694503, -3.417818360897226, -2.8350899538510363, -2.2917210498486495, -1.793841684371846, -1.346733679391962, -0.9547628942913494, -0.6213252646114258, -0.34881078015904055, -0.1385851660415253, 0.009011198802901254, 0.09464683589727492, 0.11996541458215655, 0.08753592823755853, 0.0007879104880700444, -0.13606696762960152, -0.3181253406188536, -0.5398928455398527, -0.795393114616372, -1.0782829705077235, -1.3819716373535658, -1.6997417289449486, -2.024869766738739, -2.3507440149754864, -2.6709774970945475, -2.9795141315619618, -3.270726163176394, -3.5395017016302632, -3.781322886390207, -3.9923289646165787, -4.169362093084147, -4.310000454765498, -4.412576467307653, -4.47617996754209, -4.500646664932937, -4.48653244884065, -4.435074411093568, -4.348139701023733, -4.2281635596939555, -4.078078078932694, -3.9012333950669573, -3.701313153700352, -3.4822461681231056, -3.2481162384162947, -3.0030721003606753, -2.751239565946273, -2.4966381691543043, -2.2431047016709913, -1.9942191300489962, -1.753239998468888, -1.5230516117937873, -1.3061220185324571, -1.1044724251910965, -0.9196584135721032, -0.7527630528597588, -0.6044017200047014, -0.47473817122262946, -0.3635111504084505, -0.2700705826617232, -0.19342218819975962, -0.1322791684117752, -0.08511946572099255, -0.0502469855508565, -0.025855094481568176, -0.010090675189302458, -0.0011170411254591542, 0.002825998141551494, 0.0033665172549197328, 0.001950525246128141, -0.00020082796652300426, -0.002125757167899549, -0.0031471913421125854, -0.002888341931589652, -0.0012781223480445353, 0.0014536827298935171, 0.004791331651585494, 0.007957693357002317, 0.009947784883393134, 0.009570359276970067, 0.005496410631581019, -0.003686723111033356, -0.01941713286381256, -0.04309757778332409, -0.07603386093056413, -0.11937397170028897, -0.17404972438132876, -0.24072279016452802, -0.31973654768450566, -0.41107519209336435, -0.5143313730219983, -0.6286834422848636, -0.7528831550994259, -0.8852544173751585, -1.0237034038000141, -1.1657400933674524, -1.3085109872619076, -1.44884249538259, -1.5832942089143032, -1.7082210237241868, -1.819842849091569, -1.9143204339783193, -1.9878356736965122, -2.036674653561728, -2.0573121578515576, -2.046494739173402, -2.0013199084793047, -1.9193107426268607, -1.7984840621908185, -1.637410141917105, -1.4352625275398394, -1.1918567282278694, -0.9076767489952956, -0.5838886908589265, -0.2223409292152369, 0.17444932371982907, 0.6033229653790871, 1.0605190512006613, 1.541727246044669, 2.0421517030136855, 2.5565851386205103, 3.079491645218185, 3.605096771211508, 4.127484606216783, 4.64069691714425, 5.138832585432317, 5.616146690616494, 6.0671467202634775, 6.4866840635434295, 6.8700388553010425, 7.2129964873447285, 7.511914302906598, 7.763777201186372, 7.966241128714377, 8.117663705054424, 8.217121515614618, 8.264413897239134, 8.260053335881352, 8.205242883110838, 8.10184127279106, 7.952316674658758, 7.759691924876053, 7.527484100049774, 7.259626387351483, 6.960387694093193, 6.634290135391087, 6.286024519000456, 5.920365611981694, 5.5420890000705, 5.155891236978761, 4.766314815204134, 4.377679359093817, 3.994020257482442, 3.6190357441210947, 3.256043206679355, 2.907945265410439, 2.577205916898502, 2.265836792972275, 1.9753933460564177, 1.706980553841835, 1.4612683414357572, 1.2385143877384361, 1.038591895319964, 0.8610254090802945, 0.7050317050712572, 0.5695642358660502, 0.4533598280435163, 0.3549863495227016, 0.2728901919429558, 0.2054422919912812, 0.1509816583551439, 0.1078554896232065, 0.07445510317611725, 0.04924705822578309, 0.030799028906228286, 0.017800160347740783, 0.009075816652253191, 0.003596799479230824, 0.0004832747925252117, -0.0009962134370258247, -0.0014301402316789444, -0.0012731769562705924, -0.0008584862380984025, -0.0004124083012883835, -7.077352395228187e-05, 0.00010392131806233367, 0.00010520677214318473, -3.4115105255795664e-05, -0.0002575660923669048, -0.000498909917949914, -0.0006939836198214908, -0.000790146745848985, -0.0007531730899348535, -0.0005715304220554079, -0.0002581106204218309, 0.00015041848955435537, 0.0005963713088969495, 0.0010055627332139418, 0.001293174707105931, 0.0013705156088289908, 0.0011521879755783603, 0.0005631840844420485, -0.00045454920042740135, -0.001936493283953242, -0.0038912448716634353, -0.006297787439451103, -0.009104540038830404, -0.012230282138614141, -0.01556693742690166, -0.018984110578484408, -0.02233517340768987, -0.02546460694103235, -0.028216231629223973, -0.030441899471913843, -0.03201018276276152, -0.032814576711598265, -0.032780740102542956, -0.03187233297131911, -0.030095042768031485, -0.027498473155811987, -0.02417567209845493, -0.020260180560304326, -0.015920604920021973, -0.01135284542532101, -0.006770244388345349, -0.0023920457712942682, 0.0015693235373362522, 0.004921539157526637, 0.007505528748827188, 0.00920772281040695, 0.00997062574002026, 0.009800925251320043, 0.008774395220848559, 0.007036920300439942, 0.00480107916853544, 0.002337867563495752, -3.667498755568094e-05, -0.0019799985300300066, -0.003146575930932691, -0.0032160285543361916, -0.0019252051840717695, 0.0008966600976740871, 0.005290809305070362, 0.011131142582217009, 0.018087195476364414, 0.02558952069268086, 0.032799174930499574, 0.03858305052777534, 0.04149672427249747, 0.039776447494929236, 0.03134174217721024, 0.013809844644963059, -0.01547703996022057, -0.05941106045661647, -0.12106476579049216, -0.203623911977587, -0.31030715313758567, -0.44427425258126124, -0.6085243373495011, -0.8057862829263193, -1.0384037703333968, -1.308217961913401, -1.6164510880986969, -1.9635945102402936, -2.3493050102602355, -2.772313144331466, -3.2303478145238196, -3.7200814918602143, -4.237096772650302, -4.77587905194393, -5.329837901598727, -5.8913588012626255, -6.451887601914331, -7.002055958575642, -7.5318254409150285, -8.030658812207458, -8.487723097541675, -8.892116628935447, -9.233115805987586, -9.500436503381522, -9.684504290804737, -9.776726974821143, -9.769762451192515, -9.657774493076616, -9.436668915367727, -9.104302564351226, -8.660658839005059, -8.107983424371424, -7.450865377921667, -6.696267491110128, -5.853500363096568, -4.934138251706897, -3.951874122224853, -2.92229595819457, -1.8626112807936746, -0.7913175946986238, 0.2721793550262074, 1.307993030623643, 2.296221226578248, 3.217439424166599, 4.053211673832337, 4.786607256754461, 5.402710575263618, 5.889111198404699, 6.236360771519612, 6.438383608166599, 6.49282938969888, 6.40135745712603, 6.169832009894553, 5.808427483209438, 5.331640917068023, 4.758197419287322, 4.110834424677144, 3.4159875773097705, 2.7033732200233835, 2.005471191629657, 1.3569154659882603, 0.7938027308196184, 0.3529314280616459, 0.07098599586286725, -0.01631699828158098, 0.12489747791701486, 0.525789011492425, 1.2139479559284079, 2.212582484585424, 3.5397670700419024, 5.207771493694994, 7.2224878078775765, 9.582980477088933, 12.281184558832173, 15.30175271599949, 18.622039812631098, 22.212252624136884, 26.03576157711662, 30.04957235371354, 34.20495182097797, 38.4481989845599, 42.72154801810576, 46.964186976643674, 51.11337265309795, 55.10561926613518, 58.87793635202621, 62.36908944117135, 65.52085588837545, 68.27924763909473, 70.59567278173974, 72.42801059896999, 73.74159781369363, 74.51020491952364, 74.71662134243054, 74.35303577399566, 73.42130451510812, 71.9330174731701, 69.90935648941333, 67.38074614138874, 64.38630199240194, 60.97308604595174, 57.19518379249098, 53.112621593374044, 48.790147122800754, 44.29589908063831, 39.69999530518507, 35.07307067593908, 30.484797737836562, 26.002423752540658, 21.689357859654912, 17.603869005463196, 13.797928013649587, 10.316008382872457, 7.194154246678773, 4.459277380975871, 2.1286659411053708, 0.20971689583353123, -1.3001011690049398, -2.4130536917065193, -3.1507185812532983, -3.5433472982201875, -3.629023654657567, -3.452640329387534, -3.064717539921975, -2.5200921775724896, -1.876508899690594, -1.1931471001284342, -0.5291192822676655, 0.05802288789298688, 0.5137374644446231, 0.7878681374123113, 0.8359157284572482, 0.6201594594934956, 0.11060459595383378, -0.7142652901291499, -1.866949121021134, -3.3506145185328076, -5.159016120242887, -7.276646928993824, -9.67911782991556, -12.333754764240963, -15.20039769008771, -18.23238052245592, -21.377666852109655, -24.580112505670535, -27.780823019941394, -30.919571935488932, -33.9362438723386, -36.772254989510024, -39.37194750843628, -41.68392031137416, -43.66223848269915, -45.267485742486826, -46.46765315926413, -47.23884327156555, -47.565772037328685, -47.442058569882306, -46.870298127027816, -45.86191938015102, -44.43683245712214, -42.622879483516236, -40.455104206647775, -37.974861652481394, -35.22879252751851, -32.26769014433627, -29.145289948202603, -25.9170144256906, -22.638711667243438, -19.365395208080287, -16.150033674490608, -13.042426114488253, -10.08818343436337, -7.327833910546917, -4.796080276851928, -2.5212213782014095, -0.5247477995018124, 1.1788829745190772, 2.58229117661486, 3.6850432349234046, 4.493352752483153, 5.01962684821261, 5.281874489984897, 5.302996678289947, 5.109980945967482, 4.733024566513993, 4.204612908212564, 3.5585788658996624, 2.8291622284587077, 2.05010303158753, 1.2537908619375657, 0.4704899047580655, -0.27234223461614326, -0.950625797674745, -1.544110266878643, -2.036698249342005, -2.4166380807155057, -2.6765853977422007, -2.8135376580117106, -2.8286490783065292, -2.7269366229087337, -2.516890416867395, -2.210004217550025, -1.8202432980801084, -1.3634682490652998, -0.8568341779951867, -0.3181822230756021, 0.23455803251838336, 0.7839339540996771, 1.3134891362723455, 1.8082232098887203, 2.2549817056625168, 2.6427680869459538, 2.9629666765910843, 3.2094794007625027, 3.378775976000541, 3.4698597611999844, 3.4841547091921874, 3.425321117545847, 3.2990098046325733, 3.1125658749154357, 2.87469435085557, 2.5951006166977253, 2.2841189336568752, 1.952343564831473, 1.610269691509406, 1.2679574292434885, 0.934733172466217, 0.6189340156941561, 0.3277014895868907, 0.06682894541478539, -0.15933530582679514, -0.34792916436792226, -0.49756258683462246, -0.6082527151481688, -0.6813137331979482, -0.7192079535515725, -0.7253657946967053, -0.7039830427940901, -0.6598041887942598, -0.5979006904689202, -0.5234527400579271, -0.4415426175004594, -0.35696701851721463, -0.2740729070168134, -0.1966233689140098, -0.1276970858919837, -0.06962291775708983, -0.023950029987519345, 0.008547431311772028, 0.02783344973458943, 0.034544556643665736, 0.029900063531377988, 0.015593295021976946, -0.006330295588235759, -0.03360202545280039, -0.06385984958422644, -0.09477340794521329, -0.12415895543222541, -0.15007957439138964, -0.17092693490774746, -0.18548196522613258, -0.192953005263955, -0.19298994305337358, -0.18567536089701922, -0.17149440304761618, -0.15128583420066632, -0.1261776062129458, -0.09751085735734882, -0.06675667486859087, -0.03543014370483492, -0.005006178924537112, 0.023158635860263604, 0.04789436465058836, 0.0682728861665613, 0.08364752173918817, 0.09367555428526972, 0.09832298257744027, 0.09785179769774591, 0.09279098338582072, 0.08389326572584131, 0.07208046669845565, 0.05838076359419596, 0.04386149742153503, 0.029561635787002303, 0.016427878481009166, 0.005258161045429519, -0.0033441144793540114, -0.009002404218064948, -0.011583954551316137, -0.01120028439022931, -0.008191130614731678, -0.0030927621464092595, 0.0034074632333836903, 0.010527473543919818, 0.017454210451157626, 0.023410526289239727, 0.027720664928574505, 0.02986958301763629, 0.029551489202687443, 0.026703331305736995, 0.021519553711552227, 0.014445431979375785, 0.006147401879808315, -0.002539894065477215, -0.010688675715258876, -0.017372529289562344, -0.021776149646217716, -0.023314680147568802, -0.021755711941282348, -0.017335927498952627, -0.010863587870221068, -0.0037976182145004955, 0.001705984448028734, 0.0027892200470917856, -0.0040633907753630264, -0.02292418237082681, -0.05826076514724603, -0.11471098603938146, -0.19679431588091417, -0.3085622292272172, -0.45319337364179346, -0.6325423449383172, -0.8466539526338923, -1.0932577747367966, -1.3672604389453291, -1.6602553044416237, -1.9600709364993891, -2.2503808574328423, -2.510397429469356, -2.7146723047974044, -2.8330251145760084, -2.8306199522262956, -2.668200946787822, -2.302502530573906, -1.6868418239111482, -0.7718964905485827, 0.4933347097905902, 2.160411956781643, 4.2801776588224465, 6.901346276209131, 10.068990306893074, 13.822956083199417, 18.196247973720947, 23.213423705405177, 28.889046634738964, 35.226242743759016, 42.21541078418504, 49.83313324263937, 58.0413335913358, 66.78672160350197, 76.00057930584444, 85.59895176253178, 95.48313688567214, 105.54057435968363, 115.646188371465, 125.66413802605652, 135.4498007866722, 144.85214022750455, 153.7163779361021, 161.88691099700557, 169.21041684145362, 175.53907954113598, 180.73386536864209, 184.6677708773079, 187.22896406216205, 188.32373849787382, 187.8792018020544, 185.84562337841908, 182.19837212916823, 176.93938260295337, 170.09816009645425, 161.73235243195236, 151.9273566251047, 140.79551593685122, 128.47462794318548, 115.12577956831146, 100.93074896436617, 86.0889098522071, 70.81369385308776, 55.32868361076422, 39.863419982740844, 24.649015099923748, 9.913669392795928, -4.121805446432168, -17.248354294150694, -29.272835286403662, -40.021867421060826, -49.3452776732695, -57.11906520286127, -63.24781141982427, -67.6664498492009, -70.34135029852087, -71.27091443932989, -70.4853217257511, -68.04555488233699, -64.04178170181284, -58.59111849634305, -51.83483202502935, -43.93505039668849, -35.07106510985899, -25.435315862352045, -15.22915679247628, -4.6585072236950005, 6.07050833224879, 16.75582723149654, 27.203522912717236, 37.23159273638193, 46.67337467229352, 55.3805189458138, 63.22545344988187, 70.10335632841317, 75.93366832723744, 80.66063129403533, 84.25332587667334, 86.70518248962978, 88.03293977436346, 88.275096398517, 87.48991398784071, 85.75303904106778, 83.15481959789771, 79.79739803630555, 75.79166456071019, 71.25415667291298, 66.30398823152294, 61.05988771146697, 55.637419147688405, 50.146451220380264, 44.6889302987393, 39.357002784585994, 34.231565704509215, 29.381170688576603, 24.86120766563361, 20.71366317787588, 16.967260868611273, 13.637955486190492, 10.729751864239594, 8.23580343968104, 6.139738748370066, 4.4171600840913365, 3.037256185537762, 1.96447043007506, 1.1601675034487673, 0.5842447639795931, 0.19663935833248006, -0.04131164217403429, -0.16569348411041668, -0.2090455834834087, -0.1996215409704738, -0.16088743827239646, -0.11125735091689902, -0.06405902397724131, -0.027716168880546035, -0.006124000895612195, 0.0008100663632050539, -0.003504879808517433, -0.013108555321048349, -0.020310808547841765, -0.016530865043019257, 0.006882353494335162, 0.05788310730093883, 0.14304545418630016, 0.2669894282256452, 0.431937113267284, 0.6374128969526541, 0.8800958314135728, 1.153825596398033, 1.4497573699765682, 1.7566558849224716, 2.0613119707959258, 2.3490599659631517, 2.6043731976443403, 2.8115121610071023, 2.9551900898329575, 3.0212327973932394, 2.9972054071036696, 2.872979760507185, 2.6412197928139314, 2.297765796617446, 1.84190276324339, 1.2765027212700797, 0.6080359939298614, -0.1535486225460984, -0.995069790495189, -1.9004760314444675, -2.851310744923746, -3.8272639417169363, -4.806795365608958, -5.7677935283389585, -6.68825111996418, -7.54693497729576, -8.324028628072123, -9.001728466260705, -9.564756845902977, -10.000789999450879, -10.300787292854027, -10.45921092933723, -10.474131085415488, -10.347215617102693, -10.083607542082895, -9.691697337750082, -9.182800561557613, -8.570754282893258, -7.871448220126808, -7.102308286973566, -6.281757007621174, -5.428659534960319, -4.561761855259948, -3.6991687774981137, -2.857867192143193, -2.053306914151992, -1.2990506984334036, -0.6065008687208575, 0.015293653055038929, 0.5597426632034129, 1.0227356444339397, 1.402583018867678, 1.69988430756431, 1.9173320748304374, 2.059462350595106, 2.132363548531074, 2.1433567034539145, 2.1006601323632252, 2.01305159318768, 1.889543880659759, 1.7390755205563784, 1.570227154857012, 1.3909805681085077, 1.2085219885463976, 1.0290931230849372, 0.8578914641479973, 0.6990194977200145, 0.5554803139224657, 0.42921456460940377, 0.32117497976518655, 0.231431367107031, 0.15929860620679387, 0.10348000723526286, 0.06221840617402508, 0.033447700116157233, 0.01493815273560872, 0.0044296747136692, -0.00025164170972611234, -0.001097285351937714, 0.00015729209521172456, 0.0020830087695337556, 0.0035842039472109874, 0.003903676807647654, 0.0026080547728039795, -0.00044339310003322946, -0.005142828376501322, -0.011186812023106353, -0.018134101653021723, -0.025464313515236245, -0.03263382249368219, -0.039125792833652355, -0.0444918660675164, -0.048383759818804654, -0.050573801980667334, -0.05096419387888555, -0.04958552035233968, -0.04658565256771462, -0.04221071723682222, -0.03678030625462265, -0.030659115514127644, -0.024227396369064225, -0.017852512156492226, -0.011863642596014959, -0.006531318557906408, -0.002053013163509494, 0.001454504502784484, 0.003955893943157352, 0.005491425006311143, 0.006165479295117115, 0.006130653917913852, 0.005569061610325631, 0.004672599329972467, 0.003624001623604192, 0.0025803989018914294, 0.0016608700202062098, 0.000939128869756872, 0.00044203299117344326, 0.00015409625090870844, 2.7639589609470023e-05, -2.3360818835284617e-06, 4.493297968903667e-08, -8.757005370302364e-06, -3.2568088262799214e-05, -1.9193013674948988e-05, 0.0001508549389787505, 0.0006685668074044296, 0.0017919507177149867, 0.0038317495711190338, 0.007126941065000983, 0.012010383955917114, 0.018765834529631764, 0.027578429698402438, 0.03848157113378029, 0.051303895738140745, 0.06562075647123507, 0.08071477224881093, 0.09555005661300618, 0.1087650108522977, 0.11868787367074166, 0.12337853193673372, 0.12069907019615013, 0.10841423537884665, 0.08432146364341722, 0.04640841627939554, -0.006965827518259114, -0.07687158866049036, -0.16359888629928612, -0.26644654721802935, -0.3835199631304101, -0.511548503149038, -0.6457344202352342, -0.77964493018967, -0.905158816642876, -1.0124794056287407, -1.09021887086946, -1.1255598955672164, -1.104499519078225, -1.01217478609821, -0.833266886357912, -0.5524768615899258, -0.15506229722876289, 0.37257913270625526, 1.0422966791769661, 1.8635643543228406, 2.8428721276603417, 3.9831545752655244, 5.283283731131745, 6.73765691047505, 8.335887803522493, 10.062627907443396, 11.897537804199038, 13.815424026053023, 15.786559089123024, 17.777161063237354, 19.750041756326354, 21.66541631125529, 23.48185598198977, 25.1573615766476, 26.650529304137766, 27.92177570614868, 28.934584226598904, 29.656732972116572, 30.061461522799, 30.128534394623443, 29.84516001767217, 29.20672690859806, 28.21733571056798, 26.89010855408488, 25.24715027157258, 23.319256476600817, 21.14536697730432, 18.77173222685428, 16.25077742309932, 13.639764654484052, 10.999262349753844, 8.391461276796546, 5.878387144151947, 3.5200651817002986, 1.3726956389904381, -0.5130992496027826, -2.093896749482075, -3.3349060726722666, -4.21115900293873, -4.708412626292373, -4.823726635958343, -4.565687804661115, -3.954272424112779, -3.0203533146164916, -1.8048014625586946, -0.35725020498372817, 1.2654573601917845, 3.0010797152685726, 4.783981642177325, 6.5472744094550706, 8.225020591847898, 9.754428869834108, 11.077963161730741, 12.145292110182796, 12.915009273011806, 13.35606125437364, 13.448830259815033, 13.185828882268305, 12.571977958254747, 11.624452638092412, 10.37209689928977, 8.854422069000622, 7.12021958155991, 5.22583803519434, 3.233203687176176, 1.2075628176830355, -0.7849075631339717, -2.6795178742549566, -4.415447276214224, -5.93800225848437, -7.200669980467276, -8.166890390260411, -8.811480509393967, -9.121656146640936, -9.097610286973062, -8.752623008354604, -8.112694460062867, -7.215709596813067, -6.110160384079186, -4.853467450697033, -3.5099580650166913, -2.148570293554327, -0.8403620873239771, 0.3440891989051784, 1.337287918942575, 2.0773367079014915, 2.5102771670797215, 2.5921677190132812, 2.290822049499474, 1.5871434332387286, 0.4760045255720214, -1.0333616183195633, -2.917476048071518, -5.139232537316343, -7.6490007363798265, -10.386176759965824, -13.281127891422512, -16.257463760846395, -19.234554455513866, -22.13020699018877, -24.86340603136712, -27.357059528456627, -29.540633665313795, -31.352472090531847, -32.74182123383943, -33.67048808228462, -34.11406602401484, -34.06268397117047, -33.52125501440902, -32.509219021127066, -31.059791853357865, -29.218751572593657, -27.042808464558707, -24.597620352970495, -21.955526944446003, -19.193086414789526, -16.38850377511878, -13.619043529425145, -10.958518665316044, -8.474945251361243, -6.228459699031754, -4.269510039106722, -2.6374175057255234, -1.359393251962171, -0.4500022640374485, 0.088908861443573, 0.26783215616602923, 0.10879204169042869, -0.35584754628278575, -1.0849091777011888, -2.0301962126100968, -3.1384817578441275, -4.353612961274252, -5.618648716508898, -6.877949463034479, -8.079141512602726, -9.174885019951352, -10.124384039505625, -10.894587904206045, -11.461043908850586, -11.80839353005952, -11.930491685357978, -11.83015806715854, -11.518590362679921, -11.01445360803915, -10.342713741048406, -9.533271107456617, -8.619455309976468, -7.63644918958213, -6.619710809536557, -5.603460524579531, -4.619295682437168, -3.6949884541862708, -2.853513055403077, -2.1123376178002293, -1.4830036847343042, -0.9710032639034103, -0.5759494870650405, -0.292025648462787, -0.1086893025318946, -0.011583324508623307, 0.01639151956992935, -0.006104470971464409, -0.06008130714311693, -0.12744176872880247, -0.192136706538665, -0.24119813084111613, -0.2656014241401798, -0.26091616207291696, -0.22771480758013682, -0.17171957934263177, -0.1036796064860434, -0.03898256074340886, 0.002983208862432991, -0.00031107610361327386, -0.07348899146413859, -0.2420836494660656, -0.5312672618482334, -0.9645512227200407, -1.5625123484363028, -2.3416013963600943, -3.313086612404724, -4.482180067853671, -5.847388317991223, -7.400114305807878, -9.12453222764183, -10.997744953766313, -12.990221440753244, -15.066500531899218, -17.186136837540058, -19.304854718664483, -21.37586814877691, -23.3513177217513, -25.18377155376278, -26.827737775590986, -28.241203779965506, -29.3870127531715, -30.233996612776135, -30.75797200045201, -30.942507848117312, -30.779435803701766, -30.26908790435506, -29.420259987213555, -28.24990844840161, -26.782565442553874, -25.049529586878464, -23.087860565205194, -20.93921298083219, -18.648553635472428, -16.262809510516313, -13.829494925739093, -11.395365654091423, -9.005145261015745, -6.700369645139781, -4.5184022348643875, -2.4915513663727613, -0.6464117987030038, 0.996550315641742, 2.423194732862678, 3.6256915328614077, 4.602304959943036, 5.356995844816934, 5.898868115784993, 6.241489609672137, 6.402114336941118, 6.400844687550296, 6.25976819401308, 6.0021014467997205, 5.6513717204013805, 5.2306632658375705, 4.76195074457935, 4.265537160246759, 3.759610859325289, 3.2599282453072203, 2.7796016204717513, 2.329015307497334, 1.9158560152589743, 1.5452411047841006, 1.2199286928576054, 0.9405915556150926, 0.7061358058682967, 0.5140452893211083, 0.36073346576287885, 0.2418861998442884, 0.1527815296906406, 0.08857450553296306, 0.04453864173428275, 0.016258739084173197, -0.0002270850781941732, -0.008335417740227261, -0.010892328836834607, -0.01012954730662309, -0.007715040647951443, -0.004809975745370283, -0.002143922068151612, -0.00010006216122849956, 0.0011972128099253761, 0.0017988875254894901, 0.0018572965742791564, 0.0015651571311985392, 0.0011097244417817048, 0.000642581860526855, 0.0002641824532380008, 2.1109403935825273e-05, -8.681568960444575e-05, -9.293646383088724e-05, -4.7167341573718905e-05, 3.2873742827529826e-07, 1.2442558344648596e-05, -2.6584841258641198e-05, -0.0001089352232296826, -0.00020713121059141195, -0.0002832116488283034, -0.0003014277037130242, -0.0002420838267460458, -0.00011377805399626557, 3.8760395955934105e-05, 0.00013376266411014716, 6.036914913142717e-05, -0.0003035193418637612, -0.001063547838275151, -0.0022726696844283453, -0.0038889337280203135, -0.0057310424420234955, -0.0074364030951228855, -0.008427079451311955, -0.007889313169683422, -0.004772071611027442, 0.0021906552072067475, 0.014430370858733964, 0.033465770183822616, 0.060796110958216555, 0.09776925653598134, 0.14543004437645307, 0.20435726256847755, 0.2744999322085618, 0.3550255892008496, 0.4441946333973107, 0.5392753818531696, 0.636514072904284, 0.7311726089870052, 0.8176442440198944, 0.8896541971878228, 0.9405475090103694, 0.9636561696593864, 0.9527389320115389, 0.9024770780281615, 0.8090033628661184, 0.6704354349895223, 0.48737218679546834, 0.26332093128089457, 0.005014107766605519, -0.27742639076853814, -0.5705163984085772, -0.8576627596236923, -1.1196701573574424, -1.3355191877593962, -1.4834212219854004, -1.5421413230936403, -1.4925645562361234, -1.3194640325809717, -1.0134116727064426, -0.5727559958470386, -0.005573922686924286, 0.6685104857640424, 1.4167488342883015, 2.1920548307541723, 2.9322791787209255, 3.5600833187015435, 3.98351545432436, 4.0973796746732605, 3.7854651371214496, 2.9236744235579626, 1.384057360869704, -0.9602804332850171, -4.229465155473251, -8.530451357418146, -13.950082354507217, -20.54781012979429, -28.348307823199967, -37.3342403064657, -47.43948392641284, -58.543124120525405, -70.4645995674696, -82.96014430776812, -95.72109864744927, -108.37413246044592, -120.48338081343306, -131.5549815307302, -141.04401550115347, -148.36386661676673, -152.89794438787658, -154.01362731384012, -151.07819803299137, -143.476455049713, -130.62960353242215, -112.01495244833828, -87.18588025948306, -55.791479499541765, -17.59525445764005, 27.507771799590863, 79.4761829349515, 138.1101933226253, 203.04331202854547, 273.7375758068658, 349.4840097450356, 429.40762010333134, 512.4768593587353, 597.5179160143842, 683.2337188242858, 768.2273953250328, 851.029777911205, 930.1304093927997, 1004.0113687902699, 1071.1831216785233, 1130.2215020122135, 1179.804857925469, 1218.750345777127, 1246.0483372574167, 1260.8939153961994, 1262.7144776071104, 1251.1925372780026, 1226.283923159218, 1188.23168903743, 1137.5668964061115, 1075.103972399726, 1001.9297776041727, 919.3854971955051, 829.0416514371055, 732.6667222992129, 632.1900835109439, 529.660095713277, 427.1983809523134, 326.95141652276965, 231.04068288711005, 141.51266070542695, 60.289995589502645, -10.874865171826047, -70.44231202808272, -117.12332605578307, -149.9113091997438, -168.10752952188548, -171.33955357424884, -159.57046282436264, -133.09962875965832, -92.55506133038094, -38.877600378392486, 26.702606396821466, 102.69668677793882, 187.39384478505883, 278.90336856332726, 375.2006989078529, 474.1763097789199, 573.6860868693204, 671.6018634954635, 765.8607852310724, 854.5122250150358, 935.7610569987903, 1008.0062171091811, 1069.873586465165, 1120.2416643308068, 1158.2612752747573, 1183.369000983653, 1195.2927590635607, 1194.0484248279383, 1179.929726837174, 1153.491759955585, 1115.5285398539538, 1067.0454010573055, 1009.2271587551639, 943.4030419565377, 871.0094604497839, 793.5516897577979, 712.5655472666606, 629.5800903785772, 546.0822962723713, 463.48458586288314, 383.09593576161075, 306.0970342171722, 233.5190832796044, 166.22943009742963, 104.92239382990282, 50.11452824016784, 2.1447592550260564, -38.8209135152685, -72.78038067540413, -99.88268573729614, -120.41221336685281, -134.7704587266381, -143.45606394334985, -147.0438150478854, -146.16327793766388, -141.47771672911907, -133.66388462539354, -123.39320892329216, -111.31481118754496, -98.04071432489307, -84.13357540454487, -70.09705924387718, -56.368338589716274, -43.31364535232162, -31.2264837866006, -20.32817762826923, -10.770485159740979, -2.640193330502478, 4.034845062421888, 9.278557092839648, 13.158706166764015, 15.77850476371336, 17.268110438327852, 17.776303700074344, 17.462610046012497, 16.490086079803838, 15.018943360715785, 13.201135428555634, 11.175985418627455, 9.066897129791606, 6.979109886585775, 4.998431817859757, 3.1909382351406435, 1.6034951716516157, 0.264974499293543, -0.8119810182886915, -1.6287922059687558, -2.198513874758238, -2.5432754128617647, -2.6917248015819593, -2.6765856120993625, -2.532416872440274, -2.29364529659168, -1.9929183976209228, -1.659806425483896, -1.3198617289137822, -0.9940267526951458, -0.6983670263911833, -0.444093702922442, -0.23783003366042893, -0.08207352630028679, 0.024199095032202796, 0.08483803541512018, 0.10578756624871954, 0.09435898279464597, 0.05854760989234735, 0.006424225770218045, -0.05437707769857245, -0.11706008439255282, -0.17595091534540325, -0.22666733815987308, -0.26618071551022937, -0.29278339027316064, -0.3059779443470792, -0.3063070067464115, -0.29514316847621497, -0.27445835698101473, -0.24659107253289164, -0.2140237884123324, -0.17918592992763635, -0.14429215896088668, -0.11122078936763105, -0.08143459847762335, -0.05594320394564769, -0.03530352021888061, -0.019652708982182458, -0.008766571011336342, -0.002135591574874765, 0.0009494674485891962, 0.0013101279632717281, -0.00020230178980342492, -0.00277873573100729, -0.005709772451393372, -0.008426161276056372, -0.010521421148812986, -0.011757247719523469, -0.012053618516544693, -0.011466427134238772, -0.010156228331648332, -0.0083519936872739, -0.006313731716782053, -0.004297494400915241, -0.002525706077768989, -0.0011649791911779016, -0.00031269995698776783, 7.246227163020233e-06, -0.00015989283704606012, -0.0007114895607105911, -0.0015048131539260373, -0.0023775842400458164, -0.0031694013613160488, -0.003741695270766234, -0.00399413852078317, -0.003875886973362069, -0.003390628968978127, -0.0025950341790142405, -0.0015908410436596525, -0.0005116121498810821, 0.0004943729631208583, 0.0012832043955447827, 0.001734297776668527, 0.0017670830059931268, 0.0013534634926422307, 0.0005244457741602586, -0.0006301377382645012, -0.0019692469528223146, -0.0033153097461068506, -0.004474947818196836, -0.005264086255963513, -0.005535219061528217, -0.005204200161036297, -0.004273726539302864, -0.0028507036356704672, -0.001154944411023909, 0.00048285993510600384, 0.0016352400548860135, 0.0018045869442191195, 0.0004618228946420434, -0.002904432757840268, -0.00873074668745636, -0.017317255010977715, -0.028765737657844338, -0.04292208061449951, -0.05932804512200363, -0.07718716508821193, -0.09534941675565156, -0.11231897727543586, -0.12628550804079264, -0.13518114466197934, -0.1367629959271617, -0.12871900026681482, -0.10879354207863494, -0.07492770380299243, -0.025406806137546496, 0.040991761441497056, 0.12485852185378216, 0.22602840313296094, 0.34348208308898387, 0.475279842911981, 0.6185344327920742, 0.7694278646944708, 0.9232750893981123, 1.0746352743014493, 1.2174689825097886, 1.34533708403625, 1.4516349682483958, 1.5298541879185426, 1.573859369761311, 1.5781674547397706, 1.5382173492503226, 1.4506179808141892, 1.3133624206521786, 1.125988418319983, 0.8896846174321013, 0.6073341536802566, 0.28349005326314336, -0.07571908935929844, -0.46275146591573246, -0.8688775295515082, -1.2844606040628568, -1.6992818700202241, -2.1028966508772995, -2.48500717887778, -2.8358359532041217, -3.146483478570849, -3.4092567277844448, -3.617957266392471, -3.7680983879136516, -3.8570546934618304, -3.8841431230212855, -3.850624523922367, -3.7596101688051378, -3.615901567595269, -3.425764987884632, -3.196650344457649, -2.936867895385725, -2.6552380718686406, -2.3607308975819357, -2.0621117622087493, -1.767609786332424, -1.4846236770851051, -1.2194778939094992, -0.9772392281891369, -0.7616006894609767, -0.5748360509691133, -0.4178251444363728, -0.29014543321285013, -0.1902199413192025, -0.11551703314966588, -0.06278548249601901, -0.028311107284036865, -0.00818015602998231, 0.0014671241363005555, 0.004207272993504837, 0.0031415386344962504, 0.000751301302202601, -0.0011916186954918605, -0.0016557757160672747, -0.0003216466242048545, 0.0025028592839481307, 0.00601626844094345, 0.00909707952770536, 0.010504763478752406, 0.009094226379740082, 0.004028745905165045, -0.005023733263906451, -0.017725495030704107, -0.03294826615342129, -0.04870646262565831, -0.062151495232086046, -0.0696307788254851, -0.06681100213580335, -0.04886134164051287, -0.010688545975913531, 0.05278756268366799, 0.1463324305672618, 0.27408528443443714, 0.4392553386504349, 0.6438434682818356, 0.8884063817475372, 1.1718786259186333, 1.4914651661325296, 1.842613926021538, 2.2190737134422487, 2.6130386003799195, 3.015376700667163, 3.4159401123179265, 3.803932322310052, 4.168320626371907, 4.4982765572176335, 4.783622964314018, 5.01526624358486, 5.185592503791724, 5.288807850981771, 5.321205415182243, 5.281345120063611, 5.170136341519598, 4.990818307509929, 4.748838119691315, 4.451631368401392, 4.108315201493716, 3.729308137280587, 3.3258946469055406, 2.9097554223504374, 2.4924913886371036, 2.0851555814869163, 1.6978050936799916, 1.3391168113094079, 1.0160811335538518, 0.7337852221537906, 0.495294496892237, 0.3016367169227339, 0.15188762099859768, 0.04335179561348745, -0.028172518806997626, -0.068060322065237, -0.08247759170193122, -0.07797147809532093, -0.061055874461726924, -0.03781534132288718, -0.013549180220179938, 0.007524919383583372, 0.022491664124534756, 0.029871649584034477, 0.02966103461286174, 0.02327581938832852, 0.013404654543197935, 0.003778811656252846, -0.0011260656700728842, 0.0035617441130157586, 0.02273263589146565, 0.06091188250791403, 0.12189262555901674, 0.2084079775752479, 0.3218624408581839, 0.4621395711957114, 0.627498556272282, 0.8145673701667102, 1.0184346814950356, 1.2328370366685568, 1.4504323266706094, 1.6631456558303397, 1.862570474725242, 2.040400166938344, 2.188867021821651, 2.301164524572117, 2.3718279943244487, 2.3970567294947602, 2.374953291861855, 2.3056659827647543, 2.191425798726638, 2.0364742761746073, 1.846884668656779, 1.6302848585405687, 1.3954959530976774, 1.152105336091401, 0.9099967617460445, 0.678862662893315, 0.46772504035453377, 0.284491023785505, 0.13556711179783598, 0.025553468154250324, -0.04296183757765921, -0.06950106618013717, -0.05568187145370868, -0.005089934472363821, 0.0769533442897337, 0.18371464049290204, 0.30744522473218916, 0.4398272671552805, 0.5724441001237475, 0.69724719702712, 0.8069927961420673, 0.8956228636626014, 0.9585683688707277, 0.9929574670080704, 0.9977169007451796, 0.9735614196889438, 0.9228729231455133, 0.8494795259470388, 0.7583466981897599, 0.6551978353744927, 0.5460980282639718, 0.43702623766837184, 0.3334648050768739, 0.24003514996145942, 0.16020602921074156, 0.09609648207447077, 0.04839056715238634, 0.01637338131965273, -0.001909836737696721, -0.009377905684666123, -0.009535806100448787, -0.00601698163911468, -0.0020748083859475626, -5.743378497145033e-05, -0.0009035879064621298, -0.0036982518304620646, -0.005325935331883178, -0.00025554254098918643, 0.01951477596398342, 0.06433207457109683, 0.14657112584165669, 0.28012441418338085, 0.479710409895068, 0.7600225888372937, 1.134753294262212, 1.6155348210411986, 2.210849137737835, 2.924963548524714, 3.756952539859962, 4.699866292005588, 5.740103360326639, 6.857038895512615, 8.022950628988264, 9.203273013790719, 10.357202356826857, 11.438699336252077, 12.397756400445429, 13.18193702690713, 13.738179140293827, 14.01477718836259, 13.9634675511438, 13.541533358154034, 12.713839486283893, 11.454710216486355, 9.749561118036295, 7.59617669656667, 5.005596166285556, 2.0025476456931273, -1.374610662117599, -5.074460380108179, -9.03360089282176, -13.17821060029021, -17.42604561889539, -21.688815464813686, -25.874885321568023, -29.892157701543887, -33.65100086925074, -37.06713937406564, -40.064395738597455, -42.57717529105882, -44.552595493829614, -45.952174837568236, -46.75301387237559, -46.94843852778855, -46.5480994353574, -45.57738506145865, -44.0763063537516, -42.09788961230409, -39.70612964479312, -36.973589312676765, -33.97874557335601, -30.803191976742, -27.528842519389922, -24.235193683050635, -20.996695978405008, -17.88049365562249, -14.944553694607471, -12.236239633817119, -9.791373794697222, -7.633808996694543, -5.775507881043996, -4.217105537047984, -2.9489102821797446, -1.9522806308378216, -1.201297656940159, -0.6646349193107974, -0.30755043607242977, -0.09389326013683173, 0.011973465405220927, 0.0434208788858038, 0.030050656092642986, -0.0034993580824868543, -0.038396812773652214, -0.06207610679391457, -0.06831462881190084, -0.0569403446492051, -0.033204364582388485, -0.006868019419810867, 0.00893308507519362, -0.001023818836760443, -0.05268767824107872, -0.1613773881464877, -0.3405061668990656, -0.6004557237064739, -0.9476593089174034, -1.3839406981474294, -1.9061403833846569, -2.506043875189498, -3.17061042619529, -3.8824861676022966, -4.620784443869402, -5.362055821244502, -6.081395885222876, -6.753641329487013, -7.354582986396676, -7.862130310084409, -8.257365904502517, -8.525435901563762, -8.656231935984422, -8.644832537601662, -8.49168527231096, -8.202525151368725, -7.788038917738872, -7.2632991281770085, -6.64700317641604, -5.960552338349127, -5.227031612216062, -4.470144404651155, -3.713162824923863, -2.9779471967115834, -2.284038018118908, -1.6479235529963312, -1.0825014187116946, -0.5967466696171665, -0.1955942766390995, 0.11996811945890677, 0.35261269630723063, 0.5082148330691997, 0.5952613872167495, 0.6241639920549622, 0.606521125725443, 0.5543736833144545, 0.4794971388334201, 0.3927693725947813, 0.3036468344537303, 0.21977311243242273, 0.14673663936345033, 0.08798318380620446, 0.044878477892056554, 0.016907312314054023, 0.001988420562357961, -0.0031234345079790434, -0.002380982266626542, 3.140063442413768e-05, 0.00015792815668161118, -0.0053166254687646635, -0.018731505643513596, -0.041213258867931556, -0.0725524112024395, -0.11119995480571528, -0.15438148702707208, -0.1983185553648886, -0.2385392812995487, -0.2702542591340763, -0.28876939116803735, -0.2899035664196069, -0.27038082266431473, -0.22816479550455024, -0.16270975574770152, -0.07511036372725818, 0.031863853515090565, 0.15385447515099532, 0.2851173831499459, 0.4188317585182435, 0.5474959569326201, 0.6633850518280235, 0.7590401746837688, 0.8277570836556659, 0.8640408548567624, 0.8639952788387262, 0.8256193769405914, 0.7489892054409252, 0.636310437699625, 0.49183571240332974, 0.32164975450403244, 0.1333337370314285, -0.06447436953402833, -0.262590229106864, -0.45183123895083677, -0.6235676517102401, -0.7702399531686271, -0.8858074565391367, -0.96609725308313, -1.0090290588829718, -1.014699743676846, -0.9853209093672846, -0.9250131856515301, -0.8394712397259065, -0.7355231385872719, -0.6206159546135177, -0.5022657285530815, -0.3875135657715528, -0.2824303542523635, -0.1917104211045586, -0.11838817914965177, -0.06370203014881905, -0.02712393218150001, -0.006554558093776901, 0.0013292383974152964, 0.0006018027849976562, -0.004468361412606207, -0.010007502124134217, -0.01309572386528656, -0.012229036105105498, -0.00761573104846233, -0.0012418015953610288, 0.0033516641948902483, 0.0016231157390916625, -0.011056328553853507, -0.038126124949268474, -0.08021502238197703, -0.1332202859384842, -0.18615954734708207, -0.2188920865213913, -0.19982350993516257, -0.0837294460693144, 0.19015527904258434, 0.6996306125918722, 1.5404594673305994, 2.8265917503484403, 4.689564614573384, 7.276986010557199, 10.750042513289223, 15.280012376447628, 21.043809321304185, 28.218629872332855, 36.975825028467696, 47.47416346793107, 59.85269602461923, 74.22346759185926, 90.66436187526593, 109.21265269202927, 129.85925064129293, 152.54366260032444, 177.1504652477225, 203.50713956879676, 231.38360974998315, 260.493624592221, 290.4980281648609, 321.0099208466164, 351.60164020393324, 381.81341913276, 411.1635093509034, 439.15949466987377, 465.3104633392508, 489.13966470127775, 510.1972445723902, 528.0726378256129, 542.4061966327127, 552.8998765127691, 559.3279377183337, 561.5430449912106, 559.4799818269875, 553.1580916236003, 542.6814737781158, 528.2361361298305, 510.0849999990519, 488.5608120463768, 464.057100972292, 437.01748504084003, 407.923692755149, 377.28270130323506, 345.6134240031799, 313.43338794328974, 281.24583607282096, 249.5276646006321, 218.71856783861028, 189.21171035395844, 161.34633489380448, 135.40245096750928, 111.59659289291352, 90.08033788804154, 70.94109216651793, 54.204793732622875, 39.84031880097854, 27.76543324629159, 17.853902573359065, 9.943431879001459, 3.8441048331380814, -0.653017858300311, -3.7674651518260114, -5.721384672922563, -6.732292832717026, -7.0067578379964495, -6.735174165074641, -6.0877303237830604, -5.211614237701843, -4.229450465146041, -3.2388914747868576, -2.313249918978471, -1.5030632713895173, -0.8384004548947657, -0.3317153682016539, 0.01895267282884056, 0.22662738214862485, 0.3120692006554063, 0.30064197570279794, 0.21950749890343552, 0.09524861156052632, -0.04801243490974458, -0.1899684834915731, -0.3149562447826638, -0.412290798798169, -0.47616268632076675, -0.5051741106333179, -0.5016041319425536, -0.4705016214442654, -0.4186947396721688, -0.3538085605176302, -0.2833761680255969, -0.214102332614229, -0.15132295006661478, -0.09868325137085553, -0.05803753322092629, -0.029554134451534975, -0.01199318210056246, -0.003112582050194555, -0.000148423502615404, -0.00031287075840537244, -0.0012540676901261218, -0.00142845634345398, -0.00034573229065092956, 0.001340405512526574, 0.001907532611019995, -0.0011983343164532919, -0.01098368774337976, -0.030420695776483323, -0.06189821356522524, -0.10666453404096225, -0.16431961502949297, -0.23241394977828825, -0.3062060848944547, -0.37862128935513534, -0.44044084704915554, -0.4807353571993175, -0.4875340616309429, -0.44870706335185245, -0.35301784044373596, -0.19128660689784677, 0.042408231506415664, 0.349572719267808, 0.7262708700256435, 1.162315038355927, 1.6407521783140018, 2.1377155053199184, 2.622696303610703, 3.0592544350158266, 3.4061742994891944, 3.6190455987022934, 3.6522208538669636, 3.461076420514337, 3.004481197052066, 2.247358734589344, 1.1632160603956234, -0.2635025636150792, -2.035383772136296, -4.1404393040199725, -6.551042390509157, -9.223499009416866, -12.09831787249157, -15.10121183508474, -18.144829530027284, -21.131214907476146, -23.95490937790806, -26.50647000521941, -28.67638876537436, -30.359235444131347, -31.457846789209587, -31.88738278768036, -31.579071544155298, -30.48347324380547, -28.57311079890721, -25.84433929664226, -22.318399564474774, -18.041635982872627, -13.084503290270078, -7.53972052409104, -1.5196035627585514, 4.84736576759552, 11.420601682541225, 18.051949678733212, 24.59057265496351, 30.887950218825367, 36.802679256437166, 42.20498182982858, 46.98074062508953, 51.03490886570775, 54.2941715619789, 56.708768659675314, 58.25342767600028, 58.92739199365807, 58.75356930846493, 57.77686102443139, 56.06177722691107, 53.68947812602681, 50.75428257044033, 47.3598702734119, 43.61535272179834, 39.631368882695305, 35.51637240182451, 31.373296679383465, 27.296494947904012, 23.369254165274867, 19.661975902705542, 16.230994693125282, 13.118035585415958, 10.350284484157008, 7.941019180966667, 5.890727371410737, 4.188621240969102, 2.8144469439197772, 1.7404817326579545, 0.9336115585723676, 0.3573875710879456, -0.026032323163493, -0.2541340121271643, -0.36254430410933947, -0.3838234925693436, -0.34657856791305636, -0.2749010091557964, -0.18811261906220966, -0.1007982584052027, -0.023082705806794085, 0.03889917013249352, 0.08239395247320103, 0.10733922834109125, 0.11564525058619689, 0.11049756982326206, 0.0957218049461436, 0.07524226284966193, 0.052655647173614976, 0.030930371665197073, 0.012231737939437944, -0.0021358154080471157, -0.011685849950405652, -0.016629071963389776, -0.017698528029926813, -0.015947363470762827, -0.012544405413034141, -0.00858972613699102, -0.004967781599781989, -0.0022499392204349392, -0.0006520382041333028, -4.6474675945882745e-05, -2.267847173764807e-05, 1.481304282453617e-05, 0.0007248363610930394, 0.0027006222799863147, 0.006349553061663832, 0.01179649137706222, 0.018822744898420455, 0.026848829077107658, 0.03496452479206334, 0.04200471088170771, 0.046664548213934766, 0.04764336401804734, 0.04380337128526751, 0.03432588016800061, 0.01884769153801614, -0.002437458872640114, -0.028726364778427906, -0.05861258245896414, -0.09015638523214005, -0.12101779190515728, -0.14864615301275494, -0.17051411816626297, -0.1843788333614259, -0.18854937057008134, -0.1821370451382898, -0.16526470079457922, -0.1392123845781456, -0.10648010205624543, -0.07075339825552691, -0.03676406275837756, -0.010045980342527603, 0.0034056228529514196, -0.0024445227401715696, -0.03319535915563976, -0.0935082983531483, -0.18661586377087783, -0.31387740186108887, -0.4744188769715435, -0.6648908890980425, -0.8793735526164057, -1.109448960689104, -1.3444520277644965, -1.5718991043635133, -1.7780815777758165, -1.9487994846334706, -2.0701987867611247, -2.1296662134335653, -2.116728203667637, -2.0238961307430676, -1.8473997284762675, -1.5877497394078075, -1.2500751553370828, -0.8442107443735288, -0.38450782773135195, 0.11064116962175281, 0.6195552224084129, 1.1182672427309173, 1.5817323778562722, 1.9851822397702636, 2.3055524431920924, 2.5229017372928193, 2.6217363949220327, 2.5921539051849143, 2.4307256576362684, 2.141049160644525, 1.7339160367772912, 1.2270619077012828, 0.6444873337310015, 0.015358833120520868, -0.6274778288205405, -1.2492787845468734, -1.8153940993186382, -2.2933696637327143, -2.6550422465813566, -2.8785041812313765, -2.949814679216125, -2.864342505864307, -2.627639504809187, -2.255765714092433, -1.7750136784111823, -1.221010776220096, -0.637212393870186, -0.07283381452711794, 0.4196971636756784, 0.7876535513420556, 0.9811484913835271, 0.9563408933821892, 0.6785447911320586, 0.12503944949753487, -0.7126036157116706, -1.8268015468972358, -3.192978293294168, -4.769408716019631, -6.4979426265045666, -8.30561795618643, -10.107126275655395, -11.808048344151992, -13.30873443922795, -14.508666224034684, -15.31110599522875, -15.627817145387247, -15.38362798146938, -14.52061057550287, -13.001657434004683, -10.81326121354655, -7.9673444800723265, -4.502050030772567, -0.48122118823679055, 4.007272901575991, 8.854280899273508, 13.93313959719349, 19.104297394280668, 24.220587680591528, 29.132929604976983, 33.69620127451587, 37.775019006773114, 41.24915793669962, 44.01836397921817, 46.006334242342746, 47.16368121272997, 47.469743556901214, 46.93316087057834, 45.59118846800912, 43.50778840034435, 40.770659511432, 37.48739746445298, 33.78041713912305, 29.7814789602162, 25.626008444981057, 21.447414444338833, 17.371670561935243, 13.512368369016057, 9.966532854096908, 6.811362826259519, 4.102019417287823, 1.870539116338942, 0.12588982045121652, -1.1448695625793381, -1.9744203605534056, -2.4121497442266264, -2.5204350032768392, -2.370461255389426, -2.03780605133297, -1.5980346624626696, -1.122529768500395, -0.6747573963906969, -0.3071839382618692, -0.058984760245127894, 0.045360843974040624, -0.0034557806536977776, -0.20002033965289415, -0.5255066423546914, -0.9497432251180368, -1.4338884381691102, -1.9335371978673315, -2.402062970032703, -2.7939903900638363, -3.06819748660969, -3.190761330361914, -3.1372860293060167, -2.8945857331214793, -2.461636474264781, -1.8497714861811754, -1.0820842988628188, -0.19208189121467498, 0.7782787257380712, 1.7810569776832752, 2.765143820057699, 3.6792524795473467, 4.474905935049345, 5.109247173304858, 5.547495879107548, 5.764917973883188, 5.748200634788538, 5.496159774537246, 5.019748143473858, 4.341373687882775, 3.4935779680772234, 2.517160979464797, 1.4588695523526838, 0.3687913835552454, -0.7023833688779223, -1.7061024907836293, -2.5985134457565238, -3.3426949084761373, -3.9104435735326275, -4.283523590371531, -4.454319628754958, -4.42587110470357, -4.211303658849692, -3.8327084706825842, -3.3195384329165387, -2.7066434353973596, -2.032071101460883, -1.3347694974043731, -0.6523319611935197, -0.01891772429810371, 0.53653248740109, 0.9916881475521908, 1.3317581440297042, 1.5499183334141622, 1.6472206344540696, 1.6320165641341848, 1.5189508410783432, 1.3276052015192705, 1.0808933358519215, 0.8033208717657588, 0.5192297381083208, 0.25114382871705726, 0.018322939937834824, -0.16438546345322508, -0.28732801020305365, -0.3464172820714432, -0.34308253903506764, -0.2838162962151646, -0.17936106323693937, -0.04360471145204899, 0.10772787059157131, 0.25848587198882195, 0.3935021517780188, 0.4998945677068662, 0.5681585528645102, 0.5929724748761405, 0.5736563838283224, 0.5142497260351704, 0.4232012381507674, 0.3126924459889382, 0.1976430711602294, 0.09447037066434867, 0.019693589717195027, -0.011513473904898264, 0.013286075446727405, 0.10256898356480065, 0.25989433891904007, 0.4832934114749139, 0.7650663348130483, 1.0920178286197817, 1.4461312315468837, 1.8056550306843195, 2.146546003415135, 2.444178661918675, 2.6752154421304097, 2.819515614603583, 2.8619532100219747, 2.7940149218197425, 2.6150580400947985, 2.333125618244634, 1.9652403960326728, 1.5371291516489185, 1.0823633432112425, 0.6409384020757453, 0.2573499882837529, -0.021741455008198726, -0.15013563815249722, -0.08486250038870903, 0.21106373519774618, 0.7660995639800818, 1.597970912952071, 2.7119325564519627, 4.099627560288461, 5.738633056806639, 7.5927435985323966, 9.613002740012469, 11.739451311097605, 13.903519558508274, 16.03095236824298, 18.04512440166359, 19.870577150532693, 21.436594194484915, 22.680626456780793, 23.55138555338133, 24.011427154653468, 24.03908623892368, 23.62965489616182, 22.795775025494894, 21.567034533702724, 19.988442205933648, 18.118261530008823, 16.02525327529468, 13.785424531909012, 11.478456315752464, 9.183998456746618, 6.978026525514582, 4.929450694106123, 3.0971509738815444, 1.5275881437058512, 0.2531063473444258, -0.7089962542200502, -1.356595937625069, -1.7020830632196595, -1.7709687060439463, -1.599854811289833, -1.2338977704426264, -0.7239249664582487, -0.1233549221814197, 0.5148917682059274, 1.1412736742691865, 1.712161137036061, 2.1918890107974858, 2.5542285829943716, 2.7832153766683376, 2.873310152749496, 2.8289114951148813, 2.6632773819084496, 2.396947776329269, 2.055788456408782, 1.6687964095720107, 1.2658180204981557, 0.8753324354129112, 0.5224439106356749, 0.22720956484625113, 0.0034040012684951253, -0.14221262807790283, -0.21008686096969303, -0.20751639883595016, -0.14779534978569017, -0.04893822302192406, 0.06791512428772219, 0.18029149476246945, 0.26623985338950934, 0.30611471325733464, 0.28415891244746094, 0.18977313151972275, 0.01838294453202367, -0.2281563747933061, -0.5416436662178626, -0.9080955841123691, -1.3087470375357173, -1.7214138421173373, -2.122117115929236, -2.4868498258395726, -2.793357397149301, -3.022802430595435, -3.1611726791372905, -3.2003300008756317, -3.138621293779305, -2.9810016884254154, -2.738655728999646, -2.428139256720458, -2.070100654026081, -1.6876724811813764, -1.304651007647322, -0.9435997338677239, -0.6240222346093355, -0.3607486542905896, -0.16266874268742243, -0.031922933221382205, 0.03636718009610265, 0.05378470585535475, 0.03771711141716788, 0.009910366126759686, -0.005440011973722018, 0.016063683642237255, 0.09659200423583589, 0.2536533532209755, 0.4978396962930068, 0.8309369314946228, 1.2445685786893865, 1.7195137143514259, 2.2258012068731663, 2.723634374442436, 3.1651459376413524, 3.4969258389706197, 3.6632077521858326, 3.609547626594135, 3.28678301827325, 2.6550285271434033, 1.6874431731082797, 0.3735098520166327, -1.2784375282083222, -3.2396970571169303, -5.460828938050503, -7.872546803228847, -10.38791843893393, -12.905841365012355, -15.315677761203055, -17.502855192304125, -19.355168701112444, -20.76946067593817, -21.658311526884166, -21.95634994051482, -21.62578867455479, -20.66081171009052, -19.090481052794026, -16.9798952247114, -14.42941390368162, -11.571861143712127, -8.56773472963384, -5.598511815440876, -2.8583230914896154, -0.5443892874769805, 1.1533304350259157, 2.0628353744624115, 2.040575587543637, 0.9811774104310047, -1.1741416669921527, -4.430970491024917, -8.737345781151063, -13.98197422229405, -19.99525545705035, -26.55319454613884, -33.38415141939156, -40.17823152335841, -46.598983585840664, -52.296944388295536, -56.92448374168653, -60.15142728286669, -61.680353358816404, -61.26100758004965, -58.703328903867146, -53.88837171129938, -46.77609235438221, -37.41013812752652, -25.919263569690376, -12.515171014042522, 2.513199106864746, 18.80873870657795, 35.95825699311309, 53.507091839595574, 70.97563957672757, 87.8771031389361, 103.73569886390499, 118.10453804207637, 130.58241178859382, 140.8289541624856, 148.5778236079577, 153.64569953678887, 155.9380790692299, 155.45161467810888, 152.27285971111496, 146.57358827192056, 138.60218257077992, 128.6723467374297, 117.14958952834093, 104.43601106542549, 90.95408909742808, 77.13018793350751, 63.378506413302475, 50.0861411307847, 37.59987032872925, 26.215166594215493, 16.16782810092517, 7.6284855264145435, 0.7001432080275892, -4.581429403581285, -8.244580608900542, -10.375925552460863, -11.112351671358699, -10.631380673122381, -9.140425107224507, -6.865493296124176, -4.039855198090183, -0.8932593032459049, 2.3578340133586617, 5.5186172138420435, 8.42259972112673, 10.936375285224655, 12.962403148658202, 14.439818749114588, 15.343387947165631, 15.6808052978035, 15.488607597883039, 14.827023828099698, 13.774122690053945, 12.41961963476006, 10.858700337114643, 9.186195698927987, 7.49139274842994, 5.853707848655527, 4.339384290603717, 2.999300904121812, 1.8678985227692937, 0.9632040307286613, 0.28783427175808224, -0.1691801211434333, -0.4299429697022945, -0.524826186622096, -0.4894089871928097, -0.3614358012964263, -0.1779863714536992, 0.026978870304245183, 0.22457559837258412, 0.3923682097071148, 0.5151177506291987, 0.5849194709221052, 0.6007803424992132, 0.5677203598476689, 0.49550752796183967, 0.39715326599326406, 0.2873020954644965, 0.18064649927242793, 0.09048582898164999, 0.027531641978900553, -0.0009658323302175769, 0.008275823472874757, 0.05444732972314329, 0.1328920413861633, 0.23567688114267452, 0.3524255036711519, 0.47133339221686205, 0.5802758516645187, 0.6679055691914475, 0.7246536653749879, 0.743557008747671, 0.7208493493433162, 0.6562748096775621, 0.5531050663670617, 0.41786497798327654, 0.2597937540549387, 0.0900884688339795, -0.07900806808766246, -0.23520203738009857, -0.367146276013555, -0.4653642212220444, -0.5230298097149914, -0.5365446216401664, -0.5058694207500015, -0.4345859943738931, -0.3296860902406313, -0.20110125123145528, -0.061008456236482954, 0.0770310446869283, 0.19903838704814583, 0.29161944290308217, 0.3429309872633097, 0.34354214065165245, 0.2871307167901812, 0.17096644052984797, -0.0038514365909578653, -0.23241701399983353, -0.5062981102516653, -0.814052353887251, -1.1419404442182661, -1.474785770189274, -1.7969199498448325, -2.0931487986738824, -2.3496736230378423, -2.554921599458364, -2.7002027722105293, -2.7801438325433354, -2.792907124091112, -2.740175571296038, -2.626911383082126, -2.4609126738097395, -2.2522056678347018, -2.0123206281337085, -1.7535063759086778, -1.4879408318754048, -1.2269933051645032, -0.9805883720163505, -0.7567120070677718, -0.5610893852262616, -0.39704758946439517, -0.26556332992250886, -0.16548134285172728, -0.09387625235001022, -0.04652012892746797, -0.018409097563578707, -0.004304809008704039, 0.0007592082677837326, 0.0010505523626477662, -0.00017524112848306677, -0.0008508956954911937, -0.00012656773624441245, 0.0017440587307597658, 0.0036431747359574923, 0.003924004001426949, 0.0008023315040043145, -0.007241243145229065, -0.021096313975743304, -0.04074110473659298, -0.06508330683758186, -0.09195263269751017, -0.11826117027159036, -0.14033233966362926, -0.15438332411789715, -0.15712463846595684, -0.14643046715705388, -0.12202106116584985, -0.08609054259087384, -0.04381136745903606, -0.0036499020956785827, 0.022563583067435156, 0.01985300297489659, -0.029373700729520197, -0.14448167493390707, -0.3454764421739766, -0.6516295582107366, -1.0799345093434494, -1.6434863938443578, -2.3498978737954648, -3.199860418382292, -4.185971375290789, -5.291939994285813, -6.492281017210622, -7.75257293265592, -9.030311255191544, -10.276372211174905, -11.437059623587684, -12.456667726555153, -13.280454513020098, -13.85788585650151, -14.145982433752318, -14.112581536669925, -13.73931592613628, -13.024113150227349, -11.983031805667224, -10.651275961594855, -9.083264578024197, -7.351677375087228, -5.545446404419232, -3.76673719726461, -2.127042438217583, -0.7424491116954748, 0.271690852648373, 0.8063833776033731, 0.7646739435035698, 0.06710293897744395, -1.3433539819182907, -3.497135511818187, -6.394980319201696, -10.006051618718983, -14.26744817489306, -19.085184112010054, -24.336648321294458, -29.874479876055986, -35.53172259465094, -41.128053671297344, -46.47682188330756, -51.39264817761991, -55.699345762089706, -59.23737175965581, -61.87062736987481, -63.49233788653687, -64.02977719842504, -63.44755287085556, -61.74928764548999, -58.977610923069534, -55.212455741370256, -50.56773920586472, -45.186582989664025, -39.235301301220154, -32.89644294552152, -26.36121871191775, -19.821673021628342, -13.462968173187749, -7.456140221359126, -1.951658095692473, 2.925926449163377, 7.082007735639184, 10.45452932293194, 13.015036870720177, 14.768036531683945, 15.74884325535383, 16.020094607805852, 15.667150038157514, 14.79264531314193, 13.510506296534565, 11.93974389314592, 10.19835226751011, 8.39761579474844, 6.6370979233285565, 5.000539362727719, 3.5528365738223164, 2.33820777173996, 1.3795862060202753, 0.6792131292257008, 0.22033930124391282, -0.030110466547295597, -0.11811182341991577, -0.09857738127683148, -0.031092569027512573, 0.024376269030101552, 0.011552579742758362, -0.1185234127240967, -0.40449855254702033, -0.8724840893021761, -1.5346985169511538, -2.389014207779325, -3.4193925364172455, -4.597141773024649, -5.882887554821928, -7.229109538568483, -8.58307164484006, -9.889958232231026, -11.096025001413365, -12.151581788544565, -13.013656129098882, -13.648174195091242, -14.031564349712067, -14.151771737510193, -14.008472244010578, -13.612657674761694, -12.985639483761585, -12.157539803292815, -11.1653829643039, -10.050918042161422, -8.858311561553341, -7.631849270617134, -6.413777316631343, -5.242397183742341, -4.150506756892189, -3.164253531296464, -2.302437157299567, -1.5762691226567467, -0.9895694409747244, -0.5393549837038377, -0.21675090668267316, -0.008149179589165643, 0.10347696888746075, 0.13719984580076294, 0.11279996757316584, 0.04952900900304844, -0.034950622960844314, -0.12539735565110569, -0.2095627553968314, -0.27849421337584446, -0.32657687499380206, -0.3513408013865411, -0.3530733329557369, -0.33428668805755085, -0.2990965203618695, -0.25256835632647634, -0.20008574772431575, -0.1467872353839471, -0.09710919232213888, -0.05445873554976954, -0.02103006835389495, 0.0022370787786444735, 0.015569947283644886, 0.02016905759853018, 0.017938399393863984, 0.011174006763865593, 0.00224660029493688, -0.006688276475283435, -0.013924282818977538, -0.01836153501374749, -0.019575171203504896, -0.01779309482842576, -0.013790439857527226, -0.008717013046159346, -0.003880958210774343, -0.0005165489193817474, 0.000434069994119352, -0.0015039341999818635, -0.006230777335425215, -0.013050757564102443, -0.020747480963883527, -0.027756471247328555, -0.03242600089859779, -0.033347380014567676, -0.029727594401908083, -0.021770501702602137, -0.01102908023505744, -0.0006903935636159148, 0.004242701078755106, -0.0030964710139082946, -0.031330727157207056, -0.09056439846303012, -0.19194287048022757, -0.34706054189796526, -0.5672446196673425, -0.8627615543369435, -1.2419920720897921, -1.710617302725215, -2.270882378733344, -2.9209914637705547, -3.654684812247596, -4.4610398808996505, -5.324527733008038, -6.225343182647794, -7.139997196324271, -8.042159076339422, -8.903713995042237, -9.695984958133396, -10.391056668815157, -10.963129795949666, -11.389829368755045, -11.653390862645908, -11.74165214972437, -11.648798546582777, -11.375863010104423, -10.930755744657795, -10.327941818483126, -9.58782428941129, -8.735817271611838, -7.801156014814848, -6.815507258044334, -5.811455320289236, -4.820947960847651, -3.873787353346267, -2.9962448471806544, -2.209886085315232, -1.5306678489062657, -0.9683539790727622, -0.5262801591845354, -0.20147678119180248, 0.014861969184001655, 0.13659500014599954, 0.18158787804294385, 0.1704685549308477, 0.12525972417917938, 0.06797611205710744, 0.01927319247524974, -0.002773301842570291, 0.016312874534051572, 0.08664584084658185, 0.2135115970247499, 0.39721922826418227, 0.6332702612967651, 0.9128285187380434, 1.2234504708141112, 1.550023411628615, 1.8758473246797183, 2.18378817350578, 2.4574276032630005, 2.682135933438994, 2.846001930791148, 2.9405799821852296, 2.961396974004413, 2.9081400828251582, 2.784587976514541, 2.5982811488191353, 2.3599563931399405, 2.0827884306108873, 1.7814931672583167, 1.4713547190778582, 1.1672417998927558, 0.8826781821755011, 0.6290271211974635, 0.4148400614982911, 0.24540716037791688, 0.12253791015152611, 0.04457898683394194, 0.006661866136351457, 0.0011583193320571815, 0.018308731418082765, 0.04697745912949736, 0.07548436075560364, 0.0924559844305359, 0.08763584261209006, 0.0526003253292384, -0.01866508244598623, -0.12936420152844563, -0.27968564206131247, -0.4668042153669248, -0.6850832713131693, -0.9264598050527976, -1.1809825730477521, -1.4374643970289895, -1.6842034755393813, -1.9097223303127293, -2.10347726896719, -2.25649315912507, -2.3618842182231443, -2.415230543591174, -2.4147923486958622, -2.361550134173691, -2.259071301579363, -2.1132203185712277, -1.9317369136408484, -1.7237145372181168, -1.4990167297398271, -1.2676717114704874, -1.0392853703854372, -0.8225099818264411, -0.6246007367100498, -0.4510849292780472, -0.30556002639534824, -0.18962714317696655, -0.10295776958796382, -0.04348436918694103, -0.007690933430355283, 0.009020706694224922, 0.01191756968879567, 0.0065062393293367216, -0.0018819960864242726, -0.008463538615484064, -0.009308615507187866, -0.0015636192694911267, 0.016420928358009474, 0.04506004375059295, 0.08359764517602486, 0.13025313640567923, 0.18243528418251725, 0.2370034523677104, 0.290553908895679, 0.33970833429767067, 0.3813827938123818, 0.41301914843447424, 0.43276490002595014, 0.4395823787158438, 0.43329063873731516, 0.4145413777054473, 0.3847331424781969, 0.34587255534403916, 0.30039927529835575, 0.25098976027055686, 0.20035619490496764, 0.1510564327399344, 0.10532893325846127, 0.0649638083045803, 0.03121750970550168, 0.0047747155053944265, -0.014243052845991583, -0.026226296310829258, -0.03199127708639742, -0.03266839476803977, -0.029576382046064432, -0.02409394492193099, -0.01753975608050494, -0.011069886857433086, -0.005600696714736797, -0.0017613187845687067, 0.0001226744561030678, 1.5791718989620816e-05, -0.0018664346501358505, -0.005115946827087756, -0.00920264199438249, -0.013548840231550794, -0.01760000488634737, -0.020884970060085235, -0.023060515823194728, -0.023937129402548753, -0.023484982265097, -0.02182130993942641, -0.01918228580414358, -0.01588394621140776, -0.012277616272572244, -0.008705570517679522, -0.0054621796148626375, -0.002764543169056592, -0.0007359626399071421, 0.0005967166340855897, 0.0012927154902332067, 0.0014763207466614125, 0.0013090111689496526, 0.0009592422961988705, 0.0005746005994193476, 0.00026056665963562997, 6.90555739252857e-05, -1.6458595228582762e-06, 4.237248550852227e-06, 2.0156088826695838e-05, -1.7293246704774016e-05, -0.00014263799194552332, -0.00034110217206767177, -0.0005387790020434905, -0.0006075333998966125, -0.0003867582550888705, 0.00027857156827287334, 0.0014871898085534042, 0.003225053605466398, 0.005312721144159977, 0.007368177163982441, 0.008797380016962116, 0.00882387055445831, 0.006565999606324573, 0.0011656364105620384, -0.008034241265222371, -0.02127353546308233, -0.0381397218385693, -0.05734105013772555, -0.07652377264103594, -0.0921746275324278, -0.09965241934202047, -0.09339106914743756, -0.06731014848379571, -0.015457329895463154, 0.06711054976221764, 0.18322290908117012, 0.3323076099621849, 0.5089912206611615, 0.7016880652637852, 0.8913075327162617, 1.0502337347387622, 1.1417492119863493, 1.1200821626258004, 0.9312519785840138, 0.5148685469722702, -0.19299468345051896, -1.2557860498965636, -2.7313200250896643, -4.665564085618521, -7.085546067511347, -9.991661671318166, -13.349770225030623, -17.083682243767136, -21.068441931013844, -25.124906614578382, -29.016532000052624, -32.448918218985966, -35.072771563441805, -36.49085366137233, -36.26936176638169, -33.95402575922222, -29.091003859889366, -21.252419193029638, -10.06611123818916, 4.751109609515499, 23.357706819149012, 45.750445203976284, 71.72773974851275, 100.85507774668682, 132.4344215451965, 165.47967521320123, 198.70091031725232, 230.49748324400895, 258.96189986561035, 281.89644392941244, 296.8432407290029, 301.12823807028, 291.91895647323105, 266.2953699106795, 221.33265749373984, 154.19394908094912, 62.230603594188864, -56.91297170807154, -205.19340195044998, -384.065108208757, -594.3837484697297, -836.3203933867946, -1109.2903951179374, -1411.900639687221, -1741.9226252439714, -2096.303348458675, -2471.18186603329, -2861.9341159006235, -3263.2470619688743, -3669.218917291934, -4073.4848922279098, -4469.3583739811365, -4849.988960609492, -5208.532746209317, -5538.328995630894, -5833.0776277095765, -6087.011720067896, -6295.059256656483, -6452.988566925081, -6557.532349359293, -6606.485819461429, -6598.775351675066, -6534.495149432503, -6414.9314940806125, -6242.548294415652, -6020.878869704602, -5754.420956971288, -5448.509560779826, -5109.166987185094, -4742.9367135095445, -4356.707233654505, -3957.5198149664275, -3552.3812607921195, -3148.084983758699, -2751.0442832845574, -2367.142959833448, -2001.6076533712933, -1658.905397447384, -1342.6688719889542, -1055.6507600407733, -799.7075112425274, -575.811831115178, -384.09305802676, -223.89696112069652, -93.86803712466839, 7.947619257310281, 83.98770377063418, 137.05235241629168, 170.18088959970157, 186.53136559169138, 189.2671871090103, 181.45383489035967, 165.9693056674552, 145.430632882368, 122.13786941320419, 98.03615314212243, 74.69568774146015, 53.30874273034601, 34.702137129072774, 19.36314285955704, 7.476347284735838, -1.0313162028971958, -6.440234569790295, -9.184916755278019, -9.800904216094436, -8.874348266270417, -6.99634116866917, -4.723654137800652, -2.547061123954894, -0.8679384989027238, 0.016651334499225637, -0.07938150699304633, -1.2321378777118484, -3.4153799014157022, -6.513634417813187, -10.33937715462131, -14.65285082588075, -19.18307882424453, -23.648719871685195, -27.777589960205987, -31.323917064409244, -34.08226090066016, -35.89773655288228, -36.67231756555703, -36.367200633761186, -35.00146247076361, -32.64743122108967, -29.42334409963629, -25.48396529931653, -21.0099026239624, -16.196349491116397, -11.241869604447272, -6.33798162809422, -1.6600400300164333, 2.640204203623082, 6.440100561330552, 9.649529256816866, 12.21227237546762, 14.105484607243662, 15.337469392881925, 15.943935846807918, 15.983223757078152, 15.530867605498047, 14.67387327608758, 13.505061699394815, 12.117790298301925, 10.601305659882094, 9.03691437280741, 7.495088514115004, 6.033556232210698, 4.6963573319543395, 3.5137651039242717, 2.502999361729108, 1.6695672559619086, 1.0090566530125316, 0.5092068780710038, 0.1520883041499333, -0.08376282229300379, -0.2213776572365264, -0.2836495044225473, -0.29196299289482486, -0.265190602825093, -0.21905842307246068, -0.16585718984484968, -0.11445431393670047, -0.07054850576588081, -0.03710092474112217, -0.01487519029931561, -0.003022360496148194, 0.00034493696006030497, -0.002366130511307311, -0.008660062348145346, -0.016278745085103057, -0.02341551539242678, -0.028822848184465295, -0.03182768655222635, -0.03227448083672082, -0.03041838947540577, -0.026792273610275235, -0.022069133646707782, -0.016937488821330667, -0.012002308354018543, -0.007718663067350214, -0.004359985860793121, -0.0020182372279964286, -0.0006297587605384174, -1.839343609230476e-05, 5.3379505305116304e-05, -0.0001659036785911492, -0.0004589625235374309, -0.000668935228711759, -0.0007130441030527599, -0.0005809749103775751, -0.0003204907330742801, -1.450555886746712e-05, 0.0002452580005233088, 0.0003828433352612475, 0.00035642226423858117, 0.0001674247276899193, -0.00014076656868945478, -0.0004938088799355371, -0.0008045420925341391, -0.0009943832952361668, -0.0010133539391685123, -0.0008541644475016765, -0.0005566157660271141, -0.00020012079173604066, 0.00011578098853313441, 0.0003007090149543055, 0.0003080413845482822, 0.0001684576293718105, 1.4905835861087024e-05, 9.124159066675414e-05, 0.0007376993475511624, 0.002348487631215555, 0.005299934273334077, 0.009851510741115992, 0.016026459004186196, 0.02348311685194896, 0.03139188033090327, 0.03833553380963478, 0.04225194214050495, 0.040437457834103324, 0.029626619472019104, 0.006158763190113793, -0.03376479351308693, -0.09373791792679129, -0.1767357039781918, -0.284653767990387, -0.4178343649150069, -0.5746207749035486, -0.7509866452030626, -0.94029419118748, -1.1332211059978765, -1.317884720465488, -1.4802003612805255, -1.6044832640208129, -1.6742873488555023, -1.6734540173324033, -1.5873230288471585, -1.4040372281368558, -1.115855108531551, -0.7203715927313201, -0.2215395426976769, 0.36961634176665203, 1.0346945099342009, 1.7481063109680237, 2.4778228158224516, 3.1867100322877593, 3.8344479676360885, 4.379988918842487, 4.784457284751811, 5.014367523108493, 5.044973401011059, 4.863557209346593, 4.4724473421117805, 3.8915417493818834, 3.1601210824257264, 2.3377558903639795, 1.5041468935012678, 0.7577851487367719, 0.21337792736561773, -0.0019464130847206902, 0.2464311495675349, 1.0947136581760641, 2.67403428875998, 5.103346194437773, 8.482196868591084, 12.883761639095878, 18.348582189259727, 24.879583678711484, 32.43830057336377, 40.94276223724383, 50.26730194559716, 60.244386463077696, 70.66849385940638, 81.3019614113652, 91.88261901563784, 102.132922478765, 111.77021124278939, 120.51764200109642, 128.115297945951, 134.33094668968656, 138.96992052750687, 141.88362148797356, 142.97620979612225, 142.2091156224584, 139.60312203333083, 135.23852144391012, 129.25257851631918, 121.83271389230259, 113.20825318908763, 103.64063363726765, 93.4123451203509, 82.81510800683971, 72.13787142892103, 61.655222509907006, 51.61677197668165, 42.238025912608336, 33.693170160384376, 26.11008770837119, 19.56780624922655, 14.096439934817656, 9.679553703588358, 6.258748115960898, 3.7401447961222742, 2.0023555088310934, 0.9054547258313765, 0.30034082459442735, 0.038058537557238994, -0.02145984999689025, -0.0017988258899286527, -0.0040170286131107884, -0.10245885541063955, -0.34259902187376856, -0.7409702413552725, -1.2870954129101797, -1.9472241667358978, -2.6695665074785566, -3.3906298605289735, -4.042204992641958, -4.558514376626242, -4.883035149042887, -4.974537560157704, -4.811936605443621, -4.397639067263089, -3.75918923014274, -2.94903409823194, -2.042433718591418, -1.1336759793230033, -0.33082415401302034, 0.25067087582626235, 0.49508444963632986, 0.2938118913256358, -0.44742156455426774, -1.8019865593559727, -3.816822840450652, -6.508306699730008, -9.859773917788123, -13.820859046883474, -18.308702737107854, -23.210967774266635, -28.390498315513295, -33.691361829376845, -38.94593208984906, -43.98262164373676, -48.63386068757034, -52.74384424604118, -56.17563589024052, -58.81725830355137, -60.58645837677331, -61.433921340370375, -61.34480591474003, -60.33856155019698, -58.46708778780746, -55.8113866854254, -52.47693799777761, -48.58808950581897, -44.28179834343616, -39.701081435529844, -34.98853367014943, -30.28025196440658, -25.700464052182124, -21.357109468304966, -17.33853382776364, -13.711405947859456, -10.519910926801908, -7.786149567628202, -5.511625760713679, -3.679646861903708, -2.258428244776448, -1.2046801786898274, -0.4673852534129948, 0.00845855185481928, 0.27834320994102024, 0.395189924919788, 0.4068645021913513, 0.3543614998552113, 0.27069792548159466, 0.1805064515389138, 0.10027180191141517, 0.039114967894312215, 4.680308058214703e-07, -0.018776391141752502, -0.02197291850613071, -0.015799325526813453, -0.0064661528168371615, 0.0010146366983676905, 0.0036982012137466752, 0.0012017918323701424, -0.004182970972345103, -0.007735806256799029, -0.0028566953363431814, 0.01815677514094439, 0.06319344580288176, 0.13937071009894922, 0.2521301035150679, 0.4044727314594194, 0.5964053274589, 0.8246470725719778, 1.0826246755211077, 1.3607673153578104, 1.6470566931673651, 1.9277883493812702, 2.1884907305653365, 2.4149244447125904, 2.594082288002594, 2.7151118709507553, 2.770090020718439, 2.754596650985748, 2.6680504940847447, 2.513736395541893, 2.2985758293903817, 2.0326566506772457, 1.7285551974844386, 1.4005043778960538, 1.0634714531218565, 0.732214175879153, 0.42038353930519806, 0.1397365451881034, -0.10049074959631489, -0.29401427733625035, -0.43770180378844054, -0.5315433679433318, -0.5784070424353558, -0.5836086122206697, -0.5543365165356587, -0.4989824915347893, -0.4264332161062235, -0.34537944827951655, -0.26369396967923664, -0.18791658662742797, -0.12288891155299596, -0.07155658243717962, -0.034943062982422876, -0.012286189861104914, -0.0013159303739671336, 0.0013585990588102065, -0.00020784134910004152, -0.001780254836299065, 0.000590107547751642, 0.010156192108639607, 0.029155329252832252, 0.05860280040802483, 0.09821161197543964, 0.14643985059341416, 0.2006558773461595, 0.257401755128504, 0.3127274788932996, 0.36256408509398746, 0.4031025630340789, 0.4311385342608269, 0.4443553470257986, 0.44152238485412487, 0.4225928146677144, 0.3886948998416588, 0.3420208075405883, 0.2856274054535388, 0.22316393371881824, 0.15855562289321423, 0.0956774518559227, 0.03804489641446295, -0.011451363906762808, -0.050744563343440435, -0.07870934114866471, -0.0951901657966103, -0.10094174675506504, -0.09749067974243654, -0.08693470574667218, -0.07170133901229368, -0.054291062168484366, -0.03703100950349834, -0.02186240270403388, -0.010182395935974007, -0.002754360261352543, 0.0003069507940890073, -0.00052301567410665, -0.004300953105971096, -0.009785871503602498, -0.015635448329410568, -0.02060433823134236, -0.02372016521376864, -0.024415457951365464, -0.022598796789503318, -0.018655472140346168, -0.013376343131587445, -0.007822504161387555, -0.0031418955164309354, -0.00036120339549046974, -0.00018143209409475126, -0.00280773279752536, -0.007843124395841427, -0.014270987839167502, -0.020543048645787543, -0.02477886272590483, -0.025070025585015355, -0.019867696116646905, -0.008420048166087218, 0.008785182183557375, 0.029626154315885972, 0.05005734280972175, 0.06398069368410542, 0.0633265479873477, 0.03838102096290779, -0.02162097547530776, -0.12763961494910386, -0.2897380936484029, -0.515807499458598, -0.8101863363794112, -1.1722729472304094, -1.5952431898687047, -2.0650106085979756, -2.5595527178104676, -3.0487292613672365, -3.4946922041022135, -3.8529238150740297, -4.0739579797576715, -4.105768651265784, -3.8967632376267667, -3.399270988139449, -2.573369713778982, -1.3908530786068445, 0.1608915014862765, 2.075344708185933, 4.323913521735217, 6.853832915782706, 9.587132374875873, 12.420846774658184, 15.228594834381749, 17.86357590457812, 20.16295576956879, 21.953581374394762, 23.058982460869593, 23.30710159744424, 22.538285149985104, 20.613494849198563, 17.42221983689432, 12.889663939470406, 6.982804396161577, -0.28504375209364174, -8.851463539508986, -18.604198973021095, -29.38257704269234, -40.981115625006545, -53.155233706291405, -65.62887101669033, -78.10372199711061, -90.26969990543893, -101.81617606073489, -112.44348486358194, -121.87421263594423, -129.86420803333047, -136.2117791450725, -140.76492319407905, -143.42665805774993, -144.1580466024524, -142.9787924561961, -139.9654084194151, -135.2470784086365, -128.9994458376071, -121.43665956102582, -112.80208768249885, -103.358165560257, -93.37587451846412, -83.12435090919162, -72.86110167593309, -62.823254388168905, -53.22020019070719, -44.227901757990445, -35.985094776331806, -28.591431798453176, -22.107146850954333, -16.55472606532676, -11.92219640441117, -8.167668587336347, -5.224798774043848, -3.008808476537832, -1.4226994023801263, -0.36331844915447664, 0.273034475430212, 0.5857101420918497, 0.6657152260224273, 0.5927382060055838, 0.4332424936343588, 0.2396038340165026, 0.050206852113440725, -0.10963564333128262, -0.22611472463042276, -0.29490601966143526, -0.3189029866676936, -0.305895244652077, -0.26637211398665006, -0.21159584855839395, -0.1520490571624676, -0.09631824354433463, -0.05043193318633507, -0.017631682739616548, 0.001479851606656752, 0.008495447379938223, 0.006562234978369918, -0.0003533615404706619, -0.008195133223651636, -0.01345446033412447, -0.013648949509376701, -0.007600447552737363, 0.004502599503563985, 0.02124713280405214, 0.04030710617179853, 0.05887208208722072, 0.07412851710712454, 0.08372550084733571, 0.08615942308034835, 0.08102544977655582, 0.06910010601549071, 0.052239953434304105, 0.0331042259342415, 0.014731549633161355, 2.0304813126606077e-05, -0.008823262963514876, -0.010797021281591015, -0.006502322221057344, 0.00163461404660972, 0.009369918672372681, 0.010907414018243518, -0.0005740872674901561, -0.032155685596231456, -0.09022761155073238, -0.1794302713661833, -0.30158215131582494, -0.4547019084487775, -0.6322361900895705, -0.8225923740925457, -1.0090612942154396, -1.1701889156286136, -1.2806218890801122, -1.3124138278445998, -1.2367389303312861, -1.0259205970321683, -0.6556482533462471, -0.10722879165898962, 0.6302974557857208, 1.5583505264967115, 2.6674795653949532, 3.9366489546809063, 5.333270398305602, 6.814085575957279, 8.326724139684977, 9.812000404417688, 11.206848343771165, 12.447730971349438, 13.474340094248133, 14.233267433566157, 14.681462606056312, 14.789236264819435, 14.542576887036248, 13.944594139104307, 13.0159531307455, 11.794227039162397, 10.332166522127082, 8.694958312456835, 6.956617265583932, 5.195720743497283, 3.4907466288654874, 1.9152950973961458, 0.5334940149589553, -0.6039964400542067, -1.4631393958016783, -2.0286331521201793, -2.304816757103641, -2.315287275988496, -2.1012312333464735, -1.7185395877948133, -1.2339012829483098, -0.7201269581746657, -0.25100799352107395, 0.10394461025069916, 0.28452239260926826, 0.24425337904789082, -0.04606724817729082, -0.5960081448983839, -1.3944771706958572, -2.410133801288618, -3.5932373310108368, -4.878857602874273, -6.1912063801701445, -7.4487819059063645, -8.56999073350625, -9.478862779224523, -10.110464060018845, -10.415642664900187, -10.36479553857711, -9.950254836492904, -9.18720383671155, -8.113042302325558, -6.785214828520959, -5.2776345884698745, -3.675933830579356, -2.0718564344065644, -0.5571708013342537, 0.782481279097183, 1.8733770217838988, 2.6587622335379617, 3.102764169713407, 3.1928582103009906, 2.9407446314113477, 2.381571107029273, 1.5715485229399786, 0.5841192155582976, -0.49506248313688733, -1.5739946829071052, -2.560638011597139, -3.3692397638637805, -3.9262298277363077, -4.175278438570184, -4.081166231450125, -3.6321998503564, -2.8410079097673475, -1.7436653542776606, -0.3972112763060828, 1.1242649680114234, 2.7347266718783665, 4.3420965799823, 5.8544904308567665, 7.1863617379804205, 8.264131473249027, 9.030912637796346, 9.45000788523702, 9.506949198388703, 9.209955477657518, 8.588799885043764, 7.692194555777452, 6.583895834413627, 5.337838417110148, 4.03267237010605, 2.7461145089224606, 1.5495354258299054, 0.5031815041620398, -0.3476203598285744, -0.975011209188298, -1.3697435066718695, -1.5408019026543505, -1.5135621282087186, -1.3266820946603917, -1.0279954252040417, -0.6697532804515909, -0.30360999658766996, 0.024232954936440853, 0.27732335565102806, 0.43233808582709876, 0.48126256306591525, 0.43218181502953396, 0.3085977974161536, 0.14731399889269706, -0.004955353508779122, -0.09599041484283495, -0.07313737575862853, 0.1113617466175908, 0.4952191238401988, 1.1015713218479894, 1.9354710907526276, 2.981722618241442, 4.204285851433335, 5.547357579696658, 6.938108578636738, 8.290926766397503, 9.51289579639093, 10.510136075370733, 11.194558889484501, 11.490540336918823, 11.341013093808552, 10.712504816823376, 9.598724136662064, 8.022375369768302, 6.03501714937301, 3.714918221621886, 1.1630089988099936, -1.502848182695036, -4.154953923935847, -6.663654796424499, -8.905484035558477, -10.771011622059772, -12.171848756157582, -13.046305354487137, -13.363290310951125, -13.124166472123466, -12.362416930963505, -11.141135919607667, -9.548514846612564, -7.691640257695755, -5.689045006163427, -3.6625460014992823, -1.7289550910724765, 0.0077338392217306635, 1.46311720756071, 2.5776283388595553, 3.3199027031147943, 3.6879727569542378, 3.708209004476964, 3.4321386733300607, 2.931407635032154, 2.2912918582303075, 1.6032765529521815, 0.9572936493392393, 0.4342353555639789, 0.09934064143027617, -0.003016379994542752, 0.14728259690122755, 0.5448040095931637, 1.1594673646749043, 1.9395783998042078, 2.8167418165136615, 3.7122462211764713, 4.544385859467545, 5.2361038780230125, 5.7223008229731915, 5.956122088708722, 5.91365799605807, 5.596600824358799, 5.032562405713686, 4.272948205193091, 3.388490742903426, 2.4627513533696317, 1.58408804460666, 0.8367427892099979, 0.29181011842268334, -0.0011003199033056271, -0.020708204300226213, 0.22130505778813503, 0.678451748124726, 1.2707581433807755, 1.8893844400693156, 2.40441718158733, 2.6754368922842207, 2.5642045902217347, 1.948572560233497, 0.7365675131524922, -1.1204970293508227, -3.6170382135540797, -6.68543662779133, -10.192408765703503, -13.940201901552474, -17.672984711519486, -21.0884483738625, -23.854248117404833, -25.628530442451346, -26.08343412669111, -24.9301508302355, -21.94390844452775, -16.987117890358753, -10.028830774232706, -1.1586972804808235, 9.405320832617296, 21.31712260288841, 34.11089397826567, 47.217846836248306, 59.99085709400506, 71.73600247700534, 81.74948639801958, 89.35798870668728, 93.96013929297743, 95.06659435526657, 92.33612826775058, 85.60524845742316, 74.9090987942384, 60.49183061637053, 42.805171271149696, 22.494580000753782, 0.37311398558500947, -22.616109044715238, -45.44735207277671, -67.06765665872767, -86.45596804625913, -102.68312782112564, -114.96952996812557, -122.73687603508854, -125.65071229372643, -123.65082313576322, -116.96713396790734, -106.11951634333784, -91.90075043283075, -75.3428392247704, -57.66783312826553, -40.22525793929412, -24.419088469794694, -11.627922842988458, -3.1225431832326462, 0.014639016749668034, -3.0363150912710015, -12.769615370731335, -29.30555927680608, -52.36131788570711, -81.24162175586665, -114.8505510281126, -151.72479991370417, -190.08734019102786, -227.9193562101393, -263.04732362572526, -293.2412518668923, -316.3194534047152, -330.2547782465126, -333.2770846047308, -323.96681757399296, -301.33493383662613, -264.8850246745848, -214.65432138923856, -151.23127445477127, -75.74843598914404, 10.151969435626793, 104.37651735450868, 204.456531339273, 307.64308789708366, 411.01393528191915, 511.5870391546217, 606.4363898175473, 692.8048352849044, 768.2089347533674, 830.5312851535881, 878.0964433245492, 909.7274095836041, 924.7806087233998, 923.158350073134, 905.2988150436998, 872.144654771046, 825.092231524873, 765.9243606660552, 696.7312014009, 619.8287081808932, 537.6566353439184, 452.6776365773411, 367.2865485612953, 283.72778081799345, 204.02155086494773, 129.9054570910759, 62.791982933682995, 3.742279741167494, -46.54376073519087, -87.72189322973513, -119.78378760826982, -143.0251597450451, -158.0041670519569, -165.49274446141388, -166.42367767526122, -161.83618361837227, -152.8226052856486, -140.47863564541444, -125.85919418430396, -109.94053013670126, -93.5901910376929, -77.54570559693855, -62.40202505241285, -48.607272551314225, -36.46563600326953, -26.146938955142552, -17.70140365750801, -11.078100801800208, -6.1456336010342, -2.7136641507636066, -0.5540206969980572, 0.5796894525477262, 0.9348118485394419, 0.7453259722743011, 0.22082905966343533, -0.46106362820983104, -1.1589994291873662, -1.7691543353205332, -2.2239063774816197, -2.4883958618407886, -2.5555704768233007, -2.4403052333630115, -2.173156159866545, -1.7942421785735139, -1.3476318479319926, -0.8765659150677936, -0.4197119257621337, -0.008538847615620838, 0.33419360932546066, 0.5949175307017259, 0.7688603376493459, 0.8589605045568299, 0.8743079334971835, 0.8283233867194939, 0.7368766587719042, 0.6165171803454486, 0.4829435071441645, 0.34980635945255395, 0.22790098850742108, 0.12475277340866216, 0.04456749928665721, -0.011509641167721381, -0.04490066245915041, -0.05895088571524537, -0.05821979764210122, -0.04778176634353029, -0.03260133598275721, -0.01703069071764282, -0.004457886547144417, 0.0028842417748432695, 0.0039555175766062866, -0.0011869349338443627, -0.01158608938448019, -0.02564818821457315, -0.041434336473990016, -0.056945299577303786, -0.0703702589302347, -0.0802782097225742, -0.08573960919072242, -0.08637502956001814, -0.08233576173894697, -0.07422790490736972, -0.06299595702847334, -0.04978418509563326, -0.03579428309576158, -0.02215521240990679, -0.009818015525184395, 0.0005160540631802868, 0.008430589238046208, 0.013793380611225918, 0.01672507818457449, 0.017545036005882256, 0.016703835623126634, 0.014712251550568706, 0.012075307272803804, 0.009238731625074633, 0.006552312902704335, 0.0042518780173185855, 0.0024590146024048966, 0.0011954563072725328, 0.00040753409516996146, -4.60737209416251e-06, -0.00015820159215543475, -0.00016376925885124407, -0.0001086531925748133, -4.936346374476966e-05, -1.219858139898006e-05, -1.6890732317874462e-07, -3.2822884915763337e-06, -8.918670851172495e-06, -9.374783203710538e-06, -4.6509143546648234e-06, -2.825734692276492e-08, 2.869578178762793e-07, 4.857186223793242e-07, 1.713134201396282e-05, 7.475228617100548e-05, 0.00018813785831623125, 0.00032750423257326214, 0.0003647399603326614, 1.8053469969915553e-06, -0.0013142178545279915, -0.004481343164677379, -0.01082689375947745, -0.02217188308671476, -0.04086033526786355, -0.06973864003397563, -0.11207212707362377, -0.171390068540979, -0.25125618736730443, -0.35497028446007334, -0.48521325178666147, -0.6436547152814123, -0.8305535881821204, -1.0443863506352562, -1.281542264011248, -1.5361258811492766, -1.7999048344745103, -2.06243473451867, -2.311383133946089, -2.5330612865034623, -2.7131565747938895, -2.8376451159904614, -2.893846255585204, -2.871524330822533, -2.7639969186114, -2.569165923482056, -2.2903815034503063, -1.9370557838649525, -1.524955783177738, -1.0760879914100445, -0.618162361130827, -0.18362783011657605, 0.19171151341276227, 0.47045260326849725, 0.6156449361416826, 0.5930334709688709, 0.3733668464490628, -0.06537020202753267, -0.7359479018124041, -1.6402506324866462, -2.7681358599406223, -4.096905609537362, -5.591482475290293, -7.205295333350992, -8.881872927263133, -10.55709815412935, -12.162043296330449, -13.626281419209445, -14.881344000712803, -15.864245701282703, -16.520872937535934, -16.809019172079452, -16.70087972421934, -16.18484628175209, -15.266479642360997, -13.968586294837596, -12.33037737163631, -10.405743901483614, -8.260736552880434, -5.970387573757896, -3.6150540370769297, -1.2764731143262174, 0.9662828906832315, 3.04055738363232, 4.8834485149866, 6.444603698624245, 7.688306117553235, 8.594545331465598, 9.159181462732748, 9.393239649044872, 9.321405791642723, 8.97984672321658, 8.413515809622556, 7.673131276963356, 6.812027733122918, 5.883080867487249, 4.935891551120951, 4.014389818104432, 3.154983588633188, 2.385334243981356, 1.7237944743973705, 1.1795006855965615, 0.7530589531539182, 0.4377052662006311, 0.22087029663710692, 0.08597073877002191, 0.014275955220994839, -0.013284191625802319, -0.014510863801911668, -0.0046408610458866075, 0.004555098249638506, 0.005238587300714958, -0.00646662055242376, -0.03084205191879045, -0.06526579651055804, -0.10512721547533913, -0.14484860788442422, -0.17889314086447974, -0.20264643444527136, -0.21307871255947236, -0.2091233860107398, -0.19174340804232032, -0.1636963660908432, -0.12904399448337164, -0.09245447902087141, -0.05845810140532358, -0.03075990504274649, -0.011689472690898591, -0.0018611980892415095, -9.31800220494995e-05, -0.003603809989370187, -0.008475301444096342, -0.01034555712134408, -0.005266191508763891, 0.009353069778605958, 0.03380395862955383, 0.06523672023466778, 0.0970042282390517, 0.11827247787710811, 0.11396145040163702], 'positive_zeros': ['0.25058437214685426705092563484228', '0.74981324281426474452348118127879', '0.77675366221029648630479549200375', '0.78013692954593520188534338256475', '0.834270937622890388404645060926426', '1.05833807787673860532738349407219', '1.20409186776586971186591664080490', '1.30848551940982463972500533557952', '1.31052850057348970742833483500226', '1.34131330051587332243974591868927', '1.36635764966846977664107319026493', '1.46371333911714546572000144716593', '1.56580408154131896545746167658683', '1.70601316779693346808504191427803', '1.71877173131364251103765454545961', '1.87873824757950734773047908810767', '1.89033792249303889225798080601796', '1.90471808279101364566139858662627', '1.92396805846462193651753545083064', '2.02990870405955612772494251085467', '2.22888131728605547888213517135108', '2.24780729396689834654220839488253', '2.25566987190041024852053203382848', '2.28015760169691997900397378553892', '2.30189539363183973687411219214351', '2.37683732662891089545188100086549', '2.40932342191619966262381874123178', '2.42417610226503866323467457319719', '2.45789893253740072714744237390461', '2.59606979862661149265299690383409', '2.67034235501626597056442182920161', '2.67279301325216371979197014575390', '2.83476509779901124047496344955491', '2.87153747814947029730983796927917', '2.88800159536392013868473406188337', '3.01965643453862398129280909373427', '3.06757751943100905601618131468412', '3.11430215489300614301822085637706', '3.18837304230988450899383410122901', '3.24591646334143777466553396372620', '3.26168518920719522078407128373761', '3.31616004102099955462028965113794', '3.36428496973883130393230587895742', '3.38279868236033452294047202971275', '3.41783181661121038027233531369732', '3.44570795786319182664878070015398', '3.45182561978225815309448757252514', '3.52076365169014484282905946206240', '3.66781413705781745566072192142155', '3.72948311000713283926289227190474', '3.85868764790337319854708798765272', '3.88647500905352424242191305007426', '3.88887070901806041916838386996644', '3.90247672294825859014856242855378', '3.97439739436826483705263048355389', '4.07179316521485776434082872495701', '4.16220166879366969082371544872719', '4.16847249803136486653455573689114', '4.18401183263406485549334778801284', '4.24859249849273138223160330670424', '4.29292890692739074674162545216647', '4.29678381926428295317233497240380', '4.29748153294518533191978231049228', '4.30696059718996257610469105566615', '4.37151614359186969442927176143911', '4.42288187896433487145460670898944', '4.54285062351812153769900753360030', '4.57571429529819229330426077792410', '4.63938154721005546425678867658675', '4.69279655854435554776725499589446', '4.71670132346117829273010500337523', '4.82429965677008361381380925331343', '4.83218735098955768742336071013538', '4.93507184461083917332952191345124', '4.94013167194391144526728518004059', '4.97463943873717710346550188887185', '4.97809616828662235496163925368863', '5.11055797280014996622541608332414', '5.20931458847559574711442426043828', '5.23143987499839356894013279964291', '5.25665324000270944055012613715461', '5.26872052822808582137330530896617', '5.27338682498172800505431739507048', '5.29604841475368165602305303639783', '5.30392090876750069065430585651778', '5.33358750446299411154841082811591', '5.40630781545527489534915825945270', '5.44377791158495785400083255964524', '5.47697982270806702570884028257143', '5.55752743255877003827058471593968', '5.67448960376001204185061751612097', '5.70504220636725671912912246605962', '5.81889938307694167384779505718298', '5.88553099208171364699703323144529', '5.93820236073883342019170951700773', '5.98977438207854076712943071730058', '6.00659364934111803166950206045255', '6.07364890467420421466885286431241', '6.08095230423935097949998535520174', '6.12785761575212108942683008318131', '6.12921653190200053962411457583629', '6.16715796239147213799966737168048', '6.18588430074037569554844520407532', '6.21776658104563226621153850355858', '6.22870992842793684330217292524284', '6.27942341867022313063179919793825', '6.34936306711045908531042890061413', '6.46178902389421309554979240640410', '6.47289996189798824062539316180350', '6.48169018871819946275047997624301', '6.50156151593461874942843213453108', '6.52876409973761510140501475268055', '6.65483391169058050090419208283082', '6.67692103931155859581600598546004', '6.69872368875411893669303484159553', '6.70175053243265172177749654427450', '6.80408575411055134538712595636105', '6.81585631408945222558681284307342', '6.89329623241011403775788525833098', '6.90987354410814484668949855303069', '6.91012143065843412597402602206914', '6.92194673787073960680615328828726', '7.01751737889818520577796100568778', '7.14321435342044073146494406443224', '7.15282933722899709790493402674151', '7.17286967312797324524649902350963', '7.17800813123031985411720819629741', '7.28933644545552521585538109308833', '7.33825426232417507381955075817857', '7.34682220414954683930926035551228', '7.35020562226797525650063859400440', '7.39912024776371993676567998696447', '7.44898899392761418597560296098648', '7.51777935441074721809665694091657', '7.52235501141626450669696998938060', '7.54127311443040482791781825654906', '7.54753555186015960751204008527261', '7.57308886083401195585744431826584', '7.77134877082206580826346868797624', '7.81541423600741605023747117234466', '7.83334317869006983094715219404320', '7.891393113305773517162213415009100', '7.892168546315422070751781389303665', '7.903779545037192575651305247595212', '7.911777791009666691137662180366458', '7.958875000373936378000675633865632', '8.005725632106410590705254395725625', '8.078885286097677235739821161751547', '8.193484206199597210154094152471737', '8.219815253924897567320308193308229', '8.252586605276868676026028410567433', '8.285449986039602807744766878481412', '8.286442945030976019392086338227231', '8.290434763199087572419937786203428', '8.334054270784681713975803613446288', '8.383122937567332481429692950139174', '8.387006220362710576812231513238089', '8.455562958826803320180759752654624', '8.500074641361582407553497672118307', '8.544177666035973828132921082837375', '8.563042809421856102121183236275787', '8.622225044946990304837027504070003', '8.712766281998653418440993536335600', '8.748102216920390505250695137178412', '8.753037791917441182523449130221122', '8.800635539812696745081056966156597', '8.851062339963067194084271440084469', '8.900098994450919775592676475853790', '8.940899656742199463227352547713914', '8.963418836935571209798236054663949', '9.004480526526558610164889865347092', '9.008490958622187021382428984634693', '9.074689183829569506791279269075482', '9.082453181757606203227935951262872', '9.181979351585543849449919037706467', '9.206860264918749177654162610385446', '9.259432607436513308913707085708260', '9.276332269329475282040364019877281', '9.297148333045202716785031944541258', '9.369900345082452541799251653529045', '9.382652201562331356760512366791636', '9.386049440721987109165884987244218', '9.438264201712786275889343843464011', '9.507123126682662988404672937816583', '9.520370728922123205415009714886317', '9.583871757158535660387555527922636', '9.672239130689262438269895501860158', '9.700861513819088756167862340722559', '9.767417633926379323777858603130938', '9.787090766530453380297860695431111', '9.827859461109248523859724496742674', '9.829998291672720327009954762154926', '9.879774148544559560266427649542031', '9.913856571416741217556997865362379', '9.937439336123001280872130921063325', '10.03350918506062950373787078470505', '10.04714295112230554821681564047393', '10.05981317531458937756450252300517', '10.21581852423989760853176982583528', '10.38584108554395385853932879840904'], 'prelabel': '40-1380e20-1.1-c0e20-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.8298853640314079, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c0e20-0', 'trace_hash': 748308434146385983, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.25058437214685426705092563484', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.74981324281426474452348118128', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.77675366221029648630479549200', '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': 0.0005764003225726267, 'bad_primes': [2, 3, 5, 23], 'central_character': '1.1', 'conductor': 627453762719724095122406062634362166417817600000000000000000000, 'conductor_radical': 690, 'degree': 40, 'dirichlet_coefficients': [1, 0, 0, 1, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -4, 0, 0, 4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'euler11': [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 10, 0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], 'euler13': [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 10, 0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], 'euler17': [1, 0, 9, 0, 36, 0, 84, 0, 126, 0, 126, 0, 84, 0, 36, 0, 9, 0, 1, 0, 0, 0, 1, 0, 9, 0, 36, 0, 84, 0, 126, 0, 126, 0, 84, 0, 36, 0, 9, 0, 1], 'euler19': [1, 4, 10, 20, 35, 56, 84, 120, 165, 220, 286, 360, 439, 520, 600, 676, 745, 804, 850, 880, 891, 880, 850, 804, 745, 676, 600, 520, 439, 360, 286, 220, 165, 120, 84, 56, 35, 20, 10, 4, 1], 'euler2': [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler29': [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 10, 0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], 'euler3': [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 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, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 10, 0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], 'euler37': [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -6, 0, 7, 0, -8, 0, 9, 0, -10, 0, 11, 0, -10, 0, 9, 0, -8, 0, 7, 0, -6, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], 'euler41': [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 10, 0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], 'euler43': [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 10, 0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], 'euler47': [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -6, 0, 7, 0, -8, 0, 9, 0, -10, 0, 11, 0, -10, 0, 9, 0, -8, 0, 7, 0, -6, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], 'euler5': [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler53': [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -6, 0, 7, 0, -8, 0, 9, 0, -10, 0, 11, 0, -10, 0, 9, 0, -8, 0, 7, 0, -6, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], 'euler59': [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -6, 0, 7, 0, -8, 0, 9, 0, -10, 0, 11, 0, -10, 0, 9, 0, -8, 0, 7, 0, -6, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], 'euler61': [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 10, 0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], 'euler67': [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 10, 0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], 'euler7': [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 10, 0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], 'euler71': [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -6, 0, 7, 0, -8, 0, 9, 0, -10, 0, 11, 0, -10, 0, 9, 0, -8, 0, 7, 0, -6, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], 'euler73': [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 10, 0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], 'euler79': [1, -4, 10, -20, 35, -56, 84, -120, 165, -220, 286, -360, 439, -520, 600, -676, 745, -804, 850, -880, 891, -880, 850, -804, 745, -676, 600, -520, 439, -360, 286, -220, 165, -120, 84, -56, 35, -20, 10, -4, 1], 'euler83': [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -6, 0, 7, 0, -8, 0, 9, 0, -10, 0, 11, 0, -10, 0, 9, 0, -8, 0, 7, 0, -6, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], 'euler89': [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -6, 0, 7, 0, -8, 0, 9, 0, -10, 0, 11, 0, -10, 0, 9, 0, -8, 0, 7, 0, -6, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], 'euler97': [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -6, 0, 7, 0, -8, 0, 9, 0, -10, 0, 11, 0, -10, 0, 9, 0, -8, 0, 7, 0, -6, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], 'euler_factors': [[1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 10, 0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 10, 0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 10, 0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, 0, 9, 0, 36, 0, 84, 0, 126, 0, 126, 0, 84, 0, 36, 0, 9, 0, 1, 0, 0, 0, 1, 0, 9, 0, 36, 0, 84, 0, 126, 0, 126, 0, 84, 0, 36, 0, 9, 0, 1], [1, 4, 10, 20, 35, 56, 84, 120, 165, 220, 286, 360, 439, 520, 600, 676, 745, 804, 850, 880, 891, 880, 850, 804, 745, 676, 600, 520, 439, 360, 286, 220, 165, 120, 84, 56, 35, 20, 10, 4, 1], [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 10, 0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 10, 0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -6, 0, 7, 0, -8, 0, 9, 0, -10, 0, 11, 0, -10, 0, 9, 0, -8, 0, 7, 0, -6, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 10, 0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 10, 0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -6, 0, 7, 0, -8, 0, 9, 0, -10, 0, 11, 0, -10, 0, 9, 0, -8, 0, 7, 0, -6, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -6, 0, 7, 0, -8, 0, 9, 0, -10, 0, 11, 0, -10, 0, 9, 0, -8, 0, 7, 0, -6, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -6, 0, 7, 0, -8, 0, 9, 0, -10, 0, 11, 0, -10, 0, 9, 0, -8, 0, 7, 0, -6, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 10, 0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 10, 0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -6, 0, 7, 0, -8, 0, 9, 0, -10, 0, 11, 0, -10, 0, 9, 0, -8, 0, 7, 0, -6, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 6, 0, 7, 0, 8, 0, 9, 0, 10, 0, 11, 0, 10, 0, 9, 0, 8, 0, 7, 0, 6, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, -4, 10, -20, 35, -56, 84, -120, 165, -220, 286, -360, 439, -520, 600, -676, 745, -804, 850, -880, 891, -880, 850, -804, 745, -676, 600, -520, 439, -360, 286, -220, 165, -120, 84, -56, 35, -20, 10, -4, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -6, 0, 7, 0, -8, 0, 9, 0, -10, 0, 11, 0, -10, 0, 9, 0, -8, 0, 7, 0, -6, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -6, 0, 7, 0, -8, 0, 9, 0, -10, 0, 11, 0, -10, 0, 9, 0, -8, 0, 7, 0, -6, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1], [1, 0, -2, 0, 3, 0, -4, 0, 5, 0, -6, 0, 7, 0, -8, 0, 9, 0, -10, 0, 11, 0, -10, 0, 9, 0, -8, 0, 7, 0, -6, 0, 5, 0, -4, 0, 3, 0, -2, 0, 1]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1380/1/bn/c'], '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': '40-1380e20-1.1-c0e20-0-1', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__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, 0, 0, 0, 0], 'order_of_vanishing': 0, 'prelabel': '40-1380e20-1.1-c0e20-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.8298853640314079, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e20-0', 'trace_hash': 748308434146385983, 'z1': {'__RealLiteral__': 0, 'data': '0.25058437214685426705092563484', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '317653429759773821019169805829,950501207312577819595839471574,984652246130357690478794125225,988941046999112670746821176763,1057564054830624731375147040374,1341602899664838285181400202071,1526367778903334566095908292136,1658702454069810717404193951369,1661292240368185707045612529969,1700316610493054258511042752826,1732064094728668502055199344273,1855477092893915339256686352263,1984892483805664439744800859331,2162628616155045753209873057576,2178802016855051960849554408820,2396288002082484940271272321933,2414517020915590790586200344768,2573214987109603609664660932134,2859401267031288376621177363319,3073008291095205881415193721261', 'Lhash_array': ['317653429759773821019169805829', '950501207312577819595839471574', '984652246130357690478794125225', '988941046999112670746821176763', '1057564054830624731375147040374', '1341602899664838285181400202071', '1526367778903334566095908292136', '1658702454069810717404193951369', '1661292240368185707045612529969', '1700316610493054258511042752826', '1732064094728668502055199344273', '1855477092893915339256686352263', '1984892483805664439744800859331', '2162628616155045753209873057576', '2178802016855051960849554408820', '2396288002082484940271272321933', '2414517020915590790586200344768', '2573214987109603609664660932134', '2859401267031288376621177363319', '3073008291095205881415193721261'], 'label': '40-1380e20-1.1-c0e20-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1380/1/bn/c'}