Lfunction data - 16-3332e8-1.1-c0e8-0-4

Formats: - HTML - YAML - JSON - 2024-04-25T09:03:50.105423

• 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': '433597792481605051857145456918,445821697257164027114719767581,955026011324088708605183788157,1107701055491958514382366695096,1732610209907514782599944362720,1822339201327631631138923432770,1875772237694089486452089113159,2422728759653019357257089636012', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 58.46513229529397, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[2, [1, 0, 0, 0, 0, 0, 0, 0, 1]], [7, [1]], [17, [1, 0, 0, 0, 0, 0, 0, 0, 1]]], 'bad_primes': [2, 7, 17], 'central_character': '3332.1', 'coefficient_field': '1.1.1.1', 'conductor': 15192874202374507341482622976, 'conductor_radical': 238, 'degree': 16, 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1], [1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 8, 32, 88, 188, 328, 480, 600, 646, 600, 480, 328, 188, 88, 32, 8, 1], [1, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 8, 28, 56, 70, 56, 28, 8, 2, 8, 28, 56, 70, 56, 28, 8, 1], [1, -8, 28, -56, 70, -56, 28, -8, 2, -8, 28, -56, 70, -56, 28, -8, 1], [1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 4, 0, 0, 0, 6, 0, 0, 0, 4, 0, 0, 0, 1], [1, 0, 4, 0, 8, 0, 12, 0, 14, 0, 12, 0, 8, 0, 4, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1], [1, 8, 28, 56, 70, 56, 28, 8, 2, 8, 28, 56, 70, 56, 28, 8, 1], [1, 0, 8, 0, 28, 0, 56, 0, 70, 0, 56, 0, 28, 0, 8, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 4, 0, 0, 0, 6, 0, 0, 0, 4, 0, 0, 0, 1], [1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1], [1, -16, 120, -560, 1820, -4368, 8008, -11440, 12870, -11440, 8008, -4368, 1820, -560, 120, -16, 1], [1, 0, 8, 0, 28, 0, 56, 0, 70, 0, 56, 0, 28, 0, 8, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 4, 0, 6, 0, 4, 0, 2, 0, 4, 0, 6, 0, 4, 0, 1], [1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1]], 'euler_factors_factorization': [[[[1, 0, 0, 0, 0, 0, 0, 0, 1], 1]], [[[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 1]], [[[1, 0, 0, 0, 1], 2], [[1, 0, 0, 0, 0, 0, 0, 0, 1], 1]], [1], [[[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 1]], [[[1, 1], 8], [[1, 0, 1], 4]], [[[1, 0, 0, 0, 0, 0, 0, 0, 1], 1]], [[[1, 0, 0, 0, 0, 0, 0, 0, 1], 2]], [[[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 1]], [[[1, 0, 0, 0, 1], 2], [[1, 0, 0, 0, 0, 0, 0, 0, 1], 1]], [[[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 1]], [[[1, 1], 8], [[1, 0, 0, 0, 0, 0, 0, 0, 1], 1]], [[[1, -1], 8], [[1, 0, 0, 0, 0, 0, 0, 0, 1], 1]], [[[1, 0, 0, 0, 0, 0, 0, 0, 1], 2]], [[[1, 0, 0, 0, 1], 4]], [[[1, 0, 1], 4], [[1, 0, 0, 0, 1], 2]], [[[1, 0, 0, 0, 0, 0, 0, 0, 1], 2]], [[[1, 1], 8], [[1, 0, 0, 0, 0, 0, 0, 0, 1], 1]], [[[1, 0, 1], 8]], [[[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 1]], [[[1, 0, 0, 0, 1], 2], [[1, 0, 0, 0, 0, 0, 0, 0, 1], 1]], [[[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 1]], [[[1, 0, 0, 0, 0, 0, 0, 0, 1], 2]], [[[1, 0, 0, 0, 1], 4]], [[[1, 0, 0, 0, 1], 2], [[1, 0, 0, 0, 0, 0, 0, 0, 1], 1]], [[[1, -1], 16]], [[[1, 0, 1], 8]], [[[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 1]], [[[1, 0, 1], 4], [[1, 0, 0, 0, 0, 0, 0, 0, 1], 1]], [[[1, 0, 0, 0, 1], 2], [[1, 0, 0, 0, 0, 0, 0, 0, 1], 1]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 4, 'label': '16-3332e8-1.1-c0e8-0-4', 'leading_term': '0.37716120778498090175957831494630732095440508523452474628714112543535835704753770179098820', '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}], 'nu_real_doubled': [0, 0, 0, 0, 0, 0, 0, 0], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3332/1/bn/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.00732421875', 'prec': 44}, 'plot_values': [0.3771612077849808, 0.3773292303590963, 0.37705228967209026, 0.376357397634036, 0.3752710395347368, 0.3738189120607701, 0.3720256810040104, 0.36991475599119406, 0.36750222991532305, 0.36478059574124305, 0.3617259048867465, 0.3583109267780573, 0.35450826289271886, 0.3502905707820113, 0.34563081909019266, 0.34050334870181437, 0.3348855035025342, 0.32875655848698315, 0.3220987013019731, 0.31489621663907685, 0.3071354969702893, 0.298805455506776, 0.289897205578195, 0.2804037728178309, 0.27032237993876845, 0.25965507493241285, 0.248408740034066, 0.23659680900251795, 0.224240349207329, 0.2113691182231758, 0.19802266651578126, 0.18425087713483806, 0.17011479945492566, 0.15568748797429832, 0.14105478766274862, 0.12631640386035942, 0.1115871891962877, 0.09699807819340413, 0.08269611188717535, 0.06884492849189325, 0.055625198508752624, 0.04323491341063639, 0.03188952957086546, 0.021822317604491784, 0.013283846164041145, 0.006540702628484397, 0.0018745320513921212, -0.0004191836827734248, -3.267036895892268e-05, 0.0033522389024684103, 0.010061507734617265, 0.020425546437367832, 0.03477594245299355, 0.0534418437563478, 0.07674591962655583, 0.10499990297858086, 0.13849965779211953, 0.17751854087702304, 0.2223010362526029, 0.27305753166588176, 0.32995806393499355, 0.39312579294299405, 0.4626303104100592, 0.5384807024696346, 0.6206164733692803, 0.7089008699301685, 0.8031160163961341, 0.9029570082209802, 1.008026429842708, 1.1178294731935872, 1.2317695885744684, 1.349142951583508, 1.469137446825399, 1.5908337695992871, 1.713206428639396, 1.8351260717513131, 1.9553635445709108, 2.0725956867961575, 2.185412557046034, 2.2923291292086065, 2.3917987005101997, 2.482227812250745, 2.5619937436010267, 2.629463425814522, 2.6830151480035256, 2.721065023030095, 2.7420933426833747, 2.7446718147798466, 2.7274931469866623, 2.6894023465853847, 2.629429660159543, 2.5468240610774338, 2.441093140769141, 2.3120336771450707, 2.1597621007603762, 1.9847462573961032, 1.7878356923985206, 1.5702901050089877, 1.333807439417423, 1.080553230064127, 0.8131709419710088, 0.5347915889708339, 0.24904133041092258, -0.039956555533813345, -0.32758583526016444, -0.6087462776185874, -0.8778685280832491, -1.1289501335617684, -1.3555928980275553, -1.5510457454633932, -1.7082555046443177, -1.8199255928869762, -1.8785833486259558, -1.8766611710788499, -1.8065846142871385, -1.6608606062434175, -1.4321715485619289, -1.1134745465203886, -0.6981045321995674, -0.17988745264231593, 0.4467331785383337, 1.1865956956748775, 2.043717879329652, 3.021195413593477, 4.121103937655356, 5.344407075681426, 6.690856664586834, 8.158892967234895, 9.7456051306771, 11.44668882916487, 13.256423555566355, 15.167651776194706, 17.171775469230703, 19.258751780817246, 21.417109194774124, 23.63403698136319, 25.8954660343533, 28.186173175010424, 30.489926770671254, 32.78960612359107, 35.06733092288181, 37.304627557272454, 39.48264315393386, 41.58234740641841, 43.58474245148755, 45.47109606566451, 47.22321684619394, 48.823647205242615, 50.25588784653465, 51.5046266675376, 52.55595351159464, 53.39756377466264, 54.01894793681918, 54.4115858652456, 54.5691929979858, 54.48780534230066, 54.16583579442996, 53.604140859899324, 52.806057862543724, 51.77740995900881, 50.52648046919004, 49.06402086717737, 47.403218622834444, 45.55945019185318, 43.55008513110896, 41.394283365680394, 39.11276396392882, 36.727551836716216, 34.261747675677626, 31.73922686668259, 29.184322964595598, 26.621433961081546, 24.074668074487626, 21.567508746947194, 19.122488812095515, 16.760904402020792, 14.502485757468104, 12.365094628457422, 10.36448497226666, 8.514039312800783, 6.824570029599206, 5.30417207319482, 3.958126205478109, 2.7888202452215087, 1.7957244798575709, 0.9754263269904192, 0.3217091852526843, -0.1743302318266816, -0.5241085045814691, -0.7413385458143048, -0.8417733143484962, -0.8429108685725836, -0.7636687189373039, -0.6240353536514256, -0.4447068251784922, -0.24669907367631208, -0.05095523434487062, 0.12204684315925529, 0.2526767296979501, 0.32251722907936403, 0.314707981830938, 0.21426032345224102, 0.00833994350666603, -0.31348590634286116, -0.7590521503023072, -1.3334486300258204, -2.038923675529667, -2.8748406144445235, -3.837688055329411, -4.921146244759452, -6.1162148746959755, -7.411380933459541, -8.792833799405983, -10.244724498670648, -11.749462564820085, -13.288044834760687, -14.840429102383206, -16.38595859317552, -17.903699773711356, -19.37282441863029, -20.772994469349374, -22.084732360596462, -23.289772824792422, -24.371431335685404, -25.314977641276045, -26.1077999287837, -26.739577463019817, -27.202452459646207, -27.49114813067016, -27.603033036712482, -27.53819565592086, -27.299477826136137, -26.89225924276528, -26.324289699801234, -25.605480301731927, -24.747701635920414, -23.764540317326997, -22.671084524340124, -21.483661102408576, -20.21939536053392, -18.895873790866258, -17.530811585398286, -16.141706494479862, -14.745571672334062, -13.358714286549509, -11.996483663028753, -10.672961452439024, -9.400767736834036, -8.19091172051391, -7.052670747841959, -5.993492086241643, -5.019021324713552, -4.133111419037953, -3.3378335000025015, -2.6335622433676873, -2.0190940942704434, -1.4917916491839471, -1.047742964784172, -0.6819322259560281, -0.3884570375503406, -0.16073233618506483, 0.008303682049227237, 0.12598845766840291, 0.1997436973621349, 0.23689783580815782, 0.244529341644325, 0.2293287628555449, 0.19746575727025306, 0.15449338640480742, 0.10528137408851024, 0.05397472821794644, 0.003976800270676503, -0.04204523043558496, -0.08213514029268043, -0.11500438005133906, -0.13997028002071196, -0.15688033735898832, -0.16602819054359913, -0.16806500730045135, -0.16391104289900843, -0.15466656731049222, -0.14152735301619335, -0.12570937283584857, -0.10837986226730216, -0.09060158173295495, -0.07329058843840959, -0.05718783343163355, -0.042841905460878626, -0.030604818473669904, -0.02064012303687267, -0.0129408544991642, -0.0073550581885944615, -0.0036178508574835335, -0.0013871388972775851, -0.00028025884724165446, 9.016023537087527e-05, 8.346137803744096e-05, 3.3299837673695363e-06, 7.675447608663527e-05, 0.00044068611698703283, 0.0011370268333409323, 0.00211607422641215, 0.0032480730322786634, 0.004341968789678596, 0.005170019760681937, 0.005496605776673059, 0.005109379453133659, 0.003850032250079563, 0.001642539027661795, -0.0014835085394307407, -0.005376717295041262, -0.009756799074152694, -0.014218158338473987, -0.01824524414522949, -0.02124041550937749, -0.022564865789631468, -0.021591103431159345, -0.017765724552809666, -0.010680533855891416, -0.00014939172736416992, 0.0137123662527113, 0.03040928521856793, 0.04899125772297592, 0.06798942349762828, 0.0853653513580505, 0.09847730160259709, 0.10406736583366855, 0.0982724119239374, 0.07666060206988173, 0.03429570140535203, -0.03416952579125093, -0.13437030603880817, -0.27208069869092727, -0.4530403612765171, -0.6827641009024394, -0.9663417105793841, -1.308220275151548, -1.7119839767102698, -2.1801349809013124, -2.713889557874846, -3.3129932754808826, -3.975579724949901, -4.69807604224918, -5.475108105229359, -6.299465190269696, -7.162117151549579, -8.052284138642953, -8.957564901519646, -9.864168987635189, -10.757203757621221, -11.620909928874543, -12.438985435823446, -13.194950994780422, -13.87254666074862, -14.456155922756503, -14.931305232362066, -15.285117925995905, -15.506605568374333, -15.58701672630926, -15.520151479115253, -15.302623781934017, -14.934072809143194, -14.417417957845396, -13.75888900700642, -12.96785793868354, -12.056705636960213, -11.040613507164588, -9.937276785446608, -8.76654950574728, -7.550104707992969, -6.310922063468182, -5.072640094578681, -3.8589892842228397, -2.693222835458144, -1.5975506736754133, -0.5925947474923614, 0.30309341890725194, 1.0735337207744442, 1.7057602494245774, 2.1901420831416574, 2.520610184030986, 2.6947912680128683, 2.7140441416513323, 2.583390433706967, 2.3113566147439712, 1.9097194677324902, 1.3931588872675198, 0.7788205699960633, 0.08582314320068693, -0.6652823997962969, -1.4531136543667842, -2.256048936498214, -3.052800535762367, -3.8229798365269465, -4.547639027045028, -5.209740357537878, -5.794566033907217, -6.290110131733097, -6.6872880867948, -6.980045697736939, -7.1654015140760965, -7.243405127850455, -7.217024867422998, -7.091913241535455, -6.876165633665083, -6.579892042657827, -6.214767236502607, -5.7935841404894015, -5.32979369559122, -4.837053891056307, -4.328817258037474, -3.8179274290828893, -3.3161865309898695, -2.834028554693285, -2.3802814029342656, -1.9620022062284137, -1.5843883164096255, -1.2507705060971246, -0.9626812005325343, -0.7199431228781614, -0.5208512257787167, -0.3624121841702255, -0.24061860729401535, -0.15074438146823171, -0.08764773335319566, -0.04606695658107431, -0.020894432569084593, -0.0074228762061249514, -0.001551191627111659, 6.0377519238198534e-05, -0.00010873936468433386, -0.00047997766697236636, -0.00035831424867238996, 0.0001396359069973611, 0.00020620884102256373, -0.001496427898248187, -0.006645841019265048, -0.01705156518205219, -0.034442988269978866, -0.0602662905307854, -0.09550362080804065, -0.1405258463296653, -0.1949886384907852, -0.257780345103991, -0.32702591451668006, -0.4001498347459429, -0.4739967335054931, -0.544999504580709, -0.6093898927488346, -0.6634399643749714, -0.7037212395504029, -0.7273626632420295, -0.7322960104766228, -0.7174652275064778, -0.6829729058812907, -0.6301632905174324, -0.5616244001573464, -0.48109927759311694, -0.39330053174543245, -0.3036235236072875, -0.21775856483660927, -0.14121108345732605, -0.07875560909066037, -0.03383705372135747, -0.007942693447929942, 2.7380063864587852e-05, -0.0056386942569606625, -0.016925825018959752, -0.021654442477791264, -0.003174460840544075, 0.0597803163311094, 0.19305061019306233, 0.42680110005237915, 0.7950453320309957, 1.334936874044994, 2.085833190087041, 3.088142869034078, 4.381974766890086, 6.005618208801519, 7.99389377464105, 10.376449064810215, 13.176029744041763, 16.406767719084478, 20.072573885416297, 24.16569146814086, 28.66547499926531, 33.537468426878746, 38.73296929398447, 44.18888180396856, 49.827929696579254, 55.559433556970426, 61.28047171220847, 66.87752091934823, 72.22859662132777, 77.20608072463503, 81.67953285805304, 85.51871389785569, 88.59702169755212, 90.79516356657716, 92.00460682802928, 92.13107495360259, 91.09806642217724, 88.8496098986415, 85.35271088851945, 80.59947108550153, 74.60870656869768, 67.42700266633719, 59.12872724716255, 49.81508857513864, 39.61274055666844, 28.671853401320657, 17.163466136037176, 5.276215782937808, -6.787496437874898, -18.81615560761974, -30.59513646694663, -41.91109249381198, -52.55657159317099, -62.33491295864229, -71.06497255676265, -78.58555136870008, -84.75996516573869, -89.48127563359199, -92.67345888677238, -94.29271599746828, -94.32852530663602, -92.80387754108523, -89.77468337926317, -85.32889097887322, -79.5853521280478, -72.68928767382438, -64.80789122277064, -56.12597538131937, -46.841301842648974, -37.15964686522944, -27.289997405055185, -17.439610725306586, -7.8080748708729875, 1.417506024345621, 10.06681996142963, 17.989997024845078, 25.060606181232455, 31.17805395827437, 36.269451950699725, 40.290351705718564, 43.224632232252894, 45.08374904809393, 45.90503132467916, 45.74937182901264, 44.69865867353344, 42.85267795008882, 40.324953514785626, 37.23876085046472, 33.723154437636644, 29.909086406175582, 25.925457448627558, 21.895678803114663, 17.934429057753896, 14.144562649592745, 10.614870608713936, 7.418436686097403, 4.611584509285004, 2.233402102418255, 0.30580166751111176, -1.1659041180587884, -2.1918860495486263, -2.796185714572307, -3.0147604826944896, -2.893275770300859, -2.4847382662752624, -1.8470759454578096, -1.0406619373978123, -0.125916028193692, 0.8388806251226173, 1.7995205149392037, 2.707505322810652, 3.5213467895373673, 4.207549273737461, 4.741220457946017, 5.106241694405266, 5.295105628808151, 5.308441563435311, 5.154266742479786, 4.847016080396648, 4.406443472757145, 3.856349542501824, 3.2232251277481514, 2.534908452907857, 1.8193167445028868, 1.1032867297167606, 0.41155901941260803, -0.23405286509100515, -0.8153260050682838, -1.3180844811941903, -1.7324396134644926, -2.0528207689153444, -2.2778157083712527, -2.409847220067265, -2.454707173516225, -2.42098701716407, -2.3194439543160446, -2.162333128590623, -1.962739121506418, -1.7339194462221472, -1.4887062050314808, -1.2389733169853172, -0.9952247782205481, -0.7662924393714488, -0.5591360181720398, -0.3787513275599192, -0.22818020641063166, -0.1086082159090458, -0.019541015675121218, 0.04093069670768167, 0.07583562934425661, 0.08901119109195058, 0.08478875369060054, 0.06769133088885908, 0.042156130875789205, 0.012286226425138908, -0.018337616668384325, -0.046785297879729876, -0.07085201548891575, -0.08908021353720974, -0.10073351223747365, -0.1057329447872841, -0.10456518457682837, -0.09814379872002177, -0.08766763957070743, -0.07448267580602091, -0.0599525171291762, -0.04534524558001844, -0.0317435461151587, -0.019979617101693006, -0.010592540170106106, -0.0038212611249410435, 0.00037521306478002125, 0.0022760566667358365, 0.0023407131173955446, 0.001141279611646295, -0.0007085367642000687, -0.002623667158522734, -0.004109026552631624, -0.004806702324680882, -0.004525805568868307, -0.003253408016262597, -0.001146566738803179, 0.0014928688253272693, 0.004258393828633884, 0.006689816494919925, 0.008329584250716657, 0.008778723594904364, 0.007746957341101461, 0.005092105442939344, 0.0008447595569573052, -0.004784730468118294, -0.011418369294208804, -0.01854116507615232, -0.025548254141375872, -0.031804316841397694, -0.03671052366491142, -0.039772677872617006, -0.0406622836682248, -0.039264640813475034, -0.03570734524962411, -0.030363833744722495, -0.023828102049474057, -0.016858558542879296, -0.010290719839923442, -0.004921544178180517, -0.0013730277588819184, 5.7752738769873895e-05, -0.00044777356103934237, -0.0020839813574876896, -0.003295735973968975, -0.0016868621403850997, 0.006025058792846654, 0.023997810159400265, 0.05718963864296617, 0.11121543846465247, 0.19213281111315722, 0.3061601360908122, 0.4593355681182451, 0.6571310880633273, 0.9040360216432138, 1.2031302371350892, 1.5556698765987258, 1.960710842040716, 2.414804394571666, 2.9117814881450883, 3.4426476218079216, 3.995598657881238, 4.556180196814908, 5.107599515826994, 5.631193865400113, 6.107086311381454, 6.514925551902227, 6.834715312017453, 7.047759308298842, 7.137606686146063, 7.091009543949575, 6.898852692804578, 6.557038019852023, 6.067126769119675, 5.4368056533285065, 4.680184466997087, 3.817855857203687, 2.8766553462332114, 1.8891654190360128, 0.8929092474190333, -0.07072991952194131, -0.9577687444614057, -1.723067521300397, -2.3219211034920026, -2.7117491885002902, -2.8538243745878478, -2.7150757388425104, -2.269550101707611, -1.4996821345371851, -0.3973726008411646, 1.0352253172169679, 2.7852568079593056, 4.829079875141034, 7.132546268235952, 9.651908009401174, 12.334993009700913, 15.122659712194665, 17.95053388991694, 20.750970830319922, 23.455242716962793, 25.99605078249763, 28.309708984790326, 30.338188561350258, 32.03101575331818, 33.34691342642399, 34.255125384022485, 34.736514760634115, 34.784496374530896, 34.40487189288943, 33.6152679916975, 32.44428950102088, 30.93031970798288, 29.119995419079878, 27.06658188293487, 24.828208729350827, 22.46530848601364, 20.038387358601664, 17.605921667444793, 15.222441316038095, 12.936855325077913, 10.791162112749225, 8.819437012488667, 7.046902499473007, 5.489641396726947, 4.154734746179326, 3.04080767389906, 2.138888561508261, 1.4335536937617603, 0.9042453500582512, 0.526702544505537, 0.2745247846490683, 0.12071840065564292, 0.03914638992427821, 0.005818373815028523, -5.542187098340115e-05, 0.0047216601339411255, 0.007828443106677836, 0.0016142587692582545, -0.01701797541695904, -0.04701177979038695, -0.08380491357516877, -0.1201720318871795, -0.14720140689021452, -0.1553382987255854, -0.1354267671918957, -0.07968281881288777, 0.01746270185730003, 0.1587048519319137, 0.3434343825446464, 0.5675670359906084, 0.8236364687030522, 1.1011400725468528, 1.3871182772312534, 1.6669308616397693, 1.9251817290280322, 2.1467509993862044, 2.317862297687327, 2.427046444277391, 2.4659993072909407, 2.4302693918930065, 2.3197188244742937, 2.1387209281153523, 1.8960822661111, 1.6046491868184176, 1.2806295207782936, 0.9426497893637632, 0.6106308489153812, 0.30453331711845594, 0.043039110698699715, -0.15775606729287722, -0.28554697615493246, -0.3328326704778627, -0.2976733060702634, -0.18412687941621303, -0.002326538013198648, 0.2318270549646195, 0.4973722807077258, 0.7693713259465147, 1.0203119150795288, 1.2217804282471547, 1.346338234350367, 1.3694328198770587, 1.2712971386302199, 1.0387330349540465, 0.6666057373987858, 0.15899333978862445, -0.4700845410670618, -1.1964452621547554, -1.9861194389158692, -2.796310194500512, -3.576950082961926, -4.272709756250107, -4.825416814084474, -5.1768275989455494, -5.2716250223051935, -5.06054970777557, -4.503604111046416, -3.572837635912307, -2.254568230286537, -0.5511727662004986, 1.5177111348468644, 3.914697885750415, 6.584943703693945, 9.457282189789755, 12.446417195583642, 15.455810424816388, 18.381062195743773, 21.113796750851225, 23.54590582032827, 25.573982191404163, 27.103986737139426, 28.05618665210069, 28.36870250594296, 28.00039149426973, 26.933147404235715, 25.173362471780266, 22.752427045202413, 19.726530037687944, 16.17558254464458, 12.199841779316651, 7.916203152384769, 3.453667415245192, -1.0515915809399754, -5.461463506563845, -9.64111025006278, -13.46425470444907, -16.818716959638888, -19.610947624312633, -21.769867080763657, -23.24947181211983, -24.03036967717199, -24.12025458047261, -23.553320499278133, -22.38839039722955, -20.705902966838458, -18.604026165319848, -16.194078444715835, -13.595046255671544, -10.928014559178774, -8.310557850249806, -5.851213666326125, -3.6445259029740456, -1.7668021949189894, -0.2727666284387748, 0.8067697201303093, 1.466095590230965, 1.7245130609516206, 1.6249998946517092, 1.231717962861792, 0.6264997263734698, -0.09552124531564436, -0.8309354432310554, -1.4735438713043625, -1.9200274632821448, -2.075456673218019, -1.858408722272062, -1.2054628364053808, -0.07486438262187194, 1.5508138974743626, 3.663156951879704, 6.2276400282764115, 9.18463229717213, 12.451553970121665, 15.926104781343335, 19.49042861494288, 23.016038596710366, 26.36941886773586, 29.41783888924571, 32.03516645987764, 34.10722142007515, 35.536697210005606, 36.24742361852224, 36.187752890531264, 35.3329460364209, 33.6862388068932, 31.2788305543853, 28.16887093350536, 24.43889178300049, 20.19247404827274, 15.550137696298556, 10.644220572724523, 5.613771846045628, 0.5994575319765127, -4.261654769944994, -8.841159089363947, -13.02389334079795, -16.71185398219725, -19.82788368951491, -22.317252811576257, -24.148339191081675, -25.31271952042879, -25.82441360252176, -25.71840824587834, -25.04812870428671, -23.882717247423205, -22.302835642845686, -20.396576414805253, -18.255598199494596, -15.971362407706295, -13.631656512140324, -11.317566454643732, -9.100735713946086, -7.041027419547658, -5.185161964565296, -3.5661148037833734, -2.203158307554808, -1.1024994452473182, -0.258436398523206, 0.3450786832847501, 0.7324889901373888, 0.9344277834597623, 0.9854449533871408, 0.9217824158511004, 0.779300499221073, 0.591639754007326, 0.38867438414213634, 0.19534290711040903, 0.030889444394743153, -0.09148633570479453, -0.16459665843361382, -0.18689057240977494, -0.16179443982968295, -0.09681308712013263, -0.0024407244798518605, 0.10898417815970655, 0.22441335342674484, 0.33115155555758496, 0.41779264712230163, 0.474998573735633, 0.4960890207894018, 0.4773533088150085, 0.41814303751540616, 0.32075443910370477, 0.19010350483519825, 0.03325613044505566, -0.1411369460797201, -0.32348736098475617, -0.503974153499359, -0.673191266098386, -0.8227269744284786, -0.9456564683714224, -1.036888088609084, -1.0933748109247223, -1.1141909488192354, -1.1004518415123792, -1.0551073502034005, -0.9826342430014386, -0.8886592129002456, -0.7795447334593223, -0.661935343409608, -0.5423209080069729, -0.42663639094490324, -0.31994212665308286, -0.22618902940460484, -0.14807669424951025, -0.0870072515834251, -0.043129736334752984, -0.015456869052816008, -0.002056050768499857, -0.0002921884899355537, -0.007096533179627901, -0.019240187203319718, -0.03359240063473464, -0.04734732475845496, -0.05820536992319524, -0.06449694301065056, -0.06524475179947686, -0.06016531488460329, -0.049614759481760896, -0.03448797917929534, -0.01608465467287881, 0.004048191057630594, 0.024282543779322045, 0.04306725974236615, 0.05906446300402115, 0.07125539288132708, 0.07900897520092398, 0.08210880510272768, 0.08074164230233567, 0.075450825821927, 0.06706010876773594, 0.05657313506801872, 0.045063957855909456, 0.03356884186782932, 0.022988277364397458, 0.014011126389628233, 0.007065083704198234, 0.002296176894442023, -0.0004214400370309381, -0.0014471901646552015, -0.0013110921864180598, -0.0006341474913068134, -4.1182860263424284e-05, -7.663762523113086e-05, -0.001131800898563739, -0.0033911202807738994, -0.006803430200823585, -0.011082753765405061, -0.01574050956073413, -0.020144288971374037, -0.02359757563666855, -0.025433144657339746, -0.02511041987256634, -0.022306287599527845, -0.016989459358809165, -0.009468185877396534, -0.0003999493690618165, 0.009236732737765634, 0.018209466097020115, 0.02513567630823921, 0.0286162210170089, 0.027389041850966706, 0.02048936594978975, 0.007398257943119314, -0.011833788588755754, -0.036502249405794704, -0.06521534310095846, -0.09592105319513808, -0.12600199190205427, -0.15244338072984714, -0.17204528202654404, -0.18167763571358236, -0.17856074825655607, -0.16054837208907127, -0.1263895675037588, -0.0759507443374999, -0.010368929750091394, 0.06791581655275845, 0.15522154548869255, 0.24679231698545642, 0.3370731195329035, 0.42007955474259334, 0.4898451621710003, 0.5409237307721464, 0.5688831987790919, 0.5707531217114575, 0.5453876024489174, 0.49370162328415435, 0.418746943626356, 0.3256108088092007, 0.22110687842233157, 0.1132416170665884, 0.01052728967422277, -0.07882678250927451, -0.1477839809482458, -0.19133031408883452, -0.20721467307442704, -0.1964746602517141, -0.16361768164359958, -0.11636670289462872, -0.06488458101385366, -0.02040815780180907, 0.00674897309203442, 0.009831336625316553, -0.011116049218903143, -0.04549577914245706, -0.06803440273397697, -0.0344578547740135, 0.12281618136925676, 0.4987150353090909, 1.2189834580523236, 2.4427903489058647, 4.364210309332534, 7.212292773166807, 11.24947553315806, 16.768145048240765, 24.085212461430825, 33.53482417963567, 45.45931004862947, 60.19811657037258, 78.07519461008184, 99.38514968904252, 124.37854362415176, 153.24694961698572, 186.11007253230395, 223.0031162323763, 263.8649330354726, 308.5280252398887, 356.71123960700345, 408.01571247835733, 461.9249192287925, 517.8151593918114, 574.9634294485444, 632.5560302731554, 689.7061805392827, 745.4715532263855, 798.8753102904905, 848.9316545191868, 894.6855324438665, 935.2344325400171, 969.7464730939138, 997.4854706224517, 1017.8365615803083, 1030.3231474953293, 1034.6244583244288, 1030.6041122219515, 1018.3047594186224, 997.9394089234225, 969.8866571709913, 934.6819888433604, 893.0060821438884, 845.6666031572263, 793.5876955700285, 737.7700146079325, 679.25615047393, 619.1024397750917, 558.3510818974291, 498.0037257635066, 438.99924381259507, 382.1955247316073, 328.3409032739092, 278.0573692320224, 231.83178718541726, 190.01181704039183, 152.80646040961233, 120.2914787348632, 92.41878812292006, 69.02630977905388, 49.853708976748884, 34.5608990342818, 22.747704782451798, 13.973880028776211, 7.778709664921607, 3.6993927697452484, 1.287833272509798, 0.12549654228913076, -0.16481119833159988, 0.08969875402570159, 0.6172905879261138, 1.2041673900872996, 1.6941412563686316, 1.9854978335261728, 2.0256483813660986, 1.8039969401369895, 1.3436835908239093, 0.6927606055970417, -0.08465192307373967, -0.9168628545949015, -1.732416711735718, -2.4665734518529434, -3.0663519511791586, -3.4939338626025584, -3.728439145911202, -3.7662013320628804, -3.619669361612035, -3.3150320472145216, -2.8889778989373838, -2.38490976190595, -1.8489278655260108, -1.3258464573593574, -0.855628333142282, -0.47042275667617633, -0.19239762331667884, -0.032522414364989094, 0.009686829818167991, -0.054508088389151936, -0.20458527308650457, -0.4129901491338516, -0.6478752582841363, -0.8760913947938901, -1.0662110505217048, -1.191359840275954, -1.2316502875259334, -1.1760487161577937, -1.0235626450121236, -0.7835755534073586, -0.4753477637415303, -0.12678742415481625, 0.22744945210508952, 0.5483994806200568, 0.7956077794569753, 0.9301524302393328, 0.9176252027966167, 0.7308122289706622, 0.3519578063635562, -0.22554279552033749, -0.9961368895826732, -1.9418695028168353, -3.033012881819395, -4.229476711367528, -5.482836796727221, -6.738890054090842, -7.940586259115221, -9.031173487712735, -9.95739537076184, -10.67280946944209, -11.140381590843884, -11.334414508035518, -11.242067657942185, -10.864043681228404, -10.214552695085864, -9.320588711344076, -8.220693643564713, -6.96263061321546, -5.6006470959475, -4.192629706802103, -2.7971259504198502, -1.470347313970872, -0.26338753537155857, 0.780275189829356, 1.6267870238316584, 2.2532316725778117, 2.648301949448019, 2.8123336857166343, 2.756726737842816, 2.5028285387233216, 2.080381466348125, 1.525357978797809, 0.8776443250859417, 0.17870728434839359, -0.5306801458739533, -1.2125445401376092, -1.8335675707347667, -2.3665871179421014, -2.7915848392754503, -3.0961466360889562, -3.2754665844541146, -3.331920398246357, -3.274264950630002, -3.1165904502445123, -2.8771308392483954, -2.5766014545765175, -2.2366641221789134, -1.878542382855582, -1.5218054133046761, -1.1833804856915364, -0.8768531921606004, -0.6120506042697353, -0.39481758094783403, -0.22715326773089614, -0.10762073991871648, -0.03194272964838478, 0.006280909555173155, 0.014798560223246575, 0.0019399334490749266, -0.024102143940138907, -0.055889358967383944, -0.08720742619838358, -0.11336647967319598, -0.1313290331650197, -0.13967675898630189, -0.13844048294432254, -0.12881950376885595, -0.11282820192729312, -0.09291427245913986, -0.07159039469921594, -0.051115629621523315, -0.033254309650891004, -0.01912801753368671, -0.009167371019593567, -0.0031638680469061663, -0.00040505655230480545, 0.00013069665728596263, -0.0004504722802535069, -0.0011803602455374993, -0.001418260865275344, -0.0009803180175026367, -0.00018809934766829495, 0.00017455335308628827, -0.001003594592416564, -0.004947202982318122, -0.012723505189475983, -0.02494422837005705, -0.041478179466657564, -0.0612139260287842, -0.08191110727166394, -0.1001742523083912, -0.11157782050459734, -0.11096384395614717, -0.09288252873442958, -0.05217071191125418, 0.015363364657245762, 0.11219856000095502, 0.2383616864624936, 0.3907577607315736, 0.5626428153876498, 0.7433174905373284, 0.9181117945029444, 1.0686791349419003, 1.173631674619544, 1.2095238141091036, 1.152163697665516, 0.9782126356382479, 0.6669741902015089, 0.2023182241259492, -0.4254223998902625, -1.2176900224298564, -2.1661959910179815, -3.251804543088443, -4.443962162529207, -5.7007086780819, -6.96931053712743, -8.187601671303858, -9.285905950918371, -10.189607297912392, -10.822280474119843, -11.10925604167525, -10.981269992518543, -10.378167637453, -9.25254967795536, -7.573102364196074, -5.327180788658155, -2.522791985171514, 0.8106248398046244, 4.622112962442152, 8.839882764609158, 13.373038178511944, 18.114287303962755, 22.943730886558317, 27.73324045019604, 32.3523647897926, 36.67287261640986, 40.573247125352445, 43.94336651062543, 46.68877691046545, 48.7345487322186, 50.0291207399299, 50.54718785063717, 50.28898511039374, 49.27927584000817, 47.56590064303918, 45.2174204484588, 42.31997259875294, 38.97398984216461, 35.29112717814455, 31.387641989558702, 27.379212616594334, 23.376595280064738, 19.481729951216558, 15.784446723657576, 12.360031738251108, 9.267623241009957, 6.548685485280812, 4.226655883046711, 2.3077814313131007, 0.7827179066477852, -0.37130569245098344, -1.187904011746718, -1.7087376494783788, -1.9806347313668906, -2.0527196095332956, -1.9736984399179756, -1.7895006321223454, -1.5413857799163906, -1.264570384662555, -0.9873800418756963, -0.7309043916942429, -0.5091562172015035, -0.32964428429479137, -0.194256804715741, -0.10038705245777323, -0.042180108208668965, -0.011797169576783425, -0.000605728952063903, -0.00021038290531684125, -0.0032706890288820476, -0.004073196185817348, 0.0011542113164507161, 0.014176801760037201, 0.03490922108332154, 0.06174622168022231, 0.09200953593534332, 0.12245208664431749, 0.14976264224357363, 0.17102149233879566, 0.1840629776124617, 0.18770928509484297, 0.18185523345328541, 0.1674208686167368, 0.14618429400347427, 0.12052184642982773, 0.09309192063196292, 0.06650343186665982, 0.042997455199558936, 0.024191657069271778, 0.010919366364203527, 0.0031752966864726116, 0.00017246404820822292, 0.0005023509192567823, 0.002378437245966347, 0.003932845648378906, 0.003528194321469414, 4.3542575077476115e-05, -0.006904897594276132, -0.016841943385495196, -0.02843524134714769, -0.03963670628906594, -0.04795735145228144, -0.050852855643830734, -0.046190263712286524, -0.03275071478649725, -0.010714715537730648, 0.017927633470003965, 0.04909444576562455, 0.07652501718604135, 0.09191800026877973, 0.08530899292953248, 0.045690071993085835, -0.03814712369535062, -0.1765879311521243, -0.37807844034824684, -0.6479763431818316, -0.9874554937529602, -1.3925794213610134, -1.8536482235820058, -2.3548714077512125, -2.8744665750370495, -3.3853649014694533, -3.856227154917565, -4.252842319354698, -4.539948938753296, -4.683361959343498, -4.652303626839834, -4.421714352525814, -3.9746517235466987, -3.303937872841434, -2.4134024465586577, -1.3186676716439825, -0.0472769468107716, 1.3618970012248328, 2.8600227071250988, 4.390498183577608, 5.891880790227649, 7.3010889072050125, 8.556825249273912, 9.60306789293135, 10.392418360816913, 10.889246022506203, 11.072654244385346, 10.937739723783416, 10.49602564890416, 9.77502842363486, 8.816826064716913, 7.675680984490406, 6.414955685372645, 5.103441860676367, 3.810537310065066, 2.601481441603996, 1.5329627464826612, 0.6492310993956151, -0.021044797669689117, -0.466934790974081, -0.6963186809963927, -0.7357001849111761, -0.6285481307707476, -0.4323316667392502, -0.21445879580040406, -0.047366883098396345, -0.003061801645697279, -0.14739647782124374, -0.5345010861958331, -1.2018421364447882, -2.166283852980546, -3.421462133165433, -4.9366948602378535, -6.657547778961011, -8.508144875160724, -10.395255487857664, -12.2138257370713, -13.853741757247718, -15.207572243424755, -16.178405237367357, -16.687586636427717, -16.681768619488633, -16.138552885611453, -15.070547438862286, -13.527426788498916, -11.595784426402025, -9.396687889245515, -7.080666230181453, -4.820429097693782, -2.801726774408969, -1.2130353700846643, -0.23447112054059194, -0.026548164587406987, -0.7194455990507486, -2.4035218901262883, -5.1217777234111885, -8.864700721145834, -13.567844271751001, -19.11238568019261, -25.328747474021572, -32.0032195650701, -38.88807662489694, -45.71436541568861, -52.20450180401058, -58.086082896859665, -63.10594970251988, -67.04355592041053, -69.72296796145693, -71.0238521610721, -70.88861607224727, -69.32584149084506, -66.40870599579017, -62.27075815927131, -57.09876654901855, -51.12270355051495, -44.603983140483834, -37.82034159409743, -31.049888891943667, -24.55591710681083, -18.57154581455514, -13.286972566049979, -8.839487907248602, -5.306635046378135, -2.7025872437159584, -0.978557214581013, -0.027140237843292767, 0.309809387867452, 0.23012160688665398, -0.04229956594682601, -0.2727819820892743, -0.23191922333334555, 0.2886445104984614, 1.461551308625327, 3.411055888088605, 6.203247852893612, 9.839769417188576, 14.25557716785239, 19.320664216966577, 24.845536558789583, 30.590273520703207, 36.276681631661894, 41.603218553719636, 46.26288137126275, 49.961092015538085, 52.43175034411375, 53.45227564137031, 52.85679101088948, 50.546488792386086, 46.49663161476697, 40.760633805588654, 33.4716138785086, 24.834605754450877, 15.116741389821568, 4.635199036442987, -6.2572609250705025, -17.18841186139074, -27.78366910461181, -37.68348020954878, -46.55871231001693, -54.12620167659239, -60.16076347995076, -64.50373305507216, -67.06810988754448, -67.84053311248329, -66.87993457456119, -64.31118384843188, -60.316577442037115, -55.12515053254028, -49.000048771739806, -42.224884876443916, -35.089836673149804, -27.87793055842638, -20.852464420297242, -14.246510483951983, -8.25459031868169, -3.026588473318608, 1.3355569250206223, 4.778806023246154, 7.297356089048262, 8.927872564380811, 9.743397582074243, 9.846027063435091, 9.358823735456962, 8.417222893114776, 7.1607449170737105, 5.725065843577336, 4.2348799201629355, 2.7984705843208513, 1.5038014909840363, 0.4161778683885362, -0.4225454598760441, -0.9933518905020824, -1.2981452754210223, -1.3567269758416662, -1.203039446925347, -0.8810088868186697, -0.44028229580952716, 0.06787093065165893, 0.5943314556314444, 1.0952936269504774, 1.5345571127666078, 1.8850342036812582, 2.129448458496424, 2.2602732763427404, 2.279009564615762, 2.195004977109926, 2.023765634188803, 1.7849337325993653, 1.500323982561019, 1.1920717500477014, 0.8810009724358958, 0.5853031412931263, 0.3195932778079131, 0.0943222410602527, -0.08440795467458853, -0.21465406169221193, -0.2981403727123, -0.33955443364340254, -0.3457145922210913, -0.3246906787287885, -0.2849511310389579, -0.23461218125284297, -0.1808369001078131, -0.12940494347617051, -0.0844758330540581, -0.048535984061899594, -0.022504949985527878, -0.005977859396341165, 0.0024468125655467718, 0.0048009410130798675, 0.003380563891935199, 0.0004151945632769585, -0.002198873602212064, -0.003083125797063778, -0.0014665568513676668, 0.0028139003236505424, 0.009387454353399976, 0.017479942396594634, 0.026078897814848873, 0.03410960648640286, 0.040602437624792, 0.04482353017041481, 0.0463583796754509, 0.04514516899736983, 0.04145777445956598, 0.03584529545897162, 0.029040063966816618, 0.02184670522730945, 0.015024504296654712, 0.009188022135460704, 0.0047367279156304625, 0.0018204125094728673, 0.0003434252434865557, 5.5223728881519625e-06, 0.00037224977767375667, 0.0009641721087798888, 0.001350451737135571, 0.0012311690922664708, 0.0004948617771938318, -0.0007590923132512349, -0.002239189105941304, -0.003522286850244967, -0.004149871323961427, -0.0037487384612986106, -0.0021595384446248217, 0.0004457488094100197, 0.0034770699137125828, 0.005888851738271819, 0.006207719519792427, 0.002631971547429242, -0.006797410542775936, -0.02396175072437777, -0.050382641857533876, -0.086917340817272, -0.13346234189227962, -0.18870292915702622, -0.2499427215163374, -0.3130408080886505, -0.3724815170166652, -0.4215902125865161, -0.4528979902231848, -0.4586557578049608, -0.43146587068883363, -0.3649514594828942, -0.2544524374937511, -0.09768276428750902, 0.10471610109152692, 0.3487864680615047, 0.6270659328711568, 0.9286657583979274, 1.2396509158735145, 1.5436734760955224, 1.8228586434028142, 2.058906984628286, 2.2343546551553537, 2.333865118007507, 2.3454670942792655, 2.2616737392606656, 2.080373955291856, 1.8054144648642356, 1.4468039469587886, 1.020489360273351, 0.5475576181557424, 0.053009255373709305, -0.4356378648174142, -0.8900807444980815, -1.2831401058763643, -1.5907192575994868, -1.7936908293842502, -1.8797651784252896, -1.844719433914648, -1.6928887378936561, -1.4372982156547411, -1.0992181708600366, -0.7071294235851602, -0.29514001003747276, 0.0990664983848767, 0.43684853566200205, 0.6813361439599281, 0.8000363719682844, 0.7672414922011855, 0.5660847753142851, 0.19010778240726675, -0.35568760089202167, -1.054729930804764, -1.879647514566622, -2.7937211580652184, -3.752978544701948, -4.708801297937366, -5.610900498595701, -6.41058855309059, -7.064047230380166, -7.535177813757561, -7.797966138815384, -7.838232927459772, -7.654510925488289, -7.258144887368013, -6.672798949123915, -5.932702423058312, -5.08011486794778, -4.16237296521237, -3.2286261290419347, -2.326488157644139, -1.4987893985195597, -0.7807101481632472, -0.19765086005768234, 0.2361335112995938, 0.5180961113956676, 0.6571128658599352, 0.6723839928272762, 0.5916456256345307, 0.4489692509720608, 0.28177518795506407, 0.12725758362352327, 0.01882126785874835, -0.017124079693075098, 0.03630451392235797, 0.1850891321528745, 0.425726338554385, 0.7476129156498484, 1.134828309802455, 1.5678772046582865, 2.025296083911209], 'positive_zeros': ['0.34204834707887138799949925467727', '0.35169130766545429036568927327266', '0.75338268380273288994846534573602', '0.873822057349656624008884387723987', '1.36678845858280938826912420401107', '1.43757215197905116700486468789496', '1.47972338541580235422754902440262', '1.91119600244485999334217766605916', '1.98546723564408394121380620456821', '2.15756330160943100376000468339619', '2.17660335775675869784094409657856', '2.17677687779652228402065222306598', '2.25995878626728419718030403788249', '2.33651516849284271809292187031221', '2.41371966081223272242639332675306', '2.75131713674030097519448378644149', '2.84265920237594508674792660421011', '3.14119178614123357838605142706180', '3.14755882911110498273843616743247', '3.16936810715799331158382917919683', '3.18059585951141172184598278915638', '3.40537319376834261299344118881377', '3.40630547501026447624257053266031', '3.43566043374277552351188392069304', '3.75320897067519182747173004984789', '3.93927756871623078463662209014337', '4.12488680894187369611997215340984', '4.19042157806563526349719489177428', '4.32588279678546734717344980966546', '4.48445383698681709180413472505036', '4.53660559270539343346669981377842', '4.65732308723604154785255643208602', '4.68484316696547438128147266509453', '4.73474772549740485192416813519953', '4.79125151442604023245042200565827', '4.91370637756199033564322352477711', '4.91838261180442431730302125228928', '4.94626846915300455026515513030260', '5.19964099480412437751180263358635', '5.26832140116316583273203288118601', '5.59319404863814753206424202649517', '5.59590349200690638336022499284191', '5.61858089353086012755213700493800', '5.68248807870316830422451670137488', '5.84611087122032345307195353669578', '5.88875164885539569733987236704693', '5.97121923036487830064745367110566', '6.07385649387455849445724317849196', '6.23851949515265335598200283215943', '6.39564889153704908392412907398575', '6.44437371002927748019496787789076', '6.49697655073959609450608583920591', '6.68057311485731805435311437747290', '6.86559836332598586463346721843858', '6.93764564457216459236238502470545', '6.98015004168892720751281188725145', '7.06198957331507211452827745007017', '7.23962112203092582071172051827213', '7.24281537781091256121382202001287', '7.33009259371484456636303457079247', '7.45449487662231679895942417661300', '7.48630868532192889407489944523917', '7.49126400908310215419479802858916', '7.58819793376078127658295681259721', '7.64225282545585870761945626611517', '7.73541175356816709009287910830926', '7.85236135718373616006071895424694', '7.922318879497863688501989508852164', '7.936445552035025418717927714435143', '7.963859740913043842546921787914105', '8.461068250966191666386714341939612', '8.472475640258405937113208501865089', '8.539277637454586823114180111844595', '8.667756180408643802515503377018018', '8.674204149084784285894324916275758', '8.769684432833278011057139629083645', '8.823109206667194693202719294953888', '8.995875103157909156648558030439142', '9.076546363754481332859427693114398', '9.436159429142385511348501309755909'], 'prelabel': '16-3332e8-1.1-c0e8-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.289528837247606, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c0e8-0', 'trace_hash': 1008794948443345841, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.34204834707887138799949925468', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.35169130766545429036568927327', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.75338268380273288994846534574', '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': 58.46513229529397, 'bad_primes': [2, 7, 17], 'central_character': '1.1', 'conductor': 15192874202374507341482622976, 'conductor_radical': 238, 'degree': 16, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -8, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler11': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'euler13': [1, 8, 32, 88, 188, 328, 480, 600, 646, 600, 480, 328, 188, 88, 32, 8, 1], 'euler17': [1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler19': [1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'euler29': [1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'euler31': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'euler37': [1, 8, 28, 56, 70, 56, 28, 8, 2, 8, 28, 56, 70, 56, 28, 8, 1], 'euler41': [1, -8, 28, -56, 70, -56, 28, -8, 2, -8, 28, -56, 70, -56, 28, -8, 1], 'euler43': [1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1], 'euler47': [1, 0, 0, 0, 4, 0, 0, 0, 6, 0, 0, 0, 4, 0, 0, 0, 1], 'euler5': [1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1], 'euler53': [1, 0, 4, 0, 8, 0, 12, 0, 14, 0, 12, 0, 8, 0, 4, 0, 1], 'euler59': [1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1], 'euler61': [1, 8, 28, 56, 70, 56, 28, 8, 2, 8, 28, 56, 70, 56, 28, 8, 1], 'euler67': [1, 0, 8, 0, 28, 0, 56, 0, 70, 0, 56, 0, 28, 0, 8, 0, 1], 'euler7': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler71': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'euler73': [1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1], 'euler79': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], 'euler83': [1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1], 'euler89': [1, 0, 0, 0, 4, 0, 0, 0, 6, 0, 0, 0, 4, 0, 0, 0, 1], 'euler97': [1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 8, 32, 88, 188, 328, 480, 600, 646, 600, 480, 328, 188, 88, 32, 8, 1], [1, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 8, 28, 56, 70, 56, 28, 8, 2, 8, 28, 56, 70, 56, 28, 8, 1], [1, -8, 28, -56, 70, -56, 28, -8, 2, -8, 28, -56, 70, -56, 28, -8, 1], [1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 4, 0, 0, 0, 6, 0, 0, 0, 4, 0, 0, 0, 1], [1, 0, 4, 0, 8, 0, 12, 0, 14, 0, 12, 0, 8, 0, 4, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1], [1, 8, 28, 56, 70, 56, 28, 8, 2, 8, 28, 56, 70, 56, 28, 8, 1], [1, 0, 8, 0, 28, 0, 56, 0, 70, 0, 56, 0, 28, 0, 8, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 1], [1, 0, 0, 0, 4, 0, 0, 0, 6, 0, 0, 0, 4, 0, 0, 0, 1], [1, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 2, 0, 0, 0, 1]], 'index': 4, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3332/1/bn/b'], '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': '16-3332e8-1.1-c0e8-0-4', '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}], 'nu_real_doubled': [0, 0, 0, 0, 0, 0, 0, 0], 'order_of_vanishing': 0, 'prelabel': '16-3332e8-1.1-c0e8-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.289528837247606, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e8-0', 'trace_hash': 1008794948443345841, 'z1': {'__RealLiteral__': 0, 'data': '0.34204834707887138799949925468', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '433597792481605051857145456918,445821697257164027114719767581,955026011324088708605183788157,1107701055491958514382366695096,1732610209907514782599944362720,1822339201327631631138923432770,1875772237694089486452089113159,2422728759653019357257089636012', 'Lhash_array': ['433597792481605051857145456918', '445821697257164027114719767581', '955026011324088708605183788157', '1107701055491958514382366695096', '1732610209907514782599944362720', '1822339201327631631138923432770', '1875772237694089486452089113159', '2422728759653019357257089636012'], 'label': '16-3332e8-1.1-c0e8-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3332/1/bn/b'}