-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '49027054088937242156286636113,1608353312980992110382815321440', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': -2, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 17, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1825.4175458562395, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1]]], 'bad_primes': [2, 7], 'central_character': '1568.1', 'coefficient_field': '1.1.1.1', 'conductor': 2458624, 'conductor_radical': 14, 'degree': 4, 'euler_factors': [[1], [1, 0, -17, 0, 81], [1, 2, 51, 50, 625], [1], [1, 0, 47, 0, 14641], [1, 48, 914, 8112, 28561], [1, 2, 579, 578, 83521], [1, 0, -673, 0, 130321], [1, 0, -1009, 0, 279841], [1, -48, 2258, -40368, 707281], [1, 0, -241, 0, 923521], [1, 98, 5139, 134162, 1874161], [1, -96, 5666, -161376, 2825761], [1, 0, -3122, 0, 3418801], [1, 0, -1393, 0, 4879681], [1, 50, 6243, 140450, 7890481], [1, 0, -6673, 0, 12117361], [1, -2, 7443, -7442, 13845841], [1, 0, -4753, 0, 20151121], [1, 0, -866, 0, 25411681], [1, 190, 19683, 1012510, 28398241], [1, 0, -10801, 0, 38950081], [1, 0, -8594, 0, 47458321], [1, 190, 24867, 1504990, 62742241], [1, 288, 39554, 2709792, 88529281], [1, 146, 25731, 1489346, 104060401], [1, 0, -13297, 0, 112550881], [1, 0, 11327, 0, 131079601], [1, 142, 28803, 1687102, 141158161], [1, -192, 34754, -2451648, 163047361]], 'euler_factors_factorization': [[1], [[[1, 0, -17, 0, 81], 1]], [[[1, 1, 25], 2]], [1], [[[1, 0, 47, 0, 14641], 1]], [[[1, 24, 169], 2]], [[[1, 1, 289], 2]], [[[1, 0, -673, 0, 130321], 1]], [[[1, 0, -1009, 0, 279841], 1]], [[[1, -24, 841], 2]], [[[1, 0, -241, 0, 923521], 1]], [[[1, 49, 1369], 2]], [[[1, -48, 1681], 2]], [[[1, 0, -3122, 0, 3418801], 1]], [[[1, 0, -1393, 0, 4879681], 1]], [[[1, 25, 2809], 2]], [[[1, 0, -6673, 0, 12117361], 1]], [[[1, -1, 3721], 2]], [[[1, 0, -4753, 0, 20151121], 1]], [[[1, 0, -866, 0, 25411681], 1]], [[[1, 95, 5329], 2]], [[[1, 0, -10801, 0, 38950081], 1]], [[[1, 0, -8594, 0, 47458321], 1]], [[[1, 95, 7921], 2]], [[[1, 144, 9409], 2]], [[[1, 73, 10201], 2]], [[[1, 0, -13297, 0, 112550881], 1]], [[[1, 0, 11327, 0, 131079601], 1]], [[[1, 71, 11881], 2]], [[[1, -96, 12769], 2]]], 'gamma_factors': [[], [0, 0]], 'group': 'GL2', 'index': 0, 'label': '4-1568e2-1.1-c2e2-0-0', 'leading_term': '0.0203750004712529265641106594871107986840365180624562158283071458621547698037494666101403989', 'load_key': 'CMFs-workshop', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2, 2], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1568/3/d/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.029296875', 'prec': 37}, 'plot_values': [0.020375000471252926, 0.008557139214913717, -0.026292688902574773, -0.08410957835425793, -0.16421555987912925, -0.2656251905560068, -0.3871932192470986, -0.5275411320788734, -0.6850310858057542, -0.8577984827953837, -1.043767552939863, -1.2406632164534792, -1.446024968304437, -1.6572291092866316, -1.871510299165239, -2.085986435945149, -2.297689306484663, -2.503591996799845, -2.700650103977423, -2.885829186913713, -3.05615808046053, -3.2087533199569904, -3.340884946521852, -3.4499942435047037, -3.5337714797618065, -3.5901628839547657, -3.617458433556275, -3.6142839473229045, -3.5796956936532673, -3.513153804746007, -3.414619197355328, -3.2845052752478736, -3.123771629977093, -2.9338521970485147, -2.7167395880194514, -2.4748894689361562, -2.2112893172080796, -1.9293407140518428, -1.6329069246759134, -1.3261769080566312, -1.0136874339910575, -0.7001747359958761, -0.3905688756673859, -0.0898408848489918, 0.19703034572891062, 0.46520610315175837, 0.7100452241463542, 0.9272371576309044, 1.112877346570768, 1.2635752074255535, 1.3765384716349134, 1.44964702492288, 1.4815349522768375, 1.471623296510403, 1.4201872857801832, 1.3283441995468592, 1.1980932234092239, 1.0322585762773195, 0.8344908206976672, 0.6091699074654288, 0.36135961483838613, 0.09667979448583695, -0.17879020780975102, -0.458656560729204, -0.7363574911737006, -1.005308638433083, -1.2590927701927885, -1.4915866086910954, -1.697181276838292, -1.8708715735011623, -2.0084898517362912, -2.1067406463337064, -2.1634273324803135, -2.177419057144721, -2.148848293811055, -2.0790029956671634, -1.9704744859152803, -1.8269751662175757, -1.6534202307134576, -1.4556794148835193, -1.2405826349029188, -1.0156222487786264, -0.7888813876293973, -0.5687100225826602, -0.36358462299190164, -0.18178599671657975, -0.031208867048229876, 0.0809288526249711, 0.14829919474317219, 0.16569560826190527, 0.12923511324718287, 0.036508233425859335, -0.11326629828104859, -0.3191864992705048, -0.5785948097197624, -0.887119764054322, -1.2387148465587252, -1.6257857849103239, -2.0393589969809724, -2.469270687972001, -2.9044695483109764, -3.333233000609005, -3.7435931850874886, -4.123538409980793, -4.461535847784321, -4.7466738428960085, -4.96924121516362, -5.120769398107681, -5.194618799158536, -5.185888907092361, -5.0919584094045165, -4.912245747297284, -4.648652612795363, -4.3051754812331975, -3.8882118261394405, -3.406042791489018, -2.868977140889722, -2.2887438796015274, -1.678468843344062, -1.0520310689192642, -0.42388852290586926, 0.19153905641750582, 0.7801584421165633, 1.3287297831721505, 1.825215950317908, 2.2591628004153588, 2.622047383287831, 2.9074710418486545, 3.1114436425877168, 3.232371297780453, 3.2712223607542024, 3.231317793163236, 3.118341691379606, 2.939968932334024, 2.70570634411836, 2.4264154081496527, 2.113996594310038, 1.7808809655840452, 1.4395956929499043, 1.102304596410576, 0.7803133296263304, 0.4837336990362388, 0.22099887068818222, -0.0012901178998046862, -0.1787679785078985, -0.30924381778709437, -0.39296352280981545, -0.4323325320869685, -0.4319988183085864, -0.3983915857536048, -0.3396164372721357, -0.26487071486906494, -0.18417557440083046, -0.10774885332659116, -0.04562991668441359, -0.007098635169942469, -0.0002725665196683153, -0.03165394451138394, -0.10579043100696274, -0.22501129301051234, -0.3892397171982968, -0.5959472896058524, -0.8401871581071207, -1.114757306412363, -1.4104917522744347, -1.7165841204587666, -2.021133121410361, -2.3115452362303217, -2.5752873651262753, -2.800267055265109, -2.975706795530033, -3.0923964300461124, -3.1435771761603593, -3.1249753597690395, -3.0355753770396183, -2.8773752708572884, -2.655939444679219, -2.3798604236547747, -2.0610137195518066, -1.7137594416156563, -1.354869339493111, -1.0025483561182191, -0.6760604798485712, -0.39468540976985755, -0.17712628130678632, -0.04053332622050149, 0.0001769793105626894, -0.06689474551324559, -0.2500187133124491, -0.5533426980618193, -0.9765091619589087, -1.5145007598998792, -2.157623255714087, -2.891678089184432, -3.6983993501670964, -4.555879268492821, -5.43948152811641, -6.322392191720993, -7.176958291681817, -7.975202626511105, -8.690468019750591, -9.297727018272601, -9.775360409694395, -10.105115177787741, -10.273820394296076, -10.272896742775643, -10.09981912194539, -9.75715142467617, -9.253603088355376, -8.602642290025186, -7.823057595682265, -6.937277699375395, -5.971428737050818, -4.953545622946607, -3.9131968431978663, -2.8798003523244797, -1.8819563381420348, -0.9460732736501929, -0.09559273788080969, 0.6499115767000786, 1.2754225934667636, 1.770817024618631, 2.131298423602101, 2.3571688928064267, 2.453893437414793, 2.4313955957364786, 2.3037168770771532, 2.0880022195950416, 1.803801078428546, 1.471956459899673, 1.1136669027240753, 0.7495027909111861, 0.39839660171425423, 0.07697992015499279, -0.2013169630809742, -0.42647920444150494, -0.5925412767497998, -0.6973124353813169, -0.7426440169179566, -0.7337209148119056, -0.6789413686673907, -0.5889117021058861, -0.4760025654712609, -0.3532384941453972, -0.23366741375875988, -0.12935168227614627, -0.050732538116181315, -0.005901910589382998, -0.00014981417382551926, -0.035631626305008726, -0.11125142858329598, -0.22275067716568211, -0.36301011621941964, -0.5224911234388561, -0.6899468941370197, -0.8530672189714359, -0.9994952834493286, -1.1174777547116044, -1.1970073675845752, -1.2302742534150004, -1.2127142433050742, -1.1430967971497095, -1.0242655898784925, -0.8627759098210647, -0.6691690203400428, -0.4571716679005775, -0.24343999050325277, -0.04643449265943919, 0.11431504797642822, 0.2194665499231114, 0.2509148098058679, 0.19294880663961586, 0.03336335972181175, -0.2357028844566522, -0.6168845985592307, -1.107227756665187, -1.6978080736242946, -2.373898754788393, -3.1152858001451036, -3.8968971975447153, -4.689888269538791, -5.4625485681138715, -6.182085481682667, -6.815542349122212, -7.332069833943087, -7.703559015730621, -7.907086466629502, -7.924999198305466, -7.747173773912154, -7.370382772234513, -6.800032297292059, -6.048775743337092, -5.137485271500162, -4.093231549553842, -2.949386547964226, -1.743226011144531, -0.5152255398719348, 0.6933641671078987, 1.8418118871417846, 2.891981193473959, 3.8098880808795346, 4.567098822802774, 5.142177810546871, 5.521196795625186, 5.698731363207417, 5.677433671190803, 5.4683377566863625, 5.089625053847256, 4.566149813436374, 3.927681260273487, 3.2077286185994436, 2.4416430110509415, 1.6649706318104953, 0.9118196232590647, 0.21306734217913206, -0.4046632557300068, -0.9205919312594696, -1.3199822971802009, -1.5952293187416962, -1.7451998827568678, -1.775643041627647, -1.6978127848566003, -1.5281831929477463, -1.2866438706147223, -0.995662962900084, -0.6784279968353161, -0.35772533130107875, -0.054398038986642215, 0.21372875795463298, 0.43278531047259144, 0.5935751645028942, 0.6917678056156851, 0.7280431726918412, 0.7075767169243169, 0.6395416173510116, 0.5360894607741709, 0.41130727313388, 0.28001312291237435, 0.15640870748062108, 0.05304806323590722, -0.020488561395112376, -0.058142365201461314, -0.058351764062682616, -0.023928907700464134, 0.03756188589539153, 0.1146173488179428, 0.19211068517033045, 0.2526393337097169, 0.27744648842583397, 0.2480125902673288, 0.1473214006005315, -0.038658424975918794, -0.3197438468011474, -0.700491884589987, -1.179420780308593, -1.7486128931729228, -2.393733997821521, -3.0943230474903856, -3.8248016820260267, -4.555296579990177, -5.2536197064481485, -5.886305513180568, -6.421322503602252, -6.828915914412896, -7.0846347316992695, -7.169577304343023, -7.073228818930492, -6.792815988808492, -6.335473057531396, -5.716600750813933, -4.961013383238231, -4.1004244159641985, -3.173446060145089, -2.2225355848895436, -1.2929739803312368, -0.42975151101129766, 0.3241145289733066, 0.9302375977292944, 1.3566878771202118, 1.5797565333961716, 1.585365491215809, 1.3696871874140186, 0.9396619346160094, 0.3124733382610535, -0.48511026551177155, -1.418145203449075, -2.4453722099211763, -3.5210444652143624, -4.597749420104391, -5.628085543443223, -6.567998131865599, -7.377760901376206, -8.025272752420602, -8.485952900294457, -8.745468662003715, -8.79839826719102, -8.650004049082007, -8.313799010529474, -7.812209160173096, -7.173432340672423, -6.431091024244808, -5.620935124336241, -4.779808844663543, -3.9427843793277146, -3.141899039867079, -2.40420575294985, -1.7507481944786005, -1.1958016701486955, -0.74644387911345, -0.40298813907478276, -0.15930650866843996, -0.00419290739876793, 0.07764192985017473, 0.10373259119366517, 0.09248223973189247, 0.06137988730248719, 0.02565653618191244, -0.00297204637024144, -0.0171968300320792, -0.014552583797443593, 0.0024441536787017477, 0.02672882497431609, 0.04739428498293907, 0.05079919266760698, 0.021958467698806394, -0.05405333674864992, -0.19040237290343728, -0.39724755860897215, -0.6802326134292963, -1.0397826208994838, -1.4702827208715097, -1.9601310607231566, -2.491957533694201, -3.0434001333378555, -3.588471818369509, -4.098782430788852, -4.545873884720093, -4.902434394775919, -5.145166908867929, -5.255488772711196, -5.222345305595176, -5.0419767581011365, -4.720083513992599, -4.270455428634514, -3.7160453830516005, -3.086541072011329, -2.418176737221883, -1.7506095951105836, -1.1256290285240562, -0.5839020011677578, -0.16304090857539344, 0.10515434588003396, 0.19661401342751958, 0.09673163390850105, -0.19842143570064477, -0.6816720003288236, -1.3347791920274137, -2.129273793966751, -3.0279989469710804, -3.9868340491110374, -4.957637330387098, -5.8902271827611825, -6.736275732366789, -7.450825296945459, -7.996441332993306, -8.343630572729698, -8.474490112159696, -8.381650214357833, -8.070774806928359, -7.558015102189669, -6.87099722712507, -6.045152124519605, -5.123197597974001, -4.151008117287425, -3.175965600744376, -2.243171152496302, -1.393305877396642, -0.6599264650102503, -0.06757408518274723, 0.3693507365159221, 0.6475923160479403, 0.7744621207230628, 0.7675863196695586, 0.6529046589810216, 0.46315891623187916, 0.23507799182355021, 0.00697175709394184, -0.18411581559902598, -0.30507558743122315, -0.32886057340459995, -0.23669132874665172, -0.01893603250035195, 0.3237688269023188, 0.7810561764707812, 1.3331349679187487, 1.9525230746341165, 2.605748553570642, 3.255727167273639, 3.8644474020440547, 4.395285568315813, 4.816006626701305, 5.100306124479247, 5.2303498348654465, 5.197162652776731, 5.002010866665223, 4.655393002438726, 4.177363432928964, 3.5953429252507285, 2.9406573006821515, 2.2482892675320048, 1.563278736296918, 0.9256769547160223], 'positive_zeros': ['0.03867552626891854107382691626427', '1.26876705039339875343631158994697', '1.79748825101306848895504491385160', '2.52668993365403805641694438733238', '2.67428628889902789518317161806796', '3.53569745841225698389206515270620', '4.18926273854097998308499131918131', '4.55318899343814814947202738878149', '4.56957747946361817481303712848331', '5.44252710686740174706948520645845', '5.44964170641966762550519063799242', '6.39024359585340319699812337715991', '6.83378794036345885091336655282892', '7.24493519917293213811890555274053', '7.26532360147701610936480437098660', '7.82994512642282414238231101193211', '7.973158524482111106585256454299281', '8.684249048673170416666209227501575', '9.208845359957239238337697286014637', '9.585671589860434202168201371447229'], 'prelabel': '4-1568e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.536429105535725, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c2e2-0', 'trace_hash': 2191433870743197898, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.03867552626891854107382691626', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.26876705039339875343631158995', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.79748825101306848895504491385', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1825.4175458562395, 'bad_primes': [2, 7], 'central_character': '1.1', 'conductor': 2458624, 'conductor_radical': 14, 'degree': 4, 'dirichlet_coefficients': [1, 0, 0, 0, -2, 0, 0, 0, 17, 0, 0, 0, -48, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 0, -47, 0, 0, 0, 48, 0, 0, 0, 0, 0, 0, 0, -98, 0, 0, 0, 96, 0, 0, 0, -34, 0, 0, 0, 0, 0, 0, 0, -50, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 96, 0, 0, 0, 0, 0, 0, 0, -190, 0, 0, 0, 0, 0, 0, 0, 208, 0, 0, 0, 4, 0, 0, 0, -190, 0, 0, 0, 0, 0, 0, 0, -288, 0, 0, 0], 'euler11': [1, 0, 47, 0, 14641], 'euler13': [1, 48, 914, 8112, 28561], 'euler17': [1, 2, 579, 578, 83521], 'euler19': [1, 0, -673, 0, 130321], 'euler2': [1, 0, 0, 0, 0], 'euler23': [1, 0, -1009, 0, 279841], 'euler29': [1, -48, 2258, -40368, 707281], 'euler3': [1, 0, -17, 0, 81], 'euler31': [1, 0, -241, 0, 923521], 'euler37': [1, 98, 5139, 134162, 1874161], 'euler41': [1, -96, 5666, -161376, 2825761], 'euler43': [1, 0, -3122, 0, 3418801], 'euler47': [1, 0, -1393, 0, 4879681], 'euler5': [1, 2, 51, 50, 625], 'euler53': [1, 50, 6243, 140450, 7890481], 'euler59': [1, 0, -6673, 0, 12117361], 'euler61': [1, -2, 7443, -7442, 13845841], 'euler67': [1, 0, -4753, 0, 20151121], 'euler7': [1, 0, 0, 0, 0], 'euler71': [1, 0, -866, 0, 25411681], 'euler73': [1, 190, 19683, 1012510, 28398241], 'euler79': [1, 0, -10801, 0, 38950081], 'euler83': [1, 0, -8594, 0, 47458321], 'euler89': [1, 190, 24867, 1504990, 62742241], 'euler97': [1, 288, 39554, 2709792, 88529281], 'euler_factors': [[1, 0, 0, 0, 0], [1, 0, -17, 0, 81], [1, 2, 51, 50, 625], [1, 0, 0, 0, 0], [1, 0, 47, 0, 14641], [1, 48, 914, 8112, 28561], [1, 2, 579, 578, 83521], [1, 0, -673, 0, 130321], [1, 0, -1009, 0, 279841], [1, -48, 2258, -40368, 707281], [1, 0, -241, 0, 923521], [1, 98, 5139, 134162, 1874161], [1, -96, 5666, -161376, 2825761], [1, 0, -3122, 0, 3418801], [1, 0, -1393, 0, 4879681], [1, 50, 6243, 140450, 7890481], [1, 0, -6673, 0, 12117361], [1, -2, 7443, -7442, 13845841], [1, 0, -4753, 0, 20151121], [1, 0, -866, 0, 25411681], [1, 190, 19683, 1012510, 28398241], [1, 0, -10801, 0, 38950081], [1, 0, -8594, 0, 47458321], [1, 190, 24867, 1504990, 62742241], [1, 288, 39554, 2709792, 88529281]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1568/3/d/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': '4-1568e2-1.1-c2e2-0-0', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2, 2], 'order_of_vanishing': 0, 'prelabel': '4-1568e2-1.1-c2e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 6.536429105535725, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c2e2-0', 'trace_hash': 2191433870743197898, 'z1': {'__RealLiteral__': 0, 'data': '0.03867552626891854107382691626', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '49027054088937242156286636113,1608353312980992110382815321440', 'Lhash_array': ['49027054088937242156286636113', '1608353312980992110382815321440'], 'label': '4-1568e2-1.1-c2e2-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1568/3/d/c'}