Lfunction data - 8-8512e4-1.1-c1e4-0-5

Formats: - HTML - YAML - JSON - 2025-02-11T14:09:13.615313

• 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': '1547433270503185949882168500654,1576301040883079164918756193779,1595678442112843546510195804262,2427652931508709565751442899614', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 4, 'a8': 0, 'a9': -5, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 21341988.809966147, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [7, [1, -4, 6, -4, 1]], [19, [1, 4, 6, 4, 1]]], 'bad_primes': [2, 7, 19], 'central_character': '8512.1', 'coefficient_field': '1.1.1.1', 'conductor': 5249602982772736, 'conductor_radical': 266, 'degree': 8, 'euler_factors': [[1], [1, -2, 9, -12, 35, -36, 81, -54, 81], [1, 0, 12, 4, 77, 20, 300, 0, 625], [1, -4, 6, -4, 1], [1, -2, 41, -64, 661, -704, 4961, -2662, 14641], [1, 0, 36, -12, 597, -156, 6084, 0, 28561], [1, 6, 55, 240, 1363, 4080, 15895, 29478, 83521], [1, 4, 6, 4, 1], [1, -4, 62, -208, 2083, -4784, 32798, -48668, 279841], [1, 2, 73, -20, 2329, -580, 61393, 48778, 707281], [1, 18, 191, 1548, 9967, 47988, 183551, 536238, 923521], [1, -16, 214, -1824, 12995, -67488, 292966, -810448, 1874161], [1, 10, 149, 1044, 9119, 42804, 250469, 689210, 2825761], [1, 4, 136, 564, 7982, 24252, 251464, 318028, 3418801], [1, 4, 100, 236, 5869, 11092, 220900, 415292, 4879681], [1, 10, 149, 1160, 12025, 61480, 418541, 1488770, 7890481], [1, 4, 164, 276, 11933, 16284, 570884, 821516, 12117361], [1, -16, 268, -2708, 24829, -165188, 997228, -3631696, 13845841], [1, 10, 63, 500, 6785, 33500, 282807, 3007630, 20151121], [1, -4, 186, -648, 16883, -46008, 937626, -1431644, 25411681], [1, 18, 241, 2728, 28175, 199144, 1284289, 7002306, 28398241], [1, -4, 232, -1028, 24574, -81212, 1447912, -1972156, 38950081], [1, 14, 143, 444, 2903, 36852, 985127, 8005018, 47458321], [1, 24, 324, 2760, 23334, 245640, 2566404, 16919256, 62742241], [1, 16, 292, 2196, 28373, 213012, 2747428, 14602768, 88529281], [1, 0, 396, -4, 59597, -404, 4039596, 0, 104060401], [1, 4, 212, 1948, 23085, 200644, 2249108, 4370908, 112550881], [1, -16, 378, -4624, 57275, -494768, 4327722, -19600688, 131079601], [1, -28, 614, -8776, 108315, -956584, 7294934, -36260812, 141158161], [1, 34, 781, 12296, 150217, 1389448, 9972589, 49058498, 163047361]], 'euler_factors_factorization': [[1], [[[1, -2, 9, -12, 35, -36, 81, -54, 81], 1]], [[[1, 0, 12, 4, 77, 20, 300, 0, 625], 1]], [[[1, -1], 4]], [[[1, -2, 41, -64, 661, -704, 4961, -2662, 14641], 1]], [[[1, 0, 36, -12, 597, -156, 6084, 0, 28561], 1]], [[[1, 6, 55, 240, 1363, 4080, 15895, 29478, 83521], 1]], [[[1, 1], 4]], [[[1, -2, 29, -46, 529], 2]], [[[1, 2, 73, -20, 2329, -580, 61393, 48778, 707281], 1]], [[[1, 18, 191, 1548, 9967, 47988, 183551, 536238, 923521], 1]], [[[1, -16, 214, -1824, 12995, -67488, 292966, -810448, 1874161], 1]], [[[1, 10, 149, 1044, 9119, 42804, 250469, 689210, 2825761], 1]], [[[1, 4, 136, 564, 7982, 24252, 251464, 318028, 3418801], 1]], [[[1, 4, 100, 236, 5869, 11092, 220900, 415292, 4879681], 1]], [[[1, 10, 149, 1160, 12025, 61480, 418541, 1488770, 7890481], 1]], [[[1, 4, 164, 276, 11933, 16284, 570884, 821516, 12117361], 1]], [[[1, -16, 268, -2708, 24829, -165188, 997228, -3631696, 13845841], 1]], [[[1, 10, 63, 500, 6785, 33500, 282807, 3007630, 20151121], 1]], [[[1, -4, 186, -648, 16883, -46008, 937626, -1431644, 25411681], 1]], [[[1, 18, 241, 2728, 28175, 199144, 1284289, 7002306, 28398241], 1]], [[[1, -4, 232, -1028, 24574, -81212, 1447912, -1972156, 38950081], 1]], [[[1, 14, 143, 444, 2903, 36852, 985127, 8005018, 47458321], 1]], [[[1, 24, 324, 2760, 23334, 245640, 2566404, 16919256, 62742241], 1]], [[[1, 16, 292, 2196, 28373, 213012, 2747428, 14602768, 88529281], 1]], [[[1, 0, 396, -4, 59597, -404, 4039596, 0, 104060401], 1]], [[[1, 4, 212, 1948, 23085, 200644, 2249108, 4370908, 112550881], 1]], [[[1, -16, 378, -4624, 57275, -494768, 4327722, -19600688, 131079601], 1]], [[[1, -28, 614, -8776, 108315, -956584, 7294934, -36260812, 141158161], 1]], [[[1, 34, 781, 12296, 150217, 1389448, 9972589, 49058498, 163047361], 1]]], 'gamma_factors': [[], [0, 0, 0, 0]], 'group': 'GL2', 'index': 5, 'label': '8-8512e4-1.1-c1e4-0-5', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, '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}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 4, 'origin': 'ModularForm/GL2/Q/holomorphic/8512/2/a/bv', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.01171875', 'prec': 34}, 'plot_values': [-7.351884716096771e-240, 9.126111028671912e-06, 0.00014589574584321653, 0.000737568418081228, 0.002326533889658475, 0.005665757203746226, 0.011712371238982801, 0.02161946951785494, 0.03672615794699205, 0.05854581533775109, 0.08875224176621631, 0.12916443462413082, 0.18172987605807614, 0.2485059354736789, 0.33163834806276526, 0.4333399904538322, 0.5558685081322552, 0.7015016467564209, 0.8725081293653443, 1.0711226109057737, 1.2995197068593354, 1.559784898938866, 1.853878915400397, 2.183612343012166, 2.55061923676337, 2.9563265225400173, 3.4019148946300413, 3.8882975529753088, 4.416097578947864, 4.985620278051195, 5.596816196539775, 6.249268618267922, 6.942179403706188, 7.67435009649206, 8.444155368242718, 9.249542797378378, 10.088031478369336, 10.956708420468193, 11.852222711690093, 12.77079845547505, 13.708248840406055, 14.65999382875394, 15.621085654405892, 16.586231695982146, 17.549823757135915, 18.505980886268365, 19.448614754755187, 20.371454225451963, 21.268085594603818, 22.13202058493623, 22.956805461181542, 23.736034105320016, 24.463390611676598, 25.132737557790534, 25.738265910005094, 26.27447989447998, 26.73622970583331, 27.118810126826308, 27.418140649265148, 27.630704782177684, 27.75355901189218, 27.78442812719248, 27.721898409803924, 27.565297395456415, 27.314666737183046, 26.970839627922583, 26.53562641864541, 26.01162863440465, 25.40216859368135, 24.711337075781366, 23.94415184194383, 23.106311162947712, 22.20408153210331, 21.244310247506505, 20.234543485143274, 19.182737702110334, 18.097117016202727, 16.986154512694693, 15.858646698993107, 14.723412858835744, 13.589143154868468, 12.464361949262088, 11.357467137815322, 10.27645441674941, 9.228782972245481, 8.221341012845862, 7.260468190096585, 6.351740967059817, 5.499882400603361, 4.708751725215468, 3.9813724349642614, 3.3198053195729913, 2.7251212061088137, 2.197431314637435, 1.7359404723244656, 1.338917124114772, 1.003733943189498, 0.7269442980429812, 0.5043696034234268, 0.33115447426883843, 0.20186302171742193, 0.11059186906585333, 0.051085536309335065, 0.01684547404248684, 0.0012544199053940912, -0.002297562153376479, -0.00029070690073829835, 0.0010442898837482986, -0.0041576704336080085, -0.021288667013233512, -0.05516871557270602, -0.1099580875647144, -0.18908431783281757, -0.29518364868249014, -0.43005500741772656, -0.594634429989203, -0.7889873404653197, -1.012317375012583, -1.2629913354753641, -1.538582978577475, -1.8359322897175203, -2.1512208859932023, -2.4800658599995895, -2.8176147236821447, -3.1586512077897457, -3.49771546967762, -3.829242737241012, -4.147671514986944, -4.447559103898821, -4.723709522413687, -4.971316840495084, -5.186042205475821, -5.364098071279841, -5.502343192600335, -5.598387173610478, -5.65060166664202, -5.6581426657979454, -5.620982528846714, -5.53994412600958, -5.4166350827219505, -5.253399613379293, -5.053279471241476, -4.819970071417527, -4.557695780883662, -4.271109036745301, -3.965197924673104, -3.6451845344849105, -3.3163830421574128, -2.9840843492549687, -2.6534479026516116, -2.329383709534566, -2.016443509559865, -1.7187354005555842, -1.4398432804291459, -1.1827395431203958, -0.9497485329812982, -0.7425241805179194, -0.5620289021103114, -0.40851084337629856, -0.28155129463508105, -0.18011288472061654, -0.10258472253771499, -0.046830627186426096, -0.010298645588258205, 0.009882294915030974, 0.01681289112607906, 0.01372851542125752, 0.0038752368730734193, -0.009591843699333101, -0.023700545113634345, -0.03575834121448513, -0.04343666556164038, -0.044830975577835004, -0.03851139017105277, -0.023575572964661794, 0.00034398970435493717, 0.03309049400427922, 0.07399889590234672, 0.12191166158684007, 0.17525186296567324, 0.23210130662156697, 0.2902771360759323, 0.3474069111247549, 0.40104850604327913, 0.448800388590525, 0.48840161021423995, 0.5178250541011006, 0.5353875055910509, 0.5398386315713031, 0.5304318703003426, 0.5069810886787297, 0.4699066252222577, 0.42025579970926474, 0.35970150616247265, 0.2905211054071318, 0.21555263746708583, 0.13812926723127478, 0.06199443327852979, -0.008800809132400734, -0.07001488693057753, -0.11734436545836104, -0.14656177409554133, -0.15365798115987322, -0.13497983207351247, -0.08736634386145152, -0.008277247642169298, 0.10409894423675205, 0.2507507668419203, 0.4317632843993353, 0.6462662328924743, 0.8924352580240663, 1.1674831034999102, 1.4676742771818283, 1.788390174177974, 2.124279726443576, 2.469330117358634, 2.8169697011628294, 3.1602407763194753, 3.4920814704172995, 3.8054186399975434, 4.093304042247579, 4.3491353208339545, 4.566994736968117, 4.741678184514566, 4.8687843098194, 4.944898407651527, 4.967886739122173, 4.936787940245815, 4.851787922348859, 4.714294989038873, 4.527106550636444, 4.29414221326915, 4.020286735159377, 3.711334666861684, 3.3740040102784485, 3.0155626117938237, 2.643586174598903, 2.2658151341134487, 1.8900614736161745, 1.5238377406947514, 1.1741257314552718, 0.8472354653172873, 0.5487017388535789, 0.28303739566239455, 0.05361400787297132, -0.13738338066374817, -0.28897177821912234, -0.4014155082246442, -0.4761771747052935, -0.5158192816082211, -0.5238853291406848, -0.5047513831208702, -0.4634304556194464, -0.40535887557465555, -0.33617803843236466, -0.261487202482962, -0.18659772186665194, -0.11630186427690391, -0.05465977729688523, -0.0047945595740959196, 0.03127471514412238, 0.05275968560065704, 0.06018893553897839, 0.05545046385174896, 0.041781332578653844, 0.02370691622279831, 0.0069310322318911705, -0.0018229628795831314, 0.004984804170811697, 0.035469046791220406, 0.09804704842104474, 0.20114224808737374, 0.35287031110931705, 0.5607214863306454, 0.8312650007467898, 1.169849618241501, 1.5803215935432953, 2.064792688430851, 2.6235122007812204, 3.2546963597618643, 3.9544103490833984, 4.7165643033042866, 5.533108000059483, 6.394040098350744, 7.28750358164098, 8.200059118662292, 9.117241351587362, 10.023677406986957, 10.903328187085421, 11.739963172728572, 12.517971049261046, 13.222418578110771, 13.839279217822282, 14.355937629593493, 14.762041122073716, 15.049313011256366, 15.211596603099592, 15.245202549155547, 15.149575980653266, 14.92676277347318, 14.581175147553024, 14.119672813862458, 13.551912942660564, 12.889520067347432, 12.145615174744625, 11.334655851746204, 10.472488069606413, 9.575417374731614, 8.659668131851198, 7.741129766382718, 6.835263336517619, 5.956335789693982, 5.117022366974773, 4.3282497018026875, 3.599155954050593, 2.9366917282351364, 2.3455168052608424, 1.828070030493978, 1.3847152045936675, 1.01375465721801, 0.71162885759511, 0.47320824037204157, 0.29211595325045264, 0.1610203897086545, 0.07199627453085332, 0.01689863633299338, -0.01228033848031886, -0.023082446978341418, -0.022278123139206848, -0.015607355817867392, -0.007577038702221142, -0.0013187484640456175, 0.0014860729778536368, 0.0006110700412078195, -0.0027792514068527515, -0.006260050917928191, -0.006336796185584039, 0.001311480042209435, 0.02154719783480621, 0.05946105428631292, 0.1200404654947613, 0.20783536867548716, 0.3266488478415051, 0.47924412238314057, 0.6670825192061224, 0.8901224174550075, 1.146728967207389, 1.4335841703803134, 1.7456624259220728, 2.076322053252094, 2.417581080224321, 2.760268599795141, 3.094254277192324, 3.4088244217777435, 3.6932739219423736, 3.9371525727002985, 4.130591014974149, 4.264776555056804, 4.332622881830122, 4.32885736800481, 4.25019747451727, 4.0956630404307575, 3.867020220932343, 3.568503933021176, 3.2066603948830235, 2.7903100264551868, 2.330571619788834, 1.8402074417832122, 1.3331371251970467, 0.8240663239288261, 0.32813200248860797, -0.13990656562977868, -0.5662637125221185, -0.9386045996260295, -1.2465083438882052, -1.482070856554819, -1.6402840907838332, -1.719295721286346, -1.720626444007504, -1.6492647853679139, -1.513580944751632, -1.325140395058811, -1.0984490936239686, -0.850480746029773, -0.6001145483085134, -0.36752248103621404, -0.1734996841498467, -0.03866704703539684, 0.017304425778473614, -0.023555262721876944, -0.17677038673258894, -0.4547302053243949, -0.8661123718786672, -1.4154097637583494, -2.102559827609088, -2.922752096905638, -3.8663884939168223, -4.919201722059693, -6.0625588576557075, -7.273883590970164, -8.527216271598393, -9.793941020668969, -11.043717231305385, -12.245280064825124, -13.367332381777667, -14.379563077618762, -15.253799493957041, -15.964715773095493, -16.490591215275735, -16.814119804528634, -16.92320864983969, -16.811157511033784, -16.47687704630003, -15.925073659488204, -15.166253497047082, -14.216235396612225, -13.095717675491732, -11.829739073861793, -10.446825473930367, -8.978101587770746, -7.456465364728487, -5.915603369629509, -4.388635820251955, -2.9073661102353188, -1.501553953442177, -0.19798794550357682, 0.9807895009745783, 2.0165809808376904, 2.895718326061659, 3.6094897489874054, 4.154847030835638, 4.533663592342681, 4.752238610045341, 4.821090521172472, 4.75496354093811, 4.571502174844553, 4.290327478449993, 3.932439758417764, 3.519795470637613, 3.0739664019239212, 2.6152826046140007, 2.162303566508681, 1.7314473110132653, 1.3361946301384442, 0.9867412392662985, 0.6899225545888912, 0.44927200229602926, 0.26500738122179607, 0.13431855189807584, 0.051814316634713434, 0.01004168490020402, 4.5990827330331276e-05, 0.012033150964475237, 0.03604938836046348, 0.06263664625667781, 0.08345880395125337, 0.09185924039662059, 0.08331655721362961, 0.055783461456153774, 0.009896231179406592, -0.05096416517946374, -0.12076058956942487, -0.19103386356655294, -0.2512698019954772, -0.2893889872386932, -0.29233975870610196, -0.2467587142447238, -0.1396689431185227, 0.04079394375447369, 0.3046773374589109, 0.6596196160629857, 1.110282412053813, 1.6578606305328936, 2.29977082496093, 3.0296754557413013, 3.8373863986865033, 4.7089196743278245, 5.626865025635249, 6.571273369737343, 7.519989727443173, 8.449177336011486, 9.334240718564898, 10.15134067149089, 10.877728898203962, 11.492315160108772, 11.976665709188145, 12.316547151140751, 12.501720749237546, 12.52605121411004, 12.388051762897941, 12.091852627064284, 11.646176071543092, 11.06375485079988, 10.361189212013885, 9.559101308804754, 8.680506782590893, 7.749762948434543, 6.791957815320354, 5.832517850574855, 4.8956037117536635, 4.003146711694574, 3.174304661545816, 2.425105552862295, 1.7675415454962045, 1.2092392683343811, 0.7534716411330663, 0.399329572750452, 0.14181253299103252, -0.027700984093839597, -0.12078825197278323, -0.15123233516225987, -0.13421397031604215, -0.08538757605596145, -0.019949877025557276, 0.048246009922308146, 0.10752515616552162, 0.14911269595788948, 0.16770060669971484, 0.16183867616428554, 0.13413234602056645, 0.09122203446193712, 0.04354302349625151, 0.004873011032387688, -0.008310323049518738, 0.022352036596616713, 0.11613815978730702, 0.29220298128387273, 0.5684824233360404, 0.9605665054411578, 1.4806303717896412, 2.136587154235444, 2.9312413383646585, 3.8615781020797173, 4.918372228842354, 6.086399413476252, 7.344345215379388, 8.664976914232428, 10.015873131289226, 11.3610724453812, 12.66164035530941, 13.876581641091335, 14.964465271645638, 15.886099482613634, 16.605046457474383, 17.088567967997403, 17.309342993762304, 17.248145871145507, 16.893416727899794, 16.241404331232484, 15.297074069063203, 14.075732420531226, 12.601192150598083, 10.904710184293375, 9.024655831954629, 7.006621622721628, 4.9005446144591405, 2.7587894746726414, 0.6349136364855339, -1.4173215334893865, -3.346803945953856, -5.106896575542513, -6.656662805517696, -7.96193459348796, -8.996949148952394, -9.745101147410908, -10.19924315211314, -10.361861309376897, -10.244891761520599, -9.868998003354102, -9.262622448707937, -8.460972023943352, -7.504379447276353, -6.436561500171646, -5.302915778942892, -4.14887994971194, -3.0179680527255486, -1.9500638428214874, -0.9799734395058458, -0.1362019346061107, 0.5601166632547752, 1.0958811647671114, 1.4663328649233505, 1.675045210976995, 1.7335205103041078, 1.6604620154238006, 1.480767673605507, 1.2242663575724242, 0.9242161545287582, 0.6157061752643265, 0.3339861513933848, 0.11277715190854194, -0.01729471081517302, -0.0301360106412812, 0.09455144520997925, 0.37032177947177736, 0.8033376455180972, 1.391960759557669, 2.1267076932251707, 2.990804370412132, 3.9607361689324083, 5.007017053237834, 6.095403504340925, 7.188824409934715, 8.24853210603271, 9.235409036220926, 10.111702957058462, 10.843397510802337, 11.400911594729008, 11.759958131159554, 11.902780807174524, 11.819819435908267, 11.509169543132401, 10.976326235520002, 10.234279918053636, 9.303829635322804, 8.211815689038138, 6.989834559486468, 5.67331723101342, 4.300703011550796, 2.91125608431226, 1.5435139960537658, 0.23410973445209107, -0.9833324966108401, -2.079717356027512, -3.0313787309281097, -3.820655516925501, -4.43637816765327, -4.8740684928043745, -5.13572002507672, -5.229389454305303, -5.168724923848956, -4.972000521106749, -4.661036218222824, -4.260119392529199, -3.794960264356943, -3.2913710569115064, -2.774096830646295, -2.2658153570916117, -1.7862937664673104, -1.3516075938052985, -0.9736242023565862, -0.6597227287193035, -0.4127326838420299, -0.2310967442464226, -0.10923754122112181, -0.03810129147545919, -0.005858013378292142, 0.0012745511438955397, -0.0018411515713948824, -0.00016374125165348856, 0.020645014344681585, 0.07341494924942028, 0.168751632987406, 0.3144481749984546, 0.515124778791141, 0.771985286897832, 1.0827113437183773, 1.4415824170979346, 1.8399658348592924, 2.2666587929877062, 2.708339641460537, 3.1502668109792813, 3.5773699145944597, 3.974711672296192, 4.328027948764965, 4.624494273031996, 4.853807415200871, 5.008203232006218, 5.082587569900313, 5.074879485875845, 4.986564502901594, 4.822045420811596, 4.58821349041562, 4.294248425312574, 3.951560837516386, 3.572753217634358, 3.1709176336481466, 2.7591888935594207, 2.3504239932221176, 1.9563270360969311, 1.58695110998716, 1.250447056680166, 0.9529360644763702, 0.6982118773265689, 0.4877420222632319, 0.32084295175351185, 0.19494202919654263, 0.10584409261427546, 0.04813484623331905, 0.015637141425065424, 0.0018721570961544422, 0.0005037613317690642, 0.005759948466456262, 0.012794406500848126, 0.017968345518373074, 0.01904086488243476, 0.015257981747026224, 0.007336311343584972, -0.0026562897778613583, -0.011509691776919411, -0.015159403629231835, -0.009037216031733812, 0.011546581162829963, 0.05101037605167103, 0.11310777140969014, 0.20057108139634167, 0.314860754056423, 0.45593852861310663, 0.6221072916487383, 0.8099853101072437, 1.0147147186051004, 1.2300588009218574, 1.4485873574720027, 1.6620459304426713, 1.8620086341239013, 2.0401173764646985, 2.1884036076631017, 2.299791597618884, 2.3688394795881775, 2.391751486107523, 2.3664875176915383, 2.293031658274424, 2.1738020380739846, 2.013206787874164, 1.8173581893242101, 1.5939365178766027, 1.352115221582042, 1.1017933575117589, 0.8530666297922893, 0.615856401523499, 0.399573403854801, 0.21244557152854066, 0.06112199584208165, -0.04956712772679708, -0.11680606903757304, -0.13998715201996684, -0.12068055845154577, -0.062491854543758205, 0.029123321859479086, 0.14718479255101388, 0.28360761778360416, 0.4296481284519258, 0.5763498150057167, 0.7150502289855114, 0.8378460049384219, 0.9379956999140885, 1.0102576770845995, 1.0511341758235535, 1.0590098556422811, 1.0341909228319492, 0.9788468443286398, 0.8967997379919678, 0.7932449894370657, 0.6744104933926135, 0.5471573696580317, 0.41852195255471913, 0.29528142379987615, 0.18354215982017286, 0.0883618993495349, 0.013458986904573873, -0.03898839555383281, -0.0684544347254973, -0.07606712893093186, -0.06448025183511873, -0.03766825476289236, -0.0006354700822150643, 0.04098079637184589, 0.08131592373693548, 0.1146862276676398, 0.1360157631273286, 0.14127809754954665, 0.1277662489800973, 0.0943013287132345, 0.04138571111432488, -0.028738473004115025, -0.11226047139385972, -0.20402344285862992, -0.29781968508518836, -0.3868195387319769, -0.4640708615717391, -0.5229698118156973, -0.5577502892231505, -0.5640420392582444, -0.5392213205410121, -0.48265527785831647, -0.39589192937011425, -0.28280907754649337, -0.14938377174179304, -0.0033632400745122345, 0.14613116772244575, 0.2890856658150706, 0.41536205446267965, 0.5154515489422798, 0.5812102816736283, 0.6065950995395658, 0.5883909421130399, 0.5267759470672585, 0.4257330495384575, 0.2933010187636405, 0.14157383277456353, -0.013534332193736896, -0.15275076723140107, -0.2541459012951646, -0.29405999124370624, -0.24819291026616241, -0.09283272696196802, 0.19382870226891172, 0.6303939439253978, 1.2309800640117574, 2.0040591526983995, 2.95161705121553, 4.068407266802513, 5.34142522124905, 6.749840493913882, 8.265750622461333, 9.854521966776074, 11.475480567682785, 13.083341628158582, 14.63081905103279, 16.069607734771328, 17.351788014538265, 18.432107486528157, 19.27148503820666, 19.83737432855709, 20.104661594197907, 20.057454496471955, 19.691837829452087, 19.014437703285978, 18.041761118078824, 16.80040207331591, 15.327854131617087, 13.669178694576214, 11.874789810477143, 9.999110153003434, 8.099587674840528, 6.23276279911124, 4.451721330233469, 2.804427104075402, 1.332364290402845, 0.06794960818701018, -0.9666896205410634, -1.7601523990838766, -2.311862067959839, -2.6320543370590017, -2.740807944245444, -2.666582597733921, -2.4445099115368336, -2.114188734931661, -1.7171970553706049, -1.294574223701553, -0.8843649426787707, -0.5191054422258893, -0.22366478184368963, -0.013511987742835851, 0.10656427763605514, 0.14321380527964492, 0.11462482038203309, 0.04999417298851803, -0.011617113531534575, -0.02303378318472121, 0.06876813885175773, 0.31997272344529354, 0.7869621110812773, 1.5231801767182824, 2.57592841350991, 3.9833208862978107, 5.7718292339017285, 7.953899975096755, 10.52598495589617, 13.467473628148936, 16.741303712960576, 20.293801271482838, 24.05525314106671, 27.942020864296236, 31.861189558305774, 35.712168970760914, 39.38920485979316, 42.78580941577391, 45.80200797735806, 48.345480891186874, 50.333843532053145, 51.698972086156814, 52.39382038019418, 52.390684184639404, 51.68104739417524, 50.27746814874286, 48.21729264351692, 45.55726563905385, 42.370332393679966, 38.7444351386592, 34.78249878719584, 30.59500593857517, 26.295248754548556, 21.996469361651478, 17.809791904024628, 13.837839730606099, 10.171041787904011, 6.885554871968723, 4.041787037390136, 1.6816091072232693, -0.17235315887942596, -1.5163200957247793, -2.3645286694119054, -2.7480218785410866, -2.712391144948442, -2.3150826502291415, -1.6225647373037442, -0.7069816338628608, 0.3572261997133816, 1.4965203976870796, 2.6412303129846433, 3.728308320344228, 4.7035452755937905, 5.523270218653013, 6.155552672274832, 6.580631357222008, 6.790806024993628, 6.789850523005992, 6.591937498724166, 6.219961617903145, 5.703696185980627, 5.077763106487517, 4.379392073786744, 3.6462985277524087, 2.914755788387243, 2.217788261640005, 1.583514033554636, 1.0342190924368797, 0.5857067448430507, 0.24689562546119562, 0.019782551824288074, -0.0998761911857001, -0.1218033015305074, -0.06027007409642637, 0.06717047449057155, 0.24105920394333857, 0.4412411013463772, 0.6480898229338888, 0.8438850501770615, 1.0135892194099163, 1.145397605263127, 1.2312371960091257, 1.2672617745259662, 1.2534526645299824, 1.1931682234727583, 1.0927225262840972, 0.9609469305109066, 0.8081035022578484, 0.6450049633417608, 0.48230342911850543, 0.3298545964357417, 0.19591483406665722, 0.086671286040117, 0.005997650975832668, -0.04465185368953991, -0.06621350086668207, -0.06174688751581257, -0.03603387667492562, 0.004899717565783323, 0.05436235838768468, 0.10559442791675051, 0.15232815306196107, 0.1892818166437183, 0.21256447273573514, 0.21994275922455236, 0.21095943784250068, 0.18689869468615516, 0.15060456094811447, 0.10617335486157717, 0.05853490582662836, 0.012946439481999365, -0.025504379193670938, -0.05239447021715635, -0.0644310357045585, -0.05982994323522848, -0.03851417793810869, -0.002214015132303636, 0.045573569975655204, 0.09983977156205938, 0.15443058149608932, 0.2024827808729216, 0.23698485823324517, 0.2515068904241318, 0.2407212684441661, 0.20088791961902844, 0.13034929976641335, 0.03000934215813042, -0.09668601169189675, -0.24384562698072598, -0.4033067711974003, -0.5649769209415205, -0.7176083184470132, -0.8495458694058341, -0.9495064481891324, -1.0074910899136311, -1.015689531479739, -0.9691796530423118, -0.8665127416160036, -0.7102308987031556, -0.5069205462062187, -0.26698836867611453, -0.004236480543402555, 0.26478355045990215, 0.5219357469415348, 0.7487863478530692, 0.9279808769712387, 1.0447399332289022, 1.0883897387090038, 1.0537159240773883, 0.9421405505700798, 0.7627485201337133, 0.532776468819568, 0.27757988970405617, 0.03004712226770135, -0.17057692161793478, -0.27975224362650125, -0.24907596790133743, -0.02816029479935832, 0.43161738729759186, 1.1714254427461759, 2.2199068524694017, 3.5924611154108135, 5.309580014363208, 7.403039453648183], 'positive_zeros': ['1.22070961053825409467541695215763', '1.24348226601184896814241054871200', '1.25876834028679164557137661539794', '1.91508048911240360072665558368745', '1.96061400315172222764464276271139', '2.05064063720648113313294429441798', '2.31878075705183782272250273568368', '2.40334438065332715198733716393696', '2.86243340239432620345550528425589', '3.03648104188588296086412550086017', '3.12459966626566605167462391434464', '3.13609457594094352079327535665771', '3.81427374526897454527801807570030', '3.88267534284319733310169273772744', '3.90498032103384897440003823014757', '3.94798416184443200992526932712904', '4.34405853922864981738932537058368', '4.54094416207378581137257641033709', '4.55504931034111227194636656235540', '4.98234702550663700359205703621883', '5.28262813211443446544550377372041', '5.28493770556389679439676733274684', '5.38099612166610403782668872592791', '5.48212765585664647992745999754900', '5.95075545999582350825606007644562', '6.01509914866101311720821131258886', '6.11934820242407011091555387311444', '6.13462888534252111308643670632791', '6.53091314536818354087975956976341', '6.77553898293449632089166583376570', '6.92344912623762417840631201785990', '6.94193606986133298281466520745643', '7.27952159875144301791169487256876', '7.57629365802598121821071150462371', '7.58805005420593826325325626452282', '7.60567844901625741373070497367642'], 'prelabel': '8-8512e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.244310899069363, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e4-0', 'trace_hash': 335144255803684283, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.22070961053825409467541695216', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.24348226601184896814241054871', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.25876834028679164557137661540', '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': 21341988.809966147, 'bad_primes': [2, 7, 19], 'central_character': '1.1', 'conductor': 5249602982772736, 'conductor_radical': 266, 'degree': 8, 'dirichlet_coefficients': [1, 0, 2, 0, 0, 0, 4, 0, -5, 0, 2, 0, 0, 0, 0, 0, -6, 0, -4, 0, 8, 0, 4, 0, -12, 0, -16, 0, -2, 0, -18, 0, 4, 0, 0, 0, 16, 0, 0, 0, -10, 0, -4, 0, 0, 0, -4, 0, 10, 0, -12, 0, -10, 0, 0, 0, -8, 0, -4, 0, 16, 0, -20, 0, 0, 0, -10, 0, 8, 0, 4, 0, -18, 0, -24, 0, 8, 0, 4, 0, 2, 0, -14, 0, 0, 0, -4, 0, -24, 0, 0, 0, -36, 0, 0, 0, -16, 0, -10, 0], 'euler11': [1, -2, 41, -64, 661, -704, 4961, -2662, 14641], 'euler13': [1, 0, 36, -12, 597, -156, 6084, 0, 28561], 'euler17': [1, 6, 55, 240, 1363, 4080, 15895, 29478, 83521], 'euler19': [1, 4, 6, 4, 1, 0, 0, 0, 0], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, -4, 62, -208, 2083, -4784, 32798, -48668, 279841], 'euler29': [1, 2, 73, -20, 2329, -580, 61393, 48778, 707281], 'euler3': [1, -2, 9, -12, 35, -36, 81, -54, 81], 'euler31': [1, 18, 191, 1548, 9967, 47988, 183551, 536238, 923521], 'euler37': [1, -16, 214, -1824, 12995, -67488, 292966, -810448, 1874161], 'euler41': [1, 10, 149, 1044, 9119, 42804, 250469, 689210, 2825761], 'euler43': [1, 4, 136, 564, 7982, 24252, 251464, 318028, 3418801], 'euler47': [1, 4, 100, 236, 5869, 11092, 220900, 415292, 4879681], 'euler5': [1, 0, 12, 4, 77, 20, 300, 0, 625], 'euler53': [1, 10, 149, 1160, 12025, 61480, 418541, 1488770, 7890481], 'euler59': [1, 4, 164, 276, 11933, 16284, 570884, 821516, 12117361], 'euler61': [1, -16, 268, -2708, 24829, -165188, 997228, -3631696, 13845841], 'euler67': [1, 10, 63, 500, 6785, 33500, 282807, 3007630, 20151121], 'euler7': [1, -4, 6, -4, 1, 0, 0, 0, 0], 'euler71': [1, -4, 186, -648, 16883, -46008, 937626, -1431644, 25411681], 'euler73': [1, 18, 241, 2728, 28175, 199144, 1284289, 7002306, 28398241], 'euler79': [1, -4, 232, -1028, 24574, -81212, 1447912, -1972156, 38950081], 'euler83': [1, 14, 143, 444, 2903, 36852, 985127, 8005018, 47458321], 'euler89': [1, 24, 324, 2760, 23334, 245640, 2566404, 16919256, 62742241], 'euler97': [1, 16, 292, 2196, 28373, 213012, 2747428, 14602768, 88529281], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0], [1, -2, 9, -12, 35, -36, 81, -54, 81], [1, 0, 12, 4, 77, 20, 300, 0, 625], [1, -4, 6, -4, 1, 0, 0, 0, 0], [1, -2, 41, -64, 661, -704, 4961, -2662, 14641], [1, 0, 36, -12, 597, -156, 6084, 0, 28561], [1, 6, 55, 240, 1363, 4080, 15895, 29478, 83521], [1, 4, 6, 4, 1, 0, 0, 0, 0], [1, -4, 62, -208, 2083, -4784, 32798, -48668, 279841], [1, 2, 73, -20, 2329, -580, 61393, 48778, 707281], [1, 18, 191, 1548, 9967, 47988, 183551, 536238, 923521], [1, -16, 214, -1824, 12995, -67488, 292966, -810448, 1874161], [1, 10, 149, 1044, 9119, 42804, 250469, 689210, 2825761], [1, 4, 136, 564, 7982, 24252, 251464, 318028, 3418801], [1, 4, 100, 236, 5869, 11092, 220900, 415292, 4879681], [1, 10, 149, 1160, 12025, 61480, 418541, 1488770, 7890481], [1, 4, 164, 276, 11933, 16284, 570884, 821516, 12117361], [1, -16, 268, -2708, 24829, -165188, 997228, -3631696, 13845841], [1, 10, 63, 500, 6785, 33500, 282807, 3007630, 20151121], [1, -4, 186, -648, 16883, -46008, 937626, -1431644, 25411681], [1, 18, 241, 2728, 28175, 199144, 1284289, 7002306, 28398241], [1, -4, 232, -1028, 24574, -81212, 1447912, -1972156, 38950081], [1, 14, 143, 444, 2903, 36852, 985127, 8005018, 47458321], [1, 24, 324, 2760, 23334, 245640, 2566404, 16919256, 62742241], [1, 16, 292, 2196, 28373, 213012, 2747428, 14602768, 88529281]], 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8512/2/a/bv'], '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': '8-8512e4-1.1-c1e4-0-5', 'motivic_weight': 1, '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}], 'nu_real_doubled': [1, 1, 1, 1], 'order_of_vanishing': 4, 'prelabel': '8-8512e4-1.1-c1e4-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 8.244310899069363, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e4-0', 'trace_hash': 335144255803684283, 'z1': {'__RealLiteral__': 0, 'data': '1.22070961053825409467541695216', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '1547433270503185949882168500654,1576301040883079164918756193779,1595678442112843546510195804262,2427652931508709565751442899614', 'Lhash_array': ['1547433270503185949882168500654', '1576301040883079164918756193779', '1595678442112843546510195804262', '2427652931508709565751442899614'], 'label': '8-8512e4-1.1-c1e4-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8512/2/a/bv'}