-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1946993504070021913041854836230', 'a10': [0.0, 0.0], 'a2': [2.419870349137736, 0.0], 'a3': [-0.5370800561629734, 0.0], 'a4': [3.8557725066359887, 0.0], 'a5': [0.0, 0.0], 'a6': [-1.2996641030220093, 0.0], 'a7': [-3.1867595782641023, 0.0], 'a8': [4.490728863553442, 0.0], 'a9': [-2.7115450132719774, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 72.06498782420559, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [0, 0]]]], 'bad_primes': [5, 19], 'central_character': '9025.1', 'coefficient_field': 'CDF', 'conductor': 9025, 'conductor_radical': 95, 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.419870349137736, 0], [2.0, 0]], [[1.0, 0], [0.5370800561629734, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.1867595782641023, 0], [7.0, 0]], [[1.0, 0], [-4.155436609657998, 0], [11.0, 0]], [[1.0, 0], [2.0708585144157055, 0], [13.0, 0]], [[1.0, 0], [-5.794698148842781, 0], [17.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [2.607938570578679, 0], [23.0, 0]], [[1.0, 0], [6.0, 0], [29.0, 0]], [[1.0, 0], [2.5993282060440186, 0], [31.0, 0]], [[1.0, 0], [4.302660642112499, 0], [37.0, 0]], [[1.0, 0], [-0.5993282060440186, 0], [41.0, 0]], [[1.0, 0], [-3.1867595782641023, 0], [43.0, 0]], [[1.0, 0], [-11.708598959444199, 0], [47.0, 0]], [[1.0, 0], [11.75033991096665, 0], [53.0, 0]], [[1.0, 0], [-1.7115450132719774, 0], [59.0, 0]], [[1.0, 0], [8.754764815702016, 0], [61.0, 0]], [[1.0, 0], [4.762278988039284, 0], [67.0, 0]], [[1.0, 0], [13.711545013271977, 0], [71.0, 0]], [[1.0, 0], [2.727141232337317, 0], [73.0, 0]], [[1.0, 0], [-1.4006717939559814, 0], [79.0, 0]], [[1.0, 0], [7.071542825972266, 0], [83.0, 0]], [[1.0, 0], [16.535306833771912, 0], [89.0, 0]], [[1.0, 0], [2.0708585144157055, 0], [97.0, 0]], [[1.0, 0], [1.7115450132719774, 0], [101.0, 0]], [[1.0, 0], [5.752957197320331, 0], [103.0, 0]], [[1.0, 0], [-15.432438593871275, 0], [107.0, 0]], [[1.0, 0], [11.711545013271977, 0], [109.0, 0]], [[1.0, 0], [-10.592697895595803, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 466, 'label': '2-95e2-1.1-c1-0-466', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/9025/2/a/bx/1/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-3.855133655981548e-58, 0.42282406305247056, 0.8439776238493574, 1.2617095852472733, 1.6741131628647128, 2.0790613966580715, 2.474157617634184, 2.8567042144529653, 3.2236918959602883, 3.5718104684965457, 3.8974810366664747, 4.196908559575907, 4.466152886056361, 4.701215759145371, 4.898140809433701, 5.053123225599602, 5.162625572657772, 5.223496101317118, 5.233085838667806, 5.189360761562697, 5.09100542628969, 4.937514563075534, 4.729269346183263, 4.467595325459094, 4.154799358093199, 3.7941833130224905, 3.3900328347638595, 2.947580044810049, 2.4729397193284175, 1.9730191999684132, 1.4554030543631469, 0.9282142850802806, 0.39995466796859047, -0.12067244166368506, -0.6249527900664157, -1.104360719554755, -1.5507622782986916, -1.956616351868941, -2.315167979263698, -2.6206279427288237, -2.8683328317637757, -3.0548800859268184, -3.1782330208160903, -3.2377915324984023, -3.2344250461257387, -3.170465305720975, -3.0496577682727817, -2.8770716339103837, -2.6589698767575296, -2.402641995027667, -2.116203527466289, -1.80836763786029, -1.4881952012623796, -1.1648307876650912, -0.8472326874559122, -0.5439056198534958, -0.2626449796501423, -0.010301386827854503, 0.2074261038842757, 0.38616050117368195, 0.522974481067671, 0.616469806757287, 0.666804832250528, 0.6756681138207494, 0.6461980498969614, 0.5828504413138572, 0.49121783736876506, 0.3778064328687463, 0.2497780303883321, 0.11466610560850876, -0.01992375744095075, -0.1466179209751654, -0.2585716290688773, -0.3497471871004781, -0.41516217865696853, -0.45109740467788956, -0.4552555633465644, -0.4268634287367953, -0.36671237619150515, -0.27713447047178785, -0.1619138916443906, -0.026136124378691495, 0.12402002850537353, 0.2815400390705209, 0.4388710139392671, 0.5882470527626987, 0.7220293476170793, 0.8330467935287972, 0.9149224875526084, 0.9623717186304216, 0.9714579058369726, 0.9397944143989343, 0.8666822250788622, 0.7531759839605873, 0.6020739218168757, 0.41783038827612196, 0.20639316111579162, -0.025028882342142386, -0.26825886070419586, -0.5144938923433189, -0.7546816049921395, -0.9799147802611042, -1.1818264814103545, -1.3529675036096094, -1.4871483006723059, -1.5797286968049578, -1.6278406637104303, -1.630532170673421, -1.5888234982348708, -1.5056713098679089, -1.3858400355814384, -1.2356845476896392, -1.0628524973131936, -0.8759188189173771, -0.6839685907363671, -0.4961474658173494, -0.32120108932101, -0.1670261528260309, -0.04025590665037848, 0.054097995006248414, 0.11292750348968152, 0.13521735028059007, 0.12212877223336331, 0.07697003871958163, 0.005051481719623438, -0.08657148116563597, -0.18945798540026662, -0.2942290409380295, -0.3910824361944312, -0.47035079393860874, -0.5230750609212339, -0.5415636803597275, -0.5199070780505916, -0.45441798544973117, -0.3439705524439016, -0.19021511927203988, 0.002349204798486125, 0.2264555686968158, 0.47230809128135326, 0.7279744324926406, 0.9799202941239262, 1.2136660109926816, 1.4145380847746147, 1.5684822002259402, 1.6628993113728796, 1.6874631075811948, 1.6348758119725213, 1.501519989335803, 1.287966913545235, 0.9993070279458909, 0.6452749819812404, 0.24015039487298223, -0.19757446309975998, -0.6457578989193028, -1.0793893334959628, -1.4715622121220953, -1.7946036774465333, -2.0213159282079616, -2.1262764525890248, -2.0871387796512915, -1.885872406255287, -1.5098803908738063, -0.9529358931865743, -0.21588467338767564, 0.6929309030685742, 1.7575597752865302, 2.954662323632189, 4.254068412631936, 5.61966350580762, 7.010577337403462, 8.382634527280947, 9.690012758283526, 10.887042412907347, 11.930072527524729, 12.779322099290914, 13.400633566846755, 13.767046912275466, 13.86011835026428, 13.670916844639168, 13.200644398167631, 12.460841696609524, 11.473158591471838, 10.268688285742792, 8.886884055136989, 7.3740969514795625, 5.781791242707799, 4.164510431066936, 2.5776797270731144, 1.0753401392172564, -0.2920856679567213, -1.479895230487523, -2.4509797226607883, -3.1773818608871154, -3.6414644706041615, -3.8366329551842755, -3.767574920182162, -3.4500022720107317, -2.9099041869259916, -2.1823423240431943, -1.3098414100303681, -0.34044776981969105, 0.6744554688069676, 1.682475745287805, 2.6325730080971876, 3.4773461578910907, 4.175137194391221, 4.691854771581388, 5.002432220522137, 5.091852679342386, 4.955694927228927, 4.6001768243982255, 4.041697754369977, 3.30590591857442, 2.4263395087157837, 1.4427114982449503, 0.3989249885410735, -0.6590811684863684, -1.6855490341363806, -2.6370708523946917, -3.474604590711145, -4.1652381780823236, -4.68361858059856, -5.012979799264073, -5.145725101324012, -5.08354217998575, -4.837054237608624, -4.425033913820978, -3.873229262379396, -3.212870437964872, -2.4789413595975214, -1.7083115547435486, -0.9378290973786289, -0.20247576167339157, 0.4663197489090669, 1.042125037143536, 1.5046331741176286, 1.8404258284813877, 2.043339573055496, 2.11442713269997, 2.061527996218096, 1.898484300490521, 1.6440570017659413, 1.3206130142121986, 0.9526653599657763, 0.5653548313130112, 0.18296289526310594, -0.17245843953776666, -0.48226303081530253, -0.7321298453811874, -0.9126784486958914, -1.0197534961062653, -1.0543716320570322, -1.0223449109654508, -0.9336143676583504, -0.8013445160658291, -0.6408433214139367, -0.46838176373481827], 'positive_zeros': ['1.53590705808010721915145214042361', '2.67392876795961646102982202851542', '3.27419653689933536535042735090494', '3.80530448652832527833496737767975', '4.54194782625180799476303768328149', '5.54923860720704785328756139941862', '5.81533005065001967900723051325083', '6.37447459732746793902973298625433', '7.10412972735096657386278615641496'], 'prelabel': '2-95e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.489109954771795, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.53590705808010721915145214042', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.67392876795961646102982202852', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.27419653689933536535042735090', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 72.06498782420559, 'bad_primes': [5, 19], 'central_character': '1.1', 'conductor': 9025, 'conductor_radical': 95, 'degree': 2, 'index': 466, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9025/2/a/bx/1/6'], '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': '2-95e2-1.1-c1-0-466', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-95e2-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.489109954771795, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.53590705808010721915145214042', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1946993504070021913041854836230', 'Lhash_array': ['1946993504070021913041854836230'], 'label': '2-95e2-1.1-c1-0-466', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9025/2/a/bx/1/6'}