-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3604271115054551902923534951062', 'a10': [0.0, 0.0], 'a2': [0.5, -0.8660254037844386], 'a3': [2.598076211353316, -1.5], 'a4': [-0.5, -0.8660254037844386], 'a5': [0.0, 0.0], 'a6': [3.111507638930571e-61, -3.0], 'a7': [-1.7320508075688772, 2.0], 'a8': [-1.0, 0.0], 'a9': [3.0, -5.196152422706632], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.900439568106474, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.5, 0.8660254037844386]]], [7, [[1.0, 0], [1.7320508075688772, -2.0]]], [17, [[1.0, 0], [3.9641016151377544, -1.1339745962155614]]]], 'bad_primes': [2, 7, 17], 'central_character': '238.135', 'coefficient_field': 'CDF', 'conductor': 238, 'conductor_radical': 238, 'conjugate': '2371425491089577203523080608342', 'degree': 2, 'euler_factors': [[[1.0, 0], [-0.5, 0.8660254037844386]], [[1.0, 0], [-2.598076211353316, 1.5], [1.5, -2.598076211353316]], [[1.0, 0], [0, 0], [2.5, 4.330127018922194]], [[1.0, 0], [1.7320508075688772, -2.0]], [[1.0, 0], [2.598076211353316, -1.5], [5.5, -9.526279441628825]], [[1.0, 0], [-5.0, 0], [13.0, 0]], [[1.0, 0], [3.9641016151377544, -1.1339745962155614]], [[1.0, 0], [2.0, -3.4641016151377544], [-9.5, -16.454482671904334]], [[1.0, 0], [-3.4641016151377544, -2.0], [11.5, 19.91858428704209]], [[1.0, 0], [0, -4.0], [-29.0, 0]], [[1.0, 0], [-3.4641016151377544, 2.0], [15.5, -26.846787517317598]], [[1.0, 0], [6.928203230275509, 4.0], [18.5, 32.04293994002423]], [[1.0, 0], [0, 4.0], [-41.0, 0]], [[1.0, 0], [-8.0, 0], [43.0, 0]], [[1.0, 0], [2.0, -3.4641016151377544], [-23.5, -40.703193977868615]], [[1.0, 0], [-0.5, -0.8660254037844386], [-26.5, 45.89934640057525]], [[1.0, 0], [6.0, 10.392304845413264], [-29.5, 51.09549882328188]], [[1.0, 0], [0, 0], [30.5, 52.827549630850754]], [[1.0, 0], [-8.0, -13.856406460551018], [-33.5, 58.023702053557386]], [[1.0, 0], [0, 1.0], [-71.0, 0]], [[1.0, 0], [6.928203230275509, -4.0], [36.5, -63.21985447626402]], [[1.0, 0], [-6.06217782649107, -3.5], [39.5, 68.41600689897065]], [[1.0, 0], [16.0, 0], [83.0, 0]], [[1.0, 0], [4.5, -7.794228634059948], [-44.5, -77.07626093681505]], [[1.0, 0], [0, 8.0], [-97.0, 0]], [[1.0, 0], [5.0, 8.660254037844387], [-50.5, 87.4685657822283]], [[1.0, 0], [-4.0, 6.928203230275509], [-51.5, -89.20061658979718]], [[1.0, 0], [2.598076211353316, 1.5], [53.5, 92.66471820493493]], [[1.0, 0], [-17.320508075688775, 10.0], [54.5, -94.39676901250381]], [[1.0, 0], [0, 12.0], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-238-119.16-c1-0-9', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/238/2/j/a/135/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [2.057526988651771, 2.1677897801491675, 2.3015856238788808, 2.4581628274106926, 2.633807745231917, 2.822208282862093, 3.0149374042621995, 3.2019514092330925, 3.3720800081642843, 3.5135359410250904, 3.614482985633888, 3.6636869967520407, 3.6512502251207555, 3.569403538021554, 3.4133083500548307, 3.181801888773871, 2.878007108806917, 2.5097234054832986, 2.0895175637852295, 1.6344471666519007, 1.1653714523195335, 0.705836928863712, 0.2805653630888633, -0.08638275907433447, -0.3736495944718801, -0.564663734346114, -0.6495709307190215, -0.6267984415912942, -0.5040421641838259, -0.2984920920554926, -0.03616325112117427, 0.2497253156111018, 0.5212863990021207, 0.7392724210454423, 0.8669060325192701, 0.8738903580103844, 0.7401874063807066, 0.45912300792693245, 0.039394402104342904, -0.4943724895396355, -1.102745776399387, -1.7343519625395054, -2.3303456021905755, -2.8301407274990615, -3.1778694518260977, -3.3288849564155902, -3.255545693623859, -2.9515244391515574, -2.4339900454565657, -1.7432097660678647, -0.9394008685372706, -0.09699385608629903, 0.7031830305752591, 1.3829730962929803, 1.8761531284854407, 2.13671119218731, 2.1449975403568744, 1.9108007370872093, 1.4727457716145205, 0.8938714187386522, 0.2537655371254162, -0.3618504678989786, -0.8727692147049648, -1.2155869119991718, -1.3529852150861277, -1.2795362866217768, -1.022977721090582, -0.6405128944594576, -0.21041821835900695, 0.18002021965594028, 0.4485762987083935, 0.5320623288313702, 0.3979812761677205, 0.05182334254631223, -0.4614766368990787, -1.0625767650623388, -1.648916276155337, -2.1106850602760634, -2.3493203652476917, -2.2956881947591405, -1.9249362831797312, -1.2653149124390048, -0.3990389858854732, 0.5455817165831569, 1.4101492903059, 2.028355476060008, 2.2512183343827803, 1.9715525872320643, 1.1437184961934668, -0.20479044848538513, -1.9722436484409085, -3.9928067775062304, -6.056882002009547, -7.938915888850685, -9.428597314687913, -10.360647976323717, -10.638462356843613, -10.247710406245016, -9.257563180975769, -7.809199723143208, -6.093370997777679, -4.320665293572331, -2.6893990843126736, -1.3565002335120568, -0.4162516113276261, 0.10961318213383386, 0.26899508109803, 0.16454368862272478, -0.07017232566869779, -0.2987805600543266, -0.4090879329624057, -0.3337874956698035, -0.061019933862743306, 0.3670349189578205, 0.8669386595228639, 1.3352276176494715, 1.6734330590508273, 1.8114227982335844, 1.723934993045675, 1.4366067833385041, 1.0200567668180263, 0.5732056830547827, 0.19946225854096047, -0.01887470775988061, -0.04204566779880114, 0.11515973851999978, 0.38415309199492986, 0.6566436030710093, 0.8096319315138057, 0.7361975512234417, 0.3753101606529131, -0.2663532178249197, -1.1062964213085233, -1.9948404045844768, -2.7400283116674915, -3.1446693133431327, -3.0484082391905742, -2.3660898538239503, -1.1138711356011652, 0.5834102701465049, 2.50651687166605, 4.376222299914217, 5.901985448262521, 6.8356966070821175, 7.019775887022944, 6.41958926582703, 5.133000104086024, 3.3743715277181994, 1.4355720567495605, -0.36859241265432835, -1.7596620258966833, -2.5474579035082847, -2.663959234711834, -2.1721035913175246, -1.2477682761208713, -0.1389284477435275, 0.88907320843484, 1.6101848527263836, 1.8838706169388402, 1.6808990383406595, 1.0833169727888852, 0.2591038770813296, -0.5822080716815676, -1.242291844869395, -1.582589062690263, -1.5571265709186461, -1.221790148728395, -0.717902762883698, -0.2341692326303757, 0.04364467525529547, -0.017174141712539278, -0.4589652483188805, -1.218787385538515, -2.1401640568661975, -3.009187330351202, -3.6065756034988037, -3.763107413419607, -3.404689520882114, -2.5755235632088693, -1.432949576866465, -0.21437422904190154, 0.8164108034819594, 1.4309552690545122, 1.491076984489969, 0.9834786157240009, 0.025242582299487365, -1.1616414228465926, -2.301012996358306, -3.1265752974948184, -3.4438673361313574, -3.175184842618126, -2.3765565241161832, -1.2227254903835107, 0.036015564773224394, 1.1343171745230747, 1.854511272213902, 2.076059884058365, 1.799679475066095, 1.140678372964897, 0.2940012545274481, -0.5192527952989863, -1.1093949930282592, -1.3645157157931616, -1.273625729047289, -0.9210168735527268, -0.45426842303713866, -0.03564029430037783, 0.20877441144993364, 0.22713862626074485, 0.05582590190285344, -0.195193277040138, -0.38158300883748125, -0.377053691001608, -0.12308977476767362, 0.3398552710483973, 0.8709037931265806, 1.260087996777806, 1.285999189768823, 0.7850236411737381, -0.28714187272418, -1.8204033831099413, -3.55441014777165, -5.124829766235517, -6.1432945083461705, -6.292739126196745, -5.414351987888645, -3.56290392493658, -1.0139706953938425, 1.7819737409921004, 4.290273411476303, 6.007518354538672, 6.574531243797305, 5.859437001566262, 3.9900389456355665, 1.3268840191667752, -1.617023794465568, -4.290652390260157, -6.225836945349469, -7.1355246582468155, -6.9662408001162675, -5.893506139660405, -4.263536197819587, -2.4980367321494223, -0.9877280539623191, -0.0021086812075699446, 0.3624727891080235, 0.18551385745476548, -0.32141033685799175, -0.8896908223895414, -1.277064799555234, -1.3353529341719272, -1.0443528525218138, -0.5044456935397024, 0.10702806171016248, 0.6000186432477437, 0.8355066138793253, 0.7686252753724507], 'positive_zeros': ['2.84326857448387940484128249191681', '3.76605421545594811879256021513509', '4.76011602936817966651137700161612', '6.38956897147667516533394771779445', '7.54996769182271527692556209778006', '8.564029696573533914418462573056615', '9.139395021082871822422959133033434', '10.30291718521800745403703180383643', '11.10851031989385042745150611801588', '13.08927072110243034878179995580841'], 'prelabel': '2-238-119.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3785643140987198, 'root_angle': 0.451658369818595, 'root_number': '0.15128658560229583 + 0.9884899438116703*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.225829184909', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.84326857448387940484128249192', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.76605421545594811879256021514', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.76011602936817966651137700162', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 1.900439568106474, 'bad_primes': [2, 7, 17], 'central_character': '119.16', 'conductor': 238, 'conductor_radical': 238, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/238/2/j/a/135/2'], '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': '2-238-119.16-c1-0-9', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-238-119.16-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3785643140987198, 'root_angle': 0.2258291849092975, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.84326857448387940484128249192', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3604271115054551902923534951062', 'Lhash_array': ['3604271115054551902923534951062'], 'label': '2-238-119.16-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/238/2/j/a/135/2'}