-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '3121289578322544564787020158229', 'a10': [1.5667861817025317, -1.138336793298024], 'a2': [-0.2101043682882193, -0.4123530404549824], 'a3': [1.442935046936875, -0.9580910449019333], 'a4': [1.0496793201862695, -1.4447596385968535], 'a5': [0.6546304647052377, 4.133174088085122], 'a6': [-0.6982387119156075, -0.39369954003175245], 'a7': [-0.6632064881996703, 0.5664318520453929], 'a8': [-1.730486973239603, -0.27408221074545536], 'a9': [1.1641230993574432, -2.7649262936907415], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9821599448617492, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.442935046936875, 0.9580910449019333]]], [41, [[1.0, 0], [-1.1910157537745123, 6.2913815235018875]]]], 'bad_primes': [3, 41], 'central_character': '123.101', 'coefficient_field': 'CDF', 'conductor': 123, 'conductor_radical': 123, 'conjugate': '3015619979005686668190778444516', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.2101043682882193, 0.4123530404549824], [-1.1755705045849463, 1.618033988749895]], [[1.0, 0], [-1.442935046936875, 0.9580910449019333]], [[1.0, 0], [-0.6546304647052377, -4.133174088085122], [-4.755282581475768, 1.545084971874737]], [[1.0, 0], [0.6632064881996703, -0.5664318520453929], [1.095041255281616, -6.913818384165964]], [[1.0, 0], [2.719791667571502, 1.6666904774642364], [4.993895497135015, 9.801071766072047]], [[1.0, 0], [4.334223072379001, -0.3411107535548692], [12.83994842773679, -2.0336480455230013]], [[1.0, 0], [0.884963548964725, -0.21246095066658668], [15.147110911202253, -7.717838495572296]], [[1.0, 0], [-4.24406550012979, -0.3340151987356924], [18.766078471307615, 2.9722548357643865]], [[1.0, 0], [0.047090546220648254, -0.14492979885987947], [-18.607390870623792, -13.519060802726882]], [[1.0, 0], [2.4719460921589174, 0.593461750318455], [25.839189201462666, 13.165724492446857]], [[1.0, 0], [-2.547164947595928, -3.5058717823289394], [-9.57952682562337, 29.48275200514976]], [[1.0, 0], [-7.305909456210656, -5.308053925693561], [11.433628791873055, 35.189091102920685]], [[1.0, 0], [-1.1910157537745123, 6.2913815235018875]], [[1.0, 0], [-4.24467008880948, 2.162767434956207], [25.274765848576344, -34.78773075812274]], [[1.0, 0], [-2.900009949398206, 3.3954753909749362], [-7.352419856890851, -46.42135200797147]], [[1.0, 0], [2.1517870745997594, -8.962838207113908], [-47.2233457819835, -24.06149648619598]], [[1.0, 0], [-5.5498920335599475, -1.803269233669725], [47.7320026681219, 34.67932988525592]], [[1.0, 0], [-5.189811516596256, 10.18557860406343], [-35.854900389840864, -49.350036656871794]], [[1.0, 0], [1.2656503261951324, -0.7755915174019392], [30.417363482549636, -59.69743712062065]], [[1.0, 0], [-3.0435073251377522, 4.96655256331487], [-32.23332548150782, -63.26146321737412]], [[1.0, 0], [5.109879696858169, 5.109879696858169], [0, 73.0]], [[1.0, 0], [3.1382295816361037, -1.299897254554118], [55.86143571373726, -55.86143571373726]], [[1.0, 0], [0, -6.737195316342686], [-83.0, 0]], [[1.0, 0], [4.102578943902579, 4.803502776410773], [-13.922667388580548, 87.90426231296726]], [[1.0, 0], [-1.8256394612383886, -2.979172834910759], [-44.03707847473604, 86.42763284627168]], [[1.0, 0], [0.2860209987545462, -3.6342413690204336], [-99.7565224001089, -15.799880969063318]], [[1.0, 0], [-5.711068529257245, -2.909934759463284], [60.54188098612473, 83.32875042061958]], [[1.0, 0], [5.057317318468613, 15.564822253322147], [-86.56481839811937, 62.893021995294625]], [[1.0, 0], [13.799218157198238, 5.715823310856578], [77.07463914933368, 77.07463914933368]], [[1.0, 0], [-5.047573378886275, 3.6672767229885954], [34.91892036436906, -107.46938634135235]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 5, 'label': '2-123-123.101-c1-0-5', '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/123/2/o/a/101/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.3129229732634298, 1.3415275389931025, 1.3853612113329683, 1.4428052561116715, 1.510792553933571, 1.5850917839771976, 1.6605905950984117, 1.7315332609337113, 1.7917174953344965, 1.8346800252900881, 1.8539027998094095, 1.8430622486577497, 1.7963313204748959, 1.7087320238420893, 1.5765258666152566, 1.397620882347118, 1.171966713797478, 0.9019036044659138, 0.5924275014821002, 0.2513323318156485, -0.11080754648488725, -0.48084620247082127, -0.8434883987206694, -1.1819341053489159, -1.4787373420574823, -1.7168519750103415, -1.8808161977469169, -1.9580067513622226, -1.9398754902048152, -1.8230668730299202, -1.6103075600589163, -1.3109605027684361, -0.9411472229963048, -0.5233641500832125, -0.08555171136304643, 0.3403829895518562, 0.720540170336874, 1.0213963527066954, 1.212416316661899, 1.2687126445282055, 1.1735265550674874, 0.9202903510237421, 0.5140400213027365, -0.02802125989679982, -0.6769516325375973, -1.3935558375547261, -2.130897384772448, -2.8377041574850876, -3.4624314801849296, -3.9576563059214154, -4.284409322907635, -4.416018704286985, -4.3410477532655865, -4.064962935282267, -3.6102681220686614, -3.0149793772083573, -2.329481050414487, -1.611982406864504, -0.922965230495588, -0.3191560998730912, 0.15234744059749145, 0.4591360984415439, 0.5871156109281356, 0.542202899756791, 0.3497829772970562, 0.05186115183842467, -0.2978829027896945, -0.6406628205192175, -0.9200649310207203, -1.0895647675022784, -1.1191379289824561, -1.000068332506898, -0.7472211094066854, -0.3983193665741484, -0.010117806014500633, 0.34823753113478856, 0.6039840676934023, 0.690641297425302, 0.5577990430939255, 0.1794849948559377, -0.44010525742426115, -1.2644677923012515, -2.2267780138152613, -3.236027134210331, -4.186769423830152, -4.971416487821793, -5.493597901559287, -5.680865800875097, -5.495001371545231, -4.938402528080176, -4.055480260429637, -2.9286182723084044, -1.668979291380251, -0.40317402058049373, 0.7425602465834781, 1.6585927064147852, 2.2663082657561366, 2.5286148055606614, 2.454937722340479, 2.0998170376334135, 1.5551138316812507, 0.9367655095889782, 0.3678654808746649, -0.03954920542159642, -0.20134295845155978, -0.0742153293098911, 0.3373134284437727, 0.9810617511862438, 1.7646308610392, 2.5691546500132802, 3.267369626549888, 3.743288621669409, 3.9104358070708263, 3.725747995026881, 3.1968636666022494, 2.381525317157834, 1.3790635822953485, 0.3152179479177399, -0.6773326927832145, -1.4795984992598887, -2.004678245189497, -2.2108481490940766, -2.1070955920469623, -1.7500981681276513, -1.2331010822362365, -0.6685619111136525, -0.1675626929291633, 0.18037400388610872, 0.32341703706005187, 0.25649852440560983, 0.021519304576029998, -0.30154810128957826, -0.6112255843416843, -0.8058610292659725, -0.8058273886836539, -0.5723747598483829, -0.11936996427329498, 0.4846762197875048, 1.125194713526231, 1.6597142926170598, 1.9427079816866673, 1.8528621337900928, 1.3178418217507213, 0.3318509940806301, -1.0376081784148876, -2.6555524413510048, -4.337461242539003, -5.876664100503366, -7.076664049581103, -7.782831097579621, -7.907834257272667, -7.4461571002524725, -6.474912854469561, -5.140618006994582, -3.6341543383604424, -2.158364018771937, -0.8941480938697547, 0.02871988872531341, 0.5506912495231746, 0.6879625577593281, 0.5235245426419112, 0.18565614168047648, -0.1817393287658995, -0.45090898251529177, -0.5376196408629453, -0.4184402370370894, -0.1342619651484183, 0.22081722265986303, 0.5230675085540237, 0.6503047422979443, 0.514064647110405, 0.08574017666699296, -0.5893250709888469, -1.3934766227944428, -2.1546369509412604, -2.6775529450980917, -2.7825801688137335, -2.344341155348426, -1.322271083905956, 0.22362187908947323, 2.135716265023027, 4.180746465371116, 6.087241081962824, 7.591660575788487, 8.484519367629733, 8.64755496802378, 8.074597923004236, 6.87191674743211, 5.237849974993874, 3.4256743699551353, 1.6970363156066877, 0.2751762933033585, -0.692814226703447, -1.1573726211187447, -1.1675934207319454, -0.8524755860204762, -0.38683012494913305, 0.05042511182240048, 0.3163517991736722, 0.33373957532033344, 0.10422484185577557, -0.29769694394318374, -0.7478828993053349, -1.1071675022720002, -1.2589851938619023, -1.1409002261163723, -0.7623832456394444, -0.20440644099634014, 0.3992594787110592, 0.8947595280421854, 1.147126338160798, 1.0760611387023584, 0.6795929813226683, 0.039349905732649786, -0.6945845870599376, -1.336400230201076, -1.707704186367863, -1.6811328615408194, -1.2139778514174824, -0.3633368064904734, 0.7216454586523554, 1.8296218394020747, 2.7328889089931123, 3.239128720814698, 3.2371551161122234, 2.725721994403061, 1.8180071602521506, 0.7198021238443458, -0.31449492240024535, -1.0386726031246585, -1.2715883826312209, -0.9410141619297089, -0.10394138730608024, 1.0620143683978587, 2.2949362511966447, 3.305053804342555, 3.8388953039734104, 3.736685824698614, 2.9698121619368063, 1.6495437009928757, 0.00468869734441069, -1.6670090974445846, -3.0628341564361343, -3.9399117505055865, -4.166112557423987, -3.745509599199778, -2.8127967532421128, -1.598364112589585, -0.3726158003165684, 0.6170457767382573, 1.2015350164901628, 1.3246839718043988, 1.0492872141160743, 0.5338160980666549, -0.013742420606744573, -0.39286195630309323, -0.46362522503934783], 'positive_zeros': ['2.46226332221243273219859838064514', '4.27452366427808116285918108049866', '5.36914963372050459797324852327248', '7.45493021591467685250194043414857', '8.144222999300983639955298212478631', '9.253284770334073351238668041356094', '9.916371293635257229419632999669983', '11.66688037839373729069839091181751', '12.85911490787057971579744367288050', '13.15506501451826156480816098035737'], 'prelabel': '2-123-123.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9910398301086335, 'root_angle': 0.17712027095231292, 'root_number': '0.8491408972565808 + 0.5281663910230268*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0885601354762', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.46226332221243273219859838065', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.27452366427808116285918108050', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.36914963372050459797324852327', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.9821599448617492, 'bad_primes': [3, 41], 'central_character': '123.101', 'conductor': 123, 'conductor_radical': 123, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/123/2/o/a/101/6'], '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': '2-123-123.101-c1-0-5', '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': '2-123-123.101-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9910398301086335, 'root_angle': 0.08856013547615646, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.46226332221243273219859838065', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '3121289578322544564787020158229', 'Lhash_array': ['3121289578322544564787020158229'], 'label': '2-123-123.101-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/123/2/o/a/101/6'}