-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1239325994649656663657225772246', 'a10': [0, 0], 'a2': [0, 0], 'a3': [1.701659167912, 0.3230419109976908], 'a4': [0, 0], 'a5': [0, 1.5548068384992908], 'a6': [0, 0], 'a7': [0, 0], 'a8': [0, 0], 'a9': [2.79128784747792, 1.0994144589380659], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 18.780814555405154, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.701659167912, -0.3230419109976908]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 7], 'central_character': '2352.2255', 'coefficient_field': 'CDF', 'conductor': 2352, 'conductor_radical': 42, 'conjugate': '1657933780346059892304387034528', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.701659167912, -0.3230419109976908]], [[1.0, 0], [0, -1.5548068384992908], [-5.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 0], [11.0, 0]], [[1.0, 0], [-2.5332635680173827, 0], [13.0, 0]], [[1.0, 0], [0, -4.339913433478635], [-17.0, 0]], [[1.0, 0], [0, 6.837230951552501], [-19.0, 0]], [[1.0, 0], [-3.8084834029131542, 0], [23.0, 0]], [[1.0, 0], [0, 8.336393355026804], [-29.0, 0]], [[1.0, 0], [0, -4.898979485566356], [-31.0, 0]], [[1.0, 0], [-1.58257569495584, 0], [37.0, 0]], [[1.0, 0], [0, -7.449527110477217], [-41.0, 0]], [[1.0, 0], [0, -6.2052031256248945], [-43.0, 0]], [[1.0, 0], [5.38600888047262, 0], [47.0, 0]], [[1.0, 0], [0, -10.535222272902935], [-53.0, 0]], [[1.0, 0], [-10.209955007471999, 0], [59.0, 0]], [[1.0, 0], [8.190117817509762, 0], [61.0, 0]], [[1.0, 0], [0, 3.4641016151377544], [-67.0, 0]], [[1.0, 0], [14.439056842785996, 0], [71.0, 0]], [[1.0, 0], [-11.547267834442625, 0], [73.0, 0]], [[1.0, 0], [0, 6.928203230275509], [-79.0, 0]], [[1.0, 0], [-4.82394612699938, 0], [83.0, 0]], [[1.0, 0], [0, -4.339913433478635], [-89.0, 0]], [[1.0, 0], [9.899494936611665, 0], [97.0, 0]], [[1.0, 0], [0, -19.563474736452307], [-101.0, 0]], [[1.0, 0], [0, -3.87650293197229], [-103.0, 0]], [[1.0, 0], [-14.439056842785996, 0], [107.0, 0]], [[1.0, 0], [13.58257569495584, 0], [109.0, 0]], [[1.0, 0], [0, 14.473957792177474], [-113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 42, 'label': '2-2352-12.11-c1-0-42', 'leading_term': '2.8102739436451916866640960292922931450549523371733676997', '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/2352/2/h/p/2255/16', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [2.810273943645192, 2.7403202469029173, 2.6621167937655965, 2.5755660476105526, 2.4804545482900138, 2.376494992373098, 2.263373783595405, 2.140801485078165, 2.0085636415475485, 1.8665696454787355, 1.7148976379327607, 1.5538338029945562, 1.3839047840548782, 1.2059022867384366, 1.0208992203266536, 0.8302569648383706, 0.6356235422476653, 0.438922630534135, 0.2423335024794838, 0.04826210991303991, -0.14069632203326676, -0.3218026713310609, -0.49222657888074967, -0.6491055244260059, -0.7896092625684926, -0.9110083713014209, -1.0107454780583522, -1.0865075530765393, -1.1362975054518591, -1.1585031922519728, -1.1519618638092017, -1.1160180265618806, -1.0505727153326792, -0.9561222352569476, -0.8337845637103249, -0.6853117967635202, -0.5130872831532465, -0.3201064095798042, -0.1099403801224548, 0.11331723683172595, 0.3451209473740455, 0.5805600047324768, 0.8144600403128301, 1.0414978503165773, 1.2563270204811516, 1.453711586858027, 1.628664493786723, 1.776587239139241, 1.8934068086320248, 1.9757058113538342, 2.02084165149676, 2.0270506178572565, 1.9935329510363704, 1.9205152626989523, 1.8092871318211368, 1.6622092850714134, 1.4826914730621632, 1.2751389670628603, 1.044867503032786, 0.7979874682041469, 0.5412591326290359, 0.2819217434534611, 0.027500290028239935, -0.21440532141524557, -0.43634310908058405, -0.6312375920701472, -0.7926172764521885, -0.9148338714302907, -0.993265917346496, -1.0244996023027357, -1.00647988480289, -0.9386256299467877, -0.8219033018105447, -0.6588548212787657, -0.4535764742712818, -0.21164720871026144, 0.059993749916017136, 0.3532183519511967, 0.6589269130531697, 0.9673060064753425, 1.2681204051999393, 1.5510309435748084, 1.805928893061956, 2.023276430401237, 2.1944420692735873, 2.3120195704928523, 2.3701188726049276, 2.3646180141253645, 2.2933658564971524, 2.15632665456048, 1.9556591350871695, 1.6957246947772895, 1.3830215635138374, 1.0260442297205337, 0.6350700138700612, 0.2218773157842835, -0.2005973428445077, -0.6186539046970406, -1.0182631994802676, -1.3855275254895882, -1.7071522436983522, -1.9709122588755459, -2.1660968313676277, -2.283916321011111, -2.31785523107993, -2.2639572927885183, -2.121030283886902, -1.8907607590243305, -1.5777318128479514, -1.1893403063065227, -0.7356135511176732, -0.2289291408497287, 0.3163546968579108, 0.8843473156788654, 1.4581382769462543, 2.020357412702563, 2.5537630864590857, 3.041837809097549, 3.4693695112804392, 3.822996725157106, 4.091696717119198, 4.267197237532185, 4.344294976762151, 4.321066969884834, 4.198964973599216, 3.9827871172948814, 3.680525750239612, 3.303095193304187, 2.8639478684342277, 2.378591828529758, 1.8640268531076427, 1.3381198301061714, 0.8189429488496013, 0.32410014686298827, -0.12993182008483814, -0.5284214453765419, -0.8589346471544081, -1.1117982915137998, -1.2804555626187217, -1.3616978190478748, -1.3557624433541278, -1.266291599152905, -1.1001525402260366, -0.8671259320320861, -0.5794742999569223, -0.2514079628512513, 0.10152959205566887, 0.46313120120821044, 0.8172220019268253, 1.148352010604889, 1.4424551969529673, 1.6874460494391292, 1.8737270295385997, 1.9945839399069605, 2.0464509496590897, 2.029032641304496, 1.9452767353929503, 1.8011978407316434, 1.6055593748794623, 1.369427393578362, 1.1056161520454175, 0.8280505041388839, 0.5510744651103726, 0.2887382000562906, 0.0540971871847247, -0.14144276032219405, -0.2887025808349936, -0.38120032198439585, -0.41549055905596716, -0.3913545365190812, -0.3118295657292743, -0.18307377751633833, -0.014070245350251514, 0.18381760675256814, 0.3974198964223091, 0.612437326782951, 0.8141896114365826, 0.9883992986661827, 1.1219724518969323, 1.2037368993668331, 1.2250999221015753, 1.180590299147709, 1.068254473945461, 0.8898830570282444, 0.6510516657301058, 0.36096887640135555, 0.03213342595850768, -0.3201876953291788, -0.6786394312507035, -1.0245878898972514, -1.3390221825212094, -1.6035068384944156, -1.8011390828196652, -1.9174637320190553, -1.9412992175663129, -1.8654313079091909, -1.6871363817691059, -1.40850340588942, -1.0365327834769682, -0.5830005659190889, -0.0640876848370516, 0.5002146652031856, 1.0869011396564456, 1.6709170864918441, 2.226250285685686, 2.727100514970663, 3.1490728643894608, 3.470338249318088, 3.6727048160591598, 3.742546948230002, 3.6715442812477375, 3.4571912951939643, 3.103048333596088, 2.6187168234498976, 2.019534492924884, 1.3259998729153233, 0.5629486647279095, -0.24148300822220323, -1.0570625097296418, -1.8527769433048087, -2.5982006243374944, -3.264849263118221, -3.8274561075788274, -4.265108262482913, -4.562187485179539, -4.709068701738928, -4.702540885451405, -4.545928253614407, -4.248904321935186, -3.8270064860929, -3.3008737140447466, -2.695243866053105, -2.037759385950224, -1.3576399774812788, -0.6842878564799971, -0.04589485823707525, 0.5318791496522582, 1.0270904943485277, 1.4224993352064912, 1.7063114173772453, 1.8726372056254343, 1.921646211363718, 1.8594101195906882, 1.697444539172027, 1.451974985086244, 1.1429672125335717, 0.7929744755961523, 0.4258639937356297, 0.06549133342619523, -0.265605823895383, -0.5474241325207502, -0.7635557465393266, -0.9020371612100901, -0.9559403118612099, -0.923674664438091, -0.8089849674995616, -0.6206461903587217], 'positive_zeros': ['0.977655826003258989203126608043230', '1.95500393922573853964274194190859', '3.15405230307011067506379939769287', '3.84855251123148603809533982105172', '4.85092451330527943574722344152722', '5.65839486864211910471222936865270', '6.78957606281475232990130153655907', '7.39968277281819967265459983549038', '8.341101997699372652374092286804774', '8.738204191559513176282917909837090'], 'prelabel': '2-2352-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.33368371658629, 'root_angle': -0.27361619840082063, 'root_number': '0.65274764483033928770181796571157138753372582899463871214 - 0.75757541681897600746842032108637056205616916279559885460*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.13680809920041032', 'prec': 67}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.977655826003258989203126608043', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.95500393922573853964274194191', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.15405230307011067506379939769', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 18.780814555405154, 'bad_primes': [2, 3, 7], 'central_character': '12.11', 'conductor': 2352, 'conductor_radical': 42, 'degree': 2, 'index': 42, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2352/2/h/p/2255/16'], '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': '2-2352-12.11-c1-0-42', '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': '2-2352-12.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.33368371658629, 'root_angle': -0.13680809920041032, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.977655826003258989203126608043', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1239325994649656663657225772246', 'Lhash_array': ['1239325994649656663657225772246'], 'label': '2-2352-12.11-c1-0-42', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2352/2/h/p/2255/16'}