-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '2181982676351763732221990392360', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.15891862259789113, 1.724744871391589], 'a4': [0.0, 0.0], 'a5': [-1.224744871391589, -0.7071067811865476], 'a6': [0.0, 0.0], 'a7': [0.2679491924311227, 0.0], 'a8': [0.0, 0.0], 'a9': [-2.949489742783178, 0.5481881585886564], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.282356664340774, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.15891862259789113, -1.724744871391589]]], [19, [[1.0, 0], [1.7320508075688772, -4.0]]]], 'bad_primes': [2, 3, 19], 'central_character': '912.65', 'coefficient_field': 'CDF', 'conductor': 912, 'conductor_radical': 114, 'conjugate': '309305512785822729394281004294', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.15891862259789113, -1.724744871391589]], [[1.0, 0], [1.224744871391589, 0.7071067811865476], [2.5, 4.330127018922194]], [[1.0, 0], [-0.2679491924311227, 0], [7.0, 0]], [[1.0, 0], [0, 5.277916867529369], [-11.0, 0]], [[1.0, 0], [0.2320508075688773, -0.13397459621556135], [6.5, -11.258330249197702]], [[1.0, 0], [4.242640687119285, 2.449489742783178], [8.5, 14.722431864335457]], [[1.0, 0], [1.7320508075688772, -4.0]], [[1.0, 0], [4.570810086342821, -2.6389584337646843], [11.5, -19.91858428704209]], [[1.0, 0], [1.035276180410083, 1.793150944336107], [-14.5, 25.11473670974872]], [[1.0, 0], [0, 2.4641016151377544], [-31.0, 0]], [[1.0, 0], [0, 7.732050807568878], [-37.0, 0]], [[1.0, 0], [-2.8284271247461903, 4.898979485566356], [-20.5, -35.50704155516198]], [[1.0, 0], [-2.866025403784439, 4.964101615137754], [-21.5, -37.239092362730865]], [[1.0, 0], [0.6563387984470711, -0.378937381963012], [23.5, -40.703193977868615]], [[1.0, 0], [-5.467385558510874, -9.469789571909176], [-26.5, 45.89934640057525]], [[1.0, 0], [-5.606086266752904, 9.710026245630159], [-29.5, -51.09549882328188]], [[1.0, 0], [-5.232050807568878, -9.062177826491071], [-30.5, 52.827549630850754]], [[1.0, 0], [-0.8660254037844386, 0.5], [33.5, -58.023702053557386]], [[1.0, 0], [6.6921304299024635, -11.59110991546882], [-35.5, -61.48780366869514]], [[1.0, 0], [-1.5, 2.598076211353316], [-36.5, -63.21985447626402]], [[1.0, 0], [9.062177826491071, 5.232050807568878], [39.5, 68.41600689897065]], [[1.0, 0], [0, -2.070552360820166], [-83.0, 0]], [[1.0, 0], [3.6742346141747673, 6.363961030678928], [-44.5, 77.07626093681505]], [[1.0, 0], [0.4641016151377546, 0.2679491924311227], [48.5, 84.00446416709055]], [[1.0, 0], [-1.793150944336107, 1.035276180410083], [50.5, -87.4685657822283]], [[1.0, 0], [0, 3.5358983848622456], [-103.0, 0]], [[1.0, 0], [-4.898979485566356, 0], [107.0, 0]], [[1.0, 0], [5.535898384862246, 3.196152422706632], [54.5, 94.39676901250381]], [[1.0, 0], [3.965239270635226, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 32, 'label': '2-912-57.8-c1-0-32', '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/912/2/bn/m/65/3', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.5489778009562563, 0.79402728169387, 1.0191142384879486, 1.223299656302294, 1.401198920190293, 1.5434357009491355, 1.6379347783758726, 1.671772404971452, 1.6333297044341162, 1.5145339316093551, 1.3129798453574197, 1.0337034300658938, 0.6903575663129738, 0.3055385942700063, -0.08994919868924099, -0.4590196836214635, -0.7614206851847422, -0.9578743907933669, -1.014896942772009, -0.9097807991737927, -0.6350917379562239, -0.20197019097414706, 0.3584405166063787, 0.9959730779736059, 1.6451021924356712, 2.231230914113287, 2.6791291672920456, 2.922654568800455, 2.914549441678516, 2.6349042754418637, 2.0968641614660624, 1.348366131072553, 0.4691345459725274, -0.43720761293306787, -1.255307466679136, -1.8731738496093493, -2.1982023918002294, -2.1717592071681513, -1.7799110949824881, -1.0582551030354852, -0.08955654277707807, 1.006031406410854, 2.0871727246132967, 3.011807335483088, 3.6587771461760483, 3.947075144341128, 3.8493078612720826, 3.3967261417974823, 2.6744957432380425, 1.8075544064045377, 0.9391512553077844, 0.20565803791682152, -0.28783412681347137, -0.486497109829968, -0.3954679082554831, -0.07800805401525651, 0.3579766997109711, 0.7828125810369728, 1.0730368521661025, 1.13887860327366, 0.9454079783944707, 0.5225009884759816, -0.03915001859448819, -0.6059222602221913, -1.029964533758969, -1.1830597288787668, -0.9884628563723677, -0.44346614594002365, 0.37302418228293355, 1.3106995401295414, 2.174893215584748, 2.7656807552410685, 2.921227998262537, 2.5560783032153744, 1.6855558893139657, 0.4299678057509016, -1.003612959248761, -2.359330853925672, -3.3830679781303985, -3.875056974933444, -3.733117807890937, -2.9765861923105508, -1.7448941358901777, -0.2702389951422942, 1.17035804270336, 2.313408006809244, 2.9648073310271394, 3.0404729377079627, 2.5822543971080467, 1.7451967417735599, 0.7589239698891592, -0.1278571182398902, -0.7065146625879262, -0.857001176897525, -0.5738232157268486, 0.03697458974220822, 0.7890549455698878, 1.4673204460020712, 1.8864630492615941, 1.9412289964354108, 1.6350031605771067, 1.078794676106339, 0.46043509545262024, -0.008191703191352782, -0.15191241735815206, 0.11553545509030931, 0.7625909285848209, 1.6430522028203827, 2.531610203141278, 3.1830376136441463, 3.3994360307918905, 3.0870854990268723, 2.2865943417611856, 1.1668353314860689, -0.017108676331821865, -0.991668942710933, -1.5402181521215799, -1.5652973153208876, -1.1195517698604707, -0.3953182753737583, 0.3259715253857342, 0.7520177063172357, 0.6646141867115748, -0.012347214898732299, -1.181749286830393, -2.5893599376424277, -3.8846764806181473, -4.711345801773261, -4.8031642576540685, -4.059291902666978, -2.577315983928998, -0.6339864463363629, 1.382181276971809, 3.068703507431448, 4.110794870589102, 4.35896083641736, 3.8611184387281496, 2.840616865522239, 1.6269235184756705, 0.5593047078449858, -0.10844774459586047, -0.27467173345172313, -0.008938449698949767, 0.48102097470995675, 0.9234600051249345, 1.0743274398402036, 0.7977944026796877, 0.11045112593917633, -0.8245295585067466, -1.7511463344659923, -2.404832953558127, -2.5998965674860814, -2.2914879219691744, -1.5913627871873819, -0.7314749658914467, 0.013498703871593574, 0.4197271545960326, 0.3928301929099468, 0.004400928940165765, -0.5276570968461216, -0.9109143147046503, -0.8806893165020206, -0.29998428711965985, 0.7766493545259608, 2.098927308712697, 3.281633478204307, 3.914816202053112, 3.690985834745115, 2.509811582071718, 0.5260862479630705, -1.876844100391896, -4.183272994027688, -5.884099846167269, -6.617605679382052, -6.269514178444136, -5.001625911108035, -3.200022777316988, -1.3586955574285022, 0.06545864449727665, 0.7815021722309666, 0.7378286515827139, 0.1186847098809244, -0.7326989424612117, -1.4373535110431401, -1.7086244865133307, -1.4427156517394903, -0.742727465215007, 0.1298906033364664, 0.8577655289924413, 1.186950883657071, 1.0207950205198757, 0.4551720577585915, -0.25725987569187625, -0.8008974676580515, -0.9154395527382053, -0.49580824996094197, 0.3629234480398131, 1.3930083646069724, 2.2454935707641206, 2.613960731728448, 2.3464100615737435, 1.5043422298266953, 0.3461083762988145, -0.7616320748998812, -1.4743584810730077, -1.5959430778254424, -1.1546309627837066, -0.39929759752145955, 0.2856703893228489, 0.5191947891588966, 0.06795820943056499, -1.0554297993572512, -2.577868156745038, -4.043685682369578, -4.96138754250505, -4.970376769448513, -3.9701459835252484, -2.165850893464339, -0.012144578347906661, 1.9278332634698245, 3.16159201732182, 3.4238534844340043, 2.7569503486930236, 1.4874753934708707, 0.10755440880479937, -0.8976171874036373, -1.2156033712187502, -0.8081367224077007, 0.08657770857534013, 1.0499221987334013, 1.6414873109348151, 1.5623954830444091, 0.7643991881855104, -0.5338866072156583, -1.9280478502676974, -2.9750919973996277, -3.351850988063928, -2.966262697438504, -1.9815725298378726, -0.7465932776114312, 0.3394648515847805, 0.974798307379478, 1.058672804147478, 0.7120187774120085, 0.2088926382666349, -0.1520467516426124, -0.18301672706853828, 0.10655870018956949, 0.5097256391595522, 0.7101653049214155, 0.42508193249438847, -0.45474666642514344, -1.7868472503001118, -3.197860631880723, -4.202447610899816, -4.380172863784924, -3.5448788571765144], 'positive_zeros': ['1.72128082924341836682443571601654', '2.67288254076284268713814859926133', '4.06418091952156900545821215911606', '5.01056250342754943947983008074336', '6.41912833207372144341487067993787', '6.89889128135846713628218821820527', '7.74168347229201480685589194694682', '8.446711060340473634434965915963429', '9.413153470421490451716819562830545', '10.39752056417284564200039685410969'], 'prelabel': '2-912-57.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.698584196266771, 'root_angle': 0.5696667692557529, 'root_number': '-0.21712145893434867 + 0.9761445958823006*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.284833384628', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.72128082924341836682443571602', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.67288254076284268713814859926', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.06418091952156900545821215912', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 7.282356664340774, 'bad_primes': [2, 3, 19], 'central_character': '57.8', 'conductor': 912, 'conductor_radical': 114, 'degree': 2, 'index': 32, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/912/2/bn/m/65/3'], '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': '2-912-57.8-c1-0-32', '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': '2-912-57.8-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.698584196266771, 'root_angle': 0.28483338462787644, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.72128082924341836682443571602', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '2181982676351763732221990392360', 'Lhash_array': ['2181982676351763732221990392360'], 'label': '2-912-57.8-c1-0-32', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/912/2/bn/m/65/3'}