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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': -1, 'A4': 0, 'A5': -1, 'A6': 0, 'A7': 1, 'A8': 0, 'A9': 1, 'Lhash': '14314369748366822', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [-0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.0, 0], 'a7': [0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1841.6696722188117, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, 1]], [31, [1]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '230640.1', 'coefficient_field': '1.1.1.1', 'conductor': 230640, 'conductor_radical': 930, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 1], [1, -1, 7], [1, 3, 11], [1, -6, 13], [1, -4, 17], [1, 1, 19], [1, 3, 23], [1, 8, 29], [1], [1, -12, 37], [1, 0, 41], [1, -9, 43], [1, -2, 47], [1, -1, 53], [1, 6, 59], [1, 10, 61], [1, 2, 67], [1, 3, 71], [1, 1, 73], [1, 7, 79], [1, -12, 83], [1, -5, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 19, 'label': '2-230640-1.1-c1-0-19', 'leading_term': '1.68309830255', 'load_key': 'Cremona', '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': 'EllipticCurve/Q/230640/m', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.683098302546041, 0.9872149197828766, -0.5312270781243928, -1.450508597504316, -0.6959058751643717, 0.9305090686385933, 1.115971145501516, -1.09399616052805, -3.296085790305054, -2.209907012955657, 1.645526607076625, 3.82148091261284, 1.757173677477828, -1.387160957575148, -1.222921011941383, 1.313642170352009, 1.788771348315357, -0.2006929289962174, -0.4641235392514958, 2.155818585791339, 3.404507104140421, 1.113808437417702, -0.9270737158570941, -0.07731054724658724, 0.4645500630847288, -1.322020638367236, -1.317625234094458, 2.798321714326259, 5.666691835766632, 3.157798238990633, -0.2306672738895751, -0.1716360806058261, -0.2150620213531261, -2.878404248999298, -2.986907276762362, 1.56878586088543, 3.667664057458341, 0.221595498512696, -1.089065865272225, 3.380255621820808, 5.970105418105376, 2.68516896428322, -0.02726281845694239, 0.901422552149918, 0.7696223151672132, -0.7849744972191435, 0.2244147949705883, 1.309253259748878, -1.334078790471536, -2.945629469886433, -0.005439160259083004, 1.452512483039602, -0.8835700338049841, -0.5131505633272785, 2.094133264549369, -0.5044538088373361, -4.824136111384123, -2.080928103193016, 2.709510927859712, 0.9847186966158972, -1.577537663069773, 1.306113035711503, 3.132062667064186, 0.439316595022216, -0.4248715459581849, 0.6777600921867644, -1.05238415626256, -1.634718632826267, 1.988242973105766, 2.439482186545331, -1.704783628935406, -1.926073382823838, 1.275373414048245, 0.9156887106489154, -0.3643076907571547, 0.1506288065997334, -2.823743832533296, -6.256355836228653, -1.515707937454464, 4.4929394269259, 1.768810256349911, -1.805080780426219, 0.8427087492841824, 1.874646311796886, -0.4666940345634575, 0.4187906723332012, 0.4983217073115224, -4.227962875818192, -4.815145157254496, 0.2276463838251933, 0.7208067877807818, -2.161594302467812, -1.060233459883431, 0.1757685496256464, -0.9838269404988234, -0.009791635671913, 0.3400413005821088, -1.818426610234393, 1.188486779714442, 6.342626410869572, 2.531150396993097, -3.269838177659278, -0.7280009535030737, 1.48716014489967, -1.023254625992588, 0.6304557801270402, 2.958492649383871, -1.664531320985987, -4.095904084193723, 0.2629616907324979, 1.62248665049374, -0.1200893669487648, 0.6832073338580547, -0.05795552056515877, -1.589155765553763, 1.461516660527277, 2.612690436837152, -0.5466135598724027, 1.494076791764379, 5.483854375593236, 2.343840323396657], 'positive_zeros': ['0.4147404639288312', '1.104475806160263', '1.649336458806602', '2.398793324058172', '3.123206628328498', '3.621797626026672', '4.224217612673676', '4.559289272080714', '5.348744982986570', '5.763105699599839', '6.086313283328998', '6.600002249452454', '7.470454228504245', '7.795395678461657', '7.961551577001215', '8.672670357645560', '9.264190620078041', '9.584006933848156', '10.48810360450955', '10.56679428868984', '11.10727382935304', '11.47277589564674', '11.90264463179851', '12.50038619714108', '12.91178855123616', '13.29343438429679', '13.72543877907437', '14.33741529226503', '14.81125538089117', '15.16834099816133', '15.79255424935592', '16.07709533665337', '16.39242788386705', '16.87622548107361', '17.39800670907221', '17.88940310961086', '18.37099582973540', '18.63824302128846', '18.79389378335150', '19.54759141945283'], 'prelabel': '2-230640-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 42.91467898305674, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 14314369748366822, 'z1': {'__RealLiteral__': 0, 'data': '0.4147404639288312', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.104475806160263', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.649336458806602', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1841.6696722188117, 'bad_primes': [2, 3, 5, 31], 'central_character': '1.1', 'conductor': 230640, 'conductor_radical': 930, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -3, 0, 6, 0, 1, 0, 4, 0, -1, 0, -1, 0, -3, 0, 1, 0, -1, 0, -8, 0, 0, 0, 3, 0, -1, 0, 12, 0, -6, 0, 0, 0, 9, 0, -1, 0, 2, 0, -6, 0, -4, 0, 1, 0, 3, 0, 1, 0, -6, 0, -10, 0, 1, 0, -6, 0, -2, 0, 3, 0, -3, 0, -1, 0, -1, 0, -3, 0, -7, 0, 1, 0, 12, 0, -4, 0, 8, 0, 5, 0, 6, 0, 0, 0, 1, 0, 2, 0, -3, 0], 'euler11': [1, 3, 11], 'euler13': [1, -6, 13], 'euler17': [1, -4, 17], 'euler19': [1, 1, 19], 'euler2': [1, 0, 0], 'euler23': [1, 3, 23], 'euler29': [1, 8, 29], 'euler3': [1, 1, 0], 'euler31': [1, 0, 0], 'euler37': [1, -12, 37], 'euler41': [1, 0, 41], 'euler43': [1, -9, 43], 'euler47': [1, -2, 47], 'euler5': [1, 1, 0], 'euler53': [1, -1, 53], 'euler59': [1, 6, 59], 'euler61': [1, 10, 61], 'euler67': [1, 2, 67], 'euler7': [1, -1, 7], 'euler71': [1, 3, 71], 'euler73': [1, 1, 73], 'euler79': [1, 7, 79], 'euler83': [1, -12, 83], 'euler89': [1, -5, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 1, 0], [1, -1, 7], [1, 3, 11], [1, -6, 13], [1, -4, 17], [1, 1, 19], [1, 3, 23], [1, 8, 29], [1, 0, 0], [1, -12, 37], [1, 0, 41], [1, -9, 43], [1, -2, 47], [1, -1, 53], [1, 6, 59], [1, 10, 61], [1, 2, 67], [1, 3, 71], [1, 1, 73], [1, 7, 79], [1, -12, 83], [1, -5, 89], [1, -2, 97]], 'index': 19, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/230640/m'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': True, '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': '2-230640-1.1-c1-0-19', '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': '2-230640-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 42.91467898305674, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 14314369748366822, 'z1': {'__RealLiteral__': 0, 'data': '0.4147404639288312', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '14314369748366822', 'Lhash_array': ['14314369748366822'], 'label': '2-230640-1.1-c1-0-19', 'type': 'ECQ', 'url': 'EllipticCurve/Q/230640/m'}