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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': '466189646202093001', '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': 231.88556746979836, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, 1]], [11, [1]]], 'bad_primes': [2, 3, 5, 11], 'central_character': '29040.1', 'coefficient_field': '1.1.1.1', 'conductor': 29040, 'conductor_radical': 330, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 1], [1, -1, 7], [1], [1, 1, 13], [1, 3, 17], [1, -1, 19], [1, 6, 23], [1, -3, 29], [1, -4, 31], [1, 1, 37], [1, 0, 41], [1, -4, 43], [1, 6, 47], [1, -6, 53], [1, -6, 59], [1, 10, 61], [1, 2, 67], [1, -15, 71], [1, 4, 73], [1, -10, 79], [1, 3, 83], [1, -12, 89], [1, -8, 97]], 'gamma_factors': [[], [0]], 'index': 56, 'label': '2-29040-1.1-c1-0-56', 'leading_term': '4.0977232692', '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': 1, 'origin': 'EllipticCurve/Q/29040/r', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 0.9343194371431713, 1.334384122310256, 0.7950668763063509, -0.5975500174641942, -2.017153861717685, -2.296023663706681, -0.9346647240286471, 1.133991740614485, 2.025281155696364, 0.5864979232669801, -2.213106859553073, -3.865479427470688, -2.725295435881115, 0.146484087622138, 1.944777543049463, 1.149675277261635, -0.7918018826602132, -1.314887634340245, -0.01329352819587234, 0.8594136313826488, -0.4789977256395528, -2.674590544803498, -2.890564032739536, -0.7899065190654605, 0.7790446832327625, -0.2658086373274887, -2.130028130831641, -1.645565135214526, 0.9540363505946965, 2.167408354537659, 0.4698135983571408, -1.182974444568268, 0.1591638140681884, 2.543577485705955, 1.742005961011564, -2.067048667922585, -3.982280732889595, -1.522543143980892, 1.589292676771081, 1.07838163138636, -1.521145222075631, -1.7569833586188, 0.514902974585708, 1.371847642206202, -0.3120413712532525, -1.26533177120906, 0.05448034281330421, 0.7831573454990607, -0.6623270077838938, -1.059517574050951, 1.832839690792047, 4.287276052205385, 2.342030305503545, -0.9665637023328205, -0.1692100958118674, 3.291438839050082, 3.339202779464437, -0.2526221793519416, -1.450613620699119, 1.544722411365245, 3.450199372600933, 1.467281199150683, -0.2566712555237362, 1.067337154276093, 1.800104867743797, -0.5843301076050743, -2.167605475568905, 0.05076197740589167, 2.278478087956248, 1.042142445199853, -0.4784791115120609, 0.7582496514728008, 1.345989468837142, -1.439401740133129, -3.141400293487581, -0.1045189217498456, 3.003743734882025, 1.51992714800195, -0.5414595171761216, 1.402315483081037, 3.210450055353963, 0.1068763070990563, -3.446256057098556, -1.831070479793169, 1.158404293589592, -0.1137014648403681, -2.457951075718524, -0.8196566248199243, 1.745754213329236, 0.8569278815343289, -0.3991031457849083, 1.335903483620761, 2.258173067006839, -0.4237255020438803, -2.209796705527848, -0.4813989067339419, 0.4885193261557783, -0.4199053959889729, 1.755041606974203, 6.147698730790687, 5.075846643994404, -1.023391832050045, -2.716316909697696, 1.398039857675159, 2.742312380039577, -0.4733479968854528, -1.169119929699182, 1.508334806144209, 1.56958662789006, -0.5343406124074368, 0.2707598647109649, 2.054117699868206, 0.530737687815949, -0.8796651541651028, 1.418936960099025, 2.739086752417815, 0.269228636509093, -0.2712472975223604, 2.961359450967121, 3.308924142724688], 'positive_zeros': ['0.9041645862580797', '1.860770975861024', '2.555969003907213', '3.487066091315940', '4.142736722984458', '4.752132018254764', '5.193180419517382', '6.088399971116731', '6.466228189110522', '7.162104656498170', '7.799606330808023', '8.234485577338447', '8.871945351171085', '9.602189247414716', '10.10147396566855', '10.69552966775721', '11.21133069842995', '11.74182927848859', '12.15647370918830', '12.61807402495277', '13.40682178350372', '13.76331738472025', '14.48199539131920', '14.89216056836532', '15.66166123838191', '15.84914392648904', '16.45115486441754', '16.99605838770783', '17.62348480978067', '17.89447969814492', '18.39386264947865', '19.00601768607468', '19.63734667395069', '19.87563425266797'], 'prelabel': '2-29040-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 15.22778931656852, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 466189646202093001, 'z1': {'__RealLiteral__': 0, 'data': '0.9041645862580797', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.860770975861024', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.555969003907213', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 231.88556746979836, 'bad_primes': [2, 3, 5, 11], 'central_character': '1.1', 'conductor': 29040, 'conductor_radical': 330, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -1, 0, 1, 0, 1, 0, 0, 0, -1, 0, 1, 0, -3, 0, 1, 0, -1, 0, -6, 0, 1, 0, -1, 0, 3, 0, 4, 0, 0, 0, -1, 0, -1, 0, 1, 0, 0, 0, 4, 0, -1, 0, -6, 0, -6, 0, 3, 0, 6, 0, 0, 0, -1, 0, 6, 0, -10, 0, 1, 0, 1, 0, -2, 0, 6, 0, 15, 0, -4, 0, -1, 0, 0, 0, 10, 0, 1, 0, -3, 0, 3, 0, -3, 0, 12, 0, -1, 0, -4, 0, -1, 0, 8, 0, 0, 0], 'euler11': [1, 0, 0], 'euler13': [1, 1, 13], 'euler17': [1, 3, 17], 'euler19': [1, -1, 19], 'euler2': [1, 0, 0], 'euler23': [1, 6, 23], 'euler29': [1, -3, 29], 'euler3': [1, 1, 0], 'euler31': [1, -4, 31], 'euler37': [1, 1, 37], 'euler41': [1, 0, 41], 'euler43': [1, -4, 43], 'euler47': [1, 6, 47], 'euler5': [1, 1, 0], 'euler53': [1, -6, 53], 'euler59': [1, -6, 59], 'euler61': [1, 10, 61], 'euler67': [1, 2, 67], 'euler7': [1, -1, 7], 'euler71': [1, -15, 71], 'euler73': [1, 4, 73], 'euler79': [1, -10, 79], 'euler83': [1, 3, 83], 'euler89': [1, -12, 89], 'euler97': [1, -8, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 1, 0], [1, -1, 7], [1, 0, 0], [1, 1, 13], [1, 3, 17], [1, -1, 19], [1, 6, 23], [1, -3, 29], [1, -4, 31], [1, 1, 37], [1, 0, 41], [1, -4, 43], [1, 6, 47], [1, -6, 53], [1, -6, 59], [1, 10, 61], [1, 2, 67], [1, -15, 71], [1, 4, 73], [1, -10, 79], [1, 3, 83], [1, -12, 89], [1, -8, 97]], 'index': 56, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/29040/r'], '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': '2-29040-1.1-c1-0-56', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-29040-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 15.22778931656852, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 466189646202093001, 'z1': {'__RealLiteral__': 0, 'data': '0.9041645862580797', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '466189646202093001', 'Lhash_array': ['466189646202093001'], 'label': '2-29040-1.1-c1-0-56', 'type': 'ECQ', 'url': 'EllipticCurve/Q/29040/r'}