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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 2, 'A4': 0, 'A5': -2, 'A6': 0, 'A7': 5, 'A8': 0, 'A9': 1, 'Lhash': '8079942552512156', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [1.1547005383792517, 0], 'a4': [0.0, 0], 'a5': [-0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [1.889822365046136, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 839.5151866909339, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [6571, [1, 1]]], 'bad_primes': [2, 6571], 'central_character': '105136.1', 'coefficient_field': '1.1.1.1', 'conductor': 105136, 'conductor_radical': 13142, 'degree': 2, 'euler_factors': [[1], [1, -2, 3], [1, 2, 5], [1, -5, 7], [1, -6, 11], [1, 6, 13], [1, 3, 17], [1, -8, 19], [1, -2, 23], [1, -2, 29], [1, -9, 31], [1, 4, 37], [1, 6, 41], [1, -12, 43], [1, 3, 47], [1, -3, 53], [1, 6, 59], [1, 0, 61], [1, -5, 67], [1, -16, 71], [1, 10, 73], [1, -7, 79], [1, -1, 83], [1, 6, 89], [1, 15, 97]], 'gamma_factors': [[], [0]], 'index': 0, 'label': '2-105136-1.1-c1-0-0', 'leading_term': '5.22724717567', '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/105136/d', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [5.227247175668888, 4.330791992562731, 2.029329991239263, -0.4672664397271743, -1.585167387667877, -0.7010822631765594, 0.9695210234927683, 1.407112663519031, 0.0780248502093786, -1.262179833591773, -0.7201513420997736, 1.070058699849007, 1.559153438206473, -0.1745591915617081, -1.888068884740061, -1.321770940576097, 0.3475391637560954, 0.3179617548372327, -1.178226847301168, -1.118774562268626, 0.7139990929485426, 0.0841297514576555, -5.030549428020539, -9.309516607272009, -6.282795708513539, 1.920351079444152, 6.574533094031167, 4.12935629877149, 0.04287378351054166, -0.5080970963274507, 0.6114098883516685, 0.0807095667336983, -0.7123341354658335, 0.3109553737559997, 1.125861474122233, 0.01764646935233851, -0.2763657849333956, 1.778307589821646, 2.331562733936827, -0.305418723388121, -0.3911034291223873, 5.529653047027124, 10.49690389994933, 7.530715450590046, 1.267724465367059, -0.4072522796681286, 0.9242047519130089, 0.1539194656922783, -0.7557670425723927, 0.7226953508133332, -0.7499055762242731, -8.430785921512882, -14.05586533141849, -10.15180164546115, -2.514562587689458, 0.35078366608205, -0.03780104707345774, 0.6205028204036017, 0.817670425179503, -0.3901469390589222, -0.1764809856575713, 0.514664643886553, -1.213589621811833, -1.107827277811935, 5.001684324163803, 9.405314039649525, 4.317558563505332, -2.7297234632006, -2.155898864343509, 1.07212657587675, 0.3523464072520188, 0.9690904663888341, 5.782859499824188, 6.240863207980724, -0.1032788135803205, -3.382164813731666, -0.3060371758427536, 1.536075444940668, 0.1556862423436113, -0.007695370129721051, 0.1739300290290389, -1.238472079333433, -0.9157390718056074, 0.5888378486325211, -1.590967098151891, -3.923213775095845, -0.4509202547593116, 2.708548173043206, -0.530503963502761, -2.411527944719371, 1.246216234292616, 0.866362038807683, -4.727639585511941, -3.365615784496275, 4.769855823089147, 6.656508894354409, 1.853119528197065, -0.2389940623489491, 0.2576516155056692, -0.03754961120917959, 1.212834103384439, 1.520644804295572, -4.000060511323402, -8.332298774511194, -4.042618968154257, 1.278198503325258, 0.7207428166325779, -0.3698613492904208, 0.3650573530783998, -0.4836027125932086, -0.6499166178694478, 0.0390454607307351, -4.486420898006619, -8.885952643636514, -2.377008597734579, 5.646480764721967, 1.208960726716958, -5.13229356996303, -0.237031804355213, 5.556970889876699, 2.608406030768167], 'positive_zeros': ['0.6965568344241447', '1.351140720885502', '2.011146449372398', '2.602735710289077', '3.230684805574466', '3.937257283717921', '4.308527691662332', '4.901263293152584', '5.256543698943850', '6.191687651249469', '7.004184239241558', '7.350100568422867', '7.766379684537998', '8.198039048917873', '8.753248764007925', '9.048663601893880', '9.722430440071853', '10.02700545529568', '11.08819414187222', '11.32823223013953', '11.77255325163238', '12.14384315245348', '12.45719082999505', '13.66196508964497', '13.96036663659987', '14.06597595217917', '14.66578458410797', '15.03743949132392', '15.35897039771488', '15.81509237545613', '16.63082251603641', '17.13987658012247', '17.58395682024353', '17.62578822479976', '18.49611294750191', '19.02078745448427', '19.53387181491412', '19.75278754018764'], 'prelabel': '2-105136-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 28.974388461034582, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 8079942552512156, 'z1': {'__RealLiteral__': 0, 'data': '0.6965568344241447', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.351140720885502', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.011146449372398', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 839.5151866909339, 'bad_primes': [2, 6571], 'central_character': '1.1', 'conductor': 105136, 'conductor_radical': 13142, 'degree': 2, 'dirichlet_coefficients': [1, 0, 2, 0, -2, 0, 5, 0, 1, 0, 6, 0, -6, 0, -4, 0, -3, 0, 8, 0, 10, 0, 2, 0, -1, 0, -4, 0, 2, 0, 9, 0, 12, 0, -10, 0, -4, 0, -12, 0, -6, 0, 12, 0, -2, 0, -3, 0, 18, 0, -6, 0, 3, 0, -12, 0, 16, 0, -6, 0, 0, 0, 5, 0, 12, 0, 5, 0, 4, 0, 16, 0, -10, 0, -2, 0, 30, 0, 7, 0, -11, 0, 1, 0, 6, 0, 4, 0, -6, 0, -30, 0, 18, 0, -16, 0, -15, 0, 6, 0], 'euler11': [1, -6, 11], 'euler13': [1, 6, 13], 'euler17': [1, 3, 17], 'euler19': [1, -8, 19], 'euler2': [1, 0, 0], 'euler23': [1, -2, 23], 'euler29': [1, -2, 29], 'euler3': [1, -2, 3], 'euler31': [1, -9, 31], 'euler37': [1, 4, 37], 'euler41': [1, 6, 41], 'euler43': [1, -12, 43], 'euler47': [1, 3, 47], 'euler5': [1, 2, 5], 'euler53': [1, -3, 53], 'euler59': [1, 6, 59], 'euler61': [1, 0, 61], 'euler67': [1, -5, 67], 'euler7': [1, -5, 7], 'euler71': [1, -16, 71], 'euler73': [1, 10, 73], 'euler79': [1, -7, 79], 'euler83': [1, -1, 83], 'euler89': [1, 6, 89], 'euler97': [1, 15, 97], 'euler_factors': [[1, 0, 0], [1, -2, 3], [1, 2, 5], [1, -5, 7], [1, -6, 11], [1, 6, 13], [1, 3, 17], [1, -8, 19], [1, -2, 23], [1, -2, 29], [1, -9, 31], [1, 4, 37], [1, 6, 41], [1, -12, 43], [1, 3, 47], [1, -3, 53], [1, 6, 59], [1, 0, 61], [1, -5, 67], [1, -16, 71], [1, 10, 73], [1, -7, 79], [1, -1, 83], [1, 6, 89], [1, 15, 97]], 'index': 0, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/105136/d'], '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': '2-105136-1.1-c1-0-0', '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': '2-105136-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 28.974388461034582, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 8079942552512156, 'z1': {'__RealLiteral__': 0, 'data': '0.6965568344241447', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '8079942552512156', 'Lhash_array': ['8079942552512156'], 'label': '2-105136-1.1-c1-0-0', 'type': 'ECQ', 'url': 'EllipticCurve/Q/105136/d'}