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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 2, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': -3, 'Lhash': '1686740431120359243', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.8944271909999159, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [-1.0, 0], 'algebraic': True, 'analytic_conductor': 491.1119125916831, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [31, [1]]], 'bad_primes': [2, 31], 'central_character': '61504.1', 'coefficient_field': '1.1.1.1', 'conductor': 61504, 'conductor_radical': 62, 'degree': 2, 'euler_factors': [[1], [1, 0, 3], [1, -2, 5], [1, 0, 7], [1, 0, 11], [1, -2, 13], [1, -6, 17], [1, 4, 19], [1, 8, 23], [1, -2, 29], [1], [1, -10, 37], [1, 6, 41], [1, -8, 43], [1, 8, 47], [1, 6, 53], [1, -12, 59], [1, 6, 61], [1, -12, 67], [1, -8, 71], [1, 10, 73], [1, -8, 79], [1, -8, 83], [1, -6, 89], [1, -2, 97]], 'gamma_factors': [[], [0]], 'index': 9, 'label': '2-248e2-1.1-c1-0-9', 'leading_term': '2.2749363403', '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/61504/bd', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.274936340295349, 1.652229641130351, 0.05026164373220199, -1.676201691266141, -2.339691496326166, -1.335023158616005, 0.5421960520457675, 1.55401588267202, 0.7485206256203139, -0.7950996364765625, -0.9770886983115524, 0.7684653430200707, 2.449191654086347, 1.811856453023747, -0.5204692694480374, -1.387320829741735, 0.8517392097400148, 3.71267493186308, 3.470289428248357, 0.1496382610053231, -2.343844501785074, -1.499044935432313, 0.5839280879823089, 0.776561986507816, -0.2922155389775675, 0.09151557973113085, 1.339140871488105, -0.1697891345928178, -4.753042031745485, -7.494323255322054, -5.04478258467296, -0.8190582763628874, 0.2303671952485663, -0.8644167696865536, 0.3418213329662465, 3.528773127158725, 4.050175903928734, 1.214391020115168, -0.4058067489643443, 0.9181549328106389, 1.313246687052108, -0.9656429229000988, -1.844797701019675, 0.8264899360342814, 2.551022549869571, 0.1328906601138471, -2.133661647781912, -0.2184177660440694, 2.013641254754984, -0.001561589594540003, -2.741814778688712, -1.088010647205091, 2.023611878792727, 1.21449210071828, -1.354574606008187, -0.7586528783130421, 1.192769036392524, 0.5603535533517674, -0.290736097643388, 1.559037476509118, 1.79776789030718, -3.084971349581113, -7.036964037039675, -4.157676712008996, 0.5179055061882037, 0.3908911962269925, -1.195212823362023, 0.7866292479063286, 2.869863482116716, 1.267154188871851, -0.08630777290990284, 1.38527946097392, 1.159873320458119, -1.786200985983313, -1.581675547677479, 1.919643558576025, 1.63810932415504, -2.227586254765669, -2.096217835980874, 1.470983748635012, 1.031178297056052, -2.259004346063356, -1.577355681021988, 1.150379371068635, 0.2758612890999025, -1.185933266829664, 0.8509027863715188, 1.912498716557982, -0.5167227565867635, -0.4527666882599479, 3.23777652739971, 3.382438975437877, -0.1965466596167905, -0.398019373870136, 1.488627929941234, -0.5567239804463943, -2.410125272331961, 1.796345402845816, 5.632339728190347, 2.563148333206058, -1.256037036980966, -0.3975502729557733, 0.5811315247854705, -0.2171860009696774, 0.5937424423406389, 0.06997247671691081, -5.201007467008116, -7.590325233341932, -1.933226324316247, 2.6038809049163, 0.1974211470026737, -1.316312120446808, 1.251986084871122, 1.046278373846457, -1.556616208775873, -0.3417832650987029, 1.566159417843775, -0.4132102988818082, -0.9884792932094528, 1.993717141908958, 1.887422530242957], 'positive_zeros': ['0.5067663842404504', '1.426544336743667', '2.114853207762413', '2.659840811455148', '3.443637143394505', '3.931123344525700', '4.760311383625453', '5.417338575922606', '5.919767400693519', '6.232185953253571', '6.737692965125393', '7.835446497356291', '8.057112360297133', '8.468097537812307', '9.372105537268707', '9.614753695745830', '10.15765595037748', '10.68741898422632', '11.25958485897620', '11.76686413985853', '12.24989029631141', '12.82414930107008', '13.35365220054425', '13.83213001913330', '14.34151309103945', '14.56832180415608', '15.11609500341845', '15.95833835830160', '16.29411790366936', '16.68556480363879', '17.41739645787844', '17.53469468126970', '18.10215419325057', '18.61295717269431', '19.10563656527761', '19.63994986145899'], 'prelabel': '2-248e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 22.16104493456216, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1686740431120359243, 'z1': {'__RealLiteral__': 0, 'data': '0.5067663842404504', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.426544336743667', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.114853207762413', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 491.1119125916831, 'bad_primes': [2, 31], 'central_character': '1.1', 'conductor': 61504, 'conductor_radical': 62, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 2, 0, 0, 0, -3, 0, 0, 0, 2, 0, 0, 0, 6, 0, -4, 0, 0, 0, -8, 0, -1, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 10, 0, 0, 0, -6, 0, 8, 0, -6, 0, -8, 0, -7, 0, 0, 0, -6, 0, 0, 0, 0, 0, 12, 0, -6, 0, 0, 0, 4, 0, 12, 0, 0, 0, 8, 0, -10, 0, 0, 0, 0, 0, 8, 0, 9, 0, 8, 0, 12, 0, 0, 0, 6, 0, 0, 0, 0, 0, -8, 0, 2, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, -2, 13], 'euler17': [1, -6, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 8, 23], 'euler29': [1, -2, 29], 'euler3': [1, 0, 3], 'euler31': [1, 0, 0], 'euler37': [1, -10, 37], 'euler41': [1, 6, 41], 'euler43': [1, -8, 43], 'euler47': [1, 8, 47], 'euler5': [1, -2, 5], 'euler53': [1, 6, 53], 'euler59': [1, -12, 59], 'euler61': [1, 6, 61], 'euler67': [1, -12, 67], 'euler7': [1, 0, 7], 'euler71': [1, -8, 71], 'euler73': [1, 10, 73], 'euler79': [1, -8, 79], 'euler83': [1, -8, 83], 'euler89': [1, -6, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, 0, 0], [1, 0, 3], [1, -2, 5], [1, 0, 7], [1, 0, 11], [1, -2, 13], [1, -6, 17], [1, 4, 19], [1, 8, 23], [1, -2, 29], [1, 0, 0], [1, -10, 37], [1, 6, 41], [1, -8, 43], [1, 8, 47], [1, 6, 53], [1, -12, 59], [1, 6, 61], [1, -12, 67], [1, -8, 71], [1, 10, 73], [1, -8, 79], [1, -8, 83], [1, -6, 89], [1, -2, 97]], 'index': 9, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/61504/bd'], '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': '2-248e2-1.1-c1-0-9', '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': '2-248e2-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 22.16104493456216, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1686740431120359243, 'z1': {'__RealLiteral__': 0, 'data': '0.5067663842404504', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1686740431120359243', 'Lhash_array': ['1686740431120359243'], 'label': '2-248e2-1.1-c1-0-9', 'type': 'ECQ', 'url': 'EllipticCurve/Q/61504/bd'}