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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': -3, 'A8': 0, 'A9': 1, 'Lhash': '2097118627207845446', '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': [-1.1338934190276817, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 3182.3898623169184, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [19, [1]], [23, [1, -1]]], 'bad_primes': [2, 3, 19, 23], 'central_character': '398544.1', 'coefficient_field': '1.1.1.1', 'conductor': 398544, 'conductor_radical': 2622, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, 1, 5], [1, 3, 7], [1, -3, 11], [1, 4, 13], [1, 7, 17], [1], [1, -1], [1, 4, 29], [1, -10, 31], [1, 2, 37], [1, 10, 41], [1, -1, 43], [1, -7, 47], [1, 2, 53], [1, -2, 59], [1, 7, 61], [1, -8, 67], [1, 6, 71], [1, -9, 73], [1, -14, 79], [1, -4, 83], [1, 0, 89], [1, 4, 97]], 'gamma_factors': [[], [0]], 'index': 1, 'label': '2-398544-1.1-c1-0-1', 'leading_term': '0.326632411182', '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/398544/m', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.3266324111821953, -0.2463779471862078, -1.216847458964919, -0.9257768615988632, 1.345234959209245, 3.741545670734914, 3.328255928291501, 0.07408706768587528, -2.18784090685296, -0.6283333711503447, 2.12488511919614, 1.475050215883712, -1.95535320345224, -3.008382749379757, -0.3160374702690804, 1.502463543697338, -0.02573997214881647, -1.068015526265753, 0.8971356846856364, 1.971590119456839, -0.4325956378758885, -1.738424220154055, 1.414545860708727, 4.215808152974271, 2.337384080985207, -0.3764131192668751, -0.1844663683620378, -0.1841444033741915, -1.816797012794836, -0.80003300166674, 2.263650665382747, 0.6810192267423327, -4.131096264860733, -3.21778898852187, 2.400810075948674, 3.064081447524352, -0.7573531475698608, -0.8254678684198492, 1.483996544290552, 0.1990455159944671, -1.035577771393963, 1.766221740621441, 2.492405549300135, -1.40212100903893, -2.437052518183229, 0.5708107398688781, 0.62153473125923, -1.400435482824628, -0.3390595213710414, 0.510041135064594, -1.057600823249482, 0.5635443186273466, 4.106133332831125, 2.404247761359191, -0.449586299817986, 1.408358791939071, 0.1404528234445418, -7.353996874787988, -8.715157102991824, -1.607507247396079, 1.396397661193483, -0.7957553190701823, -0.1660086736890111, 0.3024492871464118, -2.454853686965726, -1.73562067929025, 1.784935133860641, 1.127911513860253, -0.1288657835261937, 1.536233121513257, 0.5968890239634081, -0.707168086056935, 3.600626449413664, 5.309827767892481, -0.7775155946416967, -3.582529393127699, -0.2726252956542866, 0.3605761226532522, 0.1323987964956742, 2.38520159852606, 1.075115635624692, -0.558902172851921, 3.995921400055909, 3.959306666877515, -5.38744785266647, -8.143203170187334, -1.455725718017436, 0.8199768986379466, -0.8355822042975843, 0.2951216222574961, 0.4328387511646179, 0.1789993932580437, 2.490726621066252, 1.175740661095245, -2.215973603045986, 0.3742876946901739, 2.45097549909207, -0.7628756596345133, -0.2889982051410147, 2.084060252669377, -0.1393560576416732, 1.703608565251732, 7.33438056846114, 3.945850494820492, -1.726288283561785, 0.9251695876768515, 2.043759303325496, -1.33286934960334, -0.6842869042152361, -0.547115814846164, -2.915201435092899, 0.6806503459117517, 4.562373887350322, 1.490749042630663, 0.0767270060310266, 1.151620501655841, -1.125916462182433, -1.248990269947909, 0.197996688102767, -2.564384436293898, -1.951270486302565], 'positive_zeros': ['0.1838861475615287', '0.8734176452049560', '1.755245152458984', '2.300274144041143', '2.861603274951265', '3.525324619389314', '3.997054909144861', '4.410484225252943', '4.964259454278442', '5.414273422922072', '6.193537638688529', '6.557297002234315', '6.704885973906500', '7.310783995345384', '7.785181377153441', '8.389692997152640', '8.944102555242554', '9.326615087899518', '9.769330943829394', '10.11881611924943', '10.66699651820091', '11.19922894298288', '11.56620202633672', '12.04279347763566', '12.33926383529466', '12.71157237961609', '13.41749556013520', '13.61095522794464', '14.00616513380701', '14.81602517821292', '15.15652920377824', '15.52209555098114', '15.78658963199461', '16.36053547472449', '16.88946788206022', '17.03352412159097', '17.55607502222184', '17.81898470793986', '18.47148540273020', '19.02451968023736', '19.32964222516084', '19.47592999566612'], 'prelabel': '2-398544-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 56.41267466019421, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 2097118627207845446, 'z1': {'__RealLiteral__': 0, 'data': '0.1838861475615287', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '0.8734176452049560', 'prec': 60}, 'z3': {'__RealLiteral__': 0, 'data': '1.755245152458984', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3182.3898623169184, 'bad_primes': [2, 3, 19, 23], 'central_character': '1.1', 'conductor': 398544, 'conductor_radical': 2622, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, -1, 0, -3, 0, 1, 0, 3, 0, -4, 0, 1, 0, -7, 0, 0, 0, 3, 0, 1, 0, -4, 0, -1, 0, -4, 0, 10, 0, -3, 0, 3, 0, -2, 0, 4, 0, -10, 0, 1, 0, -1, 0, 7, 0, 2, 0, 7, 0, -2, 0, -3, 0, 0, 0, 2, 0, -7, 0, -3, 0, 4, 0, 8, 0, -1, 0, -6, 0, 9, 0, 4, 0, -9, 0, 14, 0, 1, 0, 4, 0, 7, 0, 4, 0, 0, 0, 12, 0, -10, 0, 0, 0, -4, 0, 3, 0], 'euler11': [1, -3, 11], 'euler13': [1, 4, 13], 'euler17': [1, 7, 17], 'euler19': [1, 0, 0], 'euler2': [1, 0, 0], 'euler23': [1, -1, 0], 'euler29': [1, 4, 29], 'euler3': [1, 1, 0], 'euler31': [1, -10, 31], 'euler37': [1, 2, 37], 'euler41': [1, 10, 41], 'euler43': [1, -1, 43], 'euler47': [1, -7, 47], 'euler5': [1, 1, 5], 'euler53': [1, 2, 53], 'euler59': [1, -2, 59], 'euler61': [1, 7, 61], 'euler67': [1, -8, 67], 'euler7': [1, 3, 7], 'euler71': [1, 6, 71], 'euler73': [1, -9, 73], 'euler79': [1, -14, 79], 'euler83': [1, -4, 83], 'euler89': [1, 0, 89], 'euler97': [1, 4, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 1, 5], [1, 3, 7], [1, -3, 11], [1, 4, 13], [1, 7, 17], [1, 0, 0], [1, -1, 0], [1, 4, 29], [1, -10, 31], [1, 2, 37], [1, 10, 41], [1, -1, 43], [1, -7, 47], [1, 2, 53], [1, -2, 59], [1, 7, 61], [1, -8, 67], [1, 6, 71], [1, -9, 73], [1, -14, 79], [1, -4, 83], [1, 0, 89], [1, 4, 97]], 'index': 1, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/398544/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': '2-398544-1.1-c1-0-1', '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': '2-398544-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 56.41267466019421, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 2097118627207845446, 'z1': {'__RealLiteral__': 0, 'data': '0.1838861475615287', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '2097118627207845446', 'Lhash_array': ['2097118627207845446'], 'factors': ['2-398544-1.1-c1-0-1'], 'label': '2-398544-1.1-c1-0-1', 'type': 'ECQ', 'url': 'EllipticCurve/Q/398544/m'}