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lfunc_lfunctions • Show schema
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{'A10': 2, 'A2': -2, 'A3': -1, 'A4': 2, 'A5': -1, 'A6': 2, 'A7': -1, 'A8': 0, 'A9': 1, 'Lhash': '1128609032263624703', 'a10': [0.6324555320336759, 0], 'a2': [-1.414213562373095, 0], 'a3': [-0.5773502691896258, 0], 'a4': [1.0, 0], 'a5': [-0.4472135954999579, 0], 'a6': [0.8164965809277261, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 2665.36649426933, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1, 1]], [5, [1, 1]], [7, [1, 1]], [11, [1, -1]], [17, [1]]], 'bad_primes': [3, 5, 7, 11, 17], 'central_character': '333795.1', 'coefficient_field': '1.1.1.1', 'conductor': 333795, 'conductor_radical': 19635, 'degree': 2, 'euler_factors': [[1, 2, 2], [1, 1], [1, 1], [1, 1], [1, -1], [1, 3, 13], [1], [1, 6, 19], [1, -3, 23], [1, 0, 29], [1, -3, 31], [1, -11, 37], [1, -3, 41], [1, 8, 43], [1, 11, 47], [1, -6, 53], [1, 4, 59], [1, 7, 61], [1, 14, 67], [1, 14, 71], [1, 4, 73], [1, 8, 79], [1, -3, 83], [1, -6, 89], [1, -12, 97]], 'gamma_factors': [[], [0]], 'index': 2, 'label': '2-333795-1.1-c1-0-2', 'leading_term': '0.232320531704', '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/333795/b', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.232320531704275, -0.07347348796951934, -0.5725124002232451, -0.3998379574994012, 0.637887850515717, 1.320624331537837, 0.3395341516213983, -1.325160119441479, -0.8651991113381716, 2.197520215508274, 3.994525186656808, 1.348315778467823, -2.195948149744504, -0.0001289300660421789, 7.317501543999903, 10.98075909130891, 6.507637876274077, 0.6968492013323582, 0.580431677867415, 1.893457343096751, -2.68286678453394, -9.253195964223057, -8.283561787871669, -1.068994364897843, 2.319124375212654, -0.1817533493712145, -1.330752685464245, 0.9291027858090606, 1.447913714926257, -0.3519424164022499, -0.06903257953441647, 1.558007014919774, 0.5625872701418057, -1.193582319068046, -0.1874165813987137, 0.9065942692625975, -0.6149383732165452, -1.406875388686784, 0.1208037471358775, 0.2730836744937995, -1.118329906549466, -0.5315266274331508, 0.4016110448417048, -1.156783755997296, -1.642157706996867, 0.5261782245028686, 0.228535115977755, -1.843186313753667, 0.4706433699034611, 2.87895571388631, -1.809346705308488, -5.503030288182197, -0.8918168047531495, 0.4281611445902541, -6.33863176674672, -3.472431749123165, 13.04397230029049, 19.75518314489393, 8.753491300766543, 0.08006758787205995, 0.7956192301916651, -1.728769068392212, -7.051855112541577, -5.071143464467928, -0.1400664894290366, 0.1174868928089726, -0.382734914998483, 0.670118020227443, 0.005202267987655179, -0.5924304953968162, 0.4270071310539855, -0.427151148889615, -1.783927988478068, -0.3170255155200494, 0.3039576261696895, -1.179148483850228, -0.5106673249173318, 0.6173203912186817, -0.28579814088744, 0.4249389268440171, 0.5929662783531268, -3.265989298748914, -1.975079691842522, 6.38288203192566, 6.594118076349058, -0.5253492382750781, 1.30755473526227, 5.995787297697242, 0.7639180363284332, -2.186713803967912, 4.036220399193971, 4.587167027699607, -0.2671031401585568, 0.99278190997352, 0.2009008935034018, -6.766112240068555, -5.118189418349095, 2.891952796778797, 2.149824242625288, -1.012459668187959, 1.807611764173539, 1.726474468153301, -1.369583227281453, 0.6672261441268588, 2.370040338474705, -0.2087530549850706, -0.3243439054277668, 1.083683222237435, 0.0574327389501013, 0.09617383539797725, 0.7030521353483747, -0.4505492379170356, -0.04957261433873207, 0.5017333835439028, -1.109548624302534, -0.3042371206200345, 1.087203398554438, -0.6725148689726865, 0.4946485115754642, 2.65839167660638, -0.01305297216613093], 'positive_zeros': ['0.2144153939632357', '0.8617526174660022', '1.547072352961161', '2.084473377179514', '2.827627176139451', '3.250005553856405', '4.330542784381715', '4.412136227167613', '4.895843163635157', '5.792032894993210', '6.235409654195706', '6.657625925658935', '7.194608945982867', '7.509886044832887', '8.061634632982506', '8.524615357967101', '8.923591905925521', '9.480463492862467', '9.799490207319319', '10.33701051458639', '10.60047804028393', '11.18766537258237', '11.52392178801871', '11.97130922949322', '12.43080564609328', '13.04209169451664', '13.27234251030621', '13.81178935386225', '14.75861839744394', '14.87636169040330', '15.16168217347740', '16.01316361025943', '16.27302353354099', '16.59088002035670', '17.00094475109023', '17.39199986535353', '17.69176097717260', '18.29315024408006', '18.55768364168000', '19.07141351634933', '19.42477988120737', '19.68193636689595'], 'prelabel': '2-333795-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 51.62718754948143, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1128609032263624703, 'z1': {'__RealLiteral__': 0, 'data': '0.2144153939632357', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '0.8617526174660022', 'prec': 60}, 'z3': {'__RealLiteral__': 0, 'data': '1.547072352961161', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2665.36649426933, 'bad_primes': [3, 5, 7, 11, 17], 'central_character': '1.1', 'conductor': 333795, 'conductor_radical': 19635, 'degree': 2, 'dirichlet_coefficients': [1, -2, -1, 2, -1, 2, -1, 0, 1, 2, 1, -2, -3, 2, 1, -4, 0, -2, -6, -2, 1, -2, 3, 0, 1, 6, -1, -2, 0, -2, 3, 8, -1, 0, 1, 2, 11, 12, 3, 0, 3, -2, -8, 2, -1, -6, -11, 4, 1, -2, 0, -6, 6, 2, -1, 0, 6, 0, -4, 2, -7, -6, -1, -8, 3, 2, -14, 0, -3, -2, -14, 0, -4, -22, -1, -12, -1, -6, -8, 4, 1, -6, 3, 2, 0, 16, 0, 0, 6, 2, 3, 6, -3, 22, 6, -8, 12, -2, 1, 2], 'euler11': [1, -1, 0], 'euler13': [1, 3, 13], 'euler17': [1, 0, 0], 'euler19': [1, 6, 19], 'euler2': [1, 2, 2], 'euler23': [1, -3, 23], 'euler29': [1, 0, 29], 'euler3': [1, 1, 0], 'euler31': [1, -3, 31], 'euler37': [1, -11, 37], 'euler41': [1, -3, 41], 'euler43': [1, 8, 43], 'euler47': [1, 11, 47], 'euler5': [1, 1, 0], 'euler53': [1, -6, 53], 'euler59': [1, 4, 59], 'euler61': [1, 7, 61], 'euler67': [1, 14, 67], 'euler7': [1, 1, 0], 'euler71': [1, 14, 71], 'euler73': [1, 4, 73], 'euler79': [1, 8, 79], 'euler83': [1, -3, 83], 'euler89': [1, -6, 89], 'euler97': [1, -12, 97], 'euler_factors': [[1, 2, 2], [1, 1, 0], [1, 1, 0], [1, 1, 0], [1, -1, 0], [1, 3, 13], [1, 0, 0], [1, 6, 19], [1, -3, 23], [1, 0, 29], [1, -3, 31], [1, -11, 37], [1, -3, 41], [1, 8, 43], [1, 11, 47], [1, -6, 53], [1, 4, 59], [1, 7, 61], [1, 14, 67], [1, 14, 71], [1, 4, 73], [1, 8, 79], [1, -3, 83], [1, -6, 89], [1, -12, 97]], 'index': 2, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/333795/b'], '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': '2-333795-1.1-c1-0-2', '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': '2-333795-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 51.62718754948143, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1128609032263624703, 'z1': {'__RealLiteral__': 0, 'data': '0.2144153939632357', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1128609032263624703', 'Lhash_array': ['1128609032263624703'], 'label': '2-333795-1.1-c1-0-2', 'type': 'ECQ', 'url': 'EllipticCurve/Q/333795/b'}