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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 0, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': 0, 'A8': 0, 'A9': 0, 'Lhash': '1084471049641239274', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.0, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [0.0, 0], 'a8': [0.0, 0], 'a9': [0.0, 0], 'algebraic': True, 'analytic_conductor': 373.6998814595924, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1]], [13, [1, 1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '46800.1', 'coefficient_field': '1.1.1.1', 'conductor': 46800, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[1], [1], [1], [1, 0, 7], [1, 0, 11], [1, 1], [1, 6, 17], [1, 4, 19], [1, 0, 23], [1, -2, 29], [1, 0, 31], [1, -2, 37], [1, -2, 41], [1, 4, 43], [1, 4, 47], [1, 10, 53], [1, -8, 59], [1, 2, 61], [1, 4, 67], [1, 12, 71], [1, -6, 73], [1, 0, 79], [1, -16, 83], [1, -10, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 12, 'label': '2-46800-1.1-c1-0-12', 'leading_term': '1.07171998227', '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/46800/cw', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [1.071719982270381, 0.5262006381556479, -0.8828874366831773, -2.411183025081084, -2.978746075578538, -1.943120986078461, 0.09503428223797972, 1.498619725618513, 1.051229948975067, -0.6264531129731578, -1.461709869954103, -0.1657470415914247, 2.035670615441666, 2.531411093164886, 0.4413899213104133, -2.039794517811627, -2.170097623863685, -0.1696048144659421, 1.025531013958104, -0.1699279728228997, -1.584672904974122, -0.2808500050005361, 2.965451505369702, 4.341888628803329, 2.330362264114618, -0.06262673480746775, 0.1798550631217506, 1.494082783636192, 0.3506206305450118, -2.779627585229173, -3.754385105459854, -1.314509938955022, 0.6454581499935322, -0.8172106324533976, -2.986450115240473, -2.141515640774752, 0.0735201833806974, -0.4789748453628372, -3.023284793067272, -2.909577680588908, 0.2788297877553257, 1.705873190750748, -0.4660589015102815, -1.969919278829045, -0.1510801015299321, 1.309015449986273, -0.6138285477617047, -2.337202518038021, -0.08737827457735518, 2.853110830995108, 1.75749398352074, -1.101516856927146, -0.8918211176894767, 0.7607406308565462, -0.6630866323826766, -3.248500464755543, -1.849560887961608, 1.882384606418743, 2.138937546667698, -0.3597817901438869, -0.1939359620606822, 1.988923621762421, 0.978947000961699, -2.226579576276508, -2.105579721446475, 0.2863147194123825, -0.7751531092934045, -4.093271349714981, -3.553074027934569, -0.02584674838723468, 0.6751326488981614, -0.5411790059641, 1.277354031880924, 3.825292218446537, 1.611945677089517, -2.417098161677584, -2.031530442870938, 0.3152152854809082, -0.8617178916590237, -2.756130976059579, -0.8948260360584226, 0.733779963816981, -1.938571240403611, -3.862712443336021, -1.056288875752899, 0.9560556466384653, -1.414621105798094, -2.570717283406406, 0.06638423246171359, 0.8268580023931035, -1.322112765582503, -0.2609521122023153, 3.495928619901546, 3.036237685695584, -0.4269751934889098, -0.1549419868759206, 1.873213845772066, 0.009019005490467488, -2.201939201222914, 0.02370684655395108, 1.770019194205827, -0.7210497876942253, -1.482177896256114, 1.883439666338396, 2.491598749966902, -0.8517003447511908, -1.178923247072995, 1.222180435456331, 0.1682373595093402, -1.788524409981521, 0.8111706982148063, 3.191023026787066, 0.4672846928529701, -1.334108606302282, 1.429306367557326, 2.285799138853156, -0.2643045856562857, 0.3310432515356733, 2.913696644625678, 0.9672595086473414, -2.005637453314516], 'positive_zeros': ['0.3566354593083553', '1.488328825348248', '2.159872171848166', '2.768854493267974', '3.538632722270980', '4.270296936584620', '4.727536596771065', '5.274178971866294', '6.238174739209557', '6.465904220535080', '7.030958937131245', '7.871752444820437', '8.164912114463387', '8.986630559943733', '9.186626111614066', '9.978593309638912', '10.45839166432566', '11.01484412958511', '11.44485604542293', '12.00596123613498', '12.63859357264529', '13.11136568361687', '13.43910268433716', '14.11676604754833', '14.70721325601361', '15.02272247911772', '15.57341809051215', '16.20721198172620', '16.42878887209378', '17.25232511951738', '17.61353347359351', '17.88665006064966', '18.58752883754557', '19.19469244865536', '19.40764230190940'], 'prelabel': '2-46800-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 19.331318668409363, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1084471049641239274, 'z1': {'__RealLiteral__': 0, 'data': '0.3566354593083553', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.488328825348248', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.159872171848166', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 373.6998814595924, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 46800, 'conductor_radical': 390, 'degree': 2, 'dirichlet_coefficients': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1, 0, 0, 0, -6, 0, -4, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 0, 2, 0, 0, 0, 2, 0, -4, 0, 0, 0, -4, 0, -7, 0, 0, 0, -10, 0, 0, 0, 0, 0, 8, 0, -2, 0, 0, 0, 0, 0, -4, 0, 0, 0, -12, 0, 6, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 10, 0, 0, 0, 0, 0, 0, 0, -2, 0, 0, 0], 'euler11': [1, 0, 11], 'euler13': [1, 1, 0], 'euler17': [1, 6, 17], 'euler19': [1, 4, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, -2, 29], 'euler3': [1, 0, 0], 'euler31': [1, 0, 31], 'euler37': [1, -2, 37], 'euler41': [1, -2, 41], 'euler43': [1, 4, 43], 'euler47': [1, 4, 47], 'euler5': [1, 0, 0], 'euler53': [1, 10, 53], 'euler59': [1, -8, 59], 'euler61': [1, 2, 61], 'euler67': [1, 4, 67], 'euler7': [1, 0, 7], 'euler71': [1, 12, 71], 'euler73': [1, -6, 73], 'euler79': [1, 0, 79], 'euler83': [1, -16, 83], 'euler89': [1, -10, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 0, 0], [1, 0, 0], [1, 0, 0], [1, 0, 7], [1, 0, 11], [1, 1, 0], [1, 6, 17], [1, 4, 19], [1, 0, 23], [1, -2, 29], [1, 0, 31], [1, -2, 37], [1, -2, 41], [1, 4, 43], [1, 4, 47], [1, 10, 53], [1, -8, 59], [1, 2, 61], [1, 4, 67], [1, 12, 71], [1, -6, 73], [1, 0, 79], [1, -16, 83], [1, -10, 89], [1, 2, 97]], 'index': 12, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/46800/cw'], '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': '2-46800-1.1-c1-0-12', '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': '2-46800-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 19.331318668409363, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1084471049641239274, 'z1': {'__RealLiteral__': 0, 'data': '0.3566354593083553', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1084471049641239274', 'Lhash_array': ['1084471049641239274'], 'label': '2-46800-1.1-c1-0-12', 'type': 'ECQ', 'url': 'EllipticCurve/Q/46800/cw'}