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lfunc_lfunctions • Show schema
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{'A10': 0, 'A2': 0, 'A3': 1, 'A4': 0, 'A5': 0, 'A6': 0, 'A7': -1, 'A8': 0, 'A9': 1, 'Lhash': '571590572631566265', 'a10': [0.0, 0], 'a2': [0.0, 0], 'a3': [0.5773502691896258, 0], 'a4': [0.0, 0], 'a5': [0.0, 0], 'a6': [0.0, 0], 'a7': [-0.3779644730092272, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 737.8177146766311, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, -1]], [5, [1]], [7, [1, 1]], [11, [1, -1]]], 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '92400.1', 'coefficient_field': '1.1.1.1', 'conductor': 92400, 'conductor_radical': 2310, 'degree': 2, 'euler_factors': [[1], [1, -1], [1], [1, 1], [1, -1], [1, 2, 13], [1, 6, 17], [1, 0, 19], [1, 0, 23], [1, 2, 29], [1, 0, 31], [1, -2, 37], [1, 6, 41], [1, 4, 43], [1, -8, 47], [1, -6, 53], [1, 0, 59], [1, -10, 61], [1, -8, 67], [1, 16, 71], [1, -10, 73], [1, 8, 79], [1, -12, 83], [1, 10, 89], [1, -10, 97]], 'gamma_factors': [[], [0]], 'index': 126, 'label': '2-92400-1.1-c1-0-126', 'leading_term': '7.29513948309', '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': 1, 'origin': 'EllipticCurve/Q/92400/fo', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [0.0, 1.63223781211881, 2.178297454733939, 1.020207006986658, -1.302488936035173, -3.080723333982992, -2.804266475633372, -0.8341603558492418, 0.7143742086694255, 0.2915980055830538, -1.11518899628354, -1.144517754720082, 0.6976171682451799, 2.088297489015426, 1.045293784706013, -0.9908220565304209, -1.018109994580747, 0.8978539497294413, 1.34673580020018, -1.134681753538121, -3.126780145314853, -1.163286200757332, 2.464270085204009, 2.522557992093681, -1.23773856361348, -3.530085210899641, -1.693924108031744, 0.5176513068428163, -0.2697849649762704, -1.356930929241375, 0.7499203635669479, 3.564659086950574, 2.751482179491162, -0.09537719836131445, -0.2778723043271817, 1.649717796679361, 1.48342632151538, -0.2955127120290928, 0.3253694987715968, 2.424246181977003, 1.48688001164693, -1.274101521730071, -0.4121565049851897, 2.963751914065806, 2.2895029380968, -2.087872061004828, -2.963544319428231, 0.3281261417313784, 0.7196432851014966, -2.964369729034847, -3.950354112246911, -0.7456927510758784, 0.6192880082674116, -1.048334438594976, -0.704445095675328, 1.441598982274668, 0.3911097281567867, -2.404636424404557, -1.573544297171282, 0.9029687589449024, -0.001766545487364006, -1.633321356938826, 0.0387167943082709, 0.9410170270276649, -2.085294759795118, -3.12279035490287, 0.7690542915496585, 2.449005579133239, -0.7938914825805542, -1.442607204231889, 2.167101241585778, 2.125906826512774, -2.011830457452033, -2.091495385191246, 1.402093808535269, 0.922528592925412, -1.957904715374502, -0.9811652293563637, 1.108611265735737, -0.08331955321106292, -0.7970186762556619, 0.7658754892239664, -0.2041392691720741, -2.42415836432622, 0.3751541273067131, 4.583200726180368, 2.832185001006894, -0.6996545560302937, -0.1181065165346031, -0.2262837559323467, -3.141625780612118, -1.567095652256263, 3.644464053458009, 2.72948873507079, -2.297143081150184, -1.722124924053343, 1.41335276214955, -0.3806361393704058, -2.496331876250303, -0.3923272548631931, 0.2861698017984495, -1.503656554262961, 0.1221985918537738, 2.611042858129438, 0.4145515736231372, -1.667111168320332, 0.06330960955618668, 0.1473778016079862, -1.205159268941999, 1.488000387243039, 3.220633801282835, -1.411333504355454, -3.803796469510144, 0.5720430750599705, 1.96295116042244, -1.42001874648126, -0.5033637670293626, 2.49995308359324, 0.2518808627743285, -1.47345454499236, 1.865866916385059], 'positive_zeros': ['0.8661508758121926', '1.854736864434101', '2.302330584886371', '2.918727079416475', '3.618432670535508', '4.139313540853744', '4.656644994205697', '5.324671188846983', '5.925653385254443', '6.659004552443692', '6.961042688605471', '7.441339717518335', '8.238765985201386', '8.539994930251041', '9.195398564211206', '9.457955303653753', '10.12175763572010', '10.53113355258649', '11.13153341353942', '11.72401238713566', '12.06021345403914', '12.81384670903657', '13.10736697251031', '13.57587022798030', '14.03207510477350', '14.63631733269897', '14.99981119236897', '15.49606097277566', '15.85168832346696', '16.45666333370031', '16.94520637249547', '17.35790497458016', '17.87803867337735', '18.39188740828556', '18.82121272208233', '19.33828469014667', '19.73941004829763'], 'prelabel': '2-92400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 27.16280019947559, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 571590572631566265, 'z1': {'__RealLiteral__': 0, 'data': '0.8661508758121926', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.854736864434101', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.302330584886371', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 737.8177146766311, 'bad_primes': [2, 3, 5, 7, 11], 'central_character': '1.1', 'conductor': 92400, 'conductor_radical': 2310, 'degree': 2, 'dirichlet_coefficients': [1, 0, 1, 0, 0, 0, -1, 0, 1, 0, 1, 0, -2, 0, 0, 0, -6, 0, 0, 0, -1, 0, 0, 0, 0, 0, 1, 0, -2, 0, 0, 0, 1, 0, 0, 0, 2, 0, -2, 0, -6, 0, -4, 0, 0, 0, 8, 0, 1, 0, -6, 0, 6, 0, 0, 0, 0, 0, 0, 0, 10, 0, -1, 0, 0, 0, 8, 0, 0, 0, -16, 0, 10, 0, 0, 0, -1, 0, -8, 0, 1, 0, 12, 0, 0, 0, -2, 0, -10, 0, 2, 0, 0, 0, 0, 0, 10, 0, 1, 0], 'euler11': [1, -1, 0], 'euler13': [1, 2, 13], 'euler17': [1, 6, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, 0, 23], 'euler29': [1, 2, 29], 'euler3': [1, -1, 0], 'euler31': [1, 0, 31], 'euler37': [1, -2, 37], 'euler41': [1, 6, 41], 'euler43': [1, 4, 43], 'euler47': [1, -8, 47], 'euler5': [1, 0, 0], 'euler53': [1, -6, 53], 'euler59': [1, 0, 59], 'euler61': [1, -10, 61], 'euler67': [1, -8, 67], 'euler7': [1, 1, 0], 'euler71': [1, 16, 71], 'euler73': [1, -10, 73], 'euler79': [1, 8, 79], 'euler83': [1, -12, 83], 'euler89': [1, 10, 89], 'euler97': [1, -10, 97], 'euler_factors': [[1, 0, 0], [1, -1, 0], [1, 0, 0], [1, 1, 0], [1, -1, 0], [1, 2, 13], [1, 6, 17], [1, 0, 19], [1, 0, 23], [1, 2, 29], [1, 0, 31], [1, -2, 37], [1, 6, 41], [1, 4, 43], [1, -8, 47], [1, -6, 53], [1, 0, 59], [1, -10, 61], [1, -8, 67], [1, 16, 71], [1, -10, 73], [1, 8, 79], [1, -12, 83], [1, 10, 89], [1, -10, 97]], 'index': 126, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/92400/fo'], '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': '2-92400-1.1-c1-0-126', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-92400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 27.16280019947559, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 571590572631566265, 'z1': {'__RealLiteral__': 0, 'data': '0.8661508758121926', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '571590572631566265', 'Lhash_array': ['571590572631566265'], 'label': '2-92400-1.1-c1-0-126', 'type': 'ECQ', 'url': 'EllipticCurve/Q/92400/fo'}