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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': '1601346051229641985', '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': 498.26650861278983, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1]], [13, [1, 1]]], 'bad_primes': [2, 3, 5, 13], 'central_character': '62400.1', 'coefficient_field': '1.1.1.1', 'conductor': 62400, 'conductor_radical': 390, 'degree': 2, 'euler_factors': [[1], [1, 1], [1], [1, 1, 7], [1, -5, 11], [1, 1], [1, -7, 17], [1, 6, 19], [1, -3, 23], [1, 2, 29], [1, 2, 31], [1, -7, 37], [1, -9, 41], [1, -8, 43], [1, -10, 47], [1, -5, 53], [1, 0, 59], [1, 5, 61], [1, -4, 67], [1, 9, 71], [1, -6, 73], [1, -3, 79], [1, -4, 83], [1, -11, 89], [1, -11, 97]], 'gamma_factors': [[], [0]], 'index': 63, 'label': '2-62400-1.1-c1-0-63', 'leading_term': '2.44054546842', '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/62400/cf', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [2.440545468423183, 1.952312717980234, 0.743600305914172, -0.4015091227341774, -0.4923750555628192, 0.7639152666622644, 2.283114996204477, 2.279682610870954, 0.1388060037256944, -2.432500858132207, -2.766737354065262, -0.1909283759330783, 2.808853833812474, 3.154437560065576, 0.8232414421196491, -1.096017546299272, -0.4332782489725958, 1.137772417633765, 0.5262073094485255, -2.129486504397807, -3.371373790548566, -1.384802245094261, 1.244208694008687, 1.35786418700944, -0.103692332272791, -0.0001832414615872713, 1.546378725138928, 1.29649363236266, -1.259162060440802, -2.401485049799706, 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0.02806989632754309, -4.225809926351104, -8.392908940660076, -5.228797600372753, -0.09269470973195759, -0.7372532698824101, -2.802895225423222, -0.4242689597589394, 1.787733886757863, 0.01251414957974969, -0.6367000196070276, 1.705054772020091, 1.767451601941248, -0.3143919567268171, 0.2485793891383973, 0.9190809269228297, -2.296751903926296, -4.037693093330667, -0.4673385294576822, 1.437772196967116, -1.549143683625168, -2.146707514866655, 1.061722367192181, 1.182581476206049, -0.1883450448633357, 3.480198872895121, 6.80547894872204, 2.164603150142291, -3.499274199789371, -2.092493087729028, 0.7547887312820775, -0.1532397289120981, -0.3249262028967164, 0.6898998200730727, -1.702590561182211, -3.722761432423224, -0.195662613300457, 2.921747507404445, 0.8995924192056203, -0.3879188611113386, 0.9601539309801876, -0.1888024804930679], 'positive_zeros': ['0.6459081257183999', '1.124541182145256', '2.012288516494566', '2.764028802437582', '3.579639123782833', '4.061035734706900', '4.557257208193279', '5.365336027411700', '5.977585956629026', '6.250036367733908', '6.886114879138565', '7.544476962525016', '7.841828724856541', '8.855699029369857', '9.138689267109644', '9.650617444954906', '10.21356818262292', '10.81126476155189', '11.17381728986228', '11.87707053317996', '12.19979088942014', '12.73782147186518', '13.01883298723358', '13.87494703085784', '14.34192473916758', '14.85930288756523', '14.98203630054012', '15.98406443785479', '16.25615559061309', '16.86049509061678', '17.14402322592578', '17.38860838934272', '18.21450783818182', '18.68292339324013', '19.10387840724613', '19.61374422936789', '19.75452790125289'], 'prelabel': '2-62400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 22.321884073993168, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1601346051229641985, 'z1': {'__RealLiteral__': 0, 'data': '0.6459081257183999', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.124541182145256', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '2.012288516494566', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 498.26650861278983, 'bad_primes': [2, 3, 5, 13], 'central_character': '1.1', 'conductor': 62400, 'conductor_radical': 390, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 5, 0, -1, 0, 0, 0, 7, 0, -6, 0, 1, 0, 3, 0, 0, 0, -1, 0, -2, 0, -2, 0, -5, 0, 0, 0, 7, 0, 1, 0, 9, 0, 8, 0, 0, 0, 10, 0, -6, 0, -7, 0, 5, 0, 0, 0, 6, 0, 0, 0, -5, 0, -1, 0, 0, 0, 4, 0, -3, 0, -9, 0, 6, 0, 0, 0, -5, 0, 3, 0, 1, 0, 4, 0, 0, 0, 2, 0, 11, 0, 1, 0, 2, 0, 0, 0, 11, 0, 5, 0], 'euler11': [1, -5, 11], 'euler13': [1, 1, 0], 'euler17': [1, -7, 17], 'euler19': [1, 6, 19], 'euler2': [1, 0, 0], 'euler23': [1, -3, 23], 'euler29': [1, 2, 29], 'euler3': [1, 1, 0], 'euler31': [1, 2, 31], 'euler37': [1, -7, 37], 'euler41': [1, -9, 41], 'euler43': [1, -8, 43], 'euler47': [1, -10, 47], 'euler5': [1, 0, 0], 'euler53': [1, -5, 53], 'euler59': [1, 0, 59], 'euler61': [1, 5, 61], 'euler67': [1, -4, 67], 'euler7': [1, 1, 7], 'euler71': [1, 9, 71], 'euler73': [1, -6, 73], 'euler79': [1, -3, 79], 'euler83': [1, -4, 83], 'euler89': [1, -11, 89], 'euler97': [1, -11, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, 0, 0], [1, 1, 7], [1, -5, 11], [1, 1, 0], [1, -7, 17], [1, 6, 19], [1, -3, 23], [1, 2, 29], [1, 2, 31], [1, -7, 37], [1, -9, 41], [1, -8, 43], [1, -10, 47], [1, -5, 53], [1, 0, 59], [1, 5, 61], [1, -4, 67], [1, 9, 71], [1, -6, 73], [1, -3, 79], [1, -4, 83], [1, -11, 89], [1, -11, 97]], 'index': 63, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/62400/cf'], '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': '2-62400-1.1-c1-0-63', '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': '2-62400-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 22.321884073993168, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1601346051229641985, 'z1': {'__RealLiteral__': 0, 'data': '0.6459081257183999', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1601346051229641985', 'Lhash_array': ['1601346051229641985'], 'label': '2-62400-1.1-c1-0-63', 'type': 'ECQ', 'url': 'EllipticCurve/Q/62400/cf'}