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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': 4, 'A8': 0, 'A9': 1, 'Lhash': '1869569192572788676', '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': [1.5118578920369088, 0], 'a8': [0.0, 0], 'a9': [0.3333333333333333, 0], 'algebraic': True, 'analytic_conductor': 1841.6696722188117, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 1]], [5, [1, -1]], [31, [1]]], 'bad_primes': [2, 3, 5, 31], 'central_character': '230640.1', 'coefficient_field': '1.1.1.1', 'conductor': 230640, 'conductor_radical': 930, 'degree': 2, 'euler_factors': [[1], [1, 1], [1, -1], [1, -4, 7], [1, -2, 11], [1, 2, 13], [1, 0, 17], [1, 0, 19], [1, 6, 23], [1, -8, 29], [1], [1, -2, 37], [1, -6, 41], [1, -4, 43], [1, -12, 47], [1, -2, 53], [1, -12, 59], [1, -8, 61], [1, -4, 67], [1, -8, 71], [1, 4, 73], [1, -4, 79], [1, 16, 83], [1, -2, 89], [1, 2, 97]], 'gamma_factors': [[], [0]], 'index': 41, 'label': '2-230640-1.1-c1-0-41', 'leading_term': '4.00045305387', '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/230640/bp', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.25', 'prec': 14}, 'plot_values': [4.000453053868373, 3.15968808565399, 1.212918084426115, -0.3344936240041501, -0.1577799683046806, 1.301100769820709, 1.959738334691491, 0.680484521913435, -0.8109640289854528, -0.1038121397658603, 1.821909217264969, 0.9702647598007662, -3.905313927058739, -8.205148682727916, -6.958782244910075, -1.851098462258454, 1.099299580985504, 0.2119536847808113, -0.413159029259961, 1.362302579523281, 2.371720736309367, 0.7293559475258787, -0.3732002023002653, 0.9057819319798388, 1.013672512804852, -1.939871890421888, -3.560476137262294, -1.216984143296248, 0.3004906045325936, 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2.832325760378037, -0.1791054928251148, -3.22266943079524, 0.4618905101040454, 2.213365341568457, -0.4701301455768518, 0.197984665214258, 2.142866123896041, 0.3433476705697502, -0.1176840909618802, 1.069374274243095, -2.024815552083762, -3.969052741790207, 0.7558253245137262, 3.19077237199842, 0.08112978097832323, 0.07701958262482082, 2.088268924955937, 0.4899598577002447, 0.2220072340633799, 1.828536021577488, -0.787191017887439, -1.922785067087352, 2.575192458883013, 1.504190889784188, -5.137475385665336, -3.196662866113274, 3.495063108214946, 2.463834951246486, -0.6013920369535276, 0.1057058825795101, -1.357845825214073, -2.792952951010749, 0.2781780460023226, 1.147240949380948, -0.2484679795630108, 2.582696601943205, 3.421641839547385, -1.41339269754757, -2.187999817426371, 0.7757821131080774, 0.1482903382388758], 'positive_zeros': ['0.6725355286892447', '1.033584403479774', '1.841525143278839', '2.263615219957031', '2.814618335447183', '3.860684436999883', '4.284777015597180', '4.584205063497133', '5.348826710196702', '5.606282704152356', '6.104608830046943', '6.868772835236043', '7.057108379440890', '7.866273525487215', '8.119307367437770', '8.675945127398647', '9.186135490271503', '9.820268620229190', '10.12049049580715', '10.70090791765007', '11.08268186537877', '11.56847257816041', '12.02815406791597', '12.25546499510542', '12.82486033735720', '13.45511863882546', '14.00330595215712', '14.28708160752881', '14.56407257549174', '15.09469238867858', '15.81313458628493', '15.92740957377073', '16.63416029331464', '17.10722655137278', '17.46568505735125', '17.66571520063707', '18.16388509231969', '18.45947408416659', '19.12056354913776', '19.56424898896468', '19.99162181539169'], 'prelabel': '2-230640-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 42.91467898305674, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'spectral_label': 'c1-0', 'st_group': 'SU(2)', 'trace_hash': 1869569192572788676, 'z1': {'__RealLiteral__': 0, 'data': '0.6725355286892447', 'prec': 60}, 'z2': {'__RealLiteral__': 0, 'data': '1.033584403479774', 'prec': 57}, 'z3': {'__RealLiteral__': 0, 'data': '1.841525143278839', 'prec': 57}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1841.6696722188117, 'bad_primes': [2, 3, 5, 31], 'central_character': '1.1', 'conductor': 230640, 'conductor_radical': 930, 'degree': 2, 'dirichlet_coefficients': [1, 0, -1, 0, 1, 0, 4, 0, 1, 0, 2, 0, -2, 0, -1, 0, 0, 0, 0, 0, -4, 0, -6, 0, 1, 0, -1, 0, 8, 0, 0, 0, -2, 0, 4, 0, 2, 0, 2, 0, 6, 0, 4, 0, 1, 0, 12, 0, 9, 0, 0, 0, 2, 0, 2, 0, 0, 0, 12, 0, 8, 0, 4, 0, -2, 0, 4, 0, 6, 0, 8, 0, -4, 0, -1, 0, 8, 0, 4, 0, 1, 0, -16, 0, 0, 0, -8, 0, 2, 0, -8, 0, 0, 0, 0, 0, -2, 0, 2, 0], 'euler11': [1, -2, 11], 'euler13': [1, 2, 13], 'euler17': [1, 0, 17], 'euler19': [1, 0, 19], 'euler2': [1, 0, 0], 'euler23': [1, 6, 23], 'euler29': [1, -8, 29], 'euler3': [1, 1, 0], 'euler31': [1, 0, 0], 'euler37': [1, -2, 37], 'euler41': [1, -6, 41], 'euler43': [1, -4, 43], 'euler47': [1, -12, 47], 'euler5': [1, -1, 0], 'euler53': [1, -2, 53], 'euler59': [1, -12, 59], 'euler61': [1, -8, 61], 'euler67': [1, -4, 67], 'euler7': [1, -4, 7], 'euler71': [1, -8, 71], 'euler73': [1, 4, 73], 'euler79': [1, -4, 79], 'euler83': [1, 16, 83], 'euler89': [1, -2, 89], 'euler97': [1, 2, 97], 'euler_factors': [[1, 0, 0], [1, 1, 0], [1, -1, 0], [1, -4, 7], [1, -2, 11], [1, 2, 13], [1, 0, 17], [1, 0, 19], [1, 6, 23], [1, -8, 29], [1, 0, 0], [1, -2, 37], [1, -6, 41], [1, -4, 43], [1, -12, 47], [1, -2, 53], [1, -12, 59], [1, -8, 61], [1, -4, 67], [1, -8, 71], [1, 4, 73], [1, -4, 79], [1, 16, 83], [1, -2, 89], [1, 2, 97]], 'index': 41, 'instance_types': ['ECQ'], 'instance_urls': ['EllipticCurve/Q/230640/bp'], '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': '2-230640-1.1-c1-0-41', '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': '2-230640-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 42.91467898305674, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1869569192572788676, 'z1': {'__RealLiteral__': 0, 'data': '0.6725355286892447', 'prec': 60}}
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lfunc_instances • Show schema
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{'Lhash': '1869569192572788676', 'Lhash_array': ['1869569192572788676'], 'label': '2-230640-1.1-c1-0-41', 'type': 'ECQ', 'url': 'EllipticCurve/Q/230640/bp'}