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lfunc_lfunctions • Show schema
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{'Lhash': '879559727123982003916043912033,1232717008155088392381708534460', 'a10': -4, 'a2': -2, 'a3': 2, 'a4': 3, 'a5': 2, 'a6': -4, 'a7': 2, 'a8': -4, 'a9': 3, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3212.3747533820165, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 2, 1]], [3, [1, -2, 1]], [7, [1, -2, 1]], [13, [1]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '7098.1', 'coefficient_field': '1.1.1.1', 'conductor': 50381604, 'conductor_radical': 546, 'degree': 4, 'euler_factors': [[1, 2, 1], [1, -2, 1], [1, -2, 8, -10, 25], [1, -2, 1], [1, 0, 19, 0, 121], [1], [1, -4, 35, -68, 289], [1, 2, 39, 38, 361], [1, 0, 34, 0, 529], [1, -6, 55, -174, 841], [1, -6, 44, -186, 961], [1, 10, 96, 370, 1369], [1, -6, 91, -246, 1681], [1, -10, 108, -430, 1849], [1, 2, 83, 94, 2209], [1, -14, 155, -742, 2809], [1, 12, 106, 708, 3481], [1, 0, 95, 0, 3721], [1, -4, 90, -268, 4489], [1, 6, 124, 426, 5041], [1, 4, 138, 292, 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7.528466998978268, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e2-0', 'trace_hash': 1383803145824069640, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.69385028253497057407204253047', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.972442254934560421103330310643', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.77865485860307062731330305620', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3212.3747533820165, 'bad_primes': [2, 3, 7, 13], 'central_character': '1.1', 'conductor': 50381604, 'conductor_radical': 546, 'degree': 4, 'dirichlet_coefficients': [1, -2, 2, 3, 2, -4, 2, -4, 3, -4, 0, 6, 0, -4, 4, 5, 4, -6, -2, 6, 4, 0, 0, -8, -4, 0, 4, 6, 6, -8, 6, -6, 0, -8, 4, 9, -10, 4, 0, -8, 6, -8, 10, 0, 6, 0, -2, 10, 3, 8, 8, 0, 14, -8, 0, -8, -4, -12, -12, 12, 0, -12, 6, 7, 0, 0, 4, 12, 0, -8, -6, -12, -4, 20, -8, -6, 0, 0, 18, 10, 5, -12, 10, 12, 8, -20, 12, 0, 14, -12, 0, 0, 12, 4, -4, -12, -14, -6, 0, -12], 'euler11': [1, 0, 19, 0, 121], 'euler13': [1, 0, 0, 0, 0], 'euler17': [1, -4, 35, -68, 289], 'euler19': [1, 2, 39, 38, 361], 'euler2': [1, 2, 1, 0, 0], 'euler23': [1, 0, 34, 0, 529], 'euler29': [1, -6, 55, -174, 841], 'euler3': [1, -2, 1, 0, 0], 'euler31': [1, -6, 44, -186, 961], 'euler37': [1, 10, 96, 370, 1369], 'euler41': [1, -6, 91, -246, 1681], 'euler43': [1, -10, 108, -430, 1849], 'euler47': [1, 2, 83, 94, 2209], 'euler5': [1, -2, 8, -10, 25], 'euler53': [1, -14, 155, -742, 2809], 'euler59': [1, 12, 106, 708, 3481], 'euler61': [1, 0, 95, 0, 3721], 'euler67': [1, -4, 90, -268, 4489], 'euler7': [1, -2, 1, 0, 0], 'euler71': [1, 6, 124, 426, 5041], 'euler73': [1, 4, 138, 292, 5329], 'euler79': [1, -18, 191, -1422, 6241], 'euler83': [1, -10, 164, -830, 6889], 'euler89': [1, -14, 215, -1246, 7921], 'euler97': [1, 14, 168, 1358, 9409], 'euler_factors': [[1, 2, 1, 0, 0], [1, -2, 1, 0, 0], [1, -2, 8, -10, 25], [1, -2, 1, 0, 0], [1, 0, 19, 0, 121], [1, 0, 0, 0, 0], [1, -4, 35, -68, 289], [1, 2, 39, 38, 361], [1, 0, 34, 0, 529], [1, -6, 55, -174, 841], [1, -6, 44, -186, 961], [1, 10, 96, 370, 1369], [1, -6, 91, -246, 1681], [1, -10, 108, -430, 1849], [1, 2, 83, 94, 2209], [1, -14, 155, -742, 2809], [1, 12, 106, 708, 3481], [1, 0, 95, 0, 3721], [1, -4, 90, -268, 4489], [1, 6, 124, 426, 5041], [1, 4, 138, 292, 5329], [1, -18, 191, -1422, 6241], [1, -10, 164, -830, 6889], [1, -14, 215, -1246, 7921], [1, 14, 168, 1358, 9409]], 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/7098/2/a/bp'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, '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': '4-7098e2-1.1-c1e2-0-6', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1], 'order_of_vanishing': 0, 'prelabel': '4-7098e2-1.1-c1e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.528466998978268, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e2-0', 'trace_hash': 1383803145824069640, 'z1': {'__RealLiteral__': 0, 'data': '0.69385028253497057407204253047', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '879559727123982003916043912033,1232717008155088392381708534460', 'Lhash_array': ['879559727123982003916043912033', '1232717008155088392381708534460'], 'label': '4-7098e2-1.1-c1e2-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/7098/2/a/bp'}