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lfunc_lfunctions • Show schema
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{'Lhash': '867374109606801717178120583160,963702714868814496034237918652', 'a10': 0, 'a2': -1, 'a3': -2, 'a4': 0, 'a5': 0, 'a6': 2, 'a7': 0, 'a8': 1, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.5965114058884313, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1, 1, 1]], [5, [1]], [19, [1, -2, 1]]], 'bad_primes': [2, 5, 19], 'central_character': '3800.1', 'coefficient_field': '1.1.1.1', 'conductor': 14440000, 'conductor_radical': 190, 'degree': 4, 'euler_factors': [[1, 1, 1], [1, 2, 3, 2, 1], [1], [1, 0, -2, 0, 1], [1, 2, 3, 2, 1], [1, 0, 1, 0, 1], [1, -1, 0, -1, 1], [1, -2, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, -1, 0, -1, 1], [1, 2, 3, 2, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, -1, 0, -1, 1], [1, 0, 1, 0, 1], [1, -1, 0, -1, 1], [1, 0, 1, 0, 1], [1, 2, 3, 2, 1], [1, 0, 1, 0, 1], [1, -4, 6, -4, 1], [1, -1, 0, -1, 1], [1, -1, 0, -1, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, 2, 3, 2, 1], [1, 0, 1, 0, 1], [1, -4, 6, -4, 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'5.72537649953636185351604359329270', '6.24465723971237284711489609819829', '6.60107986511674122415307284123960', '7.21711840564239426605320191310929', '7.45468440700127506174417905294714', '7.66431842077474198234987457278259', '8.204904509616653978322091610269180', '8.332069598149599117981018553842232', '9.122071345926588598575568097106071'], 'prelabel': '4-3800e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.3771154809983837, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c0e2-0', 'trace_hash': 727482753906394407, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.68423752526969071470027603493', 'prec': 97}, 'z2': {'__RealLiteral__': 0, 'data': '0.76022739601535963651202880162', 'prec': 97}, 'z3': {'__RealLiteral__': 0, 'data': '1.68287882945680099695377238636', 'prec': 100}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.5965114058884313, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 14440000, 'conductor_radical': 190, 'degree': 4, 'dirichlet_coefficients': [1, -1, -2, 0, 0, 2, 0, 1, 1, 0, -2, 0, 0, 0, 0, -1, 1, -1, 2, 0, 0, 2, 0, -2, 0, 0, 2, 0, 0, 0, 0, 0, 4, -1, 0, 0, 0, -2, 0, 0, 1, 0, -2, 0, 0, 0, 0, 2, 2, 0, -2, 0, 0, -2, 0, 0, -4, 0, 1, 0, 0, 0, 0, 1, 0, -4, 1, 0, 0, 0, 0, 1, -2, 0, 0, 0, 0, 0, 0, 0, -4, -1, 4, 0, 0, 2, 0, -2, 1, 0, 0, 0, 0, 0, 0, 0, 1, -2, -2, 0], 'euler11': [1, 2, 3, 2, 1], 'euler13': [1, 0, 1, 0, 1], 'euler17': [1, -1, 0, -1, 1], 'euler19': [1, -2, 1, 0, 0], 'euler2': [1, 1, 1, 0, 0], 'euler23': [1, 0, 1, 0, 1], 'euler29': [1, 0, 1, 0, 1], 'euler3': [1, 2, 3, 2, 1], 'euler31': [1, 0, -2, 0, 1], 'euler37': [1, 0, -2, 0, 1], 'euler41': [1, -1, 0, -1, 1], 'euler43': [1, 2, 3, 2, 1], 'euler47': [1, 0, 1, 0, 1], 'euler5': [1, 0, 0, 0, 0], 'euler53': [1, 0, 1, 0, 1], 'euler59': [1, -1, 0, -1, 1], 'euler61': [1, 0, 1, 0, 1], 'euler67': [1, -1, 0, -1, 1], 'euler7': [1, 0, -2, 0, 1], 'euler71': [1, 0, 1, 0, 1], 'euler73': [1, 2, 3, 2, 1], 'euler79': [1, 0, 1, 0, 1], 'euler83': [1, -4, 6, -4, 1], 'euler89': [1, -1, 0, -1, 1], 'euler97': [1, -1, 0, -1, 1], 'euler_factors': [[1, 1, 1, 0, 0], [1, 2, 3, 2, 1], [1, 0, 0, 0, 0], [1, 0, -2, 0, 1], [1, 2, 3, 2, 1], [1, 0, 1, 0, 1], [1, -1, 0, -1, 1], [1, -2, 1, 0, 0], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, 0, -2, 0, 1], [1, 0, -2, 0, 1], [1, -1, 0, -1, 1], [1, 2, 3, 2, 1], [1, 0, 1, 0, 1], [1, 0, 1, 0, 1], [1, -1, 0, -1, 1], [1, 0, 1, 0, 1], [1, -1, 0, -1, 1], [1, 0, 1, 0, 1], [1, 2, 3, 2, 1], [1, 0, 1, 0, 1], [1, -4, 6, -4, 1], [1, -1, 0, -1, 1], [1, -1, 0, -1, 1]], 'index': 4, 'instance_types': ['CMF', 'Artin'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3800/1/bd/a', 'ArtinRepresentation/2.3800.6t5.d'], 'is_instance_Artin': True, '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': '4-3800e2-1.1-c0e2-0-4', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0, 0], 'nu_real_doubled': [0, 0], 'order_of_vanishing': 0, 'prelabel': '4-3800e2-1.1-c0e2-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.3771154809983837, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e2-0', 'trace_hash': 727482753906394407, 'z1': {'__RealLiteral__': 0, 'data': '0.68423752526969071470027603493', 'prec': 97}}
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lfunc_instances • Show schema
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id: 19953765
{'Lhash': '867374109606801717178120583160,963702714868814496034237918652', 'Lhash_array': ['867374109606801717178120583160', '963702714868814496034237918652'], 'factors': ['2-3800-152.11-c0-0-0', '2-3800-152.83-c0-0-3'], 'label': '4-3800e2-1.1-c0e2-0-4', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3800/1/bd/a'}
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id: 24609440
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