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lfunc_lfunctions • Show schema
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{'Lhash': '2115526388833247514775931639164', 'a10': 0, 'a2': 1, 'a3': 0, 'a4': 1, 'a5': 0, 'a6': 0, 'a7': 1, 'a8': 1, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 51.88679123342802, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, -1]], [3, [1]], [19, [1]]], 'bad_primes': [2, 3, 19], 'central_character': '6498.1', 'coefficient_field': '1.1.1.1', 'conductor': 6498, 'conductor_radical': 114, 'degree': 2, 'euler_factors': [[1, -1], [1], [1, 0, 5], [1, -1, 7], [1, -2, 11], [1, 3, 13], [1, 4, 17], [1], [1, 4, 23], [1, 0, 29], [1, 3, 31], [1, 5, 37], [1, 4, 41], [1, 9, 43], [1, 10, 47], [1, -4, 53], [1, -14, 59], [1, -11, 61], [1, -3, 67], [1, 14, 71], [1, 11, 73], [1, -1, 79], [1, 8, 83], [1, -14, 89], [1, -2, 97], [1, -10, 101], [1, 3, 103], [1, -10, 107], [1, -14, 109], [1, 10, 113]], 'euler_factors_factorization': [[[[1, -1], 1]], [1], [[[1, 0, 5], 1]], [[[1, -1, 7], 1]], [[[1, -2, 11], 1]], [[[1, 3, 13], 1]], 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0.0797712659064059, -0.1164388840312591, -0.3052725162510506, -0.46624410599451965, -0.5810085774833671, -0.6344480683457062, -0.6155645852319046, -0.5181278675245813, -0.34104170061603806], 'positive_zeros': ['1.66885606211393383518733282723363', '2.23651451653199078821675184261845', '3.37023256108413759660766045527577', '4.03962720202051060719646779226684', '4.80065633486119479778731610427789', '5.38621693677820962887664692170210', '6.27075428503338386215963543011369', '6.85545217444089561847219939247921', '7.50727163341642116560481426828342'], 'prelabel': '2-6498-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.203248658308834, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'trace_hash': 1688758016473305407, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.66885606211393383518733282723', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 51.88679123342802, 'bad_primes': [2, 3, 19], 'central_character': '1.1', 'conductor': 6498, 'conductor_radical': 114, 'degree': 2, 'dirichlet_coefficients': [1, 1, 0, 1, 0, 0, 1, 1, 0, 0, 2, 0, -3, 1, 0, 1, -4, 0, 0, 0, 0, 2, -4, 0, -5, -3, 0, 1, 0, 0, -3, 1, 0, -4, 0, 0, -5, 0, 0, 0, -4, 0, -9, 2, 0, -4, -10, 0, -6, -5, 0, -3, 4, 0, 0, 1, 0, 0, 14, 0, 11, -3, 0, 1, 0, 0, 3, -4, 0, 0, -14, 0, -11, -5, 0, 0, 2, 0, 1, 0, 0, -4, -8, 0, 0, -9, 0, 2, 14, 0, -3, -4, 0, -10, 0, 0, 2, -6, 0, -5], 'euler11': [1, -2, 11], 'euler13': [1, 3, 13], 'euler17': [1, 4, 17], 'euler19': [1, 0, 0], 'euler2': [1, -1, 0], 'euler23': [1, 4, 23], 'euler29': [1, 0, 29], 'euler3': [1, 0, 0], 'euler31': [1, 3, 31], 'euler37': [1, 5, 37], 'euler41': [1, 4, 41], 'euler43': [1, 9, 43], 'euler47': [1, 10, 47], 'euler5': [1, 0, 5], 'euler53': [1, -4, 53], 'euler59': [1, -14, 59], 'euler61': [1, -11, 61], 'euler67': [1, -3, 67], 'euler7': [1, -1, 7], 'euler71': [1, 14, 71], 'euler73': [1, 11, 73], 'euler79': [1, -1, 79], 'euler83': [1, 8, 83], 'euler89': [1, -14, 89], 'euler97': [1, -2, 97], 'euler_factors': [[1, -1, 0], [1, 0, 0], [1, 0, 5], [1, -1, 7], [1, -2, 11], [1, 3, 13], [1, 4, 17], [1, 0, 0], [1, 4, 23], [1, 0, 29], [1, 3, 31], [1, 5, 37], [1, 4, 41], [1, 9, 43], [1, 10, 47], [1, -4, 53], [1, -14, 59], [1, -11, 61], [1, -3, 67], [1, 14, 71], [1, 11, 73], [1, -1, 79], [1, 8, 83], [1, -14, 89], [1, -2, 97]], 'index': 138, 'instance_types': ['ECQ', 'CMF', 'CMF'], 'instance_urls': ['EllipticCurve/Q/6498/u', 'ModularForm/GL2/Q/holomorphic/6498/2/a/u/1/1', 'ModularForm/GL2/Q/holomorphic/6498/2/a/u'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, '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': '2-6498-1.1-c1-0-138', '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': '2-6498-1.1-c1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.203248658308834, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'trace_hash': 1688758016473305407, 'z1': {'__RealLiteral__': 0, 'data': '1.66885606211393383518733282723', 'prec': 103}}
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lfunc_instances • Show schema
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id: 21714798
{'Lhash': '2115526388833247514775931639164', 'Lhash_array': ['2115526388833247514775931639164'], 'label': '2-6498-1.1-c1-0-138', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6498/2/a/u'}
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id: 24575356
{'Lhash': '2115526388833247514775931639164', 'Lhash_array': ['2115526388833247514775931639164'], 'label': '2-6498-1.1-c1-0-138', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6498/2/a/u/1/1'}
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id: 23555
{'Lhash': '1688758016473305407', 'Lhash_array': ['1688758016473305407'], 'label': '2-6498-1.1-c1-0-138', 'type': 'ECQ', 'url': 'EllipticCurve/Q/6498/u'}