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lfunc_lfunctions • Show schema
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{'Lhash': '1954221353666103736139328472116', 'a10': [-3383.931508629795, 0.0], 'a2': [-16.013798716329703, 0.0], 'a3': [27.0, 0.0], 'a4': [128.4417493271229, 0.0], 'a5': [211.31347836782214, 0.0], 'a6': [-432.37256534090204, 0.0], 'a7': [0.0, 0.0], 'a8': [-7.074084807619985, 0.0], 'a9': [729.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 45.920598746165915, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-27.0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '147.1', 'coefficient_field': 'CDF', 'conductor': 147, 'conductor_radical': 21, 'degree': 2, 'euler_factors': [[[1.0, 0], [16.013798716329703, 0], [128.0, 0]], [[1.0, 0], [-27.0, 0]], [[1.0, 0], [-211.31347836782214, 0], [78125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [954.3810311224836, 0], [19487171.0, 0]], [[1.0, 0], [-1309.212109341577, 0], [62748517.0, 0]], [[1.0, 0], [30323.23861638486, 0], [410338673.0, 0]], [[1.0, 0], 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-0.35663930813253075], 'positive_zeros': ['1.54160882605527365066264957283702', '2.49292197254431025626536931958805', '4.38107566889524032456741847490299', '6.12443361380815810382015305651794', '7.30032175236316333265622404811135', '8.364192346475987549672672974279126', '9.099320106872103845267485591117256', '10.00063185928293416759461557114971', '10.69616803117664377812804893609148'], 'prelabel': '2-147-1.1-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.776473916880808, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c7-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.54160882605527365066264957284', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.49292197254431025626536931959', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.38107566889524032456741847490', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 45.920598746165915, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 147, 'conductor_radical': 21, 'degree': 2, 'index': 36, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/147/8/a/m/1/2'], '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': '2-147-1.1-c7-0-36', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 1, 'prelabel': '2-147-1.1-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.776473916880808, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '1.54160882605527365066264957284', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1954221353666103736139328472116', 'Lhash_array': ['1954221353666103736139328472116'], 'factors': ['2-147-1.1-c7-0-36'], 'label': '2-147-1.1-c7-0-36', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/147/8/a/m/1/2'}