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lfunc_lfunctions • Show schema
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{'Lhash': '1162987474093429153864209451548', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.1738248013306656, 0.0], 'a4': [0.0, 0.0], 'a5': [1.0, 0.0], 'a6': [0.0, 0.0], 'a7': [1.0, 0.0], 'a8': [0.0, 0.0], 'a9': [-1.6221353357810235, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 29.065546335746074, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-1.0, 0]]], [7, [[1.0, 0], [-1.0, 0]]], [13, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 5, 7, 13], 'central_character': '3640.1', 'coefficient_field': 'CDF', 'conductor': 3640, 'conductor_radical': 910, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.1738248013306656, 0], [3.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [0.49041095729549217, 0], [11.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [7.574213494772216, 0], [17.0, 0]], [[1.0, 0], [-3.549398030665237, 0], [19.0, 0]], [[1.0, 0], [4.519182969107591, 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'5.62058023716131726194585272044056', '6.29597843341692810778441861871634', '7.06820396774009992809563482099225', '8.141390428416471476334758970281389', '8.390096997522863667278313329540685'], 'prelabel': '2-3640-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.3912471966833495, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.917435351574040538191319195143', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '2.40323080787449136596337429545', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.61188113059511580442812722334', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 29.065546335746074, 'bad_primes': [2, 5, 7, 13], 'central_character': '1.1', 'conductor': 3640, 'conductor_radical': 910, 'degree': 2, 'index': 24, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3640/2/a/ba/1/4'], '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': '2-3640-1.1-c1-0-24', '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': '2-3640-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.3912471966833495, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.917435351574040538191319195143', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1162987474093429153864209451548', 'Lhash_array': ['1162987474093429153864209451548'], 'label': '2-3640-1.1-c1-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3640/2/a/ba/1/4'}