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lfunc_lfunctions • Show schema
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{'Lhash': '1967422185606867179563920702039', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.9328293835915458, 0.0], 'a4': [0.0, 0.0], 'a5': [0.0, 0.0], 'a6': [0.0, 0.0], 'a7': [2.3823584151802217, 0.0], 'a8': [0.0, 0.0], 'a9': [0.7358294260748746, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 73.46236985957799, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [0, 0]]], [23, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 5, 23], 'central_character': '9200.1', 'coefficient_field': 'CDF', 'conductor': 9200, 'conductor_radical': 230, 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.9328293835915458, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.3823584151802217, 0], [7.0, 0]], [[1.0, 0], [5.333675535903341, 0], [11.0, 0]], [[1.0, 0], [-4.537521730698465, 0], [13.0, 0]], [[1.0, 0], [1.8146415423364495, 0], [17.0, 0]], [[1.0, 0], [7.0023343455697615, 0], [19.0, 0]], [[1.0, 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[113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 191, 'label': '2-9200-1.1-c1-0-191', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/9200/2/a/cu/1/4', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.046875', 'prec': 27}, 'plot_values': [-2.4357270736003375e-60, 0.29102581397559163, 0.5806415917014326, 0.867384420389714, 1.149689792027508, 1.4258508894500406, 1.6939891416716661, 1.9520385294540763, 2.1977452242496485, 2.428683218582196, 2.642285727480376, 2.835891361203401, 3.0068034180902945, 3.1523601311529545, 3.2700133164340963, 3.357412600436232, 3.4124922310910217, 3.4335573866637903, 3.419366878723766, 3.36920919270354, 3.2829689207317148, 3.1611808175092264, 3.00506895373118, 2.816568755734555, 2.598330106270388, 2.3537001389110306, 2.086684883986605, 1.8018895100465762, 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'6.84162157960168621035114708693691', '7.65883101044741792956930681883115'], 'prelabel': '2-9200-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.571019184413135, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.55202244628973474673365463989', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.28563678076206809989920213104', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.88611777185810853705314722059', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 73.46236985957799, 'bad_primes': [2, 5, 23], 'central_character': '1.1', 'conductor': 9200, 'conductor_radical': 230, 'degree': 2, 'index': 191, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/9200/2/a/cu/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': '2-9200-1.1-c1-0-191', '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': '2-9200-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.571019184413135, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.55202244628973474673365463989', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1967422185606867179563920702039', 'Lhash_array': ['1967422185606867179563920702039'], 'label': '2-9200-1.1-c1-0-191', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/9200/2/a/cu/1/4'}