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lfunc_lfunctions • Show schema
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{'Lhash': '1232430147299324891013776446419', 'a10': [-7716.897562372538, 0.0], 'a2': [-21.307095467237477, 0.0], 'a3': [27.0, 0.0], 'a4': [325.99231724997185, 0.0], 'a5': [362.17501227411805, 0.0], 'a6': [-575.2915776154119, 0.0], 'a7': [343.0, 0.0], 'a8': [-4218.64120542472, 0.0], 'a9': [729.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 150.88196730883087, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '3.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-27.0, 0]]], [7, [[1.0, 0], [-343.0, 0]]], [23, [[1.0, 0], [12167.0, 0]]]], 'bad_primes': [3, 7, 23], 'central_character': '483.1', 'coefficient_field': 'CDF', 'conductor': 483, 'conductor_radical': 483, 'degree': 2, 'euler_factors': [[[1.0, 0], [21.307095467237477, 0], [128.0, 0]], [[1.0, 0], [-27.0, 0]], [[1.0, 0], [-362.17501227411805, 0], [78125.0, 0]], [[1.0, 0], [-343.0, 0]], [[1.0, 0], [-5512.737822286874, 0], [19487171.0, 0]], [[1.0, 0], [-8637.817699535695, 0], [62748517.0, 0]], [[1.0, 0], 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'2.38315507392720889465081564119', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 150.88196730883087, 'bad_primes': [3, 7, 23], 'central_character': '1.1', 'conductor': 483, 'conductor_radical': 483, 'degree': 2, 'index': 82, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/483/8/a/h/1/1'], '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': '2-483-1.1-c7-0-82', 'motivic_weight': 7, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [7], 'order_of_vanishing': 0, 'prelabel': '2-483-1.1-c7-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.283402106453687, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c7-0', 'z1': {'__RealLiteral__': 0, 'data': '0.972215961620210351312620420793', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1232430147299324891013776446419', 'Lhash_array': ['1232430147299324891013776446419'], 'label': '2-483-1.1-c7-0-82', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/483/8/a/h/1/1'}