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lfunc_lfunctions • Show schema
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{'Lhash': '1721547329416558483200886275776', 'a10': [-1.408408562549739, 2.831322186000134], 'a2': [-1.3119896781181348, 0.5279044274406806], 'a3': [-0.10858219739999883, 0.12940322384322228], 'a4': [1.4426338309770546, -1.3852103196700736], 'a5': [1.671242507069477, -1.4855801838218392], 'a6': [0.07414618742424976, -0.2270967167462155], 'a7': [0.17627727346187164, 0.3053211938556746], 'a8': [-1.1614620348555653, 2.578954427978356], 'a9': [0.5159894322519842, 2.9263214862455422], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.034315276808656, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.3119896781181348, -0.5279044274406806]]], [5, [[1.0, 0], [-1.671242507069477, 1.4855801838218392]]], [19, [[1.0, 0], [1.5720831162746691, 4.065532520534564]]]], 'bad_primes': [2, 5, 19], 'central_character': '380.59', 'coefficient_field': 'CDF', 'conductor': 380, 'conductor_radical': 190, 'conjugate': 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'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0146783382551', 'prec': 54}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.35806138466436173041937184358', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.79923639280983123155569193114', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.99427948129228935546634108004', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.034315276808656, 'bad_primes': [2, 5, 19], 'central_character': '380.59', 'conductor': 380, 'conductor_radical': 190, 'degree': 2, 'index': 30, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/380/2/bb/a/59/7'], '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': '2-380-380.59-c1-0-30', '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': '2-380-380.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.7419286084132886, 'root_angle': -0.014678338255115045, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.35806138466436173041937184358', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1721547329416558483200886275776', 'Lhash_array': ['1721547329416558483200886275776'], 'label': '2-380-380.59-c1-0-30', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/380/2/bb/a/59/7'}