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lfunc_lfunctions • Show schema
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{'Lhash': '601881643707294597537906570163', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-0.5802342224082742, -3.2906717966640637], 'a4': [0.0, 0.0], 'a5': [-11.90653776709357, 9.99077144896657], 'a6': [0.0, 0.0], 'a7': [-13.765940169464749, 23.843307787466266], 'a8': [0.0, 0.0], 'a9': [14.879851640712966, -5.4158230875166335], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.484145160436289, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [76.22190107249149, -32.391693331706506]]]], 'bad_primes': [2, 19], 'central_character': '76.61', 'coefficient_field': 'CDF', 'conductor': 76, 'conductor_radical': 38, 'conjugate': '3105098256922608747464321116939', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0.5802342224082742, 3.2906717966640637], [-25.371700761219525, 9.234543869793056]], [[1.0, 0], [11.90653776709357, -9.99077144896657], [21.706022208366292, -123.10096912652601]], 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'data': '3.85112403285144590173660406094', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.51488146588137490508030350138', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.484145160436289, 'bad_primes': [2, 19], 'central_character': '19.4', 'conductor': 76, 'conductor_radical': 38, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/76/4/i/a/61/2'], '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': '2-76-19.4-c3-0-0', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-76-19.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.1175800245649015, 'root_angle': -0.3077523285432479, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.47480089829084692003529168505', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '601881643707294597537906570163', 'Lhash_array': ['601881643707294597537906570163'], 'label': '2-76-19.4-c3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/76/4/i/a/61/2'}