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lfunc_lfunctions • Show schema
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{'Lhash': '4157089727217332953044819780998', 'a10': [2.045796382905387, -3.543423277132764], 'a2': [1.392728480640038, -0.2455756079379457], 'a3': [-1.569007106987643, -2.556993683649271], 'a4': [1.8793852415718169, -0.6840402866513374], 'a5': [1.8597086067630257, -2.2163144132882087], 'a6': [-2.8131361625839784, -3.175888053877575], 'a7': [2.174268603472515, 0.79136905296354], 'a8': [2.449489742783178, -1.4142135623730951], 'a9': [-4.076433396444534, 8.023882524336438], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.4713934275456033, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.0', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.392728480640038, 0.2455756079379457]]], [3, [[1.0, 0], [1.569007106987643, 2.556993683649271]]]], 'bad_primes': [2, 3], 'central_character': '54.41', 'coefficient_field': 'CDF', 'conductor': 54, 'conductor_radical': 6, 'conjugate': '2464254482825301488430901428742', 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.392728480640038, 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'spectral_label': 'c2-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.27936556529763431089611201038', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '5.02302622160369566363924687004', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.07257726493750000589360452713', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.4713934275456033, 'bad_primes': [2, 3], 'central_character': '27.14', 'conductor': 54, 'conductor_radical': 6, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/54/3/f/a/41/4'], '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': '2-54-27.14-c2-0-5', 'motivic_weight': 2, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [2], 'order_of_vanishing': 0, 'prelabel': '2-54-27.14-c2-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2130100690207, 'root_angle': 0.14462523397200527, 'self_dual': False, 'spectral_label': 'c2-0', 'z1': {'__RealLiteral__': 0, 'data': '3.27936556529763431089611201038', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4157089727217332953044819780998', 'Lhash_array': ['4157089727217332953044819780998'], 'label': '2-54-27.14-c2-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/54/3/f/a/41/4'}