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lfunc_lfunctions • Show schema
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{'Lhash': '942178192745380645796110005506', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [2.5, -4.330127018922194], 'a6': [0, 0], 'a7': [-1.0, -1.7320508075688772], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 95.58309420929984, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [-2.5, 4.330127018922194]]]], 'bad_primes': [2, 3, 5], 'central_character': '1620.1081', 'coefficient_field': 'CDF', 'conductor': 1620, 'conductor_radical': 30, 'conjugate': '825788884999446905165304525521', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-2.5, 4.330127018922194]], [[1.0, 0], [1.0, 1.7320508075688772], [-171.5, 297.04671349806245]], [[1.0, 0], [-15.0, -25.98076211353316], [-665.5, 1152.6798124370878]], [[1.0, 0], [-2.0, 3.4641016151377544], [-1098.5, -1902.6578121144116]], [[1.0, 0], [90.0, 0], 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{'__RealLiteral__': 0, 'data': '0.05555555555555555', 'prec': 64}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.74324754200861791421041994190', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.05587660198820689938867939007', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.99694672027115655748303861153', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 95.58309420929984, 'bad_primes': [2, 3, 5], 'central_character': '9.4', 'conductor': 1620, 'conductor_radical': 30, 'degree': 2, 'index': 24, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1620/4/i/i/1081/1'], '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': '2-1620-9.4-c3-0-24', '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': '2-1620-9.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.776660688051921, 'root_angle': 0.05555555555555555, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.74324754200861791421041994190', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '942178192745380645796110005506', 'Lhash_array': ['942178192745380645796110005506'], 'label': '2-1620-9.4-c3-0-24', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1620/4/i/i/1081/1'}