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lfunc_lfunctions • Show schema
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{'Lhash': '838850414989562270705955811701', 'a10': [13.5, -23.382685902179844], 'a2': [-1.5, 2.598076211353316], 'a3': [-1.5, 2.598076211353316], 'a4': [-0.5, -0.8660254037844386], 'a5': [-9.0, 0.0], 'a6': [-4.5, -7.794228634059948], 'a7': [-1.0, -1.7320508075688772], 'a8': [-21.0, 0.0], 'a9': [-4.5, -7.794228634059948], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.301074490223885, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.5, -2.598076211353316]]], [13, [[1.0, 0], [-32.5, -33.77499074759311]]]], 'bad_primes': [3, 13], 'central_character': '39.22', 'coefficient_field': 'CDF', 'conductor': 39, 'conductor_radical': 39, 'conjugate': '4938547880503047761167019148596', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.5, -2.598076211353316], [-4.0, -6.928203230275509]], [[1.0, 0], [1.5, -2.598076211353316]], [[1.0, 0], [9.0, 0], [125.0, 0]], [[1.0, 0], [1.0, 1.7320508075688772], [-171.5, 297.04671349806245]], 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0, 'data': '-0.495918097215', 'prec': 50}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.66173629771368750311017618197', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.07740421174496972295053312568', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.69451087536718866451308193320', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.301074490223885, 'bad_primes': [3, 13], 'central_character': '13.9', 'conductor': 39, 'conductor_radical': 39, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/39/4/e/a/22/1'], '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': '2-39-13.9-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': '2-39-13.9-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.5169292963826246, 'root_angle': -0.4959180972148666, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.66173629771368750311017618197', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '838850414989562270705955811701', 'Lhash_array': ['838850414989562270705955811701'], 'label': '2-39-13.9-c3-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/39/4/e/a/22/1'}