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lfunc_lfunctions • Show schema
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{'Lhash': '771403251706906519501336237823', 'a10': [0.0, 0.0], 'a2': [-0.8165941601528085, 0.0], 'a3': [-1.538444565037812, 0.0], 'a4': [-1.3331739776043292, 0.0], 'a5': [0.0, 0.0], 'a6': [1.256284847528705, 0.0], 'a7': [-5.033159634903042, 0.0], 'a8': [2.7218504048850036, 0.0], 'a9': [-0.6331883203056171, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.79289409601082, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [5, 19], 'central_character': '475.1', 'coefficient_field': 'CDF', 'conductor': 475, 'conductor_radical': 95, 'conjugate': '771403251706906519501336237823', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.8165941601528085, 0], [2.0, 0]], [[1.0, 0], [1.538444565037812, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [5.033159634903042, 0], [7.0, 0]], [[1.0, 0], [3.033159634903041, 0], [11.0, 0]], [[1.0, 0], [-4.571604199940854, 0], [13.0, 0]], 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'5.67595031944522013313221045088507', '6.13384615958499342549676490382665', '7.37293913524197533799493645968913', '8.495178541244963706394724501282930', '9.292832878707652797997066644687095', '10.23071942198849525938986948919594', '10.63206226457689822574229513158856'], 'prelabel': '2-475-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.60852986743194229708444574820', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.02795612468554015068081966573', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.21642320315638735892081658755', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.79289409601082, 'bad_primes': [5, 19], 'central_character': '1.1', 'conductor': 475, 'conductor_radical': 95, 'degree': 2, 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/475/2/a/i/1/2'], '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': '2-475-1.1-c1-0-1', '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': '2-475-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.60852986743194229708444574820', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '771403251706906519501336237823', 'Lhash_array': ['771403251706906519501336237823'], 'label': '2-475-1.1-c1-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/2/a/i/1/2'}