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lfunc_lfunctions • Show schema
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{'Lhash': '3211442778080235478625587905446', 'a10': [0.0, 0.0], 'a2': [2.142434334394992, 0.0], 'a3': [2.8783447793462797, 0.0], 'a4': [2.5900248771945127, 0.0], 'a5': [0.0, 0.0], 'a6': [6.166664681498047, 0.0], 'a7': [-3.1048189144009593, 0.0], 'a8': [1.2640895550487123, 0.0], 'a9': [5.284868668789984, 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': '3211442778080235478625587905446', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.142434334394992, 0], [2.0, 0]], [[1.0, 0], [-2.8783447793462797, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [3.1048189144009593, 0], [7.0, 0]], [[1.0, 0], [1.104818914400959, 0], [11.0, 0]], [[1.0, 0], [1.7735258649453207, 0], [13.0, 0]], 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'4.92466216797136882337836470724739', '6.49472017848852510188881082873310', '7.00563683171543417120531968408776', '8.366950422454006530385427726972293', '9.169833876468508841162276552094078', '9.966452785722532456931604020407118', '11.20239957506913439228659537595876'], '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': '2.53338165698185548864165943671', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.95177043823742787400304234771', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.05262928251473097624945113995', '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': 25, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/475/2/a/i/1/3'], '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-c1-0-25', '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': '2.53338165698185548864165943671', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3211442778080235478625587905446', 'Lhash_array': ['3211442778080235478625587905446'], 'factors': ['2-475-1.1-c1-0-25'], 'label': '2-475-1.1-c1-0-25', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/2/a/i/1/3'}