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lfunc_lfunctions • Show schema
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{'Lhash': '2458595371163888587099238110846', 'a10': [0.0, 0.0], 'a2': [2.419870349137736, 0.0], 'a3': [-0.5370800561629734, 0.0], 'a4': [3.8557725066359887, 0.0], 'a5': [0.0, 0.0], 'a6': [-1.2996641030220093, 0.0], 'a7': [3.1867595782641023, 0.0], 'a8': [4.490728863553442, 0.0], 'a9': [-2.7115450132719774, 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': '2458595371163888587099238110846', 'degree': 2, 'euler_factors': [[[1.0, 0], [-2.419870349137736, 0], [2.0, 0]], [[1.0, 0], [0.5370800561629734, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-3.1867595782641023, 0], [7.0, 0]], [[1.0, 0], [-4.155436609657998, 0], [11.0, 0]], [[1.0, 0], [2.0708585144157055, 0], [13.0, 0]], 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'6.23747713927914624437019652328135', '6.77589657797894483872649228641946', '8.161361446199647684270679948434051', '9.125612398491009934797537683859935', '10.72963131554115289684461111800503', '11.42914549877807920452444824912880'], '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': '1.93948977006853465589612621317', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.23585636369928182955420610606', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.61746627410580203861480523527', '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': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/475/2/a/j/1/6'], '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-c1-0-16', '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': '1.93948977006853465589612621317', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2458595371163888587099238110846', 'Lhash_array': ['2458595371163888587099238110846'], 'label': '2-475-1.1-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/2/a/j/1/6'}