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lfunc_lfunctions • Show schema
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{'Lhash': '1154958804463909298450937485604', 'a10': [0.23325200448479122, 0.0], 'a2': [-0.10336277020963638, 0.0], 'a3': [1.0, 0.0], 'a4': [-1.9893161377345898, 0.0], 'a5': [-2.25663460849316, 0.0], 'a6': [-0.10336277020963638, 0.0], 'a7': [4.11146919998558, 0.0], 'a8': [0.41234676723825453, 0.0], 'a9': [1.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.17172697437388, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.0, 0]]], [17, [[1.0, 0], [-1.0, 0]]], [79, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [3, 17, 79], 'central_character': '4029.1', 'coefficient_field': 'CDF', 'conductor': 4029, 'conductor_radical': 4029, 'degree': 2, 'euler_factors': [[[1.0, 0], [0.10336277020963638, 0], [2.0, 0]], [[1.0, 0], [-1.0, 0]], [[1.0, 0], [2.25663460849316, 0], [5.0, 0]], [[1.0, 0], [-4.11146919998558, 0], [7.0, 0]], [[1.0, 0], [-3.4154868256472195, 0], [11.0, 0]], [[1.0, 0], [-3.8804694888281777, 0], [13.0, 0]], 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'3.91623326885732624894126512549593', '4.55536077631780489526528568021155', '5.11196388958246587072339423576960', '6.32856217893966083930727775280672', '7.18513551942727134899896724551862', '8.149320257112475149941774597414357', '8.416573934092287313410647397669089'], 'prelabel': '2-4029-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.6720126035097875, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.911101847982377059564661825922', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.71314437977392451508145501802', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.27591555514979695880352230487', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 32.17172697437388, 'bad_primes': [3, 17, 79], 'central_character': '1.1', 'conductor': 4029, 'conductor_radical': 4029, 'degree': 2, 'index': 77, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4029/2/a/k/1/14'], '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': '2-4029-1.1-c1-0-77', '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': '2-4029-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.6720126035097875, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.911101847982377059564661825922', 'prec': 107}}
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lfunc_instances • Show schema
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{'Lhash': '1154958804463909298450937485604', 'Lhash_array': ['1154958804463909298450937485604'], 'label': '2-4029-1.1-c1-0-77', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4029/2/a/k/1/14'}