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lfunc_lfunctions • Show schema
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{'Lhash': '733742163838105574757276740316', 'a10': [4.684225109893684, -8.113315884425768], 'a2': [-1.110003899047093, 1.92258314974912], 'a3': [-0.27477556591051805, 0.475925240835508], 'a4': [-1.464217311799498, -2.536098777358651], 'a5': [-4.220007798094186, 0.0], 'a6': [-0.610003899047093, -1.0565577459646813], 'a7': [0.5, 0.8660254037844386], 'a8': [2.061132104410412, 0.0], 'a9': [1.3489967767571092, 2.3365309565899635], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[7, [[1.0, 0], [-0.5, -0.8660254037844386]]], [13, [[1.0, 0], [2.959000675804202, -2.060173536523143]]]], 'bad_primes': [7, 13], 'central_character': '91.22', 'coefficient_field': 'CDF', 'conductor': 91, 'conductor_radical': 91, 'conjugate': '5155773014862663694679336783296', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.110003899047093, -1.92258314974912], [-1.0, -1.7320508075688772]], [[1.0, 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'10.48478029384537397027395553832994', '11.44040697046566554777701428811006', '12.17586700928181408089458016102773', '12.72098732622981601294405891411620'], 'prelabel': '2-91-13.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': 0.8917789232628712, 'root_number': '-0.9427591542989431 + 0.3334744022943015*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.445889461631', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.57882050756415191752513853396', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.15821707461235387314895124712', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.39589751016946934774997453766', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.7266386583936518, 'bad_primes': [7, 13], 'central_character': '13.9', 'conductor': 91, 'conductor_radical': 91, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/91/2/f/c/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': '2-91-13.9-c1-0-0', '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': '2-91-13.9-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8524310285258578, 'root_angle': 0.4458894616314356, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.57882050756415191752513853396', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '733742163838105574757276740316', 'Lhash_array': ['733742163838105574757276740316'], 'label': '2-91-13.9-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/91/2/f/c/22/1'}