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lfunc_lfunctions • Show schema
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{'Lhash': '2052965354928165658538348906670', 'a10': [-0.7443511339634102, -0.13124918803869026], 'a2': [0.17364817766693036, 0.984807753012208], 'a3': [0.5178738639389258, 1.6528177942680091], 'a4': [-0.9396926207859084, 0.3420201433256687], 'a5': [-0.25851043591411865, 0.7102515853674123], 'a6': [-1.5377799253773459, 0.7970149942795586], 'a7': [0.7779430100600899, -1.3474368188171422], 'a8': [-0.5, -0.8660254037844386], 'a9': [-2.463613322097934, 1.7119022750091726], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9102945830425968, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.17364817766693036, -0.984807753012208]]], [3, [[1.0, 0], [-0.5178738639389258, -1.6528177942680091]]], [19, [[1.0, 0], [4.143636822345215, 1.3528761526854014]]]], 'bad_primes': [2, 3, 19], 'central_character': '114.29', 'coefficient_field': 'CDF', 'conductor': 114, 'conductor_radical': 114, 'conjugate': 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0.9827969340312221*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.279563961602', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.61950410827600855092488691341', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.31321013956548319010295501370', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.16396058582476973217693566769', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.9102945830425968, 'bad_primes': [2, 3, 19], 'central_character': '57.29', 'conductor': 114, 'conductor_radical': 114, 'degree': 2, 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/114/2/l/b/29/2'], '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': '2-114-57.29-c1-0-2', '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': '2-114-57.29-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9540935923915415, 'root_angle': -0.27956396160184044, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.61950410827600855092488691341', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2052965354928165658538348906670', 'Lhash_array': ['2052965354928165658538348906670'], 'label': '2-114-57.29-c1-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/114/2/l/b/29/2'}