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lfunc_lfunctions • Show schema
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{'Lhash': '3503516536742513163580713800535', 'a10': [0.40001903933453936, 0.6928533001223154], 'a2': [-0.6427876096865394, 0.766044443118978], 'a3': [1.4396926207859084, -1.2080455471101075], 'a4': [-0.17364817766693036, -0.984807753012208], 'a5': [0.27362913833239094, -0.7517898788730694], 'a6': [-4.7720212980954226e-61, 1.8793852415718169], 'a7': [-0.13844908042023066, -0.05039134423449164], 'a8': [0.8660254037844386, 0.5], 'a9': [0.09239626545204768, -0.5240052604587699], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.5908929749574752, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.6427876096865394, -0.766044443118978]]], [37, [[1.0, 0], [-6.082271935422356, 0.07725350201502051]]]], 'bad_primes': [2, 37], 'central_character': '74.3', 'coefficient_field': 'CDF', 'conductor': 74, 'conductor_radical': 74, 'conjugate': '2812974083869995825354483945426', 'degree': 2, 'euler_factors': [[[1.0, 0], 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['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.76378722663148320127200442087', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.06126131264194166663343268673', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.25434991670005036183902371270', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.5908929749574752, 'bad_primes': [2, 37], 'central_character': '37.3', 'conductor': 74, 'conductor_radical': 74, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/74/2/h/a/3/1'], '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': '2-74-37.3-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': '2-74-37.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7686956321961738, 'root_angle': 0.0028035007153645267, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.76378722663148320127200442087', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3503516536742513163580713800535', 'Lhash_array': ['3503516536742513163580713800535'], 'label': '2-74-37.3-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/74/2/h/a/3/1'}