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lfunc_lfunctions • Show schema
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{'Lhash': '1291295359269777160025982445157', 'a10': [-0.3614488497912558, -0.6260477721757864], 'a2': [-0.25881904510252074, -0.9659258262890683], 'a3': [-0.8660254037844386, 0.5], 'a4': [-0.8660254037844386, 0.5], 'a5': [0.6982655577917042, -0.18709969231275458], 'a6': [0.7071067811865476, 0.7071067811865476], 'a7': [2.638390541105545, -0.19721904726671008], 'a8': [0.7071067811865476, 0.7071067811865476], 'a9': [0.5, -0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 4.359831950361911, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.25881904510252074, 0.9659258262890683]]], [3, [[1.0, 0], [0.8660254037844386, -0.5]]], [7, [[1.0, 0], [-2.638390541105545, 0.19721904726671008]]], [13, [[1.0, 0], [3.558954345079214, 0.577792323972708]]]], 'bad_primes': [2, 3, 7, 13], 'central_character': '546.187', 'coefficient_field': 'CDF', 'conductor': 546, 'conductor_radical': 546, 'conjugate': 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'2.78400432214332930497955359158789', '4.65358401189921774178286314316459', '5.33294247400045082524086130563302', '6.19296698259553532342245800055789', '7.40846523151268024276197809619930', '7.84176219695853945370943842573291', '8.989685510688214729253226602544218', '9.907464798840992453006036347087836', '10.76737383069003694595125189999380'], 'prelabel': '2-546-91.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': 0.057576585732055915, 'root_number': '0.983685373889568 + 0.17989742965295763*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.028788292866', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.01865242602124806827842645291', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.78400432214332930497955359159', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.65358401189921774178286314316', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.359831950361911, 'bad_primes': [2, 3, 7, 13], 'central_character': '91.5', 'conductor': 546, 'conductor_radical': 546, 'degree': 2, 'index': 5, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/546/2/bz/a/187/4'], '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': '2-546-91.5-c1-0-5', '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': '2-546-91.5-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.0880210608042034, 'root_angle': 0.028788292866027958, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.01865242602124806827842645291', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1291295359269777160025982445157', 'Lhash_array': ['1291295359269777160025982445157'], 'label': '2-546-91.5-c1-0-5', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/546/2/bz/a/187/4'}