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lfunc_lfunctions • Show schema
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{'Lhash': '740634071663553695003285047690', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.9281934015534656, 1.6076781307407833], 'a4': [0.0, 0.0], 'a5': [-1.5181667194588018, 1.5181667194588018], 'a6': [0.0, 0.0], 'a7': [-2.977677740534301, 0.797866345896296], 'a8': [0.0, 0.0], 'a9': [-0.22308598137478616, 0.3863962541974939], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.3217767240852654, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-0.15951641373009595, -3.602020893019735]]]], 'bad_primes': [2, 13], 'central_character': '416.271', 'coefficient_field': 'CDF', 'conductor': 416, 'conductor_radical': 26, 'conjugate': '3321720200786326744662871644397', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.9281934015534656, -1.6076781307407833], [-1.5, 2.598076211353316]], [[1.0, 0], [1.5181667194588018, -1.5181667194588018], [0, -5.0]], [[1.0, 0], [2.977677740534301, 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'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 0, 'label': '2-416-104.11-c1-0-0', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/416/2/bk/a/271/9', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [0.9904509006286575, 0.7858635377228289, 0.5825845720073594, 0.3740169005486004, 0.15499258856965908, -0.07713469385757829, -0.3217949424618446, -0.5748895531828426, -0.8288095119281953, -1.0727480856443434, -1.2932990564063345, -1.4753437743307223, -1.6032211376796797, -1.6621475827057108, -1.6398160549184533, -1.5280609154655056, -1.3244368058692837, -1.0335304388826505, -0.6678114886911529, -0.2478376822478156, 0.19833638725690036, 0.6366360809415545, 1.029332807441779, 1.338198638684104, 1.5282354295725733, 1.5716554243635932, 1.4517009798515008, 1.165837203891322, 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'9.971210224866643484570630443668535', '10.74682628725668672945377490982504'], 'prelabel': '2-416-104.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.822574202628048, 'root_angle': -0.8156521258386683, 'root_number': '-0.8369303971380077 - 0.5473093369808493*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.407826062919', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.58425726421003469668418697927', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.44476016849574478644300608231', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.65919645881682509264509302341', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.3217767240852654, 'bad_primes': [2, 13], 'central_character': '104.11', 'conductor': 416, 'conductor_radical': 26, 'degree': 2, 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/416/2/bk/a/271/9'], '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': '2-416-104.11-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': '2-416-104.11-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.822574202628048, 'root_angle': -0.40782606291933415, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.58425726421003469668418697927', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '740634071663553695003285047690', 'Lhash_array': ['740634071663553695003285047690'], 'label': '2-416-104.11-c1-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/416/2/bk/a/271/9'}