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lfunc_lfunctions • Show schema
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{'Lhash': '1998735352268969185638174514963', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [0.5362146574003032, 1.6469589676701346], 'a4': [0.0, 0.0], 'a5': [-1.6520844195398077, 0.0], 'a6': [0.0, 0.0], 'a7': [-3.1856205544675515, -1.8392188846578457], 'a8': [0.0, 0.0], 'a9': [-2.424947682378151, 1.7662470772031964], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.419972322510946, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-0.5362146574003032, -1.6469589676701346]]], [67, [[1.0, 0], [8.087899896778003, 1.2593153932587167]]]], 'bad_primes': [2, 3, 67], 'central_character': '804.365', 'coefficient_field': 'CDF', 'conductor': 804, 'conductor_radical': 402, 'conjugate': '328045804070516385871191721289', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-0.5362146574003032, -1.6469589676701346]], [[1.0, 0], [1.6520844195398077, 0], [5.0, 0]], [[1.0, 0], [3.1856205544675515, 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'9.457489114506575342358045636105256', '10.48725719686714249186312219318083'], 'prelabel': '2-804-201.164-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.533766430141292, 'root_angle': 0.5148429046229231, 'root_number': '-0.046613463189879974 + 0.9989130017421165*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.257421452311', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.57672417928813694394485551460', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.20958053232017753072350463371', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.54648767411658269852696920894', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.419972322510946, 'bad_primes': [2, 3, 67], 'central_character': '201.164', 'conductor': 804, 'conductor_radical': 402, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/804/2/o/d/365/11'], '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': '2-804-201.164-c1-0-15', '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': '2-804-201.164-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.533766430141292, 'root_angle': 0.2574214523114616, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.57672417928813694394485551460', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1998735352268969185638174514963', 'Lhash_array': ['1998735352268969185638174514963'], 'label': '2-804-201.164-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/804/2/o/d/365/11'}