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lfunc_lfunctions • Show schema
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{'Lhash': '2451822990982179231167024406647', 'a10': [90.29437168288781, 0.0], 'a2': [0.0, 4.427815632505942], 'a3': [0.0, 0.0], 'a4': [-11.60555127546399, 0.0], 'a5': [0.0, -20.392531933807128], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, -15.964716301301188], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.903223470671655, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [13, [[1.0, 0], [-46.87216658103186, 0]]]], 'bad_primes': [3, 13], 'central_character': '117.64', 'coefficient_field': 'CDF', 'conductor': 117, 'conductor_radical': 39, 'conjugate': '950075984033797491194071016219', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -4.427815632505942], [-8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, 20.392531933807128], [-125.0, 0]], [[1.0, 0], [0, 0], [-343.0, 0]], [[1.0, 0], [0, 70.03322706643327], [-1331.0, 0]], [[1.0, 0], [-46.87216658103186, 0]], [[1.0, 0], [0, 0], [4913.0, 0]], 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'11.78041628046654923804559932266785', '12.80056317237265360561319787637850'], 'prelabel': '2-117-13.12-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6273986128244142, 'root_angle': 1.383202515268798e-61, 'root_number': '1.0 + 4.34545886039538e-61*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0000000000000000000000000000000000000000000000000000000000000691601257634', 'prec': 250}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.93414730410789057295757879670', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.07536055520435076079127533659', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.28916520528875930588625783628', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.903223470671655, 'bad_primes': [3, 13], 'central_character': '13.12', 'conductor': 117, 'conductor_radical': 39, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/117/4/b/c/64/4'], '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': '2-117-13.12-c3-0-9', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 0, 'prelabel': '2-117-13.12-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6273986128244142, 'root_angle': 6.91601257634399e-62, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.93414730410789057295757879670', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2451822990982179231167024406647', 'Lhash_array': ['2451822990982179231167024406647'], 'label': '2-117-13.12-c3-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/117/4/b/c/64/4'}