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  • lfunc_lfunctions • Show schema
    {'Lhash': '3183353065076914602031151839796', 'a10': [-247.47359318619675, 0.0], 'a2': [6.38986691902975, 0.0], 'a3': [9.0, 0.0], 'a4': [8.83039924291075, 0.0], 'a5': [-38.72906843320825, 0.0], 'a6': [57.50880227126775, 0.0], 'a7': [0.0, 0.0], 'a8': [-148.05066540485126, 0.0], 'a9': [81.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 23.57642151250816, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 7}, 'bad_lfactors': [[3, [[1.0, 0], [-9.0, 0]]], [7, [[1.0, 0], [0, 0]]]], 'bad_primes': [3, 7], 'central_character': '147.1', 'coefficient_field': 'CDF', 'conductor': 147, 'conductor_radical': 21, 'degree': 2, 'euler_factors': [[[1.0, 0], [-6.38986691902975, 0], [32.0, 0]], [[1.0, 0], [-9.0, 0]], [[1.0, 0], [38.72906843320825, 0], [3125.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [576.3898669190297, 0], [161051.0, 0]], [[1.0, 0], [391.49119772873223, 0], [371293.0, 0]], [[1.0, 0], [-1329.700304016403, 0], [1419857.0, 0]], [[1.0, 0], 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'4.71988752942268134871114721621504', '5.80905837720830070576998366879531', '7.43894621286793819805019524319779', '8.252508069274632845332126271264265', '9.597832961713370677363959296156844', '10.75025679854187434642862371754760', '12.18531646024113554861615028484886'], 'prelabel': '2-147-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.855555736731704, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'spectral_label': 'c5-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.51122278055465735574161802883', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.61859773359340275618543275722', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '4.71988752942268134871114721622', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 23.57642151250816, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 147, 'conductor_radical': 21, 'degree': 2, 'index': 33, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/147/6/a/k/1/2'], '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': '2-147-1.1-c5-0-33', 'motivic_weight': 5, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [5], 'order_of_vanishing': 1, 'prelabel': '2-147-1.1-c5-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.855555736731704, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c5-0', 'z1': {'__RealLiteral__': 0, 'data': '2.51122278055465735574161802883', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '3183353065076914602031151839796', 'Lhash_array': ['3183353065076914602031151839796'], 'factors': ['2-147-1.1-c5-0-33'], 'label': '2-147-1.1-c5-0-33', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/147/6/a/k/1/2'}