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lfunc_lfunctions • Show schema
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{'Lhash': '2411197183867046726103864463545', 'a10': [0.6180339887498949, 0.6180339887498949], 'a2': [1.260073510670101, 0.6420395219202062], 'a3': [-0.4510565162951536, 1.672288258377628], 'a4': [1.1755705045849463, 1.618033988749895], 'a5': [0.5877852522924731, 0.19098300562505258], 'a6': [-1.6420395219202062, 1.8176100265051525], 'a7': [-2.48989828488278, -3.4270509831248424], 'a8': [0.4424634841649486, 2.793604493334841], 'a9': [-2.59309603821536, -1.508593032130205], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.0540253066809016, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.260073510670101, -0.6420395219202062]]], [3, [[1.0, 0], [0.4510565162951536, -1.672288258377628]]], [11, [[1.0, 0], [-3.3090169943749475, 0.2245139882897927]]]], 'bad_primes': [2, 3, 11], 'central_character': '132.71', 'coefficient_field': 'CDF', 'conductor': 132, 'conductor_radical': 66, 'conjugate': 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'-0.211569014628', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.90209919313171292284171327879', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.39499250571953280246355319957', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.53399332298812593735813647921', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.0540253066809016, 'bad_primes': [2, 3, 11], 'central_character': '132.71', 'conductor': 132, 'conductor_radical': 66, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/132/2/o/a/71/2'], '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': '2-132-132.71-c1-0-6', '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': '2-132-132.71-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.0266573462849724, 'root_angle': -0.211569014627914, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.90209919313171292284171327879', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2411197183867046726103864463545', 'Lhash_array': ['2411197183867046726103864463545'], 'label': '2-132-132.71-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/132/2/o/a/71/2'}