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lfunc_lfunctions • Show schema
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{'Lhash': '922901832287977134213377690358', 'a10': [-32.29437168288782, 0.0], 'a2': [0.0, 3.5205750559441293], 'a3': [0.0, 0.0], 'a4': [-4.39444872453601, 0.0], 'a5': [0.0, 9.173038827381932], 'a6': [0.0, 0.0], 'a7': [0.0, 0.0], 'a8': [0.0, 12.693613883326062], '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': '3266900046999523928909627273357', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, -3.5205750559441293], [-8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [0, -9.173038827381932], [-125.0, 0]], [[1.0, 0], [0, 0], [-343.0, 0]], [[1.0, 0], [0, -20.477966370257537], [-1331.0, 0]], [[1.0, 0], [46.87216658103186, 0]], [[1.0, 0], [0, 0], [4913.0, 0]], 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'10.54108261706540084823297753015561', '11.60160341664841070800638665386842', '12.41310089328677827003160573589729'], 'prelabel': '2-117-13.12-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6273986128244142, 'root_angle': -1.0, 'root_number': '-1.0 - 1.2246467991473532e-16*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.5', 'prec': 14}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.72804117484882406288662974146', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.39050690219638523959115644465', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.93244288367769326776970706608', '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': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/117/4/b/c/64/3'], '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-c3-0-2', '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': -0.5, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '0.72804117484882406288662974146', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '922901832287977134213377690358', 'Lhash_array': ['922901832287977134213377690358'], 'label': '2-117-13.12-c3-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/117/4/b/c/64/3'}