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{'Lhash': '1268436184437309724792528502400,1475759425790651369735593941634,1956955833354560571990908121945,2061587004155847517510288822743,2298008766328891209662335284984,2311215438828197630166692852726,2432494175891500201441761850362,2889742923364878208073661204361', 'a10': 8, 'a2': 2, 'a3': 0, 'a4': 3, 'a5': 4, 'a6': 0, 'a7': -1, 'a8': 2, 'a9': 1, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.0027992655294255013, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'bad_lfactors': [[31, [1]]], 'bad_primes': [31], 'central_character': '961.1', 'coefficient_field': '1.1.1.1', 'conductor': 727423121747185263828481, 'conductor_radical': 31, 'degree': 16, 'euler_factors': [[1, -2, 1, 2, -4, 4, -1, -4, 7, -4, -1, 4, -4, 2, 1, -2, 1], [1, 0, -1, 0, 0, 0, 1, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1], [1, -4, 6, -8, 17, -24, 22, -28, 36, -28, 22, -24, 17, -8, 6, -4, 1], [1, 1, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 1, 1], [1, 0, -1, 0, 0, 0, 1, 0, -1, 0, 1, 0, 0, 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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.0027992655294255013, 'bad_primes': [31], 'central_character': '1.1', 'conductor': 727423121747185263828481, 'conductor_radical': 31, 'degree': 16, 'dirichlet_coefficients': [1, 2, 0, 3, 4, 0, -1, 2, 1, 8, 0, 0, 0, -2, 0, 1, 0, 2, -1, 12, 0, 0, 0, 0, 10, 0, 0, -3, 0, 0, 0, -2, 0, 0, -4, 3, 0, -2, 0, 8, -1, 0, 0, 0, 4, 0, -4, 0, 0, 20, 0, 0, 0, 0, 0, -2, 0, 0, -1, 0, 0, 0, -1, -4, 0, 0, -8, 0, 0, -8, -1, 2, 0, 0, 0, -3, 0, 0, 0, 4, 1, -2, 0, 0, 0, 0, 0, 0, 0, 8, 0, 0, 0, -8, -4, 0, 2, 0, 0, 30], 'euler11': [1, 0, -1, 0, 0, 0, 1, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1], 'euler13': [1, 0, -1, 0, 0, 0, 1, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1], 'euler17': [1, 0, -1, 0, 0, 0, 1, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1], 'euler19': [1, 1, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 1, 1], 'euler2': [1, -2, 1, 2, -4, 4, -1, -4, 7, -4, -1, 4, -4, 2, 1, -2, 1], 'euler23': [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], 'euler29': [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 4, 0, 3, 0, 2, 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[1, 0, -1, 0, 0, 0, 1, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1], [1, 4, 10, 20, 35, 52, 68, 80, 85, 80, 68, 52, 35, 20, 10, 4, 1], [1, 0, -1, 0, 0, 0, 1, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1], [1, 1, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 1, 1], [1, 0, -8, 0, 28, 0, -56, 0, 70, 0, -56, 0, 28, 0, -8, 0, 1], [1, 8, 36, 112, 266, 504, 784, 1016, 1107, 1016, 784, 504, 266, 112, 36, 8, 1], [1, 1, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 2, 2, 1, 1, 1], [1, 0, -1, 0, 0, 0, 1, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1], [1, 0, -1, 0, 0, 0, 1, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1], [1, 0, -1, 0, 0, 0, 1, 0, -1, 0, 1, 0, 0, 0, -1, 0, 1], [1, 0, 2, 0, 3, 0, 4, 0, 5, 0, 4, 0, 3, 0, 2, 0, 1], [1, -2, 1, 2, -4, 4, -1, -4, 7, -4, -1, 4, -4, 2, 1, -2, 1]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/961/1/h/a'], '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': '16-31e16-1.1-c0e8-0-0', 'motivic_weight': 0, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [0, 0, 0, 0, 0, 0, 0, 0], 'order_of_vanishing': 0, 'prelabel': '16-31e16-1.1-c0e8-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 0.692532654205067, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c0e8-0', 'trace_hash': 980821932395392381, 'z1': {'__RealLiteral__': 0, 'data': '1.00061971667030243643718911363', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1268436184437309724792528502400,1475759425790651369735593941634,1956955833354560571990908121945,2061587004155847517510288822743,2298008766328891209662335284984,2311215438828197630166692852726,2432494175891500201441761850362,2889742923364878208073661204361', 'Lhash_array': ['1268436184437309724792528502400', '1475759425790651369735593941634', '1956955833354560571990908121945', '2061587004155847517510288822743', '2298008766328891209662335284984', '2311215438828197630166692852726', '2432494175891500201441761850362', '2889742923364878208073661204361'], 'label': '16-31e16-1.1-c0e8-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/961/1/h/a'}