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lfunc_lfunctions • Show schema
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{'Lhash': '2164461758754175184067007758743', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, -3.0], 'a4': [0, 0], 'a5': [2.0, -11.0], 'a6': [0, 0], 'a7': [0, -10.0], 'a8': [0, 0], 'a9': [-9.0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 56.64183360551102, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 3.0]]], [5, [[1.0, 0], [-2.0, 11.0]]]], 'bad_primes': [2, 3, 5], 'central_character': '960.769', 'coefficient_field': 'CDF', 'conductor': 960, 'conductor_radical': 30, 'conjugate': '539252825576305796854953231537', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 3.0]], [[1.0, 0], [-2.0, 11.0]], [[1.0, 0], [0, 10.0], [-343.0, 0]], [[1.0, 0], [14.0, 0], [1331.0, 0]], [[1.0, 0], [0, 82.0], [-2197.0, 0]], [[1.0, 0], [0, -18.0], [-4913.0, 0]], [[1.0, 0], [-136.0, 0], [6859.0, 0]], [[1.0, 0], [0, 140.0], [-12167.0, 0]], [[1.0, 0], [-112.0, 0], [24389.0, 0]], [[1.0, 0], [72.0, 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'2-960-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.526076906696543, 'root_angle': -0.9427508529512999, 'root_number': '-0.98386991009990746642003641424176154359387207822907131868 - 0.17888543819998317571273389349850209883524946876892205794*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.47137542647564995', 'prec': 67}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.70745926232708190927854686446', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.86057124007904460095454866060', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.68706189128463260069871149483', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 56.64183360551102, 'bad_primes': [2, 3, 5], 'central_character': '5.4', 'conductor': 960, 'conductor_radical': 30, 'degree': 2, 'index': 67, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/960/4/f/e/769/1'], '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': '2-960-5.4-c3-0-67', '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': '2-960-5.4-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.526076906696543, 'root_angle': -0.47137542647564995, 'self_dual': False, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.70745926232708190927854686446', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2164461758754175184067007758743', 'Lhash_array': ['2164461758754175184067007758743'], 'label': '2-960-5.4-c3-0-67', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/960/4/f/e/769/1'}