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lfunc_lfunctions • Show schema
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{'Lhash': '845572050307490330150672065167', 'a10': [0, 0], 'a2': [0, 0], 'a3': [0, 0], 'a4': [0, 0], 'a5': [-1.0, 2.0], 'a6': [0, 0], 'a7': [0, -1.0], 'a8': [0, 0], 'a9': [0, 0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 40.24460261872533, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [1.0, -2.0]]], [7, [[1.0, 0], [0, 1.0]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '5040.1009', 'coefficient_field': 'CDF', 'conductor': 5040, 'conductor_radical': 210, 'conjugate': '485308944201038707842495962556', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.0, -2.0]], [[1.0, 0], [0, 1.0]], [[1.0, 0], [6.0, 0], [11.0, 0]], [[1.0, 0], [0, 2.0], [-13.0, 0]], [[1.0, 0], [0, -4.0], [-17.0, 0]], [[1.0, 0], [6.0, 0], [19.0, 0]], [[1.0, 0], [0, 0], [-23.0, 0]], [[1.0, 0], [2.0, 0], [29.0, 0]], [[1.0, 0], [-10.0, 0], [31.0, 0]], [[1.0, 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'root_number': '0.89442719099991587856366946749251049417624734384461028971 + 0.4472135954999579392818347337462552470881236719223051449*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.07379180882521663', 'prec': 64}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.66703873303515375556556336169', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.11936001204954947106587096675', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.75377545149421420779722922875', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 40.24460261872533, 'bad_primes': [2, 3, 5, 7], 'central_character': '5.4', 'conductor': 5040, 'conductor_radical': 210, 'degree': 2, 'index': 35, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5040/2/t/e/1009/2'], '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': '2-5040-5.4-c1-0-35', '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': '2-5040-5.4-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.343863382728645, 'root_angle': 0.07379180882521663, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.66703873303515375556556336169', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '845572050307490330150672065167', 'Lhash_array': ['845572050307490330150672065167'], 'label': '2-5040-5.4-c1-0-35', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5040/2/t/e/1009/2'}