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lfunc_lfunctions • Show schema
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{'Lhash': '3028385290414022608345213026422', 'a10': [-1.6645576070099766, -0.9610327824888494], 'a2': [0.15744470824065074, -0.432575780703809], 'a3': [0.8880013665548426, 1.4870956838740175], 'a4': [1.36975591633943, 1.1493616842033128], 'a5': [0.7250401291000776, -4.111906902658547], 'a6': [0.7830926925075942, -0.14999253833003462], 'a7': [-1.0996940726843891, -2.4063817125516103], 'a8': [1.510174840330518, -0.8718998505882247], 'a9': [-1.422907145993464, 2.6410859989558717], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5091725982022, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-0.8880013665548426, -1.4870956838740175]]], [7, [[1.0, 0], [1.0996940726843891, 2.4063817125516103]]]], 'bad_primes': [3, 7], 'central_character': '189.104', 'coefficient_field': 'CDF', 'conductor': 189, 'conductor_radical': 21, 'conjugate': '2471744399054602125351608007855', 'degree': 2, 'euler_factors': [[[1.0, 0], 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50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.38897476155400260002639036517', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.95410343953467303503480125713', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.75267192967562608122340344430', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 1.5091725982022, 'bad_primes': [3, 7], 'central_character': '189.104', 'conductor': 189, 'conductor_radical': 21, 'degree': 2, 'index': 16, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/189/2/be/a/104/14'], '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': '2-189-189.104-c1-0-16', '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': '2-189-189.104-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2284838615961546, 'root_angle': 0.026604481784181663, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.38897476155400260002639036517', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '3028385290414022608345213026422', 'Lhash_array': ['3028385290414022608345213026422'], 'factors': ['2-189-189.104-c1-0-16'], 'label': '2-189-189.104-c1-0-16', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/189/2/be/a/104/14'}