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lfunc_lfunctions • Show schema
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{'Lhash': '2918420669236990902840964972281', 'a10': [0.1512702185075827, -0.08733590137572639], 'a2': [-0.04484600881649469, -0.12321339657598207], 'a3': [1.6294114815891538, 0.5873825190329028], 'a4': [1.518918509648935, -1.2745239612347652], 'a5': [0.23132412027529056, 1.3119042777563157], 'a6': [-0.0006992064096444704, -0.22710708469370733], 'a7': [-0.7726955431230763, -2.530403445626356], 'a8': [-0.452264020189215, -0.2611147538010256], 'a9': [2.309963552669123, 1.9141756411939432], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 1.5091725982022, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [-1.6294114815891538, -0.5873825190329028]]], [7, [[1.0, 0], [0.7726955431230763, 2.530403445626356]]]], 'bad_primes': [3, 7], 'central_character': '189.20', 'coefficient_field': 'CDF', 'conductor': 189, 'conductor_radical': 21, 'conjugate': '2690148337886332805572292265265', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'0.016175895421', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.30222797095000372415086318635', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.17674697030904953857823489889', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.11927155393591232900286323589', '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': '189.20', 'conductor': 189, 'conductor_radical': 21, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/189/2/be/a/20/12'], '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': '2-189-189.20-c1-0-12', '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': '2-189-189.20-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.2284838615961546, 'root_angle': 0.016175895420998017, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.30222797095000372415086318635', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2918420669236990902840964972281', 'Lhash_array': ['2918420669236990902840964972281'], 'factors': ['2-189-189.20-c1-0-12'], 'label': '2-189-189.20-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/189/2/be/a/20/12'}