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lfunc_lfunctions • Show schema
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{'Lhash': '1882275595900771232138454340572', 'a10': [-12.374270034807358, 0.0], 'a2': [-2.0, 0.0], 'a3': [0.0, 0.0], 'a4': [4.0, 0.0], 'a5': [6.187135017403679, 0.0], 'a6': [0.0, 0.0], 'a7': [25.719198683643192, 0.0], 'a8': [-8.0, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 128.50615999250311, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [2.0, 0]]], [3, [[1.0, 0], [0, 0]]], [11, [[1.0, 0], [0, 0]]]], 'bad_primes': [2, 3, 11], 'central_character': '2178.1', 'coefficient_field': 'CDF', 'conductor': 2178, 'conductor_radical': 66, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-6.187135017403679, 0], [125.0, 0]], [[1.0, 0], [-25.719198683643192, 0], [343.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [-30.763031175962194, 0], [2197.0, 0]], [[1.0, 0], [47.98495213987338, 0], [4913.0, 0]], [[1.0, 0], [46.74798331583557, 0], [6859.0, 0]], [[1.0, 0], 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'3.13832287133698409318842007126032', '4.40297850189619770213841651274011', '5.12553417237832862525395729672167', '6.15597952401815853154636196105717', '6.73947516012261210248154851713434', '7.87389890658920936884407934341189', '8.307025828237981956318660278106252'], 'prelabel': '2-2178-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.336055751120101, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.48485363045770181211517285788', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.88988053026649869168680314098', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.13832287133698409318842007126', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 128.50615999250311, 'bad_primes': [2, 3, 11], 'central_character': '1.1', 'conductor': 2178, 'conductor_radical': 66, 'degree': 2, 'index': 119, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2178/4/a/bu/1/3'], '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': '2-2178-1.1-c3-0-119', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-2178-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 11.336055751120101, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.48485363045770181211517285788', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1882275595900771232138454340572', 'Lhash_array': ['1882275595900771232138454340572'], 'label': '2-2178-1.1-c3-0-119', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2178/4/a/bu/1/3'}