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lfunc_lfunctions • Show schema
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{'Lhash': '1776065610965773690776643513421', 'a10': [0, 0], 'a2': [-0.9659258262890683, -0.25881904510252074], 'a3': [0.25881904510252074, 0.9659258262890683], 'a4': [0.8660254037844386, 0.5], 'a5': [0, 0], 'a6': [0, -1.0], 'a7': [-2.633061469448106, 0.25881904510252074], 'a8': [-0.7071067811865476, -0.7071067811865476], 'a9': [-0.8660254037844386, 0.5], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 8.384292212234444, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0.9659258262890683, 0.25881904510252074]]], [3, [[1.0, 0], [-0.25881904510252074, -0.9659258262890683]]], [5, [[1.0, 0], [0, 0]]], [7, [[1.0, 0], [2.633061469448106, -0.25881904510252074]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '1050.493', 'coefficient_field': 'CDF', 'conductor': 1050, 'conductor_radical': 210, 'conjugate': '368540837192049471168806259248', 'degree': 2, 'euler_factors': [[[1.0, 0], [0.9659258262890683, 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'3.75442477652222610550032249719634', '5.14794624542592895915996158790046', '6.30561911435558494845958858692203', '6.87627978036826328989910858206587', '7.53732090363414458536431408132280', '8.629708988974667321702235891564937', '9.226115827716238522499713111872359', '9.990784976984925511900450173601103'], 'prelabel': '2-1050-35.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8955642303762565, 'root_angle': 0.5726268227839914, 'root_number': '-0.226189384481261607014336804947666875086655937373934351 + 0.974083344662040718798720938866176273342486029309073608*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.2863134113919957', 'prec': 60}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.40106872559836962494048353733', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.64449560318579642161326065986', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.75442477652222610550032249720', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 8.384292212234444, 'bad_primes': [2, 3, 5, 7], 'central_character': '35.3', 'conductor': 1050, 'conductor_radical': 210, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1050/2/bc/f/493/1'], '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': '2-1050-35.3-c1-0-15', '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': '2-1050-35.3-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.8955642303762565, 'root_angle': 0.2863134113919957, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.40106872559836962494048353733', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1776065610965773690776643513421', 'Lhash_array': ['1776065610965773690776643513421'], 'label': '2-1050-35.3-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1050/2/bc/f/493/1'}