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lfunc_lfunctions • Show schema
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{'Lhash': '2276035195663981837295770299475', 'a10': [1.2738905549642177, 0.0], 'a2': [1.0, 0.0], 'a3': [1.6510934089371754, 0.0], 'a4': [1.0, 0.0], 'a5': [1.2738905549642177, 0.0], 'a6': [1.6510934089371754, 0.0], 'a7': [-2.651093408937175, 0.0], 'a8': [1.0, 0.0], 'a9': [-0.2738905549642176, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 51.279928178066285, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-1.0, 0]]], [13, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [-1.0, 0]]]], 'bad_primes': [2, 13, 19], 'central_character': '6422.1', 'coefficient_field': 'CDF', 'conductor': 6422, 'conductor_radical': 494, 'degree': 2, 'euler_factors': [[[1.0, 0], [-1.0, 0]], [[1.0, 0], [-1.6510934089371754, 0], [3.0, 0]], [[1.0, 0], [-1.2738905549642177, 0], [5.0, 0]], [[1.0, 0], [2.651093408937175, 0], [7.0, 0]], [[1.0, 0], [3.2738905549642174, 0], [11.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [5.30218681787435, 0], [17.0, 0]], 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'5.52099739220083971780658402989696', '6.22898555292719715285877859987949', '6.88852847107395876350750786855046', '7.62560960166538454926323736714265'], 'prelabel': '2-6422-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.161000501191595, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.79547518476637143584703761611', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.58176134129582938742176235720', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.08759137113016327027651779366', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 51.279928178066285, 'bad_primes': [2, 13, 19], 'central_character': '1.1', 'conductor': 6422, 'conductor_radical': 494, 'degree': 2, 'index': 225, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/6422/2/a/u/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': '2-6422-1.1-c1-0-225', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-6422-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 7.161000501191595, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.79547518476637143584703761611', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2276035195663981837295770299475', 'Lhash_array': ['2276035195663981837295770299475'], 'label': '2-6422-1.1-c1-0-225', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/6422/2/a/u/1/3'}