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lfunc_lfunctions • Show schema
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{'Lhash': '4634404608930712530939971813200', 'a10': [1.2542766367752762, -0.533167268996591], 'a2': [0.8505163071989118, -1.1298769894058054], 'a3': [-0.5, -0.8660254037844386], 'a4': [-0.5532440223774525, -1.921957609236899], 'a5': [0.8345980810297811, 0.48185542674768916], 'a6': [-1.4037603295763643, -0.17163023366428462], 'a7': [-1.2010326143978236, 2.35743942852255], 'a8': [-2.64211874018251, -1.0095585979904225], 'a9': [-0.5, 0.8660254037844386], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.6707433769787555, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [-0.8505163071989118, 1.1298769894058054]]], [3, [[1.0, 0], [0.5, 0.8660254037844386]]], [7, [[1.0, 0], [1.2010326143978236, -2.35743942852255]]]], 'bad_primes': [2, 3, 7], 'central_character': '84.19', 'coefficient_field': 'CDF', 'conductor': 84, 'conductor_radical': 42, 'conjugate': '2591267927914369357589147894753', 'degree': 2, 'euler_factors': 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'9.964443132429470133609176157021816', '11.42636560185512385382373144098263', '12.68222743155963042098115350627609', '13.49893133365043778622683676854804', '14.66000853670635082592881585360891'], 'prelabel': '2-84-28.19-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8189892410641031, 'root_angle': 0.43444894168294124, 'root_number': '0.20448222190187437 + 0.9788702778847015*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.217224470841', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '3.65590061496151109908035932221', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.86017595218788734689164314285', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '6.29472772579348900009523934977', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6707433769787555, 'bad_primes': [2, 3, 7], 'central_character': '28.19', 'conductor': 84, 'conductor_radical': 42, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/84/2/o/a/19/3'], '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': '2-84-28.19-c1-0-6', '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': '2-84-28.19-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.8189892410641031, 'root_angle': 0.21722447084147062, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '3.65590061496151109908035932221', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '4634404608930712530939971813200', 'Lhash_array': ['4634404608930712530939971813200'], 'label': '2-84-28.19-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/84/2/o/a/19/3'}