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lfunc_lfunctions • Show schema
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{'Lhash': '2180802819240863011026395141620', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [-1.7055643787113128, -0.30174517406429835], 'a4': [0.0, 0.0], 'a5': [2.04578783618262, -0.9026362109550191], 'a6': [0.0, 0.0], 'a7': [1.3023152501905195, -2.303036037304064], 'a8': [0.0, 0.0], 'a9': [2.8178996998578127, 1.0292916406642239], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 6.7074337697875555, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [1.7055643787113128, 0.30174517406429835]]], [5, [[1.0, 0], [-2.04578783618262, 0.9026362109550191]]], [7, [[1.0, 0], [-1.3023152501905195, 2.303036037304064]]]], 'bad_primes': [2, 3, 5, 7], 'central_character': '840.209', 'coefficient_field': 'CDF', 'conductor': 840, 'conductor_radical': 210, 'conjugate': '840574146625001611065498338274', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [1.7055643787113128, 0.30174517406429835]], [[1.0, 0], 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0.10093504146160162, -0.20495228216698652, 0.4248224884687307, 1.27630840102333, 1.3446143519940812], 'positive_zeros': ['1.72035008609488177618671773006133', '2.70124724245694961788580114146145', '4.70693864172483391383890236294621', '4.97440983334945251558615346507173', '6.06296781000340126921295335071643', '6.89529110174459552608214348157201', '7.62592593329275285964838369762215', '9.105191749380001654419507007978122', '9.865783300738871199954698665566977', '10.17532920249796167077916127263014'], 'prelabel': '2-840-105.104-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5898713809352687, 'root_angle': 0.5872896969645629, 'root_number': '-0.2708045095147426 + 0.9626343634145208*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.293644848482', 'prec': 47}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.72035008609488177618671773006', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '2.70124724245694961788580114146', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.70693864172483391383890236295', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 6.7074337697875555, 'bad_primes': [2, 3, 5, 7], 'central_character': '105.104', 'conductor': 840, 'conductor_radical': 210, 'degree': 2, 'index': 38, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/840/2/k/a/209/1'], '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': '2-840-105.104-c1-0-38', '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': '2-840-105.104-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.5898713809352687, 'root_angle': 0.29364484848228145, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.72035008609488177618671773006', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '2180802819240863011026395141620', 'Lhash_array': ['2180802819240863011026395141620'], 'label': '2-840-105.104-c1-0-38', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/840/2/k/a/209/1'}