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lfunc_lfunctions • Show schema
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{'Lhash': '1860255102000114937578922909013', 'a10': [1.1887912389152873, -0.6863489417980099], 'a2': [0.0, 0.5462082665232075], 'a3': [-1.7280335610299014, -0.11789831192310721], 'a4': [1.7016565295817128, 0.0], 'a5': [-1.256570037225623, -2.1764431477434942], 'a6': [0.0643970325815328, -0.9438662158640677], 'a7': [-0.6127048635947892, 2.573828422822176], 'a8': [0.0, 2.0218753962871396], 'a9': [2.9721999760913635, 0.40746447958380205], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [1.7280335610299014, 0.11789831192310721]]], [7, [[1.0, 0], [0.6127048635947892, -2.573828422822176]]], [13, [[1.0, 0], [-1.897155475711012, 3.066072585732393]]]], 'bad_primes': [3, 7, 13], 'central_character': '273.269', 'coefficient_field': 'CDF', 'conductor': 273, 'conductor_radical': 273, 'conjugate': '1607435766486119321444233809109', 'degree': 2, 'euler_factors': 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'6.34322733865003574507879834908604', '6.83385493809338824141358350769774', '7.45420939744281520268750655292727', '9.511166988885278413642598106583473', '10.30159754679929098747312606828535', '11.16832353566685011979798372904946', '11.63624679304217676424204153357532'], 'prelabel': '2-273-273.269-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': -0.015856759105267158, 'root_number': '0.9987594656525177 - 0.04979487694027695*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.00792837955263', 'prec': 57}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.46748252370581631838195231170', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.50705792284743348659747024857', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.34705405631353394375081884466', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 2.1799159751809554, 'bad_primes': [3, 7, 13], 'central_character': '273.269', 'conductor': 273, 'conductor_radical': 273, 'degree': 2, 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/273/2/r/b/269/18'], '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': '2-273-273.269-c1-0-8', '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': '2-273-273.269-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.4764538513549808, 'root_angle': -0.007928379552633579, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.46748252370581631838195231170', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1860255102000114937578922909013', 'Lhash_array': ['1860255102000114937578922909013'], 'label': '2-273-273.269-c1-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/273/2/r/b/269/18'}