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  • lfunc_lfunctions • Show schema
    {'Lhash': '3143898142407313018611723038118', 'a10': [2.137054624375387, 2.3308791329530094], 'a2': [0.541196100146197, 1.3065629648763766], 'a3': [1.3065629648763766, -1.137054624375387], 'a4': [-1.4142135623730951, 1.4142135623730951], 'a5': [2.1010029896154587, -0.7653668647301796], 'a6': [2.1927402424368476, 1.0917372528213891], 'a7': [-2.274109248750774, 0.0], 'a8': [-2.613125929752753, -1.082392200292394], 'a9': [0.41421356237309503, -2.9712669225006008], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 0.9582048242553651, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 4}, 'bad_lfactors': [[2, [[1.0, 0], [-0.541196100146197, -1.3065629648763766]]], [3, [[1.0, 0], [-1.3065629648763766, 1.137054624375387]]], [5, [[1.0, 0], [-2.1010029896154587, 0.7653668647301796]]]], 'bad_primes': [2, 3, 5], 'central_character': '120.59', 'coefficient_field': 'CDF', 'conductor': 120, 'conductor_radical': 30, 'conjugate': '3238647454599265101213148933821', 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2.82213749401176, 2.3084356116337266, 1.5862097546844511, 0.8293632458644514, 0.20495673188854, -0.17181923238047964, -0.2686155650054116], 'positive_zeros': ['2.48009833454209043096434564647107', '3.50207224093443734710015805363470', '5.12056728808378425870375499290665', '6.39932684106204987704310751492259', '8.495596996186060220843132942189836', '9.480476106158081012508620652034863', '10.20744571437767667737739833959498', '11.01157329627151345804455378007964', '12.58790517604808832053006694507390', '13.42517704310427999401719126873682'], 'prelabel': '2-120-120.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9788793716568784, 'root_angle': -0.10707741865851042, 'root_number': '0.7820877717656567 - 0.623168289673528*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.107077418659', 'prec': 40}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '2.48009833454209043096434564647', 'prec': 100}, 'z2': {'__RealLiteral__': 0, 'data': '3.50207224093443734710015805363', 'prec': 100}, 'z3': {'__RealLiteral__': 0, 'data': '5.12056728808378425870375499291', 'prec': 100}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 0.9582048242553651, 'bad_primes': [2, 3, 5], 'central_character': '120.59', 'conductor': 120, 'conductor_radical': 30, 'degree': 2, 'index': 12, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/120/2/m/b/59/11'], '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': '2-120-120.59-c1-0-12', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [0], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-120-120.59-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.9788793716568784, 'root_angle': -0.10707741865851042, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.48009833454209043096434564647', 'prec': 100}}
  • lfunc_instances • Show schema
    {'Lhash': '3143898142407313018611723038118', 'Lhash_array': ['3143898142407313018611723038118'], 'factors': ['2-120-120.59-c1-0-12'], 'label': '2-120-120.59-c1-0-12', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/120/2/m/b/59/11'}