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lfunc_lfunctions • Show schema
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{'Lhash': '1631108164049834607688226262842', 'a10': [-2.619438962528829, -4.426889293235504], 'a2': [-1.1150510065015462, -0.8698627782011877], 'a3': [0.26404642479943397, 1.7518335643634622], 'a4': [0.4866774942002226, 1.9398827327029313], 'a5': [3.3857971355200323, 1.3288274544097018], 'a6': [1.2294295795075467, -2.1830679358167964], 'a7': [-0.35777825971405924, 2.621448972777456], 'a8': [1.144761553503875, -2.5864108307883718], 'a9': [-0.13248190542260754, 0.04086525579492999], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.1301357592341925, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.1150510065015462, 0.8698627782011877]]], [7, [[1.0, 0], [0.35777825971405924, -2.621448972777456]]]], 'bad_primes': [2, 7], 'central_character': '392.109', 'coefficient_field': 'CDF', 'conductor': 392, 'conductor_radical': 14, 'conjugate': '2443389965723214869295009159390', 'degree': 2, 'euler_factors': [[[1.0, 0], 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'sign_arg': {'__RealLiteral__': 0, 'data': '-0.147308201097', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.28671746280573515387971800835', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.98645950248718964027269074997', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.50811223609099962409392311979', 'prec': 103}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 3.1301357592341925, 'bad_primes': [2, 7], 'central_character': '392.109', 'conductor': 392, 'conductor_radical': 14, 'degree': 2, 'index': 15, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/392/2/z/a/109/14'], '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': '2-392-392.109-c1-0-15', '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': '2-392-392.109-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.769218968707433, 'root_angle': -0.14730820109680542, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.28671746280573515387971800835', 'prec': 103}}
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lfunc_instances • Show schema
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{'Lhash': '1631108164049834607688226262842', 'Lhash_array': ['1631108164049834607688226262842'], 'label': '2-392-392.109-c1-0-15', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/392/2/z/a/109/14'}