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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_4021.98', 'a10': [-0.6818078215504377, -0.731531335263669], 'a2': [-0.31050309998335557, 0.9505723669982872], 'a3': [0.934973602016122, -0.3547173008650668], 'a4': [-0.8071756498014526, -0.5903113334229683], 'a5': [-0.483670030710694, 0.8752504221034779], 'a6': [0.046872262469940064, 0.9989008914857115], 'a7': [0.9510565162951535, 0.30901699437494745], 'a8': [0.8117641829722164, -0.5839853690320074], 'a9': [0.7483512729340034, -0.6633026249744959], 'algebraic': True, 'analytic_conductor': 432.11646259918723, 'analytic_normalization': 0, 'bad_lfactors': [[4021, [1]]], 'bad_primes': [4021], 'central_character': '4021.98', 'coeff_info': ['x^4020 - 1', '0.999998778544789 + 0.00156298078332576*I', '\\\\zeta_{4020}'], 'conductor': 4021, 'conductor_radical': 4021, 'conjugate': 'dirichlet_L_4021.2667', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1207', 'a^3788', 'a^2414', 'a^1328', 'a^975', 'a^201', 'a^3621', 'a^3556', 'a^2535', 'a^2959', 'a^2182', 'a^3090', 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'-0.222401270946516974414212798084-0.974955216756838500856199448283*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 17}, 'spectral_label': 'r1-0', 'st_group': 'mu(4020)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.07973359731164158885842213396+0.191332483307421869763271087487*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.204961095845', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.01738977313', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.18449640625', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 432.11646259918723, 'bad_primes': [4021], 'central_character': '4021.98', 'conductor': 4021, 'conductor_radical': 4021, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4021/98'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, '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': '1-4021-4021.98-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-4021-4021.98-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 432.11646259918723, 'root_angle': -0.2856947512517244, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.204961095845', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_4021.98', 'Lhash_array': ['dirichlet_L_4021.98'], 'label': '1-4021-4021.98-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4021/98'}