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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_1053.119', 'a10': [-0.766044443118978, -0.6427876096865394], 'a2': [0.9983081582712682, -0.05814482891047583], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.993238357741943, -0.11609291412523023], 'a5': [-0.7273736415730487, -0.6862416378687336], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.918216106880274, 0.39607976603915684], 'a8': [0.984807753012208, -0.17364817766693036], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 4.890111441541118, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [13, [1]]], 'bad_primes': [3, 13], 'central_character': '1053.119', 'coeff_info': ['x^108 - 1', '0.998308158271268 + 0.0581448289104758*I', '\\\\zeta_{108}'], 'conductor': 1053, 'conductor_radical': 39, 'conjugate': 'dirichlet_L_1053.761', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^107', 0, 'a^106', 'a^67', 0, 'a^47', 'a^105', 0, 'a^66', 'a^41', 0, 0, 'a^46', 0, 'a^104', 'a^12', 0, 'a^105', 'a^65', 0, 'a^40', 'a^88', 0, 'a^26', 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False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0627465933984', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(108)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.66632881783191280281398580404-0.180486528513029340949725815045*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.918136651472', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.35929687422', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.18162786415', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 4.890111441541118, 'bad_primes': [3, 13], 'central_character': '1053.119', 'conductor': 1053, 'conductor_radical': 39, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1053/119'], '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': '1-1053-1053.119-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-1053-1053.119-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.890111441541118, 'root_angle': -0.06274659339844167, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.918136651472', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_1053.119', 'Lhash_array': ['dirichlet_L_1053.119'], 'factors': ['1-1053-1053.119-r0-0-0'], 'label': '1-1053-1053.119-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1053/119'}