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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_3920.93', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.36534102436639504, -0.9308737486442042], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.7330518718298263, 0.6801727377709194], 'algebraic': True, 'analytic_conductor': 421.2625051949301, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [7, [1]]], 'bad_primes': [2, 5, 7], 'central_character': '3920.93', 'coeff_info': ['x^84 - 1', '0.997203797181180 + 0.0747300935864243*I', '\\\\zeta_{84}'], 'conductor': 3920, 'conductor_radical': 70, 'conjugate': 'dirichlet_L_3920.3077', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^58', 0, 0, 0, 0, 0, 'a^116', 0, 'a^115', 0, 'a^66', 0, 0, 0, 'a^43', 0, 'a^35', 0, 0, 0, 'a^83', 0, 0, 0, 'a^90', 0, 'a^99', 0, 'a^28', 0, 'a^5', 0, 0, 0, 'a^134', 0, 'a^124', 0, 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'root_analytic_conductor': 421.2625051949301, 'root_angle': -0.8437251979775046, 'root_number': '-0.881884531450219776000080166653-0.471465452805214909086720946014*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 17}, 'spectral_label': 'r1-0', 'st_group': 'mu(84)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.739572079697180934258954746889-0.154463971892910170822404518545*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.0949828759021', 'prec': 50}, 'z2': {'__RealLiteral__': 0, 'data': '1.09449382966', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '1.96616551601', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 421.2625051949301, 'bad_primes': [2, 5, 7], 'central_character': '3920.93', 'conductor': 3920, 'conductor_radical': 70, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3920/93'], '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': '1-3920-3920.93-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': '1-3920-3920.93-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 421.2625051949301, 'root_angle': -0.4218625989887523, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.0949828759021', 'prec': 50}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_3920.93', 'Lhash_array': ['dirichlet_L_3920.93'], 'label': '1-3920-3920.93-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3920/93'}