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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_3920.2267', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.2225209339563144, -0.9749279121818236], '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': [-0.9009688679024191, -0.4338837391175581], 'algebraic': True, 'analytic_conductor': 421.2625051949301, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [7, [1]]], 'bad_primes': [2, 5, 7], 'central_character': '3920.2267', 'coeff_info': ['x^28 - 1', '0.974927912181824 + 0.222520933956314*I', '\\\\zeta_{28}'], 'conductor': 3920, 'conductor_radical': 70, 'conjugate': 'dirichlet_L_3920.83', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^22', 0, 0, 0, 0, 0, 'a^16', 0, 'a^33', 0, 'a^40', 0, 0, 0, 'a^25', 0, 'a^7', 0, 0, 0, 'a^17', 0, 0, 0, 'a^38', 0, 'a^39', 0, 'a^0', 0, 'a^27', 0, 0, 0, 'a^18', 0, 'a^6', 0, 'a^36', 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'198.10396156174235861613389425689', '198.3358089204184472443647293135', '199.01645640034696182430785844218', '199.923503911433654761216249153855'], 'prelabel': '1-3920-3920.2267-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 421.2625051949301, 'root_angle': -0.673281604743584, 'root_number': '-0.517887997152641326848554013036-0.855448433516144659106678962085*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 17}, 'spectral_label': 'r1-0', 'st_group': 'mu(28)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.954903216480894775665401287783-0.254509112416710824981825181818*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.231813570987', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.35456312403', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '1.96009211238', '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': '3920.2267', 'conductor': 3920, 'conductor_radical': 70, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/3920/2267'], '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': '1-3920-3920.2267-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': '1-3920-3920.2267-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 421.2625051949301, 'root_angle': -0.336640802371792, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.231813570987', 'prec': 47}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_3920.2267', 'Lhash_array': ['dirichlet_L_3920.2267'], 'label': '1-3920-3920.2267-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/3920/2267'}