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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_113.32', 'a10': [0.7818314824680298, -0.6234898018587335], 'a2': [-0.9009688679024191, 0.4338837391175581], 'a3': [-0.9749279121818236, -0.2225209339563144], 'a4': [0.6234898018587335, -0.7818314824680298], 'a5': [-0.9749279121818236, 0.2225209339563144], 'a6': [0.9749279121818236, -0.2225209339563144], 'a7': [-0.2225209339563144, 0.9749279121818236], 'a8': [-0.2225209339563144, 0.9749279121818236], 'a9': [0.9009688679024191, 0.4338837391175581], 'algebraic': True, 'analytic_conductor': 0.5247697938216015, 'analytic_normalization': 0, 'bad_lfactors': [[113, [1]]], 'bad_primes': [113], 'central_character': '113.32', 'coeff_info': ['x^28 - 1', '0.974927912181824 + 0.222520933956314*I', '\\\\zeta_{28}'], 'conductor': 113, 'conductor_radical': 113, 'conjugate': 'dirichlet_L_113.53', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^12', 'a^15', 'a^24', 'a^13', 'a^27', 'a^8', 'a^8', 'a^2', 'a^25', 'a^18', 'a^11', 'a^22', 'a^20', 'a^0', 'a^20', 'a^19', 'a^14', 'a^1', 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'index': 0, 'label': '1-113-113.32-r0-0-0', 'leading_term': '0.302243606578501495338174624874-0.132906573704259144660470193129*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/113/32', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.33017473412026205, 0.20291765236038042, -0.0843017261767918, -0.6450574771095228, -1.4261609636430121, -2.221544838954854, -2.721148216647575, -2.6060801658849346, -1.6779164367643444, 0.022064619775560186, 2.1623118517540525, 4.183507744312781, 5.4754619273974585, 5.612901893474719, 4.551541941525962, 2.683855527993073, 0.7048068956083562, -0.6741461388746097, -1.0399605414705702, -0.46618340112716294, 0.533909486108391, 1.2827371963677348, 1.308804807557142, 0.6115102779328988, -0.33827504743889325, -0.8794479445873467, -0.5736043849660253, 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lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.5247697938216015, 'bad_primes': [113], 'central_character': '113.32', 'conductor': 113, 'conductor_radical': 113, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/113/32'], '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': '1-113-113.32-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': '1-113-113.32-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5247697938216015, 'root_angle': -0.1318705011268451, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.557077030206', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_113.32', 'Lhash_array': ['dirichlet_L_113.32'], 'factors': ['1-113-113.32-r0-0-0'], 'label': '1-113-113.32-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/113/32'}
Lfunction data - 1-113-113.32-r0-0-0