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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_113.52', 'a10': [0.9937122098932426, 0.11196447610330786], 'a2': [0.9009688679024191, -0.4338837391175581], 'a3': [-0.8467241992282841, 0.5320320765153366], 'a4': [0.6234898018587335, -0.7818314824680298], 'a5': [0.8467241992282841, 0.5320320765153366], 'a6': [-0.5320320765153366, 0.8467241992282841], 'a7': [-0.2225209339563144, 0.9749279121818236], 'a8': [0.2225209339563144, -0.9749279121818236], 'a9': [0.4338837391175581, -0.9009688679024191], 'algebraic': True, 'analytic_conductor': 0.5247697938216015, 'analytic_normalization': 0, 'bad_lfactors': [[113, [1]]], 'bad_primes': [113], 'central_character': '113.52', 'coeff_info': ['x^56 - 1', '0.993712209893243 + 0.111964476103308*I', '\\\\zeta_{56}'], 'conductor': 113, 'conductor_radical': 113, 'conjugate': 'dirichlet_L_113.50', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^52', 'a^23', 'a^48', 'a^5', 'a^19', 'a^16', 'a^44', 'a^46', 'a^1', 'a^22', 'a^15', 'a^2', 'a^12', 'a^28', 'a^40', 'a^3', 'a^42', 'a^37', 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'gamma_factors': [[0], []], 'index': 0, 'label': '1-113-113.52-r0-0-0', 'leading_term': '1.47903500609473592897330535889+0.117522361580865891784839302806*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/113/52', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.4836967529536484, 1.747091180497644, 2.156917679805372, 2.3367499902922324, 2.0830168668270783, 1.3790104998211072, 0.384369209199651, -0.6073612953339016, -1.2637178190952933, -1.3429951903266397, -0.8094562238264081, 0.12444216865030433, 1.065571367510519, 1.6054904016089553, 1.5166481863234886, 0.8809541695169196, 0.06880560659935728, -0.44620296820563116, -0.36095981400796556, 0.23731021195202406, 0.8441714890767221, 0.7573783764637823, -0.538903810538573, -3.0190379372292058, -6.0020203412458635, -8.385730352975125, 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'198.401525528532793600357400395748', '199.26468651630384539248869008835', '199.986493113540587649945037278934'], 'prelabel': '1-113-113.52-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5247697938216015, 'root_angle': 0.02523949569363915, 'root_number': '0.987451820488650658141682673140+0.157920556653178107738469927118*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0252394956936', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(56)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.44413517713038913449703750955+0.0200970325711120568682711980517*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.99031384179', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.39897012524', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.02977581577', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.5247697938216015, 'bad_primes': [113], 'central_character': '113.52', 'conductor': 113, 'conductor_radical': 113, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/113/52'], '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': '1-113-113.52-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': '1-113-113.52-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.5247697938216015, 'root_angle': 0.02523949569363915, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.99031384179', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_113.52', 'Lhash_array': ['dirichlet_L_113.52'], 'factors': ['1-113-113.52-r0-0-0'], 'label': '1-113-113.52-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/113/52'}
Lfunction data - 1-113-113.52-r0-0-0