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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_569.18', 'a10': [-0.9756263315525068, -0.21943851344146056], 'a2': [-0.19780192098551724, -0.9802420109618029], 'a3': [0.8141868867035742, -0.5806028879707207], 'a4': [-0.9217488001088784, 0.3877875055979021], 'a5': [0.4080836122434649, -0.9129445576913887], 'a6': [-0.7301790727058343, -0.6832558245506934], 'a7': [0.7596870845832849, 0.6502888077749369], 'a8': [0.5624492876407806, 0.8268317838789087], 'a9': [0.3258005729601175, -0.9454385155359702], 'algebraic': True, 'analytic_conductor': 2.6424248910131967, 'analytic_normalization': 0, 'bad_lfactors': [[569, [1]]], 'bad_primes': [569], 'central_character': '569.18', 'coeff_info': ['x^71 - 1', '0.996086822074945 + 0.0883801045973425*I', '\\\\zeta_{71}'], 'conductor': 569, 'conductor_radical': 569, 'conjugate': 'dirichlet_L_569.411', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^51', 'a^64', 'a^31', 'a^58', 'a^44', 'a^8', 'a^11', 'a^57', 'a^38', 'a^15', 'a^24', 'a^18', 'a^59', 'a^51', 'a^62', 'a^3', 'a^37', 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'gamma_factors': [[0], []], 'index': 0, 'label': '1-569-569.18-r0-0-0', 'leading_term': '1.21693191526128307081311017049-1.41310205458449593218970720998*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/569/18', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.8648808817327764, 1.7130520376994345, 1.4056740087724664, 0.7286321982929471, 0.01100920146505387, -0.28551166922240323, -0.008859841026703839, 0.4868831019593741, 0.5566544286903319, -0.20826000924674337, -1.5343842400852, -2.5317363205052406, -2.35115344815891, -0.9851523371601811, 0.4938066627192389, 0.6284214491750961, -1.1964017767934267, -3.9854244902550238, -5.619122628546736, -4.414270739870279, -0.5776371839220833, 3.7244597485854376, 5.902696087939409, 4.912412462892279, 1.9975722825469524, -0.4536622048890252, 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'197.61584044395702946706630427097', '198.27362680214553169237156931700', '198.77293847607169557266388617497', '199.48482459383343979762401646786'], 'prelabel': '1-569-569.18-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6424248910131967, 'root_angle': -0.5473967115534251, 'root_number': '-0.148351542072965701808326127974-0.988934689433317981251518619970*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.273698355777', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(71)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.11192877603530833242667891350-0.823263227970750805070588400199*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.25607597061', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.88069684113', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.75294843714', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.6424248910131967, 'bad_primes': [569], 'central_character': '569.18', 'conductor': 569, 'conductor_radical': 569, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/569/18'], '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': '1-569-569.18-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': '1-569-569.18-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.6424248910131967, 'root_angle': -0.27369835577671253, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.25607597061', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_569.18', 'Lhash_array': ['dirichlet_L_569.18'], 'label': '1-569-569.18-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/569/18'}
Lfunction data - 1-569-569.18-r0-0-0