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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_5245.52', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [0.07188282077798921, -0.9974130839712297], 'a3': [0.9913139401830674, 0.13151681260858564], 'a4': [-0.989665720153999, -0.1433937319134508], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.20243503195489745, -0.9792956947916291], 'a7': [-0.6031973613821136, 0.7975919653692958], 'a8': [-0.21416274796188828, 0.9767979921075866], 'a9': [0.9654066560025564, 0.2607488994146703], 'algebraic': True, 'analytic_conductor': 563.6535305478083, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [1049, [1]]], 'bad_primes': [5, 1049], 'central_character': '5245.52', 'coeff_info': ['x^524 - 1', '0.999928111079281 + 0.0119905243180430*I', '\\\\zeta_{524}'], 'conductor': 5245, 'conductor_radical': 5245, 'conjugate': 'dirichlet_L_5245.1513', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^399', 'a^11', 'a^274', 0, 'a^410', 'a^185', 'a^149', 'a^22', 0, 'a^144', 'a^285', 'a^361', 'a^60', 0, 'a^24', 'a^205', 'a^421', 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'gamma_factors': [[1], []], 'index': 0, 'label': '1-5245-5245.52-r1-0-0', 'leading_term': '0.0307013649698868977697677254579+0.209161989954951814953964145576*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/5245/52', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.21140319735739505, 2.3710577140942672, 3.1307848266489393, 1.8459949982199648, -0.3450404011429353, -1.5340373994157397, -1.0217384105395786, -0.016645219406438445, 0.03222751259521894, -0.5920498786342445, -0.40670388988122863, 0.8130226358462971, 1.3455598388556285, 0.09938949085505326, -1.1922484404662164, -0.0961174076928703, 2.4205178048707783, 2.3242183317058593, -1.8419958604089113, -5.629512941114417, -3.587508987121172, 3.192670776505467, 7.574758557444596, 5.215344580738078, -0.06224060593898591, 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'-0.957818476480796720422105359597+0.287373913415963105452113783293*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.25', 'prec': 17}, 'spectral_label': 'r1-0', 'st_group': 'mu(524)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.06882795305794736917014680699-0.244543107677082521648146893778*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.19753008543', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.19554641444', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.51901944809', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 563.6535305478083, 'bad_primes': [5, 1049], 'central_character': '5245.52', 'conductor': 5245, 'conductor_radical': 5245, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/5245/52'], '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': '1-5245-5245.52-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': '1-5245-5245.52-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 563.6535305478083, 'root_angle': 0.45360888558732415, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.19753008543', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_5245.52', 'Lhash_array': ['dirichlet_L_5245.52'], 'factors': ['1-5245-5245.52-r1-0-0'], 'label': '1-5245-5245.52-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/5245/52'}
Lfunction data - 1-5245-5245.52-r1-0-0