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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_4031.104', 'a10': [-0.9976687691905392, 0.06824241336467098], 'a2': [0.09093486230884695, 0.9958568425315313], 'a3': [-0.5579340481846333, -0.8298852919990252], 'a4': [-0.9834617016337421, 0.18111620970985576], 'a5': [-0.022763197856105682, 0.9997408848413492], 'a6': [0.7757112907044198, -0.6310879443260528], 'a7': [-0.1586825464562513, 0.9873296559154696], 'a8': [-0.2697967711570243, -0.9629172873477992], 'a9': [-0.37741919575261446, 0.9260425209878053], 'algebraic': True, 'analytic_conductor': 18.71988529995465, 'analytic_normalization': 0, 'bad_lfactors': [[29, [1]], [139, [1]]], 'bad_primes': [29, 139], 'central_character': '4031.104', 'coeff_info': ['x^276 - 1', '0.999740884841349 + 0.0227631978561057*I', '\\\\zeta_{276}'], 'conductor': 4031, 'conductor_radical': 4031, 'conjugate': 'dirichlet_L_4031.969', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^65', 'a^181', 'a^130', 'a^70', 'a^246', 'a^76', 'a^195', 'a^86', 'a^135', 'a^179', 'a^35', 'a^158', 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'a^74'], [1, 'a^254'], [1, 'a^11'], [1, 'a^243'], [1, 'a^64'], [1, 'a^67'], [1, 'a^115'], [1, 'a^97']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-4031-4031.104-r0-0-0', 'leading_term': '0.229337400622799400913460292435+0.640929558523754423658291802803*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/4031/104', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.6807248653559502, 0.9985517159516234, 0.32886319739940295, -2.0067108842963766, -4.993103320532076, -6.238869918572242, -4.329783656584082, -0.7655913613053968, 1.093135473937699, -0.4393451109218621, -3.1795826084583734, -3.20668698795779, 0.6357658726404343, 5.139187848686268, 6.247756475802383, 3.6113006582277034, 0.6003053242776885, -0.047857665075568934, 0.8363838227466887, 0.9229062310181442, 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'types': ['DIR'], 'values': [[1, '0.597145667490253787630859348414+0.329121207272919161950540031263*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.686307064412', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '2.26764471529', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.76082073904', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 18.71988529995465, 'bad_primes': [29, 139], 'central_character': '4031.104', 'conductor': 4031, 'conductor_radical': 4031, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4031/104'], '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': '1-4031-4031.104-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': '1-4031-4031.104-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.71988529995465, 'root_angle': 0.3906209769779011, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.686307064412', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_4031.104', 'Lhash_array': ['dirichlet_L_4031.104'], 'label': '1-4031-4031.104-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4031/104'}
Lfunction data - 1-4031-4031.104-r0-0-0