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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_67.23', 'a10': [0.23575893550942723, -0.9718115683235417], 'a2': [-0.8888354486549235, 0.4582265217274104], 'a3': [-0.9594929736144974, -0.28173255684142967], 'a4': [0.5800569095711982, -0.8145759520503357], 'a5': [-0.6548607339452851, 0.7557495743542583], 'a6': [0.9819286972627067, -0.18925124436041021], 'a7': [0.0475819158237423, -0.998867339183008], 'a8': [-0.14231483827328514, 0.9898214418809327], 'a9': [0.8412535328311812, 0.5406408174555976], 'algebraic': True, 'analytic_conductor': 0.311146691911923, 'analytic_normalization': 0, 'bad_lfactors': [[67, [1]]], 'bad_primes': [67], 'central_character': '67.23', 'coeff_info': ['x^33 - 1', '0.981928697262707 + 0.189251244360410*I', '\\\\zeta_{33}'], 'conductor': 67, 'conductor_radical': 67, 'conjugate': 'dirichlet_L_67.35', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^14', 'a^18', 'a^28', 'a^12', 'a^32', 'a^25', 'a^9', 'a^3', 'a^26', 'a^1', 'a^13', 'a^2', 'a^6', 'a^30', 'a^23', 'a^5', 'a^17', 'a^8', 'a^7', 'a^10', 'a^15', 'a^29', 'a^27', 'a^24', 'a^16', 'a^21', 'a^20', 'a^22', 'a^11', 'a^31', 'a^4', 'a^19', 'a^19', 'a^4', 'a^31', 'a^11', 'a^22', 'a^20', 'a^21', 'a^16', 'a^24', 'a^27', 'a^29', 'a^15', 'a^10', 'a^7', 'a^8', 'a^17', 'a^5', 'a^23', 'a^30', 'a^6', 'a^2', 'a^13', 'a^1', 'a^26', 'a^3', 'a^9', 'a^25', 'a^32', 'a^12', 'a^28', 'a^18', 'a^14', 'a^0', 0, 'a^0', 'a^14', 'a^18', 'a^28', 'a^12', 'a^32', 'a^25', 'a^9', 'a^3', 'a^26', 'a^1', 'a^13', 'a^2', 'a^6', 'a^30', 'a^23', 'a^5', 'a^17', 'a^8', 'a^7', 'a^10', 'a^15', 'a^29', 'a^27', 'a^24', 'a^16', 'a^21', 'a^20', 'a^22', 'a^11', 'a^31', 'a^4', 'a^19'], 'euler_factors': [[1, 'a^14'], [1, 'a^18'], [1, 'a^12'], [1, 'a^25'], [1, 'a^1'], [1, 'a^2'], [1, 'a^5'], [1, 'a^8'], [1, 'a^29'], [1, 'a^22'], [1, 'a^31'], [1, 'a^11'], [1, 'a^16'], [1, 'a^27'], [1, 'a^7'], [1, 'a^6'], [1, 'a^9'], [1, 'a^32'], [0], [1, 'a^28'], [1, 'a^32'], [1, 'a^13'], [1, 'a^23'], [1, 'a^15'], [1, 'a^11'], [1, 'a^19']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-67-67.23-r0-0-0', 'leading_term': '0.447609501938891960857017757572+0.120136514536638092374900796710*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/67/23', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.46345123621692386, 0.5388531052351453, 0.6049227484302103, 0.4884690281544413, 0.06809414135224189, -0.698166585743208, -1.7509753458737345, -2.919579698421686, -3.941827680133758, -4.5217508836823495, -4.416382175794067, -3.527485572037457, -1.9640991386129392, -0.04428452745256583, 1.7783922381715453, 3.0501197022319686, 3.4714222957688246, 3.0120117068999455, 1.9331338734283643, 0.6960330752421544, -0.21784782060570576, -0.5060141180386764, -0.17647373555532403, 0.45465378277183593, 0.9101663392862125, 0.7854343658420643, -0.03842574904597812, 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'0.542351021964958358822498931338+0.0935805611984411267437951082249*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.28467241472', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '4.06959345364', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '6.15590436368', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.311146691911923, 'bad_primes': [67], 'central_character': '67.23', 'conductor': 67, 'conductor_radical': 67, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/67/23'], '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': '1-67-67.23-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': '1-67-67.23-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.311146691911923, 'root_angle': 0.08346595800502893, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.28467241472', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_67.23', 'Lhash_array': ['dirichlet_L_67.23'], 'factors': ['1-67-67.23-r0-0-0'], 'label': '1-67-67.23-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/67/23'}
Lfunction data - 1-67-67.23-r0-0-0