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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_4009.18', 'a10': [-0.8090169943749475, -0.5877852522924731], 'a2': [0.8584487936018661, -0.5128992774059061], 'a3': [-0.3930250316539236, 0.9195277725514507], 'a4': [0.4738686624729987, -0.880595531856738], 'a5': [-0.3930250316539236, -0.9195277725514507], 'a6': [0.1342332658176555, 0.9909497617679347], 'a7': [-0.8584487936018661, -0.5128992774059061], 'a8': [-0.044864830350514924, -0.9989930665413147], 'a9': [-0.6910626489868646, -0.7227948638273916], 'algebraic': True, 'analytic_conductor': 18.61771772947611, 'analytic_normalization': 0, 'bad_lfactors': [[19, [1]], [211, [1]]], 'bad_primes': [19, 211], 'central_character': '4009.18', 'coeff_info': ['x^70 - 1', '0.995974293995239 + 0.0896393089034335*I', '\\\\zeta_{70}'], 'conductor': 4009, 'conductor_radical': 4009, 'conjugate': 'dirichlet_L_4009.2450', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^64', 'a^22', 'a^58', 'a^48', 'a^16', 'a^41', 'a^52', 'a^44', 'a^42', 'a^8', 'a^10', 'a^11', 'a^35', 'a^0', 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'gamma_factors': [[0], []], 'index': 0, 'label': '1-4009-4009.18-r0-0-0', 'leading_term': '0.911854274687845615606064369814+0.502639108787437395535506883449*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/4009/18', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.0412128946325665, 1.796112548093395, 1.5866216752114857, -0.039802799896956675, -1.8898655885838886, -1.9806850611545577, 0.21908399582365468, 2.864371399671347, 3.4762510411038363, 1.6104400926391789, -0.6894528634495974, -1.326026040053502, -0.48824750741875356, 0.07903925965736823, -0.24259104774450624, -0.2011158125574649, 1.0020917093717336, 1.9216967903376907, 0.787991544975125, -1.3896558148326197, -1.6904061376022368, 0.16985896636882594, 0.24284153039228915, -4.670621906056987, -11.511113561315367, 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{'__RealLiteral__': 0, 'data': '0.93149079329', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.85103863771', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.01543438229', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 18.61771772947611, 'bad_primes': [19, 211], 'central_character': '4009.18', 'conductor': 4009, 'conductor_radical': 4009, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4009/18'], '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': '1-4009-4009.18-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': '1-4009-4009.18-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 18.61771772947611, 'root_angle': 0.16035977922036343, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.93149079329', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_4009.18', 'Lhash_array': ['dirichlet_L_4009.18'], 'label': '1-4009-4009.18-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4009/18'}