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lfunc_lfunctions • Show schema
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{'Lhash': 'dirichlet_L_149.144', 'a10': [-0.2106792699957263, 0.9775552389476861], 'a2': [0.2928227712765504, 0.956166734739251], 'a3': [-0.6606747233900815, -0.7506723052527243], 'a4': [-0.8285096492438421, 0.5599747861375954], 'a5': [0.8730141131611882, 0.48769494381363454], 'a6': [0.5243072835572317, -0.8515291377333113], 'a7': [0.2106792699957263, -0.9775552389476861], 'a8': [-0.7780357543184395, -0.6282199972956423], 'a9': [-0.12701781974687876, 0.9919004352588768], 'algebraic': True, 'analytic_conductor': 0.6919530909683064, 'analytic_normalization': 0, 'bad_lfactors': [[149, [1]]], 'bad_primes': [149], 'central_character': '149.144', 'coeff_info': ['x^74 - 1', '0.996397488542527 + 0.0848059244755092*I', '\\\\zeta_{74}'], 'conductor': 149, 'conductor_radical': 149, 'conjugate': 'dirichlet_L_149.119', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^15', 'a^47', 'a^30', 'a^6', 'a^62', 'a^58', 'a^45', 'a^20', 'a^21', 'a^7', 'a^3', 'a^55', 'a^73', 'a^53', 'a^60', 'a^10', 'a^35', 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'gamma_factors': [[0], []], 'index': 0, 'label': '1-149-149.144-r0-0-0', 'leading_term': '1.05064927296410641675668052476+0.447138535072001835940053078230*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/149/144', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.1418392024827053, 1.3303721607261356, 1.5240741678404746, 1.3423842929342187, 0.5784324898053408, -0.7355635202888855, -2.31681862857869, -3.6937070261945033, -4.359554506486205, -3.9807081938007474, -2.5730891307935613, -0.5512686570855622, 1.4024229155675996, 2.6156681145295173, 2.7305416697546616, 1.8777292544826492, 0.6118579069384185, -0.3795593827252271, -0.6471232530652907, -0.21904148626402858, 0.4448379599696841, 0.7747886626872259, 0.49927603625200406, -0.12903901585414806, -0.466456651323601, 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'types': ['DIR'], 'values': [[1, '1.04182407731755746736026902239+0.336471112456200607083490620361*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.40107994262', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.51978204511', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.17009168103', 'prec': 44}}
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lfunc_search • Show schema
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{'algebraic': True, 'analytic_conductor': 0.6919530909683064, 'bad_primes': [149], 'central_character': '149.144', 'conductor': 149, 'conductor_radical': 149, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/149/144'], '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': '1-149-149.144-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': '1-149-149.144-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6919530909683064, 'root_angle': 0.128076567274425, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.40107994262', 'prec': 44}}
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lfunc_instances • Show schema
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{'Lhash': 'dirichlet_L_149.144', 'Lhash_array': ['dirichlet_L_149.144'], 'label': '1-149-149.144-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/149/144'}