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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_229.13', 'a10': [0.9157733266550574, 0.4016954246529695], 'a2': [0.1645945902807339, -0.9863613034027223], 'a3': [-0.08257934547233232, -0.9965844930066698], 'a4': [-0.9458172417006346, -0.3246994692046835], 'a5': [-0.24548548714079915, 0.9694002659393304], 'a6': [-0.9965844930066698, -0.08257934547233232], 'a7': [0.8371664782625285, -0.5469481581224269], 'a8': [-0.47594739303707356, 0.8794737512064891], 'a9': [-0.9863613034027223, 0.1645945902807339], 'algebraic': True, 'analytic_conductor': 24.60946777796913, 'analytic_normalization': 0, 'bad_lfactors': [[229, [1]]], 'bad_primes': [229], 'central_character': '229.13', 'coeff_info': ['x^76 - 1', '0.996584493006670 + 0.0825793454723323*I', '\\\\zeta_{76}'], 'conductor': 229, 'conductor_radical': 229, 'conjugate': 'dirichlet_L_229.141', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^59', 'a^56', 'a^42', 'a^22', 'a^39', 'a^69', 'a^25', 'a^36', 'a^5', 'a^10', 'a^22', 'a^3', 'a^52', 'a^2', 'a^8', 'a^60', 'a^19', 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'197.89139533080101788251408555904', '198.37377349509646202581259053640', '199.421273934938722858052137257162'], 'prelabel': '1-229-229.13-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 24.60946777796913, 'root_angle': -0.5436388983419456, 'root_number': '-0.136666588831523366875652901750-0.990617102364559084903285951571*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.271819449171', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(76)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.949362706297747169500265035595-0.718545056145790759152691845651*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.939609608196', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.96076254053', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.22266446032', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 24.60946777796913, 'bad_primes': [229], 'central_character': '229.13', 'conductor': 229, 'conductor_radical': 229, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/229/13'], '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': '1-229-229.13-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': '1-229-229.13-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 24.60946777796913, 'root_angle': -0.2718194491709728, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.939609608196', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_229.13', 'Lhash_array': ['dirichlet_L_229.13'], 'label': '1-229-229.13-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/229/13'}
Lfunction data - 1-229-229.13-r1-0-0