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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_555.173', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.984807753012208, -0.17364817766693036], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.9396926207859084, 0.3420201433256687], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.6427876096865394, -0.766044443118978], 'a8': [-0.8660254037844386, -0.5], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 2.577409164345034, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [5, [1]], [37, [1]]], 'bad_primes': [3, 5, 37], 'central_character': '555.173', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 555, 'conductor_radical': 555, 'conjugate': 'dirichlet_L_555.77', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^19', 0, 'a^2', 0, 0, 'a^23', 'a^21', 0, 0, 'a^30', 0, 'a^11', 'a^6', 0, 'a^4', 'a^7', 0, 'a^8', 0, 0, 'a^13', 'a^33', 0, 0, 'a^30', 0, 'a^25', 'a^30', 0, 'a^18', 'a^23', 0, 'a^26', 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'187.70193447893376707391132673932', '188.69601472495814196386115404977', '188.98811860167734945099805300503', '189.9731476211226231419979300313', '190.311421201052221256938454118121', '190.99566645207680266080145332031', '191.62794076855089926125766665713', '192.11003089185404475218054315334', '192.93003172999315474915844565280', '193.401778283209818378431532758398', '194.19599247829913845514875444773', '194.7193781082781164077497993162', '195.57284800465958664491111141592', '196.36247777863401938640182449432', '197.21334798622796017371499167940', '197.46142119354904452065087110819', '198.05785924477896565227435427892', '198.76959787897656002631992359275', '199.51791620740077662600166268931'], 'prelabel': '1-555-555.173-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.577409164345034, 'root_angle': -0.11105698726482227, 'root_number': '0.766262991701675219779677798066-0.642527063670004808669692486698*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.111056987265', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.691153079519372248371023771144-0.114005470222795550105506333649*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.762395968506', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.94958477688', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.30828338227', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.577409164345034, 'bad_primes': [3, 5, 37], 'central_character': '555.173', 'conductor': 555, 'conductor_radical': 555, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/555/173'], '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': '1-555-555.173-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': '1-555-555.173-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.577409164345034, 'root_angle': -0.11105698726482227, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.762395968506', 'prec': 47}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_555.173', 'Lhash_array': ['dirichlet_L_555.173'], 'factors': ['1-555-555.173-r0-0-0'], 'label': '1-555-555.173-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/555/173'}
Lfunction data - 1-555-555.173-r0-0-0