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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1976.1051', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.9396926207859084, 0.3420201433256687], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.3420201433256687, 0.9396926207859084], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.8660254037844386, -0.5], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.766044443118978, -0.6427876096865394], 'algebraic': True, 'analytic_conductor': 9.17650542116358, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [13, [1]], [19, [1]]], 'bad_primes': [2, 13, 19], 'central_character': '1976.1051', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 1976, 'conductor_radical': 494, 'conjugate': 'dirichlet_L_1976.643', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^16', 0, 'a^43', 0, 'a^21', 0, 'a^32', 0, 'a^15', 0, 0, 0, 'a^23', 0, 'a^34', 0, 0, 0, 'a^37', 0, 'a^32', 0, 'a^14', 0, 'a^12', 0, 'a^38', 0, 'a^51', 0, 'a^31', 0, 'a^28', 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'196.62353822347250401300186421295', '196.980580135701576501869955901582', '197.68619327328043341848345441353', '198.281506651099724625652157035080', '198.760069039751115500833699939714', '199.20969650318422388972093909123', '199.90399457741807636014881663173'], 'prelabel': '1-1976-1976.1051-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.17650542116358, 'root_angle': 0.031511685009576046, 'root_number': '0.980463184285599729177391255549+0.196702679850941797688290227053*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0315116850096', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.729116537729173008899832218740+0.124963705633736725549197349382*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.5341898346', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '1.90642186014', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.09347224392', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 9.17650542116358, 'bad_primes': [2, 13, 19], 'central_character': '1976.1051', 'conductor': 1976, 'conductor_radical': 494, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1976/1051'], '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': '1-1976-1976.1051-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': '1-1976-1976.1051-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.17650542116358, 'root_angle': 0.031511685009576046, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.5341898346', 'prec': 40}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1976.1051', 'Lhash_array': ['dirichlet_L_1976.1051'], 'factors': ['1-1976-1976.1051-r0-0-0'], 'label': '1-1976-1976.1051-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1976/1051'}
Lfunction data - 1-1976-1976.1051-r0-0-0