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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_547.129', 'a10': [0.12053668025532305, 0.992708874098054], 'a2': [0.9485364419471455, 0.3166679938014725], 'a3': [1.0, 0.0], 'a4': [0.7994427634035012, 0.6007422642379789], 'a5': [0.4286925614030542, 0.9034504346103823], 'a6': [0.9485364419471455, 0.3166679938014725], 'a7': [-0.20002569377604443, 0.9797906520422677], 'a8': [0.5680647467311558, 0.8229838658936564], 'a9': [1.0, 0.0], 'algebraic': True, 'analytic_conductor': 2.540257320534655, 'analytic_normalization': 0, 'bad_lfactors': [[547, [1]]], 'bad_primes': [547], 'central_character': '547.129', 'coeff_info': ['x^39 - 1', '0.987050262637913 + 0.160411280857760*I', '\\\\zeta_{39}'], 'conductor': 547, 'conductor_radical': 547, 'conjugate': 'dirichlet_L_547.441', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^2', 'a^0', 'a^4', 'a^7', 'a^2', 'a^11', 'a^6', 'a^0', 'a^9', 'a^23', 'a^4', 'a^26', 'a^13', 'a^7', 'a^8', 'a^29', 'a^2', 'a^31', 'a^11', 'a^11', 'a^25', 'a^1', 'a^6', 'a^14', 'a^28', 'a^0', 'a^15', 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False, 'root_analytic_conductor': 2.540257320534655, 'root_angle': 0.4038774478615957, 'root_number': '0.297409190898259811548559795293+0.954750110326907714711779938024*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.201938723931', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(39)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '2.29717939854434225042769777847+1.00319797808151622271074478711*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.10456713101', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.95908737828', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.20590236114', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 2.540257320534655, 'bad_primes': [547], 'central_character': '547.129', 'conductor': 547, 'conductor_radical': 547, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/547/129'], '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': '1-547-547.129-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': '1-547-547.129-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.540257320534655, 'root_angle': 0.20193872393079784, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.10456713101', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_547.129', 'Lhash_array': ['dirichlet_L_547.129'], 'label': '1-547-547.129-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/547/129'}
Lfunction data - 1-547-547.129-r0-0-0