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  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_287.17', 'a10': [0.10452846326765347, -0.9945218953682733], 'a2': [0.20791169081775934, -0.9781476007338057], 'a3': [-0.9659258262890683, -0.25881904510252074], 'a4': [-0.9135454576426009, -0.4067366430758002], 'a5': [0.9945218953682733, -0.10452846326765347], 'a6': [-0.4539904997395468, 0.8910065241883679], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [-0.5877852522924731, 0.8090169943749475], 'a9': [0.8660254037844386, 0.5], 'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'analytic_normalization': 0, 'bad_lfactors': [[7, [1]], [41, [1]]], 'bad_primes': [7, 41], 'central_character': '287.17', 'coeff_info': ['x^120 - 1', '0.998629534754574 + 0.0523359562429438*I', '\\\\zeta_{120}'], 'conductor': 287, 'conductor_radical': 287, 'conjugate': 'dirichlet_L_287.152', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^94', 'a^65', 'a^68', 'a^118', 'a^39', 0, 'a^42', 'a^10', 'a^92', 'a^17', 'a^13', 'a^9', 0, 'a^63', 'a^16', 'a^47', 'a^104', 'a^31', 'a^66', 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'3.84932411268', 'prec': 44}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 1.3328223966973418, 'bad_primes': [7, 41], 'central_character': '287.17', 'conductor': 287, 'conductor_radical': 287, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/287/17'], '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': '1-287-287.17-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': '1-287-287.17-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.3328223966973418, 'root_angle': -0.15118778487824236, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.33776751988', 'prec': 44}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_287.17', 'Lhash_array': ['dirichlet_L_287.17'], 'factors': ['1-287-287.17-r0-0-0'], 'label': '1-287-287.17-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/287/17'}