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  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_4729.73', 'a10': [-0.824953294004347, 0.5652009047333323], 'a2': [-0.9918730395931648, -0.12723157362941068], 'a3': [0.7099202423246631, -0.7042820809432053], 'a4': [0.9676242533435677, 0.25239513533605024], 'a5': [0.746337530720497, -0.665567645125596], 'a6': [-0.7937576660606797, 0.608234138773797], 'a7': [-0.6103416861215312, -0.7921382620365754], 'a8': [-0.9276477791027373, -0.373456286499182], 'a9': [0.00797350092461664, -0.9999682111362367], 'algebraic': True, 'analytic_conductor': 21.961383672410207, 'analytic_normalization': 0, 'bad_lfactors': [[4729, [1]]], 'bad_primes': [4729], 'central_character': '4729.73', 'coeff_info': ['x^2364 - 1', '0.999996467887392 + 0.00265785867577771*I', '\\\\zeta_{2364}'], 'conductor': 4729, 'conductor_radical': 4729, 'conjugate': 'dirichlet_L_4729.2073', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1230', 'a^2070', 'a^96', 'a^2090', 'a^936', 'a^1526', 'a^1326', 'a^1776', 'a^956', 'a^513', 'a^2166', 'a^224', 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-0.04126404061079424, 'root_number': '0.966577488468698388175669283842-0.256374645364051619267602693787*I', 'self_dual': False, 'sign_arg': 0, 'spectral_label': 'r0-0', 'st_group': 'mu(2364)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.979902550959421173720524606186-0.281802870193958038054430201185*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.08353359285', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '1.41097616008', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.110090033', 'prec': 34}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 21.961383672410207, 'bad_primes': [4729], 'central_character': '4729.73', 'conductor': 4729, 'conductor_radical': 4729, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4729/73'], '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': '1-4729-4729.73-r0-0-0', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-4729-4729.73-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.961383672410207, 'root_angle': -0.04126404061079424, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.08353359285', 'prec': 40}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_4729.73', 'Lhash_array': ['dirichlet_L_4729.73'], 'factors': ['1-4729-4729.73-r0-0-0'], 'label': '1-4729-4729.73-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4729/73'}