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  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_4729.486', 'a10': [0.9590835257019713, -0.2831232783207275], 'a2': [-0.9334851442746663, -0.35861606966016646], 'a3': [-0.4814741573567515, 0.8764602876329344], 'a4': [0.7427890291629893, 0.6695255470518686], 'a5': [-0.7937576660606797, 0.608234138773797], 'a6': [0.7637617168088325, -0.6454982880978266], 'a7': [-0.5091786732784713, 0.8606608383552581], 'a8': [-0.4532799038330384, -0.8913682341104104], 'a9': [-0.5363652715952123, -0.8439859568894462], 'algebraic': True, 'analytic_conductor': 21.961383672410207, 'analytic_normalization': 0, 'bad_lfactors': [[4729, [1]]], 'bad_primes': [4729], 'central_character': '4729.486', 'coeff_info': ['x^394 - 1', '0.999872846566010 + 0.0159464949121641*I', '\\\\zeta_{394}'], 'conductor': 4729, 'conductor_radical': 4729, 'conjugate': 'dirichlet_L_4729.3610', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^220', 'a^130', 'a^46', 'a^156', 'a^350', 'a^132', 'a^266', 'a^260', 'a^376', 'a^135', 'a^176', 'a^370', 'a^352', 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'-0.999962748116961299222648077699+0.00863147602525846245898113671932*I', 'self_dual': False, 'sign_arg': 0, 'spectral_label': 'r0-0', 'st_group': 'mu(394)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.422897231865972286860988874180+0.185731062915843604968790906350*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.819665628278', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.35086572914', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '2.74731034672', 'prec': 40}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 21.961383672410207, 'bad_primes': [4729], 'central_character': '4729.486', 'conductor': 4729, 'conductor_radical': 4729, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4729/486'], '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': '1-4729-4729.486-r0-0-0', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-4729-4729.486-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.961383672410207, 'root_angle': 0.498626240865987, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.819665628278', 'prec': 40}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_4729.486', 'Lhash_array': ['dirichlet_L_4729.486'], 'factors': ['1-4729-4729.486-r0-0-0'], 'label': '1-4729-4729.486-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4729/486'}