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  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_68.67', 'a10': [1.0, 0.0], 'a2': [1.0, 0.0], 'a3': [1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [-1.0, 0.0], 'a6': [1.0, 0.0], 'a7': [1.0, 0.0], 'a8': [1.0, 0.0], 'a9': [1.0, 0.0], 'algebraic': True, 'analytic_conductor': 7.307614886034502, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [17, [1]]], 'bad_primes': [2, 17], 'central_character': '68.67', 'coeff_info': ['x^2 - 1', -1, '\\\\zeta_{2}'], 'conductor': 68, 'conductor_radical': 34, 'conjugate': 'dirichlet_L_68.67', 'degree': 1, 'dirichlet_coefficients': [1, 0, 1, 0, -1, 0, 1, 0, 1, 0, 1, 0, 1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, -1, 0, -1, 0, -1, 0, -1, 0, 1, 0, 0, 0, 1, 0, -1, 0, -1, 0, -1, 0, -1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, 1, 0, 1, 0, -1, 0, 0, 0, -1, 0, 1, 0, 1, 0, 1, 0, 1, 0, -1, 0, 1, 0], 'euler_factors': [[0], [1, 1], [1, -1], [1, 1], [1, 1], [1, 1], [0], [1, -1], [1, 1], [1, -1], [1, 1], [1, -1], [1, -1], [1, -1], [1, 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'185.809280250520931547533472022495', '186.61915720779922658597829780566', '187.54469730815925283394790152363', '187.85126161556861101408752752225', '189.36051430015789324056360326286', '189.99105637517733475648582559263', '190.92930852566013638513804976941', '191.680109968545068101282875646947', '192.30549000897779589684397958591', '192.79227016367765651843472746570', '194.205900751909318013858219201079', '195.15526593568162659557899605253', '195.571601326461701012125468303470', '196.47682555477103580394192189263', '197.48233791957418457959090034171', '198.179486071937736065973837848885', '198.80039262442268863635413851570', '199.57957149656738813532395401366'], 'prelabel': '1-68-68.67-r1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.307614886034502, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'r1-0', 'st_group': 'mu(2)', 'symmetry_type': 'orthogonal', 'types': ['DIR'], 'values': [[1, '1.52389627569590479880276058442']], 'z1': {'__RealLiteral__': 0, 'data': '1.50090041534', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '3.46477752662', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '4.5444054213', 'prec': 37}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 7.307614886034502, 'bad_primes': [2, 17], 'central_character': '68.67', 'conductor': 68, 'conductor_radical': 34, 'degree': 1, 'dirichlet_coefficients': [1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, -1, 0, -1, 0, 0, 0, 1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 0, -1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, -1, 0, 1, 0, 1, 0, 0, 0, -1, 0, -1, 0, 1, 0, 1, 0, 1, 0, 1, 0, -1, 0], 'euler11': [1, 1], 'euler13': [1, 1], 'euler17': [1, 0], 'euler19': [1, -1], 'euler2': [1, 0], 'euler23': [1, 1], 'euler29': [1, -1], 'euler3': [1, 1], 'euler31': [1, 1], 'euler37': [1, -1], 'euler41': [1, -1], 'euler43': [1, -1], 'euler47': [1, -1], 'euler5': [1, -1], 'euler53': [1, 1], 'euler59': [1, -1], 'euler61': [1, -1], 'euler67': [1, -1], 'euler7': [1, 1], 'euler71': [1, 1], 'euler73': [1, -1], 'euler79': [1, 1], 'euler83': [1, -1], 'euler89': [1, 1], 'euler97': [1, -1], 'euler_factors': [[1, 0], [1, 1], [1, -1], [1, 1], [1, 1], [1, 1], [1, 0], [1, -1], [1, 1], [1, -1], [1, 1], [1, -1], [1, -1], [1, -1], [1, -1], [1, 1], [1, -1], [1, -1], [1, -1], [1, 1], [1, -1], [1, 1], [1, -1], [1, 1], [1, -1]], 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/68/67'], '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': '1-68-68.67-r1-0-0', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-68-68.67-r1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 7.307614886034502, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.50090041534', 'prec': 40}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_68.67', 'Lhash_array': ['dirichlet_L_68.67'], 'factors': ['1-68-68.67-r1-0-0'], 'label': '1-68-68.67-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/68/67'}