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  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_4195.4194', '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': 450.815359513452, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [839, [1]]], 'bad_primes': [5, 839], 'central_character': '4195.4194', 'coeff_info': ['x^2 - 1', -1, '\\\\zeta_{2}'], 'conductor': 4195, 'conductor_radical': 4195, 'conjugate': 'dirichlet_L_4195.4194', 'degree': 1, 'dirichlet_coefficients': [1, -1, -1, 1, 0, 1, -1, -1, 1, 0, -1, -1, 1, 1, 0, 1, 1, -1, 1, 0, 1, 1, -1, 1, 0, -1, -1, -1, -1, 0, -1, -1, 1, -1, 0, 1, -1, -1, -1, 0, -1, -1, -1, -1, 0, 1, -1, -1, 1, 0, -1, 1, -1, 1, 0, 1, -1, 1, 1, 0, 1, 1, -1, 1, 0, -1, 1, 1, 1, 0, -1, -1, -1, 1, 0, 1, 1, 1, -1, 0, 1, 1, 1, 1, 0, 1, 1, 1, -1, 0, -1, -1, 1, 1, 0, 1, 1, -1, -1, 0], 'euler_factors': [[1, -1], [1, -1], [0], [1, -1], [1, -1], [1, 1], [1, 1], [1, 1], [1, -1], [1, 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['DIR'], 'values': [[1, '0.388037660113296699399144194350']], 'z1': {'__RealLiteral__': 0, 'data': '0.241093817147', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.24444859291', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.00029791622', 'prec': 44}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 450.815359513452, 'bad_primes': [5, 839], 'central_character': '4195.4194', 'conductor': 4195, 'conductor_radical': 4195, 'degree': 1, 'dirichlet_coefficients': [1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, -1, 1, 0, 1, -1, 1, -1, 0, 1, 1, 1, 1, 0, -1, 1, 1, 1, 0, 1, 1, 1, -1, 0, 1, 1, -1, -1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, -1, -1, 1, 1, 0, 1, -1, 1, -1, 0, -1, 1, 1, 1, 0, 1, -1, -1, 1, 0, 1, 1, 1, 1, 0, -1, 1, -1, 1, 0, 1, 1, -1, 1, 0, 1, 1, 1, 1, 0, -1, 1, 1, 1, 0, 1, -1, 1, 1, 0], 'euler11': [1, -1], 'euler13': [1, 1], 'euler17': [1, 1], 'euler19': [1, 1], 'euler2': [1, -1], '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, 0], '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, -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], [1, -1], [1, 1], [1, -1], [1, 1]], 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/4195/4194'], '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': '1-4195-4195.4194-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-4195-4195.4194-r1-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 450.815359513452, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.241093817147', 'prec': 47}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_4195.4194', 'Lhash_array': ['dirichlet_L_4195.4194'], 'factors': ['1-4195-4195.4194-r1-0-0'], 'label': '1-4195-4195.4194-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/4195/4194'}