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  • lfunc_lfunctions • Show schema
    {'Lhash': 'dirichlet_L_1480.987', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.984807753012208, -0.17364817766693036], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.6427876096865394, -0.766044443118978], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.9396926207859084, -0.3420201433256687], 'algebraic': True, 'analytic_conductor': 6.87309110492009, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [37, [1]]], 'bad_primes': [2, 5, 37], 'central_character': '1480.987', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 1480, 'conductor_radical': 370, 'conjugate': 'dirichlet_L_1480.3', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^35', 0, 0, 0, 'a^23', 0, 'a^34', 0, 'a^12', 0, 'a^47', 0, 0, 0, 'a^7', 0, 'a^8', 0, 'a^22', 0, 'a^51', 0, 0, 0, 'a^33', 0, 'a^30', 0, 'a^0', 0, 'a^11', 0, 0, 0, 0, 0, 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'0.446909401652038285340185862817+0.894579223274840605390636054220*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.176262315021', 'prec': 40}, 'spectral_label': 'r0-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.28427289312764496988006425171+0.141320203751502157644169816294*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.34005857387', 'prec': 40}, 'z2': {'__RealLiteral__': 0, 'data': '2.12739209492', 'prec': 40}, 'z3': {'__RealLiteral__': 0, 'data': '3.17041443818', 'prec': 40}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 6.87309110492009, 'bad_primes': [2, 5, 37], 'central_character': '1480.987', 'conductor': 1480, 'conductor_radical': 370, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1480/987'], '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': '1-1480-1480.987-r0-0-0', 'motivic_weight': 0, 'mu_imag': [0], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-1480-1480.987-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.87309110492009, 'root_angle': 0.1762623150210722, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.34005857387', 'prec': 40}}
  • lfunc_instances • Show schema
    {'Lhash': 'dirichlet_L_1480.987', 'Lhash_array': ['dirichlet_L_1480.987'], 'factors': ['1-1480-1480.987-r0-0-0'], 'label': '1-1480-1480.987-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1480/987'}