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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_2808.2165', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.6427876096865394, 0.766044443118978], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.984807753012208, -0.17364817766693036], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 13.040297177442982, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [13, [1]]], 'bad_primes': [2, 3, 13], 'central_character': '2808.2165', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 2808, 'conductor_radical': 78, 'conjugate': 'dirichlet_L_2808.821', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^41', 0, 'a^19', 0, 0, 0, 'a^19', 0, 0, 0, 0, 0, 'a^0', 0, 'a^51', 0, 0, 0, 'a^8', 0, 'a^10', 0, 0, 0, 'a^52', 0, 'a^29', 0, 0, 0, 'a^24', 0, 'a^21', 0, 0, 0, 'a^23', 0, 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'spectral_label': 'r0-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.832128812579341171472999109572+0.0691357635728230553804276418512*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.12551537137', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.63836184632', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.46255695205', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 13.040297177442982, 'bad_primes': [2, 3, 13], 'central_character': '2808.2165', 'conductor': 2808, 'conductor_radical': 78, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2808/2165'], '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': '1-2808-2808.2165-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-2808-2808.2165-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 13.040297177442982, 'root_angle': -0.3199694559842744, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.12551537137', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_2808.2165', 'Lhash_array': ['dirichlet_L_2808.2165'], 'factors': ['1-2808-2808.2165-r0-0-0'], 'label': '1-2808-2808.2165-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2808/2165'}
Lfunction data - 1-2808-2808.2165-r0-0-0