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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_143.38', 'a10': [1.0, 0.0], 'a2': [0.8090169943749475, -0.5877852522924731], 'a3': [0.30901699437494745, 0.9510565162951535], 'a4': [0.30901699437494745, -0.9510565162951535], 'a5': [0.8090169943749475, 0.5877852522924731], 'a6': [0.8090169943749475, 0.5877852522924731], 'a7': [-0.30901699437494745, 0.9510565162951535], 'a8': [-0.30901699437494745, -0.9510565162951535], 'a9': [-0.8090169943749475, 0.5877852522924731], 'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [13, [1]]], 'bad_primes': [11, 13], 'central_character': '143.38', 'coeff_info': ['x^10 - 1', '0.809016994374947 + 0.587785252292473*I', '\\\\zeta_{10}'], 'conductor': 143, 'conductor_radical': 143, 'conjugate': 'dirichlet_L_143.64', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^9', 'a^2', 'a^8', 'a^1', 'a^1', 'a^3', 'a^7', 'a^4', 'a^0', 0, 'a^0', 0, 'a^2', 'a^3', 'a^6', 'a^6', 'a^3', 'a^7', 'a^9', 'a^5', 0, 'a^0', 'a^9', 'a^2', 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'194.25063084314326305878665373184', '194.65845065982075299516122423771', '195.83376000886489319451249758356', '196.66857411587720738191145840492', '197.110516233131848537065034319546', '197.92287979529276329525401259861', '198.7734122563076742358099470309', '199.78225489344148800490555288722'], 'prelabel': '1-143-143.38-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': 0.04271713006960679, 'root_number': '0.964196527258429889770384438615+0.265188719260046705618715810899*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0427171300696', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(10)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.74039779727039754937325407397+0.0847518232927868809741355846987*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.35893887997', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.97867548232', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.55763963863', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'bad_primes': [11, 13], 'central_character': '143.38', 'conductor': 143, 'conductor_radical': 143, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/143/38'], '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': '1-143-143.38-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': '1-143-143.38-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': 0.04271713006960679, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '2.35893887997', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_143.38', 'Lhash_array': ['dirichlet_L_143.38'], 'factors': ['1-143-143.38-r0-0-0'], 'label': '1-143-143.38-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/143/38'}
Lfunction data - 1-143-143.38-r0-0-0