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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_81.70', 'a10': [0.17364817766693036, -0.984807753012208], 'a2': [-0.05814482891047583, -0.9983081582712682], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [-0.993238357741943, 0.11609291412523023], 'a5': [0.9730448705798238, 0.23061587074244017], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.5971585917027862, -0.8021231927550437], 'a8': [0.17364817766693036, 0.984807753012208], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.37616241858008603, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]]], 'bad_primes': [3], 'central_character': '81.70', 'coeff_info': ['x^27 - 1', '0.973044870579824 + 0.230615870742440*I', '\\\\zeta_{27}'], 'conductor': 81, 'conductor_radical': 3, 'conjugate': 'dirichlet_L_81.22', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^20', 0, 'a^13', 'a^1', 0, 'a^23', 'a^6', 0, 'a^21', 'a^17', 0, 'a^25', 'a^16', 0, 'a^26', 'a^12', 0, 'a^15', 'a^14', 0, 'a^10', 'a^4', 0, 'a^2', 'a^18', 0, 'a^9', 'a^11', 0, 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'187.07969193707284289900809020468', '188.34334209959768414035202898630', '189.114204172066276185936815170486', '189.788410372201498238402906034871', '190.59725385046229830582188465534', '191.52721116478093295595587886913', '192.22610531773240543230378509625', '192.72724999733848904052821246747', '194.02392342571853652774500634357', '194.169335368520982183123501327963', '195.02052208690818448441255998908', '196.0369512002463663041147395885', '197.113139255970423004953250506128', '197.727466897822644994902469353755', '198.71993806545445209182070199146', '199.51584267504945764545095677671'], 'prelabel': '1-3e4-81.70-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.37616241858008603, 'root_angle': -0.2345679012345679, 'root_number': '0.0968108707031790957914761200182-0.995302795793165819361360709688*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.234567901235', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(27)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.910984964208508777916736398365-0.533498595113642652192440106495*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.44794418125', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.97550073932', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.56299343698', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.37616241858008603, 'bad_primes': [3], 'central_character': '81.70', 'conductor': 81, 'conductor_radical': 3, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/81/70'], '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': '1-3e4-81.70-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': '1-3e4-81.70-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.37616241858008603, 'root_angle': -0.2345679012345679, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.44794418125', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_81.70', 'Lhash_array': ['dirichlet_L_81.70'], 'factors': ['1-3e4-81.70-r0-0-0'], 'label': '1-3e4-81.70-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/81/70'}
Lfunction data - 1-3e4-81.70-r0-0-0