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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_171.167', 'a10': [-0.766044443118978, 0.6427876096865394], 'a2': [-0.9396926207859084, 0.3420201433256687], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.766044443118978, -0.6427876096865394], 'a5': [0.9396926207859084, -0.3420201433256687], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, 0.0], 'a8': [-0.5, 0.8660254037844386], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 0.7941206614468482, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [19, [1]]], 'bad_primes': [3, 19], 'central_character': '171.167', 'coeff_info': ['x^18 - 1', '0.939692620785908 + 0.342020143325669*I', '\\\\zeta_{18}'], 'conductor': 171, 'conductor_radical': 57, 'conjugate': 'dirichlet_L_171.128', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^8', 0, 'a^16', 'a^17', 0, 'a^0', 'a^6', 0, 'a^7', 'a^3', 0, 'a^13', 'a^8', 0, 'a^14', 'a^11', 0, 0, 'a^15', 0, 'a^11', 'a^7', 0, 'a^16', 'a^3', 0, 'a^16', 'a^4', 0, 'a^15', 'a^4', 0, 'a^1', 'a^17', 0, 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'194.72899212614816171847941735954', '195.742159763617599286690984625921', '196.1294629109094301251107045017', '196.89195188112296357454382718681', '197.81052457809069710494628981086', '198.15533894386856190736286067062', '198.98591857767571566250135643197', '199.68689703034370127742615090879'], 'prelabel': '1-171-171.167-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7941206614468482, 'root_angle': 0.017228818925864475, 'root_number': '0.998535549374040374159262190552+0.0540995068025890430254211263802*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.00861440946293', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(18)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.901797935039747645043048731555+0.0472051940111280521354686965321*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.34698723395', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.40212875993', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.76492468029', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 0.7941206614468482, 'bad_primes': [3, 19], 'central_character': '171.167', 'conductor': 171, 'conductor_radical': 57, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/171/167'], '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': '1-171-171.167-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': '1-171-171.167-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.7941206614468482, 'root_angle': 0.008614409462932238, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.34698723395', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_171.167', 'Lhash_array': ['dirichlet_L_171.167'], 'label': '1-171-171.167-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/171/167'}
Lfunction data - 1-171-171.167-r0-0-0