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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1960.163', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.14904226617617444, -0.9888308262251285], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.9555728057861407, 0.2947551744109042], 'algebraic': True, 'analytic_conductor': 9.102201733542822, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [7, [1]]], 'bad_primes': [2, 5, 7], 'central_character': '1960.163', 'coeff_info': ['x^84 - 1', '0.997203797181180 + 0.0747300935864243*I', '\\\\zeta_{84}'], 'conductor': 1960, 'conductor_radical': 70, 'conjugate': 'dirichlet_L_1960.1467', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^61', 0, 0, 0, 0, 0, 'a^38', 0, 'a^4', 0, 'a^123', 0, 0, 0, 'a^55', 0, 'a^14', 0, 0, 0, 'a^71', 0, 0, 0, 'a^15', 0, 'a^48', 0, 'a^70', 0, 'a^65', 0, 0, 0, 'a^125', 0, 'a^100', 0, 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'195.935725542511259760252621971613', '196.065000073260132506616747199469', '196.83872680710619434783204015260', '197.68423644029306644785717629706', '197.82153095548510221469615743027', '198.47615745021619173679822107109', '199.45392860273729880360027743957', '199.839451638956455537450226458686'], 'prelabel': '1-1960-1960.163-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.102201733542822, 'root_angle': -0.40613130647174545, 'root_number': '-0.831055051598571335701898083152-0.556190166411179850521561920263*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.406131306472', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(84)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.819797228580779339583944712494-0.359540564229594226160091323328*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.34902140649', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.53359674924', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.28608624191', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 9.102201733542822, 'bad_primes': [2, 5, 7], 'central_character': '1960.163', 'conductor': 1960, 'conductor_radical': 70, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1960/163'], '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': '1-1960-1960.163-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': '1-1960-1960.163-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.102201733542822, 'root_angle': -0.40613130647174545, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.34902140649', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1960.163', 'Lhash_array': ['dirichlet_L_1960.163'], 'factors': ['1-1960-1960.163-r0-0-0'], 'label': '1-1960-1960.163-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1960/163'}
Lfunction data - 1-1960-1960.163-r0-0-0