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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_37.32', 'a10': [-0.5, 0.8660254037844386], 'a2': [0.6427876096865394, 0.766044443118978], 'a3': [-0.766044443118978, -0.6427876096865394], 'a4': [-0.17364817766693036, 0.984807753012208], 'a5': [0.3420201433256687, 0.9396926207859084], 'a6': [2.9010907910729803e-30, -1.0], 'a7': [-0.9396926207859084, 0.3420201433256687], 'a8': [-0.8660254037844386, 0.5], 'a9': [0.17364817766693036, 0.984807753012208], 'algebraic': True, 'analytic_conductor': 3.976202217401126, 'analytic_normalization': 0, 'bad_lfactors': [[37, [1]]], 'bad_primes': [37], 'central_character': '37.32', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 37, 'conductor_radical': 37, 'conjugate': 'dirichlet_L_37.22', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^5', 'a^22', 'a^10', 'a^7', 'a^27', 'a^16', 'a^15', 'a^8', 'a^12', 'a^6', 'a^32', 'a^19', 'a^21', 'a^29', 'a^20', 'a^35', 'a^13', 'a^31', 'a^17', 'a^2', 'a^11', 'a^3', 'a^1', 'a^14', 'a^24', 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'182.68596117468073720191757123050', '183.64850069763806989422224776714', '184.383948488009026113310430565388', '185.38798412154953543686296606885', '186.1044404663161090949694675713', '187.23559424841747173247287479890', '187.76276026697936835371148776464', '188.9684370689885913386988320903', '189.57736046552900692249999856478', '190.402451013980274233241751469179', '190.93431625100544087668421580776', '193.11682062553113726728431617812', '193.57519508141671682071381181465', '194.22422538898162773516952626144', '195.17487471212108211716904881746', '195.950790765907977061127742337241', '196.72227403237279881832436234408', '197.581559376841139006367327261854', '198.5750160397210921062191933914', '199.33366890666190281954318214677'], 'prelabel': '1-37-37.32-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.976202217401126, 'root_angle': 0.3723584676175512, 'root_number': '-0.695273910330786569570406126395+0.718744871017064967472221764699*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.372358467618', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.857336961746232118304198732589+0.644878940804298121234406622009*I']], 'z1': {'__RealLiteral__': 0, 'data': '2.86376886724', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '5.20135100307', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '6.57869448505', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 3.976202217401126, 'bad_primes': [37], 'central_character': '37.32', 'conductor': 37, 'conductor_radical': 37, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/37/32'], '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': '1-37-37.32-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-37-37.32-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 3.976202217401126, 'root_angle': 0.3723584676175512, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '2.86376886724', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_37.32', 'Lhash_array': ['dirichlet_L_37.32'], 'factors': ['1-37-37.32-r1-0-0'], 'label': '1-37-37.32-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/37/32'}
Lfunction data - 1-37-37.32-r1-0-0