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lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1480.83', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.3420201433256687, -0.9396926207859084], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.984807753012208, 0.17364817766693036], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.766044443118978, -0.6427876096865394], 'algebraic': True, 'analytic_conductor': 6.87309110492009, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [37, [1]]], 'bad_primes': [2, 5, 37], 'central_character': '1480.83', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 1480, 'conductor_radical': 370, 'conjugate': 'dirichlet_L_1480.107', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^29', 0, 0, 0, 'a^53', 0, 'a^22', 0, 'a^12', 0, 'a^23', 0, 0, 0, 'a^31', 0, 'a^2', 0, 'a^46', 0, 'a^51', 0, 0, 0, 'a^15', 0, 'a^48', 0, 'a^18', 0, 'a^5', 0, 0, 0, 0, 0, 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'186.45022903331568179254803624402', '186.97195030297265381062540010046', '187.82666351336792497415580470380', '188.542776878089072163335108937110', '188.87320838381759739060429179122', '189.75051111924594176860082018777', '190.14188856798014257156546715200', '190.65606605924935815886950185452', '191.32579069505352083500783562537', '191.58793431642371052259118942265', '192.316183835150544336204681786268', '193.259574724924088770466688863812', '193.73333947138215066885955663376', '194.02417359066721898190562104614', '194.89684533539914000740410091809', '195.67346633825621273744650231520', '195.93051743914623476199718311606', '196.59457724116840264411154683758', '196.89795679150437547817624957866', '197.73125996254731629702856379503', '198.16374306519608258553352667121', '198.83515278618946211162822255112', '199.69637323849132640900126659605'], 'prelabel': '1-1480-1480.83-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.87309110492009, 'root_angle': 0.335159029898743, 'root_number': '0.495024632090010493263079767050+0.868878940718527113148943290668*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.167579514949', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.842761317230793608011916102097-0.154169461185479928886381805747*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.07428864638', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.26520659265', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.95605336438', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 6.87309110492009, 'bad_primes': [2, 5, 37], 'central_character': '1480.83', 'conductor': 1480, 'conductor_radical': 370, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1480/83'], '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': '1-1480-1480.83-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': '1-1480-1480.83-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.87309110492009, 'root_angle': 0.1675795149493715, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.07428864638', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1480.83', 'Lhash_array': ['dirichlet_L_1480.83'], 'label': '1-1480-1480.83-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1480/83'}
Lfunction data - 1-1480-1480.83-r0-0-0