-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1883860340756020065443919734409', 'a10': [0.0, 0.0], 'a2': [-1.445041867912629, 0.0], 'a3': [-2.246979603717467, 0.0], 'a4': [0.08814600002041936, 0.0], 'a5': [0.0, 0.0], 'a6': [3.246979603717467, 0.0], 'a7': [-1.3568958678922094, 0.0], 'a8': [2.762709075306724, 0.0], 'a9': [2.0489173395223053, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.79289409601082, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [[1.0, 0], [0, 0]]], [19, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [5, 19], 'central_character': '475.1', 'coefficient_field': 'CDF', 'conductor': 475, 'conductor_radical': 95, 'conjugate': '1883860340756020065443919734409', 'degree': 2, 'euler_factors': [[[1.0, 0], [1.445041867912629, 0], [2.0, 0]], [[1.0, 0], [2.246979603717467, 0], [3.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [1.3568958678922094, 0], [7.0, 0]], [[1.0, 0], [-4.850855075327144, 0], [11.0, 0]], [[1.0, 0], [0.19806226419516174, 0], [13.0, 0]], [[1.0, 0], [-1.1370633395427248, 0], [17.0, 0]], [[1.0, 0], [1.0, 0]], [[1.0, 0], [2.5549581320873713, 0], [23.0, 0]], [[1.0, 0], [10.234898018587335, 0], [29.0, 0]], [[1.0, 0], [-2.5157294715892573, 0], [31.0, 0]], [[1.0, 0], [-0.13706333954272468, 0], [37.0, 0]], [[1.0, 0], [11.750627490176592, 0], [41.0, 0]], [[1.0, 0], [-7.591793886479545, 0], [43.0, 0]], [[1.0, 0], [2.692021471630096, 0], [47.0, 0]], [[1.0, 0], [12.878002150695126, 0], [53.0, 0]], [[1.0, 0], [-5.823707999959161, 0], [59.0, 0]], [[1.0, 0], [7.582105207455354, 0], [61.0, 0]], [[1.0, 0], [8.01506549023785, 0], [67.0, 0]], [[1.0, 0], [8.823707999959161, 0], [71.0, 0]], [[1.0, 0], [-11.970460018526078, 0], [73.0, 0]], [[1.0, 0], [-10.740938811152402, 0], [79.0, 0]], [[1.0, 0], [3.7747906604368557, 0], [83.0, 0]], [[1.0, 0], [-9.366584546916402, 0], [89.0, 0]], [[1.0, 0], [0.19806226419516174, 0], [97.0, 0]], [[1.0, 0], [-11.509024697672785, 0], [101.0, 0]], [[1.0, 0], [15.156440697591107, 0], [103.0, 0]], [[1.0, 0], [2.652792811131982, 0], [107.0, 0]], [[1.0, 0], [2.4993360186485933, 0], [109.0, 0]], [[1.0, 0], [8.527811056719388, 0], [113.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 9, 'label': '2-475-1.1-c1-0-9', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/475/2/a/d/1/2', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [-8.14958064159963e-121, 0.10941093979554146, 0.21879888849717005, 0.3270160528741029, 0.4308859752498706, 0.5246562641427348, 0.5998418293022637, 0.6454349580700596, 0.6484500267620915, 0.5947813392982557, 0.4703554390573199, 0.2625438627941209, -0.03822936814328489, -0.4367921839942434, -0.931589606357848, -1.5132936308918747, -2.1638627702715336, -2.856255963162757, -3.5549790499016423, -4.21758640461977, -4.7971760986924705, -5.245808704192398, -5.518656470697147, -5.5785642210509945, -5.40059223790644, -4.976032568395858, -4.315360793849204, -3.4496192630483433, -2.429832800758569, -1.324233135671761, -0.21330269694040446, 0.817079637208391, 1.6838298580086497, 2.3153789801507254, 2.6599373773478954, 2.692249153201874, 2.4178462076039002, 1.874019664203806, 1.1270696557195365, 0.26584258047750525, -0.6079330984361655, -1.3915122131990298, -1.9937967181851295, -2.3471507288852633, -2.416688886466458, -2.205573510768937, -1.7553088272726658, -1.140669798023131, -0.45966906660866763, 0.18025970712816095, 0.6780221797344774, 0.9542959795296311, 0.9642553476445179, 0.7054693596972901, 0.21947970293662192, -0.4135196877952531, -1.0863977727223952, -1.6816151009033828, -2.0900936252009994, -2.2294188327328563, -2.0583051493759155, -1.5847194591076246, -0.8660043285267726, -0.000640570485231219, 0.8872681836346684, 1.6683680464419868, 2.2298812093975915, 2.495060728755352, 2.436703166617412, 2.082077501062757, 1.508101400967718, 0.8273679024678398, 0.16737658997658345, -0.3532857823841719, -0.6473328712867176, -0.6753531851437723, -0.4531607405827607, -0.048210699319556724, 0.4345011782270359, 0.8744821516036663, 1.1614172518740635, 1.2192242111036171, 1.0233431432038957, 0.6073086705405065, 0.05674970290948915, -0.5084239758710287, -0.9602844431786091, -1.1921995694019456, -1.1448147607259127, -0.8226686530252041, -0.2971091506834334, 0.3060511423954707, 0.8323904185331652, 1.1333385962253897, 1.102047729930405, 0.7026231089200414, -0.014452735041931716, -0.9153231597468833, -1.8050367778554568, -2.465707570019119, -2.703353257305971, -2.393720758410155, -1.5168875540730185, -0.17213341920540287, 1.431714418974992, 3.0102343394709496, 4.256118728213945, 4.90065133476827, 4.771434593372356, 3.833903092636527, 2.206940378574929, 0.14795842486040905, -1.9908948513535925, -3.8274980413536266, -5.022803791926196, -5.347279875135707, -4.726813217553294, -3.25817555476295, -1.1904487836290143, 1.1239641429578937, 3.2985575797725475, 4.987585495283128, 5.9507757496044915, 6.09441266114569, 5.480639960951235, 4.303996729923609, 2.8415342694575285, 1.388659502171226, 0.1957459044234505, -0.5801332647116615, -0.8980792424160738, -0.8270476069052869, -0.5137768830700435, -0.13462545122040245, 0.15538824500650406, 0.2628931782105628, 0.17570858859284796, -0.04255938476295273, -0.280105868284022, -0.4178443750953159, -0.37120169533914504, -0.1202370592469077, 0.28102171762390765, 0.7190573753546209, 1.0551537814629566, 1.1694737195587925, 1.0016423540063337, 0.5750834192495632, -0.0033445318984959773, -0.5698803217222971, -0.9502607077600463, -1.0133464276088469, -0.716323469420607, -0.1272107264533952, 0.583969330152008, 1.1854947622463283, 1.44673658203286, 1.2072767973656633, 0.4331239276012018, -0.7570318672315555, -2.105463119288588, -3.2685170562425236, -3.8978456833132524, -3.72994806062489, -2.660708207139054, -0.7842839362091678, 1.6158626964087228, 4.123842772002501, 6.283457005417666, 7.703067344669972, 8.146630137208795, 7.587228154853575, 6.208844251188281, 4.355618664539359, 2.441828768823583, 0.8464786979298919, -0.17933643196227753, -0.5675441569636067, -0.43624804894975505, -0.04092167168814804, 0.3117819582148494, 0.3624433243517548, -0.019174478265792615, -0.7926662531456791, -1.7583997170714447, -2.6188090598368903, -3.0718396329093274, -2.9090273472471946, -2.088796100502887, -0.7622539975341593, 0.7577235010639837, 2.076836898008289, 2.8271323541202436, 2.7716207065314196, 1.8753656060988304, 0.321740716936333, -1.5319830218356842, -3.248143234134577, -4.425413735835664, -4.805943047110624, -4.342628853596046, -3.207610480909976, -1.739966144503413, -0.3481060674770077, 0.604705032221411, 0.8987116883222291, 0.5121092006301721, -0.3829214426080365, -1.4796280826059107, -2.4323040269174525, -2.958624148531764, -2.918072723195015, -2.344011806890114, -1.4217922321526775, -0.42214207936801934, 0.3873991019919649, 0.8241970402355824, 0.8398414868131169, 0.5228750589393265, 0.05641617503278361, -0.3530077802394727, -0.5499791767923846, -0.48218861389310824, -0.21238990043670478, 0.11292115095889493, 0.3259673125081621, 0.3079849653716128, 0.04100535737233475, -0.3789355335656176, -0.7735740716990632, -0.9491893210060782, -0.7748938961712518, -0.24331618318039128, 0.5109132301774187, 1.245781877352946, 1.6920155833503276, 1.653933637505298, 1.0965577125783472, 0.18609544514368034, -0.7359263225384094, -1.2435871688481681, -0.9589704524785354, 0.3137067939585743, 2.496156515973441, 5.220226191292779, 7.90042603457478, 9.87974829049475, 10.609604427202692, 9.811554594597828, 7.57111307917006, 4.332196558747742, 0.7896279123394556, -2.2921589952812984, -4.283022959751263, -4.854506248368561, -4.061613668559869, -2.3150823045823077], 'positive_zeros': ['1.48610377371875774807829192300584', '3.77476908895374431764903359800898', '4.91253673733910429662711263351319', '6.08772087408116031085258817944838', '6.79567546001537173163653958636915', '7.87508911704190464041888948152804', '9.035674999455596344268413788226384', '9.637895505596095622010197420773015', '10.51222991718351149872969050042242'], 'prelabel': '2-475-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.48610377371875774807829192301', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.77476908895374431764903359801', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.91253673733910429662711263351', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.79289409601082, 'bad_primes': [5, 19], 'central_character': '1.1', 'conductor': 475, 'conductor_radical': 95, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/475/2/a/d/1/2'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, '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': '2-475-1.1-c1-0-9', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-475-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.9475353901818626, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.48610377371875774807829192301', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1883860340756020065443919734409', 'Lhash_array': ['1883860340756020065443919734409'], 'label': '2-475-1.1-c1-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/475/2/a/d/1/2'}