-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1284781965505370327314336627214', 'a10': [0.0, 0.0], 'a2': [0.0, 0.0], 'a3': [1.704243251095381, -0.30911962263150794], 'a4': [0.0, 0.0], 'a5': [-1.4539504011428581, 1.732750614015794], 'a6': [0.0, 0.0], 'a7': [-1.4927648536121987, 4.101337727855], 'a8': [0.0, 0.0], 'a9': [2.8088901178083083, -1.0536300613017968], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 3.4495373673193144, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [0, 0]]], [3, [[1.0, 0], [-1.704243251095381, 0.30911962263150794]]]], 'bad_primes': [2, 3], 'central_character': '432.95', 'coefficient_field': 'CDF', 'conductor': 432, 'conductor_radical': 6, 'conjugate': '2700968485523002751446737127605', 'degree': 2, 'euler_factors': [[[1.0, 0], [0, 0]], [[1.0, 0], [-1.704243251095381, 0.30911962263150794]], [[1.0, 0], [1.4539504011428581, -1.732750614015794], [-0.8682408883346517, -4.924038765061041]], [[1.0, 0], [1.4927648536121987, -4.101337727855], [-5.362311101832846, -4.499513267805775]], [[1.0, 0], [-1.8362947360773716, 1.5408342357753033], [1.9101299543362338, -10.832885283134289]], [[1.0, 0], [0.21957689199442693, -1.245282435576155], [-12.216004070216808, -4.446261863233693]], [[1.0, 0], [-4.235126410605354, -2.445151373215095], [8.5, 14.722431864335457]], [[1.0, 0], [5.935255856448432, -3.426721566429805], [9.5, -16.454482671904334]], [[1.0, 0], [2.4327518673899498, -0.8854492670854613], [17.619022191736494, -14.784115022790404]], [[1.0, 0], [-9.764279881382517, 1.7217059902765879], [27.251086002791343, -9.918584156444393]], [[1.0, 0], [2.1542133350164887, 5.918652494645838], [-23.747377736688318, 19.92641590028272]], [[1.0, 0], [-2.4978064427759623, 4.32632766636085], [-18.5, -32.04293994002423]], [[1.0, 0], [-0.20647719573313955, -0.036407500508775247], [38.527397452222246, 14.022825876352417]], [[1.0, 0], [-0.8638710102587558, -1.0295213800138618], [-7.466871639678005, 42.34673337952495]], [[1.0, 0], [-5.300349216993191, -1.9291693462016941], [36.00408882659197, 30.211017655267348]], [[1.0, 0], [0, 12.006822235013622], [-53.0, 0]], [[1.0, 0], [6.165757029031949, 5.173684448989431], [10.24524248234889, 58.10365742772028]], [[1.0, 0], [3.5970845118723895, 1.3092316924615217], [46.728711030257664, 39.2100441908789]], [[1.0, 0], [-2.97797345254924, -0.5250970675179706], [62.95940559265586, 22.915349602819806]], [[1.0, 0], [-1.2942574866669494, 2.241719724983555], [-35.5, -61.48780366869514]], [[1.0, 0], [-4.413579276513919, -7.644543550155195], [-36.5, 63.21985447626402]], [[1.0, 0], [1.3924915903437354, -0.24553383778723953], [74.23571704208676, -27.01959132272783]], [[1.0, 0], [1.5558559673199828, 8.823697661405543], [-77.9944875252304, 28.387671896030504]], [[1.0, 0], [15.446219196946238, -8.917878811318875], [44.5, -77.07626093681505]], [[1.0, 0], [-11.898629127055907, 9.984135312027853], [16.843873233692243, -95.52635204218419]], [[1.0, 0], [-4.098202380730169, 11.259718501411314], [-77.37048875501678, -64.92154857834048]], [[1.0, 0], [11.481466420668854, -13.683078855081892], [-17.885762299693827, -101.43519856025743]], [[1.0, 0], [-16.388136097904844, 0], [107.0, 0]], [[1.0, 0], [1.5929459694524126, 0], [109.0, 0]], [[1.0, 0], [3.8252130266012925, -4.558711366890262], [-19.62224407636313, -111.28327609037952]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 6, 'label': '2-432-108.95-c1-0-6', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/432/2/be/b/95/6', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.125', 'prec': 17}, 'plot_values': [1.6367151064963232, 1.5075934197579517, 1.3731688501632096, 1.225631184812101, 1.0563407354140288, 0.8572874823982044, 0.6223708077264296, 0.34841763136106935, 0.035935521780709904, -0.3103907821646717, -0.6814745426125379, -1.0639148034465309, -1.440448024843809, -1.7908047264215965, -2.0929833066567456, -2.32490944940934, -2.4663964020418834, -2.5012653699760414, -2.4194337687203844, -2.2187402211624123, -1.906257072751713, -1.4988508732809485, -1.022793568397384, -0.5123034602534038, -0.007002320961375152, 0.4515946283835462, 0.8242987715419311, 1.0787877128241725, 1.193967227384784, 1.163597924235163, 0.9986319766188859, 0.727782807495214, 0.3960052414657332, 0.06078716709649723, -0.21357351276855552, -0.3632413374619374, -0.33292796960009047, -0.08384174972640816, 0.3995538303684981, 1.105004586036172, 1.991011922037924, 2.9890018484591687, 4.009221056561458, 4.949957624470406, 5.70917317622854, 6.197194697219473, 6.348823088183019, 6.133134356366718, 5.559415702494415, 4.678095916956994, 3.576161177179892, 2.367318485974479, 1.1779731569538543, 0.13079981256399642, -0.6718149179700289, -1.161996924740425, -1.3160082381308067, -1.1575738779704026, -0.7541075966239764, -0.20612273340876774, 0.368762122870818, 0.8548442951277749, 1.1573713124500746, 1.2184093731792942, 1.0267379782143693, 0.6198467136447724, 0.07738998062773748, -0.493067623812494, -0.9757601206068905, -1.2685227332176001, -1.3027657530570382, -1.0578219598166674, -0.5667082181199139, 0.088211752391356, 0.7893513348814314, 1.405615510167286, 1.8179227796711424, 1.9437881802363841, 1.7561121564839322, 1.2921470447107652, 0.6502799773813687, -0.0254904270792579, -0.5710978228024597, -0.8335732462373854, -0.7020539292806504, -0.13253824251895283, 0.838838514707354, 2.097266291804988, 3.4659852328184075, 4.735801360851644, 5.702252818753052, 6.203508996672738, 6.151611834124208, 5.550669374397894, 4.497959795500566, 3.1671849142911768, 1.7766920586292585, 0.5486308876389915, -0.33295201806838653, -0.7566318469705725, -0.7035962064112333, -0.2488233304200074, 0.4569787537978608, 1.2210312018977947, 1.8506965661067982, 2.1952256817194753, 2.177962420869099, 1.8118677380741128, 1.1947980633952864, 0.4854387768310678, -0.13482441179653423, -0.5055116212506632, -0.5261172527543042, -0.18145881475356782, 0.4528926906897001, 1.2267850544581975, 1.949899289270966, 2.4366374429263584, 2.551007858719357, 2.2407310404522374, 1.5520560692313994, 0.6211658656667515, -0.35641522379496027, -1.171608856200943, -1.6520321790054846, -1.7045199509068503, -1.3392029418019964, -0.6685876988829609, 0.11897892535313669, 0.8057508954500902, 1.200052210584204, 1.1872150213310326, 0.7630027298698967, 0.04036207301789482, -0.7733850410654585, -1.4245506480936099, -1.6754663056677543, -1.3663833085046975, -0.46152210155011825, 0.9327986056849837, 2.583603765500739, 4.177871695778059, 5.390174037812726, 5.955739439141468, 5.731572450270813, 4.730756818447339, 3.1213207260013283, 1.1895637350702442, -0.723556449021275, -2.297703325554542, -3.3019142509059187, -3.640280170710498, -3.3638632837851223, -2.646774634350809, -1.7334942939362112, -0.8718367081086486, -0.24949587356975708, 0.0491249860453989, 0.05480347510472783, -0.1081952584717452, -0.27035391335735126, -0.2771990761238679, -0.043726189157385346, 0.4134084641029107, 0.9760400666799489, 1.457825833191948, 1.661831314186355, 1.4459715036382763, 0.7769063315032639, -0.24452290000616886, -1.39576685903596, -2.381902291273268, -2.9101120176779274, -2.769789738603824, -1.8961324640289428, -0.3986070660508585, 1.4554105810192266, 3.299528026681848, 4.75564057387661, 5.52720409063337, 5.473663213116548, 4.645662426118458, 3.2708805717982763, 1.6936165689844513, 0.2839712764839629, -0.6589648768234051, -0.9835955079814603, -0.7210611477382016, -0.06967167964089853, 0.666879898826894, 1.1699297507121458, 1.1991707976322763, 0.6623353289819853, -0.3585780667010768, -1.6318568939319358, -2.8440610842859986, -3.691489911049832, -3.968329436129019, -3.6256550104084684, -2.784042315714536, -1.6962548486463516, -0.6712994338160287, 0.01733519293924049, 0.21169837148615328, -0.0863761851269395, -0.7200191667799527, -1.429399440952416, -1.9349715714322662, -2.0261081272819546, -1.6275530993452707, -0.8228733513486262, 0.17262204454054694, 1.0812066626778765, 1.6525642373826637, 1.745542258025318, 1.3753188253800939, 0.7099799759537438, 0.01634831054236005, -0.4287867938558159, -0.43425600839479145, 0.03400656334500476, 0.8299035242466585, 1.6623029576831785, 2.1799562227407994, 2.0816445344073253, 1.2179924638669588, -0.3473948232239679, -2.3384309011295303, -4.331343421147093, -5.866712976921747, -6.576681030711384, -6.289715924128485, -5.0812266426223305, -3.2540775878376804, -1.253996593887018, 0.4554138178701921, 1.5209857674378133, 1.7934557932553168, 1.3585875921261654, 0.49760819777420406, -0.40963180317538966, -1.007833371679936, -1.0770307987522125, -0.5966745936687275, 0.2560599572179566, 1.1716404120332267, 1.814795508355673, 1.93701794037973, 1.4582006364445708, 0.49125101909617314, -0.6973864585347894, -1.7770834698789735, -2.461598110901371, -2.600077575409069, -2.2199683057190605, -1.5078937013310214, -0.7359180828642954], 'positive_zeros': ['1.01351426432019720052210487981059', '3.00179184258271350959936924028842', '4.14956469756620712709239849668871', '4.65178801451809941107000948691796', '6.64274007153779813955319036070305', '7.41913870883790614038143948170385', '8.266755151011347566119409537843365', '9.109162427264404448111020942355119', '10.12002724801066682212820952411709', '10.64529918211749458642057035305960'], 'prelabel': '2-432-108.95-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.857293021394124, 'root_angle': -0.3565297121616833, 'root_number': '0.43561842596860767 - 0.900131427601899*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.178264856081', 'prec': 50}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.01351426432019720052210487981', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '3.00179184258271350959936924029', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '4.14956469756620712709239849669', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 3.4495373673193144, 'bad_primes': [2, 3], 'central_character': '108.95', 'conductor': 432, 'conductor_radical': 6, 'degree': 2, 'index': 6, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/432/2/be/b/95/6'], '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': '2-432-108.95-c1-0-6', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-432-108.95-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 1.857293021394124, 'root_angle': -0.17826485608084164, 'self_dual': False, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.01351426432019720052210487981', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1284781965505370327314336627214', 'Lhash_array': ['1284781965505370327314336627214'], 'label': '2-432-108.95-c1-0-6', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/432/2/be/b/95/6'}