-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_1181.12', 'a10': [-0.6860981774633227, -0.7275089627499491], 'a2': [0.9968120070307501, -0.07978610555308308], 'a3': [0.9510565162951535, 0.30901699437494745], 'a4': [0.9872683547213446, -0.15906349601907205], 'a5': [-0.625865794404573, -0.7799307708985027], 'a6': [0.9726798173387414, 0.23215075477342878], 'a7': [-0.9171190430327487, -0.3986134228882605], 'a8': [0.97142989326471, -0.23732669987111482], 'a9': [0.8090169943749475, 0.5877852522924731], 'algebraic': True, 'analytic_conductor': 126.91607618245214, 'analytic_normalization': 0, 'bad_lfactors': [[1181, [1]]], 'bad_primes': [1181], 'central_character': '1181.12', 'coeff_info': ['x^1180 - 1', '0.999985823641077 + 0.00532470814936850*I', '\\\\zeta_{1180}'], 'conductor': 1181, 'conductor_radical': 1181, 'conjugate': 'dirichlet_L_1181.689', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^1165', 'a^59', 'a^1150', 'a^758', 'a^44', 'a^667', 'a^1135', 'a^118', 'a^743', 'a^520', 'a^29', 'a^249', 'a^652', 'a^817', 'a^1120', 'a^1068', 'a^103', 'a^335', 'a^728', 'a^726', 'a^505', 'a^598', 'a^14', 'a^336', 'a^234', 'a^177', 'a^637', 'a^603', 'a^802', 'a^329', 'a^1105', 'a^579', 'a^1053', 'a^245', 'a^88', 'a^134', 'a^320', 'a^308', 'a^713', 'a^532', 'a^711', 'a^1141', 'a^490', 'a^876', 'a^583', 'a^298', 'a^1179', 'a^154', 'a^321', 'a^1127', 'a^219', 'a^902', 'a^162', 'a^98', 'a^622', 'a^394', 'a^588', 'a^1042', 'a^787', 'a^760', 'a^314', 'a^785', 'a^1090', 'a^1007', 'a^564', 'a^233', 'a^1038', 'a^657', 'a^230', 'a^346', 'a^73', 'a^899', 'a^119', 'a^395', 'a^305', 'a^7', 'a^293', 'a^333', 'a^698', 'a^236', 'a^517', 'a^273', 'a^696', 'a^646', 'a^1126', 'a^662', 'a^475', 'a^355', 'a^861', 'a^916', 'a^568', 'a^388', 'a^283', 'a^1093', 'a^1164', 'a^449', 'a^139', 'a^638', 'a^306'], 'euler_factors': [[1, 'a^1165'], [1, 'a^59'], [1, 'a^758'], [1, 'a^667'], [1, 'a^520'], [1, 'a^249'], [1, 'a^1068'], [1, 'a^335'], [1, 'a^598'], [1, 'a^603'], [1, 'a^329'], [1, 'a^134'], [1, 'a^532'], [1, 'a^1141'], [1, 'a^298'], [1, 'a^902'], [1, 'a^1042'], [1, 'a^760'], [1, 'a^233'], [1, 'a^346'], [1, 'a^899'], [1, 'a^333'], [1, 'a^273'], [1, 'a^355'], [1, 'a^449'], [1, 'a^300']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-1181-1181.12-r1-0-0', 'leading_term': '2.74052055691034695371615048674+2.43571489804808125361071750369*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/1181/12', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [3.666491509252621, 5.090059937958428, 4.7414563916754435, 2.798675132415191, 0.2075051030745106, -1.6628843449079793, -1.8645476465558743, -0.5938445228578746, 0.9283046754781554, 1.4618794272143072, 0.8041386400036895, -0.11577444378814106, -0.26081378622733664, 0.37431737262950493, 0.7501247007001235, 0.022889780332295676, -1.2699653001462479, -1.5334020372256112, 0.15250972848578476, 2.709633193667744, 3.8246017798674026, 2.2934417245215655, -0.5216131064508602, -1.9435429486569802, -0.8433712856396407, 1.0180276324696995, 0.882820703254235, -1.7964320949769044, -4.505833993683414, -4.382204883746245, -1.5429571880571045, 0.8845555594782226, 0.27682803872666284, -2.418380132362315, -3.7216022747324273, -1.6547802132535545, 1.9606572836344691, 3.6514450188884364, 2.2596167190322904, -0.03159523057119592, -0.6418375383652891, 0.37016305725260096, 0.9251777515509079, 0.04122357049240481, -0.8957090173261215, -0.3340261758284813, 1.020375973401355, 1.108360187698789, -0.47573487550991345, -1.761541114203579, -1.211947380190109, -0.052958310543829844, -0.38546019254894925, -1.3682141942090245, 0.7668347128057643, 7.785789153309732, 15.700441624466903, 17.87191876379387, 12.153496232097039, 3.518482221815873, -1.2820705591607804, -0.6572143667053723, 1.4578614630266482, 1.39525263883219, -0.21094292976111734, -0.7572615301718979, -0.011602703561491033, -0.03975543185075851, -1.4269732263072847, -2.010427910978032, -0.2323925571740952, 2.0720975171566067, 1.9851287096379817, -0.2975492863970282, -1.699383204700365, -0.7435998815274294, 0.3825237105062913, -0.6602640990436526, -2.597050368779044, -2.3945434897606406, -0.04029466291310851, 1.2104873503692646, -0.16380576781036224, -1.3309428403751156, 0.6388194994281633, 3.7249068890125185, 3.1635857623364703, -1.5637682491180185, -5.153604842455049, -3.282880456273043, 1.5007548920933333, 3.2460061683782064, 0.6147661565493124, -1.8106481541612238, -0.388457694179842, 2.685896806332564, 3.103298249655571, 0.6491423053197594, -1.1603853466661587, -0.5754504808929004, 0.46753489562193495, 0.17564431127767308, -0.4190331757633914, -0.04404368212448834, 0.0877353871305171, -1.4466147303560402, -2.9980016496420556, -2.0219556309782223, 0.05976803837839063, -1.15100565133913, -6.246131859823877, -9.70357968326048, -6.849615190445361, -0.6096285497292215, 2.243799504566356, 0.34624272370915427, -1.005650320880234, 1.7146937478748179, 4.958595196534769, 3.713168441099522, -0.8746758834876414, -3.3694948732144345, -1.950035221784853, -0.09702138780287642, -0.38713143996258337, -0.9592714021848008, 0.19378699397343063, 1.1723559755801118, -0.5159742099224924, -3.085086165197181, -2.74062945321874, 0.2741464824535201, 1.868084367692619, 0.3867285604382547, -1.2076018774146073, -0.5389669656723519, 0.5640773386049016, -0.09309295454685237, -0.926250526982757, 0.3150444230936935, 1.776349652602358, 0.35846033655122495, -1.8365246694831565, 0.6632640097521635, 7.564783712071979, 10.894497117045224, 5.299344169922891, -3.85559041355492, -7.115702447013573, -3.080079662042708, 1.2250011464449524, 1.0004417040573956, -1.0482172525614428, -0.9965256244482411, 0.22835213691067546, 0.018558590307500858, -0.7944420848754818, -0.015967195846013256, 1.3166108138584127, 0.6969882110706198, -1.0103276549564006, -0.8697073913469191, 0.7001512743888987, 0.4012126302985953, -1.880643677960802, -2.360872880372321, -0.012393998481160002, 1.0542759238736246, -1.3398156552130158, -2.6452017213837635, 1.6293427192029513, 7.77930811233277, 8.354326933205353, 3.083638051180154, -0.9200464005173604, 0.11219017697480553, 2.106775131506681, 1.1378427181378954, -0.3399339017460508, 0.9188221453479569, 2.2475629442598595, -0.5518422857391289, -5.318207314104874, -6.116577936132803, -2.3536319202228544, 0.6448491597214457, 0.0872358315841574, -1.0301594541670327, -0.19096204373013634, 0.6472060306897527, -0.3791620416571174, -1.3328345039642298, -0.47323002378098034, 0.1813777723215448, -1.0752461991842557, -1.7569331676264668, 0.31537181017324944, 2.0713522311624035, 0.11991301429034074, -2.151474327836443, 0.8676665282642841, 6.6315664030520916, 6.373358477417548, -1.5351211899183599, -7.832380769767711, -5.246342002742197, 1.5857131044518489, 3.9649346061802904, 1.3622296214608707, -0.5020133879604721, 0.09963427592469196, -0.11705206450881583, -1.9444108452084403, -2.3243448227535835, -0.5426009823385235, 0.4893391736971063, -0.09458797770575753, 0.05874920928761358, 0.905723653173508, -0.8690006202240872, -5.126618068072411, -6.547829208944578, -2.7053351265058843, 1.535710429646092, 1.5110252630649288, -0.43133166822880836, -0.25372551932885123, 0.5337081367184634, -1.068602962772227, -2.402742460325878, 0.5652264263530198, 4.5037471261278625, 2.545674498925889, -4.000744937719033, -6.345223128208062, -1.5557577934526472, 3.1995153813231925, 2.324165137866653, -0.3097315364638568, 0.5708975759860058, 2.7842460604124724, 1.7645891163582932, -1.013117430726868, -1.2888467356879676, 0.16675148098589887, -0.3799023084073712, -2.4227771449598223, -2.47747454381129, -0.6512780558476757, 0.11987121554848243, -0.17211883667955752, 0.40765815530048766, 0.6106422017709171, -1.6313936690752038, -3.1631929164031267, 0.53834479643244, 6.073273643339399, 5.244572653056758, -1.5890697035553853, -4.390478008737868, 1.4446340226903773, 7.797107104707071, 6.471963950961748, 0.9829882317999205, -0.8398844671444697, 0.8394971155605044, 0.8162857628280193, -0.9888000711597952, -0.7980965915549212, 0.8365211313317303, 0.3617918812960541, -1.2703600444092582, -0.22333015026188935, 2.4245266059523773, 2.09188334000107, -0.8599358183744229, -1.583410058246269, 0.6136133087682362, 1.5247726787081493, 0.09963578056407496, -0.3054695725542959, 0.6506550420638983, -0.607249779760177, -3.80503652190918, -4.083870469805098, -0.9092221592627658, 0.4189669276678653, -1.3393565088474044, -0.6383492281442285, 4.025146451138124, 5.681573736313065, 0.8178677804443717, -3.002074626949865, 1.1062868585861805, 7.466032616890876, 6.553779478079553, -0.18920005631295406, -3.7744070944071657, -1.8358039184671162, 0.2309786356040064, -0.19115140786797474, -0.503351620746557, 0.178208788810124, -0.02301129830271543, -0.44369916525197034, 1.112044846978323, 2.8744575649055357, 1.5924334445196346, -0.7775451517901095, -0.09547815542026289, 1.915880420515947, 0.6460824387955502, -2.0562900103459993, -0.6286416879012902, 3.1752964493007143, 2.1944319989868486, -3.056265452528125, -4.081679445286134, 1.1515025683342268, 4.497145250580483, 1.5545183820236947, -1.4531497097487023, 0.6200716635462384, 3.353180831992046, 1.8525149026434204, -0.6850741475448164, -0.07645621653903091, 1.1349716119030728, -0.10854127431458206, -0.6245292413973436, 2.5563122208279894, 5.425929836706347, 3.6921666223941907, 0.4240600124780228, 0.239661180896667, 1.3995626906999046, 0.35495954212655223, -1.206182749365865, -0.4616671067307929, 0.6173396423128235, -0.27542684450916877, -0.8526897698616924, 0.3022949853084834, -0.1558634891461469, -2.3020567255778692, 1.223427596763599, 12.913998511540406, 21.578831652799273, 16.294320893067674, 3.003049779887296, -4.011814563667219, -2.0941857772041583, 0.2008699750971487, -0.6428797125093835, -0.16830487591489313, 2.5642632091755875, 2.9194189801029413, 0.2577560877883667, -0.8924350039434323, 0.4272894870717605, 0.7397698021486698, -0.28634322028800874, 0.1325012029734157, 1.1826006367588493, 0.022701248166914052, -1.5097480700339179, -0.13535755924291284, 1.2044967641855058, -2.0748599324040384, -6.56941764128374, -5.623672677207545, -1.1400114774377985, -0.20599692189839403, -2.3880597045455687, -1.6331008263719158, 1.2684228181289185, 0.21990196683990665, -3.5110580661271706, -2.714083369498436, 2.108067977779844, 3.1609283062807565, -0.27963126824082984, -0.660524489781016, 3.596132999841985, 5.259693241662054, 1.7361599933967207, -0.7031995806974889, 1.1777633141798602, 2.6282858031767593, 0.7732685227452735, -0.8049429464564, -0.07782534238039843, 0.1603465860606419, -0.8947797311411012, -0.675605255160943, 0.27766005208761985, -0.9958877700426201, -2.7989825053043473, -1.2530963628281695, 1.3412020433821508, 0.2731511486999478, -1.6408497030525475, 1.0291700282360012, 4.107492746419078, -0.45321671107940786, -8.464211132473597, -7.64941141321032, 2.2550789997368987, 8.322842220982015, 4.652695909755048, -0.595145957027543, -0.6959357860487331, 0.823668988855426, 0.14573369341515152, -0.4432763000102229, 0.35142434127481903, 0.019336978735114394, -0.9206939449452181, 0.9825493779464841, 4.019684772190949, 3.031188281776209, -0.6645233522977859, -1.0051982236726797, 1.7645327934170805, 2.010850055703648, -0.481992971632576, -1.0473865893211713, 0.20196003884188984, -0.2798738910589811, -0.9374017328169416, 1.334150352079524, 2.4938056252635343, -2.320478356949769, -7.732913839826004, -5.665057398881972, 0.3615961987572718, 1.5415976036777397, -0.12818757010454565, 3.6035675974670696, 10.477498302869106, 10.631960348722806, 3.8537050162143456, -0.6382358642145739, -0.017732479158417178, 0.14306360595160422, -1.734961543574085, -1.601525121522397, 0.5788629093561145, 0.843081334303911, -0.5215911302863686, -0.333378376058661, 0.49125636435559017, -0.3431444074144209, -0.9521179201763795, 0.0976069102361694, -0.37561615362133494, -2.6291933079861467, -0.48553630128875364, 7.024461379607678, 10.379623530929083, 4.610535614407217, -1.1489640895158293, 1.2085596641782501, 5.385222242658056, 3.069924968783117, -1.5670245696128222, -1.2485412753647387, 1.096450395798977, -0.059882443250878284, -1.6764703003897128, 0.461880387116392, 2.3802615011742323, -0.05113716298472892, -2.6170846104605894, -1.0798949774316409, 0.9456998925506017, -0.04691268176783038, -0.9192503414157814, 0.309741042400443, -0.13346960662372973, -3.163914705371075, -3.6699311396259153, -0.3349338445074226, 1.5661816529507182, 0.23217653269875474, -0.30075629358819067, 0.622806795958885, -0.24569510509934928, -1.4261516193491404, 0.5695243109068033, 1.632939294981751, -3.4758091205331016, -8.01609282915503, -1.9901382693161564, 8.927556497348114, 9.978410653589878, 0.7251808620168954, -5.271078936515716, -2.714913430218325, 0.47869150927088716, -0.22499411231570382, -0.6213952356501024, 0.9385612876013554, 1.016510568247951, -0.32916910929414106, -0.01810326764242232, 0.7793924028429248, -0.45566025124090476, -1.3550622211306822, 0.11926056071724439, 0.256536804994325, -2.7860417871334975, -3.873932264590412, -0.6733931447649202, 1.0770280378715544, -1.1775954840335903, -1.5373307042146969, 2.0174236908560634, 2.859975151771906, -0.4909004016764147, 0.01942596721997815, 6.201320339098664, 8.376137565955691, 2.4380857300696883, -2.8380412827843973, -1.6936353720886816, 0.3233264938555087, -0.6506038358958015, -0.428675772772273, 1.926504303955325, 1.070278893533909, -2.562257172118259, -1.7677635244983623, 3.707413373986846, 5.96457125111029, 2.8220887735210196, 0.10931384358907997, 0.17119923185544908, 0.04258499870274445, -0.42361037593100215, 0.5401438093176283, 0.7922085796221116, -1.258191956252588, -1.9038368665914012, 0.08564826322339837, -0.5755102069863328, -4.5008586982680745, -3.938085440895169, 2.0040901609691484, 2.488412649850679, -6.018175184652939, -11.345521674439563, -5.849067166962664, 0.9256811799641755, -0.15211604477541876, -3.3791705530916385, -1.542714469409676, 1.3588469902615703, 0.3327058914733897, -1.1906950435420731, -0.05800927710356456, 0.6310069292689987, -0.47456962534489294, -0.39043284308818343, 0.39318312762894736, -1.3151780090365852, -3.185864420339247, -1.1373404699894594, 1.497468085787852, -0.1660637616531547, -2.602501026975415, -0.9994395588920076, 0.7682843137620039, -1.5884444894490117, -3.322567735383015, -0.20808432643214744, 2.619366819887093, 1.1008905902950337, -0.27371390696263903, 0.0916162622482914, -4.006906965961861, -12.044214988636586, -13.05574666492153, -4.431100665689274, 1.885207204377461, -0.670185378910719, -3.778227762731326, -1.2103811316284694, 1.4132155568234488, -0.15574353202255936, -1.4926403410771178, -0.19938483295433945, 0.10266396983098797, -1.0042691293032209, -0.09890701956777517, 1.6115816175492486, 0.5672990669043161, -1.151438295507905, -0.23700190512972635, 0.8104619483361537, -0.23663685199514253, -0.32892758449990295, 0.684233801598644, -1.840575954174092, -5.196879101725866, -0.01957647258697531, 11.168340830972772, 13.378651365558149, 3.191028779899878, -5.062651804800657, -3.0021405514911255, 0.9417304628134169, -0.14305111211841665, -1.4616505432319038, 0.14450029232914258, 0.248763250630969, -1.8767839505583117, -1.5346669238801056, 0.6127420971912918, -0.03796239866974816, -1.6943215278649617, -0.2165386156281645, 1.13128337707866, -1.8308857971409536, -4.733521182733934, -2.7590750087624234, 0.24070715923945937, 0.10669699729317976, -0.18770886989228344, 1.2053062833377532, 0.797940238210711, -1.16595613362745, -0.11283694177671863, 2.217059645154851, 0.587882733671373, -1.1475531577841014, 3.803567812136695, 9.763393036078895, 6.959916546899328, 0.26601260587522146, 0.8600415880529019], 'positive_zeros': ['1.27677311834491742946526704366', '2.29952717455626483792885635509', '3.38675686497956495111020571057', '3.90160651441303020852984121992', '4.69328421774149383575258829921', '5.60544173759309549670009382553', '6.813787256523900539104200220642', '7.628210539671941127431132548757', '8.25341845628965914330886703837', '9.537577065080599726552722112206', '10.03814190171605560453255683473', '11.07823185997564961956887308153', '12.18179808780983555397132792387', '12.71550634366342545662452494724', '13.447655218535760424719587015363', '14.138426893551703040321385253011', '14.92038322791126836581933506209', '15.96893698698262392345008551749', '16.10454738285337278438420034987', '16.818448146599330220898976381020', '18.6188351522948059967170122746', '19.149495710082625294381734575143', '19.95600730134136324819347430466', '20.63017183634051122624401496095', '20.92291081925493182907634651821', '21.90270985783948540643709926966', '22.77437938476443464100922052478', '23.59263850005973428848722879513', '23.94325128055435914775565001560', '25.005284026346813777656281174731', '25.599200514412603709341344858393', '26.1863110164387021612269764796', '27.09604464422728229344166221569', '28.02233170144845610243711576975', '28.80588792432720134652380869263', '29.41365462484736093591681970072', '30.39029323757193214220951621903', '31.07708879260526194672275668097', '31.63100216676210175306142623581', '32.20980566720617271593344991481', '32.5347540304335342156538591851', '33.73415357147927762068085771134', '33.92269912962465301566801842745', '35.34886145811930842757297109432', '35.9786089581083819165460403348', '36.414734889772343496874438014201', '37.44038025387170190808572614871', '38.48841227979719076757115743621', '38.587165542887972336206103499184', '39.33828415799310663189042176975', '39.939728217638242775379461071519', '40.90959784435984604893338726040', '41.61752954898397420565901750812', '42.30427589722916841659987303481', '42.78961207364878226401090200614', '43.38726079341266099359319628058', '44.10305591745113289979228729042', '44.647872445213484890779636654177', '45.79776794975459244083831514781', '46.75364039846276192923032623704', '47.32667271426632220034218892012', '48.04874837666928419101410065258', '48.44350621490815539672024966475', '49.06573790025552398510558265845', '49.806503400909933612000505485932', '50.47887730420833074453502236802', '51.001052640446994929388967580929', '51.87651963140969627176660245395', '52.35957752601751259700089242502', '53.041908134102899407875378514035', '54.257877521526503231655244905717', '54.67367020726992335933708798652', '55.5009149316316435645880361470', '55.78823386508003489610827617033', '56.52505815244172239610244885782', '57.70304899151042286549071547335', '58.14219090537277436028234761339', '58.79319715222443816639480039726', '59.29562826984752013367940875592', '60.128367318432161278141979292775', '60.39586187579667700797529905547', '61.21456559472938185218584166152', '61.8865138549611185408086106519', '62.44975677258165577147748769474', '63.38505248879989459945370229539', '64.295295778575280199006976938042', '65.16485018218796158748320051498', '65.5875748818311859697332346156', '65.908636661375363090978552012037', '66.97402532139594104529846149030', '67.45594163061570108444288293656', '67.79201759846985650124734396712', '68.351534467724503199037623391578', '69.54593092063187277128189297049', '70.22459626698112179788907641133', '70.6894108174644635266348723441', '71.096547202164762950982894496327', '71.83660375362521275200826816225', '72.62619085265777493640314653706', '73.51575379281301344151906150863', '74.31512743596215382371723501113', '74.607143713686848189736850116851', '75.498104143916522455149946075686', '76.20115252698764016865422168555', '76.48883338127736933902582591896', '77.66765341050227808733755182118', '77.936629742841562254306315658904', '78.28709502845727487880263218973', '78.87071520022795909161177710412', '79.65885929957520261179518582412', '80.554432447809684318624342181408', '81.19335274947619763704759812789', '82.26659648323271325170071572740', '82.67019106830122346008901810969', '83.26269641367725184477221499820', '83.8906669100493203105119105723', '84.43634303365898295196111549986', '85.02609480599644003771758796969', '85.84440894067828927032532775350', '86.48310099472097988749442914830', '87.20937906010203084980115467741', '87.59813566897937052246817000460', '88.05046408283773761036084281180', '89.169110475404155560346232532843', '89.47397218979931039124479485399', '90.053621861064673618956050986232', '90.97963378941642195231707509243', '91.51206027458905962077421517039', '92.490966980670621386996725048044', '93.36590764639507155364850434185', '93.68348603383405651039730878989', '94.286631400497154670911147050153', '94.67788581518239927567964408214', '95.14104373285743567304604836135', '96.12093134478519825082652239461', '96.5757269020502575314342311448', '97.25201741570445263087861926170', '97.86202562638647093277411773042', '98.57219541095503335368481006087', '99.31556660411344820417479679347', '100.11438265318447583172002188802', '100.570849610044791070028517175718', '101.44500951675358759067851193107', '101.88841633673013868938483193905', '102.48118777827939601496112335240', '102.906774619189166914424276060646', '104.151930509234728790581674888990', '104.30417143940650944710270529825', '105.05486480777093284214070505307', '105.7177221378424981542055947998', '106.18691283141598748008690769212', '106.7970745856034021475264231379', '107.16268891146210260633696329229', '107.762279169110387588389052036965', '109.148934977425597181483147139884', '109.9259238053618031020759342939', '110.14392722185622908011746967142', '110.64820634801368225686985870902', '111.59429708092811597177449095801', '112.09872666219300790508771762041', '112.71215505034230304460023030065', '113.09175772981354178478917902598', '113.753375816292536835322915857900', '114.39269711689785372615746322716', '114.85728232610355254048798755422', '116.09186630368591783038070202605', '116.19833543249743316293985193518', '117.03456271462037736485755586029', '117.5189725686448923475703164882', '118.30067082179084463306251499238', '119.03603766163403929908660622936', '119.438498351090154103569705095516', '120.4633362637465307765085746246', '120.79725773632088216460245672493', '121.665537538690226074232057718521', '122.21161182397452837983654080303', '122.55734842877102824169751908735', '123.300862473539588158956707511870', '123.585759232582262299254882293194', '124.49962815188132293892846218941', '125.031459140679082260615550269281', '125.549803245304810640424553435970', '126.23265509280200552372172433563', '127.12130022859859250123139071037', '128.07003637488212764943721785452', '128.55055899228893248702146933058', '129.09956926476109538622063069694', '129.55854286433240086839979991155', '130.004935344586918925069315834907', '130.52342916683181611059721528400', '131.49724001056607114660839166028', '131.9952404977991679173248856945', '132.74920797918813072867987974624', '133.37122678084699491546032336135', '133.680339027483521510845401058873', '134.23123409929835631077982260389', '134.88732155487021311462422147513', '135.913613356437837264164489974893', '136.49093020973648548348574732690', '136.61688075703346562859433351875', '138.036745113284025968329104913378', '138.44154038039886651567445384420', '138.78040879485891902132004104585', '139.59835120112449179990856923722', '140.1826065164655426597211194805', '140.71823898657050314071526735143', '141.16688572784207997336288164645', '141.845276630109311946402704197678', '142.11968405325246894055432821597', '142.83771605540838335971004889102', '143.95821190167380968331071883929', '144.29727122549064409786798043343', '145.18333690663401115081259505177', '145.76301207100853985706316184958', '146.24252605636894703229834323245', '146.82982620282641947697026036469', '147.49566959872680748928384371571', '148.24863633403583742065704481055', '148.74166109599462312884736452671', '149.30288125109489119261582225764', '149.66834020422677144307074471138', '150.65506646450069406098987621854', '151.29773038621020209286785501828', '151.66331721484279506156146555618', '152.14404267408401980957486925016', '152.75082005234995712658781665241', '153.26642774554024280642665985325', '154.1170425528740784264559683882', '155.02327697337862677580188826853', '155.850296453259634366851627352927', '156.20221452122793425037743225355', '156.69939436898639017406103066185', '157.4072094197982961343434644425', '157.81730626120135277053475927360', '158.35738163688562220226559625381', '159.04087328991064597441387353859', '159.41349804031124760679571762817', '160.37356648916134720077978080030', '160.8029799090563584872715692053', '161.40001270278311893201870755999', '162.139285055781759621343067228796', '162.49859131850245565287358603348', '163.54499888594928749250773983348', '164.27106972034289989297367853628', '164.542324329683250924500333157947', '165.06105201216482593241929871467', '165.71617742733487554806140171131', '166.360960715053540282851760913855', '167.54253169354857141410808208086', '167.69925721610250983160400124382', '168.14374825255127915245339898040', '168.61699938500884553794756910549', '169.20565011354420758677759602512', '169.98442093711149729498524556619', '170.24529294359372351713402468818', '171.145356638021451192612259528764', '171.67672341528663990437445153311', '172.74284207941050154026940928642', '173.11294224409375114782841136359', '173.88077417415816738746601237503', '174.420320188772126865602990924969', '175.01120235393982796294836669641', '175.50089597570653314902569920758', '176.0453297532046174560278410680', '176.38372782724521628699465395623', '177.2891892137432003525650058719', '177.79649076355951067243399330591', '178.550104029468812057993117603307', '178.90549515325538675588866182324', '179.70267178071856005749281773039', '180.47991176496395758708310856493', '180.77356052372653759049462254368', '180.96502378764587053580895477882', '182.35226002572008437322596038872', '182.76833805362172291374140203272', '183.5358912622195208188363209401', '184.04294250123697223761988920943', '184.73430284736118578689361208534', '185.031500946805773608936849068512', '185.63992891084972887445432539673', '186.328788365880730710893488114591', '186.91744899101272399541273517470', '187.44319612037426283818870771455', '187.89223476994316295657258069896', '188.28080460357387639480947053676', '189.06309690518866561324220431203', '190.08704703658023064710317719288', '190.8229676020125164293971602410', '191.231766820643948393254830493454', '191.84963896476809547721786639888', '192.22978905795238863232833118312', '193.01510725964604855779615679006', '193.43180283171105999926651033573', '194.0893039040808048254752918216', '194.54154429836052750344041633180', '195.58202163189555278359483944716', '195.97010317483303495623818931619', '196.30553758485040528060743518200', '196.98979372778316763933254876983', '197.51269121688834267235586859066', '198.182499909960528290493392703711', '198.56180899477499766538479340992', '199.70941071981635530255675906321', '199.932316266483748094062152287019'], 'prelabel': '1-1181-1181.12-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 126.91607618245214, 'root_angle': 0.46255551133790496, 'root_number': '0.117364210479610486400802208666+0.993088939671818965164378530153*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.231277755669', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(1180)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '2.04953813552258723569053554597+0.198356454559828212019241062456*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.27677311834', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.29952717456', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.38675686498', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 126.91607618245214, 'bad_primes': [1181], 'central_character': '1181.12', 'conductor': 1181, 'conductor_radical': 1181, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1181/12'], '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': '1-1181-1181.12-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': '1-1181-1181.12-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 126.91607618245214, 'root_angle': 0.23127775566895248, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.27677311834', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_1181.12', 'Lhash_array': ['dirichlet_L_1181.12'], 'label': '1-1181-1181.12-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1181/12'}