-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_1045.339', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.4383711467890774, 0.898794046299167], 'a3': [0.374606593415912, 0.9271838545667874], 'a4': [-0.6156614753256583, -0.7880107536067219], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [-0.9975640502598242, -0.0697564737441253], 'a7': [0.9781476007338057, 0.20791169081775934], 'a8': [0.9781476007338057, -0.20791169081775934], 'a9': [-0.7193398003386512, 0.6946583704589973], 'algebraic': True, 'analytic_conductor': 4.852959597730739, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]], [19, [1]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.339', 'coeff_info': ['x^90 - 1', '0.997564050259824 + 0.0697564737441253*I', '\\\\zeta_{90}'], 'conductor': 1045, 'conductor_radical': 1045, 'conjugate': 'dirichlet_L_1045.709', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^29', 'a^17', 'a^58', 0, 'a^46', 'a^3', 'a^87', 'a^34', 0, 0, 'a^75', 'a^19', 'a^32', 0, 'a^26', 'a^11', 'a^63', 0, 0, 'a^20', 0, 'a^85', 'a^14', 0, 'a^48', 'a^51', 'a^61', 'a^88', 0, 'a^84', 'a^55', 0, 'a^40', 0, 'a^2', 'a^63', 0, 'a^36', 0, 'a^62', 'a^49', 'a^5', 0, 0, 'a^24', 'a^7', 'a^43', 'a^6', 0, 'a^28', 'a^77', 'a^49', 'a^80', 0, 'a^0', 0, 'a^27', 'a^38', 0, 'a^76', 'a^23', 'a^37', 'a^84', 0, 0, 'a^25', 'a^69', 'a^12', 0, 'a^86', 'a^31', 'a^53', 'a^2', 0, 0, 0, 'a^65', 'a^44', 0, 'a^68', 'a^1', 'a^21', 'a^78', 0, 'a^34', 'a^15', 0, 'a^10', 0, 'a^22', 'a^53', 'a^11', 'a^36', 0, 'a^72', 'a^29', 'a^35', 0, 0], 'euler_factors': [[1, 'a^29'], [1, 'a^17'], [0], [1, 'a^3'], [0], [1, 'a^19'], [1, 'a^11'], [0], [1, 'a^85'], [1, 'a^88'], [1, 'a^84'], [1, 'a^63'], [1, 'a^62'], [1, 'a^5'], [1, 'a^7'], [1, 'a^49'], [1, 'a^38'], [1, 'a^76'], [1, 'a^25'], [1, 'a^86'], [1, 'a^53'], [1, 'a^44'], [1, 'a^21'], [1, 'a^10'], [1, 'a^29'], [1, 'a^64']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1045-1045.339-r0-0-0', 'leading_term': '0.502054086393607998084155726832+1.43726041506151503423438871748*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/1045/339', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.52242431876508, 2.1148482797775316, 2.5147854669761593, 1.8900031110460154, 0.03286514907957716, -2.218224496977165, -3.366291489427661, -2.2984662188807867, 0.7124419700175969, 3.933992304074632, 5.312455492185552, 4.053836401187196, 1.3078635696975445, -0.7709485703389706, -0.8732211145878475, 0.3733362486580306, 1.1509583443715439, 0.3636628005985346, -1.1971161300990034, -1.6849109788687993, -0.22578467854042916, 2.0109014247078023, 2.9334297876702364, 1.7135009233865954, -0.34492151129548254, -1.2578265393842019, -0.526123883613812, 0.4675342948141432, 0.2880743604503055, -0.7150369696065216, -0.8771732094421995, 0.49984876223446983, 1.9595175650658132, 1.5720596546931918, -0.3576294146401315, -1.0958514543033444, 1.3891566393909083, 5.4119572696687195, 6.598598127102746, 2.440216174431429, -4.565722500595725, -9.002739376174869, -7.850481111664455, -3.232395015063625, 0.31109497414539244, 0.6602648793555006, -0.4572515910786461, -0.5256132540243917, 0.5287687189191637, 0.8982428000773716, -0.08516270704086511, -0.9110660320346124, -0.19694121498985068, 1.1447004884442977, 1.1726670166220798, -0.09405380045455376, -0.39935165427429264, 1.5645962667405724, 3.9036332395757656, 3.7366854302115504, 1.2279897545690928, -0.21725556954214034, 1.6396337353186836, 4.6062393954976315, 4.634974575362108, 1.14916276514819, -2.022224329458947, -1.5948893416476513, 0.8718570673762898, 1.192680132683222, -1.6521175417508362, -4.062601216650683, -2.7318018398275488, 0.8119977112879968, 2.2601798841730494, 0.2752342155115515, -1.9809869335003465, -1.4202909922171567, 0.8821067952033628, 1.6346386057658937, 0.11906092010555586, -1.1319712942037254, -0.3493446929879004, 1.006780104863304, 0.8321274702695469, -0.3024362665071684, -0.31220717721424235, 0.8016283136024694, 0.920670811059649, -0.41489430866163485, -0.7428428253087902, 1.2357242871408136, 2.2701932082241068, -1.8476285140040207, -9.63359700139336, -13.965007493080723, -10.205459647930931, -2.1180520597304504, 2.5763300420935917, 1.3177359897659824, -1.3960319916588784, -1.0332613471406769, 1.3127867317751671, 1.861035303991842, 0.1591050136430132, -0.8574170730836184, 0.11676407706256409, 1.015262551013518, 0.28368843470084776, -0.4475764588931275, 0.6035469931309968, 1.8394210084970648, 0.5176457734500586, -2.503296137079277, -3.379526812157279, -0.8699154480287095, 1.7074259225753656, 1.4150389626857227, -0.08843684176815701, 0.32853402159163714, 1.9235183526730677, 1.3621852726303707, -1.2500695584130397, -1.682887341519661, 1.791198266462505, 4.70767342120334, 2.318026225191254, -3.142488393412468, -5.058517213239596, -1.6178503319847803, 1.8716991082522045, 0.8665831369250737, -2.155327797082487, -2.024488835351966, 1.354601335804155, 3.437588470163034, 2.0893953983821305, 0.047066637703908155, -0.08791525622781071, 0.5170099673534646, 0.003259241042153824, -0.6444847263089688, 0.1604202731845886, 1.0983617416720988, 0.014296630098154378, -1.8356493571974273, -1.4229272585936033, 0.4948553819857034, -0.2711864163467869, -4.317058030984443, -6.28193811238935, -2.4250320400405916, 2.8345149304576696, 2.360936990634872, -3.460462993007541, -7.034492980380227, -4.199329771066075, 0.5642952050691563, 1.4571199963163166, -0.6788608726534104, -1.3204049798790722, 0.1384971183362071, 0.6028607683490084, -0.3932266331004166, 0.16904195753668988, 2.9128531274591527, 4.166775336892317, 1.8073151740340896, -1.009253831320455, -0.7460475090067556, 1.0948710460887143, 0.9753087648222745, -0.6651149256241637, -0.6480099451974457, 1.0230753317144654, 1.2027583294685327, -0.5304767923083225, -0.9106814283691644, 0.9942144120557775, 1.6574893425597514, -0.5282712811811227, -1.3866304553603468, 2.3114176941209084, 5.882716243075231, 2.3757729544856874, -6.378900392565403, -10.82571186694417, -6.462355358652625, 0.4695534966616749, 2.4053544629682957, 0.15523562448251133, -0.7832128165529966, 0.6812832221215374, 1.258994225698594, 0.08060343776212353, -0.3287468053235636, 0.5829855464914122, 0.36423526657435584, -1.4487755290318596, -2.092652443751191, -0.6431827312017735, 0.22570270544906845, -0.49232040567964735, 0.3060647993595353, 3.9622472147379533, 6.092030384788247, 2.951414818365743, -1.6645701649454046, -1.4746082045364082, 2.4926815254478125, 3.569174954426413, 0.28904125054664564, -1.4434380004136067, 1.5839806293753091, 4.519668563492612, 2.6151260240035015, -1.0815914219649918, -1.261945670570003, 0.8307627843902102, 0.2685137843273749, -2.645785498808703, -3.060830379053825, -0.20260807361516875, 1.3693916586198023, -0.2794506040877859, -1.4952340263305168, 0.1477036670666284, 1.730968502516962, 0.5362575390613892, -1.2090555966157255, -0.6825945132309916, 0.6226324134106082, 0.32654720591660835, -0.22467692690671986, 0.7352191865616415, 0.9356241959301761, -1.6892671881496697, -3.2872178739301745, 0.6781330534829815, 6.213273224694177, 4.651354644430358, -3.943313163523758, -9.288235661459924, -5.271668174833993, 1.6848878279061708, 2.930131292092314, -0.3820096898830489, -1.5840666325341424, 0.27244211616374336, 0.8109620117006898, -0.9178212403698992, -1.5370671432938776, -0.2159096061083679, 0.32596883183291814, -0.3384205467173487, 0.2696484046225323, 1.8284766415855447, 1.0326040299051436, -1.8001714429286442, -2.094941910866585, 1.1511238190177142, 3.0179531715040273, 0.8246700669606338, -1.4032147137824291, -0.24298489472941354, 1.3235814224777729, 0.25918328563081483, -0.016225826210841794, 4.169897479343151, 8.623415043821968, 6.984607745774926, 1.4773776954788058, -0.2952576153604222, 2.3481626252754295, 2.8608650684697947, -0.5659285892582875, -1.8638439746098874, 1.9849167044547789, 5.415117691265467, 3.5889858802629853, -0.00874033435543697, -0.21214256193448264, 1.601245439913368, 1.4343132799768206, -0.0689579539194893, -0.07975626954777602, 0.5649070572016945, -0.3240124650214363, -1.3682725808991754, -0.553027318716024, 0.04067379257489252, -1.8659803887537691, -3.324347294598791, -1.006523898352513, 1.6923178586346874, -0.00036097103303738606, -2.3614195720398943, 2.1821620790424605, 11.365896997881078, 14.098135200269999, 6.688261925427765, -1.6171645899303742, -2.6261978910639194, 0.32292724568439013, 0.7033982085975159, -0.6626936815794862, 0.0904936697840502, 1.637794508412035, 0.810755192665503, -0.6263958552714299, 0.4388874858275252, 1.968870554295127, 0.5985308398436191, -1.4795868483985024, -0.26641274137246734, 2.4226338261998284, 2.0805566596473555, -0.3329029110240969, -0.5690029841704793, 0.7680347212854466, -0.18355608949596963, -2.504079918283663, -1.9496810940268303, 0.7194592930142677, 1.0855835425508786, -0.04356354772416235, 1.9752558382578087, 5.454570342695852, 3.5572551699023576, -2.8996203104224643, -4.276392331315359, 2.751808274740178, 8.888369392604487, 6.27398271006502, -0.1950080795189178, -2.116169836298446, -0.18443923999668774, 0.0911111103047108, -1.1957416415967772, -0.487354089250493, 1.3217894688566696, 0.9736798168832217, -0.5459837323350337, -0.3869176539108734, 0.3537724551435303, -0.544507485380239, -1.284197467785408, 0.11739177300407908, 0.8317840254293868, -1.3939390622052312, -2.298978624504016, 1.900978322155173, 6.058602422103609, 3.472430759661896, -2.138846530709447, -2.0400690375637134, 2.9634311447231547, 4.295885653467562, 0.49485458032757196, -1.1963940712367955, 1.6142967935624983, 2.8178227241986034, -0.3335424640335961, -2.511388078552291, -0.5930642959863939, 1.1799481396738192, 0.02349837034050512, -0.5293493282913102, 1.3489855870674412, 1.5028985757495266, -1.9932399957237437, -4.318549213674666, -2.2399749795301034, 0.42553319758885955, 0.1759819658375716, -0.5189866098640042, 0.6658835446768814, 1.2495148921023922, -0.22926934879086874, -0.8127303609378922, 0.3472023329161295, -0.3450393291016299, -2.7066645358558876, -0.9577981051471453, 4.9323909413700795, 5.728456595570465, -2.5125919909163184, -9.908284552803435, -7.221103041386228, -0.11585565088511708, 0.8359564586453819, -3.231923942900893, -3.8199067643804807, -0.10528611321539896, 1.749406252024268, 0.43930300127314464, 0.0012794594295675772, 1.0204414899621008, 0.7387794853386256, -0.23810615858385478, 0.4446985621410192, 1.1324630089044896, -0.4689036039791843, -1.481503209402001, 1.1231496870234285, 3.683073790411616, 1.8312039078602147, -1.1448649799887316, -0.26187326984280207, 1.688153139427388, -0.2291708626567029, -2.945774965740653, -1.0273350842802897, 2.179976834417336, 0.09256294762418266, -4.396998825696118, -3.45091986946877, 1.632062505876568, 2.924168043002091, 0.06275158918931019, -0.3719709793794378, 1.9236731489906616, 0.8899759292379106, -3.2826457229312105, -3.687756304776351, 0.650781146991511, 3.053971041194417, 1.0299293754407528, -0.6805214107340571, 0.19980708143196185, 0.6164932348184385, -0.2323709378778786, 0.32694717847411925, 1.7246054500596357, 0.8156349542294721, -1.210608700261542, -0.9033096031644021, 0.16874900365922582, -1.130177713290142, -1.809936353830263, 1.5295418626770234, 3.0886825837675675, -4.060198403158589, -13.528705512703638, -12.785898611323452, -2.959573271123963, 2.6441825514656365, -0.7187644944775109, -4.266828034597234, -2.2498422865988648, 0.5915650597289044, 0.3827962648394142, 0.09792800301272558, 1.215098394560791, 0.5647598080676903, -1.8849880879545862, -2.0045636370973896, 0.1709319527114894, 0.4315426241682997, -0.919241793992361, 0.17882736897205226, 2.593778064495454, 1.6553089540362012, -1.2185911703996468, -0.6656124472909104, 2.24721551799515, 2.109408741922853, -0.2859057107648678, -0.08824037339360905, 1.4075449988877158, -0.20164379522486306, -2.2372180540388467, 0.3387836148279687, 3.3806721352083864, -0.36424024169793834, -6.814311040062352, -5.996296396747894, 0.5944940803173968, 2.3891934358972673, -2.1731198509269003, -4.364543637402166, -1.2512065285080982, 0.9232118400141882, -0.4049817560562502, -0.8173500205738613, 0.9665759651345308, 1.1816659892813994, -0.4888891070873345, -0.5900092106231578, 0.6008632726262588, 0.19565346016020746, -0.7430697071312795, -0.013652881429653083, 0.1100338742834266, -1.847006750259038, -1.2819370437568898, 3.844613500489688, 6.233235316101021, 0.862642939618824, -4.675015238038066, -2.397215345798452, 2.0357067900595056, -0.26685524360193225, -5.371174019429005, -4.256487973014511, 0.8563209918787135, 1.6316134061983727, -1.280924910832813, -1.4581078829232985, 0.639176316527037, 0.4539709585253716, -0.613077482763216, 0.9711522737837903, 2.5568674304292083, 0.7635000730638364, -0.8910224622869666, 1.148304206499355, 2.8390077940655187, 0.18515299558232445, -2.8781593083799186, -2.0025486013790537, -0.01947535518250665, -0.18293987469207612, -0.23812624702845692, 0.9500763089403726, 0.12801587305647333, -2.1896002660512615, -0.7132884717240668, 3.6106769632342854, 3.5545958893677536, -0.09340474941248404, 1.9210062414996165, 9.67343728161568, 11.332679764465915, 3.1450052050163206, -3.4997445590014054, -1.10434403397723, 2.9981108036431015, 1.448678167187957, -1.670253170676145, -1.1537529417538877, 0.2794171688038839, -0.35299039231743257, -0.622593747352881, 0.5803063721816086, 0.5181379856466908, -0.640943136351766, 0.019923303893614068, 0.9861750854119078, -1.0689698134404488, -3.224275179137916, -1.034319151816789, 2.1122348154011257, 1.1050999062987066, -0.42110663561271067, 2.709296348617581, 5.840325450180906, 2.890928666990539, -0.8842249528557079, 2.0607936238484794, 7.050550685137813, 5.511276619127148, 0.4109520102930734, -0.3805708409883037, 1.3841558748001523, -0.04268362121083737, -1.9590537300645179, 0.48698823773268607, 3.233070561722234, 0.8520606627661003, -2.5723365525911164, -1.2944054882943064, 1.4355467509482411, 0.5871431162957458, -1.2012315314579942, -0.22365343622828068, 0.9015597132423637, -0.18260913580526553, -0.5001804795953503, 1.1464977923592101, 1.342101791626603, -0.07567439059156347, 0.5971256142688388, 2.213908123696306, 0.6241870299288338, -1.5177924397868143, 0.25513441348094157, 0.009392135136851214, -10.21374437784543, -22.594369507578698, -21.67944992010208, -8.511126528456764, 1.1608317203116723, 1.1890948039633817, -0.2021228059827953, 1.4748199138233926, 1.7237978018652635, -0.46410705423563137, -0.5953429086675615, 1.2166683715690383, 0.9865592058091248, -0.34968853581927184, 0.2978863067421782, 0.8260569105220433, -1.1329633924228952, -2.1161724366411816, -0.04708338101482448, 0.502003776446608, -2.3232034542570905, -2.822297080415829, 1.1138838574747714, 3.2208726618471033, 0.9615968516783349, 0.040439326805170955, 2.1675230273974377, 1.8477131771603024, -1.0657046473514136, -0.310014255510534, 2.803554065275693, 0.19156865010644392, -6.480115058390245, -6.780388662043628, -0.24045433966409208, 2.941667677564218, 0.5314904840450636, 0.4391342843135747, 4.100616577044808, 4.508610363692367, 0.8328847547260828, -0.547410955275783, 1.1108248955838245, 0.8664216390885303, -1.1602928634528433, -1.108090626870672, 0.0870196379465579, -0.31405944035575245, -0.5869731521986212, 0.556462205811886, 0.15378193035601329, -1.7342666155794058, -0.6637769568208706], 'positive_zeros': ['1.25450694734100319043569341955', '2.435368526148383689798122092517', '3.91552118881095869085020982045', '4.602305122602681741471155944997', '5.38622804764235828824259611109', '6.28162019361679414151255709688', '7.44203556622502237490892281193', '8.26521930260823718904742224188', '8.84548445303114934498445828283', '9.59811012934944603821657557868', '10.568092923982257151530583863525', '11.122691151065915923809413400776', '12.29890228666652350886425437207', '13.70558620586709834417050222226', '14.24279196774416099301122357602', '14.8534004550579430442467554250', '15.60387819475640014614309722426', '16.29356240155346695799878677025', '17.16402605303620299553786981241', '17.59820588530243831527654636684', '18.9381976293806744724076023578', '19.15505962440752573157568681189', '20.40191747888186631557083536500', '21.134520127402839483032307180338', '21.72007047610908427560234674663', '22.73753934365930440241689065831', '23.46763106204564735346959770179', '24.25323512431628607769524541446', '25.01969684917822539644599115522', '25.69481445305572779795113910713', '26.46929911553105228875253682716', '26.97229564284837352939704300740', '27.72301909516537241903159589293', '28.27249782403097694071314963959', '28.96831694366238653086078119018', '30.410099410866762200908583564069', '31.068413064757374863836115539500', '31.70049686007718221837645340748', '32.52699185847966549687733813445', '33.09918874586315401036436311493', '33.82625734278021540172865767497', '34.25208802402951365961972895106', '35.05621763204433183588005843083', '36.02136337239296563807774782454', '36.84608603126249934796895102316', '37.10952776979978860946128607282', '37.97816648831471296784027482446', '38.61625294007156627380162588071', '39.5071295408383257944500488783', '40.4257531305967680892496750963', '41.02243300494696523333213622599', '41.76024885121207689100199813916', '42.82516343801989995795206114745', '43.16352577341004951059346369976', '43.75106140535422530687253781633', '44.33677384284148953532176185799', '45.002218739484263586498105197229', '45.842040268610534854005640537079', '46.218788090507002499527176302608', '47.31374048838314415054453244588', '47.95380197322675803209223114499', '49.014671003119141637902658850338', '49.59219700755770085570507581446', '50.28378378224626587355387473388', '50.8141980257222554333499462703', '51.2219902428515521526784806413', '52.35960772678393468768961948554', '52.932361457617134922790793081210', '53.617317910853060536506795751711', '54.18997546645998114284057613726', '54.908542379556939001626416197882', '55.48056312296194886788841804388', '56.18642200034464134455590137340', '56.71906138187041167942479288451', '57.59087185899762202965321199056', '58.722696696023822072274608504621', '59.3961601696301515001699044915', '59.87491852646412270513640070544', '60.646073505606869256998549490970', '61.06521771884149252743299309070', '61.63702134099081338791297138995', '62.643536823273064007405110906392', '62.94234674901965474344936607894', '63.39561842507555701303616723489', '64.554131741204653164185449174600', '65.12363278460409224597374731199', '65.96266543192825526720677140492', '66.439237733163018387571924431754', '67.39063036591757549332122256123', '67.98991190957162685546373160845', '68.470203477820620276084910649297', '69.39615633833538462285753357577', '69.96134904412872298428932604465', '70.60550515752905799313491064449', '71.32682454937995734773184049950', '72.01325545208654828538603102053', '72.61347342233576554360527693802', '72.93232712015381630198628638595', '73.57980790931047775533349607589', '74.340219890550996056101050825088', '75.18000560140856537568343550396', '76.159183130410610648990411894787', '76.83883569066906279483270072265', '77.4573742150731597491869454835', '77.97590090863700464589606292293', '78.80263283978791287164124098315', '79.216920076025258493123125722169', '79.6281519100133442381263478949', '80.428722653697173107812694550159', '81.15226316578850411776824050186', '81.9577341408571672269205115194', '82.53385936401143782712521455329', '83.17662703498190792751929793773', '83.44012175809793719984116707497', '84.81656138200785912232176919618', '85.05519243233322294620445999742', '85.889976260678515326251783210335', '86.433783797822723754866781945224', '87.49882184775214151814233103475', '87.851393979797655684111229846791', '88.73000111594853181113798239738', '89.09253493300541349295490424748', '89.616603988448471273311931409542', '90.46557805783094796797669791773', '90.64186048273987416901018083464', '91.650231252936248690671066177628', '92.187467210163603532237855817620', '92.72104088064036949432555865684', '93.98047570905137165132218540284', '94.6468151923331901709877409415', '95.14328766283681352459718230735', '95.60937053870906503328889121427', '96.3868325301775214774818982527', '96.804546020128082679846215786716', '97.57140955689942787281573739297', '98.15398384050522284655271558900', '99.01114119009536295345367393079', '99.49658089787991273434149974197', '99.97477852082914470123631776124', '100.84466603730741857642507673635', '101.52107197968033036087516703421', '101.61541656946100739286922200345', '102.67239927950054223409957556439', '103.33760799577372155146315735310', '104.36311214512207025685492409910', '105.03572550728212522250596543735', '105.336314690946082155347210026909', '106.013625775475150812608146604991', '106.74393948575581617111813029637', '107.30555959316603463282138805689', '107.68393565874063409431456243732', '108.41755390994091424237391571245', '108.90064629034495210426148353', '109.578765397501620802368896195827', '110.49060410820452755218991648815', '111.07193854591949318897017482092', '111.91543075453917942817342612080', '112.35008172687939149341955593360', '113.097933782103399547853246125564', '113.81757049574432792921460443889', '114.379413676732326704210496654744', '114.79976929913443239955814583565', '115.46980756852682045475107816253', '116.48444075828925493584037365788', '116.92045896562482281014912206071', '117.363604080953317339830975587755', '118.08287549214206690929973645854', '118.65330927009700934283114586259', '119.00958330183113437875581006162', '119.7442549329807004676301310722', '120.54744015178869416783936902716', '121.56970072880042948077522464874', '121.94942725875608419632174131604', '122.821407041268175411864772870', '123.55514163873371204289058655010', '123.749434073405450472326058160765', '124.5732010398807644306145701556', '124.88303217331549543217841099427', '125.55732182828093248795156535418', '126.15071321519721184490026723221', '127.03638800629900356721231166633', '127.531801682015140443832684719488', '128.10434772144398248676607112205', '128.82986803708731776102721359582', '129.38111378171174358558590392769', '130.20811839692455011824485942690', '130.945153947430862343117458822672', '131.30640011184281685593805589989', '131.945756916015445491325727907858', '132.76912756148619177025487434265', '133.56545969510413121101768611487', '134.01373310353234414078399516186', '134.59081984056343725837822696854', '134.92448250472868489846022725879', '135.7363311968597684980423409085', '136.45618463233433914057951010057', '136.66535474455832071689068383746', '137.38532003142867939125441124226', '137.99176691233965398935881628778', '139.16804333667547260799234689066', '139.64499329696014772071086261406', '140.526228869485336321388322959276', '141.10062027671373404160428152585', '141.19238011010894646020406870387', '141.94997348626711607262431559196', '142.7843319144849253171896126172', '143.218693662139026159971888691553', '143.72770839301263039137640437647', '144.53906475951740532751202923096', '145.07129247303530804493722792818', '145.88946050899840997418365459092', '146.26561082430346111541983975437', '146.85336643546759275688268995505', '147.475313731899634943000359463139', '148.1082480592102286444386753814', '149.03152555259490323247593620201', '149.557038997973960700972343351154', '150.4272802358011462109414130918', '150.8670602306333057115064018324', '151.404475755848453591530792098845', '152.092121910697724787468910090970', '152.64248723849363388903766978985', '153.173300186149658650025738991279', '153.753942279134795037678953758932', '154.08812716578472516073393539287', '154.783643317493422874286467345473', '155.66111371229814016306452558773', '156.38792799126905711162007796588', '156.85950255635932130960263007504', '157.75139500127410221931488754794', '158.299260808894113128814735094542', '158.954164304162317023601540891311', '159.46865052539339930877655995868', '159.868005169364930129893664821636', '160.71538064624846557875715323848', '161.12476242589362194383556569', '161.88944242103311041028167988919', '162.81912428486713192697289954679', '163.04476761037575586888413959599', '163.50685064734937531964676308330', '164.07927165294608897816088156364', '164.74012091224275666363453890720', '165.61246494111311685342116447669', '165.80773664149003659414324500222', '166.98222098794945607442090300209', '167.56532505602341364126462853866', '168.24514957297649610994284543685', '168.95671582649243635094267298599', '169.271449382314387950967766236063', '169.856503753844047453694365513926', '170.437324429001931427694808348528', '170.93346999898935648204151801277', '171.44876135066955328195358650511', '172.26973600996954163923998220872', '172.95574635741290828726702635417', '173.21425348317421764093026894949', '174.25445768828398237264411937568', '174.55618534468244281788715028307', '175.663368352437204267919204985896', '175.999585428876810687539830765903', '176.55779693236896016993090831000', '177.14837736997914795869631275911', '177.87394621416516090439494369888', '178.55974505682375302747988490382', '179.14071772975262371654792894947', '179.725565173087346716117149899836', '180.272566007127785575910415470311', '180.73637271605908574652716670611', '181.53725334728444415261891351324', '181.75668006470529559677766278002', '182.56492788434544628277129019989', '183.09549841045738204787443372923', '183.438099435552888835816843319', '184.93346431894837574611314203997', '185.49053170372386021397016196945', '185.696604004038570207577015668797', '186.49239791994379511133176343375', '186.97775943455713216194894126842', '187.69754569756092338143513945733', '188.05291652002591112666184866791', '188.60103283516008518625846734319', '189.381470760799924824216981947026', '189.76209481177321565882475053579', '190.5468264717961619991039734814', '191.40057901431523168682588877065', '191.55141923996313365115298546639', '192.37445659069013358186416296352', '192.84144497888699269868604764446', '193.44703322467021032682097401724', '194.38673521030688247531609769518', '195.07993642387068949504148013451', '195.24810104471457667686682576415', '196.33662479810226972445971765238', '196.68308232960599717311319564464', '197.31551552961812484680787975936', '198.083722738855341102812728823199', '198.32120335275428083862264432087', '198.91892548263881552713260067908', '199.40090924586953533571423344316'], 'prelabel': '1-1045-1045.339-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': 0.3930278655142947, 'root_number': '-0.782499838878226303951685028454+0.622650786681868630632957347958*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.393027865514', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(90)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.769279261131096562422044115250+0.767480286291831022096683110038*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.25450694734', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.43536852615', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.91552118881', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 4.852959597730739, 'bad_primes': [5, 11, 19], 'central_character': '1045.339', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1045/339'], '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': '1-1045-1045.339-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': '1-1045-1045.339-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': 0.3930278655142947, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.25450694734', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_1045.339', 'Lhash_array': ['dirichlet_L_1045.339'], 'factors': ['1-1045-1045.339-r0-0-0'], 'label': '1-1045-1045.339-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1045/339'}
Lfunction data - 1-1045-1045.339-r0-0-0