-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_504.205', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-1.0, -1.4081532572346456e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 2.3405661600538683, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [7, [1]]], 'bad_primes': [2, 3, 7], 'central_character': '504.205', 'coeff_info': ['x^6 - 1', '0.500000000000000 + 0.866025403784439*I', '\\\\zeta_{6}'], 'conductor': 504, 'conductor_radical': 42, 'conjugate': 'dirichlet_L_504.445', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^3', 0, 0, 0, 0, 0, 'a^3', 0, 'a^5', 0, 0, 0, 'a^2', 0, 'a^7', 0, 0, 0, 'a^0', 0, 'a^0', 0, 0, 0, 'a^7', 0, 'a^4', 0, 0, 0, 0, 0, 'a^7', 0, 0, 0, 'a^2', 0, 'a^7', 0, 0, 0, 'a^2', 0, 0, 0, 0, 0, 'a^5', 0, 'a^0', 0, 0, 0, 'a^7', 0, 'a^5', 0, 0, 0, 'a^2', 0, 'a^7', 0, 0, 0, 'a^0', 0, 'a^2', 0, 0, 0, 0, 0, 'a^2', 0, 0, 0, 'a^7', 0, 'a^5', 0, 0, 0, 'a^4', 0, 0, 0, 0, 0, 'a^4', 0, 'a^4', 0, 0, 0], 'euler_factors': [[0], [0], [1, 'a^3'], [0], [1, 'a^3'], [1, 'a^5'], [1, 'a^2'], [1, 'a^7'], [1, 'a^0'], [1, 'a^7'], [1, 'a^4'], [1, 'a^7'], [1, 'a^2'], [1, 'a^7'], [1, 'a^2'], [1, 'a^5'], [1, 'a^7'], [1, 'a^5'], [1, 'a^7'], [1, 'a^0'], [1, 'a^2'], [1, 'a^2'], [1, 'a^7'], [1, 'a^4'], [1, 'a^4'], [1, 'a^3']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-504-504.205-r0-0-0', 'leading_term': '0.825994703681667887293313326434+0.417521646976553873510082730416*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/504/205', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.9255223261511203, 1.2151316913039594, 1.284662132239154, 0.6887825977753057, -0.6193078758591083, -2.1488632440309408, -3.10813637321216, -2.8919962289498287, -1.5431375087636279, 0.16123851878469667, 1.1518357483300936, 0.8080067766195882, -0.531983254616077, -1.7438345421404748, -1.7448288438208739, -0.38907353486402124, 1.3146219192323794, 1.9403085766163872, 0.8233096432569083, -1.2946380725960305, -2.7787889163389337, -2.434446868917326, -0.5431937880206661, 1.3538391799408809, 1.8130722369788141, 0.8001826911579215, -0.2798223290744847, 0.06214876228835309, 1.8895565501998486, 3.650898486245905, 3.591672874246859, 1.4756061203648125, -1.0801191638716854, -2.0750618773882232, -1.026996529421267, 0.5834489039436457, 0.8229208193488081, -0.717185624114306, -2.5094902090553033, -2.7196528190604363, -1.2073570239257754, 0.24150045911835188, -0.21413793842185147, -2.4284811304673894, -4.275859588769196, -3.8047220753151834, -1.2973427797929393, 0.9976954058753524, 1.2257096911621173, -0.1614404078027799, -1.0454445994823456, -0.13455372618136913, 1.4974573116991199, 1.6202691071563688, -0.5074692291235143, -3.084069460650923, -3.613514763342233, -1.6559345067455744, 0.6485607759116352, 0.9472600844987585, -0.72437717917369, -2.091557022810713, -1.3667566401501725, 0.6426150803748992, 1.5497057318852656, 0.337026991302224, -1.3102929501178062, -0.9742063513797481, 1.5077128295215938, 3.6504919738397654, 3.1166823871808873, 0.43843316087883394, -1.5966085421751337, -1.1930269477643418, 0.467393862543681, 0.8853794838739626, -0.5316815756316077, -1.7113387924405385, -0.6093962579292715, 2.006148320603367, 3.2578563024448624, 1.6165026759593586, -1.1420230220843077, -1.9881860442045345, -0.24027918434063048, 1.7280771919102187, 1.5374854490577818, -0.24588876750927333, -0.9853250595157288, 0.48468790711220083, 2.2576181124991512, 1.8328843649773368, -0.49395989005361435, -1.790142966292744, -0.14177809388563983, 2.826360044441601, 3.861952402937961, 2.058414428580139, -0.1691047086667085, -0.31326502803907713, 1.0355444556503528, 1.2040111286887072, -0.7503879703606631, -2.5792041833539114, -1.7900474154780235, 0.8709092919771588, 2.129624079832182, 0.32315197486468666, -2.421713515344539, -2.8813459843420315, -0.7993393145497929, 1.0039227846188103, 0.5327737709782893, -0.7697017544769957, -0.21292080460935076, 2.1909425920873242, 3.515849141836913, 1.8674626954530371, -0.8659206710068043, -1.331675637485635, 0.8876771118331216, 2.712610891847267, 1.647317114162334, -0.9793903810614304, -1.9518287966459302, -0.5470432002749622, 0.691746595576318, -0.21313043776333623, -1.6884148874462341, -0.776692311542477, 2.482678961900582, 4.654035557919828, 3.270670387550876, 0.07969016513836363, -1.30371688469112, -0.13401144341955498, 0.8182587461873305, -0.5355136656822752, -2.566631141004327, -2.3483800353913455, -0.023962509898988585, 1.2165042087134188, -0.3478061285265893, -2.3662646174243798, -1.572872124598593, 1.6101581712096265, 3.511139862836582, 2.150512188116432, -0.2055981086569084, -0.38786170876473536, 1.2836751782121654, 1.8087486240723791, 0.2036550514469592, -0.8766404728496063, 0.9223536036251818, 3.8594343625468097, 4.140150914920797, 1.1157184905775899, -1.735415020027319, -1.5140821103512958, 0.3457853067943141, 0.5193607845607198, -1.2638948716982732, -1.997470058325481, -0.11458243156670468, 1.937682650763722, 1.1981206560738396, -1.3394123562188773, -1.986693758341689, 0.3035825113263165, 2.28753936122581, 0.9867363203117513, -2.0735365581686773, -3.050134359958089, -1.1474358837747516, 0.6492187197449556, 0.3440742608576218, -0.08032871700189362, 2.0157491381155603, 5.353853107420958, 6.015385319269102, 2.9786585636603684, -0.2199277217474917, -0.30995308897482965, 1.3418112710059407, 1.1162797634068264, -1.377496846332947, -2.873998786641761, -1.5493195057930864, 0.18629842473391114, -0.5330986702740396, -2.4737539218422624, -2.0515744354250613, 1.09539619800097, 3.1712227508257786, 1.5655665397178982, -1.3642817400891525, -1.7075435295185881, 0.4620113416948478, 1.6008316546013903, 0.25259486596817776, -0.9123670213921626, 0.4069922803172761, 2.2218918232868816, 1.1709611146906305, -2.0739405698323856, -3.336900019936392, -0.9103456097034015, 1.9248371425517805, 1.6678271420961504, -0.475833557977545, -0.8119204712794412, 1.0817916185515026, 1.9366536478559906, 0.19588968127158626, -1.3495662402032549, 0.06129399825520093, 2.573914131185126, 2.261221473230476, -0.8779576768804933, -2.682872178490281, -0.8866831887820017, 1.6636938897527125, 1.4363924377621813, -0.589454980038485, -0.859024195134535, 0.9694639529507751, 1.5885041976640915, -0.3968453117375337, -1.8552554463025006, 0.13038904532924805, 3.4414591906398377, 3.7226925254724876, 0.7551963630011974, -1.3063568707852258, -0.1548503288718774, 1.5669488284714868, 0.8501832701031864, -0.8671261182859119, -0.27142841631732745, 2.131953262458322, 2.508417345428176, -0.1927220083239284, -2.221219855489973, -0.5788551934725851, 2.3643501539833407, 2.432688479400168, -0.09111551302435927, -1.1745825005396908, 0.5775611976534992, 1.9754660133957054, 0.6205225308070318, -1.207888870786945, -0.4581165277422111, 1.3737749119195488, 0.34144559597633384, -3.4958892377171034, -5.576788492199944, -3.412881380008524, -0.13615114920530574, 0.41402862207299307, -0.741065922696732, -0.09823475550159015, 2.2120669743588017, 2.627484688259127, 0.2832548369038402, -1.1056866409647352, 1.018811528131048, 3.8239895238776667, 3.3493254707582496, 0.6781551403849098, 0.21273767321550785, 2.754979529101999, 4.3481684051539995, 2.5752226900311577, 0.138619883050165, 0.1523939128432054, 1.0796379307582904, -0.3196471871505159, -2.9753271200931937, -2.621670148212293, 1.3531074657377031, 4.357092189322698, 3.163771580984185, 0.4026257105633297, 0.03733690411521626, 1.2592001718880854, 0.4889291206355255, -2.1903325567426966, -2.9706097382630645, -0.7275450653928951, 0.8508417516010722, -0.7998013164321569, -2.7648534290825126, -1.2152274523287487, 2.310670181871769, 3.111706046969826, 0.5662319394973536, -1.1698802438984937, 0.07441819256734807, 1.3612221812899552, 0.011424096022895562, -1.7520943069330486, -0.7295882200862662, 1.4025476992890107, 0.4060023843161873, -3.4741176388365176, -5.341689877284234, -2.990916742249007, -0.09649305542349836, -0.25584986329218196, -1.6632820297026991, -0.8575171179408512, 1.10247366445916, 0.48327021756996275, -2.4696432977277487, -3.497831741583921, -1.269527504748254, 0.2578918502770721, -1.7438553405524624, -4.199451718685028, -2.947058736412755, 0.6250407491234656, 1.8818522426143405, 0.23114688510860082, -0.5701437031749527, 0.8097495763715604, 1.102376896676686, -1.4758234732081807, -3.4324192840826324, -1.3701434104562495, 2.1895065250442647, 2.440372440325578, -0.263391411994181, -1.243699199751572, 0.8687518753811625, 2.269050967973348, 0.6304305398180431, -1.1344302848924608, -0.21381403493819276, 1.034457428215289, -0.8302280366581489, -3.9691557608046724, -3.718350980067343, -0.17103139370491843, 1.7237098149682408, -0.08209777595645057, -1.8114057175643643, -0.39440579141165244, 1.602505004523244, 0.7089519975827344, -1.4205578733677195, -1.0271180641695488, 1.0167102400043742, 0.5700284101217888, -2.4116158979766302, -3.1966934820126633, 0.10069840006480921, 3.179924251205984, 2.1951373650662402, -0.5076767997189905, -0.8009886268174735, 0.45495842188455504, -0.34512998012258567, -2.6251177399106664, -2.3280769298787316, 0.8238705616060285, 2.228463816288673, -0.16340927749740444, -2.3178424200521945, -0.6670952008852161, 2.0905435655977267, 1.5898138485058504, -1.0439660863006088, -1.442105546990124, 0.5198254838569775, 0.8911150387859113, -1.0971555521808618, -1.5532364475963902, 1.0520762045710006, 2.664230891190804, 0.25217642899936543, -2.786156617938164, -1.834354558286143, 1.6008387009233105, 2.5705904722551116, 0.6394347022160018, -0.25514811195428455, 0.8007323639951381, 0.24471653815015507, -3.0115893424640667, -4.745146699025861, -2.193975480504156, 1.0272523618197755, 0.6114413948811647, -1.5279642712099464, -0.7808470543933188, 2.2553290230323313, 2.9142898992222435, 0.4550458587449269, -0.8986899974898126, 0.6125599765681348, 1.5415153670136768, -0.1257547132025485, -0.9177341636991304, 2.053117749978581, 5.336251537229482, 4.129217347271204, -0.0012589482215045638, -1.6638913399521589, -0.12298262238785632, 0.49091668258354926, -1.0440244556419904, -1.1315545901431265, 1.6103063052504911, 3.2399968186569468, 1.1953395195247563, -0.9113493364160751, 0.8076298905216707, 3.832720104993017, 3.4004922724017477, 0.5080949378756866, 0.0715272382142832, 2.5338790073694804, 3.3794284391197564, 1.0545620006460417, -0.7179246443277916, -0.01106013863963351, -0.22871949895390095, -3.585046146518465, -6.195262408691814, -4.039203933966754, 0.1053837145156653, 0.870815595945371, -1.287810156419968, -1.6209830976259672, 0.5234751772212574, 1.0910159409919145, -0.955036506105136, -1.6755089794325044, 0.5308392581497656, 1.6492430200254617, -0.9275250887414641, -3.3613258779551805, -1.5628906262908668, 1.8400434490867175, 1.8733263318760631, -0.5718347733458504, -0.7535020389090973, 1.5552672396264544, 2.066240831348436, -0.08419152937566637, -0.9094047419288958, 0.8394721498639396, 0.9895049353554588, -2.570801199345103, -5.4443017934499505, -3.658462693384386, -0.2846119408504468, -0.279810323940512, -2.470868312015215, -2.3373002775166114, -0.15397948342612522, 0.0016173000321956185, -1.871266513691738, -1.531344025736879, 1.4948190230909726, 2.3824739311142964, -0.7307294264922914, -3.1530056227621777, -1.3754200379454928, 1.142148882994456, 0.11397918571845948, -2.3726528056198903, -2.0159001050743504, 0.03387474661736364, -0.27641545362524966, -2.1183548044604694, -1.1887549059620826, 2.097898278424995, 2.693351252815577, -0.3285768167066339, -1.8274204411537553, 0.7455749257747295, 3.0775257828505103, 1.47712019506319, -1.110359908896261, -0.7938255076431511, 0.5403405669216009, -0.5229071174290746, -1.9538537761118897, 0.2003095475337641, 3.9527582220897415, 3.813368857050061, -0.08377652200381548, -2.1345028938007746, -0.5804151807872384, 0.21532900964403967, -1.9006618005358797, -3.074890634541924, -0.7370922343025864, 1.5491168618654063, 0.5087990124863384, -1.0111338256157734, 0.39457469953654295, 1.8951867841498247, -0.812479870862837, -5.322026975317951, -5.752266687933766, -2.1645179098207645, 0.09455227299953751, -0.44664354479372287, 0.013708358041562394, 2.47375827846247, 2.9339577262484955, 0.15173182955220985, -1.2876927563480474, 1.1338350060763005, 3.078853227846988, 0.71651176106447, -2.5604578691471107, -1.994453238485537, 0.5143897446313805, 0.3056856580687015, -1.632598722113074, -0.9150757200417696, 1.8659210165729752, 2.2125982615210598, 0.17290780846059256, 0.3295451588320922, 3.0443424535614754, 3.1299222169593626, -1.030859256618244, -4.099243724911536, -2.4481899221351475, 0.24198243997920574, -0.06253036964138661, -1.1498836631772853, 0.1510890104936805, 1.344453058248288, -1.018711840607676, -4.092797539022618, -2.9690325685575423, 0.6748838826931818, 1.2486461793145147, -1.182341261110087, -1.4165975136177402, 1.3924853933051486, 2.4027530454444745, -0.009320857527637389, -1.498647483531357, 0.11528081595623178, 1.1324638957747295, -0.5215326940297578, -0.8681620280162798, 2.728723653825971, 5.807508121128884, 3.8268243207725394, -0.11475459003754337, -0.6062662748862001, 1.214786878230317, 0.7838444581236435, -1.2090834844512366, -0.6129423857605549, 1.792207525307329, 1.4384846522597607, -1.2794012718631627, -1.215059777012777, 2.150577736475722, 3.29283172333064, 0.21098112867621713, -2.088874428020876, -0.40004085565835684, 1.5101548847393709, 0.3025318023678836, -0.9840111325167005, 0.7933428937197016, 2.5880392069600977, 0.914699401914706, -1.1572817937237099, 0.699032885008829, 3.8452972555240805, 2.9029576439575253, -0.7931707104719776, -1.524286644254598, 0.9490262404562202, 1.6708069505593712, -0.2351782103379646, -0.601451430307674, 1.202360866114206, 0.8175728094919672, -2.4552825583133755, -3.4256267086137164, -0.12869638118478638, 2.2361672885843267, 0.16539022203507533, -2.2486602473895263, -0.8578904018189338, 1.4547129470703821, 0.7221920502630286, -0.7249113228962273, 0.8285663755593158, 2.953002891497615, 1.4857420600766038, -1.3114955062971374, -0.5363365035238699, 2.20385224130313, 1.3604612369500506, -2.554835759146461, -3.712654973346212, -1.1022300715071418, 0.2794009723285728, -1.2379494487677016, -1.686161704569705, 0.1074958173452602, -0.049983097171717866, -3.2591587565302396, -4.332291863462959, -0.756564382168166, 2.3745848520044266, 0.9182911798684442, -1.4982038228220427, -0.4922522466079031, 1.3941846950686116, 0.17691896568434276, -1.815936109201109, -0.5868425836250764, 1.606631429852626, 0.40116873661307184, -2.1747256260822416, -1.2140858678082291, 1.7304922245376158, 1.088519424013315, -2.5759951732425903, -3.3306542476961694, -0.2424628570705777, 1.4704441724104638, 0.006066611806459374, -0.7487074551873945, 0.24620523841636588, -1.1071521590093973], 'positive_zeros': ['1.117931979127501033151806049276', '2.780007424532864848546682014780', '3.63832414625329459249927871459', '4.75500982857319301848813797611', '5.75175001485831156495494532077', '6.9529324834232920650195273897', '8.01384694978710106020568697251', '8.42118154207769640692268674985', '9.85695561711862577031342626475', '10.810255923969549777334129830638', '11.44576521926785764368801363496', '12.73204774396025089363096501919', '13.07778466471778557280157038383', '14.52682685687533435993831242580', '15.27963897069174080533263402238', '15.96278485081679750965086096351', '16.81727238032137025095457744506', '18.01816864161809421163507279833', '18.634844824813402910159347767038', '19.58679069963466265500385660037', '20.36755676654061897452067894329', '21.0798932820559949812196007427', '22.23669326630852897652671135066', '23.03175921240794221890658319720', '23.655446137473973451270927784172', '24.45292660583071705238924448404', '25.487181213097093238283504123551', '26.281321577056012275987961725505', '27.14412427384629575480430004631', '27.738683213221553287277661942924', '28.68694470156498230853282015660', '29.39035702689071538564376120762', '30.59036985590661194325778307791', '31.02027120558647488677330116205', '31.777123505532633402703671090971', '32.71191832937638967926631297694', '33.47197860695313022595440539255', '34.48038949827694430988507359837', '35.11257486939845368157783039858', '35.659534344326420959073322371492', '36.76335259296772417131224852529', '37.395640814479670373729163471231', '38.31700251150973878615008630848', '39.15889085947394772111844752143', '39.64759235786605750962120544063', '40.39900260202596708044711625109', '41.57156573866716891711060838684', '42.21328669426413443830714402185', '42.73263934509479445451063520612', '43.75317585877338049582002113431', '44.329526994131795182401484260471', '45.16332262873613137664181258327', '46.21302207129403332471471611533', '46.64828591247401579238016455932', '47.53327571950279318382596080013', '48.01808682707776334967717009396', '49.16045075872546659441235087619', '49.93381269520395234114636975270', '50.42123116580053011259176043411', '51.263679174872635664805327793169', '52.022750595756983292671478831784', '52.77953674455115064074274003782', '53.53826730719047575498604800436', '54.535091616386914436181765498426', '55.12119264919681120680102641193', '55.344326509506783618375073308321', '56.84132623600921283629396016242', '57.24959515878896087866826190459', '57.96716327193718430585507232641', '59.00314785648225560321278468856', '59.27103472666211552156274426923', '60.213983855920110853782581613349', '61.09162502719932215124518410930', '61.81375377519917134842747280201', '62.54252029176670259789963153631', '63.06539972207079399955617672399', '63.86807427311015475726276709426', '64.77040835403360702918061020473', '65.549300158323614614918062906023', '66.0898109278168778299129487316', '66.9013949008190667283280825171', '67.49274527956488175171068468203', '68.35632193870673931499436036658', '69.15506183594890458039823628830', '69.90309789425982969401239548464', '70.473791237388568919594575459501', '71.20019965896900755350152548321', '71.8629608244420586852716462405', '72.88854607863795626307539710954', '73.45984788764921817992654439646', '74.19844260394202854485028969433', '74.726858838343114120385412620825', '75.60619657809894439569449768118', '76.30667334836406950849492636015', '77.17609897097268279632564874136', '77.73353263425708195895620604082', '78.5220018432971655684699146101', '79.13155280629222665786007910436', '79.7214605478214324269723367353', '80.9575724151147118534462956378', '81.3613222153229337746593477901', '81.89036299553544607044734514623', '82.84685344884386820352110747756', '83.333636363845572722722597849717', '84.516427891794535135001883012073', '84.62537267090761299194988729339', '85.972766386921838775775242210471', '86.20256545632827796476813156302', '86.836027554967089151909698697582', '87.71844184993754624572653934391', '88.83284658495369362859611230755', '89.05059390470825282049997093963', '89.75049723199358267961250198314', '90.71536842823585256589406055185', '91.14957211753568821054349486480', '91.980777855237905844395952316425', '92.876064557458800973254929789242', '93.42585264668794918216718774022', '94.064073795115585763415588004284', '94.78077758254234472119632444448', '95.35155350421051244846392738828', '96.583603973618197314035435721571', '96.81438531403595352048105099069', '97.623018997724092290658454689937', '98.1835942555818254590701868525', '99.24214310330870719166304125495', '99.46799889631233573214836658399', '100.565476611482236529882662837393', '101.290042861784030886759835031045', '101.720522517426313912648007073874', '102.34967580137755879735434498819', '103.23511340811295099637213403699', '104.03185349723227047463355420895', '104.582678034538153749847574934244', '105.39403593825792230402433606149', '105.97341551627246640754304759070', '106.476683030250752752307277638050', '107.515135627985429591452912701586', '108.11528409393983996723693336879', '108.79873391169083431285043809688', '109.46843475551302776587153918999', '110.148136184637096335811219616754', '110.693857586570325984951607165765', '111.55499252645661877489568203329', '112.4279483015898682654659541699', '112.99342432692715877022129181718', '113.382306412753064814052027496073', '114.29732972565391045580187116445', '114.98421491617350865844100146321', '115.69027836169093227628692292119', '116.43311152278412557400901631832', '117.10626355078611557692234486658', '117.65552849819356456272567937720', '118.33100694251783267115566593749', '119.08355937560129607564392293216', '119.851664647816713740591576575437', '120.74194887224652005262226335490', '121.03779692203806467093936672692', '121.59398934492809514729806463452', '122.68413511446586189216937599163', '123.207257949446081002568755030637', '123.8345383780782226256921848809', '124.74374160278614278411595593957', '125.21690072701202453616186693795', '125.91881775679238321871549965398', '126.38891287841019985080960178469', '127.49989171013131714616727171687', '128.14714170103750525906705663432', '128.55985301217731120986849720959', '129.21307151740719695121796716911', '130.12992327683692450432680589940', '130.5415664674636464983048392380', '131.64588454883432257873018213283', '131.859811068677655132887123270820', '132.943580463640914476447736953425', '133.44088167447303016298017491436', '133.70757439023888329027747791870', '134.989413701479824753310198734677', '135.45017148126585647519193454782', '136.176560691626847222737468579663', '136.74606229736396984093098327504', '137.4368650226738361178069976483', '138.04105624812855567678849394562', '138.87970210294034160309884783545', '139.608195963604679284026896998518', '140.11358694282960404974665535211', '140.92575609718289224241872926141', '141.431912286500404407036958821127', '141.98908368580384826621570889148', '143.17412639180996841570656412427', '143.38365541819340483206923401262', '144.404895187641422561835787144327', '144.687853649721595171075732522126', '145.478393448923481211287412702739', '146.190687270591083716293144280', '147.012808292141134396002855853492', '147.51343469369622658243533334267', '148.42968087326343716324138538967', '148.69521946995429735837249174399', '149.49053239354023995878320438160', '150.28164459731897690576197163155', '150.87026063352298254509578055390', '151.71489286086806499282184425372', '152.33615128347809622955558509857', '152.72711807869556212444524836699', '153.42115691679453352066745895315', '154.36832479865707482635077609063', '155.101439212237943183430497987707', '155.36804702309963150992201820647', '156.32291275439779472157530602259', '156.94873775282359365084359706013', '157.44749882630688638967856387236', '158.06727643645657208471490547693', '159.33304344764712695583399086988', '159.5224044505746837635272133033', '159.99769440104459023324156807590', '160.953241200625459893749879871673', '161.45150927161897262361543763298', '162.244408334628231066910952391283', '163.045103489058135875551729583968', '163.48612746741387809017945158655', '164.16595329587101527683023518084', '165.03670458360062047271526943675', '165.25254084248261249722825272854', '166.183251712443842692579556935156', '167.141367063281422902042732427179', '167.48666572322182756340850696719', '168.102261583471926301661676863932', '168.658712978063741934394023951441', '169.62099309086420243839638988149', '170.16724243985047071968100028165', '170.79488544757512968073522894542', '171.56147058337812986623907291405', '172.17079036153835188851588212540', '172.73249752941623002373815019909', '173.230713145148873700667731534846', '174.36222274558876843713574222176', '174.79188010503612382916449716757', '175.426306843540991830093331810613', '176.015622677109658320752507568819', '176.72512775993923693225142877974', '177.31332747088116817673366148746', '178.14268982190219080822808674091', '178.79537320644365131847918299319', '179.41985071233555826051654233926', '179.904189568066353102451413080551', '180.72573049640409015083072314866', '181.18432620234083211632978543108', '182.113365222731142743949409579', '182.70043068702752153721862537947', '183.39946419735760007986264808628', '183.864285380142427251152373844161', '184.46493658112051689315909269158', '185.32270234894985054249034635328', '185.95297500175573262090420470695', '186.6562507842550184413139492276', '187.30151785790553141783910717464', '187.7094286149503124346030618203', '188.58126580868996971530337029573', '189.12056134436477898499264364970', '189.801159011755478985154781149226', '190.77562247942911317909298471000', '191.03157529908795113969176571268', '191.85486990179552965740852103734', '192.18016897684685064086021478931', '193.17799028601434761896696509474', '193.84374953584702547097332594731', '194.43826796091565150015949815379', '195.02190685807835188570993931531', '195.69277744173495514595979438033', '196.292844588245545873722101664563', '196.99369677662031176347144796181', '197.598023083652263926302413260643', '198.46086006387927775920945247502', '199.06353261093937274433843380284', '199.59847342331913269411700976697', '199.86309787023096773607965247185'], 'prelabel': '1-504-504.205-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3405661600538683, 'root_angle': 0.2979507308317239, 'root_number': '0.592981461558381071312685918416+0.805216111517949094101307634942*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.148975365416', 'prec': 47}, 'spectral_label': 'r0-0', 'st_group': 'mu(6)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.853111266184336264389586476416+0.0987776635314158889448159027966*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.11793197913', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.78000742453', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.63832414625', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 2.3405661600538683, 'bad_primes': [2, 3, 7], 'central_character': '504.205', 'conductor': 504, 'conductor_radical': 42, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/504/205'], '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': '1-504-504.205-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': '1-504-504.205-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.3405661600538683, 'root_angle': 0.14897536541586195, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.11793197913', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_504.205', 'Lhash_array': ['dirichlet_L_504.205'], 'label': '1-504-504.205-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/504/205'}