-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_1960.163', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.14904226617617444, -0.9888308262251285], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.9555728057861407, 0.2947551744109042], 'algebraic': True, 'analytic_conductor': 9.102201733542822, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [7, [1]]], 'bad_primes': [2, 5, 7], 'central_character': '1960.163', 'coeff_info': ['x^84 - 1', '0.997203797181180 + 0.0747300935864243*I', '\\\\zeta_{84}'], 'conductor': 1960, 'conductor_radical': 70, 'conjugate': 'dirichlet_L_1960.1467', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^61', 0, 0, 0, 0, 0, 'a^38', 0, 'a^4', 0, 'a^123', 0, 0, 0, 'a^55', 0, 'a^14', 0, 0, 0, 'a^71', 0, 0, 0, 'a^15', 0, 'a^48', 0, 'a^70', 0, 'a^65', 0, 0, 0, 'a^125', 0, 'a^100', 0, 'a^12', 0, 'a^9', 0, 0, 0, 'a^53', 0, 0, 0, 'a^32', 0, 'a^43', 0, 0, 0, 'a^75', 0, 'a^58', 0, 'a^62', 0, 0, 0, 0, 0, 'a^7', 0, 'a^48', 0, 'a^78', 0, 'a^73', 0, 0, 0, 0, 0, 'a^56', 0, 'a^76', 0, 'a^45', 0, 0, 0, 'a^109', 0, 'a^38', 0, 0, 0, 'a^47', 0, 0, 0, 'a^63', 0, 'a^42', 0], 'euler_factors': [[0], [1, 'a^61'], [0], [0], [1, 'a^4'], [1, 'a^123'], [1, 'a^55'], [1, 'a^14'], [1, 'a^71'], [1, 'a^48'], [1, 'a^70'], [1, 'a^125'], [1, 'a^12'], [1, 'a^9'], [1, 'a^53'], [1, 'a^43'], [1, 'a^58'], [1, 'a^62'], [1, 'a^7'], [1, 'a^78'], [1, 'a^73'], [1, 'a^56'], [1, 'a^45'], [1, 'a^38'], [1, 'a^63'], [1, 'a^82']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1960-1960.163-r0-0-0', 'leading_term': '0.273492000746411274462797827540-0.900373540887634371556418811466*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/1960/163', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.9409943610898057, 0.11261093941376361, -0.9095199302588689, -1.5550453894484735, -1.1301047961628161, 0.12162625492245194, 0.9924325860243288, 0.44942619506127, -1.116804637720579, -1.9690144157819578, -0.6917767540559685, 2.0978913489882705, 3.9848532187873476, 3.075861408650749, 0.11650307563435289, -2.051907403591157, -1.4031617228227544, 1.1022759448162907, 2.6265922313376766, 1.683984879793025, -0.27810282645945583, -0.8498563360857811, 0.2786523606453272, 1.0764205302150591, 0.08981350373066994, -1.37005157980589, -0.885757860121262, 1.5880385442665577, 3.2291533284168126, 1.9261684286714464, -0.6380910323095991, -0.8015424722503798, 2.3314407606845355, 5.4296375325211255, 4.965764250103812, 1.6154239619771897, -0.7773643120084871, -0.2229686706525628, 1.2273678776283556, 0.9073586734852689, -0.551909463768931, -0.4673079260404156, 1.5234220598089139, 2.6762441363741134, 1.285128975404056, -0.5247347070091599, 0.08777319850225485, 2.0682324125532783, 1.5547537769129511, -2.3636282612235435, -5.619293352123443, -4.345435908560336, -0.1590174979197333, 2.076132643062174, 0.8316223839516457, -0.614535692513488, 0.42143615970093756, 2.1489066838794644, 1.6091488408250005, -0.41714458194854553, -0.754831420905689, 0.886584536746815, 1.4170163385887773, -0.3872541382846614, -1.5348312303786502, 0.330829991365713, 2.4514407622061225, 0.5752602277071143, -4.291948370632177, -6.608239022667936, -3.9708514724709514, -0.30050626075133263, 0.20827800414201647, -1.0509341587775471, -0.2126143289878538, 2.490142770451393, 3.3015325428996682, 1.2472393382031417, -0.4845713236839684, -0.14370213212361246, -0.2150280779143513, -2.524153195753408, -4.215014516985564, -2.1284220547717903, 1.3243434188096215, 1.1502647007482463, -2.3862780678813746, -3.7976259967675396, -0.7813152914841693, 2.242682431815613, 1.1181823879286847, -1.7979040332444978, -1.9049127797878869, 0.3548258034882211, 1.07012436513872, -0.1520003910560844, 0.010672663586739142, 2.1509240882975207, 2.8386840784845284, 0.9047210255900214, -0.09608497395438256, 1.797489834341397, 2.813500329115569, -0.4845724303393616, -4.700969558322795, -4.257385372365883, -0.20845977941736274, 1.3564262581815572, -1.1251584741426799, -2.818359613925412, -0.9012670201880106, 1.184986108773237, 0.23256261272282325, -1.414699280101283, -0.7013756392510516, 0.5135393477681561, -0.677598332902569, -2.3013659961724757, -0.9013454730734258, 1.6292271493650374, 0.7550389151352473, -2.4267314417108934, -2.275216760221462, 1.830227108102521, 3.8383213157247735, 0.7359686107147814, -2.6073260831567397, -1.577443090686541, 1.0601196517371374, 0.7185973061315005, -1.2624154429469128, -1.010359583020856, 0.5200826780373606, -0.15383431834285707, -1.9732424751729583, -1.2048839030516572, 1.163770989580728, 0.8366115764600067, -1.5270022059087998, -0.7666803873496402, 3.3763016382732896, 4.821226224581141, 1.2673120548219103, -1.5374153240716217, 0.7672128140071488, 4.1374498425615105, 3.3571345012468603, 0.428339929863097, -0.06528195762933037, 0.908898959361192, -0.10050167305104603, -1.6601595504381177, -0.2134603593817222, 2.551939748940686, 2.3370524655605696, 0.2146222999344368, 0.45879133901883384, 1.8072882925640896, -0.8871533515676404, -6.517288073265646, -7.878033211948818, -3.2211944354909456, 0.7591529629029461, -0.11415695884204508, -1.7095860123289262, -0.20758620928988256, 1.3502859366488578, -0.17009144504458124, -1.7357318105997388, -0.17111417479451957, 1.689853350361642, 0.6634076090069472, -0.6435471945591501, 0.5407601449749875, 0.9224726312375595, -2.5912426675777813, -5.551690403732321, -2.694071581944661, 2.345276408165664, 2.4774691255848174, -1.1655413228833824, -1.9449885254853094, 0.5268584684335597, 0.7894612467173117, -1.7814302300666012, -2.256247080694255, 0.20916063545139113, 1.208953969063357, -0.13663503494004203, -0.12495497349158213, 1.2478794272285736, -0.0760670202528872, -3.367280347374236, -3.124533108238363, 0.5684251887589712, 1.1748685369165313, -2.6245749173095345, -4.097326016841535, -0.3925230575225549, 2.3951540282571475, 0.2033626699595479, -2.30492860714236, -0.9523515147481895, 0.847879376884952, -0.3379518968710735, -1.4972623826037952, 0.030896866292152464, 1.0514480517061182, -0.5086624582011804, -0.779480577797872, 2.166332650612805, 3.4501823171567634, 0.45434488537633383, -1.3192158609594968, 1.894528831386936, 4.545489176744391, 1.4939984228448198, -2.5354994496346706, -1.3727854318554158, 2.0110261743362687, 1.8605543498302097, -0.1390932110188002, 0.3334779859035926, 1.4373033291504638, -0.1976234327661906, -1.8929271102211433, -0.31383815457766806, 1.409179753278053, -0.005097624885890126, -0.8541080670969305, 2.1555563720204542, 4.151916079353221, 0.5726090327953198, -3.4189586483181986, -1.4341605843265843, 2.7930187642563493, 2.388668249330582, -0.5991233768942751, -0.23260956757570253, 2.065602724695834, 1.444961407898818, -0.5738930384177634, -0.016585042214129733, 1.0796863144125564, -0.6222051341291174, -2.148360698825109, -0.22523317724117142, 1.2467858738184259, -1.4059403132303019, -3.572146071740178, -0.8759255000990319, 1.558918532539969, -1.8681221670309878, -6.307482434730864, -4.772245534777923, -0.29526763579417914, 0.4655949417828278, -1.124278499601015, -0.49511761237652213, 0.4841306248829252, -1.5019979400040613, -3.2587575375210975, -1.2768776592364826, 0.9730433278644994, 0.18398944101645845, -0.10061901222303615, 2.2716432710919574, 2.0385442446578694, -3.213876569428188, -6.3103915629059575, -2.3827903640759036, 2.2385119436772185, 1.3868451316542068, -0.7071099066738846, 1.0773607374844154, 3.1471453158587006, 1.48882313991059, -0.25923171063357786, 1.14263244187411, 2.01320870039982, 0.04959184922399146, -0.6896567283688312, 1.2775667119396095, 1.4229812716989512, -0.6858610597856171, 0.6678773462833069, 5.270428718956867, 5.275989154470591, -0.5619404737682631, -3.8802389995841895, -1.4971642443794078, 0.03859648249314862, -2.0767981452974045, -2.3813447531035856, 0.8010214408533632, 1.9635119454381993, -0.3210302244865445, -1.1888471889678534, 0.13618678716711036, -0.17316086080904075, -0.9659426045514783, 1.7709957306022082, 4.905157875909275, 2.73646693835891, -1.3654097379511314, -0.6194588831634443, 2.0721630468554117, -0.11776688043259112, -4.145795493400694, -2.673827456744412, 1.8943045495933244, 2.298909975974353, -0.2978736869006493, -0.45438885172860316, 0.43498995889930386, -1.2398020049629157, -2.6334080753894518, -0.8026801075334459, 0.30096783461099985, -1.7948125744522252, -2.1704919972003203, 1.1996169094542068, 2.3150061642311814, -0.6551552272508533, -0.5570580042101616, 4.764049195297664, 7.1240740533972176, 2.8336348300884486, -0.9426444810980097, -0.044433304064244485, 0.44117754397436953, -1.8428775864061246, -2.224891367528234, 0.12477239442523694, 0.447916379744654, -1.0662184637321108, 0.018003048806202213, 1.9713682793203604, 0.12160320647857369, -2.5258051545636775, -0.949258164424524, 0.6628902976441202, -3.293081162975436, -7.49999479662382, -4.7558073844781825, 0.40114816118476815, 0.3402412190926159, -2.055574952974887, -0.9089850782264026, 1.0333143126570106, -0.2812459301934055, -1.3550240926986377, 0.6460166135960832, 1.5360899062075348, -0.47909883595139113, -0.7526700044883597, 1.1999692971306966, 0.06499166783238779, -3.169753040599271, -1.8291530133149358, 2.377481535652995, 1.3277346088437831, -3.590756007005133, -3.562642442259425, 1.0719107066859512, 2.3596523939165808, 0.11815162060136786, 0.2567885775411617, 1.8373246576753581, 0.31514851804889055, -1.842648296835228, -0.6754979225801132, 0.4521061355226279, -1.5016457278752375, -2.260260077838807, 0.05381975131520717, -0.0451086691092933, -3.2321593928823718, -2.0764949147615366, 3.9947859593946937, 5.766410942632789, 1.031042980703687, -1.7933470780998644, 0.03315121672295859, 0.16866906318467959, -2.4566824041488466, -2.243936914279558, 0.35985140777883234, 0.09677699841236516, -1.6295008565291254, -0.44404328984754976, 1.0557853021127654, -0.45403869074618175, -0.9489545064474805, 1.6380206853594594, 0.9691227423216491, -4.858713985631664, -7.227047328753002, -2.475992054443083, 1.3294481740043627, 0.1613596909090088, 0.43063790596236484, 4.21358623254147, 4.835074798714457, 0.9955803582513962, -0.895076085502637, 0.21865008634859892, -0.11444725889742807, -0.8587519717882923, 1.2418000296105995, 2.4176444898640703, -0.801410906201985, -3.035972071120898, -0.6670694051531639, 0.12337591217188268, -3.611130078008014, -4.349620036553238, 0.822578789302067, 3.514443749699313, 0.11629578079355915, -1.9183696824667948, 0.540397805529135, 1.4631208665064555, -0.681459529076595, -0.9184001009225252, 0.34072291697660206, -1.0679563075643606, -2.579087606834287, -0.3094537774297417, 1.548994167633777, -0.5216584658206219, -1.1782312631675838, 2.107131547449327, 2.3251756710733056, -2.5447834465432515, -3.8494964979212636, 1.0313237906658037, 3.3115480281363174, -0.1466118358233712, -2.0476922454479034, -0.07822289932948387, 0.4171315720404062, -0.5746057139933325, 1.2528603787909613, 3.3882567223232303, 1.4772883455816779, -0.782116563789157, 0.3531620906004386, 0.6097828500955323, -1.7277434803389073, -0.5430465735386836, 4.285975884774898, 3.8748506883772285, -2.4952412484442044, -4.923483424668927, -1.3481474858331597, 0.12507155138138568, -1.762834221220934, -0.7906408918602611, 2.1630391998800746, 1.5390828262256697, -0.4870701218732776, 0.614230100114342, 1.7429809857517817, 0.14008561981517995, 0.20788893938398997, 2.815780616307363, 1.8701065552693734, -2.1549095314943147, -1.7718544005243335, 1.5743136681132186, -0.5273318987025509, -5.860593380513578, -5.182155685984804, -0.22680300762872369, 0.6410998675827074, -1.2925042089282832, -0.3613910312074247, 0.8020085855449613, -1.343749937665537, -2.408652828530347, 0.004017346453670285, 0.8042151554083985, -1.0596998384994922, -0.7847219104811018, 0.06197376860487358, -3.614000027207341, -7.131289012710626, -3.3747982327967874, 2.157305207638015, 1.2163332319188067, -1.5123582524837154, 0.9150465496884341, 3.634876019368861, 1.2504131102254505, -1.1374380305377034, 0.23049949587148413, 0.5070635116975418, -1.6989288745021807, -1.3845645689784578, 0.8518547007561812, 0.2945369568978107, -0.56193572801197, 1.9763104335616637, 2.6686800825257335, -1.9052221134188596, -4.0930196584828415, 0.11279795814612172, 2.3289428696613115, -1.4532380452151603, -3.2635556325779547, -0.1560886995152215, 0.5756740094339521, -2.374856719299393, -2.3495429256124307, 0.505728859893106, 0.7011799669338589, -0.24969463385943022, 1.081111776085895, 1.0222699560282205, -2.035572243284986, -2.0045588752933985, 1.8425191762267819, 2.165892840192529, -0.673441996200516, 1.1150287546720252, 5.427928886434881, 3.6146771962576905, -1.3861864914885875, -0.6907997804768218, 2.9315608311206933, 1.997803971816303, -0.7600696081787779, -0.41234816520721795, -0.18949595789178725, -1.861783021495154, -0.7343826879990798, 2.6435934758998103, 2.278800050663687, -0.1415775922324466, 0.8951343161702809, 1.918144360796661, -1.2804170841733191, -2.094918106549963, 3.773457924184275, 7.361259240288248, 2.972336414367413, -1.1343121783858807, 0.42242705024195637, 1.556802777971034, -0.15191166815770568, 0.49401421815686053, 2.769459724003564, 1.4714503916978663, -0.7938561900493233, 0.46825729435413505, 1.4525305886910802, -0.5339624809076347, -0.44310641528855516, 1.8543606101677312, -0.6094673830280276, -5.791298633437979, -4.332063475257651, 1.4828413070331354, 1.6887490356427444, -1.887840367176409, -1.0433789495877395, 1.7119038986836093, 0.5208422834915328, -0.7896070955853061, 1.487020020626668, 2.411114743488926, 0.1269588378700114, -0.30052969924222944, 0.6919662573435879, -1.494364503292721, -3.5617803527504304, -1.217935215963007, -0.34649671572774304, -4.834643425908062, -6.509668125477732, -1.4501664427130019, 1.198992616801481, -2.402026605421354, -3.9110182226178445, -0.8711330309793086, -0.22082656059117495, -2.043478316053779, -0.5793104335541942, 1.9427679379010834, 0.7824788823605446, -0.5637633315933457, 0.5971918669558884, -0.2615007702852996, -2.8849104248493176, -1.0533714094958957, 2.7331407736660367, 1.0398558069552197, -2.0626003732482014, 1.0280313343823753, 4.686504810941362, 1.313536305046373, -2.9762405477450726, -1.4346854961293207, 0.5002490362902209, -1.263721985894268, -1.5398275657136136, 0.6355855188510412, -0.12172652002575596, -2.409096515440372, -1.2622252715754687, 0.33607053222990896, -0.6149771711909077, 0.9782558420041852, 5.566959430020093, 4.848177045517971, -0.9093357068055072, -1.8559255066876124, 1.6349582302659005, 0.6444961738772815, -2.824531222589527, -0.813174189121481, 3.1228063562110595, 2.0236015882317155, -0.23463449093839744, 0.9146955326978607, 1.4285966450460759, -0.004241214945676227, 1.0317651880399397, 2.514668329488897, -0.5198642835847596, -3.531471307942924, -1.4479258854550734, 0.03229227218309677, -2.2613440732232593, -0.6982927657551038, 5.806186139764709, 6.905220752496057, 1.2346556419117964, -1.0682687518239202, 1.3609646669681061], 'positive_zeros': ['0.34902140649029950387241038627', '1.533596749236149255028073618592', '2.286086241905071093066647918184', '3.21002505176831909674063370117', '4.38688155533076055375375010789', '5.18130164948182987151349777375', '6.19866451362383279700920291979', '6.812582685137353184026413192968', '7.51682232096377901602708605956', '8.251948223176006964779294976860', '9.285366598428830977699170282858', '9.79448260976411990169611823033', '11.10345618771063830924337066670', '11.60529367141937536667325369803', '12.3729383733706978895893063482', '12.903053912083512908754236062293', '13.94023155767785472371837641950', '14.35999331605213649541900692156', '15.14474847117338792876074179456', '16.26277666007983393354424361123', '17.007403865523796120336447785852', '17.42933512848806363715724400516', '18.36601432071654617933633593923', '18.90932103085238401512639146871', '19.632530990921878296384189413792', '20.27553876118565000325755791341', '20.97894720609235106326687110365', '22.23194500120567935400148932402', '22.553520885078881001996142468335', '23.15288645211460602975027867602', '24.24090555650084254909168425467', '24.75648310962596039073119481149', '24.93062763303227154217391763464', '26.11248287740334360148741992695', '26.67665337874786197971245824071', '27.56060677761102867248597281367', '28.236398987145974660883930375852', '29.01157143986704113938411764125', '29.646872715424246316059383673652', '29.99779883434954863076000404578', '31.10286745591888353718045975463', '31.28591854605010093935164728071', '32.155828743014444978889745993696', '33.142840912996041104830645233112', '33.63652213852881438908046838414', '34.475657519566610956352273841785', '35.035016449494429914735352037918', '35.7594444476815135002463117823', '36.140964108289376483964246755262', '36.97127087421995221645575948676', '37.57495002332368847590696769186', '38.309676342767551613766196815784', '39.114790334613092084496551047541', '39.85322808186524745237375368773', '40.418134158037927995460111802633', '41.12085070456438507832164147103', '41.53642634076498857378317355994', '42.33506037259407494155947965000', '42.920319745307516567344448997907', '43.504763302633683208155588758949', '44.46929729012734560611374793391', '44.9379583331217229393089653361', '46.01446892956636942997546628436', '46.270990476788927204495093588949', '46.85908780011003296084692463560', '47.52252627269087359040767223815', '48.49883611753413847979341160528', '48.63504689524117457902999124511', '49.317121831032144434400924914897', '50.52532064098729958848255114050', '50.92198734995455197426129757930', '51.58934221154267039690524020082', '52.16544119228655852510313384063', '52.833316352791435460255452636183', '53.54592524172646363808902716925', '53.964915341645440949407472063012', '54.49090491806879658622386302609', '55.463874439191082448887033352348', '56.14796839004346684527812431466', '56.80763354840619324281642057300', '57.29558933878945556181993552092', '58.09919477491996374307575649730', '58.71783526172855533535072347242', '59.091268151765235003722382941227', '59.67978105091728794166036832220', '60.57400179100405892037608626425', '61.053934898518593446803783707541', '61.90212041428636490391086437791', '62.51788884867775232038054021217', '63.244927165481400675463795037917', '63.69715532098969135339953027017', '64.37036108296894976419305900585', '64.9169164698018962173496694994', '65.41810553222940671725650830490', '66.29007880341429182457812971971', '66.73318345832390967034281579294', '67.59323549261753064184164351250', '68.23929274567943569523488180679', '69.02783536868697181376943527856', '69.303771827209320020235795304327', '69.97567780340119191858444543717', '70.662882918377845721521069213054', '71.24926495804834659074991695379', '71.6882581230969467298613832179', '72.533656384600254616680586174630', '73.21892192879208406904732917129', '73.983412105039865832764882065277', '74.40556871960485518056420357243', '75.19699204593980301449789379740', '75.62811365934905196679025897573', '76.172214824433878970745332851660', '76.90044643218323303968778558660', '77.37643274564676018015590897857', '78.1947005342883226992399839067', '78.63411576588032544012304663161', '79.71829991752530561683032932204', '80.08829049362747485411636529888', '80.719612705378143146484740116621', '81.064893464342700144183710632185', '82.00985266932608575325428272248', '82.54112446318407462718412709656', '82.83320351003241387280325498043', '83.57954650568857466770242978337', '84.50432219075840103843858964567', '85.156504356331890048882361308290', '85.50540350407641922066314496805', '86.454826065134855154643260423055', '86.68468163811800615873109352671', '87.50707088220952496461580499132', '87.9419244240241166875970223860', '88.63548847508234744430921644688', '89.003990159141201321034500252650', '89.97176506496272396757075809552', '90.82616000164254438474174457900', '90.951500850555812648847584559742', '91.80112825079625278186693440536', '92.459732789343775671298007186766', '93.08675412221635618636723472837', '93.395473257482505942833423222883', '93.91241572877197079693199657261', '94.87123508297998496436223747728', '95.37162767061202612250634496671', '95.929357292313097087441435818914', '96.733781209242347104254629230059', '97.45585789760516051854509197397', '97.91987790882559951323683382633', '98.26209686000237416572228718912', '99.17962347211737014299543148154', '99.448746696387084065264297513367', '100.21160462571302319742532206388', '100.87153133036157145971532820060', '101.29443928749484002248635292719', '102.37379303272822470232163087939', '102.820232888852478657159704965573', '103.204074943007743868590306552742', '104.04403055703148713134503800290', '104.462552952401523042224794408256', '104.99773533041933401003577476986', '105.63600124090995600125068439580', '106.35315713762630997300627702066', '106.66108948160191684608153640807', '107.776293793344731725558842444680', '108.16450849718194528768802935667', '108.85756864190898050669536367396', '109.33503144851672547627247632804', '109.91900357956809712118024004665', '110.55623923223245524560899431075', '111.05605630712423186515047342676', '111.56868449591489092122726138660', '112.31234757056331161459528586707', '112.89715798704790900906302301451', '113.675034489270120920572582124677', '114.39770572454916035942497252526', '114.63743269061996171352444838924', '115.346705757639415527573534218512', '116.04188081014364750132613546584', '116.36203631382897505020422841808', '117.17973030650279693089407463537', '117.494350140296426074338729184616', '118.23990302995847851214104455550', '119.127659717370678385128803192722', '119.6825476532576591363671715863', '120.02462660263757443282355640476', '120.88234698383243291752172346591', '121.2653312517341369937723686052', '121.93493447824759446212101407149', '122.432718708509628741190424991232', '122.94241308725182271678371936742', '123.50222740571970642031716240703', '124.52315390808434825811300588114', '125.03090344484547095453194907865', '125.253326944060309185239064435290', '126.34101385638883242424720780359', '126.81355297272840303443398268694', '127.159849662941414360055732686711', '127.6692875181274650847090673162', '128.37678896872927071257880285979', '129.14165239633239850483030517168', '129.39228097359598826450880445101', '130.26804152888415174671641047728', '130.94619953518349244245079599412', '131.5053194828945103375137028168', '132.09137568409508580809133334989', '132.68775261506669689006102739479', '132.96961515641172809937162779530', '133.77997028889828675732530501932', '134.3152582969477231253000022853', '134.818354147239492144480892278156', '135.474172195720330499071650429778', '136.191039063803877199291530680339', '136.86371904995546998594811942025', '137.51214292686301935799955487731', '137.916062494039787069652418451762', '138.29104269331954234856588223855', '139.21541891044707068219532325235', '139.6262787538344347212915845418', '140.09064533505859588504662629613', '140.66347691940615789282333824847', '141.44525742804847636183544571331', '142.334704700409353388061729976350', '142.53026008001608546020363028849', '143.2013089341765266018295856641', '143.94837174653078435592838507422', '144.279465018512768831554708814775', '145.027353763602246298880447766368', '145.27792939988555804638859944969', '146.07640557450240027981173688158', '146.70890846462788944023847310121', '147.15519614684424709113659718534', '148.1444714264628335956728273982', '148.53372722433892301260142290548', '149.11603411310119238659094381318', '149.53239717806278843554074603758', '150.31201257459447298664860050648', '150.76642569060089401398693082635', '151.40629849047490827429232250588', '151.577680939463831964581667049767', '152.661617207288262052151474648638', '153.22797826446241840326645342431', '153.67868815891843599806462886292', '154.48599388030097228808003074367', '154.96243483978639163658445438642', '155.39336209961485309986000927100', '156.111270936057813103515544128937', '156.6142457100144379496864753819', '156.980076788908601280019833213832', '157.70088536032224833788638942375', '158.430484398810982659417267707195', '158.96410231829880217267056348707', '159.70312453961369323430650507462', '160.07269066159772430712594273901', '160.87224606050739863371777449060', '161.41140012676212604045466681104', '161.66904820663289480618357267117', '162.30293712213221293158106684281', '162.97768958041375903300590475038', '163.655454004030991768975676183516', '163.97594044463065027576901753396', '164.893025854272879350015850182096', '165.36697801067692913170985489608', '166.13426927161936476357119532879', '166.69634884887551686284029227201', '166.80869582085324354006783680240', '167.56591170262220138753844285362', '168.40311402805120548595001426030', '168.61164279457540310136572492578', '169.27250580442383125559306797762', '169.82652966585313645834505732962', '170.79784278044846952647197147176', '171.20108631562890938990100081543', '171.842553060988655828043826106586', '172.11489453349366039453833423639', '172.971833287242283806536962611044', '173.37143544526010999317885437510', '173.98557521703049697304037620617', '174.43188629130371519738283143518', '174.96306561692742732203214523630', '175.84519753263553765474428068323', '176.386462217766278233385459657478', '176.97150455329783601205989968327', '177.56649187327002778020162883041', '177.95839085392654028796726844091', '178.76933144080072980224983535983', '179.13263182302983021706984228600', '179.53351960057345635401330223946', '180.48878095341327595876468452678', '180.55427747716083258269139916510', '181.65082219248259625839688786127', '182.01365528199799628689837407670', '182.94702058269136125131123745850', '183.07108946430028769425477939148', '183.80616128843800595702503640563', '184.4871475388149550251382281394', '184.86226134351215094636845680415', '185.28074904519648565266953723633', '186.01086062251204920550018852724', '186.63880602301047303730180056034', '187.125235087328437874125514522698', '187.884208247162999298140167783', '188.59320862086332027307978929896', '188.884402619719312767566074268960', '189.583683787029327192731602635891', '189.98494593618434353359129136395', '190.80597615500014329717869363650', '191.08688583074209627226742854100', '191.47449930398510418670031216601', '192.445351212561347691449245269919', '192.972375542837381176390927938267', '193.48778162164085082347811328213', '194.11619004363709600146973997934', '194.92697167637158514994094591793', '195.14738409014861956961827416415', '195.935725542511259760252621971613', '196.065000073260132506616747199469', '196.83872680710619434783204015260', '197.68423644029306644785717629706', '197.82153095548510221469615743027', '198.47615745021619173679822107109', '199.45392860273729880360027743957', '199.839451638956455537450226458686'], 'prelabel': '1-1960-1960.163-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.102201733542822, 'root_angle': -0.40613130647174545, 'root_number': '-0.831055051598571335701898083152-0.556190166411179850521561920263*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.406131306472', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(84)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.819797228580779339583944712494-0.359540564229594226160091323328*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.34902140649', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.53359674924', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.28608624191', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 9.102201733542822, 'bad_primes': [2, 5, 7], 'central_character': '1960.163', 'conductor': 1960, 'conductor_radical': 70, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1960/163'], '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': '1-1960-1960.163-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': '1-1960-1960.163-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.102201733542822, 'root_angle': -0.40613130647174545, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.34902140649', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_1960.163', 'Lhash_array': ['dirichlet_L_1960.163'], 'factors': ['1-1960-1960.163-r0-0-0'], 'label': '1-1960-1960.163-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1960/163'}