-
lfunc_lfunctions • Show schema
{'Lhash': 'dirichlet_L_79.30', 'a10': [-0.3546048870425356, -0.9350162426854148], 'a2': [-0.9199794436588242, 0.3919666098600751], 'a3': [0.6324453755953773, -0.7746049618276546], 'a4': [0.6927243535095994, -0.7212024473438146], 'a5': [-0.040265940109415144, 0.9991889981715696], 'a6': [-0.27821746391645263, 0.9605181116313724], 'a7': [-0.9870502626379128, -0.16041128085776024], 'a8': [-0.3546048870425356, 0.9350162426854148], 'a9': [-0.20002569377604443, -0.9797906520422677], 'algebraic': True, 'analytic_conductor': 8.489729058775376, 'analytic_normalization': 0, 'bad_lfactors': [[79, [1]]], 'bad_primes': [79], 'central_character': '79.30', 'coeff_info': ['x^78 - 1', '0.996757308134210 + 0.0804665687167259*I', '\\\\zeta_{78}'], 'conductor': 79, 'conductor_radical': 79, 'conjugate': 'dirichlet_L_79.29', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^34', 'a^67', 'a^68', 'a^20', 'a^23', 'a^41', 'a^24', 'a^56', 'a^54', 'a^32', 'a^57', 'a^16', 'a^75', 'a^9', 'a^58', 'a^3', 'a^12', 'a^38', 'a^10', 'a^30', 'a^66', 'a^26', 'a^13', 'a^40', 'a^50', 'a^45', 'a^31', 'a^35', 'a^43', 'a^8', 'a^14', 'a^21', 'a^37', 'a^61', 'a^46', 'a^25', 'a^72', 'a^5', 'a^44', 'a^33', 'a^64', 'a^7', 'a^22', 'a^76', 'a^60', 'a^53', 'a^47', 'a^4', 'a^74', 'a^70', 'a^6', 'a^11', 'a^1', 'a^52', 'a^65', 'a^27', 'a^69', 'a^49', 'a^77', 'a^51', 'a^42', 'a^19', 'a^48', 'a^36', 'a^55', 'a^18', 'a^71', 'a^15', 'a^17', 'a^63', 'a^2', 'a^62', 'a^59', 'a^29', 'a^28', 'a^73', 'a^39', 0, 'a^0', 'a^34', 'a^67', 'a^68', 'a^20', 'a^23', 'a^41', 'a^24', 'a^56', 'a^54', 'a^32', 'a^57', 'a^16', 'a^75', 'a^9', 'a^58', 'a^3', 'a^12', 'a^38', 'a^10', 'a^30'], 'euler_factors': [[1, 'a^34'], [1, 'a^67'], [1, 'a^20'], [1, 'a^41'], [1, 'a^32'], [1, 'a^16'], [1, 'a^3'], [1, 'a^38'], [1, 'a^26'], [1, 'a^35'], [1, 'a^8'], [1, 'a^25'], [1, 'a^33'], [1, 'a^7'], [1, 'a^53'], [1, 'a^11'], [1, 'a^49'], [1, 'a^51'], [1, 'a^18'], [1, 'a^63'], [1, 'a^62'], [0], [1, 'a^68'], [1, 'a^54'], [1, 'a^12'], [1, 'a^66']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-79-79.30-r1-0-0', 'leading_term': '0.224045291865431186828919053827+0.501898187015071963911268095725*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/79/30', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.5496344994049068, 1.0157764379982763, 1.34119020485305, 1.4521266598864073, 1.274553766665941, 0.7846072555688663, 0.057076898553247796, -0.7155657023328552, -1.2509543272602623, -1.2533355760556568, -0.5208988065350918, 0.9524363839178949, 2.925256297783025, 4.941674223869382, 6.455412045679682, 7.012324663318894, 6.425562481827981, 4.8677428784815024, 2.828365779711054, 0.9378647196595866, -0.27835150606875037, -0.6112333229537763, -0.24430414213516052, 0.35061359224981153, 0.6579623820880124, 0.3876749029249763, -0.3699691066394887, -1.194208555945718, -1.574952918456169, -1.2234909431885903, -0.2789721450986555, 0.7216695287100781, 1.119424164446821, 0.5198932254334233, -0.9258752720471175, -2.5271396879342323, -3.3785274531484215, -2.8516832576550266, -0.9846125163942987, 1.4689660681634968, 3.391468381901606, 3.8849348719667507, 2.7658401170948292, 0.6794153765440198, -1.2519325354147233, -2.0589571271335774, -1.471475320651395, -0.052855110045642174, 1.1643753465178421, 1.3247478650897961, 0.2803919191592636, -1.3268320605101054, -2.484781397456889, -2.463396141924904, -1.2765942118712654, 0.3484411536327507, 1.4706668571831594, 1.5620435502802121, 0.8299132150947868, 0.01053893667420278, -0.218000997481414, 0.22501686675508778, 0.7423851586797005, 0.5270889420378098, -0.7393671421526011, -2.479752244721669, -3.45813086856925, -2.568585335959419, 0.33575685570071756, 4.168168406132826, 7.142933176577411, 7.823761953485754, 6.011477815905976, 2.8701890606940963, 0.18958848113412163, -0.7316763833568505, 0.16495019023638405, 1.804202273020132, 2.823767479999959, 2.531398666996508, 1.2887578198074614, 0.08536375568326478, -0.32106980971700694, -0.005694882228031044, 0.25090333054530606, -0.30102695073412433, -1.6512984664846901, -2.9300955101964186, -3.058506051287184, -1.6498978510387454, 0.576141701133782, 2.2499024709693765, 2.3693966597723306, 1.0912599015853044, -0.3597615411024964, -0.6418839258222314, 0.6115074293644469, 2.4338685264074016, 3.23359679092421, 2.059039185381057, -0.5637633766629365, -2.9131472568679646, -3.3076823924008085, -1.369326261940833, 1.663289224973115, 3.8279452467436728, 3.859328715732042, 2.0495320013821883, -0.08972317556265268, -1.0520214757612167, -0.4519386599757581, 0.8353024485615507, 1.54982612977312, 1.1459374285222612, 0.1757735941510898, -0.3275429854942723, 0.12988870244834436, 1.022228978099197, 1.3105383954740462, 0.4772439298664887, -0.8838845855026025, -1.5340993290659288, -0.7746056213170122, 0.6977340889336249, 1.1209031102789129, -0.9454269834927866, -5.267943110321577, -9.797151353108667, -11.979582867771633, -10.568765652163231, -6.519218291778598, -2.249852771527852, 0.13085163917016118, 0.22166987563367363, -0.7176188213568652, -1.0964250169448924, -0.39807324952838974, 0.5358312040253798, 0.49559867547156294, -0.8120451993670292, -2.391034630910185, -2.833416309205386, -1.6235356176475624, 0.351700126734975, 1.575327531317578, 1.2540133183120736, 0.001636807079170027, -0.7870019211001713, -0.29044092005341904, 0.9379188991636752, 1.5056672640561393, 0.5801217371494332, -1.1804101061400492, -2.114981686157745, -1.1079170370019518, 1.2131894206217684, 2.81723927181373, 1.9774452647879734, -1.111216219831563, -4.283284477119729, -5.071361010610771, -2.7172127163281585, 1.1933444759987166, 4.017988391900945, 4.153698875320284, 2.157262596596799, 0.015034797163926117, -0.668772878877824, 0.09119181481048749, 1.0140212644807538, 0.9879142613055317, 0.1264325416046292, -0.5350795216317201, -0.28219369293457675, 0.44875344802337397, 0.5533676436974058, -0.4257026528898568, -1.551571205577879, -1.2164806923906974, 1.2376307247338283, 4.580203633104109, 6.494289438925282, 5.546377527690215, 2.5475977594265102, -0.03023698978220223, -0.1648300935598741, 1.9503125439770301, 4.101918228867087, 4.058817733913346, 1.561317092901485, -1.5047447251085133, -2.8617283843031807, -1.857171807528133, 0.11260525444368882, 1.0767304201348369, 0.3730970441358439, -0.8679772584530168, -1.023765999502575, 0.3023491893851859, 1.870697867229378, 2.079549135998366, 0.6052368049618136, -1.2556657330513787, -1.8726513674880156, -0.8738858906236481, 0.57130273730681, 1.034225108396439, 0.303560638468009, -0.5170777157021555, -0.4099968587880533, 0.17029561426582393, -0.47286132268247016, -3.4648666542067525, -7.7382868636303614, -10.403766106981315, -9.06252870259619, -4.03751058097712, 1.6100694141360936, 4.442813926029057, 3.3399116336655803, 0.14922666792369385, -2.1764089132693165, -2.136089467201136, -0.6018990154755722, 0.5202023717937005, 0.3361129963386046, -0.351495464784712, -0.22809190738935692, 0.9221287387174991, 1.9635515938984944, 1.742530673066565, 0.482842457175501, -0.3541491551677248, 0.3409093760770795, 2.003687822451015, 2.8579071567717884, 1.7909736029720755, -0.31605256820794103, -1.3161720287659688, 0.021637632354308954, 2.5878253067066495, 3.834189249598103, 2.2356541783751895, -1.1174348630552238, -3.451812237340837, -2.9190908248998517, -0.3161543077903084, 1.7908881954911833, 1.6523154251952783, 0.029040862333123363, -0.6886898040229329, 0.9934976380875813, 4.083021401320915, 6.032668786565958, 5.20646145996238, 2.378378516570903, -0.16498141360192242, -0.8687723635798753, -0.16481097373472703, 0.4142842469644877, 0.10068279195603667, -0.3711558044533524, 0.1177676685605217, 1.5018838736791977, 2.4192621165365162, 1.7755184021198254, 0.1996738832565446, -0.4194949326183846, 0.9639197045658919, 3.0572142741915553, 3.179359988809009, -0.027924191839637815, -4.837701457000832, -7.608685740917461, -5.983595040276142, -1.0800850513174227, 3.4762794310864744, 4.753973432715354, 2.8731022669109607, 0.37907501213452727, -0.48548558316266194, 0.24651236758118722, 0.8760472889152525, 0.2451683595818942, -1.004866629363566, -1.4091433272716842, -0.5971413522277441, 0.1513340493780707, -0.6074505308705241, -2.661471907331027, -4.141168918930386, -3.459715499412445, -1.0864323303721528, 0.8592467305612179, 0.8226756465502794, -0.575398532769805, -1.3311322029377772, -0.39043789746443036, 1.1104177647326985, 1.1763055054321945, -0.5527628398560475, -1.9903913492822998, -0.6090302155890205, 3.708893363055349, 8.056527057848918, 8.998595839452102, 5.784010239029807, 1.0411525020960917, -1.7397968925072933, -1.3688643517717811, 0.36538970601918364, 0.951660281785134, -0.2117951073938332, -1.5326304440436402, -1.3095510392286536, 0.3135168330716831, 1.655158820904458, 1.5127414760333013, 0.4469209655290873, -0.1042899792756673, 0.3088786819573795, 0.6429618728526016, -0.12519166480024216, -1.3401716501583953, -1.0802466363665553, 1.5346284946762117, 4.736886763014536, 5.345794864046741, 1.9160898807728965, -3.453892581651463, -6.770272469807821, -5.789521364322786, -2.013240773542356, 0.9771652607576349, 1.067343517086766, -0.6269429537990208, -1.4298061593849531, -0.17632229763136814, 1.690037226627916, 2.009190165301474, 0.4630548571323728, -1.124703653044985, -0.981698806681067, 0.5413235608911001, 1.4130846368851486, 0.3177286050180263, -1.8011049744478584, -2.819847846878907, -1.8429765729864855, -0.12515000711854463, 0.5235091418217466, -0.09744066258982811, -0.4510038062104501, 0.6735695020719794, 2.4338079467989653, 2.760655143688805, 0.9128390754173725, -1.292805098012782, -1.2940083781701752, 1.1754361336174828, 3.3095588565804204, 1.9229432955649923, -3.0574313039517196, -8.084196113579933, -9.204559127026943, -5.7724341811048046, -0.883357316693673, 1.7693079519503307, 1.232226429662534, -0.4942072291771224, -1.1269329126559224, -0.4365791244307805, 0.166478419762819, -0.1725401292544325, -0.6710085737202791, -0.1849287771518711, 0.9641640246269112, 1.1111887775453095, -0.6690312657439741, -3.0926911322657213, -3.8269293696874493, -2.1320359318038173, 0.13310588454475147, 0.5266345716468461, -1.1183127386826726, -2.3565365813082915, -0.908384425969634, 2.507774094584416, 4.61075183007005, 2.9791067254344217, -1.2585419078640996, -4.4857213039468045, -4.293991016422409, -1.7755708975683961, 0.010810682317439894, -0.47121182487059454, -1.7513362917738768, -1.3984628051619936, 0.9456700554525657, 3.099228203590317, 2.887374583090595, 0.6429167385506782, -1.235427541360202, -1.0385488142145913, 0.468126382045443, 1.2188977507823848, 0.3932523361284271, -0.7826024178039286, -0.8095368623459166, 0.11618865909499423, 0.48834447364337885, -0.29362371747317106, -0.8628974907779197, 0.36897747311799545, 2.6382098018541864, 2.840224214003881, -1.2720485533013641, -8.052719306064795, -12.760131264412454, -11.821139924767248, -6.241052695865173, -0.5485323114385525, 1.5968029780106452, 0.5019921575297834, -0.7728635135689429, -0.15543716099184007, 1.4732166525502681, 1.9571448975001706, 0.7560309875873975, -0.5034308103381087, -0.2401598841890464, 1.0683314610997434, 1.6008058495430748, 0.6180335746867222, -0.5781116150216485, -0.4235760424524742, 0.6707632213636616, 0.6007157827687619, -1.7769084737779153, -4.866265552671338, -5.815421226002795, -3.704515358391139, -0.6532070381446209, 0.5941528131319489, -0.18491450813868918, -0.5947359709282842, 1.2371767462738714, 4.052175331859822, 4.662111665392028, 1.7281333138912667, -2.3180572508063424, -3.639267951859986, -1.1063767923220258, 2.481075315860857, 3.441238867834617, 1.0624675471393406, -1.9842353336733716, -2.85347646943668, -1.4854530158130104, -0.08243744039198839, -0.16343856876657523, -0.9435029316771707, -0.792127684106582, 0.41662978944953877, 1.1850026491652492, 0.5441382079856794, -0.5080878410152143, -0.3197467681094884, 1.0236645892382, 1.525484793098165, -0.11788111891077596, -2.336530038002613, -2.019699538134871, 1.7588242159159835, 6.007252220347648, 6.536854648838382, 2.439689397782951, -2.6919684002413877, -4.340274732963824, -1.581354710396289, 2.3366597567931033, 3.734127912383128, 2.1720463126496634, 0.12636608264517113, -0.3868295720550078, 0.07135299309730403, -0.18991902598903793, -1.261532945839077, -1.3347854805608321, 0.7896354373245652, 3.7282759377912, 4.788523020941319, 3.050099295352683, 0.44505006934343017, -0.5285952194079957, 0.3648938747499725, 1.1889661582414468, 0.5738121015773858, -0.5218196359220327, -0.33368505402656645, 0.9424116591957754, 0.9671787361704999, -1.7528820567357615, -5.388533063996575, -6.283714040560487, -3.1055676865439397, 1.218207895215023, 2.376326266773218, -0.6656562069811548, -4.522639906798428, -5.111683425936201, -2.003856899118821, 1.446469273725027, 2.054344616313894, 0.104261804163736, -1.588565395483603, -1.2415051388299063, 0.1594027829265846, 0.6908300095883397, 0.1083403228844369, -0.16647573009408784, 0.6480568165633046, 1.4716013231920684, 0.9760405539709698, -0.23196224835417653, -0.09030842778108597, 2.078510049346099, 4.100300450696459, 3.202687056059562, -0.4246571932291117, -3.2596700997197896, -2.178243867843921, 1.8957368156604106, 4.828997717490763, 3.8075046148270677, 0.3231904244059579, -1.8193558411377257, -0.9903098600286075, 0.6492529624971716, 0.14923554813757275, -2.4737739446822644, -4.328652994370474, -3.3007198696786397, -0.6246576495301583, 0.7350060000549312, -0.29277380197642633, -1.8170142770466955, -1.6277906958651036, -0.013704604786468799, 0.8139903099438753, -0.23952712226011233, -1.7111603071112476, -1.5751942181795227, 0.047309750527615234, 1.0855627453864636, 0.33000137330241686, -0.9579787620880632, -0.8618881959832615, 0.3995720933698302, 0.6764893082194815, -0.8429165395768525, -1.604458885994308, 1.8619426509238166, 9.395963742625163, 16.12074382157373, 16.750044972375655, 10.847994135192419, 3.2082852535051094, -1.022942670458731, -0.9909023150476824, 0.3046709809368077, 0.2506768815983172, -0.6912664617695037, -0.5993617689450725, 0.7958694697960322, 1.7501270619340359, 1.064644886913936, -0.1977027280366681, -0.25769053961142135, 0.754918899241751, 0.8350537833044647, -1.0814502986629364, -3.3172157455899054, -3.3146683271671717, -0.9329244659218829, 1.1848876410440206, 0.8926059012231387, -0.6584138890412279, -0.45649541239799635, 2.3245335990732237, 4.851878950322277, 3.870420273018408, -0.20167136317361103, -3.4794968704741875, -3.053442831482173, -0.3017913612053982, 0.956551481869334, -0.8639326996711368, -3.3809772720749756, -3.451861342250425, -1.1644958929518234, 0.3663738804819899, -1.0225248783041856, -3.8824702510402505, -5.028804935327386, -3.379396193885169, -0.9311037467117336, 0.018004353314620972, -0.46478918664178503, -0.7036877269428768, -0.10586885130453962, 0.1581013162124084, -0.6638609709000608, -1.2445130918730325, 0.18146492204833659, 2.86448034001293, 3.618011541514772, 0.5782339339369592, -3.880874451152636, -5.2191334257334825, -1.8835057527831618, 2.57569088370568, 3.270356345098749, -0.5917452311107, -4.947685364337908, -5.579117152885629, -2.6146057111369654, 0.2799042281609605, 0.5194499873572389, -0.8094238254768709, -1.1308215903873289, 0.06681835732922861, 0.9882679074379704, 0.46875645667527377, -0.2670280121121372, 0.5179015175675996, 2.2947483373478024, 2.643171040747729, 0.48176341630228975, -2.204296213348244, -2.6541342238413845], 'positive_zeros': ['1.89748842145217392828857748873', '3.252773934254870768015161285015', '6.15495865702598995945369761152', '7.0013599274810898867803074459', '7.9882752593510202148866877069', '9.45529809321928318438308619617', '10.44066925961418162489474220214', '12.00166554872353840431101027486', '13.53582748344248632676057193543', '14.698556999575344789765941961573', '15.68214508531592239707832190602', '17.11802855626229649527025834648', '18.44304518503837746812837119525', '18.94139232312938578295320439849', '19.84637028096088940795184911994', '21.22076786363975658508434255147', '23.15741316662524489685270965373', '23.714699323419554211465621503951', '25.3448259881013093221337622640', '25.94151815566062482276877896851', '26.45504360026874976150528345574', '28.044725167764028870268503109623', '29.28198879489977474580161765070', '29.883353165287253943266547789757', '31.18782024429143671079914228262', '32.330460749186462943203928198', '33.73411761503562498226983806452', '34.48696499772621761853362756772', '35.69091493260352587708603748643', '36.198825864401019246304339475823', '37.2970154611521629760537503188', '38.287153953397814583593421659536', '38.96424235749387041462416057592', '41.21762101529193746718550700506', '41.64532459162315499024173121711', '42.61824995103567959129060613160', '43.27262863539406402053990211913', '44.62970589424638555553917532479', '45.62540915640538174959370200178', '46.32870786620362206956585164414', '47.293746273228519526883334312778', '48.28145345682742387935624994541', '49.276531113620896806624356749710', '50.52999557073253908156787266854', '51.87802241902990422303672388452', '52.47374766108987222564969877083', '53.479854912122167402708846602176', '54.182388685658578158372026338073', '54.89324850707776192035769506633', '55.80796131446339235554381673786', '57.49396987958530894967966306517', '57.8498678264923091635782076462', '59.2126914934076849774014964253', '60.29262621468688031549141478731', '61.02560067377728420723239685493', '61.81981485389312116263930729726', '62.90675844795483617403199813584', '63.92770199769306983520644073580', '64.78209583273655024210152646026', '65.51065479130022802364414044294', '65.82748298677645857746405613029', '67.71416140974094040088787350657', '68.76468371160894364770263952679', '69.815852031696267109980665587166', '70.45349687539949950276798579042', '71.01852256531047451434179564990', '72.31469799609702636113074391410', '72.727859319114236387506268713622', '74.01305442202093721454895048190', '74.68458677925229438268533699088', '75.83617076664687169269658239510', '76.91070964825829197936073326935', '77.818270229099493189231645474116', '78.30619187618552159802956505516', '79.97158709344997894381196641570', '80.68481310382297958840000758461', '81.30094384566482690910193155765', '81.83913414630277752701798090304', '83.171687719274512515977733489717', '83.58367189839569663193421394979', '84.68557838641987902035047733829', '86.00091500372124146783354219105', '87.25846277391292835246824571237', '87.73496778218855711897541223902', '88.49927075846687401492062268428', '89.57418057430243769035632375312', '89.84299691613783192632186015839', '91.394235892080211004030292558133', '92.06742500503769372252821646329', '92.88774131621428481860319899269', '93.66649002548341823245841561101', '94.430981528397224214532729309087', '96.020744871502203716540506430526', '96.80425704711183010825627334624', '97.458325947950726935313824378456', '98.3835186160956369696093753851', '99.553823726576549284904894067666', '99.82821032298937461462871006774', '100.59325052473042975201473487458', '101.40853544792267749674037594688', '102.612677518925877524039412968001', '103.928757626292754486264738206759', '104.57776560933565217619940947792', '105.34023844821275608562000155888', '106.32450521174737421553326747591', '107.08432973931945196814725506738', '107.86162109002535710307740038333', '109.09161678894681086231523548730', '109.65016346339798810398658289092', '110.175246921269537061478220796057', '111.36367143102237642491122105090', '112.06019817713751070427657216905', '112.95158124128299122345057594328', '114.445302451999068966066994432392', '115.21601717874084518098037722103', '116.11035905217417270524447607516', '116.473252077076027896892643905965', '117.24035526959988787389860091812', '118.035972459101827160155704704652', '119.35052490098510198795458735111', '119.815431409410757608271541679872', '120.715666157051660397174624114712', '121.78701519958388263112718904013', '123.11991220930199018758768712377', '123.29315014111496134793584517593', '124.2654093886473858469469871075', '125.395722861677562859183578181825', '126.15535374833375153261467254754', '126.96667209832416713058652138503', '127.77379424375292598394007472783', '128.34717755981996091894254246737', '129.00509349323512916537445057808', '129.93054334284110488089537692756', '131.60582642097613176114987693321', '132.279879008244769408741459792937', '132.844141801468078558061259707141', '133.906241242786053737209554349456', '134.43968478213695430260550285434', '135.449967383460333794760025837048', '136.06133049542394671583539598132', '136.672996668391434891394364592770', '138.22100777358979092853660436865', '138.69750449582468033194007496395', '139.212199428970259378962217020848', '140.43840176801785658694904822427', '141.33969607078454395613729527939', '142.2865048263789207190587080191', '143.48016090683418740832490740195', '143.663546127433883601211392444123', '144.58926740088129841741148115803', '145.45511660067675990830628652583', '146.02373652312606392302351849122', '146.85972935645756981395609246369', '147.69138949647516733686717628680', '148.88767772700491665665318452449', '149.80536777012270797025247608655', '150.96731884716119117663364934073', '151.50537298431524648964963171300', '151.791958880091352610959789166396', '152.72439696097907346851370730884', '154.13820907390499002909055409459', '154.594140978340404027757707794006', '155.45775972314340039496077306726', '156.02691674603156734128464564900', '156.70955903188643700876285819896', '158.024972670786497874817146244773', '158.69997399441821657406090312392', '159.84924899692868844895614472203', '160.63908206118203403469824013697', '161.52318084199432929697272553604', '162.23890241899325726703352915723', '162.60256046454733443090142033991', '163.678530710641958468289642447031', '164.08312763093799769452839200239', '165.27920169288189793471128459161', '166.11452317975279885498983428190', '167.21791285965537425603438335885', '167.9778014137652018008450918232', '168.46105554648439302251237369509', '169.77574434034115348185610618190', '170.258159506126268406032078897358', '171.25268184222730032847047690516', '171.82878073615142898107266037620', '172.80389096651884588157470403243', '173.508957541239002999948308463115', '174.27705166468968121375613446366', '174.8540297971408515887140738201', '175.5109706584709187651698334059', '177.38234044430768133335476861841', '178.03338326860357251208007637634', '178.52225382962336458479185527644', '179.21448599461750757935876091404', '180.25021303684673803744515665560', '180.71641510007998228222317118671', '181.41884144522661342800133976483', '182.60935328676679329306617309197', '183.2965751331932219997004943160', '183.82073759898576203960169120686', '184.985791666252025827683421619286', '185.97542063544015041976574776287', '186.45841004780463956518359787998', '187.67544384301112732057581570727', '187.9752271178972633865415220614', '189.641883344294455430621858101627', '189.73615483435104774710023655705', '190.67593518715134645930923836757', '191.03343334444318594630138755753', '191.85142227449905985008084632127', '192.85198728998882445288404966948', '193.87007123903998934396455528211', '194.65023195931052019548887224103', '195.89176040802049416020556974387', '196.37940980091064232048223826107', '197.17286595338829882475935126595', '197.96533912443357013172533207993', '198.316013462801395801352437209946', '199.42541232265933798686291636324'], 'prelabel': '1-79-79.30-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.489729058775376, 'root_angle': 0.7327134613982299, 'root_number': '-0.667682149325742487077522315757+0.744446470521391424582208815984*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.366356730699', 'prec': 47}, 'spectral_label': 'r1-0', 'st_group': 'mu(78)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.622398894365524570058514870873+0.152408455285041257712811925505*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.89748842145', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.25277393425', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '6.15495865703', 'prec': 44}} -
lfunc_search • Show schema
{'algebraic': True, 'analytic_conductor': 8.489729058775376, 'bad_primes': [79], 'central_character': '79.30', 'conductor': 79, 'conductor_radical': 79, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/79/30'], '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': '1-79-79.30-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': '1-79-79.30-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 8.489729058775376, 'root_angle': 0.36635673069911495, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.89748842145', 'prec': 44}} -
lfunc_instances • Show schema
{'Lhash': 'dirichlet_L_79.30', 'Lhash_array': ['dirichlet_L_79.30'], 'label': '1-79-79.30-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/79/30'}
Lfunction data - 1-79-79.30-r1-0-0