-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': 'dirichlet_L_143.81', 'a10': [-0.5, 0.8660254037844386], 'a2': [-0.9781476007338057, -0.20791169081775934], 'a3': [0.9135454576426009, -0.4067366430758002], 'a4': [0.9135454576426009, 0.4067366430758002], 'a5': [0.30901699437494745, -0.9510565162951535], 'a6': [-0.9781476007338057, 0.20791169081775934], 'a7': [0.9135454576426009, 0.4067366430758002], 'a8': [-0.8090169943749475, -0.5877852522924731], 'a9': [0.6691306063588582, -0.7431448254773942], 'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'analytic_normalization': 0, 'bad_lfactors': [[11, [1]], [13, [1]]], 'bad_primes': [11, 13], 'central_character': '143.81', 'coeff_info': ['x^15 - 1', '0.913545457642601 + 0.406736643075800*I', '\\\\zeta_{15}'], 'conductor': 143, 'conductor_radical': 143, 'conjugate': 'dirichlet_L_143.113', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^8', 'a^14', 'a^1', 'a^12', 'a^7', 'a^1', 'a^9', 'a^13', 'a^5', 0, 'a^0', 0, 'a^9', 'a^11', 'a^2', 'a^7', 'a^6', 'a^4', 'a^13', 'a^0', 0, 'a^5', 'a^8', 'a^9', 0, 'a^12', 'a^2', 'a^11', 'a^4', 'a^3', 'a^10', 0, 'a^0', 'a^13', 'a^14', 'a^11', 'a^12', 0, 'a^6', 'a^14', 'a^8', 'a^10', 0, 'a^10', 'a^13', 'a^9', 'a^1', 'a^2', 'a^2', 'a^6', 0, 'a^3', 'a^5', 0, 'a^10', 'a^3', 'a^4', 'a^1', 'a^12', 'a^7', 'a^11', 'a^14', 'a^3', 0, 0, 'a^5', 'a^8', 'a^4', 'a^6', 'a^7', 'a^7', 'a^6', 'a^4', 'a^8', 'a^5', 0, 0, 'a^3', 'a^14', 'a^11', 'a^7', 'a^12', 'a^1', 'a^4', 'a^3', 'a^10', 0, 'a^5', 'a^3', 0, 'a^6', 'a^2', 'a^2', 'a^1', 'a^9', 'a^13', 'a^10', 0, 'a^10'], 'euler_factors': [[1, 'a^8'], [1, 'a^14'], [1, 'a^12'], [1, 'a^1'], [0], [0], [1, 'a^7'], [1, 'a^4'], [1, 'a^5'], [1, 'a^11'], [1, 'a^3'], [1, 'a^11'], [1, 'a^14'], [1, 'a^10'], [1, 'a^9'], [1, 'a^3'], [1, 'a^1'], [1, 'a^7'], [1, 'a^5'], [1, 'a^7'], [1, 'a^6'], [1, 'a^3'], [1, 'a^12'], [1, 'a^5'], [1, 'a^13'], [1, 'a^8']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-143-143.81-r0-0-0', 'leading_term': '0.958263862508591260910286082339-0.501718985066852797686879591600*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/143/81', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.0816614859402165, 1.074441968312766, 1.055245637713846, 0.7981600306988313, 0.3201751636142418, -0.18026351728808138, -0.420724809474347, -0.16766362419228656, 0.6216469325347128, 1.7122288946984612, 2.623870320316393, 2.803911056283887, 1.8890000850165762, -0.06113326702664573, -2.491561390363646, -4.5187473717767155, -5.297155239826115, -4.427124735975438, -2.192226267987467, 0.5251878598817827, 2.6417367777324205, 3.396008862876053, 2.7164962288652768, 1.219614198547271, -0.17320391079464864, -0.7800684631990897, -0.5340324768280678, 0.0485682450450007, 0.2882048074831328, -0.13075336617268524, -0.8962873429799917, -1.2745806848643073, -0.6661415270005465, 0.8761552934949353, 2.565710272660537, 3.3517917712851415, 2.653415205782358, 0.8392790446131049, -0.9337561915192276, -1.4751316999516908, -0.41217591080082605, 1.4796782715330048, 2.75785659122106, 2.317367535818502, 0.21873567307196776, -2.2829512158809475, -3.578086313901383, -2.8388374336181084, -0.6275604021238662, 1.4891921541957327, 2.0595172738864314, 0.7783012023044906, -1.336435930187753, -2.7490304906862213, -2.5673083769495584, -1.1610707027874156, 0.22569542582728416, 0.5268494378911787, -0.30088486519502466, -1.3259028443646244, -1.5127427290564386, -0.6471677873046613, 0.49750855313198133, 0.8996123122328206, 0.2660522543235635, -0.6655510859760416, -0.8365954742276777, 0.0012601767914618366, 0.7848439920558544, -0.1457405181014146, -3.584335922941757, -8.461935146883844, -12.269660389503837, -12.728474243125993, -9.455977603507973, -4.2930453765130645, 0.010638805175850195, 1.7268055782530958, 1.1733160016942739, 0.08426599078571717, -0.03453363553177105, 0.8855664309784578, 1.6893860776652219, 1.312074288546048, -0.09846444883852476, -1.3065356105638006, -1.2071330377807423, 0.06337121344176314, 1.2227924579753022, 1.0794028134069684, -0.27884341993271394, -1.5217706825934592, -1.3551830165390708, 0.17224827091649703, 1.6321566482964065, 1.5574517469454394, -0.09199824875929488, -1.7912403852321503, -1.8676097778920302, -0.1759658966201794, 1.6103227134110365, 1.4882257015407458, -0.9247553660689872, -3.836025802069317, -4.750582178105983, -2.704893424048841, 0.7831517672792594, 2.9665872575556715, 2.2224881994115178, -0.6158681515367846, -3.1163740169849405, -3.4344055240095632, -1.7872545275648728, 0.054889131689719074, 0.6016629269011802, -0.05798549408707344, -0.6749926638942064, -0.3626493913820228, 0.4718102057673705, 0.7563571979532407, 0.17831485368801378, -0.25985543914428033, 0.7065109859806074, 3.0031164070711918, 4.876588719684426, 4.4239633773755385, 1.6013980960047156, -1.3814630144052087, -1.914462174960024, 0.5465419712175806, 3.8059158368512755, 4.832279614101806, 2.522194131346166, -1.2939842341366348, -3.56243570975991, -2.773369575298523, -0.14348378102950987, 1.807096739202843, 1.7277028000121708, 0.471795567249672, -0.19151522680190908, 0.3490838071237927, 0.9469057556104653, 0.14732099351630967, -1.9797321329878013, -3.6929082215692572, -3.3303064833131453, -1.0783576242583581, 1.1700050426233841, 1.7359304822381816, 0.7886607264293571, -0.054553918850296215, 0.33522510121190635, 1.3348698511216592, 1.4392745993055929, 0.29078314031010555, -0.532816517344821, 0.8933000871930237, 4.430934745150555, 7.362021114671464, 6.676659289279678, 2.0802768134938017, -3.3556380664065526, -5.753597357443974, -3.8205248593617567, 0.1969518290915311, 2.8276852935874843, 2.5560524419994533, 0.7561005715058513, -0.2546291745278554, 0.2777420299158305, 1.1175450358891144, 0.8512114414650774, -0.3521661331994874, -1.052146994087299, -0.4063489059938899, 0.7380469160008452, 0.8854331621992649, -0.18414592943915992, -0.9996988705814087, -0.15183173862756022, 1.7759037350067475, 2.51081526653963, 0.5781975002665513, -2.71969858157428, -4.234067015793694, -2.098725324247053, 2.205053312806823, 5.161331521998364, 4.650161651695664, 1.9137694809323542, 0.014051038696661855, 0.513665872620734, 1.9922845811154486, 1.922319263719309, -0.29823122464941404, -2.5809761704476886, -2.468914628446112, 0.10582711232441955, 2.714090257983028, 3.0295189217082643, 1.1838746784018956, -0.6767241781957023, -0.9374446059433172, -0.15197800802646694, -0.00015305659299347994, -1.0222130351906134, -1.9562713613717422, -1.4409904915673608, 0.11203126012652247, 0.907887705766633, 0.03414446731908135, -1.2380079441076932, -0.9507227275941091, 0.8464699923086308, 1.5579166088590033, -1.2528493825651645, -6.698931127896972, -10.670817037472997, -9.552422558833772, -3.8352369914730153, 2.215539872644782, 4.566029499406209, 2.940719152160608, 0.3736103441955762, -0.34231393474630534, 0.7277575737940147, 1.5534134327186375, 0.9730759633164623, -0.06534992357593244, -0.09600345917184396, 0.757459675389876, 0.9531818788954562, -0.26577094908232995, -1.5645284256048173, -0.9685574961787424, 1.5807011320590074, 3.789631410638809, 3.4600750910710487, 1.0118997519125712, -0.9885627640933298, -0.8271008822335131, 0.4168077466660311, 0.3913643239778271, -1.339229336961297, -2.402637033540543, -0.3473144449331625, 4.111252623894671, 7.306969884226474, 6.363268005882034, 2.3219979837011935, -0.9369092840089107, -0.8179091982556647, 1.4535601935406732, 2.6192496087937536, 1.2456298169035687, -0.8404985773069362, -0.9908730258182781, 1.0644089796432994, 3.042121007968001, 2.921803084425237, 1.1849621776192487, -0.11553937293081815, -0.0028905273094596874, 0.49581951184218265, 0.1297095424708283, -0.6923919472868596, -0.5757327398105384, 0.5181404151236291, 0.6275346129088603, -1.8113520947842616, -5.325461385383665, -6.2000383423225545, -2.4446895521609657, 3.4834556653029014, 6.685245748659402, 4.720980387458977, 0.05714803814950448, -2.678610130852065, -1.528739332184657, 1.2317230520782285, 2.2207512245918637, 0.8086443828211292, -0.7233579726598236, -0.43809357828286505, 0.887264970944104, 1.0985333265314636, -0.30094302630504255, -1.4569696016124272, -0.6575363953602331, 1.319438686307229, 2.117646701351811, 0.816843291384354, -0.8716773462232571, -0.8129864493551249, 0.787093478834865, 1.67423440093286, 0.5502169192845239, -1.1419557907955205, -1.0778357934798055, 0.7900143734197353, 1.9756188015723628, 0.6583243633161462, -1.7181270590746913, -2.034339564269248, 0.3959789105368774, 2.3603086942613545, 0.1692209544366754, -5.802797732005915, -10.91464367856259, -10.911874988753624, -6.239357042950596, -1.2291141948777475, 0.6219189574639147, -0.23837222629429305, -1.0502550277645066, -0.44549748115431487, 0.4503822803231615, 0.3159862023627231, -0.26223677315276406, 0.22635532229740643, 1.7482903102552716, 2.4543146977028787, 1.170736549528241, -0.7762609723800218, -1.1421056880340001, 0.14752550727856134, 0.6433541861244021, -1.393962868548662, -4.237645976052569, -4.318754562110628, -0.6622642575068967, 3.3514955122883534, 3.4633476554662783, -0.6262108832283623, -4.838464475788973, -5.283234477465535, -2.38933462887113, 0.16649290395379365, 0.07462061718139654, -1.2409122947256865, -1.1167067149470107, 0.6035723547728111, 1.490003906791398, 0.0002601658466505297, -2.2603286327244545, -2.521943088842855, -0.4345992448274566, 1.4710908965028362, 1.0080997113808745, -1.0099954909778275, -2.0542040995664377, -1.208985420964663, -0.06894614788391465, -0.2106781719316304, -0.9565042609474479, -0.6237928153846939, 0.5874137497627979, 0.463734638255197, -1.916216888668421, -3.884239136010533, -1.6628251144691497, 4.774263954965852, 10.578317637945501, 10.708282282055286, 5.321011392340791, -0.45477845507572423, -2.12468135214894, -0.24144982621690333, 1.24826196223158, 0.1389969201644054, -1.840279753204064, -1.940142784197503, -0.08969299517273151, 1.3699966498114482, 1.0306215565117085, 0.0454322305255387, 0.057801345620066655, 0.7160325566148186, 0.43576394783273015, -0.7933638936050595, -0.8781284544201328, 1.4683274600254235, 4.327649349070374, 4.405098234535234, 1.1487533312290938, -2.2424306406553924, -2.564016586114148, -0.4553843210716294, 0.6695926303027224, -0.7210874009126974, -2.170048238483859, -0.5563663036821944, 3.4644238777753644, 5.861196489764905, 4.167104718445994, 0.6419810374152186, -0.47586941557001505, 1.8418876088188427, 4.359188974459682, 3.830266813978489, 0.9725973727480071, -0.7899227860018021, 0.17980285539108967, 1.9644141805247572, 2.0183362477464346, 0.5006872755735967, -0.3998317621896009, 0.20926244317362458, 0.8099021618281048, -0.015338173403409535, -1.3156621540375653, -1.1795359033409845, 0.2357401674741052, 0.6832767918872541, -0.8161703639658713, -2.064324502142454, -0.512856996279843, 2.566871948611771, 2.5840420619494147, -2.9002220424579326, -10.33964592937691, -13.295563189496232, -9.28130971961514, -2.3108399996769795, 1.7555781252802412, 1.2880797494646907, -0.6367900887731891, -0.9772978691059432, -0.11566993911784845, -0.05961367988963483, -0.8962363769218074, -0.7723777046779985, 0.8996769561016992, 2.055190119897133, 0.7071404539639548, -2.0285310840509787, -3.0820202677520583, -1.3863745271566212, 0.785780096497704, 0.9735000933301395, -0.23205470581645893, -0.37873099231398616, 1.0017476029445576, 1.523911329406671, -0.505712683997985, -3.1545597091242397, -3.0571919417818965, -0.10366976307452823, 1.9099322466961097, 0.04907174937023314, -3.7030868414795117, -4.713378556169596, -1.630215441094365, 1.729059058454511, 1.1169272475862821, -2.8384921029478765, -5.519632069367114, -4.054310681086814, -0.4658264359073715, 1.409129552164577, 0.6841046916043676, -0.2982081540826549, 0.21811280199295885, 1.189651043946619, 0.899727516030105, -0.2505075643748485, -0.53270866869411, 0.1916561347643974, 0.17819027084867392, -1.1930115951065428, -1.7945781896279922, 0.41697400581873784, 3.7597642097257893, 4.01895897840549, -0.22285930528649808, -5.051228748611219, -5.428427178697874, -1.229579739648142, 2.626853107542702, 2.2355368821457087, -0.7918903017067421, -1.977936614845511, 0.04311981511615916, 2.1379229055896167, 1.2895868070176706, -1.3696992344784242, -2.4204621774361605, -0.9001171365167089, 0.7570224403870314, 0.532387971706699, -0.35429001422521916, 0.40471744339728, 2.455201756921706, 3.061154202143158, 1.0705733938757176, -1.2207896008403654, -1.1044058665915024, 0.8898378462205528, 1.9062573944258894, 0.8259462813985695, -0.4361679806188847, -0.14242566000738593, 0.5610447142793152, -0.243482239432807, -1.3870317255992346, 0.7049305046143916, 6.75985853042706, 12.009284912052367, 10.778152420691086, 3.2881135675452424, -4.023350375251888, -5.490086495827885, -2.041123180930987, 0.983482628354238, 0.5846275145807646, -1.2607538994085934, -1.5083066464098929, -0.29696408096335036, 0.07388241111246288, -0.9525296209709518, -1.4783349912738732, -0.34234847688255166, 0.9929917264480624, 0.8084147886467661, -0.016462464647485176, 0.7130398644020086, 2.8410696394345645, 3.5414874416088513, 1.3170758131782452, -1.4189767597586922, -1.3906076774155023, 0.7854358272142139, 1.0695296632259157, -2.41246402839384, -6.263776109362371, -5.85141883956178, -1.3601254106109748, 2.295437559097425, 1.661659512678102, -1.2309336585944333, -2.1667099258907845, -0.46915298271668093, 0.7340705055488459, -0.3963092816202331, -1.5393055213403848, 0.3383879570436987, 4.291359943240844, 6.256917604089281, 4.291620843009599, 0.8997655169067474, -0.5157693741729994, 0.17298444057750684, 0.6340600776578259, -0.029575708675423144, -0.3413844251078162, 0.5286910918750825, 0.9890554395497901, -0.41750819013327006, -2.1491121854729447, -1.475695664130215, 1.1898593708275336, 2.143390319148221, -0.4541341685101663, -3.1771197090775463, -1.232880728876681, 4.866124570560537, 8.982332954997009, 6.505737294258911, -0.018238615561180834, -4.035167186186495, -2.702887357493407, 0.6584729579789118, 1.7341120285340967, 0.42544268057344986, -0.4233474083101023, 0.23724070914163461, 0.6341283566127005, -0.36771057648636646, -1.2635475545455466, -0.507534289108988, 0.6342029950001611, -0.19243592375354351, -2.5376650497410274, -3.242272974010135, -0.8794685693605938, 1.8873568617863534, 1.7922877852006942, -0.51548998260065, -1.5068119917397507, 0.06639660435931728, 1.4611731226645348, 0.27382042722506716, -1.6378298759282903, -0.7503543806459453, 2.5166592713047224, 3.580224317853217, -0.15549466872271375, -5.191033966949901, -5.947255037840758, -1.799937817422792, 2.286160425012924, 2.217853481380818, -0.49305952579206935, -1.6752427137204668, -0.32660816871540294, 0.8087942424713208, -0.09096288170801023, -1.323384585757617, -0.6412565443870166, 1.1827265223744428, 1.6474984375697865, 0.38566939613669854, -0.4902481232022472, 0.10948624462425001, 0.667807744456368, -0.017514818892433885, -0.3193333175134682, 1.6329471949844843, 3.7956574470256874, 1.5703195577812141, -5.817586544981837, -12.637036586012414, -12.488067113576761, -5.849543974663828, 0.5035734141121384, 1.572225674187666, -0.7509618174456141, -1.5851361342974344, 0.17822162967337898, 1.4441998886507599, 0.31816565133757024, -1.1270590873440476, -0.4171680747190793, 1.3769248545601487, 1.3954375442373554, -0.4580185102707227, -1.2895122428482861, 0.33638426453220754, 2.132955240153769, 1.5168534209303601], 'positive_zeros': ['1.440641715066081773855425400747', '2.273186206653290942052512443300', '4.05424039608559974233924021111', '5.87540648308775186960588773784', '7.45216907664782097265095154206', '8.40865467819631807481894855062', '8.99976728472106933536029731680', '10.151610547253041952093962002356', '11.695622211049001878770223396219', '12.57228179007561942961950699355', '13.7763500977420462936232611962', '15.08089507141423922918388478083', '16.05458617193517680957461131659', '17.434174857523689697674641104716', '18.03812870005045708784962780408', '19.22900264376852358647308708495', '20.08315285913682280975383494886', '20.93713577365220126368113123674', '21.540826372873087110384860003362', '23.7489409255119697796898878758', '24.72599338499788142557468969781', '25.019301329380723122974494332057', '26.23026775419642305917352321681', '27.17406825671983719481108473449', '28.069680531452958915002070802873', '29.03249741263442139847218077897', '29.985649757276703488137753541489', '30.963444063723258745729444862366', '31.77752301855177115152204119607', '33.05329792927116334244996734093', '34.00087555676058540858462844029', '35.299863816554256548995114994409', '35.91670179317962861916679718394', '36.69845743629324668184954099452', '37.57685894858539215902823924712', '37.966415415529518662270697722972', '39.52562921168123969621894117402', '40.26083027317022653479032695919', '41.45432025588917114406541509109', '42.51683047690594155328438688079', '43.58594736708127932763181292000', '43.922410171389738570148353679794', '44.714397830656662276925322447932', '46.06963092275202578217663860965', '47.14241415558795381905170255388', '47.3553631240166836507283421555', '48.50670125917914377097097625715', '48.93836111154713196166395068635', '50.424803159969198087846047769339', '51.54657284830394271352566033723', '52.6715967976621631537107311555', '53.02942525321291618158322175656', '53.97555182139674713902450861581', '54.79164588051298096843292037980', '55.57991898564327105913227106289', '56.277312546205766681849126654460', '57.2440328665626283730782117494', '58.28179605145228240115411718126', '59.69401521253922659040465239744', '59.84894446113192345863404761017', '60.9033736755409507335526227192', '61.864317453813000839508888130462', '62.986965665584875004508575826445', '63.82774843576358753231528711809', '64.06240793128234005357710670015', '65.28934663073507041817440432668', '65.944904265061804908245258403047', '66.73798849294227683940266555737', '67.40528295629289855228539114769', '68.93366495934889996517302028729', '70.07088524322081561036016716950', '70.44591993350859258492725673661', '71.53495946580270028837641689552', '71.91947437990172074014138596204', '72.76067168361966745881415200771', '73.5736297746146839279183659487', '74.81360625251412480165056217822', '75.5117100860114403151311894266', '76.02836207123738313664957724282', '76.903369602283570115639003414194', '78.31550575259826834769781784798', '78.87342820413329820206430023219', '79.857983136790196361798952087', '80.487278411588074083230546167532', '81.82348472842770501240743779993', '82.18904557231774019037600845098', '82.86001679967271303479321986134', '83.60917919913077080659149917814', '84.18126699500285753970174717812', '85.44074665838370721569752591587', '86.56658374667132967199754414808', '87.35540078366904426298242026980', '88.259676904915460294877374926980', '88.85483516449570615412356804701', '89.63208282188168349293145076695', '90.41940234375286975224559574439', '91.38175337120997389917710616237', '92.04625324398659738902585354489', '92.903267256412815355260011327766', '93.63155601768418097866254824906', '94.45797280353210345041342006951', '95.27074164901682911031292375981', '95.9488196154994502843228276994', '97.631101317389633833522096366761', '98.06718850495908813335067997528', '98.88070514375853069681423911988', '99.52092265472372112210426220336', '99.9342574522050489941532333810', '101.11238194742967085992163354618', '101.84254787792736276496571389726', '102.331717326956808399217746016975', '103.481797970842546460864889851010', '104.33577856569387995791656236042', '105.58956697281171972794935082411', '105.95645387270150488806440611860', '106.773872446839467645698753684921', '107.50003430259886831353532617688', '108.49204001161266541653079946401', '109.22383081183513988868424921292', '110.3565793974631719838874726211', '110.5091162629682915607032133210', '111.40805937260672725189481436067', '111.95877935779794861710991212816', '112.90755451687205080757249995750', '114.342286907914838422079210983612', '115.032445122670337294937913786177', '115.64565213747317582814625356474', '116.576017267586117432056315329039', '117.52415064833435545999537137263', '117.77908163338569972521802774364', '118.554698644474329730830126946018', '119.2143102987252410255616387714', '120.402470042641663486718364199020', '121.32025818258645831072297450849', '121.75940486115125937584907883907', '122.54921873391962095783984422782', '123.829699376348648560206287833562', '124.16473592543327231047022463689', '125.43172957171555801718565018401', '125.90714024139694076211448789285', '126.98768140236924322498802351332', '127.43123053083314407996742545764', '128.12159419471635282113058148571', '129.01024486606386937024576141218', '129.55077300703614641682239170339', '130.3646805017532026639236186909', '131.11774326711880553023542387888', '132.63249602510526365727180188734', '133.32041227797092445202887155521', '134.12150530345115599771481278185', '134.34161317859802813944269183993', '135.16449692759574149287040644404', '136.01983623582937899260157518061', '137.05306685400747300725205715089', '137.74926283659505687765144989094', '138.23103976097939967048726995271', '139.007119785142948542774195428247', '140.01001632599770911068325117855', '140.62930566672772710297927291702', '141.68885473103334737705325981723', '142.28974388157610579011011903842', '143.48487984253153647008365992050', '144.23490948807333886453889399859', '144.62107397599917297557942795919', '145.55128563578476039817439982872', '146.17079894961384408335558971870', '146.61914163133829468887372934558', '147.46070797806250571549835546094', '148.42483665520204168875964405154', '149.4536606553676292981675692126', '150.22994681693588939921088164313', '150.93264484927401010353996425903', '151.715056795861231611479264694221', '152.63848691341711054081821936147', '153.281305468547189148691424071744', '153.66776340278839069576024872889', '154.81193554487174689490146430157', '155.49364336346357943381837907187', '156.41891269624021642013486151505', '156.92282732254026990808589766078', '157.44703258259475299480782327407', '158.07043561795156777997447703049', '159.49668304571624778641132649884', '160.485477841706969740287685475530', '161.03317242797828023627140932179', '161.97325639377116422756023667748', '162.22569041579573994038859778114', '163.19029738090982095860656972201', '164.04826203790600351211386945759', '164.17762992138689604265406570111', '165.44353685583118428132346695025', '166.13874505719192854413424976633', '166.69165798448395334450709252535', '167.90121399125975187620715487508', '168.6146405980254775711441524917', '169.45040709765789580876635730003', '169.92861722461128383531622220009', '170.59345438161041658879292359186', '171.99940918939113159898823670913', '172.445014363585419626032186110921', '173.11363191350680349193643221101', '173.59358410668497371695587450226', '174.309852138016857182850008264900', '175.177159592435279281311781390904', '175.89759952233648012020242715135', '176.63602527326812617988994086455', '177.81159366877517294878801231063', '178.680167595479948326739005142088', '179.47026220124444530053888449688', '179.92002301514440462634245593843', '180.538276852978347552358379719', '181.36188450214754364265172683291', '181.84331411537743836667493937862', '182.896759728641752507472393842568', '183.681635398727570378853595641547', '184.365213713917097509683606746149', '185.038164722251262838910309239300', '185.7045507499375308687856394982', '186.55346590409002260945346599905', '187.61327262813765974584060922791', '188.379919390290349406394358674722', '189.120814670134409578668636394981', '189.66913930482696493107539056649', '190.42188338958795684015164793921', '191.33842053261698008223799543666', '191.83893023478149031260898105246', '192.4942815652678048062732917970', '192.90061844768618820345323639214', '193.83175534748789868902062944624', '195.27616863924010913818300499561', '195.84206925082068237104623641237', '196.53662921117298547672594835005', '197.24073945224445653150417518218', '197.88277540015262330911612767826', '198.67756203714000404962534973211', '199.32870942836001978657781024596'], 'prelabel': '1-143-143.81-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': -0.30705824106975654, 'root_number': '0.569702985226273449590287194532-0.821850660779847798032412880492*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.153529120535', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(15)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.973979160494658311221878680203-0.320987768552520676688909916902*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.44064171507', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.27318620665', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '4.05424039609', 'prec': 44}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 0.6640892081105222, 'bad_primes': [11, 13], 'central_character': '143.81', 'conductor': 143, 'conductor_radical': 143, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/143/81'], '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': '1-143-143.81-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': '1-143-143.81-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.6640892081105222, 'root_angle': -0.15352912053487827, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.44064171507', 'prec': 44}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': 'dirichlet_L_143.81', 'Lhash_array': ['dirichlet_L_143.81'], 'label': '1-143-143.81-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/143/81'}