Lfunction data - 1-76-76.71-r0-0-0

Formats: - HTML - YAML - JSON - 2025-12-07T17:08:15.765197

• lfunc_lfunctions •

  Column	Type
  A10	numeric
  A2	numeric
  A3	numeric
  A4	numeric
  A5	numeric
  A6	numeric
  A7	numeric
  A8	numeric
  A9	numeric
  Lhash	text
  a10	jsonb
  a2	jsonb
  a3	jsonb
  a4	jsonb
  a5	jsonb
  a6	jsonb
  a7	jsonb
  a8	jsonb
  a9	jsonb
  accuracy	smallint
  algebraic	boolean
  analytic_conductor	double precision
  analytic_normalization	numeric
  bad_lfactors	jsonb
  bad_primes	bigint[]
  central_character	text
  coeff_info	jsonb
  coefficient_field	text
  conductor	numeric
  conductor_radical	integer
  conjugate	text
  credit	text
  degree	smallint
  dirichlet_coefficients	jsonb
  euler_factors	jsonb
  euler_factors_factorization	jsonb
  gamma_factors	jsonb
  group	text
  index	smallint
  label	text
  leading_term	text
  load_key	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  origin	text
  plot_delta	numeric
  plot_values	jsonb
  positive_zeros	jsonb
  precision	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  root_number	text
  self_dual	boolean
  sign_arg	numeric
  spectral_label	text
  st_group	text
  symmetry_type	text
  trace_hash	bigint
  types	jsonb
  values	jsonb
  z1	numeric
  z2	numeric
  z3	numeric

  
  {'Lhash': 'dirichlet_L_76.71', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.9396926207859084, -0.3420201433256687], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.17364817766693036, 0.984807753012208], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.5, -0.8660254037844386], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.766044443118978, 0.6427876096865394], 'algebraic': True, 'analytic_conductor': 0.35294251619859923, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [19, [1]]], 'bad_primes': [2, 19], 'central_character': '76.71', 'coeff_info': ['x^18 - 1', '0.939692620785908 + 0.342020143325669*I', '\\\\zeta_{18}'], 'conductor': 76, 'conductor_radical': 38, 'conjugate': 'dirichlet_L_76.15', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^10', 0, 'a^4', 0, 'a^15', 0, 'a^2', 0, 'a^21', 0, 'a^17', 0, 'a^14', 0, 'a^16', 0, 0, 0, 'a^7', 0, 'a^23', 0, 'a^8', 0, 'a^12', 0, 'a^11', 0, 'a^24', 0, 'a^13', 0, 'a^19', 0, 'a^9', 0, 'a^9', 0, 'a^1', 0, 'a^13', 0, 'a^6', 0, 'a^11', 0, 'a^12', 0, 'a^26', 0, 'a^5', 0, 'a^25', 0, 0, 0, 'a^16', 0, 'a^14', 0, 'a^17', 0, 'a^3', 0, 'a^20', 0, 'a^15', 0, 'a^22', 0, 'a^10', 0, 'a^0', 0, 'a^0', 0, 'a^10', 0, 'a^4', 0, 'a^15', 0, 'a^2', 0, 'a^21', 0, 'a^17', 0, 'a^14', 0, 'a^16', 0, 0, 0, 'a^7', 0, 'a^23', 0], 'euler_factors': [[0], [1, 'a^10'], [1, 'a^4'], [1, 'a^15'], [1, 'a^21'], [1, 'a^17'], [1, 'a^16'], [0], [1, 'a^23'], [1, 'a^11'], [1, 'a^24'], [1, 'a^9'], [1, 'a^1'], [1, 'a^13'], [1, 'a^11'], [1, 'a^5'], [1, 'a^16'], [1, 'a^14'], [1, 'a^20'], [1, 'a^22'], [1, 'a^10'], [1, 'a^10'], [1, 'a^15'], [1, 'a^17'], [1, 'a^7'], [1, 'a^8']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-76-76.71-r0-0-0', 'leading_term': '0.813582498741258362211025691400+0.0490397735207949062291329666722*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/76/71', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.8150591276987461, 0.9365130073465379, 1.1034610299696337, 1.084726393772854, 0.7465568973889132, 0.06593815457715829, -0.8628690163240759, -1.836489545463172, -2.5850967984789373, -2.8505947738331043, -2.4812822527083833, -1.5089303183886855, -0.1714715995050086, 1.1414220221141014, 2.013811093729202, 2.1604293183138523, 1.5524457364816677, 0.45083861724951585, -0.6826275586267001, -1.3745484079776076, -1.355159077964522, -0.7009369650557156, 0.17413550953060386, 0.6939752738458909, 0.39627098083766543, -0.8175856851076722, -2.5884726912646085, -4.227337489748319, -5.023141046075356, -4.58990007586846, -3.0759312649830775, -1.1141584800018953, 0.4796030264668328, 1.1159260483113824, 0.7334961883412907, -0.17812900558050365, -0.861144350059647, -0.7314049936312456, 0.2683251237645926, 1.616095807458573, 2.507240526940544, 2.3412424635515308, 1.1142402676360221, -0.530070655134222, -1.6460318464880834, -1.5420160353408174, -0.2173568270954165, 1.59733885352884, 2.8444670684264586, 2.7611860708023994, 1.3428380941740088, -0.6463677384133515, -2.1357560030913, -2.402915924617911, -1.5065577441233629, -0.21453838278715898, 0.532374657346026, 0.2701327643225596, -0.6642400273281294, -1.3663112868529628, -1.01386738808464, 0.50487302442717, 2.429190882583493, 3.572829901214079, 3.104879077713367, 1.1411449540938854, -1.2726801983581373, -2.801903529144244, -2.6713489850113383, -1.1471468013621091, 0.6823048130561152, 1.6765161731048224, 1.4237172888140681, 0.47812448617859876, -0.11441060052995276, 0.3473759846229953, 1.6456444509365176, 2.7731093290248507, 2.691419996400434, 1.1627454335932796, -0.9805631701340325, -2.365395696102665, -2.048337504775615, -0.21907844530247883, 1.900052647410234, 2.911152833645261, 2.2378321802264196, 0.5248921261461785, -0.862181389204463, -0.865839218842305, 0.48304269369978386, 2.1245288118258006, 2.8164558134245397, 2.1038865295616977, 0.646132298451039, -0.3607617421817868, -0.20626864971678044, 0.6978175647968905, 1.1071769876902628, -0.034870008672541454, -2.6489523129993864, -5.424457290957921, -6.704765406148078, -5.697663028063991, -3.072457777940556, -0.46594893046702796, 0.7264596245913018, 0.33038270533405895, -0.6178427103170296, -0.8336353636870791, 0.10974568521691752, 1.450369937233719, 1.950733902466379, 1.0426478238669161, -0.5855245037644005, -1.4934610201823526, -0.6960683910659698, 1.4366660937205988, 3.3772572924422066, 3.6244337225738965, 1.9220498818839609, -0.5007595628285214, -1.8914746156399276, -1.3630418812151472, 0.43159786928438143, 1.8918458062780135, 1.8209804605630313, 0.3927302477478488, -1.0761393550057257, -1.327697346054522, -0.2785586783509906, 0.9329446402553088, 1.0102141835921397, -0.2746947552871115, -1.8034201673799723, -2.0723045142042835, -0.5752656798203217, 1.621152526035098, 2.671011021515291, 1.4800374641113871, -1.3290032877397444, -3.8658877089482178, -4.478072421224061, -3.037856585346792, -0.927146383615659, 0.22745050844308293, -0.07003874266736178, -0.9097959097112472, -1.0021456363597099, -0.02000826313238787, 1.014063849123965, 0.6860193258235956, -1.3756965908303116, -3.941624815783328, -5.088774833085953, -3.8276050202793956, -1.0042997963704288, 1.362889098085148, 1.7661806399675384, 0.43754238038912047, -0.9566071689901092, -0.8645793294326763, 0.7632643302620125, 2.4937141381398797, 2.7854220996218926, 1.4254883476293536, -0.3073310322724731, -0.8869133615244058, 0.0011475064007947576, 1.1846639659941922, 1.1919441601184022, -0.2258296491748376, -1.7193332539239639, -1.5384206768035285, 0.7712737064978495, 3.7710034178872602, 5.253947700802052, 4.122156053078437, 1.3214559928484322, -1.0158691666252804, -1.428868002012007, -0.2859580965490119, 0.7775079820780735, 0.536527594967005, -0.6685415552678653, -1.3934676142878997, -0.6702555703531661, 0.8944422862052727, 1.6383561071631634, 0.5189406778065722, -1.6970104428200945, -2.9634494881520252, -1.797117630328171, 1.2800737693902442, 4.093662236017216, 4.686818401624963, 2.988263878996322, 0.7395664650250033, -0.20810612990347477, 0.4202342778215897, 1.2486503651666694, 0.7902743705346725, -0.9672381667055123, -2.517297311838755, -2.364989661811393, -0.5809034837635902, 1.2121891722504108, 1.4462528301712878, 0.21452381885565566, -0.7642476411087958, 0.14345941339856907, 2.7585051491311443, 5.082286395551375, 5.0942299003668845, 2.656803525692774, -0.3117844075153032, -1.5753873452249585, -0.560537172509822, 1.300111687155635, 2.112843668038437, 1.3592770573081472, 0.19771348542860565, 0.00762522428356917, 0.761122098798357, 0.9729456455281408, -0.66930904148428, -3.6800114578669594, -5.916785647988005, -5.490256283708117, -2.6098257072102253, 0.4937766402980824, 1.5670460216047366, 0.34374714069226825, -1.3715837233465975, -1.5826872356824806, -0.046860296201725736, 1.6301452013902826, 1.7634778544807594, 0.35222638697300007, -0.9814476044635859, -0.7727252876389041, 0.6888675812620499, 1.6552009427718142, 0.8232156809258151, -1.160424446293453, -2.2349154157629108, -1.0296976425950881, 1.6143529222859474, 3.333170169553584, 2.5232171312906857, -0.058041114430131456, -2.005737947735481, -1.5964256261351015, 0.5995541052892351, 2.4093312581922777, 2.2835235302125554, 0.7523888046037163, -0.33040530195527784, 0.13988854285804203, 1.3825926113052096, 1.7352811472597043, 0.6706404927951024, -0.4268777064412822, 0.3272284285937723, 3.147543377551315, 5.995509895401626, 6.349940349885206, 3.6343255615927617, -0.15620856661497856, -2.2981859746459565, -1.8150232259569394, -0.12450946409593289, 0.6872132933185808, 0.06889168635337632, -0.6248931674441599, 0.11687529027973069, 2.085808309758644, 3.448246286276, 2.7302282003321228, 0.5157207384801037, -1.0548628645660851, -0.5256510102105202, 1.2852521677154, 2.110795669371964, 0.670393616339694, -1.8581183701093285, -2.9447781676250138, -1.2929064493751903, 1.7858745191920538, 3.6495908689992196, 2.921175699790992, 0.7066465610910606, -0.7584668173003736, -0.4931427101310584, 0.38806577113613183, 0.19261035339958144, -1.2645553985463365, -2.3967364408448173, -1.7276882689466309, 0.204698206954549, 1.1567062105934074, -0.4756814294445863, -3.7606501123211538, -5.915365444852563, -4.9879059260528, -1.78283386936932, 0.9767721941693682, 1.3594167480220363, -0.030492168662296162, -1.0190745434525588, -0.35614541904537916, 1.027430629621134, 1.2985601941501694, -0.014577237855532565, -1.3998956510163358, -1.1176302234695688, 0.6596568807103005, 1.8213781178591593, 0.5714149581122858, -2.475623612442121, -4.728621519679876, -4.232965452515294, -1.6909695396751285, 0.3015059676312192, -0.0012772586793243607, -1.7201267409142735, -2.430238729745952, -0.8674482236273806, 1.7082898219761782, 2.9319081562324265, 1.8915747764707846, -0.024458359544211897, -0.8576389710437761, -0.3301852933757695, -0.006202473478105323, -1.1869010275939404, -3.0233616010043582, -3.1617708023309996, -0.3683087135583756, 3.7702383023044854, 6.1016806481481325, 4.938855944207872, 1.6808205196878712, -0.69233192034473, -0.6117880737504576, 0.7886749134516111, 1.3196364422755194, 0.3122566401581542, -0.8011403445894414, -0.43933818065948926, 1.0374588462834964, 1.6197438865740388, 0.03380935992143257, -2.5712066310264188, -3.7047100089595038, -2.283702747494631, 0.052345689692619296, 0.6448142922976878, -1.2675028909927224, -3.6533501276324207, -3.85125003826011, -1.4275768764497667, 1.4073727257151416, 2.2348654904811047, 0.9635532628634962, -0.32307606525569754, 0.0944605898028252, 1.6255255303418183, 2.219420782016776, 0.9242772804562074, -0.9148429046295341, -1.264163688930659, 0.07770674860660587, 1.085834162116546, -0.15475448055380475, -3.0171604688221105, -4.696390621815304, -3.142579287267309, 0.6345526506792196, 3.485162274389891, 3.3014042639480774, 1.0016887057757784, -0.7576369439160202, -0.5446595263347286, 0.580357190467184, 0.7595435832478591, -0.20940481531372176, -0.6600750774483379, 0.6844627108914731, 2.7831065124249554, 3.1618519075245057, 0.7550843897573274, -2.595831482120971, -3.884228758290365, -2.1067559669349105, 0.6813847351503435, 1.6403023957433027, 0.20458259269915402, -1.4915856686119775, -1.2163265530990321, 0.7793919456490705, 2.147185749694762, 1.2494203385330755, -0.9414127259080449, -2.04064106319769, -1.0517943560201186, 0.5881726287538511, 0.9297340246406579, 0.021101181831277696, -0.10577133750077802, 1.9447950071131963, 4.840329601644349, 5.616342696177164, 2.91183982447558, -1.319687154767176, -3.6756377054697276, -2.7494488215477224, -0.3545622725800637, 0.7301107353304376, -0.1876509978330879, -1.3160741751291853, -0.8676903697246463, 0.7007622301178651, 1.3825547807518546, 0.28835020167400877, -1.0974832152901302, -0.7247889565298312, 1.30039351254166, 2.485904493818906, 0.7235104346572647, -3.0869403191776033, -5.713173618716779, -4.954050083039782, -1.9238605305652325, 0.31304196593506217, 0.13951227599311, -1.085752699909828, -0.9922374042236524, 0.8296314957549037, 2.408876610376844, 1.9220522739684522, 0.0013358091915635082, -1.0216761685110884, 0.00014257050134023542, 1.5848338851887085, 1.4457748595467792, -0.6051478609905507, -2.2715042712033084, -1.5091425268631617, 0.8422969829788899, 1.7805026038642524, -0.46382496408901935, -4.266279670456452, -6.24076836690829, -4.832348288718609, -1.7912224074637613, 0.017756196020964784, -0.2506038181142903, -0.9927487870851791, -0.6617908006300619, 0.11222872688123262, -0.5186444866111045, -2.8530139939337498, -4.707189085051625, -3.753046831280089, -0.4377709651941657, 2.1479894297274003, 1.5546912778923083, -1.3112919650245662, -3.224585696306249, -2.25334748820914, 0.2339155804985445, 1.4085299552006645, 0.35525628107550317, -1.0488523341036122, -0.6540059120279278, 1.2561036012313482, 2.397255754141752, 1.4307480328865634, -0.3177091715768539, -0.544928354458646, 1.0485208012265208, 2.2750779361818942, 1.1999572748368945, -1.2387124881818525, -2.07555912560463, 0.20471450994982796, 3.6920444028278503, 5.038913268904304, 3.162812245429992, 0.3443901150125718, -0.5057614502560122, 0.8890954119161644, 2.189559998679696, 1.500500662467057, -0.3868987190075244, -1.2395860453786411, -0.3556854729911239, 0.6077057321636271, 0.016266443659877575, -1.2631003819495752, -0.6464511569645842, 2.8502950212798317, 6.846479608240195, 7.806469183237562, 4.856859492794784, 0.7693210622308139, -1.0690362310278727, -0.1637531086636241, 1.1033173832815446, 0.7155992135533511, -0.6070290220378417, -0.7069540275539662, 0.9094855172532867, 2.2307514558920016, 1.2619335133728369, -1.3244048552711252, -2.8634019124913235, -1.9528149469268614, -0.2061332452895121, -0.2137883052539259, -2.1804461381687035, -3.476042011911446, -1.8081879279329038, 1.8022947532635842, 3.9454727154680613, 2.6461556840478533, -0.45143234829332424, -2.0955012162744824, -1.1297093962092355, 0.5434651070961359, 0.6653800122861199, -0.5815664770578775, -1.1595702062788102, -0.17512559941590883, 0.7715010997088713, -0.24213334430389055, -2.564395881692478, -3.2726157759810555, -0.6218046772249521, 3.5377516352883465, 5.529158520934325, 3.8944714648428085, 0.9417719428446961, -0.031170489173118356, 1.5274411958067824, 3.147395747799777, 2.6138429101230782, 0.5998189198360415, -0.5159907520290024, 0.10385997840249894, 0.7351076172470238, -0.41424839179947565, -2.5383251688293593, -3.0185841460172664, -0.8115875542735164, 1.90383693741947, 2.116902161237504, -0.39789029846196433, -2.742522660537594, -2.362927789837175, -0.10559656010513896, 0.8947526787943885, -0.8901221342404386, -3.5147780335598506, -3.9673542179981105, -1.7894420811525216, 0.5564898993400285, 0.8553961787394607, -0.277795536733728, -0.5950497871646686, 0.5775448407420247, 1.4549932608710239, 0.43121514376572845, -1.3070698667339191, -0.8774203331889895, 2.583580914207381, 6.2796408371279675, 6.5474005495693195, 2.9486976220198873, -1.2234343797657712, -2.6259588879975286, -1.303248652622795, 0.08475836391752378, -0.08233731347331748, -0.5919603649936043, 0.4527945965012089, 2.6407422073642133, 3.513841662028453, 1.78734983784274, -0.7667583049985226, -1.4120438698695763, 0.06009109169417173, 0.9916494844051791, -0.7231155276789278, -3.7435289043613467, -4.688214331008563, -2.225619790926884, 1.2240149846938748, 2.325603271915119, 0.7002476672466147, -0.9163458825731947, -0.2627088186435178, 1.7265662596975537, 2.397902687444688, 0.9357310968473925, -0.6844428670266123, -0.47973601058024257, 0.8346532096763989, 0.8885492054311279, -0.9180039574592177, -2.2615424698597932, -0.7924509473256967, 2.5289210619489726, 4.110623194340075, 1.8852817543531548, -2.110732406582355, -3.9856721186160025, -2.371768839095022, 0.3480116413914309, 1.234241705708131, 0.21444161567665976, -0.45167972419135455, 0.4248360197383759, 1.3949159740340602, 0.6695473942594505, -0.9920953127883779, -0.9381243671682337, 1.8088700994164288, 4.789403085176343, 4.7518576647221975, 1.5898265099812257, -1.4166873308128585, -1.4845969809746629, 0.4680046344520674, 1.2604863794837418, -0.38979379882313797, -2.3031266135280006, -1.7678625519017732, 0.9121665380504942, 2.8158574210066023], 'positive_zeros': ['1.58702375544705554397572365317', '3.78841354528954967058726514752', '5.430224701022469086446899090009', '6.80925897549110393407668749628', '7.62785468129583486173104795162', '9.88861948418508800898628498257', '10.8784468559433808113359796931', '11.80809742068884956155103291722', '13.33452569963245920101842441130', '14.41342742065765652512589367934', '15.83534712446400949601791846478', '17.24886603199047623073591687519', '17.915022662519050517483964441084', '18.976383269193511961462989099337', '20.45657833054174825351098652330', '21.750625251265996760353467417601', '23.01099611950523159293441405803', '23.2972217558275348145847923915', '24.85565164898485520735629335208', '25.968040538201862069060932334053', '27.28338056096053307003648750105', '28.03398395302858755309407811843', '29.53707602879429471948455519356', '30.08166788066724711132897728453', '30.93203897624112577887447555378', '32.891293751216152252609275512292', '33.54325475580060021386955409002', '34.34915281686612777381591055393', '35.51182116106194883595471049192', '36.36520349762342068053899592552', '37.74378547394870842599076765691', '38.680284301107246775724413347174', '39.75968513396389617330195354531', '40.687727333480283238237359502558', '41.51022664480208042087624175634', '42.58111888559776454532786481240', '43.61240559587694396185265576602', '45.20422909778203128184851075149', '45.59669749513017405862582638584', '46.56745597242620940172693117699', '47.317716502421812878091802263192', '48.86156102065680043128796416050', '49.769179818790425926257628540', '50.50029267255586775277189000308', '51.80964799103927548279522012849', '52.49972687337803824370703230294', '53.39743218398479336612156783142', '54.291665574433657732232220410', '55.77695143079786329152059624462', '56.627477906872303738016659142868', '57.33725426441155433854484290850', '58.26152004906034694629603741796', '59.14032393083867011869897972049', '60.193220774907245291713512505845', '61.731664484481975090600616085575', '62.04463190212428274423450725045', '62.969166260810084060465791682255', '64.14908472390091082341532544662', '65.04689283188958906611498653222', '65.60150303471905834973735549413', '67.14867955610268056587291301407', '67.90537763074723779153070207991', '69.15890273777807529274682784467', '69.36948084798525653773204652332', '70.223492595302025850112938849768', '71.81441725129735480081583086541', '72.55654927378148697308712317508', '73.44497830115517015303808749985', '74.44060727625519926352336991528', '75.1772832763489287373616671986', '76.07236915347094797621684114894', '77.002874283276926385696384249176', '78.11828139248838362206508949166', '78.98513554002035213545713807322', '80.16899455327370530933117301335', '80.58395222111243423738204577218', '81.716661578881938086358454233', '82.12882902161817935494122715530', '83.73556502203922052988815646183', '84.71378069959457161038530529298', '85.33455693098103818461125297299', '85.913407333628218194650542547705', '87.261808507952787454519813399580', '87.91006168656314311071442877145', '88.83361888068835868921475782551', '89.82099886311523913804265884582', '91.04907938061105130380622596953', '91.721591284040732020719409871213', '92.24226122312477915219039488677', '93.40393951448892718582604750946', '94.00669879294340966218864421165', '95.48844530957299810493927172184', '96.24389564468145600289053281298', '96.95377380249573539785898370956', '97.80983002148478207661162557708', '98.64416746396762222444083501735', '99.44171180285538996291295573389', '100.861256137999991015929525283702', '101.24970832028906383280886173781', '102.29183428554657094768844424309', '103.43279341404037994413416583494', '104.24067331954078397192108116268', '104.36939684955914672323302474003', '105.65365037670921454369252827056', '107.06098359072629624835492328323', '107.64180722339687551408355950232', '108.50731671279375669328837186039', '109.16400138681985385620850880747', '110.00424246023410744596846870683', '111.24120550880329573479466355204', '111.70719479929546870434256659004', '112.95581481801386512424425747003', '113.94823853158360240583322321827', '114.350820243854654694017228885207', '115.45725955196533741667389709571', '116.23497778615985852250852495014', '116.85438932458275487299233014091', '118.07457125190683092800520176534', '119.20304462749543401388857220719', '119.834752448816530057115608050640', '120.56498055697498661243346108239', '121.13650147206000902206472424887', '122.25531814178644363975521423363', '123.351793234060776585460215736809', '124.09363589484255577731196351088', '124.88844376593498673543880204596', '125.80377160596546062263750698872', '126.74945143073488013378933568552', '127.50732642101672691915822653375', '127.84383481068483768573544097891', '129.27375611963359200074172675797', '130.36919962443897032667147638463', '130.89582440772317385391625213712', '131.73838057177936694329134259705', '132.55445381506468183437964927357', '133.25100268461590788175523399693', '134.12827128125616001411349680255', '135.5526715895010874328322943400', '135.97434213674168410529659606367', '136.75195384722965622656256110413', '137.81272441571016494809940789084', '138.43747416317931511697302144509', '139.29485312457094079426851096449', '140.2012737030272639500859011525', '140.895235053515919452591336160296', '142.49192403815693813559702917819', '142.70856971876020252475041745941', '143.67952452606600447145269299166', '143.93107979468726610103657060802', '145.35174067743773442201447835654', '146.11625276431887231717621432116', '147.15584959411997533162309016251', '147.87774801304126947646450401974', '148.556312670572724639261548393290', '149.619339171983615619498218895580', '150.13286002146307986925323480257', '151.09090457710939615602626619554', '151.856217686105406914981058494294', '153.17975839321787171788741047657', '153.58861918136402822689890450100', '154.6208052369566731688627302133', '155.39863547365008472318173013048', '155.94135062401740476928349267782', '156.64101136024903610932500659390', '158.20477677159221360658788649090', '158.7821630242628896975069337195', '159.53823635962583740522829056457', '160.16144594261736960862927345813', '161.095678378768937015395547836120', '162.25442104746885670231726110286', '162.4330465796612572667101612845', '163.59772751066392493502867148949', '164.63979733134016009164359355919', '165.50561465517084796231401815396', '166.11587516055002060544085256175', '166.914949905693991647723251635217', '167.4611372088488029713576956339', '168.48479178977368861746124132056', '169.87407167576324674956814939642', '170.016325422398661903801407400571', '171.36024688159145264181306218104', '171.84361562377462939017285631770', '172.430764287588475422499755096803', '173.52023105898914005464157216976', '174.334025065350914962837492014047', '175.32812822318984260733303990859', '175.82702921881228902763279499203', '177.092067102237128111085630424502', '177.73767084733992391085322982880', '178.31059161186623726920619997941', '179.13325718276014818995860882486', '179.79051562615698857279474459688', '181.14382496072316244771595910114', '182.15163254594860256411868973861', '182.46266791537990412309093249608', '183.04362928883824657983149261911', '184.268799084078539786350819540', '184.98929288223080906514528425564', '185.53938415767946041898591583713', '186.75242783670467559966329981447', '187.60385085961763347273080471830', '188.16968616803515331813923804553', '189.21452488200512748056400670603', '189.802764298938916340777989026954', '190.48840056346685082113876030282', '191.32945773916774615225323848499', '192.33285060291539039954427430029', '193.38963118984228544544700460073', '194.11875355364932484443901309883', '194.58099690153315163665421260053', '195.43357328732538344280816472144', '196.0732608198961357760769822516', '197.32674164520554541165271641896', '198.0520035800565620298984960197', '198.69694557391981082010103602809', '199.589388814619106933460278754433'], 'prelabel': '1-76-76.71-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.35294251619859923, 'root_angle': 0.019163368314845542, 'root_number': '0.992759831450808727819719377972+0.120116264751122884346980219288*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0191633683148', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(18)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.889053561819422050317307985967+0.0183537808416836338423537107732*I']], 'z1': {'__RealLiteral__': 0, 'data': '1.58702375545', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '3.78841354529', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '5.43022470102', 'prec': 44}}
• lfunc_search •

  Column	Type
  algebraic	boolean
  analytic_conductor	double precision
  bad_primes	bigint[]
  central_character	text
  conductor	numeric
  conductor_radical	bigint
  degree	smallint
  dirichlet_coefficients	numeric[]
  euler11	numeric[]
  euler13	numeric[]
  euler17	numeric[]
  euler19	numeric[]
  euler2	numeric[]
  euler23	numeric[]
  euler29	numeric[]
  euler3	numeric[]
  euler31	numeric[]
  euler37	numeric[]
  euler41	numeric[]
  euler43	numeric[]
  euler47	numeric[]
  euler5	numeric[]
  euler53	numeric[]
  euler59	numeric[]
  euler61	numeric[]
  euler67	numeric[]
  euler7	numeric[]
  euler71	numeric[]
  euler73	numeric[]
  euler79	numeric[]
  euler83	numeric[]
  euler89	numeric[]
  euler97	numeric[]
  euler_factors	numeric[]
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  is_instance_Artin	boolean
  is_instance_BMF	boolean
  is_instance_CMF	boolean
  is_instance_DIR	boolean
  is_instance_ECNF	boolean
  is_instance_ECQ	boolean
  is_instance_G2Q	boolean
  is_instance_HMF	boolean
  is_instance_MaassGL3	boolean
  is_instance_MaassGL4	boolean
  is_instance_MaassGSp4	boolean
  is_instance_NF	boolean
  label	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  self_dual	boolean
  spectral_label	text
  trace_hash	bigint
  z1	numeric

  
  {'algebraic': True, 'analytic_conductor': 0.35294251619859923, 'bad_primes': [2, 19], 'central_character': '76.71', 'conductor': 76, 'conductor_radical': 38, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/76/71'], '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': '1-76-76.71-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': '1-76-76.71-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 0.35294251619859923, 'root_angle': 0.019163368314845542, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.58702375545', 'prec': 44}}
• lfunc_instances •

  Column	Type
  Lhash	text
  Lhash_array	text[]
  factors	text[]
  label	text
  type	text
  url	text

  
  {'Lhash': 'dirichlet_L_76.71', 'Lhash_array': ['dirichlet_L_76.71'], 'factors': ['1-76-76.71-r0-0-0'], 'label': '1-76-76.71-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/76/71'}