Lfunction data - 1-828-828.83-r1-0-0

Formats: - HTML - YAML - JSON - 2026-01-01T16:32:16.131731

• 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_828.83', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [0.23575893550942723, -0.9718115683235417], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.32706796331742166, 0.9450008187146685], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 88.98095772994952, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [3, [1]], [23, [1]]], 'bad_primes': [2, 3, 23], 'central_character': '828.83', 'coeff_info': ['x^66 - 1', '0.995471922573085 + 0.0950560433041827*I', '\\\\zeta_{66}'], 'conductor': 828, 'conductor_radical': 138, 'conjugate': 'dirichlet_L_828.419', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 0, 0, 'a^52', 0, 'a^86', 0, 0, 0, 'a^83', 0, 'a^46', 0, 0, 0, 'a^12', 0, 'a^54', 0, 0, 0, 0, 0, 'a^38', 0, 0, 0, 'a^23', 0, 'a^37', 0, 0, 0, 'a^72', 0, 'a^3', 0, 0, 0, 'a^19', 0, 'a^62', 0, 0, 0, 'a^44', 0, 'a^40', 0, 0, 0, 'a^42', 0, 'a^69', 0, 0, 0, 'a^46', 0, 'a^59', 0, 0, 0, 'a^32', 0, 'a^82', 0, 0, 0, 'a^60', 0, 'a^54', 0, 0, 0, 'a^37', 0, 'a^68', 0, 0, 0, 'a^47', 0, 'a^64', 0, 0, 0, 'a^18', 0, 'a^0', 0, 0, 0, 'a^40', 0, 'a^41', 0, 0, 0], 'euler_factors': [[0], [0], [1, 'a^52'], [1, 'a^86'], [1, 'a^83'], [1, 'a^46'], [1, 'a^12'], [1, 'a^54'], [0], [1, 'a^23'], [1, 'a^37'], [1, 'a^3'], [1, 'a^19'], [1, 'a^62'], [1, 'a^44'], [1, 'a^42'], [1, 'a^46'], [1, 'a^59'], [1, 'a^82'], [1, 'a^60'], [1, 'a^54'], [1, 'a^68'], [1, 'a^47'], [1, 'a^18'], [1, 'a^41'], [1, 'a^47']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-828-828.83-r1-0-0', 'leading_term': '0.400135896324105148689451018331-0.825338239304230965359645043851*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/828/83', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.9172196818564806, -0.4522416439953804, -1.6387238284848684, -2.0288126277710883, -1.3422054461170645, 0.05905121874855014, 1.2326164996079079, 1.2414539412136678, -0.07951730506173643, -1.8236528147555064, -2.578531218698282, -1.544688170940359, 0.7000273484543313, 2.5526657170293365, 2.697541467712637, 1.276779703349109, -0.2091892642981001, -0.30516333186520606, 0.9513056868634435, 1.9912326853389875, 1.2585029072854774, -1.111342151717766, -3.22350146861662, -3.1950921878048906, -1.065603570773035, 1.1535920169090206, 1.461377661515971, -0.12098086018379726, -1.6615971322987355, -1.4927215639489404, -0.09198340201083385, 0.47270741604220884, -0.9952557109205712, -3.2238520433656523, -3.6853529441496646, -1.4078622452249994, 1.7814100874336232, 3.110787231807364, 1.8117212019504505, -0.20099613757841256, -0.7139073784496268, 0.15188563513101194, 0.23053922417860911, -1.79307331987334, -4.43621309370406, -4.944773526635014, -2.5866945798074172, 0.30789631842465914, 0.9719973529858332, -0.5995906799894146, -1.7919984788641392, -0.7058620478679563, 1.4611609987945902, 1.9923813017136776, 0.1932792015239382, -1.6625443818275103, -1.2708926356943677, 0.641738563959662, 1.178928746856415, -0.9289528252425043, -3.4998280778021282, -3.537250967236534, -1.0207498040954281, 1.0761726681212014, 0.61196220549276, -1.0454956444526926, -1.0089939998299324, 1.1487612995999084, 2.800064168842457, 1.89106088463285, -0.137296671706437, -0.2173688747191462, 2.1075966696329176, 3.8681136907053726, 2.5489831403447374, -0.4893516256663338, -1.7217684456404063, -0.052618753081063216, 1.9111585025257176, 1.5720332223080544, -0.16635499970381395, -0.4865060401932112, 0.9952230985787398, 1.4215993098623732, -1.2190892752587417, -4.815387571580794, -5.489519160571225, -2.589040985965631, 0.5147247214442087, 0.9223229266126368, -0.25316950165212876, -0.1114040028711554, 1.4789829917580397, 1.7074281562120572, -0.711275455433004, -3.083135423451152, -2.1844920176147, 1.1261385425135353, 2.8405941273436563, 1.1755651207268896, -1.149724725083729, -0.9095835472014004, 1.1688375916095353, 1.8606857257382956, 0.46650939677555225, -0.17018959209955573, 1.8017406628953891, 4.013985738486302, 3.0349345893742363, -0.5418604969231293, -2.6471294851114666, -1.3294792306730931, 0.6942999066701184, 0.218210886100396, -1.771383787988197, -1.8171046783148317, 0.6084674513875239, 2.2600780466127106, 1.122707486048746, -0.4093275461096828, 0.8399877271622507, 3.814632320647304, 4.54498606220165, 1.9961419125698654, -0.3438545229103977, 0.38899103530985385, 2.272628075696565, 1.683584172128699, -1.1175755330103896, -2.4230527502821606, -0.778509798013389, 0.9091442438437074, 0.09887074460748477, -1.2757546081777162, 0.10841683332545621, 3.3747887267131835, 4.2037250777753945, 1.121331063804471, -2.17502220340281, -2.064400980109576, 0.09825888840117088, 0.6953574104213067, -0.39050745312045354, -0.07155676698858239, 2.2956991473394157, 3.249638894041453, 0.5786620537319593, -2.680474850186008, -2.2589774701856613, 1.14113723335689, 2.9452159715553297, 1.4226701232866534, -0.27241862646738463, 0.4442549500438644, 1.5583581693055741, 0.20159605468431166, -2.1557454977750643, -1.7793977921331205, 1.1137268195150665, 2.1532071582959706, -0.5994105902133596, -3.5031931410712054, -2.7113926239850743, 0.22376952965589653, 1.1257923079356105, -0.33433177166065864, -0.7981727500369645, 0.633859728294468, 0.6609023429563741, -2.509284391505421, -5.433149932983963, -4.2168042765543, -0.49223708981111247, 1.0068598566638245, -0.4579453463244796, -1.0710639663085009, 0.9128160009300185, 2.2633157184643067, 0.25932303140850976, -2.570142602913924, -2.341560389845093, 0.02442424407194036, 0.5448204344082035, -1.0627276411583049, -0.8744572159818893, 2.490780604747085, 5.0237929700087465, 3.355238268670316, 0.049529276665244835, -0.424701442458684, 1.4945321089182855, 1.812710119132554, -0.1084887869843719, -0.7121924540554868, 1.2895589818085667, 2.3109135048896507, -0.15396563155732634, -2.9253099783985075, -1.9206463941402445, 1.2279050358499348, 1.6334476416945072, -1.1808237281794296, -2.818140361308629, -1.2361574714558536, 0.3890603358326645, -0.43380898317154193, -1.2430663741034775, 0.6427126240226197, 2.6797357790298353, 0.7749132169919963, -3.6102422796362084, -4.9775570683402695, -1.9735320539655712, 0.8777883106612705, 0.4798745437800956, -0.617869312952255, 0.42912137173981574, 1.5751115413875538, -0.1264559808866421, -2.541336683013158, -1.3821078758034275, 2.432547517756158, 3.6150828811252236, 0.6958180392868614, -1.8107440591401205, -0.7647130947739847, 1.002658009571743, 0.190940027248658, -1.1867079251722326, 0.33444614197966654, 3.138098093497167, 2.9731093159140216, 0.3525087673611867, -0.016584885226570704, 2.8513389965963207, 4.4157971483887675, 2.164848106096091, -0.22431941432975402, 0.8507231424138589, 2.9652877944509988, 2.092604313127808, -0.4265477494041289, -0.4235005738243593, 1.655508005694109, 1.5394282804981452, -1.1871924706122667, -2.086824789086494, 0.4218102358802017, 2.008786441293425, -0.3799453521514828, -3.2638714981483745, -2.3589282951336195, 0.45848864777488246, 0.7129415708570455, -1.0506736477190595, -0.798328479247701, 1.4088234546556861, 1.4741357881867758, -1.078755949891662, -1.6825808050942692, 1.4143892494833998, 3.601979297991508, 1.270241574804878, -2.217028231297599, -2.0664486365963897, 0.4174558519394521, 0.8862716634822951, -0.457838476397157, -0.21646027963902847, 0.9230182162263973, -1.1950582728832329, -6.186689464746015, -8.190755480724961, -4.673288579797385, -0.3799725360133433, 0.2873193968479486, -0.4680510720788927, 0.9245139690505595, 2.65291474728716, 1.2449835681729216, -1.4516285327471767, -1.1184467202145147, 1.2152707952806276, 0.6664630041247286, -2.8325961444877827, -3.9830500780340117, -1.015294327740376, 1.3335386475345563, -0.12996474383639278, -2.082523937294378, -1.1306234255566847, 0.24931639440109862, -1.1713803874932402, -2.882182274953728, -0.9543480083553553, 2.4405706495135338, 2.1908819047133954, -1.0336614981422327, -1.9001221690398729, 0.46109461246185407, 1.3403164416945792, -0.9226376754618375, -2.0940868462546063, 0.09441742738385656, 1.7426098412851707, -0.1651845158837959, -2.3011105437625985, -1.05346246477948, 0.9705119830788906, -0.052559305974627296, -1.7420038435248826, 0.512271758915767, 4.930923006167494, 5.633473431920235, 2.1803353650566577, -0.1763158750557729, 0.4865993909744415, 0.6299178699364156, -0.9664283511343903, -0.5660159883921849, 2.9335521630553645, 4.593265098776007, 1.4446683215923517, -2.02658583712221, -1.1390627411905612, 1.39097429263241, 0.6606959876792352, -1.9566963963519886, -1.9541979099212692, -0.014569819422008296, -0.15619602182548625, -1.6548566338727477, -0.3098230912268901, 3.0032946936565277, 2.745726819846534, -1.6844874235288267, -4.23920008910322, -1.9256971756758863, 0.8740428557035326, 0.5599685227491747, -0.07727422236535927, 1.6742520770192229, 2.77895035718046, 0.4228039149682139, -1.8367036030641481, 0.035474232978508324, 2.946786564904892, 1.6445746553305693, -2.1576582618697957, -2.789887769212294, -0.3070799473897162, 0.4358012893259755, -1.0006425648398065, -0.3136716849846862, 2.7754590113024564, 3.464106838315222, 0.7484123218584149, -0.4077767549348528, 1.9860651022712639, 3.31394450466673, 0.9056465189616839, -0.9226136560310761, 1.2679056801003237, 3.678551443965313, 2.1177114935974846, -0.5413000543504634, 0.15251211518347238, 2.2150454342786015, 1.4451354228976054, -0.4667226338468819, 0.5683314163284778, 2.613902153810729, 0.7314362870358522, -3.5865739387868922, -4.219450656679162, -0.7878846575238996, 0.9914718641689568, -0.6086848820080025, -1.1474445433454172, 1.0295505060050878, 1.931941654594148, 0.1814707288357259, 0.06733491207202767, 3.110702929222433, 4.242383932187456, 0.6530251779232186, -2.6402652457293962, -1.1630616177909348, 1.5522984793723875, 0.6602980734668218, -1.7044520818165878, -1.3004625487098647, 0.26870451544439466, -0.37054800714666347, -0.8085341714130643, 2.772316220391985, 7.1330276557836045, 6.187824452403887, 1.3330183157370257, -0.7607486329795075, 0.9078175961180073, 1.416899625059259, -0.29656991203086536, -0.2820864844495199, 1.6234933206797517, 0.8171056788541368, -2.9049692737409134, -3.8799221666072015, -0.4912888211911132, 1.8078922309398011, 0.27199695757804854, -0.5752574045095833, 2.098982806226326, 3.9292824627598835, 1.5493618561857003, -1.1286421951672476, -0.279785182641824, 1.0451852173130405, -0.5064210598222924, -1.6781377975694192, 0.9999965905699141, 3.729366665655988, 1.7370233213484891, -1.9780910206954099, -1.941592687111025, 0.16277194096530637, -0.6736977159688396, -3.0910227910614463, -2.172730218753395, 0.9327174678176251, 1.0916958112662676, -1.1950422720311993, -1.2134538601812033, 0.4300030321797641, -1.0434435585737951, -4.627613370865462, -4.226257707012976, 0.4031218561384857, 2.738519713208462, 0.5698376912936616, -1.1420287040720853, -0.03961669036200044, 0.17261991293712284, -1.6970303577505104, -1.4775649656796568, 1.5122574119764767, 1.704569915500727, -2.703397712404034, -5.510737293699634, -2.8032976215522574, 0.6591081208266101, 0.29895809447059113, -0.9729729806361067, 0.16736243939115467, 0.7939921039831701, -1.595635274383461, -2.9615899078445316, -0.09834993071628637, 2.517904634336302, 0.43491193986325255, -2.455778822476575, -0.8838127436849335, 2.3314878302687934, 1.7999246906701747, -0.7567379154491027, -0.7116213929950245, 0.401368431007755, -1.2481207225695432, -3.1724012487228164, -0.9000788753246218, 2.7550568576185683, 2.0191658579251355, -1.378049350131368, -1.4248728938530955, 1.2327557589001827, 1.2022175801565436, -1.0513102177083693, -0.4265802966961338, 2.54857042767602, 2.6308922454635666, 0.052709147952344784, -0.10912236452000622, 1.8520090371267155, 0.7178705663549123, -3.124828076999871, -3.7433630717837865, -0.6820478060565431, 0.20313502853615023, -2.1515890693306314, -2.2316172977980284, 1.2730136690099307, 2.957286713627222, 0.9347229341989622, -0.2687702111767769, 0.7518842932002436, -0.21966684138139925, -3.394229462236975, -2.9118640271489764, 2.288123081020603, 5.301665829897824, 2.7038785781093067, -0.27186639716925043, 0.15735520292835745, 0.5206617251612993, -1.3957692779026958, -1.7494171998062291, 0.8829365260118125, 1.4777071139506517, -1.887851668983418, -3.4799628412891996, -0.23022615406840316, 2.3123408771764855, 0.005646063429750428, -2.6917521589526325, -1.5268358005483773, 0.1421512633895262, -1.0220069543482286, -1.73987326719628, 0.36482042063745546, 0.969500427667905, -2.442414568804876, -4.423163866480735, -0.968161810743639, 2.8116135434980394, 1.633500864937758, -1.0774963848906642, -0.5812919131869686, 0.6242172526652983, -0.7410356142495244, -1.3321853632186658, 1.8151847359767088, 4.153946740042591, 1.569976290904609, -1.569220974363242, -0.3239504101646966, 1.9232942033571643, 0.6392529220118062, -0.9316222363478942, 1.4284332828258026, 4.0599878583709605, 2.1771813587460143, -1.0243062503999678, -0.6736707086718285, 0.8115329723741344, -0.31823541953076956, -0.8553165250548164, 2.7630260718400916, 6.0688581467568286, 3.9515056062348712, 0.21486492456961387, 0.645610703867562, 2.7250200277709955, 1.4213788564248977, -0.955828703469878, -0.030103151601580266, 1.5772768315158963, -0.20603461364692027, -2.29264008682428, -0.6574419936510896, 0.9479412694362342, -2.058010929913139, -5.543976334486182, -3.6957259566030887, 0.35128023404426784, 0.49955963081484844, -1.5623096057847596, -1.0712127116766674, 0.35276856011923824, -0.5382081774121898, -0.54252223686706, 3.640120645934479, 7.067112202420336, 4.303172475303865, -0.4504170693025076, -0.5486337517378048, 1.871486662099716, 1.3732701432435157, -0.3888368833907168, 0.5588871482456922, 1.647091835499349, -0.6242254895090331, -2.468994952904754, 0.22371771982171537, 3.089604686818555, 0.9256957645598142, -2.4290320398782996, -1.303857985076518, 1.4351572902823042, 0.7001166552354489, -0.9765978332815636, 0.5905154186181554, 2.3131155285823186, 0.28659874805271796, -1.7541951177148787, 0.3477672878139552, 2.624966948392643, 0.705273200410098, -1.3536667253934225, 1.0019370022494976, 3.6853547032901885, 1.8307301504097049, -0.9079340788238819, 0.1486666071403829, 1.7314847824812707, -0.11082076907481242, -1.7800302976432487, 0.26851507003332337, 1.8908779158501994, -0.4339585929596997, -2.1399568422224164, 0.40407631311675873, 2.2095942147700183, -0.8544406627494626, -3.8483885002757257, -2.047602331812818, 0.5645206566443918, -0.21204718821736276, -1.016833637905795, 0.9932088903097257, 1.8024538698883807, -0.6213389887827286, -0.968596899104667, 3.0191611914188603, 4.883009101095131, 0.9290755000846548, -2.8134393161609164, -1.560935355869198, 0.6126110616089565, 0.12312812335912872, 0.20801501368222722, 2.2466801423860927, 1.6677054774442681, -2.0441191663553084, -2.304636080405962, 2.5354723143877633, 5.266294123380451, 2.4857626371937305, -0.20315602025308097, 0.28464513116774537, -0.4008827391786759, -3.5832715648782596], 'positive_zeros': ['0.21206738827590890392206635667', '1.549989256109399403285380506957', '2.48578254780025282355458594246', '3.65799803155595016373745636074', '4.93964720588280422428703042533', '5.41154301460369502025945321851', '6.42966899431695355128238489626', '7.63131776737502745773058751585', '8.418120898524093999189882915112', '9.39692791150460573100591186017', '9.837832482975082344752158321825', '11.069244068967442591633575952604', '12.148135379171990391352055123379', '12.76158630398251596708568185952', '13.18491347916957245405824039019', '14.644654643994402580706932282733', '15.21416544230198605128806567837', '16.03701062472360825985076231323', '16.900736419055913434079913361659', '17.70702385838122023031165158119', '18.33227970963080345814145903048', '19.492966948674254403361553288170', '20.11088175807336569649345097825', '20.79107899321335000467668666208', '21.84754041731744848794490532177', '22.23034670951459866947979247678', '23.38326700505251289613357162880', '24.06927970624798860588833383583', '24.965550768726773115674196751501', '25.43615492347950389010489230993', '26.1414771854838504619683178433', '27.42926660683280285196577008818', '28.04992205668059636859305254860', '28.46493305776681182208160895170', '29.30191301153732935049855206227', '30.2089671736441722677860972833', '31.07322582844277948834602319680', '31.704307828226330648729449558727', '32.605208430221802812404386331934', '32.86728079016616457582457872216', '34.01610889270139391295965751619', '34.86431832166590421151640397396', '35.34885166494840270913202049915', '36.18077966782963340123130816340', '37.06021459843544294917154177836', '37.38309983699422175158672306362', '38.67051748239470570257701611911', '38.99537771306583763311650210633', '39.87985279948488616761558609659', '40.73272351900821012730707101781', '41.26748611640956898777368318761', '41.86326993999511394055870344096', '42.89995235523004954703774335122', '43.73365242602413011520913412028', '44.26457963315129869788085043383', '44.70050303967397792058541927913', '45.67183367742255814329243413205', '46.462413593756443200273595756810', '47.41028195131057158058939527352', '47.71404867710004778464377853166', '48.46222536987851395271696028067', '49.25930251439473920436661788050', '49.94922446913151492874249858505', '50.910142826665091043661905206134', '51.49829498121554506881363902620', '52.062973853291819867554206523627', '52.5914210041425053321389141979', '53.80079690874681415693650504343', '54.29694843549717116010028581972', '54.88313112839840452819453958493', '55.649967312864820465781225720983', '56.55869058221676499168402948047', '56.99511965873599487893429925435', '57.60314346600241026963521564474', '58.75664907044545404445224318514', '59.14414280582909993196953688826', '59.98261522537786739761357386731', '60.452171042673929293809152682983', '61.23628146911338847361912687470', '62.057907209093529974498304940332', '62.69593308852277240836776521295', '63.625150068224112187704039577953', '63.96883933826733240579152562948', '64.6132638490162940009148901539', '65.370036900174970162241353017140', '66.42804550055614346034580493345', '66.974019286143214350593677710627', '67.42164687997352901318558876682', '68.11108621783935885458997938124', '68.86688359220139157777418773276', '69.74843569805304534583827406789', '70.4188893465618865711667947382', '70.96954020319759925792852536998', '71.5252881912191920399828379358', '72.55603558450511563232881170847', '72.8155226437207535860946221360', '74.003015281636945697432919817992', '74.24402979958889705181044416860', '75.247157249848623673295070149006', '75.69448432711414399374963268642', '76.43400303532954774931367186636', '77.14424719700809272700899724129', '77.779312223151588479536914152616', '78.68799493961615268350282675931', '79.18993089873318628929493326752', '79.80413115616350492753147590256', '80.500481313204945324466974063620', '81.13075351494059478493755641349', '81.97353598071279572903258677055', '82.75335881240399750705199733915', '83.324575844901063551040613811036', '83.7980132994564154043981782409', '84.272088470936172949919426752', '85.67620038965272325129224144946', '86.0269815540001441614690885343', '86.41952701666642151341771310774', '87.3162060960512096387598848009', '87.95463958227682568716990147443', '88.50617391412732694454039990918', '89.46671749662567620797136957273', '89.98434571708455862577542418716', '90.824836867429845650895429176816', '91.06608754165221738608334576492', '91.95455739194297366719070537238', '92.71157757228480711025523651372', '93.382003041554759461166317989045', '93.9556898949146943991057713119', '94.677148514978611561403829526738', '95.29493244513503912998582903664', '96.067368762427290299747577062519', '96.55526695576911316015111974840', '97.14858191403558844431455033615', '98.376774620403783492613273693814', '98.61321786542005696100435231739', '99.195846380468952165498084668110', '99.75179020264116875491430216846', '100.72777529238954385179136653157', '101.37237814581248175344137928949', '101.951358069360665972573327338136', '102.81585542889906396926190818530', '103.09007590159773825187659424056', '103.77986337256815472675714262334', '104.578996889379576376575868347006', '105.49216752145426073316606562767', '106.090212782388540882998410608754', '106.282205973798758668876182646920', '107.22759392166481859995959316919', '107.80930011210763579084576519530', '108.56827287927074231897111483687', '109.41979520447724762570346929795', '109.79315582781153906859495180353', '110.34947674257957254879356999210', '111.343665038531117040149460482734', '111.64662289398170778190254484041', '112.59593528206869576316265648704', '112.9980312388928976222536932739', '113.97104930412661051726871438610', '114.35319930590041201518134871273', '115.20426529323636504520323004260', '115.54504162586006983128002992584', '116.30332373455214364973270241114', '117.26333864882986912493705462198', '117.71889326375698131941339757995', '118.30802431831579232447694727662', '119.09677314710832368403241854353', '119.36342019621859144617809568866', '120.35671563209760722453717275478', '121.04769642671245056628613988890', '121.63956730487507752486461578252', '122.41685948885026618843906135985', '122.72700063286261274472493105427', '123.23695453523622566098029387025', '124.48821573441522672119205660772', '124.86220862799338075407377010414', '125.56893226630501857067580481748', '125.988063903964906067215512143561', '126.63899460038645453420178347485', '127.54019605653342661197968896339', '128.164718260853970083739855832757', '128.53834505659371368121007041545', '129.51715005840285955425416639461', '130.04309718658046974727250186606', '130.556477860129460150229604398449', '131.16620077225429271449315346673', '132.00512700379095390545908900140', '132.774673387984815083004621220645', '133.024558782657543653710523827896', '133.957227599174379533376992637621', '134.52337642580082669500264589631', '135.20378025163195364313399365316', '135.50944187625454741472959285502', '136.535722648927917531127952012697', '137.251054301018828788394446347262', '137.8214028551450992870626794730', '138.16323979742678168840330771238', '138.91026952445161387824403088936', '139.51789272823871870779460038107', '140.536299135663860988813718254090', '140.98968305295368382424282088440', '141.53244690020497043906762970364', '142.012618190443886737594359695967', '142.820312279731629016567580972488', '143.47373867550459391410439105524', '144.137749141950096506396023045523', '144.89105323637396837781845397303', '145.46100789781196957701200278501', '145.77085656406844390928633033751', '146.6291109372149143673907348761', '147.36300990613947307191380488193', '147.97611904649674904448503392046', '148.59534982906252370384627137032', '149.11001696254297548493687546613', '150.008161907994432093923091985500', '150.33190788945081391328152399866', '150.99941575536001886741444261487', '151.961339681593013585937360322550', '152.22697706624270867677360312131', '153.02098629211273078518450453803', '153.89580267311837709118039452297', '154.17025301659663721846161569179', '154.66168099042027252048063259752', '155.49962495579472359005283624593', '156.50830727720398159008061883527', '156.83627716727029686655411040467', '157.29601159330712075902648790038', '158.028736455495940423405110894210', '158.59687563188638302571564095210', '159.39227839696135039915240631125', '160.00047733461493437773349213603', '160.86688842974703178114754885314', '161.04889938613255369391659330345', '161.82869655505007591678359598851', '162.30500399861427747194620736614', '163.18595548865038058911811746738', '163.91063206918937790184438151327', '164.47740872149875996370139670278', '164.879879887659768647765423451036', '165.477179003428792540976979685', '166.371737660943562210445505531419', '166.90960830216457362984912836913', '167.58048181501687546737825011583', '167.99173376061939820640023546921', '168.93572853802900377411581063985', '169.482632754499430515722422584312', '169.94649557745648888508125487196', '170.42208279050625010933039288986', '171.60153607306997514896668010053', '171.76759444779879778771018142615', '172.65463662502197127876344812367', '173.12916281881767272015646927244', '173.7282127611367344293580489246', '174.45025847509619302735048179456', '174.8410735386584694436827712341', '175.899705095230770484192214968485', '176.32229316229262044436358059085', '177.065478885184475269011751689585', '177.38304932408777326657934618015', '177.87545872531270840635800722606', '179.02014921743290551097578614367', '179.44314746100703442402438418907', '180.20811242097093130237920953331', '180.52863953879891017259560493200', '181.18851175003873894180141553400', '181.85783234912511708501239618901', '182.56980108335568928394218559156', '183.25093800485273043506489630787', '183.8458529434598100033264766225', '184.30381121377860748844943476358', '185.02837034568820478215599213159', '185.59255691728117893032011963420', '186.31963873299406030845076873615', '186.78818721812752943170248467101', '187.67030471716046798276577835196', '188.10538306927745059372252722699', '188.73770867568316752525732989498', '189.34668288780944770188128884239', '189.9579001327803326039569579456', '190.588749633317146460188580187914', '191.187997633346617544441478898493', '192.08164405714694700395684782593', '192.46197045588164458791501207102', '192.999020712149320193500750080267', '193.678302130512397508754755409515', '194.16042084709267364798515065023', '195.05583253063164191329970346630', '195.80832820016239028378966863570', '196.29145783870188023650328369445', '196.511291733378608578147243449766', '197.33231849720817309499726861998', '197.97887798637494184219416650432', '199.00820019586933589892022340775', '199.280026663660200331812280052828', '199.62932106439797109746739648892'], 'prelabel': '1-828-828.83-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 88.98095772994952, 'root_angle': -0.356306792111866, 'root_number': '-0.619374138740789307427297951673-0.785095966273617710781592028569*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.356306792112', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(66)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.935052118940955183365935789688-0.115627948757926176902034740261*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.212067388276', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.54998925611', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.4857825478', 'prec': 40}}
• 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': 88.98095772994952, 'bad_primes': [2, 3, 23], 'central_character': '828.83', 'conductor': 828, 'conductor_radical': 138, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/828/83'], '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': '1-828-828.83-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': '1-828-828.83-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 88.98095772994952, 'root_angle': -0.356306792111866, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.212067388276', 'prec': 47}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_828.83', 'Lhash_array': ['dirichlet_L_828.83'], 'factors': ['1-828-828.83-r1-0-0'], 'label': '1-828-828.83-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/828/83'}