Lfunction data - 1-1045-1045.64-r0-0-0

Formats: - HTML - YAML - JSON - 2024-12-10T03:21:32.017445

• 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
  instance_types	text[]
  instance_urls	text[]
  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_1045.64', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [-0.9135454576426009, 0.4067366430758002], 'a3': [-0.6691306063588582, -0.7431448254773942], 'a4': [0.6691306063588582, -0.7431448254773942], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [0.9135454576426009, 0.4067366430758002], 'a7': [-0.30901699437494745, -0.9510565162951535], 'a8': [-0.30901699437494745, 0.9510565162951535], 'a9': [-0.10452846326765347, 0.9945218953682733], 'algebraic': True, 'analytic_conductor': 4.852959597730739, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]], [19, [1]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.64', 'coeff_info': ['x^30 - 1', '0.978147600733806 + 0.207911690817759*I', '\\\\zeta_{30}'], 'conductor': 1045, 'conductor_radical': 1045, 'conjugate': 'dirichlet_L_1045.49', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^13', 'a^19', 'a^26', 0, 'a^2', 'a^21', 'a^9', 'a^8', 0, 0, 'a^15', 'a^23', 'a^4', 0, 'a^22', 'a^7', 'a^21', 0, 0, 'a^10', 0, 'a^5', 'a^28', 0, 'a^6', 'a^27', 'a^17', 'a^26', 0, 'a^18', 'a^5', 0, 'a^20', 0, 'a^4', 'a^21', 0, 'a^12', 0, 'a^4', 'a^23', 'a^25', 0, 0, 'a^18', 'a^29', 'a^11', 'a^12', 0, 'a^26', 'a^19', 'a^23', 'a^10', 0, 'a^0', 0, 'a^9', 'a^16', 0, 'a^2', 'a^1', 'a^29', 'a^18', 0, 0, 'a^5', 'a^3', 'a^24', 0, 'a^22', 'a^17', 'a^1', 'a^4', 0, 0, 0, 'a^25', 'a^28', 0, 'a^16', 'a^17', 'a^27', 'a^6', 0, 'a^8', 'a^15', 0, 'a^20', 0, 'a^14', 'a^1', 'a^7', 'a^12', 0, 'a^24', 'a^13', 'a^25', 0, 0], 'euler_factors': [[1, 'a^13'], [1, 'a^19'], [0], [1, 'a^21'], [0], [1, 'a^23'], [1, 'a^7'], [0], [1, 'a^5'], [1, 'a^26'], [1, 'a^18'], [1, 'a^21'], [1, 'a^4'], [1, 'a^25'], [1, 'a^29'], [1, 'a^23'], [1, 'a^16'], [1, 'a^2'], [1, 'a^5'], [1, 'a^22'], [1, 'a^1'], [1, 'a^28'], [1, 'a^27'], [1, 'a^20'], [1, 'a^13'], [1, 'a^8']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1045-1045.64-r0-0-0', 'leading_term': '0.325431613189999145206438447309-0.478622276482193184140667520982*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/1045/64', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [0.5787789028708994, 0.2127029642140948, -0.27437095410030826, -0.574166287241686, -0.18798707222486416, 0.8954729719876178, 1.8687829131699578, 1.5308638154066343, -0.6815365025201097, -3.8555595596524257, -5.858467138918643, -4.8097639016894895, -0.7339193315227218, 4.093454636449328, 6.6804284372116625, 5.632614604699666, 2.2480662897705974, -0.6708981567574367, -1.2645802213686612, -0.04654305413525578, 0.9975200925783255, 0.6174988604376935, -0.5360390742585401, -0.9628241276836885, -0.26930956256192295, 0.3149053643131904, -0.47753215514259356, -2.1597710481040426, -2.783073283190203, -1.1809289249993757, 1.451030070426317, 2.6968914011371092, 1.6375311712460803, -0.08178509607282825, -0.26867415539232975, 1.0488597199766607, 1.5808024410764085, -0.2703497583397485, -3.0476565016112223, -3.6524474931822075, -1.1329171027672007, 1.795856455980876, 1.7181110506985875, -1.33365160419416, -3.6520720759907492, -2.122149224129441, 2.010339870519201, 4.474931535698937, 2.888359543300644, -0.6553131489399903, -2.311095301891056, -0.9671485786184311, 1.0005177275205122, 1.1866611811032057, 0.02551323697960712, -0.4724379223521604, 0.14088444356519786, 0.31696117808771984, -0.8179095020120619, -1.8709158097423972, -1.2162002530637448, 0.33929059724043076, 0.5108555665702086, -0.8940469694541963, -1.1327351850508687, 1.630433565697782, 4.813811255750085, 3.76006409710802, -2.222522463598804, -7.988447322821122, -8.010605186596418, -2.7355234543811484, 2.165056679457706, 2.630650839574807, 0.3710224771623065, -0.5145765745251186, 0.7783971442545505, 1.4853505962154507, 0.006527517902595355, -1.654694724663687, -1.1311344975153816, 0.5784884115359319, 0.6205212835699597, -1.286572948384057, -2.297791854213219, -0.6958524028229369, 1.4502857614311502, 1.2988713617084382, -0.5833597281001155, -1.1943111853205508, 0.28645865078202853, 1.3398675372317734, 0.17551021045411153, -1.3932930677129016, -0.9237768984591166, 0.4946012575569805, -0.1285702904506626, -2.2630868474110355, -1.3820985975315354, 4.565695431094019, 10.741660112838499, 10.40529438114125, 3.4508608176706446, -3.144845909322663, -3.854805218732362, -0.6914427812623205, 0.8233539260968467, -0.7013013790380465, -1.9016042961406558, -0.615571772202637, 1.1482937800313242, 1.0010421015029458, -0.1095113481951869, -0.034124998710778, 0.7681313031368686, 0.2932776083912264, -1.1523130603836629, -1.2771788134307624, -0.0657292758191778, -0.4692484605463301, -3.4767252624390688, -5.399724498577399, -2.7595726377146934, 2.0084759966263395, 3.2934559324147155, 0.2247347164948025, -2.076305469870985, -0.1913835430226208, 2.4223877424721514, 0.7361203648851659, -4.060967052403981, -6.133312795441198, -3.443477715580793, -0.22912129525561414, -0.21392322018698, -1.4564759485627683, -0.46229188175906, 1.7391483108100425, 1.4673275916208135, -1.1915075191854174, -2.1547554185474045, 0.2768314057156942, 2.789660328032772, 2.273803915546734, 0.3007611521716097, -0.03581328271848129, 0.9033319572425533, 0.7392092930175278, -0.24389100210417547, 0.26975939939791865, 1.918185882495948, 1.8094522544573008, 0.010615492453761236, 0.4995516293922605, 4.430157050336039, 6.479140659230692, 1.9398408637775848, -5.158233924175459, -6.236251960111068, 0.11332052220625684, 5.953878101667034, 4.820123000600909, -0.2331580150684881, -2.329207164533955, -0.45522219777016015, 1.0340017535615984, 0.189343537996297, -0.5634414717708099, 0.16630864375472432, 0.45499512423633826, -0.6121167096124427, -0.731352883227792, 1.291945468268376, 2.6854653506393893, 1.1565417127976636, -0.8236745727138928, 0.10947361157437872, 2.344684788070319, 1.7703956937185465, -1.1417971043062618, -1.8407611959157546, 0.6192117728546366, 1.815725040015209, -0.40124026829272796, -1.750509059367454, 1.501551367260009, 5.744861026058165, 5.210330619338282, 1.0918366426368848, -0.47457409741263423, 1.5931103949341243, 1.856541100524173, -2.189357483441972, -5.49482223283737, -3.3171580346186484, 1.3852648919486656, 2.780054203715494, 0.7449314579700977, -0.4281705570178093, 0.39148554334172136, 0.4122804326158172, -1.0889092193204228, -1.488899859942195, -0.024343345360404004, 0.7147954675619413, -0.2334427380041321, -0.3981160226528184, 1.0982492490313516, 1.405974845433147, -0.41773093625019003, -0.429152928461008, 3.3036810074786374, 5.114759618182513, -0.8612948235090776, -10.307726432357146, -12.890112249644055, -6.374782283484807, 0.5738115910662963, 1.031663101233857, -1.7479432337874607, -1.7255640090007782, 0.46932108708611564, 0.7083808694114331, -0.62136180059448, -0.08196358192972311, 1.8976870557404029, 1.8521446286383032, -0.11222994971599518, -0.5301022927157388, 0.8368940193288353, 0.5302367310084112, -1.8433703919807323, -2.257833691502233, 0.6349592836895958, 2.6670597773139666, 1.0633192167180276, -1.0290835922498076, -0.39272978074603027, 0.7622324734996696, -0.44639416540822496, -1.8078362509730623, -0.56111402436617, 0.07643071375782734, -4.211049587457149, -9.863545864955466, -9.248550849460758, -2.914872730651313, 0.18072475343460428, -3.8474820777607377, -8.089845150306024, -5.944136243260469, -0.7093382373488938, 1.01512383548283, -0.3739434357090497, -0.16328732108339017, 1.82446888892058, 1.9599913260564013, 0.0641169909192989, -0.6493676341401542, 0.2638598827616082, 0.37307614528082855, -0.297588938522859, 0.3369879339810914, 1.2100887512406668, -0.569727013813715, -3.2310699006214856, -1.8630844222105414, 2.7866226586086937, 4.235784148410064, 0.9820834917544867, -0.28033516494659066, 4.161790183725233, 8.08395859259042, 5.210477578458368, -0.34391585741733227, -0.7941207833860562, 2.9515427912547323, 3.8995069171544654, 0.8985495614730712, -0.7530104413296681, 0.6385237848480498, 1.1453094423162227, -0.44380122141293465, -0.4806708798122251, 1.7967184212012164, 2.0000987219322983, -1.385314620098687, -3.6326290171589823, -1.64816741533579, 1.0557682014286862, 0.9009937625688926, -0.10450247251067599, 0.6660088427255091, 1.3827300783257295, 0.22743703916489655, -0.28317948814393196, 1.5501603034290057, 2.2123832126881737, -0.6924264622250733, -2.8600283403180278, -0.7213366322964596, 0.538645580983798, -5.166071606139942, -12.754743918719804, -11.737278997158331, -2.4337669288121226, 3.9086891721903765, 1.6655664548110338, -2.5845897747643205, -2.2083114390078533, 0.3582964292769201, 0.6282565200814568, -0.1318464411202373, 0.6900563733447487, 1.4466292216192649, 0.29084347683795164, -0.58425273831806, 0.45929894671859595, 0.783642894395511, -1.125100364561175, -1.8192014339035678, 0.7843207451503057, 2.7111937416611913, 0.8743348552308433, -0.9052713618628077, 1.0088462689346347, 2.5579538425638675, -1.021906910838238, -5.728256678996574, -4.880965757630869, -0.6725538472200978, -0.2486839107739464, -3.1654756492467593, -2.8804153569843827, 0.7930597941137334, 1.3353934663169849, -2.2936916119709214, -3.638312105089471, -0.5085498880012751, 1.2658271858543948, -1.3405421431516742, -3.3158442932626926, -1.0161357276163296, 1.651671933390423, 0.8893578492449851, -0.6920527358265799, -0.10913759083221596, 0.47915839220065737, -0.9849719351512171, -1.9669647681563847, -0.6466745828689989, 0.26269392538786424, -0.8105768366458626, -1.0431261147847242, 0.4030475573651032, -0.09776550459898595, -2.2483273564153787, 0.749013587312238, 10.154904439864827, 15.526140140564952, 8.918296690552673, -2.0771548287571697, -5.06728587035054, -0.4794621683067865, 2.059767568717916, 0.0548059813381674, -0.6924033250402868, 1.5417988658131327, 2.3101445611476605, 0.53439341403893, 0.006975288004836684, 1.323066955729944, 1.1922753642465387, -0.2798019811303665, 0.09466252905629743, 1.423386059433136, 0.10077275641863964, -2.3158713330501515, -1.0539112374823536, 2.676530257933453, 3.16227157396436, 0.35924352965578255, -0.43103366028197265, 1.3478734520526627, 1.2039505919709876, -0.8107408225779819, -0.25623994492115854, 1.742139791676417, -0.5386178505371725, -5.540260599790356, -4.918034399514841, 1.9580803134385132, 5.611394974314308, 1.895333449776873, -1.7198324088670105, 0.18364735003474575, 2.3000477186884964, -0.4628318413412389, -3.696392773781133, -2.137813235658601, 1.1421203744794095, 1.253841222503148, -0.25304378297070773, -0.14387906225692115, 0.20738552044167236, -0.9064886867325703, -1.2898703058651373, 0.1604472894511944, 0.639431963518011, -0.3782998556079406, 0.6161219172444442, 3.195504181877002, 1.828210371789926, -3.4196666901647954, -4.739118528183717, 0.0007642761283993321, 2.226523975677838, -2.684988538418821, -6.573709342667876, -2.301040698853509, 3.8861767635224758, 3.197176926878917, -1.524965475826691, -2.521918460659855, -0.2832875135332159, 0.1454017951662769, -0.5834388615936229, 0.6508688853764073, 1.6990895651483284, -0.2689860588266994, -1.8237508100788649, 0.6870411554761104, 3.6112621450332067, 2.410568938286567, -0.08277174450074623, 0.5266855300897927, 2.0665828222614557, 0.9701059563296782, -0.5312895498516407, 0.34768182442141327, 0.8982783239736918, -0.9551989497616846, -1.4766136886285688, 1.182183335323644, 2.0281349421040065, -1.0570050891954401, -1.716114068675347, 2.8430227137365978, 4.130378326380274, -3.6528034191450125, -11.595170644206906, -9.218064270780058, -1.11044951664473, 1.4486614771096136, -1.8447432114837832, -3.163207124382063, -1.0039481623611082, 0.10595337702864562, -0.2506229798752003, 0.7347692056617955, 1.887768379268053, 0.7580569105749707, -0.4880771837877161, 0.5879366234423907, 1.3920945238035054, -0.14182749659101163, -0.8868789417382373, 0.5311827061509989, -0.2756734967988168, -4.3565757509808645, -5.144571517585108, 0.0055988462436859935, 3.688307766829579, 1.2204235047208039, -0.8153013290241099, 2.955675353398867, 6.3661015372855125, 3.1534899589187617, -1.5695783100655265, -1.1833972354210658, 0.8496694722056044, -0.698242099926843, -2.242668844701104, 0.7397174406226614, 3.965768065833415, 2.325524806212417, -0.5206623725174564, 0.33006955220454426, 1.8765452806158194, 0.11704989405519196, -1.820633378785012, -0.39498641456884864, 1.2478505088166632, -0.03061679910345662, -1.2788708661531676, -0.05729056410737639, 0.8353808991065798, -0.010324451502368884, 0.1850789224142298, 1.1355092112131342, -0.8600510607201929, -3.715059933626945, -1.5051108722369362, 2.485347929525929, -1.713599674719839, -12.455525867262413, -15.69480884731405, -6.7204362704989835, 2.465428475970715, 2.7264857843479184, -0.1872164101850371, 0.6869572875624853, 2.156719684817654, 0.25866802275404865, -1.526752940169409, -0.2494259506986781, 0.8816762668214477, -0.05461504900396172, -0.2434455591514424, 0.7582118840312522, 0.005658818544825281, -1.3925047961362598, 0.3070705529211619, 2.7587635695193082, 0.6764175985502165, -3.5606164918740895, -3.4366143485365384, -0.20884436680057417, 0.12037576474924808, -1.4994988539916287, -0.46178530769229736, 0.6554578748023966, -2.780885595182094, -6.205360308956179, -2.9839740714229186, 2.2845205735653673, 1.1893592282442356, -3.259841419904442, -2.780405991449297, 0.5621829142242596, -0.7151359181509125, -4.486451358525153, -3.3657830752535065, 0.8954710279311217, 1.1258611589712921, -1.8002768055128533, -1.8549962195475698, 0.4453160953030272, 0.5492715759727301, -0.8053815468640763, -0.4909766530169776, 0.24646688310545675, -0.15708928230550748, 0.6753239725900455, 3.0107637302048547, 2.7184225936990525, -0.18182617503585255, -0.45204667590728365, 1.3868169820261704, -0.9488722526014588, -5.589481846019658, -3.0684508232650063, 5.6279200108537655, 7.580901259234662, -0.7946653527247092, -7.357574371713554, -4.502568500387556, 0.33172947506509787, 0.16014193892482473, -1.0996602772984116, 0.39323659338236716, 1.1676410196468043, -0.535498637945528, -1.0305442830812794, 0.08418487210421002, -0.9368112287639849, -2.869709972491609, -1.0105836999374465, 2.7079418579899492, 2.487078115581683, -0.43204793061298136, -0.7905072678404139, 0.28826704214572957, -1.0908869671521282, -2.492364639900314, -0.36253378093473215, 1.7785612772388593, 0.3657868420983321, -0.6590960098681848, 1.4287712102135186, 1.5265946669327728, -2.2352479363147992, -2.5258813569689136, 2.8470348898139632, 3.952578325800236, -3.9041572116987, -9.896284805884166, -5.415354091491224, 1.842404156411702, 2.2504640773942928, -0.7699711923721727, -0.507729359185716, 0.9460749178570498, -0.12384024477559426, -1.109248173046674, 0.06022788570703766, 0.35286542781926433, -1.0999517354899635, -1.061388981715886, 0.2579024686690061, -0.3328149844493164, -1.3755920450497467, 0.1925468713801761, 1.3893022015461334, -0.7123591166015681, -0.841919748235926, 4.81944507939311, 8.510504874583658, 3.267981160920507, -3.496347317852132, -2.4006441234656677, 1.7830744008016057, 0.4650247238617632, -2.792856632780246, -0.9922451684881999, 2.060713067341478, 0.11832468612510993, -3.022983295960008, -1.8691220348031936, 0.14072783027724364, -0.9913251973370477, -1.5280856508807785, 0.998567018104683, 1.745173212025993, -1.2435173037243266, -2.4223050569660405, 0.22972524229921, 1.4765782084892667, -0.31726544802523093, -0.6559858891996359, 1.057031982597837], 'positive_zeros': ['0.45439393155846958877973368519', '1.316715171158199425275962285745', '2.424829742177262428284824260305', '3.795715851683234527285099731015', '5.2191536813369509407031887730', '5.947399458241295926572679125216', '6.7286640961441604374714410136', '7.595729918084366170668911734601', '8.007020823100449489079182308580', '9.200539006312648934121342281910', '10.29214113494351269269778482618', '10.7066396031508703452714786847', '11.53178690306137284604794290772', '12.60428152670888658692868295857', '13.31730925326901109711456340409', '14.2282266139100252082371777095', '15.25082787118605323855034410797', '16.07321900662639357184139115986', '16.882182120774116394363595231590', '17.440473185891822393751473844006', '17.93367502047533401350943314055', '18.98447002408466519528044255283', '19.50536930299862772498951948215', '20.16426970118919753702460790821', '21.1498559043222966173766910241', '22.33537893139576967073722194338', '23.18503355271456821777974247681', '23.59475007918535395501704528634', '24.375966875717212783429838102835', '25.196412472079715394900498096518', '25.744932483001871330299640189167', '26.649527011367201837264601391067', '27.40358317997648999821876272126', '28.07603165724804887133607028705', '28.7785529361636257743090601130', '29.556573653550050624627116540024', '29.9784516348403390752057870069', '30.72097809464562540733744416929', '32.01390136751539685370684496848', '32.88968759447385848836159983316', '33.32973872059233916484183158700', '34.153745026842775048272627273893', '34.958430828388870130556366645120', '35.3258752372689514345432882933', '36.00275147671926270086939861797', '36.89881159820787998038606754021', '37.08612741253579767157840867474', '38.297956450238423382782804864824', '39.081563779884922619931845958933', '39.705596050113755153931981485908', '40.36531714229899691641782879501', '41.61077147942321941944295721992', '41.81832501604619184024341361686', '42.562005592600969667754614037069', '43.30405923036874535935607616465', '44.0358690654163803540152404345', '45.07851342606528809736561547837', '45.32769449668035703387931795907', '46.15176188910832550470182041844', '46.499431919268890211819090773743', '47.50245434895296177962438279849', '47.73851347595078507120892607583', '48.83042018133125075361847137072', '49.68293597883302418464960563280', '50.60892535414644790583250436791', '51.31045089833295208441011184316', '51.92061744216834913845648041034', '52.44631862022668302998444627605', '52.96702948946116594031903855326', '53.576896297095259460526969841919', '54.52280102308906284714511725335', '54.984940986792510119273947301727', '55.814387185559662934016032607634', '56.493641260011024324473936512451', '57.14358220179150201581653582847', '57.70972826793135677740097538681', '58.86063873587101547392058080994', '59.164588581762526914742460087854', '59.857159362154275031213396659332', '60.83616384347910812530037903277', '61.6827829016470335105066400233', '62.06828211774008516792722790926', '62.6002689144383661462328075852', '63.44229261520433282160194400629', '63.99748240914095062053249765785', '64.47679199349443973535376826590', '65.244551691753320243324038997538', '65.67746584506492180566180196299', '66.53314621583173933736229775741', '67.772535275523501515120614962863', '68.23880931411194853115626784801', '68.98759873493796053795905611252', '69.53192707570059015381033755353', '70.013935606686021245952389948192', '70.91757519430284934651208783145', '71.37979508865239373322360219016', '71.954440564075302727662587701276', '72.75436162802178497531286676382', '73.5632919270865911694810133423', '74.13707638831133239224818425661', '74.615824975946694390075797900005', '75.412363071481862589864362112426', '75.63885811481643050960243909464', '77.083406820176086157170809132816', '77.22808989280708422079379544883', '78.496728040059327278189964624193', '78.98080302610290284514523196325', '79.40455574296817792320253809491', '80.32390667849474339006873816680', '80.85321984710706379294739251362', '81.40091288649711612553648608980', '81.78633987619195726980039397053', '82.43832994864122331014474094097', '83.25416948654366643127440807378', '84.16136031744082371734871062651', '84.41345004653683638069775314373', '85.59860747181421359388217519899', '86.01440303515922587052936221670', '86.97304992312746424325258621872', '87.38804962216309068622171801389', '88.04184468669800810521045072502', '88.51612416795680095298165051827', '89.26437484470390502335854072554', '90.161450662150251835008391070902', '90.86515625796103646458500512810', '91.06212326044060321807219640702', '91.92589004035763170297352336115', '92.262188851296798373017328173273', '93.06579737324340077043782945891', '93.82555270738508824268619479318', '94.12374949317565221204104170228', '95.39519458399949291007090993210', '96.04094540440353324054273277398', '96.81893282071976277873947814758', '97.3970866570564103170562532941', '97.62260097844413997060999694061', '98.49661454363207039225306544548', '98.95763217083499555969782574773', '99.52745539619703384071110274228', '100.23718169715355683554418932835', '101.03813816390531052942665888026', '101.450062957179644069133266884529', '102.12749345731069075198611120521', '103.2093401885088040393199779739', '103.39758712676409561877636371990', '104.30415631448942809879391030178', '104.81975668273757846070697688557', '105.67058869412783219344508640293', '106.12687935304417552501200332170', '106.96644096666841341412458592444', '107.63990809625222307362645450984', '108.15277875141837993756290712286', '108.57938474368857540523666036243', '109.508928459362340647222992103798', '109.80460208584114214763615700658', '110.53355046237283902864352143280', '110.92274943237103667048598311516', '111.52748841894994804084556578704', '112.742729678589059658119784512825', '113.468359617197874278677589915444', '114.06972451151893338246196699457', '114.493814313202081620073134287644', '115.43551679056068456071886177850', '115.622348967311762986826929409014', '116.48820101017572175403384205577', '116.85464985413940361829731826758', '117.51150318503333658621588384986', '118.21316494572146339039561723212', '119.10985171389952732109544277845', '119.46521183720608835576838375559', '120.17537804696630429568305732104', '120.65978994462316905921998370847', '121.21371697735070200591268457834', '122.10435222104030991343870401257', '122.93024060583960658543417771646', '123.42079648700640515818552494648', '124.02859139793948239051579871781', '124.8708289839213096426331352479', '125.55449377991373655750911387091', '125.99600345164707369489862528140', '126.33993437018613870918533034661', '127.15542352231970182444415436285', '127.68708812456330614772050535336', '128.03560641955692948136842564287', '128.86507199459326497855984744667', '129.68745436810693529314173719337', '130.17772342005868477729412768535', '131.0360510390036072469523400137', '131.76618303938781578646554161697', '132.55376981568452055846568797253', '132.86207038006966970250070765943', '133.32609680785366301557007931833', '134.03206378539897999256540772099', '134.63004461443748698450459502583', '135.60543212761822198259592763342', '135.838711127669900217428335563941', '136.71598715351154550763894335036', '137.113602664907851532492856800480', '137.67624847437363050990705972404', '138.31576354609795761173109283529', '138.96789643016957824132998820131', '139.515183807216354043555630976122', '140.196708514846224490463481686284', '141.3079843174318183850499094919', '141.722225866451010100772664475366', '142.698810523784821881867846402', '142.91127272220295236019259590816', '143.27414176000924352163814958667', '144.19631046573264504623135065487', '144.57304156793521654720605244255', '145.28915857625488542875461465295', '145.826786760827354999422118296004', '146.22000401411826707841592684678', '147.187209984554998885019377714798', '147.91861073451226138043747602326', '148.23962914399822618028274639065', '149.24316868728304379219917147193', '149.82923111002649515813432125391', '150.22999170186067373101344341212', '150.88419567554390773410241620131', '151.78628344399028764613383425911', '152.1394912090833205170142516121', '152.82543170203591095288594119822', '153.4881133234087637480014699036', '154.05787165861801619889223592880', '154.69798527141942919382744011520', '155.30853294411345947001207118095', '155.56929244537052308030296233143', '156.16705256894312996403332985385', '156.96980318693324255580966844782', '157.43646351141954427317027711249', '158.6361393070535814531042527545', '159.33863184233283353515585023561', '159.583003339672798423381621110010', '160.341559156242256636581531549793', '160.977666068196990902757684860384', '161.54738379130649808885086925257', '161.95155039089492682987392631863', '162.500988781148571126731558847907', '163.09343798551210146550838039844', '163.79683260690829414739039138125', '164.71622938972533568522264858529', '165.02303909801236748430743953104', '165.6918774602630055157273118976', '166.04280932551567663006736512463', '167.02767418164903664721826344840', '167.57865874168182063480746110794', '168.36433978774507906851284095631', '168.68610911045528773795333056757', '169.61004677582389497086477576877', '170.12109969463522753749866115185', '170.86717765402304852583893393342', '171.36564739500192943546945320264', '172.025032347044489453302759968', '172.396593853465007299591035360508', '172.676629515083507823717184974232', '173.726934808425129477996296934960', '174.1332159567599820579585400968', '174.62191109691898405992836860338', '175.426851486742760110457172578875', '176.22523376491480733517498260760', '177.15125777768474583484841149428', '177.52574964941574659970744322546', '178.06458879768562975778118091576', '178.66287742440144532779185607653', '179.33618600274893682549141553823', '179.517053766303830031707973386447', '180.390407528268549838283559336945', '181.19501196881859564435479559922', '181.74467850261124289828067826768', '182.01458330640355405752357392590', '182.84820293413029077214143634348', '183.48973651686660242349546781957', '183.87953609519249423570205453011', '184.51488256537678259396687360278', '185.16091123627639921683921246490', '185.80750358457300397459768166910', '186.77388557494721729194704200474', '187.4021488683275496904008363159', '187.89503939821715604630930261150', '188.41597857457775057133892881846', '189.04893057764784751925800610335', '189.46337188936218115943509395359', '190.22982907242426893873300902161', '190.55175637639239602178398564342', '191.22421659800711557645755281803', '191.790516643157475339041916040841', '192.25571257267737492509276713176', '193.25003717166986415366665469739', '193.90448486561389390667305521513', '194.4115738393208824400680582363', '195.0777718079834526361311556914', '195.6344270475799354348466911789', '196.50653474029817334200793239688', '196.68669198413968309853891742111', '197.39198416561716655552412504038', '198.01075031577585011106860407200', '198.72602119026571762417620712603', '199.32431689905892585053223465249', '199.81168006176579871506993875800'], 'prelabel': '1-1045-1045.64-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': -0.6198542148681571, 'root_number': '-0.367698678784995965696155257428-0.929944988491130241727241366574*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.309927107434', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(30)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.532725115552034034034083048884-0.161962736634601621832112605162*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.454393931558', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.31671517116', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.42482974218', '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': 4.852959597730739, 'bad_primes': [5, 11, 19], 'central_character': '1045.64', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1045/64'], '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': '1-1045-1045.64-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': '1-1045-1045.64-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 4.852959597730739, 'root_angle': -0.30992710743407853, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.454393931558', 'prec': 47}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_1045.64', 'Lhash_array': ['dirichlet_L_1045.64'], 'label': '1-1045-1045.64-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1045/64'}