Lfunction data - 1-1480-1480.573-r0-0-0

Formats: - HTML - YAML - JSON - 2023-12-03T14:33:28.667439

• 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_1480.573', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.984807753012208, 0.17364817766693036], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [1.0, -2.8163065144692913e-30], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [0.6427876096865394, -0.766044443118978], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.9396926207859084, 0.3420201433256687], 'algebraic': True, 'analytic_conductor': 6.87309110492009, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [5, [1]], [37, [1]]], 'bad_primes': [2, 5, 37], 'central_character': '1480.573', 'coeff_info': ['x^36 - 1', '0.984807753012208 + 0.173648177666930*I', '\\\\zeta_{36}'], 'conductor': 1480, 'conductor_radical': 370, 'conjugate': 'dirichlet_L_1480.997', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^37', 0, 0, 0, 'a^31', 0, 'a^2', 0, 'a^24', 0, 'a^34', 0, 0, 0, 'a^2', 0, 'a^19', 0, 'a^32', 0, 'a^12', 0, 0, 0, 'a^39', 0, 'a^33', 0, 'a^9', 0, 'a^25', 0, 0, 0, 0, 0, 'a^35', 0, 'a^34', 0, 'a^18', 0, 0, 0, 'a^3', 0, 'a^26', 0, 'a^39', 0, 'a^23', 0, 0, 0, 'a^20', 0, 'a^23', 0, 'a^43', 0, 'a^33', 0, 0, 0, 'a^31', 0, 'a^49', 0, 'a^28', 0, 'a^27', 0, 0, 0, 'a^19', 0, 'a^13', 0, 'a^4', 0, 'a^47', 0, 0, 0, 'a^34', 0, 'a^23', 0, 'a^29', 0, 'a^46', 0, 0, 0, 'a^30', 0, 'a^26', 0], 'euler_factors': [[0], [1, 'a^37'], [0], [1, 'a^31'], [1, 'a^24'], [1, 'a^34'], [1, 'a^2'], [1, 'a^19'], [1, 'a^12'], [1, 'a^33'], [1, 'a^9'], [0], [1, 'a^34'], [1, 'a^18'], [1, 'a^3'], [1, 'a^23'], [1, 'a^23'], [1, 'a^43'], [1, 'a^31'], [1, 'a^28'], [1, 'a^27'], [1, 'a^13'], [1, 'a^47'], [1, 'a^23'], [1, 'a^30'], [1, 'a^48']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1480-1480.573-r0-0-0', 'leading_term': '2.56082013607878201922332173120-0.597040278176183854966632149254*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/1480/573', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [2.6294974544789427, 2.423416987443004, 1.7200809671182062, 0.26391556916149056, -1.0936697730285303, -1.264612262996731, -0.019756109295443372, 1.6401100168788076, 2.2743295340323253, 1.3492071413112439, -0.1651438302732236, -0.706212384012718, 0.22111148094197594, 1.3771374520369482, 1.032399571305632, -1.007790719539325, -2.846566109360248, -2.31827896839184, 0.5498220425713878, 3.2057107840796735, 3.0424599051095997, 0.16191786690547041, -2.671377834464327, -2.9764362077111994, -1.1278308355654487, 0.3933900417357511, 0.12206107732231229, -0.7281119613179627, -0.10568869996262134, 1.9304496887753257, 3.067349534784155, 1.7408769277991607, -0.6177400662061443, -1.2607333575816138, 0.2230241433456265, 1.1331963527507267, -0.8735968497266801, -4.391181478835, -5.568014228084689, -2.7834245494285383, 1.2200446159779053, 2.598654296618877, 0.9255674123112119, -0.8178899363546668, -0.5051928162430652, 0.531128747939344, -0.040360099976355215, -1.8116160205455623, -2.1572759723753454, -0.2893727966932069, 1.2280040522347202, 0.06857493856776709, -2.1936551310786223, -1.9488895356017042, 1.275473494442467, 3.699045674947954, 2.2204695056840738, -1.2837941277938427, -2.4100844767006686, -0.12097076242025451, 2.137627804976677, 1.4984933448267714, -0.47574744353405657, -0.5349260157161846, 1.322429603542657, 2.1385682029884814, 0.7733227714153614, -0.43910559309128155, 0.22671193735885112, 0.6521816394293493, -1.9496506111467768, -6.003115471932494, -6.806184835369506, -2.978948219336881, 1.2575549935989567, 1.696774024046703, -0.3116064682298179, -0.4016692226299475, 2.172136064172412, 3.7457777393430645, 2.1322853841368237, -0.10830049798515472, 0.11456271763368887, 1.6657076964657627, 1.406884734798278, -0.47445833270273874, -0.8788714613923988, 0.7338902388707766, 1.0848256372323708, -1.380483769816181, -3.068133753383089, -0.20485095358684458, 4.952509507754234, 6.598295694525875, 3.364352187515115, -0.09672686430300978, -0.13834479237608036, 1.1414353215958133, 0.2829912635241252, -1.6994493454138848, -1.404937699902621, 0.9322553200075002, 1.7676281709340418, 0.2632446806021929, -0.3559515433350625, 1.4532320100813716, 2.554810962573973, 0.40535330803919006, -2.072209966894212, -0.7324999182193431, 2.7774758786062517, 2.929118302859763, -1.2280221577724297, -4.367930272638991, -2.7868565771255787, 0.49176607693862806, 1.04479130953733, -0.32733743283569605, -0.11388801700300101, 1.4628160991399408, 1.300379845860128, -0.45491285082595845, -0.29996653349020186, 2.1976431347921874, 2.9151179578714435, -0.038870595860430554, -2.6661127132935323, -1.3828071343319464, 0.89516039878704, -0.5853041597011682, -4.346079175901498, -4.692075814935366, -0.7728901571282873, 2.0984878182411832, 0.8284420050515663, -1.2531702741257482, -0.6411947125584766, 0.9019724207159973, 0.5551960630167561, -0.10544116079391305, 1.5745729622645148, 3.584335140625383, 2.18554608714264, -1.1273657227201428, -1.434242821462906, 1.2301750358321373, 1.4155615070221488, -2.6839587408339485, -5.72536659793295, -3.5377983992394912, 0.404733657073664, 0.9394131515076879, -0.7630475127334182, -0.35492085144761243, 1.704138062204166, 1.40022680031604, -1.2365750395937096, -2.1026161763046014, -0.3311476936434334, 0.5806443420515381, -0.2705957693823929, 0.582241842029283, 3.7334813455786646, 4.116737138704609, -0.8405217334974046, -5.689660827365554, -4.545763763043899, 0.07908758550805811, 1.752886030580482, 0.1235834570504599, -0.1334378741500196, 1.664253434308876, 1.496196595435081, -1.329157285060499, -2.577877345767613, -0.707605829385402, 0.5365809760809264, -0.771051866306768, -1.3745452448358821, 0.41715503127632375, 0.8069606106655216, -2.4119217670350817, -4.5138440073456945, -1.1317915502335594, 3.7484601067628347, 3.5893156651336153, -0.35001168041873887, -1.6059170801988225, 0.7878151252444425, 1.8244023478639702, -0.11299560388277653, -1.210249436059347, -0.08177160661553896, -0.10230413632596069, -2.1831339253502033, -2.404832692364253, 0.5087951991434931, 2.1865747101178106, 0.5047812843998888, -0.14162280257272586, 3.12704742303615, 5.707396165108179, 3.2298548747857723, -0.3528950858757314, 0.8383326160423916, 4.609173898236258, 4.61703296174713, 1.050722973573592, -0.5595588192985194, 0.831520060671513, 1.234889976031958, -0.08388590692686237, 0.12891829516292952, 1.6115177167111063, 0.4146424947525427, -2.979835369357729, -3.3917126800867905, -0.34574879424605737, 0.3580713123208562, -3.06270869310651, -4.6888503607989795, -1.1595894206810404, 2.3132489562017797, 1.0689360953012916, -1.1941101267667296, 0.32937038274348474, 2.977741561546374, 2.052461422059964, -0.6364319308463857, -0.7860402158521531, 0.4400536203315828, -0.270509379773321, -1.2192608555294009, 0.5756347251062793, 2.2020322038909947, -0.5064404107534877, -4.290950827643659, -3.0654390765456703, 1.215295987959533, 1.4332463754010962, -2.466906177961751, -3.6924252718342254, -0.610754319347188, 1.1635965949144462, -0.6085945059000911, -1.6061790699004215, -0.0503910780425713, 0.15927744014485734, -2.188252702133369, -2.803325460912081, -0.276473037915158, 1.0668523274211255, -0.3531691732163567, -0.5029498580551384, 1.3582256021256702, -0.16631911099732022, -6.220735005616294, -9.346559953595776, -4.997892270072732, 0.8258054201990922, 1.5062323057067313, -0.4349195598886636, -0.08309404234112941, 0.8455336080864476, -0.8828695221447695, -2.5259610115584987, -0.7009574540037945, 1.5684579497928341, 0.5916108171166614, -0.7896631397034869, 0.9110929982116598, 2.5346852879561563, 0.6273236686791392, -0.8219054668495203, 2.491507443076877, 5.941930047417956, 3.138136999105088, -2.61256468757833, -3.707607954776514, -0.8376795024489201, -0.24039664836958774, -2.063886873274263, -1.6275229752184586, 0.6347053403533656, 0.48963551686073015, -1.245168266217903, -0.7059606656368289, 0.6409359834693525, -0.9335094539417088, -2.7259353994123074, 0.18385758782389922, 4.714813245687994, 4.064639959106401, -0.2509429605285663, -1.2969978884893065, 0.570412867463602, -0.8743383387664079, -5.166857139379431, -5.559921181589063, -1.3800451389362065, 1.1371615839764606, 0.16968777028792453, -0.12119324203542481, 0.956329111480674, 0.026499502941313053, -1.9037117100874625, -0.7269356608063797, 1.6781769411958032, 0.06955527100908807, -3.43663068483018, -2.194131049433636, 2.417363275304988, 2.752916015217247, -1.4307658529216727, -2.8829501901687458, -0.2227088551855998, 0.5422679029213515, -1.8641514176926561, -2.1384527822024952, 0.6475912410407888, 1.5451779273390591, -0.14633655035661156, -0.04454380327954699, 1.8052977734824935, 1.176477789205523, -0.9996980538629081, -0.32044575944021086, 1.0781791246871977, -2.4173292415300978, -8.007739420640142, -7.647004827835282, -2.1598152842576517, 0.018437750859635397, -2.554200971551798, -3.3044876002966803, -0.6251376071805994, 0.4440741128975259, -0.8139423278530648, -0.06261687990917172, 2.219898015923838, 1.4897806917032075, -1.1014922472698807, -0.6126090569996296, 1.7078012505374904, 1.1840474440263893, -0.21046786576464951, 2.1697035885582707, 4.914533901232801, 1.8134029313137248, -3.5713237001180818, -3.0061060068694827, 2.003006496375841, 3.320685788055143, 0.4439583771306217, -0.6194186661665074, 0.5800204017164062, -0.03371696996030977, -1.355765156645032, 0.1925591424531505, 2.03570384469771, 0.1654437505138484, -2.1569426455207794, -0.5561368951216807, 1.4097414625078655, -0.543808773241761, -2.0766661752986004, 1.419777973650716, 4.643147358788387, 1.4822948682144412, -3.3661375700812384, -2.8362907300826583, 0.18490253670784193, -0.3288761104106095, -2.258393230498864, -1.178885535351249, 0.3677011745379787, -1.016702644952048, -2.1908001119655056, -0.5399433800738124, 0.24739154087759732, -1.3035583920445035, -0.052094611501409746, 4.974512690338931, 6.396010127639649, 1.571648586620865, -1.799136658623829, 0.6171680986105039, 2.7152468046030327, 0.5210493097274624, -0.8430680886299947, 1.4096937763971054, 1.956346003177855, -1.5052357390611926, -3.4776321905263696, -1.4656342900139792, 0.16203013157209983, -0.041182958867807144, 1.168936394621557, 2.463801032822153, -0.6128762088862093, -4.89198888705894, -3.275763967798561, 1.815108010966767, 2.133131056869622, -1.2704294759823966, -0.6142006983080669, 3.5172164333914706, 3.917638966833621, 0.7610276586341284, 0.015373094610977685, 1.1914299854968438, -0.26268547601794345, -2.4694435597817868, -1.1664093122206238, 0.929499526541943, -0.16947836770984853, -1.255583578331265, 0.7787726266486539, 1.5123478652768931, -1.6309733594761375, -2.5048040580367297, 1.986360627181836, 4.350678740978694, -0.13887499318591362, -4.355925027919255, -2.2945807968442273, 1.0089078165564678, 0.4752824994064398, -0.4228403727804395, 1.0336479466181503, 1.2490705351510196, -0.4697377905453066, 0.5389390091354792, 3.8717306971980583, 3.6939447495743094, 0.4302900584236008, -0.12491238164848001, 1.0258613278951114, -1.41697600554114, -4.412442140961013, -1.1096964567573224, 4.909959565797781, 4.803842753743004, 0.15955327908327044, -0.982933095924806, 0.9728837113103408, 0.276368361099152, -1.8251885426149317, -0.9491498959963588, 0.6469704210681657, -0.34925854854460286, -0.7086766653390928, 1.5911582267588444, 1.5995719544227038, -2.2487914064136083, -3.3491786806962063, 0.297200028678699, 1.4206015100820644, -2.253154462595682, -3.2876784852483745, 0.6162935051215389, 2.064067773209818, -1.2990807563973603, -2.6701501986578418, 0.015427454476975626, 0.9660726649912814, -0.9573122313193235, -0.9680411180488047, 0.5783721049167332, -0.5095057833866385, -2.2598947782392296, -0.7210931094163114, 0.7612209877622468, -1.222775245536174, -1.1383913755024453, 5.010948062126219, 9.62945426726323, 6.041526476189033, 0.401334199325962, -0.12238319212227637, 0.808892709361546, -1.1339153435204192, -1.7857048453951712, 1.357153064936454, 2.8102302894191418, 0.21176997755539784, -1.20228851543356, 0.15107881021945813, -0.1699075281755555, -1.8760336637707078, -0.7007015860203363, 0.8643610656964871, -2.0127066276450094, -4.624271794619323, -0.20902343056748054, 5.939465499942079, 4.9344904225975705, 0.019388826737489328, -0.7735693520378354, 0.6801878947565801, -0.9389435029876538, -2.7379254954446064, -0.9082604164157895, 0.5677783443179976, -1.2652436389052029, -2.0588266884479083, -0.18317722178906898, -0.3884430493854231, -2.6115057611685204, -1.1385073726701433, 2.6891235916464593, 2.054340526310125, -1.1240739524525483, 0.4212007408687353, 3.9834756892888454, 1.5967768048226088, -3.865889516445782, -3.811717495846278, 0.1857823673423457, 1.0128388111386557, -0.38781728754018946, 0.24153873486411212, 0.7423733040785437, -0.8452839878151537, -0.2493085572352241, 3.356487427485752, 3.7494350294784806, 0.152006926188051, -0.5930574809722272, 1.8823523325980083, 0.8530988924248433, -2.5702582929584885, -0.8738343692543211, 3.9173863218731286, 3.151507412849672, -1.7848228220988662, -2.6479664195515107, -0.014701936972764795, 0.07954925161323839, -1.0291804958521285, 0.5547504885588312, 1.7501227532090475, -0.22142064091335092, -1.0952875181885666, 0.7446261996481403, 0.23298741669206005, -2.3892714323579862, -0.33911065032355214, 4.981757090516044, 4.563610545818669, -1.0637624089255335, -2.65662868806448, 0.21746159918348262, 0.13653880055851353, -2.378533028038354, -1.3046018661048373, 1.3016091481676928, 0.0724080980697175, -2.0236010969202156, -0.5116370429816528, 1.1152505998777715, -0.17544253025843243, -0.41150773463211954, 1.3456738152943148, 0.0993345066454282, -2.7616514564518404, -0.08073326695318798, 5.61742088755043, 4.68083268031285, -1.5587936601511303, -3.2057638365161987, -0.004394444502640129, 0.6660988519018818, -0.7016563518175781, 0.8751507513464224, 2.758356921676298, 0.9058987815686925, -0.6489460066472627, 1.332921578043865, 2.0987337857177066, -0.4423539719891847, -1.2307829662866894, 0.13956606813691638, -1.534755727157421, -3.9583860767711223, -0.28976235426978786, 5.539191813027777, 4.370340814470499, -0.7804041316864132, -0.7198837389585551, 2.6248685835137704, 1.9576904858483848, -0.6721315679457706, -0.21651932202864752, 0.5056083876814588, -1.2231665089155064, -1.21535778246801, 1.4615878965467344, 1.3010835462605514, -1.521018992348606, -1.1334570925709972, 0.7774415557126536, -1.7354097471023895, -4.908865713201099, -1.8799029078729919, 2.5305542398591765, 0.7072342871898082, -2.7939141384754484, -1.1749840506267633, 0.9631192278493125, -1.7707127157436813, -4.3225993370957365, -2.2613063515997487, -0.029170832634421863, -0.22213570471528593, 0.4434650337407178, 0.930723789513493, -2.594113564263212, -5.820353382957579, -2.891641236528681, 1.0001983050929786, -0.779715300970738, -3.125579812960183, -0.462220057285387, 1.251597836731899, -2.5192680429845615, -4.680421959726151, -0.8659676787583496, 2.0952298446209876, 0.5388394963828074, -0.09781508461282123, 1.5574089346116198, 0.7646729588123382, -1.4026152092048474, -0.36521749245031637, 1.226951687758479, -0.16601511468838087, -0.026355784156753968, 3.7529102374226837, 3.8539945577351142, -1.7439434776583278], 'positive_zeros': ['0.98916050886957563681300281388', '1.87862649459296909555114989785', '3.08573652275005701598641119434', '3.69790977155262169261702897702', '4.55196410368460148352912944086', '5.57304015324578234774301307842', '6.57732537981852090008132173670', '7.69278003376585223977523453171', '8.16396356402307127359554671323', '8.77009398095330943975232641138', '9.9088378352447527312055967030', '10.58637529627322329996088025789', '11.160045218633715803396871501692', '12.39386329740768456838740299864', '13.257533706450259496141255328046', '13.87998906714487344529685976298', '14.36668426515367051872510901044', '15.35281723618172320757819534859', '15.946702947343016627150761707527', '16.766231840557575068049146128893', '17.692789278539304869034365221683', '18.450046206036716018105761575607', '19.28669602103966645633881229797', '19.79218333866175096716957197510', '20.77214216300178674174535060307', '21.18836033701498863215419690828', '21.689024007420962845840990344136', '23.00934299977514581052334133641', '23.69688095612282403830379484069', '24.12775430755018189549040357629', '25.287422766230253746620837710207', '25.59890807243054904237228520174', '26.48086939739104576244510523140', '27.059428661958784552931619959016', '27.665524543493990102814855763175', '28.450324121528294056415347059030', '29.67222226022063369484787377016', '30.030615473741116717737349663054', '30.66737264552115774105868081241', '31.44093837649169677408827852491', '32.23934633145133709756863475955', '32.59305440582417688072148193308', '33.477011026176707380237472740524', '34.1277043985524224913363043590', '34.92012692361239599541313550564', '35.87857801868950812732393150186', '36.47934070873648241364882808736', '36.8998646407473540606357932047', '37.72431902127714721962077051777', '38.17253696715665235042168002055', '39.05926074627310526597504152828', '39.84308141197437584092015208884', '40.25579275399552041588874955087', '41.30659897949176392965234978449', '41.97500907082778761279196107637', '42.61000445573305818188042525551', '43.29379964320554572595906309602', '43.49090927795530934965774497661', '44.570408731438059912710348765609', '45.17424483124211090649880980089', '45.75759088442812614771188864370', '46.83229186554645320504216788422', '47.35307371555810955565358401157', '47.86758026184930444909735318778', '48.60805216085893686837632401285', '49.43144430221659433427092670269', '49.90245369687866404927717204445', '50.22365282286977646387112350384', '51.207982113298493937613718665575', '52.1812850236749104121548628907', '52.83705419776616389566782633652', '53.15518397269707784929442853454', '53.92596525802170617110878497504', '54.7931908482545025920440149655', '55.17106245974156311889728681820', '55.87422275547084836954935514495', '56.356765777601497903740977683443', '57.251162982258186943563724541915', '58.09508515562213219845677445595', '58.66029332934312328114766670175', '59.35942129921544426559282305503', '60.02245428973698541430786968044', '60.28866120224909192603660357924', '61.20144090317206623631461257824', '61.956617581271620464464875746208', '62.21371226862052772062843472368', '63.38549662411011576694752554908', '63.66539823718857680461596717360', '64.802830163523542475886999668134', '65.158847671018153605885234259323', '65.913828422823250634064381419634', '66.21987271764173275093576667780', '66.915761774226348192275797107977', '67.85247589448563938860399224632', '68.17460141834782771875243879477', '69.139806143614922619884308885579', '69.80114951023046751439537171005', '70.27832007155140587648747499778', '71.16037243918460698982478507697', '71.735137261627181180753558610954', '72.13051709588638989949022931893', '72.74402035444041908690340354647', '73.40108802769974462014650199580', '74.27583985100698101268315018856', '74.81396279682863180811635498167', '75.683420026285136050883981717066', '76.1680322171331699266947499373', '76.88475756617277967290332041419', '77.21783294428082206783269191658', '78.15724358371565400027934225866', '78.68405139320783451515497644375', '79.15136389782603900775976011112', '79.67564832559816095496795367824', '80.87653729521488279798915851446', '81.474463984658826517629419315247', '81.89283298673030320916934368222', '82.38712491791289783648685558120', '83.1981668358029060917782419025', '83.83872623612008177830794738524', '84.26076078769895708153067006736', '85.071957883974410174155802936557', '85.43926334932224027111922195898', '86.41000114842725746396154040954', '87.36015823205072728644751887919', '87.41378190526964134314723513003', '88.336631293239504123634550069216', '88.83271530303271851334084152718', '89.49753037318699974452091089341', '89.8824348127311259597412090354', '90.613413949706029524325815446', '91.54121659271224979504837928247', '92.07773269232469189847659213766', '92.41715519112086514871153285846', '93.54935339287361309661945395712', '94.10523498741275143820752576396', '94.41360645616039466867739503696', '95.00380102676417745984769445305', '95.70328397518132795861272345072', '96.255812536901033772097697082927', '97.01958843383974267298977879043', '97.71012261690397068660814577720', '98.46420702811265330278949424148', '98.8378657421353068994315261623', '99.616788730708605115219149479684', '100.28289873264733039384664187608', '100.63338223875014939793999848527', '101.40030157240499589785072594077', '101.92113935593824819829908065132', '102.34711358151483001685804281074', '103.643970675040493236499847593434', '103.755554589093798547990978480430', '104.77050056694255950826742567512', '105.12171682615283904119802625699', '105.63354963077014211039076977822', '106.41389908991598475448913068549', '106.95153938731843762637887813991', '107.69960905603326393287782041880', '107.89278321385715766031632611030', '108.84385538783315012169584939639', '109.56088602664217001231879800094', '110.36644361067665803146868963283', '110.785312031796941345038694259440', '111.24385703434080681638838341201', '111.852169813336695610958330674575', '112.51612795771807795241015184591', '113.18423868895014617621827847051', '113.69379916925189751775342058726', '114.28223775238277644379807991089', '115.081050325065042394425856513275', '115.90748375528920492423712132610', '116.20055087418404247767059303505', '117.05429183396736285880620356802', '117.33931073893024764641017226315', '118.21760641884980965255096796391', '118.50390630500004087593620580007', '119.066635888810584827109242084467', '120.09317527285252418777779210097', '120.5725033249586255903658880293', '121.30799133106039531494724758657', '121.71147996777700124372470669232', '122.38209189009443449048612398134', '123.35821418910387216307336415287', '123.666771093599333029063633868694', '123.802402089447064962461901399124', '124.648350487148084953023365359', '125.502202994977422890486794731834', '126.124320397276218888162881757053', '126.612658371472647247218037875811', '127.62008997382054364201150921639', '127.80785983221184498116907766440', '128.40722624012612499854597468635', '129.197691344314598767656220492449', '129.662068445864057047911781161068', '130.21847738078404747162255324616', '130.79695171012049791510088537932', '131.44506606051641201338728912387', '132.18039886911547728995722402501', '132.99462486719574924476756701621', '133.52784158392588151303303227809', '133.875277506771128559380475182438', '134.58948425858616406560813417226', '134.93756782101265102228146639920', '135.997014837468981787443374881922', '136.278304598485089251442616023822', '136.75484103197671004095547511151', '137.55312319254561704621278708844', '138.450782781519753152284403893272', '138.90284140661651209001323220728', '139.41089359624430253558867292939', '140.14002181289356610172763864188', '140.556747323287510970384900984952', '141.05341043060079374451970996341', '141.70638748647883922681537082716', '142.475966918928614157792161337453', '142.95437049710545741395223706003', '143.70455226887250272383349506264', '144.27027778302459730205172395295', '144.99829005413129188089669875432', '145.47859502580755827606668407553', '146.1066510841759359003729431605', '146.489843132307029392558862230142', '147.278094548249306517160057871286', '147.66112653096316423037054288194', '148.2061851676138471983702352407', '149.41754988631717059356831863539', '149.71262524762697189813378122194', '150.16833958082713612953804628741', '150.820963994174100826620391178911', '151.58501968274550928366614177677', '152.15162752589796279453356980778', '152.46814855272129015381348219606', '153.21313824172131510357096552321', '153.58812104157032576237813815670', '154.38407733429548074975014519471', '155.31420018847682276666754295878', '155.75858224649036049803200695981', '156.13636582727580887135969748275', '156.98965775549898433540529677550', '157.327618780314101066916986568831', '158.1644719932668616684712983203', '158.366266904155927824106794093618', '159.14885982284430570261777748519', '159.8652150307522727935952423354', '160.27877079647412738433782853167', '161.02235488094017955974306234832', '161.85725960385784254978772780919', '162.38882723479292608038782773772', '162.756171574667261237238967466332', '163.28586546453735120183767281495', '163.77628797056902421558442808619', '164.702569778452369155517295638325', '165.08121390618114882583338601827', '165.69599970010472620543426657620', '166.30454322005222415489085139655', '167.068233935815040860301522194540', '167.814838661315538471744839087278', '168.14190304307947350489077580451', '168.67603324494309336863523770652', '169.34659044775873131548763813385', '169.87937184770556714410677021638', '170.33979428793774344724380632171', '170.95789052307550196449870299354', '171.81282876613360718737612812392', '172.473104253834426114997153622380', '172.829898535586843520094506508114', '173.566639135777792860329128766244', '174.07049756107011551560649550392', '174.749674786143793286495685255047', '175.28002776784887083681440337093', '175.70149048421225576910813282085', '176.25948710210665517828273247187', '176.87932857113135949544738851440', '177.72989873578278198023295858603', '178.43798152427455033787006935940', '178.87638210458066648909933597996', '179.269747656654807237983433320881', '180.10803023626270212101940121762', '180.45790993005793715692116548275', '181.199159569354399971250934610805', '181.81934677851705374726174369606', '181.99364392676143091987012709855', '182.826269604904172515206821846726', '183.68990041177610459289576350670', '184.12768206262754092487058894369', '184.893700657176020602127052597705', '185.35601184080111108159983314337', '185.744940086230251242982428742302', '186.39525383409513179735742516098', '187.01380870659314076691509815292', '187.64156488963517585252441838842', '187.98272451404705375752830171410', '188.8559632715451196358200290566', '189.42473148707756571371140065542', '190.11182681401770322343581636667', '190.478046757289886939585301779933', '191.57666344647946863812939744655', '191.720600413654425232256262323276', '192.07694626274280300952495272224', '192.623748736594041041676880730225', '193.62777376388916076258189179702', '193.993371313207176598579928985579', '194.72659874650960692418307437082', '195.140771195958449990032599152522', '195.99484894993459467544508562359', '196.6539535183614073668645240892', '196.89921050682451194937684921984', '197.59280493817068043358760321910', '198.17294951772255016996112593806', '198.72179832846760180342220286227', '199.06564808272860148495988570175', '199.90902122675233695265207500041'], 'prelabel': '1-1480-1480.573-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.87309110492009, 'root_angle': -0.1458193675872074, 'root_number': '0.896892145946600538538714238567-0.442249339783907194888030994095*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.0729096837936', 'prec': 54}, 'spectral_label': 'r0-0', 'st_group': 'mu(36)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.65440310309158438435051315321-0.149689751139701975403483012924*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.98916050887', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '1.87862649459', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.08573652275', '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': 6.87309110492009, 'bad_primes': [2, 5, 37], 'central_character': '1480.573', 'conductor': 1480, 'conductor_radical': 370, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1480/573'], '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': '1-1480-1480.573-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': '1-1480-1480.573-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.87309110492009, 'root_angle': -0.0729096837936037, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.98916050887', 'prec': 44}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_1480.573', 'Lhash_array': ['dirichlet_L_1480.573'], 'label': '1-1480-1480.573-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1480/573'}