Lfunction data - 6-2205e3-1.1-c3e3-0-1

Formats: - HTML - YAML - JSON - 2024-05-10T01:56:45.537558

• 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': '1125610399505924266158756148206,1221482502430313819213487962034,1550269307539088875376629284518', 'a10': 45, 'a2': -3, 'a3': 0, 'a4': -7, 'a5': -15, 'a6': 0, 'a7': 0, 'a8': 35, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 2202033.865947624, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [5, [1, 15, 75, 125]], [7, [1]]], 'bad_primes': [3, 5, 7], 'central_character': '2205.1', 'coefficient_field': '1.1.1.1', 'conductor': 10720765125, 'conductor_radical': 105, 'degree': 6, 'euler_factors': [[1, 3, 16, 34, 128, 192, 512], [1], [1, 15, 75, 125], [1], [1, -1, 3485, -6442, 4638535, -1771561, 2357947691], [1, 79, 6542, 346439, 14372774, 381317911, 10604499373], [1, -72, 14635, -688048, 71901755, -1737904968, 118587876497], [1, 29, 18484, 332301, 126781756, 1364330549, 322687697779], [1, -63, 32377, -1479946, 393930959, -9326261007, 1801152661463], [1, 220, 74711, 10703064, 1822126579, 130861130620, 14507145975869], [1, -136, 27042, -3338174, 805608222, -120700500616, 26439622160671], [1, -43, 33294, -1889771, 1686440982, -110326235587, 129961739795077], [1, -599, 272999, -79436618, 18815364079, -2845312440359, 327381934393961], [1, -170, 62886, -25979064, 4999877202, -1074631718330, 502592611936843], [1, -3, 72213, -31379318, 7497370299, -32337645987, 1119130473102767], [1, 331, 442671, 98567438, 65903530467, 7336403533699, 3299763591802133], [1, -1520, 1161665, -599760000, 238581596035, -64114411134320, 8662995818654939], [1, 1160, 1094643, 571897312, 248463162783, 59763634258760, 11694146092834141], [1, -806, 956790, -441427296, 287767030770, -72909456028214, 27206534396294947], [1, -406, 391273, -58294156, 140040910703, -52008715271926, 45848500718449031], [1, 1192, 1524996, 931572678, 593249368932, 180390397736488, 58871586708267913], [1, 2590, 3310582, 2751421632, 1632246038698, 629596509799390, 119851595982618319], [1, -508, 1655669, -550491384, 946690010503, -166085709671452, 186940255267540403], [1, 42, 566539, -649223388, 399392432291, 20873214220362, 350356403707485209], [1, 1020, 828679, -17707848, 756312948967, 849631445027580, 760231058654565217], [1, -4240, 8865723, -11246297696, 9134363272623, -4500845438548240, 1093685272684360901], [1, -2982, 5991802, -7216691164, 6547403824054, -3560663948249478, 1304773183829244583], [1, -1166, 1984153, -3135311588, 2430672743579, -1749851590255934, 1838459212420154507], [1, -200, 2684500, -144846430, 3476505350500, -335420022168200, 2171893279442309389], [1, 2038, 5440543, 5987348788, 7850143173071, 4243017671817142, 3004041937984268273]], 'euler_factors_factorization': [[[[1, 3, 16, 34, 128, 192, 512], 1]], [1], [[[1, 5], 3]], [1], [[[1, -1, 3485, -6442, 4638535, -1771561, 2357947691], 1]], [[[1, 79, 6542, 346439, 14372774, 381317911, 10604499373], 1]], [[[1, -72, 14635, -688048, 71901755, -1737904968, 118587876497], 1]], [[[1, 29, 18484, 332301, 126781756, 1364330549, 322687697779], 1]], [[[1, -63, 32377, -1479946, 393930959, -9326261007, 1801152661463], 1]], [[[1, 220, 74711, 10703064, 1822126579, 130861130620, 14507145975869], 1]], [[[1, -136, 27042, -3338174, 805608222, -120700500616, 26439622160671], 1]], [[[1, -43, 33294, -1889771, 1686440982, -110326235587, 129961739795077], 1]], [[[1, -599, 272999, -79436618, 18815364079, -2845312440359, 327381934393961], 1]], [[[1, -170, 62886, -25979064, 4999877202, -1074631718330, 502592611936843], 1]], [[[1, -3, 72213, -31379318, 7497370299, -32337645987, 1119130473102767], 1]], [[[1, 331, 442671, 98567438, 65903530467, 7336403533699, 3299763591802133], 1]], [[[1, -1520, 1161665, -599760000, 238581596035, -64114411134320, 8662995818654939], 1]], [[[1, 1160, 1094643, 571897312, 248463162783, 59763634258760, 11694146092834141], 1]], [[[1, -806, 956790, -441427296, 287767030770, -72909456028214, 27206534396294947], 1]], [[[1, -406, 391273, -58294156, 140040910703, -52008715271926, 45848500718449031], 1]], [[[1, 1192, 1524996, 931572678, 593249368932, 180390397736488, 58871586708267913], 1]], [[[1, 2590, 3310582, 2751421632, 1632246038698, 629596509799390, 119851595982618319], 1]], [[[1, -508, 1655669, -550491384, 946690010503, -166085709671452, 186940255267540403], 1]], [[[1, 42, 566539, -649223388, 399392432291, 20873214220362, 350356403707485209], 1]], [[[1, 1020, 828679, -17707848, 756312948967, 849631445027580, 760231058654565217], 1]], [[[1, -4240, 8865723, -11246297696, 9134363272623, -4500845438548240, 1093685272684360901], 1]], [[[1, -2982, 5991802, -7216691164, 6547403824054, -3560663948249478, 1304773183829244583], 1]], [[[1, -1166, 1984153, -3135311588, 2430672743579, -1749851590255934, 1838459212420154507], 1]], [[[1, -200, 2684500, -144846430, 3476505350500, -335420022168200, 2171893279442309389], 1]], [[[1, 2038, 5440543, 5987348788, 7850143173071, 4243017671817142, 3004041937984268273], 1]]], 'gamma_factors': [[], [0, 0, 0]], 'group': 'GL2', 'index': 1, 'label': '6-2205e3-1.1-c3e3-0-1', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3, 3], 'order_of_vanishing': 3, 'origin': 'ModularForm/GL2/Q/holomorphic/2205/4/a/bi', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.016927083333333332', 'prec': 67}, 'plot_values': [2.2431810396545712e-182, 0.00016051954313199747, 0.001279769995566182, 0.004294623664193082, 0.010098614745075268, 0.01952138472220032, 0.03330915177160147, 0.052106680827521484, 0.07644187133553954, 0.10671146211473011, 0.14316941197357075, 0.18592012577967934, 0.23491114829745097, 0.2899299945319927, 0.35060864849578016, 0.4164235579302394, 0.4867017057344646, 0.5606377232575225, 0.6372999530792279, 0.7156451303773096, 0.7945478712644781, 0.8728101348551826, 0.9491824696797376, 1.022403954985292, 1.091211284134554, 1.1543633248201328, 1.2106880261948236, 1.2590867609254224, 1.298558141261875, 1.3282471875809916, 1.3474406541897812, 1.3555857970331615, 1.3523364451277204, 1.3375358650347007, 1.3112265929597822, 1.2736881290084099, 1.225405434651863, 1.1670670426797893, 1.0995899955075665, 1.0240741714280144, 0.9417875906298157, 0.8541759240197767, 0.7628052475678408, 0.6693355848757471, 0.575514673275299, 0.4831141001708668, 0.39389437788399145, 0.3095853856294876, 0.2318227470555761, 0.16210976565972463, 0.1017896635908702, 0.051990124699448095, 0.013588847048053455, -0.012815104050547007, -0.02694074985249079, -0.028848796107278744, -0.01896264333308903, 0.001914599599073567, 0.03259387622628585, 0.07149513438980588, 0.11665652115405488, 0.16575000661101305, 0.21609877922229875, 0.26471276515555353, 0.3083274639915516, 0.3434467781402271, 0.3664008543344811, 0.37340553618296324, 0.36062878078783756, 0.3242629348372969, 0.26059804995273683, 0.16610446123511793, 0.0375087402459249, -0.12812953575026745, -0.3333319252366456, -0.5801333732749565, -0.8700147897226731, -1.2038311183209498, -1.5817625177648473, -2.0032695581490034, -2.4670546264095083, -2.97103914735052, -3.5123527978757747, -4.087346948224505, -4.691599216975178, -5.3199438431094865, -5.966551855423094, -6.6249569879562475, -7.288128102807587, -7.948623634850218, -8.598625350192236, -9.230046330861475, -9.834757733191639, -10.404610503208623, -10.931565136425364, -11.407978262923637, -11.826588728725048, -12.180649536811304, -12.464251982752115, -12.672252704177698, -12.800385238993705, -12.845592261988546, -12.805874979650753, -12.680362612089105, -12.469620376117541, -12.175411857233225, -11.800709832699047, -11.349950068706429, -10.828710028266082, -10.24365341840554, -9.60270777748763, -8.914677214437404, -8.189124663468753, -7.4364637261049396, -6.66753660110856, -5.893450331905701, -5.12558849589743, -4.375195379141379, -3.6531931479918973, -2.970134027697474, -2.3358357093222692, -1.7592130170317708, -1.2482031543849135, -0.809493754725461, -0.44840339929793666, -0.1688185810818861, 0.026955535234408176, 0.1382373454413921, 0.16598311333548893, 0.1128012789582684, -0.01709866853997929, -0.21796785078580727, -0.48262925081542546, -0.8026214766105256, -1.1683469933359474, -1.5692780607865833, -1.9941740071521008, -2.43130604522508, -2.8687098978285293, -3.294441147674282, -3.6968461893885105, -4.06480463800526, -4.387976755325393, -4.657074282184759, -4.864037580883064, -5.002227139409602, -5.0666408569879975, -5.053984017428258, -4.96276471498578, -4.79340811879149, -4.548199978860485, -4.2312627593004875, -3.8485327396934417, -3.4075857657613313, -2.917494091720309, -2.388656603330475, -1.8325433241627598, -1.2614579541118314, -0.6882404376537405, -0.12598823507939458, 0.4122290450923623, 0.9137481244521996, 1.366546047418569, 1.759514268467931, 2.082852034185135, 2.3281923500907813, 2.488804990736908, 2.559932033525649, 2.5387618897044146, 2.4245140973782484, 2.2186531103782516, 1.9246972641520217, 1.5481622602706826, 1.0966127866954716, 0.5793292774671543, 0.007117757339542117, -0.6078073894090693, -1.2522427050742342, -1.9122809473938622, -2.5735669790442026, -3.2217241983543023, -3.8426727172806374, -4.4229621463924325, -4.950120060519816, -5.412930223179844, -5.801762053494197, -6.108768813265688, -6.328058917559286, -6.455941757518261, -6.490933185297902, -6.433774916082893, -6.287535735144338, -6.057422667221529, -5.7506371870397555, -5.376306093993628, -4.945139241148957, -4.46914922266735, -3.961429624179268, -3.4357341115631796, -2.906119416165614, -2.386630001503804, -1.8908899265805625, -1.4317488986823328, -1.0209612613409784, -0.6688764192031417, -0.3841688822846714, -0.17360802358376168, -0.0419053914270117, 0.008409123411630115, -0.02295476802262923, -0.13406699742872738, -0.3208267045736529, -0.5771224213272549, -0.8949896305918086, -1.2648183210823216, -1.6757288276422475, -2.1157924745371153, -2.572341901497738, -3.032511024104435, -3.4834202528934632, -3.9125079258397637, -4.3081456042639354, -4.659691483050683, -4.957755638896653, -5.1947864295351485, -5.3649239375708895, -5.464129174965069, -5.490648255900055, -5.444645799030242, -5.328164816505558, -5.145410166381582, -4.902197851881979, -4.605758746340578, -4.264832521386745, -3.889018048694572, -3.4884778996429544, -3.073884943565116, -2.6557880235169544, -2.2443030081146067, -1.848992140287682, -1.4783592165101151, -1.139618186082073, -0.8385988860188496, -0.5794561226788424, -0.3645860562544244, -0.19463657311350388, -0.06846228832747923, 0.016782778017457676, 0.06549255562753857, 0.08343689585415776, 0.0775154679548828, 0.05547965263789887, 0.025624804512021516, -0.0035401277237307517, -0.02362723023246153, -0.026703087351426024, -0.005607058679614305, 0.045759973225178066, 0.1321823779465971, 0.2569191212255706, 0.42156650269292506, 0.6259548067869188, 0.8681107675780302, 1.1443473143957177, 1.449321201664768, 1.7761826325232575, 2.1169112443367526, 2.4624824173765107, 2.8031599174651918, 3.129030541501144, 3.4301782765443427, 3.697028628155369, 3.9209770691823254, 4.0944528222050875, 4.211202757409152, 4.266879544503318, 4.258898095400761, 4.186560757716382, 4.051480891511563, 3.857190831015639, 3.609056488828195, 3.314460482734094, 2.9821955945474103, 2.6221833490444735, 2.245415037801341, 1.8632366454242226, 1.48695270867595, 1.127601620026788, 0.7952838026393091, 0.49877780259834936, 0.24528307580517197, 0.03994637111843077, -0.11437481306650195, -0.21725349439736436, -0.2708572506223269, -0.2799373281552853, -0.2517405641757902, -0.19583242565904946, -0.12380937279044311, -0.04894680503595071, 0.014256891866506598, 0.05058714173034312, 0.04466268862887878, -0.018469521947268516, -0.1527426269730476, -0.37048241227392487, -0.6818500002220442, -1.094340479079066, -1.6123710788412928, -2.23691783400855, -2.965268992173788, -3.7909958421523973, -4.703865285361801, -5.689948616201384, -6.732110636143985, -7.8101711505792455, -8.901368427092965, -9.981381407912814, -11.02460262563675, -12.00484564601681, -12.896777245559583, -13.676088398223994, -14.320250172569326, -14.810118019917722, -15.129774713703569, -15.267108206390414, -15.215295115766038, -14.972150514682223, -14.540338212249614, -13.928465978044139, -13.149899994260638, -12.22251671975133, -11.169245937459833, -10.016459889281736, -8.793310295006943, -7.53171034727409, -6.2645453790555825, -5.02476963152304, -3.844980690176777, -2.7557764144744423, -1.784872843873613, -0.956545141890229, -0.29044580144904536, 0.19898219389263475, 0.5028841685315275, 0.6185001833933765, 0.5492525851409239, 0.30468827242429697, -0.09973651557831768, -0.6431355244637039, -1.2998013479345982, -2.0400003315906723, -2.8309215486315376, -3.6377652528812456, -4.4248224204618705, -5.156651893343499, -5.799401821920051, -6.32180853808116, -6.696281772324903, -6.900103285332596, -6.916016985249087, -6.732916136044379, -6.346556943606213, -5.759549127426155, -4.981445232378737, -4.0287100196035, -2.924119444516722, -1.6962216389710145, -0.3784888622774256, 0.9916661611817105, 2.373904800668529, 3.726485551602108, 5.007280176462934, 6.174969340663295, 7.190916342829536, 8.019829736656533, 8.630789443870702, 8.999053714984829, 9.106066011517342, 8.940008952959609, 8.497151142806011, 7.781076934649741, 6.802604302143316, 5.580412687702276, 4.139598930521556, 2.5109830283428938, 0.7309624927758959, -1.1603017659017145, -3.1199880336103756, -5.103375163401185, -7.06560810767701, -8.96288836801817, -10.753536733347593, -12.399298127811287, -13.86628088510853, -15.12595093347262, -16.155690019782085, -16.93922866878346, -17.467260173810228, -17.737173289860177, -17.75288198289129, -17.524896368499807, -17.069375315772838, -16.4074375860442, -15.564714880379675, -14.570043422532692, -13.45448843784571, -12.250569841279185, -10.990983973589817, -9.707641637363889, -8.430847777640402, -7.188397561273439, -6.004899335592556, -4.901180907456936, -3.893958686418639, -2.995605159286576, -2.2139554320411943, -1.5525552774503344, -1.0108788729108944, -0.5845595094696496, -0.26604596683460585, -0.04513333961429112, 0.09050398957036927, 0.1545230628180162, 0.16129080926967385, 0.1252620050823253, 0.06033742005661061, -0.020623369086779197, -0.1062918249412699, -0.1871726636528561, -0.2558064956651156, -0.3069788398479702, -0.33763372002554787, -0.3467621572600116, -0.3353032637094338, -0.30576415030335247, -0.261884650238148, -0.20832551869621588, -0.15018334441748635, -0.09259763673102114, -0.04039727927460145, 0.002286495492602, 0.032298133419079576, 0.04767916959458049, 0.04781732635007068, 0.03349818331752597, 0.006889611850987631, -0.028576859168041386, -0.06839100404841704, -0.1072098321136031, -0.1391634949644025, -0.15818732453188727, -0.1583829605892989, -0.13436472816374018, -0.08159018911335505, 0.003340909460465823, 0.1224444342327743, 0.2761673672002405, 0.4633195328123982, 0.681013561766683, 0.9247073461487326, 1.1884584937196445, 1.4650235458962504, 1.7461120435860542, 2.0229419365494, 2.286383886352706, 2.527322549230356, 2.737384791165523, 2.9089728580195477, 3.0355830693829735, 3.1125214320889847, 3.1366957751414577, 3.106758784918094, 3.023639447567982, 2.890049799998944, 2.7103912766515066, 2.4910088931308776, 2.2394792037275013, 1.9643168312272086, 1.6749691597766068, 1.3810434476625053, 1.0919340281174237, 0.8166734082761786, 0.5632904486191563, 0.3385135123601488, 0.14763957323755486, -0.005823153913764119, -0.12024964533585408, -0.1958741940097254, -0.23480682757328616, -0.2408800125129223, -0.21941770383864426, -0.17697153920935813, -0.1209750945247874, -0.05936189788792417, -0.0001730136067718561, 0.04884715512355439, 0.08064150418509305, 0.08918144660806031, 0.06977145007215052, 0.0192787689451633, -0.06371090329558829, -0.17880571276434412, -0.3238635620964622, -0.4950566211550857, -0.6870280091022465, -0.8932585408666355, -1.1062738572309847, -1.3179718690045334, -1.5202117625773577, -1.7050091674112766, -1.8648901585960038, -1.993533239084488, -2.0857892584307685, -2.137907892598608, -2.1480497480137375, -2.116032180026324, -2.043329810153134, -1.9333337552978183, -1.7908359142136483, -1.6218033517092116, -1.4333701935773897, -1.2331847126071656, -1.0290568363547687, -0.8287795629599933, -0.6395275402305557, -0.4675347608051895, -0.31790857353261764, -0.1942568849572827, -0.09854349351151379, -0.031049598654388957, 0.009677398093753424, 0.026717799250107928, 0.024595838912790085, 0.009038502400848159, -0.013346209343921639, -0.0354319845476648, -0.04996996010011428, -0.04999522928812744, -0.029220833153627397, 0.017597766288208236, 0.09434324005275478, 0.20330184517651761, 0.3449820253588052, 0.5180204057667955, 0.7192570855235481, 0.9437867163297451, 1.1851328446172684, 1.4356734663202777, 1.6868476834169832, 1.9295239632210897, 2.154681898543384, 2.3536037795822287, 2.5182744294112016, 2.6421239889637786, 2.7200165698165786, 2.748501069455678, 2.7263975894293284, 2.6544663637311876, 2.5353912450595613, 2.3740615741377296, 2.1769364226260555, 1.951760684194184, 1.7075272244158035, 1.4536881697798778, 1.1997269703368492, 0.9549251270512993, 0.7276528450835068, 0.5249935033913437, 0.3525222830249505, 0.21389401116147266, 0.11070344858527961, 0.04246923023046246, 0.006628715535984008, -0.0012804305065151828, 0.012652971053212704, 0.041067278740206235, 0.07577316638773775, 0.10824020222852511, 0.13012136605639493, 0.13377800680838622, 0.11276488034002309, 0.062279646436978836, -0.020466245374300966, -0.1360303224856843, -0.2825564540558385, -0.455738194950972, -0.6490674109038108, -0.8539634959523499, -1.0601106092157406, -1.2562023813433774, -1.430251089007198, -1.5701688595741934, -1.664837834786704, -1.7043413884025702, -1.680535725194439, -1.5881278683876197, -1.4245594388762794, -1.1902972352101937, -0.8895779868852364, -0.5297942579403676, -0.12133727012049572, 0.32221223415711187, 0.7851389158352159, 1.2501744445807599, 1.6988589166625159, 2.112769636002484, 2.4743067084079216, 2.767371153713562, 2.978382826823856, 3.0969330857385926, 3.116400304089212, 3.034408173727787, 2.8530313886609147, 2.57898548029459, 2.223364797327505, 1.8012508562609806, 1.331293914590083, 0.8348411077354528, 0.33504114124331363, -0.14408764835428933, -0.5787852065220374, -0.9466311102003687, -1.2276356977316525, -1.4051621019328466, -1.4667711398778964, -1.4049903361800533, -1.217651444588995, -0.9081446393976447, -0.48545473137715184, 0.03621272384982307, 0.6378982007600288, 1.2967436753171053, 1.9868823201643233, 2.6804628572018117, 3.3492181549352105, 3.9654165560706267, 4.503038581802405, 4.939595183828482, 5.2566075875654175, 5.44044750993765, 5.483832608510721, 5.385447689384143, 5.150078554574052, 4.7893337183516875, 4.320341885344295, 3.765090743534957, 3.1502348323710985, 2.505175188233663, 1.8608458532004706, 1.2488440433047678, 0.6994629350334989, 0.24041151917243275, -0.10421183593225085, -0.3153205657842288, -0.37965382242698764, -0.2903682631009566, -0.047468923772590606, 0.3422001252678101, 0.8652096916065578, 1.502108325384515, 2.228280140480997, 3.0150958437876247, 3.8310943976675618, 4.643363357447965, 5.419249678099514, 6.127536810003155, 6.7398003886714, 7.232090536474159, 7.585491071559396, 7.786909929037531, 7.830142807782763, 7.715470452084057, 7.4495794419741905, 7.04566951312087, 6.522162759789226, 5.901818740622058, 5.210948586934917, 4.4776992748006625, 3.73076983633682, 2.998170817202598, 2.305739043755298, 1.6760291867219854, 1.1272410399164747, 0.6725295550694661, 0.3195619970439882, 0.07014332040530423, -0.07945116329696796, -0.13806487768724512, -0.11913736591109585, -0.03956075288232548, 0.08138389546325152, 0.22322131232169948, 0.3656759207928538, 0.48988370989439106, 0.5797087613811176, 0.6227233908668062, 0.6109844962741118, 0.541848524122822, 0.4180629667297481, 0.2477094865301137, 0.0441166920469339, -0.1750131078734953, -0.3885178518024821, -0.5727371410337948, -0.7029973633011066, -0.7550096298342283, -0.7062302013589304, -0.5373420632218567, -0.23352375820879756, 0.21452840623950273, 0.8097092892652585, 1.547947112058555, 2.418205142277261, 3.402454917207397, 4.476114356888536, 5.609401364701749, 6.7679856241254965, 7.9142708026960635, 9.009909239299697, 10.016551917944499, 10.897440010656373, 11.620431348577494, 12.158127674215576, 12.48908652105669, 12.600513088188304, 12.487237214759816, 12.152007229398055, 11.607154764929641, 10.872350366593636, 9.973836432546937, 8.944812633427265, 7.822424385589151, 6.646259654424257, 5.457735958653377, 4.297136445876028, 3.202025319528555, 2.206307287361026, 1.338154456325077, 0.6190360466768444, 0.06319506820400735, -0.32301864889470383, -0.5410806650688128, -0.599925189720267, -0.5152356154634117, -0.30837892217823404, -0.005165748914244221, 0.36567525701160425, 0.7740767449763176, 1.1902653808974424, 1.586265586606068, 1.9372707630337547, 2.2229262213815297, 2.4281037942940333, 2.5435026814763706, 2.5660270243318637, 2.498393239034909, 2.3486699867936114, 2.1296535159612473, 1.8579164220229458, 1.5524996402232432, 1.2326684977981646, 0.9165623949699684, 0.6211401244006658, 0.36416974113075073, 0.1614057324671072, 0.02012823712757106, -0.07232909277662077], 'positive_zeros': ['0.887950038680428156048478633861104', '0.963579792578804111999718284081224', '1.22294684928163679163864429143179', '2.12997157977917079782719366324215', '2.19874225135401749005514921917444', '2.69528710070449305188675872734389', '2.96244211844016406723936010423703', '3.51485445750503009873811372483724', '3.53069213668194569851421416131923', '4.17696195862044241446232115207131', '4.28029753934786921402762023723654', '4.33585728364535005459578551362952', '4.92966232592713789277376912833672', '5.07378539741429688660896089179499', '5.12540188769477338580568131053907', '5.79832658248926588059688951324312', '5.88697566185318166127259745865745', '6.23388669851040478126330731773788', '6.54049467637934465317542234817775', '7.13094383991726968268867384125433', '7.22372719601776456806403496570499', '7.46380255277666238963259005028845', '7.55305459313433055108012034846214', '7.70126417313012848988247776653835', '8.225831870938833719537358327650386', '8.378959175471211672075197055799818', '8.468131963275563228620286797408082'], 'prelabel': '6-2205e3-1.1-c3e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 11.406104136060572, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3e3-0', 'trace_hash': 2215095421233952256, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.887950038680428156048478633861', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '0.963579792578804111999718284081', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '1.22294684928163679163864429143', 'prec': 103}}
• 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': 2202033.865947624, 'bad_primes': [3, 5, 7], 'central_character': '1.1', 'conductor': 10720765125, 'conductor_radical': 105, 'degree': 6, 'dirichlet_coefficients': [1, -3, 0, -7, -15, 0, 0, 35, 0, 45, 1, 0, -79, 0, 0, -19, 72, 0, -29, 105, 0, -3, 63, 0, 150, 237, 0, 0, -220, 0, 136, -73, 0, -216, 0, 0, 43, 87, 0, -525, 599, 0, 170, -7, 0, -189, 3, 0, 0, -450, 0, 553, -331, 0, -15, 0, 0, 660, 1520, 0, -1160, -408, 0, 293, 1185, 0, 806, -504, 0, 0, 406, 0, -1192, -129, 0, 203, 0, 0, -2590, 285, 0, -1797, 508, 0, -1080, -510, 0, 35, -42, 0, 0, -441, 0, -9, 435, 0, -1020, 0, 0, -1050], 'euler11': [1, -1, 3485, -6442, 4638535, -1771561, 2357947691], 'euler13': [1, 79, 6542, 346439, 14372774, 381317911, 10604499373], 'euler17': [1, -72, 14635, -688048, 71901755, -1737904968, 118587876497], 'euler19': [1, 29, 18484, 332301, 126781756, 1364330549, 322687697779], 'euler2': [1, 3, 16, 34, 128, 192, 512], 'euler23': [1, -63, 32377, -1479946, 393930959, -9326261007, 1801152661463], 'euler29': [1, 220, 74711, 10703064, 1822126579, 130861130620, 14507145975869], 'euler3': [1, 0, 0, 0, 0, 0, 0], 'euler31': [1, -136, 27042, -3338174, 805608222, -120700500616, 26439622160671], 'euler37': [1, -43, 33294, -1889771, 1686440982, -110326235587, 129961739795077], 'euler41': [1, -599, 272999, -79436618, 18815364079, -2845312440359, 327381934393961], 'euler43': [1, -170, 62886, -25979064, 4999877202, -1074631718330, 502592611936843], 'euler47': [1, -3, 72213, -31379318, 7497370299, -32337645987, 1119130473102767], 'euler5': [1, 15, 75, 125, 0, 0, 0], 'euler53': [1, 331, 442671, 98567438, 65903530467, 7336403533699, 3299763591802133], 'euler59': [1, -1520, 1161665, -599760000, 238581596035, -64114411134320, 8662995818654939], 'euler61': [1, 1160, 1094643, 571897312, 248463162783, 59763634258760, 11694146092834141], 'euler67': [1, -806, 956790, -441427296, 287767030770, -72909456028214, 27206534396294947], 'euler7': [1, 0, 0, 0, 0, 0, 0], 'euler71': [1, -406, 391273, -58294156, 140040910703, -52008715271926, 45848500718449031], 'euler73': [1, 1192, 1524996, 931572678, 593249368932, 180390397736488, 58871586708267913], 'euler79': [1, 2590, 3310582, 2751421632, 1632246038698, 629596509799390, 119851595982618319], 'euler83': [1, -508, 1655669, -550491384, 946690010503, -166085709671452, 186940255267540403], 'euler89': [1, 42, 566539, -649223388, 399392432291, 20873214220362, 350356403707485209], 'euler97': [1, 1020, 828679, -17707848, 756312948967, 849631445027580, 760231058654565217], 'euler_factors': [[1, 3, 16, 34, 128, 192, 512], [1, 0, 0, 0, 0, 0, 0], [1, 15, 75, 125, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0], [1, -1, 3485, -6442, 4638535, -1771561, 2357947691], [1, 79, 6542, 346439, 14372774, 381317911, 10604499373], [1, -72, 14635, -688048, 71901755, -1737904968, 118587876497], [1, 29, 18484, 332301, 126781756, 1364330549, 322687697779], [1, -63, 32377, -1479946, 393930959, -9326261007, 1801152661463], [1, 220, 74711, 10703064, 1822126579, 130861130620, 14507145975869], [1, -136, 27042, -3338174, 805608222, -120700500616, 26439622160671], [1, -43, 33294, -1889771, 1686440982, -110326235587, 129961739795077], [1, -599, 272999, -79436618, 18815364079, -2845312440359, 327381934393961], [1, -170, 62886, -25979064, 4999877202, -1074631718330, 502592611936843], [1, -3, 72213, -31379318, 7497370299, -32337645987, 1119130473102767], [1, 331, 442671, 98567438, 65903530467, 7336403533699, 3299763591802133], [1, -1520, 1161665, -599760000, 238581596035, -64114411134320, 8662995818654939], [1, 1160, 1094643, 571897312, 248463162783, 59763634258760, 11694146092834141], [1, -806, 956790, -441427296, 287767030770, -72909456028214, 27206534396294947], [1, -406, 391273, -58294156, 140040910703, -52008715271926, 45848500718449031], [1, 1192, 1524996, 931572678, 593249368932, 180390397736488, 58871586708267913], [1, 2590, 3310582, 2751421632, 1632246038698, 629596509799390, 119851595982618319], [1, -508, 1655669, -550491384, 946690010503, -166085709671452, 186940255267540403], [1, 42, 566539, -649223388, 399392432291, 20873214220362, 350356403707485209], [1, 1020, 828679, -17707848, 756312948967, 849631445027580, 760231058654565217]], 'index': 1, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/2205/4/a/bi'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, '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': '6-2205e3-1.1-c3e3-0-1', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3, 3], 'order_of_vanishing': 3, 'prelabel': '6-2205e3-1.1-c3e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 11.406104136060572, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3e3-0', 'trace_hash': 2215095421233952256, 'z1': {'__RealLiteral__': 0, 'data': '0.887950038680428156048478633861', 'prec': 107}}
• lfunc_instances •

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

  
  {'Lhash': '1125610399505924266158756148206,1221482502430313819213487962034,1550269307539088875376629284518', 'Lhash_array': ['1125610399505924266158756148206', '1221482502430313819213487962034', '1550269307539088875376629284518'], 'label': '6-2205e3-1.1-c3e3-0-1', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/2205/4/a/bi'}