Lfunction data - 1-51e2-2601.1546-r0-0-0

Formats: - HTML - YAML - JSON - 2024-06-11T17:51:49.935129

• 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_2601.1546', 'a10': [0.8502171357296141, -0.5264321628773558], 'a2': [0.9697969360350095, -0.24391372010837714], 'a3': [1.0, -2.8163065144692913e-30], 'a4': [0.8810121942857845, -0.47309355683601007], 'a5': [0.9529420004271566, -0.3031526741130435], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [-0.3323547994796597, -0.9431544344712774], 'a8': [0.7390089172206591, -0.6736956436465572], 'a9': [1.0, -2.8163065144692913e-30], 'algebraic': True, 'analytic_conductor': 12.078993218849428, 'analytic_normalization': 0, 'bad_lfactors': [[3, [1]], [17, [1]]], 'bad_primes': [3, 17], 'central_character': '2601.1546', 'coeff_info': ['x^102 - 1', '0.998103328737044 + 0.0615609061339428*I', '\\\\zeta_{102}'], 'conductor': 2601, 'conductor_radical': 51, 'conjugate': 'dirichlet_L_2601.2209', 'degree': 1, 'dirichlet_coefficients': ['a^0', 'a^98', 0, 'a^94', 'a^97', 0, 'a^71', 'a^90', 0, 'a^93', 'a^77', 0, 'a^22', 'a^67', 0, 'a^86', 0, 0, 'a^72', 'a^89', 0, 'a^73', 'a^37', 0, 'a^92', 'a^18', 0, 'a^63', 'a^77', 0, 'a^73', 'a^82', 0, 0, 'a^66', 0, 'a^15', 'a^68', 0, 'a^85', 'a^61', 0, 'a^50', 'a^69', 0, 'a^33', 'a^14', 0, 'a^40', 'a^88', 0, 'a^14', 'a^54', 0, 'a^72', 'a^59', 0, 'a^73', 'a^28', 0, 'a^23', 'a^69', 0, 'a^78', 'a^17', 0, 'a^4', 0, 0, 'a^62', 'a^3', 0, 'a^69', 'a^11', 0, 'a^64', 'a^46', 0, 'a^89', 'a^81', 0, 'a^57', 'a^92', 0, 0, 'a^46', 0, 'a^65', 'a^12', 0, 'a^93', 'a^29', 0, 'a^10', 'a^67', 0, 'a^71', 'a^36', 0, 'a^84'], 'euler_factors': [[1, 'a^98'], [0], [1, 'a^97'], [1, 'a^71'], [1, 'a^77'], [1, 'a^22'], [0], [1, 'a^72'], [1, 'a^37'], [1, 'a^77'], [1, 'a^73'], [1, 'a^15'], [1, 'a^61'], [1, 'a^50'], [1, 'a^14'], [1, 'a^54'], [1, 'a^28'], [1, 'a^23'], [1, 'a^4'], [1, 'a^3'], [1, 'a^69'], [1, 'a^89'], [1, 'a^92'], [1, 'a^12'], [1, 'a^71'], [1, 'a^74']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-51e2-2601.1546-r0-0-0', 'leading_term': '2.11199486942010010672644544936-3.03766617918499867606967783333*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/2601/1546', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [3.6997213604028634, 2.501350912753156, 0.8086911554831052, -1.016331009846613, -1.6209074443069018, -0.5566011393999957, 0.9979167781592279, 1.3403896668939186, 0.0582342800450845, -1.4499811378582312, -1.50004144045049, -0.08382149420342015, 1.0824181633135754, 0.642999912088895, -0.6652428502673923, -0.9158758715723196, 0.46275029043720717, 1.822722778954824, 1.4588009318800244, 0.0257443111825952, -0.27097419412551166, 1.0552569223408532, 1.6047102232423294, -0.7453113764032092, -4.216018719139258, -4.421279527737179, 0.18290520378903913, 5.601696693584861, 6.51734215237376, 2.590634373087839, -1.2521735408900765, -1.0629392823924984, 1.511854821409478, 2.1714143058039332, 0.04589055430946278, -1.5736508435429215, -0.4524422423186517, 1.3092340133255502, 0.6174873265254626, -1.9180385326358405, -2.992341049838907, -1.5209892866748556, 0.1468928270606475, 0.23227757426696594, 0.03516794018138152, 0.9959031834991598, 1.5785775192736478, -0.29255469071146556, -2.9991572878157102, -2.7641799583254856, 0.5538469699063154, 2.6544451893961316, 1.0900327777044614, -0.9121446075270724, 0.34434149842392225, 2.5764062375316676, 0.5258169872664115, -5.424490655857754, -8.533589853095643, -4.941938407445372, 0.699321160524975, 1.8155611489714985, -1.1499513844768732, -2.566966293672314, -0.4901330931149957, 1.345406765715086, 0.36818516021166875, -1.0381365558069064, -0.33679621371780827, 0.8641899850216116, 0.29173341094202027, -0.5346317278586296, 0.8919534483810961, 3.0986252255896405, 2.753825235021293, 0.43283441276410317, -0.3366097433557398, 0.6691955812509705, 0.07594390031146787, -2.5136677447603217, -3.0093060544184556, 0.029530066899763285, 2.037091884849904, -0.07901372954193125, -1.8603254785390189, 1.8418998686774977, 7.381157118603966, 6.612630337044303, -0.6492263581454762, -5.817709699559915, -3.9169157497710407, 0.2900611107592458, 0.9895896956707085, -0.4428352447434901, -0.05022840607846874, 1.3397300876383167, 0.8661471697066955, -0.11285901265340384, 1.4659956751997876, 4.038514483271093, 3.580825009077023, 0.6460438246975811, -0.6338013378740798, 0.2922856631440173, 0.19906343652628786, -1.3131877691147689, -1.322020709165677, 0.011193576789086732, -0.7294399766195523, -2.820062669708746, -1.1139384554700769, 4.341804005847911, 5.969094313035647, 0.22887611659405419, -5.60402379358163, -4.158093493960129, 0.8291491879583397, 1.3760720509022895, -1.8360518291489365, -2.1587026573331585, 0.8307782768361072, 1.369303374910452, -1.5489089485844767, -2.628767386273885, -0.09576267781974274, 1.5618010438498247, 0.12128480699344822, -0.9930746015746044, 0.11202259210001311, 0.577991449405058, -0.860098011330121, -1.2571349852236284, 0.2407888272032908, 0.27486817518209566, -1.8694939143428086, -2.23147390266535, 0.1195208528955797, 0.7288354327453059, -1.5361169458678587, -1.4522970956914942, 2.5035728780477675, 3.5598759966645663, -1.9666554142284114, -6.998339914399738, -4.809016360590435, -0.11248447472472364, -0.35833310076218766, -2.847871215221512, -0.5876406492495887, 4.4433380755866665, 4.749884041197065, 0.4481132295581195, -1.7084946541419637, -0.15699503791838793, 0.6396282946671237, -0.381593015033837, -0.08111600482549909, 1.3683894816340656, 0.9533345853347732, -0.30190926673959234, 0.8155358016093246, 2.521966563217534, 0.9018615272655979, -2.0325904627861533, -1.5781732111503635, 0.740920756377995, 0.31120687417564197, -1.327607441121204, 0.12108835541208643, 2.2889287281827566, 0.7497170700686361, -0.22025647168002307, 6.299849349364407, 15.38354970381479, 15.135897433618709, 5.315455194317168, -2.205296254328746, -1.8055427102813812, 0.2491692879270636, -0.4991818499168482, -0.6135416398360465, 1.3634221183711874, 1.2109990705369922, -1.8322875226298514, -2.9111524844523555, -0.8796784125581928, -0.016547233418756455, -1.1175577427759538, -0.4909087645047142, 1.6219388864231754, 1.2162595971556565, -1.0422766311683855, -1.0199108801600212, 0.38278135311159617, -0.5015893194338872, -1.686474387713958, 0.45776142792166785, 2.252181162391789, -0.9981296954364591, -4.010498053030034, 0.5365396738152259, 7.421429179699952, 6.14680653764948, -1.0784077329506228, -3.267609977478331, 0.6841796168757215, 2.2531744416406356, -0.3376734296393834, -0.8752918060194775, 1.4672528974408452, 1.5598542542228964, -0.327140955374773, 0.5815296750271801, 3.1071279881867047, 2.2269288018799402, -0.8385296020682818, -1.2259149510363816, 0.3178698018676793, 0.30424772632775565, -0.04854499502088192, 1.1632250593830278, 1.1632187219287649, -1.0390049930519252, -0.5558114255504885, 3.740027249989423, 4.940534140984544, 0.47284305591747927, -2.3398962830904915, -0.0006748336067397641, 0.5890422246266225, -3.5213009967607496, -4.468184209588496, 1.0371832393184746, 4.072714793826335, -0.31850640409512654, -3.860338094589722, -0.41277270578289027, 3.573410571037643, 2.085312975397253, -0.5023366755095279, 0.20491799785320902, 1.007244500068659, -0.2277277127044789, -0.189079992129435, 1.5494294089315979, 1.098337238146432, -1.0318581760083387, -0.7284329342477701, 0.7432228855362104, -0.5340985703216988, -2.170820550367737, -0.1705445381225552, 2.1864315265779313, 0.8953251305569645, -0.24744492437756993, 1.866342576230144, 1.930006217681192, -2.485482389668333, -3.4189050209274723, 2.7531779069087845, 6.213138206874115, 0.6717189792951561, -4.709019797630277, -1.83843321938477, 2.5003125965208577, 0.6810966462202557, -2.452462726669272, -0.9325086639032736, 1.4570660083182831, 0.6695863762337833, -0.16350692818009402, 0.6809461170790264, -0.055291463958583385, -1.8467001477584404, -0.35303784017353, 2.7793305409432807, 2.2128411341947025, -0.4872938073528265, -0.286502826734453, 1.2957902144326325, 0.6056074170188396, -0.23488637640127483, 0.27532833857375033, -1.8951472950807018, -6.036354395256431, -3.9745390629187947, 4.265831474687427, 7.183849993409494, 1.7551521741671567, -0.5713920634522386, 5.048354275962228, 8.473485464621383, 4.08334929661055, -0.3050447446920044, 0.061821880607217994, -0.10152546179348058, -2.312534650059407, -1.1403807526163778, 2.822255112550466, 3.0307706818235567, -0.03392122599222815, -0.5118049575680397, 1.0746887689517517, 0.6402350072385772, -0.34094492931775894, 0.4334787952674623, 0.03960427571550671, -2.3448466637697485, -2.1230702450156778, 0.7695216168683484, 0.7901264631781795, -1.3730866042592607, -0.08603512030261666, 2.2680056440354326, -0.24458275203435237, -2.753927216473466, 2.4464486516449013, 9.033041174444055, 6.569813877401499, -0.17707955317602006, -0.6865316815414743, 2.033960304360449, 0.005032688742480299, -2.931136471493528, -0.23293115909961357, 3.232380065079804, 1.3030487185345296, -1.6128100150626972, -0.6471067437197352, 0.5864559265974076, -0.5279244158204793, -0.6074425643068329, 0.6918490195974328, -0.0791126677322703, -1.3830934679703168, 0.07286996982916712, 1.0243174251588245, -1.4500845211372506, -2.350565908271, 1.1083617481369095, 2.8130271454866653, 0.11982956257491671, -1.0805176698206636, 0.13891590050181252, -1.902114329058647, -4.473548592456644, 0.4260195166079366, 7.339364660426801, 3.654787623975591, -6.85998981751114, -9.370045466451025, -3.192602602233327, 0.293647758469843, -0.8469765552604435, -0.2826870763944844, 1.3648240044432793, 0.24805707187539558, -0.6949547915236384, 1.0131852601223097, 1.0821378019704997, -1.598675550719783, -1.6727944884364638, 1.1972899779827777, 1.6068476330821575, -0.1772344338530533, -0.14248605387705862, -0.21844724621040637, -2.8419592962901965, -3.624816584265392, -0.7550527657615071, 0.04190553378042734, -1.6805596116726218, 0.7688023855776864, 5.06614210263782, 1.697009837348798, -5.658790634858057, -4.134967370480197, 4.151051181466936, 5.694644273896281, 0.3803814697879865, -0.9593471213910362, 1.879983193539487, 1.4378090736817184, -0.8768129885131027, -0.23138095486274113, 0.004864212227646759, -3.060531227693927, -4.161085050655985, -1.1107054004454417, 0.5557691738045906, -0.4505283644208361, 0.33471568821798225, 2.1081826055776753, 1.0288303784350092, -0.4923738123765769, 0.41634155227925496, 0.5187588821470205, -0.6180077388087459, 1.6985975447341168, 4.69278422159814, 0.5306795804310848, -6.4697777659549, -5.307696150919253, 0.896571938410128, 1.3947439898470402, -1.215320413148075, 1.0554567331507958, 3.0548483898934684, -2.1448273433538243, -6.784385048789878, -3.0202994706259947, 1.782169743095403, 0.2753068324366645, -1.990478048712991, -0.37882825780589835, 0.5638987695580948, -0.7563925973130821, -0.2969466698710609, 0.9881350218180764, -0.33737129240665037, -1.3824379211055142, 0.33552911053795736, 0.6942924745468303, -1.1313825099644381, 0.0231401647615737, 3.121426061722696, 2.1082816319387883, -0.7908177120792966, -0.07277430559800642, 0.5796275447221889, -2.2842126973356227, -1.9095222829893115, 3.4728359676354796, 2.952279573425123, -5.744437551382393, -8.997144739710428, -2.2574239140492116, 2.2450672413338237, -0.16447103369634922, -0.3768029511465451, 3.3663536713187248, 3.2188068146713196, -0.41498622453562345, -0.8339881406368911, 0.6602059251271234, -0.07605056012534656, -0.5290943926354661, 0.5796333238130869, -0.6593876748094076, -2.9782429393691845, -1.1150128514747417, 2.2050370162062976, 1.3155751938982174, -0.7291931468038435, 0.19804673410251034, 0.6737721605495449, -0.4369861691997521, 1.2595162387074486, 3.4654308581044626, 0.7312878607786459, -0.5509606100842038, 7.093394936099056, 13.42497616262229, 6.592650238019207, -3.949237233782112, -4.262744001623764, 0.5568394532168155, 0.6699057354155191, -0.23013613874217054, 2.1776621917804313, 2.6280094457685825, 0.024970015820666564, 0.5658529068803327, 3.180778595478289, 1.7093757396668703, -1.2834136061045696, -0.4768487009289422, 0.9616436418685179, -0.27020164607418773, -0.7055592566156872, 0.33989958073810433, -0.5342220284175413, -1.1110753528016433, 1.6112709238984844, 2.5393518402664217, -0.8800411426011827, -1.6416064291229644, 1.547673512026976, 0.6219664782391079, -3.0498244424839522, 0.22883273200172938, 6.686443745947106, 4.849726452013213, -0.7165877538182047, 1.4759083893705012, 6.476303617692427, 4.150078630565948, -0.5490015933005779, -0.18565570964309963, 0.3564946034143305, -2.4113019064321177, -2.444326887565219, 1.0597332563397701, 1.4113122744259836, -1.0233436059062488, -0.9203193755619432, 0.25083985001703407, -0.1859580311412547, 0.576728547397522, 2.1601729331075274, 0.4011346412278446, -1.617582012346038, 1.1278341567926529, 3.648323059608248, 1.092660024149901, -0.6768336845149007, 1.125922999896833, -0.20224896200701847, -3.9465539511361394, -1.6836287343596172, 2.8504886107295704, -0.04680522940308379, -3.857379710250859, 2.302525444194174, 10.093514740831163, 7.130192130986745, 0.11394755601506587, -0.2789332139070429, 1.7534938444861867, 0.4836340158915451, -0.3028877558950869, 0.7755775323646548, 0.22590798891865202, 0.19306236050204365, 3.361824412256982, 4.431440675418348, 0.9004934255001092, -0.8959911394876319, 0.8482131711138134, 0.9528574479104222, -0.16518100885947118, 0.6989509305377425, -0.02859897764594222, -3.6222668220326306, -3.5525611865922597, -0.14955287277028984, -1.1241948544224134, -3.149318320069156, 2.193931068606714, 7.265372328254795, 1.0620877553037356, -7.143271909041328, -4.4876967228827285, 1.5982899230627046, 0.44037202052855606, -2.2995784216903483, -0.6461463753103227, 0.032132215203002405, -1.6457814334171297, -0.038340339796590454, 2.9122780092863145, 1.664268505895066, -0.3936167969954073, 0.42381133547945266, -0.16700649420866984, -2.962278652320547, -2.597137689509407, -0.11468449205402632, -0.34217465112830575, -0.9004436041948043, 0.670549093573791, 0.6458250833760939, 0.17958791736060467, 4.3680875566538475, 7.559797615967366, 2.391124778070241, -2.3208666594665464, 2.6162946910542098, 7.283192082460264, 2.467698539070263, -2.3966224346020066, -0.41181553495887535, 0.19853228211806107, -2.673043612466249, -0.388093725791315, 5.0984883851958855, 3.9685025183691978, -0.875720149695393, -1.0465292899804473, 0.515135120833782, -0.8722229902449616, -1.5004319820420098, -0.12604026333330576, -0.6107954745893003, -1.4314995103237433, 0.08775536962274097, -0.10571181595609269, -2.8036819288477495, -2.0143635626044807, 1.1421591786975747, 0.14082722887084942, -1.995138054796113, 0.0042829844139958126, 1.026648103358915, -1.2966023402010953, 0.7190642828012255, 5.6184762740812815, 2.1441936794059506, -5.991411290989789, -5.155816683395479, 0.4782766631768977, -1.9202388172048823, -7.268426401952166, -4.766957873829001, 0.21423368146982708, 0.10336222054124761, -0.3614608690588593, 1.4967367868594097, 0.6320429163718703, -1.8771237818098472, -1.0898837173687912, 0.13224451194708692, -1.1331405993298418, -0.9729587097277286, 0.38202721186170996, -1.6722419096702539, -3.7536027492715607, -0.947510720772734, 1.6335210861171665, 0.20116058435077588, 0.035229411896988964, 1.641206408668325, 0.003748933522303908, -1.3533898677123717, 0.7440401757768582, -3.5998788018108545, -16.94052993884397, -21.871982594973286, -10.722191476955281, -0.13045723325069147, -0.1872512493135199], 'positive_zeros': ['0.75306985645082385276288917335', '1.66687674596639526043692889468', '2.510500732233599698710893083524', '3.45360747135344379628714183399', '4.213301283815464039067378251825', '4.91632797612785761831857783509', '5.9442912050817579498045605086', '6.337823756682697968153692054964', '7.11873538936344259267608136245', '8.115493110240123823621953939387', '9.24293909775926727205872737158', '9.819873518612201543938208110641', '10.6306554811960777421649654329', '11.31661615037356605923666212022', '11.95771327692741126804508556157', '13.08074619999531291894869097145', '13.62937381127562415367575041019', '13.70906053139856062138689175738', '14.6554918379458232961830273919', '15.57714740718263252049988980660', '16.38144529306515415747489706184', '16.8328655000721804440741438859', '17.53268941381008534945999213652', '18.700921541828338220738883625028', '19.26627803425286197909410893991', '20.05686436888117205716618458541', '20.68673771228680095912491970806', '21.318796493319065000641425767933', '21.947360605787197751380222977846', '22.36786991721911181897726075266', '23.51356666663990102752981734690', '23.86897964074196270955966130308', '24.386375619237592769571202513619', '25.30988652444116928411038171878', '25.92972462620294652062948302104', '26.457257063063384124753720752713', '27.47432611561283282486637313232', '28.408146511458528310768697278596', '28.95176223071754344665531021782', '29.38555739654093672676697091364', '30.21890749310342346212852674878', '30.39073701815092420144200174697', '31.64749316300176033937624211767', '32.10161565763105951622240212524', '32.54731644860852576969178495114', '33.43301765266347386971355077205', '33.60363247055825796016097535680', '34.445999266484637381099225108644', '35.32193642792485121241704434632', '36.18733354296958723780712638032', '36.70180344008846379400544379507', '37.41349724156028398106178399872', '37.97449807115042845244163182237', '38.76008355628836962317661763166', '39.39393151206428886782429827461', '39.975467328755662257354412342655', '40.46075139150308472971717215036', '41.19983911322770005142578779375', '41.613337345815588794153100280', '42.48409747936570960610072611964', '42.93058302959595819081064035076', '43.56802654185088690797166974681', '44.28659566501891562278351238603', '45.325624431708773671231319167619', '45.57993792386170269518274518920', '46.286148635693241222250366476630', '47.22170289857573580326508323968', '47.83883248519956340106078679407', '48.324594563665749996747731034507', '48.767865882481980201774409004315', '49.57257868822935100691023348316', '49.863268472776628657982987728183', '50.7095539674043017338398541157', '51.44379075894111524163243407932', '51.92358895753291826254634970769', '52.48648766027336338177015278800', '53.21599806147108881874805950650', '53.46329277119575954620517017201', '54.86763496569795686238265249507', '55.54908154023284938689604548191', '55.81540293125696461569325194369', '56.35895133537284544548501360163', '57.01084297882459854462325302333', '58.00274213195330766087478235242', '58.11575769862069997333546040506', '58.82064091578262073150937226832', '59.53463993021782152385976932368', '60.1973253142268378160754784168', '60.535268631657466701908525439528', '61.20469431064141245097317243433', '61.80894353762928976597174116948', '62.4779363594963269908178994085', '63.38691737922936216295537908915', '64.01294590992498101357434198414', '64.64844343732546292135349526403', '65.12554979554277875634026351750', '65.86504168787807546926029489634', '66.1704868979060779862606811154', '67.090532319054883743659007772930', '67.735605689143204044593647766716', '68.25395799552869218259581554172', '68.46248368094950424366957577940', '69.231714604694519690090675942449', '69.73804166975298906445248108530', '70.654364385698339838329365252881', '71.250072175898308136557278579067', '71.62459594727053517770010616370', '72.448893214546576460466463517713', '73.10821073083807432560267785879', '73.77377262570196131671928716222', '74.58958580782576463046372723654', '74.960077427631687189383057285811', '75.57229823171685319356577755852', '75.97573496991684101019944893094', '76.71216836651763909495996646335', '77.311544225086230760804865925652', '77.73969860919534466617007019442', '78.45379780360270983806445158370', '79.2004135893777567607114805543', '79.440667569915591565400959391141', '80.15220407416836840561531274461', '80.81832404761932613465953691457', '81.589649807408142752865927390487', '82.28991547017209234929962361616', '82.86426750828826537603818990386', '83.53013424302999419720155016147', '84.214569482234726419545429033930', '84.45952489406086423070675904863', '84.99117458261834776232539918122', '85.65756134203043859419263339449', '86.490057098026714414826166266455', '86.92368693153646298293661477574', '87.64266691941042577737757080317', '87.94979249075107375906376733531', '88.23740666866373562239676479838', '89.21849298932034377311039617609', '90.10634621371272818195716926223', '90.36749636927753599763819387361', '91.517762026876417028688143642924', '91.859219654271321451292703516119', '92.16953172312015091496919789697', '92.90206421809222035169528201313', '93.74575082461735650567808787036', '94.16022450004424814217506735376', '94.83267676185975663819961778698', '95.18074047144737091957306355502', '95.63142041020437239558295797216', '96.47215852441193268989281799292', '96.978914753403998284426190931017', '97.508632754238652076472184042015', '98.10713758843365544620002212126', '98.64922661046694816478567273395', '99.67570773842833226291322608900', '100.068628484158218266534479419400', '100.625385376831215204161021138780', '101.26547263130904312756883545052', '101.98264033262579875243289527798', '102.60156954585187999086602784272', '103.00717760299651387770412007146', '103.57083334362819766584733227803', '104.048891315431621841163712514290', '104.67718495891322482919750410662', '105.161137213476859625584145480077', '105.85209917277022256280443194193', '106.57505446416429229949686657900', '107.12325803489552674865790103373', '107.28439174601435778340646399931', '108.10871137695305096093560921202', '108.85798509465766710823280199001', '109.91389559624528273800089995508', '110.13070547003481873958569516175', '110.66785003602444396440529092837', '111.29020696770471339208489402883', '111.71803707197884530794921508997', '112.32139826920083880860186618946', '112.99439598826136018782273034510', '113.7091521072722587004476307168', '114.12097764445753318799187594322', '114.32048794060054783252000391692', '115.4147520516181883138153096419', '115.63398840168007786238436210702', '116.19922244540525998736514943509', '116.941477092349226645978399237002', '117.65413111210643535105049127930', '118.463755527127471585463792173029', '118.8607543453406393950822738997', '119.54072500845681292680911487271', '120.049603193740027164963189994332', '120.313373344703047050142373394493', '121.3727231692651261055325418994', '121.744423677839001785933246054035', '122.13337575404869298799647401948', '122.968795092554976499339492875672', '123.339721622375866218044751771656', '123.8639503184669413206059438412', '124.22012717118385382073368094234', '125.021417944192666022156539902165', '125.88181700836366921259905108262', '126.38595341681742646159084974879', '126.78997964618450827126778132098', '127.4041720002348270310601408251', '128.28099036266842148576397582264', '128.77497667566545448722868064385', '129.430175673549947349653509425969', '129.83081637899460831008864604251', '130.36625651039566795310858359780', '130.88716140663232122358290914337', '131.510573515823740087985379120146', '131.99350178774891717821610054668', '132.49772510237802422938915278899', '133.32346384620027247842515786274', '133.76167378065744350637952086428', '134.14833793130788443766500032178', '134.80630359810525270229622824777', '135.432441514314949452906226342444', '136.34797208161005599913635285608', '136.85789632396308292572449392024', '137.22527663790814153035346902021', '138.081883951572807712183676402915', '138.583958871618701619021109896707', '139.045165295459271352422665930', '139.51844685824369468600691142536', '139.91642460830208137474565651508', '140.71254160514743850309010301073', '141.40773623177258193338564031857', '141.83635847078213497089671974643', '142.352322510324874039810117521347', '142.66569509332336634045293020098', '143.49649635983383350897394040953', '143.79315284236826535932523664487', '144.86052916098134805123954921893', '145.575684192094738474984495558266', '146.053756165437247279402996350025', '146.3020171588941776113428078602', '147.19170866391134078151340663749', '147.42388625109644058687996956111', '148.2742460631647719940695059730', '148.81767387957152555741013126338', '149.32392848527217924152041065675', '149.87446060810833070439921430395', '150.20523758959891933688554056777', '150.78129257426079337744791873639', '151.48896450273946209617121128340', '152.03636759628331575246756213904', '152.5466128162175270328987782355', '153.11475144572142181664872091822', '153.99900779634497744617631912229', '154.28588142705503812804082949223', '155.2543759420455501335656097578', '155.655954605432894009254418167705', '155.993865882417365765685338325293', '156.776741377854237953392509828004', '157.35960944276344120088939514223', '158.01131772262259094789124891012', '158.3404578984803883070617910423', '158.634417065351499385368613980167', '159.41476503620975484119456348684', '159.91284425563876323370881418988', '160.73156927623075057475655027854', '161.0750716412073307302387887935', '161.54599412209198367947060803364', '162.28051904111662749586840316344', '162.81001878599484914701201998030', '163.36119545896247029562589409685', '164.383498448094817774843570116954', '164.72146333915803755001499256554', '165.39776858465697883260990820349', '165.72043815859772892544864472793', '166.31302217131962290891520533611', '166.52382898499777700949956777711', '167.58076941258414328118013971621', '167.991521807130586096476883480609', '168.65730978769293371674919002269', '168.875070876771445323578327037880', '169.37185958335042639328397507498', '170.33806348004059741894785335896', '170.48991357545836443542170263588', '171.15987013030308454034390786911', '171.90698101327586977014338445346', '172.70020571584262756584928723807', '173.16036313359913887110426110953', '173.85228557591864407047022940689', '174.06996531823477308838416053943', '174.69091771614424283518456375030', '175.51567292851810947970361199234', '175.829911691591680128172961495185', '176.22750993761879628762719754617', '177.215274290927829691426347503051', '177.40907807459822442877809850695', '178.00324122940822338046306638533', '178.61068508847890258801967471704', '178.70103097854894496039658339312', '179.7918384115640437055815210984', '180.199560540208791916831258774', '181.049492017961746782955583485799', '181.608049995453535861205327662596', '181.90026888517469094319508788729', '182.52098241733845152781199367162', '183.36527382903739098740234351438', '183.90499885581176139209985235166', '184.23471114443105776109675957418', '185.06785978352734405909589849763', '185.12161138578568993693880265119', '185.92075584889743239817083705657', '186.23445870001684857742064987089', '187.05229160447361829730512428269', '187.51469280094748408758847628720', '188.124536768984861363972167696142', '188.57926673484828294656051395666', '189.016667783228680179109612847324', '189.76356589005634052487161841828', '190.5807451112151697993914236130', '190.824728046902911760255025201781', '191.8512871938700840583113589353', '192.20769538653507604877373247551', '192.571008465131080430477356195728', '193.19327781852846825094731957906', '193.94895741618258208143454181996', '194.129521725300902346585609155316', '194.86086361522184373830111054454', '195.127776492247967749066482245455', '196.01212321873815849731328538089', '196.5995457385656026914014311237', '196.86800410366694787067851995419', '197.50041149989228596389270494440', '198.00829703025105248862442275276', '198.28722907605695885300852687051', '199.69633782221426238484610050496', '199.97764521320191189412927423184'], 'prelabel': '1-51e2-2601.1546-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.078993218849428, 'root_angle': -0.6132256824298348, 'root_number': '-0.348255043041727366994744631209-0.937399821312125394531504513857*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.306612841215', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(102)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.92660593054883791215771589072-0.997534911121207885338236571513*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.753069856451', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.66687674597', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.51050073223', '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': 12.078993218849428, 'bad_primes': [3, 17], 'central_character': '2601.1546', 'conductor': 2601, 'conductor_radical': 51, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/2601/1546'], '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': '1-51e2-2601.1546-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': '1-51e2-2601.1546-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 12.078993218849428, 'root_angle': -0.3066128412149174, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.753069856451', 'prec': 47}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_2601.1546', 'Lhash_array': ['dirichlet_L_2601.1546'], 'label': '1-51e2-2601.1546-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/2601/1546'}