Lfunction data - 1-1976-1976.997-r0-0-0

Formats: - HTML - YAML - JSON - 2025-10-23T14:00:31.205796

• lfunc_lfunctions •

  Column	Type
  A10	numeric
  A2	numeric
  A3	numeric
  A4	numeric
  A5	numeric
  A6	numeric
  A7	numeric
  A8	numeric
  A9	numeric
  Lhash	text
  a10	jsonb
  a2	jsonb
  a3	jsonb
  a4	jsonb
  a5	jsonb
  a6	jsonb
  a7	jsonb
  a8	jsonb
  a9	jsonb
  accuracy	smallint
  algebraic	boolean
  analytic_conductor	double precision
  analytic_normalization	numeric
  bad_lfactors	jsonb
  bad_primes	bigint[]
  central_character	text
  coeff_info	jsonb
  coefficient_field	text
  conductor	numeric
  conductor_radical	integer
  conjugate	text
  credit	text
  degree	smallint
  dirichlet_coefficients	jsonb
  euler_factors	jsonb
  euler_factors_factorization	jsonb
  gamma_factors	jsonb
  group	text
  index	smallint
  label	text
  leading_term	text
  load_key	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  origin	text
  plot_delta	numeric
  plot_values	jsonb
  positive_zeros	jsonb
  precision	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  root_number	text
  self_dual	boolean
  sign_arg	numeric
  spectral_label	text
  st_group	text
  symmetry_type	text
  trace_hash	bigint
  types	jsonb
  values	jsonb
  z1	numeric
  z2	numeric
  z3	numeric

  
  {'Lhash': 'dirichlet_L_1976.997', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [0.9396926207859084, -0.3420201433256687], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.766044443118978, -0.6427876096865394], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, 0.0], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [0.766044443118978, -0.6427876096865394], 'algebraic': True, 'analytic_conductor': 9.17650542116358, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [13, [1]], [19, [1]]], 'bad_primes': [2, 13, 19], 'central_character': '1976.997', 'coeff_info': ['x^18 - 1', '0.939692620785908 + 0.342020143325669*I', '\\\\zeta_{18}'], 'conductor': 1976, 'conductor_radical': 494, 'conjugate': 'dirichlet_L_1976.549', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^17', 0, 'a^11', 0, 'a^0', 0, 'a^16', 0, 'a^9', 0, 0, 0, 'a^10', 0, 'a^14', 0, 0, 0, 'a^17', 0, 'a^10', 0, 'a^4', 0, 'a^15', 0, 'a^13', 0, 'a^12', 0, 'a^8', 0, 'a^11', 0, 'a^21', 0, 0, 0, 'a^8', 0, 'a^17', 0, 'a^9', 0, 'a^10', 0, 'a^0', 0, 'a^13', 0, 'a^25', 0, 'a^2', 0, 0, 0, 'a^23', 0, 'a^13', 0, 'a^16', 0, 0, 0, 'a^13', 0, 'a^9', 0, 'a^8', 0, 'a^14', 0, 'a^21', 0, 'a^9', 0, 'a^14', 0, 'a^14', 0, 'a^21', 0, 'a^25', 0, 'a^12', 0, 'a^16', 0, 0, 0, 'a^11', 0, 0, 0, 'a^14', 0, 'a^25', 0], 'euler_factors': [[0], [1, 'a^17'], [1, 'a^11'], [1, 'a^0'], [1, 'a^9'], [0], [1, 'a^14'], [0], [1, 'a^10'], [1, 'a^13'], [1, 'a^12'], [1, 'a^21'], [1, 'a^8'], [1, 'a^17'], [1, 'a^10'], [1, 'a^25'], [1, 'a^23'], [1, 'a^13'], [1, 'a^13'], [1, 'a^8'], [1, 'a^14'], [1, 'a^14'], [1, 'a^21'], [1, 'a^16'], [1, 'a^14'], [1, 'a^25']], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1976-1976.997-r0-0-0', 'leading_term': '0.621110401673417415495024675004-1.47979586762095584740841271991*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/1976/997', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.6048594769932258, 0.5832744119541473, -0.7061195685780884, -1.7213452370304672, -1.5555241378934714, -0.22011003094309242, 1.0971694346365395, 1.0773157647326257, -0.3315956674289526, -1.6687291378609617, -1.3751974306517423, 0.45921668537662774, 2.009592327461776, 1.6675174464810498, -0.003661061583553131, -0.7094359979105506, 0.9026981397295335, 3.3187704156329065, 3.5077312400677636, 0.35983910192528235, -3.728339223236473, -5.229025628073848, -3.257672942403082, -0.3225220517604586, 0.812792924369119, 0.2188543781384696, 0.023895222216533597, 1.0507317188799208, 1.6066580424955657, 0.1855629424848219, -1.76563222278827, -1.299217887489229, 1.8868043074549194, 4.357810540620467, 2.980097423456206, -0.9438616062859191, -3.125223127851395, -1.687031426696548, 0.6350514485500008, 0.43220630774348545, -1.781197582495521, -2.654133178372399, -1.0089667002912848, 0.5458415738546466, -0.3453787188625245, -2.2089073071401484, -2.026764315108128, 0.09129004115698075, 1.0541504078632096, -0.34529191932720626, -1.3862852196834112, 0.3215901287710449, 2.641913913307337, 1.604783916706312, -2.5150705248403895, -4.905690036086668, -2.67908566600308, 1.158373725569398, 2.0719649650828162, 0.2434665244899364, -0.4203141141523892, 1.442239545834095, 2.8567632034152157, 1.5682992897659687, -0.45005339658396826, -0.541084983612843, 0.21642238425943355, -0.7207410400509431, -2.183766604671598, -0.41489547956621714, 4.428286540638023, 6.93951782545994, 3.585139148782844, -1.9959983556168508, -3.8120860706352095, -1.4763368138410886, 0.4019855675793674, -0.31209086330558383, -0.9069640363827133, 0.493288774118917, 1.3834405182211793, -0.5521837092639832, -2.8717234681265364, -2.02657492316211, 0.6901206003345374, 1.1235470325780919, -0.8872405503144959, -1.3753186449822918, 0.742414284121427, 1.4841665401374802, -1.3811289949247936, -3.8583388311621585, -1.691511249212675, 2.543133184860415, 3.0256742660296476, -0.4969791618258386, -2.7205182284065295, -1.1921891738939774, 0.6863343382068723, 0.12167682437269145, -0.8266797281001733, 0.02420827425572704, 0.6573793328646114, -0.9179876071028524, -1.8596340019191613, 1.1648745969838201, 5.331663555191387, 5.035482980041294, 0.839978701936097, -0.9855433357828093, 1.732805147718025, 3.8665008692899945, 1.5504117892645393, -1.8287776512216076, -1.7383445362283445, 0.3165961255451185, 0.43844833113090836, -0.633325767187449, 0.2746071851863426, 2.1081775210892517, 1.2921382971889854, -1.1755774659943534, -0.779933692087461, 2.3895160939307205, 3.1442369231093776, 0.05983943124583752, -1.7259218336654318, 0.8011425981688497, 3.31268227222862, 1.6697511669232936, -0.9003149919986899, 0.4243715504410768, 3.546532495566873, 3.113300766612048, -0.3319980393307656, -1.7229549291680115, -0.26399598058375817, 0.16314343390206268, -1.2580027726381289, -1.2343481841819126, 0.5849495722350124, 0.7125527010327913, -0.6558798217888047, 1.396832911732334, 7.2962721688702965, 9.927099774533161, 5.056573924618153, -1.5542431208001553, -2.7151628165547184, 0.06382773453807496, 1.0414884925470977, -0.03745725473067635, 0.23530614977762376, 1.1007049639667534, -0.6281421970410301, -3.273839072940495, -2.484443171597275, 0.5851102635100938, 0.908233659695904, -1.361839786760244, -1.3943165292502426, 0.8617563839138394, 0.19124946116938757, -3.815666468523802, -4.884049399374338, -0.7516683995958913, 2.6206595375201864, 1.1839412526324407, -0.7777130854405304, 0.9810186068003112, 3.261493077192681, 2.024142722983112, -0.1675708450516637, 0.43603764595171285, 1.6590321401101504, 0.24796423861152309, -1.4000812938958727, -0.17636648451531003, 1.0362744287431802, -1.0779927948977552, -2.7364279815623913, 0.7425327285343223, 5.320656793470647, 3.8264341675908797, -1.9215963307219945, -3.989961436088956, -1.226986808338335, 0.33800846009512836, -1.192515189634497, -1.6133499060617702, 0.21211532091255947, 0.6573594468450026, -0.7099864757467654, -0.5327477353669934, 0.3634938105644588, -2.40983579810963, -7.30280896237808, -7.460283722930614, -2.388534850602299, 0.6251282754389371, -1.205675044473355, -2.3142344076913473, 0.09269072899857503, 1.1912852421315439, -1.3919518500191517, -2.5486186186960516, 0.5411819926984849, 2.804852678911426, 0.602087727673694, -1.932860866369178, -1.0780680972039176, 0.2352923973612434, -0.47585709136677823, -0.19413498548411998, 2.3513787311896936, 2.8676611614538112, 0.32869195305635923, 0.8025924112060299, 6.49654303935592, 9.9635955904938, 5.980084264209434, 0.46501059431554304, 0.26486395902340376, 2.4642360768210496, 1.6088796150586004, -0.4410050810754708, 0.056160242197324524, 0.8453098141280555, -0.8563090093017771, -2.0015995791017316, -0.22018570170520813, 0.4927020560574365, -2.33082416031799, -3.7644941817310857, -0.6935710751406506, 1.3672112058147114, -1.6850143340204609, -4.212133486488668, -0.8401067453446003, 3.5976151386985835, 2.845314152703995, -0.09591642717090619, 0.11544888575575606, 1.389536206587702, 0.13799948825288072, -0.6542049978923706, 2.0491235087154465, 4.138464045043878, 1.8804718586698097, -0.7916265706483716, -0.022350327638813755, 0.9409394018233568, -0.44155688177062224, -0.1097914988589084, 3.401127494624498, 3.522263022482387, -2.755775551619477, -7.617336728855992, -4.905063505846515, -0.22056238787610988, -0.40716953801225625, -2.5617007143903887, -1.676108544626325, 0.13260039303131196, -0.1685108185575235, -0.14630414961305058, 1.3988532536029903, 0.5854005732643266, -2.8736899076451916, -3.1320422232487246, 0.5338882932663187, 0.888803436270557, -3.964416646087951, -6.231981700791593, -2.3141790999420953, 1.156829306226118, 0.09165070958525769, -0.6602682988084089, 1.469926431724499, 1.6014498244025823, -1.8357615857670826, -3.2416900657467593, -0.8375676562333406, 0.147190171522011, -1.7694222964377362, -2.023662491112635, -0.16929543284329446, -0.4140261723681363, -1.4867332640095858, 1.57433400069776, 5.963317891471448, 4.478526135439566, -0.804808244619914, -1.660271197500382, 1.3250364538707031, 0.7219430916605145, -3.07510929317049, -3.1611009920927438, 0.25538784706988843, 1.0314298464876468, -0.8224370880995051, -0.7270723556132581, 0.45760062322982875, -0.4947598886060573, -1.1251762805566579, 1.0360489385058196, 1.4653924666204765, -2.4609334190716425, -3.9931089196452176, 1.291933915292939, 5.925884058768016, 3.0387843062503963, -1.8770481306445588, -1.773202719135359, 0.1829748588667786, -0.7690003833838723, -1.6627306518054878, 0.11115885955571847, 0.5207607910347157, -1.9112172207239522, -1.984991586738209, 1.4237796806631184, 2.4120024008281846, -0.18710237565224633, -0.7186395030754137, 1.3135594677174944, 0.5864309519396724, -1.9805093473343383, -0.7279713364139531, 1.7597447288645398, -1.8398810584589842, -8.550840942193233, -8.793050864888071, -2.962326717877014, 0.4268311692563035, -0.05764729240898493, 0.48950699195700514, 1.7573487912802457, 0.6170999266675153, -0.3701732962846304, 1.5223734991125293, 2.250885601043979, -0.4658674011274967, -1.0743012631176347, 2.4827584495140647, 2.955329230547077, -2.378866597712937, -5.210518144200329, -1.311177774266045, 1.8850053047373696, -0.24760154289756867, -1.9728630385614552, 0.08392117938781454, 1.2064450661161248, -0.12920495544244034, 0.519543905665125, 2.7929590761264578, 1.8334763281266517, -0.801215699986185, -0.06396727657461534, 1.521790156225946, -0.8512322416388856, -3.1874501175532663, -0.2799708432589046, 2.947601132723266, 0.7906307959880963, -1.6921023583767831, 0.9805302862719367, 3.5330967149413133, 0.8658575522494686, -1.6563666125488505, 0.5570617784543297, 2.348263584076485, -0.003984059527322321, -1.6304762785575597, 0.13942726216164533, 1.0412184241739197, -0.0960527495584051, -0.05000971254689775, -0.6258004953171263, -5.1222188539814795, -7.689731400225321, -1.5125691606253373, 6.812237732255136, 6.709028631554414, 1.1763095145388112, -0.36292036290965934, 1.3348079965401283, 0.5981277906896002, -0.610429106674432, 1.1615327402876237, 2.2251601002261894, 0.17519571685106083, -0.2948864300813039, 2.0832419405580893, 1.6886279081026339, -1.8013187505071855, -2.0695485811729712, 0.5747168655539373, -0.025845745370675105, -2.1554763303431015, 0.47647537224289094, 4.497849303229543, 2.539368099606185, -1.7849266262074017, -0.7975274415784692, 2.3187538420283995, 0.8296641000097839, -2.107392296718472, -1.105680983807329, 0.6027267057749843, -0.5443270887585736, -0.9530519351629151, 0.7901092940281221, 0.16994778451562415, -2.40321947500749, -1.428100671710284, 1.161830838570645, -0.9217959387256376, -4.122131212610412, -0.8538137033120539, 4.524635796368435, 2.9744863270507653, -2.1159940470568124, -1.967251776177399, 1.406422454222435, 1.4398214341509112, -0.14384988360338508, 0.27847763983110707, 0.13318491955766062, -1.3133437094960507, 0.3429427013417785, 3.7545236835622138, 2.2152498208029696, -2.440020013203837, -2.3159004463254433, 0.9547652481188686, 0.030331551045669272, -2.6479093033465375, -0.4341305903880181, 3.0081600694894393, 1.3574033167424588, -1.1516078595047794, 0.8358860436729406, 2.397348634972054, -0.7349028582915202, -2.9252296341071187, -0.531059481506651, 1.202768177450467, -0.10335609021713013, -0.33083288737381766, 0.3025852500675447, -1.734818637598607, -3.024712986426373, 0.32500269171520496, 1.8067973080621325, -4.0683654279172465, -8.970671243642688, -4.811742955637792, 1.5270575839875067, 1.5774585123314, -0.730635391638512, -0.25871808662155754, -0.35679180047451237, -2.488788723300483, -2.0423685515093717, 0.4801437905430991, -0.20389071042120735, -2.3047841170047, -0.8809047251569453, 0.8403447042371586, -0.9764668906886607, -0.7518121839640411, 4.819853432126959, 7.524357672134519, 2.7812312116154843, -1.066027316237454, 1.0505877680918267, 2.5190023029245907, 0.2129990137557468, -0.21800549522489543, 1.6637414175714136, 0.14958991280129794, -3.149326728063386, -2.2870502200641027, 0.22045658450537522, -0.7431676008529402, -1.99601196899441, -0.34767946898174573, -0.23443616339520412, -2.723680705332634, -1.775883593044826, 1.6580724091292312, -0.43046896463822987, -5.754839899693401, -4.088298662637947, 2.921871356528631, 4.615401013104801, 0.9365226069944396, -0.20835236416561717, 0.9976320090612055, 0.0980220398637343, -0.8088176027418253, 0.3218177879889956, -0.16215728591814899, -1.7570647777043114, 0.9134299673755983, 4.886296853951735, 2.2859503801647962, -3.3376539785713533, -2.801715466498496, 1.0586739129980165, 0.3100341165005786, -1.920509792259103, 0.055301950341263624, 1.5305783775645405, -1.5996605898199932, -3.1335640204132815, 0.2083766434039495, 1.962862024669027, -0.15579708047782354, -0.7646087902493858, 0.15313955842571828, -1.7796372920733927, -3.6916771813022433, -1.3475244591101905, 0.6812292931116375, -0.7888960869262372, 0.41962509104969986, 5.628947982280685, 5.8044080848411985, -0.45891694705386765, -2.8459030327617048, 0.9745802654179212, 2.2517038630935904, -0.4397702793701888, -0.3932785019355496, 1.8036963333843639, 1.0217593291825229, -0.4341938172576672, 0.7443138897565469, 0.8282912047025281, -1.2389712378138122, -0.3621803379266464, 2.069254120639622, -0.38076956457123345, -3.7573245064755803, 0.40468929456401376, 6.99583928431664, 5.725711594735939, 0.272970297144999, -0.3767099039226461, 1.3584366959275618, 0.3485143642065097, -0.030417550709122533, 1.8963778199608878, 1.0041421854145403, -2.0157307733107905, -0.6335998062978017, 3.146207929061759, 2.4292303848419032, -0.3948160382899893, -0.04395648902790091, 0.36994386596226786, -1.082923617361383, 1.350128724484326, 6.8177009127177985, 5.501301399854216, -2.1050895855271765, -4.465457209264125, -0.40240594248296563, 0.6773380966586531, -1.8220846649047981, -1.3295544669241317, 0.7731336974227768, 0.11250225502823774, -0.38243428909099103, 1.191626519243909, 0.6653600585307665, -1.0777944901634902, 1.2171267245313344, 3.6545384801324725, -0.557937788052605, -5.474882432201947, -2.804222946496912, 1.506698869410513, -0.23314480215787434, -2.3685316237922978, 0.5908677734574754, 2.6220086273768337, 0.37496594320305376, -0.28428857526944457, 1.5469536879018366, 0.5318425984566042, -1.6363997841593143, -0.21746310271472277, 1.1413319703986524, -0.940010149867841, -1.133220692145432, 1.9100935624429334, 0.9866851585418165, -3.5788863017710733, -3.192675655084592, 0.9954071800298647, 0.8623326976215239, -0.9995427634582706, 2.0239549286134393, 4.666857764285704, 0.5790399887384621, -3.7324334632429785, -2.067284522849599, 0.34522039413826733, -0.1669367604062812, 0.33577009430579474, 1.7338567108732774, 0.44034433986685023, -0.5449052090621045, 0.9565676431557991, -1.4930516102604292, -8.66553820971902, -9.781439038730388, -2.635281666104227, 1.03620285835679, -2.1784996873800293, -2.867732259165839, 0.8410697195292098, 1.7914681535360026, 0.14689513726907233, 0.29333483074539785, -0.5626037205860431, -4.019889644134024, -3.972922337894488, 0.20978776923131304, 1.1280610079410525, -1.0939842303856149, -0.07529385977140407, 1.8832935190248783, -0.09474746774010737, -0.9042042501213174, 2.8756168273896, 3.268248071303273], 'positive_zeros': ['0.46021731900085176716955169324', '1.60599557605970994296066780785', '2.43851934389615271554793357993', '3.36846031296153794228426271114', '4.37428360281750265311364770491', '4.87315196051689631701321161301', '5.963726376723185540618183849251', '7.23441511806773362815493846478', '7.9252185385050033178189251064', '8.10965309777984077861436037371', '9.08876597547088162103897446289', '9.83348487771707589616513531484', '10.86262764821905798242914787969', '11.76714097706774024888808375201', '12.258134405486288691838565615095', '13.28163771875448950455738666812', '13.689849073059252676428712558484', '14.67393232625259874651001024714', '15.25480751822089934074486083890', '15.899950801082227400413961312393', '16.69528801133203419000429904095', '17.705382360393858418895431405793', '18.48039068575170236206310039331', '18.85272090360409509405359749980', '19.90984217727469092441213438260', '20.494583453152610735197104929348', '20.78305189408598358867711273430', '21.59427727764456821586291254155', '22.69076648186894325837464284523', '23.6298306525627649061978746981', '23.98555963153209939634113736851', '24.6024415706643043813237094660', '25.25082026531375496993426446101', '26.16203986181322838706963330957', '26.74664109571836222946448242964', '27.403307843363980476085681495857', '28.00513725453157938833267624661', '28.86728819960592951844444329210', '29.64765372232119441391073144181', '30.47058892240314553453091079656', '30.96508550610273725949241230745', '31.55683444032925976905282723747', '32.045201663396020465500488018885', '32.72864930259370510154625822825', '33.82143416516560791861114699840', '34.21662866646558213109540247602', '35.123628142931514048640903169687', '35.87901876346904247160297129866', '36.361471786642603151265275529472', '36.829851597928879178049936586510', '37.65275069130229882584357725670', '38.21081970692976338947124300240', '39.06787872383363773078449602263', '39.61726980938236772914416756674', '40.47981921815820343739841863389', '40.89361908576600790534670523785', '41.84330300375442777220387175549', '42.55774186662943586811970653014', '42.86090595432443836000546617085', '43.64736365007503473694676492296', '44.2058292366545490094461456221', '44.571074403564469865029011901425', '45.84677348574592355631135078926', '46.554834878034099940408419574277', '47.17350243684573678778220078725', '47.42906199648360820964689028723', '48.05493607670354747042180264201', '48.99415183417549679797531394497', '49.50591939113278058283234281194', '50.18646046211807955430500999212', '50.6437851191092269584108433201', '51.61012707069463493848634808941', '52.32344222812877900291440654980', '52.70229585152780091880754384068', '53.70703208634277836435655378570', '53.97372316520350993705299743094', '54.72056638494398906704360714986', '55.338590088974567415280475471021', '55.82227569372316597302597185981', '56.518777943458701671832477692796', '57.39314598016120587761142004177', '58.27542752771292053112228638924', '58.54480224738708959461804547007', '59.33876746907741864525255725566', '59.841323792406939276595561123767', '60.43598655524006903585854529202', '60.72355114699725641476855352813', '62.052570242389578301585119522641', '62.35351648876245335454330965712', '63.11471703394126309091627668013', '63.6095079105225298178915796219', '64.33157299296680709139817704639', '65.0548657727825297002197494627', '65.8265786246540239588094683883', '66.10395044932699236598845533504', '66.5937569595640541079291293149', '67.55499809861819519437116338681', '67.718958603838892434043819614039', '69.11648467739969552003331696897', '69.33348890466263588931263629749', '70.21622662501377971065492879201', '70.61271790895905742127794921910', '71.13034925479889413928792830688', '71.90730425117838436644565102728', '72.26920952838247883945566129893', '73.18295298508413712224576655002', '73.62191528102566884197848501187', '74.42327939636083522464924931229', '75.29612936405105305496921182674', '75.60247244486277258924155594283', '76.27238000576087237535238232858', '76.675988440055539525858071001230', '77.67888026136633117256100938612', '78.12892685409871384636150630175', '78.66545629012793645418726960403', '79.07580250648298465270132447979', '79.88336010479597351014760600213', '80.96680452253093900042034475861', '81.188584153785319745990768112121', '82.144589699000047894827214380664', '82.43531496950886434918891872036', '82.848661340775376650768917422532', '83.49611229301413113913266814892', '84.32798809837608864446003183185', '84.76246719465797638491883186362', '85.78343896303443668872388988967', '86.26429758613679458741114904785', '86.68355271575012823735333600774', '87.34783467656376047855298743615', '88.247845187645130324931338524048', '88.47606897186491245442756188762', '89.42268635886371585770694275135', '89.5845488079317929814676915542', '90.204630831994933715774580303273', '91.19444277928964812440469466117', '91.73309687286253987677532889459', '92.2500695955766122695121294455', '93.09875798711448080167400360590', '93.6100687269373488314284563300', '94.21589982865296639314265159884', '94.58923703628224514077721594619', '95.186858485930383442350428277337', '95.76555593393149732443000235782', '96.5034514951656838869191747678', '97.35589634090130098659150240189', '98.0677668258015643725288120669', '98.29213882059407641349535203921', '99.04536996279669173226536939224', '99.45814943980885310305946825145', '100.18923097452725968761893153579', '100.91471836388752017637247485654', '101.36377041647980862177613239150', '101.93959393322290629897160302524', '102.5677708785109529712538425523', '103.029727371270960762590825757135', '104.28429977246097617624410387498', '104.660957426906851519599664117413', '104.87969388856507266014002712310', '105.73281131918454772986011820540', '106.03767099253233994674280304451', '106.82642335250674029928141693382', '107.30113010970294077376305488106', '108.002521298611865445560996375239', '108.83311121927054900659089554082', '109.3512929227918399588651413049', '109.98981532628333293325561961472', '110.59026587370960296489448564541', '110.85198128000502663430717373943', '111.754945673846322166275668791723', '112.1961878947177516197394627114', '112.73870317429901954577193390740', '113.45654031731814078379690306809', '114.127224139118239911189440346151', '114.611702049620374329373343152971', '115.381222384710622691347202484644', '115.885031876042093505662130818932', '116.56209897357966983913584161144', '117.16769187803290837095270789038', '117.782104143647789478826594559810', '118.15133300322623105421415677533', '118.32278077386685900324987015328', '119.42428383132639653691512406507', '120.4146239910960302230686257090', '120.69777535096680236112535524232', '121.3475333119539979034562936966', '121.71968301515216980846547115467', '122.525677804287805836290526691544', '122.86208381334868345225294010252', '123.58898704179873881744404448577', '124.29399197524109190072731175030', '124.68435168396063449740427755264', '125.281064528104148966618550051216', '126.09687752083019505896566275861', '126.62960573377712594898607728038', '127.25894428884995642906964153766', '127.96024934249474963359028550947', '128.337498502504803359612563044125', '128.92219892307182309433497873728', '129.39575280457009598926484101608', '130.14001801029034312537806962158', '130.551834982209196587461585774020', '131.292323253409498962198469952482', '132.04219415063111513936821511846', '132.66975889425218660760971117165', '133.38569196902851058806110224863', '133.650591789470865505857050248', '134.09163797726332136424581901186', '134.65686276020451880195609112705', '135.4515547946260368573828775114', '136.13989760617377077702273637093', '136.56545840434601018853494147895', '137.218471522496535480397412168768', '137.93442737595024499885612927245', '138.35418783468939255167634089926', '139.00627627753711662884166397399', '139.74165982593912521027228321317', '140.290794354109755758345700719', '140.725090996054638804866049886207', '141.02845015985935773620508890142', '141.85090915555347999176306955348', '142.32088701454717374195317689416', '143.33745243266829353526953984433', '143.93127835134652892715732031128', '144.467379615641024787263380990628', '144.59070155188623883052855954330', '145.547807785097440262617464574974', '145.910644612405681285446820471868', '146.66583382958851050124497093859', '147.06030594359775286664705015066', '147.55799044529757587752929031835', '148.602006875241696660355255126072', '148.96127785416895722691059204503', '149.71733556765892720886683865234', '150.03855874451906691103224159709', '150.63797632394527033485360179595', '151.51193931850592124952808870654', '151.75622524655453498839148237859', '152.56806362911701281650844714825', '152.76818157704631517883636271405', '153.58020592346007460641339031293', '154.03671183711967400534415191618', '154.865876437184151232828648001880', '155.73571428267231715448676653787', '155.9936090826790657031727948365', '156.5804398803341079921441317805', '157.10477446411665705092220030180', '157.47229155266440518182998995256', '158.06236599398017043946654010751', '158.86376357316140226920023944837', '159.58036315312082592554569178802', '160.03226523448883647311910527393', '160.61950856592357774947269257508', '161.12135839113945236985427412408', '161.8582508644428166564490203781', '162.478692068155627893347630377516', '163.01359937680448944569958777856', '163.19988422824299567991062710932', '164.19905450825786885962875956803', '164.55186103047655231793509903016', '164.96647040928303756017014838551', '165.914506412684910168020385219427', '166.49132345413795432145164376860', '167.13261529327202240589540263137', '167.5530490682916615765132887995', '168.28377361437024729916025390373', '168.60570668185571657827127952124', '169.18723731492259882081081387709', '169.72588189935021132639389405523', '170.28661767897182422275554508211', '170.920413086415210941833264030584', '171.899066124835061811465882795970', '172.245257885515256630975369812782', '172.88479500016534308681738850919', '173.13199357496627321299729016059', '173.84410363299831386341775098979', '174.42333176911829904611352523991', '175.247230711320771905618240467113', '175.634909048557116561963634055895', '176.020364484796652372993763939290', '176.47066003276710621605853782832', '177.41156549126454202490946489504', '178.15919401452945347049000910418', '178.52872587438011926510330830004', '179.229231858009525359325178664128', '179.71155971755980251137785797578', '180.09096283088297067194032039208', '180.71641445898821200543822863959', '181.14613404143401502245970611541', '181.84828130268403817801113949252', '182.66369708739027006901095931401', '183.10502937405144791404790999522', '183.70401753347553125625753345249', '184.42547215157864513708190531335', '184.74153791802127529463352688249', '185.37243150246214447362293834977', '185.96402907511326987113889743053', '186.44684672562699386240578726908', '186.99588368254539850992958830062', '187.56898529232256491930193174109', '188.34989761107809583380930350530', '188.85050404992807917140253112497', '189.224871443935095484568942290564', '190.03005701126334135389099726384', '190.84982335417213783848555019544', '191.18790951364858350976739313639', '191.49177151024706057133669945758', '192.25491041024011712459176260460', '192.625723215735310488446038420676', '193.03187180617867157412694123238', '194.19659896129559233458249432690', '194.51254636145408237371629090823', '195.240950577104594374891893884754', '196.00709313951960650657455804153', '196.09046817590595218632335085486', '196.48435680964378633399094002446', '197.48251892969238344270133836399', '197.96217187603673242661906877086', '198.44603861047069980332926820893', '199.05214492520790814462132831397', '199.47224848338602550678174602969'], 'prelabel': '1-1976-1976.997-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.17650542116358, 'root_angle': -0.37350493248671174, 'root_number': '-0.700433270471076365326889182064-0.713717894981758168475304291040*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '-0.373504932487', 'prec': 50}, 'spectral_label': 'r0-0', 'st_group': 'mu(18)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '1.13625699289604589887846561274-0.502621730533921698791502841953*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.460217319001', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '1.60599557606', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.4385193439', 'prec': 40}}
• lfunc_search •

  Column	Type
  algebraic	boolean
  analytic_conductor	double precision
  bad_primes	bigint[]
  central_character	text
  conductor	numeric
  conductor_radical	bigint
  degree	smallint
  dirichlet_coefficients	numeric[]
  euler11	numeric[]
  euler13	numeric[]
  euler17	numeric[]
  euler19	numeric[]
  euler2	numeric[]
  euler23	numeric[]
  euler29	numeric[]
  euler3	numeric[]
  euler31	numeric[]
  euler37	numeric[]
  euler41	numeric[]
  euler43	numeric[]
  euler47	numeric[]
  euler5	numeric[]
  euler53	numeric[]
  euler59	numeric[]
  euler61	numeric[]
  euler67	numeric[]
  euler7	numeric[]
  euler71	numeric[]
  euler73	numeric[]
  euler79	numeric[]
  euler83	numeric[]
  euler89	numeric[]
  euler97	numeric[]
  euler_factors	numeric[]
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  is_instance_Artin	boolean
  is_instance_BMF	boolean
  is_instance_CMF	boolean
  is_instance_DIR	boolean
  is_instance_ECNF	boolean
  is_instance_ECQ	boolean
  is_instance_G2Q	boolean
  is_instance_HMF	boolean
  is_instance_MaassGL3	boolean
  is_instance_MaassGL4	boolean
  is_instance_MaassGSp4	boolean
  is_instance_NF	boolean
  label	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  self_dual	boolean
  spectral_label	text
  trace_hash	bigint
  z1	numeric

  
  {'algebraic': True, 'analytic_conductor': 9.17650542116358, 'bad_primes': [2, 13, 19], 'central_character': '1976.997', 'conductor': 1976, 'conductor_radical': 494, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1976/997'], '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': '1-1976-1976.997-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': '1-1976-1976.997-r0-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 9.17650542116358, 'root_angle': -0.37350493248671174, 'self_dual': False, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '0.460217319001', 'prec': 47}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_1976.997', 'Lhash_array': ['dirichlet_L_1976.997'], 'factors': ['1-1976-1976.997-r0-0-0'], 'label': '1-1976-1976.997-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1976/997'}