Lfunction data - 1-1045-1045.1044-r0-0-0

Formats: - HTML - YAML - JSON - 2024-04-19T22:44:33.290618

• lfunc_lfunctions •

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

  
  {'Lhash': 'dirichlet_L_1045.1044', 'a10': [1.0, 0.0], 'a2': [-1.0, 0.0], 'a3': [1.0, 0.0], 'a4': [1.0, 0.0], 'a5': [1.0, 0.0], 'a6': [-1.0, 0.0], 'a7': [1.0, 0.0], 'a8': [-1.0, 0.0], 'a9': [1.0, 0.0], 'algebraic': True, 'analytic_conductor': 4.852959597730739, 'analytic_normalization': 0, 'bad_lfactors': [[5, [1]], [11, [1]], [19, [1]]], 'bad_primes': [5, 11, 19], 'central_character': '1045.1044', 'coeff_info': ['x^2 - 1', -1, '\\\\zeta_{2}'], 'conductor': 1045, 'conductor_radical': 1045, 'conjugate': 'dirichlet_L_1045.1044', 'degree': 1, 'dirichlet_coefficients': [1, -1, 1, 1, 0, -1, 1, -1, 1, 0, 0, 1, -1, -1, 0, 1, 1, -1, 0, 0, 1, 0, -1, -1, 0, 1, 1, 1, 1, 0, -1, -1, 0, -1, 0, 1, 1, 0, -1, 0, 1, -1, 1, 0, 0, 1, -1, 1, 1, 0, 1, -1, 1, -1, 0, -1, 0, -1, -1, 0, -1, 1, 1, 1, 0, 0, 1, 1, -1, 0, -1, -1, 1, -1, 0, 0, 0, 1, 1, 0, 1, -1, 1, 1, 0, -1, 1, 0, -1, 0, -1, -1, -1, 1, 0, -1, 1, -1, 0, 0], 'euler_factors': [[1, -1], [1, 1], [0], [1, 1], [0], [1, -1], [1, 1], [0], [1, -1], [1, 1], [1, -1], [1, 1], [1, 1], [1, 1], [1, -1], [1, 1], [1, -1], [1, -1], [1, 1], [1, -1], [1, 1], [1, 1], [1, 1], [1, -1], [1, 1], [1, -1]], 'gamma_factors': [[0], []], 'index': 0, 'label': '1-1045-1045.1044-r0-0-0', 'leading_term': '1.63503062587961956067801268642', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/1045/1044', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.635030625879619, 1.6716589195694207, 1.3841847146914201, 0.48329466136307137, -0.5864571093157167, -1.0471958353760906, -0.534273157220081, 0.43067663593974626, 0.7455272396289493, -0.2787301406855937, -2.057211931865365, -2.9408625916794424, -1.5969078189609731, 1.5346035392646626, 4.177846314538367, 3.9516749871548376, 0.5546276616038422, -3.6538423659250334, -5.47037956433189, -3.5838299623405367, 0.3066777920785507, 3.1093991455584638, 3.1468133848337785, 1.4032887531960299, 0.0889153524501077, 0.21180380490265133, 0.8135598844110087, 0.5308476383486331, -0.5556134854190822, -1.0791182930136216, -0.3059786624414417, 0.7138515418554325, 0.41395738024440126, -1.0802602529723229, -1.7485908878616614, -0.10590652984542882, 2.5965538037814047, 3.4263815126724566, 1.266489270227619, -1.4054621788658614, -1.0098346221064922, 2.9221628576063923, 6.825657694333105, 6.87646678910211, 3.217772435361806, -0.3528201592461795, -0.8518089743544051, 0.6825106151223004, 1.0348043589790061, -0.8416937602067995, -2.585726490020407, -1.7595173746875603, 0.7579934891781441, 1.8319151135976308, 0.1474588305585328, -2.1383011934955998, -2.3140917597099073, -0.608426090867033, 0.4015869307488492, -0.5393480528612498, -1.7856865287914556, -1.3798589532906147, 0.06634151109204275, 0.40597267449992247, -0.6858003132010109, -1.1539313605087615, 0.17088042738607895, 1.417397965657656, 0.3862135722223329, -1.3760373757837288, 0.4595581412526901, 7.1493638336041325, 13.757943780032132, 13.849027141465033, 6.892992405519265, -0.8993792758077569, -3.5634189914461194, -1.5013529541448998, 0.5034090230518914, -0.11188597412414913, -1.3645066521982363, -0.8013853592619132, 0.7185982933960253, 0.8093731845778416, -0.5146919327781285, -1.0110719022553134, 0.06779531316951902, 0.8329514909944747, 0.08147093320292707, -0.3555705252783169, 1.610056951289883, 4.492217069204515, 4.677325888245416, 1.623756127641282, -0.9445947867266844, -0.12116230259457206, 2.093316262153672, 1.9258842643814953, -0.31826753250366396, -0.6010911323945173, 2.5271714662909543, 5.154127527764569, 3.405561666613032, -0.6725427477101062, -1.6513306378637052, 1.678440132239793, 4.640355244153257, 3.3576328946781313, 0.003529921338234769, -0.831968749918361, 1.1092164164968663, 1.8810575139967634, -0.39147606704094634, -2.8389498987540858, -2.4272804239336216, -0.302713676548834, 0.5372519329889397, -0.10696957074029875, -0.12373531157171916, 0.7869975540762206, 0.7124900987792095, -0.5929908982506757, -0.7217243223735454, 1.1116690718060702, 1.8120832675734122, -0.8894510185758413, -3.638673030899324, -1.2721979038712452, 5.084260148336517, 8.041839855817756, 3.5066607455111374, -3.449035004717903, -5.153838490309145, -1.2146525641604313, 2.0672733431699997, 0.9910883177440004, -1.4048105742264543, -1.2448730620419795, 0.47937545366589784, 0.7146010803210883, -0.2859145815166123, -0.12898698145907073, 0.8075881439496961, -0.21495483901849327, -3.105604183443317, -4.20318184299622, -1.8977930175148332, 0.5504656363964668, -0.03558255250657458, -1.9375749237395516, -1.7081084393216655, 0.0910985438313504, 0.23974249835989556, -1.1701958422332013, -0.6842031242470491, 2.194203213791904, 3.3218541933331993, 0.6206330882765074, -1.7496390893220262, 0.3959945825228318, 3.9905099510620703, 2.689726771473617, -3.1724286278550107, -6.251523083411809, -2.651841009732474, 2.553637112075663, 2.9097355795301367, -0.6097201420303602, -2.4038634593407844, -0.9272996206885163, 0.39249400378518107, -0.2745274709926283, -0.8312265131905179, 0.02546148455198655, 0.426152725484836, -0.664825594793339, -1.0547036432358263, 0.6462766652544925, 2.0329920228792733, 1.0062923145535532, -0.18167829232173333, 1.0531381204653338, 2.02700212483408, -1.5812812116441692, -7.533645998289388, -8.482988973629817, -2.6479689233193002, 2.758634324725218, 1.6141859537470518, -2.6443849789218423, -3.0131111248643476, 0.5475953638081825, 2.3707942090693432, 0.7384845118002469, -0.2746577657148742, 1.364453563306477, 2.337510455043857, 0.4240695741256102, -1.2598185563511402, 0.23528081110678628, 2.35872971330325, 1.3900186852644707, -1.2035361885156604, -1.4706060462247645, 0.2188329525469864, 0.22309130656882908, -1.6793741817400365, -2.0224840846575636, -0.030940358147538573, 1.0731531184707856, 0.041638852206940136, -0.4144507371065285, 0.6159164546902871, -0.02750113081082049, -2.9705702819769177, -2.8451126571750165, 3.496384067807105, 9.601654280064468, 6.9767622851618825, -2.2332107140410264, -7.430883508805765, -4.11251674232522, 1.1388327727918173, 1.6656321493993382, -0.48220504137188835, -0.36937976571766834, 1.339702781034621, 1.0421081759757742, -0.7901215533104822, -1.038604392832642, 0.09401970467391262, 0.0519225455694376, -0.7474415457973562, 0.0737442184104066, 1.5966697563115186, 0.9333902407370203, -0.6711233761224572, 0.950594488897251, 5.133889251003645, 6.14731582011938, 2.3585066800359042, -0.7120482749586429, 0.5938243554389903, 2.2716086456950366, 0.31471708579980767, -1.6218200408258336, 1.4990763406027918, 6.511088319343825, 6.284047042139619, 1.1316425948235893, -1.9298397278271144, -0.5510366528579476, 0.3828292882299868, -1.5913594588700573, -2.302727418849457, 0.8298496051751444, 3.5065027464639003, 1.7403378929138373, -1.4433451497045418, -1.4418677078373763, 0.46428606587349763, 0.4114295891919099, -1.0565300928017956, -0.9174083719760405, 0.32250205733452186, 0.23933871973979032, -0.23428678845885892, 1.0763907122067362, 2.286965515113306, 0.5229546559545051, -1.4921040754574242, 0.8910942876150891, 4.974414178974735, 3.4401246657606754, -2.9878437034903254, -4.6117210586143855, 2.542846276285395, 9.690424791560613, 8.023847220117652, 1.0950326669495023, -2.1049132678816256, -0.4569858199160237, 0.6274011742196703, -0.3612634883659245, -0.2829486663197263, 1.1547706695225526, 1.0697814784402135, -0.2531275532804853, 0.19201111339007626, 1.711492052541282, 0.737295200017885, -1.9964160969742144, -1.9865484749795237, 0.903578468630073, 1.860670490397913, -0.3262032395942291, -1.352443087271177, 0.2545942561175883, 0.3592997776208145, -2.5180750911198997, -3.735289510290249, -1.1602492142769034, 0.1735553082314282, -2.9203179370041563, -5.25827351515783, -2.158532691168026, 1.6951500189995374, 0.08175050691808787, -3.4739163791781946, -1.350335095179111, 4.927280844899984, 6.854259428464953, 2.6042926600099223, -1.1029853396797087, -0.5933835623058601, 0.4783773461103391, -0.4988176865823145, -0.9610758403162412, 0.4751891612124115, 1.019669844056985, -0.4471183411025278, -1.1347393118498932, -0.16882533187481044, -0.2717266223033488, -1.6903861953083934, -1.2134639534626963, 0.7782820876168618, -0.15938617274125783, -3.3746639478717326, -1.9829076072221405, 5.027632316999703, 8.381426084076464, 2.260267569326602, -5.695787811413759, -5.750692925422393, -0.35922962421750093, 1.703549208764627, -0.35989884557699076, -0.8261283129621473, 0.8888778087764195, 0.3314074106854132, -2.357404408127463, -2.6015705930119943, -0.25441264251519646, 0.49590837053228665, -0.5078367291777124, 0.44992996327684753, 2.803073641537411, 2.121389477215729, -1.2258710543434912, -2.0941773614568864, 0.2943096306285471, 1.3392444783227848, -0.19369678373987875, -0.5855874904743761, 0.8731564757005243, 0.6757810544653546, -1.1522633668389355, -0.7739900749260189, 0.8581883535593963, -1.356923495896579, -5.610149966050954, -3.3132246226113935, 6.23127571756153, 12.040696052061246, 7.6274058271120575, 0.8058115819224858, 0.6561298496458342, 4.118359250404986, 3.699735766002615, 0.4245057584817364, -0.10042543477587626, 1.618015377804756, 1.3091075270630774, -0.5348171643104352, -0.6598746654695734, 0.19008437133942832, -0.34411981823838067, -0.8933318597777213, 0.19150797536493128, 0.3885579297155535, -1.7852604095834912, -2.1783712620582896, 1.7939723619321706, 4.970818617065152, 2.7690758425105204, -0.29106161359724736, 1.3179151358012196, 3.608023946261962, 0.3323707216011662, -4.770885465575236, -3.946081711989098, 0.6999294655377554, 0.8982092943599673, -3.2496303513072426, -4.251637249804705, -0.8638614109566172, 0.949534107973639, -0.1939960268927928, 0.26120856652234853, 2.4799548414565873, 1.5629024608716104, -2.2044531082211067, -2.846772845124683, 0.5467613482161808, 2.289691794205011, 0.3491469747629592, -1.1062103322391685, -0.2852101124852642, 0.02375071317611349, -0.5183030154975872, 0.7396464109934294, 2.6848682123169705, 1.7173770257092766, -0.6516966993675042, -0.34354281339202275, 0.5252924260551224, -2.4687485475069013, -5.155625899038702, 0.17589147956311038, 9.51767867368849, 10.333097166947157, 1.166483586873065, -5.492405257301595, -2.6396236350147415, 2.23374788636893, 1.6294852960108428, -1.1088600883539028, -0.8777724849394164, 0.38204204410779, -0.10543938611567102, -0.26933782091267966, 1.0587117351470934, 0.9554152268891768, -1.0136301924235465, -1.0308530075429385, 1.24058064861237, 1.501056395924714, -0.5007965582576374, -0.1410657555004103, 2.5270652807170215, 2.1670844942595284, -1.2745519869997366, -1.8282314410735219, 0.9888466454716016, 0.9768641858914903, -2.5714539384317403, -3.187835066536335, 0.043898770233592996, 0.31375530050972256, -3.576278481151846, -4.345332936706689, -0.2023645067811018, 1.1477356923851456, -3.2003282338280155, -5.7113328225502515, -2.178808185655162, 0.9999005824944034, -1.0138903259105343, -3.407988177959924, -1.6769027192062775, 0.7211267884744226, 0.32314177489950663, -0.20590796748408471, 1.1006843951331855, 1.3554614882429399, -0.4664844166805043, -1.0294453882361525, 0.35348394655940896, 0.5644887739402725, -0.16775872982408083, 1.0587367196831532, 2.125801534893547, -0.7372003292509071, -2.868620448066557, 3.184624817142474, 12.594193116962568, 12.748444615073145, 3.2619224751797384, -3.1057403202325196, -0.9360656117911492, 1.4470989933676426, -1.3666638626526693, -3.7504200375148464, -1.6105281954365602, 0.5343252007625723, -0.409011423844576, -0.8857894033634747, 0.6525987579685653, 0.6587141385330006, -1.2243166141971789, -1.0010082529096422, 1.052522149491484, 0.6822861722653217, -1.0957999133251, 0.6088316842738677, 4.379229746797174, 4.2844655048229034, 0.8112455475724283, -0.5324280715077607, 0.3240922109328275, -0.4939414116426434, -1.7494951769194378, -0.36569439993674585, 0.17710851661514682, -3.8868895226274427, -6.821381726222482, -2.180980413235794, 4.0575198736770215, 2.5202434577806088, -2.944505818718696, -2.029881385499227, 3.741472692824522, 4.545664355115431, -0.01735120624411612, -1.6888821115165376, 0.9687491340367177, 1.884575084729599, -0.07466231556844322, -0.5280965372204333, 0.8071564904698477, 0.7246067123022569, -0.11637801849040423, 0.4757570905670001, 0.6362044984781418, -1.1194933423582678, -1.6019356856893479, 0.19574256079810198, -0.4293935547487191, -4.281153072428564, -4.628993134774952, 0.45748935478376845, 3.2563542918204726, 0.6131868552345485, 0.46333694784440665, 6.529898472633669, 9.886859199887088, 4.578644495998155, -1.4966485384232913, -0.5833849290023156, 2.6272047164831793, 1.7651316956967424, -0.2385439646098903, 0.42046923640602774, 0.5340835663600761, -1.7774224867955282, -1.876230177106628, 1.6610357798038753, 2.988654065296485, -0.05082641775449315, -1.840844442722394, 0.08841032707394594, 1.124442394593395, -0.4854890107240885, -0.8196943891108712, 0.7591327127729639, 0.6449090801259352, -0.6546145469914936, 0.19532598754858654, 1.2098263531611257, -1.0383937069058164, -2.8860759798644624, -0.18206352678248477, 2.126551538706397, -0.5661079275729393, -0.7922445622524636, 8.814866895368407, 19.17747369372561, 16.701736547229483, 4.951383814284775, -1.7799861485398096, -0.5151415978085601, 0.6358266285421459, -0.8313015807477642, -0.6915821196901539, 0.8908649428943844, 0.4769264403295163, -0.5165608195542108, 0.6679342891161241, 1.6879148389760885, 0.42868412604072365, -0.06177433279799717, 1.484333827881098, 1.1649333907403516, -1.3962660015893789, -1.0937883159825672, 1.9390939663790807, 1.3521038054341041, -2.635474295540703, -2.5958064437740207, 1.6445453722481698, 2.221424892596471, -1.3717612585232737, -1.3619737655271456, 2.620824220443649, 2.844079114815484, -0.7878022919832413, -0.5255847762046657, 3.4108128969219775, 3.0780803351742247, -1.3461794771898, -1.9537774659882174, 1.4519355545314359, 1.7228941291228401, -1.313864910532495, -1.5279331039032833, 0.7721762697596888, 0.3304904829081261, -1.9246116123140449, -1.4405555040461604, 0.4106812131348271, -0.04372223449384014, -1.0114190257513498, 0.030689754954048926, 0.7076764559985285, -0.1603226296603081, 0.5263083730291725, 2.1220983029792335, 0.038196164745841144, -3.0971688629763343, 0.2268884015889811, 6.357172109062056, 3.142900559175279, -8.455766680309626, -13.375087695793646, -6.5572297005399305, 0.34502356825504377, 0.04317500477457984, -1.0432684686363267, 1.5253649593160579, 2.7408083862351473, 0.3926265751153793, -0.6349156534819224, 0.9842115777328468, 1.2746201287514973, 0.09978648197358723, 0.2835280151016588, 0.030768627306242188, -2.8814447150955496, -4.1750379474263735, -0.5614668345656301], 'positive_zeros': ['1.07136547264467266957227068153', '2.04460835684569280896362943688', '2.75567243030322196957325020494', '3.91991528553599080000997397346', '5.03932646373993168302293034692', '6.225268278116929425298914412779', '7.56929590638183264232915705025', '7.66563745787259578805685599829', '8.59749343606639663331373171069', '9.45391331242561928641935457592', '10.098371436516175758172201267262', '10.95001475736373849873783436404', '12.0036000947278337129896913272', '12.60232669165728615618304049872', '14.01785228587880129295060213688', '14.55610468482603603046112626021', '15.19872774539021180981353834881', '16.15508739501892846330661532778', '16.89300672451798079274714166037', '17.93329571795847741735044032882', '18.31657383622425928214176155920', '19.35816659286193409060258896254', '19.82751625309575683545823048511', '20.595095077484943238239596582555', '21.30723621187722643428886238116', '21.841574694572319411361031823982', '23.39205934215883122680950469114', '24.25234480681816122419638812873', '24.6636993675754862947140296252', '25.46749391949714227919390797308', '26.13573690501968049251283475222', '26.859145363111460736344965742701', '27.52370075790687566944496817036', '27.91332001451056130082618687526', '29.21884039856484814418715731756', '29.70424070869921567186644101529', '30.5776461646165972714539405341', '31.02277785503778437175879819539', '32.12923381134705649756948330937', '32.68321489216356876432656377771', '33.7504153025760861033115669982', '34.2180451679838276868826485920', '34.959930937236437532930120790911', '35.993271656882278104361437902743', '36.51524777558721157659008712785', '36.92549688463395176388238186497', '37.675784539192189033520509449209', '38.26886937687110506778540496077', '38.98585751247264268256309731284', '39.75660138871892327339642132132', '40.77152320191428117865195912586', '41.64582618308724999614477703318', '42.30082973556032385159194306165', '43.0291767003305828229639199583', '43.6516625399141355200280836912', '44.10217692380954406423099398012', '44.658043499881153123852464484142', '45.83369014041633367338094599619', '46.24413241815862037746851373777', '47.16801506593460915011039097486', '47.55967179914717308585858989533', '48.21157292542662339153130725332', '49.11768982593488089487242524784', '49.65573788757280605075682492958', '50.4654208769105436433778135540', '51.391423019337341660439278626923', '52.1351623173213198290263553951', '52.97373091526532746548754623058', '53.35848727597406115546823072175', '54.055012154399849361114875446161', '54.52652318263992029105790440533', '55.21794771036141306570583395741', '56.14342022664562105571319543048', '56.363589598314137639337481070186', '57.095076608747935026117560251542', '58.24593890601086861464357108260', '58.863788853429721960841001162956', '59.64172933447034466325580684584', '60.43944641981245980376319709156', '60.71480745549489793036920982576', '61.61436281659180373226980314439', '62.158994228134857336994182407745', '62.97009930665790828471405265062', '63.70431156592966886982892566275', '64.10754532105570729609367378058', '65.00452301197274326141889563401', '65.63524472136352801293214382050', '66.07627900007685481368997647780', '66.55870339795928005425625468692', '67.35594270908356203998330054049', '68.36317463369331532186272296372', '69.28747260986122004491135559898', '69.91819403012254503475878661879', '70.379671220101540726738948557', '71.10977368087791980621922445836', '71.84319397146508059207273403522', '72.20619422369069962910253701932', '72.79874541224956077029229865972', '73.58792312134160454098819338535', '73.96713032211561922533258086608', '75.19002182657705139136004091903', '75.54962200380491588838750604371', '76.28179628945554973904584685065', '76.77843920556977179485952943012', '77.88487707348676162693521938729', '78.525387888602877877067486227768', '78.84281237525298448393012091491', '79.6222513219348361562733837285', '80.464191383016656646014308933825', '81.1615334867271114808892059300', '81.64934687476234265278730326521', '82.40296209672755813033400987920', '82.90683453791298244926699243976', '83.230371541494934516389136376928', '84.11964779231455868398392725265', '84.62051901642430298665693579839', '85.482460474275184488028932734413', '86.16250332560728705441305535222', '87.24750205519234048577452342446', '87.88161638756838935299199696324', '88.33719265808573890001159176913', '88.816505777203712522854826250727', '89.61174028987234156036964675002', '89.95889721004199726319673186136', '90.7083621946121661514355385296', '91.46801696254343412580899887294', '92.14653792285509877613989333078', '92.76767062330740093576993599450', '93.17874659881624220677373749824', '94.20835634706909409639932095435', '94.41320721222998278026936510702', '95.45325733280086544970809190965', '95.94381727490361185855943336539', '96.63347441528606456370384180464', '97.67693836974710060757234838969', '98.24026453893632570595989887164', '98.63494533485222310982292008881', '99.28571071592006466938711926012', '99.91790764516702050791794091960', '100.698721730704348049381653224318', '100.83968689286375384975722324222', '101.73724304172491957667429282075', '102.17023534722687580389855476877', '102.91437092306915665792362925299', '103.82620250021551223322007669523', '104.71152668198649280623706325365', '105.26252879368591091426797034443', '105.775346978141490289869509463977', '106.29219324211702674035989429138', '107.22705188769942957994575763499', '107.64957476970848083646091168186', '108.05811482351138233489783001033', '108.946759276563119486661394226616', '109.65192884101588843296730263743', '110.276513917357967629656593307195', '110.75928585070028562077686245298', '111.36332418184043696700374685301', '111.99490415089280563254767875134', '112.38887964536288833369250835554', '113.24661638095300207570396819705', '114.45907526472627132813489455285', '114.604174233369070740795946849061', '115.68612822074027951821354745738', '115.95956711879065754134532174821', '116.7723191193412534087638080832', '117.39710265450463697125708653362', '117.70157748182544610722467066531', '118.39271484863771861532224988080', '118.825816832549891596702926353432', '119.571190750543575674825580503448', '120.56447116108634686138845721523', '120.79044428087119040259471341745', '121.580538783027944952461760608519', '122.44410844202594190966863600567', '122.89059151119714040000440294310', '123.83369519958594617022460613118', '124.32503082522372945669589761074', '124.64301655215822140405716942211', '125.44407454989295364860188844151', '126.203789035492307104773428165427', '126.919917003666405279672296085679', '127.60212283534592721281431447213', '127.82626031433798061395916494781', '128.32081513779251093706452215850', '129.267579807453168265272220563158', '129.75466427643000835191693319168', '130.10137200722126296270382438631', '130.931558267074053787537933633276', '131.91121445331821925902109522356', '132.64200000361634720279745112924', '133.28880757949804938738652464263', '133.92810828287307073365582391589', '134.33872553981017261901147605753', '134.76630998683642818825563205471', '135.46739021746349651727067817566', '136.08515383778555556223168473917', '136.79020885051870099470433306013', '137.20639903774186658995922474457', '138.0082648997498073220054005659', '138.641357208624008159724798330016', '139.15925538746701164585444274725', '139.99530779434444342946220847876', '140.34635710140299956537818220833', '141.26536973166585950223243434749', '141.67365998505283639105080361602', '142.65757320684082231956268867800', '143.02915008765107294021599356257', '143.931780063015923559451386954347', '144.46441554581331844423785174079', '144.76395513895260249018159559559', '145.54977778064370672420642201531', '146.172184024414788705699550069541', '146.75352533525207792660466380361', '146.98503161576121499758116154582', '147.75542060506687183512669911765', '148.32405165784809377821779762667', '149.486196882601852689028393503702', '150.07369420206398697060841681002', '150.515382412307464967774568988525', '151.4295093109664612605792004842', '151.79155725544845661432324907707', '152.37686979818213843812229684386', '152.92546822346845810806099255139', '153.58245221671588048135266284851', '154.16373982327179807610014683298', '154.632508345804289023545701002423', '155.72105672864971766480587046027', '156.12298016437342236470314556902', '156.465439841965468038746334408392', '157.24647276156155877461148284454', '157.52657257938043544039912844614', '158.52801174856320658084597764421', '159.19451385730274698746208270117', '159.79903202757184698316888301059', '160.62375883057249288879975299989', '161.14926445625509564589416645078', '161.862648949716605073787219362568', '162.3148429662506839490617405117', '163.042585041829244900380411222271', '163.270653656999920113396958110594', '163.884966372097240012042539716367', '164.64978037974022506533991842104', '164.9481847226386678624686002966', '165.91180095355105753826519659696', '166.63591830769931210593390109264', '166.8262311972138360516206864486', '168.01506721910260382821365059893', '168.485902669751437364763051899778', '169.30525241786774086358482391775', '169.58280408097178237292316149727', '170.08870202215921263395401724611', '170.80337609879472349658714219802', '171.55801092815530780393319106192', '172.17607534825391313677265888004', '172.72947222270944694094588514499', '173.28877574432845313495102023484', '173.88245753989846738695123572996', '174.339978906766965360452828158856', '174.895445687242198359124105501970', '175.6395152056758581512333756798', '176.20121475583035787722545348486', '176.6075213046724944132204702975', '177.98535963767697131476280776526', '178.50462675720248377522033901926', '178.90257622571718089208055765671', '179.4999427915932720213300432247', '180.10482507805403255969394030388', '180.50445031068490936046429084836', '181.34953425913286223727607880924', '181.58212972286066955752667591849', '182.329269250437568567348235410610', '182.92541074819679148368042334151', '183.54582688109668124029144104485', '184.2539814710569282267761645700', '184.88089858132674435651575679215', '185.425355441332572588069445495939', '186.174975009025433233840737920060', '186.60852295617677498275508386922', '187.40077678921659114577020706194', '187.993468204581340166392159405244', '188.613954747729104164391245402762', '189.25870154918003122240741284803', '189.73173680522995643917517187913', '190.53022146323472066609256655812', '190.92781323967758662935020499362', '191.556041859248183813372666753279', '192.12336592982651660957164960348', '192.394869269805177123862040684819', '193.12801289067026474501692093645', '193.73927795957082935964390413971', '194.46744576262915179390234939921', '195.59460070394313372398622811670', '195.94343805463207583827939726450', '196.408884244133669243758907547243', '197.2383153202066026230302239165', '197.64321320759888232715443484011', '198.4984621625609392358545637793', '198.59355469677409990250620428125', '199.06795327151025988753571745675'], 'prelabel': '1-1045-1045.1044-r0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.852959597730739, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'r0-0', 'st_group': 'mu(2)', 'symmetry_type': 'orthogonal', 'types': ['DIR'], 'values': [[1, '1.13210161969969338016690911041']], 'z1': {'__RealLiteral__': 0, 'data': '1.07136547264', 'prec': 44}, 'z2': {'__RealLiteral__': 0, 'data': '2.04460835685', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '2.7556724303', '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': 4.852959597730739, 'bad_primes': [5, 11, 19], 'central_character': '1045.1044', 'conductor': 1045, 'conductor_radical': 1045, 'degree': 1, 'dirichlet_coefficients': [1, 1, -1, 1, 0, -1, -1, 1, 1, 0, 0, -1, 1, -1, 0, 1, -1, 1, 0, 0, 1, 0, 1, -1, 0, 1, -1, -1, -1, 0, 1, 1, 0, -1, 0, 1, -1, 0, -1, 0, -1, 1, -1, 0, 0, 1, 1, -1, 1, 0, 1, 1, -1, -1, 0, -1, 0, -1, 1, 0, 1, 1, -1, 1, 0, 0, -1, -1, -1, 0, 1, 1, -1, -1, 0, 0, 0, -1, -1, 0, 1, -1, -1, 1, 0, -1, 1, 0, 1, 0, -1, 1, -1, 1, 0, -1, -1, 1, 0, 0], 'euler11': [1, 0], 'euler13': [1, -1], 'euler17': [1, 1], 'euler19': [1, 0], 'euler2': [1, -1], 'euler23': [1, -1], 'euler29': [1, 1], 'euler3': [1, 1], 'euler31': [1, -1], 'euler37': [1, 1], 'euler41': [1, 1], 'euler43': [1, 1], 'euler47': [1, -1], 'euler5': [1, 0], 'euler53': [1, 1], 'euler59': [1, -1], 'euler61': [1, -1], 'euler67': [1, 1], 'euler7': [1, 1], 'euler71': [1, -1], 'euler73': [1, 1], 'euler79': [1, 1], 'euler83': [1, 1], 'euler89': [1, -1], 'euler97': [1, 1], 'euler_factors': [[1, -1], [1, 1], [1, 0], [1, 1], [1, 0], [1, -1], [1, 1], [1, 0], [1, -1], [1, 1], [1, -1], [1, 1], [1, 1], [1, 1], [1, -1], [1, 1], [1, -1], [1, -1], [1, 1], [1, -1], [1, 1], [1, 1], [1, 1], [1, -1], [1, 1]], 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/1045/1044'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': False, 'is_instance_DIR': True, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '1-1045-1045.1044-r0-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [0], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-1045-1045.1044-r0-0', 'primitive': True, 'rational': True, 'root_analytic_conductor': 4.852959597730739, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'r0-0', 'z1': {'__RealLiteral__': 0, 'data': '1.07136547264', 'prec': 44}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_1045.1044', 'Lhash_array': ['dirichlet_L_1045.1044'], 'label': '1-1045-1045.1044-r0-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/1045/1044'}