Lfunction data - 1-14e2-196.39-r1-0-0

Formats: - HTML - YAML - JSON - 2023-03-27T11:07:46.023767

• 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_196.39', 'a10': [1.0, -2.8163065144692913e-30], 'a2': [1.0, -2.8163065144692913e-30], 'a3': [-0.36534102436639504, 0.9308737486442042], 'a4': [1.0, -2.8163065144692913e-30], 'a5': [-0.9888308262251285, 0.14904226617617444], 'a6': [1.0, -2.8163065144692913e-30], 'a7': [1.0, -2.8163065144692913e-30], 'a8': [1.0, -2.8163065144692913e-30], 'a9': [-0.7330518718298263, -0.6801727377709194], 'algebraic': True, 'analytic_conductor': 21.063125259746503, 'analytic_normalization': 0, 'bad_lfactors': [[2, [1]], [7, [1]]], 'bad_primes': [2, 7], 'central_character': '196.39', 'coeff_info': ['x^42 - 1', '0.988830826225129 + 0.149042266176174*I', '\\\\zeta_{42}'], 'conductor': 196, 'conductor_radical': 14, 'conjugate': 'dirichlet_L_196.191', 'degree': 1, 'dirichlet_coefficients': ['a^0', 0, 'a^55', 0, 'a^20', 0, 0, 0, 'a^26', 0, 'a^37', 0, 'a^30', 0, 'a^33', 0, 'a^10', 0, 'a^35', 0, 0, 0, 'a^53', 0, 'a^40', 0, 'a^39', 0, 'a^24', 0, 'a^49', 0, 'a^8', 0, 0, 0, 'a^38', 0, 'a^43', 0, 'a^6', 0, 'a^57', 0, 'a^4', 0, 'a^23', 0, 0, 0, 'a^23', 0, 'a^4', 0, 'a^57', 0, 'a^6', 0, 'a^43', 0, 'a^38', 0, 0, 0, 'a^8', 0, 'a^49', 0, 'a^24', 0, 'a^39', 0, 'a^40', 0, 'a^53', 0, 0, 0, 'a^35', 0, 'a^10', 0, 'a^33', 0, 'a^30', 0, 'a^37', 0, 'a^26', 0, 0, 0, 'a^20', 0, 'a^55', 0, 'a^0', 0, 'a^21', 0], 'euler_factors': [[0], [1, 'a^55'], [1, 'a^20'], [0], [1, 'a^37'], [1, 'a^30'], [1, 'a^10'], [1, 'a^35'], [1, 'a^53'], [1, 'a^24'], [1, 'a^49'], [1, 'a^38'], [1, 'a^6'], [1, 'a^57'], [1, 'a^23'], [1, 'a^4'], [1, 'a^43'], [1, 'a^38'], [1, 'a^49'], [1, 'a^39'], [1, 'a^40'], [1, 'a^35'], [1, 'a^33'], [1, 'a^26'], [1, 'a^0'], [1, 'a^34']], 'gamma_factors': [[1], []], 'index': 0, 'label': '1-14e2-196.39-r1-0-0', 'leading_term': '1.16611096661213688887937720462+0.279299612917982896539657012312*I', 'load_key': 'dirichlet', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'origin': 'Character/Dirichlet/196/39', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.3125', 'prec': 20}, 'plot_values': [1.1990925986883694, 0.9597559815524099, 0.23193418221245043, -0.9351867718136043, -2.3359371431662836, -3.5982848544822685, -4.288216958343983, -4.1001986696705455, -3.0398005821912504, -1.485316544453013, -0.05965671595742991, 0.6575876771384501, 0.44197209978062074, -0.42243736496462003, -1.2703302918938282, -1.431216451959469, -0.6557658720972237, 0.674932809334237, 1.7268880731422342, 1.7159720799908191, 0.4443661249662738, -1.4881438160844538, -2.9848403049881362, -3.1222555315337184, -1.7715213366243387, 0.2630180692839913, 1.728781963407721, 1.7455240903119613, 0.4073743164116858, -1.2747858911035301, -2.0824327139301295, -1.460348262941972, 0.09036999024451232, 1.409771768041449, 1.587094079910002, 0.684682592209825, -0.3096944943720497, -0.30292250338490384, 0.9410942826595304, 2.490188942045062, 2.899172521930018, 1.3691234400131376, -1.5077749842464203, -4.064316758932691, -4.752247204619907, -3.2979481425243233, -0.8889509687569392, 0.7787714639755478, 0.8263181076841342, -0.20067657993467655, -0.9398326608842048, -0.4944119797549984, 0.7450193051521946, 1.4840167847801917, 0.7866376828870301, -0.927810229540721, -2.1098953140925945, -1.406142333397828, 1.0636187517665046, 3.6589862763035566, 4.529670677744775, 3.1806050014528577, 0.90237602804385, -0.3508564412506908, 0.33786263336012134, 2.088327984932815, 3.0882039442848215, 2.282947002397931, 0.3245590124998618, -1.097428742502168, -0.8927075486933822, 0.40297899104150353, 1.2109894281638314, 0.5400411233456235, -0.9503444444819265, -1.554679865716398, -0.26615207686005227, 2.0446111618186404, 3.2543924747440696, 1.9266413672032, -1.2546943340028833, -3.9735900242399786, -4.298563051770213, -2.3496107565339366, -0.051956460888711725, 0.7437648947251171, -0.08004443917777501, -1.066371313327751, -0.9064172147177136, 0.10727014492812079, 0.4314445441665966, -0.9366300550546183, -3.1429844987817206, -4.121830828928352, -2.658997492271769, 0.22145415899511817, 2.0615675333519152, 1.2776016195178743, -1.30246337671874, -3.2403739079683587, -2.8533537183648696, -0.7740529534524626, 0.8447830539090493, 0.6101239428883621, -0.7337189199817312, -1.236751523938277, 0.06288907203981235, 2.063089942257598, 2.8013331788738247, 1.6183845285269318, -0.10638630049869854, -0.5015248985363511, 0.6317704721049571, 1.4563643391407108, 0.05763435915182996, -3.3153758067189134, -6.191426120936227, -6.207728023329624, -3.4627717008436503, -0.42575401853090356, 0.5173606369330459, -0.6852156067904068, -2.0131193572277333, -1.7319334715996741, -0.20346169271656322, 0.7917494673708574, 0.3247052961306271, -0.5062736359155007, 0.09318826963089974, 2.286005012534974, 4.040800357596487, 3.178094898421244, -0.1265925472253072, -3.2133800415886427, -3.497252051303179, -1.0475624596840543, 1.5838302011169343, 2.0893576131982696, 0.7123256672748347, -0.3302075511109777, 0.46496193710288747, 2.1857491066343253, 2.6819799859823723, 1.17513407852275, -0.7829766274774297, -1.134422740699778, 0.22888097768960933, 1.310738265876838, 0.4114127930262185, -1.715257405978443, -2.569582911100088, -0.7986066337054398, 2.0382791423350537, 2.9799334429508124, 0.8755506764069154, -2.2947666202193333, -3.5101153694427567, -1.8855546309862332, 0.5915830141861342, 1.468095617154158, 0.5029820325401589, -0.43266987229850934, 0.08720686183884054, 1.2506102667113304, 1.1826746092418026, -0.40302311402324714, -1.4682613995926435, 0.04214689812496012, 3.492457060217023, 5.799192500068416, 4.617602327617208, 0.9327772931776562, -1.9474030361700003, -1.9083093308263994, -0.08156617101449258, 0.8025148927221372, -0.3150728042194645, -1.802183671287612, -1.6218989061212616, 0.015602018649460857, 0.929021660587321, -0.21516336356758262, -2.1071396770394912, -2.341757075234237, -0.45737030665805184, 1.3370896927582359, 0.7855911325041419, -1.5684285103272977, -2.8623526341270713, -1.2997658586846659, 1.577902592965828, 2.535949689934325, 0.3471943619646841, -2.8046558050294155, -3.8460458295316666, -2.2182448652917133, -0.16647457551887343, 0.21837726337902474, -0.5696928911442835, -0.48497744793455394, 1.092891533209043, 2.403530607998377, 1.6863050456291393, -0.18246289585230274, -0.3855799529276335, 2.375738043580874, 5.892459919827688, 6.610122785729934, 3.5941024849521224, -0.3761828966207086, -1.9042055219801668, -0.5863612077608358, 1.0631069376203162, 1.0036485244385773, 0.03630044686232963, 0.31858018847527014, 2.1771313228103026, 3.475255941281269, 2.3878156348903565, -0.06693354337374911, -1.1566597108032626, 0.08983011434366293, 1.5335875120394555, 0.5897563769273738, -2.3568651813937995, -4.169548651794683, -2.710128764806315, 0.48233057945305735, 1.9616148506185291, 0.4570090333709099, -1.7483327254195296, -1.7638554287450814, 0.39909548518327415, 2.091038155696885, 1.5144385902269977, -0.1450829999022448, -0.5854435156527531, 0.4121786223656373, 0.8168691018690997, -0.5454746293019922, -1.8797891087392748, -0.4260985399333701, 3.749807576338404, 7.150347013070509, 6.575891810783521, 2.7937962663120226, -0.3713061776001467, -0.43201230083803477, 1.247427491397025, 1.6965210488491218, 0.21178482505500604, -1.104381311412141, -0.53197878276574, 0.8373407212372561, 0.7218339247472614, -0.9628925618721372, -1.700447023046861, 0.29093235269183776, 3.385484443165602, 4.290021778283814, 2.1678322391518647, -0.19560186367940355, 0.15137950863501942, 2.592176626305553, 3.73583760730363, 1.7461058354639616, -1.3458768938286887, -2.263701636336858, -0.5763707710908984, 1.0052489053742786, 0.3206031574078858, -1.5434658498604286, -2.013155529925442, -0.6457463409630925, 0.4128491278603185, -0.2971807755867016, -1.201952024401417, 0.24100820790588967, 3.6858285907684825, 5.622517171857851, 3.5023027555837696, -0.8793219500923409, -3.2330239620247267, -1.71026908800335, 1.21012381876669, 2.084081400623328, 0.6231259828226132, -0.6079695241259575, -0.057036484227380654, 0.8425509753489026, 0.1372707442343153, -1.4581366385908505, -1.338091259947663, 1.1944406949882762, 3.4765101151494533, 2.723784797714699, -0.19395417340781307, -1.62725047690317, 0.22987231363571775, 2.9853045184730034, 3.1221582091390605, 0.5034766171418115, -1.5840403494175446, -0.8041947353686008, 1.2977845083716983, 1.5954499304501484, -0.3717410782040338, -1.966221603123323, -1.2331726041147555, 0.4588270226963063, 0.5307414843906841, -1.0467230582958607, -1.7579863739468795, -0.3699683776432358, 0.908678514609908, -0.7052302538797608, -4.3769320706295485, -6.040823919592572, -3.298440590558054, 1.4377684270332927, 3.7308381773918624, 2.283846684776504, -0.08776660992430366, -0.555747482104825, 0.28830253512220144, 0.06259666147664368, -1.4956570557349664, -2.0949214773578957, -0.46028863064824144, 1.4416403988099036, 1.0157897418724113, -1.0497237031527402, -1.2965893910853288, 1.8557073946284237, 5.579272996509925, 5.912284994086242, 2.691244727994421, -0.37835920196393663, -0.5536707458241593, 0.7103904618272887, 0.2969906130580895, -2.012226762547833, -3.289749453826015, -1.6848106531029954, 0.9406382506401647, 1.6256443316013802, 0.35293241636105643, -0.24642744493953964, 1.0069697167395362, 1.985611197896085, 0.47882444290588455, -2.1099049012016486, -2.1741730040622596, 1.1377907122224167, 4.27027323035973, 3.5319899737699902, -0.21345166986706518, -2.6887734345209915, -1.620297974319088, 0.7769047369949651, 1.2442404061389831, -0.22666186702425883, -1.0723273309862165, -0.3081981122998057, 0.14926247777772295, -1.1632345433694993, -2.450557234231411, -0.9417003314622581, 2.7627275262750928, 4.742254788855403, 2.699083321002545, -0.8278117827669901, -1.584214137965391, 0.9742946428901476, 3.2271861305068503, 2.3837115420757335, 0.004807233374471493, -0.5964510379026037, 0.8910672617289668, 1.6191552145267292, -0.0212264514278818, -1.9847388520587952, -1.6203133510771608, 0.37434393115900527, 0.9575353160381361, -0.7391402161642804, -2.075793393594101, -0.8688003469527187, 1.090370814710887, 0.3349347745516652, -3.140385875142382, -5.272209373217678, -3.086582791272332, 1.3011469465141143, 3.3460670004320345, 1.7641628464800045, -0.4032052811361379, -0.3795628405086956, 0.8205021645432207, 0.6250334509938382, -0.9200104077181569, -1.3969368646558125, -0.12770597745001308, 0.36944541204173903, -1.8407640243862176, -4.596269434699522, -4.001287968219945, 0.1562521900635142, 3.5833626979794273, 2.7919835612968176, -0.5450995947219663, -2.079049673322334, -0.5400025560689091, 1.1537916290567243, 0.5392170713755594, -0.9542737725648754, -0.5675403903468745, 1.3687231555029975, 1.8665207224786224, -0.12737411313259966, -1.9536533496039103, -1.0674742040401732, 1.1801377073278694, 1.5444487449704334, -0.16156918610650245, -0.5851846549157645, 2.169333680039497, 5.258383140770685, 4.578298391232394, 0.37252585406218514, -2.9193343074905647, -2.4286840258708366, -0.24547205490971033, 0.024318568756205958, -1.711422940770467, -2.509298002362559, -1.1322933825796646, 0.25498369434246043, -0.23717706144976602, -1.1335051249964188, -0.0833733524970737, 1.8285769613603198, 0.9161761496061193, -3.6990430083095767, -7.917720714050369, -7.426174062915935, -3.1594577969179127, 0.07229801016028574, -0.14752459014244038, -1.3423409369933488, -0.44637362767473476, 1.7211381212352488, 2.174719122902663, 0.6159947924425482, -0.09943075199906437, 1.515615805477324, 3.134047592663662, 2.12816214426451, -0.2612104500799751, -0.6036933161612223, 1.489557592715668, 2.4824516500481755, 0.014798979674562073, -3.4027841919126556, -3.724351779988522, -1.10326863608827, 0.2832649597355776, -1.8513477256018598, -4.723197987137917, -4.4852720350120086, -1.495454899280838, 0.6135425867495166, 0.23411717565517148, -0.5297702632181579, 0.13384099034666225, 0.6802003778835938, -1.0297085645903117, -3.604876976799532, -3.5393456048327376, -0.5700799093635394, 1.1748302018957115, -1.3697210123504093, -5.6665336972228, -6.65115359951243, -3.336846914194972, 0.21191267084174756, 0.6012484435951808, -0.8138415169884601, -0.9112961579645249, 0.265148430434053, 0.11726476691290155, -1.76324120164869, -2.4824758800436095, -0.2910132523657527, 2.3655899280162997, 2.235378996333357, 0.17846179529184766, 0.017427092363134788, 2.7511488433341817, 4.785105594734637, 3.076363975413007, -0.28210597053520936, -0.9013062411258916, 1.6850153479048844, 3.4787290015153305, 1.8353502220095945, -0.9481548771828989, -1.3095687937071436, 0.42843609144609107, 1.0475854329829495, -0.40172100642733394, -1.3968318065095904, -0.33283648077813804, 0.7239921265338681, -0.48099701288101604, -2.137514603624834, -0.5019907777422103, 4.18986701417099, 7.012258299243277, 4.605363719424809, -0.251577712359855, -2.3179723955510854, -0.6014028544262386, 1.2510230083764768, 0.7614122153081886, -0.2673181254319566, 0.5371967064852178, 1.9967956894015897, 1.418401120362803, -0.6933131874470112, -1.0622843327061207, 1.1597658554092898, 2.6343036392482313, 0.7089151222112879, -2.2948947831160877, -2.167151938521213, 1.0186029629398865, 2.869963524130245, 0.9956664591100288, -1.6284152171962434, -1.167958617434717, 1.5043763021075265, 2.4021608025538783, 0.4957578986211485, -0.9795505806516317, 0.3269986591320896, 2.394388239258015, 2.2057920140412013, 0.3959174629096623, -0.18317826319892144, 0.5332607886566914, -0.42482177783148983, -3.803732700958023, -5.775122973530026, -2.9463129683012284, 2.2922896501127483, 4.34221279039935, 1.6670066393979324, -1.544214779450985, -1.48584073482784, 0.42278580804102406, 0.5937185702674987, -1.11134163850404, -1.780611363543465, -0.5637061135373728, 0.03961595059818336, -1.3023697972690607, -2.0496102435506174, 0.2632184446768363, 3.4747464134463395, 3.2554989004506623, -0.5542347451890978, -3.328498497467691, -2.070145191648136, 0.5279061088179524, 0.3664860142448383, -1.9560272235608989, -2.3440429753522394, 0.3782395527707532, 2.709288890875697, 1.8369866112070903, -0.32297650860532534, -0.4731167114598174, 0.9033768748185644, 0.7007517053145481, -1.4589570322696221, -2.475870217703182, -0.8993387110267282, 0.4571997029642173, -0.9878500215239001, -2.906319741129816, -1.0219423634954867, 4.205099192478342, 7.364163487516406, 5.192273820157322, 0.815229367398139, -0.8684671628752425, 0.3782909574933531, 1.064453258854434, -0.0897256054109897, -0.7125813990827088, 0.530662466710892, 1.3530486692336905, -0.21980807922855256, -2.003103678282651, -0.7040607979688722, 2.5470578545796005, 3.2246868898747953, 0.0902990402394377, -2.5757581298426118, -0.9653928783377692, 2.8021477316115746, 3.871856467541277, 1.5762466148087901, -0.24717170395238627, 0.4812148084091814, 1.1817605757450118, -0.7175514573992796, -3.326015311589023, -3.1833879775831155, -0.7364693897355752, 0.4233315924339509, -0.7502598437094853, -1.3973859593630065, 0.09229096845376979, 0.9544860371847959, -1.549032701231604, -4.999268061368823, -4.56733948369754, -0.10861333433993388, 3.1642044118912924, 1.8105622195097906, -1.3330202635476087, -1.7033994039189588, 0.5531395230265889, 1.7135563413065993, 0.5832225569571372, -0.25333637602931064, 0.619692727707817, 0.9871530945869276, -0.8240492822124359], 'positive_zeros': ['0.696246239103063253262169218120', '3.14153171876136634477530421573', '3.92514416377923000002622706144', '5.15932969591582036108609231939', '6.32557510733513289891572074432', '7.771235351826238195627474086825', '8.82245581906435456580961076274', '9.98285013149463943373181172958', '11.13102558818373547582542425246', '11.66704261898831851709783459907', '12.96965849875302568722524920057', '14.50911728893069806970291104953', '15.25731686656675998680149435169', '16.069863030313316844059517321577', '17.02668547064937016028588214622', '18.00641523093752053678638974681', '19.543483351803390759925153856857', '19.9208240231943327494822827188', '21.30284726203822986180787469048', '22.09609355923404520719626241778', '22.928127654144071507105680380513', '23.78837070077820784163022561487', '24.88505771390736647047053128482', '26.259459491798742158075870630260', '26.854116734570365902136585790777', '27.7784848280668127564987099905', '28.27042564161452893996698405762', '29.66296247669710906722960740224', '30.4770852296751944242526718405', '31.67934923315570067050978093015', '32.334594239921449647359636337593', '33.1150034741092935689930266482', '34.35030171647793119314174643334', '34.85496275658536698889279755798', '35.63171096128324044005776538013', '37.25489883899403351451481206108', '37.67577546260439796037307215383', '38.7918982920841582842771562064', '39.475986253230199329735012392563', '39.98092275710574988863816593601', '41.23944311682549694549638265644', '42.295987508189841211178970577866', '43.28291401718907080388619751446', '43.64498277195419829829815641060', '44.85931939822763590755660789670', '45.58153919453215302964338237790', '46.31455992830863641730148744314', '47.27326522737133207564792310350', '48.20830132681155717991948105502', '49.29022452232360974555761995331', '50.12620378081867895580467844011', '50.60071103638008874547073880529', '51.49301275366666758282802820150', '52.18287545170137482853897870418', '53.51621185977664511899375464510', '54.38965280142393374421942298370', '54.94092110472306425575279459083', '55.9345946226822090352575553883', '56.52667565399044423863973133378', '57.56196975879424016798619020107', '58.239832439285403578378055670580', '59.2001246552010436804334176251', '60.03297573827608812966043891789', '61.291611076246264891270429824795', '61.66233179936828669303129166954', '62.30731543913552918367284001859', '63.4018791121020285816276837170', '63.820010474731721532411366920787', '65.276815556430386375976908615873', '66.02962577384426011362464883832', '66.894106463985039050058497704818', '67.08187277806776645105510596152', '68.42806187377165890333525343704', '69.04749597691597755234737990374', '69.75929990630578828946171755022', '70.88715276715388647949662261973', '71.62002214472554815051773829349', '72.449287133414473882366643906111', '73.40534714782534487885962765845', '73.95126542604757710642519972711', '74.592822375166999378342456094951', '75.35204558003122559788716056793', '76.81769885880131575183032360311', '77.27542130430693821611732089371', '78.16109516758714650442270459926', '78.86244160087760809490980951371', '79.52278665477763304223677080247', '80.282403408281836795721045173648', '81.52092016409603829341623262968', '81.84779989910863314157105677787', '82.97899307612896263031888015425', '83.83479341434775933591768072366', '84.430326395755713182279223682578', '85.44878715979515396595867716329', '85.861581189004547943180725310559', '86.53506484144648090299193207912', '87.74767535589351515241891369223', '88.61114779672094796094300901987', '89.48967024103637401427759535418', '90.01544080227677006014460335926', '90.65214913658754487554684132671', '91.43667742324507999932953166108', '92.478711216757417025980024081186', '93.10049293056434261409816760444', '94.11641877292999348594129577101', '94.803001924761002149711652508986', '95.57530714874932300586146880040', '96.46370184397148949932837922760', '96.996303246138425537062058512798', '97.8737430919953480196501512170', '98.359968856860145908130737798623', '99.58769435820614630543881183743', '100.6088802573633725259710153410', '101.13943499150554393614943356809', '101.57906938651178634621172176172', '102.56210874191407576526139792765', '103.27985186852464514755068025985', '103.91188017972552607988990007731', '105.25469008321854502144385053618', '105.75586290216799766962437264663', '106.30008951860527711487689245626', '107.37610262824830515140159508386', '108.2136676152793704160621638417', '108.53733201654977246918327550844', '109.43018845976089317835937661702', '110.2233549915916237419336360535', '111.2328027293022806313986703884', '112.07411013137438157653378382542', '112.76916355203172782854685176758', '113.54006957407331431875959373846', '113.81953261825066854086185310737', '114.773909141913515335985311619081', '115.85295757507851352251118344246', '116.46509172342558668748939206175', '117.50078811491636772305505546854', '117.96244047277391612681847992647', '118.74719373390949125079654403538', '119.62593388300473289355688208555', '120.20217866118646579343995159495', '121.0567928333577699910316069618', '121.60065932383848189812309725183', '122.71577366508095065204750847288', '123.66936749981863392313509054248', '124.15909167087132215178788969866', '124.82155881070108647377587030706', '125.65365963035667173216556710554', '126.02720955778138085574408408620', '127.17707085875193611058531267027', '128.07217535963683867032183826350', '128.825567976456599553481808282261', '129.47531015743595672685490422412', '130.098328043384667653531997114136', '130.92179446224406152055229305485', '131.70485654609193389422739619904', '132.47138797091252237405112253490', '132.91305170826421186736732603131', '134.08822564956675343563759829112', '135.05354191667896436115860063901', '135.31923069198810431793487728644', '136.46674954853462575486101363738', '136.80797986095550855593339815538', '137.512717331066289649506247284748', '138.20456674568900746475038079398', '139.67286403989039849348710278718', '139.96502598382487208019912246266', '140.68995452382741548064953891163', '141.70734658864246964027374243934', '141.91761204016236894228802878820', '143.0838608084025477954383504650', '143.54924913762436974229839163938', '144.37624621699870325853325474419', '145.467798917958005716086477587568', '145.71356767464451346749986653329', '147.05032067255908039193840134544', '147.567089196501417518413146318326', '148.08641181224926621438007043297', '148.6142872174398946648708842885', '149.74604410887726486463885943857', '150.20016547297453644427771063346', '151.5339872336894575805028108528', '152.01009525869431780938100335742', '152.73570243325646726849275488193', '153.15135984151846650430945167122', '154.09160634490247579726804708123', '155.035601430213309663298413247816', '155.30901768272342031942901784760', '156.53002742503769484345425196', '157.00947444910482277777518948856', '158.00273195117042254904356835326', '158.67620813815062562264374003668', '159.30460326844913564270872093031', '160.065247682882817317455500789837', '160.54856593326783313084886061656', '161.28983648812786921642736770368', '162.48146350041918538064892125674', '163.20117279921838576242229294022', '163.93746650630694249469963092422', '164.25481135378176429157327523609', '165.20588242503177466412607220464', '165.79805338920061367971941371310', '166.628960499419620123498439066027', '167.40829705154534209655013730549', '168.22511831943022075272549997152', '168.8909239444130687508047032866', '169.75542059929072987445697477693', '170.266773656839352308831142160030', '171.34440628483543526378864413024', '171.652816842527962427658367128620', '172.12684402394465116300561983', '173.29632151159227257690335734292', '174.199860877946236532621301019408', '174.92256492458753836698176812753', '175.43581135606618414238435668202', '176.411471223232876597376693798071', '176.58395711726878829751953729717', '177.47629895218285985292697297956', '178.39672017720908801243435715405', '179.29334779474507560171591734980', '179.74386309616874846265284874337', '180.589237143886899412150446402047', '181.5032715959277692796556276655', '181.98601774646703622732372074989', '182.61572321246721008447782414369', '183.58254464841066783094866950290', '183.91834725704459731079404097623', '184.756910564639421550189396130193', '186.01875648735540187715578092109', '186.48892789577444324178169683308', '187.16759181772697166048948916488', '187.70881894477233898611552612693', '188.40800987290817393854646677146', '189.132227408931792846773107668527', '190.00732932865833959026234348015', '190.70496743864389574261150236082', '191.78768708597942540341766391341', '192.07028083943514137107755380586', '192.73106550975616129509006766654', '193.86452691177415565543669085607', '194.21831334266510488347088540536', '194.98475578618438895680663665802', '195.48118432840705816821090230314', '196.56948912711300876420337314715', '197.35494905402255188830271275855', '198.05370330899937995350702932560', '198.88920454985165124888086466134', '199.20325373674741705183348850878', '199.88803315154268027101079950533'], 'prelabel': '1-14e2-196.39-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.063125259746503, 'root_angle': 0.14965986394557826, 'root_number': '0.891491135545289584096248464203+0.453038138840616943309900146760*I', 'self_dual': False, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0748299319728', 'prec': 50}, 'spectral_label': 'r1-0', 'st_group': 'mu(42)', 'symmetry_type': 'unitary', 'types': ['DIR'], 'values': [[1, '0.827300150336454951731217978375+0.181184072159306181455289609206*I']], 'z1': {'__RealLiteral__': 0, 'data': '0.696246239103', 'prec': 47}, 'z2': {'__RealLiteral__': 0, 'data': '3.14153171876', 'prec': 44}, 'z3': {'__RealLiteral__': 0, 'data': '3.92514416378', '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': 21.063125259746503, 'bad_primes': [2, 7], 'central_character': '196.39', 'conductor': 196, 'conductor_radical': 14, 'degree': 1, 'index': 0, 'instance_types': ['DIR'], 'instance_urls': ['Character/Dirichlet/196/39'], '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': '1-14e2-196.39-r1-0-0', 'motivic_weight': 0, 'mu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'mu_real': [1], 'nu_imag': [], 'nu_real_doubled': [], 'order_of_vanishing': 0, 'prelabel': '1-14e2-196.39-r1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 21.063125259746503, 'root_angle': 0.07482993197278913, 'self_dual': False, 'spectral_label': 'r1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.696246239103', 'prec': 47}}
• lfunc_instances •

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

  
  {'Lhash': 'dirichlet_L_196.39', 'Lhash_array': ['dirichlet_L_196.39'], 'label': '1-14e2-196.39-r1-0-0', 'type': 'DIR', 'url': 'Character/Dirichlet/196/39'}