-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '759220746601567081074560039991,958335622663639833137818193859,1354265606890046078713628873609', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 15, 'a6': 0, 'a7': -8, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 258743.5181162607, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1]], [5, [1, -15, 75, -125]]], 'bad_primes': [2, 3, 5], 'central_character': '1080.1', 'coefficient_field': '1.1.1.1', 'conductor': 1259712000, 'conductor_radical': 30, 'degree': 6, 'euler_factors': [[1], [1], [1, -15, 75, -125], [1, 8, 273, 11320, 93639, 941192, 40353607], [1, 10, 1129, -32780, 1502699, 17715610, 2357947691], [1, -48, 3891, -92328, 8548527, -231686832, 10604499373], [1, -37, 14418, -347965, 70835634, -893090053, 118587876497], [1, -29, 17960, -420497, 123187640, -1364330549, 322687697779], [1, 11, 30456, 222899, 370558152, 1628394779, 1801152661463], [1, -28, 55099, -1662544, 1343809511, -16655052988, 14507145975869], [1, -41, 78964, -2734453, 2352416524, -36387650921, 26439622160671], [1, -230, 114787, -19298596, 5814305911, -590117074070, 129961739795077], [1, -370, 214275, -48796108, 14768047275, -1757538569170, 327381934393961], [1, 130, 44673, 3936068, 3551816211, 821777196370, 502592611936843], [1, 56, 115517, 4195536, 11993321491, 603636058424, 1119130473102767], [1, -805, 594702, -247415005, 88537449654, -17842310708845, 3299763591802133], [1, -576, 214701, -9306072, 44095076679, -24295987377216, 8662995818654939], [1, 257, 202474, 153986701, 45957750994, 13240736210777, 11694146092834141], [1, 14, 651149, -22117636, 195841526687, 1266417350366, 27206534396294947], [1, -1238, 1448677, -895305068, 518497433747, -158588151494198, 45848500718449031], [1, 398, 1211307, 310732420, 471219015219, 60231022063022, 58871586708267913], [1, 321, 774636, 459949637, 381925758804, 78031073222241, 119851595982618319], [1, -687, 1037148, -349696983, 593027743476, -224608036504503, 186940255267540403], [1, -2358, 3793395, -3699365060, 2674225879755, -1171881884086038, 350356403707485209], [1, -576, 2295459, -793944704, 2095003451907, -479791874839104, 760231058654565217], [1, -628, 2170695, -1049646856, 2236469229195, -666634654577428, 1093685272684360901], [1, 764, 2102613, 1368609928, 2297581995651, 912255954548156, 1304773183829244583], [1, -1884, 2766105, -3192320488, 3388597567515, -2827375982883516, 1838459212420154507], [1, 757, 2321922, 1522526681, 3006956325738, 1269564783906637, 2171893279442309389], [1, -2142, 4748271, -5775804612, 6851265981087, -4459540654088478, 3004041937984268273]], 'euler_factors_factorization': [[1], [1], [[[1, -5], 3]], [[[1, 8, 273, 11320, 93639, 941192, 40353607], 1]], [[[1, 10, 1129, -32780, 1502699, 17715610, 2357947691], 1]], [[[1, -48, 3891, -92328, 8548527, -231686832, 10604499373], 1]], [[[1, -37, 14418, -347965, 70835634, -893090053, 118587876497], 1]], [[[1, -29, 17960, -420497, 123187640, -1364330549, 322687697779], 1]], [[[1, 11, 30456, 222899, 370558152, 1628394779, 1801152661463], 1]], [[[1, -28, 55099, -1662544, 1343809511, -16655052988, 14507145975869], 1]], [[[1, -41, 78964, -2734453, 2352416524, -36387650921, 26439622160671], 1]], [[[1, -230, 114787, -19298596, 5814305911, -590117074070, 129961739795077], 1]], [[[1, -370, 214275, -48796108, 14768047275, -1757538569170, 327381934393961], 1]], [[[1, 130, 44673, 3936068, 3551816211, 821777196370, 502592611936843], 1]], [[[1, 56, 115517, 4195536, 11993321491, 603636058424, 1119130473102767], 1]], [[[1, -805, 594702, -247415005, 88537449654, -17842310708845, 3299763591802133], 1]], [[[1, -576, 214701, -9306072, 44095076679, -24295987377216, 8662995818654939], 1]], [[[1, 257, 202474, 153986701, 45957750994, 13240736210777, 11694146092834141], 1]], [[[1, 14, 651149, -22117636, 195841526687, 1266417350366, 27206534396294947], 1]], [[[1, -1238, 1448677, -895305068, 518497433747, -158588151494198, 45848500718449031], 1]], [[[1, 398, 1211307, 310732420, 471219015219, 60231022063022, 58871586708267913], 1]], [[[1, 321, 774636, 459949637, 381925758804, 78031073222241, 119851595982618319], 1]], [[[1, -687, 1037148, -349696983, 593027743476, -224608036504503, 186940255267540403], 1]], [[[1, -2358, 3793395, -3699365060, 2674225879755, -1171881884086038, 350356403707485209], 1]], [[[1, -576, 2295459, -793944704, 2095003451907, -479791874839104, 760231058654565217], 1]], [[[1, -628, 2170695, -1049646856, 2236469229195, -666634654577428, 1093685272684360901], 1]], [[[1, 764, 2102613, 1368609928, 2297581995651, 912255954548156, 1304773183829244583], 1]], [[[1, -1884, 2766105, -3192320488, 3388597567515, -2827375982883516, 1838459212420154507], 1]], [[[1, 757, 2321922, 1522526681, 3006956325738, 1269564783906637, 2171893279442309389], 1]], [[[1, -2142, 4748271, -5775804612, 6851265981087, -4459540654088478, 3004041937984268273], 1]]], 'gamma_factors': [[], [0, 0, 0]], 'group': 'GL2', 'index': 3, 'label': '6-1080e3-1.1-c3e3-0-3', 'leading_term': '9.7256690297362415609793105101802147057371098675732810911661527009729443050333837766562240', 'load_key': 'CMFs-workshop', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3, 3], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1080/4/a/k', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.01953125', 'prec': 34}, 'plot_values': [9.725669029736244, 9.680558484698913, 9.615410461382298, 9.51045028561892, 9.35092658046062, 9.139950649638916, 8.885226106769716, 8.593496103447276, 8.26744407908708, 7.909068080418157, 7.521055424041094, 7.107574467528246, 6.673236011540515, 6.222693621722667, 5.760490356527981, 5.291151534039332, 4.819216841552517, 4.34928411122498, 3.885830504483798, 3.433142411723984, 2.995305405795154, 2.576110668818772, 2.1790167644251643, 1.8071463428533119, 1.4632015114617796, 1.1494341639313725, 0.867644769420969, 0.6191309961475078, 0.4046774090738811, 0.22456376405453712, 0.07854522462092808, -0.034137185636805324, -0.11473488984915675, -0.16497976691658903, -0.18705249689274156, -0.18354541685522233, -0.15742303826445925, -0.11197178064497826, -0.05074808599770086, 0.02248125516983123, 0.1038026558998993, 0.18921852473386974, 0.27471733057244635, 0.35634272884150625, 0.4302603498069075, 0.4928272109054482, 0.5406571368572578, 0.5706820818523474, 0.5802101999259648, 0.5669779039033847, 0.5291947613481616, 0.46558166259463973, 0.375400937104649, 0.2584738778607381, 0.11519425222814594, -0.053469523315524445, -0.24599335940208497, -0.46030832522934995, -0.693828517761888, -0.9435120319353965, -1.2058901973881508, -1.4771228502219487, -1.7531016552470866, -2.029486573237873, -2.3017810133981227, -2.5654718997034562, -2.8160583678759967, -3.0491351246628264, -3.2605578105193085, -3.446447446608994, -3.603267783972828, -3.7279999081869923, -3.8181074674997695, -3.871593582399786, -3.8871663202917626, -3.8641544033633295, -3.8025317504943663, -3.7030561923233036, -3.567132752512487, -3.3967990105311756, -3.1948234960041977, -2.9645227157403933, -2.7097076065579397, -2.4347350524227442, -2.1442940417830645, -1.8433213581185373, -1.5370085240464155, -1.2305800018121655, -0.9291934235627394, -0.6379133309712297, -0.36150843398765853, -0.10435650540582599, 0.12959639945163787, 0.3369932123583376, 0.5151350290682567, 0.662014015036941, 0.7764045537950657, 0.8578885213559294, 0.9068591366156108, 0.9245356694197605, 0.9129344303007135, 0.8748289019089821, 0.8136909044066708, 0.7336076914861831, 0.6391947157311877, 0.5354796997058557, 0.4277781712258173, 0.32156874287790055, 0.2223474540452993, 0.13548461440531123, 0.06608563036190726, 0.01884851336510984, -0.0020685830421083343, 0.006831596953537402, 0.04827727058758225, 0.12413569916623354, 0.23534600052666158, 0.3818672133717297, 0.562650331353314, 0.7756557321347602, 1.017863756818047, 1.2853214341619257, 1.5732623393551661, 1.8761673428119974, 2.1878801835382737, 2.50182870483028, 2.8111059364257693, 3.108631769040638, 3.3874535758832613, 3.6408060143636916, 3.862282961496823, 4.046177395055124, 4.187475942806406, 4.281999682998939, 4.326732627083764, 4.319715909625307, 4.260120324136712, 4.1485132860610054, 3.986636817468232, 3.777388828306329, 3.524991080842691, 3.234661173914047, 2.9125010896752834, 2.565551431040884, 2.2013946309136787, 1.8279734163073162, 1.4535445382788195, 1.0862716243761636, 0.7340169320869868, 0.40423404557949144, 0.10361805201163655, -0.16207460743818192, -0.3881377020919026, -0.5711463857271115, -0.7090563893490343, -0.8012604345221983, -0.8486613735180768, -0.8536538869132393, -0.8200807108413943, -0.7531416816440137, -0.6592492822816501, -0.5458689785362139, -0.42129505921454924, -0.2944045152290669, -0.1744035767213218, -0.07053223191171908, 0.008229175570133362, 0.053448500920330926, 0.057530675459077085, 0.013985922796690444, -0.08233024925230363, -0.2350079949548428, -0.44591256893888764, -0.7150813645056873, -1.0406418589646866, -1.418791195896731, -1.8438996243308976, -2.3085606317555136, -2.8037367357802396, -3.3190982308261283, -3.8431633071685076, -4.363581831739843, -4.867685362179148, -5.342635500640012, -5.775777043874246, -6.155323189102802, -6.470411088168056, -6.711431104497287, -6.870734549117365, -6.942504283607168, -6.922966492696412, -6.81099873618847, -6.60776105496144, -6.316723033502537, -5.944072371083677, -5.498110513159919, -4.989075684050903, -4.429302721843217, -3.8324520929921664, -3.2131670659778138, -2.5870018395428547, -1.9696058785986776, -1.3763045672607037, -0.8218766108906452, -0.31984060675533654, 0.11792215584423947, 0.48141735339672276, 0.7630146816624764, 0.9576671900826703, 1.0630570980006306, 1.0797522521493192, 1.0111888496298334, 0.8636154582432986, 0.6459201011212072, 0.3693603368707461, 0.047273663160359324, -0.30535273450631606, -0.6723488104735952, -1.0368349807310713, -1.381774806164271, -1.6905229138061644, -1.9473585853129958, -2.138000690964545, -2.250091269368289, -2.273623549063883, -2.201280901221175, -2.028722342164278, -1.7547431778490696, -1.3813647743783724, -0.9138402390113425, -0.3604383574990493, 0.26769861845946263, 0.9568320659366182, 1.6912408320205046, 2.453489236484962, 3.224906941932266, 3.9865220729425297, 4.719289318293821, 5.404630740345808, 6.025528116669041, 6.566536071446773, 7.0142213691508495, 7.358216115625991, 7.590887668998791, 7.707542737457902, 7.707260892607195, 7.592184655569735, 7.367425790876412, 7.041568267872761, 6.625652073830981, 6.1328114992675005, 5.57843736681958, 4.9790230961775155, 4.351649723196216, 3.7138974443066624, 3.0827716554811233, 2.4741993495830767, 1.9028476294032641, 1.3813335104437443, 0.9198939829118228, 0.5262818992179118, 0.20538853134422203, -0.04080563570677526, -0.21313376703877507, -0.31519194255942506, -0.35309165027473116, -0.33512778017230804, -0.2714011175878619, -0.17335545372909975, -0.05328009367887258, 0.07621052804515176, 0.20270296400824883, 0.3144988335415087, 0.4010731432844471, 0.45349178903466947, 0.46476629639446077, 0.4300924848364009, 0.3470266532437553, 0.21554172084651935, 0.0379880973478363, -0.181018848809558, -0.43489144789350365, -0.7153278994454114, -1.0126588112826447, -1.3164280429333526, -1.61571830750204, -1.8995942959370242, -2.157818178566671, -2.3810559531452125, -2.5612466919648718, -2.6922586189824163, -2.7698258468600208, -2.7917029752799998, -2.758095754133836, -2.6712734340628, -2.5354506891538615, -2.3569148119987613, -2.1433793526851916, -1.9036413414775781, -1.647442979970723, -1.3847328695449246, -1.1252361266790516, -0.8781888722159756, -0.6517154907568078, -0.45248750734389254, -0.28551422759573325, -0.15381036062096193, -0.05828974986950103, 0.002234639294145699, 0.031017947086329482, 0.03319768532234076, 0.01552792775322856, -0.013964938811330357, -0.04640139292336644, -0.07250912745025892, -0.08311702734183757, -0.06965136787237784, -0.024610742425419246, 0.057996233409996725, 0.1822741305591828, 0.35017493606578287, 0.5612829293915408, 0.812716495126058, 1.099251099640637, 1.413381908400435, 1.7455592208747943, 2.0847582991250344, 2.418734421411934, 2.7345136340011234, 3.019311135070092, 3.260780436432943, 3.447570761776058, 3.5703640297739057, 3.6218837192678754, 3.597289357269983, 3.4950495136874067, 3.316538551186393, 3.0660890672973102, 2.7514714124572746, 2.3830508265205625, 1.9734469292302101, 1.537535343704239, 1.09131212794282, 0.6512693834188296, 0.234019754195666, -0.14484856652615447, -0.47144185797049326, -0.7340594803203798, -0.9240249434984851, -1.036119952575188, -1.0688956154215132, -1.0249465008332392, -0.9108942847592844, -0.7372721616070185, -0.5181767836734275, -0.2707468457826586, -0.014561765454937488, 0.2291816484206576, 0.43855469269379105, 0.5918168519186212, 0.6684038273201786, 0.6498801496868323, 0.52082713173266, 0.2696383131234116, -0.11080874931293488, -0.6227118465611365, -1.2630017605903618, -2.023217098979372, -2.889834825166581, -3.8444309796574228, -4.864175872645542, -5.9230357074254645, -6.992240186749286, -8.041238526749735, -9.039592619160016, -9.957371749743077, -10.766225169024615, -11.441556014952067, -11.96242249457433, -12.312322591479607, -12.481145899545314, -12.464290663978403, -12.26285146787968, -11.884934161453835, -11.343960481103133, -10.658170723506396, -9.851127002617858, -8.949477441145866, -7.981951407599095, -6.979178961821501, -5.97140935208143, -4.987382859756327, -4.053841684851546, -3.193751287055159, -2.425495418994608, -1.762545863971351, -1.2125908773432459, -0.7773877158646667, -0.45295468104330683, -0.22971662223415043, -0.09310039616055228, -0.024349939119626806, -0.001464115782276146, -0.0003299929017341723, 0.004056274331859212, 0.03632941743614135, 0.11950589803094602, 0.2738175548912614, 0.5156579532174569, 0.8566927712110616, 1.3032725722046676, 1.8559603259646682, 2.50934087663915, 3.2523884636021925, 4.0686448808938716, 4.9367927664586615, 5.832043414404982, 6.72670227601957, 7.591265904360806, 8.396544317766525, 9.11412886953865, 9.717561658210702, 10.18465442426958, 10.4973591002322, 10.642529524783935, 10.613848510635329, 10.410805665203624, 10.038738963862254, 9.509955130184837, 8.8418633459738, 8.056281754276373, 7.179663615852699, 6.24077950617477, 5.269578874047197, 4.2967812030387496, 3.351700073546515, 2.4611352097279555, 1.648810894290893, 0.9339066111151231, 0.3304420436826261, -0.15294720872877982, -0.5134574636577702, -0.7539832811516313, -0.8827219597227999, -0.9126545993097478, -0.8607215618456875, -0.7468553697088652, -0.5928868793182623, -0.4213747103273572, -0.25442282488884144, -0.11256887158537726, -0.013750208316568742, 0.027588349510257685, 0.0011399685042189816, -0.09877925558760393, -0.2730569373050824, -0.5178141652375603, -0.8246354018543999, -1.181272332149558, -1.5722042715718474, -1.979434557678098, -2.383884306460271, -2.7660642502900057, -3.1070463485984336, -3.3900919071624256, -3.6009417845562943, -3.7285075686013824, -3.766206382852101, -3.711535392253804, -3.5661685388614353, -3.336625419813317, -3.0331151000885863, -2.6690067209420665, -2.2607706159837644, -1.826410166143701, -1.3845682143709082, -0.9540027057930437, -0.552121064692371, -0.19415433324979692, 0.10738156800895564, 0.3435668562380822, 0.5094363190505189, 0.6041141371898959, 0.6308744135333788, 0.5968521188053572, 0.5125932140484782, 0.39140559908273986, 0.24854722052321662, 0.10033943342792187, -0.03679387930132436, -0.1472898636783916, -0.217360238053406, -0.23577258741586424, -0.1945233510027477, -0.08930160969925227, 0.08025826495362204, 0.31049670518348543, 0.5940264707218483, 0.9200485173227194, 1.2748821616829307, 1.6430127628974585, 2.007690015852811, 2.351790031706951, 2.6592739182218645, 2.915600040896132, 3.1084784789135322, 3.2292261257276222, 3.272579140653406, 3.236953918449439, 3.125249882130615, 2.9439195558293068, 2.702596900876134, 2.4141772471901466, 2.093362575324081, 1.7558401769807896, 1.4178266503636006, 1.0945797345399597, 0.7995492002751686, 0.5438316899288425, 0.33518934031189, 0.17762794529514586, 0.0712375636270206, 0.012050205189536459, -0.007697023057829493, 0.0009129625534704191, 0.024135656605319016, 0.046432615444490684, 0.05145286155328054, 0.02309911056141351, -0.05339538168349741, -0.19044676478726882, -0.39720074720301163, -0.6787730163866508, -1.0357843695984865, -1.4640215645282841, -1.9543928819451968, -2.493443735511205, -3.0636818448468515, -3.6443080383793296, -4.212737790434947, -4.745262491427323, -5.218227187765124, -5.61013572165942, -5.902056830134446, -6.078674543189455, -6.1302777486999664, -6.052352360562582, -5.845959303420938, -5.518950408454354, -5.084521980163404, -4.560682210439111, -3.9703918208064817, -3.339344004598512, -2.694731162954839, -2.0645209367099713, -1.475138788856242, -0.9501175312338525, -0.5091406510208243, -0.16642674737133625, 0.07004728995885366, 0.1989894532460367, 0.22615220872460046, 0.1640744577405268, 0.031533664879335774, -0.147389496252636, -0.34459088718544617, -0.5294178476156989, -0.6703905122336494, -0.736990179703455, -0.7014356519514369, -0.5403671916511421, -0.23634952023518768, 0.2209794153754584, 0.8340009644097455, 1.5966036128248342, 2.494467058767424, 3.5052116213885616, 4.599147475545227, 5.74127653522999, 6.892157194487831, 8.009598435315715, 9.051972513822593, 9.978971962084675, 10.753471154227602, 11.345198324902869, 11.730471234975235, 11.893343732836932, 11.828550774571715, 11.539680329438392, 11.039039235971927, 10.349134645417335, 9.499419533262527, 8.524913515354287, 7.466162735786426, 6.36537241043137, 5.264422810955768, 4.203938315719872, 3.2199671577045934, 2.3423472439725765, 1.5938823680909862, 0.9885667742843156, 0.5311180552441169, 0.21712170941916864, 0.033185424559152535, -0.04207963067439926, -0.036665868367598435, 0.016514535721538628, 0.08165534531645653, 0.12223145550542146, 0.10322226415843762, -0.0067284552377992485, -0.23336521481259487, -0.5951616892840139, -1.1020153626361606, -1.7546032746396245, -2.543974230879856, -3.451691987254752, -4.45110748054381, -5.508145013402067, -6.582804748267197, -7.632184700860038, -8.61169664582191, -9.4771946795703, -10.188849261809827, -10.711709854048737, -11.017433600682866, -11.0877799373131, -10.91366932425635, -10.49568730221544, -9.84618960693026, -8.986682303609477, -7.946873106694163, -6.765042997999685, -5.4843651643545535, -4.150975351996842, -2.8130519116917614, -1.5172122242948367, -0.30653533779596825, 0.7806799089150452, 1.7133068653551855, 2.4684814050678336, 3.03217053189434, 3.399745548187658, 3.57570092645847, 3.5730215244716432, 3.4121191689642845, 3.1193657382896607, 2.7254363217682394, 2.2634583952241525, 1.7670977629242168, 1.268632636786709, 0.7973922811503001, 0.37829981903745064, 0.03059209669114078, -0.23267751205289006, -0.40502554090023835, -0.48658260674132414, -0.48340683203347734, -0.40676548241789645, -0.2719763198297573, -0.0970767006084462, 0.09847337501455408, 0.2955341506602495, 0.4763967174296754, 0.6258811318783388, 0.7328045156001985, 0.7901676728781314, 0.7954531039435065, 0.7511794138627189, 0.6639987945608442, 0.5440852209233463, 0.4046825914684828, 0.2605582326087187, 0.12690025837353658, 0.018331396272915294, -0.05248995157248701, -0.07577040560640676, -0.045359241355456194, 0.040690247347180276, 0.17998692938624955, 0.36580841189056984, 0.5875836316572586, 0.8316392137673443, 1.082062705611871, 1.3218465807219484, 1.534111160676344, 1.7033493513372582, 1.8164887728666423, 1.8639007354988948, 1.84027762323525, 1.7449413855242315, 1.5820579046660372, 1.3605636515244353, 1.093512245789673, 0.7973629235618648, 0.49089355501910714, 0.19396826203917403, -0.0736946866473192, -0.2941020494981344, -0.4520361572785836, -0.53608636785593, -0.5398878731672995, -0.46229100042183086, -0.30756524752050907, -0.08561890190649994, 0.18893316748294134, 0.4975551560233069, 0.8187188887076378, 1.1295237860774212, 1.407054415328714, 1.6299399660841105, 1.7798205262995477, 1.8424938975059284, 1.809214282859724, 1.6771977641963685, 1.449846614804708, 1.137021961055413, 0.7542773642520992, 0.3219353053531316, -0.13585157155488778, -0.5927584548878959, -1.0219425377852276, -1.397655087995119, -1.696914189984087, -1.9010347991314713, -1.996916533776757, -1.9778482563856317, -1.8440872194224298, -1.6029074143205724, -1.2681640447058729, -0.8595954289881531, -0.4013246019655966, 0.07943081406842449, 0.5539502725385769, 0.9945455371999365, 1.375743224523619, 1.6758625046462534, 1.8795014440535351, 1.9776009668502037, 1.9680731278491088, 1.8571555390098498, 1.6578881515289048, 1.3893661054846356, 1.0764838228665716, 0.7472210419764577, 0.43088226385076156, 0.15664784658279024, -0.049226903522823086, -0.16519984917162278, -0.1759807649477877, -0.07414565640425916, 0.1391373278389903, 0.4536301850676969, 0.8503115349160768, 1.3023280849759897, 1.776266616795379, 2.2340725205329814, 2.6351614503228227, 2.9386027939345754, 3.10613651115333, 3.105111360181369, 2.9107327163210828, 2.506186359063569, 1.8838671586043974, 1.0507099473244788, 0.03300897821077472, -1.129874040478266, -2.4207045503910867], 'positive_zeros': ['0.59891956542668462990713863077220', '0.75599350679998091551841234850345', '1.06832719256096467193151386479566', '1.78580098908290865194078225605756', '2.18333244276845554111320200577123', '2.19999523340935722057675932173691', '2.93698384572121499904008796214162', '3.23973093975724225646417175892322', '3.30446223074629078855853957784650', '3.99832489384659573326825498306771', '4.20191843680412622711192130156033', '4.50365074674448642799495439218589', '5.11349638015423101072384069881692', '5.26200622227382572126233182091188', '5.45287213787894197085174093051650', '6.01465005967817359504035277474631', '6.08510100228363696984037264424194', '6.19829944735034210677088141100426', '6.73052969162843159400036352890823', '6.95424849503103791492725508231899', '7.10433232169747824573437845073797', '7.85720198000421645798473763491695', '7.86701083377791750343809932117075', '7.88143878609372245644428302762448', '8.587010656684076393155624881775783', '8.812658630244704444454581938964947', '8.848007971344169428480315583319550', '9.348041724711630280989260657188583', '9.545248395533446180811350578904869', '9.659614219583059727226148137827930'], 'prelabel': '6-1080e3-1.1-c3e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.982610024684901, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c3e3-0', 'trace_hash': 1862155028157104214, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.59891956542668462990713863077', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.75599350679998091551841234850', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.06832719256096467193151386480', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 258743.5181162607, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 1259712000, 'conductor_radical': 30, 'degree': 6, 'dirichlet_coefficients': [1, 0, 0, 0, 15, 0, -8, 0, 0, 0, -10, 0, 48, 0, 0, 0, 37, 0, 29, 0, 0, 0, -11, 0, 150, 0, 0, 0, 28, 0, 41, 0, 0, 0, -120, 0, 230, 0, 0, 0, 370, 0, -130, 0, 0, 0, -56, 0, -209, 0, 0, 0, 805, 0, -150, 0, 0, 0, 576, 0, -257, 0, 0, 0, 720, 0, -14, 0, 0, 0, 1238, 0, -398, 0, 0, 0, 80, 0, -321, 0, 0, 0, 687, 0, 555, 0, 0, 0, 2358, 0, -384, 0, 0, 0, 435, 0, 576, 0, 0, 0], 'euler11': [1, 10, 1129, -32780, 1502699, 17715610, 2357947691], 'euler13': [1, -48, 3891, -92328, 8548527, -231686832, 10604499373], 'euler17': [1, -37, 14418, -347965, 70835634, -893090053, 118587876497], 'euler19': [1, -29, 17960, -420497, 123187640, -1364330549, 322687697779], 'euler2': [1, 0, 0, 0, 0, 0, 0], 'euler23': [1, 11, 30456, 222899, 370558152, 1628394779, 1801152661463], 'euler29': [1, -28, 55099, -1662544, 1343809511, -16655052988, 14507145975869], 'euler3': [1, 0, 0, 0, 0, 0, 0], 'euler31': [1, -41, 78964, -2734453, 2352416524, -36387650921, 26439622160671], 'euler37': [1, -230, 114787, -19298596, 5814305911, -590117074070, 129961739795077], 'euler41': [1, -370, 214275, -48796108, 14768047275, -1757538569170, 327381934393961], 'euler43': [1, 130, 44673, 3936068, 3551816211, 821777196370, 502592611936843], 'euler47': [1, 56, 115517, 4195536, 11993321491, 603636058424, 1119130473102767], 'euler5': [1, -15, 75, -125, 0, 0, 0], 'euler53': [1, -805, 594702, -247415005, 88537449654, -17842310708845, 3299763591802133], 'euler59': [1, -576, 214701, -9306072, 44095076679, -24295987377216, 8662995818654939], 'euler61': [1, 257, 202474, 153986701, 45957750994, 13240736210777, 11694146092834141], 'euler67': [1, 14, 651149, -22117636, 195841526687, 1266417350366, 27206534396294947], 'euler7': [1, 8, 273, 11320, 93639, 941192, 40353607], 'euler71': [1, -1238, 1448677, -895305068, 518497433747, -158588151494198, 45848500718449031], 'euler73': [1, 398, 1211307, 310732420, 471219015219, 60231022063022, 58871586708267913], 'euler79': [1, 321, 774636, 459949637, 381925758804, 78031073222241, 119851595982618319], 'euler83': [1, -687, 1037148, -349696983, 593027743476, -224608036504503, 186940255267540403], 'euler89': [1, -2358, 3793395, -3699365060, 2674225879755, -1171881884086038, 350356403707485209], 'euler97': [1, -576, 2295459, -793944704, 2095003451907, -479791874839104, 760231058654565217], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0], [1, 0, 0, 0, 0, 0, 0], [1, -15, 75, -125, 0, 0, 0], [1, 8, 273, 11320, 93639, 941192, 40353607], [1, 10, 1129, -32780, 1502699, 17715610, 2357947691], [1, -48, 3891, -92328, 8548527, -231686832, 10604499373], [1, -37, 14418, -347965, 70835634, -893090053, 118587876497], [1, -29, 17960, -420497, 123187640, -1364330549, 322687697779], [1, 11, 30456, 222899, 370558152, 1628394779, 1801152661463], [1, -28, 55099, -1662544, 1343809511, -16655052988, 14507145975869], [1, -41, 78964, -2734453, 2352416524, -36387650921, 26439622160671], [1, -230, 114787, -19298596, 5814305911, -590117074070, 129961739795077], [1, -370, 214275, -48796108, 14768047275, -1757538569170, 327381934393961], [1, 130, 44673, 3936068, 3551816211, 821777196370, 502592611936843], [1, 56, 115517, 4195536, 11993321491, 603636058424, 1119130473102767], [1, -805, 594702, -247415005, 88537449654, -17842310708845, 3299763591802133], [1, -576, 214701, -9306072, 44095076679, -24295987377216, 8662995818654939], [1, 257, 202474, 153986701, 45957750994, 13240736210777, 11694146092834141], [1, 14, 651149, -22117636, 195841526687, 1266417350366, 27206534396294947], [1, -1238, 1448677, -895305068, 518497433747, -158588151494198, 45848500718449031], [1, 398, 1211307, 310732420, 471219015219, 60231022063022, 58871586708267913], [1, 321, 774636, 459949637, 381925758804, 78031073222241, 119851595982618319], [1, -687, 1037148, -349696983, 593027743476, -224608036504503, 186940255267540403], [1, -2358, 3793395, -3699365060, 2674225879755, -1171881884086038, 350356403707485209], [1, -576, 2295459, -793944704, 2095003451907, -479791874839104, 760231058654565217]], 'index': 3, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1080/4/a/k'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '6-1080e3-1.1-c3e3-0-3', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3, 3, 3], 'order_of_vanishing': 0, 'prelabel': '6-1080e3-1.1-c3e3-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.982610024684901, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c3e3-0', 'trace_hash': 1862155028157104214, 'z1': {'__RealLiteral__': 0, 'data': '0.59891956542668462990713863077', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '759220746601567081074560039991,958335622663639833137818193859,1354265606890046078713628873609', 'Lhash_array': ['759220746601567081074560039991', '958335622663639833137818193859', '1354265606890046078713628873609'], 'label': '6-1080e3-1.1-c3e3-0-3', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1080/4/a/k'}