-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '378683065102866803671093049240,770011961111945298204940875154,877048807455824618412223339527,1383307556676526426056629747909,2476350368001491483956297949134,2622724221088464567098852169890', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': 0, 'a5': 50, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': -243, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 50821887.74931882, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '2.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [3, [1, 0, 243, 0, 19683, 0, 531441]], [5, [1, -50, -625, 283500, -1953125, -488281250, 30517578125]]], 'bad_primes': [2, 3, 5], 'central_character': '120.1', 'coefficient_field': '1.1.1.1', 'conductor': 2985984000000, 'conductor_radical': 30, 'degree': 12, 'euler_factors': [[1], [1, 0, 243, 0, 19683, 0, 531441], [1, -50, -625, 283500, -1953125, -488281250, 30517578125], [1, 0, -64626, 0, 2028003087, 0, -41058323262556, 0, 572860676973093663, 0, -5156655001749473176626, 0, 22539340290692258087863249], [1, 664, 927242, 486628904, 369966973095, 148891760318192, 79421624285476108, 23979166891005139792, 9595990469511758110095, 2032769698418744566576504, 623802050801256808051553642, 71942447464098791435775286664, 17449402268886407318558803753801], [1, 0, -2165574, 0, 1976112655671, 0, -972719104225889812, 0, 272423910434526297125679, 0, -41156655421823712363882036774, 0, 2619995643649944960380551432833049], [1, 0, -6393390, 0, 19617942041247, 0, -35338776492878157220, 0, 39549651494515956369819903, 0, -25984216432946523688997171817390, 0, 8193465725814765556554001028792218849], [1, -288, 3843858, 3191500576, 12581641677063, 4024206089052864, 52212874685887107612, 9964332672897707497536, 77138878753983745146518463, 48450575660174587979142320224, 144490520194575691769195473748658, -26806030758217753786543567760783712, 230466617897195215045509519405933293401], [1, 0, -12847386, 0, 119828345726079, 0, -792017135162474667756, 0, 4964070307934420916400052271, 0, -22048116401306325897871650270794586, 0, 71094348791151363024389554286420996798449], [1, 1892, 73729778, 221122236196, 2964156539596023, 7752710730372195304, 78209112393556434399292, 159017004944562923337444296, 1247042096842140531477624700623, 1908105512426271167652296992390004, 13049770806825416556907599088131560978, 6868645137902773390761209451789433777108, 74462898441675122902293018227199467668020601], [1, 10248, 148847370, 1071971809752, 9540988611950607, 53587080545652756816, 354342595920577956102476, 1534152620590655168451543216, 7820064152116406303659369296207, 25154099363702568241233624570682152, 99994253405629603494678071193266639370, 197097657436816560205164793859373139456248, 550618520345910837374536871905139185678862401], [1, 0, -290752854, 0, 38769784471186119, 0, -3247030100434017898649524, 0, 186427779730153771798232916638031, 0, -6722928117650116550731034251080698280054, 0, 111186413610993811950185637819224232932533011049], [1, 1324, 287461202, 1075890738524, 54435387698127135, 166919514855955817432, 8090401066538794557515068, 19338660863974103231521095832, 730667663488021665691959123501135, 1673115874593673703756481030983164924, 51791247450327874012898222191662665350802, 27636586655722684142621449283999820233645324, 2418330769289520463963038742566759257517431737201], [1, 0, -502572210, 0, 127464803683947447, 0, -22067384193417129455383580, 0, 2754703350381879235844363288862303, 0, -234729450434017657910032766127984084312210, 0, 10093776109231555797740541116805209814919811290249], [1, 0, -288722058, 0, 116437215277524783, 0, -17624967958799601181845964, 0, 6124496483554336878610574173604367, 0, -798798284321974813391715815474185359381258, 0, 145524373433240498178471282244561013997462983607649], [1, 0, -1963456710, 0, 1786491383741543655, 0, -952189813368729684101162964, 0, 312434958932343616401103499305654095, 0, -60053555133775029535329947571301467588100710, 0, 5349042986438842598594824161669986924013455633256649], [1, 10296, 1221513450, 6893206196616, 1215172084818479367, 10103537901516419485872, 1268522834127048461073756364, 7223264751661557237926980003728, 621094810693992806494453818584473167, 2518845005023774992609249183577508789784, 319108583501367661231750384779464117437173450, 1922953688175847336543867180052165925029772553704, 133524312114275664899926313757566191470823300027804201], [1, 52116, 2451197130, 72357973266932, 2964089342279684487, 99376072009915887993576, 3671325684468772606291509612, 83932662827484594320504601362376, 2114412121850708760924858179201910687, 43594722649066273461711408776005473161732, 1247311537876982874821482091141970259223873130, 22398397652714704004624434344351993662393704306116, 362990325539372200679554918670984996723331903112927801], [1, 0, -7507145634, 0, 24155236685124504999, 0, -42778648868588803994265375484, 0, 44031078607540520553286435819655983551, 0, -24944275529981688609573892755733633012784612034, 0, 6056811824360306133893955506189170373758117309785601849], [1, 28288, 4692808010, 91249558850432, 13544019195862931487, 268968750522951962214656, 31449780336124998500740130956, 485281314195306529390725317568256, 44089081142086844779033770331472275887, 535927452831654510604455387334748113148032, 49727858991740377517362774544782884694364032010, 540830233202224245462032061776797132102814676092288, 34494548241361273407325608100987789752280917290697963601], [1, 0, -2138297622, 0, 9645229369668502143, 0, -18586449024559316458871195956, 0, 41451586872502718876888374824080541807, 0, -39493475612476959537418946015142599562781976022, 0, 79375377473505188618758459764796980252025727125812230449], [1, -220200, 36179470890, -3995254606507192, 366969270786989572335, -26432219350603783266026640, 1631543209177325947238142759564, -81333429692546995812336391916469360, 3474566369651468344768724872104381784335, -116399423745434526323683256783746705417419208, 3243426322735597815484837626072566527702313086890, -60742770574473318937993308150149117007907653176179800, 848814400041653188432880077486808325583024422374372061601], [1, 0, -5878219362, 0, 30391064056477835847, 0, -175857560153428632986323559676, 0, 471549001623321500509482923690160786303, 0, -1415166816435976536990313395605862765404915426562, 0, 3735448655171776399347824699993039078892536706537925477849], [1, -351420, 79254204978, -12402973117333356, 1540954763286670371903, -152819228915756925200160504, 12615370151932131067487813141500, -853351659215926483151142478677802296, 48049619853552292297792034530112249762703, -2159612845764374987866974456193030042961639244, 77058836378595304165427726980095566011465621006578, -1907992400280974404156456707340479466039619461863743580, 30317975617236256833580920126868226118402514553481681430801], [1, 0, -18122177670, 0, 229144433332479834447, 0, -2179324713417119565558839920660, 0, 16897663368303703845290662038165689109903, 0, -98547376984594215946936555232011112335083019745670, 0, 401007068543157803727680343536350900670553508041935397795649], [1, 496500, 150118375362, 31784901991817172, 5324791336912936675623, 720090180776838312749434632, 81181204313349797023605756067420, 7568220169747828920023827613249950632, 588188232395193726321789091060471402648623, 36901284461977767905292877361743085249008175172, 1831729464298826587064244996193523344580581736899362, 63672748552605648914880138254665062324569665940741746500, 1347848915332905650585522351309777516867383425202804564353001], [1, 0, -69371088690, 0, 2007280502569214653647, 0, -31009911293969874449623502726620, 0, 269761714534086837570926590997705582252703, 0, -1252919026442573083657275462163691555723980374984690, 0, 2427262471189660338642479878258204290900786637085454027093649], [1, 0, -44651077938, 0, 1237237059961488960567, 0, -20624140103878511634372039869724, 0, 243383256179219432478422155726615824825183, 0, -1727855825299380194934201508431389677766931121201938, 0, 7612255042662029206648128983778031607830320888857736765034249], [1, -847068, 379217333418, -114695101014542652, 25788796649887004288295, -4506087613503825458068543224, 625303637657578742525406341142572, -69331743450151585725727260905924765976, 6105146040038538109756925375406024401891295, -417774893657559896887709356003373661686149727148, 21252897067360099047426746818503911921549990042575818, -730433568884640174630632758963221402706010030435042149932, 13267678469131246220534960856572201266909465533192540861850201], [1, 0, -70310439534, 0, 2404348334908018746591, 0, -53370443261461536224340192761892, 0, 816172245169255644326402554392809547429759, 0, -8101933655265580461049877595604857895609063116394734, 0, 39115897957341730208009052194412390955771656152457329084502049]], 'euler_factors_factorization': [[1], [[[1, 0, 81], 3]], [[[1, -50, -625, 283500, -1953125, -488281250, 30517578125], 1]], [[[1, 0, -64626, 0, 2028003087, 0, -41058323262556, 0, 572860676973093663, 0, -5156655001749473176626, 0, 22539340290692258087863249], 1]], [[[1, 332, 408509, 107689464, 65790782959, 8611224967532, 4177248169415651], 2]], [[[1, 0, -2165574, 0, 1976112655671, 0, -972719104225889812, 0, 272423910434526297125679, 0, -41156655421823712363882036774, 0, 2619995643649944960380551432833049], 1]], [[[1, 0, -6393390, 0, 19617942041247, 0, -35338776492878157220, 0, 39549651494515956369819903, 0, -25984216432946523688997171817390, 0, 8193465725814765556554001028792218849], 1]], [[[1, -144, 1911561, 1871015072, 4733214280539, -882873541123344, 15181127029874798299], 2]], [[[1, 0, -12847386, 0, 119828345726079, 0, -792017135162474667756, 0, 4964070307934420916400052271, 0, -22048116401306325897871650270794586, 0, 71094348791151363024389554286420996798449], 1]], [[[1, 946, 36417431, 76110228372, 746963353438219, 397989042701990146, 8629188747598184440949], 2]], [[[1, 5124, 61295997, 221905216248, 1754852353808547, 4199775342489624324, 23465261991844685929951], 2]], [[[1, 0, -290752854, 0, 38769784471186119, 0, -3247030100434017898649524, 0, 186427779730153771798232916638031, 0, -6722928117650116550731034251080698280054, 0, 111186413610993811950185637819224232932533011049], 1]], [[[1, 662, 143511479, 442940770164, 16626694756831279, 8885800463320889462, 1555098314991537910888601], 2]], [[[1, 0, -502572210, 0, 127464803683947447, 0, -22067384193417129455383580, 0, 2754703350381879235844363288862303, 0, -234729450434017657910032766127984084312210, 0, 10093776109231555797740541116805209814919811290249], 1]], [[[1, 0, -288722058, 0, 116437215277524783, 0, -17624967958799601181845964, 0, 6124496483554336878610574173604367, 0, -798798284321974813391715815474185359381258, 0, 145524373433240498178471282244561013997462983607649], 1]], [[[1, 0, -1963456710, 0, 1786491383741543655, 0, -952189813368729684101162964, 0, 312434958932343616401103499305654095, 0, -60053555133775029535329947571301467588100710, 0, 5349042986438842598594824161669986924013455633256649], 1]], [[[1, 5148, 597505773, 370643378904, 427171395910478127, 2631229045991701932348, 365409786560616989860302899], 2]], [[[1, 26058, 886088883, 13089282520252, 748387392939021783, 18588289592111394816858, 602486784535040403801858901], 2]], [[[1, 0, -7507145634, 0, 24155236685124504999, 0, -42778648868588803994265375484, 0, 44031078607540520553286435819655983551, 0, -24944275529981688609573892755733633012784612034, 0, 6056811824360306133893955506189170373758117309785601849], 1]], [[[1, 14144, 2246377637, 13852014127488, 4052980466105423587, 46042164785483759706944, 5873205959385493353867330551], 2]], [[[1, 0, -2138297622, 0, 9645229369668502143, 0, -18586449024559316458871195956, 0, 41451586872502718876888374824080541807, 0, -39493475612476959537418946015142599562781976022, 0, 79375377473505188618758459764796980252025727125812230449], 1]], [[[1, -110100, 12028730445, -673264081259096, 37013081987633367555, -1042457196697215876830100, 29134419507545592909032289199], 2]], [[[1, 0, -5878219362, 0, 30391064056477835847, 0, -175857560153428632986323559676, 0, 471549001623321500509482923690160786303, 0, -1415166816435976536990313395605862765404915426562, 0, 3735448655171776399347824699993039078892536706537925477849], 1]], [[[1, -175710, 24190100439, -1951044010529988, 135078958928656998111, -5478940008894358120531710, 174120577810999285787632895849], 2]], [[[1, 0, -18122177670, 0, 229144433332479834447, 0, -2179324713417119565558839920660, 0, 16897663368303703845290662038165689109903, 0, -98547376984594215946936555232011112335083019745670, 0, 401007068543157803727680343536350900670553508041935397795649], 1]], [[[1, 248250, 44245156431, 4908590911912836, 465021040772276471931, 27422244263333151960998250, 1160968955369998535166956051501], 2]], [[[1, 0, -69371088690, 0, 2007280502569214653647, 0, -31009911293969874449623502726620, 0, 269761714534086837570926590997705582252703, 0, -1252919026442573083657275462163691555723980374984690, 0, 2427262471189660338642479878258204290900786637085454027093649], 1]], [[[1, 0, -44651077938, 0, 1237237059961488960567, 0, -20624140103878511634372039869724, 0, 243383256179219432478422155726615824825183, 0, -1727855825299380194934201508431389677766931121201938, 0, 7612255042662029206648128983778031607830320888857736765034249], 1]], [[[1, -423534, 99918142131, -15028820097960372, 1537364470118595338919, -100265900655469778058919134, 3642482459687520062956914986149], 2]], [[[1, 0, -70310439534, 0, 2404348334908018746591, 0, -53370443261461536224340192761892, 0, 816172245169255644326402554392809547429759, 0, -8101933655265580461049877595604857895609063116394734, 0, 39115897957341730208009052194412390955771656152457329084502049], 1]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 0, 'label': '12-120e6-1.1-c5e6-0-0', 'leading_term': '5.0481626388680612975111216188237136932936168348887196080756601518487783068738785549771109', 'load_key': 'CMFs-workshop', 'motivic_weight': 5, '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}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5, 5, 5, 5, 5, 5], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/120/6/f/a', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.013671875', 'prec': 37}, 'plot_values': [5.048162638868061, 5.018288440156082, 4.9621839739774, 4.877889257634189, 4.763802229803869, 4.618774430097629, 4.442287783018879, 4.235827356829498, 4.002654428698384, 3.746378977131682, 3.4707883671851607, 3.179775591575019, 2.8771427786484876, 2.566377952763611, 2.2509455737858617, 1.9343396220211642, 1.620046372212909, 1.3115027526762186, 1.0120902418933735, 0.7250340361035497, 0.4533171981058758, 0.19963417035434397, -0.03364637325923903, -0.24451464263861, -0.43134328563253654, -0.5929008919140244, -0.7283663768833575, -0.8373382544930382, -0.9198382171512496, -0.9763106797115689, -1.0076136807550624, -1.0150022116300466, -1.000106164895134, -0.9649015045020871, -0.9116771751393514, -0.8429963101244308, -0.7616518018110948, -0.6706192122540043, -0.5730066969302288, -0.47200222039636236, -0.3708194105477662, -0.27264062684572576, -0.1805610808809613, -0.09753410373888906, -0.02631790577056829, 0.030575890755251394, 0.0709304540654136, 0.09286718071470909, 0.09488446546559672, 0.07589122225531329, 0.03523499820001278, -0.027276207238599928, -0.1113608828694476, -0.21625741252346178, -0.3407245979785491, -0.4830496430862397, -0.6410641878079547, -0.8121686755273184, -0.9933632600332635, -1.181285149115843, -1.3722523036107162, -1.5623148381437029, -1.7473137634811742, -1.9229392883050258, -2.084793708192779, -2.228457459763567, -2.3495582262663675, -2.443847150394328, -2.5072669386966604, -2.5360161578229206, -2.526614124068139, -2.4759632953340422, -2.381414279917846, -2.2408217883894554, -2.0525851045714463, -1.8156856393019023, -1.5297185620697107, -1.1949196551105872, -0.812188423552568, -0.38308525965376244, 0.09017524285757363, 0.6047385382803737, 1.157132207325937, 1.743293558019804, 2.358614413579403, 2.9979959621846795, 3.655908536666384, 4.326455399987455, 5.003444154424469, 5.680468959271292, 6.3509911060775925, 7.00842267348648, 7.646216665748003, 8.257950987774716, 8.83742845839175, 9.378758119146385, 9.87642585355512, 10.325370321203193, 10.721059789760067, 11.0595649546036, 11.337626983885349, 11.552677529845809, 11.70286948841288, 11.787103880597176, 11.805060265942188, 11.757227574880153, 11.644866436947655, 11.469971713235864, 11.235240612039966, 10.944035130572802, 10.600370019990478, 10.208846221058296, 9.774541124457778, 9.302929679007068, 8.799802675343203, 8.271194409662986, 7.723329515602775, 7.162484617526603, 6.594883003465565, 6.026605743621912, 5.4635078633966465, 4.911161503222186, 4.374771955739647, 3.859079749290214, 3.368299698016532, 2.906072285890067, 2.475432570038376, 2.0787898112828462, 1.7178913796932953, 1.3938132635690503, 1.1069688899331909, 0.8571313510021709, 0.64347132687618, 0.46459175412103054, 0.318576578321379, 0.2030531632520945, 0.11526315101410921, 0.052140570001347905, 0.010392381216435083, -0.013419375393717306, -0.02279054480330647, -0.02118815776031972, -0.01196598075303932, 0.0017157798482448923, 0.01696513062437096, 0.031226416608717306, 0.04233976680996042, 0.048590405616679606, 0.048746936260348865, 0.04208785862622991, 0.02841543902696944, 0.008056523288568726, -0.018149770514462336, -0.048877311593804665, -0.08235076836730285, -0.1163949889875943, -0.1484949523676979, -0.17586517149621703, -0.19552725522728437, -0.20439430092488933, -0.19935908610720718, -0.1773835619981037, -0.13558928127398842, -0.07134622385525466, 0.01764157612693655, 0.1332565129486687, 0.2768986513521015, 0.4494251046743517, 0.6511000992908177, 0.8815579751653252, 1.1397831334479636, 1.4241036887184182, 1.7321984046329209, 2.061118497628928, 2.4073242061759403, 2.7667422810362363, 3.1348455685236924, 3.506724109451693, 3.877171165967355, 4.240780046113916, 4.592051190652508, 4.925524583265677, 5.235896394562893, 5.5181138539131265, 5.767478316503235, 5.979746975428733, 6.151248340662926, 6.278979183963708, 6.360668490515311, 6.394815800390784, 6.380724483125252, 6.318533860612909, 6.20925378937957, 6.054724728163756, 5.857591070922146, 5.6212295336329605, 5.349675774057606, 5.04756739921606, 4.720035408775609, 4.372573292940114, 4.010931294439137, 3.6409716338683618, 3.2685444988154346, 2.899370518565818, 2.5388873252277997, 2.1921305656381604, 1.8636334471550389, 1.5573173642335023, 1.276416544451416, 1.0234032748653068, 0.799937558122173, 0.6068482575482209, 0.44413646639561233, 0.31099312889498676, 0.2058423056445576, 0.12640501071420843, 0.06978860196367455, 0.03259437494837272, 0.011039863689035683, 0.0010926689845185643, -0.001384626464020128, -0.0004830485107440193, -9.471584081370649e-05, -0.0037634520533280404, -0.014542056423118505, -0.03486067583415337, -0.06641109980320564, -0.11005046995751419, -0.16572748087274664, -0.23243384753018986, -0.30818437520703773, -0.39002682714637343, -0.4740814415138755, -0.5556102874351365, -0.629116114913333, -0.6884757127112611, -0.7270927935158153, -0.7380704598345512, -0.7144044681266702, -0.6491896283789165, -0.5358409988292634, -0.36832305258571424, -0.1413532153655278, 0.14939223472576468, 0.5070855232341737, 0.9335737029194182, 1.4292254120714925, 1.9928262224095674, 2.621503791722462, 3.3106864981199755, 4.05410244518687, 4.843830118567108, 5.67040628223736, 6.522952813576791, 7.389340967092675, 8.25639987205757, 9.11016798243436, 9.93622804654676, 10.719987615422196, 11.446968280887633, 12.103120888220673, 12.675148680208027, 13.150897348848357, 13.51968933857144, 13.772522168419666, 13.902304503669919, 13.90406213568625, 13.775134910756314, 13.51539972749591, 13.127222621130135, 12.615420792855721, 11.987206017202164, 11.252081253660288, 10.421759537430926, 9.509902892052585, 8.531757849122357, 7.503837290491745, 6.443573471949079, 5.368974258627217, 4.298248025248386, 3.249309694847737, 2.239368929071295, 1.2845473397283687, 0.39952068160742554, -0.4028065841205753, -1.1116260269260412, -1.718472371136941, -2.21739532555483, -2.6050700570871546, -2.8808574233765314, -3.0468046012057224, -3.1075334976681526, -3.0700707814997514, -2.9436189372042296, -2.7392758864781044, -2.4697213944182153, -2.1488130291654937, -1.7911543391871714, -1.411657989824035, -1.0251019747461108, -0.6456899463751004, -0.2866113069733289, 0.0403695598402213, 0.3252737222216698, 0.560215961268553, 0.7396593769736207, 0.8606179998179558, 0.9227565163612721, 0.928415416056132, 0.8825595176569767, 0.7926503986727853, 0.6684575038945214, 0.521772324658504, 0.36604926558927, 0.21600739603642544, 0.08718760556758519, -0.004520746965015987, -0.043380124831790906, -0.014315329470476628, 0.0965960073760158, 0.3016571268282393, 0.611121673076965, 1.032809020583325, 1.5717903598760135, 2.23014717583216, 3.006804666441818, 3.897452402520076, 4.894564956504621, 5.987530799265331, 7.162826329255949, 8.40427546368594, 9.693387811511217, 11.009795612997237, 12.331830879298822, 13.636994439723692, 14.902443112941752, 16.10552588941612, 17.22433170620859, 18.238398062212667, 19.129258983708553, 19.880717045406314, 20.47920637745123, 20.914100864288088, 21.17804073314686, 21.267368029418325, 21.181922856544706, 20.924913261542127, 20.502791923540524, 19.92507162885278, 19.204299025330368, 18.355655900582413, 17.39630000553171, 16.344898543409386, 15.22115246146006, 14.04540402083865, 12.838265101833617, 11.619885694907193, 10.409442102630578, 9.224727520554158, 8.081816178376252, 6.994880685687068, 5.97584699808903, 5.0341595604565725, 4.176711598840829, 3.4078569961778498, 2.7295257025730377, 2.1413658967618625, 1.6408815253653777, 1.2236996589216154, 0.8838833065477717, 0.6142728584177536, 0.40684511466507006, 0.2530451317295225, 0.14412984815710803, 0.07149766033090724, 0.02698339744379862, 0.0031093633283802427, -0.006716481402598839, -0.008055949898248845, -0.005352152259872843, -0.0019009280021758275, 0.00011960278627982857, -0.00043396875163188603, -0.003800705075519597, -0.009484802706632881, -0.016454875093339757, -0.023362625769306426, -0.028769355971514334, -0.03136837661981471, -0.03019157307305199, -0.024790704932773373, -0.015384158352571824, -0.0029613109206632297, 0.010662743644345109, 0.022844891367552685, 0.030163481169944807, 0.02851930545350191, 0.013285268973662447, -0.020498912199216058, -0.07790117251106188, -0.16384881121148612, -0.28286502225423177, -0.4388023548898239, -0.6345875434297461, -0.871999261263637, -1.151475438007014, -1.4719607933112944, -1.830805774900618, -2.223727962929204, -2.64487124092326, -3.08691666536721, -3.541225211961981, -3.9980481822723575, -4.446795607573045, -4.876405481848696, -5.2757398764434145, -5.633939949317756, -5.9407764433857455, -6.187006560077003, -6.364752677801207, -6.467924273678654, -6.492398973696466, -6.436215686730333, -6.299659106683589, -6.085297143552517, -5.798053158917197, -5.445054788315559, -5.03533763774266, -4.579586259956009, -4.089757283658831, -3.5787189593294135, -3.0598675775696504, -2.5465544144994987, -2.0516133966244596, -1.5869266667235136, -1.163000736525306, -0.7886373725153666, -0.47058614524362335, -0.21329610205459185, -0.01879217757245965, 0.11335812624904058, 0.18597797736265168, 0.20412606103937936, 0.1748574578678305, 0.10688386991162195, 0.010166176996741787, -0.10454653782724073, -0.22621906389349564, -0.3440398251053497, -0.447922805781853, -0.528980338560481, -0.5799472182651864, -0.5955493518034386, -0.5727721180483454, -0.5110145503615935, -0.41214281741770303, -0.2804307973044896, -0.12238925157501135, 0.05351775306711862, 0.23727954280195176, 0.4178195681522307, 0.5835400786716631, 0.7229146899012372, 0.8251229359496003, 0.8806755143600381, 0.8819852260043444, 0.8238880446119925, 0.7040846396045554, 0.523491176879199, 0.28647217983164647, 0.0008845690945916375, -0.3220086903906145, -0.6677629411822025, -1.019119783769356, -1.3565193020063195, -1.658760177239078, -1.9037551453214059, -2.0693414862206905, -2.134139706860885, -2.0784496388232814, -1.8851370065663957, -1.5404259959087345, -1.034619666066759, -0.36268780203198625, 0.47527286636987137, 1.47374964085146, 2.6217344844803736, 3.9028203166988864, 5.295508817745378, 6.773681859748987, 8.307324497081055, 9.863410274893138, 11.406777865348008, 12.901174288199359, 14.310429659655748, 15.599610207941842, 16.736363415923012, 17.691791151643677, 18.441312734117147, 18.96550359805424, 19.250874393595357, 19.290530040235517, 19.084327753624446, 18.638633071186764, 17.966104129793504, 17.085317643971283, 16.020385963551117, 14.800207794406404, 13.457142616880338, 12.02589496547402, 10.542397067194306, 9.04270429708787, 7.562020579888787, 6.133355239462344, 4.786408361227799, 3.5467416628910575, 2.435115104792243, 1.4670211478250594, 0.652363915725735, -0.004684117887508977, -0.5055130610053136, -0.8566974898815363, -1.0694463928005078, -1.158925137230429, -1.1434071511411266, -1.0433122476673986, -0.8802117022557687, -0.6758355061151877, -0.45112180290919496, -0.225322689261005, -0.01522085098907254, 0.1655005620711075, 0.3067102253589403, 0.40209980225996983, 0.4492735025468925, 0.4496139382848782, 0.4079779351233772, 0.3322211311422427, 0.2325850381569042, 0.12098111255464553, 0.010182397446915258, -0.08700772207722872, -0.15856159052535365, -0.1939957814188978, -0.18505369595044271, -0.12626934584444743, -0.015360233834934515, 0.14654707093619584, 0.35486631632309995, 0.6016826957381332, 0.8760824385937942, 1.1646542114581555, 1.452113316512517, 1.7220348517566644, 1.9576642478953707, 2.142799154888658, 2.2626837960763475, 2.3047618661801126, 2.2593721100596604, 2.1203319487427588, 1.8853884029095913, 1.556530936819, 1.1399820227347843, 0.6460142412850808, 0.08861216405835388, -0.5150413139426713, -1.1452442499414885, -1.7806402670923787, -2.3991574751281175, -2.978957567316348, -3.499387537778662, -3.9419263096625072, -4.291148040737606, -4.535381474410334, -4.667215631360812, -4.683844407386228, -4.587217149213808, -4.384092219687962, -4.085742502206078, -3.7073160291474574, -3.2671268309059904, -2.7858098070699695, -2.2854031673857254, -1.7883573299617506, -1.3163558276675351, -0.8892439849547146, -0.5240755900089469, -0.23429162951299565, -0.029075474707508524, 0.08715412700398993, 0.1150009386556479, 0.06007976463047844, -0.06723906982138245, -0.2523225175313066, -0.4769832669153273, -0.7203639677955461, -0.959981739186273, -1.1728651539119885, -1.3367383608559038, -1.4312212254511552, -1.438915650568342, -1.3463773848794731, -1.1449397700576092, -0.8313083343055715, -0.40792324594541784, 0.11697205836969511, 0.7295300876612681, 1.4107378421989312, 2.1371215412631592, 2.8816946566697346, 3.615164089931387, 4.307130989146568, 4.927363054732377, 5.447121017727762, 5.840516242152711, 6.085837349767722, 6.166542541959135, 6.071926826036739, 5.797672274853972, 5.346171906342374, 4.726706535395587, 3.955167794870984, 3.053256600365948, 2.0476310958579016, 0.9688875490397267, -0.14959821396240566, -1.2729563657375833, -2.3663804998997175, -3.3965295324932874, -4.33279702736067, -5.1484559718285885, -5.821733714840537, -6.336708495486884, -6.683713510291975, -6.859525274241539, -6.8672900125283585, -6.716230178842368, -6.421273006097865, -6.002075262070703, -5.481901673220085, -4.8864876761031155, -4.24284566247547, -3.5781517738780346, -2.9185407789101916, -2.2878780936660736, -1.7068133856609804, -1.192050215752637, -0.7558480831401532, -0.405753621931545, -0.1445017373930872, 0.02978025449267902, 0.12313327645354616, 0.14513589145011535, 0.10813148322804551, 0.026351300405624445, -0.08502890465043297, -0.21083368453332263, -0.33678056026101805, -0.45027079157330396, -0.5410383619204566, -0.6016269328084659, -0.6276712150085723, -0.6179754004097084, -0.5743807814583706, -0.5014301041473916, -0.4058703037539942, -0.2960357602203573, -0.1811406558118481, -0.07052580182332278, 0.027111867503633324, 0.1044317879414223, 0.15601054454775135, 0.17878395462455662, 0.17232575999186864, 0.13894244989492782, 0.08357022711058647, 0.013426992109820665, -0.06249332052646745, -0.13406359004448287, -0.19078243321296995, -0.22262066549498716, -0.22088697189202774, -0.17902397950396215, -0.0933174018121013, 0.03652739106323226, 0.20698462613216928, 0.4105521321548154, 0.6358609704777572, 0.8680033764780408, 1.089089398852853, 1.2790245016131292, 1.4165825366482554, 1.4805985649324793, 1.45112023310029, 1.3106187228424562, 1.0451628522197138, 0.6455773715950179, 0.10851605791675074, -0.5630391910076175, -1.3594604820107639, -2.2644179860383247, -3.255123465145945, -4.302797227259563, -5.3737102263528085, -6.430534524348553, -7.433786011138699, -8.34342635381853, -9.120596818089641, -9.729439979116208, -10.138794498423811, -10.323756012993636, -10.266937763619927, -9.959489676786887, -9.401917202032486, -8.604214033331973, -7.585620853786292, -6.37407574523918, -5.005254497334335, -3.5213318086003387, -1.9692821103397442, -0.39889005396680227, 1.1392403575492223, 2.5957367882221005, 3.9244110027122825, 5.084245573736312, 6.0410499674058995, 6.768748983563005, 7.250353609086548, 7.478584841444112, 7.45608737078293, 7.195102091657305, 6.716595854020986, 6.049153507542859, 5.227588080857363, 4.291365307328268, 3.28273650868414, 2.2446612777365633, 1.218914910182255, 0.24433581567770216, -0.6447427675459546, -1.4198671201361213, -2.0595106317360794, -2.5496716939609216, -2.8840917003867217, -3.064104527006896, -3.098181989656575, -3.001147770481089, -2.792957056232711, -2.4973589642617067, -2.140457421910302, -1.7492282207918768, -1.3500537354424325, -0.9673441701051165, -0.6223464504764274, -0.33221508644408404, -0.10935507391463584, 0.03897164418145167, 0.11069638846215232, 0.10865552384370729, 0.04007501558884283, -0.08416180606826804, -0.25041778157345823, -0.4433630599296295, -0.6470657847177604, -0.8460237482793658, -1.026100573608121, -1.175327553417331, -1.2846221160525546, -1.3482032646422615, -1.3636819723910922, -1.331996310581144, -1.2571157335275596, -1.145620820335701, -1.006150417228052, -0.8485414984959397, -0.6830412705534294, -0.5195629429677869, -0.366999880175401, -0.2326945156009009, -0.12194532083558575, -0.0377263787556081, 0.01935162101467746, 0.05089411949907118, 0.060398884844670014, 0.052801194554051696, 0.03391748484441825, 0.009809707094244152, -0.013849789935314199, -0.03235849433522835, -0.04245876373074536, -0.04265803954827898, -0.033362496441173256, -0.016800359269975425, 0.0032716511124837675, 0.022069289588514132, 0.03446667281188169, 0.03582013286350849, 0.022874631918572197, -0.005310703972798235, -0.046489300713519435, -0.09448526161444494, -0.13865026718523504, -0.16357600362942465, -0.1491137949892291, -0.07073752897737128, 0.0997215829170423, 0.3930102370220809, 0.8410946719100321, 1.475526079044915, 2.325603690114019, 3.416446200531876, 4.767150327592595, 6.3890469629347715, 8.284109026014063, 10.443653270939329, 12.847469894950152, 15.46382406058451, 18.249738002292247, 21.151731035046392, 24.10699304082041, 27.045088639600106, 29.890711457838197, 32.566974396191256, 34.997676475671724, 37.11043414431165, 38.83934676932967, 40.12788974473514, 40.932753783639676, 41.22502512869092, 40.991117204140586, 40.23387491460868, 38.9723718406994, 37.242219322764875, 35.09438326774719, 32.59200495784853, 29.80796029885185, 26.8222174711198, 23.718609256687557, 20.58200576293003, 17.494025538547316, 14.529723048642929, 11.754951224470322, 9.224217084865339, 6.979005310782651, 5.046481982299745, 3.439004504922979, 2.154609954390698, 1.1781573166732715, 0.4830196111905709, 0.03321448303031619, -0.21397108826470113, -0.3051183972449953, -0.287774856029999, -0.20766157857420026, -0.10612750614537578, -0.0179285465409178, 0.030454192558774972, 0.021892270047003535, -0.05093220719652812, -0.18569572905151752, -0.3712349987278776, -0.5889180077983288, -0.8144467245042574, -1.0199829545764643, -1.17647858394856, -1.256112759543039, -1.2345554851104155, -1.0929433037033212, -0.8195082179465016, -0.4107554730746841, 0.12789012939262281, 0.7821245780178976, 1.5293769462320046, 2.3399027159780985, 3.178327173747013, 4.005621311499946, 4.781584398291337, 5.467131828216302, 6.02652614691153, 6.429413708153169, 6.652617014717296, 6.681928741968782, 6.513011928048079, 6.151393358591674, 5.612181549066767, 4.91916632072497, 4.103666336058446, 3.2030166082049685, 2.2579945700427997, 1.310453810601448, 0.40100492395449605, -0.4331992091084474, -1.160297078574598, -1.7555724022027965, -2.2027487163321777, -2.494599590660342, -2.633011675610911, -2.628443765656215, -2.498918006231064, -2.2685334132016846, -1.9655524036901635, -1.6202550027576994, -1.26269890221141, -0.9205042869237723, -0.61681058142135, -0.3685551257193298, -0.18519117568388377, -0.06792332945205606, -0.009515634335927857, 0.00531232259395615, -0.0010770661685872134, -0.0007168890594690385, 0.03805728338695658, 0.1483864678239363, 0.3625313558587315, 0.7095018433578144, 1.212795217443241, 1.888388002570567, 2.74311546921199, 3.7737639849678297, 4.966749236853309, 6.298157058194366, 7.73444527922245, 9.233716724369698, 10.747777615620496, 12.2250067470562, 13.612563514767292, 14.858826146806443, 15.915918321713661, 16.74221117215147, 17.30539311067645, 17.58381480292925, 17.567115685727604, 17.256585760065953, 16.66501322208043, 15.816529489581443, 14.745616181049243, 13.49432247833551, 12.110063915832933, 10.643172153949335, 9.144525859818398, 7.663532109740848, 6.245240657866052, 4.928197104889583, 3.743026936798432, 2.7114875452358946, 1.84613795218668, 1.150335032938743, 0.6187382093424891, 0.2384934074241628, -0.00921456149628821, -0.14736436377594894, -0.201193906622471, -0.1962515353117259, -0.1565411603536186, -0.10291275033587463, -0.05179239840693369, -0.014333301702082725, 0.00400276636863146, 0.0033956946049884577, -0.010833280208715022, -0.029113352885729388, -0.03883353397134694, -0.025765315667225598, 0.024413112479403167, 0.12460420999375567, 0.28489776518245624, 0.5114040978118222, 0.8054522425191921, 1.1631510083860421, 1.5753240288665862, 2.027850136248658, 2.5023825833574196, 2.9775077169771684, 3.4302852189552264, 3.837600460964176, 4.177633076578139, 4.4313036225353155, 4.583612039195429, 4.624952171646753, 4.551794499604591, 4.366748223966856, 4.078397694107246, 3.7008047467950687, 3.252773417550246, 2.7566594563301257, 2.236824276695409, 1.7179611917090227, 1.2235279163700636, 0.7743215956864298, 0.387221914633172, 0.07413860160442773, -0.1586170173136905, -0.31056657946998434, -0.3868503896940459, -0.39764174587399, -0.35718468774778317, -0.28253929065120376, -0.19217598066961494, -0.10444132163882278, -0.036065093789820216, -0.000808385512154883, -0.008362417252505904, -0.06358656754503574, -0.16610646353582378, -0.31032250577781234, -0.485883350104528, -0.6785510594797127, -0.8713553293484233, -1.045972837512267, -1.184225129104409, -1.2696999950839096, -1.2892942130650344, -1.2343527865975563, -1.1015468908788475, -0.8933751755357751, -0.618255466821627, -0.2902406484387748, 0.07194275145073116, 0.4462048597450734, 0.8086502145315867, 1.1353360515165245, 1.4041154028376357, 1.596485845531, 1.6992293529573619, 1.705689411214091, 1.6166302807863517, 1.4406143319125975, 1.1938467742279535, 0.8993773353299428, 0.585801993410926, 0.2855272365003606, 0.0326800917149513, -0.13923753577286319, -0.19975755730218897, -0.1237192915042225, 0.10669868905927951, 0.5003253270565579, 1.0558649179725377, 1.7614736344472766, 2.5949943543193412, 3.524802545860834, 4.511261625253611, 5.508762407366955, 6.468561714603779, 7.341610210754574, 8.081341672367168, 8.6464175744524, 9.00325422023107, 9.128520200215343, 9.011037676084086, 8.652159874737897, 8.0659008218501, 7.27822818848503, 6.325799759586187, 5.254357778890928, 4.1157069686731305, 2.9645942941984003, 1.8556432446656093, 0.8402294983417454, -0.036339268993385285, -0.7374617816487591, -1.2373369503608482, -1.5222096321242111, -1.590904093595906, -1.4545841356919764, -1.1357708468527954, -0.6665856390349743, -0.08646497056354593, 0.5604910187757476, 1.2284062431401197, 1.8726873865293057, 2.452871419098863, 2.9349535288109228, 3.29324643054683, 3.511645298227999, 3.584362692409981, 3.515958715009084, 3.3202016238760343, 3.0185125634317487, 2.6379844381623005, 2.2090983997865554, 1.7633883527679226, 1.3307532432447147, 0.9370544718467271, 0.6022386521672314, 0.33897548162396934, 0.1519140792384371, 0.03755470144362466, -0.015210627850427948, -0.023859470407453363, -0.010472583876829616, 0.00042328362085907465, -0.015755586910872216, -0.08121690532836655, -0.21351271300490915, -0.42358551508071013, -0.7142938710652387, -1.0795731492373073, -1.5043337309760643, -1.9650845983486829, -2.431185347977028, -2.8667101269564683, -3.2328667520598047, -3.4908949476400384, -3.604882851516598, -3.5445932760313785, -3.2878843337150427, -2.8227570447937063, -2.1489354042086894, -1.2784889599589964, -0.23560791826444324, 0.9443416921534508, 2.216576126777023, 3.529291683663622, 4.8267706005384925, 6.052534358166081, 7.152615996322569, 8.078923194712713, 8.792035260665948, 9.263939689700626, 9.479474945644057, 9.43679291849671, 9.147342690300643, 8.63521250018916, 7.935422746899166, 7.091529117697296, 6.152180347401864, 5.167885865494562, 4.187859474420232, 3.2571144085167445, 2.413633933092094, 1.6859604518543974, 1.091805866385953, 0.637602475750075, 0.31891315150867305, 0.12164542055415746, 0.023923316409420855, -0.0013297862193840625, 0.016621844875183207, 0.04948927954052778, 0.07303261487819429, 0.06980402397510999, 0.03135196488031951, -0.04031622748585349, -0.13214711871324492, -0.2204028275185023, -0.27202793960746846, -0.24687179191409203, -0.10060414189611497, 0.21178674536196554, 0.7321576339927429, 1.4953144307049853, 2.5254943655136017, 3.8333670307772643, 5.41368659926359, 7.243834123128721, 9.283460398617379, 11.476045691506906, 13.751091940009813, 16.02683106376713, 18.213985101267202, 20.220170599647084, 21.95575602118846, 23.34005267240364, 24.304648772719073, 24.797241807025923, 24.784716881254965, 24.255713842301247, 23.223803135243223, 21.725587135344426, 19.81802950338559, 17.575665655552807, 15.086748170629651, 12.449895040171942, 9.768820941503398, 7.145332313443312, 4.674156403867954, 2.438360628912462, 0.5056599520072973, -1.0741465518452253, -2.2719498925787667, -3.080001577900609, -3.511101691243999, -3.5966659555647538, -3.3836685612847686, -2.9310567538325905, -2.3055726399539407, -1.5771621964344336, -0.8144571197412621, -0.08053761551568127, 0.570764829662061, 1.0975104146092196, 1.471438044771671, 1.6787539055692209, 1.7199149194761627, 1.6085486472157393, 1.369259778603926, 1.0348291771133953, 0.6431071923952065, 0.23373077952848453, -0.15508546226951972, -0.48949674417728994, -0.74247201325978, -0.895511219875172, -0.9396229443929065, -0.8755183592852904, -0.712938974964348, -0.4693311146930867, -0.16802537837794015, 0.16394851369918487, 0.49823240967991506, 0.8076987642878589, 1.0687438145353079, 1.262879443634802, 1.3779515464351204, 1.4088037494207537, 1.3574241087192715, 1.2326011605877754, 1.0485424003383974, 0.8232865532734722, 0.5769475473345352, 0.32988013158246565, 0.10092612968450553, -0.09428375529767635, -0.24459155469513066, -0.3440084799603817, -0.3919009892714054, -0.3926957809564211, -0.35513572194266174, -0.2910012779448184, -0.21358600529818791, -0.13607620960392527, -0.0699847135366358, -0.023789117971424963, -0.0018544898933275347, -0.0038523754197929733, -0.02474592321836664, -0.05533494138199352, -0.08332806865371443, -0.09487918446647055, -0.07647824518878686, -0.01701314670963101, 0.09018518126491473, 0.24552257349944415, 0.4417032800191971, 0.6628581478241381, 0.8843515044672128, 1.0733467003535127, 1.1901715921048037, 1.1905311070942048, 1.0282572072486447, 0.6584164382933958, 0.040747952157757346, -0.8568388430777285, -2.0549546401302163, -3.5600365489375547, -5.362530103711954, -7.435775701132312, -9.735827660197577, -12.202332997936692, -14.761075134145763, -17.327643495203027, -19.81089113154514, -22.117167746092274, -24.154961151070182, -25.84020961940869, -27.102140665375302, -27.886621849990266, -28.15853035949555, -27.903585896996553, -27.1294217015954, -25.866736844649242, -24.16698546163306, -22.098978094088462, -19.74479566492766, -17.195405105716866, -14.546515472233466, -11.89372384185957, -9.326723420818555, -6.925153812132986, -4.755023795456985, -2.866255265469127, -1.2911871876372614, -0.04390633490030839, 0.8789375970264448, 1.4962885153826704, 1.8400596652579377, 1.9520765543100367, 1.8805183203444933, 1.67597665074226, 1.3879051509086167, 1.0615315097231801, 0.7353985779765008, 0.4396614723322292, 0.194983504619623, 0.012445800115667231, -0.10571618995159691, -0.16472212006020384, -0.17537190316709964, -0.15188723269463167, -0.10962692944788319, -0.06291336954132956, -0.023177559332105628, 0.0024222145492981996, 0.011804281579395823, 0.008149729663239918, -0.0005378704699335442, -0.002437039067661872, 0.01663211070751045, 0.07146337598394084, 0.1756210689472516, 0.3396500146125486, 0.5695131057959504, 0.865409126857931, 1.2211776630479827, 1.6244366295225536, 2.057091628436663, 2.4964071189921926, 2.91656196972642, 3.2906099383384007, 3.5929513296365596, 3.801469957734411, 3.899177646997453, 3.875672123556781, 3.7281788187387344, 3.462250509104316, 3.0916061751549506, 2.637021995623889, 2.1247081107138692, 1.5843924759322532, 1.047190921035842, 0.5433133271274867, 0.09960345475147171, -0.2624855955149074, -0.5284494340876569, -0.691675637759962, -0.7538170078592791, -0.7244352864806323, -0.6199044529110322, -0.4618015720978379, -0.27483290313059083, -0.084547115454985, 0.08503475324565227, 0.21366797687244662, 0.2867101666947384, 0.29643370796875546, 0.2426853221051277, 0.13287868028692873, -0.018811091715083755, -0.19292949967743234, -0.366717692636851, -0.5164674404752765, -0.6200357634310124, -0.6593008004967505, -0.6222839949704955, -0.5047330838803457, -0.3110409681178631, -0.054409031169101216, 0.24388728529094572, 0.556105752787387, 0.8503151796956939, 1.0931954171270166, 1.2531694347523505, 1.3036967578400414, 1.2262713604516868, 1.012797934006193, 0.6673076126776138, 0.20678551248634022, -0.3389912867274892, -0.9287168531562364, -1.512113896150154, -2.033261978944797, -2.4345792137705913, -2.66125711313007, -2.6660586950971874, -2.413337611992235, -1.8818930565002476, -1.0672380980864344, 0.01710919394384578, 1.338828870127128, 2.8454534750546214, 4.466402160918508, 6.116928514094979, 7.703352186625107, 9.131133836946612, 10.32826762043097, 11.249092623267694, 11.86810047942436, 12.177882762055903], 'positive_zeros': ['0.29872826552891485273566752320830', '0.60743233267377570796642129166222', '0.69186951617261069637196147053688', '1.09123725135891072925621466639365', '1.89160739532275905641488405070636', '1.95349599294604227904756624031955', '2.06896460319291925866186484653487', '2.23976773708647889466540825461824', '2.99732660512568948067387872654823', '3.02815565891587064538755136237677', '3.03366645458857037602418252664801', '3.31562636061074473763893553931205', '3.87576034416872768577615001423058', '4.12712658511643339861966407714855', '4.31942420039526035046985094876240', '4.35024463092622852528000318585535', '5.14358375231149841087908823931498', '5.20734963208991396037238028837053', '5.21893632173749865458845505284005', '5.36237023642681970124116237716266', '5.43417153306926416711772439642867', '6.00356548035327835097324882155614', '6.08526685673050354820450443269741', '6.25766003568171610653178322454452', '6.42582129617523744449456580981355', '6.60976586868613646525143191434463', '7.09559234067085158623505792359982', '7.24715388602837838735217474846605', '7.38413315978695934683569553449108', '7.46634730290326032756194933833185', '7.71300123742824111072915362597789', '8.041670081298368417734364455623647', '8.087406235025469971395569535223588', '8.268639489663449933290232085971696', '8.543106088518173988099109871726610', '8.883833944951712736085277957549624', '8.944912427453920928395842482151528', '9.142431891011290422468107633440156', '9.244631709354459076446880382114398', '9.348139398829081648042139058328984', '9.531703581461590169460001768472941', '9.847250381055809077574625642855628', '10.09345362339370182644521114674671', '10.33157677472105715071587134615577', '10.38200234300164772813467569994899', '10.67233774509026095128536039140742', '10.75156312741107281358592450088645', '10.83960026411510810247789789955427', '10.90804041017410058760418992822781', '10.99893408258841101401546661426615', '11.60879297662174847417826431361545', '11.69315568272075917338827152820923', '11.72237937389392502573200048320228', '11.89155120871226370383948589807195', '12.17435327253941132249636061630383', '12.41912208848734165294340634823100', '12.43964842799626819281113317452467', '12.45573030489488821859504361216476', '12.98762338516399070541157262511776', '13.09299064351571710865352609578643'], 'prelabel': '12-120e6-1.1-c5e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.387032981134023, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c5e6-0', 'trace_hash': 2180489962256303769, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.29872826552891485273566752321', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.60743233267377570796642129166', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.69186951617261069637196147054', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 50821887.74931882, 'bad_primes': [2, 3, 5], 'central_character': '1.1', 'conductor': 2985984000000, 'conductor_radical': 30, 'degree': 12, 'dirichlet_coefficients': [1, 0, 0, 0, 50, 0, 0, 0, -243, 0, -664, 0, 0, 0, 0, 0, 0, 0, 288, 0, 0, 0, 0, 0, 3125, 0, 0, 0, -1892, 0, -10248, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1324, 0, 0, 0, -12150, 0, 0, 0, 64626, 0, 0, 0, 0, 0, -33200, 0, 0, 0, -10296, 0, -52116, 0, 0, 0, 0, 0, 0, 0, 0, 0, -28288, 0, 0, 0, 0, 0, 0, 0, 220200, 0, 39366, 0, 0, 0, 0, 0, 0, 0, 351420, 0, 0, 0, 0, 0, 14400, 0, 0, 0, 161352, 0], 'euler11': [1, 664, 927242, 486628904, 369966973095, 148891760318192, 79421624285476108, 23979166891005139792, 9595990469511758110095, 2032769698418744566576504, 623802050801256808051553642, 71942447464098791435775286664, 17449402268886407318558803753801], 'euler13': [1, 0, -2165574, 0, 1976112655671, 0, -972719104225889812, 0, 272423910434526297125679, 0, -41156655421823712363882036774, 0, 2619995643649944960380551432833049], 'euler17': [1, 0, -6393390, 0, 19617942041247, 0, -35338776492878157220, 0, 39549651494515956369819903, 0, -25984216432946523688997171817390, 0, 8193465725814765556554001028792218849], 'euler19': [1, -288, 3843858, 3191500576, 12581641677063, 4024206089052864, 52212874685887107612, 9964332672897707497536, 77138878753983745146518463, 48450575660174587979142320224, 144490520194575691769195473748658, -26806030758217753786543567760783712, 230466617897195215045509519405933293401], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, 0, -12847386, 0, 119828345726079, 0, -792017135162474667756, 0, 4964070307934420916400052271, 0, -22048116401306325897871650270794586, 0, 71094348791151363024389554286420996798449], 'euler29': [1, 1892, 73729778, 221122236196, 2964156539596023, 7752710730372195304, 78209112393556434399292, 159017004944562923337444296, 1247042096842140531477624700623, 1908105512426271167652296992390004, 13049770806825416556907599088131560978, 6868645137902773390761209451789433777108, 74462898441675122902293018227199467668020601], 'euler3': [1, 0, 243, 0, 19683, 0, 531441, 0, 0, 0, 0, 0, 0], 'euler31': [1, 10248, 148847370, 1071971809752, 9540988611950607, 53587080545652756816, 354342595920577956102476, 1534152620590655168451543216, 7820064152116406303659369296207, 25154099363702568241233624570682152, 99994253405629603494678071193266639370, 197097657436816560205164793859373139456248, 550618520345910837374536871905139185678862401], 'euler37': [1, 0, -290752854, 0, 38769784471186119, 0, -3247030100434017898649524, 0, 186427779730153771798232916638031, 0, -6722928117650116550731034251080698280054, 0, 111186413610993811950185637819224232932533011049], 'euler41': [1, 1324, 287461202, 1075890738524, 54435387698127135, 166919514855955817432, 8090401066538794557515068, 19338660863974103231521095832, 730667663488021665691959123501135, 1673115874593673703756481030983164924, 51791247450327874012898222191662665350802, 27636586655722684142621449283999820233645324, 2418330769289520463963038742566759257517431737201], 'euler43': [1, 0, -502572210, 0, 127464803683947447, 0, -22067384193417129455383580, 0, 2754703350381879235844363288862303, 0, -234729450434017657910032766127984084312210, 0, 10093776109231555797740541116805209814919811290249], 'euler47': [1, 0, -288722058, 0, 116437215277524783, 0, -17624967958799601181845964, 0, 6124496483554336878610574173604367, 0, -798798284321974813391715815474185359381258, 0, 145524373433240498178471282244561013997462983607649], 'euler5': [1, -50, -625, 283500, -1953125, -488281250, 30517578125, 0, 0, 0, 0, 0, 0], 'euler53': [1, 0, -1963456710, 0, 1786491383741543655, 0, -952189813368729684101162964, 0, 312434958932343616401103499305654095, 0, -60053555133775029535329947571301467588100710, 0, 5349042986438842598594824161669986924013455633256649], 'euler59': [1, 10296, 1221513450, 6893206196616, 1215172084818479367, 10103537901516419485872, 1268522834127048461073756364, 7223264751661557237926980003728, 621094810693992806494453818584473167, 2518845005023774992609249183577508789784, 319108583501367661231750384779464117437173450, 1922953688175847336543867180052165925029772553704, 133524312114275664899926313757566191470823300027804201], 'euler61': [1, 52116, 2451197130, 72357973266932, 2964089342279684487, 99376072009915887993576, 3671325684468772606291509612, 83932662827484594320504601362376, 2114412121850708760924858179201910687, 43594722649066273461711408776005473161732, 1247311537876982874821482091141970259223873130, 22398397652714704004624434344351993662393704306116, 362990325539372200679554918670984996723331903112927801], 'euler67': [1, 0, -7507145634, 0, 24155236685124504999, 0, -42778648868588803994265375484, 0, 44031078607540520553286435819655983551, 0, -24944275529981688609573892755733633012784612034, 0, 6056811824360306133893955506189170373758117309785601849], 'euler7': [1, 0, -64626, 0, 2028003087, 0, -41058323262556, 0, 572860676973093663, 0, -5156655001749473176626, 0, 22539340290692258087863249], 'euler71': [1, 28288, 4692808010, 91249558850432, 13544019195862931487, 268968750522951962214656, 31449780336124998500740130956, 485281314195306529390725317568256, 44089081142086844779033770331472275887, 535927452831654510604455387334748113148032, 49727858991740377517362774544782884694364032010, 540830233202224245462032061776797132102814676092288, 34494548241361273407325608100987789752280917290697963601], 'euler73': [1, 0, -2138297622, 0, 9645229369668502143, 0, -18586449024559316458871195956, 0, 41451586872502718876888374824080541807, 0, -39493475612476959537418946015142599562781976022, 0, 79375377473505188618758459764796980252025727125812230449], 'euler79': [1, -220200, 36179470890, -3995254606507192, 366969270786989572335, -26432219350603783266026640, 1631543209177325947238142759564, -81333429692546995812336391916469360, 3474566369651468344768724872104381784335, -116399423745434526323683256783746705417419208, 3243426322735597815484837626072566527702313086890, -60742770574473318937993308150149117007907653176179800, 848814400041653188432880077486808325583024422374372061601], 'euler83': [1, 0, -5878219362, 0, 30391064056477835847, 0, -175857560153428632986323559676, 0, 471549001623321500509482923690160786303, 0, -1415166816435976536990313395605862765404915426562, 0, 3735448655171776399347824699993039078892536706537925477849], 'euler89': [1, -351420, 79254204978, -12402973117333356, 1540954763286670371903, -152819228915756925200160504, 12615370151932131067487813141500, -853351659215926483151142478677802296, 48049619853552292297792034530112249762703, -2159612845764374987866974456193030042961639244, 77058836378595304165427726980095566011465621006578, -1907992400280974404156456707340479466039619461863743580, 30317975617236256833580920126868226118402514553481681430801], 'euler97': [1, 0, -18122177670, 0, 229144433332479834447, 0, -2179324713417119565558839920660, 0, 16897663368303703845290662038165689109903, 0, -98547376984594215946936555232011112335083019745670, 0, 401007068543157803727680343536350900670553508041935397795649], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, 243, 0, 19683, 0, 531441, 0, 0, 0, 0, 0, 0], [1, -50, -625, 283500, -1953125, -488281250, 30517578125, 0, 0, 0, 0, 0, 0], [1, 0, -64626, 0, 2028003087, 0, -41058323262556, 0, 572860676973093663, 0, -5156655001749473176626, 0, 22539340290692258087863249], [1, 664, 927242, 486628904, 369966973095, 148891760318192, 79421624285476108, 23979166891005139792, 9595990469511758110095, 2032769698418744566576504, 623802050801256808051553642, 71942447464098791435775286664, 17449402268886407318558803753801], [1, 0, -2165574, 0, 1976112655671, 0, -972719104225889812, 0, 272423910434526297125679, 0, -41156655421823712363882036774, 0, 2619995643649944960380551432833049], [1, 0, -6393390, 0, 19617942041247, 0, -35338776492878157220, 0, 39549651494515956369819903, 0, -25984216432946523688997171817390, 0, 8193465725814765556554001028792218849], [1, -288, 3843858, 3191500576, 12581641677063, 4024206089052864, 52212874685887107612, 9964332672897707497536, 77138878753983745146518463, 48450575660174587979142320224, 144490520194575691769195473748658, -26806030758217753786543567760783712, 230466617897195215045509519405933293401], [1, 0, -12847386, 0, 119828345726079, 0, -792017135162474667756, 0, 4964070307934420916400052271, 0, -22048116401306325897871650270794586, 0, 71094348791151363024389554286420996798449], [1, 1892, 73729778, 221122236196, 2964156539596023, 7752710730372195304, 78209112393556434399292, 159017004944562923337444296, 1247042096842140531477624700623, 1908105512426271167652296992390004, 13049770806825416556907599088131560978, 6868645137902773390761209451789433777108, 74462898441675122902293018227199467668020601], [1, 10248, 148847370, 1071971809752, 9540988611950607, 53587080545652756816, 354342595920577956102476, 1534152620590655168451543216, 7820064152116406303659369296207, 25154099363702568241233624570682152, 99994253405629603494678071193266639370, 197097657436816560205164793859373139456248, 550618520345910837374536871905139185678862401], [1, 0, -290752854, 0, 38769784471186119, 0, -3247030100434017898649524, 0, 186427779730153771798232916638031, 0, -6722928117650116550731034251080698280054, 0, 111186413610993811950185637819224232932533011049], [1, 1324, 287461202, 1075890738524, 54435387698127135, 166919514855955817432, 8090401066538794557515068, 19338660863974103231521095832, 730667663488021665691959123501135, 1673115874593673703756481030983164924, 51791247450327874012898222191662665350802, 27636586655722684142621449283999820233645324, 2418330769289520463963038742566759257517431737201], [1, 0, -502572210, 0, 127464803683947447, 0, -22067384193417129455383580, 0, 2754703350381879235844363288862303, 0, -234729450434017657910032766127984084312210, 0, 10093776109231555797740541116805209814919811290249], [1, 0, -288722058, 0, 116437215277524783, 0, -17624967958799601181845964, 0, 6124496483554336878610574173604367, 0, -798798284321974813391715815474185359381258, 0, 145524373433240498178471282244561013997462983607649], [1, 0, -1963456710, 0, 1786491383741543655, 0, -952189813368729684101162964, 0, 312434958932343616401103499305654095, 0, -60053555133775029535329947571301467588100710, 0, 5349042986438842598594824161669986924013455633256649], [1, 10296, 1221513450, 6893206196616, 1215172084818479367, 10103537901516419485872, 1268522834127048461073756364, 7223264751661557237926980003728, 621094810693992806494453818584473167, 2518845005023774992609249183577508789784, 319108583501367661231750384779464117437173450, 1922953688175847336543867180052165925029772553704, 133524312114275664899926313757566191470823300027804201], [1, 52116, 2451197130, 72357973266932, 2964089342279684487, 99376072009915887993576, 3671325684468772606291509612, 83932662827484594320504601362376, 2114412121850708760924858179201910687, 43594722649066273461711408776005473161732, 1247311537876982874821482091141970259223873130, 22398397652714704004624434344351993662393704306116, 362990325539372200679554918670984996723331903112927801], [1, 0, -7507145634, 0, 24155236685124504999, 0, -42778648868588803994265375484, 0, 44031078607540520553286435819655983551, 0, -24944275529981688609573892755733633012784612034, 0, 6056811824360306133893955506189170373758117309785601849], [1, 28288, 4692808010, 91249558850432, 13544019195862931487, 268968750522951962214656, 31449780336124998500740130956, 485281314195306529390725317568256, 44089081142086844779033770331472275887, 535927452831654510604455387334748113148032, 49727858991740377517362774544782884694364032010, 540830233202224245462032061776797132102814676092288, 34494548241361273407325608100987789752280917290697963601], [1, 0, -2138297622, 0, 9645229369668502143, 0, -18586449024559316458871195956, 0, 41451586872502718876888374824080541807, 0, -39493475612476959537418946015142599562781976022, 0, 79375377473505188618758459764796980252025727125812230449], [1, -220200, 36179470890, -3995254606507192, 366969270786989572335, -26432219350603783266026640, 1631543209177325947238142759564, -81333429692546995812336391916469360, 3474566369651468344768724872104381784335, -116399423745434526323683256783746705417419208, 3243426322735597815484837626072566527702313086890, -60742770574473318937993308150149117007907653176179800, 848814400041653188432880077486808325583024422374372061601], [1, 0, -5878219362, 0, 30391064056477835847, 0, -175857560153428632986323559676, 0, 471549001623321500509482923690160786303, 0, -1415166816435976536990313395605862765404915426562, 0, 3735448655171776399347824699993039078892536706537925477849], [1, -351420, 79254204978, -12402973117333356, 1540954763286670371903, -152819228915756925200160504, 12615370151932131067487813141500, -853351659215926483151142478677802296, 48049619853552292297792034530112249762703, -2159612845764374987866974456193030042961639244, 77058836378595304165427726980095566011465621006578, -1907992400280974404156456707340479466039619461863743580, 30317975617236256833580920126868226118402514553481681430801], [1, 0, -18122177670, 0, 229144433332479834447, 0, -2179324713417119565558839920660, 0, 16897663368303703845290662038165689109903, 0, -98547376984594215946936555232011112335083019745670, 0, 401007068543157803727680343536350900670553508041935397795649]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/120/6/f/a'], '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': '12-120e6-1.1-c5e6-0-0', 'motivic_weight': 5, '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}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [5, 5, 5, 5, 5, 5], 'order_of_vanishing': 0, 'prelabel': '12-120e6-1.1-c5e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 4.387032981134023, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c5e6-0', 'trace_hash': 2180489962256303769, 'z1': {'__RealLiteral__': 0, 'data': '0.29872826552891485273566752321', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '378683065102866803671093049240,770011961111945298204940875154,877048807455824618412223339527,1383307556676526426056629747909,2476350368001491483956297949134,2622724221088464567098852169890', 'Lhash_array': ['378683065102866803671093049240', '770011961111945298204940875154', '877048807455824618412223339527', '1383307556676526426056629747909', '2476350368001491483956297949134', '2622724221088464567098852169890'], 'label': '12-120e6-1.1-c5e6-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/120/6/f/a'}