Lfunction data - 32-8001e16-1.1-c1e16-0-2

Formats: - HTML - YAML - JSON - 2025-09-10T14:02:23.269588

• lfunc_lfunctions •

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

  
  {'Lhash': '1066431153624676436857897691903,1071482530501859812813511610795,1114825968197399805774226587029,1250994324550696608999223176746,1350129982898641701194226605716,1386881711690821173082304859301,1403104913593685131107766090532,1417822664905564827150396438883,1557597895449348864200310219434,1575455231306280425317993386170,1583514365172011409277802606898,1761420652683686481262129510499,1789395591546813398773235927688,2046736838312547510564942078505,2211553485315499991175650286382,2234187840931969738269175335503', 'a10': -5, 'a2': -5, 'a3': 0, 'a4': 6, 'a5': 1, 'a6': 0, 'a7': -16, 'a8': 13, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.704457055859471e+28, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [7, [1, 16, 120, 560, 1820, 4368, 8008, 11440, 12870, 11440, 8008, 4368, 1820, 560, 120, 16, 1]], [127, [1, -16, 120, -560, 1820, -4368, 8008, -11440, 12870, -11440, 8008, -4368, 1820, -560, 120, -16, 1]]], 'bad_primes': [3, 7, 127], 'central_character': '8001.1', 'coefficient_field': '1.1.1.1', 'conductor': 282038454737647007234373878049347083438272290079006727680128001, 'conductor_radical': 2667, 'degree': 32, 'euler_factors': [[1, 5, 19, 52, 125, 264, 529, 1006, 1858, 3287, 5617, 9208, 14687, 22750, 34532, 50960, 73260, 101920, 138128, 182000, 234992, 294656, 359488, 420736, 475648, 515072, 541696, 540672, 512000, 425984, 311296, 163840, 65536], [1], [1, -1, 24, -19, 329, -170, 3169, -250, 23164, 13164, 133265, 205344, 624119, 1857497, 2603502, 12171723, 11656934, 60858615, 65087550, 232187125, 390074375, 641700000, 2082265625, 1028437500, 9048437500, -488281250, 30947265625, -8300781250, 80322265625, -23193359375, 146484375000, -30517578125, 152587890625], [1, 16, 120, 560, 1820, 4368, 8008, 11440, 12870, 11440, 8008, 4368, 1820, 560, 120, 16, 1], [1, 11, 127, 927, 6546, 37443, 205797, 996578, 4658508, 19883514, 82587628, 319384657, 1213890104, 4356733405, 15506991000, 52671594431, 178444424018, 579387538741, 1876345911000, 5798812162055, 17772565012664, 51437218394507, 146309020847308, 387473437398894, 998592562009548, 2349878794001398, 5337844170611997, 10682924882687673, 20544152154015666, 32002554157424037, 48228228865071607, 45949729863572161, 45949729863572161], [1, -18, 219, -1948, 14614, -94646, 555983, -2985822, 14990448, -70533970, 315528362, -1344918094, 5522268604, -21859541176, 84090414036, -314220696382, 1147549597242, -4084869052966, 14211279972084, -48025411963672, 157721513598844, -499358673875542, 1522995137456858, -4425902015622490, 12228168955153008, -31663147526889606, 76646977873682567, -169620812654025902, 340478215979937334, -590000707641708844, 862285428468144291, -921346074253633626, 665416609183179841], [1, -5, 158, -540, 11588, -27066, 558089, -870456, 20459225, -20581469, 610166673, -380514409, 15256129494, -5823688053, 325009231345, -84738254968, 5951336176930, -1440550334456, 93927667858705, -28611779404389, 1274207191468374, -540276047219513, 14727940171037937, -8445372677850637, 142718591030843225, -103225528624072632, 1125104019907681961, -927603145462394778, 6751426485018470468, -5348472137769205980, 26603696596385346782, -14312115257549078965, 48661191875666868481], [1, 11, 181, 1462, 14335, 95375, 719296, 4211650, 26971845, 143986816, 822044549, 4072545605, 21330650499, 99112960004, 484717258250, 2123022393713, 9768224694024, 40337425480547, 174982930228250, 679815792667436, 2779831703680179, 10084026099994895, 38673810028952669, 128705745610993024, 458078029889580645, 1359047642350925350, 4410051434971228096, 11110258442417637125, 31727869364813417935, 61481461821819820258, 144620210126702025901, 166992397328622781289, 288441413567621167681], [1, 13, 208, 2018, 20375, 160550, 1275907, 8665917, 58792152, 357162729, 2165764215, 12076345886, 67338196417, 351022119450, 1831885262566, 9017382569929, 44472265582174, 207399799108367, 969067303897414, 4270886127348150, 18843988223529697, 77727504308934898, 320610830931912135, 1216076748419164863, 4604071349910314712, 15608639468567456571, 52856375643073254643, 152973606633080979850, 446510472802414040375, 1017145378387791178894, 2411309955504059960272, 3466258061037086192891, 6132610415680998648961], [1, 24, 472, 6622, 82320, 873128, 8519727, 75217422, 623444003, 4802217916, 35136436698, 242281577588, 1597747487582, 10006074679634, 60158248780719, 344816413108922, 1900626864033788, 9999675980158738, 50593087224584679, 244038155361593626, 1130056440764484542, 4969473537862528612, 20899971964810634058, 82837665059863752044, 311875626182796922883, 1091190120882540389718, 3584310774643021565127, 10652606690711199063112, 29126032953474211455120, 67945883337211863695558, 140447485822977346763032, 207100529942356426582776, 250246473680347348787521], [1, 42, 1103, 21297, 334685, 4460298, 52049742, 541781390, 5109757813, 44140935934, 352708311097, 2626670113330, 18362034468729, 121180561220341, 758925862323514, 4526798708422582, 25783901132438856, 140330759961100042, 729327753692896954, 3610090099315178731, 16957724434595074809, 75199335301711682830, 313029924417880648057, 1214432536850515364674, 4358066642201825276533, 14324495245283137712690, 42661440873252651003342, 113329378684080674899638, 263618918792270776760285, 520020483496687072060527, 834909160548538341314063, 985541003657476809057942, 727423121747185263828481], [1, -40, 1093, -21915, 365384, -5189918, 65263975, -735690707, 7568509040, -71598368286, 629373118507, -5166707785384, 39884876555089, -290489859017229, 2005230244594602, -13140503504719049, 81949219635694490, -486198629674604813, 2745160204850010138, -14714182828799700537, 74750680129362155329, -358279962501233324488, 1614799231268096551363, -6796967501049835804038, 26584232499815351945840, -95611644232790233249439, 313827330266869186689775, -923377867790413627716134, 2405305335701855451112904, -5337819548695421807775255, 9850182996522544071560077, -13337850718072612283539720, 12337511914217166362274241], [1, 9, 262, 2416, 37769, 315207, 3782416, 28401838, 290262313, 2011916927, 18444064407, 119441768717, 1012122769428, 6182374690503, 49052876571800, 283552719845861, 2125239007937044, 11625661513680301, 82457885517195800, 426095446044157263, 2860017049061634708, 13838069564272264117, 87611228560967850087, 391829420226777883687, 2317722866136716416873, 9298248664783908500318, 50770081337269403980816, 173467563100183522342287, 852200465154530482093289, 2235049095193072928439536, 9937457525067876406166182, 13995884834923841197997409, 63759030914653054346432641], [1, -7, 372, -3138, 73315, -666780, 10087481, -91367841, 1064678040, -9159628901, 89637382245, -716798756168, 6144361260517, -45322086179990, 347525991033990, -2355177051473659, 16357027715502558, -101272613213367337, 642575557421847510, -3603423105912464930, 21006348421816780117, -105375469088594326424, 566630435932631665005, -2489757606125356803407, 12444170162683688582040, -45920801855220173265963, 218005417217090909386769, -619634479604621876573460, 2929640331901305788839315, -5391912821997828484092534, 27485352932019523400747028, -22239492560585689633400149, 136614025729312093462315201], [1, 31, 941, 18281, 336231, 4931218, 68745838, 824945998, 9479210063, 97272427247, 962214491659, 8677297342675, 75838894223815, 611669521060006, 4799477730874298, 34983489091252572, 248573892822537796, 1644223987288870884, 10602046307501324282, 63505364685013002938, 370069611204959803015, 1990094819796879273725, 10371917198276635440811, 49280460626885284455361, 225712188137142548500943, 923222205025974279376466, 3615971423624950344086062, 12190756020288152980775054, 39067178557204889410549671, 99832535627590381064714887, 241523634002595032183641229, 373963798875431415400175633, 566977372488557307219621121], [1, 66, 2621, 76058, 1781762, 35276871, 609041687, 9347868667, 129408562699, 1632151424402, 18901860842316, 202148349366060, 2005406612147776, 18514212309862079, 159456108398381176, 1283208801034658221, 9658332823518811780, 68010066454836885713, 447912208491052723384, 2756340386055336735283, 15823622770426395720256, 84537528622275699167580, 418947669719195948734764, 1917306460145856556102474, 8056937050218939070423339, 30845756688314537134466711, 106513759986574573983473663, 326982584774827913954652987, 875306447766272906745457442, 1980300996217778127093314434, 3616839152851773816941197349, 4827052024675888901816218362, 3876269050118516845397872321], [1, -7, 442, -3508, 105593, -856382, 17639389, -139554059, 2261197320, -17115674831, 234152631353, -1678592886254, 20227940459783, -136519444242156, 1488182686904536, -9408447183719123, 94379018439678286, -555098383839428257, 5180363933114689816, -28038226939009757124, 245109256837696592663, -1200066842511527685946, 9876682943913887846273, -42594949581847336890589, 332012592005317865619720, -1208956229593324657847401, 9015787235887047621743989, -25824960058081483171999738, 187870792984166978173615433, -368244048047872565478294332, 2737476706098181517258540362, -2557868505924318929022120293, 21559177407076402401757871041], [1, -6, 323, -1803, 51999, -310708, 5859564, -41551842, 551504573, -4527561984, 47537189043, -403868693098, 3813583117651, -30173927981267, 277792860692578, -1985788550129320, 18004760530932760, -121133101557888520, 1033667234637082738, -6848908347115964927, 52802265487280039491, -341106004280275030498, 2449133775564987326523, -14228962989857025425664, 105727459795542808066013, -485913310774361559037722, 4179878444835007025045964, -13520122313214006558681988, 138023492314500182646533679, -291933263240171418450618543, 3190216908275705744721318443, -3614920707210242422811153406, 36751693856637464631913392961], [1, -16, 766, -9522, 266198, -2737347, 58496417, -519287669, 9388084842, -74027457819, 1185159368461, -8444953971409, 122332956376634, -795520428449380, 10542611262284876, -62937864816399986, 767216039759836106, -4216836942698799062, 47325781956396808364, -239263110621720876940, 2465146206233273306714, -11401744384258651065763, 107207599083415823371909, -448659072716172158370537, 3812197808495644968535722, -14128017828220325264108543, 106629480338424335805228233, -334312552917015486658098801, 2178223406975457306167849078, -5220361910464242403944159414, 28136884474779022123001696014, -39376945374625472213913600688, 164890958756244164895763202881], [1, 46, 1696, 44053, 1001168, 19136619, 332551066, 5155299858, 74144424281, 977582113019, 12099134092469, 139298259299498, 1516078883966442, 15474989005321276, 149928022065044389, 1368030361292835759, 11870282787987010192, 97130155651791338889, 755787159229888764949, 5538668789883543214436, 38526112970191238809002, 251326007971362991165798, 1549902512443529567890949, 8891226782601575743192429, 47879023801639694066722841, 236362769243333187494537598, 1082534712977961369925910266, 4422899246739704486294758749, 16428849250081879601645793488, 51325598517914925355667032883, 140295173339687277861394262176, 270167474131732694277897205346, 416997623116370028124580469121], [1, -39, 1449, -35633, 819016, -15354005, 270847213, -4181000932, 61166945860, -808996878016, 10194855445346, -118177368250479, 1310024305648818, -13487234128627491, 133088301010306108, -1225754844226755877, 10832013228567582618, -89480103628553179021, 709227556083921249532, -5246763359016280666347, 37202385947672794929138, -244990145055568123543047, 1542830560949635435900994, -8937310912148054755471552, 49328700779135877381454660, -246142158895586956358694916, 1163999978492021205416482237, -4816961098850022804218999885, 18757143782844265728875083336, -59573013496962879372736828889, 176843225343592806988184647641, -347462154971158537954010829423, 650377879817809571042122834561], [1, -4, 523, -2502, 139646, -789723, 25317681, -164597190, 3543641120, -25365204188, 414143422875, -3092572364282, 42450546057593, -314223074160542, 3907176098450002, -27774453730301147, 324801875822633630, -2194181844693790613, 24384686030426462482, -154924230261039467138, 1653452207437478015033, -9516019582884487140518, 100673070887441256442875, -487111072641691100833892, 5376089162299152917388320, -19727235915754264149923610, 239714793479876159470660881, -590707916031225410517110517, 8251893149529168823104709886, -11679909887498649809068865178, 192877232942358798625618825963, -116537678030182371636129156796, 2301619141096101839813550846721], [1, 15, 838, 11765, 347274, 4483083, 94328215, 1114931415, 18851537694, 204626105391, 2955643532351, 29598435804255, 378062838968094, 3501719008421705, 40369874910747532, 345564045988135983, 3640146863496575154, 28681815817015286589, 278108068260139747948, 2002237406668421436835, 17942227569919113810174, 116589441602186837335965, 966319200012505970360519, 5552744429698964349779157, 42459171912072529660511454, 208425563325900025086460245, 1463600469055608993395763535, 5773455139313977465109371161, 37120120547435803318414251114, 104377558106763894680900165695, 617074090655151375319620070102, 916774752822987425146690915605, 5072820298953863752478356399681], [1, -1, 543, 671, 152533, 517635, 30165176, 157224139, 4823063548, 30855005869, 665165199182, 4562642804149, 80959528623427, 549124327434249, 8716291116419723, 56211725364021865, 827104459422306710, 5002843557397945985, 69041741933160625883, 387115627986995083281, 5079582256137455079907, 25478068662920079853901, 330574659391801061193902, 1364758097795251796859701, 18986417972246561418843388, 55084483916045769840260051, 940602069670137602372478776, 1436526714039376044899023515, 37674187227020130046916968693, 14750019910513889756785970599, 1062331165745759687445895083663, -174120577810999285787632895849, 15496731425178936435099327730561], [1, -41, 1499, -38587, 902626, -17930470, 329984509, -5477364638, 85335761433, -1232122907558, 16844252420378, -216472222887038, 2649198951432652, -30719144250882281, 340398004753863806, -3588518828385646187, 36211946895519678800, -348086326353407680139, 3202804826729104550654, -28036533540885484047113, 234531678396286601483212, -1858920634120138180888766, 14030790710132423596043162, -99553417196871010173278054, 668813363456732034167545113, -4164062717383819376860596446, 24333853843817659662801674941, -128256903490287331970620863910, 626280154935868220454311677666, -2597009632821903713386320465499, 9786015799134508141019285112731, -25963298754608364827774314138313, 61425365346268570446197767595521], [1, 26, 1145, 22800, 594481, 9838746, 194974482, 2811233898, 46546875940, 601899712718, 8729531345908, 102971794250090, 1342285237970519, 14569434200810100, 173170552622401209, 1735203595795214398, 18956029210061653766, 175255563175316654198, 1766512807301114733009, 15010902626528846840100, 139678740119592633318119, 1082243906336739828295090, 9266573428984410385090708, 64531796042802109499395318, 504035967376673441950827940, 3074605112313648819357022098, 21537312670778863633526356482, 109767774830799965953232759346, 669876070737883491508391431681, 2594852679387899872738613662800, 13161479741570775472932323554145, 30185192839619961914340857339026, 117257864492369852051862561201601], [1, 32, 1597, 39960, 1168339, 24146387, 529068340, 9334990168, 167497823503, 2576543977499, 39509000009885, 537020405780394, 7203361965251599, 87233080344580087, 1037245076507240738, 11238933336780299795, 119316672737784084348, 1157610133688370878885, 11004133016665316989442, 95321942185691964727249, 810744735350958854108719, 6225538337912766234392742, 47175812195367467951189165, 316882410104386440335500013, 2121812315111438668477211983, 12180044842516054773172259944, 71102360791840487323125628660, 334242467410204332893548127189, 1665772048776977862945585106099, 5868260718952450997989859815080, 24156057905936126554313063834893, 49854957331224466576716254477024, 160470643909878751793805444097921], [1, 6, 655, 4545, 234925, 1695368, 59724708, 427001312, 11976781431, 82141047970, 2000280494735, 12968598070522, 287304599828721, 1757772758288407, 36297599429411626, 210288253746687616, 4096890271255060092, 22500843150895574912, 415571215867333706074, 2153347213131904976501, 37659772311013417020321, 181891296685633117524254, 3001881650660348342015015, 13190057328875214530028710, 205783403336117673547556631, 785024495761892669731713184, 11748754040592296033264108292, 35684986446666664863753721624, 529096109036621422613589324925, 1095274552585482801482718708315, 16889398683818165487770371985095, 16554189244292003424654318800658, 295216374856540727739668685278401], [1, -20, 1386, -24540, 925086, -14611701, 394996445, -5606443161, 120936031462, -1551364099553, 28195500386937, -328092836356389, 5184693835920754, -54804170278060238, 767746236704610264, -7364305769579431966, 92574727715551538130, -802709328884158084294, 9121593038287474546584, -70972989831026071956902, 731861847226609376373394, -5048114974490257490628561, 47286676824149501088484017, -283595426461344205982393957, 2409726183254509046624238502, -12176596222951197368005138629, 93510023548602313245718309445, -377044190868274322385282546009, 2601956812320410728223507471166, -7523484518199793144092474855660, 46316336597494521167507194227546, -72849649193750401259138299722980, 397030588105939686862303733490241], [1, 9, 1137, 9700, 603601, 4815811, 196928182, 1447342852, 43715305403, 290762744382, 6922495748213, 40883680920703, 809576669488749, 4225400713994266, 76319235813098356, 380344401701039349, 7519770145479927660, 42978917392217446437, 974520322097452907764, 6096818014020184428602, 131999339487309743641389, 753255319875794208870479, 14412302155420406129837717, 68405002594324355250968094, 1162146997897365254545826363, 4347878626049757973376934596, 66848598477386852603045174518, 184727823235904664627366361907, 2616322477798802306928771678481, 4751070770120107833858172264100, 62930136455237275732157920686993, 56288433399275557976785053068313, 706732552679793116819634555191041]], 'euler_factors_factorization': [[[[1, 5, 19, 52, 125, 264, 529, 1006, 1858, 3287, 5617, 9208, 14687, 22750, 34532, 50960, 73260, 101920, 138128, 182000, 234992, 294656, 359488, 420736, 475648, 515072, 541696, 540672, 512000, 425984, 311296, 163840, 65536], 1]], [1], [[[1, -1, 24, -19, 329, -170, 3169, -250, 23164, 13164, 133265, 205344, 624119, 1857497, 2603502, 12171723, 11656934, 60858615, 65087550, 232187125, 390074375, 641700000, 2082265625, 1028437500, 9048437500, -488281250, 30947265625, -8300781250, 80322265625, -23193359375, 146484375000, -30517578125, 152587890625], 1]], [[[1, 1], 16]], [[[1, 11, 127, 927, 6546, 37443, 205797, 996578, 4658508, 19883514, 82587628, 319384657, 1213890104, 4356733405, 15506991000, 52671594431, 178444424018, 579387538741, 1876345911000, 5798812162055, 17772565012664, 51437218394507, 146309020847308, 387473437398894, 998592562009548, 2349878794001398, 5337844170611997, 10682924882687673, 20544152154015666, 32002554157424037, 48228228865071607, 45949729863572161, 45949729863572161], 1]], [[[1, -18, 219, -1948, 14614, -94646, 555983, -2985822, 14990448, -70533970, 315528362, -1344918094, 5522268604, -21859541176, 84090414036, -314220696382, 1147549597242, -4084869052966, 14211279972084, -48025411963672, 157721513598844, -499358673875542, 1522995137456858, -4425902015622490, 12228168955153008, -31663147526889606, 76646977873682567, -169620812654025902, 340478215979937334, -590000707641708844, 862285428468144291, -921346074253633626, 665416609183179841], 1]], [[[1, -5, 158, -540, 11588, -27066, 558089, -870456, 20459225, -20581469, 610166673, -380514409, 15256129494, -5823688053, 325009231345, -84738254968, 5951336176930, -1440550334456, 93927667858705, -28611779404389, 1274207191468374, -540276047219513, 14727940171037937, -8445372677850637, 142718591030843225, -103225528624072632, 1125104019907681961, -927603145462394778, 6751426485018470468, -5348472137769205980, 26603696596385346782, -14312115257549078965, 48661191875666868481], 1]], [[[1, 11, 181, 1462, 14335, 95375, 719296, 4211650, 26971845, 143986816, 822044549, 4072545605, 21330650499, 99112960004, 484717258250, 2123022393713, 9768224694024, 40337425480547, 174982930228250, 679815792667436, 2779831703680179, 10084026099994895, 38673810028952669, 128705745610993024, 458078029889580645, 1359047642350925350, 4410051434971228096, 11110258442417637125, 31727869364813417935, 61481461821819820258, 144620210126702025901, 166992397328622781289, 288441413567621167681], 1]], [[[1, 13, 208, 2018, 20375, 160550, 1275907, 8665917, 58792152, 357162729, 2165764215, 12076345886, 67338196417, 351022119450, 1831885262566, 9017382569929, 44472265582174, 207399799108367, 969067303897414, 4270886127348150, 18843988223529697, 77727504308934898, 320610830931912135, 1216076748419164863, 4604071349910314712, 15608639468567456571, 52856375643073254643, 152973606633080979850, 446510472802414040375, 1017145378387791178894, 2411309955504059960272, 3466258061037086192891, 6132610415680998648961], 1]], [[[1, 24, 472, 6622, 82320, 873128, 8519727, 75217422, 623444003, 4802217916, 35136436698, 242281577588, 1597747487582, 10006074679634, 60158248780719, 344816413108922, 1900626864033788, 9999675980158738, 50593087224584679, 244038155361593626, 1130056440764484542, 4969473537862528612, 20899971964810634058, 82837665059863752044, 311875626182796922883, 1091190120882540389718, 3584310774643021565127, 10652606690711199063112, 29126032953474211455120, 67945883337211863695558, 140447485822977346763032, 207100529942356426582776, 250246473680347348787521], 1]], [[[1, 42, 1103, 21297, 334685, 4460298, 52049742, 541781390, 5109757813, 44140935934, 352708311097, 2626670113330, 18362034468729, 121180561220341, 758925862323514, 4526798708422582, 25783901132438856, 140330759961100042, 729327753692896954, 3610090099315178731, 16957724434595074809, 75199335301711682830, 313029924417880648057, 1214432536850515364674, 4358066642201825276533, 14324495245283137712690, 42661440873252651003342, 113329378684080674899638, 263618918792270776760285, 520020483496687072060527, 834909160548538341314063, 985541003657476809057942, 727423121747185263828481], 1]], [[[1, -40, 1093, -21915, 365384, -5189918, 65263975, -735690707, 7568509040, -71598368286, 629373118507, -5166707785384, 39884876555089, -290489859017229, 2005230244594602, -13140503504719049, 81949219635694490, -486198629674604813, 2745160204850010138, -14714182828799700537, 74750680129362155329, -358279962501233324488, 1614799231268096551363, -6796967501049835804038, 26584232499815351945840, -95611644232790233249439, 313827330266869186689775, -923377867790413627716134, 2405305335701855451112904, -5337819548695421807775255, 9850182996522544071560077, -13337850718072612283539720, 12337511914217166362274241], 1]], [[[1, 9, 262, 2416, 37769, 315207, 3782416, 28401838, 290262313, 2011916927, 18444064407, 119441768717, 1012122769428, 6182374690503, 49052876571800, 283552719845861, 2125239007937044, 11625661513680301, 82457885517195800, 426095446044157263, 2860017049061634708, 13838069564272264117, 87611228560967850087, 391829420226777883687, 2317722866136716416873, 9298248664783908500318, 50770081337269403980816, 173467563100183522342287, 852200465154530482093289, 2235049095193072928439536, 9937457525067876406166182, 13995884834923841197997409, 63759030914653054346432641], 1]], [[[1, -7, 372, -3138, 73315, -666780, 10087481, -91367841, 1064678040, -9159628901, 89637382245, -716798756168, 6144361260517, -45322086179990, 347525991033990, -2355177051473659, 16357027715502558, -101272613213367337, 642575557421847510, -3603423105912464930, 21006348421816780117, -105375469088594326424, 566630435932631665005, -2489757606125356803407, 12444170162683688582040, -45920801855220173265963, 218005417217090909386769, -619634479604621876573460, 2929640331901305788839315, -5391912821997828484092534, 27485352932019523400747028, -22239492560585689633400149, 136614025729312093462315201], 1]], [[[1, 31, 941, 18281, 336231, 4931218, 68745838, 824945998, 9479210063, 97272427247, 962214491659, 8677297342675, 75838894223815, 611669521060006, 4799477730874298, 34983489091252572, 248573892822537796, 1644223987288870884, 10602046307501324282, 63505364685013002938, 370069611204959803015, 1990094819796879273725, 10371917198276635440811, 49280460626885284455361, 225712188137142548500943, 923222205025974279376466, 3615971423624950344086062, 12190756020288152980775054, 39067178557204889410549671, 99832535627590381064714887, 241523634002595032183641229, 373963798875431415400175633, 566977372488557307219621121], 1]], [[[1, 66, 2621, 76058, 1781762, 35276871, 609041687, 9347868667, 129408562699, 1632151424402, 18901860842316, 202148349366060, 2005406612147776, 18514212309862079, 159456108398381176, 1283208801034658221, 9658332823518811780, 68010066454836885713, 447912208491052723384, 2756340386055336735283, 15823622770426395720256, 84537528622275699167580, 418947669719195948734764, 1917306460145856556102474, 8056937050218939070423339, 30845756688314537134466711, 106513759986574573983473663, 326982584774827913954652987, 875306447766272906745457442, 1980300996217778127093314434, 3616839152851773816941197349, 4827052024675888901816218362, 3876269050118516845397872321], 1]], [[[1, -7, 442, -3508, 105593, -856382, 17639389, -139554059, 2261197320, -17115674831, 234152631353, -1678592886254, 20227940459783, -136519444242156, 1488182686904536, -9408447183719123, 94379018439678286, -555098383839428257, 5180363933114689816, -28038226939009757124, 245109256837696592663, -1200066842511527685946, 9876682943913887846273, -42594949581847336890589, 332012592005317865619720, -1208956229593324657847401, 9015787235887047621743989, -25824960058081483171999738, 187870792984166978173615433, -368244048047872565478294332, 2737476706098181517258540362, -2557868505924318929022120293, 21559177407076402401757871041], 1]], [[[1, -6, 323, -1803, 51999, -310708, 5859564, -41551842, 551504573, -4527561984, 47537189043, -403868693098, 3813583117651, -30173927981267, 277792860692578, -1985788550129320, 18004760530932760, -121133101557888520, 1033667234637082738, -6848908347115964927, 52802265487280039491, -341106004280275030498, 2449133775564987326523, -14228962989857025425664, 105727459795542808066013, -485913310774361559037722, 4179878444835007025045964, -13520122313214006558681988, 138023492314500182646533679, -291933263240171418450618543, 3190216908275705744721318443, -3614920707210242422811153406, 36751693856637464631913392961], 1]], [[[1, -16, 766, -9522, 266198, -2737347, 58496417, -519287669, 9388084842, -74027457819, 1185159368461, -8444953971409, 122332956376634, -795520428449380, 10542611262284876, -62937864816399986, 767216039759836106, -4216836942698799062, 47325781956396808364, -239263110621720876940, 2465146206233273306714, -11401744384258651065763, 107207599083415823371909, -448659072716172158370537, 3812197808495644968535722, -14128017828220325264108543, 106629480338424335805228233, -334312552917015486658098801, 2178223406975457306167849078, -5220361910464242403944159414, 28136884474779022123001696014, -39376945374625472213913600688, 164890958756244164895763202881], 1]], [[[1, 46, 1696, 44053, 1001168, 19136619, 332551066, 5155299858, 74144424281, 977582113019, 12099134092469, 139298259299498, 1516078883966442, 15474989005321276, 149928022065044389, 1368030361292835759, 11870282787987010192, 97130155651791338889, 755787159229888764949, 5538668789883543214436, 38526112970191238809002, 251326007971362991165798, 1549902512443529567890949, 8891226782601575743192429, 47879023801639694066722841, 236362769243333187494537598, 1082534712977961369925910266, 4422899246739704486294758749, 16428849250081879601645793488, 51325598517914925355667032883, 140295173339687277861394262176, 270167474131732694277897205346, 416997623116370028124580469121], 1]], [[[1, -39, 1449, -35633, 819016, -15354005, 270847213, -4181000932, 61166945860, -808996878016, 10194855445346, -118177368250479, 1310024305648818, -13487234128627491, 133088301010306108, -1225754844226755877, 10832013228567582618, -89480103628553179021, 709227556083921249532, -5246763359016280666347, 37202385947672794929138, -244990145055568123543047, 1542830560949635435900994, -8937310912148054755471552, 49328700779135877381454660, -246142158895586956358694916, 1163999978492021205416482237, -4816961098850022804218999885, 18757143782844265728875083336, -59573013496962879372736828889, 176843225343592806988184647641, -347462154971158537954010829423, 650377879817809571042122834561], 1]], [[[1, -4, 523, -2502, 139646, -789723, 25317681, -164597190, 3543641120, -25365204188, 414143422875, -3092572364282, 42450546057593, -314223074160542, 3907176098450002, -27774453730301147, 324801875822633630, -2194181844693790613, 24384686030426462482, -154924230261039467138, 1653452207437478015033, -9516019582884487140518, 100673070887441256442875, -487111072641691100833892, 5376089162299152917388320, -19727235915754264149923610, 239714793479876159470660881, -590707916031225410517110517, 8251893149529168823104709886, -11679909887498649809068865178, 192877232942358798625618825963, -116537678030182371636129156796, 2301619141096101839813550846721], 1]], [[[1, 15, 838, 11765, 347274, 4483083, 94328215, 1114931415, 18851537694, 204626105391, 2955643532351, 29598435804255, 378062838968094, 3501719008421705, 40369874910747532, 345564045988135983, 3640146863496575154, 28681815817015286589, 278108068260139747948, 2002237406668421436835, 17942227569919113810174, 116589441602186837335965, 966319200012505970360519, 5552744429698964349779157, 42459171912072529660511454, 208425563325900025086460245, 1463600469055608993395763535, 5773455139313977465109371161, 37120120547435803318414251114, 104377558106763894680900165695, 617074090655151375319620070102, 916774752822987425146690915605, 5072820298953863752478356399681], 1]], [[[1, -1, 543, 671, 152533, 517635, 30165176, 157224139, 4823063548, 30855005869, 665165199182, 4562642804149, 80959528623427, 549124327434249, 8716291116419723, 56211725364021865, 827104459422306710, 5002843557397945985, 69041741933160625883, 387115627986995083281, 5079582256137455079907, 25478068662920079853901, 330574659391801061193902, 1364758097795251796859701, 18986417972246561418843388, 55084483916045769840260051, 940602069670137602372478776, 1436526714039376044899023515, 37674187227020130046916968693, 14750019910513889756785970599, 1062331165745759687445895083663, -174120577810999285787632895849, 15496731425178936435099327730561], 1]], [[[1, -41, 1499, -38587, 902626, -17930470, 329984509, -5477364638, 85335761433, -1232122907558, 16844252420378, -216472222887038, 2649198951432652, -30719144250882281, 340398004753863806, -3588518828385646187, 36211946895519678800, -348086326353407680139, 3202804826729104550654, -28036533540885484047113, 234531678396286601483212, -1858920634120138180888766, 14030790710132423596043162, -99553417196871010173278054, 668813363456732034167545113, -4164062717383819376860596446, 24333853843817659662801674941, -128256903490287331970620863910, 626280154935868220454311677666, -2597009632821903713386320465499, 9786015799134508141019285112731, -25963298754608364827774314138313, 61425365346268570446197767595521], 1]], [[[1, 26, 1145, 22800, 594481, 9838746, 194974482, 2811233898, 46546875940, 601899712718, 8729531345908, 102971794250090, 1342285237970519, 14569434200810100, 173170552622401209, 1735203595795214398, 18956029210061653766, 175255563175316654198, 1766512807301114733009, 15010902626528846840100, 139678740119592633318119, 1082243906336739828295090, 9266573428984410385090708, 64531796042802109499395318, 504035967376673441950827940, 3074605112313648819357022098, 21537312670778863633526356482, 109767774830799965953232759346, 669876070737883491508391431681, 2594852679387899872738613662800, 13161479741570775472932323554145, 30185192839619961914340857339026, 117257864492369852051862561201601], 1]], [[[1, 32, 1597, 39960, 1168339, 24146387, 529068340, 9334990168, 167497823503, 2576543977499, 39509000009885, 537020405780394, 7203361965251599, 87233080344580087, 1037245076507240738, 11238933336780299795, 119316672737784084348, 1157610133688370878885, 11004133016665316989442, 95321942185691964727249, 810744735350958854108719, 6225538337912766234392742, 47175812195367467951189165, 316882410104386440335500013, 2121812315111438668477211983, 12180044842516054773172259944, 71102360791840487323125628660, 334242467410204332893548127189, 1665772048776977862945585106099, 5868260718952450997989859815080, 24156057905936126554313063834893, 49854957331224466576716254477024, 160470643909878751793805444097921], 1]], [[[1, 6, 655, 4545, 234925, 1695368, 59724708, 427001312, 11976781431, 82141047970, 2000280494735, 12968598070522, 287304599828721, 1757772758288407, 36297599429411626, 210288253746687616, 4096890271255060092, 22500843150895574912, 415571215867333706074, 2153347213131904976501, 37659772311013417020321, 181891296685633117524254, 3001881650660348342015015, 13190057328875214530028710, 205783403336117673547556631, 785024495761892669731713184, 11748754040592296033264108292, 35684986446666664863753721624, 529096109036621422613589324925, 1095274552585482801482718708315, 16889398683818165487770371985095, 16554189244292003424654318800658, 295216374856540727739668685278401], 1]], [[[1, -20, 1386, -24540, 925086, -14611701, 394996445, -5606443161, 120936031462, -1551364099553, 28195500386937, -328092836356389, 5184693835920754, -54804170278060238, 767746236704610264, -7364305769579431966, 92574727715551538130, -802709328884158084294, 9121593038287474546584, -70972989831026071956902, 731861847226609376373394, -5048114974490257490628561, 47286676824149501088484017, -283595426461344205982393957, 2409726183254509046624238502, -12176596222951197368005138629, 93510023548602313245718309445, -377044190868274322385282546009, 2601956812320410728223507471166, -7523484518199793144092474855660, 46316336597494521167507194227546, -72849649193750401259138299722980, 397030588105939686862303733490241], 1]], [[[1, 9, 1137, 9700, 603601, 4815811, 196928182, 1447342852, 43715305403, 290762744382, 6922495748213, 40883680920703, 809576669488749, 4225400713994266, 76319235813098356, 380344401701039349, 7519770145479927660, 42978917392217446437, 974520322097452907764, 6096818014020184428602, 131999339487309743641389, 753255319875794208870479, 14412302155420406129837717, 68405002594324355250968094, 1162146997897365254545826363, 4347878626049757973376934596, 66848598477386852603045174518, 184727823235904664627366361907, 2616322477798802306928771678481, 4751070770120107833858172264100, 62930136455237275732157920686993, 56288433399275557976785053068313, 706732552679793116819634555191041], 1]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 2, 'label': '32-8001e16-1.1-c1e16-0-2', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, '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}, {'__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}, {'__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': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'order_of_vanishing': 16, 'origin': 'ModularForm/GL2/Q/holomorphic/8001/2/a/r', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0029296875', 'prec': 40}, 'plot_values': [0.0, 1.0379293340078428e-32, 6.800142319374253e-28, 4.464388174309511e-25, 4.451219834356659e-23, 1.57997440928755e-21, 2.917925940110489e-20, 3.432895838099266e-19, 2.9032399439339092e-18, 1.9080415915690266e-17, 1.0277455246910033e-16, 4.712591404727707e-16, 1.891826349711599e-15, 6.791922342573729e-15, 2.2170657228053872e-14, 6.66705718362302e-14, 1.8665981957149236e-13, 4.907766250238929e-13, 1.2205170386945842e-12, 2.888260434189239e-12, 6.536807794661521e-12, 1.421063230394222e-11, 2.978503611144732e-11, 6.038410412179748e-11, 1.187436565577916e-10, 2.2705711189373193e-10, 4.231008688476957e-10, 7.697979632780091e-10, 1.3698778927484688e-09, 2.3879686616309766e-09, 4.083366348132015e-09, 6.857931342147076e-09, 1.1325136146435154e-08, 1.840832772641083e-08, 2.9478872964153587e-08, 4.6548188643477756e-08, 7.253181472569662e-08, 1.1160888932694221e-07, 1.6970681467589233e-07, 2.551487899679622e-07, 3.7951149298366264e-07, 5.587518051601411e-07, 8.146754153660006e-07, 1.1768368144747952e-06, 1.6849799043518398e-06, 2.392151713575373e-06, 3.3686489750425377e-06, 4.706989079159002e-06, 6.528133718749352e-06, 8.989235049646166e-06, 1.229322034448344e-05, 1.6700595326469842e-05, 2.254390036390103e-05, 3.0245326752083194e-05, 4.03380808970904e-05, 5.3492171881090844e-05, 7.054539874747987e-05, 9.254042277915754e-05, 0.00012076892995307308, 0.00015682402256186496, 0.00020266212376018344, 0.00026067583649462306, 0.00033377936897155793, 0.0004255083226971906, 0.000540135836256681, 0.0006828072274139884, 0.0008596953818971462, 0.0010781799812579677, 0.0013470531923070043, 0.001676754944076695, 0.002079641276754602, 0.00257028940797527, 0.0031658434813966255, 0.0038864052362027265, 0.004755474116028346, 0.005800441615454161, 0.007053144937187656, 0.00855048529985984, 0.010335116491211058, 0.012456209500131234, 0.014970299279031183, 0.017942218471986928, 0.021446121055186493, 0.02556661307330339, 0.030399989923244455, 0.03605558640440247, 0.042657246996106526, 0.0503449227157985, 0.059276400734503173, 0.06962917267214606, 0.08160244715743717, 0.09541931180867856, 0.11132904926643133, 0.12960961128018386, 0.1505702539160949, 0.17455433414422325, 0.20194227326009787, 0.2331546740868856, 0.26865556121483586, 0.308955843437307, 0.3546169223649172, 0.4062544410617668, 0.4645421748937926, 0.5302160550370509, 0.6040783130297809, 0.6870017325636588, 0.779933992403348, 0.8839020817794236, 1.0000167589092042, 1.1294770355044808, 1.273574678751032, 1.4336986781572745, 1.6113396516842897, 1.8080940957014764, 2.0256683243218236, 2.2658825474243893, 2.530674669975628, 2.822103774554659, 3.142353288091647, 3.4937337817706093, 3.8786853508418777, 4.299779504673075, 4.759720484254417, 5.261346063806478, 5.807627686288569, 6.401669875408176, 7.046708875258456, 7.746110456866658, 8.503366831465552, 9.322092511125653, 10.206018889916235, 11.15898829305294, 12.184946791483132, 13.287935761039654, 14.472082213403201, 15.741587739529168, 17.1007163010812, 18.55378076539592, 20.105128021876535, 21.759122737039906, 23.520129742653932, 25.392495058791965, 27.380525563048888, 29.488467327191184, 31.72048265311617, 34.08062635619422, 36.57282214504937, 39.20083510134203, 41.968243539756934, 44.87841036543802, 47.93445398182937, 51.139218249679494, 54.49524181293015, 58.004726958347256, 61.66950816399052, 65.4910205038381, 69.47026808766583, 73.607792726501, 77.90364302450556, 82.35734410786537, 86.96786821004159, 91.73361010043672, 96.6523729200466, 101.7213343521234, 106.93701992881954, 112.29528175089372, 117.79127947489286, 123.41946380651149, 129.17356273553872, 135.0465707426012, 141.03074120074632, 147.11758218571777, 153.29785589752365, 159.56158188255958, 165.89804417782204, 172.29580205493997, 178.74270574250306, 185.2259302802433, 191.73204427861967, 198.247004958381, 204.75617917473946, 211.2443815063637, 217.69591679226053, 224.09462705835293, 230.42394274379598, 236.6669381044926, 242.80639063811392, 248.82484433689882, 254.70467628214763, 260.42816668411734, 265.9775725364164, 271.33520368425644, 276.4835012475172, 281.4051480434887, 286.0832447926124, 290.501310041462, 294.64333365091875, 298.4938591850504, 302.03806582936903, 305.26184933093054, 308.1519014422501, 310.69578736691096, 312.88202070195996, 314.70013516460153, 316.14075276140846, 317.19564786321257, 317.8578066600525, 318.1214815099101, 317.98223971578267, 317.43705227319805, 316.48446799687514, 315.12450337563973, 313.35861586552033, 311.18971559774786, 308.6221694752228, 305.6617979662873, 302.3158630654144, 298.59304805485453, 294.5034296445356, 290.05844211571394, 285.2708335595693, 280.15461436661934, 274.7249981804077, 268.99833558615506, 262.99204086144516, 256.72456113173786, 250.21542925664366, 243.48501005865896, 236.5543509017843, 229.44507858191136, 222.17929152671994, 214.77945004121716, 207.268264521708, 199.66858227912195, 192.00327371560314, 184.2951186093776, 176.56669326816407, 168.84025931061757, 161.13765482842413, 153.4801886686445, 145.88853855675748, 138.38268869044518, 130.9819296908006, 123.7046455671944, 116.56819664410219, 109.58884801454414, 102.78170583776958, 96.16066187057726, 89.73834655657191, 83.52609092968177, 77.53389751799347, 71.77042036200524, 66.24295418839715, 60.95743270701821, 55.91843596162208, 51.12920681789868, 46.59167541649827, 42.30650647278212, 38.2731744774986, 34.48995345096627, 30.953958628053847, 27.661211635057, 24.606711417195907, 21.78451021980393, 19.18779389390849, 16.80896577154919, 14.639733338051789, 12.671196918965709, 10.893939654398338, 9.298117838096324, 7.873550826043542, 6.609809999215799, 5.496305927432645, 4.5223755807285215, 3.677368378538135, 2.9507119581008316, 2.331984473208951, 1.810985208908984, 1.3777995963150544, 1.022858245379508, 0.736989684415958, 0.5114665693583571, 0.3380451948824769, 0.20899820785461312, 0.11714052550554813, 0.05584849891764204, 0.01907244014038718, 0.0013427002580524059, -0.0022304521641677956, 0.004037134418504081, 0.01639181684878883, 0.031625607033530824, 0.04705511581930564, 0.06049616714077164, 0.07023460163434483, 0.07499383448913483, 0.0738997430895361, 0.06644346827679712, 0.05244271307785625, 0.03200211270009726, 0.005473234495445081, -0.026585255330853926, -0.06344674948384943, -0.10425470655804153, -0.14805907045036054, -0.1938506352540304, -0.24059296908784267, -0.28725222933659245, -0.3328239579766079, -0.37635670568733764, -0.4169724064224226, -0.4538834208742248, -0.4864062132178108, -0.5139716802162038, -0.5361322028419859, -0.5525655380845227, -0.5630757122494114, -0.5675911162910626, -0.5661600381033285, -0.5589438958633286, -0.5462084602044813, -0.5283134690336554, -0.5057011026747594, -0.47888280524526866, -0.4484254393325123, -0.414937105026463, -0.3790528593535945, -0.34142063725701305, -0.3026876548597019, -0.2634875511534681, -0.22442849605903184, -0.18608246163122025, -0.14897581970028956, -0.11358139413117019, -0.08031205995344752, -0.04951594552014794, -0.0214732544676415, 0.003605255599126513, 0.025578203637819846, 0.04437235998433546, 0.0599798388533585, 0.07245397036631508, 0.08190407125289627, 0.08848928703845245, 0.09241169151038292, 0.09390883773012536, 0.09324595878395457, 0.09070801591492696, 0.08659178764906104, 0.08119818191486805, 0.07482494066816278, 0.06775989506583502, 0.06027490519420475, 0.05262061606080684, 0.04502213096095352, 0.037675512626837264, 0.030745317655966855, 0.02436316161293568, 0.01862728217901107, 0.013603061509465227, 0.009324445422694923, 0.005796175718807579, 0.0029967331039213855, 0.0008818725229248189, -0.0006113789249737006, -0.0015604007161891184, -0.0020524780813562273, -0.002180266265799816, -0.0020373615429751615, -0.0017141146013147533, -0.0012938124145963985, -0.0008493310817593895, -0.0004403594186791906, -0.00011127431875470749, 0.00011027699148548239, 0.00021405536749348326, 0.0002071599185366174, 0.00011322474632243546, -2.9079621730445997e-05, -0.00016817982083281108, -0.00024228752247312316, -0.0001825426891257489, 8.350204504011254e-05, 0.000628182194183445, 0.0015199421761712558, 0.0028196127440146303, 0.004576876290156673, 0.006827075491189756, 0.009588487883340244, 0.012860179245539428, 0.016620535668818326, 0.020826553393774826, 0.025413942046840523, 0.030298071133104305, 0.03537576197035336, 0.04052789839775095, 0.04562280035274357, 0.05052027560233839, 0.05507623738081639, 0.059147750266083925, 0.06259834414099623, 0.06530341479931456, 0.06715552353644358, 0.06806941320378337, 0.06798649421247484, 0.06687860509732442, 0.06475085597120875, 0.06164337436908102, 0.05763179479962441, 0.05282636135311952, 0.04736954656120047, 0.041432128800313384, 0.03520771414102723, 0.028905735777091653, 0.022743014024217773, 0.01693401126228528, 0.011679966279932986, 0.007157147853394767, 0.003504507892560799, 0.0008110386659148733, -0.0008967615654013595, -0.0016669240227472604, -0.0016331292864893649, -0.0010244774558468464, -0.00017347163600584778, 0.0004782136728250122, 0.00037658717472517444, -0.0011448066740277448, -0.004861707721998926, -0.011652361482899587, -0.02248694000773794, -0.038413041066941406, -0.06053723533495773, -0.09000271889476676, -0.1279632134467058, -0.17555349703216502, -0.23385692443053238, -0.30387044724969237, -0.38646777161544554, -0.48236139133337824, -0.5920643334472175, -0.7158525455770248, -0.8537289357690828, -1.0053900896332806, -1.1701967809467082, -1.3471493925721862, -1.5348693549226204, -1.7315876822295522, -1.9351416310640446, -2.142980589747329, -2.352182367599116, -2.5594792339018677, -2.761295185180461, -2.953794790031943, -3.1329436190439974, -3.294580212228266, -3.4344991143362344, -3.5485444141155016, -3.6327129846637636, -3.683266257232086, -3.696849126111526, -3.6706143232316837, -3.6023503542655213, -3.490610859703357, -3.3348430602364516, -3.135513371410047, -2.8942279569385425, -2.6138405405749254, -2.2985498719600077, -1.953983337367477, -1.587263323602789, -1.2070538080152242, -0.82358465166385, -0.44865132865332774, -0.0955881003909747, 0.22078703123467047, 0.4842568810208152, 0.6773200127457427, 0.7813364439644674, 0.776704016225576, 0.6430647890342549, 0.3595405338931439, -0.0950041964037214, -0.7416765727849153, -1.6012484636180473, -2.693831183752538, -4.038536218675599, -5.653126373066761, -7.553662219516611, -9.754149090912543, -12.266190159505944, -15.098651368209588, -18.257344117401836, -21.74473165671311, -25.559665111721902, -29.69715524667447, -34.148184827328926, -38.899573389326136, -43.93391332801592, -49.229527488929314, -54.760488676688645, -60.49670450597135, -66.40406430961097, -72.44464895208084, -78.57700345539783, -84.75647136304859, -90.93558876054121, -97.06453486491878, -103.09163573041074, -108.96391527407464, -114.62768623598373, -120.02917616620064, -125.11518011733344, -129.83376315846766, -134.1350439469155, -137.97179174295067, -141.3000597970105, -144.0798264027653, -146.2756043798283, -147.85700912900748, -148.7992757078941, -149.08371602453244, -148.6981078906862, -147.63700676367634, -145.9019748477326, -143.50172172635087, -140.4521518497629, -136.7763156729746, -132.50426262415826, -127.6728355805399, -122.32543670787148, -116.5114459938367, -110.28564284773279, -103.70758686656619, -96.84092268794551, -89.75261729850766, -82.51214078892296, -75.19060091051396, -67.85984295299929, -60.59152797638371, -53.45620268585684, -46.522374615054304, -39.855606454389424, -33.51764331421633, -27.565586443176798, -22.051135772956503, -17.01990639124073, -12.510763229451301, -8.555297270914512, -5.177419457598555, -2.393065349626466, -0.21001541562062265, 1.3721650363060593, 2.3620644681648346, 2.776242377291669, 2.6389272606705507, 1.981599242533152, 0.8424632100498917, -0.7341798892604134, -2.6986542290417055, -4.996711832535016, -7.570398929950621, -10.358969892918749, -13.299880474154708, -16.329792666732928, -19.38558134965956, -22.405332546157975, -25.329317190185993, -28.10092464305183, -30.66754081320238, -32.981356600194566, -35.000093495934756, -36.68763451559427, -38.014550176224205, -38.9585105904355, -39.504573352134884, -39.645351401381184, -39.38106054934672, -38.719447855177194, -37.675563911280165, -36.27141758844993, -34.53551921471327, -32.50231641300354, -30.211532735172693, -27.707420865657916, -25.03794359940693, -22.253897000257695, -19.407991018069122, -16.55389927949995, -13.745301864461327, -11.034944083623683, -8.473711808752341, -6.109744943513078, -3.987605234480094, -2.147511114935494, -0.6246522100873669, 0.5513967018789597, 1.3571574260017438, 1.7756193671221974, 1.7964943352849865, 1.4163517566277153, 0.638633195313891, -0.5264545860257638, -2.0621655337536766, -3.9455487193622356, -6.1478866013971265, -8.635228876324197, -11.369011444579739, -14.306748597479004, -17.402796559665717, -20.609197644813865, -23.876498181496924, -27.15458661171352, -30.393538722845452, -33.54444732173808, -36.5602287500267, -39.39637417413271, -42.01163933711746, -44.3686703544518, -46.434550751730676, -48.181261293543194, -49.58604599516446, -50.63167955808912, -51.30663338042257, -51.60513922651555, -51.52718144566401, -51.078450238775936, -50.270017012480096, -49.117982787395235, -47.64307292654368, -45.87015140674247, -43.82768495210711, -41.54716099159824, -39.062470750719825, -36.409269958023096, -33.62432974416737, -30.744890157500524, -27.808028323662153, -24.85005265058609, -21.905933641924374, -19.008780852806186, -16.18938861203077, -13.475858471339642, -10.893194143166724, -8.463018247244829, -6.203381803537537, -4.128649403227107, -2.249459100070477, -0.5727545607772385, 0.8981143899417094, 2.1632279689376563, 3.2258756409261604, 4.092285544257889, 4.771312111327389, 5.274090479977057, 5.613667140830634, 5.804614390821309, 5.8626401532037855, 5.80420663267156, 5.6461460889904735, 5.40529503903016, 5.0981561318441795, 4.740592247603681, 4.347557804823874, 3.9328711303495187, 3.509030571292648, 3.0870758373229865, 2.676494888154241, 2.2851757030256596, 1.919400647553181, 1.5838805297663063, 1.2818252874986509, 1.015046501760915, 0.7840873904213213, 0.5883744661190212, 0.4263799816164963, 0.29579766497384175, 0.19372350257482931, 0.11683490587973698, 0.0615630166643537, 0.024253424499830846, 0.001311203383152533, -0.010673102622704829, -0.014819109036552019, -0.013875564650988005, -0.010163553390228681, -0.005543939242012787, -0.0014082433164995763, 0.001308627473097757, 0.002096075061204666, 0.0008188250635840857, -0.0023454122116206206, -0.006977977749949456, -0.012496981573247357, -0.0182366118276334, -0.023524005453371653, -0.027749836950649278, -0.030429106577791357, -0.031249058675883533, -0.030101707224361, -0.02709908221831194, -0.02257001301320117, -0.01703801134775296, -0.011180583625018784, -0.005771064857413651, -0.0016048063606679747, 0.0005878023090462578, 0.00023839916515510073, -0.0029559824446936693, -0.008927283558473779, -0.01713284759958109, -0.02645836724323559, -0.03513179757254175, -0.040652520477386156, -0.03973973642722361, -0.02830361133397801, -0.0014421288971193742, 0.04653409278537445, 0.12204754925744611, 0.232169553820404, 0.38450620263511714, 0.5870556928180942, 0.8480388391725255, 1.1757071920350026, 1.5781319950379566, 2.062978654896085, 2.6372722271300617, 3.3071598402293616, 4.077676353988175, 4.952519756436185, 5.933842837664283, 7.022067532305476, 8.215727994749857, 9.511347966607909, 10.903357411595477, 12.384053427748425, 13.943606667392135, 15.570117407229066, 17.249727267191655, 18.966770265897335, 20.703972064666296, 22.442694757946178, 24.163221661650653, 25.845076870264673, 27.467373342836503, 29.00918240270257, 30.449916821659787, 31.769719159041774, 32.94984850719207, 33.97305449857482, 34.823926336685304, 35.48921448768234, 35.95811535163395, 36.22252048289326, 36.277233714378326, 36.120078588782526, 35.751961879877136, 35.1768839197369, 34.40188625387003, 33.436937236481576, 32.29475766018148, 30.990590743445573, 29.541921912170498, 27.968148221635893, 26.290211564211432, 24.53020288957005, 22.71094554703735, 20.855567205821508, 18.98707008183099, 17.127914827265922, 15.299628882522306, 13.522404943858422, 11.814752845729183, 10.193201241280166, 8.672048728819803, 7.263169809619576, 5.975877633156766, 4.816847060982231, 3.790099033472491, 2.8970446641142025, 2.1365865745270236, 1.5052735673465634, 0.9975034255433757, 0.6057674703303281, 0.32092953693143683, 0.13253132554422944, 0.029115199345771982, -0.001444199491501163, 0.028392639000590046, 0.10615352506387347, 0.21966032928366724, 0.35730946469474456, 0.5083204394579772, 0.6629469418452714, 0.812646163896447, 0.9502034197082431, 1.0698105278640018, 1.1670978618161851, 1.239121383181415, 1.2843073175846864, 1.3023583694918042, 1.294127057229086, 1.2614625756158782, 1.2070328011263611, 1.1341335011341782, 1.0464916874227512, 0.9480698345527173, 0.8428779710197617, 0.734800115187768, 0.6274407713495959, 0.5239962504168318, 0.4271544679431408, 0.3390256385835542, 0.2611049745486275, 0.1942671543741904, 0.13879100798618532, 0.09441157838710333, 0.060395667451013414, 0.03563586823861549, 0.01875726032092794, 0.008230943165584561, 0.002487605330161123, 2.4564581269985684e-05, -0.0004998976856601434, -0.00019047144322740907, 0.0001383047447738626, -1.130316242492818e-05, -0.0008222026198398645, -0.0021937015888607897, -0.0038009343365804846, -0.0051797002652265185, -0.005832194242341387, -0.005347439267478301, -0.003528705037418475, -0.0005188311106703852, 0.0030867146998311036, 0.006149744670149314, 0.006933293536265402, 0.0030905255153258976, -0.008291076045402806, -0.030581008911607005, -0.06742489074620636, -0.122485830820338, -0.19910492282835265, -0.2998806346249121, -0.42617008911032783, -0.5775187054906048, -0.7510283067206792, -0.940677493088431, -1.1366116510578883, -1.3244238041946768, -1.4844509218526338, -1.5911107422157729, -1.612307950198025, -1.5089397231457191, -1.234530256397977, -0.735026024200346, 0.051218805919103834, 1.1932406371561868, 2.7670239996741297, 4.854798429340443, 7.544059745953702, 10.926306746100906, 15.095491075923556, 20.146185495641785, 26.171492058138586, 33.26073985008518, 41.496943627032785, 50.954097524369566, 61.69434911066918, 73.76508303853873, 87.19600180444408, 101.99626346536333, 118.15174675774776, 135.6225183822819, 154.34057897068863, 174.2079643087317, 195.09527663377463, 216.84071717351657, 239.24968550320804, 262.09500377409165, 285.11796800279825, 308.03052885948205, 330.5173764883627, 352.23890964387783, 372.8350551542586, 391.92978680765555, 409.136303002029, 424.0628057906675, 436.318807483181, 445.5218751085042, 451.3047081987346, 453.3224318944175, 451.2599756751451, 444.83940471011346, 433.8271067543003, 418.04052197051396, 397.3546791149085, 371.70876548998297, 341.1098774842373, 305.6364272692071, 265.4408031287051, 220.7508572184896, 171.870134046364, 119.17677385968013, 63.12104830032018, 4.22151074298449, -56.94022986946958, -119.72608680695234, -183.4493756869003, -247.38385004501436, -310.7737863413736, -372.8449869753917, -432.8165153547805, -489.91322465539855, -543.3789537585582, -592.4893958635269, -636.5647423859297, -674.9819480220813, -707.1863786199725, -732.7026080204582, -751.1441695096483, -762.2220820938093, -765.751710411976, -761.658029184313, -749.9791295845447, -730.8678277804571, -704.5912984976272, -671.5286923266584, -632.1670828329666, -587.0961168295829, -536.9985558856946, -482.6396409216783, -424.85516617419233, -364.5381167148984, -302.62411732389575, -240.07582921213086, -177.86666873044715, -116.96417041203118, -58.313257458423465, -2.8197291396450335, 48.66572436131799, 95.36267478616323, 136.57498319129036, 171.70342644750264, 200.25663081199443, 221.8602490615137, 236.26443167413217, 243.34867106237422, 243.12419000101454, 235.73386749286578, 221.44975819973226, 200.6682219055305, 173.9027412664498, 141.7745538464409, 105.00126750904113, 64.38366820375927, 20.790965222336578, -24.85524964218808, -71.59802658066414, -118.46274331473172, -164.4749802669039, -208.6781199601394, -250.15141161810206, -288.02703772951116, -321.50598935500096, -349.87258429509626, -372.5073533169483, -388.89805263891037, -398.64859864146547, -401.48576252690265, -397.26350752424605, -385.96489830360014, -367.70156055576126, -342.71072070486287, -311.3499249420248, -274.0894630199256, -231.50252435594115, -184.25301533093733, -133.08283117891963, -78.79754386737332, -22.250887132129296, 35.67147388313804, 94.0685615262752, 152.04076243816152, 208.70623466324523, 263.216727203939, 314.77251067308435, 362.6361651713181, 406.1449528685736, 444.72148962080064, 477.8826075543555, 505.2462518907204, 526.5367036596169, 541.5884680986532, 550.3455954242932, 552.8596112659218, 549.2858029976879, 539.8775943897259, 524.9791654031881, 505.01650669544136, 480.487141755601, 451.9487652363619, 420.00693211021905, 385.30220654909886, 348.497025152702, 310.2625324642166, 271.26565706602304, 232.15668465159652, 193.5577221097073, 156.05225812750263, 120.17482839538827, 86.40257493588301, 55.148462709779714, 26.756049173273087, 1.4958616907273643, -20.436605192185876, -38.92126791457395, -53.912261539509906, -65.4352646466039, -73.58345282948017, -78.51221800232942, -80.43281279876628, -79.60509720826019, -76.32957796484321, -70.9389816708298, -63.789609255693506, -55.25231380126838, -45.703634372533266, -35.517260353386675, -25.055963026545225, -14.664165184761554, -4.661280428777932, 4.664064113672569, 13.058832059431216, 20.30934523343024, 26.24397678166204, 30.73475848500381, 33.69791615374742, 35.0933709812808, 34.92326689074368, 33.229606557879706, 30.091104463608215, 25.619332462716905, 19.95428268328397, 13.259498524753688, 5.716910305076615, -2.478487947366974, -11.12398683276837, -20.01440718557005, -28.947123756872877, -37.72675893974961, -46.169451761565355, -54.10662231069864, -61.388168387861064, -67.88505223167869, -73.4912378976399, -78.12498145940468, -81.72950348797316, -84.27295129434341, -85.74777600105433, -86.16957114338076, -85.57542138149877, -84.02183001443132, -81.5823007362368, -78.34465355543159, -74.40815700755313, -69.8805588378911, -64.87509798860741, -59.50756843309878, -53.89350158514078, -48.145541075397006, -42.371060034972786, -36.67006765584395, -31.13343425815806, -25.841444244564784, -20.862728052098575, -16.25356276233962, -12.057530183327678, -8.30551667621876, -5.01603094684618, -2.195809136063492, 0.15932943481863499, 2.063416587568474, 3.539102325512415, 4.61630042606839, 5.330758163686686, 5.722594538668238, 5.834849150177817, 5.712083611978962, 5.399070378794198, 4.939575379980268, 4.375290105509509, 3.7449253039091466, 3.0834751141783863, 2.42165835504998, 1.7855377027529638, 1.1963127249375844, 0.6702777410872255, 0.21893110590346576, -0.15078089140737716, -0.4361050617752459, -0.6380287885342596, -0.76075659627838, -0.8111388484584348, -0.7980753148178632, -0.7319149415232885, -0.6238711764055466, -0.4854722726034468, -0.3280614106624425, -0.16235869259729716, 0.0019058520978749646, 0.15628227100782013, 0.2938108228896455, 0.40915232340974755, 0.4986415226876554, 0.5602687720708439, 0.5935973133369731, 0.5996251927185374, 0.5806020358998756, 0.5398117058491915, 0.48133222659726177, 0.40978394713084215, 0.330076828184646, 0.2471678144595297, 0.16583655514277218, 0.09048673357642051, 0.02497883058641465, -0.02750150374998215, -0.06453697982062333, -0.08453326617799395, -0.0867353918927594, -0.07120812228713484, -0.03878372702628948, 0.009018406479549322, 0.07009505982212555, 0.141879571876628, 0.22147365093597252, 0.3057853281239882, 0.3916641026757807, 0.4760295589166359, 0.555988971943226, 0.6289396854983471, 0.6926531560733107, 0.745338505223552, 0.7856843950333636, 0.8128789999000452, 0.8266087524667535, 0.8270372537395322, 0.814766711230571, 0.7907849095781841, 0.7564005410153382, 0.7131704772948271, 0.6628229543976147, 0.6071802222362714, 0.5480810709672204, 0.4873101324092336, 0.4265356928586561, 0.36725756543167776, 0.3107664622088356, 0.2581157033110131, 0.21010546716743303, 0.16727924849051645, 0.12993187798471478, 0.0981274463481881, 0.07172552556120888, 0.050413770604834714, 0.033744782643762176, 0.02117506208924535, 0.012103944312102941, 0.005910550334684699, 0.001986967307914541, -0.00023364387274148543, -0.0012550905359619716, -0.0015029679073776934, -0.001316446328650887, -0.0009468125191219143, -0.0005621550811221256, -0.0002572401441415963, -6.73551613452756e-05, 1.530538981589522e-05, 2.4260234755085635e-05, 1.94902828102827e-06, -1.4946031849036135e-05, -6.679422744888514e-06, 2.304309172847311e-05, 4.609183612967166e-05, 1.5012612885942597e-05, -0.000125645654514022, -0.0004220088346801921, -0.0008881828506296902, -0.0014791747172568828, -0.0020607507776212266, -0.0023778313088829725, -0.00202323022207679, -0.0004086784358922366, 0.003259888606205751, 0.010000849524602201, 0.021067436072666895, 0.037948741471588845, 0.062359964517146184, 0.09622143677558624, 0.1416274727829876, 0.20080255055840854, 0.27604651583756623, 0.36967021423531543, 0.48392291669952603, 0.6209135314783967, 0.7825279614218894, 0.9703452567461481, 1.185555417041006, 1.4288818019655103, 1.700511110882309, 2.000033784510472, 2.326397615905935, 2.677878465345265, 3.0520667588672294, 3.445878473691897, 3.8556057517006117, 4.276950682264567, 4.705083609206016, 5.1347243001045975, 5.560238726092854, 5.975749180521185, 6.37525499377716, 6.752760711153579, 7.102408304915395, 7.418609850363044, 7.696179836394707, 7.930459531915752, 8.11742466199726, 8.253782803655774, 8.337054600007662, 8.365651266684159, 8.338961648279538, 8.25732341363227, 8.121999760441627, 7.9351488531041, 7.699771951222567, 7.4196418006722675, 7.099213413076541, 6.743520909755233, 6.358063972137898, 5.94867871808928, 5.521406285635966, 5.082361090114921, 4.637601111078204, 4.193003613009318, 3.7541494618770224, 3.3262256712663207, 2.91394969498007, 2.521464966690673, 2.15227685088414, 1.8092155983533649, 1.49441823640787, 1.2093293304628447, 0.9547178922212481, 0.7307106868676513, 0.536840402125047, 0.37210578423146523, 0.23504128300545402, 0.12379360333146851, 0.03620249717975361, -0.030116843279244094, -0.0776923197907201, -0.1091168273794182, -0.12697632965280092, -0.13378427171513466, -0.13192331366482035, -0.12359689555412517, -0.11079133970339068, -0.0952488912045816, -0.07845148855326657, -0.061614730257300986, -0.045691198787744566, -0.031382047281636356, -0.019155558414387364, -0.009271252162434967, -0.0018080504626509927, 0.0033049997998553867, 0.006256892649293008, 0.007323071837579689, 0.006835390955963515, 0.005154437634464343, 0.0026448922231221035, -0.0003452516761886858, -0.003501203717936257, -0.00655348471999785, -0.009285692884038368, -0.011538183354294646, -0.013208073475207617, -0.014246108202710111, -0.01465100446044253, -0.014461939233744557, -0.01374985577000556, -0.01260824130047565, -0.01114395226119355, -0.009468608233523338, -0.0076909898049544135, -0.00591075335802986, -0.004213604842969807, -0.0026680510126350435, -0.0013237161202440432, -0.00021111137798784552, 0.0006573311821063282, 0.0012852044724374649, 0.001689330047786218, 0.0018965109176196846, 0.0019401180996533325, 0.0018567684653076886, 0.0016833111471322964, 0.0014542947792760344, 0.001200027768750678, 0.0009452863368069922, 0.0007086690187154495, 0.0005025427380646607, 0.00033349463967005866, 0.00020316988619834285, 0.00010935930752378066, 4.719841266728344e-05, 1.0348670742402326e-05, -7.948141662667307e-06, -1.4023895220084551e-05, -1.3194925972793472e-05, -9.444189779431368e-06, -5.357021731881278e-06, -2.2654349823852844e-06, -5.363286889529844e-07, 7.107561179441141e-08, 5.291663503156335e-08, -1.2270089189631484e-07, -1.85882206883364e-07, -1.0377296372908113e-07, 3.366489540584541e-10, 6.447852049653886e-09, -3.0624629156198244e-08, 2.1893781890890884e-07, 1.300278777347159e-06, 3.6751820495372162e-06, 7.130511076767892e-06, 9.880774760484551e-06, 7.406182309938204e-06, -8.868701695466294e-06, -5.288349925899221e-05, -0.00014500290460718243, -0.00031254599647498175, -0.0005894746370582401, -0.0010149393317519949, -0.001630430530711405, -0.0024753826445902895, -0.003581230793248259, -0.004964123903753711, -0.006616748552042613, -0.008500001832034898, -0.010535548705152635, -0.012600581609838103, -0.014526331225699378, -0.0161020128186987, -0.01708588086713899, -0.017224847967923243, -0.01628364044427983, -0.014083649252569701, -0.010550420632397682, -0.005767085120962072, -2.8897550689140743e-05, 0.006108659149456346, 0.011798996026332949, 0.015905355537721946, 0.017052482152882173, 0.013752740461472053, 0.00463556781526895, -0.011185431225054318, -0.03356794032456781, -0.06057375196976201, -0.0874287607937718, -0.10515558446498562, -0.0988208097862922, -0.045336614215512, 0.08924566312752734, 0.3530112764024267, 0.8120830982882682, 1.555199559317972, 2.6990123100797914, 4.3941346090649995, 6.831956435411404, 10.252223939332124, 14.951359049627868, 21.29146997651264, 29.70997829420539, 40.72975561787024, 54.96962075771466, 73.15502654501734, 96.12872274687388, 124.86126856180688, 160.46148072456498, 204.185623328049, 257.44549361564435, 321.8151075396021, 399.03553197944296, 491.0174726561913, 599.8412202704465, 727.7536018379698, 877.1616605202857, 1050.6223794665493, 1250.8283260173582, 1480.5889463372632, 1742.8072560440978, 2040.4517705653275, 2376.523599450382, 2754.02133859237, 3175.9094253407325, 3645.0694995395957, 4164.249690907677, 4736.012418632608, 5362.679364572392, 6046.2753436523235, 6788.469645323067, 7590.516114423622, 8453.194152651758, 9376.751123637301, 10360.847265797533, 11404.504280575577, 12506.058796462674, 13663.121920403437, 14872.546075787608, 16130.416200240352, 17432.09186475368, 18772.172513009366, 20144.495167292684, 21542.15696958266, 22957.543565104435, 24382.37266626353, 25807.75018535904, 27224.23844051627, 28621.936073372217, 29990.569089875833, 31319.592206494075, 32598.29945766417, 33815.94280121404, 34961.85725150574, 36025.590880061776, 36997.07960025799, 37866.91423802497, 38626.3589091711, 39267.43426491353, 39783.03399902988, 40167.03308481622, 40414.3857978915, 40521.2116918008, 40484.86784160277, 40304.00585454637, 39978.61236411894, 39510.031971000644, 38900.97186788926, 38155.48852749739, 37278.96328514846, 36278.04578333968, 35160.61828302085, 33935.82235212148, 32613.810473490706, 31205.57738967811, 29722.82312302172, 28177.806317009254, 26583.190205566254, 24951.883653627534, 23296.879804612683, 21631.094916069396, 19967.21002019516, 18317.520924290147, 16693.793040422766, 15107.120256625529, 13567.801418505824, 12085.231378804108, 10667.82343442416, 9322.967003863569, 8056.900898431305, 6874.65892495089, 5780.054332054664, 4775.683637161546, 3862.9492065918794, 3042.0996287687967, 2312.2868010736406, 1671.6379621751769, 1117.3396677618841, 645.734163482121, 252.4251131379427, -67.60988512093336, -319.90230718827274, -510.3735571735872, -645.2162456252973, -730.7805363410083, -773.4630171264237, -779.5977232274697, -755.3554421137121, -706.653245012819, -639.0755599998234, -557.8071882176289, -467.5791557194526, -372.6278822205158, -276.6674947829763, -182.87496475514183, -93.88748405239654, -11.8112584372645, 61.75931225864267, 125.71327036282949, 179.38663536936062, 222.5196930084701, 255.21120801635874, 277.86746581629586, 291.1488936310453, 295.91608602787835, 293.1768264825391, 284.03535417958756, 269.64499328618, 251.16509029958712, 229.72301396930897, 206.38177344527207, 182.11360957299405, 157.7797172808184, 134.116069042347, 111.72513520204976, 91.07326264348879, 72.49320313479232, 56.190249956635704, 42.25260564705645, 30.664946277043942, 21.324224005884144, 14.056900238244927, 8.636824906861188, 4.803024734119224, 2.2767317243477385, 0.7770690503342769, 0.03491100370144516, -0.19545736263880215, -0.1271410887964123, 0.06595845920370624, 0.2530995615537318, 0.3480904181509295, 0.3082863636092177, 0.1314444822424989, -0.14926036433041703, -0.47167997292574243, -0.7521832381510314, -0.8937625384118616, -0.7943277756264744, -0.3547786101878973, 0.513520285679037, 1.8821885238952853, 3.800473929558136, 6.291296094155015, 9.348818177836124, 12.937603964602458, 16.993344657663275, 21.42505800255626, 26.118595555677445, 30.941367497117696, 35.74795061863001, 40.38629999733899, 44.70427612774733, 48.556182869794725, 51.80901898703093, 54.34817342870251, 56.08233106912415, 56.94732033825031, 56.90879239409844, 55.96362861896852, 54.140024508744446, 51.49626200514934, 48.1182385217656, 44.11587855545538, 39.6186021122196, 34.77000495355969, 29.722022791918324, 24.62883689184361, 19.640780822614722, 14.898519461413779, 10.527702819359769, 6.634339634366165, 3.301093665271099, 0.5846354027450381, -1.4858524984512176, -2.908967982370965, -3.710184400392538, -3.939802468003871, -3.6698629094905506, -2.9901689135891485, -2.003604203722811, -0.8209412446239243, 0.44461072796661355, 1.6828733213389324, 2.791942441795259, 3.6829765011010607, 4.284318778166136, 4.544773949661415, 4.4358965584838055, 3.95319294570931, 3.1161860974257083, 1.9673429208809117, 0.5699135437158442, -0.9952197978733388, -2.6335428904894096, -4.241579351195706, -5.712022008348858, -6.939095625429029, -7.823904059168583, -8.27952102243645, -8.235592132928574, -7.642235385163949, -6.473056528241999, -4.72713338406778, -2.4298673646475275, 0.36735048803306436, 3.5886597631501607, 7.136385618970756, 10.89472617907074, 14.734325799979379, 18.51753977772344, 22.104169947066268, 25.357433144171, 28.149851062291912, 30.368843843645333, 31.921772834172433, 32.74019523516399, 32.783129818433125, 32.039173332784124, 30.527355477681397, 28.296674426609822, 25.424312698714047, 22.01259543587529, 18.184798673268133, 14.079975917877068, 9.847036094179774, 5.638322732739367, 1.6029735562422278, -2.1196424366431765, -5.406060499194413, -8.154176657886339, -10.28775888738211, -11.759777963309947, -12.554375565250854, -12.687345251793728, -12.205068644284426, -11.18191914234769, -9.71620924378493, -7.924848719571234, -5.936937715509037, -3.886578506541595, -1.905240392621654, -0.11404881050850786, 1.383616778397978, 2.508820703041627, 3.212615420696094, 3.4801644311769047, 3.3331418548666747, 2.830172139631514, 2.0651636242025195, 1.1634805732137428, 0.27600628632232443, -0.4287434129010385, -0.7741903776142716, -0.5865763087487866, 0.29331184710284863, 1.998126370130004, 4.62227354633884, 8.211225538866413, 12.7525346395148, 18.16928566823279, 24.316491859773652, 30.981060533124456, 37.8858331831303, 44.69804130316884, 51.04241953293618, 56.51903846569648, 60.72574195525112, 63.28488378205057, 63.873862532932165, 62.25875854853429, 58.33018966266896, 52.140330236773465, 43.93988766576937, 34.2137087990537, 23.71358157943654, 13.486733468417063, 4.898912490107087, -0.3493092845738602, -0.21434689062603765, 7.689360993561393, 26.07816002839318, 57.97712854567933, 106.68672499221668, 175.73798749621903, 268.8364572283439, 389.795332302815, 542.4587015631583, 730.616074869338, 957.9100916941761, 1227.738848308431, 1543.157480547454, 1906.7885239556942, 2320.722319228629, 2786.422523152772, 3304.6402887292406, 3875.3377702128146, 4497.623335522017, 5169.700701212044, 5888.833973443885, 6651.330285788858, 7452.541415751428, 8286.887863450314, 9147.903868811487, 10028.297731971474, 10920.034170192579, 11814.435905166723, 12702.32034672811, 13574.195433361387, 14420.368453859057, 15231.08612983077, 15996.696318833549, 16707.8126695338, 17355.478832674828, 17931.328768095857, 18427.742904556413, 18838.001092088947, 19156.403058463802, 19378.376505836724, 19500.568631073118, 19520.91600434553, 19438.69110112482, 19254.524283617026, 18970.42586249306, 18589.829559572678, 18117.453394950535, 17559.19018007582, 16922.002487076883, 16213.79956448038, 15443.308327372855, 14619.913449858435, 13753.483675244821, 12854.19981081583, 11932.37989889532, 10998.305081709395, 10062.049758530411, 9133.319489264022, 8221.299875325318, 7334.5193526013445, 6480.737694057176, 5666.863091580758, 4898.829218952415, 4181.530998767558, 3518.7910492805036, 2913.340885574782, 2366.831560642067, 1879.8662772793743, 1452.0527641431381, 1082.0734628783318, 767.7712279515932, 506.247962167905, 293.9734038924702, 126.90114981685457, 0.5889407866782763, -89.67974314336097, -148.77561428122053, -181.6088591555089, -193.0210495859102, -187.68331833278438, -170.0055712599725, -144.05871595144242, -113.51101513131765, -81.57925347197175, -50.99498904375285, -23.985756773252042, -2.2707110237552146, 12.930153087410563, 20.874366919058804, 21.26436982742445, 14.205536251566423, 0.15670377021669266, -20.12488807393885, -45.64224367696723, -75.21976708763427, -107.56456057011435, -141.32587274652047, -175.1511239129635, -207.73710471622104, -237.87518103702513, -264.4895940489022, -286.66821138118905, -303.68535359893895, -315.01652623576894, -320.345289757695, -319.5627408165414, -312.7599629867709, -300.2142587550701, -282.3702208462006, -259.8168151210316, -233.26014016928715, -203.49420937052915, -171.37082604410912, -137.76947404423166, -103.56821738117976, -69.61650069587596, -36.71061709933156, -5.572479396402139, 23.167824312292954, 48.98540720894753, 71.46971238651422, 90.32937822553882, 105.39297179729456, 116.60584993500865, 124.02357021252956, 127.80242136276294, 128.18713241165193, 125.49661941348644, 120.10844492192419, 112.44257300606549, 102.94501216428783, 92.07191554161544, 80.27463004558085, 67.9861208895585, 55.60912761935995, 43.506317561575145, 31.992613180796358, 21.329780600924376, 11.723280624026824, 3.32130380502693, -3.7841519697214343, -9.55439462296343, -13.99964486962694, -17.173293656631703, -19.16518693952499, -20.09428405821192, -20.101015218647508, -19.339647417370244, -17.97094178225029, -16.15535030016072, -14.046958193780133, -11.788331874819875, -9.506383553017935, -7.3093142882593956, -5.284649485395253, -3.4983363077454106, -1.994833576050389, -0.7980879392172185, 0.08673890921228541, 0.6709280156945508, 0.9794140091977561, 1.047717173509426, 0.9187597835396961, 0.6397197154854046, 0.2590586182463133, -0.17615840505327635, -0.6225584080661886, -1.0423042044244943, -1.4044454301370053, -1.6857629504386302, -1.8711175041987187, -1.9533355253760476, -1.9326848091022364, -1.8160079465350178, -1.6155889647493138, -1.347840759808614, -1.0318993419374458, -0.6882080017119531, -0.3371682968739901, 0.002075082445104736, 0.31266098058519476, 0.5808097135216822, 0.7963673906659695, 0.9530873942043908, 1.0486547308659442, 1.0844726197522878, 1.0652429195806166, 0.9983812752710127, 0.8933140946832737, 0.7607081764624383, 0.6116892216014727, 0.4570951785435474, 0.30680873571085227, 0.16920653705643246, 0.05075324609761706, -0.044241755349280806, -0.11369828581646202, -0.1576742852647351, -0.17812466868243138, -0.17853464095537752, -0.16345999857310708, -0.13801289065176572, -0.10733519458818089, -0.0761028630468499, -0.04810307909965945, -0.025922610565725566, -0.01078072273351204, -0.002527855598414842, 0.00017533767223882688, -0.0005054562475000565, -0.002118813085958093, -0.0026270048842691827, -0.0012354098563574618, 0.0006864098315444275, -0.0013618313967616387, -0.01597100690262971, -0.05672000535234025, -0.14295387685483157, -0.30038743969873377, -0.5614833564800108, -0.9655646644378675, -1.558646889498641, -2.392945356514099, -3.5260522565127808, -5.019791039959478, -6.93876262020594, -9.348614037866056, -12.314072545699412, -15.896799685266016, -20.15312984095773, -25.13176554205128, -30.871507106369577, -37.39909681945568, -44.727257560969996, -52.853002572798495, -61.7562869686331, -71.39924076052958, -81.72638315688341, -92.66440960296113, -104.12260181739094, -115.9938690300154, -128.1562681023055, -140.47497307039555, -152.80465011701494, -164.99218073391663, -176.87966433090628, -188.3076221698009, -199.11831756546965, -209.15910303037217, -218.2857063697018, -226.3653920374162, -233.27984558738117, -238.9282435187362, -243.23103755280434, -246.13015845687434, -247.58960898048414, -247.59603568739902, -246.15877526066265, -243.30938257363457, -239.10066218941725, -233.60523834068482, -226.91371045637135, -219.13245196426072, -210.38113786462685, -200.79003861796048, -190.4971281838306, -179.64515596344268, -168.37873165959687, -156.84184245770453, -145.1760290370103, -133.5165336183718, -121.98971068076372, -110.7111650630023, -99.78424935149614, -89.29893686703376, -79.3310751060504, -69.94201677252349, -61.17861229792979, -53.07351444432252, -45.645795102251725, -38.901827358234826, -32.83638503590629, -27.433913071063376, -22.66992079212639, -18.512503630395937, -14.923931038271125, -11.861878496996711, -9.280845213319358, -7.133550585098307, -5.3722067770679285, -3.9496457116651857, -2.8202833117236863, -1.9409146825871189, -1.2713378419419856, -0.7748084606338134, -0.4183340042355541, -0.17281987002252017, -0.013083419664317746, 0.0822458044941846, 0.13091991639996417, 0.1473399104987663, 0.14287738363489047, 0.12623149405556938, 0.1037985531213747, 0.08004331259307429, 0.05785881304074343, 0.038903389998127834, 0.023906139646616874, 0.0129349031926054, 0.0056234165906815636, 0.0013566108358474814, -0.0005849297589648123, -0.000918685315341156, -0.00028815853811394604, 0.0007797385877472176, 0.0018931784520501485, 0.002795231732105009, 0.0033502924760039055, 0.003522165071817265, 0.0033479207974536026, 0.00291106887252394, 0.0023168183022222342, 0.001671366285682013, 0.0010663559272990892, 0.0005689291673016921, 0.00021719334991934726, 2.0443832245861037e-05, -3.68483013342209e-05, 1.15358043999316e-05, 0.00012148358080504072, 0.0002466491345845308, 0.0003457178984009041, 0.0003880586360618041, 0.00035725386015021595, 0.00025229233138192157, 8.650047674566606e-05, -0.000115484797992198, -0.00032220583752096816, -0.0005007111148402416, -0.0006220353911566085, -0.0006661607709746475, -0.0006258623415902123, -0.0005089726160906661, -0.00033877010807204834, -0.00015239240903163007, 2.62395318260605e-06, 7.338368878635071e-05, 7.796565684807942e-06, -0.00023871724928795781, -0.0006966491612605005, -0.001376605208949222, -0.0022649023268740756, -0.0033210776673236833, -0.00447768151950544, -0.005642543678976178, -0.0067035003010404385, -0.007535359887609712, -0.008008689017940426, -0.00799982346471079, -0.007401381675663739, -0.006132475636203331, -0.004147791917863279, -0.0014447565542642048, 0.0019319002185869756, 0.005888703074192439, 0.010285509115911525, 0.014941206766781165, 0.01964265878545407, 0.024156497721309046, 0.02824310746572878, 0.031671913222650123, 0.03423695668445993, 0.03577165937690485, 0.03616167782917716, 0.035354830065383945, 0.03336722796955309, 0.030284974845689202, 0.026261070443615486, 0.021507490380505687, 0.01628275310102155, 0.010875714427988462, 0.005586582569751282, 0.0007057409581323228, -0.0035073401809809644, -0.006843658402197552, -0.009161233035591488, -0.010397204725752632, -0.010574245335821238, -0.009800371574285689, -0.008261673216952193, -0.006207954213494746, -0.0039318157625542905, -0.0017422533325985785, 6.563976295408369e-05, 0.0012428068489351036, 0.0016177749038452998, 0.0011249444009086337, -0.00017314633069047132, -0.002072286742244677, -0.004224193363921808, -0.006147211064944404, -0.007251459339031139, -0.006878991877878628, -0.00435864578226938, 0.0009257135646421055, 0.0094558461702225, 0.021491959912215162, 0.036981866820573105, 0.055471394239761246, 0.07602153866274229, 0.09713821212394148, 0.11672033963554529, 0.13203197867473884, 0.1397037311508933, 0.13576628912221145, 0.1157195286037003, 0.07463847909569006, 0.0073156636768828675, -0.09156242736165739, -0.22720885003689353, -0.404505684037736, -0.6277571866001491, -0.9004358627636981, -1.2249322420350686, -1.602319675893089, -2.0321448880787654, -2.512256477598028, -3.0386821646332227, -3.605567301883674, -4.2051894571429855, -4.828031638155208, -5.46293092829775, -6.097303557592624, -6.7174412226334, -7.308872248077485, -7.856778051992016, -8.346453405882896, -8.763796647210246, -9.095804821172674, -9.331062141550838, -9.460202013326343, -9.476322429755808, -9.3753362282347, -9.156239316382935, -8.821290278655702, -8.376095602737855, -7.829528309689464, -7.193545140885725, -6.482895616530441, -5.7147213949306295, -4.908058166632422, -4.083250593812852, -3.261303787954744, -2.4631954676761634, -1.709172168324458, -1.0180560409691664, -0.40658925089802234, 0.11115766964618637, 0.5242889298020453, 0.8254763153504642, 1.0112245416102703, 1.0819968876484496, 1.0421859926017565, 0.8999332332188545, 0.6668025835953134, 0.3573191949848988, -0.011609501415882382, -0.4213685083577526, -0.8523794790693435, -1.284884662123569, -1.6997385475871303, -2.079174237488301, -2.407511993874734, -2.6717792486060286, -2.8622145514675217, -2.97263238831074, -3.0006342921124585, -2.947656344215927, -2.8188245630504642, -2.6226498197536996, -2.3705706207029817, -2.07635907073851, -1.7554148408331836, -1.4239773698299698, -1.098290737062741, -0.79375843963375, -0.5241265384209761, -0.30073320749822685, -0.13186060870853922, -0.022221265629461504, 0.027394169865186644, 0.02028737059824209, -0.03617241075196458, -0.1307759319531669, -0.24889476435223107, -0.3730781662387874, -0.483805180517088, -0.5603620627933715, -0.5818088129836363, -0.5279937153932147, -0.38057161292042463, -0.1239803289345261, 0.2536696934503319, 0.7598349929813132, 1.3969461881066774, 2.162013284982042, 3.0464524288319055, 4.036148521216422, 5.111761561506826, 6.249286003555511, 7.420816880188343, 8.595495839910557, 9.740609012429946, 10.822792473656078, 11.809296461706444, 12.669255982025858, 13.374915472380218, 13.90275667663887, 14.234469086907938, 14.357728648993094, 14.266748280704228, 13.962572263252461, 13.45309841125463, 12.752823513249318, 11.882336568021673, 10.86758822239316, 9.738828822191744, 8.529412069093835, 7.27449273324758, 6.009655966181626, 4.769538544326823, 3.586497508853962, 2.4893894163593515, 1.5025155724475492, 0.6447786513365764, -0.07091131694279762, -0.6379546226675219, -1.0560886879553752, -1.3311227939162735, -1.4743930917264307, -1.5019620327526906, -1.4335994076997178, -1.291603922098274, -1.0995109153567437, -0.8807544110905255, -0.6573516154199901, -0.4486769062060396, -0.27038733309018087, -0.13355542103844856, -0.04405576432736975, -0.002240137009929469, -0.0029221625395822767, -0.03567757222976386, -0.0854504092197317, -0.1334399204871695, -0.15822806181017504, -0.13709546635153866, -0.04746114094944849, 0.13164302838819816, 0.418130899394232, 0.8255304430954669, 1.3618374959767423, 2.0286224548200997, 2.8204468728476515, 3.7246331515672315, 4.7214141441714315, 5.784471180463248, 6.881849589395679, 7.9772211132171025, 9.031443821049795, 10.004354850518988, 10.85670909596964, 11.552202723868554, 12.059533721995296, 12.354121469933297, 12.419592522624404, 12.24893774146011, 11.845234569493261, 11.221872418380608, 10.402240639349642, 9.418863115236267, 8.311990137910135, 7.1276858082347285, 5.915477223914783, 4.725654636091623, 3.6063362964429926, 2.600434496373284, 1.7426679248055872, 1.0567827562768053, 0.5531234764060565, 0.22665595859154827, 0.0557036442635633, 0.0014669663202959778, 0.008395682690202598, 0.005464619194796954, -0.0916349167682608, -0.377416907938256, -0.9527068754698473, -1.9200457718746309, -3.3785440738030865, -5.418373912608632, -8.115116444176902, -11.524203541211588, -15.675705955947057, -20.569692399725263, -26.172350241474874, -32.41336567298037, -39.18458615432627, -46.34011507417219, -53.697968654201134, -61.04332243959704, -68.13337383780566, -74.70374850826029, -80.47628368286759, -85.1679912023846, -88.50093482848128, -90.21270388510301, -90.06712259862468, -87.86480358360632, -83.45313653728897, -76.73530743534688, -67.67796839009438, -56.31710157965003, -42.76157324693144, -27.194359567001502, -9.871658357465261, 8.880820418532311, 28.67422208152739, 49.06546206005737, 69.56850345145206, 89.66771771498382, 108.83296017228614, 126.53591305046554, 142.26718296424204, 155.55358994311885, 165.97505382321202, 173.18074222192797, 176.9041658125928, 176.97443615762845, 173.3252949063028, 166.0012921992688, 155.16052552582786, 141.07371956758053, 124.11954837208617, 104.77622944647267, 83.60955062780236, 61.257620223229054, 38.41275419635252, 15.801026484414653, -5.839895685450464, -25.78400321801219, -43.34053259436973, -57.876747165618454, -68.83927669244139, -75.77371976479489, -78.34121210680713, -76.33148285169604, -69.67195686782671, -58.432515673511986, -42.825671047517474, -23.20205856148792, -0.041317739630395124, 26.06141485960295, 54.4131098086434, 84.24416582433857, 114.7323720330783, 145.0287857390932, 174.2847538644402, 201.67924454963116, 226.44566740899367, 247.89666703065316, 265.4465016703658, 278.6302014791861, 287.11875911258653, 290.72979631206084, 289.43330100432127, 283.3525222023625, 272.76030094220334, 258.0682390620106, 239.81157289670068, 218.63003525719412, 195.24503776298263, 170.43395006349053, 145.00236033500119, 119.75530220122863, 95.46841876370831, 72.8599429023425, 52.56481098032453, 35.111706761689334, 20.90385040743867, 10.204387037413369, 3.1259432567099448, -0.37422952734573767, -0.49314871032592833, 2.4245757629562585, 7.898773469629157, 15.33070335182604, 24.024427112378618, 33.2118352755099, 42.08046346277135, 49.803149783516965, 55.56847703283998, 58.61075434743162, 58.23852632078278, 53.86095354624354, 45.011299624567265, 31.366043909054284, 12.759165729202287, -10.808883284608392, -39.16784214869588, -71.98006637626143, -108.7486444535836, -148.8309356191833, -191.4570723499255, -235.7528000165673, -280.76587753348775, -325.49532093120524, -368.92273736178896, -410.0432255291041, -447.8960721021465, -481.5941181528371, -510.35065699102853, -533.5029798857796, -550.5318083863965, -561.0759995944547, -564.9420784039839, -562.1083323735666, -552.7233940280984, -537.0994253020568, -515.7001613010592, -489.1239809928165, -458.08371422294846, -423.38335026728834, -385.89200655562837, -346.51541301309874, -306.1676059470381, -265.7433311463088, -226.09187463129663, -187.993176972619, -152.13699113266665, -119.10572269925837, -89.36144982825576, -63.237463101905696, -40.93448639050386, -22.521642567729632, -7.9419549386786406, 2.9779956399043708, 10.514651667235247, 15.030914395841608, 16.957071468834666, 16.769744431931873, 14.970159592282867, 12.06243703004917, 8.532643074547389, 4.8293586201616945, 1.3464427249257211, -1.5914247294992756, -3.739950559748834, -4.9428516112209575, -5.135696744601378, -4.345904439188866, -2.688979839995321, -0.36121305863676756, 2.370812689077422, 5.183434580239743, 7.71128449965285, 9.56420657571703, 10.344945739797058, 9.666968707174952, 7.171758744628238, 2.5449462258086144, -4.469298897292162, -14.056126899784527, -26.320540909268395, -41.2809134405873, -58.86568615547279, -78.91333398536456, -101.17555617034574, -125.32354205014174, -150.95705260900095, -177.61633552701667, -204.79710803880394, -231.9650131096069, -258.571237961219, -284.06877012206746, -307.9285000007212, -329.65455064847987, -348.79835943485665, -364.97107431847206, -377.85389394424556, -387.20606128912556, -392.8703087169349, -394.77564473976753, -392.9374661237191, -387.4550699012288, -378.5067252331117, -366.3430273139305, -351.27910273247835, -333.6821329903997, -313.95899598779846, -292.5437793890527, -269.885061797895, -246.43337728394366, -222.62925365469354, -198.89217733467925, -175.61078967462976, -153.13456314053397, -131.7671435026077, -111.76147834424393, -93.31678498416035, -76.57734344634565, -61.63305328016813, -48.52165234551989, -37.23237244364833, -27.71058567642283, -19.863691981559334, -13.567767393439022, -8.674627936721706, -5.019035808835131, -2.4257887941244825, -0.7164566399839521, 0.28444194328624306, 0.7439924687005162, 0.816299389865841, 0.6388520635051111, 0.3298895055673554, -0.013229655833718748, -0.3146839614816773, -0.5199434032473889, -0.5947170703360752, -0.5231723254874172, -0.30560893824089447, 0.04426260767295716, 0.5022896110016525, 1.0369425422957792, 1.6123368300417973, 2.1910849587344567, 2.736871250579625, 3.216663001151044, 3.6024950784465326, 3.8727891875326454, 4.013192810933854, 4.016945415175593, 3.8847999756408607, 3.62455211899423, 3.250237279877763, 2.781010651397172, 2.2398557590219235, 1.6521937073985418, 1.0444642763320784, 0.4427523338007984, -0.12847530503836394, -0.6474676699370091, -1.0960796998578604, -1.4604255975353135, -1.7312801050551354, -1.9042257008838575, -1.9795561918715225, -1.9619582379602578, -1.8600015895806012, -1.6854797035481812, -1.4526438401628574, -1.1773444218046134, -0.8761638973157796, -0.5655794707967262, -0.2611904688488641, 0.022956345271746052, 0.2749176335335244, 0.4852624526162414, 0.6473294825455572, 0.7573308056382944, 0.814308188795411, 0.8199546659588972, 0.7783199643902559, 0.695422760379018, 0.5787957554972681, 0.43699223954298994, 0.27908151513737645, 0.11414977963184772, -0.04915697585492809, -0.20302958223507203, -0.3408175830617229, -0.45726573989886116, -0.5486596467681282, -0.6128800253847604, -0.6493700197996517, -0.6590240046039091, -0.644009885878149, -0.6075394776765205, -0.553603205347282, -0.48668611387847466, -0.4114817366079147, -0.3326198696059899, -0.25442190667830256, -0.1806921959574562, -0.11455778606262083, -0.058360906604024404, -0.013605530648229305, 0.019043333495297795, 0.039711838478479804, 0.04922763823591499, 0.04899693355498573, 0.0408580822632266, 0.026922290669177142, 0.009411903487268818, -0.009493767937703285, -0.027796253277167282, -0.043792141156606124, -0.05615836479558584, -0.0640053042174247, -0.06689677931150032, -0.06483791460585223, -0.058233950209842476, -0.04782470226737009, -0.034600628534170896, -0.01970729585434897, -0.004345427978468734, 0.010326373963153416, 0.023279659463920552, 0.03368922312028763, 0.04098683793685613, 0.0448926626981552, 0.04542296263352946, 0.04287442415279554, 0.03778693221965351, 0.030888019868560927, 0.023023432280663978, 0.015079408081685529, 0.007902310806843796, 0.0022214637445411773, -0.0014191818150099435, -0.0027155262583533155, -0.0016398506144183122, 0.0015435137018218956, 0.006284922610219052, 0.011778655378335695, 0.017013270311534413, 0.020840309140782647, 0.02205734645873873, 0.019500380655743624, 0.01213981083471216, -0.000826490151124286, -0.01988885108756241, -0.045155416917771876, -0.07630081227590654, -0.11253780430693969, -0.15261468935647352, -0.19483973974643612, -0.23713255379110057, -0.2771006461154528, -0.3121381750788123, -0.3395424083138137, -0.35664244721443483, -0.3609339265768093, -0.35021292206639115, -0.32270216452648354, -0.27716278036431297, -0.21298344160988553, -0.13024227593317209, -0.029741200264016117, 0.08699105119311983, 0.21772834800538518, 0.3596083461345236, 0.5092232093219565, 0.6627362117122383, 0.8160193012516914, 0.9648056746648975, 1.1048506709348331, 1.2320938675883306, 1.342815209579897, 1.4337784996825402, 1.5023552818554158, 1.5466282037452346, 1.565473934242945, 1.558586112593297, 1.5264730214394655, 1.470426930146457, 1.3924626072063966, 1.2952281881481804, 1.181892770438762, 1.056016067467138, 0.92140614801541, 0.7819716894940053, 0.6415753643917036, 0.5038943885442807, 0.37229399900492705, 0.2497193545156686, 0.1386096808603317, 0.04083829733170727, -0.04232043610481602, -0.11020196293782934, -0.16273189936719526, -0.20038150610009237, -0.2241027929775612, -0.235247386155477, -0.2354738534809316, -0.22664851897010474, -0.21074484566326998, -0.18974607778911656, -0.1655557776438352, -0.13992005978525535, -0.11436451643460299, -0.09014793402133335, -0.06823391996612084, -0.04928047134534808, -0.033646649452446976, -0.02141546471065117, -0.012429527928936365, -0.006336507807709116, -0.0026411018438969583, -0.0007599872931431196, -7.62838882144497e-05, 9.679331910791166e-06, 3.6091418851552506e-05, 0.00044411542014464566, 0.0015526439852461748, 0.003544207241067017, 0.00646215131140979, 0.01021849856231413, 0.014611259983884843, 0.019349563511308114, 0.02408473504755383, 0.028443696024555307, 0.03206270869675579, 0.03461913591240518, 0.03585889567919193, 0.03561782998934362, 0.033835640121327, 0.030561592635564586, 0.02595178320855031, 0.020258324831821665, 0.013811368404376587, 0.006995334651936808, 0.0002211087355449038, -0.006103798648713978, -0.011605001426604212, -0.01596887811614423, -0.01896641306994714, -0.020470732929317784, -0.020467260838278777, -0.019056023092852665, -0.016445906293716495, -0.012941226665752762, -0.008921489169465764, -0.004815670917126862, -0.001072732528251853, 0.0018696807096738215, 0.0036162548788407404, 0.0038426519989301837, 0.0023198342193568974, -0.001067613590182898, -0.00631046265824749, -0.013271937468087016, -0.021693308147188627, -0.031208093805343708, -0.041363669255714525, -0.05164888196006302, -0.06152593502014823, -0.07046446261716688, -0.0779755563021768, -0.08364347767989054, -0.08715291847341694, -0.08830993654862257, -0.08705508868905064, -0.08346778669531588, -0.0777614741687227, -0.0702698171785363, -0.061424724754202485, -0.05172777573320122, -0.04171696327707675, -0.031929390829456596, -0.022864382117125832, -0.014949370092795128, -0.008510834628495027, -0.003752483741678256, -0.0007424193687726646, 0.0005895614538096805, 0.00044407145140327916, -0.0008660623252572169, -0.002943235078730963, -0.005339955465136927, -0.007598766060173165, -0.009294263638120852, -0.0100739614797209, -0.009694614093584719, -0.008050783571245548, -0.0051926755934691435, -0.0013307013401864765, 0.0031747308891251183, 0.007838751307177939, 0.01209236544958489, 0.015335908319468319, 0.017002787266208085, 0.016629629838339325, 0.013928053750886205, 0.008852606199755938, 0.0016590388001842017, -0.007052960007545431, -0.01631812968530716, -0.024809950017075894, -0.03087464831081396, -0.032597346551256956, -0.027901355553842756, -0.014678890925648082, 0.00905015944850345, 0.04495687326266194, 0.09420682056785525, 0.15725776173216421, 0.23366225643191843, 0.32188694745993746, 0.4191607800919169, 0.5213643161242426, 0.6229715558327519, 0.7170542750198593, 0.7953568344192063, 0.8484467750446829, 0.8659432339734359, 0.8368210925851223, 0.7497862874597361, 0.5937133039735442, 0.358131824580348, 0.03374622650297616, -0.3870314345321662, -0.9095567033284687, -1.5364596025476087, -2.2672071021470637, -3.0977448097270033, -4.020240068632551, -5.022946124157568, -6.090203514919174, -7.202591012716292, -8.337230949078995, -9.468255610279588, -10.567438679005571, -11.604923993389674, -12.550077344670003, -13.372435097795407, -14.042714177091483, -14.533849327468404, -14.822020478547186, -14.887631299124024, -14.716199772734477, -14.299122956973509, -13.634282120819972, -12.726455559512306, -11.587512778503005, -10.236377043416582, -8.69874540207103, -7.006562098397655, -5.197239204095533, -3.312675779203819, -1.3981033994886525, 0.49921899604950176, 2.3314190046153898, 4.051486486366866, 5.61476043560185, 6.9803746912305416, 8.112610613051295, 8.98210338142756, 9.566856975825859, 9.853027889130248, 9.83544474234225, 9.517840306827878, 8.912782736585795, 8.041308601144207, 6.932254786187734, 5.621275839410577, 4.149657478062332, 2.562944101301829, 0.9094199176931562, -0.7615022999312014, -2.4009273277670284, -3.9620966429538123, -5.401921408686986, -6.682373152570184, -7.771680652381546, -8.645288674021044, -9.286543147535705, -9.687077786591896, -9.846888662065686, -9.77410486427914, -9.484463467316314, -9.000435970021401, -8.350148050824655, -7.566116287684824, -6.6838405279235955, -5.740312635542357, -4.772500820375115, -3.815870720140113, -2.903002964640413, -2.062362988192332, -1.3172726495313438, -0.6851249966946846, -0.1768735879038294, 0.20318347118552976, 0.45731675141429956, 0.5939844742284431, 0.627171149212295, 0.5754426672038816, 0.460808205002817, 0.3074298195941526, 0.14022992401248893, -0.01654355037207849, -0.14073253708987857, -0.21360347920047298, -0.22104286881602292, -0.15456055975380079, -0.012055107563637008, 0.20169537937439053, 0.4748426683789142, 0.7885922118892044, 1.1176427479680868, 1.4309287860316426, 1.692641511755534, 1.8634970061871083, 1.9021879707643676, 1.766970188876053, 1.4173264766852611, 0.8156455856199292, -0.07114742382392875, -1.2700713819216478, -2.8007380824065105, -4.674222633640797, -6.892200533215466, -9.44638717160903, -12.318301472725182, -15.479367594944065, -18.89135530839682, -22.50721450230878, -26.272418070706536, -30.126229940012333, -34.0032236562076, -37.83501019943993, -41.55206736163509, -45.085610458416454, -48.36944352619432, -51.34173484445173, -53.94666579485177, -56.135876414063425, -57.86968580047148, -59.118051773984405, -59.861241689821576, -60.09019910057654, -59.80660131153021, -59.02275926679034, -57.76149961846458, -56.054862643711566, -53.94286701086839, -51.472239452682615, -48.69500822489277, -45.66701670746854, -42.44638225276114, -39.091962798233695, -35.66188715150056, -32.21218361512586, -28.79554351021733, -25.460249969783696, -22.249295338185696, -19.19970304305021, -16.342062189562657, -13.700312483383087, -11.291764494298166, -9.127071659351667, -7.21053669577072, -5.540619888200934, -4.110571103310855, -2.909159336828923, -1.9214652208196403, -1.1297048377161856, -0.5140549451087915, -0.05345220841147618, 0.2736576599650214, 0.48864103229506367, 0.612083595954965, 0.6632949351356692, 0.6599171093607025, 0.6176411367748911, 0.5500306855453719, 0.46843184543517075, 0.381976255340461, 0.29766659328925754, 0.22052905590006588, 0.1538178852837649, 0.09925664257300393, 0.05730124650578118, 0.027410713510362426, 0.0083129544330502, -0.0017452086663565093, -0.004772562447836075, -0.002839083882257601, 0.002083163103450573, 0.008241774536485722, 0.014188320137383146, 0.01882699232869743, 0.02143128601225829, 0.02163259414615079, 0.019385950832516746, 0.014918760249210312, 0.008668419069606925, 0.0012145224768793244, -0.006789149522607973, -0.01467838155411272, -0.021834394119944898, -0.027729175632639116, -0.03195864200664439, -0.03426295249658714, -0.034534142801235304, -0.03281207086536253, -0.02927032289877464, -0.024194194064585207, -0.01795273583736935, -0.01096761130504602, -0.0036811831172900867, 0.0034739829111087015, 0.010102303557579554, 0.015867565590982773, 0.02050948755077086, 0.023853908721145588, 0.0258165264918327, 0.026400530858904002, 0.02568884984891633, 0.023832004447548613, 0.021032765451028747, 0.017528903527153642, 0.013575332483809611, 0.009426864149369775, 0.005322615151732364, 0.0014729551476076758, -0.0019503876807609698, -0.004820719803329029, -0.007059194308963868, -0.008634208481690882, -0.00955776894089376, -0.009879378505843509, -0.009678115395110045, -0.009053636351406021, -0.008116840339143767, -0.006980882609944688, -0.005753137535151627, -0.004528582563737198, -0.0033849259480304003, -0.0023796413735454997, -0.001548921419572792, -0.0009084039445720944, -0.00045540822128492607, -0.0001723284467213125, -3.0774933304412636e-05, 3.967330072668872e-06, -3.14229959241455e-05, -0.00010220192927847492, -0.00017870270527988293, -0.00023852280097650823, -0.0002676585365917908, -0.00026059426512718687, -0.00021944950139660176, -0.00015236837709587647, -7.139504923881229e-05, 9.88729298305906e-06, 7.866674597082796e-05, 0.00012490333518585934, 0.00014280510612720324, 0.00013162924153421935, 9.573651997658193e-05, 4.391191254732992e-05, -1.1953318878394634e-05, -5.864976459894328e-05, -8.368378735916714e-05, -7.729892544609408e-05, -3.4218901010126877e-05, 4.513329321566594e-05, 0.00015413820446277221, 0.00028033094182518205, 0.000406638158154235, 0.0005134367972171866, 0.0005812456037721059, 0.0005937994828543312, 0.0005411665629333377, 0.0004225122444079952, 0.00024809589386352474, 4.0103905404518874e-05, -0.0001680179856557918, -0.0003339700811328448, -0.00041084087450453394, -0.00035311612362542955, -0.0001241943531588301, 0.00029505124601605123, 0.0008973181483119402, 0.0016403538322031317, 0.0024398406428723786, 0.0031647453393259957, 0.003636083102801672, 0.0036301194068662553, 0.0028868776171577367, 0.0011245909049890676, -0.0019395471846662825, -0.0065623380931898075, -0.012941660024890302, -0.021178553756470386, -0.03123565426526843, -0.042893774071709787, -0.05570887357373685, -0.06897201587427058, -0.08167517541965014, -0.09248592392347939, -0.09973423422110146, -0.10141412445126027, -0.09520026814231085, -0.0784835207653923, -0.04842659752869991, -0.002040282792969424, 0.06372008927022542, 0.15183909825386657, 0.26510876020448404, 0.4059822499208592, 0.5764179258416536, 0.7777186248856285, 1.0103719437226253, 1.2738978062465818, 1.5667099959535953, 1.8859984739516948, 2.2276488842296596, 2.5862266655680695, 2.954952582404375, 3.325725525075176, 3.6891972442013903, 4.034892523349149, 4.35137569433839, 4.62646156480993, 4.847467407880903, 5.001501099167056, 5.0757789678653, 5.057965552590221, 4.936526275297567, 4.701083118824354, 4.342762759026851, 3.8545262958151114, 3.2314957818676926, 2.471285933285713, 1.5741156516149544, 0.5429140620338189, -0.6166108366170938, -1.895971714050322, -3.2839716996419996, -4.766844427385009, -6.328462254228723, -7.9506085205976635, -9.613307773392776, -11.295206090058954, -12.973992086503005, -14.626848133154864, -16.23092240612638, -17.7638045617794, -19.2040131012735, -20.53153220634271, -21.728214529129023, -22.77813265607872, -23.667887492531733, -24.38685375844971, -24.927357274923896, -25.28478075138855, -25.45759686564658, -25.447329495495204, -25.258445994817937, -24.8981879041862, -24.376342197007975, -23.70495645456676, -22.898016442466144, -21.971092527414683, -20.941001664011868, -19.825521405530058, -18.642868731767923, -17.411274350960934, -16.148618028872605, -14.872094233838522, -13.59791493642448, -12.341054924825835, -11.115044022541188, -9.931808564250888, -8.80155839639284, -7.7327243373355214, -6.731942824155485, -5.80408378132573, -4.95231745470583, -4.1782151721658956, -3.481885616689546, -2.8621388915176906, -2.3166199646905654, -1.8419834102272827, -1.4340820504301766, -1.0881540913789653, -0.7990037852525147, -0.5611708632117165, -0.369085740642833, -0.21720782325005708, -0.10014485870792986, -0.012752284583273685, 0.049787723455355495, 0.09190712389895654, 0.1176118389304832, 0.13045909617459397, 0.13355062908843046, 0.12953993183387658, 0.1206496559067409, 0.10869808971957731, 0.09513282102244996, 0.08106921977169664, 0.06733170969289433, 0.054495958203390975, 0.04293039829983126, 0.032835786036680324, 0.02428179047007779, 0.01723989866963545, 0.011612185972693779, 0.0072557427121162825, 0.004002757178741258, 0.0016764268735336878, 0.00010300815337280365, -0.0008796059385472718, -0.0014163196025066829, -0.0016317246479569184, -0.001629000490805969, -0.0014903554228421069, -0.0012785685889743804, -0.0010392437737378201, -0.00080344590021865, -0.0005904544316965355, -0.000410430652406637, -0.00026685486790028253, -0.00015864249598294305, -8.189320761083606e-05, -3.12638591890613e-05, -9.837190990722665e-07, 1.4450048867089551e-05, 1.9847211484293312e-05, 1.91147794943492e-05, 1.5207961742969565e-05, 1.0191693321362339e-05, 5.368991466828952e-06, 1.4405713025691872e-06, -1.3311047120840634e-06, -2.9717565557920234e-06, -3.670118037309332e-06, -3.682400290033248e-06, -3.2664020045920725e-06, -2.642047952684456e-06, -1.9732677076905136e-06, -1.3654073025043161e-06, -8.725262686650019e-07, -5.096988954943262e-07, -2.6654260848326553e-07, -1.1940915245020593e-07, -4.0816549146146594e-08, -5.6495871743748265e-09, 5.649769966870434e-09, 6.26082386269171e-09, 3.7184631442437694e-09, 1.4151021330153351e-09, 2.37751987017944e-10, -7.252192902420393e-11, -2.6846833790151902e-11, 3.690347915308089e-11, 2.9353367231066984e-11, 1.7636465741865546e-12, 8.564397482583366e-12, 3.808788708058564e-11, 3.742219420734772e-11, -5.515729057432029e-12, 5.87655846879428e-12, 2.6215084946478083e-10, 9.206182522097367e-10, 1.896843741638609e-09, 2.668346331127679e-09, 2.223095825431078e-09, -7.214627515513371e-10, -7.170489806500174e-09, -1.7045597107783543e-08, -2.836571582460833e-08, -3.684553132041767e-08, -3.6485698650484765e-08, -2.1765857980860657e-08, 8.089603359377633e-09, 4.2687046182137936e-08, 5.245901737417479e-08, -1.9353012472619313e-08, -2.618705936658786e-07, -7.945160834731909e-07, -1.751662475417393e-06, -3.246305077957406e-06, -5.303664133406645e-06, -7.754704986833046e-06, -1.0079378952854757e-05, -1.1190200394430873e-05, -9.148810223892286e-06, -8.116005216892458e-07, 1.859463127635741e-05, 5.595970223264816e-05, 0.00012082604893973417, 0.00022595733474296237, 0.00038790467528826476, 0.0006275326533479151, 0.0009704605376816691, 0.0014473664337284501, 0.002094098603570166, 0.002951537265828518, 0.0040651528568245955, 0.005484213516941816, 0.007260605780179467, 0.009447248161418138, 0.012096097333573069, 0.015255770565588097, 0.018968837384947555, 0.02326885423979077, 0.028177401439714634, 0.03370163143969462, 0.03983127726760196, 0.046536025168415124, 0.053763465333784434, 0.06143768053886543, 0.0694586294139971, 0.07770246170146446, 0.08602287367498908, 0.09425357337618608, 0.10221187867669779, 0.10970342960207406, 0.11652791152310772, 0.12248561534982254, 0.127384666198959, 0.13104864775678754, 0.13332506876097977, 0.13409517160872736, 0.13327844704256372, 0.13083729131374172, 0.12678101543293493, 0.12116821726043862, 0.11410729810039588, 0.10575497798385476, 0.0963127539019903, 0.08602133442866126, 0.07515314215866348, 0.0640031668838539, 0.05287848370473054, 0.04208683699948891, 0.031924765203418796, 0.022665789407660085, 0.014549395288179936, 0.00777111867292978, 0.002473050505228176, -0.001262311001783564, -0.0034153245768510387, -0.0040296733940427135, -0.003209957303419374, -0.001116469786888937, 0.002042633319092312, 0.0060214272781501516, 0.010548106774197107, 0.015338098444272601, 0.020107750552815686, 0.02458790829901626, 0.02853667442849801, 0.03175068348827246, 0.034074367292397524, 0.035406929212675194, 0.035705872433603555, 0.03498717536882589, 0.03332223382658491, 0.030831710994239297, 0.027676685979468523, 0.024047630437814813, 0.020151881213357085, 0.01620037419992617, 0.012394457427322541, 0.00891360587829753, 0.00590481490922786, 0.0034743543942481717, 0.0016824257677367518, 0.0005410857508701079, 1.5596888610812735e-05, 2.9087516551678216e-05, 0.0004702748346176435, 0.0012038836857904702, 0.0020828797538817024, 0.0029615846086060516, 0.0037086638072967556, 0.00421894257631306, 0.004423035983592123, 0.004293883394791127, 0.0038494475295026767, 0.003151069451116762, 0.0022972510959739993, 0.0014129516945754954, 0.0006348155755830111, 9.307461576361223e-05, -0.00010881918469029634, 8.443300163617452e-05, 0.0006591251270183413, 0.0015139834026562985, 0.002445501398875064, 0.003138706635829241, 0.0031646919452784695, 0.001985932497948257, -0.001029993218106646, -0.006588134803166461, -0.015435732730656787, -0.028324498635399993, -0.04596699524626555, -0.06898914295499999, -0.09788120574242097, -0.13294994099041893, -0.17427459018088687, -0.22166927294524366, -0.27465638798792774, -0.33245234313574085, -0.39396755896661284, -0.4578222569617638, -0.5223786148211269, -0.5857890052776956, -0.646060692276666, -0.7011375569460786, -0.7489825674387252, -0.7876669731911763, -0.8154619530582763, -0.8309268466841133, -0.8329892674753165, -0.8210125487017558, -0.7948468095918838, -0.7548608271921105, -0.7019483694080508, -0.637510193667636, -0.5634114188864019], 'positive_zeros': ['0.841265845204250158921798730337699', '0.845250678940197524652540923615728', '0.879442622436091729381066234925478', '0.986860515291410759584333709491289', '1.06506476047545168073575219619354', '1.09405676251888750178416545756062', '1.10685461225756400494612377114833', '1.11846487088027115600647743452603', '1.22872808577451624965254824631591', '1.24281503990345091351649064208677', '1.24917257554006876973528623561095', '1.38951589055103835488383586934621', '1.41158422614610711790593003458644', '1.61459067502042790587790657073010', '1.63349567287706024824639619902121', '1.74460808437066896212049488996112', '1.76246344263137157951694125714799', '1.89953067478439023793761105955127', '1.99535073112783139247900384954812', '2.01398286060592675017057529030113', '2.02241749921676254492546844919408', '2.06720410513017576848885088720069', '2.07165162705821014007132020350180', '2.09777116581472295400036952387829', '2.30494108515338821678894841402771', '2.30622971864307765925059349540902', '2.40825969873832831714321913177408', '2.41544326732868787188713254829146', '2.41985090902735151250073866189437', '2.44379431195505825946881107473038', '2.45614259047245766862569958900230', '2.51058290608396911246773116682064', '2.65450289008237725206806261563140', '2.75406094859603973548801743570022', '2.80505824003724092344850755951743', '2.87515394730930890239978198200777', '2.97381943612901212999184823908299', '3.02487057619582339713580828377070', '3.06651686595406933974518162510122', '3.16970378013248089355482635561866', '3.22137982399632929622812072772620', '3.25484778840063260623141337713101', '3.30305309177115694600940191701124', '3.32177355503139947444974204167086', '3.43317424573209710697085880216737', '3.45614745866397367607113887563498', '3.46312522783334464503619288418001', '3.46954286810518333024167170090045', '3.47804729304043837410304807321082', '3.50142639794185567741827676416870', '3.69875446937873180175521976729119', '3.74503769217904669079634771105244', '3.76432505369385751655286597021914', '3.81802435264555733400081043329855', '3.86853998060277159400601222846310', '3.88990339482644356294133011584132', '3.89443005233007663127481408460745', '3.90525850200667422282806956160571', '3.90858028709383291743836612222722', '3.91217751865859907352404594327869', '3.93047790151904993453558552350609', '3.99610761124417119543404584417522', '4.01467342180095954359450986086215', '4.03543587896545814719803340300944', '4.35283992954374738017727562705906', '4.40083799147996761051749450466920', '4.48852113688735585944918606591216', '4.49614075042331598590352196950611', '4.51026226582348732767333505674835', '4.52776172792871141696572520396479', '4.62671685081520970585490830248278', '4.65132009791521198108391982333767', '4.68273518881666770640083677242993', '4.71936747576381554844286637688514', '4.78540529926063898543154602355306', '4.82832755554918666701935879838611', '4.85551564295858509489413974371246', '4.86547673485568978903368595835623', '4.93327501365447299577717791516258', '4.93668720821367733464521978303344', '5.15333642487962944991039392508976', '5.18884288756874986019231373598973', '5.20315147330267623212659132616079', '5.27984487416289318343525225146175', '5.34505198511693771318656648247016', '5.39907458610745568784509230190985', '5.41876073861727814284477398140649', '5.46091897735520380730094915150660', '5.50635158913485345429501036867963', '5.54535024510180460069908897878386', '5.54769825249617303446277152358112', '5.55928473475338978918859430351163', '5.56267532560248079876148834853541', '5.80695829971995138261692299960853', '5.84641744069337973844135865472350', '5.85437567625914374934455100829203', '5.89214867528181647443222619719895', '5.89705001538190843696687995361925', '5.91926170070473769034500855867539', '5.94720313987776003238078189709017', '5.95327312523420868141245620084163', '5.99839233534649226110630432617564', '6.05612105779823072420310720529999', '6.08776590565069923902335684569322', '6.09929454273862742227521966225972', '6.11970706599672712368948083821060', '6.15845959533143997215648127229898', '6.27471092474965026563596280571512', '6.30167071455970294425502107784974', '6.37007267811123475463567371824790', '6.37633982245748926527442844264202', '6.40537282308484128305853436789516', '6.50358733229036768497737162479747', '6.54825033902047461751270746654593', '6.55023970489334627696489779894164', '6.56931191803659984508683761244352', '6.67152700432686888632433716140864', '6.67167080511975906470285343556346', '6.67714595732105667012680909176325', '6.76914392874094003933679677400155', '6.83708145783465885178696709136415', '6.87305167653595673987491276236617', '6.96333907963454091153272053935323', '6.96757071000007201337236990568394', '7.00947263056473364366797463108704', '7.12117079656424419284762884669343', '7.14969579231394748349786233721200', '7.16935129199901123883996673816729', '7.19356943394381143985874158713480', '7.34075869943709875961150770510727', '7.35632907855141919190808873883683', '7.37370157289543967425192180325764', '7.42900819946168377328216382573573', '7.47338511280643963958061836767373', '7.51082523327725661096800631847823', '7.56554619649722185401269271626204', '7.58642643733980357293716027793935', '7.62096027933314511072916848277455', '7.65976550551885204283648499929166', '7.66870892676611306212179687451605', '7.69320590577127883248505636711787', '7.74687687340939929097547744332010', '7.899672700138229010327713636249724', '7.902761449422365607741378312908314'], 'prelabel': '32-8001e16-1.1-c1e16-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.993016117663373, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, 'spectral_label': 'c1e16-0', 'trace_hash': 1309034681367187629, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.841265845204250158921798730338', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '0.845250678940197524652540923616', 'prec': 107}, 'z3': {'__RealLiteral__': 0, 'data': '0.879442622436091729381066234925', 'prec': 107}}
• 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': 7.704457055859471e+28, 'bad_primes': [3, 7, 127], 'central_character': '1.1', 'conductor': 282038454737647007234373878049347083438272290079006727680128001, 'conductor_radical': 2667, 'degree': 32, 'dirichlet_coefficients': [1, -5, 0, 6, 1, 0, -16, 13, 0, -5, -11, 0, 18, 80, 0, -44, 5, 0, -11, 6, 0, 55, -13, 0, -23, -90, 0, -96, -24, 0, -42, 22, 0, -25, -16, 0, 40, 55, 0, 13, -9, 0, 7, -66, 0, 65, -31, 0, 136, 115, 0, 108, -66, 0, -11, -208, 0, 120, 7, 0, 6, 210, 0, 91, 18, 0, 16, 30, 0, 80, -46, 0, 39, -200, 0, -66, 176, 0, 4, -44, 0, 45, -15, 0, 5, -35, 0, -143, 1, 0, -288, -78, 0, 155, -11, 0, 41, -680, 0, -138], 'euler11': [1, 11, 127, 927, 6546, 37443, 205797, 996578, 4658508, 19883514, 82587628, 319384657, 1213890104, 4356733405, 15506991000, 52671594431, 178444424018, 579387538741, 1876345911000, 5798812162055, 17772565012664, 51437218394507, 146309020847308, 387473437398894, 998592562009548, 2349878794001398, 5337844170611997, 10682924882687673, 20544152154015666, 32002554157424037, 48228228865071607, 45949729863572161, 45949729863572161], 'euler13': [1, -18, 219, -1948, 14614, -94646, 555983, -2985822, 14990448, -70533970, 315528362, -1344918094, 5522268604, -21859541176, 84090414036, -314220696382, 1147549597242, -4084869052966, 14211279972084, -48025411963672, 157721513598844, -499358673875542, 1522995137456858, -4425902015622490, 12228168955153008, -31663147526889606, 76646977873682567, -169620812654025902, 340478215979937334, -590000707641708844, 862285428468144291, -921346074253633626, 665416609183179841], 'euler17': [1, -5, 158, -540, 11588, -27066, 558089, -870456, 20459225, -20581469, 610166673, -380514409, 15256129494, -5823688053, 325009231345, -84738254968, 5951336176930, -1440550334456, 93927667858705, -28611779404389, 1274207191468374, -540276047219513, 14727940171037937, -8445372677850637, 142718591030843225, -103225528624072632, 1125104019907681961, -927603145462394778, 6751426485018470468, -5348472137769205980, 26603696596385346782, -14312115257549078965, 48661191875666868481], 'euler19': [1, 11, 181, 1462, 14335, 95375, 719296, 4211650, 26971845, 143986816, 822044549, 4072545605, 21330650499, 99112960004, 484717258250, 2123022393713, 9768224694024, 40337425480547, 174982930228250, 679815792667436, 2779831703680179, 10084026099994895, 38673810028952669, 128705745610993024, 458078029889580645, 1359047642350925350, 4410051434971228096, 11110258442417637125, 31727869364813417935, 61481461821819820258, 144620210126702025901, 166992397328622781289, 288441413567621167681], 'euler2': [1, 5, 19, 52, 125, 264, 529, 1006, 1858, 3287, 5617, 9208, 14687, 22750, 34532, 50960, 73260, 101920, 138128, 182000, 234992, 294656, 359488, 420736, 475648, 515072, 541696, 540672, 512000, 425984, 311296, 163840, 65536], 'euler23': [1, 13, 208, 2018, 20375, 160550, 1275907, 8665917, 58792152, 357162729, 2165764215, 12076345886, 67338196417, 351022119450, 1831885262566, 9017382569929, 44472265582174, 207399799108367, 969067303897414, 4270886127348150, 18843988223529697, 77727504308934898, 320610830931912135, 1216076748419164863, 4604071349910314712, 15608639468567456571, 52856375643073254643, 152973606633080979850, 446510472802414040375, 1017145378387791178894, 2411309955504059960272, 3466258061037086192891, 6132610415680998648961], 'euler29': [1, 24, 472, 6622, 82320, 873128, 8519727, 75217422, 623444003, 4802217916, 35136436698, 242281577588, 1597747487582, 10006074679634, 60158248780719, 344816413108922, 1900626864033788, 9999675980158738, 50593087224584679, 244038155361593626, 1130056440764484542, 4969473537862528612, 20899971964810634058, 82837665059863752044, 311875626182796922883, 1091190120882540389718, 3584310774643021565127, 10652606690711199063112, 29126032953474211455120, 67945883337211863695558, 140447485822977346763032, 207100529942356426582776, 250246473680347348787521], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, 42, 1103, 21297, 334685, 4460298, 52049742, 541781390, 5109757813, 44140935934, 352708311097, 2626670113330, 18362034468729, 121180561220341, 758925862323514, 4526798708422582, 25783901132438856, 140330759961100042, 729327753692896954, 3610090099315178731, 16957724434595074809, 75199335301711682830, 313029924417880648057, 1214432536850515364674, 4358066642201825276533, 14324495245283137712690, 42661440873252651003342, 113329378684080674899638, 263618918792270776760285, 520020483496687072060527, 834909160548538341314063, 985541003657476809057942, 727423121747185263828481], 'euler37': [1, -40, 1093, -21915, 365384, -5189918, 65263975, -735690707, 7568509040, -71598368286, 629373118507, -5166707785384, 39884876555089, -290489859017229, 2005230244594602, -13140503504719049, 81949219635694490, -486198629674604813, 2745160204850010138, -14714182828799700537, 74750680129362155329, -358279962501233324488, 1614799231268096551363, -6796967501049835804038, 26584232499815351945840, -95611644232790233249439, 313827330266869186689775, -923377867790413627716134, 2405305335701855451112904, -5337819548695421807775255, 9850182996522544071560077, -13337850718072612283539720, 12337511914217166362274241], 'euler41': [1, 9, 262, 2416, 37769, 315207, 3782416, 28401838, 290262313, 2011916927, 18444064407, 119441768717, 1012122769428, 6182374690503, 49052876571800, 283552719845861, 2125239007937044, 11625661513680301, 82457885517195800, 426095446044157263, 2860017049061634708, 13838069564272264117, 87611228560967850087, 391829420226777883687, 2317722866136716416873, 9298248664783908500318, 50770081337269403980816, 173467563100183522342287, 852200465154530482093289, 2235049095193072928439536, 9937457525067876406166182, 13995884834923841197997409, 63759030914653054346432641], 'euler43': [1, -7, 372, -3138, 73315, -666780, 10087481, -91367841, 1064678040, -9159628901, 89637382245, -716798756168, 6144361260517, -45322086179990, 347525991033990, -2355177051473659, 16357027715502558, -101272613213367337, 642575557421847510, -3603423105912464930, 21006348421816780117, -105375469088594326424, 566630435932631665005, -2489757606125356803407, 12444170162683688582040, -45920801855220173265963, 218005417217090909386769, -619634479604621876573460, 2929640331901305788839315, -5391912821997828484092534, 27485352932019523400747028, -22239492560585689633400149, 136614025729312093462315201], 'euler47': [1, 31, 941, 18281, 336231, 4931218, 68745838, 824945998, 9479210063, 97272427247, 962214491659, 8677297342675, 75838894223815, 611669521060006, 4799477730874298, 34983489091252572, 248573892822537796, 1644223987288870884, 10602046307501324282, 63505364685013002938, 370069611204959803015, 1990094819796879273725, 10371917198276635440811, 49280460626885284455361, 225712188137142548500943, 923222205025974279376466, 3615971423624950344086062, 12190756020288152980775054, 39067178557204889410549671, 99832535627590381064714887, 241523634002595032183641229, 373963798875431415400175633, 566977372488557307219621121], 'euler5': [1, -1, 24, -19, 329, -170, 3169, -250, 23164, 13164, 133265, 205344, 624119, 1857497, 2603502, 12171723, 11656934, 60858615, 65087550, 232187125, 390074375, 641700000, 2082265625, 1028437500, 9048437500, -488281250, 30947265625, -8300781250, 80322265625, -23193359375, 146484375000, -30517578125, 152587890625], 'euler53': [1, 66, 2621, 76058, 1781762, 35276871, 609041687, 9347868667, 129408562699, 1632151424402, 18901860842316, 202148349366060, 2005406612147776, 18514212309862079, 159456108398381176, 1283208801034658221, 9658332823518811780, 68010066454836885713, 447912208491052723384, 2756340386055336735283, 15823622770426395720256, 84537528622275699167580, 418947669719195948734764, 1917306460145856556102474, 8056937050218939070423339, 30845756688314537134466711, 106513759986574573983473663, 326982584774827913954652987, 875306447766272906745457442, 1980300996217778127093314434, 3616839152851773816941197349, 4827052024675888901816218362, 3876269050118516845397872321], 'euler59': [1, -7, 442, -3508, 105593, -856382, 17639389, -139554059, 2261197320, -17115674831, 234152631353, -1678592886254, 20227940459783, -136519444242156, 1488182686904536, -9408447183719123, 94379018439678286, -555098383839428257, 5180363933114689816, -28038226939009757124, 245109256837696592663, -1200066842511527685946, 9876682943913887846273, -42594949581847336890589, 332012592005317865619720, -1208956229593324657847401, 9015787235887047621743989, -25824960058081483171999738, 187870792984166978173615433, -368244048047872565478294332, 2737476706098181517258540362, -2557868505924318929022120293, 21559177407076402401757871041], 'euler61': [1, -6, 323, -1803, 51999, -310708, 5859564, -41551842, 551504573, -4527561984, 47537189043, -403868693098, 3813583117651, -30173927981267, 277792860692578, -1985788550129320, 18004760530932760, -121133101557888520, 1033667234637082738, -6848908347115964927, 52802265487280039491, -341106004280275030498, 2449133775564987326523, -14228962989857025425664, 105727459795542808066013, -485913310774361559037722, 4179878444835007025045964, -13520122313214006558681988, 138023492314500182646533679, -291933263240171418450618543, 3190216908275705744721318443, -3614920707210242422811153406, 36751693856637464631913392961], 'euler67': [1, -16, 766, -9522, 266198, -2737347, 58496417, -519287669, 9388084842, -74027457819, 1185159368461, -8444953971409, 122332956376634, -795520428449380, 10542611262284876, -62937864816399986, 767216039759836106, -4216836942698799062, 47325781956396808364, -239263110621720876940, 2465146206233273306714, -11401744384258651065763, 107207599083415823371909, -448659072716172158370537, 3812197808495644968535722, -14128017828220325264108543, 106629480338424335805228233, -334312552917015486658098801, 2178223406975457306167849078, -5220361910464242403944159414, 28136884474779022123001696014, -39376945374625472213913600688, 164890958756244164895763202881], 'euler7': [1, 16, 120, 560, 1820, 4368, 8008, 11440, 12870, 11440, 8008, 4368, 1820, 560, 120, 16, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler71': [1, 46, 1696, 44053, 1001168, 19136619, 332551066, 5155299858, 74144424281, 977582113019, 12099134092469, 139298259299498, 1516078883966442, 15474989005321276, 149928022065044389, 1368030361292835759, 11870282787987010192, 97130155651791338889, 755787159229888764949, 5538668789883543214436, 38526112970191238809002, 251326007971362991165798, 1549902512443529567890949, 8891226782601575743192429, 47879023801639694066722841, 236362769243333187494537598, 1082534712977961369925910266, 4422899246739704486294758749, 16428849250081879601645793488, 51325598517914925355667032883, 140295173339687277861394262176, 270167474131732694277897205346, 416997623116370028124580469121], 'euler73': [1, -39, 1449, -35633, 819016, -15354005, 270847213, -4181000932, 61166945860, -808996878016, 10194855445346, -118177368250479, 1310024305648818, -13487234128627491, 133088301010306108, -1225754844226755877, 10832013228567582618, -89480103628553179021, 709227556083921249532, -5246763359016280666347, 37202385947672794929138, -244990145055568123543047, 1542830560949635435900994, -8937310912148054755471552, 49328700779135877381454660, -246142158895586956358694916, 1163999978492021205416482237, -4816961098850022804218999885, 18757143782844265728875083336, -59573013496962879372736828889, 176843225343592806988184647641, -347462154971158537954010829423, 650377879817809571042122834561], 'euler79': [1, -4, 523, -2502, 139646, -789723, 25317681, -164597190, 3543641120, -25365204188, 414143422875, -3092572364282, 42450546057593, -314223074160542, 3907176098450002, -27774453730301147, 324801875822633630, -2194181844693790613, 24384686030426462482, -154924230261039467138, 1653452207437478015033, -9516019582884487140518, 100673070887441256442875, -487111072641691100833892, 5376089162299152917388320, -19727235915754264149923610, 239714793479876159470660881, -590707916031225410517110517, 8251893149529168823104709886, -11679909887498649809068865178, 192877232942358798625618825963, -116537678030182371636129156796, 2301619141096101839813550846721], 'euler83': [1, 15, 838, 11765, 347274, 4483083, 94328215, 1114931415, 18851537694, 204626105391, 2955643532351, 29598435804255, 378062838968094, 3501719008421705, 40369874910747532, 345564045988135983, 3640146863496575154, 28681815817015286589, 278108068260139747948, 2002237406668421436835, 17942227569919113810174, 116589441602186837335965, 966319200012505970360519, 5552744429698964349779157, 42459171912072529660511454, 208425563325900025086460245, 1463600469055608993395763535, 5773455139313977465109371161, 37120120547435803318414251114, 104377558106763894680900165695, 617074090655151375319620070102, 916774752822987425146690915605, 5072820298953863752478356399681], 'euler89': [1, -1, 543, 671, 152533, 517635, 30165176, 157224139, 4823063548, 30855005869, 665165199182, 4562642804149, 80959528623427, 549124327434249, 8716291116419723, 56211725364021865, 827104459422306710, 5002843557397945985, 69041741933160625883, 387115627986995083281, 5079582256137455079907, 25478068662920079853901, 330574659391801061193902, 1364758097795251796859701, 18986417972246561418843388, 55084483916045769840260051, 940602069670137602372478776, 1436526714039376044899023515, 37674187227020130046916968693, 14750019910513889756785970599, 1062331165745759687445895083663, -174120577810999285787632895849, 15496731425178936435099327730561], 'euler97': [1, -41, 1499, -38587, 902626, -17930470, 329984509, -5477364638, 85335761433, -1232122907558, 16844252420378, -216472222887038, 2649198951432652, -30719144250882281, 340398004753863806, -3588518828385646187, 36211946895519678800, -348086326353407680139, 3202804826729104550654, -28036533540885484047113, 234531678396286601483212, -1858920634120138180888766, 14030790710132423596043162, -99553417196871010173278054, 668813363456732034167545113, -4164062717383819376860596446, 24333853843817659662801674941, -128256903490287331970620863910, 626280154935868220454311677666, -2597009632821903713386320465499, 9786015799134508141019285112731, -25963298754608364827774314138313, 61425365346268570446197767595521], 'euler_factors': [[1, 5, 19, 52, 125, 264, 529, 1006, 1858, 3287, 5617, 9208, 14687, 22750, 34532, 50960, 73260, 101920, 138128, 182000, 234992, 294656, 359488, 420736, 475648, 515072, 541696, 540672, 512000, 425984, 311296, 163840, 65536], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -1, 24, -19, 329, -170, 3169, -250, 23164, 13164, 133265, 205344, 624119, 1857497, 2603502, 12171723, 11656934, 60858615, 65087550, 232187125, 390074375, 641700000, 2082265625, 1028437500, 9048437500, -488281250, 30947265625, -8300781250, 80322265625, -23193359375, 146484375000, -30517578125, 152587890625], [1, 16, 120, 560, 1820, 4368, 8008, 11440, 12870, 11440, 8008, 4368, 1820, 560, 120, 16, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 11, 127, 927, 6546, 37443, 205797, 996578, 4658508, 19883514, 82587628, 319384657, 1213890104, 4356733405, 15506991000, 52671594431, 178444424018, 579387538741, 1876345911000, 5798812162055, 17772565012664, 51437218394507, 146309020847308, 387473437398894, 998592562009548, 2349878794001398, 5337844170611997, 10682924882687673, 20544152154015666, 32002554157424037, 48228228865071607, 45949729863572161, 45949729863572161], [1, -18, 219, -1948, 14614, -94646, 555983, -2985822, 14990448, -70533970, 315528362, -1344918094, 5522268604, -21859541176, 84090414036, -314220696382, 1147549597242, -4084869052966, 14211279972084, -48025411963672, 157721513598844, -499358673875542, 1522995137456858, -4425902015622490, 12228168955153008, -31663147526889606, 76646977873682567, -169620812654025902, 340478215979937334, -590000707641708844, 862285428468144291, -921346074253633626, 665416609183179841], [1, -5, 158, -540, 11588, -27066, 558089, -870456, 20459225, -20581469, 610166673, -380514409, 15256129494, -5823688053, 325009231345, -84738254968, 5951336176930, -1440550334456, 93927667858705, -28611779404389, 1274207191468374, -540276047219513, 14727940171037937, -8445372677850637, 142718591030843225, -103225528624072632, 1125104019907681961, -927603145462394778, 6751426485018470468, -5348472137769205980, 26603696596385346782, -14312115257549078965, 48661191875666868481], [1, 11, 181, 1462, 14335, 95375, 719296, 4211650, 26971845, 143986816, 822044549, 4072545605, 21330650499, 99112960004, 484717258250, 2123022393713, 9768224694024, 40337425480547, 174982930228250, 679815792667436, 2779831703680179, 10084026099994895, 38673810028952669, 128705745610993024, 458078029889580645, 1359047642350925350, 4410051434971228096, 11110258442417637125, 31727869364813417935, 61481461821819820258, 144620210126702025901, 166992397328622781289, 288441413567621167681], [1, 13, 208, 2018, 20375, 160550, 1275907, 8665917, 58792152, 357162729, 2165764215, 12076345886, 67338196417, 351022119450, 1831885262566, 9017382569929, 44472265582174, 207399799108367, 969067303897414, 4270886127348150, 18843988223529697, 77727504308934898, 320610830931912135, 1216076748419164863, 4604071349910314712, 15608639468567456571, 52856375643073254643, 152973606633080979850, 446510472802414040375, 1017145378387791178894, 2411309955504059960272, 3466258061037086192891, 6132610415680998648961], [1, 24, 472, 6622, 82320, 873128, 8519727, 75217422, 623444003, 4802217916, 35136436698, 242281577588, 1597747487582, 10006074679634, 60158248780719, 344816413108922, 1900626864033788, 9999675980158738, 50593087224584679, 244038155361593626, 1130056440764484542, 4969473537862528612, 20899971964810634058, 82837665059863752044, 311875626182796922883, 1091190120882540389718, 3584310774643021565127, 10652606690711199063112, 29126032953474211455120, 67945883337211863695558, 140447485822977346763032, 207100529942356426582776, 250246473680347348787521], [1, 42, 1103, 21297, 334685, 4460298, 52049742, 541781390, 5109757813, 44140935934, 352708311097, 2626670113330, 18362034468729, 121180561220341, 758925862323514, 4526798708422582, 25783901132438856, 140330759961100042, 729327753692896954, 3610090099315178731, 16957724434595074809, 75199335301711682830, 313029924417880648057, 1214432536850515364674, 4358066642201825276533, 14324495245283137712690, 42661440873252651003342, 113329378684080674899638, 263618918792270776760285, 520020483496687072060527, 834909160548538341314063, 985541003657476809057942, 727423121747185263828481], [1, -40, 1093, -21915, 365384, -5189918, 65263975, -735690707, 7568509040, -71598368286, 629373118507, -5166707785384, 39884876555089, -290489859017229, 2005230244594602, -13140503504719049, 81949219635694490, -486198629674604813, 2745160204850010138, -14714182828799700537, 74750680129362155329, -358279962501233324488, 1614799231268096551363, -6796967501049835804038, 26584232499815351945840, -95611644232790233249439, 313827330266869186689775, -923377867790413627716134, 2405305335701855451112904, -5337819548695421807775255, 9850182996522544071560077, -13337850718072612283539720, 12337511914217166362274241], [1, 9, 262, 2416, 37769, 315207, 3782416, 28401838, 290262313, 2011916927, 18444064407, 119441768717, 1012122769428, 6182374690503, 49052876571800, 283552719845861, 2125239007937044, 11625661513680301, 82457885517195800, 426095446044157263, 2860017049061634708, 13838069564272264117, 87611228560967850087, 391829420226777883687, 2317722866136716416873, 9298248664783908500318, 50770081337269403980816, 173467563100183522342287, 852200465154530482093289, 2235049095193072928439536, 9937457525067876406166182, 13995884834923841197997409, 63759030914653054346432641], [1, -7, 372, -3138, 73315, -666780, 10087481, -91367841, 1064678040, -9159628901, 89637382245, -716798756168, 6144361260517, -45322086179990, 347525991033990, -2355177051473659, 16357027715502558, -101272613213367337, 642575557421847510, -3603423105912464930, 21006348421816780117, -105375469088594326424, 566630435932631665005, -2489757606125356803407, 12444170162683688582040, -45920801855220173265963, 218005417217090909386769, -619634479604621876573460, 2929640331901305788839315, -5391912821997828484092534, 27485352932019523400747028, -22239492560585689633400149, 136614025729312093462315201], [1, 31, 941, 18281, 336231, 4931218, 68745838, 824945998, 9479210063, 97272427247, 962214491659, 8677297342675, 75838894223815, 611669521060006, 4799477730874298, 34983489091252572, 248573892822537796, 1644223987288870884, 10602046307501324282, 63505364685013002938, 370069611204959803015, 1990094819796879273725, 10371917198276635440811, 49280460626885284455361, 225712188137142548500943, 923222205025974279376466, 3615971423624950344086062, 12190756020288152980775054, 39067178557204889410549671, 99832535627590381064714887, 241523634002595032183641229, 373963798875431415400175633, 566977372488557307219621121], [1, 66, 2621, 76058, 1781762, 35276871, 609041687, 9347868667, 129408562699, 1632151424402, 18901860842316, 202148349366060, 2005406612147776, 18514212309862079, 159456108398381176, 1283208801034658221, 9658332823518811780, 68010066454836885713, 447912208491052723384, 2756340386055336735283, 15823622770426395720256, 84537528622275699167580, 418947669719195948734764, 1917306460145856556102474, 8056937050218939070423339, 30845756688314537134466711, 106513759986574573983473663, 326982584774827913954652987, 875306447766272906745457442, 1980300996217778127093314434, 3616839152851773816941197349, 4827052024675888901816218362, 3876269050118516845397872321], [1, -7, 442, -3508, 105593, -856382, 17639389, -139554059, 2261197320, -17115674831, 234152631353, -1678592886254, 20227940459783, -136519444242156, 1488182686904536, -9408447183719123, 94379018439678286, -555098383839428257, 5180363933114689816, -28038226939009757124, 245109256837696592663, -1200066842511527685946, 9876682943913887846273, -42594949581847336890589, 332012592005317865619720, -1208956229593324657847401, 9015787235887047621743989, -25824960058081483171999738, 187870792984166978173615433, -368244048047872565478294332, 2737476706098181517258540362, -2557868505924318929022120293, 21559177407076402401757871041], [1, -6, 323, -1803, 51999, -310708, 5859564, -41551842, 551504573, -4527561984, 47537189043, -403868693098, 3813583117651, -30173927981267, 277792860692578, -1985788550129320, 18004760530932760, -121133101557888520, 1033667234637082738, -6848908347115964927, 52802265487280039491, -341106004280275030498, 2449133775564987326523, -14228962989857025425664, 105727459795542808066013, -485913310774361559037722, 4179878444835007025045964, -13520122313214006558681988, 138023492314500182646533679, -291933263240171418450618543, 3190216908275705744721318443, -3614920707210242422811153406, 36751693856637464631913392961], [1, -16, 766, -9522, 266198, -2737347, 58496417, -519287669, 9388084842, -74027457819, 1185159368461, -8444953971409, 122332956376634, -795520428449380, 10542611262284876, -62937864816399986, 767216039759836106, -4216836942698799062, 47325781956396808364, -239263110621720876940, 2465146206233273306714, -11401744384258651065763, 107207599083415823371909, -448659072716172158370537, 3812197808495644968535722, -14128017828220325264108543, 106629480338424335805228233, -334312552917015486658098801, 2178223406975457306167849078, -5220361910464242403944159414, 28136884474779022123001696014, -39376945374625472213913600688, 164890958756244164895763202881], [1, 46, 1696, 44053, 1001168, 19136619, 332551066, 5155299858, 74144424281, 977582113019, 12099134092469, 139298259299498, 1516078883966442, 15474989005321276, 149928022065044389, 1368030361292835759, 11870282787987010192, 97130155651791338889, 755787159229888764949, 5538668789883543214436, 38526112970191238809002, 251326007971362991165798, 1549902512443529567890949, 8891226782601575743192429, 47879023801639694066722841, 236362769243333187494537598, 1082534712977961369925910266, 4422899246739704486294758749, 16428849250081879601645793488, 51325598517914925355667032883, 140295173339687277861394262176, 270167474131732694277897205346, 416997623116370028124580469121], [1, -39, 1449, -35633, 819016, -15354005, 270847213, -4181000932, 61166945860, -808996878016, 10194855445346, -118177368250479, 1310024305648818, -13487234128627491, 133088301010306108, -1225754844226755877, 10832013228567582618, -89480103628553179021, 709227556083921249532, -5246763359016280666347, 37202385947672794929138, -244990145055568123543047, 1542830560949635435900994, -8937310912148054755471552, 49328700779135877381454660, -246142158895586956358694916, 1163999978492021205416482237, -4816961098850022804218999885, 18757143782844265728875083336, -59573013496962879372736828889, 176843225343592806988184647641, -347462154971158537954010829423, 650377879817809571042122834561], [1, -4, 523, -2502, 139646, -789723, 25317681, -164597190, 3543641120, -25365204188, 414143422875, -3092572364282, 42450546057593, -314223074160542, 3907176098450002, -27774453730301147, 324801875822633630, -2194181844693790613, 24384686030426462482, -154924230261039467138, 1653452207437478015033, -9516019582884487140518, 100673070887441256442875, -487111072641691100833892, 5376089162299152917388320, -19727235915754264149923610, 239714793479876159470660881, -590707916031225410517110517, 8251893149529168823104709886, -11679909887498649809068865178, 192877232942358798625618825963, -116537678030182371636129156796, 2301619141096101839813550846721], [1, 15, 838, 11765, 347274, 4483083, 94328215, 1114931415, 18851537694, 204626105391, 2955643532351, 29598435804255, 378062838968094, 3501719008421705, 40369874910747532, 345564045988135983, 3640146863496575154, 28681815817015286589, 278108068260139747948, 2002237406668421436835, 17942227569919113810174, 116589441602186837335965, 966319200012505970360519, 5552744429698964349779157, 42459171912072529660511454, 208425563325900025086460245, 1463600469055608993395763535, 5773455139313977465109371161, 37120120547435803318414251114, 104377558106763894680900165695, 617074090655151375319620070102, 916774752822987425146690915605, 5072820298953863752478356399681], [1, -1, 543, 671, 152533, 517635, 30165176, 157224139, 4823063548, 30855005869, 665165199182, 4562642804149, 80959528623427, 549124327434249, 8716291116419723, 56211725364021865, 827104459422306710, 5002843557397945985, 69041741933160625883, 387115627986995083281, 5079582256137455079907, 25478068662920079853901, 330574659391801061193902, 1364758097795251796859701, 18986417972246561418843388, 55084483916045769840260051, 940602069670137602372478776, 1436526714039376044899023515, 37674187227020130046916968693, 14750019910513889756785970599, 1062331165745759687445895083663, -174120577810999285787632895849, 15496731425178936435099327730561], [1, -41, 1499, -38587, 902626, -17930470, 329984509, -5477364638, 85335761433, -1232122907558, 16844252420378, -216472222887038, 2649198951432652, -30719144250882281, 340398004753863806, -3588518828385646187, 36211946895519678800, -348086326353407680139, 3202804826729104550654, -28036533540885484047113, 234531678396286601483212, -1858920634120138180888766, 14030790710132423596043162, -99553417196871010173278054, 668813363456732034167545113, -4164062717383819376860596446, 24333853843817659662801674941, -128256903490287331970620863910, 626280154935868220454311677666, -2597009632821903713386320465499, 9786015799134508141019285112731, -25963298754608364827774314138313, 61425365346268570446197767595521]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/8001/2/a/r'], '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': '32-8001e16-1.1-c1e16-0-2', 'motivic_weight': 1, '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}, {'__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}, {'__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': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'order_of_vanishing': 16, 'prelabel': '32-8001e16-1.1-c1e16-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 7.993016117663373, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e16-0', 'trace_hash': 1309034681367187629, 'z1': {'__RealLiteral__': 0, 'data': '0.841265845204250158921798730338', 'prec': 107}}
• lfunc_instances •

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

  
  {'Lhash': '1066431153624676436857897691903,1071482530501859812813511610795,1114825968197399805774226587029,1250994324550696608999223176746,1350129982898641701194226605716,1386881711690821173082304859301,1403104913593685131107766090532,1417822664905564827150396438883,1557597895449348864200310219434,1575455231306280425317993386170,1583514365172011409277802606898,1761420652683686481262129510499,1789395591546813398773235927688,2046736838312547510564942078505,2211553485315499991175650286382,2234187840931969738269175335503', 'Lhash_array': ['1066431153624676436857897691903', '1071482530501859812813511610795', '1114825968197399805774226587029', '1250994324550696608999223176746', '1350129982898641701194226605716', '1386881711690821173082304859301', '1403104913593685131107766090532', '1417822664905564827150396438883', '1557597895449348864200310219434', '1575455231306280425317993386170', '1583514365172011409277802606898', '1761420652683686481262129510499', '1789395591546813398773235927688', '2046736838312547510564942078505', '2211553485315499991175650286382', '2234187840931969738269175335503'], 'factors': ['2-8001-1.1-c1-0-119', '2-8001-1.1-c1-0-121', '2-8001-1.1-c1-0-136', '2-8001-1.1-c1-0-165', '2-8001-1.1-c1-0-184', '2-8001-1.1-c1-0-194', '2-8001-1.1-c1-0-195', '2-8001-1.1-c1-0-198', '2-8001-1.1-c1-0-227', '2-8001-1.1-c1-0-230', '2-8001-1.1-c1-0-233', '2-8001-1.1-c1-0-268', '2-8001-1.1-c1-0-273', '2-8001-1.1-c1-0-286', '2-8001-1.1-c1-0-297', '2-8001-1.1-c1-0-300'], 'label': '32-8001e16-1.1-c1e16-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/8001/2/a/r'}