-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '57047605947678900956764945457,158801602094631880086309313141,699719729837549848946598120251,1110802168956060410012620922290,1314951042763612199763404314075,1356830889867970982079785255065,1366583514476693538505264480385,1886651868862624941593511878004,2003172313988824989406492839097,2315597441297642430133115322374', 'a10': 0, 'a2': 0, 'a3': 0, 'a4': -3, 'a5': 0, 'a6': 0, 'a7': 0, 'a8': 0, 'a9': 0, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 17312887701.124416, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[3, [1]], [7, [1]]], 'bad_primes': [3, 7], 'central_character': '1323.1', 'coefficient_field': '1.1.1.1', 'conductor': 16428520040413041995477810282649, 'conductor_radical': 21, 'degree': 20, 'euler_factors': [[1, 0, 3, 0, 4, -6, -2, 3, -14, 39, 1, 78, -56, 24, -32, -192, 256, 0, 768, 0, 1024], [1], [1, 0, -16, -12, 129, 147, -726, -720, 3663, 1257, -18069, 6285, 91575, -90000, -453750, 459375, 2015625, -937500, -6250000, 0, 9765625], [1], [1, 12, 105, 684, 3745, 17382, 72307, 270561, 952558, 3194589, 10673917, 35140479, 115259518, 360116691, 1058646787, 2799388482, 6634495945, 13329224964, 22507682505, 28295372292, 25937424601], [1, 6, 68, 336, 2292, 9399, 51837, 187401, 909867, 3004662, 13054461, 39060606, 153767523, 411719997, 1480516557, 3489782907, 11063046228, 21083501712, 55469689028, 63626996238, 137858491849], [1, -24, 380, -4284, 39486, -303462, 2039346, -12055428, 64101813, -306131850, 1328336013, -5204241450, 18525423957, -59228317764, 170328217266, -430872644934, 953096049534, -1757890875132, 2650787827580, -2846109035928, 2015993900449], [1, 0, -133, 0, 8580, 0, -354546, 0, 10419720, 0, -227952213, 0, 3761518920, 0, -46204789266, 0, 403653658980, 0, -2258813884453, 0, 6131066257801], [1, 15, 195, 1800, 15028, 107121, 712306, 4264599, 24178468, 125954103, 628044835, 2896944369, 12790409572, 51887376033, 199332423346, 689467498503, 2224683339892, 6128685804600, 15270642129795, 27017289921945, 41426511213649], [1, -15, 150, -1125, 6691, -30108, 81631, 232971, -5137202, 44535417, -275752187, 1291527093, -4320386882, 5681929719, 57736055311, -617549674092, 3979962840811, -19406110847625, 75036961944150, -217607189638035, 420707233300201], [1, 9, 149, 1098, 10878, 60723, 461409, 2027286, 13421802, 50078664, 374531595, 1552438584, 12898351722, 60394877226, 426120901089, 1738447936173, 9654265041918, 30208850293878, 127080764578709, 237956599446039, 819628286980801], [1, 12, 302, 2588, 38709, 264112, 3058184, 17732016, 173249698, 875160552, 7375688148, 32380940424, 237178836562, 898179806448, 5731529183624, 18314571171184, 99316703565981, 245683698020204, 1060768795084142, 1559540877540924, 4808584372417849], [1, 9, -34, -747, -2085, 20394, 110775, -623979, -5992218, 18494757, 381591615, 758285037, -10072918458, -43005256659, 313023674775, 2362771363194, -9903967342485, -145481442589107, -271487457790114, 2946437409545649, 13422659310152401], [1, -3, -79, 1100, 1674, -79931, 324899, 3229902, -28512986, -52724394, 1438527201, -2267148942, -52720511114, 256799818314, 1110765026099, -11750531857433, 10581961744026, 299000472217700, -923367821930479, -1507777835810529, 21611482313284249], [1, -15, -49, 1068, 9486, -83265, -760914, 2887821, 57371082, -59131839, -3026317959, -2779196433, 126732720138, 299822239683, -3713017588434, -19096412007855, 102251636610894, 541073492654484, -1166753046426289, -16786957096541505, 52599132235830049], [1, 0, -393, 0, 74860, 0, -9044030, 0, 764489716, 0, -47150015153, 0, 2147451612244, 0, -71361746878430, 0, 1659224074116940, 0, -24468058331664873, 0, 174887470365513049], [1, 18, -55, -1536, 19971, 205494, -1764945, -8798931, 181121100, 308804295, -11121159681, 18219453405, 630482549100, -1807115649849, -21386475710145, 146912653898706, 842387437344411, -3822568680681984, -8075674068237655, 155933924735788902, 511116753300641401], [1, -12, 251, -2436, 34779, -347730, 3716049, -34819755, 301038894, -2709237273, 20488848807, -165263473653, 1120165724574, -7903422809655, 51451823602209, -293691471746730, 1791827099901219, -7655721548547156, 48118535562317531, -140329753114009692, 713342911662882601], [1, 10, -182, -2448, 18867, 319605, -772530, -23213154, -12219093, 697872289, 3674653819, 46757443363, -54851508477, -6981657836502, -15567345506130, 431506734822735, 1706678296382523, -14836622009830704, -73904317315308662, 272065343962949470, 1822837804551761449], [1, 0, -351, 0, 63037, 0, -7800935, 0, 747809113, 0, -58386380555, 0, 3769705738633, 0, -198234871721735, 0, 8075057597528077, 0, -226659489467262111, 0, 3255243551009881201], [1, 0, -511, 0, 124869, 0, -19478727, 0, 2170586121, 0, -181575980223, 0, 11567053438809, 0, -553161583719207, 0, 18896953502481141, 0, -412101106957875391, 0, 4297625829703557649], [1, -20, 46, -144, 21153, -101181, -106944, -9264000, 7962453, 230795113, 4723714795, 18232813927, 49693669173, -4567513296000, -4165477462464, -311339643507219, 5142028946635713, -2765362894006896, 69787005255701806, -2397031919652366380, 9468276082626847201], [1, 15, -136, -1773, 22674, 93717, -3687774, -10067337, 346135869, 496605294, -27460905396, 41218239402, 2384530001541, -5756372421219, -175015562267454, 369155071940031, 7413046025768706, -48112218404608671, -306311743570909576, 2804103829013106045, 15516041187205853449], [1, 48, 1640, 40896, 851646, 14956146, 230812614, 3140740728, 38382277713, 420919956990, 4181686084101, 37461876172110, 304026021764673, 2214124850277432, 14481700653427974, 83516008391923554, 423252128521771806, 1808884671887553984, 6456005641351412840, 16817107377959290032, 31181719929966183601], [1, 6, 311, 1794, 51903, 385032, 6010353, 63309837, 574248354, 8264282925, 54719955099, 801635443725, 5403102762786, 57781178864301, 532092229646193, 3306400793833224, 43233745971829887, 144952122353734722, 2437441847851234871, 4561386351927391302, 73742412689492826049], [1, 24, 74, -4020, -48459, -7311, 5210808, 76543452, 494856327, -4853978709, -110568556605, -490251849609, 5048029391727, 78862795139052, 542238770014008, -76839344762811, -51440204977973859, -430998411547018020, 801313962164779274, 26248446544424661624, 110462212541120451001], [1, -45, 1178, -22635, 345159, -4534506, 54207117, -621172269, 7012361022, -77022211527, 806020404741, -7933287787281, 74394138082398, -678771709987563, 6101058774820077, -52567352455577958, 412137896617653111, -2783819494389193245, 14922551558746117658, -58714793272316006235, 134391637934412192049], [1, 0, -1008, 0, 463348, 0, -127901021, 0, 23478315106, 0, -2994718860389, 0, 268803229648594, 0, -16765214800172621, 0, 695360407068530452, 0, -17319316692705754608, 0, 196715135728956532249], [1, 54, 2333, 69008, 1746696, 35992198, 654949790, 10240122984, 143603877388, 1767376954770, 19638902203605, 192644088069930, 1706157667246828, 13261256227846536, 92451507903736190, 553784580323038702, 2929384055205531336, 12614932364931814352, 46486486430632181693, 117282237089884707006, 236736367459211723401], [1, 6, 339, 1962, 56389, 480210, 7585759, 89070387, 935834062, 11721114123, 105782261527, 1324485895899, 11949665137678, 128519394191139, 1236837986131999, 8847557974516530, 117399177377868901, 461581195263930954, 9012125813952804819, 18024251627905609638, 339456738992222314849]], 'euler_factors_factorization': [[[[1, 0, 3, 0, 4, -6, -2, 3, -14, 39, 1, 78, -56, 24, -32, -192, 256, 0, 768, 0, 1024], 1]], [1], [[[1, 0, -16, -12, 129, 147, -726, -720, 3663, 1257, -18069, 6285, 91575, -90000, -453750, 459375, 2015625, -937500, -6250000, 0, 9765625], 1]], [1], [[[1, 12, 105, 684, 3745, 17382, 72307, 270561, 952558, 3194589, 10673917, 35140479, 115259518, 360116691, 1058646787, 2799388482, 6634495945, 13329224964, 22507682505, 28295372292, 25937424601], 1]], [[[1, 6, 68, 336, 2292, 9399, 51837, 187401, 909867, 3004662, 13054461, 39060606, 153767523, 411719997, 1480516557, 3489782907, 11063046228, 21083501712, 55469689028, 63626996238, 137858491849], 1]], [[[1, -12, 118, -726, 4069, -17235, 69173, -209814, 579734, -1002252, 1419857], 2]], [[[1, 0, -133, 0, 8580, 0, -354546, 0, 10419720, 0, -227952213, 0, 3761518920, 0, -46204789266, 0, 403653658980, 0, -2258813884453, 0, 6131066257801], 1]], [[[1, 15, 195, 1800, 15028, 107121, 712306, 4264599, 24178468, 125954103, 628044835, 2896944369, 12790409572, 51887376033, 199332423346, 689467498503, 2224683339892, 6128685804600, 15270642129795, 27017289921945, 41426511213649], 1]], [[[1, -15, 150, -1125, 6691, -30108, 81631, 232971, -5137202, 44535417, -275752187, 1291527093, -4320386882, 5681929719, 57736055311, -617549674092, 3979962840811, -19406110847625, 75036961944150, -217607189638035, 420707233300201], 1]], [[[1, 9, 149, 1098, 10878, 60723, 461409, 2027286, 13421802, 50078664, 374531595, 1552438584, 12898351722, 60394877226, 426120901089, 1738447936173, 9654265041918, 30208850293878, 127080764578709, 237956599446039, 819628286980801], 1]], [[[1, 6, 133, 496, 7534, 20884, 278758, 679024, 6736849, 11244966, 69343957], 2]], [[[1, 9, -34, -747, -2085, 20394, 110775, -623979, -5992218, 18494757, 381591615, 758285037, -10072918458, -43005256659, 313023674775, 2362771363194, -9903967342485, -145481442589107, -271487457790114, 2946437409545649, 13422659310152401], 1]], [[[1, -3, -79, 1100, 1674, -79931, 324899, 3229902, -28512986, -52724394, 1438527201, -2267148942, -52720511114, 256799818314, 1110765026099, -11750531857433, 10581961744026, 299000472217700, -923367821930479, -1507777835810529, 21611482313284249], 1]], [[[1, -15, -49, 1068, 9486, -83265, -760914, 2887821, 57371082, -59131839, -3026317959, -2779196433, 126732720138, 299822239683, -3713017588434, -19096412007855, 102251636610894, 541073492654484, -1166753046426289, -16786957096541505, 52599132235830049], 1]], [[[1, 0, -393, 0, 74860, 0, -9044030, 0, 764489716, 0, -47150015153, 0, 2147451612244, 0, -71361746878430, 0, 1659224074116940, 0, -24468058331664873, 0, 174887470365513049], 1]], [[[1, 18, -55, -1536, 19971, 205494, -1764945, -8798931, 181121100, 308804295, -11121159681, 18219453405, 630482549100, -1807115649849, -21386475710145, 146912653898706, 842387437344411, -3822568680681984, -8075674068237655, 155933924735788902, 511116753300641401], 1]], [[[1, -12, 251, -2436, 34779, -347730, 3716049, -34819755, 301038894, -2709237273, 20488848807, -165263473653, 1120165724574, -7903422809655, 51451823602209, -293691471746730, 1791827099901219, -7655721548547156, 48118535562317531, -140329753114009692, 713342911662882601], 1]], [[[1, 10, -182, -2448, 18867, 319605, -772530, -23213154, -12219093, 697872289, 3674653819, 46757443363, -54851508477, -6981657836502, -15567345506130, 431506734822735, 1706678296382523, -14836622009830704, -73904317315308662, 272065343962949470, 1822837804551761449], 1]], [[[1, 0, -351, 0, 63037, 0, -7800935, 0, 747809113, 0, -58386380555, 0, 3769705738633, 0, -198234871721735, 0, 8075057597528077, 0, -226659489467262111, 0, 3255243551009881201], 1]], [[[1, 0, -511, 0, 124869, 0, -19478727, 0, 2170586121, 0, -181575980223, 0, 11567053438809, 0, -553161583719207, 0, 18896953502481141, 0, -412101106957875391, 0, 4297625829703557649], 1]], [[[1, -20, 46, -144, 21153, -101181, -106944, -9264000, 7962453, 230795113, 4723714795, 18232813927, 49693669173, -4567513296000, -4165477462464, -311339643507219, 5142028946635713, -2765362894006896, 69787005255701806, -2397031919652366380, 9468276082626847201], 1]], [[[1, 15, -136, -1773, 22674, 93717, -3687774, -10067337, 346135869, 496605294, -27460905396, 41218239402, 2384530001541, -5756372421219, -175015562267454, 369155071940031, 7413046025768706, -48112218404608671, -306311743570909576, 2804103829013106045, 15516041187205853449], 1]], [[[1, 24, 532, 7680, 99991, 992529, 8899199, 60833280, 375043508, 1505813784, 5584059449], 2]], [[[1, 6, 311, 1794, 51903, 385032, 6010353, 63309837, 574248354, 8264282925, 54719955099, 801635443725, 5403102762786, 57781178864301, 532092229646193, 3306400793833224, 43233745971829887, 144952122353734722, 2437441847851234871, 4561386351927391302, 73742412689492826049], 1]], [[[1, 24, 74, -4020, -48459, -7311, 5210808, 76543452, 494856327, -4853978709, -110568556605, -490251849609, 5048029391727, 78862795139052, 542238770014008, -76839344762811, -51440204977973859, -430998411547018020, 801313962164779274, 26248446544424661624, 110462212541120451001], 1]], [[[1, -45, 1178, -22635, 345159, -4534506, 54207117, -621172269, 7012361022, -77022211527, 806020404741, -7933287787281, 74394138082398, -678771709987563, 6101058774820077, -52567352455577958, 412137896617653111, -2783819494389193245, 14922551558746117658, -58714793272316006235, 134391637934412192049], 1]], [[[1, 0, -1008, 0, 463348, 0, -127901021, 0, 23478315106, 0, -2994718860389, 0, 268803229648594, 0, -16765214800172621, 0, 695360407068530452, 0, -17319316692705754608, 0, 196715135728956532249], 1]], [[[1, 27, 802, 12850, 204796, 2160907, 22322764, 152670850, 1038613258, 3811270347, 15386239549], 2]], [[[1, 6, 339, 1962, 56389, 480210, 7585759, 89070387, 935834062, 11721114123, 105782261527, 1324485895899, 11949665137678, 128519394191139, 1236837986131999, 8847557974516530, 117399177377868901, 461581195263930954, 9012125813952804819, 18024251627905609638, 339456738992222314849], 1]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 2, 'label': '20-1323e10-1.1-c1e10-0-2', 'leading_term': '0.018349500501989192862782605425191907431654646737182353218920786431024422741439910230211037', '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}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/1323/2/o/c', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.00625', 'prec': 24}, 'plot_values': [0.018349500501989188, 0.017829599544537843, 0.01656382035221127, 0.014580186957674983, 0.011928238949180726, 0.00867936577504827, 0.004927003757350306, 0.0007866626457609337, -0.003604252875483412, -0.008086862309178794, -0.012481302768816453, -0.016585691373009432, -0.020180007394191984, -0.02303034124239747, -0.02489080825705193, -0.025505481735131046, -0.024610377332247062, -0.021935472750023593, -0.017206747104550002, -0.010148224844848584, -0.0004839915540865695, 0.012059763762346153, 0.02775238884970741, 0.04685623996850122, 0.06962410311138066, 0.09629657556680829, 0.1270994214132006, 0.16224091599855586, 0.20190919526287876, 0.2462695993722603, 0.2954620181879877, 0.349598676313274, 0.4087619248774313, 0.4730021013164573, 0.5423355228808548, 0.6167426296508858, 0.6961662974928285, 0.7805103373545189, 0.8696381380388005, 0.9633701501349451, 1.0614824013213697, 1.1637068200677674, 1.2697307604545598, 1.3791969149969439, 1.4917034984383626, 1.6068047201642681, 1.724011579314593, 1.842792990266877, 1.96257661728358, 2.082749505229437, 2.202661638950631, 2.321628794834589, 2.438935360104453, 2.553837755853293, 2.6655681444259227, 2.7733384326478845, 2.876344596758383, 2.9737710839055973, 3.064794011531098, 3.148587490720827, 3.224330238905703, 3.291211331178127, 3.3484360134482887, 3.3952319833230167, 3.430855686975717, 3.4545986316960784, 3.4657937178707803, 3.4638215164469894, 3.448117054457521, 3.4181765243295232, 3.3735633622662475, 3.3139140161316725, 3.238943338345077, 3.148449873788269, 3.0423206446532274, 2.9205354221882858, 2.7831711077302943, 2.630407225078082, 2.4625272799609443, 2.279920057956781, 2.0830807022840103, 1.8726109854300732, 1.6492187384965067, 1.4137165298239178, 1.1670194121967314, 0.910142041683038, 0.6441983487527931, 0.370395775851233, 0.09002656396611107, -0.19553931678617933, -0.48486206296264356, -0.7764407831910335, -1.0687230367112723, -1.3601151391181774, -1.6489931507156863, -1.933712354901556, -2.2126177151431783, -2.4840606999217294, -2.7464129732382507, -2.9980798106894566, -3.237513628038018, -3.4632274999813717, -3.673808542222239, -3.867931019491377, -4.0443687776600985, -4.2020065366302415, -4.339853388227407, -4.457054244560101, -4.552899536236212, -4.6268337920550735, -4.678462979379748, -4.707560512533008, -4.714071846582848, -4.698117475342174, -4.659996187075514, -4.600185432140119, -4.5193375954801756, -4.418275767179149, -4.297987774098611, -4.159618414040841, -4.004459926467872, -3.8339407878260054, -3.649612930739412, -3.453139050737068, -3.246279817720432, -3.030872156579285, -2.8088097985958353, -2.5820238121912236, -2.3524624402648846, -2.122070465685857, -1.8927683397502935, -1.666431340598054, -1.4448694771496124, -1.2298104387728097, -1.0228770828178138, -0.8255667603496276, -0.6392343651738357, -0.465077042131241, -0.30412077453692893, -0.15720907252344454, -0.024993964061237776, 0.09207051618108436, 0.1937316486927146, 0.2799399602725672, 0.35084892854888855, 0.40681009299380305, 0.448365102580947, 0.4762348455505341, 0.49130574184163645, 0.49461332109641265, 0.4873232514836145, 0.4707103080313585, 0.44613594492365233, 0.41502226679272847, 0.3788246768585573, 0.33900368421746785, 0.29699605060145334, 0.25418570463681917, 0.2118748702955506, 0.17125586925333403, 0.13338411868742492, 0.09915324017857594, 0.06927099722852519, 0.044237742001223906, 0.0243285942788999, 0.00957910112090422, -0.00022528195126723336, -0.005555575308794086, -0.007141264225180596, -0.005967689728155884, -0.0032687155907287877, -0.0005145536858581301, 0.0006055164709542713, -0.001794679289361513, -0.009771439151270907, -0.025520080361178824, -0.05133983934066268, -0.08959519363450891, -0.14267409635705916, -0.21294349211360322, -0.302701762048163, -0.4141309629611752, -0.549249009498499, -0.7098619832190717, -0.8975176588286542, -1.1134610869968422, -1.3585930538979445, -1.633432231673961, -1.9380817103145438, -2.272198575842254, -2.634971225270222, -3.025106151758683, -3.4408205845411963, -3.87984214665728, -4.3394165660172055, -4.816323662877011, -5.306901606646152, -5.807079386567407, -6.312417063426294, -6.818154603080153, -7.319269705700423, -7.810541123280599, -8.286618339016139, -8.742094238975573, -9.17158195797059, -9.569794668458016, -9.931626810833178, -10.25223633775263, -10.527132611102807, -10.752253287684633, -10.92403465820182, -11.039479961892065, -11.096221925126939, -11.092574039934075, -11.027573383462686, -10.901013570133584, -10.713466677103689, -10.466303039129016, -10.161692854873, -9.80257666279175, -9.392634025619731, -8.93624072281652, -8.438414108144043, -7.904743578451233, -7.341311021282084, -6.754601735919253, -6.151410534855148, -5.538746502066257, -4.923706872072161, -4.313357493396021, -3.7146162044144484, -3.13413708404818, -2.5781976771995283, -2.0525900545739804, -1.5625197870817935, -1.1125147337802612, -0.706347112437631, -0.3469610074457725, -0.03641660673932694, 0.2241447985525088, 0.4345181591165998, 0.5954336942107861, 0.7085372541461261, 0.7763515618805572, 0.8022187804490892, 0.7902270701347567, 0.7451205299834333, 0.6721875511718775, 0.5771374142333511, 0.465966023493565, 0.3448129920248473, 0.21981294285765274, 0.09694406236597652, -0.018122922245973876, -0.12017147468746689, -0.20457890292951111, -0.2674481932545511, -0.3057229976727464, -0.3172836851104482, -0.3010223070482654, -0.2568937645316756, -0.18594084664762361, -0.09029119215661294, 0.026875272005080348, 0.16138658643720646, 0.3081723606129182, 0.4613915794703281, 0.6145876845706164, 0.7608711046382995, 0.89312690874181, 1.0042445001355966, 1.0873657382164164, 1.1361473691595736, 1.1450323360539387, 1.1095270356428137, 1.0264773869440131, 0.8943350145486597, 0.7134090192300487, 0.4860973608676215, 0.21709175342369774, -0.08644983940415722, -0.4147687455266346, -0.7554141667446563, -1.0931964239720104, -1.4101982268553896, -1.685842222592004, -1.8970139582037604, -2.0182434088979404, -2.021945276335506, -1.8787171648766985, -1.557693634601307, -1.0269531893041757, -0.25397439270016736, 0.7938655296089864, 2.148756793826834, 3.8418954335481343, 5.902901692977105, 8.359227433208531, 11.235562172053548, 14.55324782607921, 18.329712511652843, 22.577941145342987, 27.306012472836247, 32.516656407292096, 38.20687347467839, 44.36762833777216, 50.98362053283141, 58.03313932932456, 65.48800845786661, 73.31362515034522, 81.46910506899349, 89.90764875550393, 98.57692667307836, 107.4194371995457, 116.37302823673527, 125.37151236128155, 134.34536035054913, 143.22246459976589, 151.92896258861404, 160.3901107521588, 168.5313740514517, 176.27959951846208, 183.5637455499462, 190.31572682166563, 196.47129960161504, 201.97092476127625, 206.76058010730299, 210.79250893095235, 214.0258925040755, 216.4275353022091, 217.9728495448042, 218.6459002227027, 218.43949553173346, 217.35523894219827, 215.40350355936894, 212.6033056181372, 208.98205822065464, 204.57520883405837, 199.42578600081671, 193.58425191504705, 187.10777437814434, 180.0590029743448, 172.5052397521573, 164.51746764676304, 156.16938457820393, 147.5364322006174, 138.69481574023024, 129.7205305060638, 120.68856884972828, 111.67221834664971, 102.74173856251252, 93.96348392518814, 85.39920222252147, 77.10536325659484, 69.1326165341123, 61.52536443946969, 54.321443830829445, 47.55193981816952, 41.241223905937105, 35.40679630456626, 30.059304481689622, 25.202784882867242, 20.835000798408, 16.947848068161246, 13.527846658971013, 10.55669767220269, 8.01189022211739, 5.867361635013354, 4.094144125712331, 2.6610073585269536, 1.5351457250588743, 0.6828511041959875, 0.07015575107836021, -0.3365652007170502, -0.5700394620165168, -0.6616009565947834, -0.6407592902014664, -0.5348418805647512, -0.36869502741579513, -0.16446079757072593, 0.05856904019561885, 0.28402563308152484, 0.4984660429354303, 0.6913112380207633, 0.8547249883550999, 0.9834410280733954, 1.0745472919742873, 1.1272365832155182, 1.1425276046892532, 1.122967019464325, 1.0723228253361736, 0.9952778310238466, 0.8971313436322575, 0.7835155206510793, 0.6601339129869301, 0.5325286970320785, 0.40587888054852456, 0.28482972143854907, 0.1733614965363562, 0.0746964930300367, -0.00875653851557976, -0.07542201242532363, -0.12454378254537565, -0.15614130207703053, -0.17093955811532216, -0.17027709017851786, -0.15599875235515198, -0.13033688365635243, -0.0957863878724641, -0.054979224298463546, -0.010563138171538448, 0.03491100223865598, 0.07908951152591644, 0.11990073044273894, 0.15562321548061567, 0.18493323050719582, 0.2069302959492961, 0.22114359748556228, 0.22751911273375292, 0.22638900130203954, 0.21842548358745195, 0.20458197385783652, 0.186024618488286, 0.1640579443656032, 0.14004782513518227, 0.1153432835942733, 0.09120409073366358, 0.0687362179461717, 0.04883757432479195, 0.03215624877897707, 0.01906290441586225, 0.009638346374083522, 0.0036766269110968066, 0.0007033700221752735, 8.302756895323579e-06, 0.0006906605116773877, 0.001715129296870159, 0.0019756385141829758, 0.00036406687164674954, -0.00415929886049273, -0.01249681117339903, -0.025349249957601096, -0.043159669569300174, -0.0660682305819645, -0.09387985156426563, -0.1260467868758441, -0.16166732388037477, -0.1995011724419749, -0.23800145136556067, -0.2753624898182268, -0.30958199227168, -0.3385363069375235, -0.36006758727111715, -0.3720727564677768, -0.3725957425533342, -0.35991933615542687, -0.332652243976807, -0.2898076292010841, -0.23086964316285608, -0.15584480428426803, -0.06529575684384804, 0.039643104760852026, 0.15727620523185526, 0.28537994799721994, 0.4212549671159412, 0.5617985088981614, 0.703595003726889, 0.8430220723342321, 0.9763685279912433, 1.0999603762216241, 1.2102929461528675, 1.3041638742097093, 1.378792378584889, 1.4319283132382437, 1.4619455233520178, 1.467914999786644, 1.4496543247573932, 1.4077506773677064, 1.343555556045193, 1.2591518593217697, 1.1572970412867127, 1.0413241663513304, 0.9150206206324757, 0.7824894408834092, 0.6479938359504934, 0.5157903772455064, 0.3899569830437594, 0.2742222089210002, 0.17180266410895897, 0.0852557553067836, 0.016350914047633558, -0.034030290996973, -0.06595817461247984, -0.0804813884888287, -0.07961300712871955, -0.0662743143307455, -0.04419597666259594, -0.017777853449264264, 0.008089381440100784, 0.02823711944186923, 0.037461760075759264, 0.03078674514785689, 0.0037352114129451195, -0.04739465861712339, -0.1252616161290069, -0.23123120753167317, -0.36515372718691835, -0.5251803080258379, -0.7076281458737602, -0.9069021848793983, -1.115478298422259, -1.323954764886118, -1.5211763462334438, -1.6944211337869513, -1.829657219929816, -1.9118651353569172, -1.9254190901908224, -1.8545258909719287, -1.683700832247045, -1.3982552238502663, -0.9848026962524399, -0.43176394222141207, 0.27014905532530253, 1.1274874218982651, 2.1436646978071012, 3.318618241042689, 4.648550630028275, 6.125779725134715, 7.738678583576521, 9.47171290928145, 11.30558703936897, 13.217504192721266, 15.18155064466755, 17.16914714692375, 19.149594070612228, 21.090707459631474, 22.959618077624373, 24.723526201996656, 26.350410952276317, 27.809800156859332, 29.07352649817258, 30.116460390880615, 30.91721319149691, 31.45868757560597, 31.72855602429111, 31.719745883009484, 31.430800536442515, 30.865818438616174, 30.034400143386186, 28.951479861153086, 27.637021429917194, 26.11559535489103, 24.415851320852227, 22.569817281857325, 20.61216668936256, 18.579517886910075, 16.50941315110454, 14.439353571248938, 12.40590692597642, 10.443844505557085, 8.585330020054966, 6.859185062513679, 5.2902487575655, 3.8988322629225918, 2.7003343529186767, 1.704942894817596, 0.9174786534083328, 0.3374324782292617, -0.040852028460346086, -0.22785919783456482, -0.2384562765801377, -0.09133720209771595, 0.19162810739902647, 0.5861202253477161, 1.066152686556986, 1.6048872081775645, 2.1754476504300406, 2.7517085708845976, 3.309035694338282, 3.8249572265260343, 4.279747408227083, 4.656908484218037, 4.943545827705887, 5.13063887419289, 5.2131385103866945, 5.189924031886997, 5.063649434739949, 4.840473151060054, 4.529683508182544, 4.143235399714909, 3.695216173509627, 3.201262420878764, 2.6779691752415475, 2.142257012255845, 1.6107200911000887, 1.0990469243590382, 0.6214999367846645, 0.19046747269485512, -0.18389837641349102, -0.49394812335174754, -0.7346990619395025, -0.9038940215478399, -1.0019604481349054, -1.0318753331819333, -0.9989268058941064, -0.9103952100598154, -0.7751709758693436, -0.6033261895872503, -0.4056580608582706, -0.1932230837521169, 0.023119303711716943, 0.2331352377085436, 0.4276065686440148, 0.5986620902476542, 0.7400347766653931, 0.8472391036646161, 0.917663690529726, 0.9505779957504502, 0.9470554104640775, 0.9098185811429642, 0.8430175771585762, 0.7519509026124788, 0.6427392791112032, 0.521972171373648, 0.39634614001589835, 0.2723118617196047, 0.1557462808999709, 0.051665568815171474, -0.03600733649512235, -0.10460943449086076, -0.15283112119913506, -0.18072988529084313, -0.18966230245710192, -0.18213861452830596, -0.16160603168226972, -0.13217088201104943, -0.09827278146409121, -0.06432654444403905, -0.03434954718768066, -0.011593599270871432, 0.0017998923287677895, 0.005101596853818618, -0.0007653085483959693, -0.013061097449717826, -0.027154457110503228, -0.036545626908787245, -0.0329929475971037, -0.006743695698306661, 0.053135311860396564, 0.15833825068007418, 0.3208220648556609, 0.5522478081436601, 0.8633830961371939, 1.2634881095260988, 1.7597105032609155, 2.356515843287598, 3.055180046770321, 3.8533732934855753, 4.744890536776217, 5.719486780553046, 6.762844619591428, 7.856713047457797, 8.979215904608843, 10.1053104913412, 11.207402657062591, 12.25610580343217, 13.221124782036245, 14.072309136156669, 14.780751932312212, 15.319789311214775, 15.66606232336535, 15.800547359527936, 15.709514428286388, 15.385336351014807, 14.827154199181617, 14.04136381724737, 13.041920858400465, 11.850456966117456, 10.495962067186412, 9.014291084265572, 7.447460277873999, 5.842715465895561, 4.251389500069665, 2.727563441121847, 1.3265905724822549, 0.10351694221322527, -0.8885592614876485, -1.6001587362985283, -1.987026185095448, -2.0116248994758887, -1.6444875120368998, -0.8653781702511008, 0.33577736570852834, 1.958233408830963, 3.9900565668030246, 6.408110837510195, 9.178425670384565, 12.256788355070677, 15.589653577842402, 19.115339329090578, 22.765473819169028, 26.466664347753532, 30.142361712636728, 33.714797222359365, 37.10705065662355, 40.245423609989366, 43.061224742907335, 45.49245321542663, 47.48542833581175, 48.996198868625136, 49.99169142599771, 50.45058183118529, 50.36388191464611, 49.73510356115821, 48.58043408137448, 46.92819376494029, 44.81762415238461, 42.29773570156604, 39.42592261482111, 36.266370749140705, 32.8883061888031, 29.364145944850808, 25.767605676122894, 22.171818713996625, 18.647527170988877, 15.261067836667548, 12.072765220702944, 9.135582638061592, 6.494016763188857, 4.183260389708933, 2.2286496370083566, 0.6454032797121317, -0.5613513927944741, -1.396287729578755, -1.8733000476989337, -2.0146495689419583, -1.849908869860433, -1.4147483447268296, -0.7496073146023613, 0.10170577978669518, 1.093439296700246, 2.1793078905564625, 3.313878347405682, 4.453876103878104, 5.5592918884915745, 6.594326810009202, 7.528151393586629, 8.335464278211079, 8.99684500302872, 9.498902171496306, 9.834224763485153, 10.001186362284319, 10.00365493570899, 9.850331452696887, 9.554038774694565, 9.130965171372434, 8.599858292403148, 7.981200260931776, 7.296393114035386, 6.566981459978681, 5.81394055787724, 5.057088463556582, 4.3144998964347625, 3.6020193602920347, 2.9329511109908126, 2.3178713875122936, 1.7645562045039678, 1.2780169203401242, 0.8606324077635239, 0.512363949640422, 0.23103687888657767, 0.012665310181122026, -0.14818594624093048, -0.25801551077610524, -0.32400229228831673, -0.35364149139132994, -0.354412724796652, -0.33349056791266335, -0.29750502280533686, -0.25235734218552397, -0.20309371107911534, -0.153825934928282, -0.10770922397198855, -0.06697034214384548, -0.03297601527673759, -0.006333104051442041, 0.012988562234791777, 0.02551995016254787, 0.03215211981107158, 0.03399970961403838, 0.03227460101436637, 0.028175004291271587, 0.022795815866286782, 0.017062494996195398, 0.011689625791141925, 0.007163257099642295, 0.0037448564882016917, 0.0014936363324607252, 0.0003031815192046564, -5.2314462403921184e-05, 0.00013309376885069641, 0.0005485772176464436, 0.0009137553172330362, 0.001017953443907395, 0.0007486896864352157, 0.00010761000487020894, -0.0007868400995305138, -0.001709659394293994, -0.0023511149368579043, -0.002347995575582609, -0.0013213793112523255, 0.0010824541410541341, 0.005151521512296047, 0.01107154213153262, 0.018896396522757913, 0.028528279697512485, 0.03970948545827511, 0.0520271124763074, 0.06493078481157698, 0.07776207500056802, 0.08979428443246408, 0.10028003687534978, 0.10850358987182133, 0.11383377176197258, 0.11577410373322959, 0.11400637438831426, 0.10842436215598862, 0.09915475116543528, 0.08656152081300292, 0.07123457671053979, 0.05396226903238084, 0.0356885903817762, 0.01745704998464175, 0.00034415892042651187, -0.014613208165999198, -0.026492222761835084, -0.03455620694902731, -0.038317546611275455, -0.03758656361090098, -0.03250347455370077, -0.0235496635459324, -0.011535959281381616, 0.0024331788418938084, 0.0170192496216195, 0.030731011773204208, 0.04202414529546723, 0.04941495866596912, 0.05160188198111525, 0.04758725532009981, 0.036792774851324574, 0.019161320281508968, -0.004761935501917237, -0.03377573026236817, -0.06600167448899381, -0.09890025267625543, -0.12932914743566987, -0.15363778059919558, -0.16779767904876183, -0.16756629217576927, -0.14867772343813812, -0.10705275410140522, -0.039019098381082626, 0.05846870406210977, 0.1876209668600889, 0.34962271053646976, 0.544483954444597, 0.7709376971267619, 1.0263831083845874, 1.3068840786425449, 1.6072265849294018, 1.9210355171272728, 2.240950162713936, 2.5588564714094417, 2.866164348503702, 3.154131527845385, 3.4141852099114676, 3.638253318415812, 3.819089786778591, 3.9505772059877216, 4.027992816566807, 4.048225038230382, 4.009932004124899, 3.9136392766139503, 3.7617668045622072, 3.5585378705808783, 3.309814649677363, 3.0228793126156637, 2.706154666776105, 2.3688759062872293, 2.020727609448912, 1.6714619573914313, 1.330516130446034, 1.0066427201388612, 0.7075595224366145, 0.4396626375858621, 0.20781010297262853, 0.015179719834371663, -0.1367927001888413, -0.24839223282638953, -0.3215225177929841, -0.3595279065495222, -0.3669536994747189, -0.3492581830221215, -0.31245885679470276, -0.2627723653468622, -0.2062620644273106, -0.14850791374955105, -0.09431695447327881, -0.04749058205614084, -0.010661880099174176, 0.014787476968044725, 0.02872664894799757, 0.03218943956683351, 0.027203048999358347, 0.01654524554740001, 0.0034458333226994307, -0.008749219134701799, -0.01692987405318646, -0.018567487637076132, -0.012030244139219715, 0.003153642436243094, 0.026106193448032954, 0.054503902691483114, 0.08458610158701682, 0.11127322733191111, 0.1283950651091113, 0.12902237579891218, 0.10588872851269945, 0.051883104921178785, -0.03941122852099625, -0.17316069223297761, -0.3527515655989169, -0.5793169020947069, -0.851351433410981, -1.164446339889241, -1.5111711216626367, -1.8811233728317447, -2.2611596708652706, -2.6358131775709164, -2.98792498306383, -3.2994385026357835, -3.5522895253703486, -3.7294093041611704, -3.8157662316695373, -3.7994049245646773, -3.6724254684959226, -3.4318426068935333, -3.080267075324008, -2.6263952601919174, -2.0852483940388797, -1.4779119818462867, -0.8309906158206791, -0.1757240749205441, 0.45324727563206074, 1.0194316135496515, 1.4863095761077192, 1.8193741224908817, 1.988308777610109, 1.9692242326115652, 1.7469181750825846, 1.3169354711644743, 0.6873318601057193, -0.11994152852956837, -1.0681333536799773, -2.1053391912731985, -3.1647681001078882, -4.16567273735627, -5.0149109310946205, -5.609208045122794, -5.838170868709492, -5.587826482334938, -4.744635516781563, -3.1998582728417433, -0.8540992108972892, 2.378102162691527, 6.563810307682635, 11.747588962112404, 17.948010745987077, 25.15461223902764, 33.325721656279505, 42.387275373189105, 52.23271556578836, 62.72410824713271, 73.69428213623188, 84.95009162331652, 96.27680219611844, 107.4439607550869, 118.21153900286524, 128.33633537831926, 137.57910097850603, 145.71184649332298, 152.5251559196448, 157.83536099121153, 161.4906435140724, 163.37641733264508, 163.4202687447172, 161.59556673581216, 157.92217757265257, 152.46653609429134, 145.34034336493025, 136.69778298330542, 126.73139059603308, 115.66672167033884, 103.7554488822779, 91.26783140245377, 78.48482159501299, 65.68877047951507, 53.154553367829166, 41.14125053372226, 29.884395977521308, 19.58906636953793, 10.424059393814673, 2.517341591014894, -4.047098003194019, -9.23090442043079, -13.041306643847584, -15.529183063990132, -16.785662577498304, -16.937362618184505, -16.140450686142472, -14.573763160012223, -12.431254910315259, -9.914069414094872, -7.222533200176859, -4.548375827173373, -2.067314897039881, 0.06734730146683267, 1.7300152931735675, 2.8268243162370768, 3.298262134283632, 3.1203107653804207, 2.3040900292182704, 0.8940322358210072, -1.0354109977500277, -3.3842533956709686, -6.032400778565038, -8.845822086754573, -11.683173131334835, -14.402585448508196, -16.868330415238404, -18.957078003381227, -20.563496112099863, -21.605197613896312, -22.026474872387308, -21.800311946805923, -20.929314770088908, -19.44532476969426, -17.40773127272686, -14.900575877088485, -12.028592015083419, -8.912366466721645, -5.682899939746026, -2.4758025488201376, 0.5750251547118586, 3.3433468248932634, 5.716059167166471, 7.598013909092982, 8.915991376330622, 9.621663538485063, 9.693430119650351, 9.137064149530254, 7.985122849959577, 6.294948793151312, 4.145860425552663, 1.6354162079459702, -1.12509291525433, -4.015668187974503, -6.9129159990679065, -9.695411465473594, -12.248876933027724, -14.471010767332226, -16.27588307383731, -17.597568556130238, -18.392039024887758, -18.638311312220278, -18.338678081913447, -17.517906442193855, -16.2214650810508, -14.512882648344752, -12.47039870295151, -10.18311363145182, -7.746580985795422, -5.2582815781597105, -2.8129147307550406, -0.49824082263102054, 1.6085298427385186, 3.4437178487859077, 4.959405056009803, 6.124833371092055, 6.926958399549782, 7.370113950939621, 7.474834642181245, 7.276036797709375, 6.820250638885425, 6.162430893301977, 5.362521257953702, 4.481914449937755, 3.5799923104696534, 2.710925660094694, 1.920883170948656, 1.2457843538361564, 0.709752563641501, 0.3242901792845023, 0.08813138145806347, -0.012038281212937648, -0.00012082287477148262, 0.09148169826788168, 0.22445875457563425, 0.35754674491386035, 0.449669921587165, 0.46307928723999303, 0.3663195246927846, 0.1368735437868342, -0.23663319875027103, -0.7528719611676035, -1.3969780216422574, -2.1404979961504766, -2.9421381547167442, -3.7492955455176658, -4.5002870470962, -5.127173482819459, -5.559036960525959, -5.725545292361691, -5.560772615327281, -5.006956103464315, -4.01800406236603, -2.5625699536899544, -0.626453254216367, 1.7856624514556925, 4.649267152672694, 7.9199650071160805, 11.534296324988622, 15.411372824258196, 19.455406601681844, 23.558994278698002, 27.60702350096228, 31.481355103867845, 35.06538535698931, 38.248395492459935, 40.929943658436756, 43.023910841488, 44.46198710776646, 45.19641707161663, 45.20215131273779, 44.478041370679115, 43.047218619577606, 40.956384889826126, 38.273665657881814, 35.08596705557363, 31.495651755930837, 27.616628073161117, 23.570007254418275, 19.479514618588578, 15.46690924426381, 11.647478567820777, 8.12573614158917, 4.991748154708993, 2.3181824847262003, 0.1580917933214878, -1.4564808924225887, -2.5150351598432246, -3.0282816791476175, -3.026978931936584, -2.5600128554238313, -1.6918235969643003, -0.4991449786442534, 0.9326205264798718, 2.513146607160031, 4.150976585394926, 5.7572127637696315, 7.248955178551324, 8.552358511297754, 9.605196219951182, 10.358908361108853, 10.780037472097051, 10.850678754970748, 10.568365302764903, 9.94535939487568, 9.007380321417859, 7.791849548663596, 6.345750388493643, 4.723211481114486, 2.982919042446921, 1.185367523018969, -0.6097893983455548, -2.346077997840323, -3.972259418823091, -5.444030517266254, -6.725321797723206, -7.789164186078282, -8.618116817263255, -9.204273587425154, -9.549041758732413, -9.662431489512366, -9.561732204856563, -9.270174221529262, -8.815471820069076, -8.228306149835882, -7.5408205466930776, -6.785194375491609, -5.9923524807225395, -5.190888789406415, -4.406231454967367, -3.6598285861940467, -2.968714750973204, -2.3453655966364746, -1.7977781059602742, -1.329747616827851, -0.94130591340041, -0.6292803007254436, -0.38793201708390657, -0.20963327368985146, -0.08553205624954013, -0.006191557158743065, 0.037830214848717354, 0.05549338253900762, 0.05489605573742162, 0.04300721595040859, 0.025511443040974167, 0.0067578571391568466, -0.010200099708062823, -0.023491189890122333, -0.032255534466640284, -0.03643800343851182, -0.03656691954557896, -0.033536651575666834, -0.02840963778779405, -0.022249695688358048, -0.015994393685069865, -0.010370175388714797, -0.0058498651787508415, -0.002647905820317392, -0.0007483740802980786, 4.338752541451843e-05, 3.551872240345253e-05, -0.00041941858135642477, -0.0009883742200286862, -0.0014092730704980988, -0.001524797751690083, -0.0012957485166043782, -0.0007938105098387671, -0.0001760506195734548, 0.00035438629181710134, 0.0005953214530001874, 0.0003933379020478289, -0.0003148031359679832, -0.001473678041397819, -0.002898931764487865, -0.004288697272250992, -0.0052579183798183845, -0.005393843612125317, -0.004328846141488382, -0.0018244085079764467, 0.002141917661175692, 0.007295737901345211, 0.013000899146700351, 0.0182197318927971, 0.02150653088528203, 0.02104045940188507, 0.01469996755912261, 0.00017828130981914058, -0.024863064995115706, -0.06260887514114721, -0.1148868322164454, -0.18295800995097822, -0.26731660193853224, -0.36751579196289424, -0.48204133877070404, -0.6082469415898685, -0.7423516355138737, -0.8795171391980408, -1.014006394474325, -1.139420429995228, -1.249016986585386, -1.3360898938265857, -1.394392032710559, -1.4185864067074323, -1.4047037933696254, -1.3505291206649377, -1.2559358318257399, -1.123138654174489, -0.9568355821251795, -0.7642208670774748, -0.5548596252230917, -0.3404129460974347, -0.13421692622332523, 0.04928112114080535, 0.19519544675869951, 0.2889407652190533, 0.31701640803121134, 0.26779657013622, 0.13228496781071844, -0.09520805866246715, -0.41650625998702706, -0.8291641731543766, -1.326269202645989, -1.8964950230178421, -2.5243428377152153, -3.190595928275864, -3.8729802709137684, -4.54700667469826, -5.186960853411172, -5.766998754988428, -6.262300466969727, -6.650258866153161, -6.911752445319588, -7.032032952024608, -7.00144898148186, -6.816014081695592, -6.477727848833531, -5.994628553325522, -5.380568824169132, -4.654719166938575, -3.8408204678201048, -2.966285795826091, -2.060972545429849, -1.1557701129665172, -0.28124941273767645, 0.5336683470800639, 1.2629639258342353, 1.8846324674873776, 2.3816020469622354, 2.7424140067973584, 2.961651980430511, 3.040111339286249, 2.984567687436002, 2.8072643446616596, 2.525151126009271, 2.1589097138457065, 1.7318186286382855, 1.2685186497612082, 0.7937443076754244, 0.3310910419078089, -0.09811053266169448, -0.47581950196489914, -0.7880739212340566, -1.025506516477373, -1.1835875550506105, -1.2625889339494079, -1.2672789282843548, -1.2063719377810567, -1.0917713392121073, -0.9376590591991127, -0.7594731318660616, -0.5728383135067937, -0.3925379536499701, -0.23158130315696476, -0.10042058276089315, -0.006363012958170621, 0.046789360192443216, 0.05885343717950218, 0.03313035898643485, -0.023967598128588417, -0.10351342561538789, -0.1948250473722905, -0.2863370703175745, -0.36652697332283085, -0.4248331167509735, -0.4525024358987583, -0.44330996292872415, -0.3941006719560567, -0.3051180712550838, -0.18007403167478747, -0.025960976980156095, 0.14737283075680505, 0.32786531460578994, 0.5020609809030103, 0.65605834690448, 0.7765238444071626, 0.8517061079102827, 0.8723949883644893, 0.8327481674410775, 0.7308825898977591, 0.5692333416217399, 0.3546418328418661, 0.09815621577909424, -0.18545311302622217, -0.4784419214685109, -0.7610663526818543, -1.0127315136808848, -1.2132632050965468, -1.344201523984989, -1.390024178687118, -1.3392329592504915, -1.1852347833109829, -0.9269571101574721, -0.5691514695030462, -0.12235675274984965, 0.3974864604264557, 0.9697696660448307, 1.5702772683703885, 2.172477324746273, 2.7489766392012576, 3.273058144691808, 3.7202111755012046, 4.0695629846156285, 4.305122238365262, 4.4167546222542935, 4.400857115198721, 4.260668650660636, 4.006024321733009, 3.652761174714043, 3.221767178948095, 2.73770184442614, 2.227473462747761, 1.7185630536768464, 1.2372975580099528, 0.8071836524606124, 0.4474087372330503, 0.17159105018175116, -0.013068670099220981, -0.1061844648639238, -0.11410674431144839, -0.04935696611378079, 0.07040380704438663, 0.2238201129846115, 0.3876203224435094, 0.5386319285627618, 0.6559073839639684, 0.7227779163072586, 0.7287033554957897, 0.6707793619533627, 0.5547740188312529, 0.39558579153196133, 0.21704845101949577, 0.051042123176599015, -0.0640894031324714, -0.08578826142266258, 0.02988111320960541, 0.3249897444693796, 0.8362445553738712, 1.5914177303498418, 2.6059165323662796, 3.8797086845258217, 5.394814984157034, 7.113569141682824, 8.977861258190858, 10.909464705392246, 12.811458607305768, 14.57080366519421, 16.06202585674542, 17.15191160189664, 17.705066091449865, 17.590097575652457, 16.686189117717568, 14.889864015805687, 12.121421228152421, 8.330436641113744, 3.500555982794741, -2.346843096911034, -9.150379515330902, -16.807984352790623, -25.177943928944863, -34.08159085731896, -43.307838566842186, -52.620048106448074, -61.76360814132781, -70.47436217240187, -78.48792139827505, -85.54935379416231, -91.42285816771313, -95.9010687395269, -98.81362699655075, -100.03432817203391, -99.48802695150852, -97.15455120240705, -93.06917377945622, -87.3220602410544, -80.055679548218, -71.4602107292337, -61.76711564768199, -51.24114774372786, -40.17108915296421, -28.85958504111836, -17.61230123681019, -6.726242079038179, 3.520659975585198, 12.87892863431496, 21.135675106061708, 28.12117039381276, 33.71362147914723, 37.84200884225201, 40.48702795662897, 41.68057413146159, 41.50213068288983, 40.07319314115313, 37.55061387826654, 34.118828715355264, 29.98132598234768, 25.35174267792744, 20.44497590711689, 15.468696451261733, 10.615783826943561, 6.057375620766587, 1.9369969389818125, -1.6333311408703408, -4.575347612231449, -6.8451904174805085, -8.432478458881542, -9.3579646437731, -9.669946915198333, -9.439708035455443, -8.756285175660915, -7.720539478497954, -6.439138233318589, -5.018752950246503, -3.5607087460154254, -2.156315098011561, -0.8830619858040122, 0.19818711707463454, 1.0449296089711855, 1.6336679768540818, 1.959520063786988, 2.0348329885739047, 1.88695680094834, 1.5553723761979736, 1.088369318728919, 0.5394804630815341, -0.03612048367295716, -0.5850621616642224, -1.0588850776216228, -1.416645798317804, -1.6268944884635754, -1.6689832741975283, -1.5336742512983377, -1.2230603182839486, -0.7498475838504702, -0.1360797220823343, 0.5885900828707539, 1.3889845912132186, 2.2268301934916503, 3.06302738312624, 3.8598028914645925, 4.582687831449411, 5.202185915317782, 5.69506155691086, 6.045201266566747, 6.244029087535622, 6.290491227127088, 6.190795815349571, 5.95757006778624, 5.608553915770173, 5.165290011055789, 4.651708185026758, 4.092702400063701, 3.5127793283268756, 2.934847486285465, 2.379204398138645, 1.8627876431887642, 1.3986708726908097, 0.9957317617480491, 0.6586857210505354, 0.38837129902335366, 0.18222720133175338, 0.0349148734427957, -0.060968770423087446, -0.1141433653779436, -0.13391359513761794, -0.12950103711194524, -0.10947095422182718, -0.08128332417150834, -0.05099047288473342, -0.023084446730516114, -0.0004857922801274777, 0.01534363207079446, 0.024188925108379517, 0.026801483328986776, 0.024582326042412405, 0.0192592553032173, 0.0125871189961822, 0.006099433311591543, 0.0009283622795971129, -0.0022968103210492495, -0.003470457345299141, -0.0029560240051686383, -0.001468260204113725, 9.017783318501442e-05, 0.000816914443980233, 1.5795615291862725e-07, -0.002712474091717871, -0.007186431424307147, -0.01272961379888204, -0.018088784694038355, -0.021516760374651774, -0.02090741617242623, -0.013988980792667527, 0.0014409874752538325, 0.027257725189058668, 0.06475049406395882, 0.11438767941728237, 0.17562790831304295, 0.24679683534885263, 0.3250443575237731, 0.4063928198839234, 0.4858791910335868, 0.5577948288470659, 0.6160062386385966, 0.6543117782811211, 0.6668408538816054, 0.6484635355896042, 0.5951812911316472, 0.504468722376286, 0.37553597440541686, 0.20951101362467778, 0.009511686134014475, -0.21941281936751783, -0.4704769217979454, -0.7354493566679607, -1.0050339107262292, -1.2693231115235635, -1.518298848844534, -1.7423563861223355, -1.932825836449395, -2.0824142731036273, -2.1856309057539516, -2.2390842715116532, -2.2416049894520627, -2.1942776112850204, -2.1003492725841273, -1.9650200421427073, -1.7951288113601913, -1.598757880166227, -1.3847801460695308, -1.1623676026817604, -0.9405080154370974, -0.727495882564322, -0.5305256125634237, -0.3553764034555975, -0.20619624297133224, -0.08539403466979784, 0.00635826184509091, 0.07001874978940233, 0.10797650202226845, 0.12377775488420222, 0.12179253752119626, 0.10684752728016156, 0.08385828865586506, 0.05748607449940386, 0.03184101675357448, 0.010249227975563465, -0.0049039999977682795, -0.012248729161870043, -0.011423975174750104, -0.002993402891126848, 0.011708737083239915, 0.030779783667918982, 0.05198014638540554, 0.07297374359317993, 0.09155739260410889, 0.10586109887443186, 0.11450444620794242, 0.1166992710810811, 0.11229405561066068, 0.10175265314488077, 0.08607710231056324, 0.06668534163566942, 0.0452568038120103, 0.0235615785319461, 0.0032896464397743396, -0.0141039353988152, -0.027524017553161303, -0.036320307573577515, -0.04032497085923342, -0.039838633142130486, -0.03556927939073643, -0.028532117608587367, -0.01992163470558802, -0.010969649505245004, -0.002804396856615579, 0.003674529350553874, 0.007892417509568848, 0.009656475636518723, 0.009166225069029216, 0.006976324300143851, 0.0039160377424796, 0.0009742412914879901, -0.0008373426369337146, -0.000627166742352978, 0.002243684684493247, 0.008056011840585055, 0.016668512023026334, 0.02750655061378396, 0.03960749979386116, 0.05172161897731162, 0.06245985258309431, 0.0704735248258841, 0.07464568483176791, 0.07427000518289038, 0.06919161365438657, 0.05988689089961025, 0.04745700320523527, 0.03352073605944896, 0.020007555211723625, 0.008857630554266941, 0.001649395300874827, -0.0008106895574700676, 0.0011109034272936548, 0.005540562662836401, 0.008894651464205986, 0.005875331261705609, -0.010269213887525568, -0.04716585988664256, -0.11237940273581143, -0.21209814378973743, -0.34944947170515944, -0.522482997219937, -0.7218917982057963, -0.9285780463299552, -1.1112175491460334, -1.2239581710639422, -1.2044316749527069, -0.9722851933499224, -0.4284218292870061, 0.5448659212795887, 2.082708808714389, 4.3352940643676945, 7.464242915066878, 11.637810077055615, 17.025047599635528, 23.788837173437372, 32.078088429600534, 42.01937173024667, 53.70832318107987, 67.20115722588073, 82.50671841772042, 99.57950749797129, 118.31470839882488, 138.54698733144875, 160.04860919369384, 182.53018639328076, 205.64437910309744, 228.99222160400237, 252.13209526340216, 274.5908024067466, 295.87673723460836, 315.49518479480105, 332.9702797881689, 347.86112455066086, 359.7738105327512, 368.37601136801953, 373.41002617790605, 374.7036751879224, 372.17859725900735, 365.85478756348726, 355.85185189043455, 342.39070336482564, 325.7904789697285, 306.4505077490435, 284.8358461157732, 261.4613139177999, 236.8737179788143, 211.63304915616436, 186.2934374375473, 161.38424499345706, 137.39332092962673, 114.75398227361447, 93.82817353038877, 74.89580336114662, 58.149611416920074, 43.69391549136409, 31.547178268727617, 21.648160125391158, 13.865238513298488, 8.008320412708574, 3.8428665846305208, 1.1046320868089592, -0.4849508448268173, -1.2034614247020594, -1.3135352103187243, -1.050961726142671, -0.6153804632916132, -0.16395886108668145, 0.19174591452665907, 0.385737172079527, 0.3945198112091618, 0.23131473529661548, -0.061893679360292476, -0.42380377308680656, -0.7839936560731321, -1.0730927855028238, -1.2321683828693784, -1.2206313019750996, -1.0220738346410714, -0.6475864785242509, -0.13625693205146155, 0.44717842093942, 1.0173554838838477, 1.4756177062673703, 1.7191245686240633, 1.6510431774779484, 1.1910246069737045, 0.28510789061405617, -1.0857873130702653, -2.8997482729161823, -5.090852457386938, -7.549588876379885, -10.127088152524424, -12.643241685665705, -14.898530597371893, -16.689127251589614, -17.82458541573314, -18.14734403985752, -17.553147102980287, -16.009981848669973, -13.575105444761967, -10.408946357834823, -6.784625893038183, -3.092108348633001, 0.16378996627838313, 2.3720265519295873, 2.8307629958983833, 0.769424360924372, -4.623025097473619, -14.165034239373568, -28.645859042910057, -48.78674575025111, -75.20158355211443, -108.35882910795303, -148.54654400911403, -195.84234991233325, -250.09159916184151, -310.8958373441408, -377.6070579879433, -449.33228944622516, -524.9483565699271, -603.1264179418571, -682.3656192718383, -761.0348189674842, -837.4209667035736, -909.7850446577916, -976.4329487730703, -1035.7661556776961, -1086.3310085133971, -1126.8680436101565, -1156.355154809471, -1174.0428444742552, -1179.4800900020703, -1172.5297954389769, -1153.3738983964404, -1122.521150596206, -1080.7872298698032, -1029.2493366043957, -969.2066379780041, -902.1347331263164, -829.6350001894067, -753.3809133493332, -675.0634908877103, -596.3379849476879, -518.7774856449901, -443.83143882165655, -372.7751061946383, -306.67774811559565, -246.3820290217754, -192.49326047019025, -145.37772543242696, -105.16981863683299, -71.7872969743907, -44.95369850604389, -24.226980094755422, -9.030152404646376, 1.3140727545028041, 7.546825648234497, 10.437475140609376, 10.750385414976211, 9.215254878488313, 6.501968618591621, 3.200668659931619, -0.19271735561845826, -3.2850292750202628, -5.7883528107136595, -7.517425143590292, -8.382439793991443, -8.378049958611008, -7.569593691083072, -6.077480298511011, -4.060708205833857, -1.7004306361654706, 0.8157685906854352, 3.307859591759283, 5.614841120184436, 7.603532732795445, 9.17449619151818, 10.26502227195292, 10.849500869433962, 10.937390077500014, 10.569170461732478, 9.810991449533537, 8.747710440080878, 7.475300411882207, 6.093561656394508, 4.699328921240541, 3.380520565060271, 2.211330316877811, 1.2489352876412951, 0.5315313363115258, 0.07774299636451451, -0.11270583654319152, -0.05715775393072115, 0.21280866403006388, 0.6548424321396419, 1.2196254682620031, 1.8547685481517215, 2.5085888284611, 3.133316055301093, 3.6877321558758047, 4.13919796451816, 4.464850635583321, 4.652013216326494, 4.697905131888288, 4.608736394058286, 4.398312316839851, 4.086313759073523, 3.696405488683888, 3.2541775739594643, 2.785291054406654, 2.3138051216699247, 1.8607877604069307, 1.4433493634707903, 1.0740741954021966, 0.7608388319036798, 0.5069822305696247, 0.31177195152532133, 0.17109246185342294, 0.07827289625160061, 0.024987625827553924, 0.00214676589864784, 0.0007066732731528859, 0.012343912930515078, 0.02995845905183063, 0.04799040171980101, 0.06255171967490099, 0.0713900859515822, 0.07371406109744892, 0.06991552430570595, 0.061228467181681796, 0.04936900486648415, 0.03619651762290119, 0.023426556779040885, 0.012417577785848196, 0.004043255347178153, -0.0013482421095739278, -0.0038961374901073783, -0.0041259637762962285, -0.0028066707128064474, -0.0007901136366506706, 0.0011426947419410094, 0.0024070861843732273, 0.0026957507986609566, 0.00200562324788025, 0.0006084145471807081, -0.0010299912444245, -0.002369315840212712, -0.0029365137483968796, -0.002468984696057015, -0.0010381497407877165, 0.0008661135418290155, 0.002305892499992914, 0.0019305887637210146, -0.001919741814276186, -0.011047688105372279, -0.027180903546139477, -0.05172699857080576, -0.08552442719609202, -0.1286116754827611, -0.1800446591599602, -0.23778658373665595, -0.29869022318604893, -0.3585856717667073, -0.4124779992358474, -0.4548496987544097, -0.4800683434158104, -0.48286415620119355, -0.4587914998694707, -0.4046930279629247, -0.31911821393469897, -0.20265476491056605, -0.058138284687892595, 0.10928709467999234, 0.29227481103549996, 0.48155324636954167, 0.6663709267969856, 0.835109855767602, 0.9759921856220103, 1.077838254339009, 1.1308362584461076, 1.1272713420503468, 1.0621607265052626, 0.9337458787828352, 0.7438000086120863, 0.49770763731489526, 0.20429141335604464, -0.12457790089721943, -0.47457989968824593, -0.8297202594056184, -1.1732325539493906, -1.4885532307134262, -1.760308456591777, -1.9752487632582392, -2.1231057799873723, -2.197306095689222, -2.1953008558746947, -2.1186991762140415, -1.9731604390990876, -1.7680183723378344, -1.5156797156527102, -1.230834851044859, -0.9295301576676082, -0.6281655416185429, -0.34247942535739434, -0.08654088499306935, 0.12808971613886147, 0.2929923953225164, 0.4032958384371938, 0.45783549551839225, 0.459056175771782, 0.41267381859721664, 0.32712602134434454, 0.21286730456407316, 0.08152693245896822, -0.055008946616557475, -0.18546766224375497, -0.2999717397871522, -0.39068041384998015, -0.4522450604809165, -0.4820511686899567, -0.4802371897585711, -0.44950076055032906, -0.39471739067089073, -0.32237294841479175, -0.23989794963432587, -0.15496281265692613, -0.07479104947671689, -0.005547526268462318, 0.04814827128429438, 0.08354342473958694, 0.0998849546850273, 0.09836291015504049, 0.08186251282686907, 0.05455144732638415, 0.021355133419411736, -0.012627909374221978, -0.042711923986702614, -0.06515212287538669, -0.07756035761092704, -0.07916364898050703, -0.07087658889530035, -0.05517437273004717, -0.03576933509961974, -0.017122588782431107, -0.003837853824119653, 2.0528069723444705e-06, -0.008514108088542404, -0.030562421740414066, -0.06517923670224772, -0.10907819661091449, -0.1567400831735311, -0.20079679018409832, -0.23270499834492037, -0.2436821507087977, -0.22584880351736916, -0.17349733095129008, -0.08438717618302378, 0.039048076453319924, 0.18870368041499577, 0.3501255862485984, 0.5022753405929169, 0.6178064380464968, 0.6638790537992378, 0.6035296083121406, 0.3975627853880901, 0.006891453377344725, -0.6047880321499151, -1.4681296778144413, -2.6052902887526277, -4.02734339999968, -5.732088435728777, -7.7024405580865185, -9.905572855570341, -12.292933218186857, -14.801212571972236, -17.354285530419656, -19.866092384169452, -22.2444208517359, -24.39570484974393, -26.22977770169731, -27.66460861545764, -28.631059451408724, -29.07719963761241, -28.97189343929132, -28.307403626551753, -27.100801119874962, -25.394053905695745, -23.253009228554625, -20.764519993514, -18.031754028449797, -15.168887261818307, -12.29502165103619, -9.527619926171024, -6.9758289274356065, -4.734086224954794, -2.8764050874521825, -1.451712942751242, -0.4805313867232047, 0.046696780899966484, 0.16934988083119204, -0.04548713185304162, -0.5069088342097434, -1.105675926050906, -1.721030497809635, -2.2284798885146864, -2.508120639851258, -2.4530373695894356, -1.9771429319928817, -1.0219690983890009, 0.4379455609907409, 2.3914514465600347, 4.789240655276364, 7.544518741899666, 10.535936426025991, 13.612697816915414, 16.60196598743381, 19.318146777800997, 21.572427843456328, 23.18304670629713, 23.985619378231263, 23.8429166006751, 22.65353461711775, 20.358965802052836, 16.948651490561385, 12.462813875948122, 6.9929445450892995, 0.6782848595765167, -6.299748446696216, -13.725033694389097, -21.355981866644797, -28.936111160942758, -36.20543625830134, -42.91210073143691, -48.82371383032364, -53.7388557678739, -57.49648430774254, -59.98190957020266, -61.13121203548802, -60.93303453495732, -59.42791145946556, -56.70521459612368, -52.89789464193974, -48.17533466922972, -42.73525628614721, -36.79462491466181, -30.577639794086583, -24.30524167608802, -18.18559649454881, -12.405614714548644, -7.1240241397408886, -2.4662277878606793, 1.4789047326040192, 4.660259774822061, 7.063905188093433, 8.710784541368692, 9.652468666424818, 9.96561606012746, 9.745626973771504, 9.099861721622558, 8.14085806063874, 6.9799233003925965, 5.721426811376657, 4.458151194133148, 3.267625653406289, 2.209574382687446, 1.3248890210135775, 0.6358709117549897, 0.14758655618283203, -0.1498609439058976, -0.27837818843885037, -0.2685084938936631, -0.1559066483004339, 0.022081533056350872, 0.22954194901843766, 0.43461830369737015, 0.6114911792837406, 0.7416376453164092, 0.8143571117177633, 0.8266019994347465, 0.7821998748013642, 0.6905901499585172, 0.5652208483940911, 0.421783744284786, 0.2764449706907209, 0.14421263363559397, 0.03756983288876057, -0.034534372506287894, -0.06727995390133357, -0.06013908344880064, -0.016626328383794305, 0.05633492187438863, 0.14935303564307198, 0.25162557214874515, 0.35206741492740884, 0.44039853397021306, 0.5080920278677985, 0.5491033199411964, 0.5603243568933574, 0.541736228861589, 0.49626875615437055, 0.4294120045214491, 0.3484737012107345, 0.26171366653075573, 0.17744025306429134, 0.10312684152986565, 0.04463055659430991, 0.005584322131978424, -0.01298329823639075, -0.01276807723131748, 0.0019517042770753662, 0.0247173697139136, 0.04753721063417666, 0.06169675360029994, 0.05865495575398975, 0.030945232502261746, -0.027000256468193172, -0.11817791675305371, -0.24255134787456298, -0.3968463202724081, -0.5746276504708308, -0.7666596201449699, -0.9615314605397565, -1.1464958181744407, -1.30845389197962, -1.4350087574229822, -1.5155017217819586, -1.5419392309008806, -1.5097237618045234, -1.4182089776144282, -1.2709262223449713, -1.075488288070583, -0.8431954551652588, -0.5883555672734224, -0.3273641334422551, -0.07760921350563037, 0.14372024881145876, 0.32083048074854165, 0.44040002098928, 0.49250068840671996, 0.471305059942661, 0.3755095015889056, 0.20844979762978622, -0.022097774041290864, -0.3044149485574862, -0.6236033436295553, -0.9625549299686963, -1.3031072526846923, -1.6273725798748127, -1.9187661456858858, -2.162958954313308, -2.348690219409136, -2.468351635371524, -2.5183107188909974, -2.4989597157848817, -2.414496330352726, -2.272463435865707, -2.0831299573563147, -1.8587029257211687, -1.6122953558922688, -1.3569983528692182, -1.1050507080269267, -0.8671314463336852, -0.6518185846531703, -0.46524262274858624, -0.31094703107287147, -0.1899509423445129, -0.1009961244027311, -0.04094736753668358, -0.00529423517831387, 0.011283449394213793, 0.014350934351917045, 0.009205303898063108, 0.0004536807321445723, -0.008288022316815247, -0.014560184460600718, -0.017086872336900746, -0.015666876559241257, -0.01096106036472956, -0.004208259842679662, 0.0030915318431567317, 0.009486026511020937, 0.013834374944493352, 0.015494944746599775, 0.014415839887662556, 0.011119311522447783, 0.006578930287839306, 0.002005592905801716, -0.0014262311453693587, -0.00287775684894527, -0.0021313224972345224, 0.0001772710036644196, 0.002414875615688485, 0.0019230915750556006, -0.004876418958890182, -0.02223715201272021, -0.05471928422927159, -0.10672641617789487, -0.18198882619363801, -0.2830405165062851, -0.41074266961703493, -0.5639068333588977, -0.7390654720800879, -0.9304279771441262, -1.1300517898181335, -1.3282329000025173, -1.5140916487513396, -1.6763286993389348, -1.8041086645873443, -1.8879429281400113, -1.9205423625193385, -1.8975624883146094, -1.8181625122890062, -1.6853373634583986, -1.5059339824652016, -1.2903029525643432, -1.0516655715043073, -0.8052088588035006, -0.5669603444881813, -0.35249789572626394, -0.17565571030112942, -0.04732086653951376, 0.025576861428105814, 0.04078674083474838, 0.0010712508408035496, -0.08590770723131837, -0.2081569428174281, -0.35035522898255256, -0.4952434294625511, -0.625279273012193, -0.7244147175165052, -0.779840753473408, -0.7835333519338842, -0.7334123039904648, -0.6339530089284299, -0.4961406433048741, -0.33668442015865724, -0.17646819873968966, -0.038253773508708754, 0.05629722444698664, 0.0900392003348025, 0.05398574226347247, -0.04909154061463339, -0.20141636165264862, -0.36760454115340246, -0.4929896369425237, -0.503128044932556, -0.30467359436168523, 0.21221226060128737, 1.1698044674395909, 2.69732388115412, 4.92427623665355, 7.972893595394606, 11.949995059151657, 16.938734861198576, 22.99072247358575, 30.119016317361208, 38.292347649345054, 47.430729604048224, 57.40393542046926, 68.03281045132321, 79.09315557440935, 90.3217974231159, 101.42524553362708, 112.09046792035603, 121.99731329414861, 130.8320020862979, 138.30083081207243, 144.14319137551095, 148.14685006363513, 150.16217417854446, 150.10425793762104, 147.9561285359, 143.76997146552426, 137.66527355690553, 129.82396955095197, 120.48282922059023, 109.92340853751753, 98.46005688075275, 86.42858624818282, 74.17649628984779, 62.04850937400909, 50.370795126750124, 39.436105938609, 29.490750710583892, 20.72424394775269, 13.262317871266909, 7.163453327836984, 2.406004542845885, -1.1074766361346684, -3.515101388169439, -4.978377827157583, -5.668449106006496, -5.754838937393244, -5.39689050464788, -4.7378238362314535], 'positive_zeros': ['0.04500262606857755484307233915601', '0.12527237557891822934794697129779', '0.55198153948065139759623053917174', '0.876268404524141113093470062422839', '1.03731346991581652496362093992601', '1.07035084401307856404532069257001', '1.07804430829019615597331442439235', '1.48830590110788396782177042474498', '1.58022432492689337069528157751673', '1.64240301211239038508646758404259', '1.74828047137906055420398678137892', '1.82668429366951695290917973168360', '2.32589571629954348815105822732900', '2.37338275827050266595700232326056', '2.49928225857984293751525560521238', '2.56395206943660512842373511301831', '2.71168509696724299372864508610015', '2.71195474888217828530905690864286', '2.73823894941580358654853861647061', '2.87898240359564145891895896250757', '3.06429153059450682307614014419439', '3.11045496472035502636241332698511', '3.13808779889020975340504026859367', '3.26025164085007166841613895487110', '3.54913152693074962151419867221955', '3.57109107368540441078633196762840', '3.73430324435494573549746325547735', '3.81182835772548776822985390728146', '3.92227515539804276723394782364396', '3.99879372149732033535013257760441', '4.01199260948185589651148512541027', '4.04471242485751742316396139992310', '4.28183533640475143918805687014052', '4.32345760563327852013374116249889', '4.57184926295203815472586468670278', '4.61806008184864640364500136423879', '4.81917375053370944434629797921275', '4.90805959989148835628723858418285', '4.99142906743324779514155654825647', '4.99710662773931270517697819831900', '5.03207656428126614738171122268276', '5.06640742306209990035956210270486', '5.20638280614142331991325857761896', '5.26144862024979778011501527410078', '5.31761572308185820735387737978676', '5.38399410255292000329700669495056', '5.60055441033466643433441397189109', '5.68353613088282374733284207269483', '5.72040332697659077459486347975324', '5.74894380317841492428109244235411', '5.80387732233368571875779518097687', '5.95170795367845750108141679952844', '6.01164464959458122605870654868752', '6.08308567850782925076022031873928', '6.32724678743228778162694655001469', '6.41228186619927051488439113644043', '6.45308762192263227684252806929039', '6.58003512894126945490844472339684', '6.65374999265691761001395925202570', '6.77641677715062676740105875977582', '6.89856717424518901223288664801568', '6.90626937272417713402896074135292', '6.95258712611543705533003691052280', '7.04549489775618282320650382976456', '7.23802717317558159682132539245274', '7.28352900262384909927580246056253', '7.39786244359138342833540925053411', '7.58191361097430904305988544073477', '7.62111647076035463503209189611913', '7.70554019714864991561531729979780', '7.71320490131789544027415188726067', '7.75810331877842531416403731741197', '7.77898158912751168887212832046913', '7.82814855964577377427097945682750', '7.87505729895866622656035884190231', '8.035712548626290378138713516920604', '8.072684748225980311756523726013480', '8.233346423752361782111608564107926', '8.329762427710302391560808253453223', '8.425550883530506385927047485826145', '8.447718217101830631012059576869177', '8.519721177073814526644146394626056', '8.595963121756123052353017420462725', '8.670294090028806715142242652807020', '8.811926306044111704159179376530454', '8.834118807655393889480967434515360', '8.908578051328818536038195236805001', '8.923987301341477736711447862521012', '9.053866699436447616615346130708961', '9.222797834436964563360352363549048', '9.340761075172646799642405836590478', '9.430002471564280728668115765859024', '9.487105137292584139471626790165166', '9.544990258212795654862327428447854', '9.714442624946610241009271345060511', '9.768906967538032589443408260398229', '9.820190647177398666219667563765644', '9.849570366119354930218688451558218', '9.912048295771503500128706969241207', '10.02527333735762676975139318667225'], 'prelabel': '20-1323e10-1.1-c1e10-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.250262787439717, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e10-0', 'trace_hash': 10341460786436315, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.04500262606857755484307233916', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.12527237557891822934794697130', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.55198153948065139759623053917', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 17312887701.124416, 'bad_primes': [3, 7], 'central_character': '1.1', 'conductor': 16428520040413041995477810282649, 'conductor_radical': 21, 'degree': 20, 'dirichlet_coefficients': [1, 0, 0, -3, 0, 0, 0, 0, 0, 0, -12, 0, -6, 0, 0, 5, 24, 0, 0, 0, 0, 0, -15, 0, 16, 0, 0, 0, 15, 0, -9, 6, 0, 0, 0, 0, -12, 0, 0, 0, -9, 0, 3, 36, 0, 0, 15, 0, 0, 0, 0, 18, 0, 0, 0, 0, 0, 0, -18, 0, 12, 0, 0, -1, 0, 0, -10, -72, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 20, 0, 0, 0, -15, 0, 0, 0, 0, 0, -48, 0, 0, 45, 0, 0, 0, 0, -6, 0, 0, -48], 'euler11': [1, 12, 105, 684, 3745, 17382, 72307, 270561, 952558, 3194589, 10673917, 35140479, 115259518, 360116691, 1058646787, 2799388482, 6634495945, 13329224964, 22507682505, 28295372292, 25937424601], 'euler13': [1, 6, 68, 336, 2292, 9399, 51837, 187401, 909867, 3004662, 13054461, 39060606, 153767523, 411719997, 1480516557, 3489782907, 11063046228, 21083501712, 55469689028, 63626996238, 137858491849], 'euler17': [1, -24, 380, -4284, 39486, -303462, 2039346, -12055428, 64101813, -306131850, 1328336013, -5204241450, 18525423957, -59228317764, 170328217266, -430872644934, 953096049534, -1757890875132, 2650787827580, -2846109035928, 2015993900449], 'euler19': [1, 0, -133, 0, 8580, 0, -354546, 0, 10419720, 0, -227952213, 0, 3761518920, 0, -46204789266, 0, 403653658980, 0, -2258813884453, 0, 6131066257801], 'euler2': [1, 0, 3, 0, 4, -6, -2, 3, -14, 39, 1, 78, -56, 24, -32, -192, 256, 0, 768, 0, 1024], 'euler23': [1, 15, 195, 1800, 15028, 107121, 712306, 4264599, 24178468, 125954103, 628044835, 2896944369, 12790409572, 51887376033, 199332423346, 689467498503, 2224683339892, 6128685804600, 15270642129795, 27017289921945, 41426511213649], 'euler29': [1, -15, 150, -1125, 6691, -30108, 81631, 232971, -5137202, 44535417, -275752187, 1291527093, -4320386882, 5681929719, 57736055311, -617549674092, 3979962840811, -19406110847625, 75036961944150, -217607189638035, 420707233300201], 'euler3': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler31': [1, 9, 149, 1098, 10878, 60723, 461409, 2027286, 13421802, 50078664, 374531595, 1552438584, 12898351722, 60394877226, 426120901089, 1738447936173, 9654265041918, 30208850293878, 127080764578709, 237956599446039, 819628286980801], 'euler37': [1, 12, 302, 2588, 38709, 264112, 3058184, 17732016, 173249698, 875160552, 7375688148, 32380940424, 237178836562, 898179806448, 5731529183624, 18314571171184, 99316703565981, 245683698020204, 1060768795084142, 1559540877540924, 4808584372417849], 'euler41': [1, 9, -34, -747, -2085, 20394, 110775, -623979, -5992218, 18494757, 381591615, 758285037, -10072918458, -43005256659, 313023674775, 2362771363194, -9903967342485, -145481442589107, -271487457790114, 2946437409545649, 13422659310152401], 'euler43': [1, -3, -79, 1100, 1674, -79931, 324899, 3229902, -28512986, -52724394, 1438527201, -2267148942, -52720511114, 256799818314, 1110765026099, -11750531857433, 10581961744026, 299000472217700, -923367821930479, -1507777835810529, 21611482313284249], 'euler47': [1, -15, -49, 1068, 9486, -83265, -760914, 2887821, 57371082, -59131839, -3026317959, -2779196433, 126732720138, 299822239683, -3713017588434, -19096412007855, 102251636610894, 541073492654484, -1166753046426289, -16786957096541505, 52599132235830049], 'euler5': [1, 0, -16, -12, 129, 147, -726, -720, 3663, 1257, -18069, 6285, 91575, -90000, -453750, 459375, 2015625, -937500, -6250000, 0, 9765625], 'euler53': [1, 0, -393, 0, 74860, 0, -9044030, 0, 764489716, 0, -47150015153, 0, 2147451612244, 0, -71361746878430, 0, 1659224074116940, 0, -24468058331664873, 0, 174887470365513049], 'euler59': [1, 18, -55, -1536, 19971, 205494, -1764945, -8798931, 181121100, 308804295, -11121159681, 18219453405, 630482549100, -1807115649849, -21386475710145, 146912653898706, 842387437344411, -3822568680681984, -8075674068237655, 155933924735788902, 511116753300641401], 'euler61': [1, -12, 251, -2436, 34779, -347730, 3716049, -34819755, 301038894, -2709237273, 20488848807, -165263473653, 1120165724574, -7903422809655, 51451823602209, -293691471746730, 1791827099901219, -7655721548547156, 48118535562317531, -140329753114009692, 713342911662882601], 'euler67': [1, 10, -182, -2448, 18867, 319605, -772530, -23213154, -12219093, 697872289, 3674653819, 46757443363, -54851508477, -6981657836502, -15567345506130, 431506734822735, 1706678296382523, -14836622009830704, -73904317315308662, 272065343962949470, 1822837804551761449], 'euler7': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler71': [1, 0, -351, 0, 63037, 0, -7800935, 0, 747809113, 0, -58386380555, 0, 3769705738633, 0, -198234871721735, 0, 8075057597528077, 0, -226659489467262111, 0, 3255243551009881201], 'euler73': [1, 0, -511, 0, 124869, 0, -19478727, 0, 2170586121, 0, -181575980223, 0, 11567053438809, 0, -553161583719207, 0, 18896953502481141, 0, -412101106957875391, 0, 4297625829703557649], 'euler79': [1, -20, 46, -144, 21153, -101181, -106944, -9264000, 7962453, 230795113, 4723714795, 18232813927, 49693669173, -4567513296000, -4165477462464, -311339643507219, 5142028946635713, -2765362894006896, 69787005255701806, -2397031919652366380, 9468276082626847201], 'euler83': [1, 15, -136, -1773, 22674, 93717, -3687774, -10067337, 346135869, 496605294, -27460905396, 41218239402, 2384530001541, -5756372421219, -175015562267454, 369155071940031, 7413046025768706, -48112218404608671, -306311743570909576, 2804103829013106045, 15516041187205853449], 'euler89': [1, 48, 1640, 40896, 851646, 14956146, 230812614, 3140740728, 38382277713, 420919956990, 4181686084101, 37461876172110, 304026021764673, 2214124850277432, 14481700653427974, 83516008391923554, 423252128521771806, 1808884671887553984, 6456005641351412840, 16817107377959290032, 31181719929966183601], 'euler97': [1, 6, 311, 1794, 51903, 385032, 6010353, 63309837, 574248354, 8264282925, 54719955099, 801635443725, 5403102762786, 57781178864301, 532092229646193, 3306400793833224, 43233745971829887, 144952122353734722, 2437441847851234871, 4561386351927391302, 73742412689492826049], 'euler_factors': [[1, 0, 3, 0, 4, -6, -2, 3, -14, 39, 1, 78, -56, 24, -32, -192, 256, 0, 768, 0, 1024], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 0, -16, -12, 129, 147, -726, -720, 3663, 1257, -18069, 6285, 91575, -90000, -453750, 459375, 2015625, -937500, -6250000, 0, 9765625], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 12, 105, 684, 3745, 17382, 72307, 270561, 952558, 3194589, 10673917, 35140479, 115259518, 360116691, 1058646787, 2799388482, 6634495945, 13329224964, 22507682505, 28295372292, 25937424601], [1, 6, 68, 336, 2292, 9399, 51837, 187401, 909867, 3004662, 13054461, 39060606, 153767523, 411719997, 1480516557, 3489782907, 11063046228, 21083501712, 55469689028, 63626996238, 137858491849], [1, -24, 380, -4284, 39486, -303462, 2039346, -12055428, 64101813, -306131850, 1328336013, -5204241450, 18525423957, -59228317764, 170328217266, -430872644934, 953096049534, -1757890875132, 2650787827580, -2846109035928, 2015993900449], [1, 0, -133, 0, 8580, 0, -354546, 0, 10419720, 0, -227952213, 0, 3761518920, 0, -46204789266, 0, 403653658980, 0, -2258813884453, 0, 6131066257801], [1, 15, 195, 1800, 15028, 107121, 712306, 4264599, 24178468, 125954103, 628044835, 2896944369, 12790409572, 51887376033, 199332423346, 689467498503, 2224683339892, 6128685804600, 15270642129795, 27017289921945, 41426511213649], [1, -15, 150, -1125, 6691, -30108, 81631, 232971, -5137202, 44535417, -275752187, 1291527093, -4320386882, 5681929719, 57736055311, -617549674092, 3979962840811, -19406110847625, 75036961944150, -217607189638035, 420707233300201], [1, 9, 149, 1098, 10878, 60723, 461409, 2027286, 13421802, 50078664, 374531595, 1552438584, 12898351722, 60394877226, 426120901089, 1738447936173, 9654265041918, 30208850293878, 127080764578709, 237956599446039, 819628286980801], [1, 12, 302, 2588, 38709, 264112, 3058184, 17732016, 173249698, 875160552, 7375688148, 32380940424, 237178836562, 898179806448, 5731529183624, 18314571171184, 99316703565981, 245683698020204, 1060768795084142, 1559540877540924, 4808584372417849], [1, 9, -34, -747, -2085, 20394, 110775, -623979, -5992218, 18494757, 381591615, 758285037, -10072918458, -43005256659, 313023674775, 2362771363194, -9903967342485, -145481442589107, -271487457790114, 2946437409545649, 13422659310152401], [1, -3, -79, 1100, 1674, -79931, 324899, 3229902, -28512986, -52724394, 1438527201, -2267148942, -52720511114, 256799818314, 1110765026099, -11750531857433, 10581961744026, 299000472217700, -923367821930479, -1507777835810529, 21611482313284249], [1, -15, -49, 1068, 9486, -83265, -760914, 2887821, 57371082, -59131839, -3026317959, -2779196433, 126732720138, 299822239683, -3713017588434, -19096412007855, 102251636610894, 541073492654484, -1166753046426289, -16786957096541505, 52599132235830049], [1, 0, -393, 0, 74860, 0, -9044030, 0, 764489716, 0, -47150015153, 0, 2147451612244, 0, -71361746878430, 0, 1659224074116940, 0, -24468058331664873, 0, 174887470365513049], [1, 18, -55, -1536, 19971, 205494, -1764945, -8798931, 181121100, 308804295, -11121159681, 18219453405, 630482549100, -1807115649849, -21386475710145, 146912653898706, 842387437344411, -3822568680681984, -8075674068237655, 155933924735788902, 511116753300641401], [1, -12, 251, -2436, 34779, -347730, 3716049, -34819755, 301038894, -2709237273, 20488848807, -165263473653, 1120165724574, -7903422809655, 51451823602209, -293691471746730, 1791827099901219, -7655721548547156, 48118535562317531, -140329753114009692, 713342911662882601], [1, 10, -182, -2448, 18867, 319605, -772530, -23213154, -12219093, 697872289, 3674653819, 46757443363, -54851508477, -6981657836502, -15567345506130, 431506734822735, 1706678296382523, -14836622009830704, -73904317315308662, 272065343962949470, 1822837804551761449], [1, 0, -351, 0, 63037, 0, -7800935, 0, 747809113, 0, -58386380555, 0, 3769705738633, 0, -198234871721735, 0, 8075057597528077, 0, -226659489467262111, 0, 3255243551009881201], [1, 0, -511, 0, 124869, 0, -19478727, 0, 2170586121, 0, -181575980223, 0, 11567053438809, 0, -553161583719207, 0, 18896953502481141, 0, -412101106957875391, 0, 4297625829703557649], [1, -20, 46, -144, 21153, -101181, -106944, -9264000, 7962453, 230795113, 4723714795, 18232813927, 49693669173, -4567513296000, -4165477462464, -311339643507219, 5142028946635713, -2765362894006896, 69787005255701806, -2397031919652366380, 9468276082626847201], [1, 15, -136, -1773, 22674, 93717, -3687774, -10067337, 346135869, 496605294, -27460905396, 41218239402, 2384530001541, -5756372421219, -175015562267454, 369155071940031, 7413046025768706, -48112218404608671, -306311743570909576, 2804103829013106045, 15516041187205853449], [1, 48, 1640, 40896, 851646, 14956146, 230812614, 3140740728, 38382277713, 420919956990, 4181686084101, 37461876172110, 304026021764673, 2214124850277432, 14481700653427974, 83516008391923554, 423252128521771806, 1808884671887553984, 6456005641351412840, 16817107377959290032, 31181719929966183601], [1, 6, 311, 1794, 51903, 385032, 6010353, 63309837, 574248354, 8264282925, 54719955099, 801635443725, 5403102762786, 57781178864301, 532092229646193, 3306400793833224, 43233745971829887, 144952122353734722, 2437441847851234871, 4561386351927391302, 73742412689492826049]], 'index': 2, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1323/2/o/c'], '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': '20-1323e10-1.1-c1e10-0-2', '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}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '20-1323e10-1.1-c1e10-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.250262787439717, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e10-0', 'trace_hash': 10341460786436315, 'z1': {'__RealLiteral__': 0, 'data': '0.04500262606857755484307233916', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '57047605947678900956764945457,158801602094631880086309313141,699719729837549848946598120251,1110802168956060410012620922290,1314951042763612199763404314075,1356830889867970982079785255065,1366583514476693538505264480385,1886651868862624941593511878004,2003172313988824989406492839097,2315597441297642430133115322374', 'Lhash_array': ['57047605947678900956764945457', '158801602094631880086309313141', '699719729837549848946598120251', '1110802168956060410012620922290', '1314951042763612199763404314075', '1356830889867970982079785255065', '1366583514476693538505264480385', '1886651868862624941593511878004', '2003172313988824989406492839097', '2315597441297642430133115322374'], 'label': '20-1323e10-1.1-c1e10-0-2', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1323/2/o/c'}