-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1755329235791027808711831599844,2027118205245260971501576070507,2323562724015653742585568973419,3022588741062693814838088652013,3133791873330535974014870547166,3335800555479242218599141762800,3349949262859096118535438225755', 'a10': -28, 'a2': -4, 'a3': -8, 'a4': 5, 'a5': 7, 'a6': 32, 'a7': -16, 'a8': 0, 'a9': 27, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7152.532271345449, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[5, [1, -7, 21, -35, 35, -21, 7, -1]], [89, [1, -7, 21, -35, 35, -21, 7, -1]]], 'bad_primes': [5, 89], 'central_character': '445.1', 'coefficient_field': '1.1.1.1', 'conductor': 3455573038713203125, 'conductor_radical': 445, 'degree': 14, 'euler_factors': [[1, 4, 11, 24, 46, 77, 118, 171, 236, 308, 368, 384, 352, 256, 128], [1, 8, 37, 125, 340, 780, 1576, 2866, 4728, 7020, 9180, 10125, 8991, 5832, 2187], [1, -7, 21, -35, 35, -21, 7, -1], [1, 16, 143, 908, 4508, 18272, 61958, 177804, 433706, 895328, 1546244, 2180108, 2403401, 1882384, 823543], [1, 10, 91, 511, 2672, 10626, 41830, 136602, 460130, 1285746, 3556432, 7481551, 14655641, 17715610, 19487171], [1, 7, 47, 168, 622, 2167, 9118, 36132, 118534, 366223, 1366534, 4798248, 17450771, 33787663, 62748517], [1, 13, 108, 591, 3017, 14845, 78122, 344702, 1328074, 4290205, 14822521, 49360911, 153344556, 313788397, 410338673], [1, 7, 81, 366, 2784, 9257, 61132, 176376, 1161508, 3341777, 19095456, 47697486, 200564019, 329321167, 893871739], [1, 13, 144, 1105, 7943, 47855, 274740, 1359354, 6319020, 25315295, 96642481, 309224305, 926833392, 1924466557, 3404825447], [1, 4, 113, 625, 6740, 40902, 266814, 1538922, 7737606, 34398582, 164381860, 442050625, 2317759837, 2379293284, 17249876309], [1, -1, 77, -34, 3570, -2367, 134894, -138904, 4181714, -2274687, 106353870, -31399714, 2204444627, -887503681, 27512614111], [1, 5, 168, 803, 14161, 59989, 771494, 2748646, 28545278, 82124941, 717297133, 1504951283, 11649784776, 12828632045, 94931877133], [1, -5, 92, -673, 7237, -46413, 387726, -2290138, 15896766, -78020253, 498781277, -1901737153, 10658770492, -23750521205, 194754273881], [1, 31, 687, 10436, 129854, 1291529, 10962460, 77409324, 471385780, 2388037121, 10324301978, 35678607236, 100994800341, 195962254519, 271818611107], [1, 14, 271, 2621, 31508, 240678, 2207362, 13822254, 103746014, 531657702, 3271255084, 12789643901, 62152496897, 150909014606, 506623120463], [1, 13, 269, 2568, 34060, 265121, 2673394, 17174660, 141689882, 744724889, 5070750620, 20262755208, 112494587617, 288136694677, 1174711139837], [1, 14, 253, 2446, 31472, 260310, 2563464, 17624256, 151244376, 906139110, 6463687888, 29639065006, 180875847647, 590527470974, 2488651484819], [1, -3, 222, -759, 29403, -83651, 2524030, -6527094, 153965830, -311265371, 6673922343, -10508993319, 187500378822, -154561123083, 3142742836021], [1, -1, 328, -279, 53091, -39287, 5339384, -3265170, 357738728, -176359343, 15967808433, -5622162759, 442841035096, -90458382169, 6060711605323], [1, 8, 187, 1328, 22776, 168048, 2047314, 13028752, 145359294, 847129968, 8151780936, 33746712368, 337390888637, 1024802271368, 9095120158391], [1, -9, 286, -1613, 37567, -166989, 3689378, -14466938, 269324594, -889884381, 14614201639, -45806362733, 592898475598, -1362008036601, 11047398519097], [1, -9, 430, -2867, 81347, -413191, 9305818, -38366618, 735159622, -2578725031, 40107243533, -111669882227, 1323134251570, -2187787099689, 19203908986159], [1, 42, 1008, 16390, 206255, 2129142, 19880600, 179268272, 1650089800, 14667659238, 117933927685, 777841881190, 3970552968144, 13731495681498, 27136050989627], [1, -7, 21, -35, 35, -21, 7, -1], [1, 7, 609, 3724, 164856, 856227, 25710150, 108804964, 2493884550, 8056239843, 150459620088, 329683042444, 5229690216513, 5830804034503, 80798284478113], [1, 29, 762, 12225, 192941, 2287669, 27980664, 273990794, 2826047064, 23336511469, 198787305241, 1272138402225, 8008696581762, 30784084367429, 107213535210701], [1, 12, 535, 4924, 129372, 953928, 19286390, 117964020, 1986498170, 10120222152, 141368277444, 554200538044, 6202116297505, 14328627558348, 122987386542487], [1, 26, 777, 12972, 230849, 2924662, 38920257, 393926120, 4164467499, 33484455238, 282799951507, 1700364584172, 10897826947539, 39018989148074, 160578147647843], [1, -17, 704, -9257, 215365, -2271001, 37783722, -318941274, 4118425698, -26981762881, 278903920585, -1306701096377, 10831912642496, -28510701884297, 182803912081669], [1, -6, 527, -3227, 141284, -783020, 23734916, -112885446, 2682045508, -9998382380, 203858259748, -526153833947, 9709633394911, -12491710515654, 235260548044817]], 'euler_factors_factorization': [[[[1, 4, 11, 24, 46, 77, 118, 171, 236, 308, 368, 384, 352, 256, 128], 1]], [[[1, 8, 37, 125, 340, 780, 1576, 2866, 4728, 7020, 9180, 10125, 8991, 5832, 2187], 1]], [[[1, -1], 7]], [[[1, 16, 143, 908, 4508, 18272, 61958, 177804, 433706, 895328, 1546244, 2180108, 2403401, 1882384, 823543], 1]], [[[1, 10, 91, 511, 2672, 10626, 41830, 136602, 460130, 1285746, 3556432, 7481551, 14655641, 17715610, 19487171], 1]], [[[1, 7, 47, 168, 622, 2167, 9118, 36132, 118534, 366223, 1366534, 4798248, 17450771, 33787663, 62748517], 1]], [[[1, 13, 108, 591, 3017, 14845, 78122, 344702, 1328074, 4290205, 14822521, 49360911, 153344556, 313788397, 410338673], 1]], [[[1, 7, 81, 366, 2784, 9257, 61132, 176376, 1161508, 3341777, 19095456, 47697486, 200564019, 329321167, 893871739], 1]], [[[1, 13, 144, 1105, 7943, 47855, 274740, 1359354, 6319020, 25315295, 96642481, 309224305, 926833392, 1924466557, 3404825447], 1]], [[[1, 4, 113, 625, 6740, 40902, 266814, 1538922, 7737606, 34398582, 164381860, 442050625, 2317759837, 2379293284, 17249876309], 1]], [[[1, -1, 77, -34, 3570, -2367, 134894, -138904, 4181714, -2274687, 106353870, -31399714, 2204444627, -887503681, 27512614111], 1]], [[[1, 5, 168, 803, 14161, 59989, 771494, 2748646, 28545278, 82124941, 717297133, 1504951283, 11649784776, 12828632045, 94931877133], 1]], [[[1, -5, 92, -673, 7237, -46413, 387726, -2290138, 15896766, -78020253, 498781277, -1901737153, 10658770492, -23750521205, 194754273881], 1]], [[[1, 31, 687, 10436, 129854, 1291529, 10962460, 77409324, 471385780, 2388037121, 10324301978, 35678607236, 100994800341, 195962254519, 271818611107], 1]], [[[1, 14, 271, 2621, 31508, 240678, 2207362, 13822254, 103746014, 531657702, 3271255084, 12789643901, 62152496897, 150909014606, 506623120463], 1]], [[[1, 13, 269, 2568, 34060, 265121, 2673394, 17174660, 141689882, 744724889, 5070750620, 20262755208, 112494587617, 288136694677, 1174711139837], 1]], [[[1, 14, 253, 2446, 31472, 260310, 2563464, 17624256, 151244376, 906139110, 6463687888, 29639065006, 180875847647, 590527470974, 2488651484819], 1]], [[[1, -3, 222, -759, 29403, -83651, 2524030, -6527094, 153965830, -311265371, 6673922343, -10508993319, 187500378822, -154561123083, 3142742836021], 1]], [[[1, -1, 328, -279, 53091, -39287, 5339384, -3265170, 357738728, -176359343, 15967808433, -5622162759, 442841035096, -90458382169, 6060711605323], 1]], [[[1, 8, 187, 1328, 22776, 168048, 2047314, 13028752, 145359294, 847129968, 8151780936, 33746712368, 337390888637, 1024802271368, 9095120158391], 1]], [[[1, -9, 286, -1613, 37567, -166989, 3689378, -14466938, 269324594, -889884381, 14614201639, -45806362733, 592898475598, -1362008036601, 11047398519097], 1]], [[[1, -9, 430, -2867, 81347, -413191, 9305818, -38366618, 735159622, -2578725031, 40107243533, -111669882227, 1323134251570, -2187787099689, 19203908986159], 1]], [[[1, 42, 1008, 16390, 206255, 2129142, 19880600, 179268272, 1650089800, 14667659238, 117933927685, 777841881190, 3970552968144, 13731495681498, 27136050989627], 1]], [[[1, -1], 7]], [[[1, 7, 609, 3724, 164856, 856227, 25710150, 108804964, 2493884550, 8056239843, 150459620088, 329683042444, 5229690216513, 5830804034503, 80798284478113], 1]], [[[1, 29, 762, 12225, 192941, 2287669, 27980664, 273990794, 2826047064, 23336511469, 198787305241, 1272138402225, 8008696581762, 30784084367429, 107213535210701], 1]], [[[1, 12, 535, 4924, 129372, 953928, 19286390, 117964020, 1986498170, 10120222152, 141368277444, 554200538044, 6202116297505, 14328627558348, 122987386542487], 1]], [[[1, 26, 777, 12972, 230849, 2924662, 38920257, 393926120, 4164467499, 33484455238, 282799951507, 1700364584172, 10897826947539, 39018989148074, 160578147647843], 1]], [[[1, -17, 704, -9257, 215365, -2271001, 37783722, -318941274, 4118425698, -26981762881, 278903920585, -1306701096377, 10831912642496, -28510701884297, 182803912081669], 1]], [[[1, -6, 527, -3227, 141284, -783020, 23734916, -112885446, 2682045508, -9998382380, 203858259748, -526153833947, 9709633394911, -12491710515654, 235260548044817], 1]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 0, 'label': '14-445e7-1.1-c1e7-0-0', '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}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1, 1], 'order_of_vanishing': 7, 'origin': 'ModularForm/GL2/Q/holomorphic/445/2/a/f', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.0178571428571', 'prec': 50}, 'plot_values': [0.0, 4.196372887451387e-12, 5.37858942680654e-10, 9.210448155746195e-09, 6.921721659643561e-08, 3.313861317313979e-07, 1.1932737185781494e-06, 3.5309401076255e-06, 9.051708235659914e-06, 2.079810993525414e-05, 4.38374385428292e-05, 8.617524903046154e-05, 0.00015993535295994168, 0.00028285425814457443, 0.00048014385460160063, 0.000786764710661194, 0.0012500892530468192, 0.001933101843745826, 0.0029181612204535966, 0.004311363075880168, 0.00624756432678884, 0.008896123084107694, 0.012467162661047108, 0.017217540198935788, 0.023458142490701914, 0.0315616872036729, 0.041970796765642145, 0.05520638561237524, 0.07187624276730871, 0.09268220255097966, 0.1184215198890857, 0.149992923375599, 0.18840084007108399, 0.2347567644552514, 0.2902783000027589, 0.356285453000651, 0.43418853162586896, 0.5254545314987815, 0.6315918883937577, 0.7541272640874184, 0.8945728689260916, 1.0543878960802135, 1.2349341117404777, 1.4374136313847399, 1.6627639947110027, 1.9116083389826297, 2.1841931521316225, 2.4803147063061326, 2.7992455163094143, 3.139663188793598, 3.4995667370379877, 3.876152687880878, 4.2657974213284975, 4.664038453375008, 5.065561685109774, 5.464213098678024, 5.85303863835919, 6.22434716060073, 6.569788565015556, 6.880519079421498, 7.147392674304735, 7.361182878615266, 7.5128410143342785, 7.593787420424918, 7.596254903295894, 7.513706891757456, 7.341119642041241, 7.075299984227251, 6.715210982958889, 6.262268440306136, 5.7205928088047155, 5.097259303565025, 4.402566016340142, 3.6498223893543567, 2.855166298185095, 2.037327887658645, 1.2172697803177426, 0.41769974796004605, -0.3375006602216066, -1.0239588133922974, -1.6179208439044659, -2.097243451239746, -2.442370010942803, -2.637321816115567, -2.670669545264456, -2.5364710242579527, -2.235213658660238, -1.7744520018133403, -1.1691521902839417, -0.4417943180680819, 0.3778015708474449, 1.2529471011594948, 2.1408336952905813, 2.9936180012546902, 3.7601517080358824, 4.38784507036395, 4.824682041239884, 5.021371856793593, 4.933563772648395, 4.524139334709337, 3.7657682998743067, 2.6427897243284946, 1.1526443895494656, -0.6931005307672962, -2.868254507078407, -5.33208617120145, -8.029816280382269, -10.893339433990299, -13.843890624523992, -16.795003504734577, -19.65574767821285, -22.334305282800596, -24.741738168918925, -26.79571379002932, -28.42418444245012, -29.569368841784776, -30.19073863220513, -30.26713532493029, -29.798010842092786, -28.80370597375617, -27.324861427231, -25.42121907769379, -23.168666921261334, -20.65542750697221, -17.977675541004132, -15.234725306474562, -12.52405370490887, -9.936551655308046, -7.55229569753796, -5.436205133870329, -3.6349684995828917, -2.1752571594255152, -1.0632173530416131, -0.285281240064062, 0.18974700253528323, 0.40749419040091067, 0.42389306035331503, 0.30032258703313097, 0.098449681149353, -0.1248242963137982, -0.3219174910735397, -0.4582535826314133, -0.5147715628315207, -0.48896829508296946, -0.39434625669487494, -0.2582861306823959, -0.11847166537057807, -0.018124692790049687, -0.00043001425257773406, -0.10265370737900381, -0.3505679076067748, -0.7537407519120822, -1.302218545322153, -1.9650780193914232, -2.69121680276094, -3.412720733847755, -4.051143441142377, -4.525400052001768, -4.761290204525926, -4.702106412939283, -4.319442212574864, -3.6232629574856374, -2.670441881700384, -1.570584167539452, -0.48620789847063306, 0.37090542531443305, 0.7478324431650439, 0.3634141332108042, -1.0743458522010063, -3.8466880755393134, -8.198326999075066, -14.312512120593913, -22.287654035369684, -32.11666294087169, -43.670970327849915, -56.69092629240763, -70.78381389665115, -85.4319199292091, -100.01376843451145, -113.8330517945217, -126.15513703476346, -136.24996331376127, -143.43912476877028, -147.14628044861408, -146.9516638171665, -142.63116846124865, -134.18580848644987, -121.86007513793002, -106.14587433567961, -87.77073688914449, -67.67186964080334, -46.95637265872386, -26.832159387469392, -8.533531670733193, 6.756950389743949, 17.987750552621577, 24.31363612537658, 25.162499424002014, 20.2919746849643, 9.823971690763058, -5.747038173383816, -25.57054554046982, -48.48122588511775, -73.06308211208982, -97.7325548618853, -120.83683824914596, -140.7665189382986, -156.06696365994588, -165.54180765113847, -168.3418233369364, -164.03241488231052, -152.6349838199821, -134.6391742834765, -110.97769978344196, -82.96979119410418, -52.23620801864051, -20.59037553054709, 10.087240131811026, 37.98384052086599, 61.489344264225785, 79.31362271309824, 90.58439338064095, 94.9182239850814, 92.45786038126938, 83.87207061996831, 70.31640660150298, 53.35365438249304, 34.844106750764254, 16.81712477628493, 1.328359197516584, -9.688437256370047, -14.5649648964184, -12.02673668038704, -1.287401145950272, 17.898286952467743, 45.21097829077425, 79.77853955740697, 120.22364675749073, 164.74439286982096, 211.2367317354633, 257.4805569550526, 301.2622898341824, 340.49651059280336, 373.34584350735776, 398.3226061053471, 414.36661066897204, 420.9176075247615, 417.9994127519558, 406.1258993943815, 386.21921441627904, 359.52994929493104, 327.5435012318035, 291.8794034567917, 254.20365245337356, 216.1595885267393, 179.22060104031462, 144.61017899432417, 113.26240944263536, 85.80611854375094, 62.570904061941626, 43.61444563004771, 28.763826426069347, 17.651894132748833, 9.776027792971394, 4.560214701149877, 1.4113613530590743, -0.23374839237113465, -0.8731435420808151, -0.9171513521850505, -0.6777279106168285, -0.36856428678115466, -0.11478161316483791, 0.030634327428996102, 0.06679776631092033, 0.024254692493500728, -0.05379520747644606, -0.12653675950410012, -0.16571831157776756, -0.16058995611451926, -0.11797258525994676, -0.05842017684221125, -0.009827942656194997, -4.505236669200227e-05, -0.05003550853917136, -0.16869934466445322, -0.3501457151887875, -0.5737813853392271, -0.8071160209262535, -1.0108438986079091, -1.145427183948426, -1.1773856727883645, -1.084837380679426, -0.8615227460309863, -0.5186644367048969, -0.08437116652139084, 0.3994336802457146, 0.8824699784387615, 1.3125582172355177, 1.6420467667262915, 1.833679170764634, 1.865194639374342, 1.7321067343451513, 1.448376356707118, 1.0445925707423858, 0.5634216528051627, 0.05422191376990421, -0.4327569648341498, -0.852023709423382, -1.167710236035533, -1.3573523755656154, -1.4144711182355678, -1.3477040118559644, -1.1783109233933398, -0.9365912091226957, -0.6575621270587212, -0.37646562586949944, -0.12469785702730303, 0.07354852765304086, 0.20387030595900907, 0.26227693685656295, 0.25431248970158166, 0.19306845387261568, 0.09647245014551836, -0.015702290601562047, -0.12471241727808074, -0.21533691749511058, -0.2774953759469117, -0.3068745128782987, -0.304619449629447, -0.27626133355845633, -0.23015533153006174, -0.1757291293801864, -0.12174968834055869, -0.07500210149637682, -0.039525943134481274, -0.016449261617645806, -0.004368744829016891, -0.00013686240038502612, 0.0001375765132964537, 9.325640817164918e-05, 0.002329974757903365, 0.007959043781810395, 0.016542914343180164, 0.026398636919527905, 0.03517709408432347, 0.040589056340791796, 0.041040762653741195, 0.03606195559424881, 0.02644796635499471, 0.014086965847651976, 0.0015136373484586564, -0.008706312077024589, -0.014629885592559861, -0.015500147332249357, -0.012012371203583984, -0.006240798612302436, -0.0012362185180316758, -0.0003632070786746406, -0.006504617234441929, -0.021315052407535864, -0.04470018074406571, -0.07463987984879009, -0.10741418810270775, -0.13820758542615097, -0.1619897997807018, -0.1745402920045514, -0.17346520298387189, -0.15871638532928387, -0.13264619842661415, -0.09957876942809957, -0.0649450977446877, -0.03414970590542362, -0.011413726654176871, 0.001171353003396005, 0.004152107725914263, 0.00046513234686670717, -0.005507809250715817, -0.009390360802350277, -0.008440120599183958, -0.002922307060439756, 0.0032291288390837816, 0.0028571080000562416, -0.012672997016096305, -0.050539171442133206, -0.11277632115719183, -0.19259085463051762, -0.2716733879126862, -0.31970070179254495, -0.2971317976105289, -0.16172360694234592, 0.12122170409697575, 0.5655948853891233, 1.1497318033970214, 1.8024530204022038, 2.392948760117463, 2.7281927708163294, 2.560482786003403, 1.6071554956170597, -0.41667768834942454, -3.7532390850772934, -8.547898216420212, -14.79074963107224, -22.26064164482258, -30.479572897769266, -38.685716512993004, -45.83287602631018, -50.62270065482636, -51.57326146897081, -47.119112607963835, -35.7354188971836, -16.085180158872166, 12.823137989129297, 51.48200725321344, 99.75100273481209, 156.7751354908105, 221.01524815160025, 290.2692909562055, 361.74985394276035, 432.22752526016524, 498.22326522069346, 556.2379140490211, 603.0492318938417, 636.1182181291829, 653.6828316546721, 654.8507774049218, 639.6696002163605, 609.1267678191474, 565.0787209364918, 510.15321197800057, 447.6435813504864, 381.0919591861027, 313.9771348647901, 249.46925311528946, 190.22552781536308, 138.24221453454643, 94.78075845371505, 60.36037717973555, 34.76389856502903, 17.159585698616702, 6.27746268816079, 0.603719708391418, -1.4287549963838813, -1.273306405891167, -0.14136480477944502, 1.0787925056435839, 1.8511173262328147, 1.969473808397648, 1.4939508611982628, 0.6603975773830113, -0.22016288777354354, -0.8558778566300427, -1.0476991590629823, -0.7325016691339302, 0.008649230377527998, 0.975825017644574, 1.9025689539938813, 2.5244366303379273, 2.6498379391266775, 2.219261167437932, 1.3433322710208468, 0.3118959860984715, -0.42952976023303335, -0.3346460016211129, 1.1642052724117244, 4.56890562494882, 10.23309448067938, 18.290820819155627, 28.60756538111751, 40.76147687324604, 54.0592093694178, 67.59800018057948, 80.39371667238566, 91.46721595901343, 99.93390175283871, 105.09236862817774, 106.49518421130564, 103.9945492721311, 97.77328450944478, 88.36590884111378, 76.54439634753, 63.21790859279341, 49.34154269921883, 35.827712065232426, 23.46876774786553, 12.881062342930166, 4.468793348206322, -1.6106086463769045, -5.429584874730491, -7.246513067159904, -7.448783746671049, -6.491072894305217, -4.8368862714541, -2.9098693144418775, -1.0540157968334918, 0.48945150290438905, 1.5873808167405845, 2.2051096203629794, 2.3861203278606102, 2.225771079938795, 1.8439337783656726, 1.36054253260971, 0.8768950319808159, 0.46443541667035393, 0.1611728157270966, -0.025363258782714226, -0.11059105656079578, -0.12307512037727841, -0.09480057192379965, -0.05353273628647875, -0.018173365517636965, 0.002632400554107714, 0.009037174215003647, 0.006595665132629705, 0.002118466093546526, 4.737409003063334e-06, -3.5299079198224085e-05, -0.0034914068218531067, -0.019811622997831197, -0.059796543398120294, -0.13234625438386988, -0.24164630605514714, -0.38534300469471106, -0.5540210575179674, -0.7321267685674301, -0.9001505634891483, -1.0376663167896247, -1.1269647749663878, -1.1570518719225262, -1.1248005323918044, -1.0349358491044944, -0.8989881548087543, -0.7332464662318184, -0.5561195539783357, -0.3854939087092203, -0.23641037439376705, -0.11862691182193692, -0.035909678799272815, 0.013425841741921136, 0.03516244571013533, 0.037380718520248726, 0.028604502453443877, 0.01623726158292174, 0.005491835342813007, -0.0010106325777905045, -0.002986693441525366, -0.0017697153805619234, 0.000619184248344155, 0.0023457959507202693, 0.002375916810178171, 0.0007100177877300805, -0.0017666770213193258, -0.0037154598901301206, -0.0038910953529811497, -0.0016240240214620966, 0.002910259013420677, 0.008716332013606757, 0.014278192828506408, 0.018026853473598795, 0.018836523279278865, 0.01640099983965879, 0.011373840031128664, 0.0052171192069660295, -0.00022252505175933909, -0.0032571711825107345, -0.002858578229802172, 0.0010154344461935302, 0.007369288762461569, 0.014422056745791383, 0.020116382420842446, 0.02277563024197415, 0.021648012284835795, 0.01715379185293305, 0.010763993965724717, 0.0045134071680081045, 0.00025504561209438686, -0.0011465017237559164, -0.0004423831789287439, -0.00018775351433525535, -0.004295917386645791, -0.016999510883736017, -0.04140526501532095, -0.07796258190097481, -0.12325493842346823, -0.16956740604203735, -0.2055317273246473, -0.21788380780817304, -0.19412386039417237, -0.12561549897830263, -0.01048014215354851, 0.14441932985422956, 0.32313820833214796, 0.5024370570718011, 0.6554098579574247, 0.7564662773390404, 0.7867862107572041, 0.7391040934779132, 0.6207139791077644, 0.45369323890901375, 0.2711561711117612, 0.11052970255416886, 0.004756015305668097, -0.027092090136132382, 0.012173603008947905, 0.09322410957217346, 0.16066459121138868, 0.1393655309680842, -0.053835230211933066, -0.49441777192905173, -1.232773208761272, -2.2781372536259834, -3.587759632434189, -5.066468890024613, -6.573555419938779, -7.937764524097013, -8.979571902856781, -9.537639121946292, -9.495598805878956, -8.806596241873242, -7.511674905956933, -5.732287595918627, -3.653729595175114, -1.500245478706794, 0.49659387729366633, 2.13155592168578, 3.256513376779203, 3.805145027676872, 3.8018980295558156, 3.3516452838118305, 2.61541435256911, 1.7769203603124282, 1.0059934664964014, 0.42584489510005, 0.09003544920994896, -0.025967126804258577, -0.012750645655748577, 0.0024013857152360694, -0.10362258288229377, -0.40534864612021154, -0.8899489923481378, -1.4333882822613686, -1.7991609782954001, -1.6625592610079398, -0.658738928019157, 1.5517152858624652, 5.2098766403904575, 10.390975213026481, 16.958039158498952, 24.547022325662745, 32.58587347424776, 40.348681651690924, 47.03958798511151, 51.89575853995911, 54.30082683139152, 53.89938528149141, 50.6426857866248, 44.79867232704034, 36.92322556833026, 27.790618618944617, 18.292539526237324, 9.323976006476151, 1.6702374700754956, -4.113617927438991, -7.766030128032021, -9.330158127548131, -9.118675067295033, -7.639079428584771, -5.491970286034893, -3.2600119824811604, -1.41044639289889, -0.22201464721820288, 0.2491050731562873, 0.15934009725977943, -0.17294058117187075, -0.34856167424767953, 0.01826426905824174, 1.2125168687450045, 3.353115620843409, 6.360166286606317, 9.959826797731964, 13.72557696641554, 17.15293248256899, 19.76439533281494, 21.18894358651777, 21.221465171363292, 19.855286265543715, 17.280455421577436, 13.84923996797953, 10.018392384091195, 6.27717513668168, 3.0534590932555368, 0.6460380559199538, -0.8125862314332, -1.3619411184196237, -1.1890169992557034, -0.5797695928416364, 0.1431695826442686, 0.6845399570933971, 0.8302975729416424, 0.4812176899052704, -0.3385483157874259, -1.4976227404595557, -2.793732064617417, -4.0026599585938, -4.924608166932676, -5.420994468678624, -5.436327167537241, -5.001974576286629, -4.222557631954879, -3.2492920313991718, -2.245836519687278, -1.353684419737639, -0.6690422653336666, -0.232255955927257, -0.02976671763155548, -0.006718357918793815, -0.08645843290717443, -0.19246450317959218, -0.2663558706971774, -0.27760946556334926, -0.2245642666174146, -0.12801674641861335, -0.020162812678086634, 0.06761464432526153, 0.11493184282581267, 0.11768975662348283, 0.08685036192771173, 0.04243612157709892, 0.005337560404382206, -0.010219737442365236, -0.0011502161610658522, 0.024425602415827568, 0.051529944767215716, 0.06524047797292724, 0.05732819099888718, 0.029992211581189067, -0.004900116713618318, -0.031031346948294916, -0.035571569391184804, -0.016602083262886688, 0.0138729401468286, 0.03403863505960531, 0.024019561899867228, -0.017160390467192796, -0.0547659589831475, -0.008986817226805827, 0.23989929301038004, 0.8269576936940073, 1.857816035845999, 3.348635891819159, 5.162042083381168, 6.957663456508045, 8.183449626800913, 8.104800556383687, 5.88305653884318, 0.7039649284233334, -8.057414592480532, -20.65879436059381, -36.83042250356533, -55.68810746324006, -75.77753478892114, -95.20445519661773, -111.85411716874506, -123.68193645800454, -129.0365764396406, -126.98460539976143, -117.6033707617001, -101.99179102202649, -82.11405468674546, -60.4996552256534, -39.82481614247492, -22.440255948610996, -9.929989344543026, -2.7711515156469626, -0.16735338877654682, -0.19369796730513242, -0.20198378833020522, 2.5887287070223537, 10.421137303230275, 24.374986840675362, 43.915134575910834, 66.77219030630782, 89.22561406721262, 106.77176314605794, 115.08496589425934, 111.10721933445066, 94.05558783453198, 66.12586534241092, 32.676079375944454, 1.7558106858848033, -17.03473402124927, -14.248962594433344, 17.371590701704715, 80.88810660467277, 173.65952821058414, 286.5371167484527, 404.01460848501586, 505.51303212065915, 567.7741035338339, 568.156365206461, 488.4983739749803, 318.79244146021284, 59.42772872766651, -277.5013085988471, -668.2449673599554, -1079.0495596568287, -1469.366341571277, -1796.7720321778397, -2023.9682903144958, -2123.3169828492482, -2080.2780517541273, -1895.6219023824117, -1585.8249400894788, -1181.5355393638342, -724.5968960560073, -263.73666971820205, 153.4926071804368, 487.148684811473, 709.6966984402736, 809.0834291163493, 789.7477835504425, 671.5421536509921, 486.85254623774756, 275.5915384740608, 79.10357819940522, -65.77956626238448, -131.72731638944785, -104.31560412228298, 16.5024857595934, 216.90088607411002, 471.78946787149795, 748.9636957809947, 1014.0052573872977, 1235.1832426569329, 1387.6529457178933, 1456.4307406516882, 1437.8333428445217, 1339.0115487653006, 1176.029522750265, 970.8965090149155, 748.0445323006224, 530.8115731212249, 338.4253422083694, 183.86862484531093, 73.05205866643584, 5.1293698991749, -26.267704335697317, -31.153108656124132, -21.023701520371404, -6.770138514968851, 3.020775546041549, 3.0655943042828935, -8.360045128655695, -29.78878663614269, -57.40032598019682, -86.1319119252322, -110.87253397148415, -127.58603867165695, -133.92049766535982, -129.40882526131637, -115.32371900262677, -94.25138516930559, -69.49940533300203, -44.47473055895593, -22.125491399579364, -4.471298033999953, 7.560310822651354, 14.063017047213597, 15.919234441282342, 14.477302692096776, 11.213274416042875, 7.440345640492082, 4.108251199042203, 1.723878747860263, 0.3837945956290528, -0.11360094565924364, -0.11787079644426854, 0.020289020805496886, 0.059644408867819514, -0.07742239655567759, -0.31044974790354984, -0.45311834573543286, -0.2909203187684944, 0.3397288790988862, 1.4925071437823019, 3.0884249282349066, 4.929858698332215, 6.74377902144937, 8.2421132335959, 9.183798760352671, 9.424115437941504, 8.941963575280536, 7.840010904550658, 6.311450001024354, 4.594940656226289, 2.926707343032063, 1.4986611648029966, 0.4304380961981196, -0.2406543350484533, -0.5516681120712512, -0.5904677128981345, -0.46656275421283994, -0.2836741573786502, -0.11939308519718161, -0.015153083968586903, 0.022980720463029448, 0.014544735567192725, -0.0099500021298151, -0.02304672796093218, -0.01028368723895024, 0.02584573529494879, 0.06810941668258935, 0.09160664741499211, 0.07328976998295123, 0.00020319818217690808, -0.12590945671486325, -0.2884009916028113, -0.4596420648735523, -0.6077849527817787, -0.7046952146052885, -0.7334403848323079, -0.6916443925840131, -0.5909659301922289, -0.45341321374429744, -0.3055905525709388, -0.1724638525692625, -0.07221371510668297, -0.013205743987332196, 0.006555906912252127, -0.002858777027121313, -0.027252513679619016, -0.05261884614028436, -0.06867125668986929, -0.07076940529949118, -0.059934887651302185, -0.0412403449347734, -0.021336197135235546, -0.005923989309241784, 0.00208442920309689, 0.0032403266786702007, 0.0009582525236159601, -5.064766161466849e-05, 0.004377870282991526, 0.016351362590364505, 0.03514211434692462, 0.057333534532391484, 0.07782161954173951, 0.09142939584694798, 0.09474872508751539, 0.08702515560114502, 0.07023518154373187, 0.048445808427447015, 0.02663380629071766, 0.009315698067912584, -0.0006240929347444781, -0.002623711688458201, 0.0015765724544532715, 0.008748786925219505, 0.015352170310741901, 0.018664301270453425, 0.017536689824800597, 0.012582780344652926, 0.005777759395759138, -0.000421553269926596, -0.004067257917009736, -0.0044600527467708205, -0.0023865665037762266, 0.00022622772937368608, 0.0011239332770700177, -0.0012687560435731848, -0.007003417967053575, -0.014247262784572239, -0.019578900279695836, -0.018910686993388683, -0.008801640795100445, 0.012232549470530396, 0.0428887801183663, 0.07897054469469715, 0.11405539124875741, 0.14084961757597245, 0.15293192360412355, 0.14645538400020702, 0.12134927194940119, 0.0815044082830813, 0.033790512190609134, -0.013471611627478387, -0.052320345285578954, -0.07686246322827235, -0.08448715995889612, -0.07635644727784677, -0.057011075698968565, -0.03270460374176318, -0.009635538913548873, 0.007518555767032217, 0.01650161883279316, 0.017649082178484984, 0.013363452887101246, 0.007085181593765128, 0.0019803792679418727, -9.470845892168184e-05, 0.0009753755024166149, 0.0038002396111234916, 0.00624183553224649, 0.006402120125708876, 0.0034955216868148955, -0.0017125057977191147, -0.007089470049092444, -0.00988027293558937, -0.00775071455954894, 0.0002408815568807692, 0.013104151245609843, 0.02803974838040077, 0.04120836767323885, 0.04892201634672452, 0.04888650702139429, 0.04107370846210847, 0.0278907178085304, 0.01351525446311596, 0.002543946529094864, -0.0015103375740010707, 0.0026124341395082017, 0.013435608023153, 0.027151150669209995, 0.03885076250128922, 0.04427669523036315, 0.041556171805603205, 0.03183398981087129, 0.01877578080077098, 0.007118992733423891, 0.0007041511369688019, 0.0006943510661809724, 0.0047631488773285805, 0.007924807857527897, 0.005268698948775361, -0.004148585972627746, -0.01355435752448506, -0.0062798228714815146, 0.04361669640575231, 0.167184687175171, 0.3926658397731528, 0.7356624734038604, 1.1901379879985066, 1.7229427785171183, 2.2741922091624756, 2.764629034930199, 3.109552791466405, 3.2374395642163503, 3.1082534874197503, 2.7266121216612436, 2.145799346630792, 1.460191858877972, 0.7864086512253039, 0.23655736385186263, -0.11059435456167113, -0.2325241788109496, -0.17207734442982447, -0.028894947182164767, 0.06747424346802185, -0.0010982638012360184, -0.2941112360610276, -0.7726709940237033, -1.2790012409772311, -1.5419326629936396, -1.2119168419104096, 0.07691407149760765, 2.626412586982415, 6.589587934054052, 11.90497788705486, 18.276577724586733, 25.19177049841222, 31.97876197193113, 37.897466402555516, 42.250058545466835, 44.50130050644776, 44.40045870897501, 42.006570128462826, 37.66331575506398, 31.93365519571406, 25.501593228376816, 19.060174128293777, 13.209759737998096, 8.380472070082464, 4.771545493131269, 2.3601018728551604, 0.9559195310859858, 0.2789444638632739, 0.03891459603947117, -0.0014400142915025362, 0.00805848882988984, 0.007188588953351259, -6.332427589220814e-06, 0.014957621110668631, 0.06780706486208976, 0.141679553619513, 0.19218429047446225, 0.1749461090734576, 0.0845967149975457, -0.011570440841915242, 0.03705721503140733, 0.43955558284965646, 1.4008771317836324, 3.035213568985358, 5.292437572207229, 7.911038830418485, 10.417715501040059, 12.189598035637813, 12.577162800743992, 11.069903944781878, 7.4836075442765, 2.125969331160191, -4.232048333525734, -10.47971010451456, -15.376506215543253, -17.82774334533538, -17.17278092812566, -13.425053639806805, -7.404688446964286, -0.651432890102031, 4.877114768521706, 7.2455199191238995, 5.029943992675409, -2.2511179058092816, -13.867077205505854, -27.84743118850224, -41.3057013157572, -51.05634609331242, -54.402336249878665, -49.935000197150856, -38.16500030587526, -21.823995203052277, -5.71927516694546, 3.936917400875853, 0.5956221434632148, -21.33426481092932, -65.1971522871823, -131.06708543524047, -215.24974673572726, -310.572364985813, -407.25778428001195, -494.29025182890496, -561.0876400178355, -599.1854853434784, -603.6345741540251, -573.9640798721356, -514.5737493750312, -433.54110225907857, -341.0785366346584, -247.8301463799428, -163.20076928611732, -94.01403235023186, -43.75051487194484, -12.434685571239882, 2.914638344795583, 7.108229074738078, 5.38097742105246, 2.1305629980642458, 0.07528378212022502, 0.0015328411994856954, 1.1317703828164853, 1.9862215579012075, 1.4855326661204988, -0.03167033294306091, -0.1920862392161672, 5.397780237780835, 22.419975302077656, 56.524933595323226, 111.69976310723499, 188.67541355231677, 283.7511617082565, 388.35507969568425, 489.5368183434339, 571.533653813045, 618.5130192379678, 617.1339376488124, 558.9415937354445, 442.2283404456828, 272.9329723050418, 64.37656195120054, -164.12906225280994, -389.7064620190321, -589.3452086382779, -743.1042030685101, -836.7510296584517, -863.5181440250439, -824.7311363401379, -729.282528058337, -592.0146129305068, -431.07774541320146, -265.2187264550447, -111.30606305704019, 17.614064316630106, 113.49599862804472, 173.65157336295033, 200.33364356089047, 199.3777722014322, 178.62872981256265, 146.4194421465694, 110.28910097490596, 76.0953300442428, 47.58684103741052, 26.40664165414125, 12.462651495472352, 4.524651603639636, 0.8456246345365853, -0.3162467156629946, -0.3464860589675302, -0.11660011633947791, 0.0013470476137887194, -0.0002834056528506047, 0.05139675276389001, 0.34214934391637297, 0.9586480115913211, 1.8468963619181455, 2.835501993153942, 3.705844066649244, 4.2663608990180775, 4.407106451704777, 4.122757960866683, 3.5021943313900614, 2.6933326481185413, 1.8578944600301959, 1.1300181386620884, 0.5870416905334317, 0.24441035458599603, 0.06948700977632136, 0.005388986174820271, -0.004697991270268341, -0.0005901541644968428, 0.00047717343664832064, -0.001221526568970551, 0.0008630932689401467, 0.008038598302214432, 0.009700315181622303, -0.01568208010241161, -0.09238221020678072, -0.23619444894047223, -0.4450204856576224, -0.6946403614755913, -0.9416363456492302, -1.1331008320915794, -1.220598931556582, -1.1750773588283998, -0.998315421973266, -0.7207927938459656, -0.3929924819762891, -0.07271780218265789, 0.18868030352917736, 0.35754045956004393, 0.42401863030713244, 0.40217568216555544, 0.32238854132045985, 0.22001755699452274, 0.12504655377172058, 0.05552201173023771, 0.016032543093930724, 0.0007145652922982565, -0.0011254896277370762, 0.0007866960448301147, 0.0013658946856218437, 0.0004134391584256603, -3.8205510609223304e-05, 0.0006086219051295904, -0.0007622506881566992, -0.010027959875853518, -0.0312261504003928, -0.05962419799494144, -0.07524406821823286, -0.040266583955619065, 0.09684372508603915, 0.38978867335875284, 0.8791412907189339, 1.576343573004496, 2.4510191559464585, 3.4263104879899733, 4.385171046928519, 5.188169195705375, 5.703476194765865, 5.8471327683415355, 5.596013445389039, 4.990343690307919, 4.125546219161234, 3.1325681799204723, 2.1510166210208657, 1.3020932404660723, 0.6656315202302796, 0.2627492549615044, 0.062344925330362455, 0.0011654158040274114, 0.008481210616044704, 0.027862471379918978, 0.030121686287800258, 0.014573167142713471, -0.0009406787474057203, 0.003429712500692599, 0.03431982848191529, 0.07830651143395755, 0.10703708566874749, 0.09305319581251635, 0.030327590436003544, -0.04965111791130973, -0.07500125513850862, 0.05108586398342501, 0.4176335019998219, 1.0641429809014418, 1.9445781006294816, 2.916513862512348, 3.759895312203534, 4.226682910359815, 4.114252075488168, 3.3447189864732496, 2.026475308278494, 0.47561307350613014, -0.823936955154705, -1.3385564363086402, -0.6286733607098584, 1.5102592550938159, 4.94396833722736, 9.166978980177081, 13.367673575056346, 16.60875708351507, 18.062195690700214, 17.238084923874343, 14.150842086947792, 9.37148088572376, 3.939104810173192, -0.8605510525967492, -3.8220743508680193, -4.197750147975394, -1.9570014549558374, 2.142610919468727, 6.710940403229058, 10.099490936762669, 10.93234013616523, 8.689623895486852, 4.179795642144271, -0.2572933723889776, -0.9070076118293491, 6.782391499217952, 27.34442440700736, 64.26799636805595, 119.0282945042569, 190.39284410491194, 274.1628562151204, 363.4467250384663, 449.46197269818924, 522.7578537993414, 574.7529798900041, 599.4452730894421, 594.182566558209, 559.9612010635149, 501.20846251721196, 425.01916837992286, 339.990792113005, 254.92537174636857, 177.58194469907963, 113.36863101105519, 64.86302509862972, 31.960720314467874, 12.46766565667697, 2.962773395139489, -0.2765633279957036, -0.4870875165350512, 0.08298636855575356, 0.32252212439945666, 0.06653466965893666, -0.3136440353331503, -0.37755593217159805, 0.01563675687598277, 0.5496301513689994, 0.5393573819096372, -0.7860185087542284, -3.9150937787348563, -8.735385509434298, -14.383973585430397, -19.343893844636234, -21.799223988995987, -20.126906379556473, -13.394244049625609, -1.7267076481293613, 13.56912677334549, 30.182125184687308, 45.26070809833437, 56.096517981487544, 60.77328739206519, 58.62470434460457, 50.398679603055186, 38.074606868739686, 24.36983065591663, 12.054939337885992, 3.2421500258620433, -1.1617783404302173, -1.6312940737359076, 0.20761324293759692, 2.1642556356303078, 2.2911865099781767, -0.28926750497452913, -4.767658863798017, -8.448522643277084, -7.040537592992661, 4.587025747478622, 31.303116824934087, 76.47732754443916, 140.90886987951913, 222.3640994599001, 315.56335973432255, 412.69058854533824, 504.3952324613371, 581.1043496841418, 634.4269448102117, 658.5672033976002, 651.6664692777217, 615.5576740154602, 555.1551000764931, 477.5690703205454, 390.9819833475307, 303.48357466008764, 222.08969386332257, 152.03732822771397, 96.19481816886436, 55.13362362280925, 27.58743269269661, 11.093325841944816, 2.669473994351782, -0.5946239009112269, -1.1181183885319794, -0.6137254084185999, -0.06963136371359657, 0.12310295862567258, -0.032182375013445196, -0.3482268920624337, -0.6214213470845303, -0.7297944689341371, -0.657542205265422, -0.46836600654872795, -0.2557280075640031, -0.09519795511932479, -0.016229944865975243, 0.0002823156173223183, 0.002968191300227118, 0.04205186681851164, 0.14578140780360926, 0.3089150778292458, 0.4957069636633116, 0.6546467432653084, 0.7391201343567377, 0.7266882324216637, 0.6244623559906559, 0.4638386051129131, 0.28827714770422597, 0.13865264122754853, 0.04123775890149925, 0.0019163289625729134, 0.007767105016893111, 0.035140066765518375, 0.0604627219347398, 0.06873147184215217, 0.05697986344528161, 0.032383617052904656, 0.0067128223812206395, -0.010076677098554015, -0.01433690660110335, -0.009265406835634237, -0.0017926181383765758, 0.0021701388318556424, 0.0014222672692076538, -2.506322304289157e-05, 0.0038823897160305044, 0.015904938318442675, 0.030858770961251846, 0.03485153470515423, 0.010583321847608854, -0.05138336274840897, -0.13882989504897267, -0.2091160212871235, -0.18801530164434643, 0.02104849925463334, 0.5165260543441981, 1.3701610859922166, 2.5964602656480347, 4.128362236994633, 5.813137107226496, 7.437820627546838, 8.767458634584804, 9.590600333255656, 9.763221554800912, 9.241148869457694, 8.096522056804174, 6.516116738243325, 4.750559808115573, 3.054771850643557, 1.6349761335533475, 0.6118966217603051, 0.007913343020100145, -0.24054234352501436, -0.2513577029769766, -0.15536246852972185, -0.05604320521289704, -0.005139012231672919, -0.0005568596008950134, -0.00480049173732003, 0.024834456741009748, 0.1071622035657411, 0.22178329538819647, 0.3149383829293684, 0.32599109988943253, 0.2259351219384757, 0.0534500044102342, -0.06738373705997106, 0.05994277016468761, 0.6570879859039371, 1.9009706896427576, 3.8489680883755986, 6.3817865356004555, 9.185881991556506, 11.791510183977808, 13.669712262016029, 14.352626031691589, 13.55599382016219, 11.274221142471708, 7.81911603446982, 3.784829631495124, -0.06671530660193119, -2.993886043378708, -4.456492654789073, -4.251914358369877, -2.5809435782639416, -0.022753976706061985, 2.5811933653735974, 4.315121000823738, 4.4202829229646206, 2.5048689630905825, -1.341330769998831, -6.542722567447569, -12.143649864500023, -17.001702232924615, -20.030986139146815, -20.456283045852544, -17.99139158942227, -12.904340936064516, -5.962987876456775, 1.7256574569132963, 8.944555887422425, 14.613524929852488, 18.000487906158167, 18.840003876952764, 17.348276792191655, 14.13839212749913, 10.058387819057337, 5.99168000098262, 2.6659073070982915, 0.5132191955977647, -0.38220129228033334, -0.2516122813237172, 0.4547040565028606, 1.2018755624519049, 1.5113791588274985, 1.07665310937777, -0.17960737337073024, -2.115175272900936, -4.422832158394896, -6.7126545266296365, -8.601987452929457, -9.79411888661372, -10.136841633078786, -9.65610807367566, -8.513709984113506, -6.949972189386001, -5.226423421179479, -3.5758900119482617, -2.168389389711449, -1.0967802404217752, -0.3794340826421807, 0.026546043316703273, 0.19895268231748775, 0.2240480381464646, 0.17690617008094667, 0.11085257875260704, 0.05549688837838771, 0.02094225278891946, 0.004993208793540728, 0.00037234675549119967, -1.6278147907998307e-06, -0.00039380275854765027, -0.0019790343847608614, -0.003986092868810218, -0.005197402824796604, -0.004976344846662581, -0.0035560324316979653, -0.0017450931841134604, -0.00038760475227417416, 8.215108992684148e-05, -0.00021834341554468085, -0.0008098227626276751, -0.0011929971556473699, -0.0011116073554712472, -0.000632059625375328, -4.0635198896531874e-05, 0.0003563493667048622, 0.0004112848599701523, 0.00020300750993247583, -4.054705944966902e-05, -0.00011044396787496343, 4.4495547780237043e-05, 0.0002884055218671979, 0.0003901935907811369, 0.00018105822147647933, -0.0003155884690804514, -0.0008684325301704728, -0.001154996523278552, -0.0009519068083912443, -0.0002913263541411034, 0.0005171366371173683, 0.001036609989549934, 0.000968474471382035, 0.00039847458517145313, -0.00012090096336383444, 0.00026036675211731954, 0.0022917742505339025, 0.006142727750898279, 0.011084393537477588, 0.01560666608187952, 0.017918961859885865, 0.01668139738939909, 0.011718802313451631, 0.00439676309763092, -0.002588323420727239, -0.006056178786657536, -0.0036435657879699563, 0.004918641233954602, 0.01731479575003111, 0.029178709158425263, 0.035599307987881176, 0.03319867666911592, 0.022118629034660275, 0.007059890481822192, -0.003608736492611505, -0.00031349334131516746, 0.024361854997027758, 0.07244559573577428, 0.13862928194752414, 0.21051382229456816, 0.2715874599854594, 0.3060661287267786, 0.3038631339950371, 0.2640854895036325, 0.19581408838022818, 0.11576444070591423, 0.04346287408252827, -0.004782624887365898, -0.021204339852585987, -0.008542124522606978, 0.02170289684632857, 0.05395489731290595, 0.07443639661600421, 0.07604147096024091, 0.06035869270710012, 0.0358522706677972, 0.013289709283350985, 0.0005756637197717394, -0.0006894129179803941, 0.004675390726240278, 0.008765516785816368, 0.005801163248812687, -0.003817532489104626, -0.013182750396660106, -0.012863070608266495, 0.0025382525635384797, 0.028887011614252958, 0.05214548524839508, 0.05551581579983063, 0.031705498127735904, -0.007385786654767075, -0.032983835738822735, -0.02086504480106722, 0.008571079686512117, -0.05594042294551601, -0.4415709289831377, -1.4592197118969064, -3.3883670033670206, -6.276379422864602, -9.686904004304342, -12.476022505184483, -12.717174235016133, -7.932141647983881, 4.288504476978009, 25.280571453814073, 54.04585168801259, 86.02536221598132, 112.33254061960916, 119.96395751525405, 93.52619852329609, 18.614560184609378, -113.28956936677017, -298.92537624898955, -517.3762275169541, -725.6052794521507, -857.2311167144019, -826.7008586162517, -537.5679570012255, 104.67401420667113, 1176.0113734136503, 2715.730592067114, 4709.483222891205, 7077.358243542835, 9673.677006912698, 12298.15841359264, 14714.960397681714, 16679.429596872305, 17969.647346906626, 18418.5993515046, 17945.35889061452, 16583.35415272576, 14472.186708264122, 11837.290933861039, 8959.763011705252, 6137.850342552427, 3645.777395013226, 1696.7116700054833, 413.7681989888174, -188.5581241951015, -198.51343149256314, 216.42764391267872, 844.459444764194, 1469.2005686144805, 1907.4684356078135, 2039.3093169748745, 1823.4766866427617, 1296.4706295996073, 557.0002728940891, -259.9717742520137, -1013.6979813136646, -1586.387075925489, -1904.913563323041, -1950.5737644182727, -1756.4349222008193, -1394.4546989253156, -956.0127673243153, -530.6012456929745, -187.37160047732908, 36.575169215445975, 138.2523193315325, 142.9236629722709, 92.67317607573808, 32.488801200266195, -2.668285743939761, 3.2563176700183445, 44.86808209522929, 99.28392925511045, 134.26539751810964, 118.19094648008891, 29.43969050380036, -136.95317209251306, -366.88215951545305, -630.3298790396914, -888.8107482300614, -1103.7577124946627, -1244.2369681444318, -1292.49711583668, -1246.4286113000715, -1119.0608905266859, -935.6341486815331, -726.4592722590725, -520.3179201923512, -339.60097790698256, -197.63483974674148, -98.35360963803252, -37.94061005109662, -7.645748462985761, 3.101795498971027, 3.9020049947698703, 1.6440968816474235, 0.0045352842770771265, -0.032478561865629814, 0.9193948321375537, 1.8091261582544473, 1.9592274657943545, 1.3621884738193994, 0.5220949546426356, 0.02730733297217467, 0.09851887429525165, 0.33375426956792914, -0.21990702169356138, -2.6713836003215694, -7.712758384576998, -15.110365421707847, -23.50971742564516, -30.710189651500357, -34.52255659834914, -34.10474300125553, -29.945990291470928, -23.369254486629934, -15.970829162136443, -9.137297006305747], 'positive_zeros': ['1.38471060990701707155474720672030', '1.59911430237976937126415057321836', '1.83296779380478863816478260891860', '2.38440209038555509919050674647455', '2.47212589396977697230581201243091', '2.63148264583210902853824114276749', '2.64264400794348778617203117093380', '2.93780312850244441451367290352321', '2.98832092242241861645588382725622', '3.45587790298020185856735092222078', '3.56544450618704653806895186022319', '3.86899877953181198275381479500202', '4.09106058440639987689007269482761', '4.16220540712002498661950244258076', '4.74642929351272300982901740041893', '4.85190281950692521821296613565798', '4.89880680809120967132129460764603', '5.02484126305243650496672456039951', '5.03565720502203011302796914355302', '5.25319731601321216044861769517841', '5.44832777227399333657953202111598', '5.65340940362821267541754816364690', '5.76538843896948282923103507554995', '6.01957630914516778122045869529011', '6.04179844967899344415925700147998', '6.05078860209947002756367539399683', '6.25232468124830016616156134266433', '6.36863234157814022995749510549332', '6.36944103482320413140153797867913', '6.65816916178860077736678377981236', '6.69794170101574625495090298154118', '6.77553088318695637853055378468941', '6.80921750591263441589097671935156', '6.95781374742630329202725193015366', '7.10421504866325048064708776598497', '7.33206766846463897697570929283153', '7.86044296999292340328126928017823', '7.912661095778710120046847219242283', '8.013126328078941374500555446303575', '8.089113963570370123930288878668879', '8.220373631489517973132756415509119', '8.256213937658395535298854455860106', '8.673133206894176850602659056235626', '8.815249615773039709526197231051364', '8.996792902482164941132280721424532', '9.103864680273162426000067377978809', '9.178693410589626502589573472934750', '9.192531971794843889938031120647971', '9.193675616170500042491329003522477', '9.583209557981773580176371087082083', '9.692542928512956046648912166420403', '9.745372462774772993492548212404890', '9.808889374787792923180294679577982', '9.882315745353986876360803236285513', '10.03476433586651522582004550836567', '10.08576929778335642415398189563275', '10.25167788269709518976945104051546', '10.29743384694797749338665928164394', '10.29777119814374604027065380840056', '10.50135114093515880110584856330469', '10.71554038089888899654972827821209', '10.74653990101180368553200470833745', '10.81801470009708925624796640279986'], 'prelabel': '14-445e7-1.1-c1e7-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.8850312702835936, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1e7-0', 'trace_hash': 623418917423990705, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.38471060990701707155474720672', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.59911430237976937126415057322', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.83296779380478863816478260892', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 7152.532271345449, 'bad_primes': [5, 89], 'central_character': '1.1', 'conductor': 3455573038713203125, 'conductor_radical': 445, 'degree': 14, 'dirichlet_coefficients': [1, -4, -8, 5, 7, 32, -16, 0, 27, -28, -10, -40, -7, 64, -56, -5, -13, -108, -7, 35, 128, 40, -13, 0, 28, 28, -45, -80, -4, 224, 1, 7, 80, 52, -112, 135, -5, 28, 56, 0, 5, -512, -31, -50, 189, 52, -14, 40, 113, -112, 104, -35, -13, 180, -70, 0, 56, 16, -14, -280, 3, -4, -432, -13, -49, -320, 1, -65, 104, 448, -8, 0, 9, 20, -224, -35, 160, -224, 9, -35, 21, -20, -42, 640, -91, 124, 32, 0, 7, -756, 112, -65, -8, 56, -49, -56, -7, -452, -270, 140], 'euler11': [1, 10, 91, 511, 2672, 10626, 41830, 136602, 460130, 1285746, 3556432, 7481551, 14655641, 17715610, 19487171], 'euler13': [1, 7, 47, 168, 622, 2167, 9118, 36132, 118534, 366223, 1366534, 4798248, 17450771, 33787663, 62748517], 'euler17': [1, 13, 108, 591, 3017, 14845, 78122, 344702, 1328074, 4290205, 14822521, 49360911, 153344556, 313788397, 410338673], 'euler19': [1, 7, 81, 366, 2784, 9257, 61132, 176376, 1161508, 3341777, 19095456, 47697486, 200564019, 329321167, 893871739], 'euler2': [1, 4, 11, 24, 46, 77, 118, 171, 236, 308, 368, 384, 352, 256, 128], 'euler23': [1, 13, 144, 1105, 7943, 47855, 274740, 1359354, 6319020, 25315295, 96642481, 309224305, 926833392, 1924466557, 3404825447], 'euler29': [1, 4, 113, 625, 6740, 40902, 266814, 1538922, 7737606, 34398582, 164381860, 442050625, 2317759837, 2379293284, 17249876309], 'euler3': [1, 8, 37, 125, 340, 780, 1576, 2866, 4728, 7020, 9180, 10125, 8991, 5832, 2187], 'euler31': [1, -1, 77, -34, 3570, -2367, 134894, -138904, 4181714, -2274687, 106353870, -31399714, 2204444627, -887503681, 27512614111], 'euler37': [1, 5, 168, 803, 14161, 59989, 771494, 2748646, 28545278, 82124941, 717297133, 1504951283, 11649784776, 12828632045, 94931877133], 'euler41': [1, -5, 92, -673, 7237, -46413, 387726, -2290138, 15896766, -78020253, 498781277, -1901737153, 10658770492, -23750521205, 194754273881], 'euler43': [1, 31, 687, 10436, 129854, 1291529, 10962460, 77409324, 471385780, 2388037121, 10324301978, 35678607236, 100994800341, 195962254519, 271818611107], 'euler47': [1, 14, 271, 2621, 31508, 240678, 2207362, 13822254, 103746014, 531657702, 3271255084, 12789643901, 62152496897, 150909014606, 506623120463], 'euler5': [1, -7, 21, -35, 35, -21, 7, -1, 0, 0, 0, 0, 0, 0, 0], 'euler53': [1, 13, 269, 2568, 34060, 265121, 2673394, 17174660, 141689882, 744724889, 5070750620, 20262755208, 112494587617, 288136694677, 1174711139837], 'euler59': [1, 14, 253, 2446, 31472, 260310, 2563464, 17624256, 151244376, 906139110, 6463687888, 29639065006, 180875847647, 590527470974, 2488651484819], 'euler61': [1, -3, 222, -759, 29403, -83651, 2524030, -6527094, 153965830, -311265371, 6673922343, -10508993319, 187500378822, -154561123083, 3142742836021], 'euler67': [1, -1, 328, -279, 53091, -39287, 5339384, -3265170, 357738728, -176359343, 15967808433, -5622162759, 442841035096, -90458382169, 6060711605323], 'euler7': [1, 16, 143, 908, 4508, 18272, 61958, 177804, 433706, 895328, 1546244, 2180108, 2403401, 1882384, 823543], 'euler71': [1, 8, 187, 1328, 22776, 168048, 2047314, 13028752, 145359294, 847129968, 8151780936, 33746712368, 337390888637, 1024802271368, 9095120158391], 'euler73': [1, -9, 286, -1613, 37567, -166989, 3689378, -14466938, 269324594, -889884381, 14614201639, -45806362733, 592898475598, -1362008036601, 11047398519097], 'euler79': [1, -9, 430, -2867, 81347, -413191, 9305818, -38366618, 735159622, -2578725031, 40107243533, -111669882227, 1323134251570, -2187787099689, 19203908986159], 'euler83': [1, 42, 1008, 16390, 206255, 2129142, 19880600, 179268272, 1650089800, 14667659238, 117933927685, 777841881190, 3970552968144, 13731495681498, 27136050989627], 'euler89': [1, -7, 21, -35, 35, -21, 7, -1, 0, 0, 0, 0, 0, 0, 0], 'euler97': [1, 7, 609, 3724, 164856, 856227, 25710150, 108804964, 2493884550, 8056239843, 150459620088, 329683042444, 5229690216513, 5830804034503, 80798284478113], 'euler_factors': [[1, 4, 11, 24, 46, 77, 118, 171, 236, 308, 368, 384, 352, 256, 128], [1, 8, 37, 125, 340, 780, 1576, 2866, 4728, 7020, 9180, 10125, 8991, 5832, 2187], [1, -7, 21, -35, 35, -21, 7, -1, 0, 0, 0, 0, 0, 0, 0], [1, 16, 143, 908, 4508, 18272, 61958, 177804, 433706, 895328, 1546244, 2180108, 2403401, 1882384, 823543], [1, 10, 91, 511, 2672, 10626, 41830, 136602, 460130, 1285746, 3556432, 7481551, 14655641, 17715610, 19487171], [1, 7, 47, 168, 622, 2167, 9118, 36132, 118534, 366223, 1366534, 4798248, 17450771, 33787663, 62748517], [1, 13, 108, 591, 3017, 14845, 78122, 344702, 1328074, 4290205, 14822521, 49360911, 153344556, 313788397, 410338673], [1, 7, 81, 366, 2784, 9257, 61132, 176376, 1161508, 3341777, 19095456, 47697486, 200564019, 329321167, 893871739], [1, 13, 144, 1105, 7943, 47855, 274740, 1359354, 6319020, 25315295, 96642481, 309224305, 926833392, 1924466557, 3404825447], [1, 4, 113, 625, 6740, 40902, 266814, 1538922, 7737606, 34398582, 164381860, 442050625, 2317759837, 2379293284, 17249876309], [1, -1, 77, -34, 3570, -2367, 134894, -138904, 4181714, -2274687, 106353870, -31399714, 2204444627, -887503681, 27512614111], [1, 5, 168, 803, 14161, 59989, 771494, 2748646, 28545278, 82124941, 717297133, 1504951283, 11649784776, 12828632045, 94931877133], [1, -5, 92, -673, 7237, -46413, 387726, -2290138, 15896766, -78020253, 498781277, -1901737153, 10658770492, -23750521205, 194754273881], [1, 31, 687, 10436, 129854, 1291529, 10962460, 77409324, 471385780, 2388037121, 10324301978, 35678607236, 100994800341, 195962254519, 271818611107], [1, 14, 271, 2621, 31508, 240678, 2207362, 13822254, 103746014, 531657702, 3271255084, 12789643901, 62152496897, 150909014606, 506623120463], [1, 13, 269, 2568, 34060, 265121, 2673394, 17174660, 141689882, 744724889, 5070750620, 20262755208, 112494587617, 288136694677, 1174711139837], [1, 14, 253, 2446, 31472, 260310, 2563464, 17624256, 151244376, 906139110, 6463687888, 29639065006, 180875847647, 590527470974, 2488651484819], [1, -3, 222, -759, 29403, -83651, 2524030, -6527094, 153965830, -311265371, 6673922343, -10508993319, 187500378822, -154561123083, 3142742836021], [1, -1, 328, -279, 53091, -39287, 5339384, -3265170, 357738728, -176359343, 15967808433, -5622162759, 442841035096, -90458382169, 6060711605323], [1, 8, 187, 1328, 22776, 168048, 2047314, 13028752, 145359294, 847129968, 8151780936, 33746712368, 337390888637, 1024802271368, 9095120158391], [1, -9, 286, -1613, 37567, -166989, 3689378, -14466938, 269324594, -889884381, 14614201639, -45806362733, 592898475598, -1362008036601, 11047398519097], [1, -9, 430, -2867, 81347, -413191, 9305818, -38366618, 735159622, -2578725031, 40107243533, -111669882227, 1323134251570, -2187787099689, 19203908986159], [1, 42, 1008, 16390, 206255, 2129142, 19880600, 179268272, 1650089800, 14667659238, 117933927685, 777841881190, 3970552968144, 13731495681498, 27136050989627], [1, -7, 21, -35, 35, -21, 7, -1, 0, 0, 0, 0, 0, 0, 0], [1, 7, 609, 3724, 164856, 856227, 25710150, 108804964, 2493884550, 8056239843, 150459620088, 329683042444, 5229690216513, 5830804034503, 80798284478113]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/445/2/a/f'], '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': '14-445e7-1.1-c1e7-0-0', '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}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1, 1], 'order_of_vanishing': 7, 'prelabel': '14-445e7-1.1-c1e7-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 1.8850312702835936, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e7-0', 'trace_hash': 623418917423990705, 'z1': {'__RealLiteral__': 0, 'data': '1.38471060990701707155474720672', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1755329235791027808711831599844,2027118205245260971501576070507,2323562724015653742585568973419,3022588741062693814838088652013,3133791873330535974014870547166,3335800555479242218599141762800,3349949262859096118535438225755', 'Lhash_array': ['1755329235791027808711831599844', '2027118205245260971501576070507', '2323562724015653742585568973419', '3022588741062693814838088652013', '3133791873330535974014870547166', '3335800555479242218599141762800', '3349949262859096118535438225755'], 'label': '14-445e7-1.1-c1e7-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/445/2/a/f'}