-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1226353996193282218815850180680,1453453200155283476096117783357,1807346630397955803346825545423,1844102217357219203167649553107,1909083425864518847270358959054,2119997766490746859538369283567,2170464853766111690769722921581,2337674287860280891986452848276,2356958399158894747174155252164,2508041957878918501207722012516,2535892898463433962424703680751', 'a10': -11, 'a2': -11, 'a3': -4, 'a4': 66, 'a5': 1, 'a6': 44, 'a7': -6, 'a8': -286, 'a9': -7, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 738613832158.124, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1]], [751, [1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1]]], 'bad_primes': [2, 751], 'central_character': '1502.1', 'coefficient_field': '1.1.1.1', 'conductor': 87774680912726123745982623376898048, 'conductor_radical': 1502, 'degree': 22, 'euler_factors': [[1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1], [1, 4, 23, 72, 252, 654, 1771, 3959, 8994, 17649, 34770, 60227, 104310, 158841, 242838, 320679, 430353, 476766, 551124, 472392, 452709, 236196, 177147], [1, -1, 29, -20, 394, -94, 3288, 1187, 19311, 20469, 94521, 140607, 472605, 511725, 2413875, 741875, 10275000, -1468750, 30781250, -7812500, 56640625, -9765625, 48828125], [1, 6, 59, 260, 1463, 5154, 21418, 63721, 218259, 576308, 1758302, 4312446, 12308114, 28239092, 74862837, 152994121, 359972326, 606362946, 1204843409, 1498848260, 2380862813, 1694851494, 1977326743], [1, -4, 76, -218, 2543, -5171, 52856, -76251, 824629, -903598, 10686030, -10096417, 117546330, -109335358, 1097581199, -1116390891, 8512511656, -9160741931, 49555875853, -46730236058, 179204024516, -103749698404, 285311670611], [1, 19, 251, 2486, 20498, 144288, 895242, 4944973, 24659831, 111493297, 460056571, 1733530095, 5980735423, 18842367193, 54177648707, 141233373853, 332397087906, 696450616992, 1286219101466, 2027906572406, 2661729342623, 2619311345131, 1792160394037], [1, 8, 120, 743, 6373, 30365, 192554, 708204, 3751031, 10892706, 57642117, 157981491, 979915989, 3147992034, 18428815303, 59149906284, 273399144778, 732937282685, 2615088363029, 5182987778663, 14230545179640, 16127951203592, 34271896307633], [1, 9, 132, 866, 7833, 42985, 304739, 1479206, 8926075, 39204165, 208798205, 830509179, 3967165895, 14152703565, 61223948425, 192771605126, 754563933161, 2022267194785, 7001697331587, 14707765593506, 42594776106828, 55179596320209, 116490258898219], [1, -2, 116, -199, 6875, -8589, 279111, -206919, 8759964, -3090421, 229603101, -46207660, 5280871323, -1634832709, 106582481988, -57904419879, 1796454131073, -1271480250621, 23408174948125, -15583886070919, 208933708729708, -82853022427298, 952809757913927], [1, -13, 224, -2354, 25468, -217411, 1843417, -13336997, 94415573, -591192671, 3604728408, -19668193409, 104537123832, -497193036311, 2302701409897, -9433004575157, 37810600756133, -129321133041931, 439319849837612, -1177580056110194, 3249600698594656, -5469194032902613, 12200509765705829], [1, 19, 368, 4447, 51938, 471895, 4148528, 30640520, 221593872, 1398891383, 8763296259, 48830151971, 271662184029, 1344334619063, 6601503040752, 28297163670920, 118768834539728, 418808549545495, 1428950151697118, 3792806443500127, 9729780955126928, 15572937452635219, 25408476896404831], [1, 29, 530, 7415, 87962, 906024, 8377271, 70517085, 547365646, 3935903852, 26446088879, 166181713355, 978505288523, 5388252373388, 27725712066838, 132160370540685, 580913120001347, 2324609703987816, 8350397776372946, 26045035150824215, 68879722091390810, 139448946800117621, 177917621779460413], [1, 23, 524, 7801, 110137, 1250171, 13409888, 123776224, 1081864063, 8371077407, 61452377952, 403835689705, 2519547496032, 14071781121167, 74563153086023, 349762026506464, 1553618679515488, 5938442569075211, 21449651462431697, 62290401712372921, 171548133622435564, 308721164133505223, 550329031716248441], [1, 13, 238, 2106, 25816, 201269, 2028245, 14214483, 122945681, 793330591, 6220241242, 37312391727, 267470373406, 1466868262759, 9775042259267, 48596488694883, 298169139472535, 1272294419509181, 7017269264338312, 24615349784627706, 119617041640968634, 280949270072695237, 929293739471222707], [1, 16, 321, 3647, 48416, 446650, 4726823, 38156849, 349654826, 2519117392, 20488582878, 132762074369, 962963395266, 5564730318928, 36302212999798, 186193251085169, 1084073254022761, 4814536526697850, 24528665000336608, 86839762455442367, 359240881865988207, 841586115773280784, 2472159215084012303], [1, 25, 658, 10501, 166508, 2024488, 24321735, 243039987, 2399991584, 20406299116, 171381495519, 1255661569249, 9083219262507, 57321294216844, 357303547051168, 1917702399663747, 10171239958940355, 44871483133326952, 195598802471979196, 653789009009701861, 2171244443405803514, 4372186759137826225, 9269035929372191597], [1, -6, 233, -376, 19318, 21737, 1369125, -1912461, 100132738, -250397075, 3792758135, -6632269702, 223772729965, -871632218075, 20565161597702, -23173980335421, 978820730868375, 916878259754417, 48075769383733442, -55208244539224696, 2018478025746600787, -3066700519803848406, 30155888444737842659], [1, -10, 516, -4272, 119700, -822722, 16776452, -96335141, 1633182154, -8007968175, 121923996153, -532123144541, 7437363765333, -29797649579175, 370701318497074, -1333841044998581, 14169329303104052, -42386945435030642, 376186317471713700, -818973641124384432, 6034179383902416756, -7133429116628826010, 43513917611435838661], [1, 16, 615, 8234, 175581, 1993737, 30895766, 301684551, 3757993440, 31868672758, 334867476598, 2472521226173, 22436120932066, 143058472010662, 1130265380994720, 6079281891031671, 41713149376596962, 180350223490475553, 1064145804374217663, 3343561257001381994, 16732018653721392405, 29165404872828183184, 122130132904968017083], [1, -8, 368, -2391, 63944, -317254, 6876058, -22215854, 519562092, -718721756, 33189514387, -12488035445, 2356455521477, -3623076371996, 185956987909812, -564542194990574, 12405985662778358, -40640327475072934, 581578363408154104, -1543996693208614551, 16872248264389243408, -26041948408079049608, 231122292121701565271], [1, 56, 1803, 40850, 728151, 10801497, 139563167, 1620820864, 17335614757, 173046152513, 1622262774152, 14295122392183, 118425182513096, 922162946741777, 6743848845923869, 46028461513700224, 289324436936815031, 1634636191257954633, 8044174279078999647, 32943894753873208850, 106145470835007047139, 240667046463399228344, 313726685568359708377], [1, -2, 351, -590, 66579, -200805, 8944941, -40985072, 914532221, -5490048169, 80248761640, -521211788815, 6339652169560, -34263390622729, 450900051709619, -1596371874190832, 27524087942727459, -48813176505894405, 1278577056389480061, -895094197844870990, 42067910189899029969, -18936552165253694402, 747993810527520928879], [1, -21, 861, -13395, 311794, -3842050, 65761741, -670200108, 9377948350, -81917480725, 993476580480, -7651988189753, 82458556179840, -564329524714525, 5362188953201450, -31806571859698668, 259038170553439463, -1256121261502366450, 8460857882259760838, -30169454449502454195, 160955559785352286983, -325836864931322922429, 1287831418538085836267], [1, 24, 730, 11824, 220808, 2841686, 41137351, 447517393, 5494330029, 52813110330, 581943235662, 5109080651615, 51792947973918, 418332646923930, 3873332346214101, 28078244123297713, 229713413558379599, 1412264776785800246, 9766632595611967432, 46546226038621405744, 255760174706464202570, 748361278319188406424, 2775173073766990340489], [1, 84, 3898, 126840, 3203709, 66248405, 1161441294, 17698825499, 239157752199, 2912808637566, 32397739228254, 331934933022227, 3142580705140638, 27406616470858494, 218272823172717927, 1566864295970936219, 9973691580108372558, 55183066736198388245, 258854191167090921117, 994100077110773733240, 2963380666635495215866, 6194362665917397388116, 7153014030880804126753], [1, -24, 1000, -16928, 401229, -5189550, 90540917, -937980563, 13589240559, -118930331717, 1571885310821, -12561992604573, 158760416392921, -1213208313845117, 14001008137178259, -97606633515985763, 951594137122699417, -5508811897551419550, 43017179519054351529, -183305983128721399328, 1093685272684360901000, -2651093100986890824024, 11156683466653165551101], [1, 29, 681, 11978, 207223, 3097660, 44572042, 575077315, 7205045252, 82919527875, 922984533648, 9498739122389, 95067406965744, 879693271225875, 7873147483082204, 64725458446364515, 516712127292107206, 3698768036866022140, 25485815201493783601, 151733720348608656458, 888550538187715561023, 3897357500097953569421, 13842338707244455781047], [1, -4, 723, -3166, 261967, -1197702, 62764621, -287291221, 11045119097, -48465125374, 1499760787391, -6010368232945, 160474404250837, -554877220406926, 13530745833946171, -37658018619482821, 880306278102795647, -1797427743870250998, 42066175604862487181, -54397774453478590366, 1329206010579771708561, -786860542915826128996, 21048519522998348950643], [1, 35, 1292, 30370, 693335, 12592101, 218889087, 3256526977, 46253404230, 579728856433, 6936220476317, 74113598272845, 756048031918553, 6887758543280473, 59899499826572670, 459685359320209297, 3367879927243901763, 21118213982821066941, 126744350383143976115, 605141274281311340770, 2806086117039463730588, 8285772861072410319035, 25804264053054077850709], [1, -10, 394, -5796, 112095, -1306718, 23287079, -237710767, 3344656885, -34091553205, 445472167123, -3846638207045, 50338354884899, -435315042874645, 4825995385395845, -38758113240635887, 429049335727382647, -2720523830265727262, 26371531133083761615, -154083425420856804516, 1183592523565801699562, -3394567389922223148490, 38358611506121121577937]], 'euler_factors_factorization': [[[[1, 1], 11]], [[[1, 4, 23, 72, 252, 654, 1771, 3959, 8994, 17649, 34770, 60227, 104310, 158841, 242838, 320679, 430353, 476766, 551124, 472392, 452709, 236196, 177147], 1]], [[[1, -1, 29, -20, 394, -94, 3288, 1187, 19311, 20469, 94521, 140607, 472605, 511725, 2413875, 741875, 10275000, -1468750, 30781250, -7812500, 56640625, -9765625, 48828125], 1]], [[[1, 6, 59, 260, 1463, 5154, 21418, 63721, 218259, 576308, 1758302, 4312446, 12308114, 28239092, 74862837, 152994121, 359972326, 606362946, 1204843409, 1498848260, 2380862813, 1694851494, 1977326743], 1]], [[[1, -4, 76, -218, 2543, -5171, 52856, -76251, 824629, -903598, 10686030, -10096417, 117546330, -109335358, 1097581199, -1116390891, 8512511656, -9160741931, 49555875853, -46730236058, 179204024516, -103749698404, 285311670611], 1]], [[[1, 19, 251, 2486, 20498, 144288, 895242, 4944973, 24659831, 111493297, 460056571, 1733530095, 5980735423, 18842367193, 54177648707, 141233373853, 332397087906, 696450616992, 1286219101466, 2027906572406, 2661729342623, 2619311345131, 1792160394037], 1]], [[[1, 8, 120, 743, 6373, 30365, 192554, 708204, 3751031, 10892706, 57642117, 157981491, 979915989, 3147992034, 18428815303, 59149906284, 273399144778, 732937282685, 2615088363029, 5182987778663, 14230545179640, 16127951203592, 34271896307633], 1]], [[[1, 9, 132, 866, 7833, 42985, 304739, 1479206, 8926075, 39204165, 208798205, 830509179, 3967165895, 14152703565, 61223948425, 192771605126, 754563933161, 2022267194785, 7001697331587, 14707765593506, 42594776106828, 55179596320209, 116490258898219], 1]], [[[1, -2, 116, -199, 6875, -8589, 279111, -206919, 8759964, -3090421, 229603101, -46207660, 5280871323, -1634832709, 106582481988, -57904419879, 1796454131073, -1271480250621, 23408174948125, -15583886070919, 208933708729708, -82853022427298, 952809757913927], 1]], [[[1, -13, 224, -2354, 25468, -217411, 1843417, -13336997, 94415573, -591192671, 3604728408, -19668193409, 104537123832, -497193036311, 2302701409897, -9433004575157, 37810600756133, -129321133041931, 439319849837612, -1177580056110194, 3249600698594656, -5469194032902613, 12200509765705829], 1]], [[[1, 19, 368, 4447, 51938, 471895, 4148528, 30640520, 221593872, 1398891383, 8763296259, 48830151971, 271662184029, 1344334619063, 6601503040752, 28297163670920, 118768834539728, 418808549545495, 1428950151697118, 3792806443500127, 9729780955126928, 15572937452635219, 25408476896404831], 1]], [[[1, 29, 530, 7415, 87962, 906024, 8377271, 70517085, 547365646, 3935903852, 26446088879, 166181713355, 978505288523, 5388252373388, 27725712066838, 132160370540685, 580913120001347, 2324609703987816, 8350397776372946, 26045035150824215, 68879722091390810, 139448946800117621, 177917621779460413], 1]], [[[1, 23, 524, 7801, 110137, 1250171, 13409888, 123776224, 1081864063, 8371077407, 61452377952, 403835689705, 2519547496032, 14071781121167, 74563153086023, 349762026506464, 1553618679515488, 5938442569075211, 21449651462431697, 62290401712372921, 171548133622435564, 308721164133505223, 550329031716248441], 1]], [[[1, 13, 238, 2106, 25816, 201269, 2028245, 14214483, 122945681, 793330591, 6220241242, 37312391727, 267470373406, 1466868262759, 9775042259267, 48596488694883, 298169139472535, 1272294419509181, 7017269264338312, 24615349784627706, 119617041640968634, 280949270072695237, 929293739471222707], 1]], [[[1, 16, 321, 3647, 48416, 446650, 4726823, 38156849, 349654826, 2519117392, 20488582878, 132762074369, 962963395266, 5564730318928, 36302212999798, 186193251085169, 1084073254022761, 4814536526697850, 24528665000336608, 86839762455442367, 359240881865988207, 841586115773280784, 2472159215084012303], 1]], [[[1, 25, 658, 10501, 166508, 2024488, 24321735, 243039987, 2399991584, 20406299116, 171381495519, 1255661569249, 9083219262507, 57321294216844, 357303547051168, 1917702399663747, 10171239958940355, 44871483133326952, 195598802471979196, 653789009009701861, 2171244443405803514, 4372186759137826225, 9269035929372191597], 1]], [[[1, -6, 233, -376, 19318, 21737, 1369125, -1912461, 100132738, -250397075, 3792758135, -6632269702, 223772729965, -871632218075, 20565161597702, -23173980335421, 978820730868375, 916878259754417, 48075769383733442, -55208244539224696, 2018478025746600787, -3066700519803848406, 30155888444737842659], 1]], [[[1, -10, 516, -4272, 119700, -822722, 16776452, -96335141, 1633182154, -8007968175, 121923996153, -532123144541, 7437363765333, -29797649579175, 370701318497074, -1333841044998581, 14169329303104052, -42386945435030642, 376186317471713700, -818973641124384432, 6034179383902416756, -7133429116628826010, 43513917611435838661], 1]], [[[1, 16, 615, 8234, 175581, 1993737, 30895766, 301684551, 3757993440, 31868672758, 334867476598, 2472521226173, 22436120932066, 143058472010662, 1130265380994720, 6079281891031671, 41713149376596962, 180350223490475553, 1064145804374217663, 3343561257001381994, 16732018653721392405, 29165404872828183184, 122130132904968017083], 1]], [[[1, -8, 368, -2391, 63944, -317254, 6876058, -22215854, 519562092, -718721756, 33189514387, -12488035445, 2356455521477, -3623076371996, 185956987909812, -564542194990574, 12405985662778358, -40640327475072934, 581578363408154104, -1543996693208614551, 16872248264389243408, -26041948408079049608, 231122292121701565271], 1]], [[[1, 56, 1803, 40850, 728151, 10801497, 139563167, 1620820864, 17335614757, 173046152513, 1622262774152, 14295122392183, 118425182513096, 922162946741777, 6743848845923869, 46028461513700224, 289324436936815031, 1634636191257954633, 8044174279078999647, 32943894753873208850, 106145470835007047139, 240667046463399228344, 313726685568359708377], 1]], [[[1, -2, 351, -590, 66579, -200805, 8944941, -40985072, 914532221, -5490048169, 80248761640, -521211788815, 6339652169560, -34263390622729, 450900051709619, -1596371874190832, 27524087942727459, -48813176505894405, 1278577056389480061, -895094197844870990, 42067910189899029969, -18936552165253694402, 747993810527520928879], 1]], [[[1, -21, 861, -13395, 311794, -3842050, 65761741, -670200108, 9377948350, -81917480725, 993476580480, -7651988189753, 82458556179840, -564329524714525, 5362188953201450, -31806571859698668, 259038170553439463, -1256121261502366450, 8460857882259760838, -30169454449502454195, 160955559785352286983, -325836864931322922429, 1287831418538085836267], 1]], [[[1, 24, 730, 11824, 220808, 2841686, 41137351, 447517393, 5494330029, 52813110330, 581943235662, 5109080651615, 51792947973918, 418332646923930, 3873332346214101, 28078244123297713, 229713413558379599, 1412264776785800246, 9766632595611967432, 46546226038621405744, 255760174706464202570, 748361278319188406424, 2775173073766990340489], 1]], [[[1, 84, 3898, 126840, 3203709, 66248405, 1161441294, 17698825499, 239157752199, 2912808637566, 32397739228254, 331934933022227, 3142580705140638, 27406616470858494, 218272823172717927, 1566864295970936219, 9973691580108372558, 55183066736198388245, 258854191167090921117, 994100077110773733240, 2963380666635495215866, 6194362665917397388116, 7153014030880804126753], 1]], [[[1, -24, 1000, -16928, 401229, -5189550, 90540917, -937980563, 13589240559, -118930331717, 1571885310821, -12561992604573, 158760416392921, -1213208313845117, 14001008137178259, -97606633515985763, 951594137122699417, -5508811897551419550, 43017179519054351529, -183305983128721399328, 1093685272684360901000, -2651093100986890824024, 11156683466653165551101], 1]], [[[1, 29, 681, 11978, 207223, 3097660, 44572042, 575077315, 7205045252, 82919527875, 922984533648, 9498739122389, 95067406965744, 879693271225875, 7873147483082204, 64725458446364515, 516712127292107206, 3698768036866022140, 25485815201493783601, 151733720348608656458, 888550538187715561023, 3897357500097953569421, 13842338707244455781047], 1]], [[[1, -4, 723, -3166, 261967, -1197702, 62764621, -287291221, 11045119097, -48465125374, 1499760787391, -6010368232945, 160474404250837, -554877220406926, 13530745833946171, -37658018619482821, 880306278102795647, -1797427743870250998, 42066175604862487181, -54397774453478590366, 1329206010579771708561, -786860542915826128996, 21048519522998348950643], 1]], [[[1, 35, 1292, 30370, 693335, 12592101, 218889087, 3256526977, 46253404230, 579728856433, 6936220476317, 74113598272845, 756048031918553, 6887758543280473, 59899499826572670, 459685359320209297, 3367879927243901763, 21118213982821066941, 126744350383143976115, 605141274281311340770, 2806086117039463730588, 8285772861072410319035, 25804264053054077850709], 1]], [[[1, -10, 394, -5796, 112095, -1306718, 23287079, -237710767, 3344656885, -34091553205, 445472167123, -3846638207045, 50338354884899, -435315042874645, 4825995385395845, -38758113240635887, 429049335727382647, -2720523830265727262, 26371531133083761615, -154083425420856804516, 1183592523565801699562, -3394567389922223148490, 38358611506121121577937], 1]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 0, 'label': '22-1502e11-1.1-c1e11-0-0', '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}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'order_of_vanishing': 11, 'origin': 'ModularForm/GL2/Q/holomorphic/1502/2/a/e', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.005326704545454545', 'prec': 67}, 'plot_values': [0.0, 1.1475284855906596e-22, 2.3498134948402414e-19, 2.032063061649014e-17, 4.809757559092222e-16, 5.596972621398575e-15, 4.156489418601795e-14, 2.264024246508045e-13, 9.828609832242548e-13, 3.5878090251733776e-12, 1.1423022232182236e-11, 3.255962543641707e-11, 8.470153756868216e-11, 2.0406566366482634e-10, 4.6052551554694685e-10, 9.823300684729563e-10, 1.994973604660754e-09, 3.880380036196977e-09, 7.264523351587751e-09, 1.3143982591275972e-08, 2.3064769879482582e-08, 3.937010365098246e-08, 6.553776040545832e-08, 1.0663210446542764e-07, 1.6990089424026123e-07, 2.655532109556886e-07, 4.077611551538449e-07, 6.159353288150056e-07, 9.163323175127716e-07, 1.3440613103495184e-06, 1.9455657578702847e-06, 2.781667287766592e-06, 3.931272477019679e-06, 5.49585186068026e-06, 7.604812413904433e-06, 1.0421890329218771e-05, 1.4152734652285968e-05, 1.9053837846330813e-05, 2.5442991996571385e-05, 3.371146384674934e-05, 4.433807328061536e-05, 5.790544921159878e-05, 7.511868912622224e-05, 9.682666804117377e-05, 0.0001240462759600119, 0.00015798981360252057, 0.0002000956793802879, 0.00025206307522513685, 0.00031589080099441407, 0.00039392026609303175, 0.0004888831232726285, 0.0006039542428145966, 0.0007428099488622884, 0.0009096919262416216, 0.001109477127297003, 0.0013477539828991825, 0.0016309046694140557, 0.001966192367655342, 0.0023618576190495527, 0.002827219867758887, 0.0033727872524990992, 0.004010373974687202, 0.004753224347111551, 0.0056161440042466915, 0.0066156381768462036, 0.00777005686012822, 0.009099746628373963, 0.010627205657589175, 0.012377230913410793, 0.014377082006981855, 0.01665665564509823, 0.019248657306823565, 0.022188774147908003, 0.025515848619125554, 0.029272051550895864, 0.033503053325658755, 0.0382581916272448, 0.043590631643599734, 0.0495574853280377, 0.05621990750826229, 0.06364324823669466, 0.0718971700983216, 0.08105573818984148, 0.09119748989877904, 0.10240548180980308, 0.11476731098510692, 0.1283751076757741, 0.1433254673753164, 0.1597193224886766, 0.17766182662106178, 0.19726206807906116, 0.2186329152400526, 0.24189077732501324, 0.2671552847961284, 0.29454891587099713, 0.32419656680433295, 0.3562250533932922, 0.39076243727595045, 0.4279374085932345, 0.46787866405061773, 0.5107140803140038, 0.5565696171231534, 0.6055685714542725, 0.6578306768151768, 0.713471073496235, 0.7725992176934745, 0.8353176428217718, 0.9017205593537405, 0.9718927375933856, 1.045908231045858, 1.1238290261232298, 1.2057035364031103, 1.29156476215019, 1.3814291230018596, 1.4752951238161665, 1.5731419010108925, 1.6749275506949497, 1.7805877268849493, 1.8900344525034682, 2.0031548279363567, 2.1198098078055585, 2.2398330658986674, 2.363029836935668, 2.489175576491922, 2.618015481232399, 2.749263904798365, 2.882603713394411, 3.017686171863752, 3.1541309219146387, 3.291526134654401, 3.429428896855668, 3.567365844645027, 3.7048340571509457, 3.8413022074575602, 3.976211971267427, 4.108979907636335, 4.238999525243637, 4.365643536237684, 4.48826648652451, 4.60620768781523, 4.718794444181282, 4.825345566307021, 4.925175163638067, 5.017596701519362, 5.101927785926171, 5.177496219764369, 5.2436434436300345, 5.29972896950782, 5.345135416304465, 5.379273658628473, 5.401588053437574, 5.411561706298234, 5.408721736305033, 5.392644547337681, 5.362962311306486, 5.319368731586804, 5.26162405188646, 5.1895577379099125, 5.103072065791145, 5.00214592499881, 4.886838226461153, 4.757290867156339, 4.613731203744254, 4.456474621223921, 4.285928332859698, 4.102589914642758, 3.907047017309021, 3.699978373996378, 3.4821499579698, 3.2544120292026673, 3.017696145794515, 2.773011426818236, 2.5214401251455927, 2.264134595174103, 2.002311751416616, 1.7372434064595899, 1.4702486385745122, 1.2026860158045243, 0.9359453090182447, 0.6714365506430989, 0.4105799418506805, 0.1547957904193694, -0.09450531032509732, -0.33593058296628076, -0.5681184039061069, -0.7897504276622184, -0.9995623352065548, -1.1963544180262808, -1.3790023686450685, -1.5464691660461853, -1.6978139877791785, -1.832200578254541, -1.9489041018419475, -2.0473182435686788, -2.126963690499473, -2.187493640295228, -2.228698073816947, -2.2505069126971917, -2.2529920061351505, -2.2363690576296933, -2.2010007853294646, -2.1473917195284327, -2.076183148667387, -1.988149334119216, -1.884191928605074, -1.7653326636273114, -1.6327048602595327, -1.4875438309834033, -1.3311762509409184, -1.1650085892427462, -0.9905159289443727, -0.8092321274757153, -0.6227317161480866, -0.4326142085383907, -0.24048924587952605, -0.04796161495508301, 0.14338368953060107, 0.33199620091383447, 0.5163743579865183, 0.6950793690686828, 0.8667484225356555, 1.0301066090903062, 1.1839772869091763, 1.3272953765368178, 1.4591172497176983, 1.578628470495168, 1.6851500674921915, 1.7781432691427008, 1.857212651508489, 1.9221076681799167, 1.9727228290925187, 2.009096453378019, 2.031407076370003, 2.039969291305447, 2.0352274131082013, 2.0177472783928634, 1.988206768951681, 1.9473851528406911, 1.8961513899640192, 1.835451637634447, 1.7662967855089198, 1.6897483300742075, 1.6069035992248981, 1.5188818141046045, 1.4268110752777148, 1.3318127530592287, 1.2349871597793207, 1.1374003184675947, 1.0400715562596254, 0.9439623932740315, 0.8499666689375003, 0.7589006347271952, 0.6714950948965789, 0.5883891644116944, 0.510125814522933, 0.4371492908544136, 0.3698023879887806, 0.3083261701166062, 0.25286160040167127, 0.20345292605777243, 0.1600519616706469, 0.12252364134353357, 0.09065307882693417, 0.06415367725369074, 0.04267611721278972, 0.025818072895945957, 0.013134407302776235, 0.004147529087671154, -0.0016418545489555246, -0.004744015481520932, -0.00566984118628415, -0.004920805024675244, -0.0029795408603701143, -0.0003012053590551052, 0.00269422949123175, 0.005628631446456741, 0.008171205542127533, 0.010042782776902867, 0.011018886917873895, 0.010931452473876129, 0.009669217762344426, 0.007176813995094477, 0.003452612428323688, -0.0014545876466242633, -0.0074499244901029445, -0.014397766865516564, -0.02212779033382394, -0.030441652013415324, -0.03912007324449769, -0.04793038597723563, -0.05663414057757278, -0.06499459785282262, -0.07278394862892534, -0.07979008823000298, -0.08582278595375738, -0.0907191059555568, -0.09434795611411997, -0.09661368168021482, -0.09745861321340317, -0.09686453302422422, -0.09485298657356873, -0.09148442636980178, -0.08685625534990848, -0.08109983222930667, -0.07437652850382652, -0.06687295123825214, -0.058795475477146295, -0.0503642512140595, -0.041806766319414594, -0.03335125637897628, -0.025220164231092065, -0.01762359610431664, -0.01075319348486481, -0.004776574245924228, 0.0001675215344703172, 0.00397323640514084, 0.0065706362739131755, 0.007927696535564601, 0.008051134423050178, 0.006986060404381483, 0.004814449626025209, 0.0016524750013466323, -0.0023532248315908, -0.007030293247290683, -0.012186267424765897, -0.017614884537307824, -0.02310288346432265, -0.028437174778395663, -0.033412103994071164, -0.037836573285855934, -0.04154080400037848, -0.04438251607976577, -0.046252318041171546, -0.047078097921320866, -0.04682823607042479, -0.045513499269022026, -0.043187518464962424, -0.03994577515532309, -0.03592306135510051, -0.03128944629350436, -0.02624482399410278, -0.02101216437629144, -0.01582964228110435, -0.010941860609244269, -0.006590394398265307, -0.003003988929232674, -0.0003887206297630163, 0.0010815275783849494, 0.001273917270752752, 0.00010447265004501749, -0.0024554875444101833, -0.006374638874970699, -0.011558965339182336, -0.017851364061560158, -0.02503375794752548, -0.03283185319906457, -0.040922625818608845, -0.04894453823851875, -0.05651040498297368, -0.06322273899622478, -0.06869132093194165, -0.07255264487356758, -0.07449080788547215, -0.0742593324246414, -0.07170334295311541, -0.06678136538471505, -0.05958613378533954, -0.05036371064358648, -0.039530146878523346, -0.02768493763132389, -0.015620549823204027, -0.004327337421809641, 0.0050067788629369085, 0.011002411437796743, 0.01210102418520042, 0.006583734777632989, -0.00740345269193065, -0.03181794472324503, -0.06868226074299613, -0.1200395522996295, -0.18790344672462428, -0.27420288434452705, -0.3807228121736665, -0.5090419884564698, -0.6604688016410123, -0.8359762869429928, -1.0361392187743301, -1.261077622309077, -1.5103985079369084, -1.7831435933450897, -2.077744959088717, -2.391989314258406, -2.7229930603721964, -3.067189851055745, -3.4203281794209124, -3.7774832362703767, -4.133083410087602, -4.480957192637761, -4.81440933973113, -5.126281458093499, -5.409033097851761, -5.654841347810576, -5.855716413727188, -6.003624083354939, -6.090614960153634, -6.108963659295646, -6.051313286985731, -5.910822701727388, -5.681324120751518, -5.357498547701289, -4.934982681924706, -4.41048653654574, -3.7819096691859966, -3.0484356045681897, -2.210613002290946, -1.2704187558442304, -0.2312999871964156, 0.9018067547098466, 2.1224804232101775, 3.422838673249679, 4.793581197083708, 6.224112060561302, 7.702663740520058, 9.216429848453886, 10.751720239174915, 12.29413526798349, 13.828756571658262, 15.34035145861828, 16.813587657328668, 18.2332548887119, 19.584502916083636, 20.853120127351126, 22.02573582127849, 23.09001549687096, 24.034851181462997, 24.85053360366921, 25.52890293388287, 26.063475174113382, 26.44954170106517, 26.684240828986802, 26.76662141338763, 26.697675390182656, 26.48035476857444, 26.119453098664202, 25.621490551650837, 24.994590169563704, 24.24832808333953, 23.39356067081296, 22.442232075286583, 21.40717237605001, 20.30190039519803, 19.14036884066058, 17.93674177178306, 16.705216360589755, 15.459726895975564, 14.213708133571359, 12.979895950333152, 11.77014786141301, 10.59528682690103, 9.4649804207316, 8.387635265703564, 7.3703062637370484, 6.418651602766161, 5.536927061675495, 4.728018459986883, 3.9934467811216856, 3.333429276620095, 2.7469745842878206, 2.231998909178595, 1.7854606816144125, 1.4034993620748586, 1.0815872652101206, 0.8146881177660396, 0.5974155822690671, 0.42418890511750373, 0.28938085342680464, 0.18744690579424517, 0.11304724860587088, 0.061153628393514764, 0.02713667593507124, 0.006833028544874724, -0.003407770696124276, -0.006697192215900022, -0.005601701184537399, -0.0021553872440785516, 0.002110714002091805, 0.006125037950804046, 0.009220515154144916, 0.011071109434973185, 0.011623141279091018, 0.011024554320758316, 0.009555386508703247, 0.007562549179167105, 0.0054016477441090225, 0.0033881445451934265, 0.0017596465556155906, 0.0006505217751848375, 7.939512490706239e-05, -5.056632770004953e-05, 6.08122557471199e-05, 0.0001339495280198769, -0.00015845961380689313, -0.0011530815865856418, -0.003154113954529485, -0.006391121668908665, -0.010979806767266767, -0.016888962393541478, -0.023916674636020922, -0.03167852376162448, -0.039610312978279064, -0.046986830519607885, -0.05295751629065472, -0.05659907624942477, -0.05698414228367101, -0.05326411156710577, -0.04476333690521722, -0.03108092372073823, -0.012195511355711376, 0.011432149201322309, 0.03876433668053788, 0.06810703565520868, 0.09705174160366811, 0.12244462331870815, 0.14038907405774184, 0.14628687970297438, 0.1349222702168548, 0.10059190901179736, 0.037282054929879044, -0.06110729403659957, -0.20049278893127037, -0.3862948492196571, -0.623091404320116, -0.9142458368335064, -1.2615189298266234, -1.6646773419182812, -2.121113117341832, -2.625490502673418, -3.1694335002263365, -3.741272252840708, -4.325864784487626, -4.904507927312803, -5.454949204134955, -5.951528528035422, -6.3654475694406365, -6.66517464120159, -6.816993933428568, -6.785692502386878, -6.535379255456418, -6.030431066384707, -5.236549421012495, -4.1219077842843586, -2.658364985371544, -0.8227158542013654, 1.402053341157594, 4.0255451750606515, 7.048808259056676, 10.463301242961508, 14.250015126486792, 18.378794928344295, 22.807899937050742, 27.48383973545281, 32.34151887069093, 37.30472371236307, 42.28698510268278, 47.192795390302315, 51.91917229563735, 56.357568999843416, 60.39614805904612, 63.922371824868506, 66.82586887055251, 69.00152570531866, 70.35274251759051, 70.79478193742632, 70.25815432513569, 68.69195557282242, 66.06687672500031, 62.37802320688081, 57.64741112960314, 51.92602087793784, 45.29531930969187, 37.86816849631195, 29.78904817761261, 21.233528952606843, 12.406903153084665, 3.542058238206583, -5.103422140524827, -13.251046107406673, -20.605924239064333, -26.861990189295707, -31.70786803462113, -34.83329256619229, -35.93596886450936, -34.72870182298945, -30.946452701110243, -24.353492400334243, -14.750462196171021, -1.9810233117209308, 14.062162708392783, 33.43210473760675, 56.12300250900732, 82.06678596070834, 111.13083030364342, 143.11782747265218, 177.7669142427375, 214.75473733859803, 253.69860721419437, 294.16134004277956, 335.65813440153244, 377.6637055319176, 419.62067879912235, 460.9491570515038, 501.0576864389234, 539.3572980658103, 575.2713718918144, 608.2459759480804, 637.761182274956, 663.3420038516575, 684.5692844977242, 701.0910332047614, 712.6290734770985, 718.9852063848763, 720.0487971089848, 715.8013649130618, 706.3141089267891, 691.7467746813755, 672.3449215370365, 648.4352760560115, 620.4192450278541, 588.7653587664317, 554.001241420733, 516.7005596496141, 477.4726698041996, 436.94663347517474, 395.7557813982785, 354.52399484818255, 313.8523040262347, 274.3061333351801, 236.4035197230525, 200.60460986846527, 167.30299147838898, 136.8197336168648, 109.3969142028529, 85.19273839126765, 64.28099331961512, 46.652987270843205, 32.22171709061034, 20.828131948578534, 12.249300267799779, 6.208229608661708, 2.3850490732970027, 0.4292016250372441, -0.027980808582843932, 0.6397943096805502, 2.066887987059456, 3.9081550959869156, 5.85024939197513, 7.621429667290773, 8.999533831174821, 9.817844631650734, 9.968648964108722, 9.404411980949613, 8.136422587449038, 6.230904428760472, 3.8027249042263835, 1.0069387909343095, -1.9714872593124446, -4.929360797228614, -7.6578838702373, -9.955666253852266, -11.641487272736963, -12.566478481088783, -12.624979853284632, -11.763389540564129, -9.98657556300352, -7.361125350599441, -4.015191224833888, -0.13465528434941182, 4.044571289572415, 8.248134057954866, 12.17856973399895, 15.534204464556385, 18.031171791677846, 19.42793972043005, 19.55163984950768, 18.32541683616061, 15.795626844319695, 12.157809006538173, 7.780361787306425, 3.2247733783469594, -0.7387074536096935, -3.1210993369305213, -2.7114119395204677, 1.9190907908332182, 12.404397889780567, 30.56243097067279, 58.36414772543642, 97.89385341674021, 151.30093923538044, 220.74347086993515, 308.3247458835487, 416.0240280821194, 545.6229914677195, 698.6296876694512, 876.2020751477713, 1079.0733366196798, 1307.4804894137974, 1561.0971875780326, 1838.980564151892, 2139.529336421485, 2460.4550500338178, 2798.7694562751376, 3150.7897572634993, 3512.1631070292265, 3877.91132197936, 4242.496256584445, 4599.905752698873, 4943.759206349918, 5267.432306214415, 5564.201510708535, 5827.400960567084, 6050.589735745213, 6227.7261803936935, 6353.345032009262, 6422.732682582137, 6432.095588592737, 6378.7168106863, 6261.09965204053, 6079.085861520621, 5833.940616125339, 5528.409417471455, 5166.737660190909, 4754.649863067719, 4299.286083776429, 3809.0937811116833, 3293.6744296472, 2763.5864367435247, 2230.1077879945306, 1704.9496418393878, 1199.9361323702224, 726.6550651199898, 296.0833580077287, -81.8032624165215, -398.4279940693742, -647.0087839677267, -822.9420567671511, -924.1632205022529, -951.4747461622984, -908.8307011148142, -803.5653838254457, -646.5574801522724, -452.3209517647223, -239.01380829974724, -28.359594817816454, 154.5231211767249, 281.38612139342496, 321.2120089066495, 240.6683325138955, 4.652000515526663, -423.08225049649957, -1079.2177534722555, -2000.1072246727003, -3220.954166551636, -4774.956785551168, -6692.430905186707, -8999.9391012002, -11719.441481984648, -14867.466511363993, -18454.34319335462, -22483.510035506817, -26950.919307859287, -31844.554921487146, -37144.08763116677, -42820.694914563646, -48837.012030426864, -55147.32137896931, -61697.82841846114, -68427.10113007746, -75266.71175728757, -82142.04903816195, -88973.29302850782, -95676.5410115479, -102165.06931348132, -108350.72709091814, -114145.54277484672, -119463.31131846408, -124221.00543730544, -128340.33121932943, -131749.28277968796, -134383.64732262195, -136188.4296074291, -137119.16520815928, -137143.0929877587, -136240.18333371254, -134404.13471868058, -131642.7936992077, -127978.34323750909, -123447.3908365334, -118100.80491193877, -112003.2932542319, -105232.7236011485, -97879.19126553311, -90043.84408949841, -81837.54547461969, -73379.2989696517, -64794.2302222782, -56211.49498789375, -47762.34105331033, -39578.03500609034, -31787.71128594077, -24516.21761776226, -17881.99526552143, -11995.03447228118, -6954.946713742825, -2849.140308999599, 248.7824037619342, 2280.3911686096085, 3203.502333117676, 2992.8701185356585, 1640.6925739415226, -843.1487094480119, -4431.14385038715, -9078.513103720468, -14723.892385361964, -21290.29837185946, -28686.348112526455, -36807.72018242887, -45538.94581234129, -54755.70800291914, -64326.66850691495, -74115.48274965216, -83982.98439828186, -93789.5683875852, -103397.44151788013, -112672.67947749447, -121487.28216917969, -129721.10718089459, -137263.64668670166, -144015.83729132506, -149892.11751728036, -154820.92878142017, -158745.4661213504, -161624.5735491594, -163432.74401211826, -164160.050711706, -163811.89945600188, -162408.53296288496, -159984.3023129766, -156586.72456759223, -152275.54010166618, -147121.9341725753, -141206.70150502032, -134618.3936497, -127451.33854669382, -119803.92526400617, -111776.90189288095, -103471.70530824666, -94988.85138508044, -86426.41201516608, -77878.60260525953, -69434.64993436124, -61177.98866668859, -53184.64635807934, -45522.29469345382, -38249.67026412281, -31416.185835174627, -25061.72877264216, -19216.639830135482, -13901.862336623912, -9129.25153139013, -4902.077287933519, -1215.5570136918261, 1942.5670820164344, 4591.284383133295, 6755.443565159047, 8464.828394181894, 9753.212894220118, 10657.416387345582, 11216.37750489475, 11470.26519118386, 11459.650537777348, 11224.741005735143, 10804.685629218495, 10236.982228311093, 9556.904319912948, 8797.050183385612, 7987.003788486782, 7153.094414240901, 6318.251430543989, 5501.956544560621, 4720.269511031052, 3985.913579291152, 3308.4368624536633, 2694.4319864392564, 2147.8009792369767, 1670.0357406984917, 1260.533984714114, 916.9310313564133, 635.4343653070463, 411.15267058431334, 238.40359038764515, 111.0039272613822, 22.535152323985244, -33.42197579287019, -63.086631769640256, -72.31274385297803, -66.45893102989025, -50.293366648041804, -27.932674609463785, -2.812313551542857, 22.315505274501596, 45.35955185960777, 64.84686653962255, 79.86388905932914, 89.98574043177452, 95.19795077713732, 95.81473568875488, 92.39656274442503, 85.67077898579217, 76.45837485392937, 65.60862734613639, 53.94322110182601, 42.21096575193472, 31.0535995312141, 20.982661186457214, 12.366958775349307, 5.429795506874679, 0.254764694512933, -3.2014236521182036, -5.090412163427257, -5.649670455884582, -5.177639210512913, -4.008113940405337, -2.485307174423315, -0.9408460672796307, 0.32625778476097755, 1.0658759955083275, 1.088738395148929, 0.2738393684569661, -1.4287384310161944, -3.9993483678007133, -7.354238225173771, -11.354355729644197, -15.81678494653581, -20.528012778975146, -25.2581845211805, -29.77551139350441, -33.860032217411955, -37.31602051611955, -39.982441938047685, -41.740903735429484, -42.52089137532958, -42.30211975771856, -41.113986281756375, -39.032276441430994, -36.17340843407801, -32.68660392385651, -28.74452919800102, -24.53297080638518, -20.240111563945227, -16.046014746729366, -12.112975659834337, -8.57718076084315, -5.542109958519186, -3.074028335216757, -1.199780460564215, 0.09299912004479152, 0.8532492658199394, 1.1616598832562004, 1.123917212508444, 0.8623881727459817, 0.506712741681611, 0.18388662807324235, 0.008356009208057395, 0.07268843171621, 0.4393808220466853, 1.1343246414614976, 2.1423682827504744, 3.405321905324532, 4.822647638846177, 6.25495641088482, 7.530311340240056, 8.453167113400127, 8.815533836389868, 8.410118936317767, 7.044934239046113, 4.558702124517598, 0.8364781511284421, -4.175210091065942, -10.454423131904775, -17.891767033669844, -26.28090717781767, -35.3123688965616, -44.5713421235032, -53.53870003219314, -61.59614699240724, -68.0354969612878, -72.07207754888259, -72.86200336778697, -69.52295782521534, -61.157988263854776, -46.88169494346105, -25.848086787737497, 2.721081143891541, 39.51011853882769, 85.08365792263439, 139.8622168677652, 204.1005558413385, 277.8694693978225, 361.0416660678201, 453.2822873784637, 554.0444932482318, 662.5704473741787, 777.8991434334876, 898.8826942247099, 1024.2149632695794, 1152.4488393114013, 1282.0201498572162, 1411.2774274956503, 1538.5142792246384, 1662.003555723356, 1780.0324677372219, 1890.9387847558387, 1993.1496552096444, 2085.211720220023, 2165.8257406633998, 2233.892526416193, 2288.518033992044, 2329.023622556413, 2354.9571331122265, 2366.0988375196393, 2362.4623148333385, 2344.29397228033, 2312.0648978406743, 2266.451945727329, 2208.3191127372934, 2138.7013046545776, 2058.794697912738, 1969.9098636103995, 1873.4365599295634, 1770.8140167980514, 1663.502306997023, 1552.957337451718, 1440.6003046543567, 1327.7912253669724, 1215.8070638565403, 1105.8229894069734, 998.8995509868071, 895.9765604538592, 797.8543037543745, 705.1866153643791, 618.4815624579966, 538.1043981246706, 464.2816656416541, 397.10986331253883, 336.56647698883535, 282.52273860675996, 234.7576305972019, 192.973164682415, 156.8103061569235, 125.86159831868547, 99.68577184417664, 77.82144480076244, 59.79993904489549, 45.15689431601041, 33.442259953786426, 24.22856879154363, 17.117461970116672, 11.744491312397006, 7.782302327470233, 4.942292978221923, 2.9747371406102348, 1.667889340688673, 0.8461568564345153, 0.3674553120416814, 0.11996284629579118, 0.018484537696940473, 0.0006233316779400129, 0.02293273276495641, 0.05720136320164494, 0.08699143989439859, 0.10452606081385914, 0.1079882092342847, 0.09926462781248448, 0.08214704073674182, 0.06097990409891933, 0.03972381254977972, 0.021388086482883886, 0.007774993597168356, -0.0005285024053880123, -0.003977859027632196, -0.0037816924256088456, -0.0015559709882976029, 0.001026230851251871, 0.0025468256350772195, 0.002084683915227834, -0.0006328576512565385, -0.0051779536423705915, -0.010468176207782622, -0.014899767136398684, -0.016550262883836715, -0.013427206515942782, -0.003736562754668663, 0.013856357900090148, 0.03999934990297326, 0.07448186894597258, 0.11613761591204648, 0.16283309169472948, 0.21154736609539077, 0.25854128772645707, 0.2996073917606922, 0.3303857703927431, 0.34672587070947125, 0.34507020486283024, 0.3228330831813848, 0.2787480124307409, 0.21315868868185608, 0.12823003290061116, 0.02806013162241861, -0.08132078389536161, -0.1920715417185975, -0.2947820093833431, -0.37882947161680675, -0.43283606903742766, -0.44520734666786904, -0.4047229341511834, -0.301150950095002, -0.12586012186001158, 0.12760459574520977, 0.4630147769098484, 0.8810487639186133, 1.3790049443904109, 1.950658333823796, 2.5862743242464927, 3.272786197223599, 3.994147138215396, 4.7318664975390865, 5.4656098643899025, 6.173917788622293, 6.835016202440613, 7.427672786143753, 7.932063237271129, 8.33060942739303, 8.60875162665997, 8.75561893395347, 8.764565676909308, 8.63355623107786, 8.36537174236456, 7.967551448451984, 7.452178610463793, 6.835491643726476, 6.13732011438079, 5.380365791198164, 4.5893557923265424, 3.7901006838374074, 3.008494575849957, 2.269491163367308, 1.596113556260811, 1.0085235939581647, 0.5232219285551368, 0.15239099474006818, -0.09659995463029479, -0.2215037057121633, -0.22530433632399233, -0.11612116664532672, 0.09309192083347563, 0.38504516002961714, 0.7387691958441999, 1.1304223060504326, 1.5342431746787164, 1.923550300172674, 2.271765176135981, 2.5534334405228742, 2.7452030218862444, 2.8267225230648108, 2.7814077501281385, 2.597050111231884, 2.2662908431376168, 1.7869140594686876, 1.161957362888151, 0.3996178236761575, -0.4870858335406932, -1.4807840515113393, -2.560363476130025, -3.7017159346508626, -4.878677578747099, -6.063862122734488, -7.229518796155395, -8.34842101855846, -9.394716893745578, -10.344753771124216, -11.177919752818262, -11.877135653997513, -12.429242573983146, -12.825364419009661, -13.061071724430349, -13.136210167940161, -13.054710014123014, -12.824283828987378, -12.45601676758788, -11.963869042449248, -11.364159759879325, -10.67508626402434, -9.915930458979387, -9.106435236800655, -8.266113824368258, -7.413646667765416, -6.566396513340452, -5.740005856967539, -4.9480845135088005, -4.20199131459832, -3.510710116542571, -2.880832346952396, -2.316646399452731, -1.820187294783675, -1.3913941132597567, -1.0283683791297609, -0.7276714024778138, -0.48464224193110467, -0.2937216121449173, -0.14876829145059092, -0.04335627075090874, 0.028957111463012705, 0.07439943415646164, 0.09879377308615661, 0.10741587921805024, 0.10488970197114263, 0.09512686345702503, 0.08130801557531678, 0.06590077897895233, 0.050707871273514324, 0.03693837984327236, 0.025295027978465105, 0.01607000863762457, 0.009242739144498063, 0.004574557135104939, 0.0016948484529659446, 0.00017543199816464483, -0.0004094545112363641, -0.0004388668232975725, -0.00021660297411802684, 4.2622235450139386e-05, 0.00021414044687231672, 0.00025395493046203595, 0.00018187496096480816, 6.017863318427816e-05, -2.9232504041566034e-05, -6.5322786536404675e-06, 0.0001877156889653046, 0.0005792805889106984, 0.0011530207721248927, 0.0018519984888634637, 0.002582636659915042, 0.003225039767732008, 0.003647136485651183, 0.003720988615251413, 0.0033394543989814433, 0.002431400414870872, 0.00097382152757313, -0.0010004870286093612, -0.003400642134107593, -0.006081226298518815, -0.008851610961831445, -0.011490441160428216, -0.013764210892291672, -0.015448459756039031, -0.016349835680584915, -0.01632714011680027, -0.015309448160135708, -0.013309352186022833, -0.010430099340477783, -0.006865551944710203, -0.002892393500108096, 0.0011453245755102253, 0.004858656041786536, 0.007842027378062328, 0.00970554963645692, 0.010109201860394471, 0.008796441006493922, 0.005624602476131692, 0.0005893168602990493, -0.006159058073032278, -0.0143088534290692, -0.023391742686995523, -0.032799292138847955, -0.04181131755371524, -0.04963515804775878, -0.05545418508328625, -0.05848312753030051, -0.05802726471458601, -0.053541844297637184, -0.044686890189600065, -0.031374851171888825, -0.013807379299091666, 0.007502071931375382, 0.031722389174842984, 0.0577174258914532, 0.08407789007443199, 0.10917220669092298, 0.1312152174225617, 0.1483514498031245, 0.15874990264128172, 0.16070358237715818, 0.15273042793497937, 0.13367035512023437, 0.10277260400730896, 0.05976802476803518, 0.004921430484215357, -0.060940658405965055, -0.1364320739559161, -0.21963455861131687, -0.30815435114816575, -0.39921030816904607, -0.4897432402485713, -0.5765438732280342, -0.6563950473683882, -0.7262211674203861, -0.7832377014278036, -0.8250974623973052, -0.8500178633467682, -0.8568772708488014, -0.845287537353318, -0.8156359181397301, -0.7690948236636129, -0.7075744069979648, -0.6336418272556555, -0.5504077371455616, -0.46138244224902447, -0.3703086857174646, -0.2809715089280419, -0.1970046096128583, -0.1217018537485734, -0.05784220627156606, -0.00753878871211083, 0.02787917452162239, 0.047949310985350956, 0.053108241132255346, 0.044672698188861784, 0.024769279191408262, -0.0037856759622781015, -0.0376498318486017, -0.07315486946439972, -0.10653302006533069, -0.13415836857492108, -0.15279070498558567, -0.1598093567505058, -0.15341358136695238, -0.1327823987076916, -0.0981780630764455, -0.050984099879431415, 0.006328681044534751, 0.07031280943029385, 0.13673188787169385, 0.20082201314627388, 0.25761949466192785, 0.30234380887464724, 0.3308247143807188, 0.33995196232536296, 0.3281166020900749, 0.29562924427006937, 0.24509212127396685, 0.18170246207507065, 0.11346646481308073, 0.05130565572319633, 0.009040849991589398, 0.0032431287200101844, 0.05294358753460562, 0.17919636038000322, 0.40451198866181903, 0.7521774603717216, 1.245478165415437, 1.9068451627367033, 2.756955668900427, 3.813818023829038, 5.091874630089333, 6.601155419780225, 8.346522960450468, 10.327049586723748, 12.535545904610935, 14.9582842150317, 17.57491314326787, 20.358579454223655, 23.27626398137894, 26.289328777136056, 29.354267980089514, 32.42367996619229, 35.44737504294094, 38.3735816999942, 41.150276924842224, 43.72663215341018, 46.054339239007454, 48.088905069161974, 49.79087476296126, 51.12692521844184, 52.07083039217954, 52.60426790444862, 52.717253459194026, 52.40838503685137, 51.68485426474971, 50.56224783046959, 49.0641848141104, 47.22150067817187, 45.07130214956465, 42.65589944047327, 40.021669327097726, 37.217742815708085, 34.294616581489386, 31.30282047591713, 28.291632758098036, 25.307881896927395, 22.394885884552863, 19.59156234722022, 16.93161863621874, 14.442994048415885, 12.14752941667603, 10.06080676403964, 8.192214287340123, 6.545206315972844, 5.117732346810986, 3.9028099874265725, 2.889212522521711, 2.062239454820081, 1.4045357659794515, 0.8969240964486692, 0.5192241098220925, 0.2510264706271809, 0.07239404135387283, -0.03553076726710138, -0.09002832470803802, -0.10642396207414397, -0.09783438878407122, -0.07503706586337322, -0.046455820712336414, -0.01825129371237416, 0.0054972634232628255, 0.02253854100527976, 0.03214471286395833, 0.034776643018133185, 0.031739276914445114, 0.024846527766239298, 0.016112878335045593, 0.0074860857109470096, 0.0006319698869941863, -0.0032215290055990437, -0.0033774899686649183, 0.0002989515682397154, 0.007406338075287199, 0.017081917676723145, 0.02811589113131418, 0.03909287764278081, 0.048547486645760314, 0.05512054571097625, 0.057702950357628006, 0.05555575108677563, 0.04839673711167259, 0.0364455317178304, 0.02042276593500505, 0.0015040005035103774, -0.018770251337015185, -0.03862373135532795, -0.05620536799361576, -0.06977167448385165, -0.07787915639237308, -0.0795757794478768, -0.07457811243155472, -0.06342211050727369, -0.047575732003379105, -0.029501243911901506, -0.01266499766368753, -0.0014895527091835683, -0.0012463532334795549, -0.017893309748267708, -0.05786390563124946, -0.12781060340403155, -0.23431340910432247, -0.38356603366061665, -0.5810555446500488, -0.8312598647471394, -1.1373625730283334, -1.5010022517757524, -1.922093347697101, -2.398716589318561, -2.927032427018926, -3.5012793380937093, -4.113847311664934, -4.755423780503897, -5.415208417061942, -6.081213027473789, -6.740678718056739, -7.380424819191668, -7.987321872444686, -8.548655920929837, -9.052475061377605, -9.487953400453813, -9.84571980749396, -10.118139635471415, -10.299539638413485, -10.38636851898175, -10.377327688159063, -10.273566710640372, -10.078544828894232, -9.79773497009019, -9.438400024348615, -9.0093321881393, -8.520553404564241, -7.9829886920636195, -7.408124689801337, -6.80766579687103, -6.1932066963408205, -5.5759888781426685, -4.966616246952689, -4.374675621994335, -3.808517834152133, -3.2751207263681117, -2.780007677108671, -2.327220487374152, -1.919343477505874, -1.5575739362038092, -1.2418382457698287, -0.9709345582377167, -0.7426878918592211, -0.5541423805417365, -0.40173680435712905, -0.28149994916053633, -0.18924214356785543, -0.12073025731574598, -0.07184093204298948, -0.03868832633230842, -0.017724143338737636, -0.005808500599957361, -0.0002538265281168744, 0.0011573457267866304, 0.0001786383345241364, -0.0018739073059199777, -0.004080137226895147, -0.00586235084464173, -0.006924663982765581, -0.007189623061596244, -0.006736020618533336, -0.005741009604301799, -0.004429364642080079, -0.003031752683374511, -0.0017530415901709634, -0.0007508958637729046, -0.00012415268333815845, 8.996021742275605e-05, -8.876577940560677e-05, -0.0005936731267608592, -0.0013250495858796595, -0.0021656993849522056, -0.0029964334725991392, -0.003709934097634164, -0.004221800165888711, -0.004477981695575991, -0.004458238834533316, -0.004175643533741749, -0.0036725147291810445, -0.0030134966627564804, -0.0022766808171864883, -0.0015438226523654278, -0.0008907225327074999, -0.0003787594576838025, -4.8405812996173375e-05, 8.4677090408305e-05, 3.063709641345521e-05, -0.00017650560758378263, -0.0004834715657174458, -0.0008244929518605203, -0.0011295008361540569, -0.001332847848924952, -0.0013816231885827907, -0.001242641256950031, -0.0009072955461877697, -0.0003936581501185888, 0.00025454137082031944, 0.0009721290039100546, 0.001679642745222629, 0.0022928208095932294, 0.002733587957556803, 0.0029414588624428802, 0.0028841133734846514, 0.002565836014669309, 0.0020325500932156654, 0.0013723224354077715, 0.0007104652219011066, 0.00019870600596874594, -1.6843560817417247e-06, 0.0002576048675982664, 0.0010846411299585187, 0.0025164211245861066, 0.004486230225957053, 0.006791271121476462, 0.009062895175802237, 0.010741899499357506, 0.011061303201747393, 0.009038591095064916, 0.003479400602418743, -0.007005876405542002, -0.02397214347754344, -0.049096305367474065, -0.08412082274218226, -0.1307855860694845, -0.1907502579719256, -0.2655099910106581, -0.3563117870192232, -0.4640733479813752, -0.5893012009026727, -0.7320198137668551, -0.8917158021544571, -1.067304762674739, -1.257109123222445, -1.4588584969183065, -1.669714590040503, -1.8863244020006924, -2.1049189028637203, -2.3213988514804753, -2.5314379508184746, -2.7306082773071196, -2.9145155475141094, -3.078944427362905, -3.2200142877851357, -3.334296769407846, -3.418930074061104, -3.471748548641399, -3.4913797585115436, -3.4772582661146543, -3.4296453087807732, -3.3496237295958395, -3.239064553474879, -3.100566351461119, -2.937373093308606, -2.753273836467734, -2.5524667071625506, -2.339446129669356, -2.1188268085959012, -1.8951789267796317, -1.6728889172015842, -1.4560319348562172, -1.2482605239588365, -1.052713291443444, -0.8719464789930801, -0.7078901045623743, -0.5618332013229673, -0.4344292059174237, -0.32571597692771675, -0.23517215768565677, -0.16179263125153923, -0.10417719182554003, -0.06062775384223716, -0.029249277286454822, -0.00804966932569505, 0.004965796407865095, 0.011710111422733621, 0.01394270699396776, 0.013210054755750595, 0.010804986571106928, 0.007744701789171962, 0.004766590583696485, 0.002340483311569433, 0.0006951678208977327, -0.00014360054880593545, -0.0003068207620967211, -3.121173208015586e-05, 0.0003932942534576426, 0.0006740726499259191, 0.0005609107961604663, -0.00011706389812492918, -0.0014246122587968973, -0.0033050019414313644, -0.005576476520302299, -0.007940258264257932, -0.009998994708351583, -0.011284445068083165, -0.01129212551195204, -0.009520146532092075, -0.005509428517991752, 0.0011180175256117716, 0.010625055430159548, 0.023131985764440952, 0.03859762421263034, 0.05680985660469014, 0.07738604815579485, 0.09978532622229665, 0.12333078816000391, 0.14724043707572745, 0.1706656438345417, 0.192735977504758, 0.21260382589950974, 0.22948856240005586, 0.2427177806462182, 0.25176206492601433, 0.25626339689926214, 0.25605488031443835, 0.2511693322351656, 0.24183698231539408, 0.22847246999862947, 0.21165242342765989, 0.19208525551077782, 0.1705709632690789, 0.1479575726218399, 0.12509625454816886, 0.10279751809174831, 0.08179036026167, 0.0626868779478428, 0.04595436026482316, 0.03189635631497592, 0.020643669521085525, 0.012155652890996028, 0.006231516077933512, 0.00253072731264842, 0.0006013923146950764, -8.535740998859593e-05, -9.718584796230294e-05, -9.662012225533922e-07, -0.000324222551763605, -0.0015199466027283179, -0.003936908913729447, -0.00779723113938647, -0.013182560635652358, -0.02002972424915691, -0.028135780738917246, -0.03717214902274115, -0.04670691087237722, -0.05623383997239696, -0.0652063182115728, -0.07307400481915485, -0.07931995722046525, -0.08349587903687505, -0.085253391577615, -0.08436901632928344, -0.08076085234786269, -0.07449700740855197, -0.06579497917572007, -0.05501176997708831, -0.04262530340757591, -0.029208202014069096, -0.015395452800566502, -0.0018478692336382015, 0.010786531052462382, 0.021910889280471083, 0.03101541199889311, 0.037708673386384256, 0.04173972619172004, 0.043013158753456585, 0.041595551525799794, 0.03771245535697005, 0.03173596027492066, 0.024163508185539546, 0.015588918767430142, 0.006667283305761545, -0.0019240909263037336, -0.009526637427741591, -0.015540853943653012, -0.01946240598100546, -0.020913187112107823, -0.019665640420882168, -0.01565881543550295, -0.009005157734562265, 1.2630424052751019e-05, 0.010954413112314806, 0.02324451326317656, 0.03620160263807509, 0.049075951497218426, 0.061093460883290436, 0.07149612721312551, 0.07958261235849078, 0.0847470738933576, 0.0865132604510951, 0.0845616692377406, 0.07874888855158171, 0.06911797901872425, 0.055899314735434996, 0.039501815234599585, 0.020494759643885335, -0.00042124161365632225, -0.02245047754453138, -0.04474075749225937, -0.06642429416746774, -0.08665868689758495, -0.10466613523311644, -0.1197690077597495, -0.13142007444484727, -0.13922600737484303, -0.14296311421328467, -0.1425868849427235, -0.13823740844441162, -0.1302218155261936, -0.11899193834552904, -0.10511828498187722, -0.08925938975006419, -0.07212817756024634, -0.05445711620733886, -0.036963918392754765, -0.020319455620585365, -0.0051193693708800996, 0.008138941197835856, 0.019074020195529767, 0.02743501722574193, 0.03310569563437687, 0.03610064570135532, 0.03655522463173701, 0.03471014287854063, 0.030891839595582934, 0.02548993964800361, 0.018933188427637995, 0.011665122998577492, 0.004121046000898435, -0.00329209993015868, -0.010215063408855597, -0.01635081476528317, -0.021474062136505385, -0.025435975397460404, -0.028164267114299202, -0.029659042551807152, -0.029985112814372095, -0.02926131709443028, -0.027647800692576715, -0.025332320336843437, -0.02251653554579835, -0.019402848253598344, -0.01618248798420838, -0.01302563334223362, -0.010073992426833602, -0.007436062653989918, -0.005185063874972596, -0.0033593578482570574, -0.00196513095796709, -0.0009808659291709945, -0.00036308719086695543, -5.281569987723322e-05, 1.781872357505692e-05, -8.0781523914486e-05, -0.0002813096118019131, -0.0005241111601939658, -0.0007604583133051887, -0.0009544463930800365, -0.0010835416988047967, -0.0011379150961197202, -0.0011187804446293, -0.0010360171010179071, -0.0009053866155606884, -0.0007456388707983017, -0.0005758033124317959, -0.0004129051787341792, -0.00027027570358255615, -0.00015655619645785023, -7.541160875079257e-05, -2.5894869831805687e-05, -3.3401743472380527e-06, -6.167008920892139e-07, -9.54793530798132e-06, -2.229767164323537e-05, -3.2542330066740874e-05, -3.6284574148140916e-05, -3.221612686988687e-05, -2.1600037841369635e-05, -7.707100731404201e-06, 5.098521312613243e-06, 1.2479751670493464e-05, 1.1275116420638344e-05, 4.845058123026138e-07, -1.808863277914044e-05, -3.968580227534841e-05, -5.702483203367623e-05, -6.133917942961273e-05, -4.397209837115119e-05, 1.607744103038709e-06, 7.75763828968831e-05, 0.00017957664114870965, 0.0002948950627466582, 0.00040130490216382656, 0.0004668705513421066, 0.0004509099128633674, 0.0003062224028776373, -1.7382770635571003e-05, -0.0005683820465557779, -0.0013879230413455864, -0.002503704139979852, -0.0039238738660528375, -0.005631567692039729, -0.007580781261964996, -0.009694370716137787, -0.011864451416975763, -0.013955817385556148, -0.015812817452488206, -0.017269068215862417, -0.018160133413274902, -0.018338617889446355, -0.01769075538836825, -0.016153345456212744, -0.013729781903674342, -0.010503093637054506, -0.006644365145030337, -0.0024155795918684993, 0.001834779226982931, 0.005684678310533427, 0.008660525818905081, 0.010267940897876037, 0.010031041065069768, 0.007539373548037519, 0.0025015763068584455, -0.005199316246600738, -0.015450889033459604, -0.027859633962802822, -0.04170665726044831, -0.05591521430869194, -0.06903552803639772, -0.07924711417359552, -0.08438215432169145, -0.08197188602337388, -0.0693184163074995, -0.043591781080639436, -0.0019479375351663492, 0.058334198257765355, 0.13970088850977175, 0.24416246235577135, 0.37312861014216925, 0.527249027326576, 0.7062778470880072, 0.9089568518427193, 1.132929874616405, 1.3746950827975737, 1.629600103404369, 1.8918847030006463, 2.154773531627292, 2.4106194110844985, 2.651095454156595, 2.867440150762627, 3.05076907894531, 3.1923763375258343, 3.2840484979989557, 3.3183888608070538, 3.2891323739414706, 3.1914376938983864, 3.02214350170259, 2.7799770725540713, 2.465704533612417, 2.0822147698413276, 1.6345465647609718, 1.1298503164436335, 0.5771814573508429, -0.012748175219197064, -0.6278706409600109, -1.2551178170052275, -1.8808202122638593, -2.491133988281503, -3.072480156454321, -3.6119846408716083, -4.097903775201509, -4.519997330660089, -4.869868242819861, -5.141229239175761, -5.3300758034446085, -5.434773286571321, -5.456056535995025, -5.396943403437996, -5.262568630322344, -5.059959268651091, -4.797723822846892, -4.485687311523674, -4.13451486718207, -3.755336966100528, -3.359315768926826, -2.9572489123833465, -2.5592180512232376, -2.174285964515558, -1.8102554645051652, -1.4734937483688235, -1.168815991222695, -0.8994493241899019, -0.6670672564931104, -0.4718888765440038, -0.3128330240465139, -0.1877019813409031, -0.09340608021842423, -0.026208980790380906, 0.018022962546427008, 0.04358027672416118, 0.05468926330754178, 0.05532055089486841, 0.04903508181998601, 0.03887223851445141, 0.027282039994953194, 0.016100723095056373, 0.006566507967958964, -0.0006301435134022531, -0.0052686391083548055, -0.007500934690172255, -0.007743612080021949, -0.006568344126527143, -0.0045990430532743916, -0.00242282819191021, -0.0005203724692939758, 0.0007806981770398306, 0.0013277361808057594, 0.001140765524303266, 0.0003883743695291832, -0.0006540051629680408, -0.0016579756441047436, -0.0023019145379282384, -0.0023299324566620236, -0.0016035992184717193, -0.00014070001208265815, 0.0018635365011227935, 0.004035765626614744, 0.00584561479350845, 0.0066473437410878465, 0.005739463550768773, 0.002437888723454355, -0.0038433131216570843, -0.013510526835357107, -0.02671603772144608, -0.04329778105744164, -0.06274025434607156, -0.08416272901084446, -0.1063382909199765, -0.12774490696943128, -0.14664701531718694, -0.16120548183642525, -0.1696105930968105, -0.1702303797429891, -0.1617648984049644, -0.14339580657042866, -0.11492006451372441, -0.07685625676648708, -0.030511147029651988, 0.022000592560213115, 0.07779267322347928, 0.13329141678693956, 0.1843748735025045, 0.2265642322939511, 0.2552599157132631, 0.2660124494416526, 0.2548162148668395, 0.2184082612790171, 0.15455402089217518, 0.062306226386106764, -0.057785018907445626, -0.20354235706981091, -0.3710938215689454, -0.5548827787071562, -0.7477668604740002, -0.9412066625924737, -1.1255457403632974, -1.2903610408939565, -1.4248752050587465, -1.5184178027804325, -1.5609147517716917, -1.5434042253710725, -1.458576095762928, -1.3011382820217428, -1.0681453399658887, -0.7592629455988013, -0.37692308701177996, 0.07364038263282584, 0.584465623508784, 1.1450529598926595, 1.7426668897274873, 2.3627397603317104, 2.989365242934847, 3.6058970756314936, 4.195600835178278, 4.742301456057104, 5.2309801293916625, 5.648317979645852, 5.983179333893345, 6.227006834293699, 6.374112344117606, 6.4218523521226345, 6.370681751743514, 6.224118588073085, 5.988675824788789, 5.673466101622622, 5.28971634032436, 4.8502725403969835, 4.369063427927368, 3.8605440504564905, 3.3391441228671344, 2.8187447166556, 2.3122046181892553, 1.8309555552318981, 1.3846973908313138, 0.9811762229837374, 0.6259753559847309, 0.3224727923110852, 0.07191440375009785, -0.12642625324999435, -0.27501563245212846, -0.3777721401442272, -0.4397406313588537, -0.466749371658821, -0.4650670325146617, -0.4410732382345658, -0.4009661498486767, -0.3505042864312039, -0.2947997047415111, -0.2381720080137032, -0.18406375644611203, -0.1350148394286746, -0.09269024053869888, -0.05795313676660645, -0.03097240347935975, -0.011354844852401907, 0.0017091894611615266, 0.009298773760048002, 0.012624794314858445, 0.012906809661163112, 0.01127225548466917, 0.008682402072239115, 0.005886610164322401, 0.0034040780402518566, 0.0015302582190693406, 0.0003636115644221632, -0.00015293495387573894, -0.00018200961868484593, 6.049146022477535e-05, 0.00035434253182200755, 0.0005158638159683266, 0.00042715487834685733, 5.1656291534497655e-05, -0.0005643985449070426, -0.0013035391480202007, -0.001999175041169561, -0.0024648050100875957, -0.0025262112289804956, -0.002052329336631266, -0.0009807299971122667, 0.0006656915548894647, 0.002773224144253343, 0.005144188292264586, 0.007515855748551205, 0.009589792023385708, 0.01106869476313775, 0.011696785228764642, 0.01129915679519498, 0.009815269118958634, 0.007322032682257567, 0.004042624762073989, 0.0003385388639882517, -0.0033160118026888327, -0.006376717693609578, -0.00828632673313665, -0.008541962778271288, -0.00676669411062841, -0.00277824597103468, 0.0033529251698901706, 0.011264031797721452, 0.02028614472679823, 0.02946208684970941, 0.0375984932956863, 0.043354136559612524, 0.045363201811388094, 0.042388957579631875, 0.03350029649521719, 0.01826077032285715, -0.0030826724177453455, -0.029425871853244592, -0.05866565311542875, -0.08760084989032713, -0.11188862848328107, -0.12606890609843763, -0.12366366360331103, -0.09735574468742947, -0.03924656527467131, 0.058812644882354825, 0.20482649499201294, 0.4062197149673333, 0.6694089814383447, 0.9993481655309451, 1.3990933073238028, 1.8694425470107885, 2.4086319715392923, 3.012121380499602, 3.6724934752358593, 4.379477576627045, 5.120108858954954, 5.879139886224878, 6.63955659018871, 7.383004817332476, 8.090398277901395, 8.742635197708852, 9.321441042450603, 9.81000793831811, 10.193635078778259, 10.460332533986634, 10.601382607967265, 10.611992082324711, 10.491320177057885, 10.242412622763625, 9.87209349864522, 9.390704664389531, 8.811743609633096, 8.151436141981275, 7.427947613351251, 6.66063196259738, 5.869410015168681, 5.074035944625132, 4.2931697220665415, 3.543732382111085, 2.8403843067388928, 2.1951267890895014, 1.617039454558671, 1.1121647525556293, 0.6835263627256207, 0.33124635668244923, 0.05284399033423609, -0.156444210444204, -0.3032240759223194, -0.3954308423217898, -0.4418068423274288, -0.4513981689446619, -0.4330952438895051, -0.39523774354329555, -0.3453012818016876, -0.2896763035679712, -0.23352321631400383, -0.18071978817379977, -0.13389612854061936, -0.09454276638605515, -0.0631743220077227, -0.03952949756787034, -0.022787806334560533, -0.011784573724478371, -0.005208121932627289, -0.0017663771850431674, -0.0003134674128573383, 6.691051936748733e-05, 2.188209016765507e-05, -6.91255380794967e-05, -5.9079845631012643e-05, 2.5906404764876163e-05, 5.856330687266548e-05, -0.00011614098693799264, -0.0006165071067934612, -0.0014768026512649213, -0.002622702978073789, -0.0038718042459098207, -0.004958317313076867, -0.00557753779575313, -0.005442997343311064, -0.004347379159164437, -0.0022174694943565085, 0.0008462349971183668, 0.004553184900728496, 0.008435182328107934, 0.011889587476355833, 0.0142515446385798, 0.014889611449797712, 0.013315835464345302, 0.009297754330120814, 0.002958362270254299, -0.0051502873869968884, -0.014012949611978435, -0.022167052754438553, -0.02777546746082793, -0.028756515168557834, -0.022966048466204578, -0.008420115033123187, 0.016459221708937048, 0.0525980463030403, 0.10005030254725877, 0.15783000002232211, 0.22382199586756904, 0.29479240842428395, 0.366512545921952, 0.43400206049752443, 0.4918853924185364, 0.5348434525051369, 0.5581307900440606, 0.5581170328626665, 0.5327962087502947, 0.4822129876985527, 0.40874666964090894, 0.31719263116078256, 0.21460304641636158, 0.10985412101503081, 0.012927024580401332, -0.06608627232279325, -0.11821477366107393, -0.1370129012944549, -0.12004543081138792, -0.07033740259871402, 0.0023448523731037104, 0.08051815015010731, 0.1384483762796968, 0.1421880584777256, 0.05029299892256582, -0.18470769866944498, -0.6140576202560926, -1.2897573829256825, -2.260888056503385, -3.569509384560296, -5.24623268817676, -7.3057351821947005, -9.742534917841091, -12.527345617872651, -15.60434836289929, -18.889707649356733, -22.271627322789566, -25.61219873113808, -28.75156197891358, -31.51411638648456, -33.71641655633075, -35.17620138757449, -35.72284211135579, -35.208725930102176, -33.520915085775854, -30.592438529645555, -26.412515426633554, -21.035216595055875, -14.58621231131953, -7.26443236896549, 0.6596388236925549, 8.849684577409262, 16.91370029893399, 24.4178223710718, 30.903777637030377, 35.909438766160505, 38.99168789901838, 39.75089808555147, 37.85621572138569, 33.06896643993299, 25.26305588264365, 14.441355961512686, 0.7464027725695949, -15.536417194566567, -33.982319652108885, -54.03788487739317, -75.03887468810721, -96.23345804684153, -116.81516706098634, -135.96064364902938, -152.86986650917012, -166.80765283110102, -177.14524571383922, -183.40125135503703, -185.27089549280902, -182.6480059482996, -175.63738117349018, -164.5568914583017, -149.928787584751, -132.45737802462222, -112.99483922006576, -92.49652613992258, -71.9677219703601, -52.40498808792026, -34.734827005220666, -19.748662950356824, -8.045151494184035, 0.01797784693632871, 4.360000753998744, 5.197963064390082, 3.049685664937563, -1.2825129297018747, -6.74788526582023, -12.102511083720223, -15.981948830594598, -16.988832264484884, -13.791939753680657, -5.230194149105531, 9.58414365453069, 31.169221042578087, 59.59057170463583, 94.39732955176753, 134.58304109914968, 178.57545544960297, 224.2584620592335, 269.02815069763136, 309.88143417495775, 343.5388857544429, 366.5940593556024, 375.6832345817056, 367.66833594423673, 339.82405072606525, 290.0193203665182, 216.88302092569077, 119.94542941208489, -0.2544767341168809, -142.11059767965278, -302.9401907951203, -479.02870346025634, -665.7296518472114, -857.6178222118434, -1048.6910110067583, -1232.6125949788259, -1402.984449378113, -1553.6370196442456, -1678.9265768491778, -1774.020437367019, -1835.1552697275854, -1859.8577988230031, -1847.0981859445258, -1797.3779199288085, -1712.7442901468528, -1596.7258361832385, -1454.1903717944701, -1291.1291212745327, -1114.3692442392178, -931.2371048927582, -749.1867266352285, -575.4128064692519, -416.46904464632155, -277.909668467314, -163.98364553203226, -77.39934642659678, -19.176242690744036, 11.407813986319969, 16.76329450032936, 0.8260614018165914, -31.208731239943564, -73.24416496174489, -118.712629383365, -161.05700853617725, -194.23084702431626, -213.18834146232956, -214.33056587212076, -195.86138079437012, -158.035458858708, -103.27286295640228, -36.119865670602884, 36.955808178710235, 107.93841209819534, 167.80008469534954, 207.18167832272312, 217.18038699572108, 190.23842795147056, 121.10074011454174, 7.7621927787468366, -147.6556592785347, -338.16553416838, -551.3809933146231, -769.2527459369621, -968.1305880253154, -1119.2526251567906, -1189.7625855873416, -1143.6186874136145, -942.6713352976608, -547.902368134344, 79.27193220092548, 975.6892624926352, 2175.1732037964216, 3707.3549086881853], 'positive_zeros': ['0.967422723558437876828045005312006', '1.14657240717087337933250302370988', '1.42574509890387686696723514414984', '1.45474014450449100931610179924687', '1.50600127946991471987917732394228', '1.67238335714041377558229799328347', '1.71219486929232588262523554336408', '1.84409985483334531283121799001494', '1.85931233632875258013399521482748', '1.97849624922464241044315344616812', '2.00046676742539989282627255128301', '2.21703251142069649081973264087987', '2.55984113148384415249592487526385', '2.58084737601136772017862124146734', '2.64900716782881168749510961509711', '2.65574415095143538396679161077265', '2.66691331403447115272984596323848', '2.75677683343591506794633609295559', '2.80944296589361881929061826654723', '2.94242333830367144346149977731276', '3.11295197640407919981755569128956', '3.17543721925371929513680070195542', '3.46553788247114735921634116653749', '3.46832275144324940258307867381792', '3.53875215935714061926334580473817', '3.60102885942913029063314971817464', '3.66897980787409540253810437129757', '3.68448802076645253082986834076251', '3.94586261962133230686912568941478', '4.00644022618033753824806179502831', '4.03239098445538814732889255492906', '4.33543242033871787445018710167216', '4.36101032861775425181705525847841', '4.63618151711952042568864084759995', '4.80118800519933925731681664516349', '4.83723485284413282102952648147511', '4.93284797615296098017644656595774', '4.97358341237569574246844803390403', '4.99220478224152189290770428478125', '5.13979312465650487745175902371931', '5.17851019130684037495778635021305', '5.17949544049390827745601780477804', '5.25312313385447310748425330125188', '5.33690806823328166548909074933316', '5.73006730831100884526600290447457', '5.73097983098716664765662039339438', '5.79498125947806617467009963973044', '5.81452768648207405082406861341732', '5.83180263064878226273986985184089', '5.86607367106501905821519358264273', '5.95132429328681066804013331359696', '6.00072388596757961102168513199559', '6.17658014854501469640870917025745', '6.19819174438780100713157685971961', '6.28267130379128128214458443359920', '6.50150129279450815585634150371960', '6.58485110098823958150293699847935', '6.60415571299171051593120279729479', '6.62944777289356887444522518709185', '6.63740101804750598549001931982407', '6.69845664208869223917156210291772', '6.77403662204684987104502656714270', '6.81337694574586400886062018580228', '6.88564626988036370391294371090656', '6.95710599984560434414126145819260', '7.09613487061722971492208018732445', '7.12648816128736580635037507608896', '7.18517274801903311923838331875102', '7.26355419872484787370900190919117', '7.26386740276714691956976911555748', '7.59376566157405367331238928502541', '7.63180442416830979191102482505083', '7.67641239755231929206150786338977', '7.69146549742860352282434759119556', '7.75608244118295752625026160356440', '7.82121604671594229966327154155512', '7.82365277527374865018843588489890', '8.144984929349601227413505040438107', '8.155728147887373978814029737863384', '8.221012092818438912197913834601744', '8.228221037061071091308696369546728', '8.316219254811837215759054428901902', '8.326704303056040840175438892168043', '8.376913292273316499008200256054755', '8.442279954158582480449402442609833', '8.443205332594885812117009850486025', '8.498201913851313695543392587101390', '8.786666873891534300159536357093660', '8.835633630046762043090198965336173', '8.848066794977402684095861131306042', '8.868309585184943275268424799899470', '8.921470084492971995949632843688070', '9.107340202820372452893554731095157', '9.118754858886013284532866578553557', '9.119074976143354532112907950796348', '9.247908160497201446055234692872509', '9.315173270264486302608559466070333', '9.359009926785572506155897593194666', '9.444142322547607896334436762456613'], 'prelabel': '22-1502e11-1.1-c1e11-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.463167680548593, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1e11-0', 'trace_hash': 1129530279307760898, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.967422723558437876828045005312', 'prec': 107}, 'z2': {'__RealLiteral__': 0, 'data': '1.14657240717087337933250302371', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '1.42574509890387686696723514415', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 738613832158.124, 'bad_primes': [2, 751], 'central_character': '1.1', 'conductor': 87774680912726123745982623376898048, 'conductor_radical': 1502, 'degree': 22, 'dirichlet_coefficients': [1, -11, -4, 66, 1, 44, -6, -286, -7, -11, 4, -264, -19, 66, -4, 1001, -8, 77, -9, 66, 24, -44, 2, 1144, -28, 209, 48, -396, 13, 44, -19, -3003, -16, 88, -6, -462, -29, 99, 76, -286, -23, -264, -13, 264, -7, -22, -16, -4004, -23, 308, 32, -1254, -25, -528, 4, 1716, 36, -143, 6, -264, 10, 209, 42, 8008, -19, 176, -16, -528, -8, 66, 8, 2002, -56, 319, 112, -594, -24, -836, 2, 1001, 5, 253, 21, 1584, -8, 143, -52, -1144, -24, 77, 114, 132, 76, 176, -9, 12012, -84, 253, -28, -1848], 'euler11': [1, -4, 76, -218, 2543, -5171, 52856, -76251, 824629, -903598, 10686030, -10096417, 117546330, -109335358, 1097581199, -1116390891, 8512511656, -9160741931, 49555875853, -46730236058, 179204024516, -103749698404, 285311670611], 'euler13': [1, 19, 251, 2486, 20498, 144288, 895242, 4944973, 24659831, 111493297, 460056571, 1733530095, 5980735423, 18842367193, 54177648707, 141233373853, 332397087906, 696450616992, 1286219101466, 2027906572406, 2661729342623, 2619311345131, 1792160394037], 'euler17': [1, 8, 120, 743, 6373, 30365, 192554, 708204, 3751031, 10892706, 57642117, 157981491, 979915989, 3147992034, 18428815303, 59149906284, 273399144778, 732937282685, 2615088363029, 5182987778663, 14230545179640, 16127951203592, 34271896307633], 'euler19': [1, 9, 132, 866, 7833, 42985, 304739, 1479206, 8926075, 39204165, 208798205, 830509179, 3967165895, 14152703565, 61223948425, 192771605126, 754563933161, 2022267194785, 7001697331587, 14707765593506, 42594776106828, 55179596320209, 116490258898219], 'euler2': [1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, -2, 116, -199, 6875, -8589, 279111, -206919, 8759964, -3090421, 229603101, -46207660, 5280871323, -1634832709, 106582481988, -57904419879, 1796454131073, -1271480250621, 23408174948125, -15583886070919, 208933708729708, -82853022427298, 952809757913927], 'euler29': [1, -13, 224, -2354, 25468, -217411, 1843417, -13336997, 94415573, -591192671, 3604728408, -19668193409, 104537123832, -497193036311, 2302701409897, -9433004575157, 37810600756133, -129321133041931, 439319849837612, -1177580056110194, 3249600698594656, -5469194032902613, 12200509765705829], 'euler3': [1, 4, 23, 72, 252, 654, 1771, 3959, 8994, 17649, 34770, 60227, 104310, 158841, 242838, 320679, 430353, 476766, 551124, 472392, 452709, 236196, 177147], 'euler31': [1, 19, 368, 4447, 51938, 471895, 4148528, 30640520, 221593872, 1398891383, 8763296259, 48830151971, 271662184029, 1344334619063, 6601503040752, 28297163670920, 118768834539728, 418808549545495, 1428950151697118, 3792806443500127, 9729780955126928, 15572937452635219, 25408476896404831], 'euler37': [1, 29, 530, 7415, 87962, 906024, 8377271, 70517085, 547365646, 3935903852, 26446088879, 166181713355, 978505288523, 5388252373388, 27725712066838, 132160370540685, 580913120001347, 2324609703987816, 8350397776372946, 26045035150824215, 68879722091390810, 139448946800117621, 177917621779460413], 'euler41': [1, 23, 524, 7801, 110137, 1250171, 13409888, 123776224, 1081864063, 8371077407, 61452377952, 403835689705, 2519547496032, 14071781121167, 74563153086023, 349762026506464, 1553618679515488, 5938442569075211, 21449651462431697, 62290401712372921, 171548133622435564, 308721164133505223, 550329031716248441], 'euler43': [1, 13, 238, 2106, 25816, 201269, 2028245, 14214483, 122945681, 793330591, 6220241242, 37312391727, 267470373406, 1466868262759, 9775042259267, 48596488694883, 298169139472535, 1272294419509181, 7017269264338312, 24615349784627706, 119617041640968634, 280949270072695237, 929293739471222707], 'euler47': [1, 16, 321, 3647, 48416, 446650, 4726823, 38156849, 349654826, 2519117392, 20488582878, 132762074369, 962963395266, 5564730318928, 36302212999798, 186193251085169, 1084073254022761, 4814536526697850, 24528665000336608, 86839762455442367, 359240881865988207, 841586115773280784, 2472159215084012303], 'euler5': [1, -1, 29, -20, 394, -94, 3288, 1187, 19311, 20469, 94521, 140607, 472605, 511725, 2413875, 741875, 10275000, -1468750, 30781250, -7812500, 56640625, -9765625, 48828125], 'euler53': [1, 25, 658, 10501, 166508, 2024488, 24321735, 243039987, 2399991584, 20406299116, 171381495519, 1255661569249, 9083219262507, 57321294216844, 357303547051168, 1917702399663747, 10171239958940355, 44871483133326952, 195598802471979196, 653789009009701861, 2171244443405803514, 4372186759137826225, 9269035929372191597], 'euler59': [1, -6, 233, -376, 19318, 21737, 1369125, -1912461, 100132738, -250397075, 3792758135, -6632269702, 223772729965, -871632218075, 20565161597702, -23173980335421, 978820730868375, 916878259754417, 48075769383733442, -55208244539224696, 2018478025746600787, -3066700519803848406, 30155888444737842659], 'euler61': [1, -10, 516, -4272, 119700, -822722, 16776452, -96335141, 1633182154, -8007968175, 121923996153, -532123144541, 7437363765333, -29797649579175, 370701318497074, -1333841044998581, 14169329303104052, -42386945435030642, 376186317471713700, -818973641124384432, 6034179383902416756, -7133429116628826010, 43513917611435838661], 'euler67': [1, 16, 615, 8234, 175581, 1993737, 30895766, 301684551, 3757993440, 31868672758, 334867476598, 2472521226173, 22436120932066, 143058472010662, 1130265380994720, 6079281891031671, 41713149376596962, 180350223490475553, 1064145804374217663, 3343561257001381994, 16732018653721392405, 29165404872828183184, 122130132904968017083], 'euler7': [1, 6, 59, 260, 1463, 5154, 21418, 63721, 218259, 576308, 1758302, 4312446, 12308114, 28239092, 74862837, 152994121, 359972326, 606362946, 1204843409, 1498848260, 2380862813, 1694851494, 1977326743], 'euler71': [1, -8, 368, -2391, 63944, -317254, 6876058, -22215854, 519562092, -718721756, 33189514387, -12488035445, 2356455521477, -3623076371996, 185956987909812, -564542194990574, 12405985662778358, -40640327475072934, 581578363408154104, -1543996693208614551, 16872248264389243408, -26041948408079049608, 231122292121701565271], 'euler73': [1, 56, 1803, 40850, 728151, 10801497, 139563167, 1620820864, 17335614757, 173046152513, 1622262774152, 14295122392183, 118425182513096, 922162946741777, 6743848845923869, 46028461513700224, 289324436936815031, 1634636191257954633, 8044174279078999647, 32943894753873208850, 106145470835007047139, 240667046463399228344, 313726685568359708377], 'euler79': [1, -2, 351, -590, 66579, -200805, 8944941, -40985072, 914532221, -5490048169, 80248761640, -521211788815, 6339652169560, -34263390622729, 450900051709619, -1596371874190832, 27524087942727459, -48813176505894405, 1278577056389480061, -895094197844870990, 42067910189899029969, -18936552165253694402, 747993810527520928879], 'euler83': [1, -21, 861, -13395, 311794, -3842050, 65761741, -670200108, 9377948350, -81917480725, 993476580480, -7651988189753, 82458556179840, -564329524714525, 5362188953201450, -31806571859698668, 259038170553439463, -1256121261502366450, 8460857882259760838, -30169454449502454195, 160955559785352286983, -325836864931322922429, 1287831418538085836267], 'euler89': [1, 24, 730, 11824, 220808, 2841686, 41137351, 447517393, 5494330029, 52813110330, 581943235662, 5109080651615, 51792947973918, 418332646923930, 3873332346214101, 28078244123297713, 229713413558379599, 1412264776785800246, 9766632595611967432, 46546226038621405744, 255760174706464202570, 748361278319188406424, 2775173073766990340489], 'euler97': [1, 84, 3898, 126840, 3203709, 66248405, 1161441294, 17698825499, 239157752199, 2912808637566, 32397739228254, 331934933022227, 3142580705140638, 27406616470858494, 218272823172717927, 1566864295970936219, 9973691580108372558, 55183066736198388245, 258854191167090921117, 994100077110773733240, 2963380666635495215866, 6194362665917397388116, 7153014030880804126753], 'euler_factors': [[1, 11, 55, 165, 330, 462, 462, 330, 165, 55, 11, 1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, 4, 23, 72, 252, 654, 1771, 3959, 8994, 17649, 34770, 60227, 104310, 158841, 242838, 320679, 430353, 476766, 551124, 472392, 452709, 236196, 177147], [1, -1, 29, -20, 394, -94, 3288, 1187, 19311, 20469, 94521, 140607, 472605, 511725, 2413875, 741875, 10275000, -1468750, 30781250, -7812500, 56640625, -9765625, 48828125], [1, 6, 59, 260, 1463, 5154, 21418, 63721, 218259, 576308, 1758302, 4312446, 12308114, 28239092, 74862837, 152994121, 359972326, 606362946, 1204843409, 1498848260, 2380862813, 1694851494, 1977326743], [1, -4, 76, -218, 2543, -5171, 52856, -76251, 824629, -903598, 10686030, -10096417, 117546330, -109335358, 1097581199, -1116390891, 8512511656, -9160741931, 49555875853, -46730236058, 179204024516, -103749698404, 285311670611], [1, 19, 251, 2486, 20498, 144288, 895242, 4944973, 24659831, 111493297, 460056571, 1733530095, 5980735423, 18842367193, 54177648707, 141233373853, 332397087906, 696450616992, 1286219101466, 2027906572406, 2661729342623, 2619311345131, 1792160394037], [1, 8, 120, 743, 6373, 30365, 192554, 708204, 3751031, 10892706, 57642117, 157981491, 979915989, 3147992034, 18428815303, 59149906284, 273399144778, 732937282685, 2615088363029, 5182987778663, 14230545179640, 16127951203592, 34271896307633], [1, 9, 132, 866, 7833, 42985, 304739, 1479206, 8926075, 39204165, 208798205, 830509179, 3967165895, 14152703565, 61223948425, 192771605126, 754563933161, 2022267194785, 7001697331587, 14707765593506, 42594776106828, 55179596320209, 116490258898219], [1, -2, 116, -199, 6875, -8589, 279111, -206919, 8759964, -3090421, 229603101, -46207660, 5280871323, -1634832709, 106582481988, -57904419879, 1796454131073, -1271480250621, 23408174948125, -15583886070919, 208933708729708, -82853022427298, 952809757913927], [1, -13, 224, -2354, 25468, -217411, 1843417, -13336997, 94415573, -591192671, 3604728408, -19668193409, 104537123832, -497193036311, 2302701409897, -9433004575157, 37810600756133, -129321133041931, 439319849837612, -1177580056110194, 3249600698594656, -5469194032902613, 12200509765705829], [1, 19, 368, 4447, 51938, 471895, 4148528, 30640520, 221593872, 1398891383, 8763296259, 48830151971, 271662184029, 1344334619063, 6601503040752, 28297163670920, 118768834539728, 418808549545495, 1428950151697118, 3792806443500127, 9729780955126928, 15572937452635219, 25408476896404831], [1, 29, 530, 7415, 87962, 906024, 8377271, 70517085, 547365646, 3935903852, 26446088879, 166181713355, 978505288523, 5388252373388, 27725712066838, 132160370540685, 580913120001347, 2324609703987816, 8350397776372946, 26045035150824215, 68879722091390810, 139448946800117621, 177917621779460413], [1, 23, 524, 7801, 110137, 1250171, 13409888, 123776224, 1081864063, 8371077407, 61452377952, 403835689705, 2519547496032, 14071781121167, 74563153086023, 349762026506464, 1553618679515488, 5938442569075211, 21449651462431697, 62290401712372921, 171548133622435564, 308721164133505223, 550329031716248441], [1, 13, 238, 2106, 25816, 201269, 2028245, 14214483, 122945681, 793330591, 6220241242, 37312391727, 267470373406, 1466868262759, 9775042259267, 48596488694883, 298169139472535, 1272294419509181, 7017269264338312, 24615349784627706, 119617041640968634, 280949270072695237, 929293739471222707], [1, 16, 321, 3647, 48416, 446650, 4726823, 38156849, 349654826, 2519117392, 20488582878, 132762074369, 962963395266, 5564730318928, 36302212999798, 186193251085169, 1084073254022761, 4814536526697850, 24528665000336608, 86839762455442367, 359240881865988207, 841586115773280784, 2472159215084012303], [1, 25, 658, 10501, 166508, 2024488, 24321735, 243039987, 2399991584, 20406299116, 171381495519, 1255661569249, 9083219262507, 57321294216844, 357303547051168, 1917702399663747, 10171239958940355, 44871483133326952, 195598802471979196, 653789009009701861, 2171244443405803514, 4372186759137826225, 9269035929372191597], [1, -6, 233, -376, 19318, 21737, 1369125, -1912461, 100132738, -250397075, 3792758135, -6632269702, 223772729965, -871632218075, 20565161597702, -23173980335421, 978820730868375, 916878259754417, 48075769383733442, -55208244539224696, 2018478025746600787, -3066700519803848406, 30155888444737842659], [1, -10, 516, -4272, 119700, -822722, 16776452, -96335141, 1633182154, -8007968175, 121923996153, -532123144541, 7437363765333, -29797649579175, 370701318497074, -1333841044998581, 14169329303104052, -42386945435030642, 376186317471713700, -818973641124384432, 6034179383902416756, -7133429116628826010, 43513917611435838661], [1, 16, 615, 8234, 175581, 1993737, 30895766, 301684551, 3757993440, 31868672758, 334867476598, 2472521226173, 22436120932066, 143058472010662, 1130265380994720, 6079281891031671, 41713149376596962, 180350223490475553, 1064145804374217663, 3343561257001381994, 16732018653721392405, 29165404872828183184, 122130132904968017083], [1, -8, 368, -2391, 63944, -317254, 6876058, -22215854, 519562092, -718721756, 33189514387, -12488035445, 2356455521477, -3623076371996, 185956987909812, -564542194990574, 12405985662778358, -40640327475072934, 581578363408154104, -1543996693208614551, 16872248264389243408, -26041948408079049608, 231122292121701565271], [1, 56, 1803, 40850, 728151, 10801497, 139563167, 1620820864, 17335614757, 173046152513, 1622262774152, 14295122392183, 118425182513096, 922162946741777, 6743848845923869, 46028461513700224, 289324436936815031, 1634636191257954633, 8044174279078999647, 32943894753873208850, 106145470835007047139, 240667046463399228344, 313726685568359708377], [1, -2, 351, -590, 66579, -200805, 8944941, -40985072, 914532221, -5490048169, 80248761640, -521211788815, 6339652169560, -34263390622729, 450900051709619, -1596371874190832, 27524087942727459, -48813176505894405, 1278577056389480061, -895094197844870990, 42067910189899029969, -18936552165253694402, 747993810527520928879], [1, -21, 861, -13395, 311794, -3842050, 65761741, -670200108, 9377948350, -81917480725, 993476580480, -7651988189753, 82458556179840, -564329524714525, 5362188953201450, -31806571859698668, 259038170553439463, -1256121261502366450, 8460857882259760838, -30169454449502454195, 160955559785352286983, -325836864931322922429, 1287831418538085836267], [1, 24, 730, 11824, 220808, 2841686, 41137351, 447517393, 5494330029, 52813110330, 581943235662, 5109080651615, 51792947973918, 418332646923930, 3873332346214101, 28078244123297713, 229713413558379599, 1412264776785800246, 9766632595611967432, 46546226038621405744, 255760174706464202570, 748361278319188406424, 2775173073766990340489], [1, 84, 3898, 126840, 3203709, 66248405, 1161441294, 17698825499, 239157752199, 2912808637566, 32397739228254, 331934933022227, 3142580705140638, 27406616470858494, 218272823172717927, 1566864295970936219, 9973691580108372558, 55183066736198388245, 258854191167090921117, 994100077110773733240, 2963380666635495215866, 6194362665917397388116, 7153014030880804126753]], 'index': 0, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/1502/2/a/e'], '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': '22-1502e11-1.1-c1e11-0-0', '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}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}, {'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1], 'order_of_vanishing': 11, 'prelabel': '22-1502e11-1.1-c1e11-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 3.463167680548593, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1e11-0', 'trace_hash': 1129530279307760898, 'z1': {'__RealLiteral__': 0, 'data': '0.967422723558437876828045005312', 'prec': 107}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1226353996193282218815850180680,1453453200155283476096117783357,1807346630397955803346825545423,1844102217357219203167649553107,1909083425864518847270358959054,2119997766490746859538369283567,2170464853766111690769722921581,2337674287860280891986452848276,2356958399158894747174155252164,2508041957878918501207722012516,2535892898463433962424703680751', 'Lhash_array': ['1226353996193282218815850180680', '1453453200155283476096117783357', '1807346630397955803346825545423', '1844102217357219203167649553107', '1909083425864518847270358959054', '2119997766490746859538369283567', '2170464853766111690769722921581', '2337674287860280891986452848276', '2356958399158894747174155252164', '2508041957878918501207722012516', '2535892898463433962424703680751'], 'label': '22-1502e11-1.1-c1e11-0-0', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/1502/2/a/e'}