Lfunction data - 12-3800e6-1.1-c1e6-0-8

Formats: - HTML - YAML - JSON - 2024-12-02T17:20:20.418216

• lfunc_lfunctions •

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

  
  {'Lhash': '451666653568485436285272452689,673421383843490333449969298018,821901741280644182982607359569,1086351598670102217976218693701,1382628281386482274992214324142,1716091547250881169839750313129', 'a10': 0, 'a2': 0, 'a3': 2, 'a4': 0, 'a5': 0, 'a6': 0, 'a7': 2, 'a8': 0, 'a9': -4, 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 780484390.6529279, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [1]], [5, [1]], [19, [1, 6, 15, 20, 15, 6, 1]]], 'bad_primes': [2, 5, 19], 'central_character': '3800.1', 'coefficient_field': '1.1.1.1', 'conductor': 3010936384000000000000, 'conductor_radical': 190, 'degree': 12, 'euler_factors': [[1], [1, -2, 8, -14, 30, -50, 87, -150, 270, -378, 648, -486, 729], [1], [1, -2, 12, -22, 118, -126, 779, -882, 5782, -7546, 28812, -33614, 117649], [1, -3, 26, -26, 65, 749, -2288, 8239, 7865, -34606, 380666, -483153, 1771561], [1, 1, 13, 50, 38, -516, 1813, -6708, 6422, 109850, 371293, 371293, 4826809], [1, 14, 124, 848, 4842, 24018, 105929, 408306, 1399338, 4166224, 10356604, 19877998, 24137569], [1, 6, 15, 20, 15, 6, 1], [1, -12, 112, -778, 4884, -25856, 128015, -594688, 2583636, -9465926, 31342192, -77236116, 148035889], [1, -9, 107, -600, 5158, -26640, 189919, -772560, 4337878, -14633400, 75679067, -184600341, 594823321], [1, -5, 50, -176, 771, -5843, 22284, -181133, 740931, -5243216, 46176050, -143145755, 887503681], [1, 8, 132, 743, 7797, 33802, 309503, 1250674, 10674093, 37635179, 247389252, 554751656, 2565726409], [1, -3, 66, -146, 4087, -5943, 137612, -243663, 6870247, -10062466, 186500226, -347568603, 4750104241], [1, -15, 271, -2530, 26829, -185919, 1470270, -7994517, 49606821, -201152710, 926495071, -2205126645, 6321363049], [1, -4, 230, -749, 23811, -63544, 1431531, -2986568, 52598499, -77763427, 1122326630, -917380028, 10779215329], [1, -13, 126, -1554, 12921, -108347, 968797, -5742391, 36295089, -231354858, 994200606, -5436541409, 22164361129], [1, 0, 161, 255, 12605, 44407, 744938, 2620013, 43878005, 52371645, 1950895121, 0, 42180533641], [1, -9, 234, -2302, 30205, -236741, 2409968, -14441201, 112392805, -522510262, 3239926794, -7601366709, 51520374361], [1, 3, 203, 820, 23862, 100928, 1840467, 6762176, 107116518, 246625660, 4090677563, 4050375321, 90458382169], [1, -19, 351, -3254, 31709, -169223, 1652142, -12014833, 159845069, -1164642394, 8919500031, -34280357669, 128100283921], [1, -3, 133, -274, 18744, -31092, 1356111, -2269716, 99886776, -106590658, 3776966053, -6219214779, 151334226289], [1, 16, 189, 1815, 19499, 139691, 1154286, 11035589, 121693259, 894865785, 7361565309, 49232902384, 243087455521], [1, -31, 824, -13802, 205891, -2327315, 23897248, -193167145, 1418383099, -7891804174, 39105656504, -122110259933, 326940373369], [1, -14, 467, -5503, 93933, -916667, 10735038, -81583363, 744043293, -3879444407, 29300626547, -78176832286, 496981290961], [1, 11, 374, 3862, 74175, 650639, 8888572, 63111983, 697912575, 3524743126, 33109951094, 94460742827, 832972004929], [1, -12, 425, -5263, 90347, -967617, 11622638, -97729317, 921629747, -5422474163, 44225670425, -126121206012, 1061520150601], [1, -10, 425, -3177, 86075, -553367, 11135246, -56996801, 913169675, -3471593679, 47834124425, -115927407430, 1194052296529], [1, 8, 472, 4302, 102944, 916844, 13663255, 98102308, 1178605856, 5270134986, 61869571672, 112204138456, 1500730351849], [1, -17, 401, -3410, 54288, -317402, 5799063, -34596818, 644995728, -4416048890, 56604422561, -261566072333, 1677100110841], [1, 14, 501, 7073, 120649, 1494305, 17336834, 168856465, 1540567081, 10205610481, 81686727861, 257940925102, 2081951752609]], 'euler_factors_factorization': [[1], [[[1, -2, 8, -14, 30, -50, 87, -150, 270, -378, 648, -486, 729], 1]], [1], [[[1, -2, 12, -22, 118, -126, 779, -882, 5782, -7546, 28812, -33614, 117649], 1]], [[[1, -3, 26, -26, 65, 749, -2288, 8239, 7865, -34606, 380666, -483153, 1771561], 1]], [[[1, 1, 13, 50, 38, -516, 1813, -6708, 6422, 109850, 371293, 371293, 4826809], 1]], [[[1, 14, 124, 848, 4842, 24018, 105929, 408306, 1399338, 4166224, 10356604, 19877998, 24137569], 1]], [[[1, 1], 6]], [[[1, -12, 112, -778, 4884, -25856, 128015, -594688, 2583636, -9465926, 31342192, -77236116, 148035889], 1]], [[[1, -9, 107, -600, 5158, -26640, 189919, -772560, 4337878, -14633400, 75679067, -184600341, 594823321], 1]], [[[1, -5, 50, -176, 771, -5843, 22284, -181133, 740931, -5243216, 46176050, -143145755, 887503681], 1]], [[[1, 8, 132, 743, 7797, 33802, 309503, 1250674, 10674093, 37635179, 247389252, 554751656, 2565726409], 1]], [[[1, -3, 66, -146, 4087, -5943, 137612, -243663, 6870247, -10062466, 186500226, -347568603, 4750104241], 1]], [[[1, -15, 271, -2530, 26829, -185919, 1470270, -7994517, 49606821, -201152710, 926495071, -2205126645, 6321363049], 1]], [[[1, -4, 230, -749, 23811, -63544, 1431531, -2986568, 52598499, -77763427, 1122326630, -917380028, 10779215329], 1]], [[[1, -13, 126, -1554, 12921, -108347, 968797, -5742391, 36295089, -231354858, 994200606, -5436541409, 22164361129], 1]], [[[1, 0, 161, 255, 12605, 44407, 744938, 2620013, 43878005, 52371645, 1950895121, 0, 42180533641], 1]], [[[1, -9, 234, -2302, 30205, -236741, 2409968, -14441201, 112392805, -522510262, 3239926794, -7601366709, 51520374361], 1]], [[[1, 3, 203, 820, 23862, 100928, 1840467, 6762176, 107116518, 246625660, 4090677563, 4050375321, 90458382169], 1]], [[[1, -19, 351, -3254, 31709, -169223, 1652142, -12014833, 159845069, -1164642394, 8919500031, -34280357669, 128100283921], 1]], [[[1, -3, 133, -274, 18744, -31092, 1356111, -2269716, 99886776, -106590658, 3776966053, -6219214779, 151334226289], 1]], [[[1, 16, 189, 1815, 19499, 139691, 1154286, 11035589, 121693259, 894865785, 7361565309, 49232902384, 243087455521], 1]], [[[1, -31, 824, -13802, 205891, -2327315, 23897248, -193167145, 1418383099, -7891804174, 39105656504, -122110259933, 326940373369], 1]], [[[1, -14, 467, -5503, 93933, -916667, 10735038, -81583363, 744043293, -3879444407, 29300626547, -78176832286, 496981290961], 1]], [[[1, 11, 374, 3862, 74175, 650639, 8888572, 63111983, 697912575, 3524743126, 33109951094, 94460742827, 832972004929], 1]], [[[1, -12, 425, -5263, 90347, -967617, 11622638, -97729317, 921629747, -5422474163, 44225670425, -126121206012, 1061520150601], 1]], [[[1, -10, 425, -3177, 86075, -553367, 11135246, -56996801, 913169675, -3471593679, 47834124425, -115927407430, 1194052296529], 1]], [[[1, 8, 472, 4302, 102944, 916844, 13663255, 98102308, 1178605856, 5270134986, 61869571672, 112204138456, 1500730351849], 1]], [[[1, -17, 401, -3410, 54288, -317402, 5799063, -34596818, 644995728, -4416048890, 56604422561, -261566072333, 1677100110841], 1]], [[[1, 14, 501, 7073, 120649, 1494305, 17336834, 168856465, 1540567081, 10205610481, 81686727861, 257940925102, 2081951752609], 1]]], 'gamma_factors': [[], [0, 0, 0, 0, 0, 0]], 'group': 'GL2', 'index': 8, 'label': '12-3800e6-1.1-c1e6-0-8', 'leading_term': '14.1388249109664471515191175267787195823960875343428259344846389220100049710180795017911740', '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}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/3800/2/a/bc', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.008463541666666666', 'prec': 67}, 'plot_values': [14.138824910966447, 14.080678894296257, 14.015763612742012, 13.937237418388344, 13.838386553733907, 13.712682798255297, 13.55386314279592, 13.357441427001111, 13.12492330687257, 12.859383704950043, 12.563989243592914, 12.241959657967866, 11.89653162556549, 11.530580186461043, 11.145615489310408, 10.742910548153574, 10.323857410092696, 9.889962850426302, 9.442843015218667, 8.984294431787408, 8.516497565612, 8.041736626572124, 7.5623032836134705, 7.08048282902194, 6.598540379629731, 6.118692224445071, 5.643053528259918, 5.173680823301476, 4.712575712329715, 4.261672239161994, 3.822824487917769, 3.3977997635827335, 2.988280013148076, 2.5958302115157723, 2.2218820737120297, 1.8677244961394006, 1.5344948607099786, 1.223172990187227, 0.9345783981722261, 0.6693576203195584, 0.4279779753242485, 0.21072459059892729, 0.017698738726954683, -0.1511809357838349, -0.29617448402735924, -0.4177254798377695, -0.516458290104071, -0.593171841093422, -0.6488319045438937, -0.6845614906670127, -0.7016302501726979, -0.7014456323847291, -0.6855393829682042, -0.6555520006998162, -0.6132160687210105, -0.5603389593510721, -0.4987859954126049, -0.43046046077858535, -0.3572824071955396, -0.28116729989279665, -0.2040045004109454, -0.12763642027165328, -0.053838924773597044, 0.015702273570137027, 0.07941323499845158, 0.13585172977172158, 0.18372594017782823, 0.22191141855664293, 0.24946660656488723, 0.26564901963835047, 0.26992758693688185, 0.2619920843319559, 0.24175999319478964, 0.20938100492131118, 0.1652402172828147, 0.10995673140452113, 0.04437844524602788, -0.030426188762832845, -0.11317954909108421, -0.2024084928378968, -0.2964591080431225, -0.3935195340960875, -0.491644740908375, -0.5887831720770912, -0.6828057068547712, -0.7715359067021396, -0.8527810580131477, -0.924369861305689, -0.9841891773023917, -1.030220386885019, -1.0605757361162789, -1.0735341438409305, -1.0675771153803102, -1.0414245685723276, -0.9940669450102058, -0.9247943391341013, -0.8332224757256391, -0.7193159518890707, -0.5834103247895378, -0.42622517046733094, -0.24887202715399012, -0.05285754353755671, 0.15991898660706771, 0.3871724498181456, 0.6262413936651915, 0.874112264906949, 1.1274479650884082, 1.3826210862997415, 1.6357528732749886, 1.8827564299486512, 2.1193833080768454, 2.341282747361987, 2.544062207656038, 2.723349958757127, 2.874860248068471, 2.994460075623119, 3.078237992720441, 3.122575314578834, 3.124214259480246, 3.080323524329674, 2.9885607529092253, 2.8471317523802875, 2.654847602438478, 2.411171472781904, 2.1162581805997682, 1.7709862695982304, 1.3769812773427916, 0.9366303921967906, 0.4530890259080899, -0.06972856522124181, -0.6271684116765285, -1.2138663073590783, -1.8237884719244848, -2.450283950649074, -3.0861500312693475, -3.7237046492232118, -4.354868537545312, -4.971256678233312, -5.564277655985456, -6.125243104519945, -6.6454900182390615, -7.116487605615175, -7.529951608694039, -7.877962709998885, -8.153084398212428, -8.34848361836867, -8.458055725511857, -8.476511266175946, -8.399466551385796, -8.223530646781821, -7.9463820261032385, -7.5668366202608786, -7.084902614676545, -6.501795695219039, -5.819953499689678, -5.0430391906603935, -4.1759290742975335, -3.2246796679758436, -2.196458080393245, -1.0994720266155282, 0.05710739634260021, 1.2632385828878625, 2.5081156201936605, 3.780303914570303, 5.067935943780332, 6.358823725683215, 7.640589317128611, 8.900813369879854, 10.127186538578545, 11.307694481345886, 12.430880297827793, 13.48591431119194, 14.462699604776274, 15.351998289955423, 16.14554778440226, 16.83621141057226, 17.418213926530893, 17.887086060719657, 18.23966956708013, 18.474149164523993, 18.590067093733456, 18.588372267353048, 18.471551991468047, 18.243423777450673, 17.909014943016796, 17.4744795504239, 16.947001229598946, 16.334732444683002, 15.646806742565966, 14.89303153803133, 14.083689485799624, 13.229388435544038, 12.340909843316133, 11.429095910584968, 10.504795888903583, 9.578572416722983, 8.660520881953108, 7.760142630237092, 6.886230686696758, 6.046792860456983, 5.249017655268905, 4.499103107247091, 3.8021815096168208, 3.1622913470975136, 2.5823678307314104, 2.064261962991423, 1.608784195162958, 1.2156961254804444, 0.8837631851942217, 0.6108357154025426, 0.39394233158676123, 0.22939570051641056, 0.11290444313527416, 0.03967634678027247, 0.004542486857345763, 0.0020858572279337847, 0.026767842623168513, 0.07304957278609378, 0.1355045565833621, 0.20892779087671617, 0.2884359911107975, 0.3695545324817217, 0.4482900324033373, 0.5211874039905925, 0.585371868869375, 0.6385778783851821, 0.6791594581966869, 0.7060837150104018, 0.7189089428275248, 0.7177491792651539, 0.7032282072064231, 0.6764188542546556, 0.6387724698420792, 0.5920415894609578, 0.5381977260016024, 0.4793474037873191, 0.41764938899169335, 0.3552289997352567, 0.2940981075523154, 0.23608245089404672, 0.18275740035894467, 0.13539408435103617, 0.09491708446364076, 0.06187247715958302, 0.036410226312363424, 0.018280525191763805, 0.006843630838002169, 0.0010927622650472584, -0.0003107854296633312, 0.0010085893346905876, 0.003196985783120728, 0.004235282300279089, 0.0020095498296864925, -0.005614514642539024, -0.020715517326737796, -0.04524087721739967, -0.08093400515875164, -0.12926637255200712, -0.19137654131971543, -0.2680186214782858, -0.35952337592589084, -0.46576872817245596, -0.5861629864961, -0.7196418919260379, -0.8646794960585613, -1.0193150030487528, -1.1811987680315053, -1.3476386379767216, -1.515659124275403, -1.6820719045510797, -1.8435542004598757, -1.9967369592733555, -2.1383045554519824, -2.265071208709933, -2.374062457522129, -2.462596851217723, -2.5283619163956823, -2.5694859930280467, -2.584604200085554, -2.5728861106026293, -2.5340613552976903, -2.4684360083725774, -2.3768947003250323, -2.2608883322739786, -2.1224007321781007, -1.9638941064814992, -1.788251952724315, -1.598712959280066, -1.3987955518410353, -1.1922090373657814, -0.9827402610797812, -0.7741676610021592, -0.5701760008714434, -0.37426972165186173, -0.18969088612757387, -0.019332654190401467, 0.13436428398957415, 0.2694374655085863, 0.38442980672769633, 0.4784134122327551, 0.5509995643422166, 0.6023471881728284, 0.6331797647245077, 0.6447084588080864, 0.638568722423768, 0.6167594084987051, 0.5815732591956382, 0.5355299837206943, 0.4813164468936221, 0.4216623217317102, 0.3592444339561691, 0.29660595823262337, 0.23608177200056515, 0.17973594895090383, 0.12931057129511955, 0.08615872734045177, 0.051210434561501886, 0.024959053447492465, 0.007462618680634564, -0.0016400974863821816, -0.003102183712679636, 0.0019717491128332146, 0.012184424415581051, 0.02591528899233714, 0.041397018792397225, 0.05679582509703479, 0.07029299239835057, 0.080171801774728, 0.08489879098140138, 0.08319658795571226, 0.07410649583781238, 0.05703894614062514, 0.03181199620818431, -0.0013274786350408114, -0.04170215411795437, -0.0882208657179484, -0.13941310959318182, -0.19347949397772982, -0.24835551481712742, -0.30179605431607587, -0.3514701246530689, -0.3950626269871825, -0.4303804813609128, -0.45545893622473405, -0.46866483723448094, -0.46879614389075713, -0.4551678124655821, -0.4276815353916462, -0.38687660370295396, -0.33395939507217615, -0.2708100746609442, -0.19996141491099004, -0.12455039450685212, -0.04824325221769139, 0.024865202433753612, 0.09037595078994207, 0.14373131669747008, 0.18037987217388374, 0.19595385988487043, 0.18645444450086063, 0.14843943833696266, 0.07920736070438283, -0.02302886360873109, -0.1589838160937433, -0.32816353616752586, -0.5287574320512536, -0.7575634008488646, -1.009952624177654, -1.2798806945667218, -1.5599318077168247, -1.8414090704012611, -2.114471529634264, -2.368315615061767, -2.5914018127166, -2.7717216011224384, -2.897072076272824, -2.9553646546191272, -2.934956887644889, -2.8249961578831115, -2.6157619996684582, -2.298972465406683, -1.868080395776676, -1.3185576202236768, -0.6481460581284517, 0.1429318226057784, 1.0518422175883302, 2.073170009633709, 3.1988594193689965, 4.418222410572832, 5.718030945810825, 7.082672369765811, 8.494445463809297, 9.934129004907781, 11.381176172808459, 12.814023532209985, 14.210499697212398, 15.548261954468224, 16.805383042193252, 17.961253462889, 18.996713578435184, 19.89434644526768, 20.63886070256871, 21.217436639319057, 21.620192293778704, 21.840933073762724, 21.87682921984079, 21.728319987997672, 21.399110442526553, 20.896099558698317, 20.229402335601506, 19.412589393855246, 18.461840598341258, 17.39540638879673, 16.233197490240144, 14.996342661305198, 13.70684593423016, 12.387405493632489, 11.060440665520678, 9.747475294779246, 8.46869107337141, 7.242522230478694, 6.085366176445419, 5.011416708561463, 4.032123247707695, 3.1559658570052047, 2.3883927060603645, 1.7318357853401687, 1.1858236518562046, 0.747168954198369, 0.41008142084406884, 0.16645989171352624, 0.006267051494279941, -0.08205765339436732, -0.11115841396543603, -0.09431825594209269, -0.04501379405462858, 0.023544806786255888, 0.09884914609743253, 0.1694867578901384, 0.22548327881177785, 0.2585879821922599, 0.26250269774155566, 0.2330315850722517, 0.16815070317774242, 0.06799891474082591, -0.06520467668969612, -0.22730626076990113, -0.4124430768716646, -0.6133283293850582, -0.8215813887187773, -1.028092526627595, -1.2234068155708988, -1.398112931955249, -1.5432421151600775, -1.6506428523912575, -1.71332032997315, -1.7257312825881708, -1.6840233968385212, -1.5862107579483635, -1.432284984581489, -1.224251009164379, -0.9660876963141813, -0.663635534242291, -0.32441145205914146, 0.04264995092697017, 0.4274888834492907, 0.8192589508536232, 1.206700494194121, 1.5785328707969315, 1.9238617466276815, 2.2325978135580544, 2.495792265520694, 2.7059514646266507, 2.857313584492175, 2.9460679470797704, 2.97051959959976, 2.9311960321360635, 2.8308039975446166, 2.674141168224744, 2.467947294628031, 2.220686261192564, 1.9422696915677726, 1.6437239652758926, 1.3367816272828001, 1.033472320728061, 0.7457062184657123, 0.4848558871463092, 0.26134845012467556, 0.08427961965037997, -0.03891324312183431, -0.1027199782398493, -0.10376620035859452, -0.04095333821211115, 0.08447911084448692, 0.26899430663681007, 0.5068753189591594, 0.7904040560145785, 1.1101067216292948, 1.4550586148013127, 1.81326199079682, 2.1721348448431375, 2.518907658716161, 2.8410329977285365, 3.126604566019604, 3.364756774655948, 3.5460737000097136, 3.6630490434277454, 3.710239480359363, 3.6844030944099844, 3.584602859894778, 3.4122352737573367, 3.171026943210638, 2.867030384625296, 2.5082650269787683, 2.104390016185374, 1.666372095766504, 1.2061142084087142, 0.736083448295331, 0.2689483464228942, -0.18296785077622074, -0.6081220123723374, -0.9961185429911577, -1.338031135804084, -1.6266649885237068, -1.8567707380042475, -2.0252210381112747, -2.131059192993202, -2.1754587224693824, -2.161607186722854, -2.0945278712548, -1.9808602951971475, -1.8285325899063316, -1.6463920704947543, -1.443815868228608, -1.230310546439659, -1.0151226025019344, -0.8068750162746847, -0.6131879373579264, -0.44036829927985705, -0.2931688832672666, -0.17461739471855556, -0.08592292330351546, -0.026459721670656487, 0.00617821945569664, 0.016031835597333146, 0.0085564724715535, -0.0096617388112246, -0.031240762789597795, -0.048375856813032504, -0.05323904480405039, -0.038384410646314114, 0.002858946639536213, 0.07602281333761575, 0.1851799458010006, 0.33268210743231524, 0.5189723529462731, 0.7424792545400666, 0.9995986640029751, 1.284765953374724, 1.5906200595029225, 1.9082607218271679, 2.2275741080091596, 2.5376242660658095, 2.827097355361383, 3.0847806585778947, 3.3000627317330813, 3.463439987089381, 3.5669687478844345, 3.6046810559278226, 3.5729429734043303, 3.4707340632226797, 3.299833893748754, 3.0648974790213064, 2.773413157607101, 2.4355583857847454, 2.063946031323787, 1.6732641004109972, 1.2798091470660182, 0.9009186075331553, 0.5543987571427308, 0.2578997521382805, 0.02825982114775606, -0.11915098457675065, -0.17106545728033745, -0.11687663012184599, 0.050925359361861065, 0.3363703479351456, 0.7397214053641405, 1.2573058770998893, 1.8815145652249585, 2.6010839507353074, 3.401330364522702, 4.264491484655584, 5.1702018429650325, 6.096066405577727, 7.018422148004682, 7.913441119816493, 8.757670598220246, 9.528668807000955, 10.205706023571642, 10.770421887819724, 11.207571950495982, 11.506012564610419, 11.658626179827921, 11.662370412156225, 11.518345549532524, 11.231731134076453, 10.81174362547278, 10.271717415204751, 9.6280946718686, 8.89967134531083, 8.10693728833262, 7.271371825168165, 6.414816010080102, 5.558958450030629, 4.72419631919908, 3.9288829314072813, 3.188787537027343, 2.516665989343184, 1.9219923034604465, 1.4108353699978222, 0.9856326064057791, 0.645297922556945, 0.38552328393760577, 0.19920556137715542, 0.07698341184480287, 0.007848222792357168, -0.020198338177265473, -0.019406667636184916, -0.0015406774020014786, 0.022819797542943245, 0.04490462532224752, 0.058282774069997795, 0.0592760491948733, 0.047215993712023056, 0.024529486841477523, -0.003353044756479544, -0.028266272827979545, -0.03975182794081523, -0.025674564367596357, 0.027021012399777628, 0.1314443174652908, 0.29981553714778647, 0.5424796466911749, 0.8669031867473366, 1.2767331222457865, 1.7709537441920777, 2.343177964070432, 2.981113318530926, 3.6662299183081375, 4.373649742123997, 5.072329910097439, 5.725509297758238, 6.291418800876575, 6.724250518866773, 6.975366394398848, 6.994717060946929, 6.732429556344027, 6.14051956854534, 5.1746750638600885, 3.7960527688337953, 1.9730114292507965, -0.3173304335443672, -3.0876586470188525, -6.339243329875542, -10.061005665229269, -14.22891058833312, -18.805806750032414, -23.741900603617033, -28.975180368610488, -34.432280828220236, -40.02979203958293, -45.67592625533709, -51.27269631542173, -56.71879133403392, -61.91153346698726, -66.7492263921652, -71.13374535066956, -74.97312875351356, -78.18432938448781, -80.69618501634578, -82.45062341933755, -83.40409731871225, -83.52893472563461, -82.81431503253323, -81.26696243349593, -78.91138316279383, -75.78862656201196, -71.95522836699982, -67.48195934233628, -62.45221789978188, -56.959987437803285, -51.106940568001406, -44.99978564534488, -38.74781555327579, -32.46039708756606, -26.24448847796787, -20.201875347427233, -14.425576631593941, -8.998606919172387, -3.9927520109455275, 0.532636425133638, 4.53150756281485, 7.972114435601092, 10.838649222812991, 13.1294865100471, 14.855917490336443, 16.04107040944863, 16.718588026449805, 16.931526737141578, 16.73177519974059, 16.17665961690598, 15.326551789938863, 14.242988285328591, 12.98689534078746, 11.617208421236114, 10.189959502477702, 8.755952555183846, 7.359516079261002, 6.037841383683668, 4.82060552412735, 3.7299568723947254, 2.780800054197658, 1.9807212844726496, 1.3305457672335592, 0.8251900856749858, 0.45463705310662555, 0.204998298057227, 0.0595884010191186, -8.046131008650813e-05, 0.006761073264390693, 0.06112609477171201, 0.14512856448671851, 0.24268477797535784, 0.3400407653114247, 0.42615461280146205, 0.49290185385927293, 0.5351035518574386, 0.5503953757444515, 0.5389594129947077, 0.5031476506613669, 0.4470262149602724, 0.37586322743213463, 0.295596744103743, 0.21231521874359113, 0.1317796022171589, 0.05901201405896401, -0.0020309503737025174, -0.048682952227250324, -0.07968281343977049, -0.09517789936155385, -0.09662029060633542, -0.08656535670943487, -0.06838840326046602, -0.045941623917778965, -0.023173200241398483, -0.0037330721897262955, 0.009409058283251082, 0.014306973160785224, 0.010318483721298653, -0.0016922096334143935, -0.019245809368668113, -0.03824373730713386, -0.05307498583793976, -0.056832831939052184, -0.04161974453592566, 0.0010623789256067875, 0.07985196842483876, 0.2030187535616591, 0.3779368627062626, 0.6105999844492954, 0.9051564799419843, 1.2634917258645675, 1.6848906184746222, 2.1657978844029384, 2.6997351431630316, 3.2774884314378223, 3.8872293486978235, 4.514767981651196, 5.1439503920389456, 5.757161159594014, 6.3360114583660545, 6.862345799641403, 7.318740773885959, 7.689096341037734, 7.959281362937724, 8.11772803532371, 8.156080989026652, 8.070011425264454, 7.85909698684589, 7.526780026049168, 7.080310503272384, 6.530548991684162, 5.891745179278262, 5.181348791023904, 4.418976020402173, 3.6255820083158197, 2.822710764745872, 2.0317281221425794, 1.2731157063996494, 0.5658221584486528, -0.07367083346414344, -0.6319505657937529, -1.099072876009688, -1.468816049662323, -1.7387845848552261, -1.9104070257642687, -1.9887711786221967, -1.9822286916053193, -1.901863338833494, -1.7608591811763898, -1.5738143219695937, -1.3560457765288694, -1.1227704281987392, -0.8883370639164043, -0.6655440330138117, -0.4650576832384344, -0.2949623967458795, -0.16045450088120547, -0.06365302222468998, -0.0036115043139504774, 0.02349155157053553, 0.02400365098263632, 0.006309814220242995, -0.019769023528005195, -0.043667953167818616, -0.05482361506096623, -0.04342918567984825, -0.0011584424304121642, 0.07818018464461272, 0.19809898414220276, 0.359030648670762, 0.5580918907267249, 0.7890304153399716, 1.0423655172320359, 1.305736275700225, 1.5644816177382992, 1.802323942238235, 2.002187610019415, 2.147126269895036, 2.221309886194773, 2.211068655001469, 2.1060051261991393, 1.8997688941633994, 1.5907427953313031, 1.1825894771133323, 0.6845862896401994, 0.11178332177332584, -0.5149833517377845, -1.16974645484021, -1.8221971191554012, -2.438651390554495, -2.9832298737076277, -3.4191520366585304, -3.710065275719845, -3.821833379172362, -3.7241666176013033, -3.39212295683909, -2.807485398211876, -1.9598966187630693, -0.8476453886990012, 0.5214966729388787, 2.1299113265160563, 3.9501880236434435, 5.945549055448009, 8.070716889822167, 10.273279735407236, 12.494956551245739, 14.673271231586437, 16.7435171158011, 18.64088165425613, 20.30272576993241, 21.670940286481702, 22.693764080811416, 23.327626609476837, 23.538846167549366, 23.305047793794635, 22.616223192099568, 21.47518535437637, 19.89756710913671, 17.911572117664267, 15.557336260200016, 12.885899156121454, 9.957625566450524, 6.839699952706468, 3.6043212570935634, 0.32669993946152454, -2.917166512575904, -6.052739037987299, -9.009470897799293, -11.724036657498424, -14.14137026837728, -16.21581858603012, -17.912270900966117, -19.206939353658694, -20.088136921443233, -20.55737873716173, -20.62780718126691, -20.322952954089804, -19.675559047240284, -18.726152638500118, -17.521678713588113, -16.114369975130725, -14.55884447927504, -12.909910389758663, -11.220755402921005, -9.541289453929153, -7.916803587935282, -6.3869693015045925, -4.984365966792237, -3.733761973818161, -2.651872080513099, -1.7474359968659847, -1.021618449325984, -0.4686702148965743, -0.07668437987728749, 0.1713151456023617, 0.29612240132709383, 0.3210320711553762, 0.2705161695536928, 0.16895334022418076, 0.03945032654275518, -0.09719390032904289, -0.22332983167408846, -0.3250757893583645, -0.39269752585310647, -0.4207462436478468, -0.4079476280925356, -0.3568681107680821, -0.2733855745057928, -0.16599842612815524, -0.04501326333803757, 0.07834296439536562, 0.19281991942657875, 0.2880153499230506, 0.3551771686014541, 0.3878930987061838, 0.38263143145015643, 0.3390917612608894, 0.260352772183846, 0.1528376448015802, 0.026085772432250704, -0.10766260204889468, -0.23405893045197382, -0.3373926814526105, -0.40137138561458247, -0.40996258724548346, -0.34826408025926464, -0.2033559798403299, 0.034918883564108334, 0.3733657549594934, 0.8149792567324952, 1.358600121746427, 1.9987391611182983, 2.725578385677249, 3.5252433284760625, 4.3805514625673085, 5.271478942419764, 6.175763399256652, 7.069662441481598, 7.9287792769181715, 8.72910918318683, 9.448547130553823, 10.067289480828139, 10.56834935929037, 10.938124339786924, 11.166841275985304, 11.24908732894904, 11.184631857600692, 10.97769608662637, 10.636473617587932, 10.172741465506576, 9.601361293071026, 8.939870184924093, 8.20827285218744, 7.4276293512371545, 6.619104661093218, 5.803254934783409, 4.999377126318298, 4.225033276188429, 3.49576176107113, 2.824291305993548, 2.220221455441618, 1.689955498887504, 1.2367624958012022, 0.8609810046141244, 0.5603251277646538, 0.3301111985178702, 0.1636932849103325, 0.052975102270261726, -0.011066634708963132, -0.03787098973708768, -0.036823277645607305, -0.01683710111745667, 0.014017855649118996, 0.048806065710082676, 0.08192419536911326, 0.10920526267456794, 0.12793363820364062, 0.13678289323573706, 0.1356778012120102, 0.12559613324997104, 0.108328021609122, 0.08621108166370775, 0.061859310726733376, 0.03790036465894403, 0.016738952235551694, 0.0003592616836528182, -0.00982401146328328, -0.013059695923580396, -0.009296001613445869, 0.0008406296497799807, 0.016117669044244033, 0.034812441309446704, 0.05486208570182752, 0.07403683676203265, 0.09012476738340906, 0.1011059327983961, 0.10531101240876295, 0.10155436847675908, 0.08923207928408268, 0.06837846202138555, 0.03967339705104528, 0.004401131975736503, -0.0356280165995682, -0.07819135675790562, -0.12079651808226992, -0.16084777634634373, -0.1958312179133197, -0.22347514347836933, -0.24189750411985736, -0.24973315802864315, -0.24623042413438412, -0.2313138001747025, -0.20560539718684365, -0.17037708949779282, -0.12747468287363076, -0.07921166671831201, -0.028234307253264618, 0.022637355142709734, 0.0705947469062524, 0.11301311883692824, 0.14760434377356504, 0.17254997686914844, 0.1866063956664872, 0.18918276464081576, 0.1803929105693783, 0.16101971988269828, 0.13244939882383872, 0.09657743179234633, 0.05568575099323399, 0.012301254093471692, -0.03096155802107487, -0.0715849450850335, -0.10730564773280957, -0.136247967791758, -0.1570293219948131, -0.16883503251719395, -0.17146502102952316, -0.16532379180513523, -0.1513659798055134, -0.13100793608902597, -0.10601077378043093, -0.07834593796826231, -0.05005268974589631, -0.023074790044014436, 0.0008834448355977228, 0.02047497279990116, 0.034796545458545644, 0.04343764056677236, 0.04649021033153361, 0.044517413970126915, 0.03847736867156962, 0.029612159734303933, 0.0193122552035973, 0.008968240892612668, -0.00017716869233145823, -0.007164704538576351, -0.01142330400521457, -0.012830742403563225, -0.011719282019225351, -0.008818439659663788, -0.0051306997751777925, -0.0017393594763535586, 0.00044437861797782564, 0.0009837409166430346, 0.0002520954040504576, -0.00021855021110884357, 0.002599165485695079, 0.013525797136044803, 0.03940682183023939, 0.08925105485675931, 0.17425054537655868, 0.307662598287691, 0.5045489200994713, 0.7813533154658657, 1.1553180857892287, 1.6437491313674792, 2.2631459755896004, 3.0282544266737546, 3.951171477086403, 5.040308302085057, 6.29937480222702, 7.726455496209256, 9.313210882664908, 11.044393419648566, 12.898018478850284, 14.845131508796996, 16.84993496777775, 18.870322185568604, 20.85872846625857, 22.763615686015015, 24.532071536470006, 26.11085598118648, 27.447954329114765, 28.49451300623288, 29.206824210116856, 29.548759972885133, 29.49508574271689, 29.0316532307395, 28.156067099678502, 26.87845220630816, 25.221820390618348, 23.222450749558732, 20.930497797345463, 18.40711859538478, 15.722254521763926, 12.952525162018794, 10.178797530211455, 7.483743445702122, 4.949371419346036, 2.6527696616449603, 0.6629290144332121, -0.9618829944536783, -2.176425633947861, -2.9503668800435974, -3.269861029080852, -3.13865443165874, -2.578090500542322, -1.6263758382070097, -0.33719906462252663, 1.2221965569064146, 2.973409167368774, 4.8302538830428166, 6.702413975418902, 8.49921950417077, 10.133468966777189, 11.525173937944261, 12.605255248704143, 13.318823493328782, 13.62774173888994, 13.512493340625825, 12.973288650003614, 12.03045615590766, 10.72423318469426, 9.113142512629771, 7.271631357079999, 5.287082027771582, 3.256239082582053, 1.2812468878171033, -0.5345572817283673, -2.0913473355417382, -3.2972655903029495, -4.072535764928602, -4.353120665539813, -4.093761384900791, -3.2702656516060307, -1.8809838793322333, 0.05268078263486861, 2.486725832965008, 5.355943938302722, 8.576309891529839, 12.048472625842173, 15.661386383506189, 19.296501164196993, 22.832365032468978, 26.14937684268682, 29.134763773600476, 31.68788901793738, 33.72346562519986, 35.17456998254466, 35.995176438146366, 36.16185803793426, 35.67488869774618, 34.558837183657296, 32.86017192492888, 30.644813784755947, 27.995283998312132, 25.00721887449914, 21.785542488435077, 18.440329461796992, 15.081443395029803, 11.814018388063326, 8.734436376191365, 5.926732426110027, 3.4595272398274166, 1.3834228627240206, -0.2705626705133817, -1.4914643766491542, -2.2879933282101654, -2.687349763310658, -2.7333827462653355, -2.484236464161945, -2.008773141547983, -1.382832412358626, -0.6854110585800796, 0.005180460654217617, 0.6149758809032843, 1.077670796076612, 1.3378125732746708, 1.3531819685326256, 1.0964383306918781, 0.5560507710423214, -0.26356336131101543, -1.3428348429757164, -2.6483053909995196, -4.1345438082466925, -5.746585826172427, -7.422732064250153, -9.09772866214819, -10.706494052275284, -12.186953939909158, -13.48272933034124, -14.545585326995056, -15.337429078357177, -15.832006419044674, -16.01650044940275, -15.891154074983607, -15.468605212846462, -14.772873583570172, -13.837864309089328, -12.705644880858761, -11.424669932029351, -10.046691157609073, -8.624055404678268, -7.207281438202672, -5.842838501807521, -4.571285570526471, -3.4258183623098946, -2.4308220008937487, -1.6011984918216204, -0.9422882901240396, -0.4502785138987656, -0.11305989043475552, 0.08854783826766263, 0.1792852702285213, 0.18766184854902937, 0.1440451714112429, 0.0787487708792371, 0.02021903225489662, -0.006589931353115399, 0.01842747433708622, 0.10951462825266169, 0.27442303959941605, 0.514187292884694, 0.8233078651844381, 1.1903325097022288, 1.5987581686573185, 2.028203905318961, 2.455788263573721, 2.8576275471794057, 3.2103795247777356, 3.492744454533439, 3.686739160380693, 3.778788492352946, 3.760565198679267, 3.6295217705622536, 3.389072378648771, 3.048358246240505, 2.621740641330701, 2.1280441002969264, 1.5895546323104695, 1.0308302427271905, 0.4773333107920183, -0.04610261887670293, -0.5164212059605074, -0.9134503535458165, -1.220901232724528, -1.4271616147828332, -1.5258840199667085, -1.5162972180516079, -1.4028966475109637, -1.1950406503909385, -0.9063721364845799, -0.5540401274059008, -0.15772612688833768, 0.26161725559945376, 0.6829266343201086, 1.0860521497573798, 1.4527051934491084, 1.7672805337334758, 2.0176121974089924, 2.1957554789969174, 2.297953316463637, 2.3244790650335925, 2.279362639019281, 2.169940954712417, 2.0063453798187627, 1.8009881967514643, 1.567419541532049, 1.3193998793045307, 1.070116256721585, 0.8314878191019494, 0.6136230328366175, 0.42442699273218965, 0.269160554253981, 0.15034148905483796, 0.06786704371728934, 0.019291397593686897, 0.00023093221757365572, 0.004852178668795117, 0.0264218122081278, 0.05790979811192085, 0.0925657037142258, 0.12442427539474478, 0.14870900651795368, 0.16211640778999828, 0.16296786898022667, 0.1512060058501044, 0.12824707706592015, 0.09670989136777434, 0.06005082583249825, 0.022140949769100967, -0.013193066789430935, -0.04260738925036079, -0.06361618950701935, -0.07486768930858556, -0.07629053555809932, -0.06908989839639776, -0.05558289438958373, -0.03887210517220312, -0.022373299888015823, -0.00922490595793027, -0.0016175747832815987, -9.165921256825851e-05, -0.0028567642317464986, -0.005188896219779273, 0.0010383865848444319, 0.02763566279806995, 0.09014817609552586, 0.20765518187527182, 0.40229572982119494, 0.6985115423950162, 1.122019837680191, 1.6985433394754557, 2.4523836939389976, 3.4050411573650896, 4.573649780940219, 5.96942689341302, 7.596250916733393, 9.449428083017022, 11.514924665428344, 13.76958271057935, 16.180796135649512, 18.706674516575234, 21.296772516075137, 23.893247975362193, 26.432894942880854, 28.850762648855785, 31.081453049899288, 33.061029616240184, 34.72938331719826, 36.03257914873549, 36.925771314996915, 37.37734981936706, 37.36856618274922, 36.89381160309447, 35.9610772021457, 34.59192348325989, 32.821607690254694, 30.699790022249033, 28.286483514048218, 25.649154432277278, 22.860265107794252, 19.994650483281593, 17.127229036519726, 14.331165485181609, 11.673482733001395, 9.212355462539852, 6.995324918300596, 5.058000556821072, 3.423409269096547, 2.1018808145899612, 1.0906669203529715, 0.3748285450888251, -0.07120189122954762, -0.2816684601216373, -0.29725762805454964, -0.16274422005117267, 0.07548160278550671, 0.37194753676776293, 0.6844268442413662, 0.9759374492078077, 1.216324610550756, 1.383389503722254, 1.4635433543865348, 1.4518788286818742, 1.3517005530150519, 1.1735755146966844, 0.9339886521573062, 0.6537089495037748, 0.3558994941143913, 0.06415590838933302, -0.19939340947039447, -0.41580919889614637, -0.5707767051619446, -0.6556688362931133, -0.6681541294100724, -0.6123056176058009, -0.49820587468857946, -0.34106927263757536, -0.15993343412357602, 0.024004380606685798, 0.18930314473940513, 0.3163080402423598, 0.38917174818270256, 0.3977334534626189, 0.33912024664271023, 0.2189345220589104, 0.051949271402129654, -0.13774793586779446, -0.3172160142076613, -0.4457420867934217, -0.47652977000229485, -0.3588959095612197, -0.04079568717310254, 0.5283231499155892, 1.3944775438096582, 2.596074025245807, 4.1610665037188115, 6.104885791676953, 8.428472603946767, 11.116800177407397, 14.138095242336057, 17.443776813754624, 20.969588970958142, 24.638831201414632, 28.364082881464768, 32.04970442336083, 35.59512073186521, 38.89844888655011, 41.86115376870563, 44.39471739039606, 46.42230344810194, 47.88103672241341, 48.724510711778166, 48.92469777272923, 48.474138098185776, 47.38918140657943, 45.70635484910843, 43.47982061498074, 40.779145238964674, 37.68651472450705, 34.29422676978043, 30.702843098966483, 27.014442856677867, 23.327975175379013, 19.735715004820946, 16.320138583319675, 13.151648287064603, 10.287135055473518, 7.7671119570322995, 5.614974306930211, 3.837467250218594, 2.4258698627866577, 1.3578625615113205, 0.599863652036628, 0.10939092123126205, -0.1618832340635844, -0.26492981980572944, -0.2502911337502283, -0.16529236808108472, -0.051672752394967464, 0.05630733485092888, 0.13317380402174228, 0.16287376036504694, 0.13873635205674087, 0.06279860074572333, -0.05543066912998314, -0.20068214676529586, -0.353985246327221, -0.4949218266333185, -0.6039181364351169, -0.6644252667213566, -0.664848045661235, -0.6000452523018349, -0.47233622418319826, -0.2919420016308519, -0.07681955635408784, 0.14811284705912814, 0.3523353067890233, 0.501570240035557, 0.5599874601019579, 0.4926575754502315, 0.2681088859083594, -0.1391770826928591, -0.7465535386163829, -1.561388613676909, -2.5797092625640325, -3.7854336736813727, -5.150267455114282, -6.634398455887372, -8.18820399708566, -9.754131333583278, -11.269138017425531, -12.667633837736327, -13.884727302872621, -14.859849071284522, -15.540807367420774, -15.886163515311983, -15.8675469720549, -15.471663202132609, -14.701667771059322, -13.57793649135628, -12.13817565974463, -10.435856762883835, -8.53821289320868, -6.5236699932744315, -4.478665199541316, -2.4937490753422, -0.6583525714918921, 0.9433632272718406, 2.235805031323243, 3.1549047258580143, 3.6505710882666094, 3.6878287966099044, 3.246574926292219, 2.326479599989336, 0.9495495699496856, -0.8391416233775826, -2.9719185319863475, -5.360810306330098, -7.91060289697593, -10.53699991109142, -13.173401115508232, -15.773988934040291], 'positive_zeros': ['0.35630216519218056329676458584926', '0.53123580245396223865020900895315', '0.64836615162937481688212384811390', '0.856980305515190160249224023033419', '1.09070139763871223489935896850782', '1.35375753140645687279696808281929', '1.81450089913514348343164485599288', '1.81764494964424915577628759078931', '2.09438419404373246788619638318771', '2.10241663233512773714292129046262', '2.13585591453109941088560000511201', '2.49775783671414909583897896506028', '2.69761580071139637903617648115081', '2.71447115400875784857741886768743', '2.81805441937401220809702193758300', '2.99314187427319959733149592097299', '3.06211752652064591989601183391796', '3.24856094615183467759307554723439', '3.64822751435999229273070736383900', '3.68736162001612522648546472760616', '3.76237981341429066971916659831760', '3.92612465456304242242161633044383', '4.13553955410216834044883967171744', '4.16731602832766746146318495392416', '4.38910394051291516032485622432951', '4.59347935005849135591508890249829', '4.61701829129899550253402431990734', '4.66297613549990937181686433619118', '4.91861340359546945426079449182924', '4.94913892662016626665419444919265', '5.29972771255407428710353868248651', '5.32413634959572448154561838826782', '5.38180299476045708055427866308998', '5.41321279029075149395497257224035', '5.60178943150960447263163578974375', '5.93189348810692270618568733099816', '6.16989474234417847559354766663567', '6.17632277907059523307994150235210', '6.32194987077122756093635761031971', '6.40041945442112974218599089877504', '6.43133618049960926916116571015586', '6.48292021786272679408721966234429', '6.77826896861966964435603104157382', '6.94084540561536914241874896910509', '6.96766724839201932336989052012532', '7.00797499074930254407259386262233', '7.17017583187146722531641021754403', '7.28406177307473383044538228023716', '7.49954126680397315789082538925661', '7.74631570886238804258717937598843', '7.79735849558926592157435627185866', '7.88262285644955743386402446511326', '7.965851142391985490776457348671020', '8.030850053255728568508737705346034', '8.376963025151224042851706333394478', '8.409150990111643167304373408957612', '8.523013777818940021717068522526718', '8.556083496164942584725183680010848', '8.659175646472029505471538419614561', '8.789820957144421385365500408544490'], 'prelabel': '12-3800e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.508461923993535, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1e6-0', 'trace_hash': 35569433097744782, 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.35630216519218056329676458585', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '0.53123580245396223865020900895', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '0.64836615162937481688212384811', 'prec': 103}}
• lfunc_search •

  Column	Type
  algebraic	boolean
  analytic_conductor	double precision
  bad_primes	bigint[]
  central_character	text
  conductor	numeric
  conductor_radical	bigint
  degree	smallint
  dirichlet_coefficients	numeric[]
  euler11	numeric[]
  euler13	numeric[]
  euler17	numeric[]
  euler19	numeric[]
  euler2	numeric[]
  euler23	numeric[]
  euler29	numeric[]
  euler3	numeric[]
  euler31	numeric[]
  euler37	numeric[]
  euler41	numeric[]
  euler43	numeric[]
  euler47	numeric[]
  euler5	numeric[]
  euler53	numeric[]
  euler59	numeric[]
  euler61	numeric[]
  euler67	numeric[]
  euler7	numeric[]
  euler71	numeric[]
  euler73	numeric[]
  euler79	numeric[]
  euler83	numeric[]
  euler89	numeric[]
  euler97	numeric[]
  euler_factors	numeric[]
  index	smallint
  instance_types	text[]
  instance_urls	text[]
  is_instance_Artin	boolean
  is_instance_BMF	boolean
  is_instance_CMF	boolean
  is_instance_DIR	boolean
  is_instance_ECNF	boolean
  is_instance_ECQ	boolean
  is_instance_G2Q	boolean
  is_instance_HMF	boolean
  is_instance_MaassGL3	boolean
  is_instance_MaassGL4	boolean
  is_instance_MaassGSp4	boolean
  is_instance_NF	boolean
  label	text
  motivic_weight	smallint
  mu_imag	numeric[]
  mu_real	smallint[]
  nu_imag	numeric[]
  nu_real_doubled	smallint[]
  order_of_vanishing	smallint
  prelabel	text
  primitive	boolean
  rational	boolean
  root_analytic_conductor	double precision
  root_angle	double precision
  self_dual	boolean
  spectral_label	text
  trace_hash	bigint
  z1	numeric

  
  {'algebraic': True, 'analytic_conductor': 780484390.6529279, 'bad_primes': [2, 5, 19], 'central_character': '1.1', 'conductor': 3010936384000000000000, 'conductor_radical': 190, 'degree': 12, 'dirichlet_coefficients': [1, 0, 2, 0, 0, 0, 2, 0, -4, 0, 3, 0, -1, 0, 0, 0, -14, 0, -6, 0, 4, 0, 12, 0, 0, 0, -10, 0, 9, 0, 5, 0, 6, 0, 0, 0, -8, 0, -2, 0, 3, 0, 15, 0, 0, 0, 4, 0, -8, 0, -28, 0, 13, 0, 0, 0, -12, 0, 0, 0, 9, 0, -8, 0, 0, 0, -3, 0, 24, 0, 19, 0, 3, 0, 0, 0, 6, 0, -16, 0, 10, 0, 31, 0, 0, 0, 18, 0, 14, 0, -2, 0, 10, 0, 0, 0, -11, 0, -12, 0], 'euler11': [1, -3, 26, -26, 65, 749, -2288, 8239, 7865, -34606, 380666, -483153, 1771561], 'euler13': [1, 1, 13, 50, 38, -516, 1813, -6708, 6422, 109850, 371293, 371293, 4826809], 'euler17': [1, 14, 124, 848, 4842, 24018, 105929, 408306, 1399338, 4166224, 10356604, 19877998, 24137569], 'euler19': [1, 6, 15, 20, 15, 6, 1, 0, 0, 0, 0, 0, 0], 'euler2': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler23': [1, -12, 112, -778, 4884, -25856, 128015, -594688, 2583636, -9465926, 31342192, -77236116, 148035889], 'euler29': [1, -9, 107, -600, 5158, -26640, 189919, -772560, 4337878, -14633400, 75679067, -184600341, 594823321], 'euler3': [1, -2, 8, -14, 30, -50, 87, -150, 270, -378, 648, -486, 729], 'euler31': [1, -5, 50, -176, 771, -5843, 22284, -181133, 740931, -5243216, 46176050, -143145755, 887503681], 'euler37': [1, 8, 132, 743, 7797, 33802, 309503, 1250674, 10674093, 37635179, 247389252, 554751656, 2565726409], 'euler41': [1, -3, 66, -146, 4087, -5943, 137612, -243663, 6870247, -10062466, 186500226, -347568603, 4750104241], 'euler43': [1, -15, 271, -2530, 26829, -185919, 1470270, -7994517, 49606821, -201152710, 926495071, -2205126645, 6321363049], 'euler47': [1, -4, 230, -749, 23811, -63544, 1431531, -2986568, 52598499, -77763427, 1122326630, -917380028, 10779215329], 'euler5': [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], 'euler53': [1, -13, 126, -1554, 12921, -108347, 968797, -5742391, 36295089, -231354858, 994200606, -5436541409, 22164361129], 'euler59': [1, 0, 161, 255, 12605, 44407, 744938, 2620013, 43878005, 52371645, 1950895121, 0, 42180533641], 'euler61': [1, -9, 234, -2302, 30205, -236741, 2409968, -14441201, 112392805, -522510262, 3239926794, -7601366709, 51520374361], 'euler67': [1, 3, 203, 820, 23862, 100928, 1840467, 6762176, 107116518, 246625660, 4090677563, 4050375321, 90458382169], 'euler7': [1, -2, 12, -22, 118, -126, 779, -882, 5782, -7546, 28812, -33614, 117649], 'euler71': [1, -19, 351, -3254, 31709, -169223, 1652142, -12014833, 159845069, -1164642394, 8919500031, -34280357669, 128100283921], 'euler73': [1, -3, 133, -274, 18744, -31092, 1356111, -2269716, 99886776, -106590658, 3776966053, -6219214779, 151334226289], 'euler79': [1, 16, 189, 1815, 19499, 139691, 1154286, 11035589, 121693259, 894865785, 7361565309, 49232902384, 243087455521], 'euler83': [1, -31, 824, -13802, 205891, -2327315, 23897248, -193167145, 1418383099, -7891804174, 39105656504, -122110259933, 326940373369], 'euler89': [1, -14, 467, -5503, 93933, -916667, 10735038, -81583363, 744043293, -3879444407, 29300626547, -78176832286, 496981290961], 'euler97': [1, 11, 374, 3862, 74175, 650639, 8888572, 63111983, 697912575, 3524743126, 33109951094, 94460742827, 832972004929], 'euler_factors': [[1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -2, 8, -14, 30, -50, 87, -150, 270, -378, 648, -486, 729], [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [1, -2, 12, -22, 118, -126, 779, -882, 5782, -7546, 28812, -33614, 117649], [1, -3, 26, -26, 65, 749, -2288, 8239, 7865, -34606, 380666, -483153, 1771561], [1, 1, 13, 50, 38, -516, 1813, -6708, 6422, 109850, 371293, 371293, 4826809], [1, 14, 124, 848, 4842, 24018, 105929, 408306, 1399338, 4166224, 10356604, 19877998, 24137569], [1, 6, 15, 20, 15, 6, 1, 0, 0, 0, 0, 0, 0], [1, -12, 112, -778, 4884, -25856, 128015, -594688, 2583636, -9465926, 31342192, -77236116, 148035889], [1, -9, 107, -600, 5158, -26640, 189919, -772560, 4337878, -14633400, 75679067, -184600341, 594823321], [1, -5, 50, -176, 771, -5843, 22284, -181133, 740931, -5243216, 46176050, -143145755, 887503681], [1, 8, 132, 743, 7797, 33802, 309503, 1250674, 10674093, 37635179, 247389252, 554751656, 2565726409], [1, -3, 66, -146, 4087, -5943, 137612, -243663, 6870247, -10062466, 186500226, -347568603, 4750104241], [1, -15, 271, -2530, 26829, -185919, 1470270, -7994517, 49606821, -201152710, 926495071, -2205126645, 6321363049], [1, -4, 230, -749, 23811, -63544, 1431531, -2986568, 52598499, -77763427, 1122326630, -917380028, 10779215329], [1, -13, 126, -1554, 12921, -108347, 968797, -5742391, 36295089, -231354858, 994200606, -5436541409, 22164361129], [1, 0, 161, 255, 12605, 44407, 744938, 2620013, 43878005, 52371645, 1950895121, 0, 42180533641], [1, -9, 234, -2302, 30205, -236741, 2409968, -14441201, 112392805, -522510262, 3239926794, -7601366709, 51520374361], [1, 3, 203, 820, 23862, 100928, 1840467, 6762176, 107116518, 246625660, 4090677563, 4050375321, 90458382169], [1, -19, 351, -3254, 31709, -169223, 1652142, -12014833, 159845069, -1164642394, 8919500031, -34280357669, 128100283921], [1, -3, 133, -274, 18744, -31092, 1356111, -2269716, 99886776, -106590658, 3776966053, -6219214779, 151334226289], [1, 16, 189, 1815, 19499, 139691, 1154286, 11035589, 121693259, 894865785, 7361565309, 49232902384, 243087455521], [1, -31, 824, -13802, 205891, -2327315, 23897248, -193167145, 1418383099, -7891804174, 39105656504, -122110259933, 326940373369], [1, -14, 467, -5503, 93933, -916667, 10735038, -81583363, 744043293, -3879444407, 29300626547, -78176832286, 496981290961], [1, 11, 374, 3862, 74175, 650639, 8888572, 63111983, 697912575, 3524743126, 33109951094, 94460742827, 832972004929]], 'index': 8, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/3800/2/a/bc'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '12-3800e6-1.1-c1e6-0-8', '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}], 'nu_real_doubled': [1, 1, 1, 1, 1, 1], 'order_of_vanishing': 0, 'prelabel': '12-3800e6-1.1-c1e6-0', 'primitive': False, 'rational': True, 'root_analytic_conductor': 5.508461923993535, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1e6-0', 'trace_hash': 35569433097744782, 'z1': {'__RealLiteral__': 0, 'data': '0.35630216519218056329676458585', 'prec': 103}}
• lfunc_instances •

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

  
  {'Lhash': '451666653568485436285272452689,673421383843490333449969298018,821901741280644182982607359569,1086351598670102217976218693701,1382628281386482274992214324142,1716091547250881169839750313129', 'Lhash_array': ['451666653568485436285272452689', '673421383843490333449969298018', '821901741280644182982607359569', '1086351598670102217976218693701', '1382628281386482274992214324142', '1716091547250881169839750313129'], 'label': '12-3800e6-1.1-c1e6-0-8', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/3800/2/a/bc'}