-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '1978221881481606748618834065179', 'a10': [-3.057837282195013, 0.0], 'a2': [-1.0, 0.0], 'a3': [-1.1629256706065136, 0.0], 'a4': [1.0, 0.0], 'a5': [3.057837282195013, 0.0], 'a6': [1.1629256706065136, 0.0], 'a7': [2.1369123577442966, 0.0], 'a8': [-1.0, 0.0], 'a9': [-1.6476038846443908, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 32.115831692958984, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [[2, [[1.0, 0], [1.0, 0]]], [2011, [[1.0, 0], [1.0, 0]]]], 'bad_primes': [2, 2011], 'central_character': '4022.1', 'coefficient_field': 'CDF', 'conductor': 4022, 'conductor_radical': 4022, 'degree': 2, 'euler_factors': [[[1.0, 0], [1.0, 0]], [[1.0, 0], [1.1629256706065136, 0], [3.0, 0]], [[1.0, 0], [-3.057837282195013, 0], [5.0, 0]], [[1.0, 0], [-2.1369123577442966, 0], [7.0, 0]], [[1.0, 0], [-2.9650318493672865, 0], [11.0, 0]], [[1.0, 0], [2.5560726680913257, 0], [13.0, 0]], [[1.0, 0], [-0.9667463666343459, 0], [17.0, 0]], [[1.0, 0], [1.0319455517835388, 0], [19.0, 0]], [[1.0, 0], [7.180648073069294, 0], [23.0, 0]], [[1.0, 0], [3.723635698139338, 0], [29.0, 0]], [[1.0, 0], [5.133293844058798, 0], [31.0, 0]], [[1.0, 0], [-3.0441990642354635, 0], [37.0, 0]], [[1.0, 0], [9.210110453949126, 0], [41.0, 0]], [[1.0, 0], [8.730917371822175, 0], [43.0, 0]], [[1.0, 0], [1.66879367334122, 0], [47.0, 0]], [[1.0, 0], [-1.2163722814422573, 0], [53.0, 0]], [[1.0, 0], [10.465604043033998, 0], [59.0, 0]], [[1.0, 0], [4.340707510758788, 0], [61.0, 0]], [[1.0, 0], [-6.104760784464938, 0], [67.0, 0]], [[1.0, 0], [1.7070471635913065, 0], [71.0, 0]], [[1.0, 0], [15.568915653752383, 0], [73.0, 0]], [[1.0, 0], [5.888036053276255, 0], [79.0, 0]], [[1.0, 0], [8.56846642408885, 0], [83.0, 0]], [[1.0, 0], [0.6943809328354037, 0], [89.0, 0]], [[1.0, 0], [-3.168862337263849, 0], [97.0, 0]], [[1.0, 0], [-2.386705852654937, 0], [101.0, 0]], [[1.0, 0], [17.431274923832117, 0], [103.0, 0]], [[1.0, 0], [-15.8714031187509, 0], [107.0, 0]], [[1.0, 0], [-15.067939934445336, 0], [109.0, 0]], [[1.0, 0], [-7.147169243828711, 0], [113.0, 0]], [[1.0, 0], [-4.190366744691736, 0], [127.0, 0]], [[1.0, 0], [-8.083505931427537, 0], [131.0, 0]], [[1.0, 0], [4.817808285196651, 0], [137.0, 0]], [[1.0, 0], [-14.058071804280868, 0], [139.0, 0]], [[1.0, 0], [4.1726371021967665, 0], [149.0, 0]], [[1.0, 0], [-21.796723520322843, 0], [151.0, 0]], [[1.0, 0], [13.713974932635345, 0], [157.0, 0]], [[1.0, 0], [-25.206593476099457, 0], [163.0, 0]], [[1.0, 0], [-8.621197644579535, 0], [167.0, 0]], [[1.0, 0], [8.84314578081349, 0], [173.0, 0]], [[1.0, 0], [-12.587702344708813, 0], [179.0, 0]], [[1.0, 0], [1.6743294911863544, 0], [181.0, 0]], [[1.0, 0], [3.1212421885866766, 0], [191.0, 0]], [[1.0, 0], [-7.6618988085496955, 0], [193.0, 0]], [[1.0, 0], [20.31288281349419, 0], [197.0, 0]], [[1.0, 0], [-1.2531294701407494, 0], [199.0, 0]], [[1.0, 0], [-25.802760464990023, 0], [211.0, 0]], [[1.0, 0], [20.789640817143002, 0], [223.0, 0]], [[1.0, 0], [24.774656038566107, 0], [227.0, 0]], [[1.0, 0], [-14.993044163834861, 0], [229.0, 0]], [[1.0, 0], [13.210432302679695, 0], [233.0, 0]], [[1.0, 0], [-11.553107790836764, 0], [239.0, 0]], [[1.0, 0], [-24.169361775347692, 0], [241.0, 0]], [[1.0, 0], [-11.794475332988501, 0], [251.0, 0]], [[1.0, 0], [-25.98204037378631, 0], [257.0, 0]], [[1.0, 0], [1.8452513492514337, 0], [263.0, 0]], [[1.0, 0], [-25.632938888510466, 0], [269.0, 0]], [[1.0, 0], [30.054657264951402, 0], [271.0, 0]], [[1.0, 0], [19.027592766771548, 0], [277.0, 0]], [[1.0, 0], [-7.158058421675664, 0], [281.0, 0]], [[1.0, 0], [1.2447598844925765, 0], [283.0, 0]], [[1.0, 0], [2.1073429255718095, 0], [293.0, 0]], [[1.0, 0], [6.028059621672525, 0], [307.0, 0]], [[1.0, 0], [-8.47348978794134, 0], [311.0, 0]], [[1.0, 0], [13.382501311293284, 0], [313.0, 0]], [[1.0, 0], [26.446932534038506, 0], [317.0, 0]], [[1.0, 0], [26.563926540632604, 0], [331.0, 0]], [[1.0, 0], [-15.321136981532094, 0], [337.0, 0]], [[1.0, 0], [-11.290137607030813, 0], [347.0, 0]], [[1.0, 0], [-10.324473202597897, 0], [349.0, 0]], [[1.0, 0], [-7.392007530597627, 0], [353.0, 0]], [[1.0, 0], [5.479044249687184, 0], [359.0, 0]], [[1.0, 0], [0.7074766075407348, 0], [367.0, 0]], [[1.0, 0], [4.982703426283559, 0], [373.0, 0]], [[1.0, 0], [27.144960055721242, 0], [379.0, 0]], [[1.0, 0], [-20.465035081935458, 0], [383.0, 0]], [[1.0, 0], [-9.633492586169705, 0], [389.0, 0]], [[1.0, 0], [13.046148489538773, 0], [397.0, 0]], [[1.0, 0], [37.79227835553083, 0], [401.0, 0]], [[1.0, 0], [24.65389129404171, 0], [409.0, 0]], [[1.0, 0], [6.8116628733737485, 0], [419.0, 0]], [[1.0, 0], [10.39964127474297, 0], [421.0, 0]], [[1.0, 0], [-37.94594703723794, 0], [431.0, 0]], [[1.0, 0], [7.582879558256953, 0], [433.0, 0]], [[1.0, 0], [10.59829835512168, 0], [439.0, 0]], [[1.0, 0], [-28.78669038298656, 0], [443.0, 0]], [[1.0, 0], [26.559920877453063, 0], [449.0, 0]], [[1.0, 0], [23.16387617804473, 0], [457.0, 0]], [[1.0, 0], [30.067023561328725, 0], [461.0, 0]], [[1.0, 0], [22.127267610671556, 0], [463.0, 0]], [[1.0, 0], [-16.68843357629048, 0], [467.0, 0]], [[1.0, 0], [3.8241295634829244, 0], [479.0, 0]], [[1.0, 0], [-15.89140653028251, 0], [487.0, 0]], [[1.0, 0], [-29.9312721122654, 0], [491.0, 0]], [[1.0, 0], [-19.986610752559393, 0], [499.0, 0]], [[1.0, 0], [-26.02234497433364, 0], [503.0, 0]], [[1.0, 0], [3.679803127474236, 0], [509.0, 0]], [[1.0, 0], [-37.456633454591326, 0], [521.0, 0]], [[1.0, 0], [-18.080230809793957, 0], [523.0, 0]], [[1.0, 0], [7.743807002156444, 0], [541.0, 0]], [[1.0, 0], [28.782307271206598, 0], [547.0, 0]], [[1.0, 0], [-2.560675349310219, 0], [557.0, 0]], [[1.0, 0], [23.976104894191824, 0], [563.0, 0]], [[1.0, 0], [-13.172060651878168, 0], [569.0, 0]], [[1.0, 0], [-31.034084305094744, 0], [571.0, 0]], [[1.0, 0], [7.237303166408496, 0], [577.0, 0]], [[1.0, 0], [-43.83545001866783, 0], [587.0, 0]], [[1.0, 0], [-2.6903127158840907, 0], [593.0, 0]], [[1.0, 0], [9.258379918812988, 0], [599.0, 0]], [[1.0, 0], [20.478913026638274, 0], [601.0, 0]], [[1.0, 0], [-4.343941008614166, 0], [607.0, 0]], [[1.0, 0], [30.234590062958056, 0], [613.0, 0]], [[1.0, 0], [25.232431303718087, 0], [617.0, 0]], [[1.0, 0], [-27.441896791450176, 0], [619.0, 0]], [[1.0, 0], [-38.824412217898654, 0], [631.0, 0]], [[1.0, 0], [11.098348771836173, 0], [641.0, 0]], [[1.0, 0], [24.29365104251097, 0], [643.0, 0]], [[1.0, 0], [25.410281351347628, 0], [647.0, 0]], [[1.0, 0], [-15.321915892148402, 0], [653.0, 0]], [[1.0, 0], [1.3090811576862886, 0], [659.0, 0]], [[1.0, 0], [-33.40199799336939, 0], [661.0, 0]], [[1.0, 0], [34.97147037196421, 0], [673.0, 0]], [[1.0, 0], [-9.036442205602782, 0], [677.0, 0]], [[1.0, 0], [38.071124140376504, 0], [683.0, 0]], [[1.0, 0], [12.669738511194847, 0], [691.0, 0]], [[1.0, 0], [-29.505258854666238, 0], [701.0, 0]], [[1.0, 0], [9.933664562983607, 0], [709.0, 0]], [[1.0, 0], [38.20832245682198, 0], [719.0, 0]], [[1.0, 0], [20.508408381693695, 0], [727.0, 0]], [[1.0, 0], [-26.77428783503661, 0], [733.0, 0]], [[1.0, 0], [-33.420178727286846, 0], [739.0, 0]], [[1.0, 0], [-52.879796309284224, 0], [743.0, 0]], [[1.0, 0], [5.898762098471365, 0], [751.0, 0]], [[1.0, 0], [13.131385787653352, 0], [757.0, 0]], [[1.0, 0], [16.80140019505982, 0], [761.0, 0]], [[1.0, 0], [15.023474313786219, 0], [769.0, 0]], [[1.0, 0], [8.544637743647433, 0], [773.0, 0]], [[1.0, 0], [7.028190206061774, 0], [787.0, 0]], [[1.0, 0], [-26.88549226619108, 0], [797.0, 0]], [[1.0, 0], [-26.99054083460055, 0], [809.0, 0]], [[1.0, 0], [-5.460329138724102, 0], [811.0, 0]], [[1.0, 0], [-24.17309380127733, 0], [821.0, 0]], [[1.0, 0], [-16.911422972936528, 0], [823.0, 0]], [[1.0, 0], [-47.427678974284625, 0], [827.0, 0]], [[1.0, 0], [-5.7723427117264485, 0], [829.0, 0]], [[1.0, 0], [14.249738838519873, 0], [839.0, 0]], [[1.0, 0], [22.55972284763167, 0], [853.0, 0]], [[1.0, 0], [4.551682673293926, 0], [857.0, 0]], [[1.0, 0], [-21.63243911217872, 0], [859.0, 0]], [[1.0, 0], [-11.071377313333665, 0], [863.0, 0]], [[1.0, 0], [2.5824552426436576, 0], [877.0, 0]], [[1.0, 0], [-18.558228433747725, 0], [881.0, 0]], [[1.0, 0], [-8.84073855020791, 0], [883.0, 0]], [[1.0, 0], [-23.214526652870482, 0], [887.0, 0]], [[1.0, 0], [-16.86075843615573, 0], [907.0, 0]], [[1.0, 0], [-28.4955438721961, 0], [911.0, 0]], [[1.0, 0], [-32.125282056033654, 0], [919.0, 0]], [[1.0, 0], [8.076484783270185, 0], [929.0, 0]], [[1.0, 0], [0.7597302978917688, 0], [937.0, 0]], [[1.0, 0], [-13.23844246970226, 0], [941.0, 0]], [[1.0, 0], [26.177635361133483, 0], [947.0, 0]], [[1.0, 0], [-43.08600921797161, 0], [953.0, 0]], [[1.0, 0], [13.221404016955658, 0], [967.0, 0]], [[1.0, 0], [39.04410265331013, 0], [971.0, 0]], [[1.0, 0], [42.26499083169983, 0], [977.0, 0]], [[1.0, 0], [-14.672306122345638, 0], [983.0, 0]], [[1.0, 0], [21.808377949435044, 0], [991.0, 0]], [[1.0, 0], [38.717629393829405, 0], [997.0, 0]], [[1.0, 0], [-7.6675078630810685, 0], [1009.0, 0]], [[1.0, 0], [-33.14963781687915, 0], [1013.0, 0]], [[1.0, 0], [27.118530762382033, 0], [1019.0, 0]], [[1.0, 0], [28.860315414694337, 0], [1021.0, 0]], [[1.0, 0], [-2.5762200938547855, 0], [1031.0, 0]], [[1.0, 0], [33.68122128694328, 0], [1033.0, 0]], [[1.0, 0], [10.294468046415838, 0], [1039.0, 0]], [[1.0, 0], [60.73070953182479, 0], [1049.0, 0]], [[1.0, 0], [25.46252220522262, 0], [1051.0, 0]], [[1.0, 0], [41.235295105987134, 0], [1061.0, 0]], [[1.0, 0], [46.91211478419753, 0], [1063.0, 0]], [[1.0, 0], [-4.3306275060977075, 0], [1069.0, 0]], [[1.0, 0], [50.13440563296099, 0], [1087.0, 0]], [[1.0, 0], [-2.062586670097927, 0], [1091.0, 0]], [[1.0, 0], [31.19060035337306, 0], [1093.0, 0]], [[1.0, 0], [32.03874995065477, 0], [1097.0, 0]], [[1.0, 0], [-31.019801935969472, 0], [1103.0, 0]], [[1.0, 0], [26.141642305320495, 0], [1109.0, 0]], [[1.0, 0], [1.2173715373318448, 0], [1117.0, 0]], [[1.0, 0], [49.361699085248254, 0], [1123.0, 0]], [[1.0, 0], [-53.8070538295979, 0], [1129.0, 0]], [[1.0, 0], [-42.014948559648, 0], [1151.0, 0]], [[1.0, 0], [-53.31205145750849, 0], [1153.0, 0]], [[1.0, 0], [63.57386845898492, 0], [1163.0, 0]], [[1.0, 0], [-8.376076522694582, 0], [1171.0, 0]], [[1.0, 0], [-37.95427778935729, 0], [1181.0, 0]], [[1.0, 0], [65.00375315684111, 0], [1187.0, 0]], [[1.0, 0], [-43.78198048653669, 0], [1193.0, 0]], [[1.0, 0], [17.885767171649942, 0], [1201.0, 0]], [[1.0, 0], [55.716101882341455, 0], [1213.0, 0]], [[1.0, 0], [-17.168873559268125, 0], [1217.0, 0]], [[1.0, 0], [50.382735951248605, 0], [1223.0, 0]], [[1.0, 0], [20.42277558278835, 0], [1229.0, 0]], [[1.0, 0], [5.992090885973997, 0], [1231.0, 0]], [[1.0, 0], [30.64129990687012, 0], [1237.0, 0]], [[1.0, 0], [50.71071804064574, 0], [1249.0, 0]], [[1.0, 0], [-10.55076610648508, 0], [1259.0, 0]], [[1.0, 0], [33.734493506083375, 0], [1277.0, 0]], [[1.0, 0], [7.452366144685909, 0], [1279.0, 0]], [[1.0, 0], [-52.90905401198365, 0], [1283.0, 0]], [[1.0, 0], [-48.31353367322195, 0], [1289.0, 0]], [[1.0, 0], [-12.977093563635473, 0], [1291.0, 0]], [[1.0, 0], [58.155769795557156, 0], [1297.0, 0]], [[1.0, 0], [-54.31247550540347, 0], [1301.0, 0]], [[1.0, 0], [-61.57633800932465, 0], [1303.0, 0]], [[1.0, 0], [-38.98442689733616, 0], [1307.0, 0]], [[1.0, 0], [-43.80461850201595, 0], [1319.0, 0]], [[1.0, 0], [-58.088997192199976, 0], [1321.0, 0]], [[1.0, 0], [-7.704561922610295, 0], [1327.0, 0]], [[1.0, 0], [-22.160357687357518, 0], [1361.0, 0]], [[1.0, 0], [-29.662291295358354, 0], [1367.0, 0]], [[1.0, 0], [-40.777651285687966, 0], [1373.0, 0]], [[1.0, 0], [-37.13618575888838, 0], [1381.0, 0]], [[1.0, 0], [10.22145238409482, 0], [1399.0, 0]], [[1.0, 0], [-41.32056372949454, 0], [1409.0, 0]], [[1.0, 0], [-74.7904784732417, 0], [1423.0, 0]], [[1.0, 0], [19.857821078289472, 0], [1427.0, 0]], [[1.0, 0], [-25.2925824666896, 0], [1429.0, 0]], [[1.0, 0], [-2.4486343444340264, 0], [1433.0, 0]], [[1.0, 0], [42.795030504773656, 0], [1439.0, 0]], [[1.0, 0], [6.463147999785835, 0], [1447.0, 0]], [[1.0, 0], [-30.455486441476353, 0], [1451.0, 0]], [[1.0, 0], [27.313554446744288, 0], [1453.0, 0]], [[1.0, 0], [24.84315394008924, 0], [1459.0, 0]], [[1.0, 0], [-47.99776178019706, 0], [1471.0, 0]], [[1.0, 0], [-47.285062988755854, 0], [1481.0, 0]], [[1.0, 0], [-28.772336136673054, 0], [1483.0, 0]], [[1.0, 0], [21.998321082406953, 0], [1487.0, 0]], [[1.0, 0], [-44.922727444750535, 0], [1489.0, 0]], [[1.0, 0], [-13.663757481879351, 0], [1493.0, 0]], [[1.0, 0], [24.028485732054698, 0], [1499.0, 0]], [[1.0, 0], [57.5892033528306, 0], [1511.0, 0]], [[1.0, 0], [-9.603484929055057, 0], [1523.0, 0]], [[1.0, 0], [34.21661894830325, 0], [1531.0, 0]], [[1.0, 0], [16.63960554573977, 0], [1543.0, 0]], [[1.0, 0], [-40.17193753992034, 0], [1549.0, 0]], [[1.0, 0], [-17.06429478720525, 0], [1553.0, 0]], [[1.0, 0], [-51.49356025971555, 0], [1559.0, 0]], [[1.0, 0], [-12.197273127994027, 0], [1567.0, 0]], [[1.0, 0], [-49.53663420340617, 0], [1571.0, 0]], [[1.0, 0], [61.26501209413882, 0], [1579.0, 0]], [[1.0, 0], [71.12205282569724, 0], [1583.0, 0]], [[1.0, 0], [60.86617743888759, 0], [1597.0, 0]], [[1.0, 0], [19.935376091627703, 0], [1601.0, 0]], [[1.0, 0], [29.743926129265912, 0], [1607.0, 0]], [[1.0, 0], [47.613588627527754, 0], [1609.0, 0]], [[1.0, 0], [59.322214377706686, 0], [1613.0, 0]], [[1.0, 0], [-7.713522768794533, 0], [1619.0, 0]], [[1.0, 0], [-52.32742111258447, 0], [1621.0, 0]], [[1.0, 0], [28.659537659768866, 0], [1627.0, 0]], [[1.0, 0], [-36.748237786906564, 0], [1637.0, 0]], [[1.0, 0], [29.235591661528026, 0], [1657.0, 0]], [[1.0, 0], [-31.475412567842017, 0], [1663.0, 0]], [[1.0, 0], [42.33361268704586, 0], [1667.0, 0]], [[1.0, 0], [14.590157456265938, 0], [1669.0, 0]], [[1.0, 0], [54.69134425159632, 0], [1693.0, 0]], [[1.0, 0], [-41.459335206322926, 0], [1697.0, 0]], [[1.0, 0], [14.596656895559317, 0], [1699.0, 0]], [[1.0, 0], [-8.156851004321712, 0], [1709.0, 0]], [[1.0, 0], [-46.98074071200587, 0], [1721.0, 0]], [[1.0, 0], [2.8084854801127865, 0], [1723.0, 0]], [[1.0, 0], [46.148392929162455, 0], [1733.0, 0]], [[1.0, 0], [16.754821659091704, 0], [1741.0, 0]], [[1.0, 0], [-76.48592536293386, 0], [1747.0, 0]], [[1.0, 0], [-47.53115997628196, 0], [1753.0, 0]], [[1.0, 0], [42.02379498566723, 0], [1759.0, 0]], [[1.0, 0], [-67.98538759162516, 0], [1777.0, 0]], [[1.0, 0], [-51.93045183817767, 0], [1783.0, 0]], [[1.0, 0], [32.45003078426213, 0], [1787.0, 0]], [[1.0, 0], [32.83017765220022, 0], [1789.0, 0]], [[1.0, 0], [-35.4390602133714, 0], [1801.0, 0]], [[1.0, 0], [-72.45151882179726, 0], [1811.0, 0]], [[1.0, 0], [-53.557139974988665, 0], [1823.0, 0]], [[1.0, 0], [-2.240986966377201, 0], [1831.0, 0]], [[1.0, 0], [16.387815535245792, 0], [1847.0, 0]], [[1.0, 0], [1.3096054700521755, 0], [1861.0, 0]], [[1.0, 0], [-54.555337499506805, 0], [1867.0, 0]], [[1.0, 0], [-37.407055500994446, 0], [1871.0, 0]], [[1.0, 0], [83.10004040550865, 0], [1873.0, 0]], [[1.0, 0], [21.317491533389454, 0], [1877.0, 0]], [[1.0, 0], [75.49908671618034, 0], [1879.0, 0]], [[1.0, 0], [38.3371064316286, 0], [1889.0, 0]], [[1.0, 0], [-26.672272117048138, 0], [1901.0, 0]], [[1.0, 0], [33.1583304831939, 0], [1907.0, 0]], [[1.0, 0], [-17.241356386178996, 0], [1913.0, 0]], [[1.0, 0], [-54.519605754934446, 0], [1931.0, 0]], [[1.0, 0], [5.6560736500838855, 0], [1933.0, 0]], [[1.0, 0], [69.81512755860841, 0], [1949.0, 0]], [[1.0, 0], [1.6301544672101846, 0], [1951.0, 0]], [[1.0, 0], [66.59176386973665, 0], [1973.0, 0]], [[1.0, 0], [-0.5300683279654751, 0], [1979.0, 0]], [[1.0, 0], [83.99998732532697, 0], [1987.0, 0]], [[1.0, 0], [67.15392973895295, 0], [1993.0, 0]], [[1.0, 0], [36.190967091596924, 0], [1997.0, 0]], [[1.0, 0], [48.837345685268716, 0], [1999.0, 0]], [[1.0, 0], [13.238721315761357, 0], [2003.0, 0]], [[1.0, 0], [1.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 138, 'label': '2-4022-1.1-c1-0-138', 'load_key': 'CMFs-workshop', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'origin': 'ModularForm/GL2/Q/holomorphic/4022/2/a/d/1/15', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [-2.5584857734175202e-61, 0.14305435327995492, 0.2854043819563238, 0.42630734834078393, 0.5649467874537658, 0.700403138273795, 0.8316327003519633, 0.9574566807673448, 1.0765614114891102, 1.1875101360066562, 1.288766142988616, 1.3787264969400272, 1.4557651921389294, 1.5182842303590833, 1.56477087917132, 1.593859187327087, 1.6043937005087048, 1.5954932233414785, 1.5666124067563734, 1.5175989038136957, 1.448743836411491, 1.3608233570249786, 1.2551291819887442, 1.1334861238429979, 0.9982548665930808, 0.8523185138833024, 0.6990517977871099, 0.5422722636949106, 0.38617323972834866, 0.23523894878392337, 0.09414271578635404, -0.03237015320570466, -0.13961260794689095, -0.22309636878827271, -0.27867928695326305, -0.3027155797491814, -0.29220451221674465, -0.24493274296695525, -0.15960532489981044, -0.035960271254398025, 0.12513831927525046, 0.32163332544280054, 0.5502381592462032, 0.8064344931282039, 1.0845070320471082, 1.3776172326563332, 1.6779167541027793, 1.9767001875092054, 2.2645952875571926, 2.531787559307642, 2.768274681153478, 2.964144919109122, 3.1098724593545, 3.1966215065218915, 3.216550114791186, 3.163104084268189, 3.031290907801765, 2.8179237273825213, 2.5218255792882203, 2.1439848869385916, 1.6876542013553055, 1.1583855791633106, 0.5639977012414525, -0.08552816853939124, -0.778224059027654, -1.5003812866437838, -2.236862377024813, -2.9714722420329513, -3.6873795505580516, -4.367577023969528, -4.995367454867711, -5.554860679210192, -6.031465606884558, -6.412360802268152, -6.686927056645358, -6.847125942329672, -6.887809496612418, -6.8069479419106065, -6.605764672402298, -6.288770568623304, -5.863692958365909, -5.341298121893996, -4.735110020719006, -4.061031776193657, -3.336880191374503, -2.5818471469415796, -1.815904860867673, -1.0591746410738445, -0.33128075344007496, 0.3492877329156012, 0.9657838570190656, 1.5037556509333052, 1.9515236028779526, 2.3005635776701183, 2.545779178697724, 2.6856513788588967, 2.7222577018594123, 2.66115814157071, 2.511150181680694, 2.2839005173928717, 1.9934661709559436, 1.6557224162954596, 1.2877190746415708, 0.9069901186022227, 0.530843957715046, 0.17566313900001712, -0.14375761252737773, -0.41480711292613726, -0.6275615337274583, -0.7751740379663995, -0.8541323989878586, -0.8643720821737662, -0.8092382679341072, -0.6952967292187173, -0.5320000779114268, -0.33122237429948653, -0.10668116034840965, 0.12672865270742642, 0.3536602005557997, 0.5590673178531269, 0.7289504981360436, 0.8510618636422341, 0.9155360270735164, 0.9154164477136613, 0.847051064023018, 0.7103364725258424, 0.5087965014358019, 0.24948842215725042, -0.05726206921064871, -0.3982879400210508, -0.7581530237558693, -1.11984519391708, -1.4655601400202336, -1.7775404340317935, -2.0389311856246057, -2.234611950346464, -2.351964801104427, -2.3815406383421993, -2.317589844522081, -2.1584291387769627, -1.906623724959239, -1.5689722388258152, -1.156291209595884, -0.6830053297829359, -0.16655931715195335, 0.37332391231427403, 0.9155061130709913, 1.4383784651291696, 1.9208443282472318, 2.343293427229377, 2.688520452562226, 2.9425429198996755, 3.095277258899195, 3.14103834232845, 3.0788357555361325, 2.912449679629002, 2.6502798701042827, 2.304972343720656, 1.8928394884175073, 1.43309982064901, 0.9469729850019257, 0.4566733213847485, -0.015649012910258085, -0.448967116826285, -0.8243837179514099, -1.1260339980485736, -1.3418387212833773, -1.4640686600967143, -1.4896905826932416, -1.4204760136757513, -1.2628660622925003, -1.0275982162952801, -0.7291134680859576, -0.38477381154717655, -0.01393038920765992, 0.36310919001699077, 0.7261600770373503, 1.0562287287141772, 1.3365136438949239, 1.5532843320392993, 1.6965906882209856, 1.7607637541026213, 1.7446798894245341, 1.6517730955983414, 1.4897939518205716, 1.2703276056749744, 1.0080967360273037, 0.72008762024174, 0.4245476893774688, 0.13991063835532086, -0.11629020121020342, -0.32845823304186084, -0.48385992269305445, -0.573386913926996, -0.5921085619083055, -0.5395810243201631, -0.4198926812840109, -0.24144065977735713, -0.016448783276535376, 0.2397475310600739, 0.5096099301876281, 0.774447923290366, 1.0155512773990762, 1.2153377144406459, 1.3584476386444153, 1.4327196194264995, 1.429986288464991, 1.3466399164490872, 1.1839297299617468, 0.9479683291856407, 0.6494415266101747, 0.30303358203120834, -0.07340286787625058, -0.45988692941531667, -0.8355007506228318, -1.1796627206805377, -1.4734067863099614, -1.70058998013661, -1.8489527527987675, -1.9109637813875435, -1.884392284279942, -1.772565936916263, -1.584290449449819, -1.3334267363897812, -1.0381422415618529, -0.7198731644109865, -0.4020528459469763, -0.10867726174655912, 0.1372095795992428, 0.31502033424658915, 0.40802712652917505, 0.4045739434666877, 0.2990189902478642, 0.09234128489782928, -0.20763599313623665, -0.5864312943040634, -1.023501777823792, -1.4932292861436058, -1.9662489351465493, -2.411052248738817, -2.7957784288230063, -3.090093654530946, -3.267050188064515, -3.3048151592432062, -3.1881634822469436, -2.9096403204154595, -2.47031536822734, -1.880073108870652, -1.1574089536789267, -0.3287293388141656, 0.5728171722734717, 1.5089226591113838, 2.4380358837142513, 3.3175096801609794, 4.105861987874135, 4.765023625659862, 5.262443988661029], 'positive_zeros': ['1.56054190415359343010079737958780', '1.99287556329014184697603943368142', '3.19274079067380770995775457032385', '4.49294814359875909736209279942683', '5.35911390527497015112284712825141', '5.91387335733246083296374485859034', '6.49100198083967446439469581384900', '7.32831152772085139517840989866733', '8.224823017782181898111830804758960'], 'prelabel': '2-4022-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.667083173287558, 'root_angle': 1.0, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.56054190415359343010079737959', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.99287556329014184697603943368', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '3.19274079067380770995775457032', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 32.115831692958984, 'bad_primes': [2, 2011], 'central_character': '1.1', 'conductor': 4022, 'conductor_radical': 4022, 'degree': 2, 'index': 138, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/4022/2/a/d/1/15'], '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': '2-4022-1.1-c1-0-138', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 1, 'prelabel': '2-4022-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 5.667083173287558, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '1.56054190415359343010079737959', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '1978221881481606748618834065179', 'Lhash_array': ['1978221881481606748618834065179'], 'label': '2-4022-1.1-c1-0-138', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/4022/2/a/d/1/15'}