-
lfunc_lfunctions • Show schema
Hide schema
{'Lhash': '233670327362184231409050991211', 'a10': [8.735420356298196, 0.0], 'a2': [-2.459901491715527, 0.0], 'a3': [1.5881467281871502, 0.0], 'a4': [4.051115348944275, 0.0], 'a5': [-3.551126086031251, 0.0], 'a6': [-3.9066845057307042, 0.0], 'a7': [-1.7269604635737341, 0.0], 'a8': [-5.045541706548635, 0.0], 'a9': [-0.47778996974844995, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 40.54004910620407, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'bad_lfactors': [], 'bad_primes': [5077], 'central_character': '5077.1', 'coefficient_field': 'CDF', 'conductor': 5077, 'conductor_radical': 5077, 'degree': 2, 'euler_factors': [[[1.0, 0], [2.459901491715527, 0], [2.0, 0]], [[1.0, 0], [-1.5881467281871502, 0], [3.0, 0]], [[1.0, 0], [3.551126086031251, 0], [5.0, 0]], [[1.0, 0], [1.7269604635737341, 0], [7.0, 0]], [[1.0, 0], [-0.5217309188566348, 0], [11.0, 0]], [[1.0, 0], [6.4891679018290995, 0], [13.0, 0]], [[1.0, 0], [0.08231091416409757, 0], [17.0, 0]], [[1.0, 0], [1.3314492578362331, 0], [19.0, 0]], [[1.0, 0], [-1.6066406173183947, 0], [23.0, 0]], [[1.0, 0], [5.297779078438973, 0], [29.0, 0]], [[1.0, 0], [3.361368094502359, 0], [31.0, 0]], [[1.0, 0], [-1.7036108571112238, 0], [37.0, 0]], [[1.0, 0], [6.249456610400444, 0], [41.0, 0]], [[1.0, 0], [11.512489459856939, 0], [43.0, 0]], [[1.0, 0], [-0.6810143476490609, 0], [47.0, 0]], [[1.0, 0], [5.037213143948908, 0], [53.0, 0]], [[1.0, 0], [-3.9433392606965856, 0], [59.0, 0]], [[1.0, 0], [-4.734279843572587, 0], [61.0, 0]], [[1.0, 0], [-11.520431879879963, 0], [67.0, 0]], [[1.0, 0], [3.2187570011790223, 0], [71.0, 0]], [[1.0, 0], [13.067690424752533, 0], [73.0, 0]], [[1.0, 0], [15.557379134327569, 0], [79.0, 0]], [[1.0, 0], [-8.375361328518444, 0], [83.0, 0]], [[1.0, 0], [-5.069389476679887, 0], [89.0, 0]], [[1.0, 0], [9.063291655898855, 0], [97.0, 0]], [[1.0, 0], [19.194225608167176, 0], [101.0, 0]], [[1.0, 0], [12.634468827877484, 0], [103.0, 0]], [[1.0, 0], [8.245560908468029, 0], [107.0, 0]], [[1.0, 0], [16.86354167033904, 0], [109.0, 0]], [[1.0, 0], [-15.76765763380459, 0], [113.0, 0]], [[1.0, 0], [-1.1193653153629484, 0], [127.0, 0]], [[1.0, 0], [2.2912342836289254, 0], [131.0, 0]], [[1.0, 0], [-5.675458080462523, 0], [137.0, 0]], [[1.0, 0], [-16.59799905436748, 0], [139.0, 0]], [[1.0, 0], [-13.863894888906549, 0], [149.0, 0]], [[1.0, 0], [3.9798227558756754, 0], [151.0, 0]], [[1.0, 0], [2.8050438452478863, 0], [157.0, 0]], [[1.0, 0], [-18.044504630373066, 0], [163.0, 0]], [[1.0, 0], [-11.070486901283774, 0], [167.0, 0]], [[1.0, 0], [-22.73680568184517, 0], [173.0, 0]], [[1.0, 0], [10.235889384411724, 0], [179.0, 0]], [[1.0, 0], [-6.642234833478553, 0], [181.0, 0]], [[1.0, 0], [-11.286718263444227, 0], [191.0, 0]], [[1.0, 0], [-3.742382272467616, 0], [193.0, 0]], [[1.0, 0], [10.368328333748481, 0], [197.0, 0]], [[1.0, 0], [-24.88863365590346, 0], [199.0, 0]], [[1.0, 0], [28.02081217321891, 0], [211.0, 0]], [[1.0, 0], [3.745545366145419, 0], [223.0, 0]], [[1.0, 0], [-17.00298093074402, 0], [227.0, 0]], [[1.0, 0], [10.281706913980011, 0], [229.0, 0]], [[1.0, 0], [20.47522520328966, 0], [233.0, 0]], [[1.0, 0], [9.55740393591014, 0], [239.0, 0]], [[1.0, 0], [-24.520580943001033, 0], [241.0, 0]], [[1.0, 0], [-5.989187629754214, 0], [251.0, 0]], [[1.0, 0], [6.321655442565601, 0], [257.0, 0]], [[1.0, 0], [-3.3858684045601177, 0], [263.0, 0]], [[1.0, 0], [30.81700522065813, 0], [269.0, 0]], [[1.0, 0], [24.75056748717475, 0], [271.0, 0]], [[1.0, 0], [-15.232675712878835, 0], [277.0, 0]], [[1.0, 0], [-18.499446699260755, 0], [281.0, 0]], [[1.0, 0], [4.00256826478455, 0], [283.0, 0]], [[1.0, 0], [-19.935158724920697, 0], [293.0, 0]], [[1.0, 0], [23.85792400508602, 0], [307.0, 0]], [[1.0, 0], [-5.556378044887211, 0], [311.0, 0]], [[1.0, 0], [4.891317233054402, 0], [313.0, 0]], [[1.0, 0], [25.773891507566724, 0], [317.0, 0]], [[1.0, 0], [-21.86643074521235, 0], [331.0, 0]], [[1.0, 0], [-13.835197815672082, 0], [337.0, 0]], [[1.0, 0], [-16.530703386779244, 0], [347.0, 0]], [[1.0, 0], [-3.967258536442142, 0], [349.0, 0]], [[1.0, 0], [-23.075228545296994, 0], [353.0, 0]], [[1.0, 0], [17.86032076039095, 0], [359.0, 0]], [[1.0, 0], [6.249111533342257, 0], [367.0, 0]], [[1.0, 0], [-5.438198467524275, 0], [373.0, 0]], [[1.0, 0], [30.017024993074546, 0], [379.0, 0]], [[1.0, 0], [7.031070446651711, 0], [383.0, 0]], [[1.0, 0], [4.500369392035996, 0], [389.0, 0]], [[1.0, 0], [9.451050920285898, 0], [397.0, 0]], [[1.0, 0], [-13.269313280152828, 0], [401.0, 0]], [[1.0, 0], [-31.428697034329534, 0], [409.0, 0]], [[1.0, 0], [16.40096895059635, 0], [419.0, 0]], [[1.0, 0], [0.007643136320763656, 0], [421.0, 0]], [[1.0, 0], [27.058684251951284, 0], [431.0, 0]], [[1.0, 0], [-35.69670980593005, 0], [433.0, 0]], [[1.0, 0], [0.36637864411315335, 0], [439.0, 0]], [[1.0, 0], [-15.441570083647772, 0], [443.0, 0]], [[1.0, 0], [-5.181942862714959, 0], [449.0, 0]], [[1.0, 0], [-32.59370922376326, 0], [457.0, 0]], [[1.0, 0], [7.230028794778755, 0], [461.0, 0]], [[1.0, 0], [33.70035795168055, 0], [463.0, 0]], [[1.0, 0], [-10.046818880167995, 0], [467.0, 0]], [[1.0, 0], [6.201936839340095, 0], [479.0, 0]], [[1.0, 0], [21.894510139884794, 0], [487.0, 0]], [[1.0, 0], [9.161104929124015, 0], [491.0, 0]], [[1.0, 0], [-8.398253734747652, 0], [499.0, 0]], [[1.0, 0], [-6.137504054139669, 0], [503.0, 0]], [[1.0, 0], [-27.40786333370935, 0], [509.0, 0]], [[1.0, 0], [-8.257596419716041, 0], [521.0, 0]], [[1.0, 0], [10.134794815894866, 0], [523.0, 0]], [[1.0, 0], [-24.89625385110942, 0], [541.0, 0]], [[1.0, 0], [-9.35363498957077, 0], [547.0, 0]], [[1.0, 0], [14.818978316609279, 0], [557.0, 0]], [[1.0, 0], [28.378843596733233, 0], [563.0, 0]], [[1.0, 0], [-22.10327043897751, 0], [569.0, 0]], [[1.0, 0], [17.15655828144838, 0], [571.0, 0]], [[1.0, 0], [0.033049572073758825, 0], [577.0, 0]], [[1.0, 0], [-3.6522936790586282, 0], [587.0, 0]], [[1.0, 0], [36.38940015066624, 0], [593.0, 0]], [[1.0, 0], [-0.1408407096070176, 0], [599.0, 0]], [[1.0, 0], [45.58811124741696, 0], [601.0, 0]], [[1.0, 0], [31.269757584663285, 0], [607.0, 0]], [[1.0, 0], [-14.177126561936493, 0], [613.0, 0]], [[1.0, 0], [14.487448672755946, 0], [617.0, 0]], [[1.0, 0], [-11.18548514554297, 0], [619.0, 0]], [[1.0, 0], [47.89320536813666, 0], [631.0, 0]], [[1.0, 0], [-14.676967055222978, 0], [641.0, 0]], [[1.0, 0], [11.870537682888889, 0], [643.0, 0]], [[1.0, 0], [-26.130366816697105, 0], [647.0, 0]], [[1.0, 0], [-38.557705808505744, 0], [653.0, 0]], [[1.0, 0], [-10.013193341225596, 0], [659.0, 0]], [[1.0, 0], [12.043163149143917, 0], [661.0, 0]], [[1.0, 0], [28.207465522318945, 0], [673.0, 0]], [[1.0, 0], [23.876726274503053, 0], [677.0, 0]], [[1.0, 0], [20.75173743706199, 0], [683.0, 0]], [[1.0, 0], [-34.412465991908924, 0], [691.0, 0]], [[1.0, 0], [19.966014677134936, 0], [701.0, 0]], [[1.0, 0], [-34.98058929413584, 0], [709.0, 0]], [[1.0, 0], [-10.44002499563857, 0], [719.0, 0]], [[1.0, 0], [34.046624358117406, 0], [727.0, 0]], [[1.0, 0], [-46.318851319776776, 0], [733.0, 0]], [[1.0, 0], [32.505079108590785, 0], [739.0, 0]], [[1.0, 0], [-10.923468438271996, 0], [743.0, 0]], [[1.0, 0], [20.46857127200097, 0], [751.0, 0]], [[1.0, 0], [-14.132861976194164, 0], [757.0, 0]], [[1.0, 0], [33.681133533020294, 0], [761.0, 0]], [[1.0, 0], [-9.338966953673625, 0], [769.0, 0]], [[1.0, 0], [-20.372957483750525, 0], [773.0, 0]], [[1.0, 0], [3.996571393028237, 0], [787.0, 0]], [[1.0, 0], [-43.28609417843687, 0], [797.0, 0]], [[1.0, 0], [46.57626701669033, 0], [809.0, 0]], [[1.0, 0], [-44.4190842065238, 0], [811.0, 0]], [[1.0, 0], [-16.013083398302026, 0], [821.0, 0]], [[1.0, 0], [-26.109064735500656, 0], [823.0, 0]], [[1.0, 0], [-42.579226321455955, 0], [827.0, 0]], [[1.0, 0], [-2.3463162571190646, 0], [829.0, 0]], [[1.0, 0], [-48.029833118492135, 0], [839.0, 0]], [[1.0, 0], [-1.178787638090391, 0], [853.0, 0]], [[1.0, 0], [-12.607128008839629, 0], [857.0, 0]], [[1.0, 0], [-42.596783216832456, 0], [859.0, 0]], [[1.0, 0], [-23.018924621054285, 0], [863.0, 0]], [[1.0, 0], [-37.28942375567083, 0], [877.0, 0]], [[1.0, 0], [-11.294788211547003, 0], [881.0, 0]], [[1.0, 0], [11.162701733506921, 0], [883.0, 0]], [[1.0, 0], [-26.65763975074621, 0], [887.0, 0]], [[1.0, 0], [-39.353117439791, 0], [907.0, 0]], [[1.0, 0], [37.86187123158897, 0], [911.0, 0]], [[1.0, 0], [-40.05611933535279, 0], [919.0, 0]], [[1.0, 0], [12.022085739093278, 0], [929.0, 0]], [[1.0, 0], [23.309563434849125, 0], [937.0, 0]], [[1.0, 0], [-7.611777524068836, 0], [941.0, 0]], [[1.0, 0], [12.557440018742133, 0], [947.0, 0]], [[1.0, 0], [-3.0872921885228264, 0], [953.0, 0]], [[1.0, 0], [-11.679650892119724, 0], [967.0, 0]], [[1.0, 0], [29.61577995938961, 0], [971.0, 0]], [[1.0, 0], [-19.93720010654856, 0], [977.0, 0]], [[1.0, 0], [19.233458897408955, 0], [983.0, 0]], [[1.0, 0], [13.486064080872726, 0], [991.0, 0]], [[1.0, 0], [-42.83731033389911, 0], [997.0, 0]], [[1.0, 0], [-51.31791641017893, 0], [1009.0, 0]], [[1.0, 0], [18.2912143865268, 0], [1013.0, 0]], [[1.0, 0], [-3.333862484094032, 0], [1019.0, 0]], [[1.0, 0], [-7.368039580607182, 0], [1021.0, 0]], [[1.0, 0], [58.32271902419673, 0], [1031.0, 0]], [[1.0, 0], [57.16989851845001, 0], [1033.0, 0]], [[1.0, 0], [33.763283582351534, 0], [1039.0, 0]], [[1.0, 0], [2.761311924072597, 0], [1049.0, 0]], [[1.0, 0], [-22.92977030342529, 0], [1051.0, 0]], [[1.0, 0], [58.93860049919566, 0], [1061.0, 0]], [[1.0, 0], [27.614004091791394, 0], [1063.0, 0]], [[1.0, 0], [-10.688150668387118, 0], [1069.0, 0]], [[1.0, 0], [50.79378709400413, 0], [1087.0, 0]], [[1.0, 0], [0.9762074646257455, 0], [1091.0, 0]], [[1.0, 0], [63.43625208396701, 0], [1093.0, 0]], [[1.0, 0], [-18.524155174140347, 0], [1097.0, 0]], [[1.0, 0], [40.40921614984069, 0], [1103.0, 0]], [[1.0, 0], [1.7273268070298284, 0], [1109.0, 0]], [[1.0, 0], [-26.644536326864692, 0], [1117.0, 0]], [[1.0, 0], [-20.274427122294757, 0], [1123.0, 0]], [[1.0, 0], [-1.3499791558273835, 0], [1129.0, 0]], [[1.0, 0], [47.859069753551225, 0], [1151.0, 0]], [[1.0, 0], [45.79582043969185, 0], [1153.0, 0]], [[1.0, 0], [38.665669314893925, 0], [1163.0, 0]], [[1.0, 0], [20.42758391090554, 0], [1171.0, 0]], [[1.0, 0], [-33.01641919661652, 0], [1181.0, 0]], [[1.0, 0], [-4.617810140848597, 0], [1187.0, 0]], [[1.0, 0], [15.97320013149338, 0], [1193.0, 0]], [[1.0, 0], [34.35649354387567, 0], [1201.0, 0]], [[1.0, 0], [13.200924052112352, 0], [1213.0, 0]], [[1.0, 0], [44.19700802625861, 0], [1217.0, 0]], [[1.0, 0], [-5.406790235506801, 0], [1223.0, 0]], [[1.0, 0], [45.19564181760226, 0], [1229.0, 0]], [[1.0, 0], [66.87838326147498, 0], [1231.0, 0]], [[1.0, 0], [41.933069747956736, 0], [1237.0, 0]], [[1.0, 0], [3.4480718814368503, 0], [1249.0, 0]], [[1.0, 0], [-19.354634029642977, 0], [1259.0, 0]], [[1.0, 0], [-24.77394655557781, 0], [1277.0, 0]], [[1.0, 0], [-23.006196607208338, 0], [1279.0, 0]], [[1.0, 0], [20.378363207326313, 0], [1283.0, 0]], [[1.0, 0], [35.82156543662577, 0], [1289.0, 0]], [[1.0, 0], [-7.66972905922682, 0], [1291.0, 0]], [[1.0, 0], [-70.0132093377753, 0], [1297.0, 0]], [[1.0, 0], [68.88508758713631, 0], [1301.0, 0]], [[1.0, 0], [4.019052728767958, 0], [1303.0, 0]], [[1.0, 0], [29.712196709963102, 0], [1307.0, 0]], [[1.0, 0], [24.10368526179905, 0], [1319.0, 0]], [[1.0, 0], [-31.51944047722092, 0], [1321.0, 0]], [[1.0, 0], [-1.820057808679964, 0], [1327.0, 0]], [[1.0, 0], [-53.95744734282642, 0], [1361.0, 0]], [[1.0, 0], [15.73508089983274, 0], [1367.0, 0]], [[1.0, 0], [35.571177426883295, 0], [1373.0, 0]], [[1.0, 0], [-45.25115067911477, 0], [1381.0, 0]], [[1.0, 0], [60.16346288326245, 0], [1399.0, 0]], [[1.0, 0], [-1.169587787399546, 0], [1409.0, 0]], [[1.0, 0], [-30.26454191604314, 0], [1423.0, 0]], [[1.0, 0], [58.59276376813821, 0], [1427.0, 0]], [[1.0, 0], [1.7613544248653117, 0], [1429.0, 0]], [[1.0, 0], [-3.463963099122677, 0], [1433.0, 0]], [[1.0, 0], [-4.47455923082447, 0], [1439.0, 0]], [[1.0, 0], [-32.314357760728804, 0], [1447.0, 0]], [[1.0, 0], [-9.99039679668753, 0], [1451.0, 0]], [[1.0, 0], [66.7315845669074, 0], [1453.0, 0]], [[1.0, 0], [53.64952464639179, 0], [1459.0, 0]], [[1.0, 0], [30.277178686329727, 0], [1471.0, 0]], [[1.0, 0], [33.42593837005735, 0], [1481.0, 0]], [[1.0, 0], [-31.3023834806289, 0], [1483.0, 0]], [[1.0, 0], [-27.21797866367759, 0], [1487.0, 0]], [[1.0, 0], [-9.831407351470768, 0], [1489.0, 0]], [[1.0, 0], [26.00379663602099, 0], [1493.0, 0]], [[1.0, 0], [-29.17187338333667, 0], [1499.0, 0]], [[1.0, 0], [-44.68774070515435, 0], [1511.0, 0]], [[1.0, 0], [54.09531906396761, 0], [1523.0, 0]], [[1.0, 0], [74.46852882416003, 0], [1531.0, 0]], [[1.0, 0], [12.236238772480027, 0], [1543.0, 0]], [[1.0, 0], [-27.473001366007207, 0], [1549.0, 0]], [[1.0, 0], [-26.365746762594046, 0], [1553.0, 0]], [[1.0, 0], [-13.839125001684364, 0], [1559.0, 0]], [[1.0, 0], [61.940995792186314, 0], [1567.0, 0]], [[1.0, 0], [-52.51776401888657, 0], [1571.0, 0]], [[1.0, 0], [-24.550850950745744, 0], [1579.0, 0]], [[1.0, 0], [-4.967119283750422, 0], [1583.0, 0]], [[1.0, 0], [-57.09875968895166, 0], [1597.0, 0]], [[1.0, 0], [61.301895973773426, 0], [1601.0, 0]], [[1.0, 0], [-42.293323946149414, 0], [1607.0, 0]], [[1.0, 0], [-0.331664214815271, 0], [1609.0, 0]], [[1.0, 0], [41.87214412430684, 0], [1613.0, 0]], [[1.0, 0], [12.026983253553253, 0], [1619.0, 0]], [[1.0, 0], [-8.33902952726114, 0], [1621.0, 0]], [[1.0, 0], [-0.8034298486555301, 0], [1627.0, 0]], [[1.0, 0], [-68.48311013501487, 0], [1637.0, 0]], [[1.0, 0], [33.28358884610978, 0], [1657.0, 0]], [[1.0, 0], [50.16945332508331, 0], [1663.0, 0]], [[1.0, 0], [-12.571214520064652, 0], [1667.0, 0]], [[1.0, 0], [-10.2633088246034, 0], [1669.0, 0]], [[1.0, 0], [12.929330321877261, 0], [1693.0, 0]], [[1.0, 0], [-16.53832958835787, 0], [1697.0, 0]], [[1.0, 0], [-47.08002742732759, 0], [1699.0, 0]], [[1.0, 0], [29.340369817095418, 0], [1709.0, 0]], [[1.0, 0], [9.757354997888017, 0], [1721.0, 0]], [[1.0, 0], [48.053541022661946, 0], [1723.0, 0]], [[1.0, 0], [41.3431839899931, 0], [1733.0, 0]], [[1.0, 0], [-1.1254869857220058, 0], [1741.0, 0]], [[1.0, 0], [-45.55752025171324, 0], [1747.0, 0]], [[1.0, 0], [12.643840644634123, 0], [1753.0, 0]], [[1.0, 0], [33.25105931795059, 0], [1759.0, 0]], [[1.0, 0], [10.162139093075973, 0], [1777.0, 0]], [[1.0, 0], [-3.179369680549039, 0], [1783.0, 0]], [[1.0, 0], [65.28535977131315, 0], [1787.0, 0]], [[1.0, 0], [-17.89834255783095, 0], [1789.0, 0]], [[1.0, 0], [-14.48538083202366, 0], [1801.0, 0]], [[1.0, 0], [23.98366912344114, 0], [1811.0, 0]], [[1.0, 0], [-43.71994997159517, 0], [1823.0, 0]], [[1.0, 0], [63.78224099998251, 0], [1831.0, 0]], [[1.0, 0], [-16.12533392914063, 0], [1847.0, 0]], [[1.0, 0], [30.81708302527011, 0], [1861.0, 0]], [[1.0, 0], [-23.439030956404714, 0], [1867.0, 0]], [[1.0, 0], [74.29301822541173, 0], [1871.0, 0]], [[1.0, 0], [-23.60199625460903, 0], [1873.0, 0]], [[1.0, 0], [21.478131162255696, 0], [1877.0, 0]], [[1.0, 0], [-12.668737424469462, 0], [1879.0, 0]], [[1.0, 0], [-76.67265166959663, 0], [1889.0, 0]], [[1.0, 0], [-26.822596904327128, 0], [1901.0, 0]], [[1.0, 0], [81.95316251556817, 0], [1907.0, 0]], [[1.0, 0], [-22.676658407388945, 0], [1913.0, 0]], [[1.0, 0], [3.3410062245121055, 0], [1931.0, 0]], [[1.0, 0], [-21.635440388071107, 0], [1933.0, 0]], [[1.0, 0], [-21.865290926060403, 0], [1949.0, 0]], [[1.0, 0], [-37.05403641935068, 0], [1951.0, 0]], [[1.0, 0], [-47.708132160252134, 0], [1973.0, 0]], [[1.0, 0], [-47.56090900237907, 0], [1979.0, 0]], [[1.0, 0], [11.63744679621021, 0], [1987.0, 0]], [[1.0, 0], [-79.54920083546638, 0], [1993.0, 0]], [[1.0, 0], [61.662322846870296, 0], [1997.0, 0]], [[1.0, 0], [-66.9322015857812, 0], [1999.0, 0]], [[1.0, 0], [-11.424164273725435, 0], [2003.0, 0]], [[1.0, 0], [58.29271953096293, 0], [2011.0, 0]], [[1.0, 0], [29.385810133105686, 0], [2017.0, 0]], [[1.0, 0], [10.747672319453937, 0], [2027.0, 0]], [[1.0, 0], [35.87204932977046, 0], [2029.0, 0]], [[1.0, 0], [46.827449801985175, 0], [2039.0, 0]], [[1.0, 0], [64.90112670251514, 0], [2053.0, 0]], [[1.0, 0], [27.96101911562646, 0], [2063.0, 0]], [[1.0, 0], [10.96631491328188, 0], [2069.0, 0]], [[1.0, 0], [-62.22923605081109, 0], [2081.0, 0]], [[1.0, 0], [2.322666287861194, 0], [2083.0, 0]], [[1.0, 0], [40.408366258572485, 0], [2087.0, 0]], [[1.0, 0], [7.2360748404728366, 0], [2089.0, 0]], [[1.0, 0], [-72.43406571179894, 0], [2099.0, 0]], [[1.0, 0], [-35.355019762627414, 0], [2111.0, 0]], [[1.0, 0], [-11.030181553048749, 0], [2113.0, 0]], [[1.0, 0], [-23.92588419465069, 0], [2129.0, 0]], [[1.0, 0], [-7.044802264763038, 0], [2131.0, 0]], [[1.0, 0], [-20.54998882560581, 0], [2137.0, 0]], [[1.0, 0], [83.92438341348114, 0], [2141.0, 0]], [[1.0, 0], [87.6744495362175, 0], [2143.0, 0]], [[1.0, 0], [-32.218317114955475, 0], [2153.0, 0]], [[1.0, 0], [-32.54899554967543, 0], [2161.0, 0]], [[1.0, 0], [44.03669112816865, 0], [2179.0, 0]], [[1.0, 0], [-59.981135113488726, 0], [2203.0, 0]], [[1.0, 0], [-23.79760538611843, 0], [2207.0, 0]], [[1.0, 0], [70.2691970102301, 0], [2213.0, 0]], [[1.0, 0], [-42.93654345353285, 0], [2221.0, 0]], [[1.0, 0], [-68.40418326706754, 0], [2237.0, 0]], [[1.0, 0], [-67.43316518922633, 0], [2239.0, 0]], [[1.0, 0], [11.667100596821577, 0], [2243.0, 0]], [[1.0, 0], [-67.44252732055018, 0], [2251.0, 0]], [[1.0, 0], [2.3337236926197327, 0], [2267.0, 0]], [[1.0, 0], [-52.21605304798762, 0], [2269.0, 0]], [[1.0, 0], [34.05568183332015, 0], [2273.0, 0]], [[1.0, 0], [-27.858167526085563, 0], [2281.0, 0]], [[1.0, 0], [-18.61384390993724, 0], [2287.0, 0]], [[1.0, 0], [-27.508469146041858, 0], [2293.0, 0]], [[1.0, 0], [31.50094791301245, 0], [2297.0, 0]], [[1.0, 0], [72.17156865076342, 0], [2309.0, 0]], [[1.0, 0], [-53.50466704785129, 0], [2311.0, 0]], [[1.0, 0], [60.771311825514125, 0], [2333.0, 0]], [[1.0, 0], [66.578822439735, 0], [2339.0, 0]], [[1.0, 0], [46.06868663428541, 0], [2341.0, 0]], [[1.0, 0], [-31.15645269066064, 0], [2347.0, 0]], [[1.0, 0], [30.088708764606118, 0], [2351.0, 0]], [[1.0, 0], [-51.76987378522916, 0], [2357.0, 0]], [[1.0, 0], [49.437031890073186, 0], [2371.0, 0]], [[1.0, 0], [-83.20294114709702, 0], [2377.0, 0]], [[1.0, 0], [-64.68402702958548, 0], [2381.0, 0]], [[1.0, 0], [16.451957685893575, 0], [2383.0, 0]], [[1.0, 0], [-36.310123482234694, 0], [2389.0, 0]], [[1.0, 0], [-2.188952158346809, 0], [2393.0, 0]], [[1.0, 0], [39.37691318180874, 0], [2399.0, 0]], [[1.0, 0], [-13.510297287941762, 0], [2411.0, 0]], [[1.0, 0], [-11.159955771448011, 0], [2417.0, 0]], [[1.0, 0], [23.49617385006574, 0], [2423.0, 0]], [[1.0, 0], [-29.268053266825618, 0], [2437.0, 0]], [[1.0, 0], [86.95192195622889, 0], [2441.0, 0]], [[1.0, 0], [6.070353534172007, 0], [2447.0, 0]], [[1.0, 0], [52.40786923065821, 0], [2459.0, 0]], [[1.0, 0], [2.862159342322162, 0], [2467.0, 0]], [[1.0, 0], [-9.982135679365593, 0], [2473.0, 0]], [[1.0, 0], [-45.98343227017764, 0], [2477.0, 0]], [[1.0, 0], [-20.791881840198073, 0], [2503.0, 0]], [[1.0, 0], [-57.86305092377817, 0], [2521.0, 0]], [[1.0, 0], [-68.27775731207412, 0], [2531.0, 0]], [[1.0, 0], [85.20016988826276, 0], [2539.0, 0]], [[1.0, 0], [-2.28640664265448, 0], [2543.0, 0]], [[1.0, 0], [11.390848333269687, 0], [2549.0, 0]], [[1.0, 0], [65.36906382004226, 0], [2551.0, 0]], [[1.0, 0], [27.708029266763184, 0], [2557.0, 0]], [[1.0, 0], [-62.92857023258969, 0], [2579.0, 0]], [[1.0, 0], [56.01114986147929, 0], [2591.0, 0]], [[1.0, 0], [6.405874487933441, 0], [2593.0, 0]], [[1.0, 0], [7.782824733914913, 0], [2609.0, 0]], [[1.0, 0], [-30.18025395053644, 0], [2617.0, 0]], [[1.0, 0], [-59.46211363274516, 0], [2621.0, 0]], [[1.0, 0], [-34.8016615579155, 0], [2633.0, 0]], [[1.0, 0], [-41.055254328898314, 0], [2647.0, 0]], [[1.0, 0], [36.18949747801388, 0], [2657.0, 0]], [[1.0, 0], [-75.00296096222908, 0], [2659.0, 0]], [[1.0, 0], [22.821327214744276, 0], [2663.0, 0]], [[1.0, 0], [55.27080394123987, 0], [2671.0, 0]], [[1.0, 0], [2.976076335874438, 0], [2677.0, 0]], [[1.0, 0], [-79.56255940690946, 0], [2683.0, 0]], [[1.0, 0], [-26.06948036485906, 0], [2687.0, 0]], [[1.0, 0], [36.00838643659923, 0], [2689.0, 0]], [[1.0, 0], [-16.919080276920656, 0], [2693.0, 0]], [[1.0, 0], [-38.176853795470265, 0], [2699.0, 0]], [[1.0, 0], [-43.511408341144055, 0], [2707.0, 0]], [[1.0, 0], [-68.65778787977388, 0], [2711.0, 0]], [[1.0, 0], [38.689309748654004, 0], [2713.0, 0]], [[1.0, 0], [10.923176823363844, 0], [2719.0, 0]], [[1.0, 0], [73.37613504584058, 0], [2729.0, 0]], [[1.0, 0], [45.80040967524803, 0], [2731.0, 0]], [[1.0, 0], [37.844540091398514, 0], [2741.0, 0]], [[1.0, 0], [-41.446321530900434, 0], [2749.0, 0]], [[1.0, 0], [-86.47124098729853, 0], [2753.0, 0]], [[1.0, 0], [-35.15044153459071, 0], [2767.0, 0]], [[1.0, 0], [56.59256705955018, 0], [2777.0, 0]], [[1.0, 0], [31.35060867795524, 0], [2789.0, 0]], [[1.0, 0], [-57.07823954594779, 0], [2791.0, 0]], [[1.0, 0], [91.37986474701464, 0], [2797.0, 0]], [[1.0, 0], [8.024057934284976, 0], [2801.0, 0]], [[1.0, 0], [56.1396162802535, 0], [2803.0, 0]], [[1.0, 0], [72.13762349271538, 0], [2819.0, 0]], [[1.0, 0], [-49.55027699205039, 0], [2833.0, 0]], [[1.0, 0], [-1.987979068489499, 0], [2837.0, 0]], [[1.0, 0], [-73.29137023119796, 0], [2843.0, 0]], [[1.0, 0], [10.428457290840363, 0], [2851.0, 0]], [[1.0, 0], [1.1821659259744528, 0], [2857.0, 0]], [[1.0, 0], [-2.385155303167391, 0], [2861.0, 0]], [[1.0, 0], [30.198519289511307, 0], [2879.0, 0]], [[1.0, 0], [28.4722863619404, 0], [2887.0, 0]], [[1.0, 0], [-22.377615511927104, 0], [2897.0, 0]], [[1.0, 0], [-56.26872661870769, 0], [2903.0, 0]], [[1.0, 0], [59.31969295155943, 0], [2909.0, 0]], [[1.0, 0], [104.13696747455757, 0], [2917.0, 0]], [[1.0, 0], [-56.62483263128191, 0], [2927.0, 0]], [[1.0, 0], [-3.0994072605726557, 0], [2939.0, 0]], [[1.0, 0], [-1.0524074140925517, 0], [2953.0, 0]], [[1.0, 0], [-30.951022897295687, 0], [2957.0, 0]], [[1.0, 0], [-68.43391848699068, 0], [2963.0, 0]], [[1.0, 0], [74.53902812177914, 0], [2969.0, 0]], [[1.0, 0], [-41.44930869135159, 0], [2971.0, 0]], [[1.0, 0], [37.93545781021899, 0], [2999.0, 0]]], 'gamma_factors': [[], [0]], 'group': 'GL2', 'index': 13, 'label': '2-5077-1.1-c1-0-13', 'leading_term': '0.084363509354260891929360380362860', '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': 0, 'origin': 'ModularForm/GL2/Q/holomorphic/5077/2/a/c/1/16', 'plot_delta': {'__RealLiteral__': 0, 'data': '0.05078125', 'prec': 34}, 'plot_values': [0.08436350935426089, 0.07794464443124698, 0.05870257888673225, 0.0266859745333301, -0.018007553854179393, -0.07520803679036252, -0.14464297884077137, -0.22590270804816776, -0.31840382147780893, -0.421353398643416, -0.5337165871911147, -0.6541899707535419, -0.7811828454976268, -0.912808192168767, -1.04688475786204, -1.180951270369881, -1.3122934042111116, -1.4379837030259341, -1.5549342377521156, -1.6599613442334666, -1.7498613401830847, -1.8214956753420468, -1.8718835292108327, -1.898299450023757, -1.8983732414676304, -1.8701889667015557, -1.8123796702367438, -1.7242142349950005, -1.6056727113062905, -1.4575064917892118, -1.2812798732310267, -1.0793898522932284, -0.8550614501619309, -0.612316451010519, -0.3559141635166893, -0.09126366081469811, 0.17569209684943987, 0.43861882590276186, 0.6909576652141403, 0.9261125144676473, 1.1376533192659974, 1.3195296716566844, 1.4662882244944133, 1.5732867068514476, 1.636896817535919, 1.6546880028235318, 1.625584125166118, 1.5499853267428298, 1.4298480007942127, 1.268716709449605, 1.0717031219464075, 0.8454085716528305, 0.5977886108757042, 0.33795993277064834, 0.07595217116406869, -0.1775906879030464, -0.4117523234259988, -0.615720423276856, -0.7791862821849482, -0.8927548737618197, -0.9483512585333189, -0.9396082619995245, -0.8622199284563948, -0.7142453829914249, -0.4963484532626594, -0.21195973123596976, 0.13265031318200088, 0.528396050449281, 0.9635051046908244, 1.4237528684599852, 1.8928017370868733, 2.352639685557388, 2.7841087509153857, 3.1675100131245935, 3.483267948929208, 3.7126337291946263, 3.838404297430942, 3.845632050004605, 3.7222987617579593, 3.459927163256999, 3.054104344775303, 2.5048929678677374, 1.8171090982187648, 1.0004492812219576, 0.0694541694901349, -0.956698557227595, -2.0545732391151494, -3.1970221486083323, -4.353886678314491, -5.4928358524139895, -6.580318232993377, -7.5825979607819365, -8.466841227400058, -9.202216144271288, -9.760966937547668, -10.119422799725308, -10.258902654995788, -10.16647957523324, -9.835572581712508, -9.2663389839257, -8.465847077096397, -7.448016720371513, -6.233323771703556, -4.848273243624877, -3.324655016023134, -1.6986046302706879, -0.009499724697255976, 1.7012702999411848, 3.3916180982636845, 5.0201083044835695, 6.547293921159186, 7.936989235650494, 9.157431066470048, 10.182283891710597, 10.99145006098783, 11.57165364250163, 11.916775229089197, 12.027924872407908, 11.913250826998466, 11.587492520644199, 11.071296658529972, 10.390325151155924, 9.574192186844757, 8.655274849372558, 7.667446873209788, 6.644788176972815, 5.620323558286866, 4.624842312969513, 3.6858466102583645, 2.826670375010552, 2.065802462535257, 1.416438420317678, 0.8862745493544909, 0.4775468000549432, 0.1873057923587572, 0.00790847493529262, -0.07230284501641474, -0.0681716841942221, 0.003207203520008275, 0.12347992680967569, 0.2740329869026231, 0.4369508316104193, 0.5958851733916729, 0.7367952666332589, 0.8485258231667772, 0.9231983697326146, 0.9564021405202577, 0.9471815113203332, 0.897827941668424, 0.8134948135432217, 0.7016628802773084, 0.5714917630992261, 0.4330986341810403, 0.29680859063642306, 0.17242206610696711, 0.06854289610228123, -0.007993556245810404, -0.052559262483323384, -0.06301476623205043, -0.03981793226458197, 0.014044053413433974, 0.09329284978820929, 0.1907502600568893, 0.297856190635625, 0.4052789343397058, 0.5035776389069412, 0.5838734451280285, 0.6384850571363866, 0.6614865154933856, 0.6491495944597051, 0.6002402913128975, 0.5161479223117968, 0.4008358633879418, 0.2606143507380566, 0.10374729962123765, -0.06008390331742819, -0.2204269222858283, -0.36677471510425075, -0.4893054285277829, -0.5795972109189474, -0.63126958174499, -0.640506467361101, -0.6064224409920949, -0.5312427677643694, -0.4202790564906588, -0.2816950150063176, -0.1260702397248663, 0.0342166813352025, 0.18575205335678158, 0.31495357046381284, 0.4089868376045816, 0.4566741944364439, 0.4493364722801417, 0.3815103867095737, 0.25149005297696353, 0.061650373834976575, -0.18147767153797803, -0.4673951784500717, -0.7820861027326768, -1.1087131764243445, -1.4285252208572823, -1.7219274085420133, -1.9696537987607345, -2.1539725946647272, -2.259849723606169, -2.2759959823871894, -2.195727306740112, -2.0175766264457975, -1.745608871293636, -1.3894073394424322, -0.9637189239349956, -0.4877665120559796, 0.015742014298137007, 0.5218586463058882, 1.0048266525599467, 1.4396168875482696, 1.8034775946991592, 2.0774018235615657, 2.2474178981421127, 2.3056156200680133, 2.2508338443817264, 2.0889531433893653, 1.8327595515699313, 1.501370643792952, 1.1192419914842868, 0.714798769463146, 0.3187622969361962, -0.03773701877170954, -0.32515197039199567, -0.5174968182909588, -0.5941883033646956, -0.5416295987479365, -0.35442829692288513, -0.036157516946504875, 0.4004065495018709, 0.9336081065809159, 1.5338010703861134, 2.164774918543538, 2.7856541077032855, 3.353176999474147, 3.824233674533628, 4.158521752157464, 4.321166808377861, 4.285150216886153, 4.033392739964284, 3.5603569432074194, 2.8730549074428393, 1.9913786318952253, 0.9477073431991966, -0.2142133800083505, -1.4410835050368929, -2.6724729712941495, -3.8437422268120027, -4.88931029334841, -5.746097438869015, -6.356954667885124, -6.673887960139144], 'positive_zeros': ['0.18433338596622281648753936447810', '1.79469421421637012349279387168192', '2.75712617516844992772617836127662', '3.33296929733516363652261949484210', '4.26920390487367769286386673385405', '5.38309510587203931695005671105156', '6.85869669058855305395261058452351', '7.00615291994394067502165105598001', '7.915446978229926872865696640792408', '8.113992731577510558275389862433321'], 'prelabel': '2-5077-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.367106808135393, 'root_angle': 0.0, 'root_number': '1', 'self_dual': True, 'sign_arg': 0, 'spectral_label': 'c1-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '0.18433338596622281648753936448', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '1.79469421421637012349279387168', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '2.75712617516844992772617836128', 'prec': 103}}
-
lfunc_search • Show schema
Hide schema
{'algebraic': True, 'analytic_conductor': 40.54004910620407, 'bad_primes': [5077], 'central_character': '1.1', 'conductor': 5077, 'conductor_radical': 5077, 'degree': 2, 'index': 13, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/5077/2/a/c/1/16'], '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': '2-5077-1.1-c1-0-13', 'motivic_weight': 1, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [1], 'order_of_vanishing': 0, 'prelabel': '2-5077-1.1-c1-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 6.367106808135393, 'root_angle': 0.0, 'self_dual': True, 'spectral_label': 'c1-0', 'z1': {'__RealLiteral__': 0, 'data': '0.18433338596622281648753936448', 'prec': 103}}
-
lfunc_instances • Show schema
Hide schema
{'Lhash': '233670327362184231409050991211', 'Lhash_array': ['233670327362184231409050991211'], 'label': '2-5077-1.1-c1-0-13', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/5077/2/a/c/1/16'}