Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [384,5,Mod(65,384)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(384, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 5, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("384.65");
S:= CuspForms(chi, 5);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 384 = 2^{7} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 5 \) |
Character orbit: | \([\chi]\) | \(=\) | 384.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(39.6940658242\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 65.3 | ||
Character | \(\chi\) | \(=\) | 384.65 |
Dual form | 384.5.h.h.65.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/384\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(133\) | \(257\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −8.73496 | + | 2.16806i | −0.970551 | + | 0.240896i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −14.5048 | −0.580191 | −0.290095 | − | 0.956998i | \(-0.593687\pi\) | ||||
−0.290095 | + | 0.956998i | \(0.593687\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −70.6373 | −1.44158 | −0.720788 | − | 0.693155i | \(-0.756220\pi\) | ||||
−0.720788 | + | 0.693155i | \(0.756220\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 71.5990 | − | 37.8759i | 0.883938 | − | 0.467603i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 163.140 | 1.34826 | 0.674131 | − | 0.738612i | \(-0.264519\pi\) | ||||
0.674131 | + | 0.738612i | \(0.264519\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 293.353i | 1.73582i | 0.496725 | + | 0.867908i | \(0.334536\pi\) | ||||
−0.496725 | + | 0.867908i | \(0.665464\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 126.699 | − | 31.4472i | 0.563105 | − | 0.139765i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 533.139i | 1.84477i | 0.386269 | + | 0.922386i | \(0.373764\pi\) | ||||
−0.386269 | + | 0.922386i | \(0.626236\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 314.108i | − | 0.870106i | −0.900405 | − | 0.435053i | \(-0.856730\pi\) | ||
0.900405 | − | 0.435053i | \(-0.143270\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 617.014 | − | 153.146i | 1.39912 | − | 0.347270i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 547.458i | 1.03489i | 0.855716 | + | 0.517446i | \(0.173117\pi\) | ||||
−0.855716 | + | 0.517446i | \(0.826883\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −414.612 | −0.663379 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −543.297 | + | 486.075i | −0.745264 | + | 0.666770i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 493.989 | 0.587383 | 0.293692 | − | 0.955900i | \(-0.405116\pi\) | ||||
0.293692 | + | 0.955900i | \(0.405116\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1042.74 | −1.08505 | −0.542527 | − | 0.840039i | \(-0.682532\pi\) | ||||
−0.542527 | + | 0.840039i | \(0.682532\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −1425.02 | + | 353.697i | −1.30856 | + | 0.324790i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1024.58 | 0.836389 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 550.113i | − | 0.401835i | −0.979608 | − | 0.200918i | \(-0.935608\pi\) | ||
0.979608 | − | 0.200918i | \(-0.0643924\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −636.007 | − | 2562.42i | −0.418151 | − | 1.68470i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 339.288i | − | 0.201837i | −0.994895 | − | 0.100918i | \(-0.967822\pi\) | ||
0.994895 | − | 0.100918i | \(-0.0321781\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2585.68i | − | 1.39842i | −0.714915 | − | 0.699211i | \(-0.753535\pi\) | ||
0.714915 | − | 0.699211i | \(-0.246465\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1038.53 | + | 549.380i | −0.512853 | + | 0.271299i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 100.167i | 0.0453449i | 0.999743 | + | 0.0226725i | \(0.00721749\pi\) | ||||
−0.999743 | + | 0.0226725i | \(0.992783\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 2588.62 | 1.07814 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1155.88 | − | 4656.95i | −0.444398 | − | 1.79045i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1409.01 | 0.501605 | 0.250802 | − | 0.968038i | \(-0.419306\pi\) | ||||
0.250802 | + | 0.968038i | \(0.419306\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2366.30 | −0.782248 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 681.006 | + | 2743.72i | 0.209605 | + | 0.844482i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1439.43 | 0.413511 | 0.206756 | − | 0.978393i | \(-0.433710\pi\) | ||||
0.206756 | + | 0.978393i | \(0.433710\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4990.69i | 1.34122i | 0.741809 | + | 0.670611i | \(0.233968\pi\) | ||||
−0.741809 | + | 0.670611i | \(0.766032\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −5057.56 | + | 2675.45i | −1.27426 | + | 0.674086i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 4255.01i | − | 1.00710i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 168.946i | − | 0.0376355i | −0.999823 | − | 0.0188178i | \(-0.994010\pi\) | ||
0.999823 | − | 0.0188178i | \(-0.00599024\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1186.92 | − | 4782.02i | −0.249301 | − | 1.00442i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 5261.70i | − | 1.04378i | −0.853012 | − | 0.521890i | \(-0.825227\pi\) | ||
0.853012 | − | 0.521890i | \(-0.174773\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1244.91 | 0.233610 | 0.116805 | − | 0.993155i | \(-0.462735\pi\) | ||||
0.116805 | + | 0.993155i | \(0.462735\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 3621.62 | − | 898.904i | 0.643843 | − | 0.159805i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −11523.7 | −1.94362 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7421.94 | −1.18922 | −0.594611 | − | 0.804013i | \(-0.702694\pi\) | ||||
−0.594611 | + | 0.804013i | \(0.702694\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 3691.84 | − | 5423.75i | 0.562694 | − | 0.826665i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −116.567 | −0.0169207 | −0.00846037 | − | 0.999964i | \(-0.502693\pi\) | ||||
−0.00846037 | + | 0.999964i | \(0.502693\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 7733.06i | − | 1.07032i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4314.98 | + | 1071.00i | −0.570085 | + | 0.141498i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 7446.53i | − | 0.940100i | −0.882640 | − | 0.470050i | \(-0.844236\pi\) | ||
0.882640 | − | 0.470050i | \(-0.155764\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 20721.6i | − | 2.50231i | ||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 9108.26 | − | 2260.72i | 1.05310 | − | 0.261385i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4556.07i | 0.504827i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8270.40 | −0.878988 | −0.439494 | − | 0.898245i | \(-0.644842\pi\) | ||||
−0.439494 | + | 0.898245i | \(0.644842\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 11680.6 | − | 6179.05i | 1.19178 | − | 0.630451i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6550.90 | −0.642182 | −0.321091 | − | 0.947048i | \(-0.604050\pi\) | ||||
−0.321091 | + | 0.947048i | \(0.604050\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14142.4 | −1.33306 | −0.666529 | − | 0.745479i | \(-0.732221\pi\) | ||||
−0.666529 | + | 0.745479i | \(0.732221\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −8949.64 | + | 2221.35i | −0.811758 | + | 0.201483i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −3657.73 | −0.319481 | −0.159740 | − | 0.987159i | \(-0.551066\pi\) | ||||
−0.159740 | + | 0.987159i | \(0.551066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 8706.79i | − | 0.732833i | −0.930451 | − | 0.366416i | \(-0.880585\pi\) | ||
0.930451 | − | 0.366416i | \(-0.119415\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1192.68 | + | 4805.21i | 0.0968004 | + | 0.390002i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15404.2i | 1.20637i | 0.797600 | + | 0.603187i | \(0.206103\pi\) | ||||
−0.797600 | + | 0.603187i | \(0.793897\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 7940.75i | − | 0.600435i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 11111.0 | + | 21003.8i | 0.811673 | + | 1.53435i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 37659.5i | − | 2.65938i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 11973.5 | 0.817808 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 735.597 | + | 2963.67i | 0.0486217 | + | 0.195893i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 15079.3 | 0.965077 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −22620.8 | −1.40249 | −0.701247 | − | 0.712918i | \(-0.747373\pi\) | ||||
−0.701247 | + | 0.712918i | \(0.747373\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5605.92 | + | 22585.8i | 0.336874 | + | 1.35724i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9335.23 | −0.543980 | −0.271990 | − | 0.962300i | \(-0.587682\pi\) | ||||
−0.271990 | + | 0.962300i | \(0.587682\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 22187.7i | 1.25432i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7880.40 | − | 7050.41i | 0.432395 | − | 0.386854i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 18160.9i | − | 0.967602i | −0.875178 | − | 0.483801i | \(-0.839256\pi\) | ||
0.875178 | − | 0.483801i | \(-0.160744\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 9492.75i | 0.491318i | 0.969356 | + | 0.245659i | \(0.0790043\pi\) | ||||
−0.969356 | + | 0.245659i | \(0.920996\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −217.168 | − | 874.954i | −0.0109234 | − | 0.0440096i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 47857.5i | 2.34033i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −7165.20 | −0.340794 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −22611.5 | + | 5612.29i | −1.04639 | + | 0.259720i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −19050.9 | −0.858112 | −0.429056 | − | 0.903278i | \(-0.641154\pi\) | ||||
−0.429056 | + | 0.903278i | \(0.641154\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 39824.5 | 1.74661 | 0.873305 | − | 0.487174i | \(-0.161972\pi\) | ||||
0.873305 | + | 0.487174i | \(0.161972\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 20193.1 | + | 38172.2i | 0.862621 | + | 1.63066i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 15124.6 | 0.629538 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 1276.46i | − | 0.0517855i | −0.999665 | − | 0.0258928i | \(-0.991757\pi\) | ||
0.999665 | − | 0.0258928i | \(-0.00824284\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −12307.6 | + | 3054.81i | −0.486833 | + | 0.120834i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 38670.9i | − | 1.49188i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 12463.5i | − | 0.469098i | −0.972104 | − | 0.234549i | \(-0.924639\pi\) | ||
0.972104 | − | 0.234549i | \(-0.0753614\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 20669.5 | − | 5130.29i | 0.759212 | − | 0.188440i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 18549.8i | − | 0.665129i | −0.943081 | − | 0.332564i | \(-0.892086\pi\) | ||
0.943081 | − | 0.332564i | \(-0.107914\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −57494.9 | −2.01306 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −11897.1 | − | 22489.8i | −0.406864 | − | 0.769120i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2994.42 | 0.100051 | 0.0500254 | − | 0.998748i | \(-0.484070\pi\) | ||||
0.0500254 | + | 0.998748i | \(0.484070\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 29287.0 | 0.956311 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −12573.4 | + | 3120.78i | −0.401334 | + | 0.0996131i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 49036.1 | 1.53042 | 0.765208 | − | 0.643783i | \(-0.222636\pi\) | ||||
0.765208 | + | 0.643783i | \(0.222636\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 28051.5i | − | 0.856247i | −0.903720 | − | 0.428124i | \(-0.859175\pi\) | ||
0.903720 | − | 0.428124i | \(-0.140825\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −10820.1 | − | 43593.4i | −0.323095 | − | 1.30172i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 7979.25i | 0.233141i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 86976.1i | 2.48723i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 38377.0 | − | 34335.0i | 1.07435 | − | 0.961200i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 50035.7i | 1.37156i | 0.727811 | + | 0.685778i | \(0.240538\pi\) | ||||
−0.727811 | + | 0.685778i | \(0.759462\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 30906.3 | 0.829722 | 0.414861 | − | 0.909885i | \(-0.363830\pi\) | ||||
0.414861 | + | 0.909885i | \(0.363830\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 9225.13 | + | 37167.4i | 0.242607 | + | 0.977446i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −40327.4 | −1.03912 | −0.519562 | − | 0.854432i | \(-0.673905\pi\) | ||||
−0.519562 | + | 0.854432i | \(0.673905\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −706.369 | −0.0178372 | −0.00891858 | − | 0.999960i | \(-0.502839\pi\) | ||||
−0.00891858 | + | 0.999960i | \(0.502839\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 366.285 | + | 1475.74i | 0.00906624 | + | 0.0365272i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −34894.0 | −0.846758 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 4921.29i | 0.117104i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 20735.4 | + | 39197.4i | 0.483919 | + | 0.914781i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 51243.5i | − | 1.17313i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 33541.1i | 0.753376i | 0.926340 | + | 0.376688i | \(0.122937\pi\) | ||||
−0.926340 | + | 0.376688i | \(0.877063\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 11407.7 | + | 45960.7i | 0.251442 | + | 1.01304i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 37504.7i | 0.811351i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 73656.0 | 1.56419 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −10874.2 | + | 2699.04i | −0.226731 | + | 0.0562758i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −156398. | −3.20218 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 58954.5 | 1.18552 | 0.592758 | − | 0.805381i | \(-0.298039\pi\) | ||||
0.592758 | + | 0.805381i | \(0.298039\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −29685.8 | + | 15703.8i | −0.586386 | + | 0.310198i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −72396.6 | −1.40497 | −0.702484 | − | 0.711700i | \(-0.747926\pi\) | ||||
−0.702484 | + | 0.711700i | \(0.747926\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 20382.8i | − | 0.388681i | −0.980934 | − | 0.194340i | \(-0.937743\pi\) | ||
0.980934 | − | 0.194340i | \(-0.0622566\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 100659. | − | 24984.2i | 1.88638 | − | 0.468210i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 77399.0i | − | 1.42569i | −0.701324 | − | 0.712843i | \(-0.747407\pi\) | ||
0.701324 | − | 0.712843i | \(-0.252593\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 1452.90i | − | 0.0263087i | ||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 64830.3 | − | 16091.2i | 1.15420 | − | 0.286479i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 31052.7i | − | 0.543630i | −0.962349 | − | 0.271815i | \(-0.912376\pi\) | ||
0.962349 | − | 0.271815i | \(-0.0876239\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 61434.1 | 1.05773 | 0.528866 | − | 0.848706i | \(-0.322618\pi\) | ||||
0.528866 | + | 0.848706i | \(0.322618\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −20489.0 | + | 55380.4i | −0.346984 | + | 0.937871i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −37547.3 | −0.625528 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 92144.5 | 1.51034 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1018.21 | − | 252.724i | 0.0164224 | − | 0.00407613i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 58318.0 | 0.925668 | 0.462834 | − | 0.886445i | \(-0.346833\pi\) | ||||
0.462834 | + | 0.886445i | \(0.346833\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 89312.0i | 1.39530i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 16765.7 | + | 67547.9i | 0.257835 | + | 1.03880i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 19572.9i | − | 0.296339i | −0.988962 | − | 0.148170i | \(-0.952662\pi\) | ||
0.988962 | − | 0.148170i | \(-0.0473381\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 38858.4i | 0.579276i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 35369.1 | − | 18710.3i | 0.519211 | − | 0.274662i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 111228.i | − | 1.60807i | −0.594585 | − | 0.804033i | \(-0.702683\pi\) | ||
0.594585 | − | 0.804033i | \(-0.297317\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −20437.3 | −0.291026 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 16144.5 | + | 65045.1i | 0.226466 | + | 0.912415i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 38148.0 | 0.527190 | 0.263595 | − | 0.964633i | \(-0.415092\pi\) | ||||
0.263595 | + | 0.964633i | \(0.415092\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −73859.9 | −1.00570 | −0.502852 | − | 0.864373i | \(-0.667716\pi\) | ||||
−0.502852 | + | 0.864373i | \(0.667716\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 44925.8 | + | 181003.i | 0.602796 | + | 2.42862i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −67639.6 | −0.894408 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 92295.7i | − | 1.20288i | −0.798918 | − | 0.601440i | \(-0.794594\pi\) | ||
0.798918 | − | 0.601440i | \(-0.205406\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −74658.9 | + | 39494.5i | −0.959120 | + | 0.507374i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 24602.7i | − | 0.311580i | −0.987790 | − | 0.155790i | \(-0.950208\pi\) | ||
0.987790 | − | 0.155790i | \(-0.0497923\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 23094.4i | − | 0.288359i | −0.989552 | − | 0.144179i | \(-0.953946\pi\) | ||
0.989552 | − | 0.144179i | \(-0.0460542\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −9877.83 | − | 39797.0i | −0.121611 | − | 0.489961i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 23966.4i | 0.290963i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −200716. | −2.40318 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 72241.6 | − | 17930.7i | 0.853103 | − | 0.211745i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 94473.1 | 1.10046 | 0.550228 | − | 0.835014i | \(-0.314541\pi\) | ||||
0.550228 | + | 0.835014i | \(0.314541\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −20878.6 | −0.239915 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −88633.3 | + | 79298.1i | −1.00481 | + | 0.898980i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −160598. | −1.79638 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 182646.i | 2.01593i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 57221.8 | − | 14202.8i | 0.623270 | − | 0.154699i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 72388.7i | − | 0.778164i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21965.4i | 0.233057i | 0.993187 | + | 0.116529i | \(0.0371767\pi\) | ||||
−0.993187 | + | 0.116529i | \(0.962823\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 123533. | − | 30661.6i | 1.29380 | − | 0.321128i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 161.545i | 0.00167022i | 1.00000 | 0.000835109i | \(0.000265823\pi\) | |||||
−1.00000 | 0.000835109i | \(0.999734\pi\) | ||||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22811.8 | 0.232847 | 0.116424 | − | 0.993200i | \(-0.462857\pi\) | ||||
0.116424 | + | 0.993200i | \(0.462857\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 73358.7 | − | 38806.7i | 0.739317 | − | 0.391098i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −11173.0 | −0.111187 | −0.0555933 | − | 0.998453i | \(-0.517705\pi\) | ||||
−0.0555933 | + | 0.998453i | \(0.517705\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 80589.2 | 0.791946 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 31950.2 | − | 7930.19i | 0.310072 | − | 0.0769615i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 167463. | 1.60515 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 121628.i | − | 1.15150i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 18876.9 | + | 76053.4i | 0.176536 | + | 0.711252i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 7075.52i | − | 0.0653682i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 20196.8i | − | 0.184343i | −0.995743 | − | 0.0921715i | \(-0.970619\pi\) | ||
0.995743 | − | 0.0921715i | \(-0.0293808\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −20836.0 | − | 39387.5i | −0.187900 | − | 0.355198i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2450.52i | 0.0218358i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 69854.6 | 0.615085 | 0.307543 | − | 0.951534i | \(-0.400493\pi\) | ||||
0.307543 | + | 0.951534i | \(0.400493\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −33397.2 | − | 134555.i | −0.290610 | − | 1.17085i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −170112. | −1.46293 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13253.1 | −0.112649 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 17216.0 | + | 69362.1i | 0.144642 | + | 0.582752i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 118904. | 0.987503 | 0.493751 | − | 0.869603i | \(-0.335625\pi\) | ||||
0.493751 | + | 0.869603i | \(0.335625\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 32493.5i | − | 0.266775i | −0.991064 | − | 0.133388i | \(-0.957414\pi\) | ||
0.991064 | − | 0.133388i | \(-0.0425856\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −142592. | − | 159378.i | −1.15739 | − | 1.29364i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 15417.5i | − | 0.123727i | −0.998085 | − | 0.0618636i | \(-0.980296\pi\) | ||
0.998085 | − | 0.0618636i | \(-0.0197044\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 76319.7i | 0.605592i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 81648.1 | + | 328954.i | 0.640633 | + | 2.58106i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 237534.i | 1.84305i | 0.388321 | + | 0.921524i | \(0.373055\pi\) | ||||
−0.388321 | + | 0.921524i | \(0.626945\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 31657.0 | 0.242916 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −104588. | + | 25959.3i | −0.793724 | + | 0.197006i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18057.1 | −0.135539 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −84181.0 | −0.625003 | −0.312502 | − | 0.949917i | \(-0.601167\pi\) | ||||
−0.312502 | + | 0.949917i | \(0.601167\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −12850.8 | − | 24292.7i | −0.0943796 | − | 0.178411i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −99528.4 | −0.723101 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 79258.9i | 0.569679i | 0.958575 | + | 0.284840i | \(0.0919404\pi\) | ||||
−0.958575 | + | 0.284840i | \(0.908060\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −131717. | + | 32692.9i | −0.936656 | + | 0.232483i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 144913.i | 1.01959i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 115025.i | − | 0.800778i | −0.916345 | − | 0.400389i | \(-0.868875\pi\) | ||
0.916345 | − | 0.400389i | \(-0.131125\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 197592. | − | 49043.4i | 1.36119 | − | 0.337855i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 190876.i | − | 1.30123i | −0.759408 | − | 0.650615i | \(-0.774511\pi\) | ||
0.759408 | − | 0.650615i | \(-0.225489\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 167149. | 1.12767 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −97935.0 | − | 185132.i | −0.653907 | − | 1.23612i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −190095. | −1.25624 | −0.628119 | − | 0.778118i | \(-0.716175\pi\) | ||||
−0.628119 | + | 0.778118i | \(0.716175\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −291871. | −1.90914 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 81542.9 | − | 20239.4i | 0.527960 | − | 0.131042i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 107653. | 0.689976 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 73036.2i | − | 0.463401i | −0.972787 | − | 0.231700i | \(-0.925571\pi\) | ||
0.972787 | − | 0.231700i | \(-0.0744289\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −48104.4 | − | 193809.i | −0.302161 | − | 1.21739i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 141470.i | − | 0.879782i | −0.898051 | − | 0.439891i | \(-0.855017\pi\) | ||
0.898051 | − | 0.439891i | \(-0.144983\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 305890.i | − | 1.88345i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −53549.2 | + | 78670.2i | −0.326470 | + | 0.479623i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 89745.1i | − | 0.541779i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −172765. | −1.03279 | −0.516393 | − | 0.856352i | \(-0.672725\pi\) | ||||
−0.516393 | + | 0.856352i | \(0.672725\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 39374.0 | + | 158635.i | 0.233091 | + | 0.939107i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −101678. | −0.596108 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1690.78 | 0.00981725 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −20580.9 | − | 82918.8i | −0.118356 | − | 0.476849i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 192120. | 1.09432 | 0.547159 | − | 0.837029i | \(-0.315709\pi\) | ||||
0.547159 | + | 0.837029i | \(0.315709\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 307033.i | − | 1.73229i | −0.499793 | − | 0.866145i | \(-0.666591\pi\) | ||
0.499793 | − | 0.866145i | \(-0.333409\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 3793.91 | + | 7171.85i | 0.0212034 | + | 0.0400821i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 221046.i | − | 1.22378i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 352528.i | − | 1.93347i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −103758. | − | 418033.i | −0.563776 | − | 2.27141i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 106621.i | − | 0.573969i | −0.957935 | − | 0.286984i | \(-0.907347\pi\) | ||
0.957935 | − | 0.286984i | \(-0.0926528\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −174550. | −0.930990 | −0.465495 | − | 0.885051i | \(-0.654124\pi\) | ||||
−0.465495 | + | 0.885051i | \(0.654124\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 62587.7 | − | 15534.6i | 0.330758 | − | 0.0820959i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 171961. | 0.900466 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −149048. | −0.773389 | −0.386694 | − | 0.922208i | \(-0.626383\pi\) | ||||
−0.386694 | + | 0.922208i | \(0.626383\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 185343. | − | 98046.3i | 0.953012 | − | 0.504143i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 135015. | 0.687979 | 0.343989 | − | 0.938974i | \(-0.388222\pi\) | ||||
0.343989 | + | 0.938974i | \(0.388222\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 108010.i | 0.545437i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 166409. | − | 41303.6i | 0.832842 | − | 0.206716i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 94873.2i | 0.470599i | 0.971923 | + | 0.235299i | \(0.0756071\pi\) | ||||
−0.971923 | + | 0.235299i | \(0.924393\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 55351.3i | − | 0.272129i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −347865. | + | 86341.9i | −1.69517 | + | 0.420751i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 300562.i | 1.45182i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −67995.0 | −0.325570 | −0.162785 | − | 0.986662i | \(-0.552048\pi\) | ||||
−0.162785 | + | 0.986662i | \(0.552048\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −259146. | − | 289653.i | −1.23004 | − | 1.37484i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −102453. | −0.482086 | −0.241043 | − | 0.970514i | \(-0.577489\pi\) | ||||
−0.241043 | + | 0.970514i | \(0.577489\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −256628. | −1.19713 | −0.598567 | − | 0.801073i | \(-0.704263\pi\) | ||||
−0.598567 | + | 0.801073i | \(0.704263\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −132113. | + | 32791.2i | −0.610998 | + | 0.151653i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −161298. | −0.739597 | −0.369799 | − | 0.929112i | \(-0.620573\pi\) | ||||
−0.369799 | + | 0.929112i | \(0.620573\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11933.9i | 0.0542545i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2767.45 | + | 11149.8i | 0.0124749 | + | 0.0502605i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 421827.i | − | 1.88544i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 130233.i | 0.577210i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 100884. | − | 53367.4i | 0.443388 | − | 0.234552i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 179193.i | − | 0.780999i | −0.920603 | − | 0.390499i | \(-0.872302\pi\) | ||
0.920603 | − | 0.390499i | \(-0.127698\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 161377. | 0.697512 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 83840.9 | + | 337789.i | 0.359387 | + | 1.44794i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 119960. | 0.509981 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 13645.2 | 0.0575339 | 0.0287669 | − | 0.999586i | \(-0.490842\pi\) | ||||
0.0287669 | + | 0.999586i | \(0.490842\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 27021.6 | + | 108868.i | 0.113004 | + | 0.455284i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −425902. | −1.76664 | −0.883318 | − | 0.468774i | \(-0.844696\pi\) | ||||
−0.883318 | + | 0.468774i | \(0.844696\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 263365.i | 1.08359i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −169425. | + | 89625.7i | −0.691459 | + | 0.365782i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 371672.i | 1.50469i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 116410.i | 0.467507i | 0.972296 | + | 0.233753i | \(0.0751008\pi\) | ||||
−0.972296 | + | 0.233753i | \(0.924899\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 40217.0 | + | 162031.i | 0.160227 | + | 0.645541i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 395157.i | 1.56183i | 0.624637 | + | 0.780915i | \(0.285247\pi\) | ||||
−0.624637 | + | 0.780915i | \(0.714753\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 95019.3 | 0.372588 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 502215. | − | 124652.i | 1.95377 | − | 0.484936i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 492582. | 1.90126 | 0.950632 | − | 0.310319i | \(-0.100436\pi\) | ||||
0.950632 | + | 0.310319i | \(0.100436\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −87937.0 | −0.336767 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 152680. | + | 170654.i | 0.580160 | + | 0.648458i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 205132. | 0.773427 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16341.2i | 0.0611368i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −26156.2 | + | 6492.09i | −0.0971045 | + | 0.0241018i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 498910.i | 1.83801i | 0.394249 | + | 0.919003i | \(0.371005\pi\) | ||||
−0.394249 | + | 0.919003i | \(0.628995\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 174522.i | 0.638040i | 0.947748 | + | 0.319020i | \(0.103354\pi\) | ||||
−0.947748 | + | 0.319020i | \(0.896646\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −255821. | + | 63496.1i | −0.928149 | + | 0.230371i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 555923.i | − | 2.00168i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −19869.1 | −0.0710014 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 103062. | − | 54519.7i | 0.365518 | − | 0.193359i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 99531.0 | 0.350352 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 53054.6 | 0.185360 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −428328. | + | 106313.i | −1.48535 | + | 0.368671i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 422307. | 1.45362 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 185893.i | 0.635139i | 0.948235 | + | 0.317569i | \(0.102867\pi\) | ||||
−0.948235 | + | 0.317569i | \(0.897133\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 60817.4 | + | 245029.i | 0.206266 | + | 0.831032i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 126290.i | 0.425183i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 378740.i | − | 1.26580i | −0.774232 | − | 0.632902i | \(-0.781864\pi\) | ||
0.774232 | − | 0.632902i | \(-0.218136\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 189027. | + | 357328.i | 0.627160 | + | 1.18556i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 155166.i | − | 0.511086i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 524265. | 1.71436 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −17299.5 | − | 69698.5i | −0.0561627 | − | 0.226275i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 159324. | 0.513537 | 0.256768 | − | 0.966473i | \(-0.417342\pi\) | ||||
0.256768 | + | 0.966473i | \(0.417342\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 758517. | 2.42740 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −188570. | − | 759733.i | −0.599164 | − | 2.41399i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −437248. | −1.37947 | −0.689733 | − | 0.724063i | \(-0.742272\pi\) | ||||
−0.689733 | + | 0.724063i | \(0.742272\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 223434.i | − | 0.699926i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −260781. | + | 383119.i | −0.811167 | + | 1.19170i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 300156.i | 0.927092i | 0.886073 | + | 0.463546i | \(0.153423\pi\) | ||||
−0.886073 | + | 0.463546i | \(0.846577\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 202047.i | 0.619698i | 0.950786 | + | 0.309849i | \(0.100279\pi\) | ||||
−0.950786 | + | 0.309849i | \(0.899721\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −108481. | − | 437060.i | −0.330402 | − | 1.33117i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 226982.i | − | 0.686525i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −207377. | −0.622887 | −0.311443 | − | 0.950265i | \(-0.600812\pi\) | ||||
−0.311443 | + | 0.950265i | \(0.600812\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −269965. | + | 67006.8i | −0.805288 | + | 0.199877i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 8233.97 | 0.0243925 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 229865. | 0.676294 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −161162. | − | 304655.i | −0.470925 | − | 0.890218i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −545839. | −1.58412 | −0.792060 | − | 0.610443i | \(-0.790991\pi\) | ||||
−0.792060 | + | 0.610443i | \(0.790991\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 327532.i | 0.944111i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 352258. | − | 87432.3i | 1.00852 | − | 0.250321i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 124034.i | 0.352720i | 0.984326 | + | 0.176360i | \(0.0564323\pi\) | ||||
−0.984326 | + | 0.176360i | \(0.943568\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 546242.i | 1.54295i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 6170.11 | − | 1531.45i | 0.0173119 | − | 0.00429690i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 216086.i | 0.602243i | 0.953586 | + | 0.301122i | \(0.0973610\pi\) | ||||
−0.953586 | + | 0.301122i | \(0.902639\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −590209. | −1.63402 | −0.817009 | − | 0.576625i | \(-0.804369\pi\) | ||||
−0.817009 | + | 0.576625i | \(0.804369\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −6398.97 | − | 12096.4i | −0.0175985 | − | 0.0332675i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −173673. | −0.474484 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 27397.4 | 0.0743587 | 0.0371794 | − | 0.999309i | \(-0.488163\pi\) | ||||
0.0371794 | + | 0.999309i | \(0.488163\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 304798. | − | 75652.4i | 0.821822 | − | 0.203980i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −29384.3 | −0.0787104 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 594961.i | − | 1.58331i | −0.610965 | − | 0.791657i | \(-0.709219\pi\) | ||
0.610965 | − | 0.791657i | \(-0.290781\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −10669.7 | − | 42987.3i | −0.0282098 | − | 0.113655i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 614701.i | 1.61471i | 0.590068 | + | 0.807353i | \(0.299101\pi\) | ||||
−0.590068 | + | 0.807353i | \(0.700899\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 676244.i | 1.76491i | 0.470399 | + | 0.882454i | \(0.344110\pi\) | ||||
−0.470399 | + | 0.882454i | \(0.655890\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −266106. | − | 297432.i | −0.690035 | − | 0.771267i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 526002.i | 1.35523i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 40410.3 | 0.103450 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 111099. | + | 447610.i | 0.282602 | + | 1.13858i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 293287. | 0.741295 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 176191. | 0.442513 | 0.221256 | − | 0.975216i | \(-0.428984\pi\) | ||||
0.221256 | + | 0.975216i | \(0.428984\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −72719.1 | − | 292980.i | −0.181485 | − | 0.731190i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 328110. | 0.813714 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 759379.i | 1.87146i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −199291. | − | 376733.i | −0.488075 | − | 0.922638i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 191375.i | − | 0.465767i | −0.972505 | − | 0.232883i | \(-0.925184\pi\) | ||
0.972505 | − | 0.232883i | \(-0.0748161\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 323396.i | 0.782191i | 0.920350 | + | 0.391095i | \(0.127904\pi\) | ||||
−0.920350 | + | 0.391095i | \(0.872096\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −81312.6 | − | 327602.i | −0.195451 | − | 0.787458i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 451814.i | − | 1.07932i | −0.841882 | − | 0.539662i | \(-0.818552\pi\) | ||
0.841882 | − | 0.539662i | \(-0.181448\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 234828. | 0.557521 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −643382. | + | 159691.i | −1.51812 | + | 0.376806i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 467328. | 1.09596 | 0.547980 | − | 0.836491i | \(-0.315397\pi\) | ||||
0.547980 | + | 0.836491i | \(0.315397\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 135405. | 0.315612 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 89134.3 | − | 47152.0i | 0.206497 | − | 0.109237i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 163218. | 0.375835 | 0.187918 | − | 0.982185i | \(-0.439826\pi\) | ||||
0.187918 | + | 0.982185i | \(0.439826\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 698278.i | − | 1.59818i | −0.601212 | − | 0.799090i | \(-0.705315\pi\) | ||
0.601212 | − | 0.799090i | \(-0.294685\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.36613e6 | − | 339080.i | 3.10788 | − | 0.771392i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 321828.i | − | 0.727747i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 270438.i | 0.607878i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −514965. | + | 127817.i | −1.15060 | + | 0.285586i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 814178.i | 1.80832i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −397119. | −0.876779 | −0.438389 | − | 0.898785i | \(-0.644451\pi\) | ||||
−0.438389 | + | 0.898785i | \(0.644451\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 225257. | − | 201533.i | 0.494392 | − | 0.442321i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 495877. | 1.08192 | 0.540962 | − | 0.841047i | \(-0.318060\pi\) | ||||
0.540962 | + | 0.841047i | \(0.318060\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 584198. | 1.26713 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 632381. | − | 156960.i | 1.36359 | − | 0.338451i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −713524. | −1.52956 | −0.764781 | − | 0.644290i | \(-0.777153\pi\) | ||||
−0.764781 | + | 0.644290i | \(0.777153\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 263420.i | 0.561394i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 44191.2 | + | 178043.i | 0.0936315 | + | 0.377234i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 413336.i | 0.870693i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 801221.i | − | 1.67802i | −0.544118 | − | 0.839009i | \(-0.683136\pi\) | ||
0.544118 | − | 0.839009i | \(-0.316864\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −825088. | + | 436471.i | −1.71804 | + | 0.908844i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 137690.i | − | 0.285058i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 180888. | 0.372343 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 167806. | + | 676077.i | 0.343442 | + | 1.38370i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −572005. | −1.16403 | −0.582015 | − | 0.813178i | \(-0.697735\pi\) | ||||
−0.582015 | + | 0.813178i | \(0.697735\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −172795. | −0.349639 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3149.97 | + | 12691.0i | 0.00633765 | + | 0.0255339i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 462738. | 0.925755 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 447501.i | 0.890228i | 0.895474 | + | 0.445114i | \(0.146837\pi\) | ||||
−0.895474 | + | 0.445114i | \(0.853163\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −531404. | + | 281112.i | −1.05120 | + | 0.556084i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 570854.i | − | 1.12291i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 694161.i | − | 1.35784i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 67324.2 | + | 271244.i | 0.130958 | + | 0.527621i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 614041.i | 1.18779i | 0.804542 | + | 0.593895i | \(0.202411\pi\) | ||||
−0.804542 | + | 0.593895i | \(0.797589\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 998981. | 1.92170 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −536624. | + | 133193.i | −1.02658 | + | 0.254803i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −204814. | −0.389658 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −503006. | −0.951709 | −0.475855 | − | 0.879524i | \(-0.657861\pi\) | ||||
−0.475855 | + | 0.879524i | \(0.657861\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 58902.8 | − | 528167.i | 0.110836 | − | 0.993839i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.37853e6 | 2.57977 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 558326.i | − | 1.03915i | −0.854424 | − | 0.519577i | \(-0.826090\pi\) | ||
0.854424 | − | 0.519577i | \(-0.173910\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 327975. | − | 81405.0i | 0.607107 | − | 0.150687i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 27561.8i | − | 0.0507425i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 897002.i | 1.64250i | 0.570571 | + | 0.821248i | \(0.306722\pi\) | ||||
−0.570571 | + | 0.821248i | \(0.693278\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −804879. | + | 199775.i | −1.46587 | + | 0.363835i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 28448.2i | − | 0.0515319i | −0.999668 | − | 0.0257660i | \(-0.991798\pi\) | ||
0.999668 | − | 0.0257660i | \(-0.00820247\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 276330. | 0.497869 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −8346.08 | + | 4415.08i | −0.0149569 | + | 0.00791219i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 258372. | 0.460556 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 157854. | 0.279883 | 0.139941 | − | 0.990160i | \(-0.455309\pi\) | ||||
0.139941 | + | 0.990160i | \(0.455309\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −509405. | + | 126437.i | −0.898408 | + | 0.222990i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −577644. | −1.01337 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 485489.i | − | 0.847202i | −0.905849 | − | 0.423601i | \(-0.860766\pi\) | ||
0.905849 | − | 0.423601i | \(-0.139234\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −193634. | − | 780137.i | −0.336123 | − | 1.35421i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 496163.i | 0.856752i | 0.903601 | + | 0.428376i | \(0.140914\pi\) | ||||
−0.903601 | + | 0.428376i | \(0.859086\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 615024.i | 1.05643i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −292896. | − | 553679.i | −0.500485 | − | 0.946096i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 422261.i | 0.717779i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 61547.3 | 0.104077 | 0.0520386 | − | 0.998645i | \(-0.483428\pi\) | ||||
0.0520386 | + | 0.998645i | \(0.483428\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 42435.3 | + | 170968.i | 0.0713868 | + | 0.287612i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.00051e6 | 1.67441 | 0.837205 | − | 0.546889i | \(-0.184188\pi\) | ||||
0.837205 | + | 0.546889i | \(0.184188\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 432331. | 0.719801 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −84247.5 | − | 339427.i | −0.139545 | − | 0.562217i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −106573. | −0.175619 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 858392.i | − | 1.40729i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −268383. | + | 240116.i | −0.437755 | + | 0.391649i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 18514.8i | 0.0300455i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 574494.i | 0.927548i | 0.885954 | + | 0.463774i | \(0.153505\pi\) | ||||
−0.885954 | + | 0.463774i | \(0.846495\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 241150. | + | 971575.i | 0.387376 | + | 1.56071i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1.08811e6i | − | 1.73908i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.46403e6 | −2.32811 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 178519. | − | 44309.4i | 0.282456 | − | 0.0701070i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 677843. | 1.06712 | 0.533559 | − | 0.845763i | \(-0.320854\pi\) | ||||
0.533559 | + | 0.845763i | \(0.320854\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −53402.9 | −0.0836511 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −282044. | − | 533164.i | −0.439594 | − | 0.830990i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 203094. | 0.314968 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 560913.i | 0.865572i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −333221. | + | 82707.3i | −0.511665 | + | 0.126998i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.06520e6i | 1.62754i | 0.581184 | + | 0.813772i | \(0.302590\pi\) | ||||
−0.581184 | + | 0.813772i | \(0.697410\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 1.26372e6i | − | 1.92137i | −0.277643 | − | 0.960684i | \(-0.589553\pi\) | ||
0.277643 | − | 0.960684i | \(-0.410447\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 645163. | − | 160133.i | 0.976087 | − | 0.242270i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 180780.i | 0.272166i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −812184. | −1.21678 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −784850. | − | 1.48365e6i | −1.17009 | − | 2.21189i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −302546. | −0.448854 | −0.224427 | − | 0.974491i | \(-0.572051\pi\) | ||||
−0.224427 | + | 0.974491i | \(0.572051\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 279454. | 0.412583 | 0.206292 | − | 0.978491i | \(-0.433860\pi\) | ||||
0.206292 | + | 0.978491i | \(0.433860\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 590829. | − | 146647.i | 0.868069 | − | 0.215459i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −853114. | −1.24737 | −0.623686 | − | 0.781675i | \(-0.714366\pi\) | ||||
−0.623686 | + | 0.781675i | \(0.714366\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 99511.5i | 0.144799i | 0.997376 | + | 0.0723993i | \(0.0230656\pi\) | ||||
−0.997376 | + | 0.0723993i | \(0.976934\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 200103. | + | 806199.i | 0.289768 | + | 1.16746i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.38010e6i | 1.98893i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 269060.i | 0.385901i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 566516. | − | 506848.i | 0.808651 | − | 0.723481i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 239237.i | 0.339864i | 0.985456 | + | 0.169932i | \(0.0543548\pi\) | ||||
−0.985456 | + | 0.169932i | \(0.945645\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −463256. | −0.654981 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 53340.1 | + | 214903.i | 0.0750583 | + | 0.302404i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 833950. | 1.16796 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −845777. | −1.17893 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 50070.0 | + | 201728.i | 0.0694644 | + | 0.279867i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 301163. | 0.415856 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 224778.i | 0.308927i | 0.987999 | + | 0.154463i | \(0.0493649\pi\) | ||||
−0.987999 | + | 0.154463i | \(0.950635\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 172565. | + | 326210.i | 0.236059 | + | 0.446236i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 648711.i | 0.883262i | 0.897197 | + | 0.441631i | \(0.145600\pi\) | ||||
−0.897197 | + | 0.441631i | \(0.854400\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 761094.i | − | 1.03146i | −0.856752 | − | 0.515729i | \(-0.827521\pi\) | ||
0.856752 | − | 0.515729i | \(-0.172479\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −51960.6 | − | 209345.i | −0.0700918 | − | 0.282395i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 883951.i | − | 1.18688i | −0.804879 | − | 0.593440i | \(-0.797770\pi\) | ||
0.804879 | − | 0.593440i | \(-0.202230\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −43433.4 | −0.0580486 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.75325e6 | − | 435165.i | 2.33241 | − | 0.578917i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.21081e6 | −1.60338 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 49560.8 | 0.0653284 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −592153. | + | 313249.i | −0.776972 | + | 0.411018i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −1.06516e6 | −1.39123 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 763734.i | 0.992985i | 0.868041 | + | 0.496493i | \(0.165379\pi\) | ||||
−0.868041 | + | 0.496493i | \(0.834621\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −825219. | + | 204823.i | −1.06805 | + | 0.265095i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 1.42245e6i | − | 1.83267i | −0.400408 | − | 0.916337i | \(-0.631132\pi\) | ||
0.400408 | − | 0.916337i | \(-0.368868\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 526843.i | − | 0.675709i | −0.941198 | − | 0.337854i | \(-0.890299\pi\) | ||
0.941198 | − | 0.337854i | \(-0.109701\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 182374. | − | 45266.1i | 0.232850 | − | 0.0577946i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 1.22321e6i | − | 1.55473i | −0.629050 | − | 0.777365i | \(-0.716556\pi\) | ||
0.629050 | − | 0.777365i | \(-0.283444\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.59787e6 | 2.02180 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 602285. | − | 884828.i | 0.758659 | − | 1.11456i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 31463.3 | 0.0394549 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −711257. | −0.887933 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.40282e6 | − | 348187.i | 1.74348 | − | 0.432741i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −515100. | −0.637342 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 751197.i | 0.925346i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −395987. | − | 1.59540e6i | −0.485630 | − | 1.95657i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 406881.i | 0.496787i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 58073.7i | − | 0.0705935i | −0.999377 | − | 0.0352968i | \(-0.988762\pi\) | ||
0.999377 | − | 0.0352968i | \(-0.0112376\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −469038. | + | 248121.i | −0.567649 | + | 0.300286i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 101962.i | 0.122858i | 0.998111 | + | 0.0614288i | \(0.0195657\pi\) | ||||
−0.998111 | + | 0.0614288i | \(0.980434\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19016.7 | −0.0228136 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 156943. | + | 632313.i | 0.187456 | + | 0.755248i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 659415. | 0.784188 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.66618e6 | −1.97284 | −0.986420 | − | 0.164240i | \(-0.947483\pi\) | ||||
−0.986420 | + | 0.164240i | \(0.947483\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −47622.3 | − | 191867.i | −0.0561425 | − | 0.226194i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.54353e6 | 1.81181 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 228083.i | 0.266569i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.01258e6 | + | 535656.i | −1.17834 | + | 0.623342i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 545932.i | − | 0.632568i | −0.948665 | − | 0.316284i | \(-0.897565\pi\) | ||
0.948665 | − | 0.316284i | \(-0.102435\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 813107.i | − | 0.938099i | ||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −350.240 | − | 1411.09i | −0.000402348 | − | 0.00162103i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 1.26157e6i | − | 1.44307i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −69359.6 | −0.0790000 | −0.0395000 | − | 0.999220i | \(-0.512577\pi\) | ||||
−0.0395000 | + | 0.999220i | \(0.512577\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −199260. | + | 49457.4i | −0.225990 | + | 0.0560919i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −625701. | −0.706622 | −0.353311 | − | 0.935506i | \(-0.614944\pi\) | ||||
−0.353311 | + | 0.935506i | \(0.614944\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 185746. | 0.208879 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −556650. | + | 498021.i | −0.623330 | + | 0.557679i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −341934. | −0.381278 | −0.190639 | − | 0.981660i | \(-0.561056\pi\) | ||||
−0.190639 | + | 0.981660i | \(0.561056\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 365198.i | 0.405505i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 97595.9 | − | 24223.8i | 0.107912 | − | 0.0267844i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 178830.i | 0.196904i | 0.995142 | + | 0.0984518i | \(0.0313890\pi\) | ||||
−0.995142 | + | 0.0984518i | \(0.968611\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 725757.i | − | 0.795764i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −703943. | + | 174722.i | −0.768624 | + | 0.190776i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 1.28284e6i | 1.39487i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 163777. | 0.177340 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −261890. | + | 138540.i | −0.282401 | + | 0.149390i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −448289. | −0.481397 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −406495. | −0.434712 | −0.217356 | − | 0.976092i | \(-0.569743\pi\) | ||||
−0.217356 | + | 0.976092i | \(0.569743\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.46279e6 | + | 363071.i | −1.55788 | + | 0.386673i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −8629.24 | −0.00915239 | −0.00457619 | − | 0.999990i | \(-0.501457\pi\) | ||||
−0.00457619 | + | 0.999990i | \(0.501457\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 670542.i | − | 0.708273i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 263696. | + | 1.06241e6i | 0.277392 | + | 1.11759i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 455792.i | 0.477505i | 0.971080 | + | 0.238753i | \(0.0767385\pi\) | ||||
−0.971080 | + | 0.238753i | \(0.923262\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 1.21482e6i | − | 1.26750i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −329777. | − | 623397.i | −0.342675 | − | 0.647779i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.67749e6i | 1.73602i | 0.496549 | + | 0.868009i | \(0.334600\pi\) | ||||
−0.496549 | + | 0.868009i | \(0.665400\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 584939. | 0.602890 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 15340.2 | + | 61804.4i | 0.0157469 | + | 0.0634432i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 1.41555e6 | 1.44722 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.02074e6 | −1.03937 | −0.519684 | − | 0.854358i | \(-0.673950\pi\) | ||||
−0.519684 | + | 0.854358i | \(0.673950\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 43787.9 | + | 176418.i | 0.0444075 | + | 0.178914i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 10245.7 | 0.0103490 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 1.21614e6i | − | 1.22347i | −0.791064 | − | 0.611733i | \(-0.790473\pi\) | ||
0.791064 | − | 0.611733i | \(-0.209527\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 267396. | + | 298875.i | 0.267932 | + | 0.299473i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 384.5.h.h.65.3 | yes | 32 | |
3.2 | odd | 2 | inner | 384.5.h.h.65.32 | yes | 32 | |
4.3 | odd | 2 | inner | 384.5.h.h.65.29 | yes | 32 | |
8.3 | odd | 2 | inner | 384.5.h.h.65.4 | yes | 32 | |
8.5 | even | 2 | inner | 384.5.h.h.65.30 | yes | 32 | |
12.11 | even | 2 | inner | 384.5.h.h.65.2 | yes | 32 | |
24.5 | odd | 2 | inner | 384.5.h.h.65.1 | ✓ | 32 | |
24.11 | even | 2 | inner | 384.5.h.h.65.31 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
384.5.h.h.65.1 | ✓ | 32 | 24.5 | odd | 2 | inner | |
384.5.h.h.65.2 | yes | 32 | 12.11 | even | 2 | inner | |
384.5.h.h.65.3 | yes | 32 | 1.1 | even | 1 | trivial | |
384.5.h.h.65.4 | yes | 32 | 8.3 | odd | 2 | inner | |
384.5.h.h.65.29 | yes | 32 | 4.3 | odd | 2 | inner | |
384.5.h.h.65.30 | yes | 32 | 8.5 | even | 2 | inner | |
384.5.h.h.65.31 | yes | 32 | 24.11 | even | 2 | inner | |
384.5.h.h.65.32 | yes | 32 | 3.2 | odd | 2 | inner |