Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [400,2,Mod(129,400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(400, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("400.129");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 400 = 2^{4} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 400.y (of order \(10\), degree \(4\), not 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: | \(3.19401608085\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{10})\) |
Coefficient field: | 8.0.58140625.2 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 3x^{7} + 4x^{6} - 7x^{5} + 11x^{4} + 5x^{3} - 10x^{2} - 25x + 25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 25) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{10}]$ |
Embedding invariants
Embedding label | 129.1 | ||
Root | \(1.17421 + 0.0566033i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 400.129 |
Dual form | 400.2.y.c.369.1 |
$q$-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 \(\left(\mathbb{Z}/400\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(177\) | \(351\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{10}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −1.29224 | + | 1.77862i | −0.746076 | + | 1.02689i | 0.252170 | + | 0.967683i | \(0.418856\pi\) |
−0.998246 | + | 0.0592022i | \(0.981144\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.22570 | + | 1.87020i | −0.548150 | + | 0.836380i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.992398i | − | 0.375091i | −0.982256 | − | 0.187546i | \(-0.939947\pi\) | ||
0.982256 | − | 0.187546i | \(-0.0600533\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.566541 | − | 1.74363i | −0.188847 | − | 0.581211i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.618034 | + | 1.90211i | −0.186344 | + | 0.573509i | −0.999969 | − | 0.00788181i | \(-0.997491\pi\) |
0.813625 | + | 0.581390i | \(0.197491\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.20892 | + | 1.04264i | −0.889995 | + | 0.289177i | −0.718101 | − | 0.695938i | \(-0.754989\pi\) |
−0.171894 | + | 0.985115i | \(0.554989\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.74248 | − | 4.59680i | −0.449905 | − | 1.18689i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.70135 | − | 2.34171i | −0.412638 | − | 0.567948i | 0.551221 | − | 0.834359i | \(-0.314162\pi\) |
−0.963859 | + | 0.266411i | \(0.914162\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.09089 | − | 1.51912i | 0.479683 | − | 0.348510i | −0.321520 | − | 0.946903i | \(-0.604194\pi\) |
0.801203 | + | 0.598393i | \(0.204194\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.76510 | + | 1.28242i | 0.385176 | + | 0.279847i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.32696 | − | 1.40591i | −0.902233 | − | 0.293153i | −0.179075 | − | 0.983835i | \(-0.557310\pi\) |
−0.723158 | + | 0.690682i | \(0.757310\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.99532 | − | 4.58462i | −0.399064 | − | 0.916923i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.43930 | − | 0.792578i | −0.469444 | − | 0.152532i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.35599 | − | 3.16481i | −0.808886 | − | 0.587690i | 0.104621 | − | 0.994512i | \(-0.466637\pi\) |
−0.913508 | + | 0.406822i | \(0.866637\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.110461 | − | 0.0802548i | 0.0198394 | − | 0.0144142i | −0.577821 | − | 0.816163i | \(-0.696097\pi\) |
0.597661 | + | 0.801749i | \(0.296097\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.58448 | − | 3.55723i | −0.449901 | − | 0.619235i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.85599 | + | 1.21638i | 0.313719 | + | 0.205606i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.04392 | − | 0.664110i | 0.336018 | − | 0.109179i | −0.136148 | − | 0.990689i | \(-0.543472\pi\) |
0.472166 | + | 0.881510i | \(0.343472\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.29224 | − | 7.05479i | 0.367052 | − | 1.12967i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.66780 | + | 8.21064i | 0.416640 | + | 1.28229i | 0.910776 | + | 0.412902i | \(0.135485\pi\) |
−0.494135 | + | 0.869385i | \(0.664515\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.64398i | 0.708200i | 0.935208 | + | 0.354100i | \(0.115213\pi\) | ||||
−0.935208 | + | 0.354100i | \(0.884787\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.95536 | + | 1.07763i | 0.589630 | + | 0.160643i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.83453 | + | 8.03054i | −0.851054 | + | 1.17137i | 0.132576 | + | 0.991173i | \(0.457675\pi\) |
−0.983630 | + | 0.180202i | \(0.942325\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.01515 | 0.859306 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.36356 | 0.891077 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.44672 | + | 6.12038i | −0.610804 | + | 0.840699i | −0.996643 | − | 0.0818665i | \(-0.973912\pi\) |
0.385839 | + | 0.922566i | \(0.373912\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.79981 | − | 3.48727i | −0.377527 | − | 0.470223i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.68196i | 0.752594i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.51967 | + | 4.67706i | 0.197844 | + | 0.608901i | 0.999932 | + | 0.0116948i | \(0.00372266\pi\) |
−0.802088 | + | 0.597206i | \(0.796277\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.855890 | + | 2.63416i | −0.109585 | + | 0.337269i | −0.990779 | − | 0.135486i | \(-0.956740\pi\) |
0.881194 | + | 0.472755i | \(0.156740\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.73038 | + | 0.562235i | −0.218007 | + | 0.0708349i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.98322 | − | 7.27931i | 0.245989 | − | 0.902887i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.28477 | + | 1.76833i | 0.156959 | + | 0.216036i | 0.880253 | − | 0.474505i | \(-0.157373\pi\) |
−0.723294 | + | 0.690540i | \(0.757373\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.09205 | − | 5.87922i | 0.974169 | − | 0.707775i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.80098 | + | 5.66774i | 0.925806 | + | 0.672637i | 0.944962 | − | 0.327179i | \(-0.106098\pi\) |
−0.0191565 | + | 0.999816i | \(0.506098\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.737953 | − | 0.239775i | −0.0863708 | − | 0.0280636i | 0.265513 | − | 0.964107i | \(-0.414459\pi\) |
−0.351884 | + | 0.936044i | \(0.614459\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 10.7327 | + | 2.37552i | 1.23931 | + | 0.274301i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.88765 | + | 0.613336i | 0.215118 | + | 0.0698961i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −12.8236 | − | 9.31689i | −1.44277 | − | 1.04823i | −0.987455 | − | 0.157900i | \(-0.949527\pi\) |
−0.455313 | − | 0.890332i | \(-0.650473\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 9.01153 | − | 6.54726i | 1.00128 | − | 0.727474i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.04103 | + | 1.43285i | 0.114268 | + | 0.157276i | 0.862320 | − | 0.506364i | \(-0.169011\pi\) |
−0.748052 | + | 0.663640i | \(0.769011\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.46482 | − | 0.311640i | 0.701208 | − | 0.0338021i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 11.2580 | − | 3.65794i | 1.20698 | − | 0.392172i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −4.48322 | + | 13.7979i | −0.475221 | + | 1.46258i | 0.370439 | + | 0.928857i | \(0.379207\pi\) |
−0.845660 | + | 0.533722i | \(0.820793\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.03472 | + | 3.18453i | 0.108468 | + | 0.333830i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0.300177i | 0.0311269i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.278260 | + | 5.77237i | 0.0285489 | + | 0.592233i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −10.0095 | + | 13.7768i | −1.01631 | + | 1.39883i | −0.101545 | + | 0.994831i | \(0.532379\pi\) |
−0.914761 | + | 0.403995i | \(0.867621\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.66673 | 0.368520 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.54716 | −0.253452 | −0.126726 | − | 0.991938i | \(-0.540447\pi\) | ||||
−0.126726 | + | 0.991938i | \(0.540447\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.97509 | − | 8.22400i | 0.588743 | − | 0.810335i | −0.405877 | − | 0.913928i | \(-0.633034\pi\) |
0.994620 | + | 0.103593i | \(0.0330338\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −4.56186 | + | 1.72923i | −0.445192 | + | 0.168756i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.81720i | 0.465697i | 0.972513 | + | 0.232848i | \(0.0748046\pi\) | ||||
−0.972513 | + | 0.232848i | \(0.925195\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.02903 | − | 15.4778i | −0.481694 | − | 1.48250i | −0.836713 | − | 0.547642i | \(-0.815526\pi\) |
0.355019 | − | 0.934859i | \(-0.384474\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.46004 | + | 4.49354i | −0.138581 | + | 0.426508i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 6.42633 | − | 2.08804i | 0.604538 | − | 0.196426i | 0.00927487 | − | 0.999957i | \(-0.497048\pi\) |
0.595264 | + | 0.803531i | \(0.297048\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.93290 | − | 6.36906i | 0.739746 | − | 0.593918i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 3.63597 | + | 5.00449i | 0.336146 | + | 0.462665i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.32391 | + | 1.68842i | −0.213032 | + | 0.154777i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.66312 | + | 4.11450i | 0.514829 | + | 0.374045i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −18.0510 | − | 5.86513i | −1.62761 | − | 0.528841i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.0198 | + | 1.88771i | 0.985643 | + | 0.168842i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.41785 | + | 0.460687i | 0.125814 | + | 0.0408793i | 0.371247 | − | 0.928534i | \(-0.378930\pi\) |
−0.245433 | + | 0.969413i | \(0.578930\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −8.25985 | − | 6.00114i | −0.727240 | − | 0.528370i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 11.4190 | − | 8.29640i | 0.997684 | − | 0.724860i | 0.0360934 | − | 0.999348i | \(-0.488509\pi\) |
0.961590 | + | 0.274489i | \(0.0885086\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.50757 | − | 2.07500i | −0.130723 | − | 0.179925i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 4.47214 | − | 3.59053i | 0.384900 | − | 0.309024i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.655703 | − | 0.213051i | 0.0560205 | − | 0.0182022i | −0.280873 | − | 0.959745i | \(-0.590624\pi\) |
0.336893 | + | 0.941543i | \(0.390624\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.12099 | + | 15.7608i | −0.434356 | + | 1.33681i | 0.459388 | + | 0.888236i | \(0.348069\pi\) |
−0.893745 | + | 0.448576i | \(0.851931\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.74364 | − | 20.7548i | −0.567917 | − | 1.74787i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 6.74812i | − | 0.564307i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 11.2580 | − | 4.26747i | 0.934923 | − | 0.354394i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −7.77302 | + | 10.6986i | −0.641108 | + | 0.882409i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.21156 | −0.263101 | −0.131551 | − | 0.991309i | \(-0.541996\pi\) | ||||
−0.131551 | + | 0.991309i | \(0.541996\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −17.6863 | −1.43929 | −0.719647 | − | 0.694340i | \(-0.755696\pi\) | ||||
−0.719647 | + | 0.694340i | \(0.755696\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.11920 | + | 4.29321i | −0.252172 | + | 0.347085i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.0147004 | + | 0.304953i | 0.00118077 | + | 0.0244944i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.65512i | 0.132093i | 0.997817 | + | 0.0660465i | \(0.0210386\pi\) | ||||
−0.997817 | + | 0.0660465i | \(0.978961\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −5.13959 | − | 15.8180i | −0.407596 | − | 1.25445i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.39523 | + | 4.29407i | −0.109959 | + | 0.338420i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −0.849231 | + | 0.275932i | −0.0665169 | + | 0.0216127i | −0.342086 | − | 0.939668i | \(-0.611134\pi\) |
0.275570 | + | 0.961281i | \(0.411134\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.82055 | − | 0.473405i | 0.764529 | − | 0.0368545i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 3.05388 | + | 4.20331i | 0.236317 | + | 0.325262i | 0.910660 | − | 0.413156i | \(-0.135573\pi\) |
−0.674344 | + | 0.738417i | \(0.735573\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.30713 | + | 0.949687i | −0.100549 | + | 0.0730529i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.83337 | − | 2.78510i | −0.293145 | − | 0.212982i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 5.48250 | + | 1.78137i | 0.416827 | + | 0.135435i | 0.509919 | − | 0.860222i | \(-0.329675\pi\) |
−0.0930924 | + | 0.995657i | \(0.529675\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −4.54977 | + | 1.98015i | −0.343930 | + | 0.149685i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −10.2825 | − | 3.34098i | −0.772878 | − | 0.251123i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −7.01326 | − | 5.09543i | −0.524196 | − | 0.380850i | 0.293986 | − | 0.955810i | \(-0.405018\pi\) |
−0.818182 | + | 0.574959i | \(0.805018\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.5616 | + | 8.39996i | −0.859363 | + | 0.624364i | −0.927712 | − | 0.373297i | \(-0.878227\pi\) |
0.0683483 | + | 0.997662i | \(0.478227\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.57914 | − | 4.92627i | −0.264578 | − | 0.364160i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.26321 | + | 4.63655i | −0.0928732 | + | 0.340886i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.50569 | − | 1.78891i | 0.402616 | − | 0.130818i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.786553 | + | 2.42076i | −0.0572133 | + | 0.176084i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.391326 | + | 1.20438i | 0.0283154 | + | 0.0871458i | 0.964216 | − | 0.265120i | \(-0.0854114\pi\) |
−0.935900 | + | 0.352265i | \(0.885411\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − | 21.1730i | − | 1.52406i | −0.647540 | − | 0.762031i | \(-0.724202\pi\) | ||
0.647540 | − | 0.762031i | \(-0.275798\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 10.3843 | + | 12.9340i | 0.743635 | + | 0.926224i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.17176 | + | 9.87108i | −0.510967 | + | 0.703285i | −0.984082 | − | 0.177715i | \(-0.943129\pi\) |
0.473115 | + | 0.881001i | \(0.343129\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 10.4065 | 0.737695 | 0.368848 | − | 0.929490i | \(-0.379752\pi\) | ||||
0.368848 | + | 0.929490i | \(0.379752\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.80540 | −0.338947 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.14075 | + | 4.32287i | −0.220438 | + | 0.303406i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −18.6255 | − | 5.07446i | −1.30086 | − | 0.354415i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 8.34114i | 0.579749i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.59730 | + | 4.91598i | 0.110487 | + | 0.340045i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 2.67537 | − | 8.23395i | 0.184180 | − | 0.566848i | −0.815753 | − | 0.578400i | \(-0.803677\pi\) |
0.999933 | + | 0.0115520i | \(0.00367718\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −20.1615 | + | 6.55086i | −1.38144 | + | 0.448858i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.68518 | − | 5.69212i | −0.592324 | − | 0.388199i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.0796448 | − | 0.109622i | −0.00540664 | − | 0.00744160i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.38008 | − | 1.00269i | 0.0932573 | − | 0.0677554i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.90107 | + | 5.74046i | 0.531484 | + | 0.386145i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 26.9562 | + | 8.75859i | 1.80512 | + | 0.586518i | 0.999978 | − | 0.00656747i | \(-0.00209051\pi\) |
0.805139 | + | 0.593086i | \(0.202091\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −6.86346 | + | 6.07648i | −0.457564 | + | 0.405099i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −21.1529 | − | 6.87299i | −1.40397 | − | 0.456176i | −0.493495 | − | 0.869749i | \(-0.664281\pi\) |
−0.910471 | + | 0.413572i | \(0.864281\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.00280 | + | 1.45512i | 0.132348 | + | 0.0961568i | 0.651990 | − | 0.758228i | \(-0.273934\pi\) |
−0.519641 | + | 0.854384i | \(0.673934\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.53019 | + | 2.56484i | −0.232270 | + | 0.168754i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.50088 | + | 4.81854i | 0.229350 | + | 0.315673i | 0.908146 | − | 0.418654i | \(-0.137498\pi\) |
−0.678796 | + | 0.734327i | \(0.737498\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.86736 | − | 20.7548i | −0.513210 | − | 1.35389i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 33.1424 | − | 10.7686i | 2.15283 | − | 0.699496i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.17314 | + | 6.68823i | −0.140569 | + | 0.432626i | −0.996415 | − | 0.0846050i | \(-0.973037\pi\) |
0.855846 | + | 0.517231i | \(0.173037\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.364567 | + | 1.12202i | 0.0234838 | + | 0.0722758i | 0.962112 | − | 0.272656i | \(-0.0879021\pi\) |
−0.938628 | + | 0.344932i | \(0.887902\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.7942i | 1.07735i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.37276 | + | 11.2495i | −0.471029 | + | 0.718707i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.12561 | + | 7.05479i | −0.326135 | + | 0.448886i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.89375 | −0.246757 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.60867 | −0.290897 | −0.145448 | − | 0.989366i | \(-0.546462\pi\) | ||||
−0.145448 | + | 0.989366i | \(0.546462\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.34841 | − | 7.36146i | 0.336252 | − | 0.462811i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −7.79981 | + | 11.9011i | −0.488443 | + | 0.745279i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 9.75542i | − | 0.608526i | −0.952588 | − | 0.304263i | \(-0.901590\pi\) | ||
0.952588 | − | 0.304263i | \(-0.0984102\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.659062 | − | 2.02838i | −0.0409521 | − | 0.126038i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.05043 | + | 9.38824i | −0.188817 | + | 0.581118i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −0.947088 | + | 0.307728i | −0.0584000 | + | 0.0189753i | −0.338071 | − | 0.941121i | \(-0.609775\pi\) |
0.279671 | + | 0.960096i | \(0.409775\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.99602 | − | 15.8180i | −0.368333 | − | 0.971693i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −18.7479 | − | 25.8042i | −1.14735 | − | 1.57919i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.66048 | + | 1.93295i | −0.162212 | + | 0.117854i | −0.665930 | − | 0.746014i | \(-0.731965\pi\) |
0.503718 | + | 0.863868i | \(0.331965\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.82960 | + | 7.14162i | 0.597105 | + | 0.433823i | 0.844850 | − | 0.535003i | \(-0.179689\pi\) |
−0.247745 | + | 0.968825i | \(0.579689\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −7.00116 | − | 2.27482i | −0.423730 | − | 0.137678i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.95363 | − | 0.961876i | 0.600227 | − | 0.0580033i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −11.2858 | − | 3.66697i | −0.678096 | − | 0.220327i | −0.0503346 | − | 0.998732i | \(-0.516029\pi\) |
−0.627762 | + | 0.778406i | \(0.716029\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −0.202516 | − | 0.147136i | −0.0121243 | − | 0.00880883i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.9355 | − | 14.4840i | 1.18925 | − | 0.864041i | 0.196066 | − | 0.980591i | \(-0.437183\pi\) |
0.993185 | + | 0.116549i | \(0.0371833\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.97697 | + | 2.72107i | 0.117519 | + | 0.161751i | 0.863724 | − | 0.503965i | \(-0.168126\pi\) |
−0.746205 | + | 0.665716i | \(0.768126\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −10.6264 | − | 6.96438i | −0.629455 | − | 0.412534i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.14823 | − | 2.64752i | 0.480975 | − | 0.156278i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.66428 | − | 8.19982i | 0.156723 | − | 0.482342i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −11.5691 | − | 35.6060i | −0.678192 | − | 2.08726i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 8.96340i | 0.523647i | 0.965116 | + | 0.261824i | \(0.0843239\pi\) | ||||
−0.965116 | + | 0.261824i | \(0.915676\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −10.6097 | − | 2.89058i | −0.617721 | − | 0.168296i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.01515 | − | 4.14999i | 0.174956 | − | 0.240807i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 15.3507 | 0.887756 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.60867 | 0.265640 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.29155 | − | 4.53042i | 0.189094 | − | 0.260266i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.87735 | − | 4.82937i | −0.222016 | − | 0.276529i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 9.48133i | − | 0.541128i | −0.962702 | − | 0.270564i | \(-0.912790\pi\) | ||
0.962702 | − | 0.270564i | \(-0.0872102\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 6.90610 | + | 21.2548i | 0.392874 | + | 1.20914i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.06409 | + | 27.8964i | −0.513978 | + | 1.58186i | 0.271157 | + | 0.962535i | \(0.412594\pi\) |
−0.785135 | + | 0.619325i | \(0.787406\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.9655 | − | 5.83735i | 1.01547 | − | 0.329947i | 0.246440 | − | 0.969158i | \(-0.420739\pi\) |
0.769031 | + | 0.639212i | \(0.220739\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 1.06943 | − | 3.92529i | 0.0602558 | − | 0.221165i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −13.3952 | − | 18.4369i | −0.752351 | − | 1.03552i | −0.997812 | − | 0.0661157i | \(-0.978939\pi\) |
0.245461 | − | 0.969406i | \(-0.421061\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.71197 | − | 6.32962i | 0.487777 | − | 0.354391i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −8.56796 | − | 6.22499i | −0.478217 | − | 0.347445i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.11468 | − | 2.31170i | −0.395871 | − | 0.128626i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11.1829 | + | 12.6313i | 0.620318 | + | 0.700657i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 34.0277 | + | 11.0563i | 1.88174 | + | 0.611414i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.96950 | + | 5.79018i | 0.439373 | + | 0.319223i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.39711 | − | 1.74160i | 0.131757 | − | 0.0957272i | −0.519955 | − | 0.854194i | \(-0.674051\pi\) |
0.651712 | + | 0.758467i | \(0.274051\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2.31593 | − | 3.18760i | −0.126912 | − | 0.174680i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.88187 | + | 0.235333i | −0.266725 | + | 0.0128576i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 17.8916 | − | 5.81332i | 0.974615 | − | 0.316672i | 0.221937 | − | 0.975061i | \(-0.428762\pi\) |
0.752678 | + | 0.658389i | \(0.228762\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −4.59054 | + | 14.1282i | −0.249324 | + | 0.767340i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.0843849 | + | 0.259710i | 0.00456970 | + | 0.0140641i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 12.9162i | − | 0.697410i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.07691 | + | 22.3399i | 0.0579788 | + | 1.20274i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 13.3652 | − | 18.3956i | 0.717480 | − | 0.987526i | −0.282124 | − | 0.959378i | \(-0.591039\pi\) |
0.999604 | − | 0.0281483i | \(-0.00896108\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.93849 | −0.103765 | −0.0518824 | − | 0.998653i | \(-0.516522\pi\) | ||||
−0.0518824 | + | 0.998653i | \(0.516522\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.65392 | 0.461912 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.08555 | + | 4.24689i | −0.164227 | + | 0.226039i | −0.883197 | − | 0.469002i | \(-0.844614\pi\) |
0.718970 | + | 0.695041i | \(0.244614\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −20.1615 | + | 7.64246i | −1.07006 | + | 0.405620i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 6.31519i | − | 0.334235i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 6.98184 | + | 21.4879i | 0.368488 | + | 1.13409i | 0.947768 | + | 0.318960i | \(0.103334\pi\) |
−0.579281 | + | 0.815128i | \(0.696666\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.80723 | + | 11.7174i | −0.200380 | + | 0.616708i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −14.6362 | + | 4.75560i | −0.768203 | + | 0.249604i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.35294 | − | 1.08623i | 0.0708160 | − | 0.0568558i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.29008 | − | 5.90479i | −0.223940 | − | 0.308228i | 0.682232 | − | 0.731136i | \(-0.261009\pi\) |
−0.906173 | + | 0.422908i | \(0.861009\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 12.8049 | − | 9.30333i | 0.666598 | − | 0.484312i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.07386 | + | 4.41292i | 0.315339 | + | 0.229107i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 21.2156 | + | 6.89335i | 1.09850 | + | 0.356924i | 0.801525 | − | 0.597961i | \(-0.204022\pi\) |
0.296975 | + | 0.954885i | \(0.404022\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −17.5978 | + | 17.1607i | −0.908746 | + | 0.886173i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 17.2778 | + | 5.61390i | 0.889852 | + | 0.289130i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 26.6544 | + | 19.3655i | 1.36914 | + | 0.994740i | 0.997804 | + | 0.0662429i | \(0.0211012\pi\) |
0.371339 | + | 0.928497i | \(0.378899\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.65159 | + | 1.92649i | −0.135845 | + | 0.0986971i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 12.1673 | + | 16.7468i | 0.621719 | + | 0.855722i | 0.997477 | − | 0.0709955i | \(-0.0226176\pi\) |
−0.375758 | + | 0.926718i | \(0.622618\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.46076 | + | 2.77853i | −0.176377 | + | 0.141607i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.09739 | − | 2.63100i | 0.411614 | − | 0.133741i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 0.353657 | − | 1.08844i | 0.0179311 | − | 0.0551863i | −0.941691 | − | 0.336480i | \(-0.890764\pi\) |
0.959622 | + | 0.281294i | \(0.0907635\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.06943 | + | 12.5244i | 0.205800 | + | 0.633388i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 31.0310i | 1.56531i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 33.1424 | − | 12.5630i | 1.66757 | − | 0.632114i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.75385 | + | 3.79035i | −0.138212 | + | 0.190232i | −0.872512 | − | 0.488593i | \(-0.837510\pi\) |
0.734300 | + | 0.678825i | \(0.237510\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.63877 | 0.282292 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −24.0851 | −1.20275 | −0.601376 | − | 0.798966i | \(-0.705381\pi\) | ||||
−0.601376 | + | 0.798966i | \(0.705381\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.270785 | + | 0.372703i | −0.0134888 | + | 0.0185657i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.19928 | + | 24.8784i | 0.0595925 | + | 1.23622i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.29821i | 0.213054i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.586930 | + | 1.80638i | 0.0290218 | + | 0.0893199i | 0.964518 | − | 0.264016i | \(-0.0850472\pi\) |
−0.935496 | + | 0.353336i | \(0.885047\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.468391 | + | 1.44156i | −0.0231040 | + | 0.0711068i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.64151 | − | 1.50812i | 0.228394 | − | 0.0742096i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.95571 | + | 0.190687i | −0.194178 | + | 0.00936047i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −21.4148 | − | 29.4750i | −1.04869 | − | 1.44340i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.88344 | − | 1.36840i | 0.0920120 | − | 0.0668507i | −0.540828 | − | 0.841133i | \(-0.681889\pi\) |
0.632840 | + | 0.774283i | \(0.281889\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 19.3760 | + | 14.0775i | 0.944329 | + | 0.686095i | 0.949459 | − | 0.313892i | \(-0.101633\pi\) |
−0.00513010 | + | 0.999987i | \(0.501633\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 17.3078 | + | 5.62366i | 0.841536 | + | 0.273431i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −7.34110 | + | 12.4725i | −0.356095 | + | 0.605005i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.61413 | + | 0.849384i | 0.126507 | + | 0.0411045i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 12.0023 | + | 8.72020i | 0.579478 | + | 0.421015i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 0.964563 | − | 0.700796i | 0.0464614 | − | 0.0337562i | −0.564312 | − | 0.825561i | \(-0.690859\pi\) |
0.610774 | + | 0.791805i | \(0.290859\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 15.0554 | + | 20.7220i | 0.723518 | + | 0.995837i | 0.999400 | + | 0.0346454i | \(0.0110302\pi\) |
−0.275882 | + | 0.961192i | \(0.588970\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.95781 | + | 25.5382i | −0.333601 | + | 1.22446i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −11.1829 | + | 3.63356i | −0.534953 | + | 0.173817i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 5.98693 | − | 18.4259i | 0.285741 | − | 0.879420i | −0.700435 | − | 0.713716i | \(-0.747011\pi\) |
0.986176 | − | 0.165703i | \(-0.0529894\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −3.40783 | − | 10.4882i | −0.162277 | − | 0.499439i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 2.46263i | − | 0.117003i | −0.998287 | − | 0.0585016i | \(-0.981368\pi\) | ||
0.998287 | − | 0.0585016i | \(-0.0186323\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −20.3099 | − | 25.2967i | −0.962780 | − | 1.19918i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.15011 | − | 5.71214i | 0.196294 | − | 0.270175i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 14.3585 | 0.677618 | 0.338809 | − | 0.940855i | \(-0.389976\pi\) | ||||
0.338809 | + | 0.940855i | \(0.389976\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −17.2664 | −0.813041 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 22.8550 | − | 31.4572i | 1.07382 | − | 1.47799i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.22397 | − | 1.96815i | −0.338665 | − | 0.0922682i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 25.1964i | 1.17864i | 0.807901 | + | 0.589319i | \(0.200604\pi\) | ||||
−0.807901 | + | 0.589319i | \(0.799396\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 2.29413 | + | 7.06059i | 0.107081 | + | 0.329560i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.90758 | − | 27.4147i | 0.414867 | − | 1.27683i | −0.497502 | − | 0.867463i | \(-0.665749\pi\) |
0.912370 | − | 0.409367i | \(-0.134251\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.3193 | − | 9.85134i | 1.40906 | − | 0.457831i | 0.496949 | − | 0.867780i | \(-0.334453\pi\) |
0.912108 | + | 0.409949i | \(0.134453\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.561392 | − | 0.367927i | −0.0260339 | − | 0.0170622i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.3333 | − | 34.8683i | −1.17229 | − | 1.61351i | −0.646580 | − | 0.762847i | \(-0.723801\pi\) |
−0.525706 | − | 0.850666i | \(-0.676199\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.75489 | − | 1.27500i | 0.0810331 | − | 0.0588740i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.94383 | − | 2.13882i | −0.135644 | − | 0.0985514i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.83337 | − | 2.87013i | −0.406159 | − | 0.131969i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −11.1366 | − | 6.55479i | −0.510981 | − | 0.300755i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 13.1910 | + | 4.28600i | 0.603973 | + | 0.196243i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −17.0107 | − | 12.3590i | −0.777237 | − | 0.564696i | 0.126912 | − | 0.991914i | \(-0.459494\pi\) |
−0.904148 | + | 0.427218i | \(0.859494\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −5.86635 | + | 4.26216i | −0.267483 | + | 0.194338i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.83453 | − | 8.03054i | −0.265480 | − | 0.365402i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −13.4969 | − | 35.6060i | −0.612862 | − | 1.61678i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 26.5525 | − | 8.62744i | 1.20321 | − | 0.390947i | 0.362269 | − | 0.932073i | \(-0.382002\pi\) |
0.840941 | + | 0.541127i | \(0.182002\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0.606634 | − | 1.86703i | 0.0274329 | − | 0.0844299i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −4.62322 | − | 14.2288i | −0.208643 | − | 0.642137i | −0.999544 | − | 0.0301930i | \(-0.990388\pi\) |
0.790901 | − | 0.611944i | \(-0.209612\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 15.5849i | 0.701909i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −4.49431 | + | 6.85753i | −0.202004 | + | 0.308223i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 5.62466 | − | 7.74168i | 0.252300 | − | 0.347262i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −44.3253 | −1.98427 | −0.992137 | − | 0.125160i | \(-0.960056\pi\) | ||||
−0.992137 | + | 0.125160i | \(0.960056\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.4224 | −0.510316 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13.8842 | + | 19.1100i | −0.619066 | + | 0.852071i | −0.997284 | − | 0.0736453i | \(-0.976537\pi\) |
0.378219 | + | 0.925716i | \(0.376537\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 3.12205 | − | 4.76371i | 0.138930 | − | 0.211982i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 3.55211i | − | 0.157755i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8.25552 | + | 25.4079i | 0.365920 | + | 1.12618i | 0.949403 | + | 0.314060i | \(0.101689\pi\) |
−0.583484 | + | 0.812125i | \(0.698311\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.237953 | + | 0.732343i | −0.0105264 | + | 0.0323970i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −6.30434 | + | 2.04840i | −0.278343 | + | 0.0904392i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 8.05689 | + | 21.2548i | 0.355029 | + | 0.936598i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −11.6691 | − | 16.0611i | −0.513205 | − | 0.706366i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10.2531 | + | 7.44931i | −0.450061 | + | 0.326988i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −26.4607 | − | 19.2249i | −1.15927 | − | 0.842256i | −0.169581 | − | 0.985516i | \(-0.554241\pi\) |
−0.989685 | + | 0.143260i | \(0.954241\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.224417 | + | 0.0729175i | 0.00981307 | + | 0.00318846i | 0.313919 | − | 0.949450i | \(-0.398358\pi\) |
−0.304106 | + | 0.952638i | \(0.598358\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.35746 | − | 10.6511i | 0.102888 | − | 0.464853i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −0.375867 | − | 0.122127i | −0.0163730 | − | 0.00531992i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.86142 | − | 1.35240i | −0.0809313 | − | 0.0588001i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.29413 | − | 5.29949i | 0.316538 | − | 0.229978i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.1215 | − | 23.5658i | −0.741616 | − | 1.02075i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9.00915 | − | 5.90445i | −0.389499 | − | 0.255271i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 18.1256 | − | 5.88938i | 0.782179 | − | 0.254145i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.71756 | + | 11.4415i | −0.160127 | + | 0.492820i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.3698 | − | 31.9148i | −0.445830 | − | 1.37213i | −0.881570 | − | 0.472053i | \(-0.843513\pi\) |
0.435740 | − | 0.900073i | \(-0.356487\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 31.4183i | − | 1.34829i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 35.1106 | + | 9.56578i | 1.50397 | + | 0.409753i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −22.6371 | + | 31.1573i | −0.967892 | + | 1.33219i | −0.0247869 | + | 0.999693i | \(0.507891\pi\) |
−0.943105 | + | 0.332496i | \(0.892109\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 5.07790 | 0.216720 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −13.9156 | −0.592825 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.24607 | + | 12.7261i | −0.393183 | + | 0.541170i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −6.61426 | − | 8.23830i | −0.280760 | − | 0.349697i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.33445i | 0.183657i | 0.995775 | + | 0.0918283i | \(0.0292711\pi\) | ||||
−0.995775 | + | 0.0918283i | \(0.970729\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.84201 | − | 14.9022i | −0.204795 | − | 0.630294i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.93290 | + | 12.1042i | −0.166047 | + | 0.511040i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 33.1936 | − | 10.7853i | 1.39894 | − | 0.454544i | 0.490094 | − | 0.871669i | \(-0.336962\pi\) |
0.908849 | + | 0.417125i | \(0.136962\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.97169 | + | 14.5779i | −0.167090 | + | 0.613295i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.49749 | − | 8.94303i | −0.272869 | − | 0.375572i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −33.9501 | + | 24.6662i | −1.42326 | + | 1.03406i | −0.432038 | + | 0.901855i | \(0.642205\pi\) |
−0.991223 | + | 0.132204i | \(0.957795\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −11.1913 | − | 8.13093i | −0.468340 | − | 0.340269i | 0.328454 | − | 0.944520i | \(-0.393472\pi\) |
−0.796794 | + | 0.604251i | \(0.793472\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.64782 | − | 0.860328i | −0.110614 | − | 0.0359407i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 2.18809 | + | 22.6427i | 0.0912497 | + | 0.944265i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.1538 | + | 3.94902i | 0.505970 | + | 0.164400i | 0.550869 | − | 0.834592i | \(-0.314296\pi\) |
−0.0448986 | + | 0.998992i | \(0.514296\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 37.6586 | + | 27.3606i | 1.56504 | + | 1.13707i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.42196 | − | 1.03311i | 0.0589928 | − | 0.0428608i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.89344 | − | 12.2408i | −0.368329 | − | 0.506961i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −13.8160 | + | 0.666009i | −0.571222 | + | 0.0275361i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 11.5905 | − | 3.76597i | 0.478390 | − | 0.155438i | −0.0598889 | − | 0.998205i | \(-0.519075\pi\) |
0.538279 | + | 0.842767i | \(0.319075\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.109046 | − | 0.335608i | 0.00449315 | − | 0.0138285i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.28923 | − | 25.5116i | −0.340973 | − | 1.04941i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 31.2580i | − | 1.28361i | −0.766866 | − | 0.641807i | \(-0.778185\pi\) | ||
0.766866 | − | 0.641807i | \(-0.221815\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.309271 | − | 6.41567i | −0.0126789 | − | 0.263017i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −13.4477 | + | 18.5091i | −0.550376 | + | 0.757528i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −33.3707 | −1.36349 | −0.681746 | − | 0.731589i | \(-0.738779\pi\) | ||||
−0.681746 | + | 0.731589i | \(0.738779\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −46.8052 | −1.90922 | −0.954611 | − | 0.297854i | \(-0.903729\pi\) | ||||
−0.954611 | + | 0.297854i | \(0.903729\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.35544 | − | 3.24199i | 0.0959211 | − | 0.132024i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −14.6362 | + | 5.54805i | −0.595047 | + | 0.225560i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 30.7401i | 1.24770i | 0.781543 | + | 0.623851i | \(0.214433\pi\) | ||||
−0.781543 | + | 0.623851i | \(0.785567\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.63013 | − | 11.1724i | −0.147100 | − | 0.452728i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.3496 | − | 31.8527i | 0.418699 | − | 1.28862i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 36.4154 | − | 11.8321i | 1.47081 | − | 0.477894i | 0.539454 | − | 0.842015i | \(-0.318631\pi\) |
0.931352 | + | 0.364121i | \(0.118631\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 33.0941 | − | 26.5702i | 1.33448 | − | 1.07141i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 0.249989 | + | 0.344080i | 0.0100642 | + | 0.0138521i | 0.814019 | − | 0.580838i | \(-0.197275\pi\) |
−0.803955 | + | 0.594690i | \(0.797275\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.07691 | + | 4.41513i | −0.244252 | + | 0.177459i | −0.703175 | − | 0.711016i | \(-0.748235\pi\) |
0.458924 | + | 0.888476i | \(0.348235\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.44047 | + | 6.85890i | 0.378833 | + | 0.275238i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.6931 | + | 4.44914i | 0.548601 | + | 0.178251i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.0374 | + | 18.2955i | −0.681496 | + | 0.731822i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.8077 | − | 3.51165i | −0.431619 | − | 0.140242i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.03258 | − | 3.65638i | −0.200662 | − | 0.145789i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −9.11889 | + | 6.62526i | −0.363017 | + | 0.263747i | −0.754309 | − | 0.656519i | \(-0.772028\pi\) |
0.391292 | + | 0.920266i | \(0.372028\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 11.1878 | + | 15.3987i | 0.444676 | + | 0.612044i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.59943 | + | 2.08700i | −0.103155 | + | 0.0828201i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −19.3021 | + | 6.27165i | −0.764779 | + | 0.248492i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5.46290 | − | 16.8131i | 0.216109 | − | 0.665115i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 8.05994 | + | 24.8060i | 0.318349 | + | 0.979776i | 0.974354 | + | 0.225020i | \(0.0722448\pi\) |
−0.656006 | + | 0.754756i | \(0.727755\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.9492i | 1.25995i | 0.776614 | + | 0.629977i | \(0.216936\pi\) | ||||
−0.776614 | + | 0.629977i | \(0.783064\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 21.3474 | − | 8.09201i | 0.840555 | − | 0.318623i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −4.34628 | + | 5.98214i | −0.170870 | + | 0.235182i | −0.885860 | − | 0.463952i | \(-0.846431\pi\) |
0.714990 | + | 0.699134i | \(0.246431\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.83550 | −0.386077 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0.297895 | 0.0116754 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 10.9829 | − | 15.1167i | 0.429796 | − | 0.591563i | −0.538111 | − | 0.842874i | \(-0.680862\pi\) |
0.967906 | + | 0.251311i | \(0.0808618\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.51967 | + | 31.5248i | 0.0593784 | + | 1.23177i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.42256i | 0.0554994i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 3.02885 | + | 9.32184i | 0.117987 | + | 0.363128i | 0.992558 | − | 0.121770i | \(-0.0388570\pi\) |
−0.874571 | + | 0.484897i | \(0.838857\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −8.70145 | + | 26.7803i | −0.338447 | + | 1.04163i | 0.626552 | + | 0.779380i | \(0.284466\pi\) |
−0.964999 | + | 0.262253i | \(0.915534\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −20.4202 | + | 6.63492i | −0.793054 | + | 0.257679i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.72850 | − | 0.276145i | 0.222142 | − | 0.0107085i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 14.3987 | + | 19.8181i | 0.557521 | + | 0.767361i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −50.4120 | + | 36.6265i | −1.94904 | + | 1.41606i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.48150 | − | 3.25600i | −0.173006 | − | 0.125696i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −37.1153 | − | 12.0595i | −1.43069 | − | 0.464859i | −0.511707 | − | 0.859160i | \(-0.670987\pi\) |
−0.918981 | + | 0.394301i | \(0.870987\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.23353 | + | 12.7647i | 0.0474785 | + | 0.491314i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.78888 | − | 1.55600i | −0.184052 | − | 0.0598020i | 0.215541 | − | 0.976495i | \(-0.430848\pi\) |
−0.399593 | + | 0.916693i | \(0.630848\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.6721 | + | 9.93337i | 0.524687 | + | 0.381208i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 39.5590 | − | 28.7413i | 1.51591 | − | 1.10137i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17.8282 | − | 24.5384i | −0.682178 | − | 0.938937i | 0.317780 | − | 0.948165i | \(-0.397063\pi\) |
−0.999957 | + | 0.00922734i | \(0.997063\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.405247 | + | 1.48743i | −0.0154837 | + | 0.0568320i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −5.17619 | + | 1.68185i | −0.197484 | + | 0.0641664i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 7.88781 | − | 24.2762i | 0.300502 | − | 0.924849i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.56134 | + | 20.1937i | 0.249605 | + | 0.768205i | 0.994845 | + | 0.101409i | \(0.0323349\pi\) |
−0.745240 | + | 0.666796i | \(0.767665\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 3.63886i | − | 0.138229i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −23.1991 | − | 28.8953i | −0.879991 | − | 1.09606i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 14.6881 | − | 20.2164i | 0.556350 | − | 0.765751i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −13.0943 | −0.495273 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 32.7698 | 1.23770 | 0.618849 | − | 0.785510i | \(-0.287599\pi\) | ||||
0.618849 | + | 0.785510i | \(0.287599\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.26475 | − | 4.49354i | 0.123132 | − | 0.169477i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 47.0814 | + | 12.8272i | 1.77319 | + | 0.483099i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.52780i | 0.0950676i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.13273 | − | 18.8746i | −0.230320 | − | 0.708851i | −0.997708 | − | 0.0676683i | \(-0.978444\pi\) |
0.767388 | − | 0.641183i | \(-0.221556\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −8.98015 | + | 27.6381i | −0.336782 | + | 1.03651i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.590793 | + | 0.191960i | −0.0221254 | + | 0.00718897i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 12.6204 | + | 8.27117i | 0.471975 | + | 0.309324i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −9.08759 | − | 12.5080i | −0.339382 | − | 0.467120i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −19.5945 | + | 14.2362i | −0.730751 | + | 0.530922i | −0.889801 | − | 0.456349i | \(-0.849157\pi\) |
0.159050 | + | 0.987271i | \(0.449157\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.16149 | − | 5.92967i | −0.303950 | − | 0.220832i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.46676 | − | 0.801498i | −0.0917397 | − | 0.0298080i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −5.81785 | + | 26.2853i | −0.216069 | + | 0.976213i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −5.57804 | − | 1.81242i | −0.206878 | − | 0.0672188i | 0.203745 | − | 0.979024i | \(-0.434689\pi\) |
−0.410623 | + | 0.911805i | \(0.634689\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.83585 | − | 2.06037i | −0.105032 | − | 0.0763099i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.8748 | − | 7.90103i | 0.402220 | − | 0.292230i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.2795 | + | 27.9123i | 0.749039 | + | 1.03096i | 0.998047 | + | 0.0624625i | \(0.0198954\pi\) |
−0.249008 | + | 0.968501i | \(0.580105\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −10.4812 | − | 27.6504i | −0.386607 | − | 1.01990i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.15759 | + | 1.35088i | −0.153147 | + | 0.0497604i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12.2282 | − | 37.6345i | 0.449821 | − | 1.38441i | −0.427288 | − | 0.904116i | \(-0.640531\pi\) |
0.877109 | − | 0.480291i | \(-0.159469\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.92426 | − | 18.2330i | −0.217633 | − | 0.669805i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 29.7058i | − | 1.08980i | −0.838501 | − | 0.544900i | \(-0.816567\pi\) | ||
0.838501 | − | 0.544900i | \(-0.183433\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.93641 | − | 6.00627i | 0.144219 | − | 0.220053i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.90858 | − | 2.62694i | 0.0698314 | − | 0.0961147i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.78058 | 0.174679 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −26.8870 | −0.981122 | −0.490561 | − | 0.871407i | \(-0.663208\pi\) | ||||
−0.490561 | + | 0.871407i | \(0.663208\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.95552 | − | 8.19707i | 0.217031 | − | 0.298718i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 21.6781 | − | 33.0771i | 0.788949 | − | 1.20380i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 44.6792i | 1.62389i | 0.583731 | + | 0.811947i | \(0.301592\pi\) | ||||
−0.583731 | + | 0.811947i | \(0.698408\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 6.18178 | + | 19.0256i | 0.224384 | + | 0.690584i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 6.27550 | − | 19.3140i | 0.227487 | − | 0.700132i | −0.770543 | − | 0.637388i | \(-0.780015\pi\) |
0.998030 | − | 0.0627441i | \(-0.0199852\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −15.3601 | + | 4.99080i | −0.556073 | + | 0.180679i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −4.20597 | − | 11.0957i | −0.152067 | − | 0.401167i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −9.75300 | − | 13.4239i | −0.352160 | − | 0.484707i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.0811 | − | 15.3163i | 0.760205 | − | 0.552321i | −0.138768 | − | 0.990325i | \(-0.544314\pi\) |
0.898973 | + | 0.438004i | \(0.144314\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 17.3511 | + | 12.6063i | 0.624886 | + | 0.454007i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −13.0585 | − | 4.24295i | −0.469680 | − | 0.152608i | 0.0646079 | − | 0.997911i | \(-0.479420\pi\) |
−0.534288 | + | 0.845302i | \(0.679420\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.588343 | − | 0.346289i | −0.0211339 | − | 0.0124391i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4.45938 | + | 1.44894i | 0.159979 | + | 0.0519805i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 18.0510 | + | 13.1148i | 0.646745 | + | 0.469888i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −15.6020 | + | 11.3355i | −0.558282 | + | 0.405616i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 8.11722 | + | 11.1724i | 0.290086 | + | 0.399269i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.09541 | − | 2.02868i | −0.110480 | − | 0.0724068i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −18.7035 | + | 6.07714i | −0.666708 | + | 0.216627i | −0.622767 | − | 0.782408i | \(-0.713991\pi\) |
−0.0439412 | + | 0.999034i | \(0.513991\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.676537 | − | 2.08217i | 0.0240853 | − | 0.0741271i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.07217 | − | 6.37748i | −0.0736779 | − | 0.226757i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 9.34520i | − | 0.331858i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 35.8825 | + | 9.77608i | 1.27262 | + | 0.346722i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.43278 | − | 8.85396i | 0.227861 | − | 0.313623i | −0.679744 | − | 0.733450i | \(-0.737909\pi\) |
0.907604 | + | 0.419826i | \(0.137909\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 28.7318 | 1.01646 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 26.5985 | 0.939812 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.912160 | − | 1.25548i | 0.0321894 | − | 0.0443049i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.32065 | − | 7.87259i | −0.222774 | − | 0.277472i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 7.22982i | − | 0.254502i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −5.08109 | − | 15.6380i | −0.178641 | − | 0.549802i | 0.821140 | − | 0.570727i | \(-0.193339\pi\) |
−0.999781 | + | 0.0209255i | \(0.993339\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −6.99839 | + | 21.5388i | −0.245747 | + | 0.756331i | 0.749766 | + | 0.661703i | \(0.230166\pi\) |
−0.995513 | + | 0.0946276i | \(0.969834\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −25.4044 | + | 8.25439i | −0.890972 | + | 0.289494i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.524854 | − | 1.92644i | 0.0183848 | − | 0.0674804i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.05476 | + | 9.71004i | 0.246815 | + | 0.339711i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 4.96645 | − | 3.60834i | 0.173542 | − | 0.126085i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 32.1820 | + | 23.3816i | 1.12316 | + | 0.816024i | 0.984685 | − | 0.174342i | \(-0.0557800\pi\) |
0.138475 | + | 0.990366i | \(0.455780\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 15.7497 | + | 5.11738i | 0.548999 | + | 0.178381i | 0.570365 | − | 0.821391i | \(-0.306802\pi\) |
−0.0213662 | + | 0.999772i | \(0.506802\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −11.1517 | + | 18.9467i | −0.388252 | + | 0.659639i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 24.7618 | + | 8.04561i | 0.861053 | + | 0.279773i | 0.706068 | − | 0.708144i | \(-0.250467\pi\) |
0.154985 | + | 0.987917i | \(0.450467\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 4.16123 | + | 3.02331i | 0.144526 | + | 0.105004i | 0.657699 | − | 0.753281i | \(-0.271530\pi\) |
−0.513173 | + | 0.858285i | \(0.671530\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 21.1061 | − | 15.3345i | 0.732162 | − | 0.531947i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10.2339 | − | 14.0857i | −0.354583 | − | 0.488041i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −11.6042 | + | 0.559386i | −0.401579 | + | 0.0193584i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −0.333057 | + | 0.108217i | −0.0115121 | + | 0.00374052i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.9177 | − | 36.6788i | 0.411444 | − | 1.26629i | −0.503950 | − | 0.863733i | \(-0.668120\pi\) |
0.915393 | − | 0.402560i | \(-0.131880\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −0.00289251 | − | 0.00890222i | −9.97416e−5 | − | 0.000306973i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 54.1744i | 1.86586i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.173956 | − | 3.60863i | −0.00598427 | − | 0.124141i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 4.08322 | − | 5.62007i | 0.140301 | − | 0.193108i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.39447 | −0.253777 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.77764 | −0.335173 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −5.37684 | + | 7.40059i | −0.184100 | + | 0.253391i | −0.891085 | − | 0.453837i | \(-0.850055\pi\) |
0.706985 | + | 0.707228i | \(0.250055\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 9.90726 | − | 3.75547i | 0.338821 | − | 0.128434i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 13.6712i | − | 0.466998i | −0.972357 | − | 0.233499i | \(-0.924982\pi\) | ||
0.972357 | − | 0.233499i | \(-0.0750176\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −11.0182 | − | 33.9105i | −0.375936 | − | 1.15701i | −0.942845 | − | 0.333232i | \(-0.891861\pi\) |
0.566909 | − | 0.823780i | \(-0.308139\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −5.82055 | + | 17.9138i | −0.198364 | + | 0.610501i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −32.2725 | + | 10.4860i | −1.09857 | + | 0.356947i | −0.801552 | − | 0.597926i | \(-0.795992\pi\) |
−0.297017 | + | 0.954872i | \(0.595992\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −10.0514 | + | 8.06997i | −0.341759 | + | 0.274387i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.1414 | + | 15.3349i | 0.378383 | + | 0.520800i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 25.6472 | − | 18.6338i | 0.870022 | − | 0.632108i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.96645 | − | 4.33488i | −0.202165 | − | 0.146882i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 29.6925 | + | 9.64769i | 1.00494 | + | 0.326525i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.87336 | − | 10.9361i | 0.0633311 | − | 0.369706i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 27.2945 | + | 8.86851i | 0.921668 | + | 0.299468i | 0.731151 | − | 0.682216i | \(-0.238983\pi\) |
0.190517 | + | 0.981684i | \(0.438983\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −15.9425 | − | 11.5829i | −0.537726 | − | 0.390680i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −6.73943 | + | 4.89648i | −0.227057 | + | 0.164967i | −0.695498 | − | 0.718528i | \(-0.744816\pi\) |
0.468441 | + | 0.883495i | \(0.344816\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 29.5753 | + | 40.7069i | 0.995289 | + | 1.36990i | 0.928172 | + | 0.372152i | \(0.121380\pi\) |
0.0671169 | + | 0.997745i | \(0.478620\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 18.8515 | − | 15.1353i | 0.633687 | − | 0.508767i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 11.5255 | − | 3.74486i | 0.386988 | − | 0.125740i | −0.109060 | − | 0.994035i | \(-0.534784\pi\) |
0.496048 | + | 0.868295i | \(0.334784\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.457185 | − | 1.40707i | 0.0153335 | − | 0.0471916i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.88420 | + | 21.1874i | 0.230629 | + | 0.709804i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 25.6543i | 0.858490i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 18.1256 | − | 6.87075i | 0.605874 | − | 0.229664i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −19.8369 | + | 27.3031i | −0.662333 | + | 0.911624i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.735159 | −0.0245189 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.8976 | 0.729514 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.95552 | + | 8.19707i | −0.198187 | + | 0.272781i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.53864 | − | 31.9183i | −0.0511461 | − | 1.06100i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31.9105i | 1.05957i | 0.848132 | + | 0.529786i | \(0.177728\pi\) | ||||
−0.848132 | + | 0.529786i | \(0.822272\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.44307 | + | 4.44132i | 0.0478637 | + | 0.147309i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.62900 | − | 23.4797i | 0.252760 | − | 0.777916i | −0.741503 | − | 0.670950i | \(-0.765886\pi\) |
0.994263 | − | 0.106966i | \(-0.0341135\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.36884 | + | 1.09460i | −0.111492 | + | 0.0362260i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 13.6001 | − | 0.655599i | 0.449605 | − | 0.0216734i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.23333 | − | 11.3322i | −0.271889 | − | 0.374223i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.7637 | − | 11.4530i | 0.519997 | − | 0.377800i | −0.296606 | − | 0.955000i | \(-0.595855\pi\) |
0.816603 | + | 0.577200i | \(0.195855\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 16.8637 | + | 12.2522i | 0.555676 | + | 0.403723i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −30.9422 | − | 10.0537i | −1.01847 | − | 0.330922i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.12296 | − | 8.04548i | −0.234202 | − | 0.264534i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −17.7248 | − | 5.75913i | −0.582158 | − | 0.189155i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 9.51748 | + | 6.91485i | 0.312258 | + | 0.226869i | 0.732865 | − | 0.680374i | \(-0.238183\pi\) |
−0.420607 | + | 0.907243i | \(0.638183\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 12.5770 | − | 9.13773i | 0.412195 | − | 0.299477i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −37.9040 | − | 52.1704i | −1.24092 | − | 1.70798i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.40270 | + | 12.4894i | −0.111280 | + | 0.408448i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20.0371 | − | 6.51046i | 0.654585 | − | 0.212688i | 0.0371502 | − | 0.999310i | \(-0.488172\pi\) |
0.617435 | + | 0.786622i | \(0.288172\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −12.8334 | + | 39.4970i | −0.418801 | + | 1.28894i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −0.694380 | − | 2.13708i | −0.0226362 | − | 0.0696669i | 0.939100 | − | 0.343643i | \(-0.111661\pi\) |
−0.961736 | + | 0.273976i | \(0.911661\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 39.2778i | − | 1.27906i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −3.56324 | − | 4.43814i | −0.115912 | − | 0.144373i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.97122 | − | 5.46592i | 0.129047 | − | 0.177619i | −0.739604 | − | 0.673042i | \(-0.764987\pi\) |
0.868651 | + | 0.495424i | \(0.164987\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2.61803 | 0.0849850 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 50.1021 | 1.62467 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −35.2397 | + | 48.5033i | −1.14153 | + | 1.57118i | −0.377475 | + | 0.926020i | \(0.623207\pi\) |
−0.764051 | + | 0.645156i | \(0.776793\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.73208 | − | 0.744347i | −0.0884081 | − | 0.0240865i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 23.6747i | 0.765293i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −0.211431 | − | 0.650719i | −0.00682748 | − | 0.0210128i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −9.57377 | + | 29.4650i | −0.308831 | + | 0.950485i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.39944 | − | 2.72914i | 0.270668 | − | 0.0879454i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 39.5977 | + | 25.9517i | 1.27470 | + | 0.835414i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −5.32298 | − | 7.32645i | −0.171175 | − | 0.235603i | 0.714807 | − | 0.699322i | \(-0.246515\pi\) |
−0.885982 | + | 0.463719i | \(0.846515\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13.3055 | − | 9.66701i | 0.427434 | − | 0.310549i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 38.3076 | + | 27.8321i | 1.22935 | + | 0.893175i | 0.996841 | − | 0.0794192i | \(-0.0253066\pi\) |
0.232509 | + | 0.972594i | \(0.425307\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 15.6410 | + | 5.08206i | 0.501426 | + | 0.162923i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −36.9173 | + | 3.56752i | −1.18230 | + | 0.114252i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.51245 | − | 1.46618i | −0.144366 | − | 0.0469074i | 0.235943 | − | 0.971767i | \(-0.424182\pi\) |
−0.380309 | + | 0.924860i | \(0.624182\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −23.4745 | − | 17.0552i | −0.750247 | − | 0.545086i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −24.1384 | + | 17.5376i | −0.770680 | + | 0.559932i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −10.9126 | − | 15.0199i | −0.348057 | − | 0.479059i | 0.598716 | − | 0.800961i | \(-0.295678\pi\) |
−0.946773 | + | 0.321902i | \(0.895678\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.67050 | − | 25.5116i | −0.308128 | − | 0.812868i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −20.5970 | + | 6.69238i | −0.655610 | + | 0.213021i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.52903 | − | 20.0943i | 0.207611 | − | 0.638961i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 12.2741 | + | 37.7758i | 0.389900 | + | 1.19999i | 0.932863 | + | 0.360232i | \(0.117302\pi\) |
−0.542963 | + | 0.839757i | \(0.682698\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6.51411i | 0.206719i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −12.7552 | + | 19.4622i | −0.404367 | + | 0.616994i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 17.8048 | − | 24.5063i | 0.563885 | − | 0.776121i | −0.427929 | − | 0.903812i | \(-0.640757\pi\) |
0.991814 | + | 0.127691i | \(0.0407567\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −5.51210 | −0.174395 |
(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 | 400.2.y.c.129.1 | 8 | ||
4.3 | odd | 2 | 25.2.e.a.4.1 | ✓ | 8 | ||
12.11 | even | 2 | 225.2.m.a.154.2 | 8 | |||
20.3 | even | 4 | 125.2.d.b.101.1 | 16 | |||
20.7 | even | 4 | 125.2.d.b.101.4 | 16 | |||
20.19 | odd | 2 | 125.2.e.b.24.2 | 8 | |||
25.12 | odd | 20 | 10000.2.a.bj.1.2 | 8 | |||
25.13 | odd | 20 | 10000.2.a.bj.1.7 | 8 | |||
25.19 | even | 10 | inner | 400.2.y.c.369.1 | 8 | ||
100.3 | even | 20 | 625.2.d.o.251.4 | 16 | |||
100.11 | odd | 10 | 625.2.e.a.249.1 | 8 | |||
100.19 | odd | 10 | 25.2.e.a.19.1 | yes | 8 | ||
100.23 | even | 20 | 625.2.d.o.376.4 | 16 | |||
100.27 | even | 20 | 625.2.d.o.376.1 | 16 | |||
100.31 | odd | 10 | 125.2.e.b.99.2 | 8 | |||
100.39 | odd | 10 | 625.2.e.i.249.2 | 8 | |||
100.47 | even | 20 | 625.2.d.o.251.1 | 16 | |||
100.59 | odd | 10 | 625.2.b.c.624.7 | 8 | |||
100.63 | even | 20 | 625.2.a.f.1.2 | 8 | |||
100.67 | even | 20 | 125.2.d.b.26.4 | 16 | |||
100.71 | odd | 10 | 625.2.e.i.374.2 | 8 | |||
100.79 | odd | 10 | 625.2.e.a.374.1 | 8 | |||
100.83 | even | 20 | 125.2.d.b.26.1 | 16 | |||
100.87 | even | 20 | 625.2.a.f.1.7 | 8 | |||
100.91 | odd | 10 | 625.2.b.c.624.2 | 8 | |||
300.119 | even | 10 | 225.2.m.a.19.2 | 8 | |||
300.263 | odd | 20 | 5625.2.a.x.1.7 | 8 | |||
300.287 | odd | 20 | 5625.2.a.x.1.2 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
25.2.e.a.4.1 | ✓ | 8 | 4.3 | odd | 2 | ||
25.2.e.a.19.1 | yes | 8 | 100.19 | odd | 10 | ||
125.2.d.b.26.1 | 16 | 100.83 | even | 20 | |||
125.2.d.b.26.4 | 16 | 100.67 | even | 20 | |||
125.2.d.b.101.1 | 16 | 20.3 | even | 4 | |||
125.2.d.b.101.4 | 16 | 20.7 | even | 4 | |||
125.2.e.b.24.2 | 8 | 20.19 | odd | 2 | |||
125.2.e.b.99.2 | 8 | 100.31 | odd | 10 | |||
225.2.m.a.19.2 | 8 | 300.119 | even | 10 | |||
225.2.m.a.154.2 | 8 | 12.11 | even | 2 | |||
400.2.y.c.129.1 | 8 | 1.1 | even | 1 | trivial | ||
400.2.y.c.369.1 | 8 | 25.19 | even | 10 | inner | ||
625.2.a.f.1.2 | 8 | 100.63 | even | 20 | |||
625.2.a.f.1.7 | 8 | 100.87 | even | 20 | |||
625.2.b.c.624.2 | 8 | 100.91 | odd | 10 | |||
625.2.b.c.624.7 | 8 | 100.59 | odd | 10 | |||
625.2.d.o.251.1 | 16 | 100.47 | even | 20 | |||
625.2.d.o.251.4 | 16 | 100.3 | even | 20 | |||
625.2.d.o.376.1 | 16 | 100.27 | even | 20 | |||
625.2.d.o.376.4 | 16 | 100.23 | even | 20 | |||
625.2.e.a.249.1 | 8 | 100.11 | odd | 10 | |||
625.2.e.a.374.1 | 8 | 100.79 | odd | 10 | |||
625.2.e.i.249.2 | 8 | 100.39 | odd | 10 | |||
625.2.e.i.374.2 | 8 | 100.71 | odd | 10 | |||
5625.2.a.x.1.2 | 8 | 300.287 | odd | 20 | |||
5625.2.a.x.1.7 | 8 | 300.263 | odd | 20 | |||
10000.2.a.bj.1.2 | 8 | 25.12 | odd | 20 | |||
10000.2.a.bj.1.7 | 8 | 25.13 | odd | 20 |