Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(209,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 1, 3]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.209");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.cc (of order \(6\), degree \(2\), 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: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 209.1 | ||
Root | \(0.474636 - 0.274031i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.209 |
Dual form | 1008.2.cc.a.545.1 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
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 | ||||||||
\(3\) | −1.58016 | − | 0.709292i | −0.912306 | − | 0.409510i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.10552 | + | 1.91482i | 0.494405 | + | 0.856335i | 0.999979 | − | 0.00644798i | \(-0.00205247\pi\) |
−0.505574 | + | 0.862783i | \(0.668719\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.906161 | + | 2.48573i | 0.342497 | + | 0.939519i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.99381 | + | 2.24159i | 0.664603 | + | 0.747196i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.93818 | + | 1.69636i | 0.885894 | + | 0.511471i | 0.872597 | − | 0.488440i | \(-0.162434\pi\) |
0.0132968 | + | 0.999912i | \(0.495767\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.56060 | + | 0.901012i | −0.432832 | + | 0.249896i | −0.700552 | − | 0.713601i | \(-0.747063\pi\) |
0.267720 | + | 0.963497i | \(0.413730\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.388736 | − | 3.80987i | −0.100371 | − | 0.983704i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −5.96901 | −1.44770 | −0.723849 | − | 0.689959i | \(-0.757629\pi\) | ||||
−0.723849 | + | 0.689959i | \(0.757629\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 1.64419i | − | 0.377202i | −0.982054 | − | 0.188601i | \(-0.939605\pi\) | ||
0.982054 | − | 0.188601i | \(-0.0603953\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.331232 | − | 4.57059i | 0.0722807 | − | 0.997384i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.05563 | + | 1.18682i | −0.428629 | + | 0.247469i | −0.698762 | − | 0.715354i | \(-0.746266\pi\) |
0.270133 | + | 0.962823i | \(0.412932\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.0556321 | − | 0.0963576i | 0.0111264 | − | 0.0192715i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.56060 | − | 4.95626i | −0.300337 | − | 0.953833i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.44437 | + | 1.41126i | 0.453908 | + | 0.262064i | 0.709479 | − | 0.704726i | \(-0.248930\pi\) |
−0.255571 | + | 0.966790i | \(0.582264\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.28558 | + | 5.36103i | −1.66774 | + | 0.962870i | −0.698887 | + | 0.715232i | \(0.746321\pi\) |
−0.968853 | + | 0.247638i | \(0.920346\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −3.43958 | − | 4.76454i | −0.598754 | − | 0.829400i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −3.75796 | + | 4.48318i | −0.635211 | + | 0.757795i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.69963 | 0.279417 | 0.139709 | − | 0.990193i | \(-0.455383\pi\) | ||||
0.139709 | + | 0.990193i | \(0.455383\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 3.10507 | − | 0.316823i | 0.497210 | − | 0.0507323i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.455074 | − | 0.788211i | −0.0710706 | − | 0.123098i | 0.828300 | − | 0.560285i | \(-0.189308\pi\) |
−0.899371 | + | 0.437187i | \(0.855975\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.96108 | − | 3.39669i | 0.299062 | − | 0.517990i | −0.676860 | − | 0.736112i | \(-0.736660\pi\) |
0.975922 | + | 0.218122i | \(0.0699931\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.08804 | + | 6.29593i | −0.311267 | + | 0.938541i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −0.123005 | + | 0.213051i | −0.0179422 | + | 0.0310767i | −0.874857 | − | 0.484381i | \(-0.839045\pi\) |
0.856915 | + | 0.515458i | \(0.172378\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.35774 | + | 4.50495i | −0.765392 | + | 0.643564i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 9.43199 | + | 4.23377i | 1.32074 | + | 0.592846i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.87589i | 1.08184i | 0.841075 | + | 0.540919i | \(0.181923\pi\) | ||||
−0.841075 | + | 0.540919i | \(0.818077\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 7.50146i | 1.01150i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.16621 | + | 2.59808i | −0.154468 | + | 0.344124i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 5.39093 | + | 9.33736i | 0.701839 | + | 1.21562i | 0.967820 | + | 0.251643i | \(0.0809709\pi\) |
−0.265981 | + | 0.963978i | \(0.585696\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.22853 | + | 0.709292i | 0.157297 | + | 0.0908155i | 0.576582 | − | 0.817039i | \(-0.304386\pi\) |
−0.419285 | + | 0.907855i | \(0.637719\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −3.76528 | + | 6.98732i | −0.474381 | + | 0.880320i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −3.45056 | − | 1.99218i | −0.427989 | − | 0.247100i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.99381 | − | 6.91748i | −0.487922 | − | 0.845105i | 0.511982 | − | 0.858996i | \(-0.328911\pi\) |
−0.999904 | + | 0.0138913i | \(0.995578\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 4.09003 | − | 0.417322i | 0.492382 | − | 0.0502396i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 12.1743i | 1.44482i | 0.691463 | + | 0.722412i | \(0.256966\pi\) | ||||
−0.691463 | + | 0.722412i | \(0.743034\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 0.426103i | − | 0.0498715i | −0.999689 | − | 0.0249358i | \(-0.992062\pi\) | ||
0.999689 | − | 0.0249358i | \(-0.00793812\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.156253 | + | 0.112801i | −0.0180426 | + | 0.0130251i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.55423 | + | 8.84070i | −0.177121 | + | 1.00749i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.49381 | + | 4.31941i | −0.280576 | + | 0.485971i | −0.971527 | − | 0.236930i | \(-0.923859\pi\) |
0.690951 | + | 0.722902i | \(0.257192\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.04944 | + | 8.93861i | −0.116605 | + | 0.993178i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.28541 | − | 7.42254i | 0.470384 | − | 0.814730i | −0.529042 | − | 0.848596i | \(-0.677449\pi\) |
0.999426 | + | 0.0338660i | \(0.0107819\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.59888 | − | 11.4296i | −0.715750 | − | 1.23971i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −2.86150 | − | 3.96378i | −0.306785 | − | 0.424962i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 10.5358 | 1.11680 | 0.558399 | − | 0.829573i | \(-0.311416\pi\) | ||||
0.558399 | + | 0.829573i | \(0.311416\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.65383 | − | 3.06277i | −0.383025 | − | 0.321065i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 18.4752 | − | 1.88510i | 1.91579 | − | 0.195476i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.14833 | − | 1.81769i | 0.323012 | − | 0.186491i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.30108 | − | 3.63793i | −0.639777 | − | 0.369376i | 0.144751 | − | 0.989468i | \(-0.453762\pi\) |
−0.784529 | + | 0.620092i | \(0.787095\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.05563 | + | 9.96840i | 0.206599 | + | 1.00186i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.33405 | + | 4.04270i | −0.232247 | + | 0.402264i | −0.958469 | − | 0.285197i | \(-0.907941\pi\) |
0.726222 | + | 0.687460i | \(0.241274\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.40462 | − | 3.12036i | 0.532533 | − | 0.307458i | −0.209515 | − | 0.977806i | \(-0.567188\pi\) |
0.742047 | + | 0.670348i | \(0.233855\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 9.11806 | − | 4.41865i | 0.889832 | − | 0.431216i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 1.48939i | − | 0.143985i | −0.997405 | − | 0.0719925i | \(-0.977064\pi\) | ||
0.997405 | − | 0.0719925i | \(-0.0229358\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.38688 | −0.420187 | −0.210093 | − | 0.977681i | \(-0.567377\pi\) | ||||
−0.210093 | + | 0.977681i | \(0.567377\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.68568 | − | 1.20553i | −0.254914 | − | 0.114424i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.8764 | + | 8.58887i | −1.39945 | + | 0.807973i | −0.994335 | − | 0.106293i | \(-0.966102\pi\) |
−0.405115 | + | 0.914266i | \(0.632769\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.54510 | − | 2.62412i | −0.423833 | − | 0.244700i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −5.13123 | − | 1.70177i | −0.474383 | − | 0.157329i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.40888 | − | 14.8374i | −0.495831 | − | 1.36014i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0.255260 | + | 0.442124i | 0.0232055 | + | 0.0401931i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.160018 | + | 1.56828i | 0.0144283 | + | 0.141407i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.3013 | 1.01081 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.32141 | −0.560935 | −0.280467 | − | 0.959864i | \(-0.590489\pi\) | ||||
−0.280467 | + | 0.959864i | \(0.590489\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −5.50806 | + | 3.97633i | −0.484958 | + | 0.350096i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 8.51213 | + | 14.7434i | 0.743708 | + | 1.28814i | 0.950796 | + | 0.309818i | \(0.100268\pi\) |
−0.207088 | + | 0.978322i | \(0.566399\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.08701 | − | 1.48990i | 0.354389 | − | 0.129190i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.76509 | − | 8.46754i | 0.668313 | − | 0.728770i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.42580 | + | 3.13259i | 0.463557 | + | 0.267635i | 0.713539 | − | 0.700616i | \(-0.247091\pi\) |
−0.249982 | + | 0.968251i | \(0.580425\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.65488 | + | 3.84220i | −0.564460 | + | 0.325891i | −0.754934 | − | 0.655801i | \(-0.772331\pi\) |
0.190474 | + | 0.981692i | \(0.438998\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0.345483 | − | 0.249409i | 0.0290950 | − | 0.0210040i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −6.11375 | −0.511258 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.24071i | 0.518263i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 11.6614 | − | 3.31834i | 0.961817 | − | 0.273692i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.3695 | − | 7.71887i | 1.09527 | − | 0.632355i | 0.160296 | − | 0.987069i | \(-0.448755\pi\) |
0.934975 | + | 0.354714i | \(0.115422\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.84362 | − | 10.1215i | 0.475547 | − | 0.823672i | −0.524060 | − | 0.851681i | \(-0.675583\pi\) |
0.999608 | + | 0.0280089i | \(0.00891668\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −11.9011 | − | 13.3801i | −0.962145 | − | 1.08171i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −20.5309 | − | 11.8535i | −1.64908 | − | 0.952096i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.93586 | + | 2.84972i | −0.393924 | + | 0.227432i | −0.683859 | − | 0.729614i | \(-0.739700\pi\) |
0.289935 | + | 0.957046i | \(0.406366\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 5.58631 | − | 12.4452i | 0.443023 | − | 0.986966i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.81285 | − | 4.03430i | −0.379306 | − | 0.317948i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.2101 | 0.799721 | 0.399860 | − | 0.916576i | \(-0.369059\pi\) | ||||
0.399860 | + | 0.916576i | \(0.369059\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 5.32072 | − | 11.8535i | 0.414218 | − | 0.922794i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.80661 | − | 3.12914i | −0.139800 | − | 0.242140i | 0.787621 | − | 0.616160i | \(-0.211312\pi\) |
−0.927421 | + | 0.374020i | \(0.877979\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.87636 | + | 8.44610i | −0.375104 | + | 0.649700i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.68559 | − | 3.27819i | 0.281844 | − | 0.250690i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 9.03957 | − | 15.6570i | 0.687266 | − | 1.19038i | −0.285453 | − | 0.958393i | \(-0.592144\pi\) |
0.972719 | − | 0.231987i | \(-0.0745226\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0.289931 | + | 0.0509711i | 0.0219167 | + | 0.00385305i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.89561 | − | 18.5783i | −0.142483 | − | 1.39643i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.03194i | 0.376105i | 0.982159 | + | 0.188052i | \(0.0602175\pi\) | ||||
−0.982159 | + | 0.188052i | \(0.939783\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 13.5592i | 1.00785i | 0.863747 | + | 0.503925i | \(0.168111\pi\) | ||||
−0.863747 | + | 0.503925i | \(0.831889\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.43818 | − | 1.99218i | −0.106313 | − | 0.147266i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.87898 | + | 3.25449i | 0.138145 | + | 0.239275i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17.5380 | − | 10.1256i | −1.28251 | − | 0.740455i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.9058 | − | 8.37040i | 0.793280 | − | 0.608857i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.86948 | + | 5.12080i | 0.641773 | + | 0.370528i | 0.785297 | − | 0.619119i | \(-0.212510\pi\) |
−0.143524 | + | 0.989647i | \(0.545844\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.06615 | − | 13.9710i | −0.580614 | − | 1.00565i | −0.995407 | − | 0.0957374i | \(-0.969479\pi\) |
0.414792 | − | 0.909916i | \(-0.363854\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.03940 | + | 5.59542i | 0.289267 | + | 0.400696i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 3.86303i | − | 0.275230i | −0.990486 | − | 0.137615i | \(-0.956056\pi\) | ||
0.990486 | − | 0.137615i | \(-0.0439436\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 15.2034i | − | 1.07774i | −0.842388 | − | 0.538871i | \(-0.818851\pi\) | ||
0.842388 | − | 0.538871i | \(-0.181149\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.40434 | + | 13.7635i | 0.0990548 | + | 0.970803i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.29302 | + | 7.35487i | −0.0907520 | + | 0.516211i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.00619 | − | 1.74277i | 0.0702753 | − | 0.121720i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.75890 | − | 2.24159i | −0.469776 | − | 0.155801i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 2.78913 | − | 4.83091i | 0.192928 | − | 0.334161i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.9523 | − | 20.7021i | −0.822833 | − | 1.42519i | −0.903564 | − | 0.428453i | \(-0.859059\pi\) |
0.0807311 | − | 0.996736i | \(-0.474274\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.63513 | − | 19.2373i | 0.591669 | − | 1.31812i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 8.67208 | 0.591431 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −21.7403 | − | 18.2235i | −1.47583 | − | 1.23709i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −0.302231 | + | 0.673310i | −0.0204229 | + | 0.0454981i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 9.31522 | − | 5.37815i | 0.626610 | − | 0.361773i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.6198 | + | 9.59545i | 1.11294 | + | 0.642559i | 0.939591 | − | 0.342300i | \(-0.111206\pi\) |
0.173354 | + | 0.984860i | \(0.444539\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.326914 | − | 0.0674145i | 0.0217943 | − | 0.00449430i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −4.33604 | + | 7.51024i | −0.287793 | + | 0.498472i | −0.973283 | − | 0.229610i | \(-0.926255\pi\) |
0.685490 | + | 0.728082i | \(0.259588\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.4437 | − | 7.18439i | 0.822304 | − | 0.474758i | −0.0289060 | − | 0.999582i | \(-0.509202\pi\) |
0.851211 | + | 0.524824i | \(0.175869\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 8.72657 | − | 12.8673i | 0.574166 | − | 0.846607i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 29.7160i | 1.94676i | 0.229194 | + | 0.973381i | \(0.426391\pi\) | ||||
−0.229194 | + | 0.973381i | \(0.573609\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −0.543941 | −0.0354828 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.00434 | − | 5.05651i | 0.454981 | − | 0.328456i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 13.7101 | − | 7.91556i | 0.886836 | − | 0.512015i | 0.0139296 | − | 0.999903i | \(-0.495566\pi\) |
0.872906 | + | 0.487888i | \(0.162233\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.34973 | − | 2.51132i | −0.280190 | − | 0.161768i | 0.353319 | − | 0.935503i | \(-0.385053\pi\) |
−0.633510 | + | 0.773735i | \(0.718386\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.99837 | − | 13.3801i | 0.513095 | − | 0.858332i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.5493 | − | 5.27881i | −0.929521 | − | 0.337251i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.48143 | + | 2.56591i | 0.0942612 | + | 0.163265i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.0364 | + | 8.68920i | −0.762774 | + | 0.550655i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.29728 | 0.460600 | 0.230300 | − | 0.973120i | \(-0.426029\pi\) | ||||
0.230300 | + | 0.973120i | \(0.426029\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.05308 | −0.506293 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 2.32037 | + | 22.7411i | 0.145307 | + | 1.42411i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.00397 | − | 6.93508i | −0.249761 | − | 0.432598i | 0.713699 | − | 0.700453i | \(-0.247019\pi\) |
−0.963459 | + | 0.267855i | \(0.913685\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.54014 | + | 4.22482i | 0.0956994 | + | 0.262518i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.71015 | + | 8.29305i | 0.105856 | + | 0.513327i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 13.6051 | + | 7.85489i | 0.838925 | + | 0.484353i | 0.856899 | − | 0.515485i | \(-0.172388\pi\) |
−0.0179738 | + | 0.999838i | \(0.505722\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −15.0810 | + | 8.70699i | −0.926416 | + | 0.534866i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −16.6483 | − | 7.47299i | −1.01886 | − | 0.457340i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.4924 | 0.639731 | 0.319866 | − | 0.947463i | \(-0.396362\pi\) | ||||
0.319866 | + | 0.947463i | \(0.396362\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 22.2537i | 1.35181i | 0.736987 | + | 0.675907i | \(0.236248\pi\) | ||||
−0.736987 | + | 0.675907i | \(0.763752\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 3.60123 | + | 7.43130i | 0.217957 | + | 0.449762i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.326914 | − | 0.188744i | 0.0197137 | − | 0.0113817i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 11.4251 | − | 19.7889i | 0.686468 | − | 1.18900i | −0.286505 | − | 0.958079i | \(-0.592493\pi\) |
0.972973 | − | 0.230919i | \(-0.0741733\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −30.5309 | − | 10.1256i | −1.82784 | − | 0.606202i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 0.796041 | + | 0.459595i | 0.0474878 | + | 0.0274171i | 0.523556 | − | 0.851991i | \(-0.324605\pi\) |
−0.476068 | + | 0.879408i | \(0.657938\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.1573 | − | 11.0605i | 1.13878 | − | 0.657477i | 0.192654 | − | 0.981267i | \(-0.438290\pi\) |
0.946129 | + | 0.323790i | \(0.104957\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −6.26413 | + | 0.639154i | −0.371055 | + | 0.0378602i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.54691 | − | 1.84544i | 0.0913113 | − | 0.108933i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 18.6291 | 1.09583 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7.37636 | + | 10.2178i | 0.432410 | + | 0.598979i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 14.6259 | + | 25.3328i | 0.854453 | + | 1.47996i | 0.877152 | + | 0.480214i | \(0.159441\pi\) |
−0.0226986 | + | 0.999742i | \(0.507226\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −11.9196 | + | 20.6454i | −0.693986 | + | 1.20202i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 3.82228 | − | 17.2097i | 0.221791 | − | 0.998609i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.13868 | − | 3.70430i | 0.123683 | − | 0.214225i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 10.2203 | + | 1.79677i | 0.589089 | + | 0.103564i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.55563 | − | 4.73259i | 0.376611 | − | 0.271880i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 3.13656i | 0.179599i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.8451i | 0.847254i | 0.905837 | + | 0.423627i | \(0.139243\pi\) | ||||
−0.905837 | + | 0.423627i | \(0.860757\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −10.7534 | + | 1.09721i | −0.611740 | + | 0.0624182i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.69002 | − | 16.7836i | −0.549471 | − | 0.951711i | −0.998311 | − | 0.0580991i | \(-0.981496\pi\) |
0.448840 | − | 0.893612i | \(-0.351837\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.6608 | + | 7.30974i | 0.715633 | + | 0.413171i | 0.813143 | − | 0.582064i | \(-0.197755\pi\) |
−0.0975102 | + | 0.995235i | \(0.531088\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −17.5421 | + | 0.514803i | −0.988385 | + | 0.0290059i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.7046 | − | 8.48973i | −0.825895 | − | 0.476831i | 0.0265499 | − | 0.999647i | \(-0.491548\pi\) |
−0.852445 | + | 0.522817i | \(0.824881\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 4.78799 | + | 8.29305i | 0.268076 | + | 0.464321i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.05641 | + | 2.35348i | −0.0589633 | + | 0.131358i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.81416i | 0.546074i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0.200501i | 0.0111218i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 6.93197 | + | 3.11158i | 0.383339 | + | 0.172071i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −0.641051 | − | 0.112699i | −0.0353423 | − | 0.00621332i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.94801 | − | 17.2305i | 0.546792 | − | 0.947072i | −0.451700 | − | 0.892170i | \(-0.649182\pi\) |
0.998492 | − | 0.0549016i | \(-0.0174845\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 3.38874 | + | 3.80987i | 0.185702 | + | 0.208779i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 8.83051 | − | 15.2949i | 0.482462 | − | 0.835649i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.490168 | + | 0.848996i | 0.0267012 | + | 0.0462478i | 0.879067 | − | 0.476698i | \(-0.158166\pi\) |
−0.852366 | + | 0.522946i | \(0.824833\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 29.5990 | − | 3.02011i | 1.60760 | − | 0.164030i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −36.3769 | −1.96992 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.0531 | − | 9.23572i | −0.866785 | − | 0.498682i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.32072 | + | 7.37033i | 0.286458 | + | 0.396805i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.3702 | + | 10.6060i | −0.986162 | + | 0.569361i | −0.904125 | − | 0.427268i | \(-0.859476\pi\) |
−0.0820373 | + | 0.996629i | \(0.526143\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.69945 | + | 5.02263i | 0.465671 | + | 0.268855i | 0.714426 | − | 0.699711i | \(-0.246688\pi\) |
−0.248755 | + | 0.968566i | \(0.580021\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.90112 | + | 6.32862i | 0.368354 | + | 0.337797i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 1.37327 | − | 2.37858i | 0.0730920 | − | 0.126599i | −0.827163 | − | 0.561962i | \(-0.810047\pi\) |
0.900255 | + | 0.435363i | \(0.143380\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −23.3116 | + | 13.4590i | −1.23725 | + | 0.714329i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.97712 | + | 27.2819i | −0.104641 | + | 1.44391i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 10.0013i | 0.527849i | 0.964543 | + | 0.263925i | \(0.0850170\pi\) | ||||
−0.964543 | + | 0.263925i | \(0.914983\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 16.2967 | 0.857719 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −0.0897572 | − | 0.879680i | −0.00471103 | − | 0.0461712i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.815912 | − | 0.471067i | 0.0427068 | − | 0.0246568i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.03560 | + | 2.90731i | 0.262856 | + | 0.151760i | 0.625637 | − | 0.780114i | \(-0.284839\pi\) |
−0.362781 | + | 0.931875i | \(0.618173\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0.859514 | − | 2.59163i | 0.0447445 | − | 0.134915i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −19.5774 | + | 7.13683i | −1.01641 | + | 0.370526i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.75959 | + | 13.4400i | 0.401776 | + | 0.695897i | 0.993940 | − | 0.109920i | \(-0.0350596\pi\) |
−0.592164 | + | 0.805817i | \(0.701726\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −17.8578 | − | 8.01589i | −0.922172 | − | 0.413939i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.08623 | −0.261954 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2.79714 | −0.143679 | −0.0718396 | − | 0.997416i | \(-0.522887\pi\) | ||||
−0.0718396 | + | 0.997416i | \(0.522887\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9.98884 | + | 4.48373i | 0.511744 | + | 0.229708i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 1.74229 | + | 3.01773i | 0.0890268 | + | 0.154199i | 0.907100 | − | 0.420915i | \(-0.138291\pi\) |
−0.818073 | + | 0.575114i | \(0.804958\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −18.6466 | + | 6.79753i | −0.950320 | + | 0.346434i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.5240 | − | 2.37642i | 0.585798 | − | 0.120800i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.37017 | − | 3.67782i | −0.322980 | − | 0.186473i | 0.329740 | − | 0.944072i | \(-0.393039\pi\) |
−0.652720 | + | 0.757599i | \(0.726372\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 12.2701 | − | 7.08414i | 0.620525 | − | 0.358260i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.99312 | − | 29.3346i | −0.150983 | − | 1.47973i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −11.0279 | −0.554872 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 19.2838i | 0.967825i | 0.875116 | + | 0.483912i | \(0.160785\pi\) | ||||
−0.875116 | + | 0.483912i | \(0.839215\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −7.51490 | − | 0.544606i | −0.376215 | − | 0.0272644i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 9.60576 | − | 5.54589i | 0.479689 | − | 0.276949i | −0.240598 | − | 0.970625i | \(-0.577344\pi\) |
0.720287 | + | 0.693676i | \(0.244010\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.66071 | − | 16.7328i | 0.481234 | − | 0.833522i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −18.2760 | + | 7.87235i | −0.908144 | + | 0.391180i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.99381 | + | 2.88318i | 0.247534 | + | 0.142914i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.5597 | − | 10.1381i | 0.868274 | − | 0.501298i | 0.00149954 | − | 0.999999i | \(-0.499523\pi\) |
0.866774 | + | 0.498701i | \(0.166189\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.35171 | − | 8.79846i | −0.313307 | − | 0.433996i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −18.3252 | + | 21.8616i | −0.901722 | + | 1.07574i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.9505 | 0.930243 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 13.2410 | − | 1.35103i | 0.648416 | − | 0.0661604i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 5.54936 | + | 9.61177i | 0.271104 | + | 0.469566i | 0.969145 | − | 0.246492i | \(-0.0792779\pi\) |
−0.698041 | + | 0.716058i | \(0.745945\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.59269 | − | 7.95478i | 0.223834 | − | 0.387692i | −0.732135 | − | 0.681160i | \(-0.761476\pi\) |
0.955969 | + | 0.293467i | \(0.0948092\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −0.722823 | + | 0.149057i | −0.0351448 | + | 0.00724738i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.332068 | + | 0.575159i | −0.0161077 | + | 0.0278993i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.649865 | + | 3.69653i | −0.0314492 | + | 0.178888i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.66071 | + | 4.33643i | 0.466423 | + | 0.209365i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 15.1102i | − | 0.727833i | −0.931432 | − | 0.363916i | \(-0.881439\pi\) | ||
0.931432 | − | 0.363916i | \(-0.118561\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 3.33578i | − | 0.160307i | −0.996783 | − | 0.0801537i | \(-0.974459\pi\) | ||
0.996783 | − | 0.0801537i | \(-0.0255411\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.42649 | − | 9.86132i | 0.212234 | − | 0.472814i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.95135 | + | 3.37984i | 0.0933458 | + | 0.161680i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5.91032 | − | 3.41233i | −0.282084 | − | 0.162861i | 0.352282 | − | 0.935894i | \(-0.385406\pi\) |
−0.634367 | + | 0.773032i | \(0.718739\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −20.7806 | − | 3.02785i | −0.989551 | − | 0.144183i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −9.77747 | − | 5.64503i | −0.464542 | − | 0.268203i | 0.249410 | − | 0.968398i | \(-0.419763\pi\) |
−0.713952 | + | 0.700195i | \(0.753097\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 11.6476 | + | 20.1743i | 0.552151 | + | 0.956354i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −26.6008 | + | 2.71419i | −1.25818 | + | 0.128377i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 24.8554i | − | 1.17300i | −0.809950 | − | 0.586498i | \(-0.800506\pi\) | ||
0.809950 | − | 0.586498i | \(-0.199494\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 3.08787i | − | 0.145402i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −16.4129 | + | 11.8487i | −0.771146 | + | 0.556700i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.82527 | − | 10.3824i | 0.0855700 | − | 0.486735i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.30470 | − | 10.9201i | 0.294922 | − | 0.510819i | −0.680045 | − | 0.733170i | \(-0.738040\pi\) |
0.974967 | + | 0.222351i | \(0.0713732\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 9.31522 | + | 29.5840i | 0.434797 | + | 1.38086i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 14.4031 | − | 24.9470i | 0.670821 | − | 1.16190i | −0.306851 | − | 0.951758i | \(-0.599275\pi\) |
0.977672 | − | 0.210138i | \(-0.0673913\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 12.5858 | + | 21.7993i | 0.584912 | + | 1.01310i | 0.994886 | + | 0.101001i | \(0.0322045\pi\) |
−0.409974 | + | 0.912097i | \(0.634462\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 24.0345 | + | 33.2928i | 1.11457 | + | 1.54392i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −25.5951 | −1.18440 | −0.592199 | − | 0.805792i | \(-0.701740\pi\) | ||||
−0.592199 | + | 0.805792i | \(0.701740\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 13.5760 | − | 16.1959i | 0.626881 | − | 0.747857i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.82072 | − | 1.00205i | 0.452515 | − | 0.0461719i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 11.5240 | − | 6.65338i | 0.529874 | − | 0.305923i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.158430 | − | 0.0914695i | −0.00726926 | − | 0.00419691i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −17.6545 | + | 15.7030i | −0.808345 | + | 0.718993i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 0.267749 | − | 0.463755i | 0.0122338 | − | 0.0211895i | −0.859844 | − | 0.510557i | \(-0.829439\pi\) |
0.872077 | + | 0.489368i | \(0.162772\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.65244 | + | 1.53138i | −0.120941 | + | 0.0698251i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.74358 | + | 9.78856i | 0.215840 | + | 0.445395i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 16.0873i | − | 0.730485i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −34.1323 | −1.54668 | −0.773341 | − | 0.633990i | \(-0.781416\pi\) | ||||
−0.773341 | + | 0.633990i | \(0.781416\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −16.1337 | − | 7.24198i | −0.729590 | − | 0.327493i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.86948 | + | 3.38874i | −0.264886 | + | 0.152932i | −0.626561 | − | 0.779372i | \(-0.715538\pi\) |
0.361675 | + | 0.932304i | \(0.382205\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −14.5905 | − | 8.42380i | −0.657121 | − | 0.379389i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −16.8152 | + | 14.9565i | −0.755787 | + | 0.672244i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −30.2621 | + | 11.0319i | −1.35744 | + | 0.494847i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.30037 | + | 7.44846i | 0.192511 | + | 0.333439i | 0.946082 | − | 0.323928i | \(-0.105004\pi\) |
−0.753571 | + | 0.657367i | \(0.771670\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.635258 | + | 6.22595i | 0.0283812 | + | 0.278155i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.96518 | 0.132211 | 0.0661055 | − | 0.997813i | \(-0.478943\pi\) | ||||
0.0661055 | + | 0.997813i | \(0.478943\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −10.3214 | −0.459297 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 13.6962 | − | 9.88742i | 0.608268 | − | 0.439116i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.04882 | − | 5.28072i | −0.135137 | − | 0.234064i | 0.790513 | − | 0.612445i | \(-0.209814\pi\) |
−0.925650 | + | 0.378382i | \(0.876481\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.05918 | − | 0.386118i | 0.0468553 | − | 0.0170808i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.14902 | + | 2.56591i | −0.359788 | + | 0.113288i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 11.9499 | + | 6.89926i | 0.526574 | + | 0.304018i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −0.722823 | + | 0.417322i | −0.0317897 | + | 0.0183538i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −25.3893 | + | 18.3289i | −1.11447 | + | 0.804548i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −32.6929 | −1.43230 | −0.716150 | − | 0.697946i | \(-0.754097\pi\) | ||||
−0.716150 | + | 0.697946i | \(0.754097\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 2.00252i | − | 0.0875643i | −0.999041 | − | 0.0437821i | \(-0.986059\pi\) | ||
0.999041 | − | 0.0437821i | \(-0.0139407\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.421984 | − | 0.286188i | −0.0184169 | − | 0.0124903i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 55.4257 | − | 32.0001i | 2.41438 | − | 1.39394i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.68292 | + | 15.0393i | −0.377518 | + | 0.653881i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −10.1820 | + | 30.7012i | −0.441863 | + | 1.33232i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.42037 | + | 0.820053i | 0.0615232 | + | 0.0355204i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.85192 | − | 1.64656i | 0.123299 | − | 0.0711870i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 3.56911 | − | 7.95127i | 0.154019 | − | 0.343122i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −23.3840 | + | 4.14769i | −1.00722 | + | 0.178654i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −11.4451 | −0.492061 | −0.246031 | − | 0.969262i | \(-0.579126\pi\) | ||||
−0.246031 | + | 0.969262i | \(0.579126\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.61745 | − | 21.4258i | 0.412724 | − | 0.919467i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.84980 | − | 8.40010i | −0.207743 | − | 0.359821i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3.91961 | − | 6.78896i | 0.167590 | − | 0.290275i | −0.769982 | − | 0.638066i | \(-0.779735\pi\) |
0.937572 | + | 0.347791i | \(0.113068\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.859514 | + | 4.16805i | 0.0366832 | + | 0.177888i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.32037 | − | 4.01899i | 0.0988510 | − | 0.171215i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.9967 | − | 2.28487i | −0.552675 | − | 0.0971626i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.660706 | − | 6.47536i | −0.0280454 | − | 0.274864i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 0.0134996i | − | 0.000571997i | −1.00000 | 0.000285998i | \(-0.999909\pi\) | |||
1.00000 | 0.000285998i | \(-9.10361e-5\pi\) | ||||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.06782i | 0.298937i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 20.5309 | + | 28.4396i | 0.866814 | + | 1.20072i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.54528 | + | 16.5329i | 0.402286 | + | 0.696779i | 0.994001 | − | 0.109368i | \(-0.0348826\pi\) |
−0.591716 | + | 0.806147i | \(0.701549\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −32.8923 | − | 18.9904i | −1.38379 | − | 0.798932i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −23.1700 | + | 5.49118i | −0.973047 | + | 0.230608i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 32.3406 | + | 18.6719i | 1.35579 | + | 0.782765i | 0.989053 | − | 0.147561i | \(-0.0471422\pi\) |
0.366735 | + | 0.930325i | \(0.380475\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.6421 | + | 39.2173i | 0.947544 | + | 1.64119i | 0.750576 | + | 0.660784i | \(0.229776\pi\) |
0.196968 | + | 0.980410i | \(0.436890\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.3831 | − | 14.3827i | −0.433758 | − | 0.600847i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0.264101i | 0.0110138i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 37.0988i | − | 1.54444i | −0.635354 | − | 0.772221i | \(-0.719146\pi\) | ||
0.635354 | − | 0.772221i | \(-0.280854\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.83630 | + | 27.7976i | 0.117873 | + | 1.15523i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 22.3337 | + | 3.92636i | 0.926559 | + | 0.162893i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.3603 | + | 23.1408i | −0.553329 | + | 0.958393i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.41411 | − | 11.7068i | −0.0998111 | − | 0.484015i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.0612 | − | 29.5509i | 0.704191 | − | 1.21969i | −0.262792 | − | 0.964853i | \(-0.584643\pi\) |
0.966983 | − | 0.254842i | \(-0.0820235\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 8.81453 | + | 15.2672i | 0.363197 | + | 0.629075i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −2.74002 | + | 6.10421i | −0.112709 | + | 0.251094i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 19.6999 | 0.808980 | 0.404490 | − | 0.914542i | \(-0.367449\pi\) | ||||
0.404490 | + | 0.914542i | \(0.367449\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 22.4313 | − | 26.7601i | 0.919594 | − | 1.09706i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −10.7837 | + | 24.0238i | −0.441346 | + | 0.983230i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 9.74033 | − | 5.62358i | 0.397979 | − | 0.229773i | −0.287632 | − | 0.957741i | \(-0.592868\pi\) |
0.685612 | + | 0.727967i | \(0.259535\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 29.7646 | + | 17.1846i | 1.21412 | + | 0.700975i | 0.963655 | − | 0.267150i | \(-0.0860818\pi\) |
0.250469 | + | 0.968125i | \(0.419415\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.54325 | − | 22.7446i | 0.307185 | − | 0.926233i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.564393 | + | 0.977557i | −0.0229458 | + | 0.0397433i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 33.7888 | − | 19.5080i | 1.37145 | − | 0.791804i | 0.380335 | − | 0.924849i | \(-0.375809\pi\) |
0.991110 | + | 0.133044i | \(0.0424753\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.25993 | − | 10.7047i | 0.294187 | − | 0.433778i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 0.443317i | − | 0.0179347i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −16.1099 | −0.650672 | −0.325336 | − | 0.945598i | \(-0.605477\pi\) | ||||
−0.325336 | + | 0.945598i | \(0.605477\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.82607 | + | 2.04018i | −0.113958 | + | 0.0822678i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.03569 | − | 4.06205i | 0.283246 | − | 0.163532i | −0.351646 | − | 0.936133i | \(-0.614378\pi\) |
0.634892 | + | 0.772601i | \(0.281045\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −32.4018 | − | 18.7072i | −1.30234 | − | 0.751906i | −0.321535 | − | 0.946898i | \(-0.604199\pi\) |
−0.980805 | + | 0.194991i | \(0.937532\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.09020 | + | 8.33610i | 0.364777 | + | 0.334516i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 9.54718 | + | 26.1893i | 0.382499 | + | 1.04925i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 12.2156 | + | 21.1581i | 0.488626 | + | 0.846325i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.83379 | + | 5.65531i | −0.312852 | + | 0.225851i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −10.1451 | −0.404511 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 19.8268 | 0.789294 | 0.394647 | − | 0.918833i | \(-0.370867\pi\) | ||||
0.394647 | + | 0.918833i | \(0.370867\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.20281 | + | 41.1903i | 0.167047 | + | 1.63717i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −6.98848 | − | 12.1044i | −0.277329 | − | 0.480348i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.30227 | − | 11.8578i | 0.170462 | − | 0.469823i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −27.2898 | + | 24.2732i | −1.07957 | + | 0.960235i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8.01849 | − | 4.62948i | −0.316711 | − | 0.182853i | 0.333214 | − | 0.942851i | \(-0.391867\pi\) |
−0.649926 | + | 0.759998i | \(0.725200\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −36.3456 | + | 20.9841i | −1.43333 | + | 0.827534i | −0.997373 | − | 0.0724332i | \(-0.976924\pi\) |
−0.435958 | + | 0.899967i | \(0.643590\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −13.7033 | − | 6.15103i | −0.539566 | − | 0.242197i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6.28587 | −0.247123 | −0.123561 | − | 0.992337i | \(-0.539432\pi\) | ||||
−0.123561 | + | 0.992337i | \(0.539432\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 36.5798i | 1.43588i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 21.4274 | + | 44.2163i | 0.839806 | + | 1.73297i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 20.1668 | − | 11.6433i | 0.789189 | − | 0.455638i | −0.0504882 | − | 0.998725i | \(-0.516078\pi\) |
0.839677 | + | 0.543086i | \(0.182744\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.8207 | + | 32.5985i | −0.735387 | + | 1.27373i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0.955147 | − | 0.849568i | 0.0372638 | − | 0.0331448i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −25.8880 | − | 14.9464i | −1.00845 | − | 0.582230i | −0.0977141 | − | 0.995215i | \(-0.531153\pi\) |
−0.910738 | + | 0.412984i | \(0.864486\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.6184 | − | 10.1720i | 0.685278 | − | 0.395645i | −0.116563 | − | 0.993183i | \(-0.537188\pi\) |
0.801841 | + | 0.597538i | \(0.203854\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −18.5342 | + | 1.89112i | −0.719809 | + | 0.0734450i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7.37118 | + | 6.17878i | 0.285842 | + | 0.239603i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.69963 | −0.259411 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −19.4560 | − | 26.9506i | −0.752212 | − | 1.04197i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.40643 | + | 4.16805i | 0.0928990 | + | 0.160906i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.55996 | + | 14.8263i | −0.329962 | + | 0.571511i | −0.982504 | − | 0.186241i | \(-0.940369\pi\) |
0.652542 | + | 0.757753i | \(0.273703\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −0.564393 | − | 0.125352i | −0.0217235 | − | 0.00482479i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 14.2078 | − | 24.6085i | 0.546048 | − | 0.945783i | −0.452492 | − | 0.891769i | \(-0.649465\pi\) |
0.998540 | − | 0.0540148i | \(-0.0172018\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.33313 | − | 18.9593i | 0.127914 | − | 0.727593i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.1786 | − | 8.79186i | 0.466684 | − | 0.336905i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 20.9274i | − | 0.800764i | −0.916348 | − | 0.400382i | \(-0.868877\pi\) | ||
0.916348 | − | 0.400382i | \(-0.131123\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13.8526i | 0.529281i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −24.7589 | + | 2.52625i | −0.944611 | + | 0.0963824i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −7.09627 | − | 12.2911i | −0.270346 | − | 0.468254i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 20.7918 | + | 12.0041i | 0.790957 | + | 0.456659i | 0.840299 | − | 0.542123i | \(-0.182379\pi\) |
−0.0493424 | + | 0.998782i | \(0.515713\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −22.9161 | + | 14.1427i | −0.870509 | + | 0.537238i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.7143 | − | 8.49529i | −0.558144 | − | 0.322245i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.71634 | + | 4.70484i | 0.102889 | + | 0.178208i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 21.0773 | − | 46.9561i | 0.797218 | − | 1.77604i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 42.0117i | 1.58676i | 0.608728 | + | 0.793379i | \(0.291680\pi\) | ||||
−0.608728 | + | 0.793379i | \(0.708320\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 2.79450i | − | 0.105397i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.859514 | + | 0.385813i | 0.0323712 | + | 0.0145306i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −12.1641 | − | 2.13850i | −0.457478 | − | 0.0804266i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.6094 | + | 32.2324i | −0.698891 | + | 1.21051i | 0.269960 | + | 0.962871i | \(0.412989\pi\) |
−0.968851 | + | 0.247643i | \(0.920344\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −14.6545 | + | 3.02198i | −0.549587 | + | 0.113333i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.7252 | − | 22.0406i | 0.476561 | − | 0.825428i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.75890 | − | 11.7068i | −0.252769 | − | 0.437808i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −27.2787 | + | 2.78335i | −1.01874 | + | 0.103946i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −18.2978 | −0.682392 | −0.341196 | − | 0.939992i | \(-0.610832\pi\) | ||||
−0.341196 | + | 0.939992i | \(0.610832\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.6538 | + | 10.6069i | 0.471253 | + | 0.395021i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 5.09201 | + | 7.05350i | 0.189374 | + | 0.262323i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.271971 | − | 0.157022i | 0.0101007 | − | 0.00583166i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 28.3214 | + | 16.3514i | 1.05038 | + | 0.606439i | 0.922756 | − | 0.385384i | \(-0.125931\pi\) |
0.127626 | + | 0.991822i | \(0.459264\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −22.1291 | + | 15.4695i | −0.819595 | + | 0.572943i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −11.7057 | + | 20.2749i | −0.432951 | + | 0.749893i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.431812 | − | 0.249307i | 0.0159494 | − | 0.00920836i | −0.492004 | − | 0.870593i | \(-0.663736\pi\) |
0.507953 | + | 0.861385i | \(0.330402\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 19.2460 | + | 18.6611i | 0.709900 | + | 0.688324i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 27.0997i | − | 0.998231i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 47.7046 | 1.75484 | 0.877421 | − | 0.479722i | \(-0.159263\pi\) | ||||
0.877421 | + | 0.479722i | \(0.159263\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.520916 | − | 5.10532i | −0.0191363 | − | 0.187549i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −9.20534 | + | 5.31470i | −0.337711 | + | 0.194978i | −0.659259 | − | 0.751916i | \(-0.729130\pi\) |
0.321548 | + | 0.946893i | \(0.395797\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 29.5606 | + | 17.0668i | 1.08302 | + | 0.625279i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 25.1826 | − | 5.19302i | 0.921382 | − | 0.190003i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.70223 | − | 1.34963i | 0.135277 | − | 0.0493144i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 9.55927 | + | 16.5571i | 0.348823 | + | 0.604179i | 0.986041 | − | 0.166505i | \(-0.0532482\pi\) |
−0.637218 | + | 0.770684i | \(0.719915\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −11.5309 | − | 5.17590i | −0.420208 | − | 0.188620i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 25.8411 | 0.940453 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 28.5388 | 1.03726 | 0.518631 | − | 0.854998i | \(-0.326442\pi\) | ||||
0.518631 | + | 0.854998i | \(0.326442\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 12.7252 | + | 5.71199i | 0.461894 | + | 0.207332i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 21.6650 | + | 37.5249i | 0.785355 | + | 1.36028i | 0.928787 | + | 0.370615i | \(0.120853\pi\) |
−0.143431 | + | 0.989660i | \(0.545814\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.97522 | − | 10.9046i | −0.143912 | − | 0.394773i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 12.4635 | − | 37.5804i | 0.450621 | − | 1.35872i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −16.8261 | − | 9.71458i | −0.607557 | − | 0.350773i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5.75189 | − | 3.32086i | 0.207419 | − | 0.119753i | −0.392693 | − | 0.919670i | \(-0.628456\pi\) |
0.600111 | + | 0.799917i | \(0.295123\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.40792 | + | 13.7985i | 0.0507049 | + | 0.496942i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −44.4831 | −1.59995 | −0.799973 | − | 0.600036i | \(-0.795153\pi\) | ||||
−0.799973 | + | 0.600036i | \(0.795153\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.19298i | 0.0428532i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0.562971 | − | 7.76830i | 0.0201965 | − | 0.278686i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.29596 | + | 0.748226i | −0.0464328 | + | 0.0268080i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.6520 | + | 35.7703i | −0.738986 | + | 1.27996i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 3.17988 | − | 14.3173i | 0.113640 | − | 0.511660i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.9134 | − | 6.30087i | −0.389517 | − | 0.224888i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 19.0399 | − | 10.9927i | 0.678700 | − | 0.391848i | −0.120665 | − | 0.992693i | \(-0.538503\pi\) |
0.799365 | + | 0.600846i | \(0.205169\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −15.9268 | − | 22.0620i | −0.567008 | − | 0.785426i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −34.8300 | − | 29.1958i | −1.23841 | − | 1.03808i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.55632 | −0.0907776 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 30.0061 | − | 3.06164i | 1.06421 | − | 0.108585i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9.71892 | − | 16.8337i | −0.344262 | − | 0.596279i | 0.640958 | − | 0.767576i | \(-0.278537\pi\) |
−0.985219 | + | 0.171297i | \(0.945204\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0.734219 | − | 1.27171i | 0.0259748 | − | 0.0449897i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 21.0065 | + | 23.6170i | 0.742228 | + | 0.834467i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.722823 | − | 1.25197i | 0.0255079 | − | 0.0441809i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.40426 | − | 13.6758i | 0.0847390 | − | 0.482008i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −16.5796 | − | 7.44215i | −0.583630 | − | 0.261976i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 21.0058i | − | 0.738526i | −0.929325 | − | 0.369263i | \(-0.879610\pi\) | ||
0.929325 | − | 0.369263i | \(-0.120390\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 37.3291i | − | 1.31080i | −0.755281 | − | 0.655401i | \(-0.772500\pi\) | ||
0.755281 | − | 0.655401i | \(-0.227500\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 15.7844 | − | 35.1644i | 0.553581 | − | 1.23327i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 11.2876 | + | 19.5506i | 0.395386 | + | 0.684829i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.58478 | − | 3.22438i | −0.195387 | − | 0.112807i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.419569 | − | 14.2970i | −0.0146609 | − | 0.499576i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −10.9017 | − | 6.29412i | −0.380473 | − | 0.219666i | 0.297551 | − | 0.954706i | \(-0.403830\pi\) |
−0.678024 | + | 0.735040i | \(0.737163\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.4189 | − | 38.8307i | −0.781474 | − | 1.35355i | −0.931083 | − | 0.364808i | \(-0.881135\pi\) |
0.149608 | − | 0.988745i | \(-0.452199\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −0.650451 | + | 0.0663681i | −0.0226458 | + | 0.00231064i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 25.7293i | − | 0.894695i | −0.894360 | − | 0.447347i | \(-0.852369\pi\) | ||
0.894360 | − | 0.447347i | \(-0.147631\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 16.9628i | − | 0.589142i | −0.955630 | − | 0.294571i | \(-0.904823\pi\) | ||
0.955630 | − | 0.294571i | \(-0.0951767\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −32.0896 | + | 23.1658i | −1.11318 | + | 0.803614i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 31.9804 | − | 26.8901i | 1.10806 | − | 0.931686i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.99450 | − | 6.91867i | 0.138235 | − | 0.239431i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 41.0617 | + | 37.6554i | 1.41930 | + | 1.30156i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.3539 | − | 23.1296i | 0.461027 | − | 0.798522i | −0.537986 | − | 0.842954i | \(-0.680815\pi\) |
0.999012 | + | 0.0444321i | \(0.0141478\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.5167 | − | 18.2155i | −0.362645 | − | 0.628120i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −0.931886 | − | 1.29086i | −0.0320958 | − | 0.0444595i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −21.5637 | −0.741815 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −0.867695 | + | 1.03514i | −0.0298144 | + | 0.0355680i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −38.1167 | + | 3.88920i | −1.30816 | + | 0.133477i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −3.49381 | + | 2.01715i | −0.119766 | + | 0.0691471i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 37.6287 | + | 21.7249i | 1.28838 | + | 0.743848i | 0.978366 | − | 0.206883i | \(-0.0663319\pi\) |
0.310017 | + | 0.950731i | \(0.399665\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.3517 | + | 3.43313i | 0.354020 | + | 0.117411i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.83430 | + | 13.5694i | −0.267615 | + | 0.463522i | −0.968245 | − | 0.250002i | \(-0.919569\pi\) |
0.700631 | + | 0.713524i | \(0.252902\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 17.3578 | − | 10.0216i | 0.592242 | − | 0.341931i | −0.173742 | − | 0.984791i | \(-0.555586\pi\) |
0.765984 | + | 0.642860i | \(0.222252\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −3.75332 | + | 1.81887i | −0.127913 | + | 0.0619871i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 40.0219i | 1.36236i | 0.732115 | + | 0.681181i | \(0.238533\pi\) | ||||
−0.732115 | + | 0.681181i | \(0.761467\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 39.9739 | 1.35915 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −29.4369 | − | 13.2134i | −0.999730 | − | 0.448752i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.6545 | + | 8.46079i | −0.497120 | + | 0.287013i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.4655 | + | 7.19694i | 0.422376 | + | 0.243859i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.40841 | − | 21.3778i | −0.149202 | − | 0.723528i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 10.2408 | + | 28.0919i | 0.346201 | + | 0.949680i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −22.6353 | − | 39.2054i | −0.764338 | − | 1.32387i | −0.940596 | − | 0.339529i | \(-0.889732\pi\) |
0.176257 | − | 0.984344i | \(-0.443601\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.14290 | − | 50.4038i | −0.173466 | − | 1.70008i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 45.3385 | 1.52749 | 0.763746 | − | 0.645517i | \(-0.223358\pi\) | ||||
0.763746 | + | 0.645517i | \(0.223358\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −12.5650 | −0.422845 | −0.211423 | − | 0.977395i | \(-0.567810\pi\) | ||||
−0.211423 | + | 0.977395i | \(0.567810\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 33.4785 | − | 24.1685i | 1.12537 | − | 0.812415i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −17.8620 | − | 30.9379i | −0.599748 | − | 1.03879i | −0.992858 | − | 0.119303i | \(-0.961934\pi\) |
0.393110 | − | 0.919492i | \(-0.371399\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.72822 | − | 15.7133i | −0.192118 | − | 0.527009i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −18.2465 | + | 24.4830i | −0.611282 | + | 0.820211i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.350296 | + | 0.202243i | 0.0117222 | + | 0.00676782i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −9.63528 | + | 5.56293i | −0.322072 | + | 0.185948i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.00688 | + | 4.33643i | −0.200564 | + | 0.144789i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −30.2632 | −1.00933 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 47.0113i | − | 1.56617i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −14.8753 | − | 10.0884i | −0.495019 | − | 0.335720i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −25.9635 | + | 14.9901i | −0.863058 | + | 0.498287i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.52104 | + | 7.83067i | −0.150119 | + | 0.260013i | −0.931271 | − | 0.364327i | \(-0.881299\pi\) |
0.781152 | + | 0.624341i | \(0.214632\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.7157 | + | 2.82839i | −0.454922 | + | 0.0938117i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.5171 | + | 20.5058i | 1.17673 | + | 0.679388i | 0.955257 | − | 0.295777i | \(-0.0955787\pi\) |
0.221478 | + | 0.975165i | \(0.428912\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 25.1826 | − | 14.5392i | 0.833421 | − | 0.481176i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 2.22473 | − | 4.95626i | 0.0735475 | − | 0.163849i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −28.9349 | + | 34.5188i | −0.955515 | + | 1.13991i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −10.2326 | −0.337541 | −0.168771 | − | 0.985655i | \(-0.553980\pi\) | ||||
−0.168771 | + | 0.985655i | \(0.553980\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.5295 | − | 23.4576i | 0.346959 | − | 0.772954i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −10.9692 | − | 18.9992i | −0.361055 | − | 0.625366i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0.0945538 | − | 0.163772i | 0.00310891 | − | 0.00538479i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 17.7703 | + | 5.89353i | 0.583654 | + | 0.193569i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −12.8330 | + | 22.2273i | −0.421036 | + | 0.729255i | −0.996041 | − | 0.0888945i | \(-0.971667\pi\) |
0.575005 | + | 0.818150i | \(0.305000\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 7.40697 | + | 8.80913i | 0.242754 | + | 0.288707i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.40731 | + | 33.3938i | 0.111550 | + | 1.09327i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 44.7763i | − | 1.46434i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 15.9276i | 0.520333i | 0.965564 | + | 0.260167i | \(0.0837775\pi\) | ||||
−0.965564 | + | 0.260167i | \(0.916223\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −14.8214 | − | 20.5308i | −0.483679 | − | 0.669997i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 19.6767 | + | 34.0810i | 0.641442 | + | 1.11101i | 0.985111 | + | 0.171919i | \(0.0549967\pi\) |
−0.343669 | + | 0.939091i | \(0.611670\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.87093 | + | 1.08018i | 0.0609258 | + | 0.0351755i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 28.0845 | + | 11.6290i | 0.913588 | + | 0.378291i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −28.9086 | − | 16.6904i | −0.939403 | − | 0.542365i | −0.0496302 | − | 0.998768i | \(-0.515804\pi\) |
−0.889773 | + | 0.456403i | \(0.849138\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.383923 | + | 0.664975i | 0.0124627 | + | 0.0215860i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 17.2140 | + | 23.8450i | 0.558202 | + | 0.773228i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 44.4622i | − | 1.44027i | −0.693832 | − | 0.720137i | \(-0.744079\pi\) | ||
0.693832 | − | 0.720137i | \(-0.255921\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.6447i | 0.732764i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.68360 | − | 16.5004i | −0.0544232 | − | 0.533383i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.87013 | + | 16.3257i | −0.0926813 | + | 0.527185i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 41.9814 | − | 72.7138i | 1.35424 | − | 2.34561i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.33860 | − | 2.96957i | 0.107585 | − | 0.0956929i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 17.8347 | − | 30.8905i | 0.574118 | − | 0.994401i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 20.0556 | + | 34.7372i | 0.644943 | + | 1.11707i | 0.984315 | + | 0.176422i | \(0.0564523\pi\) |
−0.339371 | + | 0.940652i | \(0.610214\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 6.96110 | − | 15.5079i | 0.223623 | − | 0.498187i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 46.0026 | 1.47629 | 0.738147 | − | 0.674640i | \(-0.235701\pi\) | ||||
0.738147 | + | 0.674640i | \(0.235701\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.5811 | − | 13.0606i | −0.499506 | − | 0.418704i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0.142213 | − | 0.316823i | 0.00455448 | − | 0.0101465i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −46.8323 | + | 27.0386i | −1.49830 | + | 0.865042i | −0.999998 | − | 0.00196335i | \(-0.999375\pi\) |
−0.498299 | + | 0.867005i | \(0.666042\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 30.9562 | + | 17.8726i | 0.989365 | + | 0.571210i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −8.74660 | − | 9.83357i | −0.279257 | − | 0.313962i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 6.97890 | − | 12.0878i | 0.222592 | − | 0.385541i | −0.733002 | − | 0.680226i | \(-0.761881\pi\) |
0.955594 | + | 0.294685i | \(0.0952148\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.39703 | − | 4.27068i | 0.235689 | − | 0.136075i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0.933027 | + | 0.632776i | 0.0296986 | + | 0.0201415i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 9.30979i | 0.296034i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 37.0297 | 1.17629 | 0.588144 | − | 0.808756i | \(-0.299859\pi\) | ||||
0.588144 | + | 0.808756i | \(0.299859\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −27.9409 | + | 20.1708i | −0.886677 | + | 0.640102i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 29.1119 | − | 16.8077i | 0.922909 | − | 0.532841i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −43.4282 | − | 25.0733i | −1.37538 | − | 0.794079i | −0.383785 | − | 0.923422i | \(-0.625380\pi\) |
−0.991600 | + | 0.129344i | \(0.958713\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.65244 | − | 8.42380i | −0.0839194 | − | 0.266517i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))