Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,4,Mod(17,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.17");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.g (of order \(8\), 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: | \(7.55224448073\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 81.4 | ||
Character | \(\chi\) | \(=\) | 128.81 |
Dual form | 128.4.g.a.49.4 |
$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{3}{8}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −4.56924 | − | 1.89264i | −0.879350 | − | 0.364239i | −0.103105 | − | 0.994670i | \(-0.532878\pi\) |
−0.776245 | + | 0.630432i | \(0.782878\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.37033 | + | 3.30826i | 0.122566 | + | 0.295900i | 0.973239 | − | 0.229795i | \(-0.0738055\pi\) |
−0.850673 | + | 0.525695i | \(0.823806\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.14642 | − | 6.14642i | 0.331875 | − | 0.331875i | −0.521423 | − | 0.853298i | \(-0.674599\pi\) |
0.853298 | + | 0.521423i | \(0.174599\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.79604 | − | 1.79604i | −0.0665200 | − | 0.0665200i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −17.2398 | + | 7.14095i | −0.472544 | + | 0.195734i | −0.606230 | − | 0.795290i | \(-0.707319\pi\) |
0.133685 | + | 0.991024i | \(0.457319\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −25.9810 | + | 62.7238i | −0.554296 | + | 1.33819i | 0.359928 | + | 0.932980i | \(0.382801\pi\) |
−0.914224 | + | 0.405209i | \(0.867199\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 17.7098i | − | 0.304843i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 87.5919i | 1.24966i | 0.780762 | + | 0.624828i | \(0.214831\pi\) | ||||
−0.780762 | + | 0.624828i | \(0.785169\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −48.8193 | + | 117.860i | −0.589470 | + | 1.42311i | 0.294541 | + | 0.955639i | \(0.404833\pi\) |
−0.884011 | + | 0.467467i | \(0.845167\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −39.7174 | + | 16.4515i | −0.412716 | + | 0.170953i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 55.7254 | + | 55.7254i | 0.505198 | + | 0.505198i | 0.913049 | − | 0.407851i | \(-0.133722\pi\) |
−0.407851 | + | 0.913049i | \(0.633722\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 79.3216 | − | 79.3216i | 0.634572 | − | 0.634572i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 55.9086 | + | 134.975i | 0.398504 | + | 0.962074i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −114.139 | − | 47.2779i | −0.730865 | − | 0.302734i | −0.0139575 | − | 0.999903i | \(-0.504443\pi\) |
−0.716907 | + | 0.697168i | \(0.754443\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −229.997 | −1.33254 | −0.666269 | − | 0.745711i | \(-0.732110\pi\) | ||||
−0.666269 | + | 0.745711i | \(0.732110\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 92.2879 | 0.486826 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 28.7565 | + | 11.9113i | 0.138878 | + | 0.0575253i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −123.846 | − | 298.992i | −0.550277 | − | 1.32849i | −0.917272 | − | 0.398262i | \(-0.869613\pi\) |
0.366995 | − | 0.930223i | \(-0.380387\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 237.427 | − | 237.427i | 0.974840 | − | 0.974840i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 111.562 | + | 111.562i | 0.424952 | + | 0.424952i | 0.886904 | − | 0.461953i | \(-0.152851\pi\) |
−0.461953 | + | 0.886904i | \(0.652851\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −76.5574 | + | 31.7111i | −0.271509 | + | 0.112463i | −0.514284 | − | 0.857620i | \(-0.671942\pi\) |
0.242775 | + | 0.970083i | \(0.421942\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 3.48061 | − | 8.40293i | 0.0115302 | − | 0.0278363i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 367.843i | − | 1.14161i | −0.821087 | − | 0.570803i | \(-0.806632\pi\) | ||
0.821087 | − | 0.570803i | \(-0.193368\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 267.443i | 0.779718i | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 165.780 | − | 400.228i | 0.455173 | − | 1.09889i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −244.994 | + | 101.480i | −0.634952 | + | 0.263006i | −0.676855 | − | 0.736116i | \(-0.736658\pi\) |
0.0419036 | + | 0.999122i | \(0.486658\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −47.2482 | − | 47.2482i | −0.115835 | − | 0.115835i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 446.134 | − | 446.134i | 1.03670 | − | 1.03670i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 183.495 | + | 442.997i | 0.404899 | + | 0.977513i | 0.986459 | + | 0.164009i | \(0.0524427\pi\) |
−0.581560 | + | 0.813504i | \(0.697557\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 524.604 | + | 217.298i | 1.10113 | + | 0.456101i | 0.857873 | − | 0.513862i | \(-0.171786\pi\) |
0.243252 | + | 0.969963i | \(0.421786\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −22.0784 | −0.0441527 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −243.109 | −0.463907 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −393.028 | − | 162.797i | −0.716656 | − | 0.296849i | −0.00560040 | − | 0.999984i | \(-0.501783\pi\) |
−0.711056 | + | 0.703136i | \(0.751783\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −149.155 | − | 360.091i | −0.260233 | − | 0.628259i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 354.722 | − | 354.722i | 0.592926 | − | 0.592926i | −0.345495 | − | 0.938421i | \(-0.612289\pi\) |
0.938421 | + | 0.345495i | \(0.112289\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −22.2443 | − | 22.2443i | −0.0356644 | − | 0.0356644i | 0.689050 | − | 0.724714i | \(-0.258028\pi\) |
−0.724714 | + | 0.689050i | \(0.758028\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −512.566 | + | 212.312i | −0.789147 | + | 0.326876i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −62.0716 | + | 149.854i | −0.0918664 | + | 0.221785i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 396.453i | 0.564614i | 0.959324 | + | 0.282307i | \(0.0910996\pi\) | ||||
−0.959324 | + | 0.282307i | \(0.908900\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 653.969i | − | 0.897077i | ||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 410.445 | − | 990.903i | 0.542798 | − | 1.31043i | −0.379943 | − | 0.925010i | \(-0.624057\pi\) |
0.922741 | − | 0.385420i | \(-0.125943\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −289.777 | + | 120.029i | −0.369773 | + | 0.153165i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 432.048 | + | 432.048i | 0.532419 | + | 0.532419i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 170.977 | − | 170.977i | 0.203635 | − | 0.203635i | −0.597920 | − | 0.801555i | \(-0.704006\pi\) |
0.801555 | + | 0.597920i | \(0.204006\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 225.836 | + | 545.217i | 0.260155 | + | 0.628069i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1050.91 | + | 435.301i | 1.17177 | + | 0.485362i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −456.811 | −0.493345 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1723.11 | −1.80367 | −0.901833 | − | 0.432085i | \(-0.857778\pi\) | ||||
−0.901833 | + | 0.432085i | \(0.857778\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 43.7888 | + | 18.1379i | 0.0444539 | + | 0.0184134i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −134.279 | − | 324.178i | −0.132290 | − | 0.319376i | 0.843829 | − | 0.536612i | \(-0.180296\pi\) |
−0.976119 | + | 0.217236i | \(0.930296\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −694.181 | + | 694.181i | −0.664075 | + | 0.664075i | −0.956338 | − | 0.292263i | \(-0.905592\pi\) |
0.292263 | + | 0.956338i | \(0.405592\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −108.852 | − | 108.852i | −0.101170 | − | 0.101170i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 264.682 | − | 109.635i | 0.239138 | − | 0.0990544i | −0.259896 | − | 0.965637i | \(-0.583688\pi\) |
0.499034 | + | 0.866582i | \(0.333688\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 69.2899 | − | 167.281i | 0.0608878 | − | 0.146996i | −0.890507 | − | 0.454969i | \(-0.849650\pi\) |
0.951395 | + | 0.307973i | \(0.0996505\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1600.56i | 1.36864i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2198.94i | 1.83061i | 0.402758 | + | 0.915306i | \(0.368051\pi\) | ||||
−0.402758 | + | 0.915306i | \(0.631949\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −107.992 | + | 260.716i | −0.0875680 | + | 0.211408i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 159.318 | − | 65.9915i | 0.125888 | − | 0.0521446i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 538.376 | + | 538.376i | 0.414730 | + | 0.414730i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −694.943 | + | 694.943i | −0.522121 | + | 0.522121i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −298.606 | − | 720.898i | −0.218897 | − | 0.528465i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 784.645 | + | 325.011i | 0.561446 | + | 0.232559i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1982.34 | −1.38507 | −0.692535 | − | 0.721384i | \(-0.743506\pi\) | ||||
−0.692535 | + | 0.721384i | \(0.743506\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 409.827 | 0.279715 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −201.609 | − | 83.5090i | −0.134463 | − | 0.0556963i | 0.314437 | − | 0.949278i | \(-0.398184\pi\) |
−0.448900 | + | 0.893582i | \(0.648184\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 424.354 | + | 1024.48i | 0.276663 | + | 0.667924i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −369.920 | + | 369.920i | −0.235834 | + | 0.235834i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −332.511 | − | 332.511i | −0.207360 | − | 0.207360i | 0.595784 | − | 0.803144i | \(-0.296841\pi\) |
−0.803144 | + | 0.595784i | \(0.796841\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 917.619 | − | 380.090i | 0.559938 | − | 0.231934i | −0.0847201 | − | 0.996405i | \(-0.527000\pi\) |
0.644658 | + | 0.764471i | \(0.277000\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −696.195 | + | 1680.76i | −0.415817 | + | 1.00387i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 1266.87i | − | 0.740848i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 442.388i | − | 0.253368i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 506.174 | − | 1222.01i | 0.284003 | − | 0.685645i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2064.41 | − | 855.107i | 1.13505 | − | 0.470155i | 0.265558 | − | 0.964095i | \(-0.414444\pi\) |
0.869496 | + | 0.493940i | \(0.164444\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 609.506 | + | 609.506i | 0.328482 | + | 0.328482i | 0.852009 | − | 0.523527i | \(-0.175384\pi\) |
−0.523527 | + | 0.852009i | \(0.675384\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 157.319 | − | 157.319i | 0.0831272 | − | 0.0831272i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −315.171 | − | 760.890i | −0.163323 | − | 0.394298i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2898.83 | − | 1200.73i | −1.47358 | − | 0.610376i | −0.505906 | − | 0.862589i | \(-0.668842\pi\) |
−0.967672 | + | 0.252213i | \(0.918842\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 1311.50 | 0.654142 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 685.023 | 0.335325 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −112.364 | − | 46.5428i | −0.0539942 | − | 0.0223651i | 0.355523 | − | 0.934668i | \(-0.384303\pi\) |
−0.409517 | + | 0.912302i | \(0.634303\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 126.464 | + | 305.312i | 0.0596681 | + | 0.144052i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1557.93 | − | 1557.93i | 0.721895 | − | 0.721895i | −0.247096 | − | 0.968991i | \(-0.579476\pi\) |
0.968991 | + | 0.247096i | \(0.0794763\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1705.75 | − | 1705.75i | −0.776398 | − | 0.776398i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 299.363 | − | 124.000i | 0.133877 | − | 0.0554535i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1117.57 | − | 2698.06i | 0.491141 | − | 1.18572i | −0.462999 | − | 0.886359i | \(-0.653227\pi\) |
0.954140 | − | 0.299361i | \(-0.0967734\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 975.087i | − | 0.421198i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − | 2371.45i | − | 1.00706i | ||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1394.97 | + | 3367.75i | −0.582485 | + | 1.40624i | 0.308069 | + | 0.951364i | \(0.400317\pi\) |
−0.890553 | + | 0.454879i | \(0.849683\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −16.5037 | + | 6.83606i | −0.00677741 | + | 0.00280730i | −0.386070 | − | 0.922470i | \(-0.626168\pi\) |
0.379292 | + | 0.925277i | \(0.376168\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1985.77 | − | 1985.77i | −0.802145 | − | 0.802145i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 819.433 | − | 819.433i | 0.325653 | − | 0.325653i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −625.489 | − | 1510.06i | −0.244600 | − | 0.590518i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1173.25 | + | 485.977i | 0.451542 | + | 0.187035i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3640.57 | 1.37917 | 0.689587 | − | 0.724203i | \(-0.257792\pi\) | ||||
0.689587 | + | 0.724203i | \(0.257792\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3234.02 | 1.20616 | 0.603082 | − | 0.797679i | \(-0.293939\pi\) | ||||
0.603082 | + | 0.797679i | \(0.293939\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1110.82 | + | 460.118i | 0.407937 | + | 0.168973i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −556.709 | − | 1344.01i | −0.201339 | − | 0.486076i | 0.790670 | − | 0.612243i | \(-0.209733\pi\) |
−0.992009 | + | 0.126167i | \(0.959733\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1366.73 | + | 1366.73i | −0.486860 | + | 0.486860i | −0.907314 | − | 0.420454i | \(-0.861871\pi\) |
0.420454 | + | 0.907314i | \(0.361871\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1487.72 | + | 1487.72i | 0.522068 | + | 0.522068i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −992.136 | + | 410.956i | −0.343026 | + | 0.142086i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −216.199 | + | 521.951i | −0.0736586 | + | 0.177828i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 200.170i | − | 0.0672116i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 2380.50i | − | 0.787860i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1144.59 | + | 2763.28i | −0.373444 | + | 0.901574i | 0.619717 | + | 0.784825i | \(0.287247\pi\) |
−0.993161 | + | 0.116749i | \(0.962753\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2292.17 | + | 949.447i | −0.737356 | + | 0.305423i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −209.817 | − | 209.817i | −0.0665554 | − | 0.0665554i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1413.66 | + | 1413.66i | −0.442236 | + | 0.442236i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 59.5391 | + | 143.740i | 0.0183711 | + | 0.0443519i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5494.09 | − | 2275.73i | −1.67228 | − | 0.692679i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1712.42 | 0.514226 | 0.257113 | − | 0.966381i | \(-0.417229\pi\) | ||||
0.257113 | + | 0.966381i | \(0.417229\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −284.930 | −0.0844236 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2071.09 | + | 857.873i | 0.605564 | + | 0.250833i | 0.664330 | − | 0.747439i | \(-0.268717\pi\) |
−0.0587668 | + | 0.998272i | \(0.518717\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1656.50 | + | 3999.14i | 0.478010 | + | 1.15402i | 0.960541 | + | 0.278140i | \(0.0897179\pi\) |
−0.482530 | + | 0.875879i | \(0.660282\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 567.240 | − | 567.240i | 0.161565 | − | 0.161565i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 4732.54 | + | 4732.54i | 1.33064 | + | 1.33064i | 0.904797 | + | 0.425844i | \(0.140023\pi\) |
0.425844 | + | 0.904797i | \(0.359977\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1216.92 | − | 504.065i | 0.337801 | − | 0.139922i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 750.343 | − | 1811.49i | 0.205654 | − | 0.496493i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 3120.14i | − | 0.844457i | −0.906489 | − | 0.422229i | \(-0.861248\pi\) | ||
0.906489 | − | 0.422229i | \(-0.138752\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1994.40i | 0.533073i | 0.963825 | + | 0.266537i | \(0.0858793\pi\) | ||||
−0.963825 | + | 0.266537i | \(0.914121\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 271.803 | − | 656.192i | 0.0717539 | − | 0.173229i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −884.771 | + | 366.484i | −0.230718 | + | 0.0955666i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −6124.27 | − | 6124.27i | −1.57764 | − | 1.57764i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3750.84 | + | 3750.84i | −0.954619 | + | 0.954619i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 759.835 | + | 1834.40i | 0.191077 | + | 0.461301i | 0.990163 | − | 0.139915i | \(-0.0446830\pi\) |
−0.799086 | + | 0.601216i | \(0.794683\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1358.63 | − | 562.761i | −0.337613 | − | 0.139844i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1551.23 | 0.380948 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5357.21 | 1.30029 | 0.650143 | − | 0.759812i | \(-0.274709\pi\) | ||||
0.650143 | + | 0.759812i | \(0.274709\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2598.94 | − | 1076.52i | −0.623515 | − | 0.258268i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 120.085 | + | 289.911i | 0.0284793 | + | 0.0687551i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3387.07 | + | 3387.07i | −0.794127 | + | 0.794127i | −0.982162 | − | 0.188035i | \(-0.939788\pi\) |
0.188035 | + | 0.982162i | \(0.439788\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −671.442 | − | 671.442i | −0.155647 | − | 0.155647i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1104.83 | + | 457.636i | −0.253238 | + | 0.104895i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −225.824 | + | 545.188i | −0.0511849 | + | 0.123571i | −0.947404 | − | 0.320041i | \(-0.896303\pi\) |
0.896219 | + | 0.443612i | \(0.146303\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4177.50i | 0.936403i | 0.883622 | + | 0.468201i | \(0.155098\pi\) | ||||
−0.883622 | + | 0.468201i | \(0.844902\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 2918.65i | − | 0.647051i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −801.055 | + | 1933.92i | −0.175656 | + | 0.424071i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2459.54 | + | 1018.78i | −0.533500 | + | 0.220983i | −0.633136 | − | 0.774041i | \(-0.718232\pi\) |
0.0996351 | + | 0.995024i | \(0.468232\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 413.084 | + | 413.084i | 0.0886405 | + | 0.0886405i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1012.51 | + | 1012.51i | −0.214952 | + | 0.214952i | −0.806367 | − | 0.591415i | \(-0.798569\pi\) |
0.591415 | + | 0.806367i | \(0.298569\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −567.782 | − | 1370.75i | −0.119262 | − | 0.287924i | 0.852963 | − | 0.521971i | \(-0.174803\pi\) |
−0.972225 | + | 0.234047i | \(0.924803\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 2087.28 | + | 864.578i | 0.433823 | + | 0.179695i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1371.41 | 0.282062 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2759.34 | −0.561640 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 7873.31 | + | 3261.23i | 1.58605 | + | 0.656965i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −421.800 | − | 1018.32i | −0.0841018 | − | 0.203040i | 0.876234 | − | 0.481886i | \(-0.160048\pi\) |
−0.960336 | + | 0.278846i | \(0.910048\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1214.10 | + | 1214.10i | −0.239619 | + | 0.239619i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1927.70 | − | 1927.70i | −0.376622 | − | 0.376622i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −4943.12 | + | 2047.51i | −0.956079 | + | 0.396021i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −275.644 | + | 665.464i | −0.0527836 | + | 0.127431i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1735.39i | 0.329028i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2033.29i | 0.381725i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2140.75 | + | 5168.22i | −0.397977 | + | 0.960800i | 0.590169 | + | 0.807280i | \(0.299061\pi\) |
−0.988145 | + | 0.153521i | \(0.950939\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4485.71 | − | 1858.04i | 0.825836 | − | 0.342072i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5781.99 | + | 5781.99i | 1.05423 | + | 1.05423i | 0.998443 | + | 0.0557904i | \(0.0177679\pi\) |
0.0557904 | + | 0.998443i | \(0.482232\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 804.942 | − | 804.942i | 0.145361 | − | 0.145361i | −0.630681 | − | 0.776042i | \(-0.717224\pi\) |
0.776042 | + | 0.630681i | \(0.217224\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −30.2546 | − | 73.0412i | −0.00541161 | − | 0.0130648i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1951.08 | − | 808.164i | −0.345690 | − | 0.143189i | 0.203082 | − | 0.979162i | \(-0.434904\pi\) |
−0.548771 | + | 0.835972i | \(0.684904\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2305.34 | 0.404621 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1416.90 | −0.246366 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −10323.6 | − | 4276.18i | −1.77839 | − | 0.736634i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2914.49 | + | 7036.21i | 0.497437 | + | 1.20092i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −633.204 | + | 633.204i | −0.107083 | + | 0.107083i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2260.92 | − | 2260.92i | −0.378871 | − | 0.378871i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 7533.21 | − | 3120.36i | 1.25095 | − | 0.518158i | 0.343826 | − | 0.939033i | \(-0.388277\pi\) |
0.907119 | + | 0.420875i | \(0.138277\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −314.568 | + | 759.435i | −0.0517665 | + | 0.124975i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 1523.32i | − | 0.248442i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 3018.53i | − | 0.487922i | −0.969785 | − | 0.243961i | \(-0.921553\pi\) | ||
0.969785 | − | 0.243961i | \(-0.0784469\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 4161.81 | − | 10047.5i | 0.666780 | − | 1.60975i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3965.10 | − | 1642.40i | 0.629683 | − | 0.260823i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3752.04 | + | 3752.04i | 0.590644 | + | 0.590644i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 986.884 | − | 986.884i | 0.154006 | − | 0.154006i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1631.78 | − | 3939.46i | −0.252445 | − | 0.609456i | 0.745955 | − | 0.665996i | \(-0.231993\pi\) |
−0.998400 | + | 0.0565400i | \(0.981993\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2555.50 | + | 1058.52i | 0.391956 | + | 0.162354i | 0.569953 | − | 0.821678i | \(-0.306962\pi\) |
−0.177996 | + | 0.984031i | \(0.556962\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −9918.72 | −1.50833 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4332.58 | −0.653257 | −0.326629 | − | 0.945153i | \(-0.605913\pi\) | ||||
−0.326629 | + | 0.945153i | \(0.605913\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1659.60 | + | 687.427i | 0.248119 | + | 0.102774i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1441.02 | − | 3478.92i | −0.213632 | − | 0.515753i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9290.59 | − | 9290.59i | 1.36585 | − | 1.36585i | 0.499574 | − | 0.866271i | \(-0.333490\pi\) |
0.866271 | − | 0.499574i | \(-0.166510\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6657.67 | − | 6657.67i | −0.970648 | − | 0.970648i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 4490.63 | − | 1860.08i | 0.649303 | − | 0.268950i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 43.1080 | − | 104.072i | 0.00618186 | − | 0.0149243i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2140.92i | 0.304511i | 0.988341 | + | 0.152255i | \(0.0486536\pi\) | ||||
−0.988341 | + | 0.152255i | \(0.951346\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 400.739i | − | 0.0565356i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −882.096 | + | 2129.57i | −0.123440 | + | 0.298010i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 4123.46 | − | 1707.99i | 0.572399 | − | 0.237095i | −0.0776592 | − | 0.996980i | \(-0.524745\pi\) |
0.650058 | + | 0.759885i | \(0.274745\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2970.10 | − | 2970.10i | −0.409001 | − | 0.409001i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5930.90 | − | 5930.90i | 0.810231 | − | 0.810231i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −2989.05 | − | 7216.20i | −0.405111 | − | 0.978025i | −0.986405 | − | 0.164331i | \(-0.947453\pi\) |
0.581294 | − | 0.813694i | \(-0.302547\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 9057.77 | + | 3751.85i | 1.21796 | + | 0.504496i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6358.57 | −0.848323 | −0.424161 | − | 0.905587i | \(-0.639431\pi\) | ||||
−0.424161 | + | 0.905587i | \(0.639431\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −580.814 | −0.0768858 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 194.455 | + | 80.5458i | 0.0255418 | + | 0.0105798i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3947.57 | − | 9530.27i | −0.514523 | − | 1.24217i | −0.941226 | − | 0.337777i | \(-0.890325\pi\) |
0.426703 | − | 0.904392i | \(-0.359675\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4881.09 | + | 4881.09i | −0.631324 | + | 0.631324i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 763.145 | + | 763.145i | 0.0979531 | + | 0.0979531i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1311.57 | + | 543.270i | −0.167069 | + | 0.0692022i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1253.91 | − | 3027.20i | 0.158519 | − | 0.382698i | −0.824587 | − | 0.565735i | \(-0.808593\pi\) |
0.983106 | + | 0.183037i | \(0.0585927\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 5484.25i | − | 0.688110i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 13053.8i | 1.62562i | 0.582528 | + | 0.812810i | \(0.302063\pi\) | ||||
−0.582528 | + | 0.812810i | \(0.697937\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5975.56 | − | 14426.3i | 0.738620 | − | 1.78319i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2163.50 | − | 896.150i | 0.265445 | − | 0.109951i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4270.17 | + | 4270.17i | 0.520060 | + | 0.520060i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 652.548 | − | 652.548i | 0.0788910 | − | 0.0788910i | −0.666560 | − | 0.745451i | \(-0.732234\pi\) |
0.745451 | + | 0.666560i | \(0.232234\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 889.998 | + | 2148.65i | 0.106814 | + | 0.257871i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3850.68 | + | 1595.00i | 0.458789 | + | 0.190036i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3840.61 | 0.454284 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4912.19 | −0.576861 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 382.177 | + | 158.303i | 0.0445598 | + | 0.0184573i | 0.404852 | − | 0.914382i | \(-0.367323\pi\) |
−0.360292 | + | 0.932839i | \(0.617323\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −171.786 | − | 414.729i | −0.0198868 | − | 0.0480111i | 0.913624 | − | 0.406560i | \(-0.133272\pi\) |
−0.933511 | + | 0.358549i | \(0.883272\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −660.662 | + | 660.662i | −0.0759396 | + | 0.0759396i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 6947.92 | + | 6947.92i | 0.792997 | + | 0.792997i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4560.04 | − | 1888.83i | 0.516805 | − | 0.214068i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2397.73 | + | 5788.64i | −0.269846 | + | 0.651465i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 3644.76i | 0.407336i | 0.979040 | + | 0.203668i | \(0.0652863\pi\) | ||||
−0.979040 | + | 0.203668i | \(0.934714\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 361.093i | − | 0.0400763i | −0.999799 | − | 0.0200382i | \(-0.993621\pi\) | ||
0.999799 | − | 0.0200382i | \(-0.00637877\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −837.280 | + | 2021.37i | −0.0922863 | + | 0.222799i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9288.29 | + | 3847.34i | −1.01675 | + | 0.421151i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2187.45 | − | 2187.45i | −0.237817 | − | 0.237817i | 0.578129 | − | 0.815945i | \(-0.303783\pi\) |
−0.815945 | + | 0.578129i | \(0.803783\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 480.339 | − | 480.339i | 0.0518668 | − | 0.0518668i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 6147.99 | + | 14842.6i | 0.659367 | + | 1.59185i | 0.798783 | + | 0.601620i | \(0.205478\pi\) |
−0.139415 | + | 0.990234i | \(0.544522\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 799.930 | + | 331.342i | 0.0852142 | + | 0.0352969i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −11051.2 | −1.16936 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −13620.0 | −1.43156 | −0.715779 | − | 0.698326i | \(-0.753928\pi\) | ||||
−0.715779 | + | 0.698326i | \(0.753928\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2719.96 | − | 1126.64i | −0.283986 | − | 0.117631i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1631.40 | − | 3938.55i | −0.169205 | − | 0.408497i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1494.25 | + | 1494.25i | −0.153959 | + | 0.153959i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −3302.76 | − | 3302.76i | −0.338067 | − | 0.338067i | 0.517573 | − | 0.855639i | \(-0.326836\pi\) |
−0.855639 | + | 0.517573i | \(0.826836\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −11822.7 | + | 4897.14i | −1.20226 | + | 0.497993i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −2319.14 | + | 5598.89i | −0.234301 | + | 0.565654i | −0.996675 | − | 0.0814840i | \(-0.974034\pi\) |
0.762373 | + | 0.647138i | \(0.224034\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11103.9i | 1.11456i | 0.830326 | + | 0.557279i | \(0.188154\pi\) | ||||
−0.830326 | + | 0.557279i | \(0.811846\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4073.19i | 0.406214i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3094.31 | − | 7470.32i | 0.306611 | − | 0.740225i | −0.693199 | − | 0.720746i | \(-0.743799\pi\) |
0.999810 | − | 0.0194791i | \(-0.00620077\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3416.33 | + | 1415.09i | −0.336357 | + | 0.139324i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 10972.9 | + | 10972.9i | 1.07347 | + | 1.07347i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1093.39 | − | 1093.39i | 0.106287 | − | 0.106287i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5476.44 | + | 13221.3i | 0.529002 | + | 1.27712i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 622.280 | + | 257.757i | 0.0597322 | + | 0.0247419i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 2969.80 | 0.283285 | 0.141643 | − | 0.989918i | \(-0.454762\pi\) | ||||
0.141643 | + | 0.989918i | \(0.454762\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 21971.6 | 2.08278 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3130.03 | − | 1296.50i | −0.294868 | − | 0.122139i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2361.23 | − | 5700.50i | −0.221067 | − | 0.533704i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14166.3 | − | 14166.3i | 1.31814 | − | 1.31814i | 0.402895 | − | 0.915246i | \(-0.368004\pi\) |
0.915246 | − | 0.402895i | \(-0.131996\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 425.331 | + | 425.331i | 0.0393336 | + | 0.0393336i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16702.1 | + | 6918.24i | −1.53514 | + | 0.635877i | −0.980555 | − | 0.196247i | \(-0.937125\pi\) |
−0.554589 | + | 0.832124i | \(0.687125\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4141.16 | − | 9997.65i | 0.378314 | − | 0.913330i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 169.719i | 0.0154108i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 4360.54i | − | 0.393555i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4361.00 | + | 10528.4i | −0.391232 | + | 0.944519i | 0.598439 | + | 0.801168i | \(0.295788\pi\) |
−0.989672 | + | 0.143351i | \(0.954212\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −10067.2 | + | 4169.96i | −0.897741 | + | 0.371856i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9988.91 | − | 9988.91i | −0.885454 | − | 0.885454i | 0.108628 | − | 0.994082i | \(-0.465354\pi\) |
−0.994082 | + | 0.108628i | \(0.965354\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 888.460 | − | 888.460i | 0.0782890 | − | 0.0782890i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4565.59 | + | 11022.3i | 0.399931 | + | 0.965520i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −1708.35 | − | 707.622i | −0.148765 | − | 0.0616204i | 0.307059 | − | 0.951691i | \(-0.400655\pi\) |
−0.455824 | + | 0.890070i | \(0.650655\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −273.446 | −0.0236723 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −18637.6 | −1.60404 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3247.78 | − | 1345.28i | −0.277892 | − | 0.115107i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2626.75 | + | 6341.53i | 0.223451 | + | 0.539459i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −10212.9 | + | 10212.9i | −0.863770 | + | 0.863770i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 11373.3 | + | 11373.3i | 0.956377 | + | 0.956377i | 0.999087 | − | 0.0427108i | \(-0.0135994\pi\) |
−0.0427108 | + | 0.999087i | \(0.513599\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3452.22 | − | 1429.96i | 0.288633 | − | 0.119556i | −0.233669 | − | 0.972316i | \(-0.575073\pi\) |
0.522302 | + | 0.852760i | \(0.325073\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1845.49 | + | 4455.40i | −0.153417 | + | 0.370380i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 20145.9i | − | 1.66521i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 5956.35i | − | 0.489550i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 466.075 | − | 1125.21i | 0.0380903 | − | 0.0919581i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −9896.07 | + | 4099.08i | −0.804214 | + | 0.333116i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 725.402 | + | 725.402i | 0.0586203 | + | 0.0586203i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 12747.9 | − | 12747.9i | 1.02442 | − | 1.02442i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1909.80 | − | 4610.66i | −0.152617 | − | 0.368451i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13493.1 | + | 5589.03i | 1.07230 | + | 0.444161i | 0.847802 | − | 0.530314i | \(-0.177926\pi\) |
0.224498 | + | 0.974475i | \(0.427926\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 88.3476 | 0.00698224 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 648.357 | 0.0509588 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 10714.7 | + | 4438.16i | 0.837525 | + | 0.346914i | 0.759877 | − | 0.650067i | \(-0.225259\pi\) |
0.0776476 | + | 0.996981i | \(0.475259\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −551.934 | − | 1332.49i | −0.0429070 | − | 0.103587i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 11144.4 | − | 11144.4i | 0.861645 | − | 0.861645i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2436.77 | + | 2436.77i | 0.187381 | + | 0.187381i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −5295.07 | + | 2193.29i | −0.404979 | + | 0.167748i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −8959.38 | + | 21629.9i | −0.681546 | + | 1.64540i | 0.0796083 | + | 0.996826i | \(0.474633\pi\) |
−0.761154 | + | 0.648571i | \(0.775367\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 5625.86i | − | 0.425668i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8083.67i | 0.608365i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −144.332 | + | 348.448i | −0.0108044 | + | 0.0260841i | −0.929190 | − | 0.369603i | \(-0.879494\pi\) |
0.918385 | + | 0.395687i | \(0.129494\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7274.68 | + | 3013.27i | −0.541678 | + | 0.224370i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −4019.56 | − | 4019.56i | −0.297718 | − | 0.297718i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8107.90 | + | 8107.90i | −0.597365 | + | 0.597365i | −0.939611 | − | 0.342246i | \(-0.888813\pi\) |
0.342246 | + | 0.939611i | \(0.388813\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3680.55 | − | 8885.63i | −0.269748 | − | 0.651229i | 0.729723 | − | 0.683743i | \(-0.239649\pi\) |
−0.999471 | + | 0.0325132i | \(0.989649\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16634.6 | − | 6890.28i | −1.21278 | − | 0.502349i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 8840.46 | 0.641170 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 20668.9 | 1.49126 | 0.745629 | − | 0.666361i | \(-0.232149\pi\) | ||||
0.745629 | + | 0.666361i | \(0.232149\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14777.0 | − | 6120.83i | −1.06064 | − | 0.439331i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3567.73 | − | 8613.27i | −0.254758 | − | 0.615040i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3498.97 | − | 3498.97i | 0.248564 | − | 0.248564i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 436.634 | + | 436.634i | 0.0308591 | + | 0.0308591i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 834.858 | − | 345.810i | 0.0587024 | − | 0.0243153i | −0.353139 | − | 0.935571i | \(-0.614886\pi\) |
0.411841 | + | 0.911256i | \(0.364886\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11228.3 | − | 27107.5i | 0.785491 | − | 1.89634i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7194.77i | 0.500767i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 8473.46i | 0.586785i | 0.955992 | + | 0.293392i | \(0.0947842\pi\) | ||||
−0.955992 | + | 0.293392i | \(0.905216\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1043.34 | + | 2518.84i | −0.0718868 | + | 0.173550i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 8831.67 | − | 3658.20i | 0.605454 | − | 0.250787i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 4342.08 | + | 4342.08i | 0.296181 | + | 0.296181i | 0.839516 | − | 0.543335i | \(-0.182839\pi\) |
−0.543335 | + | 0.839516i | \(0.682839\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6136.50 | + | 6136.50i | −0.416494 | + | 0.416494i | −0.883993 | − | 0.467499i | \(-0.845155\pi\) |
0.467499 | + | 0.883993i | \(0.345155\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 413.503 | + | 998.284i | 0.0279256 | + | 0.0674184i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3251.35 | − | 1346.75i | −0.218489 | − | 0.0905013i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3622.97 | −0.242260 | −0.121130 | − | 0.992637i | \(-0.538652\pi\) | ||||
−0.121130 | + | 0.992637i | \(0.538652\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 5311.10 | 0.353393 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 23072.5 | + | 9556.95i | 1.52768 | + | 0.632787i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1515.46 | + | 3658.63i | 0.0998510 | + | 0.241062i | 0.965909 | − | 0.258882i | \(-0.0833541\pi\) |
−0.866058 | + | 0.499944i | \(0.833354\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 1975.73 | − | 1975.73i | 0.129543 | − | 0.129543i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5257.77 | − | 5257.77i | −0.343063 | − | 0.343063i | 0.514454 | − | 0.857518i | \(-0.327994\pi\) |
−0.857518 | + | 0.514454i | \(0.827994\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 23417.3 | − | 9699.75i | 1.52055 | − | 0.629831i | 0.542846 | − | 0.839832i | \(-0.317347\pi\) |
0.977701 | + | 0.210000i | \(0.0673466\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4406.02 | + | 10637.1i | −0.284714 | + | 0.687361i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 2101.79i | − | 0.135163i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 10981.0i | − | 0.702786i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4505.43 | + | 10877.1i | −0.286969 | + | 0.692804i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 26189.3 | − | 10847.9i | 1.66015 | − | 0.687656i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19776.5 | − | 19776.5i | −1.24768 | − | 1.24768i | −0.956740 | − | 0.290944i | \(-0.906031\pi\) |
−0.290944 | − | 0.956740i | \(-0.593969\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 10459.8 | − | 10459.8i | 0.656776 | − | 0.656776i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2716.45 | − | 6558.08i | −0.169762 | − | 0.409842i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −16775.0 | − | 6948.45i | −1.04341 | − | 0.432194i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1274.19 | −0.0788829 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 304.324 | 0.0187521 | 0.00937603 | − | 0.999956i | \(-0.497015\pi\) | ||||
0.00937603 | + | 0.999956i | \(0.497015\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16207.7 | − | 6713.43i | −0.994040 | − | 0.411745i | −0.174432 | − | 0.984669i | \(-0.555809\pi\) |
−0.819608 | + | 0.572924i | \(0.805809\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 561.596 | + | 1355.81i | 0.0342835 | + | 0.0827676i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13156.7 | + | 13156.7i | −0.799450 | + | 0.799450i | −0.983009 | − | 0.183559i | \(-0.941238\pi\) |
0.183559 | + | 0.983009i | \(0.441238\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −6326.83 | − | 6326.83i | −0.382666 | − | 0.382666i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 9134.88 | − | 3783.79i | 0.549960 | − | 0.227801i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 7533.14 | − | 18186.6i | 0.451447 | − | 1.08989i | −0.520326 | − | 0.853968i | \(-0.674189\pi\) |
0.971772 | − | 0.235921i | \(-0.0758106\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 781.408i | − | 0.0466139i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 79.9035i | 0.00474480i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 4387.91 | − | 10593.4i | 0.259376 | − | 0.626189i | −0.739521 | − | 0.673133i | \(-0.764948\pi\) |
0.998898 | + | 0.0469438i | \(0.0149482\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17601.5 | − | 7290.76i | 1.03573 | − | 0.429013i | 0.200953 | − | 0.979601i | \(-0.435596\pi\) |
0.834777 | + | 0.550588i | \(0.185596\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 20796.7 | + | 20796.7i | 1.21821 | + | 1.21821i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2807.75 | + | 2807.75i | −0.163729 | + | 0.163729i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3725.86 | − | 8995.03i | −0.216291 | − | 0.522172i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −7824.47 | − | 3241.00i | −0.452185 | − | 0.187301i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10595.8 | −0.609605 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1023.41 | 0.0586174 | 0.0293087 | − | 0.999570i | \(-0.490669\pi\) | ||||
0.0293087 | + | 0.999570i | \(0.490669\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 15141.2 | + | 6271.69i | 0.863385 | + | 0.357626i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −3769.24 | − | 9099.74i | −0.213979 | − | 0.516590i | 0.780049 | − | 0.625718i | \(-0.215194\pi\) |
−0.994028 | + | 0.109128i | \(0.965194\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −10591.0 | + | 10591.0i | −0.598592 | + | 0.598592i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7839.65 | − | 7839.65i | −0.441139 | − | 0.441139i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2058.49 | − | 852.656i | 0.115324 | − | 0.0477686i | −0.324276 | − | 0.945963i | \(-0.605120\pi\) |
0.439599 | + | 0.898194i | \(0.355120\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 644.384 | − | 1555.68i | 0.0359426 | − | 0.0867731i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 21408.2i | − | 1.18890i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 18003.5i | − | 0.995468i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11541.0 | + | 27862.4i | −0.635370 | + | 1.53392i | 0.197415 | + | 0.980320i | \(0.436745\pi\) |
−0.832784 | + | 0.553598i | \(0.813255\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 380.627 | − | 157.661i | 0.0208641 | − | 0.00864220i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2514.87 | + | 2514.87i | 0.137258 | + | 0.137258i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9771.90 | + | 9771.90i | −0.531043 | + | 0.531043i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −12667.1 | − | 30581.1i | −0.685428 | − | 1.65477i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 3783.29 | + | 1567.09i | 0.203841 | + | 0.0844339i | 0.482268 | − | 0.876024i | \(-0.339813\pi\) |
−0.278427 | + | 0.960457i | \(0.589813\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 41285.4 | 2.21495 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6514.41 | −0.348010 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2817.87 | − | 1167.20i | −0.149897 | − | 0.0620892i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7928.02 | + | 19139.9i | 0.419948 | + | 1.01384i | 0.982362 | + | 0.186988i | \(0.0598727\pi\) |
−0.562414 | + | 0.826856i | \(0.690127\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 712.046 | − | 712.046i | 0.0375581 | − | 0.0375581i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −12816.7 | − | 12816.7i | −0.673196 | − | 0.673196i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 4191.15 | − | 1736.03i | 0.219217 | − | 0.0908025i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −5905.31 | + | 14256.7i | −0.307584 | + | 0.742573i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 35836.7i | 1.85881i | 0.369064 | + | 0.929404i | \(0.379678\pi\) | ||||
−0.369064 | + | 0.929404i | \(0.620322\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8533.45i | 0.440780i | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3774.68 | − | 9112.89i | 0.194166 | − | 0.468758i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −12803.8 | + | 5303.53i | −0.655894 | + | 0.271680i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −17934.8 | − | 17934.8i | −0.914946 | − | 0.914946i | 0.0817100 | − | 0.996656i | \(-0.473962\pi\) |
−0.996656 | + | 0.0817100i | \(0.973962\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −14969.4 | + | 14969.4i | −0.760523 | + | 0.760523i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −2777.64 | − | 6705.81i | −0.140540 | − | 0.339293i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 12620.5 | + | 5227.58i | 0.635946 | + | 0.263418i | 0.677277 | − | 0.735728i | \(-0.263160\pi\) |
−0.0413310 | + | 0.999146i | \(0.513160\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4736.35 | 0.237691 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 7938.23 | 0.396755 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 12203.1 | + | 5054.70i | 0.607441 | + | 0.251610i | 0.665134 | − | 0.746724i | \(-0.268374\pi\) |
−0.0576928 | + | 0.998334i | \(0.518374\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 16392.2 | + | 39574.3i | 0.812662 | + | 1.96194i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3084.12 | + | 3084.12i | −0.152282 | + | 0.152282i | −0.779136 | − | 0.626854i | \(-0.784342\pi\) |
0.626854 | + | 0.779136i | \(0.284342\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 5657.83 | + | 5657.83i | 0.278237 | + | 0.278237i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2516.88 | + | 1042.53i | −0.123277 | + | 0.0510629i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 952.985 | − | 2300.71i | 0.0464904 | − | 0.112238i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 30535.2i | 1.48368i | 0.670575 | + | 0.741842i | \(0.266048\pi\) | ||||
−0.670575 | + | 0.741842i | \(0.733952\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 9819.92i | − | 0.475243i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1181.18 | + | 2851.62i | −0.0569372 | + | 0.137459i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −8109.52 | + | 3359.07i | −0.389360 | + | 0.161278i | −0.568771 | − | 0.822496i | \(-0.692581\pi\) |
0.179411 | + | 0.983774i | \(0.442581\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 5142.78 | + | 5142.78i | 0.245943 | + | 0.245943i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −13700.0 | + | 13700.0i | −0.652595 | + | 0.652595i | −0.953617 | − | 0.301022i | \(-0.902672\pi\) |
0.301022 | + | 0.953617i | \(0.402672\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −602.292 | − | 1454.06i | −0.0285772 | − | 0.0689915i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 736.028 | + | 304.873i | 0.0347858 | + | 0.0144088i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −32553.8 | −1.53253 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −5576.68 | −0.261509 | −0.130754 | − | 0.991415i | \(-0.541740\pi\) | ||||
−0.130754 | + | 0.991415i | \(0.541740\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24478.4 | − | 10139.3i | −1.14341 | − | 0.473614i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 12414.0 | + | 29969.9i | 0.577618 | + | 1.39449i | 0.894945 | + | 0.446177i | \(0.147215\pi\) |
−0.317327 | + | 0.948316i | \(0.602785\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18243.7 | + | 18243.7i | −0.845592 | + | 0.845592i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9837.72 | + | 9837.72i | 0.454216 | + | 0.454216i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18595.1 | + | 7702.33i | −0.855247 | + | 0.354255i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3582.27 | + | 8648.37i | −0.164128 | + | 0.396240i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 18049.2i | − | 0.823787i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 11235.5i | − | 0.510842i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1888.35 | + | 4558.87i | −0.0855302 | + | 0.206488i | −0.960858 | − | 0.277042i | \(-0.910646\pi\) |
0.875328 | + | 0.483530i | \(0.160646\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 21886.8 | − | 9065.82i | 0.987568 | − | 0.409064i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13515.6 | + | 13515.6i | 0.607535 | + | 0.607535i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −27259.5 | + | 27259.5i | −1.22070 | + | 1.22070i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1797.18 | + | 4338.78i | 0.0801753 | + | 0.193560i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 8355.80 | + | 3461.09i | 0.371365 | + | 0.153824i | 0.560557 | − | 0.828116i | \(-0.310587\pi\) |
−0.189192 | + | 0.981940i | \(0.560587\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 32220.1 | 1.42661 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −614.163 | −0.0270916 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 542.333 | + | 224.642i | 0.0238338 | + | 0.00987227i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 938.705 | + | 2266.23i | 0.0410994 | + | 0.0992227i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2063.69 | − | 2063.69i | 0.0900189 | − | 0.0900189i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 9416.77 | + | 9416.77i | 0.409241 | + | 0.409241i | 0.881474 | − | 0.472233i | \(-0.156552\pi\) |
−0.472233 | + | 0.881474i | \(0.656552\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4597.28 | − | 1904.26i | 0.199053 | − | 0.0824506i | −0.280930 | − | 0.959728i | \(-0.590643\pi\) |
0.479983 | + | 0.877278i | \(0.340643\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 7906.51 | − | 19088.0i | 0.341074 | − | 0.823426i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 435.509i | − | 0.0187181i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 10571.2i | − | 0.452680i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 573.621 | − | 1384.84i | 0.0244737 | − | 0.0590847i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 12716.7 | − | 5267.45i | 0.540581 | − | 0.223916i | −0.0956491 | − | 0.995415i | \(-0.530493\pi\) |
0.636231 | + | 0.771499i | \(0.280493\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18764.2 | − | 18764.2i | −0.794751 | − | 0.794751i | 0.187511 | − | 0.982262i | \(-0.439958\pi\) |
−0.982262 | + | 0.187511i | \(0.939958\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 7320.42 | − | 7320.42i | 0.308926 | − | 0.308926i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 6248.37 | + | 15084.9i | 0.262729 | + | 0.634284i | 0.999105 | − | 0.0422880i | \(-0.0134647\pi\) |
−0.736376 | + | 0.676572i | \(0.763465\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −23591.6 | − | 9771.95i | −0.988383 | − | 0.409401i | −0.170858 | − | 0.985296i | \(-0.554654\pi\) |
−0.817524 | + | 0.575894i | \(0.804654\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 13166.4 | 0.549624 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −23425.8 | −0.974379 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 7288.92 | + | 3019.17i | 0.302088 | + | 0.125129i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −12858.8 | − | 31043.9i | −0.531022 | − | 1.28200i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −26103.1 | + | 26103.1i | −1.07411 | + | 1.07411i | −0.0770872 | + | 0.997024i | \(0.524562\pi\) |
−0.997024 | + | 0.0770872i | \(0.975438\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6453.12 | − | 6453.12i | −0.264591 | − | 0.264591i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6542.73 | − | 2710.09i | 0.267312 | − | 0.110724i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3305.62 | − | 7980.48i | 0.134576 | − | 0.324896i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8542.81i | 0.346558i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 7337.88i | 0.296626i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 9760.05 | − | 23562.8i | 0.393150 | − | 0.949147i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −44742.9 | + | 18533.1i | −1.79598 | + | 0.743918i | −0.808026 | + | 0.589147i | \(0.799464\pi\) |
−0.987950 | + | 0.154770i | \(0.950536\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 820.451 | + | 820.451i | 0.0328173 | + | 0.0328173i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 21556.5 | − | 21556.5i | 0.859225 | − | 0.859225i | −0.132022 | − | 0.991247i | \(-0.542147\pi\) |
0.991247 | + | 0.132022i | \(0.0421469\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −10150.3 | − | 24505.0i | −0.403171 | − | 0.973342i | −0.986891 | − | 0.161387i | \(-0.948403\pi\) |
0.583720 | − | 0.811955i | \(-0.301597\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6266.30 | − | 2595.58i | −0.248031 | − | 0.102738i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 9799.79 | 0.386545 | 0.193273 | − | 0.981145i | \(-0.438090\pi\) | ||||
0.193273 | + | 0.981145i | \(0.438090\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10457.3 | 0.411051 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 12608.1 | + | 5222.43i | 0.493878 | + | 0.204571i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2831.05 | − | 6834.76i | −0.110514 | − | 0.266805i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20422.5 | − | 20422.5i | 0.794479 | − | 0.794479i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3094.78 | + | 3094.78i | 0.119980 | + | 0.119980i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 6820.41 | − | 2825.10i | 0.263511 | − | 0.109150i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 5253.32 | − | 12682.6i | 0.202271 | − | 0.488326i | −0.789896 | − | 0.613241i | \(-0.789866\pi\) |
0.992168 | + | 0.124914i | \(0.0398656\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 5451.24i | 0.209176i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 9710.12i | − | 0.371331i | −0.982613 | − | 0.185665i | \(-0.940556\pi\) | ||
0.982613 | − | 0.185665i | \(-0.0594440\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −6324.17 | + | 15267.9i | −0.241025 | + | 0.581887i | −0.997385 | − | 0.0722692i | \(-0.976976\pi\) |
0.756360 | + | 0.654156i | \(0.226976\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 7845.37 | − | 3249.66i | 0.297988 | − | 0.123431i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −33197.6 | − | 33197.6i | −1.25667 | − | 1.25667i | −0.952672 | − | 0.303999i | \(-0.901678\pi\) |
−0.303999 | − | 0.952672i | \(-0.598322\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12184.3 | + | 12184.3i | −0.459671 | + | 0.459671i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4669.96 | + | 11274.3i | 0.175589 | + | 0.423908i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 43354.1 | + | 17957.9i | 1.62462 | + | 0.672942i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13053.0 | −0.487499 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 26461.5 | 0.984975 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 26251.6 | + | 10873.8i | 0.973905 | + | 0.403405i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8888.79 | − | 21459.4i | −0.328667 | − | 0.793471i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2518.97 | − | 2518.97i | 0.0928305 | − | 0.0928305i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −45.2309 | − | 45.2309i | −0.00166136 | − | 0.00166136i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4347.03 | + | 1800.60i | −0.159141 | + | 0.0659183i | −0.460832 | − | 0.887487i | \(-0.652449\pi\) |
0.301691 | + | 0.953406i | \(0.402449\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −341.067 | + | 823.408i | −0.0124450 | + | 0.0300448i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 27597.7i | − | 1.00368i | −0.864961 | − | 0.501840i | \(-0.832657\pi\) | ||
0.864961 | − | 0.501840i | \(-0.167343\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20013.9i | 0.725480i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 3848.29 | − | 9290.60i | 0.139039 | − | 0.335670i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −1752.45 | + | 725.889i | −0.0631091 | + | 0.0261406i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 10437.8 | + | 10437.8i | 0.374658 | + | 0.374658i | 0.869171 | − | 0.494512i | \(-0.164653\pi\) |
−0.494512 | + | 0.869171i | \(0.664653\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19563.2 | − | 19563.2i | 0.699922 | − | 0.699922i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 13033.5 | + | 31465.5i | 0.464790 | + | 1.12210i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −33540.2 | − | 13892.8i | −1.19221 | − | 0.493830i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 2493.56 | 0.0883485 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −692.011 | −0.0244393 | −0.0122197 | − | 0.999925i | \(-0.503890\pi\) | ||||
−0.0122197 | + | 0.999925i | \(0.503890\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −31520.9 | − | 13056.4i | −1.10962 | − | 0.459620i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −15476.1 | − | 37362.5i | −0.543047 | − | 1.31103i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4138.56 | − | 4138.56i | 0.144754 | − | 0.144754i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −7694.36 | − | 7694.36i | −0.268264 | − | 0.268264i | 0.560136 | − | 0.828401i | \(-0.310749\pi\) |
−0.828401 | + | 0.560136i | \(0.810749\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −5201.44 | + | 2154.51i | −0.180769 | + | 0.0748772i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7735.22 | + | 18674.5i | −0.267971 | + | 0.646940i | −0.999388 | − | 0.0349914i | \(-0.988860\pi\) |
0.731416 | + | 0.681931i | \(0.238860\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12433.6i | 0.429369i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4547.36i | 0.156535i | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −258.346 | + | 623.702i | −0.00886496 | + | 0.0214019i | −0.928250 | − | 0.371957i | \(-0.878687\pi\) |
0.919385 | + | 0.393359i | \(0.128687\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1973.18 | − | 817.318i | 0.0674943 | − | 0.0279571i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7385.39 | + | 7385.39i | 0.251827 | + | 0.251827i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 29841.2 | − | 29841.2i | 1.01433 | − | 1.01433i | 0.0144302 | − | 0.999896i | \(-0.495407\pi\) |
0.999896 | − | 0.0144302i | \(-0.00459343\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4988.76 | + | 12043.9i | 0.169039 | + | 0.408097i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −10533.6 | − | 4363.18i | −0.355804 | − | 0.147379i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4087.50 | −0.137635 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23107.6 | 0.775657 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −672.289 | − | 278.471i | −0.0224966 | − | 0.00931840i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4431.66 | + | 10699.0i | 0.147834 | + | 0.356903i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 28561.9 | − | 28561.9i | 0.949834 | − | 0.949834i | −0.0489665 | − | 0.998800i | \(-0.515593\pi\) |
0.998800 | + | 0.0489665i | \(0.0155928\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 39077.7 | + | 39077.7i | 1.29552 | + | 1.29552i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9671.99 | − | 4006.27i | 0.319659 | − | 0.132407i | −0.217084 | − | 0.976153i | \(-0.569655\pi\) |
0.536743 | + | 0.843746i | \(0.319655\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3303.88 | − | 7976.26i | 0.108857 | − | 0.262803i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 37666.2i | − | 1.23721i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 35356.3i | − | 1.15778i | −0.815407 | − | 0.578889i | \(-0.803487\pi\) | ||
0.815407 | − | 0.578889i | \(-0.196513\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1726.67 | + | 4168.54i | −0.0563682 | + | 0.136085i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −424.890 | + | 175.995i | −0.0138284 | + | 0.00572793i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 26544.3 | + | 26544.3i | 0.861274 | + | 0.861274i | 0.991486 | − | 0.130213i | \(-0.0415660\pi\) |
−0.130213 | + | 0.991486i | \(0.541566\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3683.47 | − | 3683.47i | 0.119153 | − | 0.119153i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6051.57 | + | 14609.8i | 0.195161 | + | 0.471159i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −6033.31 | − | 2499.08i | −0.193982 | − | 0.0803500i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −40304.4 | −1.29194 | −0.645969 | − | 0.763364i | \(-0.723547\pi\) | ||||
−0.645969 | + | 0.763364i | \(0.723547\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −40326.8 | −1.28875 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −6394.38 | − | 2648.64i | −0.203734 | − | 0.0843895i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11444.4 | + | 27629.1i | 0.363537 | + | 0.877656i | 0.994777 | + | 0.102069i | \(0.0325461\pi\) |
−0.631240 | + | 0.775587i | \(0.717454\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 33432.4 | − | 33432.4i | 1.05881 | − | 1.05881i |
(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 | 128.4.g.a.81.4 | 44 | ||
4.3 | odd | 2 | 32.4.g.a.29.9 | yes | 44 | ||
8.3 | odd | 2 | 256.4.g.b.161.4 | 44 | |||
8.5 | even | 2 | 256.4.g.a.161.8 | 44 | |||
32.5 | even | 8 | 256.4.g.a.97.8 | 44 | |||
32.11 | odd | 8 | 32.4.g.a.21.9 | ✓ | 44 | ||
32.21 | even | 8 | inner | 128.4.g.a.49.4 | 44 | ||
32.27 | odd | 8 | 256.4.g.b.97.4 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.4.g.a.21.9 | ✓ | 44 | 32.11 | odd | 8 | ||
32.4.g.a.29.9 | yes | 44 | 4.3 | odd | 2 | ||
128.4.g.a.49.4 | 44 | 32.21 | even | 8 | inner | ||
128.4.g.a.81.4 | 44 | 1.1 | even | 1 | trivial | ||
256.4.g.a.97.8 | 44 | 32.5 | even | 8 | |||
256.4.g.a.161.8 | 44 | 8.5 | even | 2 | |||
256.4.g.b.97.4 | 44 | 32.27 | odd | 8 | |||
256.4.g.b.161.4 | 44 | 8.3 | odd | 2 |