Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2100,2,Mod(157,2100)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2100, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2100.157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2100 = 2^{2} \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2100.ce (of order \(12\), degree \(4\), 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: | \(16.7685844245\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 1657.3 | ||
Character | \(\chi\) | \(=\) | 2100.1657 |
Dual form | 2100.2.ce.d.493.3 |
$q$-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 \(\left(\mathbb{Z}/2100\mathbb{Z}\right)^\times\).
\(n\) | \(701\) | \(1051\) | \(1177\) | \(1501\) |
\(\chi(n)\) | \(1\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{5}{6}\right)\) |
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 | ||||||||
\(3\) | −0.258819 | + | 0.965926i | −0.149429 | + | 0.557678i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.895840 | − | 2.48947i | 0.338596 | − | 0.940932i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.866025 | − | 0.500000i | −0.288675 | − | 0.166667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.720993 | − | 1.24880i | −0.217387 | − | 0.376526i | 0.736621 | − | 0.676306i | \(-0.236420\pi\) |
−0.954008 | + | 0.299780i | \(0.903087\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.97110 | + | 1.97110i | 0.546684 | + | 0.546684i | 0.925480 | − | 0.378796i | \(-0.123662\pi\) |
−0.378796 | + | 0.925480i | \(0.623662\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.65850 | − | 0.980291i | −0.887316 | − | 0.237756i | −0.213755 | − | 0.976887i | \(-0.568569\pi\) |
−0.673561 | + | 0.739132i | \(0.735236\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.643613 | + | 1.11477i | −0.147655 | + | 0.255746i | −0.930360 | − | 0.366647i | \(-0.880506\pi\) |
0.782705 | + | 0.622392i | \(0.213839\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.17278 | + | 1.50964i | 0.474140 | + | 0.329430i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.135022 | − | 0.503908i | −0.0281540 | − | 0.105072i | 0.950419 | − | 0.310972i | \(-0.100655\pi\) |
−0.978573 | + | 0.205900i | \(0.933988\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0.707107 | − | 0.707107i | 0.136083 | − | 0.136083i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 6.13312i | − | 1.13889i | −0.822029 | − | 0.569446i | \(-0.807158\pi\) | ||
0.822029 | − | 0.569446i | \(-0.192842\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.63312 | − | 4.40699i | 1.37095 | − | 0.791518i | 0.379902 | − | 0.925027i | \(-0.375958\pi\) |
0.991048 | + | 0.133509i | \(0.0426244\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.39285 | − | 0.373213i | 0.242464 | − | 0.0649681i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.08552 | + | 1.09471i | −0.671656 | + | 0.179970i | −0.578500 | − | 0.815682i | \(-0.696362\pi\) |
−0.0931551 | + | 0.995652i | \(0.529695\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −2.41409 | + | 1.39378i | −0.386564 | + | 0.223183i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 9.57951i | − | 1.49607i | −0.663660 | − | 0.748034i | \(-0.730998\pi\) | ||
0.663660 | − | 0.748034i | \(-0.269002\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.27909 | + | 1.27909i | −0.195060 | + | 0.195060i | −0.797878 | − | 0.602819i | \(-0.794044\pi\) |
0.602819 | + | 0.797878i | \(0.294044\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.746427 | + | 2.78570i | 0.108878 | + | 0.406336i | 0.998756 | − | 0.0498609i | \(-0.0158778\pi\) |
−0.889879 | + | 0.456197i | \(0.849211\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.39494 | − | 4.46034i | −0.770706 | − | 0.637191i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.89378 | − | 3.28012i | 0.265182 | − | 0.459308i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −5.83279 | − | 1.56289i | −0.801196 | − | 0.214680i | −0.165087 | − | 0.986279i | \(-0.552790\pi\) |
−0.636109 | + | 0.771599i | \(0.719457\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.910206 | − | 0.910206i | −0.120560 | − | 0.120560i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.77048 | − | 3.06656i | −0.230497 | − | 0.399232i | 0.727458 | − | 0.686153i | \(-0.240702\pi\) |
−0.957954 | + | 0.286920i | \(0.907368\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.71119 | − | 0.987954i | −0.219095 | − | 0.126495i | 0.386436 | − | 0.922316i | \(-0.373706\pi\) |
−0.605531 | + | 0.795822i | \(0.707039\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.02056 | + | 1.70803i | −0.254566 | + | 0.215191i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.583310 | + | 2.17694i | −0.0712626 | + | 0.265956i | −0.992360 | − | 0.123377i | \(-0.960628\pi\) |
0.921097 | + | 0.389332i | \(0.127294\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.521684 | 0.0628034 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9.24915 | 1.09767 | 0.548836 | − | 0.835930i | \(-0.315071\pi\) | ||||
0.548836 | + | 0.835930i | \(0.315071\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −0.920882 | + | 3.43678i | −0.107781 | + | 0.402244i | −0.998646 | − | 0.0520242i | \(-0.983433\pi\) |
0.890865 | + | 0.454269i | \(0.150099\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.75474 | + | 0.676169i | −0.427892 | + | 0.0770566i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.09350 | − | 4.67278i | −0.910590 | − | 0.525729i | −0.0299690 | − | 0.999551i | \(-0.509541\pi\) |
−0.880621 | + | 0.473821i | \(0.842874\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.500000 | + | 0.866025i | 0.0555556 | + | 0.0962250i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −12.2773 | − | 12.2773i | −1.34760 | − | 1.34760i | −0.888257 | − | 0.459347i | \(-0.848083\pi\) |
−0.459347 | − | 0.888257i | \(-0.651917\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 5.92414 | + | 1.58737i | 0.635135 | + | 0.170184i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.94736 | − | 6.83702i | 0.418419 | − | 0.724723i | −0.577362 | − | 0.816489i | \(-0.695918\pi\) |
0.995781 | + | 0.0917656i | \(0.0292511\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.67278 | − | 3.14120i | 0.699498 | − | 0.329288i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.28122 | + | 8.51364i | 0.236552 | + | 0.882824i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.35470 | − | 9.35470i | 0.949826 | − | 0.949826i | −0.0489744 | − | 0.998800i | \(-0.515595\pi\) |
0.998800 | + | 0.0489744i | \(0.0155953\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.44199i | 0.144925i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 12.0666 | − | 6.96663i | 1.20067 | − | 0.693206i | 0.239964 | − | 0.970782i | \(-0.422864\pi\) |
0.960704 | + | 0.277576i | \(0.0895310\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.35878 | − | 0.632032i | 0.232417 | − | 0.0622760i | −0.140731 | − | 0.990048i | \(-0.544945\pi\) |
0.373148 | + | 0.927772i | \(0.378278\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −10.5421 | + | 2.82475i | −1.01914 | + | 0.273079i | −0.729445 | − | 0.684039i | \(-0.760222\pi\) |
−0.289698 | + | 0.957118i | \(0.593555\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 3.86386 | − | 2.23080i | 0.370090 | − | 0.213672i | −0.303408 | − | 0.952861i | \(-0.598124\pi\) |
0.673498 | + | 0.739189i | \(0.264791\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 4.22964i | − | 0.401460i | ||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.0939 | − | 13.0939i | 1.23177 | − | 1.23177i | 0.268489 | − | 0.963283i | \(-0.413476\pi\) |
0.963283 | − | 0.268489i | \(-0.0865244\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.721472 | − | 2.69257i | −0.0667001 | − | 0.248928i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −5.71784 | + | 8.22954i | −0.524153 | + | 0.754401i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.46034 | − | 7.72553i | 0.405485 | − | 0.702321i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.25310 | + | 2.47936i | 0.834324 | + | 0.223556i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 8.94210 | + | 8.94210i | 0.793483 | + | 0.793483i | 0.982059 | − | 0.188576i | \(-0.0603870\pi\) |
−0.188576 | + | 0.982059i | \(0.560387\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −0.904455 | − | 1.56656i | −0.0796328 | − | 0.137928i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.13312 | + | 3.54096i | 0.535853 | + | 0.309375i | 0.743397 | − | 0.668851i | \(-0.233213\pi\) |
−0.207543 | + | 0.978226i | \(0.566547\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.19861 | + | 2.60091i | 0.190644 | + | 0.225528i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.991812 | + | 3.70149i | −0.0847362 | + | 0.316240i | −0.995264 | − | 0.0972077i | \(-0.969009\pi\) |
0.910528 | + | 0.413448i | \(0.135676\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.33059 | −0.197678 | −0.0988392 | − | 0.995103i | \(-0.531513\pi\) | ||||
−0.0988392 | + | 0.995103i | \(0.531513\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.88397 | −0.242874 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1.04035 | − | 3.88265i | 0.0869986 | − | 0.324683i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.70467 | − | 4.05669i | 0.470513 | − | 0.334590i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −14.2540 | − | 8.22954i | −1.16773 | − | 0.674190i | −0.214587 | − | 0.976705i | \(-0.568841\pi\) |
−0.953145 | + | 0.302515i | \(0.902174\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.05676 | − | 3.56240i | −0.167376 | − | 0.289904i | 0.770120 | − | 0.637899i | \(-0.220196\pi\) |
−0.937497 | + | 0.347994i | \(0.886863\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.67821 | + | 2.67821i | 0.216520 | + | 0.216520i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.38514 | + | 1.44294i | 0.429781 | + | 0.115159i | 0.467223 | − | 0.884139i | \(-0.345254\pi\) |
−0.0374423 | + | 0.999299i | \(0.511921\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.01928 | − | 5.22954i | 0.239444 | − | 0.414729i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.37542 | − | 0.115288i | −0.108399 | − | 0.00908600i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.68973 | + | 10.0382i | 0.210676 | + | 0.786252i | 0.987644 | + | 0.156713i | \(0.0500897\pi\) |
−0.776969 | + | 0.629539i | \(0.783244\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.450665 | − | 0.450665i | 0.0348735 | − | 0.0348735i | −0.689455 | − | 0.724329i | \(-0.742150\pi\) |
0.724329 | + | 0.689455i | \(0.242150\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | − | 5.22954i | − | 0.402272i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.11477 | − | 0.643613i | 0.0852486 | − | 0.0492183i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 0.224151 | − | 0.0600611i | 0.0170419 | − | 0.00456636i | −0.250288 | − | 0.968171i | \(-0.580525\pi\) |
0.267330 | + | 0.963605i | \(0.413859\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.42031 | − | 0.916468i | 0.257086 | − | 0.0688860i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −5.19615 | + | 3.00000i | −0.388379 | + | 0.224231i | −0.681457 | − | 0.731858i | \(-0.738654\pi\) |
0.293079 | + | 0.956088i | \(0.405320\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 6.68435i | − | 0.496844i | −0.968652 | − | 0.248422i | \(-0.920088\pi\) | ||
0.968652 | − | 0.248422i | \(-0.0799119\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.39718 | − | 1.39718i | 0.103282 | − | 0.103282i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.41357 | + | 5.27550i | 0.103370 | + | 0.385783i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1.12687 | − | 2.39378i | −0.0819676 | − | 0.174122i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.787555 | − | 1.36408i | 0.0569854 | − | 0.0987017i | −0.836125 | − | 0.548538i | \(-0.815184\pi\) |
0.893111 | + | 0.449837i | \(0.148518\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 10.9261 | + | 2.92765i | 0.786480 | + | 0.210737i | 0.629640 | − | 0.776887i | \(-0.283203\pi\) |
0.156840 | + | 0.987624i | \(0.449869\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 15.5194 | + | 15.5194i | 1.10571 | + | 1.10571i | 0.993708 | + | 0.112003i | \(0.0357265\pi\) |
0.112003 | + | 0.993708i | \(0.464274\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.18411 | + | 10.7112i | 0.438380 | + | 0.759296i | 0.997565 | − | 0.0697470i | \(-0.0222192\pi\) |
−0.559185 | + | 0.829043i | \(0.688886\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1.95179 | − | 1.12687i | −0.137669 | − | 0.0794831i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −15.2682 | − | 5.49430i | −1.07162 | − | 0.385624i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −0.135022 | + | 0.503908i | −0.00938467 | + | 0.0350241i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.85616 | 0.128393 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.6886 | 1.35542 | 0.677710 | − | 0.735329i | \(-0.262972\pi\) | ||||
0.677710 | + | 0.735329i | \(0.262972\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −2.39386 | + | 8.93400i | −0.164024 | + | 0.612147i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.13301 | − | 22.9504i | −0.280567 | − | 1.55797i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −3.08133 | − | 1.77901i | −0.208217 | − | 0.120214i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.27901 | − | 9.14351i | −0.355104 | − | 0.615059i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3.01669 | + | 3.01669i | 0.202013 | + | 0.202013i | 0.800862 | − | 0.598849i | \(-0.204375\pi\) |
−0.598849 | + | 0.800862i | \(0.704375\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −24.3122 | − | 6.51443i | −1.61366 | − | 0.432378i | −0.664527 | − | 0.747264i | \(-0.731367\pi\) |
−0.949129 | + | 0.314886i | \(0.898034\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 11.4120 | − | 19.7662i | 0.754129 | − | 1.30619i | −0.191677 | − | 0.981458i | \(-0.561392\pi\) |
0.945806 | − | 0.324732i | \(-0.105274\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.318668 | − | 3.80180i | 0.0209668 | − | 0.250140i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.79166 | − | 25.3468i | −0.444936 | − | 1.66052i | −0.716105 | − | 0.697993i | \(-0.754077\pi\) |
0.271169 | − | 0.962532i | \(-0.412590\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.60832 | − | 6.60832i | 0.429256 | − | 0.429256i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 22.7253i | 1.46998i | 0.678078 | + | 0.734990i | \(0.262813\pi\) | ||||
−0.678078 | + | 0.734990i | \(0.737187\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −19.2070 | + | 11.0892i | −1.23723 | + | 0.714315i | −0.968527 | − | 0.248908i | \(-0.919928\pi\) |
−0.268703 | + | 0.963223i | \(0.586595\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −0.965926 | + | 0.258819i | −0.0619642 | + | 0.0166032i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.46595 | + | 0.928697i | −0.220533 | + | 0.0590916i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 15.0365 | − | 8.68133i | 0.952900 | − | 0.550157i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 28.0971i | 1.77347i | 0.462275 | + | 0.886737i | \(0.347033\pi\) | ||||
−0.462275 | + | 0.886737i | \(0.652967\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.531929 | + | 0.531929i | −0.0334421 | + | 0.0334421i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 2.19445 | + | 8.18979i | 0.136886 | + | 0.510865i | 0.999983 | + | 0.00582706i | \(0.00185482\pi\) |
−0.863097 | + | 0.505038i | \(0.831479\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.934720 | + | 11.1515i | −0.0580807 | + | 0.692919i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −3.06656 | + | 5.31144i | −0.189815 | + | 0.328770i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.47582 | − | 2.53904i | −0.584304 | − | 0.156564i | −0.0454554 | − | 0.998966i | \(-0.514474\pi\) |
−0.538849 | + | 0.842403i | \(0.681141\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 5.58241 | + | 5.58241i | 0.341638 | + | 0.341638i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 0.521684 | + | 0.903584i | 0.0318077 | + | 0.0550925i | 0.881491 | − | 0.472201i | \(-0.156540\pi\) |
−0.849683 | + | 0.527293i | \(0.823207\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −11.6148 | − | 6.70579i | −0.705547 | − | 0.407348i | 0.103863 | − | 0.994592i | \(-0.466880\pi\) |
−0.809410 | + | 0.587244i | \(0.800213\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.30713 | + | 7.25842i | 0.0791109 | + | 0.439299i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.45076 | + | 16.6104i | −0.267420 | + | 0.998025i | 0.693332 | + | 0.720618i | \(0.256142\pi\) |
−0.960752 | + | 0.277407i | \(0.910525\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.81397 | −0.527679 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −18.2662 | −1.08967 | −0.544836 | − | 0.838542i | \(-0.683408\pi\) | ||||
−0.544836 | + | 0.838542i | \(0.683408\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −1.09976 | + | 4.10437i | −0.0653740 | + | 0.243979i | −0.990879 | − | 0.134757i | \(-0.956975\pi\) |
0.925505 | + | 0.378736i | \(0.123641\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −23.8479 | − | 8.58172i | −1.40770 | − | 0.506563i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.29880 | − | 1.32722i | −0.135224 | − | 0.0780715i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 6.61477 | + | 11.4571i | 0.387765 | + | 0.671628i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −21.4015 | − | 21.4015i | −1.25029 | − | 1.25029i | −0.955591 | − | 0.294696i | \(-0.904782\pi\) |
−0.294696 | − | 0.955591i | \(-0.595218\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.39285 | − | 0.373213i | −0.0808214 | − | 0.0216560i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.727112 | − | 1.25939i | 0.0420500 | − | 0.0728327i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.03840 | + | 4.33013i | 0.117492 | + | 0.249584i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3.60619 | + | 13.4585i | 0.207170 | + | 0.773171i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.6337 | − | 21.6337i | 1.23470 | − | 1.23470i | 0.272565 | − | 0.962137i | \(-0.412128\pi\) |
0.962137 | − | 0.272565i | \(-0.0878720\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.44199i | 0.138920i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 11.1630 | − | 6.44495i | 0.632994 | − | 0.365459i | −0.148916 | − | 0.988850i | \(-0.547579\pi\) |
0.781911 | + | 0.623390i | \(0.214245\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 0.426925 | − | 0.114394i | 0.0241312 | − | 0.00646594i | −0.246733 | − | 0.969083i | \(-0.579357\pi\) |
0.270864 | + | 0.962617i | \(0.412690\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −27.4209 | + | 7.34741i | −1.54011 | + | 0.412672i | −0.926302 | − | 0.376782i | \(-0.877031\pi\) |
−0.613810 | + | 0.789454i | \(0.710364\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.65902 | + | 4.42194i | −0.428823 | + | 0.247581i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 10.9140i | − | 0.609159i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.44745 | − | 3.44745i | 0.191821 | − | 0.191821i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.15475 | + | 4.30957i | 0.0638576 | + | 0.238320i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.60361 | + | 0.637336i | 0.419200 | + | 0.0351375i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.4207 | + | 23.2453i | −0.737667 | + | 1.27768i | 0.215876 | + | 0.976421i | \(0.430739\pi\) |
−0.953543 | + | 0.301256i | \(0.902594\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 4.08552 | + | 1.09471i | 0.223885 | + | 0.0599899i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 11.2829 | + | 11.2829i | 0.614618 | + | 0.614618i | 0.944146 | − | 0.329528i | \(-0.106889\pi\) |
−0.329528 | + | 0.944146i | \(0.606889\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 9.25880 | + | 16.0367i | 0.502869 | + | 0.870994i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −11.0069 | − | 6.35481i | −0.596054 | − | 0.344132i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.9369 | + | 9.43480i | −0.860511 | + | 0.509431i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4.41863 | + | 16.4906i | −0.237205 | + | 0.885260i | 0.739938 | + | 0.672675i | \(0.234855\pi\) |
−0.977143 | + | 0.212585i | \(0.931812\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 13.1205 | 0.702323 | 0.351161 | − | 0.936315i | \(-0.385787\pi\) | ||||
0.351161 | + | 0.936315i | \(0.385787\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.78755 | 0.148789 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.40860 | − | 12.7211i | 0.181422 | − | 0.677075i | −0.813947 | − | 0.580940i | \(-0.802685\pi\) |
0.995368 | − | 0.0961351i | \(-0.0306481\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6.46924 | − | 7.65297i | −0.342388 | − | 0.405038i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 12.8042 | + | 7.39252i | 0.675781 | + | 0.390162i | 0.798263 | − | 0.602308i | \(-0.205752\pi\) |
−0.122483 | + | 0.992471i | \(0.539086\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.67153 | + | 15.0195i | 0.456396 | + | 0.790501i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.30787 | + | 6.30787i | 0.331077 | + | 0.331077i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −12.5381 | − | 3.35957i | −0.654483 | − | 0.175368i | −0.0837281 | − | 0.996489i | \(-0.526683\pi\) |
−0.570755 | + | 0.821120i | \(0.693349\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.78976 | + | 8.29610i | −0.249345 | + | 0.431878i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9.11603 | + | 13.1205i | −0.473281 | + | 0.681181i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.77184 | + | 32.7370i | 0.454189 | + | 1.69506i | 0.690461 | + | 0.723369i | \(0.257407\pi\) |
−0.236273 | + | 0.971687i | \(0.575926\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 12.0890 | − | 12.0890i | 0.622615 | − | 0.622615i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11.6911i | 0.600533i | 0.953855 | + | 0.300267i | \(0.0970757\pi\) | ||||
−0.953855 | + | 0.300267i | \(0.902924\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.9518 | + | 6.32302i | −0.561077 | + | 0.323938i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −2.78570 | + | 0.746427i | −0.142343 | + | 0.0381406i | −0.329287 | − | 0.944230i | \(-0.606808\pi\) |
0.186944 | + | 0.982371i | \(0.440142\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 1.74727 | − | 0.468180i | 0.0888189 | − | 0.0237989i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.61288 | − | 1.50855i | 0.132478 | − | 0.0764864i | −0.432296 | − | 0.901732i | \(-0.642296\pi\) |
0.564774 | + | 0.825245i | \(0.308963\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.97591i | 0.0999259i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −5.00767 | + | 5.00767i | −0.252604 | + | 0.252604i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.50329 | − | 16.8065i | −0.226014 | − | 0.843494i | −0.981996 | − | 0.188902i | \(-0.939507\pi\) |
0.755982 | − | 0.654592i | \(-0.227160\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −3.08133 | + | 1.45053i | −0.154259 | + | 0.0726175i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −15.0171 | + | 26.0104i | −0.749918 | + | 1.29890i | 0.197944 | + | 0.980213i | \(0.436574\pi\) |
−0.947862 | + | 0.318683i | \(0.896760\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 23.7322 | + | 6.35904i | 1.18219 | + | 0.316766i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.31270 | + | 4.31270i | 0.213773 | + | 0.213773i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.18674 | − | 2.05550i | −0.0586806 | − | 0.101638i | 0.835193 | − | 0.549957i | \(-0.185356\pi\) |
−0.893873 | + | 0.448320i | \(0.852023\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.31867 | − | 1.91603i | −0.163698 | − | 0.0945110i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.22019 | + | 1.66041i | −0.453696 | + | 0.0817035i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0.603202 | − | 2.25118i | 0.0295389 | − | 0.110241i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 27.4646 | 1.34173 | 0.670867 | − | 0.741578i | \(-0.265922\pi\) | ||||
0.670867 | + | 0.741578i | \(0.265922\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −31.6118 | −1.54067 | −0.770333 | − | 0.637642i | \(-0.779910\pi\) | ||||
−0.770333 | + | 0.637642i | \(0.779910\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0.746427 | − | 2.78570i | 0.0362925 | − | 0.135445i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.99243 | + | 3.37490i | −0.193207 | + | 0.163323i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.48109 | + | 2.00981i | 0.168068 | + | 0.0970344i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.9036 | − | 22.3497i | −0.621544 | − | 1.07655i | −0.989198 | − | 0.146583i | \(-0.953172\pi\) |
0.367655 | − | 0.929962i | \(-0.380161\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −13.9376 | − | 13.9376i | −0.669799 | − | 0.669799i | 0.287871 | − | 0.957669i | \(-0.407053\pi\) |
−0.957669 | + | 0.287871i | \(0.907053\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 0.648644 | + | 0.173804i | 0.0310288 | + | 0.00831415i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.3287 | + | 30.0141i | −0.827052 | + | 1.43250i | 0.0732882 | + | 0.997311i | \(0.476651\pi\) |
−0.900341 | + | 0.435186i | \(0.856683\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.44199 | + | 6.56024i | 0.116285 | + | 0.312392i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.54547 | + | 20.6960i | 0.263473 | + | 0.983295i | 0.963178 | + | 0.268863i | \(0.0866480\pi\) |
−0.699705 | + | 0.714432i | \(0.746685\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.6383 | − | 11.6383i | 0.550474 | − | 0.550474i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 12.0342i | − | 0.567928i | −0.958835 | − | 0.283964i | \(-0.908350\pi\) | ||
0.958835 | − | 0.283964i | \(-0.0916497\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.9629 | + | 6.90676i | −0.563309 | + | 0.325227i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 3.97335 | − | 1.06465i | 0.186684 | − | 0.0500219i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −18.9073 | + | 5.06619i | −0.884445 | + | 0.236986i | −0.672324 | − | 0.740257i | \(-0.734704\pi\) |
−0.212121 | + | 0.977243i | \(0.568037\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.28012 | + | 1.89378i | −0.153103 | + | 0.0883940i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 18.9284i | 0.881586i | 0.897609 | + | 0.440793i | \(0.145303\pi\) | ||||
−0.897609 | + | 0.440793i | \(0.854697\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 28.6886 | − | 28.6886i | 1.33327 | − | 1.33327i | 0.430846 | − | 0.902425i | \(-0.358215\pi\) |
0.902425 | − | 0.430846i | \(-0.141785\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.83598 | − | 10.5840i | −0.131234 | − | 0.489770i | 0.868751 | − | 0.495248i | \(-0.164923\pi\) |
−0.999985 | + | 0.00547816i | \(0.998256\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.89688 | + | 3.40232i | 0.226117 | + | 0.157105i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.78755 | + | 4.82819i | −0.128444 | + | 0.222471i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 2.51954 | + | 0.675109i | 0.115849 | + | 0.0310416i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.26990 | + | 4.26990i | 0.195505 | + | 0.195505i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.36408 | + | 2.36266i | 0.0623266 | + | 0.107953i | 0.895505 | − | 0.445051i | \(-0.146815\pi\) |
−0.833178 | + | 0.553004i | \(0.813481\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.2108 | − | 5.89518i | −0.465570 | − | 0.268797i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0.467346 | − | 1.29872i | 0.0212650 | − | 0.0590937i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.77124 | − | 29.0027i | 0.352148 | − | 1.31424i | −0.531887 | − | 0.846816i | \(-0.678517\pi\) |
0.884035 | − | 0.467420i | \(-0.154817\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −10.3923 | −0.469956 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −0.498306 | −0.0224882 | −0.0112441 | − | 0.999937i | \(-0.503579\pi\) | ||||
−0.0112441 | + | 0.999937i | \(0.503579\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −6.01225 | + | 22.4380i | −0.270778 | + | 1.01056i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.28577 | − | 23.0255i | 0.371667 | − | 1.03284i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 18.0491 | + | 10.4207i | 0.807991 | + | 0.466494i | 0.846258 | − | 0.532774i | \(-0.178850\pi\) |
−0.0382670 | + | 0.999268i | \(0.512184\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0.318668 | + | 0.551950i | 0.0142370 | + | 0.0246593i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.7279 | − | 12.7279i | −0.567510 | − | 0.567510i | 0.363920 | − | 0.931430i | \(-0.381438\pi\) |
−0.931430 | + | 0.363920i | \(0.881438\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.05135 | + | 1.35350i | 0.224338 | + | 0.0601112i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 14.2540 | − | 24.6886i | 0.631797 | − | 1.09430i | −0.355388 | − | 0.934719i | \(-0.615651\pi\) |
0.987184 | − | 0.159585i | \(-0.0510155\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.73080 | + | 5.37131i | 0.341990 | + | 0.237613i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.333158 | + | 1.24336i | 0.0147093 | + | 0.0548959i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.94061 | − | 2.94061i | 0.129328 | − | 0.129328i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.232058i | 0.0101862i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.504213 | − | 0.291107i | 0.0220900 | − | 0.0127536i | −0.488914 | − | 0.872332i | \(-0.662607\pi\) |
0.511004 | + | 0.859578i | \(0.329274\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.0931310 | − | 0.0249544i | 0.00407233 | − | 0.00109118i | −0.256782 | − | 0.966469i | \(-0.582662\pi\) |
0.260855 | + | 0.965378i | \(0.415996\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −32.2459 | + | 8.64026i | −1.40465 | + | 0.376376i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 19.6829 | − | 11.3639i | 0.855778 | − | 0.494084i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.54096i | 0.153665i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 18.8822 | − | 18.8822i | 0.817877 | − | 0.817877i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.55291 | − | 5.79555i | −0.0670132 | − | 0.250097i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.68034 | + | 9.95305i | −0.0723774 | + | 0.428708i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.51709 | + | 9.55589i | −0.237198 | + | 0.410840i | −0.959909 | − | 0.280311i | \(-0.909562\pi\) |
0.722711 | + | 0.691150i | \(0.242896\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 6.45658 | + | 1.73004i | 0.277078 | + | 0.0742430i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 32.0608 | + | 32.0608i | 1.37082 | + | 1.37082i | 0.859231 | + | 0.511588i | \(0.170943\pi\) |
0.511588 | + | 0.859231i | \(0.329057\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0.987954 | + | 1.71119i | 0.0421648 | + | 0.0730316i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 6.83702 | + | 3.94736i | 0.291267 | + | 0.168163i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −18.8833 | + | 15.9625i | −0.802997 | + | 0.678793i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −9.58541 | + | 35.7732i | −0.406147 | + | 1.51576i | 0.395784 | + | 0.918344i | \(0.370473\pi\) |
−0.801931 | + | 0.597417i | \(0.796194\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.04243 | −0.213272 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −5.46160 | −0.230589 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.04577 | − | 11.3670i | 0.128364 | − | 0.479060i | −0.871573 | − | 0.490265i | \(-0.836900\pi\) |
0.999937 | + | 0.0112048i | \(0.00356667\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.60387 | − | 0.468915i | 0.109352 | − | 0.0196926i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.4319 | + | 10.6417i | 0.772706 | + | 0.446122i | 0.833839 | − | 0.552008i | \(-0.186138\pi\) |
−0.0611330 | + | 0.998130i | \(0.519471\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 16.6899 | + | 28.9077i | 0.698450 | + | 1.20975i | 0.969004 | + | 0.247046i | \(0.0794597\pi\) |
−0.270554 | + | 0.962705i | \(0.587207\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.11377 | + | 1.11377i | 0.0465284 | + | 0.0465284i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.61457 | − | 0.432623i | −0.0672154 | − | 0.0180103i | 0.225055 | − | 0.974346i | \(-0.427744\pi\) |
−0.292270 | + | 0.956336i | \(0.594411\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −5.65578 | + | 9.79610i | −0.235046 | + | 0.407112i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −41.5623 | + | 19.5654i | −1.72430 | + | 0.811710i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.25367 | + | 8.41080i | 0.0933374 | + | 0.348340i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 19.8129 | − | 19.8129i | 0.817764 | − | 0.817764i | −0.168019 | − | 0.985784i | \(-0.553737\pi\) |
0.985784 | + | 0.168019i | \(0.0537372\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.3456i | 0.467486i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −19.0073 | + | 10.9739i | −0.781855 | + | 0.451404i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −2.17008 | + | 0.581472i | −0.0891146 | + | 0.0238782i | −0.303101 | − | 0.952958i | \(-0.598022\pi\) |
0.213986 | + | 0.976837i | \(0.431355\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −11.9468 | + | 3.20113i | −0.488949 | + | 0.131013i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −28.7089 | + | 16.5751i | −1.17302 | + | 0.677241i | −0.954388 | − | 0.298568i | \(-0.903491\pi\) |
−0.218627 | + | 0.975809i | \(0.570158\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 13.9465i | − | 0.568891i | −0.958692 | − | 0.284446i | \(-0.908190\pi\) | ||
0.958692 | − | 0.284446i | \(-0.0918096\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 1.59363 | − | 1.59363i | 0.0648977 | − | 0.0648977i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 10.2267 | + | 38.1665i | 0.415088 | + | 1.54913i | 0.784659 | + | 0.619928i | \(0.212838\pi\) |
−0.369570 | + | 0.929203i | \(0.620495\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 9.25880 | − | 13.3260i | 0.375185 | − | 0.539995i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4.01961 | + | 6.96217i | −0.162616 | + | 0.281659i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.7952 | − | 5.30411i | −0.799521 | − | 0.214231i | −0.164147 | − | 0.986436i | \(-0.552487\pi\) |
−0.635374 | + | 0.772205i | \(0.719154\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 23.5210 | + | 23.5210i | 0.946918 | + | 0.946918i | 0.998660 | − | 0.0517425i | \(-0.0164775\pi\) |
−0.0517425 | + | 0.998660i | \(0.516478\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 16.9289 | + | 29.3217i | 0.680431 | + | 1.17854i | 0.974850 | + | 0.222864i | \(0.0715406\pi\) |
−0.294419 | + | 0.955676i | \(0.595126\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −0.451792 | − | 0.260842i | −0.0181298 | − | 0.0104672i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −13.4844 | − | 15.9517i | −0.540240 | − | 0.639092i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −0.480410 | + | 1.79291i | −0.0191857 | + | 0.0716021i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 16.0200 | 0.638759 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −20.4933 | −0.815824 | −0.407912 | − | 0.913021i | \(-0.633743\pi\) | ||||
−0.407912 | + | 0.913021i | \(0.633743\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −5.09579 | + | 19.0177i | −0.202539 | + | 0.755888i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.84219 | − | 19.4257i | −0.0729902 | − | 0.769675i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −8.01000 | − | 4.62458i | −0.316871 | − | 0.182945i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.4915 | − | 18.1717i | −0.414387 | − | 0.717740i | 0.580976 | − | 0.813920i | \(-0.302671\pi\) |
−0.995364 | + | 0.0961802i | \(0.969337\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.0444 | − | 23.0444i | −0.908782 | − | 0.908782i | 0.0873921 | − | 0.996174i | \(-0.472147\pi\) |
−0.996174 | + | 0.0873921i | \(0.972147\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14.9924 | − | 4.01721i | −0.589413 | − | 0.157933i | −0.0482282 | − | 0.998836i | \(-0.515357\pi\) |
−0.541185 | + | 0.840904i | \(0.682024\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.55301 | + | 4.42194i | −0.100214 | + | 0.173576i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 23.2381 | + | 1.94782i | 0.910772 | + | 0.0763412i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.11117 | − | 4.14693i | −0.0434833 | − | 0.162282i | 0.940770 | − | 0.339045i | \(-0.110104\pi\) |
−0.984253 | + | 0.176763i | \(0.943437\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 2.51590 | − | 2.51590i | 0.0981545 | − | 0.0981545i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 22.4591i | − | 0.874882i | −0.899247 | − | 0.437441i | \(-0.855885\pi\) | ||
0.899247 | − | 0.437441i | \(-0.144115\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −2.52257 | + | 1.45640i | −0.0981165 | + | 0.0566476i | −0.548255 | − | 0.836311i | \(-0.684708\pi\) |
0.450139 | + | 0.892959i | \(0.351374\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.1983 | − | 2.73262i | 0.396068 | − | 0.106126i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3.09053 | + | 0.828106i | −0.119666 | + | 0.0320644i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.69468 | + | 2.13312i | −0.142845 | + | 0.0824713i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 2.84923i | 0.109993i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.9120 | − | 11.9120i | 0.459173 | − | 0.459173i | −0.439211 | − | 0.898384i | \(-0.644742\pi\) |
0.898384 | + | 0.439211i | \(0.144742\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.9284 | + | 44.5176i | 0.458448 | + | 1.71095i | 0.677750 | + | 0.735293i | \(0.262955\pi\) |
−0.219302 | + | 0.975657i | \(0.570378\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −14.9079 | − | 31.6686i | −0.572114 | − | 1.21533i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 12.5849 | − | 21.7977i | 0.482255 | − | 0.835290i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 22.2077 | + | 5.95053i | 0.849754 | + | 0.227691i | 0.657313 | − | 0.753618i | \(-0.271693\pi\) |
0.192441 | + | 0.981309i | \(0.438360\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 16.1391 | + | 16.1391i | 0.615744 | + | 0.615744i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.41640 | − | 14.5776i | −0.320639 | − | 0.555363i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.4182 | + | 7.74698i | 0.510451 | + | 0.294709i | 0.733019 | − | 0.680208i | \(-0.238111\pi\) |
−0.222568 | + | 0.974917i | \(0.571444\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 3.58978 | + | 1.29179i | 0.136365 | + | 0.0490710i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.39071 | + | 35.0466i | −0.355699 | + | 1.32749i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 26.2409 | 0.992524 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.8585 | 0.863352 | 0.431676 | − | 0.902029i | \(-0.357922\pi\) | ||||
0.431676 | + | 0.902029i | \(0.357922\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.40914 | − | 5.25899i | 0.0531468 | − | 0.198346i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.53352 | − | 36.2804i | −0.245718 | − | 1.36446i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9.58768 | − | 5.53545i | −0.360073 | − | 0.207888i | 0.309040 | − | 0.951049i | \(-0.399992\pi\) |
−0.669113 | + | 0.743161i | \(0.733326\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.67278 | + | 8.09350i | 0.175243 | + | 0.303530i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −3.25136 | − | 3.25136i | −0.121764 | − | 0.121764i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −21.9510 | − | 5.88175i | −0.819774 | − | 0.219658i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −22.4694 | + | 38.9182i | −0.837968 | + | 1.45140i | 0.0536236 | + | 0.998561i | \(0.482923\pi\) |
−0.891591 | + | 0.452841i | \(0.850410\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.539661 | − | 6.43831i | 0.0200980 | − | 0.239775i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.74017 | − | 21.4226i | −0.213479 | − | 0.796715i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.9289 | − | 25.9289i | 0.961650 | − | 0.961650i | −0.0376415 | − | 0.999291i | \(-0.511984\pi\) |
0.999291 | + | 0.0376415i | \(0.0119845\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1.00000i | − | 0.0370370i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 5.93344 | − | 3.42567i | 0.219456 | − | 0.126703i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31.7034 | − | 8.49489i | 1.17099 | − | 0.313766i | 0.379643 | − | 0.925133i | \(-0.376047\pi\) |
0.791347 | + | 0.611367i | \(0.209380\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 3.13912 | − | 0.841124i | 0.115631 | − | 0.0309832i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.7785 | − | 12.5738i | 0.801137 | − | 0.462537i | −0.0427317 | − | 0.999087i | \(-0.513606\pi\) |
0.843869 | + | 0.536550i | \(0.180273\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 3.58821i | − | 0.131816i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −20.3996 | + | 20.3996i | −0.748388 | + | 0.748388i | −0.974176 | − | 0.225788i | \(-0.927504\pi\) |
0.225788 | + | 0.974176i | \(0.427504\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 4.49379 | + | 16.7710i | 0.164419 | + | 0.613620i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −2.41191 | + | 28.7748i | −0.0881293 | + | 1.05141i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 20.2082 | − | 35.0017i | 0.737409 | − | 1.27723i | −0.216249 | − | 0.976338i | \(-0.569382\pi\) |
0.953658 | − | 0.300892i | \(-0.0972842\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −27.1397 | − | 7.27207i | −0.989026 | − | 0.265009i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17.8174 | − | 17.8174i | −0.647584 | − | 0.647584i | 0.304825 | − | 0.952408i | \(-0.401402\pi\) |
−0.952408 | + | 0.304825i | \(0.901402\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.376131 | − | 0.651477i | −0.0136527 | − | 0.0236471i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 29.9104 | + | 17.2688i | 1.08425 | + | 0.625993i | 0.932040 | − | 0.362354i | \(-0.118027\pi\) |
0.152212 | + | 0.988348i | \(0.451360\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −2.09211 | − | 11.6174i | −0.0757395 | − | 0.420578i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.55470 | − | 9.53429i | 0.0922450 | − | 0.344263i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −29.1538 | −1.05131 | −0.525656 | − | 0.850697i | \(-0.676180\pi\) | ||||
−0.525656 | + | 0.850697i | \(0.676180\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −8.47869 | −0.305353 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4.82370 | + | 18.0023i | −0.173496 | + | 0.647497i | 0.823307 | + | 0.567597i | \(0.192127\pi\) |
−0.996803 | + | 0.0799002i | \(0.974540\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −10.5296 | − | 3.78909i | −0.377746 | − | 0.135933i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 10.6790 | + | 6.16550i | 0.382613 | + | 0.220902i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.66857 | − | 11.5503i | −0.238620 | − | 0.413302i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −4.33677 | − | 4.33677i | −0.154984 | − | 0.154984i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −4.31201 | − | 1.15540i | −0.153706 | − | 0.0411855i | 0.181145 | − | 0.983456i | \(-0.442020\pi\) |
−0.334852 | + | 0.942271i | \(0.608686\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.90504 | − | 8.49579i | 0.174624 | − | 0.302458i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −20.8669 | − | 44.3270i | −0.741941 | − | 1.57609i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.42556 | − | 5.32027i | −0.0506232 | − | 0.188928i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 21.5240 | − | 21.5240i | 0.762418 | − | 0.762418i | −0.214341 | − | 0.976759i | \(-0.568760\pi\) |
0.976759 | + | 0.214341i | \(0.0687605\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 10.9232i | − | 0.386435i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −6.83702 | + | 3.94736i | −0.241574 | + | 0.139473i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.95578 | − | 1.32790i | 0.174886 | − | 0.0468605i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.00782 | + | 0.270044i | −0.0354768 | + | 0.00950599i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −19.4501 | + | 11.2295i | −0.683830 | + | 0.394810i | −0.801297 | − | 0.598267i | \(-0.795856\pi\) |
0.117466 | + | 0.993077i | \(0.462523\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.5465i | 0.405453i | 0.979235 | + | 0.202726i | \(0.0649802\pi\) | ||||
−0.979235 | + | 0.202726i | \(0.935020\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 9.48342 | − | 9.48342i | 0.332598 | − | 0.332598i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.602654 | − | 2.24913i | −0.0210842 | − | 0.0786872i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.34940 | − | 0.616029i | −0.256809 | − | 0.0215258i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.62458 | − | 2.81385i | 0.0566981 | − | 0.0982040i | −0.836283 | − | 0.548298i | \(-0.815276\pi\) |
0.892981 | + | 0.450094i | \(0.148609\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.8568 | + | 8.80397i | 1.14532 | + | 0.306887i | 0.781087 | − | 0.624422i | \(-0.214665\pi\) |
0.364230 | + | 0.931309i | \(0.381332\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 5.41936 | + | 5.41936i | 0.188450 | + | 0.188450i | 0.795026 | − | 0.606576i | \(-0.207457\pi\) |
−0.606576 | + | 0.795026i | \(0.707457\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.5670 | − | 21.7667i | −0.436470 | − | 0.755988i | 0.560944 | − | 0.827853i | \(-0.310438\pi\) |
−0.997414 | + | 0.0718654i | \(0.977105\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −14.8925 | − | 8.59820i | −0.516616 | − | 0.298268i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 15.3649 | + | 21.6067i | 0.532364 | + | 0.748629i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.28122 | − | 8.51364i | 0.0788506 | − | 0.294275i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −18.7482 | −0.647259 | −0.323629 | − | 0.946184i | \(-0.604903\pi\) | ||||
−0.323629 | + | 0.946184i | \(0.604903\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.61521 | −0.297076 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.72765 | − | 17.6438i | 0.162829 | − | 0.607686i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15.2367 | − | 18.0247i | −0.523541 | − | 0.619337i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.67987 | − | 2.12458i | −0.126293 | − | 0.0729153i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.10327 | + | 1.91092i | 0.0378196 | + | 0.0655054i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.0238 | − | 10.0238i | −0.343207 | − | 0.343207i | 0.514365 | − | 0.857572i | \(-0.328028\pi\) |
−0.857572 | + | 0.514365i | \(0.828028\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 44.7417 | + | 11.9885i | 1.52835 | + | 0.409520i | 0.922480 | − | 0.386045i | \(-0.126159\pi\) |
0.605869 | + | 0.795565i | \(0.292826\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 9.95564 | − | 17.2437i | 0.339682 | − | 0.588347i | −0.644691 | − | 0.764444i | \(-0.723014\pi\) |
0.984373 | + | 0.176097i | \(0.0563472\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 14.4616 | − | 20.8142i | 0.492850 | − | 0.709347i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 12.7112 | + | 47.4388i | 0.432694 | + | 1.61484i | 0.746525 | + | 0.665358i | \(0.231721\pi\) |
−0.313831 | + | 0.949479i | \(0.601612\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.87697 | − | 1.87697i | 0.0637451 | − | 0.0637451i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 13.4762i | 0.457148i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.44073 | + | 3.14120i | −0.184352 | + | 0.106436i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −12.7788 | + | 3.42406i | −0.432495 | + | 0.115887i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −35.3278 | + | 9.46606i | −1.19294 | + | 0.319646i | −0.800045 | − | 0.599940i | \(-0.795191\pi\) |
−0.392890 | + | 0.919586i | \(0.628525\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 26.2113 | − | 15.1331i | 0.884087 | − | 0.510428i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 21.4260i | 0.721862i | 0.932593 | + | 0.360931i | \(0.117541\pi\) | ||||
−0.932593 | + | 0.360931i | \(0.882459\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.71427 | + | 7.71427i | −0.259606 | + | 0.259606i | −0.824894 | − | 0.565288i | \(-0.808765\pi\) |
0.565288 | + | 0.824894i | \(0.308765\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −9.29035 | − | 34.6721i | −0.311939 | − | 1.16417i | −0.926805 | − | 0.375542i | \(-0.877457\pi\) |
0.614866 | − | 0.788632i | \(-0.289210\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 30.2718 | − | 14.2504i | 1.01528 | − | 0.477943i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.720993 | − | 1.24880i | 0.0241542 | − | 0.0418362i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.58583 | − | 0.960819i | −0.119995 | − | 0.0321526i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 1.02829 | + | 1.02829i | 0.0343336 | + | 0.0343336i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −27.0286 | − | 46.8149i | −0.901454 | − | 1.56136i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 19.8072 | + | 11.4357i | 0.659872 | + | 0.380978i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.71016 | + | 0.848226i | −0.156744 | + | 0.0282272i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.72080 | + | 17.6183i | −0.156752 | + | 0.585005i | 0.842197 | + | 0.539169i | \(0.181262\pi\) |
−0.998949 | + | 0.0458355i | \(0.985405\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.9333 | −0.462137 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 37.9403 | 1.25702 | 0.628509 | − | 0.777802i | \(-0.283666\pi\) | ||||
0.628509 | + | 0.777802i | \(0.283666\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.47998 | + | 24.1836i | −0.214456 | + | 0.800360i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 14.3094 | − | 12.0961i | 0.472539 | − | 0.399449i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.7477 | − | 11.9787i | −0.684404 | − | 0.395141i | 0.117109 | − | 0.993119i | \(-0.462637\pi\) |
−0.801512 | + | 0.597979i | \(0.795971\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 15.2974 | + | 26.4958i | 0.504065 | + | 0.873067i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 18.2310 | + | 18.2310i | 0.600080 | + | 0.600080i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.35878 | − | 0.632032i | −0.0774724 | − | 0.0207587i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.7278 | − | 23.7773i | 0.450396 | − | 0.780108i | −0.548015 | − | 0.836469i | \(-0.684616\pi\) |
0.998410 | + | 0.0563603i | \(0.0179496\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 8.44450 | − | 3.14339i | 0.276757 | − | 0.103020i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.33615 | + | 12.4507i | 0.109221 | + | 0.407617i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 19.0774 | − | 19.0774i | 0.623231 | − | 0.623231i | −0.323125 | − | 0.946356i | \(-0.604733\pi\) |
0.946356 | + | 0.323125i | \(0.104733\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.441985i | 0.0144236i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 51.3328 | − | 29.6370i | 1.67340 | − | 0.966139i | 0.707690 | − | 0.706523i | \(-0.249737\pi\) |
0.965712 | − | 0.259616i | \(-0.0835958\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.82720 | + | 1.29344i | −0.157195 | + | 0.0421203i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −35.5007 | + | 9.51238i | −1.15362 | + | 0.309111i | −0.784414 | − | 0.620238i | \(-0.787036\pi\) |
−0.369203 | + | 0.929349i | \(0.620369\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −8.58938 | + | 4.95908i | −0.278823 | + | 0.160979i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 28.3882i | − | 0.920551i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 36.0464 | − | 36.0464i | 1.16766 | − | 1.16766i | 0.184902 | − | 0.982757i | \(-0.440803\pi\) |
0.982757 | − | 0.184902i | \(-0.0591968\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2.28896 | − | 8.54253i | −0.0739917 | − | 0.276141i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8.32626 | + | 5.78504i | 0.268869 | + | 0.186809i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 23.3431 | − | 40.4313i | 0.753002 | − | 1.30424i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 10.5421 | + | 2.82475i | 0.339715 | + | 0.0910262i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 34.6587 | + | 34.6587i | 1.11455 | + | 1.11455i | 0.992528 | + | 0.122020i | \(0.0389371\pi\) |
0.122020 | + | 0.992528i | \(0.461063\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 2.43772 | + | 4.22225i | 0.0783108 | + | 0.135638i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 26.0964 | + | 15.0668i | 0.837474 | + | 0.483516i | 0.856405 | − | 0.516305i | \(-0.172693\pi\) |
−0.0189309 | + | 0.999821i | \(0.506026\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.08784 | + | 5.80195i | −0.0669331 | + | 0.186002i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.97544 | + | 11.1045i | −0.0951926 | + | 0.355264i | −0.997049 | − | 0.0767731i | \(-0.975538\pi\) |
0.901856 | + | 0.432037i | \(0.142205\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −11.3841 | −0.363836 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.46160 | −0.142448 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −6.45437 | + | 24.0880i | −0.205862 | + | 0.768289i | 0.783323 | + | 0.621616i | \(0.213523\pi\) |
−0.989185 | + | 0.146674i | \(0.953143\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.58358 | + | 7.17956i | −0.0822362 | + | 0.228528i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 0.817251 | + | 0.471840i | 0.0259871 | + | 0.0150036i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.34431 | − | 14.4528i | −0.265066 | − | 0.459107i | 0.702515 | − | 0.711669i | \(-0.252060\pi\) |
−0.967581 | + | 0.252562i | \(0.918727\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −18.9797 | − | 18.9797i | −0.602303 | − | 0.602303i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.1235 | − | 6.46387i | −0.763999 | − | 0.204713i | −0.144280 | − | 0.989537i | \(-0.546087\pi\) |
−0.619719 | + | 0.784824i | \(0.712753\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −2.11482 | + | 3.66298i | −0.0669100 | + | 0.115891i |
(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 | 2100.2.ce.d.1657.3 | yes | 24 | |
5.2 | odd | 4 | inner | 2100.2.ce.d.1993.6 | yes | 24 | |
5.3 | odd | 4 | inner | 2100.2.ce.d.1993.3 | yes | 24 | |
5.4 | even | 2 | inner | 2100.2.ce.d.1657.6 | yes | 24 | |
7.3 | odd | 6 | inner | 2100.2.ce.d.157.3 | ✓ | 24 | |
35.3 | even | 12 | inner | 2100.2.ce.d.493.3 | yes | 24 | |
35.17 | even | 12 | inner | 2100.2.ce.d.493.6 | yes | 24 | |
35.24 | odd | 6 | inner | 2100.2.ce.d.157.5 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2100.2.ce.d.157.3 | ✓ | 24 | 7.3 | odd | 6 | inner | |
2100.2.ce.d.157.5 | yes | 24 | 35.24 | odd | 6 | inner | |
2100.2.ce.d.493.3 | yes | 24 | 35.3 | even | 12 | inner | |
2100.2.ce.d.493.6 | yes | 24 | 35.17 | even | 12 | inner | |
2100.2.ce.d.1657.3 | yes | 24 | 1.1 | even | 1 | trivial | |
2100.2.ce.d.1657.6 | yes | 24 | 5.4 | even | 2 | inner | |
2100.2.ce.d.1993.3 | yes | 24 | 5.3 | odd | 4 | inner | |
2100.2.ce.d.1993.6 | yes | 24 | 5.2 | odd | 4 | inner |