Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2400,2,Mod(49,2400)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2400, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2400.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2400 = 2^{5} \cdot 3 \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2400.d (of order \(2\), degree \(1\), 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: | \(19.1640964851\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.214798336.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 2x^{5} + 9x^{4} - 4x^{3} - 16x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 600) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 49.2 | ||
Root | \(1.41216 - 0.0762223i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2400.49 |
Dual form | 2400.2.d.h.49.7 |
$q$-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 \(\left(\mathbb{Z}/2400\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1601\) | \(1951\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000 | 0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − 1.97676i | − 0.747145i | −0.927601 | − | 0.373573i | \(-0.878133\pi\) | ||||
0.927601 | − | 0.373573i | \(-0.121867\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.43055i | 0.431328i | 0.976468 | + | 0.215664i | \(0.0691915\pi\) | ||||
−0.976468 | + | 0.215664i | \(0.930808\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.241319 | −0.0669300 | −0.0334650 | − | 0.999440i | \(-0.510654\pi\) | ||||
−0.0334650 | + | 0.999440i | \(0.510654\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 7.38407i | 1.79090i | 0.445161 | + | 0.895450i | \(0.353146\pi\) | ||||
−0.445161 | + | 0.895450i | \(0.646854\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.04033i | 0.697500i | 0.937216 | + | 0.348750i | \(0.113394\pi\) | ||||
−0.937216 | + | 0.348750i | \(0.886606\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − 1.97676i | − 0.431365i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − 0.874337i | − 0.182312i | −0.995837 | − | 0.0911560i | \(-0.970944\pi\) | ||||
0.995837 | − | 0.0911560i | \(-0.0290562\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 9.07918i | 1.68596i | 0.537943 | + | 0.842981i | \(0.319201\pi\) | ||||
−0.537943 | + | 0.842981i | \(0.680799\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.44764 | 1.33764 | 0.668818 | − | 0.743426i | \(-0.266800\pi\) | ||||
0.668818 | + | 0.743426i | \(0.266800\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.43055i | 0.249027i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −8.81463 | −1.44912 | −0.724558 | − | 0.689214i | \(-0.757956\pi\) | ||||
−0.724558 | + | 0.689214i | \(0.757956\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.241319 | −0.0386420 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.91319 | −0.298790 | −0.149395 | − | 0.988778i | \(-0.547733\pi\) | ||||
−0.149395 | + | 0.988778i | \(0.547733\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 11.2452 | 1.71487 | 0.857437 | − | 0.514589i | \(-0.172056\pi\) | ||||
0.857437 | + | 0.514589i | \(0.172056\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 3.34374i | − 0.487735i | −0.969809 | − | 0.243867i | \(-0.921584\pi\) | ||||
0.969809 | − | 0.243867i | \(-0.0784162\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.09242 | 0.441774 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.38407i | 1.03398i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.20632 | 1.26459 | 0.632293 | − | 0.774729i | \(-0.282114\pi\) | ||||
0.632293 | + | 0.774729i | \(0.282114\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 3.04033i | 0.402702i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 6.43616i | − 0.837917i | −0.908005 | − | 0.418958i | \(-0.862395\pi\) | ||||
0.908005 | − | 0.418958i | \(-0.137605\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.57331i | 0.585552i | 0.956181 | + | 0.292776i | \(0.0945790\pi\) | ||||
−0.956181 | + | 0.292776i | \(0.905421\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − 1.97676i | − 0.249048i | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.86671 | 0.594563 | 0.297282 | − | 0.954790i | \(-0.403920\pi\) | ||||
0.297282 | + | 0.954790i | \(0.403920\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 0.874337i | − 0.105258i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.21808 | 0.975307 | 0.487653 | − | 0.873037i | \(-0.337853\pi\) | ||||
0.487653 | + | 0.873037i | \(0.337853\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 4.12714i | − 0.483045i | −0.970395 | − | 0.241523i | \(-0.922353\pi\) | ||||
0.970395 | − | 0.241523i | \(-0.0776468\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.82786 | 0.322264 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.6757 | −1.53864 | −0.769320 | − | 0.638864i | \(-0.779405\pi\) | ||||
−0.769320 | + | 0.638864i | \(0.779405\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 12.3320 | 1.35361 | 0.676806 | − | 0.736162i | \(-0.263364\pi\) | ||||
0.676806 | + | 0.736162i | \(0.263364\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 9.07918i | 0.973391i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 8.08066 | 0.856548 | 0.428274 | − | 0.903649i | \(-0.359122\pi\) | ||||
0.428274 | + | 0.903649i | \(0.359122\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.477031i | 0.0500064i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 7.44764 | 0.772285 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 10.6757i | − 1.08396i | −0.840393 | − | 0.541978i | \(-0.817676\pi\) | ||||
0.840393 | − | 0.541978i | \(-0.182324\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.43055i | 0.143776i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.2063i | 1.31408i | 0.753856 | + | 0.657039i | \(0.228191\pi\) | ||||
−0.753856 | + | 0.657039i | \(0.771809\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 19.4244i | − 1.91394i | −0.290181 | − | 0.956972i | \(-0.593716\pi\) | ||||
0.290181 | − | 0.956972i | \(-0.406284\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.8085 | −1.43159 | −0.715795 | − | 0.698311i | \(-0.753935\pi\) | ||||
−0.715795 | + | 0.698311i | \(0.753935\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.2296i | 1.45873i | 0.684126 | + | 0.729364i | \(0.260184\pi\) | ||||
−0.684126 | + | 0.729364i | \(0.739816\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.81463 | −0.836647 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 1.13890i | − 0.107138i | −0.998564 | − | 0.0535692i | \(-0.982940\pi\) | ||||
0.998564 | − | 0.0535692i | \(-0.0170598\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −0.241319 | −0.0223100 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 14.5965 | 1.33806 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.95352 | 0.813956 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.91319 | −0.172507 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.43616i | 0.216174i | 0.994141 | + | 0.108087i | \(0.0344725\pi\) | ||||
−0.994141 | + | 0.108087i | \(0.965527\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.2452 | 0.990083 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 6.90143i | 0.602981i | 0.953469 | + | 0.301491i | \(0.0974842\pi\) | ||||
−0.953469 | + | 0.301491i | \(0.902516\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.01001 | 0.521134 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.39022i | 0.460518i | 0.973129 | + | 0.230259i | \(0.0739573\pi\) | ||||
−0.973129 | + | 0.230259i | \(0.926043\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.4244i | 1.47792i | 0.673750 | + | 0.738959i | \(0.264682\pi\) | ||||
−0.673750 | + | 0.738959i | \(0.735318\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 3.34374i | − 0.281594i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 0.345220i | − 0.0288687i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.09242 | 0.255058 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 2.28551i | 0.187236i | 0.995608 | + | 0.0936180i | \(0.0298432\pi\) | ||||
−0.995608 | + | 0.0936180i | \(0.970157\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −6.66425 | −0.542329 | −0.271164 | − | 0.962533i | \(-0.587409\pi\) | ||||
−0.271164 | + | 0.962533i | \(0.587409\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.38407i | 0.596967i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −17.4144 | −1.38982 | −0.694910 | − | 0.719097i | \(-0.744556\pi\) | ||||
−0.694910 | + | 0.719097i | \(0.744556\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 9.20632 | 0.730109 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.72836 | −0.136214 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −4.66187 | −0.365145 | −0.182573 | − | 0.983192i | \(-0.558443\pi\) | ||||
−0.182573 | + | 0.983192i | \(0.558443\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − 0.137419i | − 0.0106338i | −0.999986 | − | 0.00531690i | \(-0.998308\pi\) | ||||
0.999986 | − | 0.00531690i | \(-0.00169243\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −12.9418 | −0.995520 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.04033i | 0.232500i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.96675 | −0.301587 | −0.150793 | − | 0.988565i | \(-0.548183\pi\) | ||||
−0.150793 | + | 0.988565i | \(0.548183\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | − 6.43616i | − 0.483771i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.68749i | 0.350359i | 0.984537 | + | 0.175180i | \(0.0560506\pi\) | ||||
−0.984537 | + | 0.175180i | \(0.943949\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 9.10242i | 0.676578i | 0.941042 | + | 0.338289i | \(0.109848\pi\) | ||||
−0.941042 | + | 0.338289i | \(0.890152\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 4.57331i | 0.338068i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.5633 | −0.772465 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 1.97676i | − 0.143788i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.2063 | −1.10029 | −0.550145 | − | 0.835069i | \(-0.685428\pi\) | ||||
−0.550145 | + | 0.835069i | \(0.685428\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | − 20.7564i | − 1.49408i | −0.664780 | − | 0.747039i | \(-0.731475\pi\) | ||||
0.664780 | − | 0.747039i | \(-0.268525\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 23.2508 | 1.65655 | 0.828275 | − | 0.560322i | \(-0.189323\pi\) | ||||
0.828275 | + | 0.560322i | \(0.189323\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.21633 | −0.511552 | −0.255776 | − | 0.966736i | \(-0.582331\pi\) | ||||
−0.255776 | + | 0.966736i | \(0.582331\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.86671 | 0.343271 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 17.9474 | 1.25966 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − 0.874337i | − 0.0607707i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.34935 | −0.300851 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.38407i | 0.301812i | 0.988548 | + | 0.150906i | \(0.0482191\pi\) | ||||
−0.988548 | + | 0.150906i | \(0.951781\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 8.21808 | 0.563094 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − 14.7222i | − 0.999409i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 4.12714i | − 0.278886i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 1.78192i | − 0.119865i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.98852i | 0.334056i | 0.985952 | + | 0.167028i | \(0.0534170\pi\) | ||||
−0.985952 | + | 0.167028i | \(0.946583\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −11.2569 | −0.747149 | −0.373574 | − | 0.927600i | \(-0.621868\pi\) | ||||
−0.373574 | + | 0.927600i | \(0.621868\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 15.8364i | − 1.04650i | −0.852180 | − | 0.523249i | \(-0.824720\pi\) | ||||
0.852180 | − | 0.523249i | \(-0.175280\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.82786 | 0.186059 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − 10.9591i | − 0.717956i | −0.933346 | − | 0.358978i | \(-0.883125\pi\) | ||||
0.933346 | − | 0.358978i | \(-0.116875\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −13.6757 | −0.888334 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.3182 | 1.12022 | 0.560111 | − | 0.828418i | \(-0.310758\pi\) | ||||
0.560111 | + | 0.828418i | \(0.310758\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.76869 | 0.307178 | 0.153589 | − | 0.988135i | \(-0.450917\pi\) | ||||
0.153589 | + | 0.988135i | \(0.450917\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000 | 0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − 0.733691i | − 0.0466836i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 12.3320 | 0.781508 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 6.15837i | − 0.388713i | −0.980931 | − | 0.194356i | \(-0.937738\pi\) | ||||
0.980931 | − | 0.194356i | \(-0.0622618\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.25079 | 0.0786362 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 14.1584i | 0.883175i | 0.897218 | + | 0.441587i | \(0.145584\pi\) | ||||
−0.897218 | + | 0.441587i | \(0.854416\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 17.4244i | 1.08270i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 9.07918i | 0.561987i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.5960i | 0.961691i | 0.876805 | + | 0.480845i | \(0.159670\pi\) | ||||
−0.876805 | + | 0.480845i | \(0.840330\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.08066 | 0.494528 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − 11.3182i | − 0.690084i | −0.938587 | − | 0.345042i | \(-0.887865\pi\) | ||||
0.938587 | − | 0.345042i | \(-0.112135\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.20485 | 0.376918 | 0.188459 | − | 0.982081i | \(-0.439651\pi\) | ||||
0.188459 | + | 0.982081i | \(0.439651\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0.477031i | 0.0288712i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.9288 | 1.13732 | 0.568661 | − | 0.822572i | \(-0.307462\pi\) | ||||
0.568661 | + | 0.822572i | \(0.307462\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.44764 | 0.445879 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.6231 | −1.28993 | −0.644963 | − | 0.764214i | \(-0.723127\pi\) | ||||
−0.644963 | + | 0.764214i | \(0.723127\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −29.1522 | −1.73292 | −0.866460 | − | 0.499247i | \(-0.833610\pi\) | ||||
−0.866460 | + | 0.499247i | \(0.833610\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.78192i | 0.223240i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −37.5245 | −2.20733 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − 10.6757i | − 0.625822i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.32427 | 0.135785 | 0.0678927 | − | 0.997693i | \(-0.478372\pi\) | ||||
0.0678927 | + | 0.997693i | \(0.478372\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1.43055i | 0.0830090i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.210995i | 0.0122021i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 22.2290i | − 1.28126i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 13.2063i | 0.758683i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.52297 | −0.201066 | −0.100533 | − | 0.994934i | \(-0.532055\pi\) | ||||
−0.100533 | + | 0.994934i | \(0.532055\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 19.4244i | − 1.10502i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 21.6757 | 1.22912 | 0.614559 | − | 0.788871i | \(-0.289334\pi\) | ||||
0.614559 | + | 0.788871i | \(0.289334\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 12.5486i | − 0.709288i | −0.935001 | − | 0.354644i | \(-0.884602\pi\) | ||||
0.935001 | − | 0.354644i | \(-0.115398\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −10.8611 | −0.610020 | −0.305010 | − | 0.952349i | \(-0.598660\pi\) | ||||
−0.305010 | + | 0.952349i | \(0.598660\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.9882 | −0.727202 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −14.8085 | −0.826529 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −22.4500 | −1.24915 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 15.2296i | 0.842197i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.60978 | −0.364409 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 1.23185i | − 0.0677088i | −0.999427 | − | 0.0338544i | \(-0.989222\pi\) | ||||
0.999427 | − | 0.0338544i | \(-0.0107783\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −8.81463 | −0.483038 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 4.13890i | − 0.225460i | −0.993626 | − | 0.112730i | \(-0.964040\pi\) | ||||
0.993626 | − | 0.112730i | \(-0.0359595\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | − 1.13890i | − 0.0618564i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.6542i | 0.576959i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − 19.9503i | − 1.07721i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 17.4586 | 0.937226 | 0.468613 | − | 0.883404i | \(-0.344754\pi\) | ||||
0.468613 | + | 0.883404i | \(0.344754\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 21.2196i | 1.13586i | 0.823078 | + | 0.567928i | \(0.192255\pi\) | ||||
−0.823078 | + | 0.567928i | \(0.807745\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −0.241319 | −0.0128807 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 21.0398i | 1.11984i | 0.828548 | + | 0.559918i | \(0.189167\pi\) | ||||
−0.828548 | + | 0.559918i | \(0.810833\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 14.5965 | 0.772531 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 23.5153 | 1.24109 | 0.620546 | − | 0.784170i | \(-0.286911\pi\) | ||||
0.620546 | + | 0.784170i | \(0.286911\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.75639 | 0.513494 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 8.95352 | 0.469938 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 25.4012i | − 1.32593i | −0.748650 | − | 0.662965i | \(-0.769298\pi\) | ||||
0.748650 | − | 0.662965i | \(-0.230702\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −1.91319 | −0.0995967 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − 18.1987i | − 0.944829i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.0677 | 0.521286 | 0.260643 | − | 0.965435i | \(-0.416065\pi\) | ||||
0.260643 | + | 0.965435i | \(0.416065\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − 2.19098i | − 0.112841i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − 18.9674i | − 0.974289i | −0.873321 | − | 0.487145i | \(-0.838038\pi\) | ||||
0.873321 | − | 0.487145i | \(-0.161962\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.43616i | 0.124808i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 28.7446i | 1.46878i | 0.678727 | + | 0.734391i | \(0.262532\pi\) | ||||
−0.678727 | + | 0.734391i | \(0.737468\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.2452 | 0.571624 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − 29.8161i | − 1.51174i | −0.654724 | − | 0.755868i | \(-0.727215\pi\) | ||||
0.654724 | − | 0.755868i | \(-0.272785\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 6.45617 | 0.326503 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.90143i | 0.348131i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.73167 | 0.137099 | 0.0685494 | − | 0.997648i | \(-0.478163\pi\) | ||||
0.0685494 | + | 0.997648i | \(0.478163\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 6.01001 | 0.300877 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 25.8744 | 1.29211 | 0.646054 | − | 0.763292i | \(-0.276418\pi\) | ||||
0.646054 | + | 0.763292i | \(0.276418\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.79726 | −0.0895279 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − 12.6098i | − 0.625044i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −22.4786 | −1.11150 | −0.555748 | − | 0.831351i | \(-0.687568\pi\) | ||||
−0.555748 | + | 0.831351i | \(0.687568\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.39022i | 0.265880i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −12.7227 | −0.626045 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 17.4244i | 0.853277i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 24.5307i | − 1.19840i | −0.800598 | − | 0.599201i | \(-0.795485\pi\) | ||||
0.800598 | − | 0.599201i | \(-0.204515\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − 33.3856i | − 1.62712i | −0.581483 | − | 0.813558i | \(-0.697527\pi\) | ||||
0.581483 | − | 0.813558i | \(-0.302473\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 3.34374i | − 0.162578i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 9.04033 | 0.437492 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 0.345220i | − 0.0166674i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.6548 | −0.561391 | −0.280696 | − | 0.959797i | \(-0.590565\pi\) | ||||
−0.280696 | + | 0.959797i | \(0.590565\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 19.7681i | 0.949996i | 0.879987 | + | 0.474998i | \(0.157551\pi\) | ||||
−0.879987 | + | 0.474998i | \(0.842449\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.65827 | 0.127163 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −25.1699 | −1.20129 | −0.600646 | − | 0.799515i | \(-0.705090\pi\) | ||||
−0.600646 | + | 0.799515i | \(0.705090\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.09242 | 0.147258 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −19.5515 | −0.928922 | −0.464461 | − | 0.885594i | \(-0.653752\pi\) | ||||
−0.464461 | + | 0.885594i | \(0.653752\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 2.28551i | 0.108101i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 19.9612 | 0.942029 | 0.471014 | − | 0.882125i | \(-0.343888\pi\) | ||||
0.471014 | + | 0.882125i | \(0.343888\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 2.73692i | − 0.128876i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.66425 | −0.313114 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 5.01176i | 0.234440i | 0.993106 | + | 0.117220i | \(0.0373983\pi\) | ||||
−0.993106 | + | 0.117220i | \(0.962602\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.38407i | 0.344659i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 5.12566i | − 0.238726i | −0.992851 | − | 0.119363i | \(-0.961915\pi\) | ||||
0.992851 | − | 0.119363i | \(-0.0380852\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.79515i | 0.269324i | 0.990892 | + | 0.134662i | \(0.0429948\pi\) | ||||
−0.990892 | + | 0.134662i | \(0.957005\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 16.8208 | 0.778373 | 0.389186 | − | 0.921159i | \(-0.372756\pi\) | ||||
0.389186 | + | 0.921159i | \(0.372756\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 9.62032i | − 0.444225i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −17.4144 | −0.802413 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 16.0868i | 0.739672i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.20632 | 0.421529 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −36.9065 | −1.68630 | −0.843151 | − | 0.537678i | \(-0.819302\pi\) | ||||
−0.843151 | + | 0.537678i | \(0.819302\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.12714 | 0.0969892 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.72836 | −0.0786429 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − 5.14984i | − 0.233361i | −0.993169 | − | 0.116681i | \(-0.962775\pi\) | ||||
0.993169 | − | 0.116681i | \(-0.0372254\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −4.66187 | −0.210817 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 23.1154i | − 1.04318i | −0.853195 | − | 0.521591i | \(-0.825339\pi\) | ||||
0.853195 | − | 0.521591i | \(-0.174661\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −67.0414 | −3.01939 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − 16.2452i | − 0.728696i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 14.3111i | − 0.640654i | −0.947307 | − | 0.320327i | \(-0.896207\pi\) | ||||
0.947307 | − | 0.320327i | \(-0.103793\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 0.137419i | − 0.00613942i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 15.4224i | − 0.687650i | −0.939034 | − | 0.343825i | \(-0.888277\pi\) | ||||
0.939034 | − | 0.343825i | \(-0.111723\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.9418 | −0.574764 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 43.1578i | 1.91294i | 0.291835 | + | 0.956469i | \(0.405734\pi\) | ||||
−0.291835 | + | 0.956469i | \(0.594266\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.15837 | −0.360905 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 3.04033i | 0.134234i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.78340 | 0.210374 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.96675 | −0.174121 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −17.8232 | −0.780848 | −0.390424 | − | 0.920635i | \(-0.627672\pi\) | ||||
−0.390424 | + | 0.920635i | \(0.627672\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −24.7502 | −1.08225 | −0.541126 | − | 0.840941i | \(-0.682002\pi\) | ||||
−0.541126 | + | 0.840941i | \(0.682002\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 54.9939i | 2.39557i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.2355 | 0.966762 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − 6.43616i | − 0.279306i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.461690 | 0.0199980 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.68749i | 0.202280i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.42386i | 0.190549i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 16.9982i | − 0.730812i | −0.930848 | − | 0.365406i | \(-0.880930\pi\) | ||||
0.930848 | − | 0.365406i | \(-0.119070\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.10242i | 0.390622i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −37.2385 | −1.59220 | −0.796101 | − | 0.605163i | \(-0.793108\pi\) | ||||
−0.796101 | + | 0.605163i | \(0.793108\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.57331i | 0.195184i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −27.6037 | −1.17596 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 27.0336i | 1.14959i | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.7604 | −0.625420 | −0.312710 | − | 0.949849i | \(-0.601237\pi\) | ||||
−0.312710 | + | 0.949849i | \(0.601237\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.71368 | −0.114776 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.5633 | −0.445983 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.00561 | 0.126671 | 0.0633356 | − | 0.997992i | \(-0.479826\pi\) | ||||
0.0633356 | + | 0.997992i | \(0.479826\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − 1.97676i | − 0.0830161i | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.1840 | 0.971923 | 0.485962 | − | 0.873980i | \(-0.338469\pi\) | ||||
0.485962 | + | 0.873980i | \(0.338469\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.202739i | 0.00848438i | 0.999991 | + | 0.00424219i | \(0.00135033\pi\) | ||||
−0.999991 | + | 0.00424219i | \(0.998650\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −15.2063 | −0.635253 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 21.8023i | − 0.907643i | −0.891093 | − | 0.453821i | \(-0.850060\pi\) | ||||
0.891093 | − | 0.453821i | \(-0.149940\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 20.7564i | − 0.862606i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 24.3774i | − 1.01134i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 13.1701i | 0.545451i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 36.7126 | 1.51529 | 0.757645 | − | 0.652667i | \(-0.226350\pi\) | ||||
0.757645 | + | 0.652667i | \(0.226350\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 22.6433i | 0.933001i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 23.2508 | 0.956409 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 10.6036i | 0.435439i | 0.976011 | + | 0.217719i | \(0.0698618\pi\) | ||||
−0.976011 | + | 0.217719i | \(0.930138\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −7.21633 | −0.295345 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −25.7988 | −1.05411 | −0.527056 | − | 0.849831i | \(-0.676704\pi\) | ||||
−0.527056 | + | 0.849831i | \(0.676704\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 18.5021 | 0.754717 | 0.377358 | − | 0.926067i | \(-0.376832\pi\) | ||||
0.377358 | + | 0.926067i | \(0.376832\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.86671 | 0.198188 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 37.5828i | − 1.52544i | −0.646730 | − | 0.762719i | \(-0.723864\pi\) | ||||
0.646730 | − | 0.762719i | \(-0.276136\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 17.9474 | 0.727264 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0.806910i | 0.0326441i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.93405 | 0.199284 | 0.0996422 | − | 0.995023i | \(-0.468230\pi\) | ||||
0.0996422 | + | 0.995023i | \(0.468230\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.26043i | 0.252035i | 0.992028 | + | 0.126018i | \(0.0402196\pi\) | ||||
−0.992028 | + | 0.126018i | \(0.959780\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 8.02562i | − 0.322577i | −0.986907 | − | 0.161288i | \(-0.948435\pi\) | ||||
0.986907 | − | 0.161288i | \(-0.0515649\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − 0.874337i | − 0.0350860i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − 15.9735i | − 0.639966i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4.34935 | −0.173696 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 65.0878i | − 2.59522i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.5248 | 1.05594 | 0.527968 | − | 0.849264i | \(-0.322954\pi\) | ||||
0.527968 | + | 0.849264i | \(0.322954\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 4.38407i | 0.174251i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.746260 | −0.0295679 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 8.21808 | 0.325102 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −26.5863 | −1.05009 | −0.525047 | − | 0.851073i | \(-0.675952\pi\) | ||||
−0.525047 | + | 0.851073i | \(0.675952\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.89233 | 0.114062 | 0.0570312 | − | 0.998372i | \(-0.481837\pi\) | ||||
0.0570312 | + | 0.998372i | \(0.481837\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − 12.3472i | − 0.485420i | −0.970099 | − | 0.242710i | \(-0.921964\pi\) | ||||
0.970099 | − | 0.242710i | \(-0.0780363\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.20726 | 0.361417 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | − 14.7222i | − 0.577009i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −39.0507 | −1.52817 | −0.764086 | − | 0.645114i | \(-0.776810\pi\) | ||||
−0.764086 | + | 0.645114i | \(0.776810\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 4.12714i | − 0.161015i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 23.7738i | − 0.926094i | −0.886334 | − | 0.463047i | \(-0.846756\pi\) | ||||
0.886334 | − | 0.463047i | \(-0.153244\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.5051i | 0.836450i | 0.908343 | + | 0.418225i | \(0.137348\pi\) | ||||
−0.908343 | + | 0.418225i | \(0.862652\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 1.78192i | − 0.0692040i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 7.93827 | 0.307371 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.98852i | 0.192867i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −6.54235 | −0.252565 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − 36.1896i | − 1.39501i | −0.716582 | − | 0.697503i | \(-0.754294\pi\) | ||||
0.716582 | − | 0.697503i | \(-0.245706\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 9.17214 | 0.352514 | 0.176257 | − | 0.984344i | \(-0.443601\pi\) | ||||
0.176257 | + | 0.984344i | \(0.443601\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −21.1034 | −0.809873 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −11.2569 | −0.431367 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.3974 | −0.627429 | −0.313714 | − | 0.949517i | \(-0.601573\pi\) | ||||
−0.313714 | + | 0.949517i | \(0.601573\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 15.8364i | − 0.604196i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.22166 | −0.0846387 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − 24.4904i | − 0.931657i | −0.884875 | − | 0.465828i | \(-0.845756\pi\) | ||||
0.884875 | − | 0.465828i | \(-0.154244\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.82786 | 0.107421 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − 14.1271i | − 0.535104i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 10.9591i | − 0.414512i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 12.3887i | − 0.467916i | −0.972247 | − | 0.233958i | \(-0.924832\pi\) | ||||
0.972247 | − | 0.233958i | \(-0.0751679\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 26.7994i | − 1.01076i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 26.1057 | 0.981807 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 33.4144i | − 1.25490i | −0.778655 | − | 0.627452i | \(-0.784098\pi\) | ||||
0.778655 | − | 0.627452i | \(-0.215902\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.6757 | −0.512880 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − 6.51175i | − 0.243867i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 17.3182 | 0.646761 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −33.8938 | −1.26403 | −0.632013 | − | 0.774958i | \(-0.717771\pi\) | ||||
−0.632013 | + | 0.774958i | \(0.717771\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −38.3974 | −1.42999 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 4.76869 | 0.177349 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 14.1846i | 0.526076i | 0.964785 | + | 0.263038i | \(0.0847245\pi\) | ||||
−0.964785 | + | 0.263038i | \(0.915275\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 83.0352i | 3.07117i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −8.09296 | −0.298920 | −0.149460 | − | 0.988768i | \(-0.547754\pi\) | ||||
−0.149460 | + | 0.988768i | \(0.547754\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.96208i | 0.256452i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 22.0919i | − 0.812663i | −0.913726 | − | 0.406331i | \(-0.866808\pi\) | ||||
0.913726 | − | 0.406331i | \(-0.133192\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − 0.733691i | − 0.0269528i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.78340i | 0.322232i | 0.986936 | + | 0.161116i | \(0.0515093\pi\) | ||||
−0.986936 | + | 0.161116i | \(0.948491\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.3320 | 0.451204 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 29.2728i | 1.06961i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −13.3779 | −0.488167 | −0.244084 | − | 0.969754i | \(-0.578487\pi\) | ||||
−0.244084 | + | 0.969754i | \(0.578487\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − 6.15837i | − 0.224423i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 9.72450 | 0.353443 | 0.176721 | − | 0.984261i | \(-0.443451\pi\) | ||||
0.176721 | + | 0.984261i | \(0.443451\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 1.25079 | 0.0454006 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 33.8835 | 1.22828 | 0.614138 | − | 0.789198i | \(-0.289504\pi\) | ||||
0.614138 | + | 0.789198i | \(0.289504\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 30.1052 | 1.08988 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.55317i | 0.0560817i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −18.7334 | −0.675545 | −0.337772 | − | 0.941228i | \(-0.609673\pi\) | ||||
−0.337772 | + | 0.941228i | \(0.609673\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.1584i | 0.509901i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 22.5006 | 0.809292 | 0.404646 | − | 0.914474i | \(-0.367395\pi\) | ||||
0.404646 | + | 0.914474i | \(0.367395\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 17.4244i | 0.625097i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 5.81673i | − 0.208406i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 11.7564i | 0.420677i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 9.07918i | 0.324464i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.1063 | 1.00188 | 0.500940 | − | 0.865482i | \(-0.332988\pi\) | ||||
0.500940 | + | 0.865482i | \(0.332988\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 15.5960i | 0.555232i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.25133 | −0.0800479 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − 1.10363i | − 0.0391910i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −38.1461 | −1.35120 | −0.675602 | − | 0.737267i | \(-0.736116\pi\) | ||||
−0.675602 | + | 0.737267i | \(0.736116\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 24.6904 | 0.873485 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 8.08066 | 0.285516 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 5.90409 | 0.208351 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − 11.3182i | − 0.398420i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.0745 | 0.354201 | 0.177101 | − | 0.984193i | \(-0.443328\pi\) | ||||
0.177101 | + | 0.984193i | \(0.443328\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 40.6001i | − 1.42566i | −0.701335 | − | 0.712832i | \(-0.747412\pi\) | ||||
0.701335 | − | 0.712832i | \(-0.252588\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 6.20485 | 0.217613 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34.1891i | 1.19612i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0.477031i | 0.0166688i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 10.3397i | − 0.360858i | −0.983588 | − | 0.180429i | \(-0.942251\pi\) | ||||
0.983588 | − | 0.180429i | \(-0.0577486\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.5013i | 0.993493i | 0.867896 | + | 0.496746i | \(0.165472\pi\) | ||||
−0.867896 | + | 0.496746i | \(0.834528\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −32.1957 | −1.11956 | −0.559778 | − | 0.828643i | \(-0.689114\pi\) | ||||
−0.559778 | + | 0.828643i | \(0.689114\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 31.5286i | 1.09503i | 0.836795 | + | 0.547516i | \(0.184427\pi\) | ||||
−0.836795 | + | 0.547516i | \(0.815573\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.9288 | 0.656633 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 22.8346i | 0.791173i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 7.44764 | 0.257428 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 54.9816 | 1.89818 | 0.949089 | − | 0.315009i | \(-0.102008\pi\) | ||||
0.949089 | + | 0.315009i | \(0.102008\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −53.4316 | −1.84247 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −21.6231 | −0.744739 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − 17.6990i | − 0.608144i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −29.1522 | −1.00050 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 7.70696i | 0.264191i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −4.22607 | −0.144698 | −0.0723489 | − | 0.997379i | \(-0.523050\pi\) | ||||
−0.0723489 | + | 0.997379i | \(0.523050\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 54.8223i | − 1.87270i | −0.351074 | − | 0.936348i | \(-0.614183\pi\) | ||||
0.351074 | − | 0.936348i | \(-0.385817\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.2126i | 0.484926i | 0.970161 | + | 0.242463i | \(0.0779554\pi\) | ||||
−0.970161 | + | 0.242463i | \(0.922045\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.78192i | 0.128887i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − 40.7446i | − 1.38696i | −0.720474 | − | 0.693482i | \(-0.756076\pi\) | ||||
0.720474 | − | 0.693482i | \(-0.243924\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −37.5245 | −1.27440 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 19.5638i | − 0.663658i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.17443 | −0.0397941 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 10.6757i | − 0.361319i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.4568 | −1.16352 | −0.581762 | − | 0.813359i | \(-0.697637\pi\) | ||||
−0.581762 | + | 0.813359i | \(0.697637\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.32427 | 0.0783957 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 23.8528 | 0.803623 | 0.401811 | − | 0.915722i | \(-0.368381\pi\) | ||||
0.401811 | + | 0.915722i | \(0.368381\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −24.2417 | −0.815798 | −0.407899 | − | 0.913027i | \(-0.633738\pi\) | ||||
−0.407899 | + | 0.913027i | \(0.633738\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 39.1843i | − 1.31568i | −0.753158 | − | 0.657840i | \(-0.771470\pi\) | ||||
0.753158 | − | 0.657840i | \(-0.228530\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.81571 | 0.161514 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.43055i | 0.0479253i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 10.1661 | 0.340195 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0.210995i | 0.00704490i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 67.6185i | 2.25520i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 67.9802i | 2.26475i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − 22.2290i | − 0.739736i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 18.9418 | 0.628951 | 0.314475 | − | 0.949266i | \(-0.398171\pi\) | ||||
0.314475 | + | 0.949266i | \(0.398171\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 13.2063i | 0.438026i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.8493 | −0.591375 | −0.295688 | − | 0.955285i | \(-0.595549\pi\) | ||||
−0.295688 | + | 0.955285i | \(0.595549\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 17.6415i | 0.583850i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.6425 | 0.450515 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 24.4983 | 0.808126 | 0.404063 | − | 0.914731i | \(-0.367598\pi\) | ||||
0.404063 | + | 0.914731i | \(0.367598\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −3.52297 | −0.116086 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.98318 | −0.0652772 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 19.4244i | − 0.637981i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −11.5577 | −0.379196 | −0.189598 | − | 0.981862i | \(-0.560718\pi\) | ||||
−0.189598 | + | 0.981862i | \(0.560718\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 9.40197i | 0.308137i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 21.6757 | 0.709632 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 59.5587i | 1.94570i | 0.231440 | + | 0.972849i | \(0.425656\pi\) | ||||
−0.231440 | + | 0.972849i | \(0.574344\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 12.5486i | − 0.409508i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 55.9289i | − 1.82323i | −0.411044 | − | 0.911615i | \(-0.634836\pi\) | ||||
0.411044 | − | 0.911615i | \(-0.365164\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.67277i | 0.0544730i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −30.0945 | −0.977941 | −0.488970 | − | 0.872300i | \(-0.662627\pi\) | ||||
−0.488970 | + | 0.872300i | \(0.662627\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.995959i | 0.0323302i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −10.8611 | −0.352195 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.4097i | 0.401989i | 0.979592 | + | 0.200995i | \(0.0644174\pi\) | ||||
−0.979592 | + | 0.200995i | \(0.935583\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.9882 | −0.419850 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 10.6552 | 0.344074 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 24.4674 | 0.789271 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −14.8085 | −0.477196 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 41.8371i | 1.34539i | 0.739920 | + | 0.672694i | \(0.234863\pi\) | ||||
−0.739920 | + | 0.672694i | \(0.765137\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −22.4500 | −0.721199 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 40.6875i | − 1.30572i | −0.757477 | − | 0.652862i | \(-0.773568\pi\) | ||||
0.757477 | − | 0.652862i | \(-0.226432\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 34.4439 | 1.10422 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − 1.67923i | − 0.0537233i | −0.999639 | − | 0.0268617i | \(-0.991449\pi\) | ||||
0.999639 | − | 0.0268617i | \(-0.00855136\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.5598i | 0.369453i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 15.2296i | 0.486243i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.4944i | 0.430404i | 0.976570 | + | 0.215202i | \(0.0690411\pi\) | ||||
−0.976570 | + | 0.215202i | \(0.930959\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −6.60978 | −0.210392 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 9.83208i | − 0.312642i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10.8502 | 0.344667 | 0.172333 | − | 0.985039i | \(-0.444869\pi\) | ||||
0.172333 | + | 0.985039i | \(0.444869\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 1.23185i | − 0.0390917i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.0972 | 1.23822 | 0.619110 | − | 0.785304i | \(-0.287493\pi\) | ||||
0.619110 | + | 0.785304i | \(0.287493\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −8.81463 | −0.278882 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))