Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(1009,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.1009");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.r (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.309123.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 2017.1 | ||
Root | \(0.500000 - 0.224437i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3024.2017 |
Dual form | 3024.2.r.g.1009.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.79418 | − | 3.10761i | −0.802383 | − | 1.38977i | −0.918044 | − | 0.396479i | \(-0.870232\pi\) |
0.115661 | − | 0.993289i | \(-0.463101\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.500000 | + | 0.866025i | −0.188982 | + | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.40545 | − | 2.43430i | 0.423758 | − | 0.733970i | −0.572546 | − | 0.819873i | \(-0.694044\pi\) |
0.996304 | + | 0.0859026i | \(0.0273774\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.500000 | − | 0.866025i | −0.138675 | − | 0.240192i | 0.788320 | − | 0.615265i | \(-0.210951\pi\) |
−0.926995 | + | 0.375073i | \(0.877618\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 4.11126 | 0.997128 | 0.498564 | − | 0.866853i | \(-0.333861\pi\) | ||||
0.498564 | + | 0.866853i | \(0.333861\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.888736 | 0.203890 | 0.101945 | − | 0.994790i | \(-0.467493\pi\) | ||||
0.101945 | + | 0.994790i | \(0.467493\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.93818 | − | 5.08907i | −0.612652 | − | 1.06115i | −0.990792 | − | 0.135396i | \(-0.956769\pi\) |
0.378139 | − | 0.925749i | \(-0.376564\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.93818 | + | 6.82112i | −0.787636 | + | 1.36422i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.849814 | + | 1.47192i | −0.157807 | + | 0.273329i | −0.934077 | − | 0.357071i | \(-0.883776\pi\) |
0.776271 | + | 0.630399i | \(0.217109\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −3.49381 | − | 6.05146i | −0.627507 | − | 1.08687i | −0.988050 | − | 0.154131i | \(-0.950742\pi\) |
0.360544 | − | 0.932742i | \(-0.382591\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.58836 | 0.606544 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 4.76509 | 0.783376 | 0.391688 | − | 0.920098i | \(-0.371891\pi\) | ||||
0.391688 | + | 0.920098i | \(0.371891\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.70582 | − | 4.68661i | −0.422578 | − | 0.731926i | 0.573613 | − | 0.819126i | \(-0.305541\pi\) |
−0.996191 | + | 0.0872002i | \(0.972208\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.60507 | − | 4.51212i | 0.397270 | − | 0.688092i | −0.596118 | − | 0.802897i | \(-0.703291\pi\) |
0.993388 | + | 0.114805i | \(0.0366243\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 1.33310 | − | 2.30900i | 0.194453 | − | 0.336803i | −0.752268 | − | 0.658857i | \(-0.771040\pi\) |
0.946721 | + | 0.322055i | \(0.104373\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | − | 0.866025i | −0.0714286 | − | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 0.123644 | 0.0169838 | 0.00849190 | − | 0.999964i | \(-0.497297\pi\) | ||||
0.00849190 | + | 0.999964i | \(0.497297\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −10.0865 | −1.36006 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 4.43818 | + | 7.68715i | 0.577802 | + | 1.00078i | 0.995731 | + | 0.0923022i | \(0.0294226\pi\) |
−0.417929 | + | 0.908479i | \(0.637244\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.93818 | + | 3.35702i | −0.248158 | + | 0.429823i | −0.963015 | − | 0.269448i | \(-0.913159\pi\) |
0.714857 | + | 0.699271i | \(0.246492\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.79418 | + | 3.10761i | −0.222541 | + | 0.385452i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.15452 | + | 10.6599i | 0.751894 | + | 1.30232i | 0.946904 | + | 0.321517i | \(0.104193\pi\) |
−0.195010 | + | 0.980801i | \(0.562474\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.87636 | −0.341361 | −0.170680 | − | 0.985326i | \(-0.554597\pi\) | ||||
−0.170680 | + | 0.985326i | \(0.554597\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.6414 | −1.24549 | −0.622744 | − | 0.782426i | \(-0.713982\pi\) | ||||
−0.622744 | + | 0.782426i | \(0.713982\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 1.40545 | + | 2.43430i | 0.160165 | + | 0.277415i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.54325 | + | 6.13709i | −0.398647 | + | 0.690477i | −0.993559 | − | 0.113314i | \(-0.963853\pi\) |
0.594912 | + | 0.803791i | \(0.297187\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.05563 | − | 3.56046i | 0.225635 | − | 0.390811i | −0.730875 | − | 0.682512i | \(-0.760888\pi\) |
0.956510 | + | 0.291700i | \(0.0942210\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −7.37636 | − | 12.7762i | −0.800078 | − | 1.38578i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.60940 | −1.01859 | −0.509297 | − | 0.860591i | \(-0.670095\pi\) | ||||
−0.509297 | + | 0.860591i | \(0.670095\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.59455 | − | 2.76185i | −0.163598 | − | 0.283360i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.66071 | + | 6.34053i | −0.371688 | + | 0.643783i | −0.989825 | − | 0.142287i | \(-0.954554\pi\) |
0.618137 | + | 0.786070i | \(0.287888\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.73236 | − | 3.00054i | 0.172376 | − | 0.298564i | −0.766874 | − | 0.641798i | \(-0.778189\pi\) |
0.939250 | + | 0.343233i | \(0.111522\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.93818 | − | 13.7493i | −0.782172 | − | 1.35476i | −0.930674 | − | 0.365849i | \(-0.880779\pi\) |
0.148502 | − | 0.988912i | \(-0.452555\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −5.35346 | −0.517538 | −0.258769 | − | 0.965939i | \(-0.583317\pi\) | ||||
−0.258769 | + | 0.965939i | \(0.583317\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −18.8640 | −1.80684 | −0.903421 | − | 0.428755i | \(-0.858952\pi\) | ||||
−0.903421 | + | 0.428755i | \(0.858952\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −9.27561 | − | 16.0658i | −0.872576 | − | 1.51135i | −0.859322 | − | 0.511434i | \(-0.829114\pi\) |
−0.0132538 | − | 0.999912i | \(-0.504219\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −10.5433 | + | 18.2614i | −0.983163 | + | 1.70289i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −2.05563 | + | 3.56046i | −0.188439 | + | 0.326387i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.54944 | + | 2.68371i | 0.140858 | + | 0.243974i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.3214 | 0.923175 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.98762 | −0.886258 | −0.443129 | − | 0.896458i | \(-0.646132\pi\) | ||||
−0.443129 | + | 0.896458i | \(0.646132\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −8.02654 | − | 13.9024i | −0.701282 | − | 1.21466i | −0.968017 | − | 0.250886i | \(-0.919278\pi\) |
0.266734 | − | 0.963770i | \(-0.414055\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.444368 | + | 0.769668i | −0.0385316 | + | 0.0667387i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −6.49381 | + | 11.2476i | −0.554804 | + | 0.960948i | 0.443115 | + | 0.896465i | \(0.353873\pi\) |
−0.997919 | + | 0.0644834i | \(0.979460\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.555632 | + | 0.962383i | 0.0471281 | + | 0.0816283i | 0.888627 | − | 0.458630i | \(-0.151660\pi\) |
−0.841499 | + | 0.540259i | \(0.818326\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.81089 | −0.235059 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.09888 | 0.506485 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.21634 | + | 7.30291i | 0.345416 | + | 0.598278i | 0.985429 | − | 0.170086i | \(-0.0544045\pi\) |
−0.640013 | + | 0.768364i | \(0.721071\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.42580 | + | 12.8619i | −0.604303 | + | 1.04668i | 0.387858 | + | 0.921719i | \(0.373215\pi\) |
−0.992161 | + | 0.124964i | \(0.960118\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −12.5371 | + | 21.7148i | −1.00700 | + | 1.74418i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.44437 | − | 2.50172i | −0.115273 | − | 0.199659i | 0.802616 | − | 0.596496i | \(-0.203441\pi\) |
−0.917889 | + | 0.396837i | \(0.870108\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 5.87636 | 0.463122 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.3090 | 0.807466 | 0.403733 | − | 0.914877i | \(-0.367713\pi\) | ||||
0.403733 | + | 0.914877i | \(0.367713\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.07598 | − | 10.5239i | −0.470174 | − | 0.814365i | 0.529244 | − | 0.848469i | \(-0.322475\pi\) |
−0.999418 | + | 0.0341045i | \(0.989142\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | − | 10.3923i | 0.461538 | − | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −3.30470 | + | 5.72391i | −0.251252 | + | 0.435181i | −0.963871 | − | 0.266370i | \(-0.914176\pi\) |
0.712619 | + | 0.701551i | \(0.247509\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.93818 | − | 6.82112i | −0.297698 | − | 0.515629i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3.84294 | −0.287234 | −0.143617 | − | 0.989633i | \(-0.545873\pi\) | ||||
−0.143617 | + | 0.989633i | \(0.545873\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 18.5426 | 1.37826 | 0.689129 | − | 0.724639i | \(-0.257993\pi\) | ||||
0.689129 | + | 0.724639i | \(0.257993\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −8.54944 | − | 14.8081i | −0.628567 | − | 1.08871i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.77816 | − | 10.0081i | 0.422541 | − | 0.731862i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.31708 | + | 4.01330i | −0.167658 | + | 0.290392i | −0.937596 | − | 0.347726i | \(-0.886954\pi\) |
0.769938 | + | 0.638119i | \(0.220287\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.6483 | + | 21.9075i | 0.910446 | + | 1.57694i | 0.813435 | + | 0.581656i | \(0.197595\pi\) |
0.0970118 | + | 0.995283i | \(0.469072\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −10.7207 | −0.763816 | −0.381908 | − | 0.924200i | \(-0.624733\pi\) | ||||
−0.381908 | + | 0.924200i | \(0.624733\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.76647 | 0.621439 | 0.310719 | − | 0.950502i | \(-0.399430\pi\) | ||||
0.310719 | + | 0.950502i | \(0.399430\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.849814 | − | 1.47192i | −0.0596453 | − | 0.103309i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −9.70946 | + | 16.8173i | −0.678138 | + | 1.17457i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.24907 | − | 2.16345i | 0.0864000 | − | 0.149649i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.26509 | + | 9.11941i | 0.362464 | + | 0.627806i | 0.988366 | − | 0.152096i | \(-0.0486023\pi\) |
−0.625902 | + | 0.779902i | \(0.715269\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −18.6959 | −1.27505 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6.98762 | 0.474351 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2.05563 | − | 3.56046i | −0.138277 | − | 0.239502i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.83379 | + | 4.90827i | −0.189765 | + | 0.328682i | −0.945172 | − | 0.326574i | \(-0.894106\pi\) |
0.755407 | + | 0.655256i | \(0.227439\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.54944 | − | 9.61192i | 0.368329 | − | 0.637965i | −0.620975 | − | 0.783830i | \(-0.713263\pi\) |
0.989304 | + | 0.145865i | \(0.0465965\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.82141 | − | 17.0112i | −0.649017 | − | 1.12413i | −0.983358 | − | 0.181679i | \(-0.941847\pi\) |
0.334341 | − | 0.942452i | \(-0.391486\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −8.96286 | −0.587177 | −0.293588 | − | 0.955932i | \(-0.594849\pi\) | ||||
−0.293588 | + | 0.955932i | \(0.594849\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.56732 | −0.624103 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.61126 | − | 9.71899i | −0.362963 | − | 0.628670i | 0.625484 | − | 0.780237i | \(-0.284901\pi\) |
−0.988447 | + | 0.151567i | \(0.951568\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.49312 | − | 6.05026i | 0.225012 | − | 0.389732i | −0.731311 | − | 0.682044i | \(-0.761091\pi\) |
0.956323 | + | 0.292312i | \(0.0944246\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.79418 | + | 3.10761i | −0.114626 | + | 0.198538i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.444368 | − | 0.769668i | −0.0282745 | − | 0.0489728i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.62041 | 0.291638 | 0.145819 | − | 0.989311i | \(-0.453418\pi\) | ||||
0.145819 | + | 0.989311i | \(0.453418\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.5178 | −1.03847 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.712008 | − | 1.23323i | −0.0444138 | − | 0.0769270i | 0.842964 | − | 0.537970i | \(-0.180809\pi\) |
−0.887378 | + | 0.461043i | \(0.847475\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.38255 | + | 4.12669i | −0.148044 | + | 0.256420i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −8.13162 | + | 14.0844i | −0.501417 | + | 0.868480i | 0.498582 | + | 0.866843i | \(0.333854\pi\) |
−0.999999 | + | 0.00163692i | \(0.999479\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.221840 | − | 0.384237i | −0.0136275 | − | 0.0236035i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 18.6538 | 1.13734 | 0.568672 | − | 0.822564i | \(-0.307457\pi\) | ||||
0.568672 | + | 0.822564i | \(0.307457\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.96286 | −0.240727 | −0.120363 | − | 0.992730i | \(-0.538406\pi\) | ||||
−0.120363 | + | 0.992730i | \(0.538406\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11.0698 | + | 19.1734i | 0.667534 | + | 1.15620i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.16690 | − | 2.02112i | 0.0701120 | − | 0.121438i | −0.828838 | − | 0.559488i | \(-0.810998\pi\) |
0.898950 | + | 0.438051i | \(0.144331\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 13.9975 | − | 24.2443i | 0.835018 | − | 1.44629i | −0.0589978 | − | 0.998258i | \(-0.518790\pi\) |
0.894016 | − | 0.448035i | \(-0.147876\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.16002 | + | 8.93741i | 0.306731 | + | 0.531274i | 0.977645 | − | 0.210261i | \(-0.0674314\pi\) |
−0.670914 | + | 0.741535i | \(0.734098\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.41164 | 0.319439 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −0.0975070 | −0.00573571 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −15.3480 | − | 26.5834i | −0.896637 | − | 1.55302i | −0.831765 | − | 0.555127i | \(-0.812670\pi\) |
−0.0648718 | − | 0.997894i | \(-0.520664\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 15.9258 | − | 27.5843i | 0.927236 | − | 1.60602i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2.93818 | + | 5.08907i | −0.169919 | + | 0.294309i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.60507 | + | 4.51212i | 0.150154 | + | 0.260074i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 13.9098 | 0.796471 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 11.4437 | 0.653125 | 0.326563 | − | 0.945176i | \(-0.394110\pi\) | ||||
0.326563 | + | 0.945176i | \(0.394110\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5.98143 | − | 10.3601i | −0.339176 | − | 0.587470i | 0.645102 | − | 0.764096i | \(-0.276815\pi\) |
−0.984278 | + | 0.176627i | \(0.943481\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.77197 | − | 11.7294i | 0.382774 | − | 0.662985i | −0.608683 | − | 0.793413i | \(-0.708302\pi\) |
0.991458 | + | 0.130429i | \(0.0416353\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −14.9814 | + | 25.9486i | −0.841441 | + | 1.45742i | 0.0472355 | + | 0.998884i | \(0.484959\pi\) |
−0.888676 | + | 0.458535i | \(0.848374\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2.38874 | + | 4.13741i | 0.133744 | + | 0.231651i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.65383 | 0.203304 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7.87636 | 0.436902 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.33310 | + | 2.30900i | 0.0734964 | + | 0.127299i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.04325 | − | 1.80697i | 0.0573423 | − | 0.0993198i | −0.835929 | − | 0.548837i | \(-0.815071\pi\) |
0.893272 | + | 0.449517i | \(0.148404\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 22.0846 | − | 38.2517i | 1.20661 | − | 2.08992i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.10439 | + | 14.0372i | 0.441474 | + | 0.764655i | 0.997799 | − | 0.0663093i | \(-0.0211224\pi\) |
−0.556325 | + | 0.830965i | \(0.687789\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −19.6414 | −1.06364 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.63348 | − | 9.75747i | −0.302421 | − | 0.523808i | 0.674263 | − | 0.738491i | \(-0.264461\pi\) |
−0.976684 | + | 0.214683i | \(0.931128\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.0988844 | − | 0.171273i | 0.00529316 | − | 0.00916803i | −0.863367 | − | 0.504577i | \(-0.831648\pi\) |
0.868660 | + | 0.495409i | \(0.164982\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −6.25093 | + | 10.8269i | −0.332703 | + | 0.576259i | −0.983041 | − | 0.183386i | \(-0.941294\pi\) |
0.650338 | + | 0.759645i | \(0.274627\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.16071 | + | 8.93861i | 0.273902 | + | 0.474412i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 20.0197 | 1.05660 | 0.528299 | − | 0.849059i | \(-0.322830\pi\) | ||||
0.528299 | + | 0.849059i | \(0.322830\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.2101 | −0.958429 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.0927 | + | 33.0695i | 0.999357 | + | 1.73094i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.0364 | − | 26.0438i | 0.784892 | − | 1.35947i | −0.144171 | − | 0.989553i | \(-0.546052\pi\) |
0.929063 | − | 0.369921i | \(-0.120615\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −0.0618219 | + | 0.107079i | −0.00320963 | + | 0.00555925i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −3.50619 | − | 6.07290i | −0.181544 | − | 0.314443i | 0.760863 | − | 0.648913i | \(-0.224776\pi\) |
−0.942406 | + | 0.334470i | \(0.891443\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.69963 | 0.0875353 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 19.0741 | 0.979772 | 0.489886 | − | 0.871787i | \(-0.337038\pi\) | ||||
0.489886 | + | 0.871787i | \(0.337038\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1.60507 | − | 2.78007i | −0.0820155 | − | 0.142055i | 0.822100 | − | 0.569343i | \(-0.192802\pi\) |
−0.904116 | + | 0.427288i | \(0.859469\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 5.04325 | − | 8.73517i | 0.257028 | − | 0.445185i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 2.56801 | − | 4.44793i | 0.130203 | − | 0.225519i | −0.793552 | − | 0.608503i | \(-0.791770\pi\) |
0.923755 | + | 0.382984i | \(0.125104\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12.0796 | − | 20.9225i | −0.610893 | − | 1.05810i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 25.4290 | 1.27947 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 22.9381 | 1.15123 | 0.575615 | − | 0.817721i | \(-0.304763\pi\) | ||||
0.575615 | + | 0.817721i | \(0.304763\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.10507 | − | 15.7705i | −0.454686 | − | 0.787539i | 0.543984 | − | 0.839095i | \(-0.316915\pi\) |
−0.998670 | + | 0.0515566i | \(0.983582\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.49381 | + | 6.05146i | −0.174039 | + | 0.301445i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 6.69708 | − | 11.5997i | 0.331962 | − | 0.574975i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.66621 | + | 13.2783i | 0.379070 | + | 0.656568i | 0.990927 | − | 0.134400i | \(-0.0429108\pi\) |
−0.611858 | + | 0.790968i | \(0.709577\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −8.87636 | −0.436777 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.7527 | −0.724182 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.28435 | − | 9.15276i | −0.258157 | − | 0.447142i | 0.707591 | − | 0.706622i | \(-0.249782\pi\) |
−0.965748 | + | 0.259481i | \(0.916449\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 18.0858 | − | 31.3256i | 0.881449 | − | 1.52671i | 0.0317181 | − | 0.999497i | \(-0.489902\pi\) |
0.849731 | − | 0.527217i | \(-0.176765\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −16.1909 | + | 28.0434i | −0.785374 | + | 1.36031i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.93818 | − | 3.35702i | −0.0937950 | − | 0.162458i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 35.0989 | 1.69065 | 0.845327 | − | 0.534249i | \(-0.179406\pi\) | ||||
0.845327 | + | 0.534249i | \(0.179406\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −41.1730 | −1.97865 | −0.989324 | − | 0.145731i | \(-0.953447\pi\) | ||||
−0.989324 | + | 0.145731i | \(0.953447\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.61126 | − | 4.52284i | −0.124914 | − | 0.216357i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.33929 | + | 4.05178i | −0.111648 | + | 0.193381i | −0.916435 | − | 0.400184i | \(-0.868946\pi\) |
0.804787 | + | 0.593564i | \(0.202280\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −15.0865 | + | 26.1306i | −0.716781 | + | 1.24150i | 0.245487 | + | 0.969400i | \(0.421052\pi\) |
−0.962268 | + | 0.272102i | \(0.912281\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.2410 | + | 29.8623i | 0.817303 | + | 1.41561i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.333792 | −0.0157526 | −0.00787632 | − | 0.999969i | \(-0.502507\pi\) | ||||
−0.00787632 | + | 0.999969i | \(0.502507\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −15.2115 | −0.716283 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.79418 | − | 3.10761i | −0.0841125 | − | 0.145687i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.65452 | − | 16.7221i | 0.451619 | − | 0.782227i | −0.546868 | − | 0.837219i | \(-0.684180\pi\) |
0.998487 | + | 0.0549917i | \(0.0175132\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 19.5538 | − | 33.8681i | 0.910710 | − | 1.57740i | 0.0976463 | − | 0.995221i | \(-0.468869\pi\) |
0.813064 | − | 0.582175i | \(-0.197798\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.9382 | + | 18.9455i | 0.508340 | + | 0.880471i | 0.999953 | + | 0.00965741i | \(0.00307410\pi\) |
−0.491613 | + | 0.870814i | \(0.663593\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −12.3200 | −0.570103 | −0.285052 | − | 0.958512i | \(-0.592011\pi\) | ||||
−0.285052 | + | 0.958512i | \(0.592011\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −12.3090 | −0.568378 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −7.32258 | − | 12.6831i | −0.336693 | − | 0.583169i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.50000 | + | 6.06218i | −0.160591 | + | 0.278152i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.74474 | + | 11.6822i | −0.308175 | + | 0.533775i | −0.977963 | − | 0.208777i | \(-0.933052\pi\) |
0.669788 | + | 0.742552i | \(0.266385\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.38255 | − | 4.12669i | −0.108635 | − | 0.188161i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 26.2719 | 1.19295 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −7.54394 | −0.341849 | −0.170924 | − | 0.985284i | \(-0.554675\pi\) | ||||
−0.170924 | + | 0.985284i | \(0.554675\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.06979 | + | 13.9773i | 0.364185 | + | 0.630786i | 0.988645 | − | 0.150270i | \(-0.0480143\pi\) |
−0.624460 | + | 0.781057i | \(0.714681\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.49381 | + | 6.05146i | −0.157353 | + | 0.272544i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.43818 | − | 2.49100i | 0.0645111 | − | 0.111737i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −15.4327 | − | 26.7302i | −0.690862 | − | 1.19661i | −0.971556 | − | 0.236810i | \(-0.923898\pi\) |
0.280694 | − | 0.959797i | \(-0.409435\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.6304 | 1.09822 | 0.549109 | − | 0.835751i | \(-0.314967\pi\) | ||||
0.549109 | + | 0.835751i | \(0.314967\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −12.4327 | −0.553247 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.79487 | + | 11.7691i | 0.301177 | + | 0.521654i | 0.976403 | − | 0.215957i | \(-0.0692870\pi\) |
−0.675226 | + | 0.737611i | \(0.735954\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.32072 | − | 9.21576i | 0.235375 | − | 0.407681i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −28.4851 | + | 49.3376i | −1.25520 | + | 2.17407i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.74721 | − | 6.49036i | −0.164802 | − | 0.285446i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 39.1730 | 1.71620 | 0.858100 | − | 0.513482i | \(-0.171645\pi\) | ||||
0.858100 | + | 0.513482i | \(0.171645\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −19.1236 | −0.836219 | −0.418109 | − | 0.908397i | \(-0.637307\pi\) | ||||
−0.418109 | + | 0.908397i | \(0.637307\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −14.3640 | − | 24.8791i | −0.625705 | − | 1.08375i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5.76578 | + | 9.98663i | −0.250686 | + | 0.434201i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.70582 | + | 4.68661i | −0.117202 | + | 0.203000i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.60507 | + | 16.6365i | 0.415264 | + | 0.719258i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2.81089 | −0.121074 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.53018 | 0.108781 | 0.0543906 | − | 0.998520i | \(-0.482678\pi\) | ||||
0.0543906 | + | 0.998520i | \(0.482678\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 33.8454 | + | 58.6220i | 1.44978 | + | 2.51109i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 8.92580 | − | 15.4599i | 0.381640 | − | 0.661019i | −0.609657 | − | 0.792665i | \(-0.708693\pi\) |
0.991297 | + | 0.131646i | \(0.0420262\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.755260 | + | 1.30815i | −0.0321752 | + | 0.0557290i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −3.54325 | − | 6.13709i | −0.150674 | − | 0.260976i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −41.3607 | −1.75251 | −0.876255 | − | 0.481847i | \(-0.839966\pi\) | ||||
−0.876255 | + | 0.481847i | \(0.839966\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5.21015 | −0.220366 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.3683 | + | 17.9584i | 0.436972 | + | 0.756858i | 0.997454 | − | 0.0713087i | \(-0.0227175\pi\) |
−0.560482 | + | 0.828166i | \(0.689384\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −33.2843 | + | 57.6501i | −1.40028 | + | 2.42536i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.134164 | + | 0.232379i | −0.00562446 | + | 0.00974185i | −0.868824 | − | 0.495121i | \(-0.835124\pi\) |
0.863199 | + | 0.504863i | \(0.168457\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 17.9684 | + | 31.1221i | 0.751953 | + | 1.30242i | 0.946875 | + | 0.321601i | \(0.104221\pi\) |
−0.194923 | + | 0.980819i | \(0.562446\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 46.2843 | 1.93019 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.43130 | 0.226108 | 0.113054 | − | 0.993589i | \(-0.463937\pi\) | ||||
0.113054 | + | 0.993589i | \(0.463937\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.05563 | + | 3.56046i | 0.0852820 | + | 0.147713i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.173775 | − | 0.300987i | 0.00719702 | − | 0.0124656i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −17.5822 | + | 30.4532i | −0.725694 | + | 1.25694i | 0.232994 | + | 0.972478i | \(0.425148\pi\) |
−0.958688 | + | 0.284461i | \(0.908185\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.10507 | − | 5.37815i | −0.127942 | − | 0.221603i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 33.5068 | 1.37596 | 0.687980 | − | 0.725730i | \(-0.258498\pi\) | ||||
0.687980 | + | 0.725730i | \(0.258498\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 14.7527 | 0.604802 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −3.12364 | − | 5.41031i | −0.127629 | − | 0.221059i | 0.795129 | − | 0.606441i | \(-0.207403\pi\) |
−0.922757 | + | 0.385381i | \(0.874070\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −11.2040 | + | 19.4058i | −0.457019 | + | 0.791580i | −0.998802 | − | 0.0489384i | \(-0.984416\pi\) |
0.541783 | + | 0.840519i | \(0.317750\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.55996 | − | 9.63014i | 0.226045 | − | 0.391521i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 7.47524 | + | 12.9475i | 0.303411 | + | 0.525523i | 0.976906 | − | 0.213669i | \(-0.0685413\pi\) |
−0.673496 | + | 0.739191i | \(0.735208\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.66621 | −0.107863 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 35.1978 | 1.42162 | 0.710812 | − | 0.703382i | \(-0.248328\pi\) | ||||
0.710812 | + | 0.703382i | \(0.248328\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.00619 | − | 1.74277i | −0.0405077 | − | 0.0701614i | 0.845061 | − | 0.534670i | \(-0.179564\pi\) |
−0.885568 | + | 0.464509i | \(0.846231\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.6909 | − | 34.1056i | 0.791444 | − | 1.37082i | −0.133629 | − | 0.991031i | \(-0.542663\pi\) |
0.925073 | − | 0.379789i | \(-0.124004\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 4.80470 | − | 8.32199i | 0.192496 | − | 0.333413i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.17240 | + | 2.03065i | 0.0468959 | + | 0.0812261i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19.5906 | 0.781126 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −44.3832 | −1.76687 | −0.883433 | − | 0.468558i | \(-0.844774\pi\) | ||||
−0.883433 | + | 0.468558i | \(0.844774\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 17.9196 | + | 31.0377i | 0.711118 | + | 1.23169i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.500000 | + | 0.866025i | −0.0198107 | + | 0.0343132i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −7.49312 | + | 12.9785i | −0.295961 | + | 0.512619i | −0.975208 | − | 0.221291i | \(-0.928973\pi\) |
0.679247 | + | 0.733909i | \(0.262306\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.32691 | − | 9.22649i | −0.210073 | − | 0.363857i | 0.741664 | − | 0.670771i | \(-0.234037\pi\) |
−0.951737 | + | 0.306914i | \(0.900703\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.12955 | 0.0837213 | 0.0418606 | − | 0.999123i | \(-0.486671\pi\) | ||||
0.0418606 | + | 0.999123i | \(0.486671\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 24.9505 | 0.979392 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 5.58582 | + | 9.67492i | 0.218590 | + | 0.378609i | 0.954377 | − | 0.298604i | \(-0.0965210\pi\) |
−0.735787 | + | 0.677213i | \(0.763188\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −28.8022 | + | 49.8868i | −1.12539 | + | 1.94924i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.65452 | − | 9.79391i | 0.220269 | − | 0.381517i | −0.734621 | − | 0.678478i | \(-0.762640\pi\) |
0.954890 | + | 0.296961i | \(0.0959733\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16.1785 | − | 28.0220i | −0.629271 | − | 1.08993i | −0.987698 | − | 0.156372i | \(-0.950020\pi\) |
0.358427 | − | 0.933558i | \(-0.383313\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.18911 | 0.123668 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 9.98762 | 0.386722 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.44801 | + | 9.43623i | 0.210318 | + | 0.364282i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 12.0803 | − | 20.9237i | 0.465662 | − | 0.806550i | −0.533569 | − | 0.845756i | \(-0.679150\pi\) |
0.999231 | + | 0.0392063i | \(0.0124830\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 12.5371 | − | 21.7148i | 0.481838 | − | 0.834569i | −0.517944 | − | 0.855414i | \(-0.673303\pi\) |
0.999783 | + | 0.0208457i | \(0.00663587\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.66071 | − | 6.34053i | −0.140485 | − | 0.243327i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −47.6784 | −1.82436 | −0.912182 | − | 0.409785i | \(-0.865604\pi\) | ||||
−0.912182 | + | 0.409785i | \(0.865604\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 46.6043 | 1.78066 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −0.0618219 | − | 0.107079i | −0.00235523 | − | 0.00407937i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.3400 | + | 21.3735i | −0.469435 | + | 0.813085i | −0.999389 | − | 0.0349408i | \(-0.988876\pi\) |
0.529954 | + | 0.848026i | \(0.322209\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.99381 | − | 3.45338i | 0.0756295 | − | 0.130994i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −11.1243 | − | 19.2679i | −0.421364 | − | 0.729824i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 29.6784 | 1.12094 | 0.560469 | − | 0.828175i | \(-0.310621\pi\) | ||||
0.560469 | + | 0.828175i | \(0.310621\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.23491 | 0.159723 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 1.73236 | + | 3.00054i | 0.0651521 | + | 0.112847i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 14.6291 | − | 25.3383i | 0.549406 | − | 0.951599i | −0.448909 | − | 0.893577i | \(-0.648187\pi\) |
0.998315 | − | 0.0580220i | \(-0.0184794\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −20.5309 | + | 35.5605i | −0.768887 | + | 1.33175i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.04325 | + | 8.73517i | 0.188607 | + | 0.326677i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.07413 | 0.0400581 | 0.0200291 | − | 0.999799i | \(-0.493624\pi\) | ||||
0.0200291 | + | 0.999799i | \(0.493624\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.8764 | 0.591266 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.69344 | − | 11.5934i | −0.248588 | − | 0.430567i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.7163 | − | 22.0253i | 0.471623 | − | 0.816875i | −0.527850 | − | 0.849338i | \(-0.677002\pi\) |
0.999473 | + | 0.0324628i | \(0.0103350\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10.7101 | − | 18.5505i | 0.396129 | − | 0.686116i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 5.69777 | + | 9.86883i | 0.210452 | + | 0.364513i | 0.951856 | − | 0.306545i | \(-0.0991731\pi\) |
−0.741404 | + | 0.671059i | \(0.765840\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 34.5994 | 1.27448 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 29.9395 | 1.10134 | 0.550671 | − | 0.834723i | \(-0.314372\pi\) | ||||
0.550671 | + | 0.834723i | \(0.314372\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 9.50069 | + | 16.4557i | 0.348546 | + | 0.603700i | 0.985991 | − | 0.166796i | \(-0.0533420\pi\) |
−0.637445 | + | 0.770496i | \(0.720009\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 15.1298 | − | 26.2055i | 0.554311 | − | 0.960096i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.67673 | − | 4.63623i | 0.0978055 | − | 0.169404i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 0.0130684 | + | 0.0226352i | 0.000476873 | + | 0.000825969i | 0.866264 | − | 0.499587i | \(-0.166515\pi\) |
−0.865787 | + | 0.500413i | \(0.833182\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 53.2929 | 1.93953 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.6910 | −0.497607 | −0.248803 | − | 0.968554i | \(-0.580037\pi\) | ||||
−0.248803 | + | 0.968554i | \(0.580037\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −7.32141 | − | 12.6811i | −0.265401 | − | 0.459688i | 0.702268 | − | 0.711913i | \(-0.252171\pi\) |
−0.967669 | + | 0.252225i | \(0.918838\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.43199 | − | 16.3367i | 0.341461 | − | 0.591428i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.43818 | − | 7.68715i | 0.160253 | − | 0.277567i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.5672 | − | 42.5517i | −0.885918 | − | 1.53445i | −0.844658 | − | 0.535306i | \(-0.820196\pi\) |
−0.0412592 | − | 0.999148i | \(-0.513137\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −12.4413 | −0.447484 | −0.223742 | − | 0.974648i | \(-0.571827\pi\) | ||||
−0.223742 | + | 0.974648i | \(0.571827\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 55.0370 | 1.97699 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.40476 | − | 4.16516i | −0.0861594 | − | 0.149232i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.04256 | + | 7.00193i | −0.144654 | + | 0.250549i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −5.18292 | + | 8.97708i | −0.184986 | + | 0.320406i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −16.4567 | − | 28.5038i | −0.586617 | − | 1.01605i | −0.994672 | − | 0.103093i | \(-0.967126\pi\) |
0.408055 | − | 0.912957i | \(-0.366207\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 18.5512 | 0.659606 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.87636 | 0.137653 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 13.1989 | + | 22.8612i | 0.467530 | + | 0.809786i | 0.999312 | − | 0.0370953i | \(-0.0118105\pi\) |
−0.531781 | + | 0.846882i | \(0.678477\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.48074 | − | 9.49292i | 0.193895 | − | 0.335835i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −14.9560 | + | 25.9045i | −0.527785 | + | 0.914151i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −10.5433 | − | 18.2614i | −0.371601 | − | 0.643631i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −35.5919 | −1.25135 | −0.625673 | − | 0.780086i | \(-0.715175\pi\) | ||||
−0.625673 | + | 0.780086i | \(0.715175\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 37.8268 | 1.32828 | 0.664140 | − | 0.747608i | \(-0.268798\pi\) | ||||
0.664140 | + | 0.747608i | \(0.268798\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −18.4963 | − | 32.0365i | −0.647896 | − | 1.12219i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.31522 | − | 4.01008i | 0.0809994 | − | 0.140295i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −9.15638 | + | 15.8593i | −0.319560 | + | 0.553494i | −0.980396 | − | 0.197036i | \(-0.936868\pi\) |
0.660836 | + | 0.750530i | \(0.270202\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −18.0000 | − | 31.1769i | −0.627441 | − | 1.08676i | −0.988063 | − | 0.154047i | \(-0.950769\pi\) |
0.360623 | − | 0.932712i | \(-0.382564\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −28.2115 | −0.981011 | −0.490505 | − | 0.871438i | \(-0.663188\pi\) | ||||
−0.490505 | + | 0.871438i | \(0.663188\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.2843 | −0.391919 | −0.195960 | − | 0.980612i | \(-0.562782\pi\) | ||||
−0.195960 | + | 0.980612i | \(0.562782\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.05563 | − | 3.56046i | −0.0712234 | − | 0.123363i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −21.8028 | + | 37.7636i | −0.754519 | + | 1.30686i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1.02152 | − | 1.76933i | 0.0352669 | − | 0.0610840i | −0.847853 | − | 0.530231i | \(-0.822105\pi\) |
0.883120 | + | 0.469147i | \(0.155439\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 13.0556 | + | 22.6130i | 0.450194 | + | 0.779759i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −43.0604 | −1.48132 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −3.09888 | −0.106479 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −14.0007 | − | 24.2499i | −0.479937 | − | 0.831276i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24.2960 | − | 42.0818i | 0.831878 | − | 1.44085i | −0.0646692 | − | 0.997907i | \(-0.520599\pi\) |
0.896547 | − | 0.442948i | \(-0.146067\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.4487 | + | 38.8823i | −0.766833 | + | 1.32819i | 0.172439 | + | 0.985020i | \(0.444835\pi\) |
−0.939272 | + | 0.343173i | \(0.888498\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 14.9065 | + | 25.8189i | 0.508605 | + | 0.880929i | 0.999950 | + | 0.00996438i | \(0.00317181\pi\) |
−0.491346 | + | 0.870965i | \(0.663495\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −42.2595 | −1.43853 | −0.719265 | − | 0.694736i | \(-0.755521\pi\) | ||||
−0.719265 | + | 0.694736i | \(0.755521\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.7170 | 0.806401 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 9.95970 | + | 17.2507i | 0.337860 | + | 0.585190i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.15452 | − | 10.6599i | 0.208538 | − | 0.361198i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −5.16071 | + | 8.93861i | −0.174464 | + | 0.302180i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.2658 | + | 26.4411i | 0.515489 | + | 0.892853i | 0.999838 | + | 0.0179782i | \(0.00572295\pi\) |
−0.484350 | + | 0.874875i | \(0.660944\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13.4079 | 0.451724 | 0.225862 | − | 0.974159i | \(-0.427480\pi\) | ||||
0.225862 | + | 0.974159i | \(0.427480\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 14.1250 | 0.475345 | 0.237672 | − | 0.971345i | \(-0.423616\pi\) | ||||
0.237672 | + | 0.971345i | \(0.423616\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 19.9716 | + | 34.5918i | 0.670581 | + | 1.16148i | 0.977740 | + | 0.209822i | \(0.0672883\pi\) |
−0.307159 | + | 0.951658i | \(0.599378\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.99381 | − | 8.64953i | 0.167487 | − | 0.290096i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.18478 | − | 2.05209i | 0.0396471 | − | 0.0686707i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.89493 | + | 11.9424i | 0.230472 | + | 0.399189i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 11.8764 | 0.396099 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.508333 | 0.0169350 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −33.2687 | − | 57.6231i | −1.10589 | − | 1.91546i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.7101 | − | 35.8710i | 0.687669 | − | 1.19108i | −0.284921 | − | 0.958551i | \(-0.591967\pi\) |
0.972590 | − | 0.232527i | \(-0.0746994\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.894237 | + | 1.54886i | −0.0296274 | + | 0.0513162i | −0.880459 | − | 0.474122i | \(-0.842765\pi\) |
0.850832 | + | 0.525439i | \(0.176099\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.77816 | − | 10.0081i | −0.191229 | − | 0.331219i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 16.0531 | 0.530120 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 57.4683 | 1.89570 | 0.947852 | − | 0.318711i | \(-0.103250\pi\) | ||||
0.947852 | + | 0.318711i | \(0.103250\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 1.43818 | + | 2.49100i | 0.0473382 | + | 0.0819922i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −18.7658 | + | 32.5033i | −0.617015 | + | 1.06870i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 17.3676 | − | 30.0816i | 0.569813 | − | 0.986945i | −0.426771 | − | 0.904360i | \(-0.640349\pi\) |
0.996584 | − | 0.0825854i | \(-0.0263177\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.444368 | − | 0.769668i | −0.0145636 | − | 0.0252248i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −41.4683 | −1.35616 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 11.6662 | 0.381118 | 0.190559 | − | 0.981676i | \(-0.438970\pi\) | ||||
0.190559 | + | 0.981676i | \(0.438970\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −25.1687 | − | 43.5934i | −0.820475 | − | 1.42111i | −0.905329 | − | 0.424712i | \(-0.860375\pi\) |
0.0848531 | − | 0.996393i | \(-0.472958\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −15.9004 | + | 27.5402i | −0.517787 | + | 0.896833i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 16.1941 | − | 28.0491i | 0.526238 | − | 0.911472i | −0.473294 | − | 0.880904i | \(-0.656935\pi\) |
0.999533 | − | 0.0305673i | \(-0.00973139\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.32072 | + | 9.21576i | 0.172718 | + | 0.299156i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 12.5367 | 0.406102 | 0.203051 | − | 0.979168i | \(-0.434914\pi\) | ||||
0.203051 | + | 0.979168i | \(0.434914\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 16.6291 | 0.538104 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −6.49381 | − | 11.2476i | −0.209696 | − | 0.363204i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −8.91342 | + | 15.4385i | −0.287530 | + | 0.498016i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 45.3868 | − | 78.6122i | 1.46105 | − | 2.53062i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.9937 | − | 50.2186i | −0.932376 | − | 1.61492i | −0.779248 | − | 0.626715i | \(-0.784399\pi\) |
−0.153127 | − | 0.988206i | \(-0.548935\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 28.0370 | 0.899750 | 0.449875 | − | 0.893092i | \(-0.351469\pi\) | ||||
0.449875 | + | 0.893092i | \(0.351469\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.11126 | −0.0356255 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.92030 | + | 8.52220i | 0.157414 | + | 0.272649i | 0.933935 | − | 0.357442i | \(-0.116351\pi\) |
−0.776521 | + | 0.630091i | \(0.783018\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.5055 | + | 23.3922i | −0.431638 | + | 0.747618i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 24.3447 | − | 42.1663i | 0.776476 | − | 1.34490i | −0.157485 | − | 0.987521i | \(-0.550339\pi\) |
0.933961 | − | 0.357374i | \(-0.116328\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 19.2348 | + | 33.3157i | 0.612873 | + | 1.06153i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −30.6167 | −0.973554 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −2.86398 | −0.0909772 | −0.0454886 | − | 0.998965i | \(-0.514484\pi\) | ||||
−0.0454886 | + | 0.998965i | \(0.514484\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −15.7286 | − | 27.2428i | −0.498631 | − | 0.863655i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 25.4203 | − | 44.0292i | 0.805069 | − | 1.39442i | −0.111176 | − | 0.993801i | \(-0.535462\pi\) |
0.916245 | − | 0.400619i | \(-0.131205\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))