Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1530,2,Mod(829,1530)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1530, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 2, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1530.829");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1530 = 2 \cdot 3^{2} \cdot 5 \cdot 17 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1530.n (of order \(4\), degree \(2\), 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: | \(12.2171115093\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(i)\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 170) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 1279.2 | ||
Root | \(0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1530.1279 |
Dual form | 1530.2.n.j.829.2 |
$q$-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 \(\left(\mathbb{Z}/1530\mathbb{Z}\right)^\times\).
\(n\) | \(307\) | \(1261\) | \(1361\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{3}{4}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | 0.707107 | + | 2.12132i | 0.316228 | + | 0.948683i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | + | 1.00000i | −0.377964 | + | 0.377964i | −0.870367 | − | 0.492403i | \(-0.836119\pi\) |
0.492403 | + | 0.870367i | \(0.336119\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.707107 | − | 2.12132i | −0.223607 | − | 0.670820i | ||||
\(11\) | 4.41421 | + | 4.41421i | 1.33094 | + | 1.33094i | 0.904534 | + | 0.426401i | \(0.140219\pi\) |
0.426401 | + | 0.904534i | \(0.359781\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.00000i | 0.832050i | 0.909353 | + | 0.416025i | \(0.136577\pi\) | ||||
−0.909353 | + | 0.416025i | \(0.863423\pi\) | |||||||
\(14\) | 1.00000 | − | 1.00000i | 0.267261 | − | 0.267261i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 2.12132 | − | 3.53553i | 0.514496 | − | 0.857493i | ||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1.24264i | 0.285081i | 0.989789 | + | 0.142541i | \(0.0455272\pi\) | ||||
−0.989789 | + | 0.142541i | \(0.954473\pi\) | |||||||
\(20\) | 0.707107 | + | 2.12132i | 0.158114 | + | 0.474342i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −4.41421 | − | 4.41421i | −0.941113 | − | 0.941113i | ||||
\(23\) | −2.82843 | + | 2.82843i | −0.589768 | + | 0.589768i | −0.937568 | − | 0.347801i | \(-0.886929\pi\) |
0.347801 | + | 0.937568i | \(0.386929\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.00000 | + | 3.00000i | −0.800000 | + | 0.600000i | ||||
\(26\) | − | 3.00000i | − | 0.588348i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −1.00000 | + | 1.00000i | −0.188982 | + | 0.188982i | ||||
\(29\) | 0.707107 | − | 0.707107i | 0.131306 | − | 0.131306i | −0.638399 | − | 0.769706i | \(-0.720403\pi\) |
0.769706 | + | 0.638399i | \(0.220403\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.36396 | − | 7.36396i | 1.32261 | − | 1.32261i | 0.410947 | − | 0.911659i | \(-0.365198\pi\) |
0.911659 | − | 0.410947i | \(-0.134802\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.12132 | + | 3.53553i | −0.363803 | + | 0.606339i | ||||
\(35\) | −2.82843 | − | 1.41421i | −0.478091 | − | 0.239046i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.24264 | + | 3.24264i | 0.533087 | + | 0.533087i | 0.921490 | − | 0.388403i | \(-0.126973\pi\) |
−0.388403 | + | 0.921490i | \(0.626973\pi\) | |||||||
\(38\) | − | 1.24264i | − | 0.201583i | ||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.707107 | − | 2.12132i | −0.111803 | − | 0.335410i | ||||
\(41\) | −1.58579 | − | 1.58579i | −0.247658 | − | 0.247658i | 0.572351 | − | 0.820009i | \(-0.306032\pi\) |
−0.820009 | + | 0.572351i | \(0.806032\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.2426 | −1.86699 | −0.933493 | − | 0.358597i | \(-0.883255\pi\) | ||||
−0.933493 | + | 0.358597i | \(0.883255\pi\) | |||||||
\(44\) | 4.41421 | + | 4.41421i | 0.665468 | + | 0.665468i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.82843 | − | 2.82843i | 0.417029 | − | 0.417029i | ||||
\(47\) | 4.41421i | 0.643879i | 0.946760 | + | 0.321940i | \(0.104335\pi\) | ||||
−0.946760 | + | 0.321940i | \(0.895665\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.00000i | 0.714286i | ||||||||
\(50\) | 4.00000 | − | 3.00000i | 0.565685 | − | 0.424264i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.00000i | 0.416025i | ||||||||
\(53\) | −3.00000 | −0.412082 | −0.206041 | − | 0.978543i | \(-0.566058\pi\) | ||||
−0.206041 | + | 0.978543i | \(0.566058\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.24264 | + | 12.4853i | −0.841757 | + | 1.68351i | ||||
\(56\) | 1.00000 | − | 1.00000i | 0.133631 | − | 0.133631i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −0.707107 | + | 0.707107i | −0.0928477 | + | 0.0928477i | ||||
\(59\) | − | 6.89949i | − | 0.898238i | −0.893472 | − | 0.449119i | \(-0.851738\pi\) | ||
0.893472 | − | 0.449119i | \(-0.148262\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.87868 | + | 1.87868i | 0.240540 | + | 0.240540i | 0.817074 | − | 0.576533i | \(-0.195595\pi\) |
−0.576533 | + | 0.817074i | \(0.695595\pi\) | |||||||
\(62\) | −7.36396 | + | 7.36396i | −0.935224 | + | 0.935224i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | −6.36396 | + | 2.12132i | −0.789352 | + | 0.263117i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 2.48528i | − | 0.303625i | −0.988409 | − | 0.151813i | \(-0.951489\pi\) | ||
0.988409 | − | 0.151813i | \(-0.0485111\pi\) | |||||||
\(68\) | 2.12132 | − | 3.53553i | 0.257248 | − | 0.428746i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.82843 | + | 1.41421i | 0.338062 | + | 0.169031i | ||||
\(71\) | −2.29289 | + | 2.29289i | −0.272116 | + | 0.272116i | −0.829952 | − | 0.557835i | \(-0.811632\pi\) |
0.557835 | + | 0.829952i | \(0.311632\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.36396 | − | 4.36396i | −0.510763 | − | 0.510763i | 0.403997 | − | 0.914760i | \(-0.367621\pi\) |
−0.914760 | + | 0.403997i | \(0.867621\pi\) | |||||||
\(74\) | −3.24264 | − | 3.24264i | −0.376949 | − | 0.376949i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.24264i | 0.142541i | ||||||||
\(77\) | −8.82843 | −1.00609 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.24264 | + | 8.24264i | 0.927370 | + | 0.927370i | 0.997535 | − | 0.0701658i | \(-0.0223528\pi\) |
−0.0701658 | + | 0.997535i | \(0.522353\pi\) | |||||||
\(80\) | 0.707107 | + | 2.12132i | 0.0790569 | + | 0.237171i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.58579 | + | 1.58579i | 0.175121 | + | 0.175121i | ||||
\(83\) | −4.24264 | −0.465690 | −0.232845 | − | 0.972514i | \(-0.574804\pi\) | ||||
−0.232845 | + | 0.972514i | \(0.574804\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 9.00000 | + | 2.00000i | 0.976187 | + | 0.216930i | ||||
\(86\) | 12.2426 | 1.32016 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −4.41421 | − | 4.41421i | −0.470557 | − | 0.470557i | ||||
\(89\) | 5.48528 | 0.581439 | 0.290719 | − | 0.956808i | \(-0.406105\pi\) | ||||
0.290719 | + | 0.956808i | \(0.406105\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.00000 | − | 3.00000i | −0.314485 | − | 0.314485i | ||||
\(92\) | −2.82843 | + | 2.82843i | −0.294884 | + | 0.294884i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 4.41421i | − | 0.455291i | ||||||
\(95\) | −2.63604 | + | 0.878680i | −0.270452 | + | 0.0901506i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.12132 | + | 4.12132i | 0.418457 | + | 0.418457i | 0.884672 | − | 0.466215i | \(-0.154383\pi\) |
−0.466215 | + | 0.884672i | \(0.654383\pi\) | |||||||
\(98\) | − | 5.00000i | − | 0.505076i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.00000 | + | 3.00000i | −0.400000 | + | 0.300000i | ||||
\(101\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(104\) | − | 3.00000i | − | 0.294174i | ||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.00000 | 0.291386 | ||||||||
\(107\) | 2.82843 | + | 2.82843i | 0.273434 | + | 0.273434i | 0.830481 | − | 0.557047i | \(-0.188066\pi\) |
−0.557047 | + | 0.830481i | \(0.688066\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −12.6066 | − | 12.6066i | −1.20749 | − | 1.20749i | −0.971836 | − | 0.235657i | \(-0.924276\pi\) |
−0.235657 | − | 0.971836i | \(-0.575724\pi\) | |||||||
\(110\) | 6.24264 | − | 12.4853i | 0.595212 | − | 1.19042i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.00000 | + | 1.00000i | −0.0944911 | + | 0.0944911i | ||||
\(113\) | 9.53553 | − | 9.53553i | 0.897028 | − | 0.897028i | −0.0981446 | − | 0.995172i | \(-0.531291\pi\) |
0.995172 | + | 0.0981446i | \(0.0312908\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −8.00000 | − | 4.00000i | −0.746004 | − | 0.373002i | ||||
\(116\) | 0.707107 | − | 0.707107i | 0.0656532 | − | 0.0656532i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.89949i | 0.635150i | ||||||||
\(119\) | 1.41421 | + | 5.65685i | 0.129641 | + | 0.518563i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 27.9706i | 2.54278i | ||||||||
\(122\) | −1.87868 | − | 1.87868i | −0.170088 | − | 0.170088i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.36396 | − | 7.36396i | 0.661303 | − | 0.661303i | ||||
\(125\) | −9.19239 | − | 6.36396i | −0.822192 | − | 0.569210i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 7.72792 | 0.685742 | 0.342871 | − | 0.939382i | \(-0.388601\pi\) | ||||
0.342871 | + | 0.939382i | \(0.388601\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.36396 | − | 2.12132i | 0.558156 | − | 0.186052i | ||||
\(131\) | −10.4142 | + | 10.4142i | −0.909894 | + | 0.909894i | −0.996263 | − | 0.0863691i | \(-0.972474\pi\) |
0.0863691 | + | 0.996263i | \(0.472474\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.24264 | − | 1.24264i | −0.107751 | − | 0.107751i | ||||
\(134\) | 2.48528i | 0.214696i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −2.12132 | + | 3.53553i | −0.181902 | + | 0.303170i | ||||
\(137\) | 7.41421i | 0.633439i | 0.948519 | + | 0.316720i | \(0.102581\pi\) | ||||
−0.948519 | + | 0.316720i | \(0.897419\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.0000 | + | 11.0000i | −0.933008 | + | 0.933008i | −0.997893 | − | 0.0648849i | \(-0.979332\pi\) |
0.0648849 | + | 0.997893i | \(0.479332\pi\) | |||||||
\(140\) | −2.82843 | − | 1.41421i | −0.239046 | − | 0.119523i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 2.29289 | − | 2.29289i | 0.192415 | − | 0.192415i | ||||
\(143\) | −13.2426 | + | 13.2426i | −1.10741 | + | 1.10741i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.00000 | + | 1.00000i | 0.166091 | + | 0.0830455i | ||||
\(146\) | 4.36396 | + | 4.36396i | 0.361164 | + | 0.361164i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 3.24264 | + | 3.24264i | 0.266543 | + | 0.266543i | ||||
\(149\) | −12.7279 | −1.04271 | −0.521356 | − | 0.853339i | \(-0.674574\pi\) | ||||
−0.521356 | + | 0.853339i | \(0.674574\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.0000i | 0.976546i | 0.872691 | + | 0.488273i | \(0.162373\pi\) | ||||
−0.872691 | + | 0.488273i | \(0.837627\pi\) | |||||||
\(152\) | − | 1.24264i | − | 0.100791i | ||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 8.82843 | 0.711415 | ||||||||
\(155\) | 20.8284 | + | 10.4142i | 1.67298 | + | 0.836490i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 12.0000i | − | 0.957704i | −0.877896 | − | 0.478852i | \(-0.841053\pi\) | ||
0.877896 | − | 0.478852i | \(-0.158947\pi\) | |||||||
\(158\) | −8.24264 | − | 8.24264i | −0.655749 | − | 0.655749i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −0.707107 | − | 2.12132i | −0.0559017 | − | 0.167705i | ||||
\(161\) | − | 5.65685i | − | 0.445823i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −12.4853 | + | 12.4853i | −0.977923 | + | 0.977923i | −0.999762 | − | 0.0218388i | \(-0.993048\pi\) |
0.0218388 | + | 0.999762i | \(0.493048\pi\) | |||||||
\(164\) | −1.58579 | − | 1.58579i | −0.123829 | − | 0.123829i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.24264 | 0.329293 | ||||||||
\(167\) | 13.0711 | + | 13.0711i | 1.01147 | + | 1.01147i | 0.999933 | + | 0.0115361i | \(0.00367215\pi\) |
0.0115361 | + | 0.999933i | \(0.496328\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 4.00000 | 0.307692 | ||||||||
\(170\) | −9.00000 | − | 2.00000i | −0.690268 | − | 0.153393i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −12.2426 | −0.933493 | ||||||||
\(173\) | 6.34315 | + | 6.34315i | 0.482260 | + | 0.482260i | 0.905853 | − | 0.423592i | \(-0.139231\pi\) |
−0.423592 | + | 0.905853i | \(0.639231\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | − | 7.00000i | 0.0755929 | − | 0.529150i | ||||
\(176\) | 4.41421 | + | 4.41421i | 0.332734 | + | 0.332734i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.48528 | −0.411139 | ||||||||
\(179\) | 23.3137i | 1.74255i | 0.490797 | + | 0.871274i | \(0.336706\pi\) | ||||
−0.490797 | + | 0.871274i | \(0.663294\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −14.0000 | − | 14.0000i | −1.04061 | − | 1.04061i | −0.999140 | − | 0.0414721i | \(-0.986795\pi\) |
−0.0414721 | − | 0.999140i | \(-0.513205\pi\) | |||||||
\(182\) | 3.00000 | + | 3.00000i | 0.222375 | + | 0.222375i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.82843 | − | 2.82843i | 0.208514 | − | 0.208514i | ||||
\(185\) | −4.58579 | + | 9.17157i | −0.337154 | + | 0.674307i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 24.9706 | − | 6.24264i | 1.82603 | − | 0.456507i | ||||
\(188\) | 4.41421i | 0.321940i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 2.63604 | − | 0.878680i | 0.191238 | − | 0.0637461i | ||||
\(191\) | 21.2132 | 1.53493 | 0.767467 | − | 0.641089i | \(-0.221517\pi\) | ||||
0.767467 | + | 0.641089i | \(0.221517\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.51472 | + | 1.51472i | −0.109032 | + | 0.109032i | −0.759518 | − | 0.650486i | \(-0.774565\pi\) |
0.650486 | + | 0.759518i | \(0.274565\pi\) | |||||||
\(194\) | −4.12132 | − | 4.12132i | −0.295894 | − | 0.295894i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 5.00000i | 0.357143i | ||||||||
\(197\) | 14.6569 | − | 14.6569i | 1.04426 | − | 1.04426i | 0.0452834 | − | 0.998974i | \(-0.485581\pi\) |
0.998974 | − | 0.0452834i | \(-0.0144191\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2.87868 | + | 2.87868i | −0.204064 | + | 0.204064i | −0.801739 | − | 0.597675i | \(-0.796091\pi\) |
0.597675 | + | 0.801739i | \(0.296091\pi\) | |||||||
\(200\) | 4.00000 | − | 3.00000i | 0.282843 | − | 0.212132i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.41421i | 0.0992583i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.24264 | − | 4.48528i | 0.156633 | − | 0.313266i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.00000i | 0.208013i | ||||||||
\(209\) | −5.48528 | + | 5.48528i | −0.379425 | + | 0.379425i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −8.00000 | − | 8.00000i | −0.550743 | − | 0.550743i | 0.375912 | − | 0.926655i | \(-0.377329\pi\) |
−0.926655 | + | 0.375912i | \(0.877329\pi\) | |||||||
\(212\) | −3.00000 | −0.206041 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.82843 | − | 2.82843i | −0.193347 | − | 0.193347i | ||||
\(215\) | −8.65685 | − | 25.9706i | −0.590393 | − | 1.77118i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 14.7279i | 0.999796i | ||||||||
\(218\) | 12.6066 | + | 12.6066i | 0.853827 | + | 0.853827i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −6.24264 | + | 12.4853i | −0.420879 | + | 0.841757i | ||||
\(221\) | 10.6066 | + | 6.36396i | 0.713477 | + | 0.428086i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 14.7574 | 0.988226 | 0.494113 | − | 0.869398i | \(-0.335493\pi\) | ||||
0.494113 | + | 0.869398i | \(0.335493\pi\) | |||||||
\(224\) | 1.00000 | − | 1.00000i | 0.0668153 | − | 0.0668153i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −9.53553 | + | 9.53553i | −0.634294 | + | 0.634294i | ||||
\(227\) | −13.9497 | + | 13.9497i | −0.925877 | + | 0.925877i | −0.997436 | − | 0.0715591i | \(-0.977203\pi\) |
0.0715591 | + | 0.997436i | \(0.477203\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 16.2426i | − | 1.07334i | −0.843791 | − | 0.536672i | \(-0.819681\pi\) | ||
0.843791 | − | 0.536672i | \(-0.180319\pi\) | |||||||
\(230\) | 8.00000 | + | 4.00000i | 0.527504 | + | 0.263752i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −0.707107 | + | 0.707107i | −0.0464238 | + | 0.0464238i | ||||
\(233\) | −1.05025 | − | 1.05025i | −0.0688043 | − | 0.0688043i | 0.671867 | − | 0.740672i | \(-0.265493\pi\) |
−0.740672 | + | 0.671867i | \(0.765493\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.36396 | + | 3.12132i | −0.610837 | + | 0.203612i | ||||
\(236\) | − | 6.89949i | − | 0.449119i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.41421 | − | 5.65685i | −0.0916698 | − | 0.366679i | ||||
\(239\) | −13.7574 | −0.889890 | −0.444945 | − | 0.895558i | \(-0.646777\pi\) | ||||
−0.444945 | + | 0.895558i | \(0.646777\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.2426 | − | 11.2426i | 0.724202 | − | 0.724202i | −0.245256 | − | 0.969458i | \(-0.578872\pi\) |
0.969458 | + | 0.245256i | \(0.0788721\pi\) | |||||||
\(242\) | − | 27.9706i | − | 1.79802i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.87868 | + | 1.87868i | 0.120270 | + | 0.120270i | ||||
\(245\) | −10.6066 | + | 3.53553i | −0.677631 | + | 0.225877i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.72792 | −0.237202 | ||||||||
\(248\) | −7.36396 | + | 7.36396i | −0.467612 | + | 0.467612i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 9.19239 | + | 6.36396i | 0.581378 | + | 0.402492i | ||||
\(251\) | −3.51472 | −0.221847 | −0.110924 | − | 0.993829i | \(-0.535381\pi\) | ||||
−0.110924 | + | 0.993829i | \(0.535381\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −24.9706 | −1.56989 | ||||||||
\(254\) | −7.72792 | −0.484893 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −18.7279 | −1.16822 | −0.584108 | − | 0.811676i | \(-0.698555\pi\) | ||||
−0.584108 | + | 0.811676i | \(0.698555\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.48528 | −0.402976 | ||||||||
\(260\) | −6.36396 | + | 2.12132i | −0.394676 | + | 0.131559i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 10.4142 | − | 10.4142i | 0.643392 | − | 0.643392i | ||||
\(263\) | 13.2426 | 0.816576 | 0.408288 | − | 0.912853i | \(-0.366126\pi\) | ||||
0.408288 | + | 0.912853i | \(0.366126\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.12132 | − | 6.36396i | −0.130312 | − | 0.390935i | ||||
\(266\) | 1.24264 | + | 1.24264i | 0.0761912 | + | 0.0761912i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | − | 2.48528i | − | 0.151813i | ||||||
\(269\) | 12.7071 | − | 12.7071i | 0.774766 | − | 0.774766i | −0.204170 | − | 0.978936i | \(-0.565449\pi\) |
0.978936 | + | 0.204170i | \(0.0654494\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.4853 | 0.636935 | 0.318468 | − | 0.947934i | \(-0.396832\pi\) | ||||
0.318468 | + | 0.947934i | \(0.396832\pi\) | |||||||
\(272\) | 2.12132 | − | 3.53553i | 0.128624 | − | 0.214373i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 7.41421i | − | 0.447909i | ||||||
\(275\) | −30.8995 | − | 4.41421i | −1.86331 | − | 0.266187i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.242641 | + | 0.242641i | 0.0145789 | + | 0.0145789i | 0.714359 | − | 0.699780i | \(-0.246719\pi\) |
−0.699780 | + | 0.714359i | \(0.746719\pi\) | |||||||
\(278\) | 11.0000 | − | 11.0000i | 0.659736 | − | 0.659736i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.82843 | + | 1.41421i | 0.169031 | + | 0.0845154i | ||||
\(281\) | − | 14.6569i | − | 0.874355i | −0.899375 | − | 0.437177i | \(-0.855978\pi\) | ||
0.899375 | − | 0.437177i | \(-0.144022\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 14.8787 | − | 14.8787i | 0.884446 | − | 0.884446i | −0.109537 | − | 0.993983i | \(-0.534937\pi\) |
0.993983 | + | 0.109537i | \(0.0349368\pi\) | |||||||
\(284\) | −2.29289 | + | 2.29289i | −0.136058 | + | 0.136058i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 13.2426 | − | 13.2426i | 0.783054 | − | 0.783054i | ||||
\(287\) | 3.17157 | 0.187212 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −8.00000 | − | 15.0000i | −0.470588 | − | 0.882353i | ||||
\(290\) | −2.00000 | − | 1.00000i | −0.117444 | − | 0.0587220i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.36396 | − | 4.36396i | −0.255382 | − | 0.255382i | ||||
\(293\) | − | 9.34315i | − | 0.545832i | −0.962038 | − | 0.272916i | \(-0.912012\pi\) | ||
0.962038 | − | 0.272916i | \(-0.0879882\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 14.6360 | − | 4.87868i | 0.852143 | − | 0.284048i | ||||
\(296\) | −3.24264 | − | 3.24264i | −0.188475 | − | 0.188475i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 12.7279 | 0.737309 | ||||||||
\(299\) | −8.48528 | − | 8.48528i | −0.490716 | − | 0.490716i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 12.2426 | − | 12.2426i | 0.705654 | − | 0.705654i | ||||
\(302\) | − | 12.0000i | − | 0.690522i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.24264i | 0.0712703i | ||||||||
\(305\) | −2.65685 | + | 5.31371i | −0.152131 | + | 0.304262i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 9.21320i | − | 0.525825i | −0.964820 | − | 0.262913i | \(-0.915317\pi\) | ||
0.964820 | − | 0.262913i | \(-0.0846831\pi\) | |||||||
\(308\) | −8.82843 | −0.503046 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −20.8284 | − | 10.4142i | −1.18298 | − | 0.591488i | ||||
\(311\) | −1.41421 | + | 1.41421i | −0.0801927 | + | 0.0801927i | −0.746065 | − | 0.665873i | \(-0.768059\pi\) |
0.665873 | + | 0.746065i | \(0.268059\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5.51472 | − | 5.51472i | 0.311710 | − | 0.311710i | −0.533862 | − | 0.845572i | \(-0.679260\pi\) |
0.845572 | + | 0.533862i | \(0.179260\pi\) | |||||||
\(314\) | 12.0000i | 0.677199i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 8.24264 | + | 8.24264i | 0.463685 | + | 0.463685i | ||||
\(317\) | 14.1421 | − | 14.1421i | 0.794301 | − | 0.794301i | −0.187889 | − | 0.982190i | \(-0.560164\pi\) |
0.982190 | + | 0.187889i | \(0.0601645\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 6.24264 | 0.349521 | ||||||||
\(320\) | 0.707107 | + | 2.12132i | 0.0395285 | + | 0.118585i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.65685i | 0.315244i | ||||||||
\(323\) | 4.39340 | + | 2.63604i | 0.244455 | + | 0.146673i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −9.00000 | − | 12.0000i | −0.499230 | − | 0.665640i | ||||
\(326\) | 12.4853 | − | 12.4853i | 0.691496 | − | 0.691496i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.58579 | + | 1.58579i | 0.0875604 | + | 0.0875604i | ||||
\(329\) | −4.41421 | − | 4.41421i | −0.243363 | − | 0.243363i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 9.72792i | − | 0.534695i | −0.963600 | − | 0.267347i | \(-0.913853\pi\) | ||
0.963600 | − | 0.267347i | \(-0.0861472\pi\) | |||||||
\(332\) | −4.24264 | −0.232845 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −13.0711 | − | 13.0711i | −0.715217 | − | 0.715217i | ||||
\(335\) | 5.27208 | − | 1.75736i | 0.288044 | − | 0.0960148i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 16.8492 | + | 16.8492i | 0.917837 | + | 0.917837i | 0.996872 | − | 0.0790351i | \(-0.0251839\pi\) |
−0.0790351 | + | 0.996872i | \(0.525184\pi\) | |||||||
\(338\) | −4.00000 | −0.217571 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 9.00000 | + | 2.00000i | 0.488094 | + | 0.108465i | ||||
\(341\) | 65.0122 | 3.52061 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −12.0000 | − | 12.0000i | −0.647939 | − | 0.647939i | ||||
\(344\) | 12.2426 | 0.660079 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −6.34315 | − | 6.34315i | −0.341010 | − | 0.341010i | ||||
\(347\) | 14.2929 | − | 14.2929i | 0.767283 | − | 0.767283i | −0.210345 | − | 0.977627i | \(-0.567459\pi\) |
0.977627 | + | 0.210345i | \(0.0674586\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 22.9706i | 1.22959i | 0.788688 | + | 0.614793i | \(0.210760\pi\) | ||||
−0.788688 | + | 0.614793i | \(0.789240\pi\) | |||||||
\(350\) | −1.00000 | + | 7.00000i | −0.0534522 | + | 0.374166i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.41421 | − | 4.41421i | −0.235278 | − | 0.235278i | ||||
\(353\) | − | 11.3137i | − | 0.602168i | −0.953598 | − | 0.301084i | \(-0.902652\pi\) | ||
0.953598 | − | 0.301084i | \(-0.0973484\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.48528 | − | 3.24264i | −0.344203 | − | 0.172101i | ||||
\(356\) | 5.48528 | 0.290719 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | − | 23.3137i | − | 1.23217i | ||||||
\(359\) | 7.07107i | 0.373197i | 0.982436 | + | 0.186598i | \(0.0597463\pi\) | ||||
−0.982436 | + | 0.186598i | \(0.940254\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 17.4558 | 0.918729 | ||||||||
\(362\) | 14.0000 | + | 14.0000i | 0.735824 | + | 0.735824i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.00000 | − | 3.00000i | −0.157243 | − | 0.157243i | ||||
\(365\) | 6.17157 | − | 12.3431i | 0.323035 | − | 0.646070i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.75736 | − | 9.75736i | 0.509330 | − | 0.509330i | −0.404991 | − | 0.914321i | \(-0.632725\pi\) |
0.914321 | + | 0.404991i | \(0.132725\pi\) | |||||||
\(368\) | −2.82843 | + | 2.82843i | −0.147442 | + | 0.147442i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.58579 | − | 9.17157i | 0.238404 | − | 0.476807i | ||||
\(371\) | 3.00000 | − | 3.00000i | 0.155752 | − | 0.155752i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 15.5147i | − | 0.803322i | −0.915788 | − | 0.401661i | \(-0.868433\pi\) | ||
0.915788 | − | 0.401661i | \(-0.131567\pi\) | |||||||
\(374\) | −24.9706 | + | 6.24264i | −1.29120 | + | 0.322799i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 4.41421i | − | 0.227646i | ||||||
\(377\) | 2.12132 | + | 2.12132i | 0.109254 | + | 0.109254i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −16.4853 | + | 16.4853i | −0.846792 | + | 0.846792i | −0.989731 | − | 0.142939i | \(-0.954345\pi\) |
0.142939 | + | 0.989731i | \(0.454345\pi\) | |||||||
\(380\) | −2.63604 | + | 0.878680i | −0.135226 | + | 0.0450753i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −21.2132 | −1.08536 | ||||||||
\(383\) | −4.75736 | −0.243090 | −0.121545 | − | 0.992586i | \(-0.538785\pi\) | ||||
−0.121545 | + | 0.992586i | \(0.538785\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.24264 | − | 18.7279i | −0.318154 | − | 0.954463i | ||||
\(386\) | 1.51472 | − | 1.51472i | 0.0770971 | − | 0.0770971i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4.12132 | + | 4.12132i | 0.209228 | + | 0.209228i | ||||
\(389\) | − | 28.6274i | − | 1.45147i | −0.687976 | − | 0.725734i | \(-0.741500\pi\) | ||
0.687976 | − | 0.725734i | \(-0.258500\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.00000 | + | 16.0000i | 0.202289 | + | 0.809155i | ||||
\(392\) | − | 5.00000i | − | 0.252538i | ||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −14.6569 | + | 14.6569i | −0.738402 | + | 0.738402i | ||||
\(395\) | −11.6569 | + | 23.3137i | −0.586520 | + | 1.17304i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.7279 | − | 20.7279i | 1.04030 | − | 1.04030i | 0.0411517 | − | 0.999153i | \(-0.486897\pi\) |
0.999153 | − | 0.0411517i | \(-0.0131027\pi\) | |||||||
\(398\) | 2.87868 | − | 2.87868i | 0.144295 | − | 0.144295i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.00000 | + | 3.00000i | −0.200000 | + | 0.150000i | ||||
\(401\) | 21.8995 | + | 21.8995i | 1.09361 | + | 1.09361i | 0.995140 | + | 0.0984684i | \(0.0313943\pi\) |
0.0984684 | + | 0.995140i | \(0.468606\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 22.0919 | + | 22.0919i | 1.10048 | + | 1.10048i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | − | 1.41421i | − | 0.0701862i | ||||||
\(407\) | 28.6274i | 1.41901i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.51472 | 0.421026 | 0.210513 | − | 0.977591i | \(-0.432487\pi\) | ||||
0.210513 | + | 0.977591i | \(0.432487\pi\) | |||||||
\(410\) | −2.24264 | + | 4.48528i | −0.110756 | + | 0.221512i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.89949 | + | 6.89949i | 0.339502 | + | 0.339502i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −3.00000 | − | 9.00000i | −0.147264 | − | 0.441793i | ||||
\(416\) | − | 3.00000i | − | 0.147087i | ||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 5.48528 | − | 5.48528i | 0.268294 | − | 0.268294i | ||||
\(419\) | −11.3137 | − | 11.3137i | −0.552711 | − | 0.552711i | 0.374511 | − | 0.927222i | \(-0.377810\pi\) |
−0.927222 | + | 0.374511i | \(0.877810\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 23.2132 | 1.13134 | 0.565671 | − | 0.824631i | \(-0.308617\pi\) | ||||
0.565671 | + | 0.824631i | \(0.308617\pi\) | |||||||
\(422\) | 8.00000 | + | 8.00000i | 0.389434 | + | 0.389434i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.00000 | 0.145693 | ||||||||
\(425\) | 2.12132 | + | 20.5061i | 0.102899 | + | 0.994692i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.75736 | −0.181831 | ||||||||
\(428\) | 2.82843 | + | 2.82843i | 0.136717 | + | 0.136717i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 8.65685 | + | 25.9706i | 0.417471 | + | 1.25241i | ||||
\(431\) | −6.34315 | − | 6.34315i | −0.305539 | − | 0.305539i | 0.537638 | − | 0.843176i | \(-0.319317\pi\) |
−0.843176 | + | 0.537638i | \(0.819317\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 14.2426 | 0.684458 | 0.342229 | − | 0.939617i | \(-0.388818\pi\) | ||||
0.342229 | + | 0.939617i | \(0.388818\pi\) | |||||||
\(434\) | − | 14.7279i | − | 0.706963i | ||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −12.6066 | − | 12.6066i | −0.603747 | − | 0.603747i | ||||
\(437\) | −3.51472 | − | 3.51472i | −0.168132 | − | 0.168132i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.9706 | + | 12.9706i | −0.619051 | + | 0.619051i | −0.945288 | − | 0.326237i | \(-0.894219\pi\) |
0.326237 | + | 0.945288i | \(0.394219\pi\) | |||||||
\(440\) | 6.24264 | − | 12.4853i | 0.297606 | − | 0.595212i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10.6066 | − | 6.36396i | −0.504505 | − | 0.302703i | ||||
\(443\) | − | 1.79899i | − | 0.0854726i | −0.999086 | − | 0.0427363i | \(-0.986392\pi\) | ||
0.999086 | − | 0.0427363i | \(-0.0136075\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.87868 | + | 11.6360i | 0.183867 | + | 0.551601i | ||||
\(446\) | −14.7574 | −0.698781 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.00000 | + | 1.00000i | −0.0472456 | + | 0.0472456i | ||||
\(449\) | −10.7990 | − | 10.7990i | −0.509636 | − | 0.509636i | 0.404779 | − | 0.914415i | \(-0.367349\pi\) |
−0.914415 | + | 0.404779i | \(0.867349\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 14.0000i | − | 0.659234i | ||||||
\(452\) | 9.53553 | − | 9.53553i | 0.448514 | − | 0.448514i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 13.9497 | − | 13.9497i | 0.654694 | − | 0.654694i | ||||
\(455\) | 4.24264 | − | 8.48528i | 0.198898 | − | 0.397796i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −6.24264 | −0.292018 | −0.146009 | − | 0.989283i | \(-0.546643\pi\) | ||||
−0.146009 | + | 0.989283i | \(0.546643\pi\) | |||||||
\(458\) | 16.2426i | 0.758969i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −8.00000 | − | 4.00000i | −0.373002 | − | 0.186501i | ||||
\(461\) | 16.2843i | 0.758434i | 0.925308 | + | 0.379217i | \(0.123807\pi\) | ||||
−0.925308 | + | 0.379217i | \(0.876193\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.7574i | 0.778781i | 0.921073 | + | 0.389390i | \(0.127314\pi\) | ||||
−0.921073 | + | 0.389390i | \(0.872686\pi\) | |||||||
\(464\) | 0.707107 | − | 0.707107i | 0.0328266 | − | 0.0328266i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.05025 | + | 1.05025i | 0.0486520 | + | 0.0486520i | ||||
\(467\) | 6.72792 | 0.311331 | 0.155666 | − | 0.987810i | \(-0.450248\pi\) | ||||
0.155666 | + | 0.987810i | \(0.450248\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.48528 | + | 2.48528i | 0.114760 | + | 0.114760i | ||||
\(470\) | 9.36396 | − | 3.12132i | 0.431927 | − | 0.143976i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 6.89949i | 0.317575i | ||||||||
\(473\) | −54.0416 | − | 54.0416i | −2.48484 | − | 2.48484i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.72792 | − | 4.97056i | −0.171049 | − | 0.228065i | ||||
\(476\) | 1.41421 | + | 5.65685i | 0.0648204 | + | 0.259281i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 13.7574 | 0.629247 | ||||||||
\(479\) | 19.9497 | − | 19.9497i | 0.911527 | − | 0.911527i | −0.0848652 | − | 0.996392i | \(-0.527046\pi\) |
0.996392 | + | 0.0848652i | \(0.0270460\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.72792 | + | 9.72792i | −0.443555 | + | 0.443555i | ||||
\(482\) | −11.2426 | + | 11.2426i | −0.512088 | + | 0.512088i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 27.9706i | 1.27139i | ||||||||
\(485\) | −5.82843 | + | 11.6569i | −0.264655 | + | 0.529310i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.75736 | + | 2.75736i | −0.124948 | + | 0.124948i | −0.766815 | − | 0.641868i | \(-0.778160\pi\) |
0.641868 | + | 0.766815i | \(0.278160\pi\) | |||||||
\(488\) | −1.87868 | − | 1.87868i | −0.0850438 | − | 0.0850438i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 10.6066 | − | 3.53553i | 0.479157 | − | 0.159719i | ||||
\(491\) | − | 12.8995i | − | 0.582146i | −0.956701 | − | 0.291073i | \(-0.905988\pi\) | ||
0.956701 | − | 0.291073i | \(-0.0940123\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.00000 | − | 4.00000i | −0.0450377 | − | 0.180151i | ||||
\(494\) | 3.72792 | 0.167727 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.36396 | − | 7.36396i | 0.330652 | − | 0.330652i | ||||
\(497\) | − | 4.58579i | − | 0.205701i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.4853 | − | 25.4853i | −1.14088 | − | 1.14088i | −0.988290 | − | 0.152588i | \(-0.951239\pi\) |
−0.152588 | − | 0.988290i | \(-0.548761\pi\) | |||||||
\(500\) | −9.19239 | − | 6.36396i | −0.411096 | − | 0.284605i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 3.51472 | 0.156870 | ||||||||
\(503\) | −1.07107 | + | 1.07107i | −0.0477566 | + | 0.0477566i | −0.730582 | − | 0.682825i | \(-0.760751\pi\) |
0.682825 | + | 0.730582i | \(0.260751\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 24.9706 | 1.11008 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 7.72792 | 0.342871 | ||||||||
\(509\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 8.72792 | 0.386101 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 18.7279 | 0.826053 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −19.4853 | + | 19.4853i | −0.856962 | + | 0.856962i | ||||
\(518\) | 6.48528 | 0.284947 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 6.36396 | − | 2.12132i | 0.279078 | − | 0.0930261i | ||||
\(521\) | −11.3137 | − | 11.3137i | −0.495663 | − | 0.495663i | 0.414422 | − | 0.910085i | \(-0.363984\pi\) |
−0.910085 | + | 0.414422i | \(0.863984\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 9.51472i | 0.416050i | 0.978124 | + | 0.208025i | \(0.0667035\pi\) | ||||
−0.978124 | + | 0.208025i | \(0.933297\pi\) | |||||||
\(524\) | −10.4142 | + | 10.4142i | −0.454947 | + | 0.454947i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −13.2426 | −0.577407 | ||||||||
\(527\) | −10.4142 | − | 41.6569i | −0.453650 | − | 1.81460i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.00000i | 0.304348i | ||||||||
\(530\) | 2.12132 | + | 6.36396i | 0.0921443 | + | 0.276433i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.24264 | − | 1.24264i | −0.0538753 | − | 0.0538753i | ||||
\(533\) | 4.75736 | − | 4.75736i | 0.206064 | − | 0.206064i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.00000 | + | 8.00000i | −0.172935 | + | 0.345870i | ||||
\(536\) | 2.48528i | 0.107348i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −12.7071 | + | 12.7071i | −0.547842 | + | 0.547842i | ||||
\(539\) | −22.0711 | + | 22.0711i | −0.950668 | + | 0.950668i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −12.9706 | + | 12.9706i | −0.557648 | + | 0.557648i | −0.928637 | − | 0.370989i | \(-0.879019\pi\) |
0.370989 | + | 0.928637i | \(0.379019\pi\) | |||||||
\(542\) | −10.4853 | −0.450381 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −2.12132 | + | 3.53553i | −0.0909509 | + | 0.151585i | ||||
\(545\) | 17.8284 | − | 35.6569i | 0.763686 | − | 1.52737i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.6066 | − | 23.6066i | −1.00935 | − | 1.00935i | −0.999956 | − | 0.00938949i | \(-0.997011\pi\) |
−0.00938949 | − | 0.999956i | \(-0.502989\pi\) | |||||||
\(548\) | 7.41421i | 0.316720i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 30.8995 | + | 4.41421i | 1.31756 | + | 0.188223i | ||||
\(551\) | 0.878680 | + | 0.878680i | 0.0374330 | + | 0.0374330i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −16.4853 | −0.701025 | ||||||||
\(554\) | −0.242641 | − | 0.242641i | −0.0103088 | − | 0.0103088i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11.0000 | + | 11.0000i | −0.466504 | + | 0.466504i | ||||
\(557\) | − | 4.79899i | − | 0.203340i | −0.994818 | − | 0.101670i | \(-0.967581\pi\) | ||
0.994818 | − | 0.101670i | \(-0.0324185\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 36.7279i | − | 1.55343i | ||||||
\(560\) | −2.82843 | − | 1.41421i | −0.119523 | − | 0.0597614i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 14.6569i | 0.618262i | ||||||||
\(563\) | 21.9411 | 0.924708 | 0.462354 | − | 0.886695i | \(-0.347005\pi\) | ||||
0.462354 | + | 0.886695i | \(0.347005\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 26.9706 | + | 13.4853i | 1.13466 | + | 0.567330i | ||||
\(566\) | −14.8787 | + | 14.8787i | −0.625398 | + | 0.625398i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.29289 | − | 2.29289i | 0.0962077 | − | 0.0962077i | ||||
\(569\) | 2.31371i | 0.0969957i | 0.998823 | + | 0.0484979i | \(0.0154434\pi\) | ||||
−0.998823 | + | 0.0484979i | \(0.984557\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.2132 | + | 22.2132i | 0.929594 | + | 0.929594i | 0.997679 | − | 0.0680858i | \(-0.0216892\pi\) |
−0.0680858 | + | 0.997679i | \(0.521689\pi\) | |||||||
\(572\) | −13.2426 | + | 13.2426i | −0.553703 | + | 0.553703i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.17157 | −0.132379 | ||||||||
\(575\) | 2.82843 | − | 19.7990i | 0.117954 | − | 0.825675i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.9706i | 1.20606i | 0.797718 | + | 0.603030i | \(0.206040\pi\) | ||||
−0.797718 | + | 0.603030i | \(0.793960\pi\) | |||||||
\(578\) | 8.00000 | + | 15.0000i | 0.332756 | + | 0.623918i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.00000 | + | 1.00000i | 0.0830455 | + | 0.0415227i | ||||
\(581\) | 4.24264 | − | 4.24264i | 0.176014 | − | 0.176014i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −13.2426 | − | 13.2426i | −0.548454 | − | 0.548454i | ||||
\(584\) | 4.36396 | + | 4.36396i | 0.180582 | + | 0.180582i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 9.34315i | 0.385962i | ||||||||
\(587\) | 24.0000 | 0.990586 | 0.495293 | − | 0.868726i | \(-0.335061\pi\) | ||||
0.495293 | + | 0.868726i | \(0.335061\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 9.15076 | + | 9.15076i | 0.377050 | + | 0.377050i | ||||
\(590\) | −14.6360 | + | 4.87868i | −0.602556 | + | 0.200852i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.24264 | + | 3.24264i | 0.133272 | + | 0.133272i | ||||
\(593\) | 18.0000 | 0.739171 | 0.369586 | − | 0.929197i | \(-0.379500\pi\) | ||||
0.369586 | + | 0.929197i | \(0.379500\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −11.0000 | + | 7.00000i | −0.450956 | + | 0.286972i | ||||
\(596\) | −12.7279 | −0.521356 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 8.48528 | + | 8.48528i | 0.346989 | + | 0.346989i | ||||
\(599\) | 12.0000 | 0.490307 | 0.245153 | − | 0.969484i | \(-0.421162\pi\) | ||||
0.245153 | + | 0.969484i | \(0.421162\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.27208 | + | 3.27208i | 0.133471 | + | 0.133471i | 0.770686 | − | 0.637215i | \(-0.219914\pi\) |
−0.637215 | + | 0.770686i | \(0.719914\pi\) | |||||||
\(602\) | −12.2426 | + | 12.2426i | −0.498973 | + | 0.498973i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 12.0000i | 0.488273i | ||||||||
\(605\) | −59.3345 | + | 19.7782i | −2.41229 | + | 0.804097i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 24.4558 | + | 24.4558i | 0.992632 | + | 0.992632i | 0.999973 | − | 0.00734096i | \(-0.00233672\pi\) |
−0.00734096 | + | 0.999973i | \(0.502337\pi\) | |||||||
\(608\) | − | 1.24264i | − | 0.0503957i | ||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.65685 | − | 5.31371i | 0.107573 | − | 0.215146i | ||||
\(611\) | −13.2426 | −0.535740 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 37.9706i | − | 1.53362i | −0.641876 | − | 0.766808i | \(-0.721844\pi\) | ||
0.641876 | − | 0.766808i | \(-0.278156\pi\) | |||||||
\(614\) | 9.21320i | 0.371815i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 8.82843 | 0.355707 | ||||||||
\(617\) | 7.43503 | + | 7.43503i | 0.299323 | + | 0.299323i | 0.840749 | − | 0.541426i | \(-0.182115\pi\) |
−0.541426 | + | 0.840749i | \(0.682115\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 14.2426 | + | 14.2426i | 0.572460 | + | 0.572460i | 0.932815 | − | 0.360355i | \(-0.117344\pi\) |
−0.360355 | + | 0.932815i | \(0.617344\pi\) | |||||||
\(620\) | 20.8284 | + | 10.4142i | 0.836490 | + | 0.418245i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.41421 | − | 1.41421i | 0.0567048 | − | 0.0567048i | ||||
\(623\) | −5.48528 | + | 5.48528i | −0.219763 | + | 0.219763i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.00000 | − | 24.0000i | 0.280000 | − | 0.960000i | ||||
\(626\) | −5.51472 | + | 5.51472i | −0.220412 | + | 0.220412i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 12.0000i | − | 0.478852i | ||||||
\(629\) | 18.3431 | − | 4.58579i | 0.731389 | − | 0.182847i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 14.4853i | − | 0.576650i | −0.957533 | − | 0.288325i | \(-0.906902\pi\) | ||
0.957533 | − | 0.288325i | \(-0.0930983\pi\) | |||||||
\(632\) | −8.24264 | − | 8.24264i | −0.327875 | − | 0.327875i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −14.1421 | + | 14.1421i | −0.561656 | + | 0.561656i | ||||
\(635\) | 5.46447 | + | 16.3934i | 0.216851 | + | 0.650552i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −15.0000 | −0.594322 | ||||||||
\(638\) | −6.24264 | −0.247149 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −0.707107 | − | 2.12132i | −0.0279508 | − | 0.0838525i | ||||
\(641\) | 27.5563 | − | 27.5563i | 1.08841 | − | 1.08841i | 0.0927179 | − | 0.995692i | \(-0.470445\pi\) |
0.995692 | − | 0.0927179i | \(-0.0295555\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.2426 | + | 12.2426i | 0.482803 | + | 0.482803i | 0.906026 | − | 0.423223i | \(-0.139101\pi\) |
−0.423223 | + | 0.906026i | \(0.639101\pi\) | |||||||
\(644\) | − | 5.65685i | − | 0.222911i | ||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −4.39340 | − | 2.63604i | −0.172856 | − | 0.103714i | ||||
\(647\) | − | 17.5269i | − | 0.689054i | −0.938776 | − | 0.344527i | \(-0.888039\pi\) | ||
0.938776 | − | 0.344527i | \(-0.111961\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 30.4558 | − | 30.4558i | 1.19550 | − | 1.19550i | ||||
\(650\) | 9.00000 | + | 12.0000i | 0.353009 | + | 0.470679i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −12.4853 | + | 12.4853i | −0.488961 | + | 0.488961i | ||||
\(653\) | −34.7990 | + | 34.7990i | −1.36179 | + | 1.36179i | −0.490154 | + | 0.871636i | \(0.663059\pi\) |
−0.871636 | + | 0.490154i | \(0.836941\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −29.4558 | − | 14.7279i | −1.15094 | − | 0.575468i | ||||
\(656\) | −1.58579 | − | 1.58579i | −0.0619146 | − | 0.0619146i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 4.41421 | + | 4.41421i | 0.172084 | + | 0.172084i | ||||
\(659\) | 12.2132 | 0.475759 | 0.237879 | − | 0.971295i | \(-0.423548\pi\) | ||||
0.237879 | + | 0.971295i | \(0.423548\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 12.0000i | 0.466746i | 0.972387 | + | 0.233373i | \(0.0749763\pi\) | ||||
−0.972387 | + | 0.233373i | \(0.925024\pi\) | |||||||
\(662\) | 9.72792i | 0.378086i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.24264 | 0.164646 | ||||||||
\(665\) | 1.75736 | − | 3.51472i | 0.0681475 | − | 0.136295i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.00000i | 0.154881i | ||||||||
\(668\) | 13.0711 | + | 13.0711i | 0.505735 | + | 0.505735i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −5.27208 | + | 1.75736i | −0.203678 | + | 0.0678927i | ||||
\(671\) | 16.5858i | 0.640287i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −30.1213 | + | 30.1213i | −1.16109 | + | 1.16109i | −0.176855 | + | 0.984237i | \(0.556592\pi\) |
−0.984237 | + | 0.176855i | \(0.943408\pi\) | |||||||
\(674\) | −16.8492 | − | 16.8492i | −0.649009 | − | 0.649009i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 4.00000 | 0.153846 | ||||||||
\(677\) | 19.5858 | + | 19.5858i | 0.752743 | + | 0.752743i | 0.974990 | − | 0.222247i | \(-0.0713393\pi\) |
−0.222247 | + | 0.974990i | \(0.571339\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −8.24264 | −0.316324 | ||||||||
\(680\) | −9.00000 | − | 2.00000i | −0.345134 | − | 0.0766965i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −65.0122 | −2.48945 | ||||||||
\(683\) | 17.4645 | + | 17.4645i | 0.668259 | + | 0.668259i | 0.957313 | − | 0.289054i | \(-0.0933406\pi\) |
−0.289054 | + | 0.957313i | \(0.593341\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.7279 | + | 5.24264i | −0.600933 | + | 0.200311i | ||||
\(686\) | 12.0000 | + | 12.0000i | 0.458162 | + | 0.458162i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −12.2426 | −0.466746 | ||||||||
\(689\) | − | 9.00000i | − | 0.342873i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.48528 | − | 7.48528i | −0.284754 | − | 0.284754i | 0.550248 | − | 0.835001i | \(-0.314533\pi\) |
−0.835001 | + | 0.550248i | \(0.814533\pi\) | |||||||
\(692\) | 6.34315 | + | 6.34315i | 0.241130 | + | 0.241130i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −14.2929 | + | 14.2929i | −0.542551 | + | 0.542551i | ||||
\(695\) | −31.1127 | − | 15.5563i | −1.18017 | − | 0.590086i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −8.97056 | + | 2.24264i | −0.339784 | + | 0.0849461i | ||||
\(698\) | − | 22.9706i | − | 0.869449i | ||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.00000 | − | 7.00000i | 0.0377964 | − | 0.264575i | ||||
\(701\) | 12.0000 | 0.453234 | 0.226617 | − | 0.973984i | \(-0.427233\pi\) | ||||
0.226617 | + | 0.973984i | \(0.427233\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −4.02944 | + | 4.02944i | −0.151973 | + | 0.151973i | ||||
\(704\) | 4.41421 | + | 4.41421i | 0.166367 | + | 0.166367i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 11.3137i | 0.425797i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −18.6066 | + | 18.6066i | −0.698786 | + | 0.698786i | −0.964149 | − | 0.265363i | \(-0.914508\pi\) |
0.265363 | + | 0.964149i | \(0.414508\pi\) | |||||||
\(710\) | 6.48528 | + | 3.24264i | 0.243388 | + | 0.121694i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.48528 | −0.205570 | ||||||||
\(713\) | 41.6569i | 1.56006i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −37.4558 | − | 18.7279i | −1.40077 | − | 0.700385i | ||||
\(716\) | 23.3137i | 0.871274i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | − | 7.07107i | − | 0.263890i | ||||||
\(719\) | −21.7487 | + | 21.7487i | −0.811091 | + | 0.811091i | −0.984797 | − | 0.173706i | \(-0.944426\pi\) |
0.173706 | + | 0.984797i | \(0.444426\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −17.4558 | −0.649639 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −14.0000 | − | 14.0000i | −0.520306 | − | 0.520306i | ||||
\(725\) | −0.707107 | + | 4.94975i | −0.0262613 | + | 0.183829i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 25.2426i | 0.936198i | 0.883676 | + | 0.468099i | \(0.155061\pi\) | ||||
−0.883676 | + | 0.468099i | \(0.844939\pi\) | |||||||
\(728\) | 3.00000 | + | 3.00000i | 0.111187 | + | 0.111187i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −6.17157 | + | 12.3431i | −0.228420 | + | 0.456840i | ||||
\(731\) | −25.9706 | + | 43.2843i | −0.960556 | + | 1.60093i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.970563 | −0.0358486 | −0.0179243 | − | 0.999839i | \(-0.505706\pi\) | ||||
−0.0179243 | + | 0.999839i | \(0.505706\pi\) | |||||||
\(734\) | −9.75736 | + | 9.75736i | −0.360151 | + | 0.360151i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 2.82843 | − | 2.82843i | 0.104257 | − | 0.104257i | ||||
\(737\) | 10.9706 | − | 10.9706i | 0.404106 | − | 0.404106i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 41.1838i | − | 1.51497i | −0.652853 | − | 0.757485i | \(-0.726428\pi\) | ||
0.652853 | − | 0.757485i | \(-0.273572\pi\) | |||||||
\(740\) | −4.58579 | + | 9.17157i | −0.168577 | + | 0.337154i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −3.00000 | + | 3.00000i | −0.110133 | + | 0.110133i | ||||
\(743\) | −12.1716 | − | 12.1716i | −0.446532 | − | 0.446532i | 0.447668 | − | 0.894200i | \(-0.352255\pi\) |
−0.894200 | + | 0.447668i | \(0.852255\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.00000 | − | 27.0000i | −0.329734 | − | 0.989203i | ||||
\(746\) | 15.5147i | 0.568034i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 24.9706 | − | 6.24264i | 0.913014 | − | 0.228254i | ||||
\(749\) | −5.65685 | −0.206697 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.63604 | − | 6.63604i | 0.242153 | − | 0.242153i | −0.575588 | − | 0.817740i | \(-0.695227\pi\) |
0.817740 | + | 0.575588i | \(0.195227\pi\) | |||||||
\(752\) | 4.41421i | 0.160970i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.12132 | − | 2.12132i | −0.0772539 | − | 0.0772539i | ||||
\(755\) | −25.4558 | + | 8.48528i | −0.926433 | + | 0.308811i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 34.9411 | 1.26996 | 0.634978 | − | 0.772530i | \(-0.281009\pi\) | ||||
0.634978 | + | 0.772530i | \(0.281009\pi\) | |||||||
\(758\) | 16.4853 | − | 16.4853i | 0.598772 | − | 0.598772i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2.63604 | − | 0.878680i | 0.0956192 | − | 0.0318731i | ||||
\(761\) | −3.51472 | −0.127408 | −0.0637042 | − | 0.997969i | \(-0.520291\pi\) | ||||
−0.0637042 | + | 0.997969i | \(0.520291\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25.2132 | 0.912779 | ||||||||
\(764\) | 21.2132 | 0.767467 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.75736 | 0.171890 | ||||||||
\(767\) | 20.6985 | 0.747379 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.4558 | 1.31463 | 0.657316 | − | 0.753615i | \(-0.271692\pi\) | ||||
0.657316 | + | 0.753615i | \(0.271692\pi\) | |||||||
\(770\) | 6.24264 | + | 18.7279i | 0.224969 | + | 0.674907i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −1.51472 | + | 1.51472i | −0.0545159 | + | 0.0545159i | ||||
\(773\) | −15.5147 | −0.558026 | −0.279013 | − | 0.960287i | \(-0.590007\pi\) | ||||
−0.279013 | + | 0.960287i | \(0.590007\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −7.36396 | + | 51.5477i | −0.264521 | + | 1.85165i | ||||
\(776\) | −4.12132 | − | 4.12132i | −0.147947 | − | 0.147947i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 28.6274i | 1.02634i | ||||||||
\(779\) | 1.97056 | − | 1.97056i | 0.0706027 | − | 0.0706027i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −20.2426 | −0.724339 | ||||||||
\(782\) | −4.00000 | − | 16.0000i | −0.143040 | − | 0.572159i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5.00000i | 0.178571i | ||||||||
\(785\) | 25.4558 | − | 8.48528i | 0.908558 | − | 0.302853i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 11.3640 | + | 11.3640i | 0.405081 | + | 0.405081i | 0.880019 | − | 0.474938i | \(-0.157529\pi\) |
−0.474938 | + | 0.880019i | \(0.657529\pi\) | |||||||
\(788\) | 14.6569 | − | 14.6569i | 0.522129 | − | 0.522129i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 11.6569 | − | 23.3137i | 0.414732 | − | 0.829465i | ||||
\(791\) | 19.0711i | 0.678089i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5.63604 | + | 5.63604i | −0.200142 | + | 0.200142i | ||||
\(794\) | −20.7279 | + | 20.7279i | −0.735606 | + | 0.735606i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −2.87868 | + | 2.87868i | −0.102032 | + | 0.102032i | ||||
\(797\) | 4.97056 | 0.176066 | 0.0880332 | − | 0.996118i | \(-0.471942\pi\) | ||||
0.0880332 | + | 0.996118i | \(0.471942\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.6066 | + | 9.36396i | 0.552122 | + | 0.331273i | ||||
\(800\) | 4.00000 | − | 3.00000i | 0.141421 | − | 0.106066i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −21.8995 | − | 21.8995i | −0.773298 | − | 0.773298i | ||||
\(803\) | − | 38.5269i | − | 1.35959i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 12.0000 | − | 4.00000i | 0.422944 | − | 0.140981i | ||||
\(806\) | −22.0919 | − | 22.0919i | −0.778153 | − | 0.778153i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −6.85786 | − | 6.85786i | −0.241110 | − | 0.241110i | 0.576199 | − | 0.817309i | \(-0.304535\pi\) |
−0.817309 | + | 0.576199i | \(0.804535\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −7.48528 | + | 7.48528i | −0.262844 | + | 0.262844i | −0.826208 | − | 0.563365i | \(-0.809507\pi\) |
0.563365 | + | 0.826208i | \(0.309507\pi\) | |||||||
\(812\) | 1.41421i | 0.0496292i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 28.6274i | − | 1.00339i | ||||||
\(815\) | −35.3137 | − | 17.6569i | −1.23699 | − | 0.618493i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 15.2132i | − | 0.532243i | ||||||
\(818\) | −8.51472 | −0.297710 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 2.24264 | − | 4.48528i | 0.0783164 | − | 0.156633i | ||||
\(821\) | −6.02082 | + | 6.02082i | −0.210128 | + | 0.210128i | −0.804322 | − | 0.594194i | \(-0.797471\pi\) |
0.594194 | + | 0.804322i | \(0.297471\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 14.7279 | − | 14.7279i | 0.513383 | − | 0.513383i | −0.402178 | − | 0.915561i | \(-0.631747\pi\) |
0.915561 | + | 0.402178i | \(0.131747\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.89949 | − | 6.89949i | −0.240064 | − | 0.240064i | ||||
\(827\) | −17.3137 | + | 17.3137i | −0.602057 | + | 0.602057i | −0.940858 | − | 0.338801i | \(-0.889979\pi\) |
0.338801 | + | 0.940858i | \(0.389979\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.0000 | 0.486240 | 0.243120 | − | 0.969996i | \(-0.421829\pi\) | ||||
0.243120 | + | 0.969996i | \(0.421829\pi\) | |||||||
\(830\) | 3.00000 | + | 9.00000i | 0.104132 | + | 0.312395i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.00000i | 0.104006i | ||||||||
\(833\) | 17.6777 | + | 10.6066i | 0.612495 | + | 0.367497i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18.4853 | + | 36.9706i | −0.639710 | + | 1.27942i | ||||
\(836\) | −5.48528 | + | 5.48528i | −0.189712 | + | 0.189712i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 11.3137 | + | 11.3137i | 0.390826 | + | 0.390826i | ||||
\(839\) | 27.0208 | + | 27.0208i | 0.932862 | + | 0.932862i | 0.997884 | − | 0.0650217i | \(-0.0207117\pi\) |
−0.0650217 | + | 0.997884i | \(0.520712\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 28.0000i | 0.965517i | ||||||||
\(842\) | −23.2132 | −0.799980 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −8.00000 | − | 8.00000i | −0.275371 | − | 0.275371i | ||||
\(845\) | 2.82843 | + | 8.48528i | 0.0973009 | + | 0.291903i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −27.9706 | − | 27.9706i | −0.961080 | − | 0.961080i | ||||
\(848\) | −3.00000 | −0.103020 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −2.12132 | − | 20.5061i | −0.0727607 | − | 0.703353i | ||||
\(851\) | −18.3431 | −0.628795 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.4853 | + | 25.4853i | 0.872599 | + | 0.872599i | 0.992755 | − | 0.120156i | \(-0.0383394\pi\) |
−0.120156 | + | 0.992755i | \(0.538339\pi\) | |||||||
\(854\) | 3.75736 | 0.128574 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.82843 | − | 2.82843i | −0.0966736 | − | 0.0966736i | ||||
\(857\) | −1.43503 | + | 1.43503i | −0.0490197 | + | 0.0490197i | −0.731192 | − | 0.682172i | \(-0.761036\pi\) |
0.682172 | + | 0.731192i | \(0.261036\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 20.2721i | 0.691674i | 0.938295 | + | 0.345837i | \(0.112405\pi\) | ||||
−0.938295 | + | 0.345837i | \(0.887595\pi\) | |||||||
\(860\) | −8.65685 | − | 25.9706i | −0.295196 | − | 0.885589i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 6.34315 | + | 6.34315i | 0.216048 | + | 0.216048i | ||||
\(863\) | 7.11270i | 0.242119i | 0.992645 | + | 0.121060i | \(0.0386292\pi\) | ||||
−0.992645 | + | 0.121060i | \(0.961371\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.97056 | + | 17.9411i | −0.305008 | + | 0.610017i | ||||
\(866\) | −14.2426 | −0.483985 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 14.7279i | 0.499898i | ||||||||
\(869\) | 72.7696i | 2.46854i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7.45584 | 0.252632 | ||||||||
\(872\) | 12.6066 | + | 12.6066i | 0.426913 | + | 0.426913i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 3.51472 | + | 3.51472i | 0.118887 | + | 0.118887i | ||||
\(875\) | 15.5563 | − | 2.82843i | 0.525901 | − | 0.0956183i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 25.4853 | − | 25.4853i | 0.860577 | − | 0.860577i | −0.130828 | − | 0.991405i | \(-0.541764\pi\) |
0.991405 | + | 0.130828i | \(0.0417636\pi\) | |||||||
\(878\) | 12.9706 | − | 12.9706i | 0.437735 | − | 0.437735i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −6.24264 | + | 12.4853i | −0.210439 | + | 0.420879i | ||||
\(881\) | 39.5563 | − | 39.5563i | 1.33269 | − | 1.33269i | 0.429730 | − | 0.902958i | \(-0.358609\pi\) |
0.902958 | − | 0.429730i | \(-0.141391\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.72792i | 0.226413i | 0.993572 | + | 0.113206i | \(0.0361121\pi\) | ||||
−0.993572 | + | 0.113206i | \(0.963888\pi\) | |||||||
\(884\) | 10.6066 | + | 6.36396i | 0.356739 | + | 0.214043i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.79899i | 0.0604382i | ||||||||
\(887\) | −22.4142 | − | 22.4142i | −0.752596 | − | 0.752596i | 0.222367 | − | 0.974963i | \(-0.428622\pi\) |
−0.974963 | + | 0.222367i | \(0.928622\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.72792 | + | 7.72792i | −0.259186 | + | 0.259186i | ||||
\(890\) | −3.87868 | − | 11.6360i | −0.130014 | − | 0.390041i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 14.7574 | 0.494113 | ||||||||
\(893\) | −5.48528 | −0.183558 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −49.4558 | + | 16.4853i | −1.65313 | + | 0.551042i | ||||
\(896\) | 1.00000 | − | 1.00000i | 0.0334077 | − | 0.0334077i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 10.7990 | + | 10.7990i | 0.360367 | + | 0.360367i | ||||
\(899\) | − | 10.4142i | − | 0.347333i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −6.36396 | + | 10.6066i | −0.212014 | + | 0.353357i | ||||
\(902\) | 14.0000i | 0.466149i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −9.53553 | + | 9.53553i | −0.317147 | + | 0.317147i | ||||
\(905\) | 19.7990 | − | 39.5980i | 0.658141 | − | 1.31628i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −21.8492 | + | 21.8492i | −0.725492 | + | 0.725492i | −0.969718 | − | 0.244226i | \(-0.921466\pi\) |
0.244226 | + | 0.969718i | \(0.421466\pi\) | |||||||
\(908\) | −13.9497 | + | 13.9497i | −0.462939 | + | 0.462939i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −4.24264 | + | 8.48528i | −0.140642 | + | 0.281284i | ||||
\(911\) | 12.6863 | + | 12.6863i | 0.420316 | + | 0.420316i | 0.885312 | − | 0.464997i | \(-0.153945\pi\) |
−0.464997 | + | 0.885312i | \(0.653945\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −18.7279 | − | 18.7279i | −0.619804 | − | 0.619804i | ||||
\(914\) | 6.24264 | 0.206488 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 16.2426i | − | 0.536672i | ||||||
\(917\) | − | 20.8284i | − | 0.687815i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 11.2132 | 0.369889 | 0.184945 | − | 0.982749i | \(-0.440789\pi\) | ||||
0.184945 | + | 0.982749i | \(0.440789\pi\) | |||||||
\(920\) | 8.00000 | + | 4.00000i | 0.263752 | + | 0.131876i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 16.2843i | − | 0.536294i | ||||||
\(923\) | −6.87868 | − | 6.87868i | −0.226414 | − | 0.226414i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −22.6985 | − | 3.24264i | −0.746322 | − | 0.106617i | ||||
\(926\) | − | 16.7574i | − | 0.550681i | ||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −0.707107 | + | 0.707107i | −0.0232119 | + | 0.0232119i | ||||
\(929\) | 26.6569 | + | 26.6569i | 0.874583 | + | 0.874583i | 0.992968 | − | 0.118385i | \(-0.0377716\pi\) |
−0.118385 | + | 0.992968i | \(0.537772\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −6.21320 | −0.203630 | ||||||||
\(932\) | −1.05025 | − | 1.05025i | −0.0344022 | − | 0.0344022i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6.72792 | −0.220144 | ||||||||
\(935\) | 30.8995 | + | 48.5563i | 1.01052 | + | 1.58796i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.78680 | −0.156378 | −0.0781889 | − | 0.996939i | \(-0.524914\pi\) | ||||
−0.0781889 | + | 0.996939i | \(0.524914\pi\) | |||||||
\(938\) | −2.48528 | − | 2.48528i | −0.0811473 | − | 0.0811473i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −9.36396 | + | 3.12132i | −0.305419 | + | 0.101806i | ||||
\(941\) | −33.1924 | − | 33.1924i | −1.08204 | − | 1.08204i | −0.996319 | − | 0.0857218i | \(-0.972680\pi\) |
−0.0857218 | − | 0.996319i | \(-0.527320\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.97056 | 0.292122 | ||||||||
\(944\) | − | 6.89949i | − | 0.224559i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 54.0416 | + | 54.0416i | 1.75704 | + | 1.75704i | ||||
\(947\) | 27.7071 | + | 27.7071i | 0.900360 | + | 0.900360i | 0.995467 | − | 0.0951071i | \(-0.0303193\pi\) |
−0.0951071 | + | 0.995467i | \(0.530319\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13.0919 | − | 13.0919i | 0.424981 | − | 0.424981i | ||||
\(950\) | 3.72792 | + | 4.97056i | 0.120950 | + | 0.161266i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.41421 | − | 5.65685i | −0.0458349 | − | 0.183340i | ||||
\(953\) | 7.41421i | 0.240170i | 0.992764 | + | 0.120085i | \(0.0383167\pi\) | ||||
−0.992764 | + | 0.120085i | \(0.961683\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.0000 | + | 45.0000i | 0.485389 | + | 1.45617i | ||||
\(956\) | −13.7574 | −0.444945 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −19.9497 | + | 19.9497i | −0.644547 | + | 0.644547i | ||||
\(959\) | −7.41421 | − | 7.41421i | −0.239417 | − | 0.239417i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | − | 77.4558i | − | 2.49858i | ||||||
\(962\) | 9.72792 | − | 9.72792i | 0.313641 | − | 0.313641i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 11.2426 | − | 11.2426i | 0.362101 | − | 0.362101i | ||||
\(965\) | −4.28427 | − | 2.14214i | −0.137916 | − | 0.0689578i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.97056 | 0.0955269 | 0.0477634 | − | 0.998859i | \(-0.484791\pi\) | ||||
0.0477634 | + | 0.998859i | \(0.484791\pi\) | |||||||
\(968\) | − | 27.9706i | − | 0.899008i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 5.82843 | − | 11.6569i | 0.187140 | − | 0.374279i | ||||
\(971\) | 0.556349i | 0.0178541i | 0.999960 | + | 0.00892705i | \(0.00284161\pi\) | ||||
−0.999960 | + | 0.00892705i | \(0.997158\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 22.0000i | − | 0.705288i | ||||||
\(974\) | 2.75736 | − | 2.75736i | 0.0883515 | − | 0.0883515i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.87868 | + | 1.87868i | 0.0601351 | + | 0.0601351i | ||||
\(977\) | −24.7279 | −0.791116 | −0.395558 | − | 0.918441i | \(-0.629449\pi\) | ||||
−0.395558 | + | 0.918441i | \(0.629449\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 24.2132 | + | 24.2132i | 0.773857 | + | 0.773857i | ||||
\(980\) | −10.6066 | + | 3.53553i | −0.338815 | + | 0.112938i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12.8995i | 0.411639i | ||||||||
\(983\) | 38.0122 | + | 38.0122i | 1.21240 | + | 1.21240i | 0.970235 | + | 0.242166i | \(0.0778578\pi\) |
0.242166 | + | 0.970235i | \(0.422142\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 41.4558 | + | 20.7279i | 1.32089 | + | 0.660447i | ||||
\(986\) | 1.00000 | + | 4.00000i | 0.0318465 | + | 0.127386i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −3.72792 | −0.118601 | ||||||||
\(989\) | 34.6274 | − | 34.6274i | 1.10109 | − | 1.10109i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 16.8787 | − | 16.8787i | 0.536169 | − | 0.536169i | −0.386233 | − | 0.922401i | \(-0.626224\pi\) |
0.922401 | + | 0.386233i | \(0.126224\pi\) | |||||||
\(992\) | −7.36396 | + | 7.36396i | −0.233806 | + | 0.233806i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4.58579i | 0.145452i | ||||||||
\(995\) | −8.14214 | − | 4.07107i | −0.258123 | − | 0.129062i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28.6985 | − | 28.6985i | 0.908890 | − | 0.908890i | −0.0872926 | − | 0.996183i | \(-0.527822\pi\) |
0.996183 | + | 0.0872926i | \(0.0278215\pi\) | |||||||
\(998\) | 25.4853 | + | 25.4853i | 0.806722 | + | 0.806722i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1530.2.n.j.1279.2 | 4 | ||
3.2 | odd | 2 | 170.2.g.f.89.2 | yes | 4 | ||
5.4 | even | 2 | 1530.2.n.o.1279.1 | 4 | |||
15.2 | even | 4 | 850.2.h.k.701.2 | 4 | |||
15.8 | even | 4 | 850.2.h.h.701.1 | 4 | |||
15.14 | odd | 2 | 170.2.g.e.89.1 | ✓ | 4 | ||
17.13 | even | 4 | 1530.2.n.o.829.1 | 4 | |||
51.47 | odd | 4 | 170.2.g.e.149.1 | yes | 4 | ||
85.64 | even | 4 | inner | 1530.2.n.j.829.2 | 4 | ||
255.47 | even | 4 | 850.2.h.k.251.2 | 4 | |||
255.98 | even | 4 | 850.2.h.h.251.1 | 4 | |||
255.149 | odd | 4 | 170.2.g.f.149.2 | yes | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
170.2.g.e.89.1 | ✓ | 4 | 15.14 | odd | 2 | ||
170.2.g.e.149.1 | yes | 4 | 51.47 | odd | 4 | ||
170.2.g.f.89.2 | yes | 4 | 3.2 | odd | 2 | ||
170.2.g.f.149.2 | yes | 4 | 255.149 | odd | 4 | ||
850.2.h.h.251.1 | 4 | 255.98 | even | 4 | |||
850.2.h.h.701.1 | 4 | 15.8 | even | 4 | |||
850.2.h.k.251.2 | 4 | 255.47 | even | 4 | |||
850.2.h.k.701.2 | 4 | 15.2 | even | 4 | |||
1530.2.n.j.829.2 | 4 | 85.64 | even | 4 | inner | ||
1530.2.n.j.1279.2 | 4 | 1.1 | even | 1 | trivial | ||
1530.2.n.o.829.1 | 4 | 17.13 | even | 4 | |||
1530.2.n.o.1279.1 | 4 | 5.4 | even | 2 |