Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [920,2,Mod(369,920)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(920, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("920.369");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 920 = 2^{3} \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 920.e (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.34623698596\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 2 x^{14} + 6 x^{13} + 100 x^{12} - 196 x^{11} + 210 x^{10} + 702 x^{9} + 1572 x^{8} + \cdots + 1024 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 369.3 | ||
Root | \(1.81400 + 1.81400i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 920.369 |
Dual form | 920.2.e.c.369.14 |
$q$-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 \(\left(\mathbb{Z}/920\mathbb{Z}\right)^\times\).
\(n\) | \(231\) | \(281\) | \(461\) | \(737\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 2.54092i | − | 1.46700i | −0.679690 | − | 0.733499i | \(-0.737886\pi\) | ||
0.679690 | − | 0.733499i | \(-0.262114\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.30744 | + | 1.81400i | −0.584704 | + | 0.811247i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.780573i | 0.295029i | 0.989060 | + | 0.147514i | \(0.0471273\pi\) | ||||
−0.989060 | + | 0.147514i | \(0.952873\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −3.45626 | −1.15209 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.16287 | 1.55666 | 0.778332 | − | 0.627853i | \(-0.216066\pi\) | ||||
0.778332 | + | 0.627853i | \(0.216066\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 3.34898i | − | 0.928839i | −0.885615 | − | 0.464419i | \(-0.846263\pi\) | ||
0.885615 | − | 0.464419i | \(-0.153737\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 4.60923 | + | 3.32209i | 1.19010 | + | 0.857760i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 6.62869i | − | 1.60769i | −0.594836 | − | 0.803847i | \(-0.702783\pi\) | ||
0.594836 | − | 0.803847i | \(-0.297217\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.40858 | −1.47023 | −0.735114 | − | 0.677943i | \(-0.762872\pi\) | ||||
−0.735114 | + | 0.677943i | \(0.762872\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.98337 | 0.432807 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 1.00000i | − | 0.208514i | ||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.58121 | − | 4.74339i | −0.316242 | − | 0.948679i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.15931i | 0.223109i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.0877744 | 0.0162993 | 0.00814965 | − | 0.999967i | \(-0.497406\pi\) | ||||
0.00814965 | + | 0.999967i | \(0.497406\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.29521 | 0.591837 | 0.295918 | − | 0.955213i | \(-0.404374\pi\) | ||||
0.295918 | + | 0.955213i | \(0.404374\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 13.1184i | − | 2.28362i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.41596 | − | 1.02055i | −0.239341 | − | 0.172505i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 4.68291i | − | 0.769865i | −0.922945 | − | 0.384933i | \(-0.874225\pi\) | ||
0.922945 | − | 0.384933i | \(-0.125775\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −8.50947 | −1.36261 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.75800 | −0.899249 | −0.449624 | − | 0.893218i | \(-0.648442\pi\) | ||||
−0.449624 | + | 0.893218i | \(0.648442\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.62914i | − | 0.400940i | −0.979700 | − | 0.200470i | \(-0.935753\pi\) | ||
0.979700 | − | 0.200470i | \(-0.0642469\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.51884 | − | 6.26966i | 0.673629 | − | 0.934625i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 5.13068i | 0.748387i | 0.927351 | + | 0.374193i | \(0.122080\pi\) | ||||
−0.927351 | + | 0.374193i | \(0.877920\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.39071 | 0.912958 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −16.8429 | −2.35848 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 8.80399i | − | 1.20932i | −0.796483 | − | 0.604660i | \(-0.793309\pi\) | ||
0.796483 | − | 0.604660i | \(-0.206691\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −6.75013 | + | 9.36546i | −0.910188 | + | 1.26284i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 16.2837i | 2.15682i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.98687 | −0.388858 | −0.194429 | − | 0.980917i | \(-0.562285\pi\) | ||||
−0.194429 | + | 0.980917i | \(0.562285\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.05559 | −0.263191 | −0.131596 | − | 0.991303i | \(-0.542010\pi\) | ||||
−0.131596 | + | 0.991303i | \(0.542010\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 2.69786i | − | 0.339898i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 6.07505 | + | 4.37858i | 0.753517 | + | 0.543096i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 3.60245i | − | 0.440109i | −0.975488 | − | 0.220054i | \(-0.929376\pi\) | ||
0.975488 | − | 0.220054i | \(-0.0706235\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −2.54092 | −0.305890 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 11.5286 | 1.36819 | 0.684096 | − | 0.729392i | \(-0.260197\pi\) | ||||
0.684096 | + | 0.729392i | \(0.260197\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.4673i | 1.22510i | 0.790431 | + | 0.612551i | \(0.209857\pi\) | ||||
−0.790431 | + | 0.612551i | \(0.790143\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −12.0526 | + | 4.01772i | −1.39171 | + | 0.463927i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 4.03000i | 0.459261i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.43878 | −0.386893 | −0.193447 | − | 0.981111i | \(-0.561967\pi\) | ||||
−0.193447 | + | 0.981111i | \(0.561967\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.42306 | −0.824785 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 3.62938i | − | 0.398376i | −0.979961 | − | 0.199188i | \(-0.936170\pi\) | ||
0.979961 | − | 0.199188i | \(-0.0638304\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 12.0245 | + | 8.66660i | 1.30424 | + | 0.940025i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − | 0.223028i | − | 0.0239111i | ||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −14.3109 | −1.51695 | −0.758477 | − | 0.651700i | \(-0.774056\pi\) | ||||
−0.758477 | + | 0.651700i | \(0.774056\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.61412 | 0.274034 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | − | 8.37284i | − | 0.868223i | ||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 8.37882 | − | 11.6252i | 0.859649 | − | 1.19272i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 0.427584i | − | 0.0434146i | −0.999764 | − | 0.0217073i | \(-0.993090\pi\) | ||
0.999764 | − | 0.0217073i | \(-0.00691018\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −17.8442 | −1.79341 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −7.99434 | −0.795467 | −0.397733 | − | 0.917501i | \(-0.630203\pi\) | ||||
−0.397733 | + | 0.917501i | \(0.630203\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.7780i | 1.06199i | 0.847376 | + | 0.530993i | \(0.178181\pi\) | ||||
−0.847376 | + | 0.530993i | \(0.821819\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.59313 | + | 3.59784i | −0.253064 | + | 0.351113i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 15.1623i | − | 1.46580i | −0.680339 | − | 0.732898i | \(-0.738167\pi\) | ||
0.680339 | − | 0.732898i | \(-0.261833\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 16.5127 | 1.58163 | 0.790816 | − | 0.612054i | \(-0.209656\pi\) | ||||
0.790816 | + | 0.612054i | \(0.209656\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −11.8989 | −1.12939 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 14.5233i | − | 1.36623i | −0.730309 | − | 0.683117i | \(-0.760624\pi\) | ||
0.730309 | − | 0.683117i | \(-0.239376\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.81400 | + | 1.30744i | 0.169157 | + | 0.121919i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 11.5749i | 1.07010i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.17418 | 0.474316 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 15.6552 | 1.42320 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 14.6306i | 1.31920i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.6719 | + | 3.33337i | 0.954520 | + | 0.298146i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 16.4865i | 1.46294i | 0.681873 | + | 0.731471i | \(0.261166\pi\) | ||||
−0.681873 | + | 0.731471i | \(0.738834\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −6.68042 | −0.588178 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.94157 | 0.431747 | 0.215874 | − | 0.976421i | \(-0.430740\pi\) | ||||
0.215874 | + | 0.976421i | \(0.430740\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 5.00236i | − | 0.433760i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −2.10299 | − | 1.51572i | −0.180996 | − | 0.130453i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 17.9516i | − | 1.53371i | −0.641821 | − | 0.766854i | \(-0.721821\pi\) | ||
0.641821 | − | 0.766854i | \(-0.278179\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 17.4812 | 1.48274 | 0.741368 | − | 0.671099i | \(-0.234177\pi\) | ||||
0.741368 | + | 0.671099i | \(0.234177\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 13.0366 | 1.09788 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 17.2903i | − | 1.44589i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.114760 | + | 0.159223i | −0.00953027 | + | 0.0132228i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 16.2382i | − | 1.33931i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 22.0079 | 1.80295 | 0.901477 | − | 0.432827i | \(-0.142484\pi\) | ||||
0.901477 | + | 0.432827i | \(0.142484\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.40875 | 0.602916 | 0.301458 | − | 0.953480i | \(-0.402527\pi\) | ||||
0.301458 | + | 0.953480i | \(0.402527\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 22.9104i | 1.85220i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.30828 | + | 5.97751i | −0.346049 | + | 0.480125i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 5.19240i | − | 0.414399i | −0.978299 | − | 0.207199i | \(-0.933565\pi\) | ||
0.978299 | − | 0.207199i | \(-0.0664348\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −22.3702 | −1.77407 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0.780573 | 0.0615178 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 11.5618i | 0.905588i | 0.891615 | + | 0.452794i | \(0.149573\pi\) | ||||
−0.891615 | + | 0.452794i | \(0.850427\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 23.7968 | + | 17.1515i | 1.85258 | + | 1.33524i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 19.4882i | 1.50804i | 0.656852 | + | 0.754019i | \(0.271888\pi\) | ||||
−0.656852 | + | 0.754019i | \(0.728112\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.78436 | 0.137258 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 22.1497 | 1.69383 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 18.9062i | − | 1.43741i | −0.695314 | − | 0.718706i | \(-0.744735\pi\) | ||
0.695314 | − | 0.718706i | \(-0.255265\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3.70256 | − | 1.23425i | 0.279888 | − | 0.0933005i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.58939i | 0.570454i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.5404 | −1.23628 | −0.618142 | − | 0.786066i | \(-0.712114\pi\) | ||||
−0.618142 | + | 0.786066i | \(0.712114\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 5.51586 | 0.409990 | 0.204995 | − | 0.978763i | \(-0.434282\pi\) | ||||
0.204995 | + | 0.978763i | \(0.434282\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.22308i | 0.386101i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.49481 | + | 6.12261i | 0.624551 | + | 0.450143i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 34.2231i | − | 2.50264i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.904924 | −0.0658235 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 24.0346 | 1.73909 | 0.869543 | − | 0.493858i | \(-0.164414\pi\) | ||||
0.869543 | + | 0.493858i | \(0.164414\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 15.2163i | 1.09530i | 0.836709 | + | 0.547648i | \(0.184477\pi\) | ||||
−0.836709 | + | 0.547648i | \(0.815523\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 11.1256 | − | 15.4362i | 0.796721 | − | 1.10541i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.82490i | 0.628748i | 0.949299 | + | 0.314374i | \(0.101795\pi\) | ||||
−0.949299 | + | 0.314374i | \(0.898205\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −15.3228 | −1.08620 | −0.543101 | − | 0.839668i | \(-0.682750\pi\) | ||||
−0.543101 | + | 0.839668i | \(0.682750\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −9.15352 | −0.645639 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.0685144i | 0.00480877i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.52823 | − | 10.4450i | 0.525795 | − | 0.729513i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 3.45626i | 0.240226i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −33.0866 | −2.28865 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.67170 | 0.321613 | 0.160806 | − | 0.986986i | \(-0.448591\pi\) | ||||
0.160806 | + | 0.986986i | \(0.448591\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 29.2932i | − | 2.00714i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4.76926 | + | 3.43744i | 0.325261 | + | 0.234431i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.57215i | 0.174609i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 26.5965 | 1.79722 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −22.1993 | −1.49329 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 20.7813i | 1.39162i | 0.718226 | + | 0.695810i | \(0.244954\pi\) | ||||
−0.718226 | + | 0.695810i | \(0.755046\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.46507 | + | 16.3944i | 0.364338 | + | 1.09296i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 13.7696i | 0.913920i | 0.889487 | + | 0.456960i | \(0.151062\pi\) | ||||
−0.889487 | + | 0.456960i | \(0.848938\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −18.6065 | −1.22955 | −0.614777 | − | 0.788701i | \(-0.710754\pi\) | ||||
−0.614777 | + | 0.788701i | \(0.710754\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 10.2399 | 0.673735 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.451458i | 0.0295760i | 0.999891 | + | 0.0147880i | \(0.00470733\pi\) | ||||
−0.999891 | + | 0.0147880i | \(0.995293\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.30707 | − | 6.70805i | −0.607126 | − | 0.437585i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.73766i | 0.567572i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.5522 | −0.811937 | −0.405969 | − | 0.913887i | \(-0.633066\pi\) | ||||
−0.405969 | + | 0.913887i | \(0.633066\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 16.7582 | 1.07949 | 0.539745 | − | 0.841828i | \(-0.318521\pi\) | ||||
0.539745 | + | 0.841828i | \(0.318521\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 22.3393i | 1.43307i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −8.35545 | + | 11.5928i | −0.533810 | + | 0.740634i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 21.4622i | 1.36561i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −9.22194 | −0.584417 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −6.77866 | −0.427865 | −0.213933 | − | 0.976848i | \(-0.568627\pi\) | ||||
−0.213933 | + | 0.976848i | \(0.568627\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 5.16287i | − | 0.324587i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 22.0211 | − | 30.5531i | 1.37902 | − | 1.91331i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 7.18182i | − | 0.447990i | −0.974590 | − | 0.223995i | \(-0.928090\pi\) | ||
0.974590 | − | 0.223995i | \(-0.0719099\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.65535 | 0.227133 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.303371 | −0.0187782 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 18.2061i | 1.12264i | 0.827600 | + | 0.561318i | \(0.189706\pi\) | ||||
−0.827600 | + | 0.561318i | \(0.810294\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 15.9705 | + | 11.5107i | 0.981057 | + | 0.707095i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 36.3628i | 2.22537i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.56736 | 0.339448 | 0.169724 | − | 0.985492i | \(-0.445712\pi\) | ||||
0.169724 | + | 0.985492i | \(0.445712\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3.85908 | 0.234422 | 0.117211 | − | 0.993107i | \(-0.462605\pi\) | ||||
0.117211 | + | 0.993107i | \(0.462605\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | − | 6.64226i | − | 0.402008i | ||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.16358 | − | 24.4895i | −0.492282 | − | 1.47677i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 6.01542i | 0.361431i | 0.983535 | + | 0.180716i | \(0.0578414\pi\) | ||||
−0.983535 | + | 0.180716i | \(0.942159\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −11.3891 | −0.681846 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.8891 | −1.00752 | −0.503761 | − | 0.863843i | \(-0.668051\pi\) | ||||
−0.503761 | + | 0.863843i | \(0.668051\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.62178i | 0.0964047i | 0.998838 | + | 0.0482023i | \(0.0153492\pi\) | ||||
−0.998838 | + | 0.0482023i | \(0.984651\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −29.5386 | − | 21.2899i | −1.74972 | − | 1.26110i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 4.49454i | − | 0.265304i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −26.9395 | −1.58468 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.08645 | −0.0636891 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 28.3659i | 1.65716i | 0.559874 | + | 0.828578i | \(0.310849\pi\) | ||||
−0.559874 | + | 0.828578i | \(0.689151\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.90515 | − | 5.41819i | 0.227367 | − | 0.315459i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.98535i | 0.347305i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.34898 | −0.193676 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.05223 | 0.118289 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 20.3130i | 1.16695i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.68756 | − | 3.72884i | 0.153889 | − | 0.213513i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.54137i | 0.316262i | 0.987418 | + | 0.158131i | \(0.0505469\pi\) | ||||
−0.987418 | + | 0.158131i | \(0.949453\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 27.3860 | 1.55793 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.09153 | 0.515533 | 0.257767 | − | 0.966207i | \(-0.417013\pi\) | ||||
0.257767 | + | 0.966207i | \(0.417013\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 24.6354i | 1.39248i | 0.717811 | + | 0.696238i | \(0.245144\pi\) | ||||
−0.717811 | + | 0.696238i | \(0.754856\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.89392 | + | 3.52729i | 0.275741 | + | 0.198740i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 23.3406i | − | 1.31094i | −0.755222 | − | 0.655469i | \(-0.772471\pi\) | ||
0.755222 | − | 0.655469i | \(-0.227529\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.453168 | 0.0253725 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −38.5262 | −2.15032 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 42.4805i | 2.36368i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −15.8855 | + | 5.29544i | −0.881169 | + | 0.293738i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | − | 41.9575i | − | 2.32025i | ||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.00487 | −0.220796 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.6239 | 1.35345 | 0.676725 | − | 0.736236i | \(-0.263399\pi\) | ||||
0.676725 | + | 0.736236i | \(0.263399\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 16.1853i | 0.886950i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.53485 | + | 4.70998i | 0.357037 | + | 0.257334i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 14.9958i | 0.816875i | 0.912786 | + | 0.408438i | \(0.133926\pi\) | ||||
−0.912786 | + | 0.408438i | \(0.866074\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −36.9024 | −2.00426 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 17.0127 | 0.921290 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 10.4524i | 0.564378i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.32209 | − | 4.60923i | 0.178855 | − | 0.248153i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 8.76366i | − | 0.470458i | −0.971940 | − | 0.235229i | \(-0.924416\pi\) | ||
0.971940 | − | 0.235229i | \(-0.0755840\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −33.1731 | −1.77572 | −0.887859 | − | 0.460116i | \(-0.847808\pi\) | ||||
−0.887859 | + | 0.460116i | \(0.847808\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.88249 | 0.207232 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 23.8513i | 1.26948i | 0.772727 | + | 0.634738i | \(0.218892\pi\) | ||||
−0.772727 | + | 0.634738i | \(0.781108\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −15.0729 | + | 20.9129i | −0.799988 | + | 1.10994i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 13.1472i | − | 0.695821i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.53298 | 0.450353 | 0.225177 | − | 0.974318i | \(-0.427704\pi\) | ||||
0.225177 | + | 0.974318i | \(0.427704\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 22.0699 | 1.16157 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 39.7786i | − | 2.08783i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −18.9877 | − | 13.6853i | −0.993860 | − | 0.716323i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 23.3388i | − | 1.21828i | −0.793064 | − | 0.609138i | \(-0.791515\pi\) | ||
0.793064 | − | 0.609138i | \(-0.208485\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 19.9011 | 1.03601 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 6.87216 | 0.356785 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 26.3073i | − | 1.36214i | −0.732218 | − | 0.681070i | \(-0.761515\pi\) | ||
0.732218 | − | 0.681070i | \(-0.238485\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 8.46982 | − | 27.1163i | 0.437380 | − | 1.40028i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 0.293955i | − | 0.0151394i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 33.0601 | 1.69818 | 0.849091 | − | 0.528246i | \(-0.177150\pi\) | ||||
0.849091 | + | 0.528246i | \(0.177150\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 41.8908 | 2.14613 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 23.7177i | − | 1.21192i | −0.795496 | − | 0.605958i | \(-0.792790\pi\) | ||
0.795496 | − | 0.605958i | \(-0.207210\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −7.31042 | − | 5.26897i | −0.372574 | − | 0.268532i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.08697i | 0.461917i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −4.39287 | −0.222728 | −0.111364 | − | 0.993780i | \(-0.535522\pi\) | ||||
−0.111364 | + | 0.993780i | \(0.535522\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6.62869 | −0.335227 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | − | 12.5561i | − | 0.633372i | ||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.49600 | − | 6.23796i | 0.226218 | − | 0.313866i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 0.668437i | 0.0335479i | 0.999859 | + | 0.0167740i | \(0.00533957\pi\) | ||||
−0.999859 | + | 0.0167740i | \(0.994660\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −12.7106 | −0.636325 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.1310 | 0.555857 | 0.277928 | − | 0.960602i | \(-0.410352\pi\) | ||||
0.277928 | + | 0.960602i | \(0.410352\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 11.0356i | − | 0.549721i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 9.70520 | − | 13.4655i | 0.482255 | − | 0.669104i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 24.1772i | − | 1.19842i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 17.7667 | 0.878506 | 0.439253 | − | 0.898364i | \(-0.355243\pi\) | ||||
0.439253 | + | 0.898364i | \(0.355243\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −45.6135 | −2.24995 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 2.33147i | − | 0.114724i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.58370 | + | 4.74519i | 0.323181 | + | 0.232932i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | − | 44.4182i | − | 2.17517i | ||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 37.4277 | 1.82846 | 0.914231 | − | 0.405194i | \(-0.132796\pi\) | ||||
0.914231 | + | 0.405194i | \(0.132796\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −27.0798 | −1.31979 | −0.659895 | − | 0.751358i | \(-0.729399\pi\) | ||||
−0.659895 | + | 0.751358i | \(0.729399\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − | 17.7329i | − | 0.862205i | ||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −31.4425 | + | 10.4814i | −1.52518 | + | 0.508420i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 1.60454i | − | 0.0776490i | ||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −43.9333 | −2.12112 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −33.3003 | −1.60402 | −0.802009 | − | 0.597312i | \(-0.796235\pi\) | ||||
−0.802009 | + | 0.597312i | \(0.796235\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 2.71773i | − | 0.130606i | −0.997865 | − | 0.0653028i | \(-0.979199\pi\) | ||
0.997865 | − | 0.0653028i | \(-0.0208013\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0.404572 | + | 0.291595i | 0.0193978 | + | 0.0139809i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 6.40858i | 0.306564i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 16.7478 | 0.799331 | 0.399665 | − | 0.916661i | \(-0.369126\pi\) | ||||
0.399665 | + | 0.916661i | \(0.369126\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −22.0879 | −1.05181 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 11.6392i | − | 0.552993i | −0.961015 | − | 0.276497i | \(-0.910827\pi\) | ||
0.961015 | − | 0.276497i | \(-0.0891735\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 18.7106 | − | 25.9600i | 0.886969 | − | 1.23062i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 55.9201i | − | 2.64493i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −10.4132 | −0.491430 | −0.245715 | − | 0.969342i | \(-0.579023\pi\) | ||||
−0.245715 | + | 0.969342i | \(0.579023\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −29.7278 | −1.39983 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 18.8250i | − | 0.884476i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −3.41780 | + | 4.74202i | −0.160229 | + | 0.222309i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | − | 6.66798i | − | 0.311915i | −0.987764 | − | 0.155957i | \(-0.950154\pi\) | ||
0.987764 | − | 0.155957i | \(-0.0498463\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 7.68469 | 0.358690 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −10.1142 | −0.471064 | −0.235532 | − | 0.971867i | \(-0.575683\pi\) | ||||
−0.235532 | + | 0.971867i | \(0.575683\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 25.4957i | 1.18489i | 0.805612 | + | 0.592443i | \(0.201836\pi\) | ||||
−0.805612 | + | 0.592443i | \(0.798164\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 15.1884 | + | 10.9470i | 0.704343 | + | 0.507654i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 9.17713i | 0.424667i | 0.977197 | + | 0.212334i | \(0.0681063\pi\) | ||||
−0.977197 | + | 0.212334i | \(0.931894\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.81197 | 0.129845 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −13.1935 | −0.607922 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 13.5739i | − | 0.624128i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.1333 | + | 30.3984i | 0.464948 | + | 1.39477i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 30.4288i | 1.39324i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 22.6115 | 1.03315 | 0.516574 | − | 0.856243i | \(-0.327207\pi\) | ||||
0.516574 | + | 0.856243i | \(0.327207\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.6829 | −0.715081 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 1.98337i | − | 0.0902465i | ||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.775638 | + | 0.559039i | 0.0352199 | + | 0.0253847i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.32242i | 0.286496i | 0.989687 | + | 0.143248i | \(0.0457547\pi\) | ||||
−0.989687 | + | 0.143248i | \(0.954245\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 29.3775 | 1.32850 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 20.5410 | 0.927002 | 0.463501 | − | 0.886096i | \(-0.346593\pi\) | ||||
0.463501 | + | 0.886096i | \(0.346593\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 0.581830i | − | 0.0262043i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 23.3302 | − | 32.3694i | 1.04861 | − | 1.45490i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.99891i | 0.403656i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 33.1588 | 1.48439 | 0.742196 | − | 0.670183i | \(-0.233784\pi\) | ||||
0.742196 | + | 0.670183i | \(0.233784\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 49.5178 | 2.21229 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 16.9045i | 0.753736i | 0.926267 | + | 0.376868i | \(0.122999\pi\) | ||||
−0.926267 | + | 0.376868i | \(0.877001\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.4521 | − | 14.5018i | 0.465113 | − | 0.645320i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 4.53391i | − | 0.201358i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −28.6358 | −1.26926 | −0.634631 | − | 0.772816i | \(-0.718848\pi\) | ||||
−0.634631 | + | 0.772816i | \(0.718848\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −8.17048 | −0.361441 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | − | 7.42951i | − | 0.328021i | ||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −19.5513 | − | 14.0915i | −0.861533 | − | 0.620948i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 26.4890i | 1.16499i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −48.0391 | −2.10868 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 38.4207 | 1.68324 | 0.841622 | − | 0.540068i | \(-0.181601\pi\) | ||||
0.841622 | + | 0.540068i | \(0.181601\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 38.6386i | 1.68955i | 0.535124 | + | 0.844773i | \(0.320265\pi\) | ||||
−0.535124 | + | 0.844773i | \(0.679735\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.13613 | − | 9.40791i | −0.136872 | − | 0.410595i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 21.8429i | − | 0.951492i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.00000 | −0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 10.3234 | 0.447997 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19.2834i | 0.835257i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 27.5045 | + | 19.8238i | 1.18912 | + | 0.857057i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 42.0277i | 1.81363i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 32.9944 | 1.42117 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.42943 | 0.190436 | 0.0952180 | − | 0.995456i | \(-0.469645\pi\) | ||||
0.0952180 | + | 0.995456i | \(0.469645\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 14.0153i | − | 0.601455i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −21.5894 | + | 29.9541i | −0.924787 | + | 1.28309i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 28.1695i | − | 1.20444i | −0.798330 | − | 0.602220i | \(-0.794283\pi\) | ||
0.798330 | − | 0.602220i | \(-0.205717\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 7.10464 | 0.303219 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.562509 | −0.0239637 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 2.68422i | − | 0.114145i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 15.5570 | − | 21.5846i | 0.660360 | − | 0.916215i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12.1942i | 0.516687i | 0.966053 | + | 0.258343i | \(0.0831766\pi\) | ||||
−0.966053 | + | 0.258343i | \(0.916823\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8.80492 | −0.372409 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −86.9579 | −3.67137 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 15.8362i | − | 0.667415i | −0.942677 | − | 0.333708i | \(-0.891700\pi\) | ||
0.942677 | − | 0.333708i | \(-0.108300\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 26.3452 | + | 18.9883i | 1.10835 | + | 0.798843i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 5.79424i | − | 0.243335i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −0.674355 | −0.0282704 | −0.0141352 | − | 0.999900i | \(-0.504500\pi\) | ||||
−0.0141352 | + | 0.999900i | \(0.504500\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −39.9107 | −1.67021 | −0.835105 | − | 0.550090i | \(-0.814593\pi\) | ||||
−0.835105 | + | 0.550090i | \(0.814593\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 61.0700i | − | 2.55124i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.74339 | + | 1.58121i | −0.197813 | + | 0.0659410i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 0.727423i | − | 0.0302830i | −0.999885 | − | 0.0151415i | \(-0.995180\pi\) | ||
0.999885 | − | 0.0151415i | \(-0.00481987\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 38.6635 | 1.60680 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.83299 | 0.117532 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 45.4538i | − | 1.88251i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −20.9969 | − | 15.1335i | −0.868116 | − | 0.625693i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 38.4075i | − | 1.58525i | −0.609712 | − | 0.792623i | \(-0.708715\pi\) | ||
0.609712 | − | 0.792623i | \(-0.291285\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −21.1176 | −0.870135 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 22.4233 | 0.922373 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.65052i | 0.396299i | 0.980172 | + | 0.198150i | \(0.0634932\pi\) | ||||
−0.980172 | + | 0.198150i | \(0.936507\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −6.76492 | + | 9.38597i | −0.277335 | + | 0.384787i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 38.9338i | 1.59346i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −35.5951 | −1.45438 | −0.727189 | − | 0.686437i | \(-0.759174\pi\) | ||||
−0.727189 | + | 0.686437i | \(0.759174\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −2.48461 | −0.101349 | −0.0506747 | − | 0.998715i | \(-0.516137\pi\) | ||||
−0.0506747 | + | 0.998715i | \(0.516137\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.4510i | 0.507043i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −20.4682 | + | 28.3986i | −0.832151 | + | 1.15457i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.0165i | 0.609500i | 0.952432 | + | 0.304750i | \(0.0985730\pi\) | ||||
−0.952432 | + | 0.304750i | \(0.901427\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0.174089 | 0.00705445 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17.1825 | 0.695131 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.41556i | 0.178343i | 0.996016 | + | 0.0891714i | \(0.0284219\pi\) | ||||
−0.996016 | + | 0.0891714i | \(0.971578\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −26.5399 | − | 19.1286i | −1.07019 | − | 0.771340i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 11.0132i | − | 0.443373i | −0.975118 | − | 0.221686i | \(-0.928844\pi\) | ||
0.975118 | − | 0.221686i | \(-0.0711561\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −28.9235 | −1.16253 | −0.581267 | − | 0.813713i | \(-0.697443\pi\) | ||||
−0.581267 | + | 0.813713i | \(0.697443\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 1.15931 | 0.0465214 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 11.1707i | − | 0.447545i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −19.9995 | + | 15.0006i | −0.799982 | + | 0.600024i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 84.0704i | 3.35745i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −31.0415 | −1.23771 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.6238 | −0.542357 | −0.271178 | − | 0.962529i | \(-0.587413\pi\) | ||||
−0.271178 | + | 0.962529i | \(0.587413\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 11.8704i | − | 0.471806i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −29.9066 | − | 21.5551i | −1.18681 | − | 0.855388i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 21.4023i | − | 0.847991i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −39.8458 | −1.57627 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −28.1924 | −1.11353 | −0.556766 | − | 0.830670i | \(-0.687958\pi\) | ||||
−0.556766 | + | 0.830670i | \(0.687958\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 18.5514i | − | 0.731596i | −0.930694 | − | 0.365798i | \(-0.880796\pi\) | ||
0.930694 | − | 0.365798i | \(-0.119204\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 8.73424 | − | 12.1183i | 0.343910 | − | 0.477158i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 13.6338i | − | 0.535999i | −0.963419 | − | 0.268000i | \(-0.913637\pi\) | ||
0.963419 | − | 0.268000i | \(-0.0863626\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −15.4208 | −0.605320 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 6.53562 | 0.256151 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 37.6196i | 1.47217i | 0.676890 | + | 0.736084i | \(0.263327\pi\) | ||||
−0.676890 | + | 0.736084i | \(0.736673\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6.46080 | + | 8.96402i | −0.252444 | + | 0.350253i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 36.1776i | − | 1.41142i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −11.7947 | −0.459455 | −0.229727 | − | 0.973255i | \(-0.573783\pi\) | ||||
−0.229727 | + | 0.973255i | \(0.573783\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6.49839 | −0.252758 | −0.126379 | − | 0.991982i | \(-0.540336\pi\) | ||||
−0.126379 | + | 0.991982i | \(0.540336\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 56.4066i | 2.19065i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 9.07430 | + | 6.54028i | 0.351886 | + | 0.253621i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 0.0877744i | − | 0.00339864i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 52.8036 | 2.04150 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −10.6127 | −0.409700 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 45.7524i | − | 1.76362i | −0.471601 | − | 0.881812i | \(-0.656324\pi\) | ||
0.471601 | − | 0.881812i | \(-0.343676\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 5.49905 | − | 1.83311i | 0.211658 | − | 0.0705564i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 25.3462i | − | 0.974133i | −0.873365 | − | 0.487066i | \(-0.838067\pi\) | ||
0.873365 | − | 0.487066i | \(-0.161933\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0.333760 | 0.0128085 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 34.9874 | 1.34072 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 24.3192i | − | 0.930548i | −0.885167 | − | 0.465274i | \(-0.845956\pi\) | ||
0.885167 | − | 0.465274i | \(-0.154044\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 32.5642 | + | 23.4706i | 1.24422 | + | 0.896766i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 47.2776i | 1.80375i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −29.4843 | −1.12326 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.4950 | 0.513374 | 0.256687 | − | 0.966495i | \(-0.417369\pi\) | ||||
0.256687 | + | 0.966495i | \(0.417369\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 13.9287i | − | 0.529107i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −22.8556 | + | 31.7109i | −0.866962 | + | 1.20286i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 38.1680i | 1.44572i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.14712 | 0.0433879 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.8467 | 0.976217 | 0.488109 | − | 0.872783i | \(-0.337687\pi\) | ||||
0.488109 | + | 0.872783i | \(0.337687\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.0108i | 1.13188i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −17.0446 | + | 23.6485i | −0.641937 | + | 0.890654i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 6.24017i | − | 0.234686i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 44.9373 | 1.68766 | 0.843828 | − | 0.536613i | \(-0.180296\pi\) | ||||
0.843828 | + | 0.536613i | \(0.180296\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 11.8853 | 0.445734 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 3.29521i | − | 0.123406i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 31.3647 | + | 22.6060i | 1.17297 | + | 0.845418i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 31.8942i | 1.19111i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −25.2188 | −0.940502 | −0.470251 | − | 0.882533i | \(-0.655837\pi\) | ||||
−0.470251 | + | 0.882533i | \(0.655837\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.41300 | −0.313317 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − | 42.5812i | − | 1.58361i | ||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −0.138790 | − | 0.416349i | −0.00515453 | − | 0.0154628i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | − | 18.6009i | − | 0.689868i | −0.938627 | − | 0.344934i | \(-0.887901\pi\) | ||
0.938627 | − | 0.344934i | \(-0.112099\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 34.4931 | 1.27752 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −17.4277 | −0.644588 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 30.0268i | − | 1.10907i | −0.832162 | − | 0.554533i | \(-0.812897\pi\) | ||
0.832162 | − | 0.554533i | \(-0.187103\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 29.4562 | + | 21.2305i | 1.08651 | + | 0.783099i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 18.5990i | − | 0.685101i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.5513 | 0.792779 | 0.396389 | − | 0.918082i | \(-0.370263\pi\) | ||||
0.396389 | + | 0.918082i | \(0.370263\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 54.5336 | 2.00334 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 0.818910i | − | 0.0300429i | −0.999887 | − | 0.0150215i | \(-0.995218\pi\) | ||
0.999887 | − | 0.0150215i | \(-0.00478166\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −28.7739 | + | 39.9223i | −1.05419 | + | 1.46264i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 12.5441i | 0.458963i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 11.8353 | 0.432452 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −40.9390 | −1.49388 | −0.746942 | − | 0.664889i | \(-0.768479\pi\) | ||||
−0.746942 | + | 0.664889i | \(0.768479\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 17.2240i | 0.627678i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −9.68649 | + | 13.4395i | −0.352527 | + | 0.489113i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.99781i | 0.217994i | 0.994042 | + | 0.108997i | \(0.0347639\pi\) | ||||
−0.994042 | + | 0.108997i | \(0.965236\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −13.1184 | −0.476168 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 35.9456 | 1.30303 | 0.651513 | − | 0.758637i | \(-0.274135\pi\) | ||||
0.651513 | + | 0.758637i | \(0.274135\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 12.8894i | 0.466627i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −41.5596 | − | 29.9540i | −1.50259 | − | 1.08299i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 10.0030i | 0.361186i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 52.5292 | 1.89425 | 0.947126 | − | 0.320861i | \(-0.103972\pi\) | ||||
0.947126 | + | 0.320861i | \(0.103972\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.2484 | −0.657201 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10.2492i | 0.368638i | 0.982866 | + | 0.184319i | \(0.0590079\pi\) | ||||
−0.982866 | + | 0.184319i | \(0.940992\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.21041 | − | 15.6305i | −0.187164 | − | 0.561463i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | − | 9.28794i | − | 0.333203i | ||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 36.9006 | 1.32210 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 59.5206 | 2.12982 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.101758i | 0.00363652i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 9.41902 | + | 6.78874i | 0.336179 | + | 0.242301i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 24.2959i | − | 0.866057i | −0.901380 | − | 0.433028i | \(-0.857445\pi\) | ||
0.901380 | − | 0.433028i | \(-0.142555\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 46.2602 | 1.64691 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 11.3365 | 0.403079 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.88412i | 0.244462i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 29.2477 | − | 40.5796i | 1.03731 | − | 1.43921i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 12.7075i | − | 0.450122i | −0.974345 | − | 0.225061i | \(-0.927742\pi\) | ||
0.974345 | − | 0.225061i | \(-0.0722582\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 34.0097 | 1.20318 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 49.4622 | 1.74766 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 54.0412i | 1.90707i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.02055 | + | 1.41596i | −0.0359697 | + | 0.0499061i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 14.1462i | − | 0.497970i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −39.2057 | −1.37840 | −0.689200 | − | 0.724571i | \(-0.742038\pi\) | ||||
−0.689200 | + | 0.724571i | \(0.742038\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −8.34215 | −0.292932 | −0.146466 | − | 0.989216i | \(-0.546790\pi\) | ||||
−0.146466 | + | 0.989216i | \(0.546790\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − | 9.80560i | − | 0.343897i | ||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −20.9731 | − | 15.1163i | −0.734655 | − | 0.529501i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 16.8490i | 0.589473i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −9.03507 | −0.315711 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −44.1654 | −1.54138 | −0.770691 | − | 0.637209i | \(-0.780089\pi\) | ||||
−0.770691 | + | 0.637209i | \(0.780089\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.3933i | 0.989727i | 0.868971 | + | 0.494863i | \(0.164782\pi\) | ||||
−0.868971 | + | 0.494863i | \(0.835218\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −62.2258 | + | 20.7430i | −2.16642 | + | 0.722178i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.1333i | 0.873970i | 0.899469 | + | 0.436985i | \(0.143954\pi\) | ||||
−0.899469 | + | 0.436985i | \(0.856046\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.477200 | −0.0165739 | −0.00828693 | − | 0.999966i | \(-0.502638\pi\) | ||||
−0.00828693 | + | 0.999966i | \(0.502638\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 15.2847 | 0.530219 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 42.3620i | − | 1.46776i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −35.3516 | − | 25.4796i | −1.22339 | − | 0.881757i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.82016i | 0.132044i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 18.7742 | 0.648159 | 0.324079 | − | 0.946030i | \(-0.394945\pi\) | ||||
0.324079 | + | 0.946030i | \(0.394945\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.9923 | −0.999734 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 42.9139i | 1.47803i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.33294 | + | 3.23683i | −0.0802556 | + | 0.111350i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 12.2200i | 0.419885i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.12080 | 0.141426 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.68291 | −0.160528 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.41061i | 0.0482983i | 0.999708 | + | 0.0241492i | \(0.00768767\pi\) | ||||
−0.999708 | + | 0.0241492i | \(0.992312\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −28.9593 | + | 40.1796i | −0.990389 | + | 1.37411i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 34.0802i | − | 1.16416i | −0.813132 | − | 0.582079i | \(-0.802239\pi\) | ||
0.813132 | − | 0.582079i | \(-0.197761\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.81779 | −0.0961418 | −0.0480709 | − | 0.998844i | \(-0.515307\pi\) | ||||
−0.0480709 | + | 0.998844i | \(0.515307\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11.4203 | −0.389201 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 43.8527i | − | 1.49276i | −0.665517 | − | 0.746382i | \(-0.731789\pi\) | ||
0.665517 | − | 0.746382i | \(-0.268211\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 34.2959 | + | 24.7187i | 1.16610 | + | 0.840461i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 68.4511i | 2.32472i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17.7540 | −0.602263 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12.0645 | −0.408790 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1.47784i | 0.0500173i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −2.60194 | + | 8.33017i | −0.0879617 | + | 0.281611i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.803651i | 0.0271374i | 0.999908 | + | 0.0135687i | \(0.00431918\pi\) | ||||
−0.999908 | + | 0.0135687i | \(0.995681\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 72.0754 | 2.43104 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 51.3971 | 1.73161 | 0.865806 | − | 0.500379i | \(-0.166806\pi\) | ||||
0.865806 | + | 0.500379i | \(0.166806\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.7742i | 0.901024i | 0.892770 | + | 0.450512i | \(0.148759\pi\) | ||||
−0.892770 | + | 0.450512i | \(0.851241\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −13.7672 | − | 9.92266i | −0.462778 | − | 0.333547i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 3.02598i | − | 0.101602i | −0.998709 | − | 0.0508012i | \(-0.983822\pi\) | ||
0.998709 | − | 0.0508012i | \(-0.0161775\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.8689 | −0.431610 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −38.3243 | −1.28391 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 32.8804i | − | 1.10030i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 21.6255 | − | 30.0043i | 0.722861 | − | 1.00293i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.50947i | 0.284123i | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.289235 | 0.00964652 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −58.3589 | −1.94422 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | − | 5.21456i | − | 0.173530i | ||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7.21164 | + | 10.0058i | −0.239723 | + | 0.332603i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36.1018i | 1.19874i | 0.800472 | + | 0.599370i | \(0.204582\pi\) | ||||
−0.800472 | + | 0.599370i | \(0.795418\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 27.6305 | 0.916446 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 55.7984 | 1.84868 | 0.924342 | − | 0.381566i | \(-0.124615\pi\) | ||||
0.924342 | + | 0.381566i | \(0.124615\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 18.7380i | − | 0.620137i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −9.47468 | − | 6.82885i | −0.313223 | − | 0.225755i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.85726i | 0.127378i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 38.9936 | 1.28628 | 0.643141 | − | 0.765748i | \(-0.277631\pi\) | ||||
0.643141 | + | 0.765748i | \(0.277631\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 14.0801 | 0.463957 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 38.6090i | − | 1.27083i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −22.2129 | + | 7.40466i | −0.730355 | + | 0.243464i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 37.2515i | − | 1.22350i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 51.1409 | 1.67788 | 0.838939 | − | 0.544226i | \(-0.183177\pi\) | ||||
0.838939 | + | 0.544226i | \(0.183177\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −40.9553 | −1.34226 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 23.1008i | − | 0.756287i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 62.0807 | + | 44.7445i | 2.03026 | + | 1.46330i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 45.7344i | − | 1.49408i | −0.664780 | − | 0.747039i | \(-0.731475\pi\) | ||
0.664780 | − | 0.747039i | \(-0.268525\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 62.5965 | 2.04276 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 46.9452 | 1.53037 | 0.765184 | − | 0.643811i | \(-0.222648\pi\) | ||||
0.765184 | + | 0.643811i | \(0.222648\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.75800i | 0.187506i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.18313 | − | 1.64153i | 0.0384873 | − | 0.0533991i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 27.3471i | − | 0.888660i | −0.895863 | − | 0.444330i | \(-0.853442\pi\) | ||
0.895863 | − | 0.444330i | \(-0.146558\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 35.0547 | 1.13792 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −59.3065 | −1.92314 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 39.4077i | 1.27654i | 0.769813 | + | 0.638270i | \(0.220350\pi\) | ||||
−0.769813 | + | 0.638270i | \(0.779650\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −31.4238 | + | 43.5989i | −1.01685 | + | 1.41083i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 1.15146i | − | 0.0372215i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 14.0125 | 0.452488 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −20.1416 | −0.649730 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 52.4048i | 1.68872i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −27.6025 | − | 19.8944i | −0.888556 | − | 0.640425i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.59634i | 0.179966i | 0.995943 | + | 0.0899831i | \(0.0286813\pi\) | ||||
−0.995943 | + | 0.0899831i | \(0.971319\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 107.939 | 3.46751 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −19.2387 | −0.617398 | −0.308699 | − | 0.951160i | \(-0.599894\pi\) | ||||
−0.308699 | + | 0.951160i | \(0.599894\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 13.6453i | 0.437450i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 13.4553 | + | 40.3637i | 0.430913 | + | 1.29267i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 41.1594i | − | 1.31681i | −0.752666 | − | 0.658403i | \(-0.771232\pi\) | ||
0.752666 | − | 0.658403i | \(-0.228768\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −73.8854 | −2.36139 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −57.0722 | −1.82218 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 53.9616i | − | 1.72111i | −0.509359 | − | 0.860554i | \(-0.670117\pi\) | ||
0.509359 | − | 0.860554i | \(-0.329883\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16.0084 | − | 11.5380i | −0.510070 | − | 0.367632i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 10.1760i | 0.323907i | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.62914 | −0.0836017 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 50.4344 | 1.60210 | 0.801051 | − | 0.598597i | \(-0.204275\pi\) | ||||
0.801051 | + | 0.598597i | \(0.204275\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 62.5672i | − | 1.98551i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.0336 | − | 27.7955i | 0.635107 | − | 0.881177i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 44.7163i | 1.41618i | 0.706122 | + | 0.708090i | \(0.250443\pi\) | ||||
−0.706122 | + | 0.708090i | \(0.749557\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 5.42893 | 0.171764 |
(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 | 920.2.e.c.369.3 | ✓ | 16 | |
4.3 | odd | 2 | 1840.2.e.h.369.14 | 16 | |||
5.2 | odd | 4 | 4600.2.a.bk.1.1 | 8 | |||
5.3 | odd | 4 | 4600.2.a.bj.1.8 | 8 | |||
5.4 | even | 2 | inner | 920.2.e.c.369.14 | yes | 16 | |
20.3 | even | 4 | 9200.2.a.de.1.1 | 8 | |||
20.7 | even | 4 | 9200.2.a.dd.1.8 | 8 | |||
20.19 | odd | 2 | 1840.2.e.h.369.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
920.2.e.c.369.3 | ✓ | 16 | 1.1 | even | 1 | trivial | |
920.2.e.c.369.14 | yes | 16 | 5.4 | even | 2 | inner | |
1840.2.e.h.369.3 | 16 | 20.19 | odd | 2 | |||
1840.2.e.h.369.14 | 16 | 4.3 | odd | 2 | |||
4600.2.a.bj.1.8 | 8 | 5.3 | odd | 4 | |||
4600.2.a.bk.1.1 | 8 | 5.2 | odd | 4 | |||
9200.2.a.dd.1.8 | 8 | 20.7 | even | 4 | |||
9200.2.a.de.1.1 | 8 | 20.3 | even | 4 |