Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2151,2,Mod(2150,2151)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2151, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2151.2150");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2151 = 3^{2} \cdot 239 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2151.b (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: | \(17.1758214748\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 2150.7 | ||
Character | \(\chi\) | \(=\) | 2151.2150 |
Dual form | 2151.2.b.a.2150.74 |
$q$-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 \(\left(\mathbb{Z}/2151\mathbb{Z}\right)^\times\).
\(n\) | \(479\) | \(1441\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − | 2.53879i | − | 1.79520i | −0.440813 | − | 0.897599i | \(-0.645310\pi\) | ||
0.440813 | − | 0.897599i | \(-0.354690\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −4.44547 | −2.22274 | ||||||||
\(5\) | 1.00261i | 0.448382i | 0.974545 | + | 0.224191i | \(0.0719740\pi\) | ||||
−0.974545 | + | 0.224191i | \(0.928026\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 0.202697i | − | 0.0766122i | −0.999266 | − | 0.0383061i | \(-0.987804\pi\) | ||
0.999266 | − | 0.0383061i | \(-0.0121962\pi\) | |||||||
\(8\) | 6.20855i | 2.19506i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2.54543 | 0.804935 | ||||||||
\(11\) | − | 2.12902i | − | 0.641924i | −0.947092 | − | 0.320962i | \(-0.895994\pi\) | ||
0.947092 | − | 0.320962i | \(-0.104006\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.58049i | 0.438350i | 0.975686 | + | 0.219175i | \(0.0703366\pi\) | ||||
−0.975686 | + | 0.219175i | \(0.929663\pi\) | |||||||
\(14\) | −0.514606 | −0.137534 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 6.87129 | 1.71782 | ||||||||
\(17\) | 4.05688i | 0.983937i | 0.870613 | + | 0.491969i | \(0.163723\pi\) | ||||
−0.870613 | + | 0.491969i | \(0.836277\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 7.85123i | − | 1.80120i | −0.434654 | − | 0.900598i | \(-0.643129\pi\) | ||
0.434654 | − | 0.900598i | \(-0.356871\pi\) | |||||||
\(20\) | − | 4.45709i | − | 0.996635i | ||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −5.40514 | −1.15238 | ||||||||
\(23\) | 7.60643 | 1.58605 | 0.793026 | − | 0.609188i | \(-0.208505\pi\) | ||||
0.793026 | + | 0.609188i | \(0.208505\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.99477 | 0.798953 | ||||||||
\(26\) | 4.01255 | 0.786926 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.901084i | 0.170289i | ||||||||
\(29\) | − | 6.23054i | − | 1.15698i | −0.815689 | − | 0.578491i | \(-0.803642\pi\) | ||
0.815689 | − | 0.578491i | \(-0.196358\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 6.20533 | 1.11451 | 0.557255 | − | 0.830342i | \(-0.311855\pi\) | ||||
0.557255 | + | 0.830342i | \(0.311855\pi\) | |||||||
\(32\) | − | 5.02768i | − | 0.888777i | ||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 10.2996 | 1.76636 | ||||||||
\(35\) | 0.203227 | 0.0343516 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.62601i | 1.25371i | 0.779136 | + | 0.626855i | \(0.215658\pi\) | ||||
−0.779136 | + | 0.626855i | \(0.784342\pi\) | |||||||
\(38\) | −19.9327 | −3.23350 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −6.22478 | −0.984224 | ||||||||
\(41\) | −8.37515 | −1.30798 | −0.653989 | − | 0.756504i | \(-0.726906\pi\) | ||||
−0.653989 | + | 0.756504i | \(0.726906\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 9.12480i | − | 1.39152i | −0.718275 | − | 0.695759i | \(-0.755068\pi\) | ||
0.718275 | − | 0.695759i | \(-0.244932\pi\) | |||||||
\(44\) | 9.46450i | 1.42683i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 19.3112i | − | 2.84728i | ||||||
\(47\) | −11.9025 | −1.73616 | −0.868082 | − | 0.496421i | \(-0.834647\pi\) | ||||
−0.868082 | + | 0.496421i | \(0.834647\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 6.95891 | 0.994131 | ||||||||
\(50\) | − | 10.1419i | − | 1.43428i | ||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | − | 7.02605i | − | 0.974337i | ||||||
\(53\) | 0.380892 | 0.0523195 | 0.0261598 | − | 0.999658i | \(-0.491672\pi\) | ||||
0.0261598 | + | 0.999658i | \(0.491672\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.13458 | 0.287827 | ||||||||
\(56\) | 1.25845 | 0.168168 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −15.8181 | −2.07701 | ||||||||
\(59\) | −7.37074 | −0.959588 | −0.479794 | − | 0.877381i | \(-0.659289\pi\) | ||||
−0.479794 | + | 0.877381i | \(0.659289\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.43937 | 0.952514 | 0.476257 | − | 0.879306i | \(-0.341993\pi\) | ||||
0.476257 | + | 0.879306i | \(0.341993\pi\) | |||||||
\(62\) | − | 15.7540i | − | 2.00077i | ||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.978334 | 0.122292 | ||||||||
\(65\) | −1.58462 | −0.196548 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.3082 | −1.74802 | −0.874011 | − | 0.485907i | \(-0.838489\pi\) | ||||
−0.874011 | + | 0.485907i | \(0.838489\pi\) | |||||||
\(68\) | − | 18.0347i | − | 2.18703i | ||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | − | 0.515950i | − | 0.0616678i | ||||||
\(71\) | − | 11.4320i | − | 1.35673i | −0.734726 | − | 0.678364i | \(-0.762689\pi\) | ||
0.734726 | − | 0.678364i | \(-0.237311\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 2.03284i | − | 0.237926i | −0.992899 | − | 0.118963i | \(-0.962043\pi\) | ||
0.992899 | − | 0.118963i | \(-0.0379569\pi\) | |||||||
\(74\) | 19.3609 | 2.25066 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 34.9024i | 4.00358i | ||||||||
\(77\) | −0.431546 | −0.0491792 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 14.3619i | − | 1.61584i | −0.589293 | − | 0.807920i | \(-0.700593\pi\) | ||
0.589293 | − | 0.807920i | \(-0.299407\pi\) | |||||||
\(80\) | 6.88924i | 0.770241i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 21.2628i | 2.34808i | ||||||||
\(83\) | − | 6.46271i | − | 0.709375i | −0.934985 | − | 0.354687i | \(-0.884587\pi\) | ||
0.934985 | − | 0.354687i | \(-0.115413\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −4.06748 | −0.441180 | ||||||||
\(86\) | −23.1660 | −2.49805 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 13.2181 | 1.40906 | ||||||||
\(89\) | −2.13672 | −0.226492 | −0.113246 | − | 0.993567i | \(-0.536125\pi\) | ||||
−0.113246 | + | 0.993567i | \(0.536125\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0.320361 | 0.0335830 | ||||||||
\(92\) | −33.8142 | −3.52537 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 30.2181i | 3.11676i | ||||||||
\(95\) | 7.87174 | 0.807624 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 3.90034i | − | 0.396020i | −0.980200 | − | 0.198010i | \(-0.936552\pi\) | ||
0.980200 | − | 0.198010i | \(-0.0634478\pi\) | |||||||
\(98\) | − | 17.6672i | − | 1.78466i | ||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −17.7586 | −1.77586 | ||||||||
\(101\) | − | 11.8944i | − | 1.18353i | −0.806110 | − | 0.591766i | \(-0.798431\pi\) | ||
0.806110 | − | 0.591766i | \(-0.201569\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 8.69316i | − | 0.856562i | −0.903646 | − | 0.428281i | \(-0.859119\pi\) | ||
0.903646 | − | 0.428281i | \(-0.140881\pi\) | |||||||
\(104\) | −9.81258 | −0.962203 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | − | 0.967006i | − | 0.0939240i | ||||||
\(107\) | −11.3388 | −1.09616 | −0.548080 | − | 0.836426i | \(-0.684641\pi\) | ||||
−0.548080 | + | 0.836426i | \(0.684641\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.40752 | −0.517947 | −0.258973 | − | 0.965884i | \(-0.583384\pi\) | ||||
−0.258973 | + | 0.965884i | \(0.583384\pi\) | |||||||
\(110\) | − | 5.41927i | − | 0.516707i | ||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | − | 1.39279i | − | 0.131606i | ||||||
\(113\) | 1.82968i | 0.172122i | 0.996290 | + | 0.0860608i | \(0.0274279\pi\) | ||||
−0.996290 | + | 0.0860608i | \(0.972572\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.62631i | 0.711157i | ||||||||
\(116\) | 27.6977i | 2.57167i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 18.7128i | 1.72265i | ||||||||
\(119\) | 0.822317 | 0.0753816 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 6.46727 | 0.587934 | ||||||||
\(122\) | − | 18.8870i | − | 1.70995i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −27.5856 | −2.47726 | ||||||||
\(125\) | 9.01827i | 0.806619i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −0.911182 | −0.0808543 | −0.0404271 | − | 0.999182i | \(-0.512872\pi\) | ||||
−0.0404271 | + | 0.999182i | \(0.512872\pi\) | |||||||
\(128\) | − | 12.5392i | − | 1.10831i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.02303i | 0.352843i | ||||||||
\(131\) | −1.17333 | −0.102515 | −0.0512574 | − | 0.998685i | \(-0.516323\pi\) | ||||
−0.0512574 | + | 0.998685i | \(0.516323\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.59142 | −0.137994 | ||||||||
\(134\) | 36.3255i | 3.13804i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −25.1873 | −2.15980 | ||||||||
\(137\) | 2.54603 | 0.217522 | 0.108761 | − | 0.994068i | \(-0.465312\pi\) | ||||
0.108761 | + | 0.994068i | \(0.465312\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.0894i | 1.70396i | 0.523572 | + | 0.851982i | \(0.324599\pi\) | ||||
−0.523572 | + | 0.851982i | \(0.675401\pi\) | |||||||
\(140\) | −0.903438 | −0.0763545 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −29.0235 | −2.43560 | ||||||||
\(143\) | 3.36490 | 0.281387 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.24682 | 0.518770 | ||||||||
\(146\) | −5.16095 | −0.427124 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 33.9013i | − | 2.78667i | ||||||
\(149\) | 22.0120 | 1.80330 | 0.901648 | − | 0.432470i | \(-0.142358\pi\) | ||||
0.901648 | + | 0.432470i | \(0.142358\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 10.0323i | − | 0.816416i | −0.912889 | − | 0.408208i | \(-0.866154\pi\) | ||
0.912889 | − | 0.408208i | \(-0.133846\pi\) | |||||||
\(152\) | 48.7448 | 3.95372 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.09561i | 0.0882864i | ||||||||
\(155\) | 6.22154i | 0.499726i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.99829 | −0.797951 | −0.398975 | − | 0.916962i | \(-0.630634\pi\) | ||||
−0.398975 | + | 0.916962i | \(0.630634\pi\) | |||||||
\(158\) | −36.4619 | −2.90075 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 5.04082 | 0.398512 | ||||||||
\(161\) | − | 1.54180i | − | 0.121511i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 24.2176 | 1.89687 | 0.948433 | − | 0.316978i | \(-0.102668\pi\) | ||||
0.948433 | + | 0.316978i | \(0.102668\pi\) | |||||||
\(164\) | 37.2315 | 2.90729 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −16.4075 | −1.27347 | ||||||||
\(167\) | −4.16262 | −0.322113 | −0.161057 | − | 0.986945i | \(-0.551490\pi\) | ||||
−0.161057 | + | 0.986945i | \(0.551490\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.5020 | 0.807849 | ||||||||
\(170\) | 10.3265i | 0.792005i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 40.5641i | 3.09298i | ||||||||
\(173\) | 7.86304 | 0.597816 | 0.298908 | − | 0.954282i | \(-0.403378\pi\) | ||||
0.298908 | + | 0.954282i | \(0.403378\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 0.809727i | − | 0.0612096i | ||||||
\(176\) | − | 14.6291i | − | 1.10271i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.42470i | 0.406598i | ||||||||
\(179\) | −10.4869 | −0.783828 | −0.391914 | − | 0.920002i | \(-0.628187\pi\) | ||||
−0.391914 | + | 0.920002i | \(0.628187\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.4370i | 1.14742i | 0.819058 | + | 0.573711i | \(0.194497\pi\) | ||||
−0.819058 | + | 0.573711i | \(0.805503\pi\) | |||||||
\(182\) | − | 0.813331i | − | 0.0602881i | ||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 47.2250i | 3.48147i | ||||||||
\(185\) | −7.64594 | −0.562141 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 8.63717 | 0.631613 | ||||||||
\(188\) | 52.9124 | 3.85903 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | − | 19.9847i | − | 1.44984i | ||||||
\(191\) | 2.69508 | 0.195009 | 0.0975046 | − | 0.995235i | \(-0.468914\pi\) | ||||
0.0975046 | + | 0.995235i | \(0.468914\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −8.42167 | −0.606205 | −0.303103 | − | 0.952958i | \(-0.598022\pi\) | ||||
−0.303103 | + | 0.952958i | \(0.598022\pi\) | |||||||
\(194\) | −9.90216 | −0.710934 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −30.9357 | −2.20969 | ||||||||
\(197\) | 9.47576i | 0.675120i | 0.941304 | + | 0.337560i | \(0.109602\pi\) | ||||
−0.941304 | + | 0.337560i | \(0.890398\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − | 22.3448i | − | 1.58398i | −0.610534 | − | 0.791990i | \(-0.709045\pi\) | ||
0.610534 | − | 0.791990i | \(-0.290955\pi\) | |||||||
\(200\) | 24.8017i | 1.75375i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −30.1973 | −2.12468 | ||||||||
\(203\) | −1.26291 | −0.0886390 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 8.39703i | − | 0.586474i | ||||||
\(206\) | −22.0701 | −1.53770 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 10.8600i | 0.753008i | ||||||||
\(209\) | −16.7154 | −1.15623 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 19.4828 | 1.34125 | 0.670626 | − | 0.741795i | \(-0.266025\pi\) | ||||
0.670626 | + | 0.741795i | \(0.266025\pi\) | |||||||
\(212\) | −1.69325 | −0.116293 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 28.7868i | 1.96782i | ||||||||
\(215\) | 9.14864 | 0.623932 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 1.25780i | − | 0.0853851i | ||||||
\(218\) | 13.7286i | 0.929817i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −9.48923 | −0.639764 | ||||||||
\(221\) | −6.41187 | −0.431309 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 23.1325i | − | 1.54906i | −0.632535 | − | 0.774532i | \(-0.717986\pi\) | ||
0.632535 | − | 0.774532i | \(-0.282014\pi\) | |||||||
\(224\) | −1.01910 | −0.0680912 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.64517 | 0.308992 | ||||||||
\(227\) | −19.5986 | −1.30081 | −0.650403 | − | 0.759590i | \(-0.725400\pi\) | ||||
−0.650403 | + | 0.759590i | \(0.725400\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 20.4918i | − | 1.35414i | −0.735920 | − | 0.677068i | \(-0.763250\pi\) | ||
0.735920 | − | 0.677068i | \(-0.236750\pi\) | |||||||
\(230\) | 19.3616 | 1.27667 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 38.6827 | 2.53964 | ||||||||
\(233\) | 6.51297 | 0.426679 | 0.213339 | − | 0.976978i | \(-0.431566\pi\) | ||||
0.213339 | + | 0.976978i | \(0.431566\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − | 11.9336i | − | 0.778465i | ||||||
\(236\) | 32.7664 | 2.13291 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | − | 2.08769i | − | 0.135325i | ||||||
\(239\) | 11.0060 | − | 10.8567i | 0.711921 | − | 0.702259i | ||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 13.2011 | 0.850358 | 0.425179 | − | 0.905109i | \(-0.360211\pi\) | ||||
0.425179 | + | 0.905109i | \(0.360211\pi\) | |||||||
\(242\) | − | 16.4191i | − | 1.05546i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −33.0715 | −2.11719 | ||||||||
\(245\) | 6.97710i | 0.445750i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.4088 | 0.789554 | ||||||||
\(248\) | 38.5261i | 2.44641i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 22.8955 | 1.44804 | ||||||||
\(251\) | 2.12359i | 0.134040i | 0.997752 | + | 0.0670198i | \(0.0213491\pi\) | ||||
−0.997752 | + | 0.0670198i | \(0.978651\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 16.1942i | − | 1.01812i | ||||||
\(254\) | 2.31330i | 0.145149i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −29.8777 | −1.86735 | ||||||||
\(257\) | − | 5.16958i | − | 0.322469i | −0.986916 | − | 0.161235i | \(-0.948452\pi\) | ||
0.986916 | − | 0.161235i | \(-0.0515476\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.54577 | 0.0960494 | ||||||||
\(260\) | 7.04440 | 0.436875 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2.97885i | 0.184034i | ||||||||
\(263\) | 10.5890i | 0.652949i | 0.945206 | + | 0.326474i | \(0.105861\pi\) | ||||
−0.945206 | + | 0.326474i | \(0.894139\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.381887i | 0.0234591i | ||||||||
\(266\) | 4.04029i | 0.247726i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 63.6066 | 3.88539 | ||||||||
\(269\) | 2.96094i | 0.180532i | 0.995918 | + | 0.0902658i | \(0.0287717\pi\) | ||||
−0.995918 | + | 0.0902658i | \(0.971228\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 31.4055 | 1.90775 | 0.953875 | − | 0.300204i | \(-0.0970547\pi\) | ||||
0.953875 | + | 0.300204i | \(0.0970547\pi\) | |||||||
\(272\) | 27.8760i | 1.69023i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 6.46384i | − | 0.390495i | ||||||
\(275\) | − | 8.50494i | − | 0.512867i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 20.5114i | 1.23241i | 0.787585 | + | 0.616206i | \(0.211331\pi\) | ||||
−0.787585 | + | 0.616206i | \(0.788669\pi\) | |||||||
\(278\) | 51.0029 | 3.05895 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.26174i | 0.0754036i | ||||||||
\(281\) | 21.8595 | 1.30403 | 0.652015 | − | 0.758206i | \(-0.273924\pi\) | ||||
0.652015 | + | 0.758206i | \(0.273924\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 23.6384 | 1.40516 | 0.702578 | − | 0.711607i | \(-0.252032\pi\) | ||||
0.702578 | + | 0.711607i | \(0.252032\pi\) | |||||||
\(284\) | 50.8206i | 3.01565i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 8.54280i | − | 0.505146i | ||||||
\(287\) | 1.69762i | 0.100207i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.541743 | 0.0318672 | ||||||||
\(290\) | − | 15.8594i | − | 0.931295i | ||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 9.03693i | 0.528846i | ||||||||
\(293\) | 0.144377i | 0.00843462i | 0.999991 | + | 0.00421731i | \(0.00134242\pi\) | ||||
−0.999991 | + | 0.00421731i | \(0.998658\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 7.39000i | − | 0.430262i | ||||||
\(296\) | −47.3465 | −2.75196 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | − | 55.8840i | − | 3.23727i | ||||||
\(299\) | 12.0219i | 0.695246i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.84957 | −0.106607 | ||||||||
\(302\) | −25.4699 | −1.46563 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 53.9481i | − | 3.09413i | ||||||
\(305\) | 7.45881i | 0.427090i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −8.36308 | −0.477306 | −0.238653 | − | 0.971105i | \(-0.576706\pi\) | ||||
−0.238653 | + | 0.971105i | \(0.576706\pi\) | |||||||
\(308\) | 1.91843 | 0.109312 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 15.7952 | 0.897108 | ||||||||
\(311\) | − | 28.3312i | − | 1.60652i | −0.595632 | − | 0.803258i | \(-0.703098\pi\) | ||
0.595632 | − | 0.803258i | \(-0.296902\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 13.5520i | − | 0.766005i | −0.923747 | − | 0.383003i | \(-0.874890\pi\) | ||
0.923747 | − | 0.383003i | \(-0.125110\pi\) | |||||||
\(314\) | 25.3836i | 1.43248i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 63.8454i | 3.59159i | ||||||||
\(317\) | −25.0488 | −1.40688 | −0.703441 | − | 0.710754i | \(-0.748354\pi\) | ||||
−0.703441 | + | 0.710754i | \(0.748354\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.2649 | −0.742694 | ||||||||
\(320\) | 0.980890i | 0.0548334i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3.91431 | −0.218136 | ||||||||
\(323\) | 31.8515 | 1.77226 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.31371i | 0.350221i | ||||||||
\(326\) | − | 61.4834i | − | 3.40525i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | − | 51.9976i | − | 2.87109i | ||||||
\(329\) | 2.41261i | 0.133011i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.9207i | 0.710184i | 0.934831 | + | 0.355092i | \(0.115551\pi\) | ||||
−0.934831 | + | 0.355092i | \(0.884449\pi\) | |||||||
\(332\) | 28.7298i | 1.57675i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 10.5680i | 0.578257i | ||||||||
\(335\) | − | 14.3456i | − | 0.783781i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.28557 | −0.396870 | −0.198435 | − | 0.980114i | \(-0.563586\pi\) | ||||
−0.198435 | + | 0.980114i | \(0.563586\pi\) | |||||||
\(338\) | − | 26.6625i | − | 1.45025i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 18.0819 | 0.980627 | ||||||||
\(341\) | − | 13.2113i | − | 0.715430i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 2.82943i | − | 0.152775i | ||||||
\(344\) | 56.6518 | 3.05446 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 19.9626i | − | 1.07320i | ||||||
\(347\) | 30.4202i | 1.63304i | 0.577316 | + | 0.816521i | \(0.304100\pi\) | ||||
−0.577316 | + | 0.816521i | \(0.695900\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −27.6480 | −1.47996 | −0.739981 | − | 0.672627i | \(-0.765166\pi\) | ||||
−0.739981 | + | 0.672627i | \(0.765166\pi\) | |||||||
\(350\) | −2.05573 | −0.109883 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −10.7040 | −0.570527 | ||||||||
\(353\) | −27.6712 | −1.47279 | −0.736395 | − | 0.676552i | \(-0.763474\pi\) | ||||
−0.736395 | + | 0.676552i | \(0.763474\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.4619 | 0.608332 | ||||||||
\(356\) | 9.49875 | 0.503432 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 26.6241i | 1.40713i | ||||||||
\(359\) | − | 2.34504i | − | 0.123767i | −0.998083 | − | 0.0618834i | \(-0.980289\pi\) | ||
0.998083 | − | 0.0618834i | \(-0.0197107\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −42.6418 | −2.24430 | ||||||||
\(362\) | 39.1913 | 2.05985 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.42416 | −0.0746461 | ||||||||
\(365\) | 2.03815 | 0.106682 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.82990 | −0.0955201 | −0.0477600 | − | 0.998859i | \(-0.515208\pi\) | ||||
−0.0477600 | + | 0.998859i | \(0.515208\pi\) | |||||||
\(368\) | 52.2660 | 2.72455 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 19.4115i | 1.00915i | ||||||||
\(371\) | − | 0.0772056i | − | 0.00400832i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.24517 | 0.0644724 | 0.0322362 | − | 0.999480i | \(-0.489737\pi\) | ||||
0.0322362 | + | 0.999480i | \(0.489737\pi\) | |||||||
\(374\) | − | 21.9280i | − | 1.13387i | ||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 73.8975i | − | 3.81098i | ||||||
\(377\) | 9.84733 | 0.507163 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 1.41319i | − | 0.0725909i | −0.999341 | − | 0.0362955i | \(-0.988444\pi\) | ||
0.999341 | − | 0.0362955i | \(-0.0115557\pi\) | |||||||
\(380\) | −34.9936 | −1.79514 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | − | 6.84225i | − | 0.350080i | ||||||
\(383\) | − | 3.82834i | − | 0.195619i | −0.995205 | − | 0.0978095i | \(-0.968816\pi\) | ||
0.995205 | − | 0.0978095i | \(-0.0311836\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 0.432673i | − | 0.0220511i | ||||||
\(386\) | 21.3809i | 1.08826i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 17.3389i | 0.880247i | ||||||||
\(389\) | 10.3854i | 0.526561i | 0.964719 | + | 0.263280i | \(0.0848045\pi\) | ||||
−0.964719 | + | 0.263280i | \(0.915196\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 30.8584i | 1.56058i | ||||||||
\(392\) | 43.2048i | 2.18217i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 24.0570 | 1.21197 | ||||||||
\(395\) | 14.3994 | 0.724513 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.66801i | 0.284469i | 0.989833 | + | 0.142235i | \(0.0454288\pi\) | ||||
−0.989833 | + | 0.142235i | \(0.954571\pi\) | |||||||
\(398\) | −56.7288 | −2.84356 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 27.4492 | 1.37246 | ||||||||
\(401\) | 2.95268i | 0.147450i | 0.997279 | + | 0.0737250i | \(0.0234887\pi\) | ||||
−0.997279 | + | 0.0737250i | \(0.976511\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.80748i | 0.488546i | ||||||||
\(404\) | 52.8760i | 2.63068i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.20627i | 0.159125i | ||||||||
\(407\) | 16.2359 | 0.804785 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.66664 | 0.131857 | 0.0659284 | − | 0.997824i | \(-0.478999\pi\) | ||||
0.0659284 | + | 0.997824i | \(0.478999\pi\) | |||||||
\(410\) | −21.3183 | −1.05284 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 38.6452i | 1.90391i | ||||||||
\(413\) | 1.49403i | 0.0735162i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 6.47960 | 0.318071 | ||||||||
\(416\) | 7.94622 | 0.389596 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 42.4370i | 2.07566i | ||||||||
\(419\) | 19.6810i | 0.961479i | 0.876863 | + | 0.480739i | \(0.159632\pi\) | ||||
−0.876863 | + | 0.480739i | \(0.840368\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −20.7305 | −1.01034 | −0.505171 | − | 0.863019i | \(-0.668571\pi\) | ||||
−0.505171 | + | 0.863019i | \(0.668571\pi\) | |||||||
\(422\) | − | 49.4629i | − | 2.40781i | ||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.36479i | 0.114844i | ||||||||
\(425\) | 16.2063i | 0.786120i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 1.50794i | − | 0.0729742i | ||||||
\(428\) | 50.4062 | 2.43647 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | − | 23.2265i | − | 1.12008i | ||||||
\(431\) | − | 8.84447i | − | 0.426023i | −0.977050 | − | 0.213012i | \(-0.931673\pi\) | ||
0.977050 | − | 0.213012i | \(-0.0683272\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 32.2277i | − | 1.54876i | −0.632718 | − | 0.774382i | \(-0.718061\pi\) | ||
0.632718 | − | 0.774382i | \(-0.281939\pi\) | |||||||
\(434\) | −3.19330 | −0.153283 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 24.0390 | 1.15126 | ||||||||
\(437\) | − | 59.7199i | − | 2.85679i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −12.6052 | −0.601612 | −0.300806 | − | 0.953685i | \(-0.597256\pi\) | ||||
−0.300806 | + | 0.953685i | \(0.597256\pi\) | |||||||
\(440\) | 13.2527i | 0.631796i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 16.2784i | 0.774285i | ||||||||
\(443\) | 27.5996i | 1.31130i | 0.755066 | + | 0.655649i | \(0.227605\pi\) | ||||
−0.755066 | + | 0.655649i | \(0.772395\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 2.14231i | − | 0.101555i | ||||||
\(446\) | −58.7285 | −2.78088 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | − | 0.198305i | − | 0.00936904i | ||||||
\(449\) | 21.6297 | 1.02077 | 0.510384 | − | 0.859947i | \(-0.329503\pi\) | ||||
0.510384 | + | 0.859947i | \(0.329503\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.8309i | 0.839623i | ||||||||
\(452\) | − | 8.13378i | − | 0.382581i | ||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 49.7568i | 2.33520i | ||||||||
\(455\) | 0.321198i | 0.0150580i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.7289 | 1.53099 | 0.765497 | − | 0.643440i | \(-0.222493\pi\) | ||||
0.765497 | + | 0.643440i | \(0.222493\pi\) | |||||||
\(458\) | −52.0245 | −2.43094 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − | 33.9026i | − | 1.58071i | ||||||
\(461\) | 17.6311 | 0.821163 | 0.410582 | − | 0.911824i | \(-0.365326\pi\) | ||||
0.410582 | + | 0.911824i | \(0.365326\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 13.6995i | 0.636668i | 0.947979 | + | 0.318334i | \(0.103123\pi\) | ||||
−0.947979 | + | 0.318334i | \(0.896877\pi\) | |||||||
\(464\) | − | 42.8119i | − | 1.98749i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | − | 16.5351i | − | 0.765973i | ||||||
\(467\) | −8.09427 | −0.374558 | −0.187279 | − | 0.982307i | \(-0.559967\pi\) | ||||
−0.187279 | + | 0.982307i | \(0.559967\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.90022i | 0.133920i | ||||||||
\(470\) | −30.2970 | −1.39750 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 45.7616i | − | 2.10635i | ||||||
\(473\) | −19.4269 | −0.893249 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 31.3638i | − | 1.43907i | ||||||
\(476\) | −3.65559 | −0.167554 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −27.5628 | − | 27.9421i | −1.26069 | − | 1.27804i | ||||
\(479\) | − | 13.0666i | − | 0.597028i | −0.954405 | − | 0.298514i | \(-0.903509\pi\) | ||
0.954405 | − | 0.298514i | \(-0.0964910\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.0529 | −0.549564 | ||||||||
\(482\) | − | 33.5149i | − | 1.52656i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −28.7501 | −1.30682 | ||||||||
\(485\) | 3.91053 | 0.177568 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −15.7929 | −0.715646 | −0.357823 | − | 0.933790i | \(-0.616481\pi\) | ||||
−0.357823 | + | 0.933790i | \(0.616481\pi\) | |||||||
\(488\) | 46.1878i | 2.09082i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 17.7134 | 0.800210 | ||||||||
\(491\) | 5.95718 | 0.268844 | 0.134422 | − | 0.990924i | \(-0.457082\pi\) | ||||
0.134422 | + | 0.990924i | \(0.457082\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 25.2765 | 1.13840 | ||||||||
\(494\) | − | 31.5034i | − | 1.41741i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 42.6386 | 1.91453 | ||||||||
\(497\) | −2.31723 | −0.103942 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 33.6073i | − | 1.50447i | −0.658896 | − | 0.752234i | \(-0.728976\pi\) | ||
0.658896 | − | 0.752234i | \(-0.271024\pi\) | |||||||
\(500\) | − | 40.0905i | − | 1.79290i | ||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.39135 | 0.240628 | ||||||||
\(503\) | 28.1240i | 1.25399i | 0.779024 | + | 0.626994i | \(0.215715\pi\) | ||||
−0.779024 | + | 0.626994i | \(0.784285\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 11.9254 | 0.530675 | ||||||||
\(506\) | −41.1139 | −1.82773 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 4.05063 | 0.179718 | ||||||||
\(509\) | 31.4716i | 1.39495i | 0.716608 | + | 0.697476i | \(0.245694\pi\) | ||||
−0.716608 | + | 0.697476i | \(0.754306\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −0.412050 | −0.0182280 | ||||||||
\(512\) | 50.7749i | 2.24395i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −13.1245 | −0.578897 | ||||||||
\(515\) | 8.71587 | 0.384067 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 25.3407i | 1.11448i | ||||||||
\(518\) | − | 3.92439i | − | 0.172428i | ||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | − | 9.83822i | − | 0.431435i | ||||||
\(521\) | −16.3465 | −0.716152 | −0.358076 | − | 0.933692i | \(-0.616567\pi\) | ||||
−0.358076 | + | 0.933692i | \(0.616567\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −34.6019 | −1.51304 | −0.756518 | − | 0.653973i | \(-0.773101\pi\) | ||||
−0.756518 | + | 0.653973i | \(0.773101\pi\) | |||||||
\(524\) | 5.21603 | 0.227863 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 26.8834 | 1.17217 | ||||||||
\(527\) | 25.1743i | 1.09661i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 34.8578 | 1.51556 | ||||||||
\(530\) | 0.969533 | 0.0421138 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 7.07461 | 0.306723 | ||||||||
\(533\) | − | 13.2369i | − | 0.573353i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 11.3684i | − | 0.491498i | ||||||
\(536\) | − | 88.8331i | − | 3.83700i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7.51721 | 0.324090 | ||||||||
\(539\) | − | 14.8157i | − | 0.638156i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 0.186320i | − | 0.00801052i | −0.999992 | − | 0.00400526i | \(-0.998725\pi\) | ||
0.999992 | − | 0.00400526i | \(-0.00127492\pi\) | |||||||
\(542\) | − | 79.7322i | − | 3.42479i | ||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 20.3967 | 0.874501 | ||||||||
\(545\) | − | 5.42165i | − | 0.232238i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 5.56344i | − | 0.237875i | −0.992902 | − | 0.118938i | \(-0.962051\pi\) | ||
0.992902 | − | 0.118938i | \(-0.0379489\pi\) | |||||||
\(548\) | −11.3183 | −0.483494 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −21.5923 | −0.920698 | ||||||||
\(551\) | −48.9174 | −2.08395 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.91111 | −0.123793 | ||||||||
\(554\) | 52.0743 | 2.21242 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 89.3070i | − | 3.78746i | ||||||
\(557\) | −7.44256 | −0.315351 | −0.157676 | − | 0.987491i | \(-0.550400\pi\) | ||||
−0.157676 | + | 0.987491i | \(0.550400\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 14.4217 | 0.609973 | ||||||||
\(560\) | 1.39643 | 0.0590099 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | − | 55.4968i | − | 2.34099i | ||||||
\(563\) | 14.1577i | 0.596674i | 0.954461 | + | 0.298337i | \(0.0964320\pi\) | ||||
−0.954461 | + | 0.298337i | \(0.903568\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.83446 | −0.0771762 | ||||||||
\(566\) | − | 60.0130i | − | 2.52253i | ||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 70.9761 | 2.97809 | ||||||||
\(569\) | − | 32.9425i | − | 1.38102i | −0.723322 | − | 0.690511i | \(-0.757386\pi\) | ||
0.723322 | − | 0.690511i | \(-0.242614\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 15.9247 | 0.666429 | 0.333214 | − | 0.942851i | \(-0.391867\pi\) | ||||
0.333214 | + | 0.942851i | \(0.391867\pi\) | |||||||
\(572\) | −14.9586 | −0.625450 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.30990 | 0.179892 | ||||||||
\(575\) | 30.3859 | 1.26718 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.46735 | 0.310870 | 0.155435 | − | 0.987846i | \(-0.450322\pi\) | ||||
0.155435 | + | 0.987846i | \(0.450322\pi\) | |||||||
\(578\) | − | 1.37537i | − | 0.0572080i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −27.7701 | −1.15309 | ||||||||
\(581\) | −1.30997 | −0.0543468 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 0.810927i | − | 0.0335852i | ||||||
\(584\) | 12.6210 | 0.522260 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0.366544 | 0.0151418 | ||||||||
\(587\) | 22.1901i | 0.915885i | 0.888982 | + | 0.457943i | \(0.151413\pi\) | ||||
−0.888982 | + | 0.457943i | \(0.848587\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 48.7194i | − | 2.00745i | ||||||
\(590\) | −18.7617 | −0.772406 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 52.4006i | 2.15365i | ||||||||
\(593\) | −13.2092 | −0.542436 | −0.271218 | − | 0.962518i | \(-0.587426\pi\) | ||||
−0.271218 | + | 0.962518i | \(0.587426\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.824465i | 0.0337998i | ||||||||
\(596\) | −97.8539 | −4.00825 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 30.5212 | 1.24810 | ||||||||
\(599\) | − | 28.3276i | − | 1.15743i | −0.815529 | − | 0.578716i | \(-0.803554\pi\) | ||
0.815529 | − | 0.578716i | \(-0.196446\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 17.2614i | 0.704106i | 0.935980 | + | 0.352053i | \(0.114516\pi\) | ||||
−0.935980 | + | 0.352053i | \(0.885484\pi\) | |||||||
\(602\) | 4.69567i | 0.191381i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 44.5983i | 1.81468i | ||||||||
\(605\) | 6.48417i | 0.263619i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 26.8071i | 1.08807i | 0.839063 | + | 0.544034i | \(0.183104\pi\) | ||||
−0.839063 | + | 0.544034i | \(0.816896\pi\) | |||||||
\(608\) | −39.4735 | −1.60086 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 18.9364 | 0.766712 | ||||||||
\(611\) | − | 18.8119i | − | 0.761048i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −10.7908 | −0.435836 | −0.217918 | − | 0.975967i | \(-0.569927\pi\) | ||||
−0.217918 | + | 0.975967i | \(0.569927\pi\) | |||||||
\(614\) | 21.2321i | 0.856859i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | − | 2.67927i | − | 0.107951i | ||||||
\(617\) | 35.4732 | 1.42810 | 0.714049 | − | 0.700096i | \(-0.246859\pi\) | ||||
0.714049 | + | 0.700096i | \(0.246859\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 37.3500i | 1.50122i | 0.660744 | + | 0.750612i | \(0.270241\pi\) | ||||
−0.660744 | + | 0.750612i | \(0.729759\pi\) | |||||||
\(620\) | − | 27.6577i | − | 1.11076i | ||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −71.9271 | −2.88401 | ||||||||
\(623\) | 0.433107i | 0.0173521i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 10.9320 | 0.437280 | ||||||||
\(626\) | −34.4058 | −1.37513 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 44.4471 | 1.77363 | ||||||||
\(629\) | −30.9378 | −1.23357 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.9840 | −1.31307 | −0.656537 | − | 0.754294i | \(-0.727979\pi\) | ||||
−0.656537 | + | 0.754294i | \(0.727979\pi\) | |||||||
\(632\) | 89.1666 | 3.54686 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 63.5938i | 2.52563i | ||||||||
\(635\) | − | 0.913562i | − | 0.0362536i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.9985i | 0.435777i | ||||||||
\(638\) | 33.6770i | 1.33328i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 12.5719 | 0.496949 | ||||||||
\(641\) | − | 26.5093i | − | 1.04705i | −0.852009 | − | 0.523527i | \(-0.824616\pi\) | ||
0.852009 | − | 0.523527i | \(-0.175384\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10.3683 | −0.408886 | −0.204443 | − | 0.978878i | \(-0.565538\pi\) | ||||
−0.204443 | + | 0.978878i | \(0.565538\pi\) | |||||||
\(644\) | 6.85403i | 0.270087i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | − | 80.8643i | − | 3.18156i | ||||||
\(647\) | 31.1998i | 1.22659i | 0.789854 | + | 0.613296i | \(0.210157\pi\) | ||||
−0.789854 | + | 0.613296i | \(0.789843\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 15.6924i | 0.615983i | ||||||||
\(650\) | 16.0292 | 0.628717 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −107.659 | −4.21623 | ||||||||
\(653\) | −31.7988 | −1.24438 | −0.622192 | − | 0.782865i | \(-0.713758\pi\) | ||||
−0.622192 | + | 0.782865i | \(0.713758\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 1.17640i | − | 0.0459658i | ||||||
\(656\) | −57.5481 | −2.24688 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 6.12511 | 0.238782 | ||||||||
\(659\) | −0.997098 | −0.0388414 | −0.0194207 | − | 0.999811i | \(-0.506182\pi\) | ||||
−0.0194207 | + | 0.999811i | \(0.506182\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.49685 | −0.213803 | −0.106901 | − | 0.994270i | \(-0.534093\pi\) | ||||
−0.106901 | + | 0.994270i | \(0.534093\pi\) | |||||||
\(662\) | 32.8029 | 1.27492 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 40.1241 | 1.55712 | ||||||||
\(665\) | − | 1.59558i | − | 0.0618739i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 47.3922i | − | 1.83503i | ||||||
\(668\) | 18.5048 | 0.715973 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −36.4204 | −1.40704 | ||||||||
\(671\) | − | 15.8386i | − | 0.611441i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.2932i | 0.782246i | 0.920338 | + | 0.391123i | \(0.127913\pi\) | ||||
−0.920338 | + | 0.391123i | \(0.872087\pi\) | |||||||
\(674\) | 18.4966i | 0.712461i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −46.6865 | −1.79564 | ||||||||
\(677\) | 41.3640 | 1.58975 | 0.794873 | − | 0.606776i | \(-0.207537\pi\) | ||||
0.794873 | + | 0.606776i | \(0.207537\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −0.790587 | −0.0303399 | ||||||||
\(680\) | − | 25.2532i | − | 0.968414i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −33.5407 | −1.28434 | ||||||||
\(683\) | −1.76522 | −0.0675444 | −0.0337722 | − | 0.999430i | \(-0.510752\pi\) | ||||
−0.0337722 | + | 0.999430i | \(0.510752\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.55268i | 0.0975329i | ||||||||
\(686\) | −7.18334 | −0.274261 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | − | 62.6991i | − | 2.39038i | ||||||
\(689\) | 0.601998i | 0.0229343i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 8.63431 | 0.328465 | 0.164232 | − | 0.986422i | \(-0.447485\pi\) | ||||
0.164232 | + | 0.986422i | \(0.447485\pi\) | |||||||
\(692\) | −34.9549 | −1.32879 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 77.2306 | 2.93163 | ||||||||
\(695\) | −20.1419 | −0.764027 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 33.9770i | − | 1.28697i | ||||||
\(698\) | 70.1925i | 2.65683i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.59962i | 0.136053i | ||||||||
\(701\) | −25.2485 | −0.953621 | −0.476811 | − | 0.879006i | \(-0.658207\pi\) | ||||
−0.476811 | + | 0.879006i | \(0.658207\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 59.8736 | 2.25818 | ||||||||
\(704\) | − | 2.08289i | − | 0.0785019i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 70.2515i | 2.64395i | ||||||||
\(707\) | −2.41095 | −0.0906731 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 42.2655i | 1.58731i | 0.608366 | + | 0.793656i | \(0.291825\pi\) | ||||
−0.608366 | + | 0.793656i | \(0.708175\pi\) | |||||||
\(710\) | − | 29.0993i | − | 1.09208i | ||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − | 13.2660i | − | 0.497163i | ||||||
\(713\) | 47.2004 | 1.76767 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.37370i | 0.126169i | ||||||||
\(716\) | 46.6192 | 1.74224 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.95358 | −0.222186 | ||||||||
\(719\) | 35.0526i | 1.30724i | 0.756822 | + | 0.653621i | \(0.226751\pi\) | ||||
−0.756822 | + | 0.653621i | \(0.773249\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.76208 | −0.0656231 | ||||||||
\(722\) | 108.259i | 4.02897i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | − | 68.6247i | − | 2.55042i | ||||||
\(725\) | − | 24.8896i | − | 0.924375i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.9131 | 0.627271 | 0.313635 | − | 0.949543i | \(-0.398453\pi\) | ||||
0.313635 | + | 0.949543i | \(0.398453\pi\) | |||||||
\(728\) | 1.98898i | 0.0737165i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | − | 5.17444i | − | 0.191515i | ||||||
\(731\) | 37.0182 | 1.36917 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −3.13835 | −0.115917 | −0.0579587 | − | 0.998319i | \(-0.518459\pi\) | ||||
−0.0579587 | + | 0.998319i | \(0.518459\pi\) | |||||||
\(734\) | 4.64574i | 0.171478i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | − | 38.2427i | − | 1.40965i | ||||||
\(737\) | 30.4624i | 1.12210i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.4927 | 0.422765 | 0.211383 | − | 0.977403i | \(-0.432203\pi\) | ||||
0.211383 | + | 0.977403i | \(0.432203\pi\) | |||||||
\(740\) | 33.9898 | 1.24949 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −0.196009 | −0.00719572 | ||||||||
\(743\) | 25.9160 | 0.950767 | 0.475383 | − | 0.879779i | \(-0.342309\pi\) | ||||
0.475383 | + | 0.879779i | \(0.342309\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 22.0696i | 0.808566i | ||||||||
\(746\) | − | 3.16123i | − | 0.115741i | ||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −38.3963 | −1.40391 | ||||||||
\(749\) | 2.29833i | 0.0839792i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 35.2543 | 1.28645 | 0.643224 | − | 0.765678i | \(-0.277596\pi\) | ||||
0.643224 | + | 0.765678i | \(0.277596\pi\) | |||||||
\(752\) | −81.7858 | −2.98242 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 25.0003i | − | 0.910459i | ||||||
\(755\) | 10.0585 | 0.366066 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.9842 | 1.34421 | 0.672107 | − | 0.740454i | \(-0.265389\pi\) | ||||
0.672107 | + | 0.740454i | \(0.265389\pi\) | |||||||
\(758\) | −3.58781 | −0.130315 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 48.8721i | 1.77278i | ||||||||
\(761\) | − | 28.2033i | − | 1.02237i | −0.859471 | − | 0.511185i | \(-0.829207\pi\) | ||
0.859471 | − | 0.511185i | \(-0.170793\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.09609i | 0.0396811i | ||||||||
\(764\) | −11.9809 | −0.433454 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −9.71937 | −0.351175 | ||||||||
\(767\) | − | 11.6494i | − | 0.420636i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.3866i | 0.482732i | 0.970434 | + | 0.241366i | \(0.0775955\pi\) | ||||
−0.970434 | + | 0.241366i | \(0.922405\pi\) | |||||||
\(770\) | −1.09847 | −0.0395860 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 37.4383 | 1.34743 | ||||||||
\(773\) | −26.2722 | −0.944945 | −0.472473 | − | 0.881345i | \(-0.656638\pi\) | ||||
−0.472473 | + | 0.881345i | \(0.656638\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 24.7888 | 0.890441 | ||||||||
\(776\) | 24.2155 | 0.869285 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 26.3664 | 0.945281 | ||||||||
\(779\) | 65.7552i | 2.35593i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −24.3389 | −0.870916 | ||||||||
\(782\) | 78.3430 | 2.80154 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 47.8167 | 1.70774 | ||||||||
\(785\) | − | 10.0244i | − | 0.357787i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 9.23638i | − | 0.329241i | −0.986357 | − | 0.164621i | \(-0.947360\pi\) | ||
0.986357 | − | 0.164621i | \(-0.0526400\pi\) | |||||||
\(788\) | − | 42.1242i | − | 1.50061i | ||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 36.5572i | − | 1.30065i | ||||||
\(791\) | 0.370870 | 0.0131866 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.7579i | 0.417535i | ||||||||
\(794\) | 14.3899 | 0.510679 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 99.3332i | 3.52077i | ||||||||
\(797\) | − | 10.1091i | − | 0.358082i | −0.983842 | − | 0.179041i | \(-0.942700\pi\) | ||
0.983842 | − | 0.179041i | \(-0.0572995\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 48.2871i | − | 1.70828i | ||||||
\(800\) | − | 20.0844i | − | 0.710091i | ||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 7.49626 | 0.264702 | ||||||||
\(803\) | −4.32795 | −0.152730 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.54583 | 0.0544833 | ||||||||
\(806\) | 24.8992 | 0.877036 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 73.8467 | 2.59792 | ||||||||
\(809\) | 37.2298 | 1.30893 | 0.654465 | − | 0.756092i | \(-0.272894\pi\) | ||||
0.654465 | + | 0.756092i | \(0.272894\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 25.9861i | − | 0.912496i | −0.889853 | − | 0.456248i | \(-0.849193\pi\) | ||
0.889853 | − | 0.456248i | \(-0.150807\pi\) | |||||||
\(812\) | 5.61424 | 0.197021 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | − | 41.2197i | − | 1.44475i | ||||||
\(815\) | 24.2808i | 0.850521i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −71.6409 | −2.50640 | ||||||||
\(818\) | − | 6.77004i | − | 0.236709i | ||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 37.3288i | 1.30358i | ||||||||
\(821\) | 37.7003 | 1.31575 | 0.657875 | − | 0.753127i | \(-0.271456\pi\) | ||||
0.657875 | + | 0.753127i | \(0.271456\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 12.3129i | 0.429201i | 0.976702 | + | 0.214600i | \(0.0688449\pi\) | ||||
−0.976702 | + | 0.214600i | \(0.931155\pi\) | |||||||
\(824\) | 53.9719 | 1.88020 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 3.79302 | 0.131976 | ||||||||
\(827\) | − | 8.16207i | − | 0.283823i | −0.989879 | − | 0.141912i | \(-0.954675\pi\) | ||
0.989879 | − | 0.141912i | \(-0.0453249\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 21.4138i | − | 0.743730i | −0.928287 | − | 0.371865i | \(-0.878718\pi\) | ||
0.928287 | − | 0.371865i | \(-0.121282\pi\) | |||||||
\(830\) | − | 16.4504i | − | 0.571001i | ||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.54625i | 0.0536066i | ||||||||
\(833\) | 28.2315i | 0.978162i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − | 4.17350i | − | 0.144430i | ||||||
\(836\) | 74.3080 | 2.56999 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 49.9660 | 1.72605 | ||||||||
\(839\) | 37.9872i | 1.31146i | 0.754993 | + | 0.655732i | \(0.227640\pi\) | ||||
−0.754993 | + | 0.655732i | \(0.772360\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.81964 | −0.338608 | ||||||||
\(842\) | 52.6304i | 1.81376i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −86.6104 | −2.98125 | ||||||||
\(845\) | 10.5295i | 0.362225i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 1.31090i | − | 0.0450429i | ||||||
\(848\) | 2.61722 | 0.0898757 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 41.1444 | 1.41124 | ||||||||
\(851\) | 58.0068i | 1.98845i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.9365 | −0.579893 | −0.289947 | − | 0.957043i | \(-0.593638\pi\) | ||||
−0.289947 | + | 0.957043i | \(0.593638\pi\) | |||||||
\(854\) | −3.82834 | −0.131003 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | − | 70.3973i | − | 2.40613i | ||||||
\(857\) | 41.2105 | 1.40772 | 0.703862 | − | 0.710337i | \(-0.251457\pi\) | ||||
0.703862 | + | 0.710337i | \(0.251457\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −46.3831 | −1.58257 | −0.791286 | − | 0.611446i | \(-0.790588\pi\) | ||||
−0.791286 | + | 0.611446i | \(0.790588\pi\) | |||||||
\(860\) | −40.6700 | −1.38684 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −22.4543 | −0.764796 | ||||||||
\(863\) | 24.3727 | 0.829656 | 0.414828 | − | 0.909900i | \(-0.363842\pi\) | ||||
0.414828 | + | 0.909900i | \(0.363842\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 7.88359i | 0.268050i | ||||||||
\(866\) | −81.8195 | −2.78034 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5.59152i | 0.189789i | ||||||||
\(869\) | −30.5768 | −1.03725 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 22.6140i | − | 0.766245i | ||||||
\(872\) | − | 33.5729i | − | 1.13692i | ||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −151.616 | −5.12850 | ||||||||
\(875\) | 1.82798 | 0.0617968 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −44.9401 | −1.51752 | −0.758759 | − | 0.651371i | \(-0.774194\pi\) | ||||
−0.758759 | + | 0.651371i | \(0.774194\pi\) | |||||||
\(878\) | 32.0020i | 1.08001i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 14.6673 | 0.494436 | ||||||||
\(881\) | −35.3645 | −1.19146 | −0.595730 | − | 0.803185i | \(-0.703137\pi\) | ||||
−0.595730 | + | 0.803185i | \(0.703137\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.76537 | −0.261326 | −0.130663 | − | 0.991427i | \(-0.541711\pi\) | ||||
−0.130663 | + | 0.991427i | \(0.541711\pi\) | |||||||
\(884\) | 28.5038 | 0.958687 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 70.0698 | 2.35404 | ||||||||
\(887\) | 7.38788i | 0.248061i | 0.992278 | + | 0.124030i | \(0.0395820\pi\) | ||||
−0.992278 | + | 0.124030i | \(0.960418\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.184694i | 0.00619443i | ||||||||
\(890\) | −5.43887 | −0.182311 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 102.835i | 3.44316i | ||||||||
\(893\) | 93.4495i | 3.12717i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − | 10.5143i | − | 0.351454i | ||||||
\(896\) | −2.54165 | −0.0849105 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | − | 54.9133i | − | 1.83248i | ||||||
\(899\) | − | 38.6625i | − | 1.28947i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.54523i | 0.0514792i | ||||||||
\(902\) | 45.2689 | 1.50729 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −11.3597 | −0.377816 | ||||||||
\(905\) | −15.4773 | −0.514484 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 43.0501i | 1.42945i | 0.699403 | + | 0.714727i | \(0.253449\pi\) | ||||
−0.699403 | + | 0.714727i | \(0.746551\pi\) | |||||||
\(908\) | 87.1251 | 2.89135 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0.815456 | 0.0270321 | ||||||||
\(911\) | 34.5957 | 1.14621 | 0.573103 | − | 0.819483i | \(-0.305739\pi\) | ||||
0.573103 | + | 0.819483i | \(0.305739\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −13.7592 | −0.455365 | ||||||||
\(914\) | − | 83.0920i | − | 2.74844i | ||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 91.0958i | 3.00989i | ||||||||
\(917\) | 0.237831i | 0.00785388i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 45.0931 | 1.48748 | 0.743742 | − | 0.668466i | \(-0.233049\pi\) | ||||
0.743742 | + | 0.668466i | \(0.233049\pi\) | |||||||
\(920\) | −47.3484 | −1.56103 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − | 44.7618i | − | 1.47415i | ||||||
\(923\) | 18.0682 | 0.594722 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 30.4642i | 1.00166i | ||||||||
\(926\) | 34.7801 | 1.14295 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −31.3252 | −1.02830 | ||||||||
\(929\) | −22.1120 | −0.725472 | −0.362736 | − | 0.931892i | \(-0.618157\pi\) | ||||
−0.362736 | + | 0.931892i | \(0.618157\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 54.6360i | − | 1.79062i | ||||||
\(932\) | −28.9532 | −0.948395 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 20.5497i | 0.672406i | ||||||||
\(935\) | 8.65974i | 0.283204i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.19854 | 0.267835 | 0.133917 | − | 0.990993i | \(-0.457244\pi\) | ||||
0.133917 | + | 0.990993i | \(0.457244\pi\) | |||||||
\(938\) | 7.36307 | 0.240413 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 53.0507i | 1.73032i | ||||||||
\(941\) | −12.6796 | −0.413343 | −0.206671 | − | 0.978410i | \(-0.566263\pi\) | ||||
−0.206671 | + | 0.978410i | \(0.566263\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −63.7050 | −2.07452 | ||||||||
\(944\) | −50.6465 | −1.64840 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 49.3208i | 1.60356i | ||||||||
\(947\) | 7.26631 | 0.236123 | 0.118062 | − | 0.993006i | \(-0.462332\pi\) | ||||
0.118062 | + | 0.993006i | \(0.462332\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.21289 | 0.104295 | ||||||||
\(950\) | −79.6263 | −2.58342 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.10540i | 0.165467i | ||||||||
\(953\) | −24.0628 | −0.779470 | −0.389735 | − | 0.920927i | \(-0.627433\pi\) | ||||
−0.389735 | + | 0.920927i | \(0.627433\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.70212i | 0.0874386i | ||||||||
\(956\) | −48.9270 | + | 48.2630i | −1.58241 | + | 1.56094i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −33.1734 | −1.07178 | ||||||||
\(959\) | − | 0.516072i | − | 0.0166648i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50608 | 0.242132 | ||||||||
\(962\) | 30.5998i | 0.986576i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −58.6852 | −1.89012 | ||||||||
\(965\) | − | 8.44367i | − | 0.271811i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 13.0184 | 0.418644 | 0.209322 | − | 0.977847i | \(-0.432874\pi\) | ||||
0.209322 | + | 0.977847i | \(0.432874\pi\) | |||||||
\(968\) | 40.1524i | 1.29055i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | − | 9.92803i | − | 0.318770i | ||||||
\(971\) | − | 4.53779i | − | 0.145625i | −0.997346 | − | 0.0728124i | \(-0.976803\pi\) | ||
0.997346 | − | 0.0728124i | \(-0.0231974\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.07207 | 0.130544 | ||||||||
\(974\) | 40.0950i | 1.28473i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 51.1181 | 1.63625 | ||||||||
\(977\) | 36.4107 | 1.16488 | 0.582441 | − | 0.812873i | \(-0.302098\pi\) | ||||
0.582441 | + | 0.812873i | \(0.302098\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 4.54912i | 0.145391i | ||||||||
\(980\) | − | 31.0165i | − | 0.990786i | ||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | − | 15.1241i | − | 0.482628i | ||||||
\(983\) | − | 44.8689i | − | 1.43109i | −0.698564 | − | 0.715547i | \(-0.746177\pi\) | ||
0.698564 | − | 0.715547i | \(-0.253823\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −9.50052 | −0.302712 | ||||||||
\(986\) | − | 64.1719i | − | 2.04365i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −55.1631 | −1.75497 | ||||||||
\(989\) | − | 69.4072i | − | 2.20702i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.1554i | 0.767321i | 0.923474 | + | 0.383661i | \(0.125337\pi\) | ||||
−0.923474 | + | 0.383661i | \(0.874663\pi\) | |||||||
\(992\) | − | 31.1984i | − | 0.990551i | ||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 5.88297i | 0.186596i | ||||||||
\(995\) | 22.4032 | 0.710228 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 5.83319i | − | 0.184739i | −0.995725 | − | 0.0923695i | \(-0.970556\pi\) | ||
0.995725 | − | 0.0923695i | \(-0.0294441\pi\) | |||||||
\(998\) | −85.3219 | −2.70082 | ||||||||
\(999\) | 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 | 2151.2.b.a.2150.7 | ✓ | 80 | |
3.2 | odd | 2 | inner | 2151.2.b.a.2150.73 | yes | 80 | |
239.238 | odd | 2 | inner | 2151.2.b.a.2150.8 | yes | 80 | |
717.716 | even | 2 | inner | 2151.2.b.a.2150.74 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2151.2.b.a.2150.7 | ✓ | 80 | 1.1 | even | 1 | trivial | |
2151.2.b.a.2150.8 | yes | 80 | 239.238 | odd | 2 | inner | |
2151.2.b.a.2150.73 | yes | 80 | 3.2 | odd | 2 | inner | |
2151.2.b.a.2150.74 | yes | 80 | 717.716 | even | 2 | inner |