Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4012,2,Mod(1,4012)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4012, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4012.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4012 = 2^{2} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4012.a (trivial) |
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: | yes |
Analytic conductor: | \(32.0359812909\) |
Analytic rank: | \(1\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 4 x^{11} - 13 x^{10} + 60 x^{9} + 48 x^{8} - 289 x^{7} - 89 x^{6} + 602 x^{5} + 161 x^{4} + \cdots + 82 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.10 | ||
Root | \(-1.18842\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4012.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.18842 | 0.686135 | 0.343067 | − | 0.939311i | \(-0.388534\pi\) | ||||
0.343067 | + | 0.939311i | \(0.388534\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.677556 | 0.303012 | 0.151506 | − | 0.988456i | \(-0.451588\pi\) | ||||
0.151506 | + | 0.988456i | \(0.451588\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.46203 | 0.552596 | 0.276298 | − | 0.961072i | \(-0.410892\pi\) | ||||
0.276298 | + | 0.961072i | \(0.410892\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.58766 | −0.529219 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.15873 | −0.650883 | −0.325442 | − | 0.945562i | \(-0.605513\pi\) | ||||
−0.325442 | + | 0.945562i | \(0.605513\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.65583 | 1.29129 | 0.645647 | − | 0.763636i | \(-0.276588\pi\) | ||||
0.645647 | + | 0.763636i | \(0.276588\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.805222 | 0.207907 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −6.39831 | −1.46787 | −0.733937 | − | 0.679218i | \(-0.762319\pi\) | ||||
−0.733937 | + | 0.679218i | \(0.762319\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.73751 | 0.379155 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.06616 | −1.68191 | −0.840955 | − | 0.541105i | \(-0.818006\pi\) | ||||
−0.840955 | + | 0.541105i | \(0.818006\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.54092 | −0.908184 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.45207 | −1.04925 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.503272 | −0.0934552 | −0.0467276 | − | 0.998908i | \(-0.514879\pi\) | ||||
−0.0467276 | + | 0.998908i | \(0.514879\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.46048 | −1.16034 | −0.580168 | − | 0.814497i | \(-0.697013\pi\) | ||||
−0.580168 | + | 0.814497i | \(0.697013\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.56548 | −0.446594 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.990608 | 0.167443 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.81150 | −0.791005 | −0.395503 | − | 0.918465i | \(-0.629430\pi\) | ||||
−0.395503 | + | 0.918465i | \(0.629430\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.53308 | 0.886002 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.96183 | 0.618735 | 0.309367 | − | 0.950943i | \(-0.399883\pi\) | ||||
0.309367 | + | 0.950943i | \(0.399883\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.76078 | −0.573514 | −0.286757 | − | 0.958003i | \(-0.592577\pi\) | ||||
−0.286757 | + | 0.958003i | \(0.592577\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.07573 | −0.160360 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.61248 | −0.818664 | −0.409332 | − | 0.912386i | \(-0.634238\pi\) | ||||
−0.409332 | + | 0.912386i | \(0.634238\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.86246 | −0.694638 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.18842 | −0.166412 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 5.58471 | 0.767119 | 0.383559 | − | 0.923516i | \(-0.374698\pi\) | ||||
0.383559 | + | 0.923516i | \(0.374698\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −1.46266 | −0.197226 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.60389 | −1.00716 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.00000 | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.84854 | −0.364719 | −0.182359 | − | 0.983232i | \(-0.558373\pi\) | ||||
−0.182359 | + | 0.983232i | \(0.558373\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.32120 | −0.292444 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.15458 | 0.391278 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.63656 | 0.444276 | 0.222138 | − | 0.975015i | \(-0.428696\pi\) | ||||
0.222138 | + | 0.975015i | \(0.428696\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.58599 | −1.15402 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 6.38829 | 0.758151 | 0.379075 | − | 0.925366i | \(-0.376242\pi\) | ||||
0.379075 | + | 0.925366i | \(0.376242\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 12.0069 | 1.40530 | 0.702651 | − | 0.711535i | \(-0.252000\pi\) | ||||
0.702651 | + | 0.711535i | \(0.252000\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −5.39652 | −0.623136 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.15614 | −0.359675 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −10.7077 | −1.20470 | −0.602352 | − | 0.798230i | \(-0.705770\pi\) | ||||
−0.602352 | + | 0.798230i | \(0.705770\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.71638 | −0.190709 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.34708 | 0.147862 | 0.0739308 | − | 0.997263i | \(-0.476446\pi\) | ||||
0.0739308 | + | 0.997263i | \(0.476446\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.677556 | −0.0734913 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −0.598098 | −0.0641229 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 18.7751 | 1.99016 | 0.995079 | − | 0.0990883i | \(-0.0315926\pi\) | ||||
0.995079 | + | 0.0990883i | \(0.0315926\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.80696 | 0.713564 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −7.67776 | −0.796147 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.33522 | −0.444784 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.8516 | 1.40642 | 0.703210 | − | 0.710982i | \(-0.251749\pi\) | ||||
0.703210 | + | 0.710982i | \(0.251749\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 3.42733 | 0.344460 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −16.4356 | −1.63541 | −0.817703 | − | 0.575640i | \(-0.804753\pi\) | ||||
−0.817703 | + | 0.575640i | \(0.804753\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.07384 | 0.302874 | 0.151437 | − | 0.988467i | \(-0.451610\pi\) | ||||
0.151437 | + | 0.988467i | \(0.451610\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.17726 | 0.114889 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.798100 | −0.0771552 | −0.0385776 | − | 0.999256i | \(-0.512283\pi\) | ||||
−0.0385776 | + | 0.999256i | \(0.512283\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 15.0629 | 1.44277 | 0.721384 | − | 0.692536i | \(-0.243507\pi\) | ||||
0.721384 | + | 0.692536i | \(0.243507\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.71808 | −0.542736 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −11.3690 | −1.06951 | −0.534754 | − | 0.845008i | \(-0.679596\pi\) | ||||
−0.534754 | + | 0.845008i | \(0.679596\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.46528 | −0.509640 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.39185 | −0.683377 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.46203 | −0.134024 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.33986 | −0.576351 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 4.70833 | 0.424535 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.46451 | −0.578203 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 4.22669 | 0.375058 | 0.187529 | − | 0.982259i | \(-0.439952\pi\) | ||||
0.187529 | + | 0.982259i | \(0.439952\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.46939 | −0.393508 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −13.1157 | −1.14593 | −0.572963 | − | 0.819581i | \(-0.694206\pi\) | ||||
−0.572963 | + | 0.819581i | \(0.694206\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.35453 | −0.811141 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.69408 | −0.317936 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.39584 | −0.460997 | −0.230499 | − | 0.973073i | \(-0.574036\pi\) | ||||
−0.230499 | + | 0.973073i | \(0.574036\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13.0896 | 1.11024 | 0.555121 | − | 0.831770i | \(-0.312672\pi\) | ||||
0.555121 | + | 0.831770i | \(0.312672\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.66998 | −0.561714 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.0507 | −0.840481 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.340995 | −0.0283181 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −5.77865 | −0.476615 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.1217 | −1.32074 | −0.660370 | − | 0.750940i | \(-0.729601\pi\) | ||||
−0.660370 | + | 0.750940i | \(0.729601\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.37058 | 0.681188 | 0.340594 | − | 0.940210i | \(-0.389372\pi\) | ||||
0.340594 | + | 0.940210i | \(0.389372\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1.58766 | 0.128354 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.37733 | −0.351596 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 4.75219 | 0.379266 | 0.189633 | − | 0.981855i | \(-0.439270\pi\) | ||||
0.189633 | + | 0.981855i | \(0.439270\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.63698 | 0.526347 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.7930 | −0.929417 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 8.94962 | 0.700988 | 0.350494 | − | 0.936565i | \(-0.386014\pi\) | ||||
0.350494 | + | 0.936565i | \(0.386014\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.73826 | −0.135323 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 0.900044 | 0.0696475 | 0.0348238 | − | 0.999393i | \(-0.488913\pi\) | ||||
0.0348238 | + | 0.999393i | \(0.488913\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.67672 | 0.667440 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 10.1583 | 0.776827 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −12.7968 | −0.972926 | −0.486463 | − | 0.873701i | \(-0.661713\pi\) | ||||
−0.486463 | + | 0.873701i | \(0.661713\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.63896 | −0.501858 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.18842 | 0.0893272 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.46621 | −0.184333 | −0.0921666 | − | 0.995744i | \(-0.529379\pi\) | ||||
−0.0921666 | + | 0.995744i | \(0.529379\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −12.0844 | −0.898228 | −0.449114 | − | 0.893474i | \(-0.648260\pi\) | ||||
−0.449114 | + | 0.893474i | \(0.648260\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −3.38527 | −0.250246 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.26006 | −0.239684 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.15873 | 0.157862 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −7.97109 | −0.579811 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −14.6034 | −1.05666 | −0.528331 | − | 0.849038i | \(-0.677182\pi\) | ||||
−0.528331 | + | 0.849038i | \(0.677182\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −7.70959 | −0.554948 | −0.277474 | − | 0.960733i | \(-0.589497\pi\) | ||||
−0.277474 | + | 0.960733i | \(0.589497\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.74897 | 0.268470 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.588856 | −0.0419543 | −0.0209771 | − | 0.999780i | \(-0.506678\pi\) | ||||
−0.0209771 | + | 0.999780i | \(0.506678\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.65566 | 0.471807 | 0.235903 | − | 0.971776i | \(-0.424195\pi\) | ||||
0.235903 | + | 0.971776i | \(0.424195\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.32176 | 0.304833 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −0.735799 | −0.0516430 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.68437 | 0.187484 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.8063 | 0.890099 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 13.8123 | 0.955414 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −19.7552 | −1.36000 | −0.680002 | − | 0.733210i | \(-0.738021\pi\) | ||||
−0.680002 | + | 0.733210i | \(0.738021\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 7.59198 | 0.520194 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −2.54814 | −0.173782 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −9.44542 | −0.641197 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 14.2693 | 0.964227 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −4.65583 | −0.313185 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 25.4341 | 1.70319 | 0.851597 | − | 0.524197i | \(-0.175634\pi\) | ||||
0.851597 | + | 0.524197i | \(0.175634\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 7.20942 | 0.480628 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.6147 | 0.970009 | 0.485004 | − | 0.874512i | \(-0.338818\pi\) | ||||
0.485004 | + | 0.874512i | \(0.338818\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.64411 | 0.505137 | 0.252568 | − | 0.967579i | \(-0.418725\pi\) | ||||
0.252568 | + | 0.967579i | \(0.418725\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.75082 | −0.246786 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 26.3790 | 1.72815 | 0.864073 | − | 0.503367i | \(-0.167906\pi\) | ||||
0.864073 | + | 0.503367i | \(0.167906\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.80277 | −0.248065 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.7252 | −0.826590 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.19929 | −0.400999 | −0.200499 | − | 0.979694i | \(-0.564256\pi\) | ||||
−0.200499 | + | 0.979694i | \(0.564256\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 15.0051 | 0.966563 | 0.483281 | − | 0.875465i | \(-0.339445\pi\) | ||||
0.483281 | + | 0.875465i | \(0.339445\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 14.3164 | 0.918399 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.29459 | −0.210484 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −29.7894 | −1.89546 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.60090 | 0.101453 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.06032 | −0.130046 | −0.0650232 | − | 0.997884i | \(-0.520712\pi\) | ||||
−0.0650232 | + | 0.997884i | \(0.520712\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 17.4127 | 1.09473 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.805222 | −0.0504249 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −24.1805 | −1.50834 | −0.754169 | − | 0.656680i | \(-0.771960\pi\) | ||||
−0.754169 | + | 0.656680i | \(0.771960\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −7.03456 | −0.437106 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.799022 | 0.0494582 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −10.5970 | −0.653439 | −0.326720 | − | 0.945121i | \(-0.605943\pi\) | ||||
−0.326720 | + | 0.945121i | \(0.605943\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.78395 | 0.232446 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 22.3127 | 1.36552 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −9.38855 | −0.572430 | −0.286215 | − | 0.958165i | \(-0.592397\pi\) | ||||
−0.286215 | + | 0.958165i | \(0.592397\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.59487 | −0.218373 | −0.109186 | − | 0.994021i | \(-0.534825\pi\) | ||||
−0.109186 | + | 0.994021i | \(0.534825\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 8.08954 | 0.489601 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 9.80264 | 0.591121 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.4200 | 0.926497 | 0.463248 | − | 0.886228i | \(-0.346684\pi\) | ||||
0.463248 | + | 0.886228i | \(0.346684\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 10.2570 | 0.614071 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 11.7653 | 0.701856 | 0.350928 | − | 0.936402i | \(-0.385866\pi\) | ||||
0.350928 | + | 0.936402i | \(0.385866\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −5.99628 | −0.356442 | −0.178221 | − | 0.983991i | \(-0.557034\pi\) | ||||
−0.178221 | + | 0.983991i | \(0.557034\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −5.15206 | −0.305182 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 5.79233 | 0.341910 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 16.4616 | 0.964994 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −14.6820 | −0.857731 | −0.428865 | − | 0.903368i | \(-0.641087\pi\) | ||||
−0.428865 | + | 0.903368i | \(0.641087\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.677556 | 0.0394488 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 11.7696 | 0.682939 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −37.5546 | −2.17184 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5.49838 | −0.316922 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −19.5324 | −1.12211 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.93005 | −0.110514 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −15.6127 | −0.891066 | −0.445533 | − | 0.895265i | \(-0.646986\pi\) | ||||
−0.445533 | + | 0.895265i | \(0.646986\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.65301 | 0.207813 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 3.87401 | 0.219675 | 0.109837 | − | 0.993950i | \(-0.464967\pi\) | ||||
0.109837 | + | 0.993950i | \(0.464967\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −16.2306 | −0.917408 | −0.458704 | − | 0.888589i | \(-0.651686\pi\) | ||||
−0.458704 | + | 0.888589i | \(0.651686\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −1.57275 | −0.0886142 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.9739 | 1.23417 | 0.617087 | − | 0.786895i | \(-0.288313\pi\) | ||||
0.617087 | + | 0.786895i | \(0.288313\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.08643 | 0.0608284 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.948478 | −0.0529389 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.39831 | 0.356012 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −21.1417 | −1.17273 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 17.9011 | 0.989933 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −8.20561 | −0.452390 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.58838 | −0.362130 | −0.181065 | − | 0.983471i | \(-0.557954\pi\) | ||||
−0.181065 | + | 0.983471i | \(0.557954\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 7.63900 | 0.418615 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.46397 | 0.134621 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −18.6130 | −1.01391 | −0.506956 | − | 0.861972i | \(-0.669230\pi\) | ||||
−0.506956 | + | 0.861972i | \(0.669230\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.5112 | −0.733827 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.9465 | 0.755243 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.3433 | −0.936450 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.49505 | −0.349682 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.0424 | −0.753833 | −0.376917 | − | 0.926247i | \(-0.623016\pi\) | ||||
−0.376917 | + | 0.926247i | \(0.623016\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 8.50135 | 0.455067 | 0.227533 | − | 0.973770i | \(-0.426934\pi\) | ||||
0.227533 | + | 0.973770i | \(0.426934\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −25.3839 | −1.35489 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 9.77220 | 0.520122 | 0.260061 | − | 0.965592i | \(-0.416257\pi\) | ||||
0.260061 | + | 0.965592i | \(0.416257\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 4.32843 | 0.229729 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.73751 | −0.0919587 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −23.4908 | −1.23980 | −0.619899 | − | 0.784681i | \(-0.712827\pi\) | ||||
−0.619899 | + | 0.784681i | \(0.712827\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 21.9384 | 1.15465 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.53443 | −0.395455 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 8.13535 | 0.425824 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 31.7892 | 1.65938 | 0.829691 | − | 0.558223i | \(-0.188517\pi\) | ||||
0.829691 | + | 0.558223i | \(0.188517\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.29003 | −0.327446 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.16502 | 0.423907 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 25.4967 | 1.32017 | 0.660085 | − | 0.751191i | \(-0.270520\pi\) | ||||
0.660085 | + | 0.751191i | \(0.270520\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.68255 | −0.396725 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −2.34315 | −0.120678 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.9453 | 0.664954 | 0.332477 | − | 0.943111i | \(-0.392116\pi\) | ||||
0.332477 | + | 0.943111i | \(0.392116\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 5.02308 | 0.257340 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 14.5875 | 0.745386 | 0.372693 | − | 0.927955i | \(-0.378434\pi\) | ||||
0.372693 | + | 0.927955i | \(0.378434\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.13846 | −0.108986 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 5.97083 | 0.303514 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.90329 | −0.147203 | −0.0736014 | − | 0.997288i | \(-0.523449\pi\) | ||||
−0.0736014 | + | 0.997288i | \(0.523449\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.06616 | 0.407923 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.5870 | −0.786259 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.25504 | −0.365040 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −13.2042 | −0.662699 | −0.331349 | − | 0.943508i | \(-0.607504\pi\) | ||||
−0.331349 | + | 0.943508i | \(0.607504\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −11.1171 | −0.556552 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −39.2650 | −1.96080 | −0.980401 | − | 0.197012i | \(-0.936876\pi\) | ||||
−0.980401 | + | 0.197012i | \(0.936876\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −30.0789 | −1.49833 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.16294 | −0.0577871 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 10.3867 | 0.514852 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 20.2798 | 1.00277 | 0.501386 | − | 0.865224i | \(-0.332824\pi\) | ||||
0.501386 | + | 0.865224i | \(0.332824\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.41252 | −0.316306 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.46203 | 0.0719418 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.912725 | 0.0448039 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 15.5559 | 0.761776 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −13.2868 | −0.649101 | −0.324550 | − | 0.945868i | \(-0.605213\pi\) | ||||
−0.324550 | + | 0.945868i | \(0.605213\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 12.3861 | 0.603661 | 0.301831 | − | 0.953362i | \(-0.402402\pi\) | ||||
0.301831 | + | 0.953362i | \(0.402402\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 8.91068 | 0.433252 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.54092 | 0.220267 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.16466 | −0.201542 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −11.9445 | −0.576684 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.8438 | −0.618665 | −0.309332 | − | 0.950954i | \(-0.600106\pi\) | ||||
−0.309332 | + | 0.950954i | \(0.600106\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −27.1939 | −1.30686 | −0.653428 | − | 0.756989i | \(-0.726670\pi\) | ||||
−0.653428 | + | 0.756989i | \(0.726670\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.405245 | −0.0194300 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 51.6098 | 2.46883 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −17.7534 | −0.847321 | −0.423661 | − | 0.905821i | \(-0.639255\pi\) | ||||
−0.423661 | + | 0.905821i | \(0.639255\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 7.71992 | 0.367615 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −1.09413 | −0.0519835 | −0.0259918 | − | 0.999662i | \(-0.508274\pi\) | ||||
−0.0259918 | + | 0.999662i | \(0.508274\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 12.7212 | 0.603042 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −19.1594 | −0.906206 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.2020 | −0.670232 | −0.335116 | − | 0.942177i | \(-0.608776\pi\) | ||||
−0.335116 | + | 0.942177i | \(0.608776\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8.55255 | −0.402724 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.94777 | 0.467387 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 4.61210 | 0.216219 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.21461 | 0.197151 | 0.0985755 | − | 0.995130i | \(-0.468571\pi\) | ||||
0.0985755 | + | 0.995130i | \(0.468571\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 5.45207 | 0.254481 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −26.6055 | −1.23914 | −0.619572 | − | 0.784940i | \(-0.712694\pi\) | ||||
−0.619572 | + | 0.784940i | \(0.712694\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.19016 | −0.287681 | −0.143841 | − | 0.989601i | \(-0.545945\pi\) | ||||
−0.143841 | + | 0.989601i | \(0.545945\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −5.20211 | −0.241242 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6.82202 | −0.315685 | −0.157843 | − | 0.987464i | \(-0.550454\pi\) | ||||
−0.157843 | + | 0.987464i | \(0.550454\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.31676 | 0.245505 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 5.64761 | 0.260228 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.11854 | 0.373291 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 29.0542 | 1.33310 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −8.86660 | −0.405974 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −12.3300 | −0.563373 | −0.281686 | − | 0.959507i | \(-0.590894\pi\) | ||||
−0.281686 | + | 0.959507i | \(0.590894\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −22.4015 | −1.02142 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −14.0150 | −0.637705 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 9.38526 | 0.426163 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −19.3105 | −0.875042 | −0.437521 | − | 0.899208i | \(-0.644143\pi\) | ||||
−0.437521 | + | 0.899208i | \(0.644143\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 10.6359 | 0.480972 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −25.5729 | −1.15409 | −0.577044 | − | 0.816713i | \(-0.695794\pi\) | ||||
−0.577044 | + | 0.816713i | \(0.695794\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0.503272 | 0.0226662 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 2.32221 | 0.104375 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 9.33988 | 0.418951 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.84685 | 0.261741 | 0.130871 | − | 0.991399i | \(-0.458223\pi\) | ||||
0.130871 | + | 0.991399i | \(0.458223\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.06963 | 0.0477876 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.4694 | 0.466809 | 0.233404 | − | 0.972380i | \(-0.425013\pi\) | ||||
0.233404 | + | 0.972380i | \(0.425013\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −11.1361 | −0.495548 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 10.3116 | 0.457954 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.7877 | 0.788427 | 0.394213 | − | 0.919019i | \(-0.371017\pi\) | ||||
0.394213 | + | 0.919019i | \(0.371017\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 17.5545 | 0.776564 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 34.8840 | 1.54017 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.08270 | 0.0917747 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.1158 | 0.532854 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −15.2080 | −0.667559 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 23.6032 | 1.03408 | 0.517038 | − | 0.855963i | \(-0.327035\pi\) | ||||
0.517038 | + | 0.855963i | \(0.327035\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −18.5438 | −0.810862 | −0.405431 | − | 0.914126i | \(-0.632878\pi\) | ||||
−0.405431 | + | 0.914126i | \(0.632878\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −7.88988 | −0.344343 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 6.46048 | 0.281423 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 42.0629 | 1.82882 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.58766 | −0.0688984 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 18.4456 | 0.798968 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.540757 | −0.0233790 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.93090 | −0.126478 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 10.4968 | 0.452128 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −23.3718 | −1.00483 | −0.502417 | − | 0.864626i | \(-0.667556\pi\) | ||||
−0.502417 | + | 0.864626i | \(0.667556\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −14.3614 | −0.616306 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 10.2060 | 0.437176 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.4644 | −1.13153 | −0.565767 | − | 0.824565i | \(-0.691420\pi\) | ||||
−0.565767 | + | 0.824565i | \(0.691420\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.52251 | 0.193016 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.22009 | 0.137180 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −15.6549 | −0.665715 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.87432 | −0.164456 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −17.6498 | −0.747847 | −0.373923 | − | 0.927460i | \(-0.621988\pi\) | ||||
−0.373923 | + | 0.927460i | \(0.621988\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17.5096 | −0.740575 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.56548 | 0.108315 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 27.4970 | 1.15886 | 0.579430 | − | 0.815022i | \(-0.303275\pi\) | ||||
0.579430 | + | 0.815022i | \(0.303275\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.70315 | −0.324074 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.50940 | −0.105385 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −29.1172 | −1.22066 | −0.610328 | − | 0.792149i | \(-0.708962\pi\) | ||||
−0.610328 | + | 0.792149i | \(0.708962\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 12.2631 | 0.513195 | 0.256598 | − | 0.966518i | \(-0.417399\pi\) | ||||
0.256598 | + | 0.966518i | \(0.417399\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −17.3549 | −0.725013 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 36.6278 | 1.52748 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 28.4697 | 1.18521 | 0.592604 | − | 0.805494i | \(-0.298100\pi\) | ||||
0.592604 | + | 0.805494i | \(0.298100\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −9.16223 | −0.380769 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.96948 | 0.0817077 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −12.0559 | −0.499305 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −5.00840 | −0.207072 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 33.0420 | 1.36379 | 0.681894 | − | 0.731451i | \(-0.261157\pi\) | ||||
0.681894 | + | 0.731451i | \(0.261157\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 41.3362 | 1.70323 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.699809 | −0.0287863 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 33.1496 | 1.36129 | 0.680645 | − | 0.732613i | \(-0.261700\pi\) | ||||
0.680645 | + | 0.732613i | \(0.261700\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.990608 | −0.0406110 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 7.90972 | 0.323723 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −21.3466 | −0.872199 | −0.436100 | − | 0.899898i | \(-0.643640\pi\) | ||||
−0.436100 | + | 0.899898i | \(0.643640\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −31.4937 | −1.28465 | −0.642327 | − | 0.766431i | \(-0.722031\pi\) | ||||
−0.642327 | + | 0.766431i | \(0.722031\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.77360 | −0.235119 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4.29561 | −0.174642 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 32.8366 | 1.33280 | 0.666398 | − | 0.745596i | \(-0.267835\pi\) | ||||
0.666398 | + | 0.745596i | \(0.267835\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −0.874438 | −0.0354340 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −26.1307 | −1.05714 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 47.3912 | 1.91411 | 0.957057 | − | 0.289900i | \(-0.0936220\pi\) | ||||
0.957057 | + | 0.289900i | \(0.0936220\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.19016 | 0.128639 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 11.9072 | 0.479367 | 0.239684 | − | 0.970851i | \(-0.422956\pi\) | ||||
0.239684 | + | 0.970851i | \(0.422956\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.47328 | 0.300376 | 0.150188 | − | 0.988657i | \(-0.452012\pi\) | ||||
0.150188 | + | 0.988657i | \(0.452012\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 43.9772 | 1.76475 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 27.4498 | 1.09975 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 18.3245 | 0.732981 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 16.4148 | 0.655543 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.81150 | 0.191847 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.45088 | 0.0577586 | 0.0288793 | − | 0.999583i | \(-0.490806\pi\) | ||||
0.0288793 | + | 0.999583i | \(0.490806\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −23.4775 | −0.933146 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.86382 | 0.113647 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −22.6388 | −0.896982 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −10.1424 | −0.401228 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −40.8584 | −1.61381 | −0.806904 | − | 0.590682i | \(-0.798859\pi\) | ||||
−0.806904 | + | 0.590682i | \(0.798859\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 20.7218 | 0.817187 | 0.408594 | − | 0.912716i | \(-0.366019\pi\) | ||||
0.408594 | + | 0.912716i | \(0.366019\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.02826 | −0.119238 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −14.3727 | −0.565051 | −0.282525 | − | 0.959260i | \(-0.591172\pi\) | ||||
−0.282525 | + | 0.959260i | \(0.591172\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.15873 | −0.0847378 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11.2251 | −0.439947 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 28.9443 | 1.13268 | 0.566339 | − | 0.824172i | \(-0.308359\pi\) | ||||
0.566339 | + | 0.824172i | \(0.308359\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −8.88663 | −0.347229 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −19.0628 | −0.743712 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −38.5731 | −1.50260 | −0.751298 | − | 0.659964i | \(-0.770572\pi\) | ||||
−0.751298 | + | 0.659964i | \(0.770572\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.1395 | −0.394382 | −0.197191 | − | 0.980365i | \(-0.563182\pi\) | ||||
−0.197191 | + | 0.980365i | \(0.563182\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.53308 | −0.214887 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6.33822 | −0.245786 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.05947 | 0.157183 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 30.2264 | 1.16862 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6.14925 | 0.237389 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.1833 | 1.24058 | 0.620288 | − | 0.784374i | \(-0.287016\pi\) | ||||
0.620288 | + | 0.784374i | \(0.287016\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 24.7574 | 0.952912 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 11.3291 | 0.435415 | 0.217707 | − | 0.976014i | \(-0.430142\pi\) | ||||
0.217707 | + | 0.976014i | \(0.430142\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.2515 | 0.777182 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.3684 | 0.665557 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 2.24154 | 0.0857701 | 0.0428850 | − | 0.999080i | \(-0.486345\pi\) | ||||
0.0428850 | + | 0.999080i | \(0.486345\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.65598 | −0.139688 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 9.08442 | 0.346592 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 26.0014 | 0.990576 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.63967 | −0.0623759 | −0.0311880 | − | 0.999514i | \(-0.509929\pi\) | ||||
−0.0311880 | + | 0.999514i | \(0.509929\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 5.01086 | 0.190347 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8.86891 | 0.336417 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −3.96183 | −0.150065 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 31.3493 | 1.18574 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.97462 | −0.263428 | −0.131714 | − | 0.991288i | \(-0.542048\pi\) | ||||
−0.131714 | + | 0.991288i | \(0.542048\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 30.7855 | 1.16110 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.51929 | −0.170206 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −24.0294 | −0.903719 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −35.4365 | −1.33085 | −0.665423 | − | 0.746467i | \(-0.731749\pi\) | ||||
−0.665423 | + | 0.746467i | \(0.731749\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 17.0001 | 0.637553 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 52.1112 | 1.95158 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.80991 | −0.254676 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −7.36736 | −0.275139 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.78953 | −0.0667381 | −0.0333691 | − | 0.999443i | \(-0.510624\pi\) | ||||
−0.0333691 | + | 0.999443i | \(0.510624\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.49405 | 0.167367 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 17.8324 | 0.663192 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.28532 | 0.0848745 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.14617 | −0.227949 | −0.113974 | − | 0.993484i | \(-0.536358\pi\) | ||||
−0.113974 | + | 0.993484i | \(0.536358\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 22.1631 | 0.820854 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.76078 | 0.139098 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.4431 | −0.792019 | −0.396010 | − | 0.918246i | \(-0.629605\pi\) | ||||
−0.396010 | + | 0.918246i | \(0.629605\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −3.91536 | −0.144420 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −7.85036 | −0.289172 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −15.0414 | −0.553306 | −0.276653 | − | 0.960970i | \(-0.589225\pi\) | ||||
−0.276653 | + | 0.960970i | \(0.589225\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −35.4024 | −1.30054 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −48.1672 | −1.76708 | −0.883542 | − | 0.468351i | \(-0.844848\pi\) | ||||
−0.883542 | + | 0.468351i | \(0.844848\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.9234 | −0.400201 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −2.13871 | −0.0782512 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −1.16685 | −0.0426356 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 15.0633 | 0.549666 | 0.274833 | − | 0.961492i | \(-0.411377\pi\) | ||||
0.274833 | + | 0.961492i | \(0.411377\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.44853 | −0.0892294 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.67154 | 0.206408 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −4.64740 | −0.168913 | −0.0844564 | − | 0.996427i | \(-0.526915\pi\) | ||||
−0.0844564 | + | 0.996427i | \(0.526915\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 20.6936 | 0.751130 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −24.2975 | −0.880784 | −0.440392 | − | 0.897806i | \(-0.645161\pi\) | ||||
−0.440392 | + | 0.897806i | \(0.645161\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 22.0225 | 0.797267 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 1.07573 | 0.0388930 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.65583 | 0.168112 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 13.7888 | 0.497236 | 0.248618 | − | 0.968602i | \(-0.420024\pi\) | ||||
0.248618 | + | 0.968602i | \(0.420024\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −28.7366 | −1.03492 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 18.4329 | 0.662987 | 0.331493 | − | 0.943458i | \(-0.392448\pi\) | ||||
0.331493 | + | 0.943458i | \(0.392448\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 29.3365 | 1.05380 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8.36001 | −0.299914 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −25.3491 | −0.908224 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −13.7906 | −0.493467 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.74387 | 0.0980579 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.21988 | 0.114922 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.7308 | 0.453805 | 0.226903 | − | 0.973917i | \(-0.427140\pi\) | ||||
0.226903 | + | 0.973917i | \(0.427140\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −12.5937 | −0.448347 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −16.6219 | −0.591006 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −13.2623 | −0.470959 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.49693 | 0.159490 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 16.5566 | 0.586463 | 0.293232 | − | 0.956041i | \(-0.405269\pi\) | ||||
0.293232 | + | 0.956041i | \(0.405269\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.61248 | 0.198555 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −29.8084 | −1.05323 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −25.9197 | −0.914687 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.99040 | −0.281625 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −11.1576 | −0.392764 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 7.62197 | 0.267974 | 0.133987 | − | 0.990983i | \(-0.457222\pi\) | ||||
0.133987 | + | 0.990983i | \(0.457222\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −56.0301 | −1.96748 | −0.983742 | − | 0.179590i | \(-0.942523\pi\) | ||||
−0.983742 | + | 0.179590i | \(0.942523\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.27222 | −0.149833 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.06387 | 0.212408 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 24.0627 | 0.841847 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −10.8071 | −0.377631 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.86489 | −0.0999853 | −0.0499926 | − | 0.998750i | \(-0.515920\pi\) | ||||
−0.0499926 | + | 0.998750i | \(0.515920\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −27.4404 | −0.956513 | −0.478256 | − | 0.878220i | \(-0.658731\pi\) | ||||
−0.478256 | + | 0.878220i | \(0.658731\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 11.6497 | 0.405589 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −7.35460 | −0.255745 | −0.127872 | − | 0.991791i | \(-0.540815\pi\) | ||||
−0.127872 | + | 0.991791i | \(0.540815\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.08547 | −0.0377001 | −0.0188500 | − | 0.999822i | \(-0.506001\pi\) | ||||
−0.0188500 | + | 0.999822i | \(0.506001\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 18.3254 | 0.635702 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4.86246 | 0.168474 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.609830 | 0.0211041 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 35.2229 | 1.21748 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −30.5467 | −1.05459 | −0.527294 | − | 0.849683i | \(-0.676793\pi\) | ||||
−0.527294 | + | 0.849683i | \(0.676793\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.7467 | −0.991266 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 13.9821 | 0.481568 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.87897 | 0.202243 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.26908 | −0.318489 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.12610 | −0.244567 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 38.8103 | 1.33040 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 14.9692 | 0.512537 | 0.256269 | − | 0.966606i | \(-0.417507\pi\) | ||||
0.256269 | + | 0.966606i | \(0.417507\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 6.88284 | 0.235388 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 31.8766 | 1.08888 | 0.544442 | − | 0.838798i | \(-0.316741\pi\) | ||||
0.544442 | + | 0.838798i | \(0.316741\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.868914 | −0.0296470 | −0.0148235 | − | 0.999890i | \(-0.504719\pi\) | ||||
−0.0148235 | + | 0.999890i | \(0.504719\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6.88372 | 0.234597 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7.18049 | 0.244427 | 0.122213 | − | 0.992504i | \(-0.461001\pi\) | ||||
0.122213 | + | 0.992504i | \(0.461001\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.67058 | −0.294809 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1.18842 | 0.0403609 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 23.1150 | 0.784122 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16.9312 | 0.573691 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −21.9916 | −0.744304 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −9.45131 | −0.319513 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 37.2504 | 1.25786 | 0.628929 | − | 0.777463i | \(-0.283494\pi\) | ||||
0.628929 | + | 0.777463i | \(0.283494\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −17.4484 | −0.588519 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 11.8301 | 0.398568 | 0.199284 | − | 0.979942i | \(-0.436138\pi\) | ||||
0.199284 | + | 0.979942i | \(0.436138\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −45.4087 | −1.52812 | −0.764062 | − | 0.645143i | \(-0.776798\pi\) | ||||
−0.764062 | + | 0.645143i | \(0.776798\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0.805222 | 0.0270672 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.62475 | 0.0545536 | 0.0272768 | − | 0.999628i | \(-0.491316\pi\) | ||||
0.0272768 | + | 0.999628i | \(0.491316\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 6.17955 | 0.207255 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3.70520 | 0.124129 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 35.9104 | 1.20170 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.67100 | −0.0558553 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −44.6307 | −1.49018 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.25137 | 0.108439 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.58471 | −0.186054 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.53439 | −0.217451 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.18788 | −0.272174 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.8412 | 0.824839 | 0.412420 | − | 0.910994i | \(-0.364684\pi\) | ||||
0.412420 | + | 0.910994i | \(0.364684\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 26.0941 | 0.865488 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −3.63895 | −0.120564 | −0.0602819 | − | 0.998181i | \(-0.519200\pi\) | ||||
−0.0602819 | + | 0.998181i | \(0.519200\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −2.90800 | −0.0962406 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.29371 | −0.0758277 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −19.1756 | −0.633234 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 37.8537 | 1.24868 | 0.624340 | − | 0.781153i | \(-0.285368\pi\) | ||||
0.624340 | + | 0.781153i | \(0.285368\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −18.5545 | −0.611392 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 29.7428 | 0.978996 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 21.8486 | 0.718378 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −4.88020 | −0.160287 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 43.5268 | 1.42807 | 0.714034 | − | 0.700111i | \(-0.246866\pi\) | ||||
0.714034 | + | 0.700111i | \(0.246866\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 31.1116 | 1.01964 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 4.60395 | 0.150727 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.46266 | 0.0478342 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −13.6024 | −0.444370 | −0.222185 | − | 0.975005i | \(-0.571319\pi\) | ||||
−0.222185 | + | 0.975005i | \(0.571319\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −19.2888 | −0.629466 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −29.5568 | −0.963524 | −0.481762 | − | 0.876302i | \(-0.660003\pi\) | ||||
−0.481762 | + | 0.876302i | \(0.660003\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −31.9568 | −1.04066 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.40086 | −0.175690 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −18.0327 | −0.585985 | −0.292993 | − | 0.956115i | \(-0.594651\pi\) | ||||
−0.292993 | + | 0.956115i | \(0.594651\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 55.9021 | 1.81466 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 26.1142 | 0.846810 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −43.6242 | −1.41313 | −0.706563 | − | 0.707650i | \(-0.749755\pi\) | ||||
−0.706563 | + | 0.707650i | \(0.749755\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −9.89460 | −0.320182 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.29114 | 0.0417365 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −7.88888 | −0.254745 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.7377 | 0.346379 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1.26711 | 0.0408320 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −5.22368 | −0.168156 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 39.0870 | 1.25695 | 0.628476 | − | 0.777829i | \(-0.283679\pi\) | ||||
0.628476 | + | 0.777829i | \(0.283679\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.60389 | 0.244272 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −21.9218 | −0.703505 | −0.351752 | − | 0.936093i | \(-0.614414\pi\) | ||||
−0.351752 | + | 0.936093i | \(0.614414\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 19.1373 | 0.613515 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −25.1253 | −0.804652 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 32.7035 | 1.04628 | 0.523140 | − | 0.852247i | \(-0.324761\pi\) | ||||
0.523140 | + | 0.852247i | \(0.324761\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −40.5305 | −1.29536 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −23.9148 | −0.763540 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −39.0597 | −1.24581 | −0.622906 | − | 0.782297i | \(-0.714048\pi\) | ||||
−0.622906 | + | 0.782297i | \(0.714048\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.398983 | −0.0127127 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −9.75172 | −0.310401 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 30.3351 | 0.964599 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.56585 | 0.303869 | 0.151935 | − | 0.988391i | \(-0.451450\pi\) | ||||
0.151935 | + | 0.988391i | \(0.451450\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −7.82977 | −0.248470 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.50958 | 0.142963 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 36.7431 | 1.16366 | 0.581832 | − | 0.813309i | \(-0.302336\pi\) | ||||
0.581832 | + | 0.813309i | \(0.302336\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 26.2326 | 0.829962 |
(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 | 4012.2.a.g.1.10 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4012.2.a.g.1.10 | ✓ | 12 | 1.1 | even | 1 | trivial |