Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8016,2,Mod(1,8016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8016, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("8016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8016 = 2^{4} \cdot 3 \cdot 167 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8016.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: | \(64.0080822603\) |
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: | \( x^{12} - 4 x^{11} - 31 x^{10} + 131 x^{9} + 309 x^{8} - 1453 x^{7} - 1072 x^{6} + 6350 x^{5} + 1411 x^{4} - 11022 x^{3} - 2450 x^{2} + 6960 x + 3008 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 4008) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-2.09997\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 8016.1 |
$q$-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 | ||||||||
\(3\) | −1.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.09997 | −0.939135 | −0.469568 | − | 0.882896i | \(-0.655590\pi\) | ||||
−0.469568 | + | 0.882896i | \(0.655590\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.97416 | −1.12413 | −0.562063 | − | 0.827094i | \(-0.689992\pi\) | ||||
−0.562063 | + | 0.827094i | \(0.689992\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.138272 | 0.0416905 | 0.0208452 | − | 0.999783i | \(-0.493364\pi\) | ||||
0.0208452 | + | 0.999783i | \(0.493364\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5.06303 | 1.40423 | 0.702116 | − | 0.712063i | \(-0.252239\pi\) | ||||
0.702116 | + | 0.712063i | \(0.252239\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.09997 | 0.542210 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.299135 | 0.0725509 | 0.0362755 | − | 0.999342i | \(-0.488451\pi\) | ||||
0.0362755 | + | 0.999342i | \(0.488451\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.432187 | −0.0991505 | −0.0495753 | − | 0.998770i | \(-0.515787\pi\) | ||||
−0.0495753 | + | 0.998770i | \(0.515787\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.97416 | 0.649015 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.72098 | −1.19291 | −0.596454 | − | 0.802647i | \(-0.703424\pi\) | ||||
−0.596454 | + | 0.802647i | \(0.703424\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.590124 | −0.118025 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.00000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.718106 | −0.133349 | −0.0666745 | − | 0.997775i | \(-0.521239\pi\) | ||||
−0.0666745 | + | 0.997775i | \(0.521239\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.27590 | 0.767974 | 0.383987 | − | 0.923339i | \(-0.374551\pi\) | ||||
0.383987 | + | 0.923339i | \(0.374551\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.138272 | −0.0240700 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 6.24565 | 1.05571 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −3.92212 | −0.644792 | −0.322396 | − | 0.946605i | \(-0.604488\pi\) | ||||
−0.322396 | + | 0.946605i | \(0.604488\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −5.06303 | −0.810733 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.57912 | 1.18366 | 0.591830 | − | 0.806063i | \(-0.298406\pi\) | ||||
0.591830 | + | 0.806063i | \(0.298406\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −12.3515 | −1.88359 | −0.941797 | − | 0.336183i | \(-0.890864\pi\) | ||||
−0.941797 | + | 0.336183i | \(0.890864\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −2.09997 | −0.313045 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 9.22989 | 1.34632 | 0.673159 | − | 0.739498i | \(-0.264937\pi\) | ||||
0.673159 | + | 0.739498i | \(0.264937\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.84562 | 0.263660 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.299135 | −0.0418873 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.26409 | 0.173636 | 0.0868178 | − | 0.996224i | \(-0.472330\pi\) | ||||
0.0868178 | + | 0.996224i | \(0.472330\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.290366 | −0.0391530 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.432187 | 0.0572446 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.01296 | −0.392253 | −0.196127 | − | 0.980579i | \(-0.562836\pi\) | ||||
−0.196127 | + | 0.980579i | \(0.562836\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.98537 | 0.382237 | 0.191118 | − | 0.981567i | \(-0.438789\pi\) | ||||
0.191118 | + | 0.981567i | \(0.438789\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −2.97416 | −0.374709 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −10.6322 | −1.31876 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.3934 | 1.39193 | 0.695964 | − | 0.718076i | \(-0.254977\pi\) | ||||
0.695964 | + | 0.718076i | \(0.254977\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.72098 | 0.688726 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.07665 | 0.839844 | 0.419922 | − | 0.907560i | \(-0.362057\pi\) | ||||
0.419922 | + | 0.907560i | \(0.362057\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 14.5486 | 1.70278 | 0.851392 | − | 0.524531i | \(-0.175759\pi\) | ||||
0.851392 | + | 0.524531i | \(0.175759\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.590124 | 0.0681417 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.411242 | −0.0468654 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −13.7670 | −1.54891 | −0.774454 | − | 0.632630i | \(-0.781975\pi\) | ||||
−0.774454 | + | 0.632630i | \(0.781975\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 15.7764 | 1.73168 | 0.865840 | − | 0.500321i | \(-0.166785\pi\) | ||||
0.865840 | + | 0.500321i | \(0.166785\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.628175 | −0.0681351 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0.718106 | 0.0769891 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −12.4982 | −1.32481 | −0.662404 | − | 0.749147i | \(-0.730464\pi\) | ||||
−0.662404 | + | 0.749147i | \(0.730464\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −15.0583 | −1.57853 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.27590 | −0.443390 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.907580 | 0.0931157 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.54510 | 0.766089 | 0.383044 | − | 0.923730i | \(-0.374876\pi\) | ||||
0.383044 | + | 0.923730i | \(0.374876\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.138272 | 0.0138968 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.4322 | 1.03804 | 0.519021 | − | 0.854761i | \(-0.326296\pi\) | ||||
0.519021 | + | 0.854761i | \(0.326296\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −12.4671 | −1.22842 | −0.614211 | − | 0.789142i | \(-0.710525\pi\) | ||||
−0.614211 | + | 0.789142i | \(0.710525\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.24565 | −0.609513 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.84644 | 0.565196 | 0.282598 | − | 0.959238i | \(-0.408804\pi\) | ||||
0.282598 | + | 0.959238i | \(0.408804\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.4163 | 1.09348 | 0.546742 | − | 0.837301i | \(-0.315868\pi\) | ||||
0.546742 | + | 0.837301i | \(0.315868\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.92212 | 0.372271 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 17.7140 | 1.66640 | 0.833198 | − | 0.552975i | \(-0.186508\pi\) | ||||
0.833198 | + | 0.552975i | \(0.186508\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 12.0139 | 1.12030 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 5.06303 | 0.468077 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.889675 | −0.0815564 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.9809 | −0.998262 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −7.57912 | −0.683387 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 11.7391 | 1.04998 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.49463 | −0.753776 | −0.376888 | − | 0.926259i | \(-0.623006\pi\) | ||||
−0.376888 | + | 0.926259i | \(0.623006\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 12.3515 | 1.08749 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.85564 | 0.249499 | 0.124749 | − | 0.992188i | \(-0.460187\pi\) | ||||
0.124749 | + | 0.992188i | \(0.460187\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1.28539 | 0.111458 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 2.09997 | 0.180737 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.64533 | 0.140570 | 0.0702850 | − | 0.997527i | \(-0.477609\pi\) | ||||
0.0702850 | + | 0.997527i | \(0.477609\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −12.1666 | −1.03196 | −0.515978 | − | 0.856602i | \(-0.672571\pi\) | ||||
−0.515978 | + | 0.856602i | \(0.672571\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.22989 | −0.777297 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.700073 | 0.0585431 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.50800 | 0.125233 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.84562 | −0.152224 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.9793 | −1.06331 | −0.531653 | − | 0.846962i | \(-0.678429\pi\) | ||||
−0.531653 | + | 0.846962i | \(0.678429\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.5738 | 1.67427 | 0.837135 | − | 0.546997i | \(-0.184229\pi\) | ||||
0.837135 | + | 0.546997i | \(0.184229\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.299135 | 0.0241836 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −8.97925 | −0.721231 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.76196 | 0.300237 | 0.150119 | − | 0.988668i | \(-0.452034\pi\) | ||||
0.150119 | + | 0.988668i | \(0.452034\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.26409 | −0.100249 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 17.0151 | 1.34098 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.3629 | −1.43829 | −0.719147 | − | 0.694858i | \(-0.755467\pi\) | ||||
−0.719147 | + | 0.694858i | \(0.755467\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.290366 | 0.0226050 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.00000 | −0.0773823 | ||||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 12.6343 | 0.971866 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −0.432187 | −0.0330502 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −24.3625 | −1.85225 | −0.926125 | − | 0.377217i | \(-0.876881\pi\) | ||||
−0.926125 | + | 0.377217i | \(0.876881\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.75512 | 0.132675 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.01296 | 0.226468 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 0.719729 | 0.0537951 | 0.0268975 | − | 0.999638i | \(-0.491437\pi\) | ||||
0.0268975 | + | 0.999638i | \(0.491437\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.81586 | −0.283630 | −0.141815 | − | 0.989893i | \(-0.545294\pi\) | ||||
−0.141815 | + | 0.989893i | \(0.545294\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.98537 | −0.220685 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 8.23633 | 0.605547 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.0413619 | 0.00302468 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.97416 | 0.216338 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −17.9273 | −1.29717 | −0.648585 | − | 0.761142i | \(-0.724639\pi\) | ||||
−0.648585 | + | 0.761142i | \(0.724639\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.31831 | −0.454802 | −0.227401 | − | 0.973801i | \(-0.573023\pi\) | ||||
−0.227401 | + | 0.973801i | \(0.573023\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 10.6322 | 0.761388 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −2.17097 | −0.154675 | −0.0773375 | − | 0.997005i | \(-0.524642\pi\) | ||||
−0.0773375 | + | 0.997005i | \(0.524642\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.0022 | −0.850816 | −0.425408 | − | 0.905002i | \(-0.639869\pi\) | ||||
−0.425408 | + | 0.905002i | \(0.639869\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.3934 | −0.803630 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.13576 | 0.149901 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.9159 | −1.11162 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −5.72098 | −0.397636 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.0597592 | −0.00413363 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.4126 | −0.854521 | −0.427260 | − | 0.904129i | \(-0.640521\pi\) | ||||
−0.427260 | + | 0.904129i | \(0.640521\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −7.07665 | −0.484884 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 25.9379 | 1.76895 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −12.7172 | −0.863299 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −14.5486 | −0.983102 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.51453 | 0.101878 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −16.6831 | −1.11719 | −0.558593 | − | 0.829442i | \(-0.688659\pi\) | ||||
−0.558593 | + | 0.829442i | \(0.688659\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.590124 | −0.0393416 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 7.20014 | 0.477890 | 0.238945 | − | 0.971033i | \(-0.423198\pi\) | ||||
0.238945 | + | 0.971033i | \(0.423198\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 16.3304 | 1.07914 | 0.539572 | − | 0.841939i | \(-0.318586\pi\) | ||||
0.539572 | + | 0.841939i | \(0.318586\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.411242 | 0.0270577 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 16.8678 | 1.10504 | 0.552522 | − | 0.833498i | \(-0.313666\pi\) | ||||
0.552522 | + | 0.833498i | \(0.313666\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −19.3825 | −1.26437 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 13.7670 | 0.894262 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −24.1014 | −1.55899 | −0.779494 | − | 0.626410i | \(-0.784524\pi\) | ||||
−0.779494 | + | 0.626410i | \(0.784524\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.37146 | −0.0883434 | −0.0441717 | − | 0.999024i | \(-0.514065\pi\) | ||||
−0.0441717 | + | 0.999024i | \(0.514065\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.00000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −3.87575 | −0.247613 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2.18818 | −0.139230 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −15.7764 | −0.999786 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −2.57248 | −0.162374 | −0.0811868 | − | 0.996699i | \(-0.525871\pi\) | ||||
−0.0811868 | + | 0.996699i | \(0.525871\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −0.791050 | −0.0497329 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0.628175 | 0.0393378 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 6.87895 | 0.429097 | 0.214549 | − | 0.976713i | \(-0.431172\pi\) | ||||
0.214549 | + | 0.976713i | \(0.431172\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.6650 | 0.724828 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −0.718106 | −0.0444497 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −30.1737 | −1.86059 | −0.930296 | − | 0.366810i | \(-0.880450\pi\) | ||||
−0.930296 | + | 0.366810i | \(0.880450\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.65454 | −0.163067 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.4982 | 0.764878 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 8.26235 | 0.503764 | 0.251882 | − | 0.967758i | \(-0.418950\pi\) | ||||
0.251882 | + | 0.967758i | \(0.418950\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.3323 | −1.41734 | −0.708669 | − | 0.705541i | \(-0.750704\pi\) | ||||
−0.708669 | + | 0.705541i | \(0.750704\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 15.0583 | 0.911367 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −0.0815975 | −0.00492051 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.10722 | −0.126610 | −0.0633052 | − | 0.997994i | \(-0.520164\pi\) | ||||
−0.0633052 | + | 0.997994i | \(0.520164\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.27590 | 0.255991 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.06113 | −0.421232 | −0.210616 | − | 0.977569i | \(-0.567547\pi\) | ||||
−0.210616 | + | 0.977569i | \(0.567547\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 10.3953 | 0.617937 | 0.308969 | − | 0.951072i | \(-0.400016\pi\) | ||||
0.308969 | + | 0.951072i | \(0.400016\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −0.907580 | −0.0537604 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −22.5415 | −1.33058 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.9105 | −0.994736 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −7.54510 | −0.442302 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −24.7202 | −1.44417 | −0.722086 | − | 0.691803i | \(-0.756817\pi\) | ||||
−0.722086 | + | 0.691803i | \(0.756817\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.32712 | 0.368379 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.138272 | −0.00802334 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −28.9655 | −1.67512 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 36.7355 | 2.11740 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −10.4322 | −0.599314 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −6.26918 | −0.358972 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 31.2025 | 1.78082 | 0.890410 | − | 0.455159i | \(-0.150418\pi\) | ||||
0.890410 | + | 0.455159i | \(0.150418\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.4671 | 0.709229 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −33.4235 | −1.89527 | −0.947636 | − | 0.319353i | \(-0.896534\pi\) | ||||
−0.947636 | + | 0.319353i | \(0.896534\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.4281 | −1.04162 | −0.520808 | − | 0.853674i | \(-0.674369\pi\) | ||||
−0.520808 | + | 0.853674i | \(0.674369\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 6.24565 | 0.351902 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −23.6150 | −1.32635 | −0.663176 | − | 0.748463i | \(-0.730792\pi\) | ||||
−0.663176 | + | 0.748463i | \(0.730792\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.0992938 | −0.00555938 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −5.84644 | −0.326316 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.129282 | −0.00719346 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.98782 | −0.165734 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −11.4163 | −0.631323 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −27.4512 | −1.51343 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.822383 | −0.0452023 | −0.0226011 | − | 0.999745i | \(-0.507195\pi\) | ||||
−0.0226011 | + | 0.999745i | \(0.507195\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −3.92212 | −0.214931 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −23.9259 | −1.30721 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −14.7926 | −0.805805 | −0.402902 | − | 0.915243i | \(-0.631999\pi\) | ||||
−0.402902 | + | 0.915243i | \(0.631999\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −17.7140 | −0.962094 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.591235 | 0.0320172 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 15.3299 | 0.827739 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −12.0139 | −0.646807 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 23.3182 | 1.25179 | 0.625894 | − | 0.779908i | \(-0.284734\pi\) | ||||
0.625894 | + | 0.779908i | \(0.284734\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −23.5530 | −1.26076 | −0.630382 | − | 0.776285i | \(-0.717102\pi\) | ||||
−0.630382 | + | 0.776285i | \(0.717102\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −5.06303 | −0.270244 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −22.7213 | −1.20933 | −0.604666 | − | 0.796479i | \(-0.706693\pi\) | ||||
−0.604666 | + | 0.796479i | \(0.706693\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.8608 | −0.788727 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.889675 | 0.0470866 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 4.45309 | 0.235025 | 0.117513 | − | 0.993071i | \(-0.462508\pi\) | ||||
0.117513 | + | 0.993071i | \(0.462508\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.8132 | −0.990169 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 10.9809 | 0.576347 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −30.5516 | −1.59914 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.0004 | −1.61821 | −0.809103 | − | 0.587667i | \(-0.800047\pi\) | ||||
−0.809103 | + | 0.587667i | \(0.800047\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 7.57912 | 0.394553 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.75960 | −0.195188 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.5252 | −0.752089 | −0.376044 | − | 0.926602i | \(-0.622716\pi\) | ||||
−0.376044 | + | 0.926602i | \(0.622716\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −11.7391 | −0.606204 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.63579 | −0.187253 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.36141 | 0.275397 | 0.137698 | − | 0.990474i | \(-0.456030\pi\) | ||||
0.137698 | + | 0.990474i | \(0.456030\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 8.49463 | 0.435193 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 35.4614 | 1.81200 | 0.905998 | − | 0.423283i | \(-0.139122\pi\) | ||||
0.905998 | + | 0.423283i | \(0.139122\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.863596 | 0.0440129 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −12.3515 | −0.627865 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −11.3561 | −0.575777 | −0.287889 | − | 0.957664i | \(-0.592953\pi\) | ||||
−0.287889 | + | 0.957664i | \(0.592953\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.71135 | −0.0865466 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.85564 | −0.144048 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 28.9103 | 1.45463 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.2022 | 1.46562 | 0.732808 | − | 0.680436i | \(-0.238210\pi\) | ||||
0.732808 | + | 0.680436i | \(0.238210\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −1.28539 | −0.0643501 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −20.5988 | −1.02866 | −0.514328 | − | 0.857594i | \(-0.671959\pi\) | ||||
−0.514328 | + | 0.857594i | \(0.671959\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 21.6490 | 1.07841 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.09997 | −0.104348 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −0.542318 | −0.0268817 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6.71740 | −0.332154 | −0.166077 | − | 0.986113i | \(-0.553110\pi\) | ||||
−0.166077 | + | 0.986113i | \(0.553110\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.64533 | −0.0811581 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 8.96101 | 0.440942 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −33.1299 | −1.62628 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 12.1666 | 0.595800 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.90625 | 0.141980 | 0.0709898 | − | 0.997477i | \(-0.477384\pi\) | ||||
0.0709898 | + | 0.997477i | \(0.477384\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −11.0417 | −0.538140 | −0.269070 | − | 0.963121i | \(-0.586716\pi\) | ||||
−0.269070 | + | 0.963121i | \(0.586716\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 9.22989 | 0.448772 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.176527 | −0.00856281 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −8.87895 | −0.429683 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −0.700073 | −0.0337999 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.6903 | 0.852110 | 0.426055 | − | 0.904697i | \(-0.359903\pi\) | ||||
0.426055 | + | 0.904697i | \(0.359903\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.4174 | −0.837025 | −0.418513 | − | 0.908211i | \(-0.637448\pi\) | ||||
−0.418513 | + | 0.908211i | \(0.637448\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.50800 | −0.0723032 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.47254 | 0.118277 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −16.5212 | −0.788512 | −0.394256 | − | 0.919001i | \(-0.628998\pi\) | ||||
−0.394256 | + | 0.919001i | \(0.628998\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.84562 | 0.0878867 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 21.4189 | 1.01764 | 0.508822 | − | 0.860871i | \(-0.330081\pi\) | ||||
0.508822 | + | 0.860871i | \(0.330081\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 26.2459 | 1.24417 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 12.9793 | 0.613900 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 31.1123 | 1.46828 | 0.734141 | − | 0.678998i | \(-0.237585\pi\) | ||||
0.734141 | + | 0.678998i | \(0.237585\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.04798 | 0.0493474 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −20.5738 | −0.966640 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 31.6219 | 1.48246 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.2728 | 0.527321 | 0.263660 | − | 0.964616i | \(-0.415070\pi\) | ||||
0.263660 | + | 0.964616i | \(0.415070\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −0.299135 | −0.0139624 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 25.0888 | 1.16850 | 0.584251 | − | 0.811573i | \(-0.301388\pi\) | ||||
0.584251 | + | 0.811573i | \(0.301388\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −29.9933 | −1.39391 | −0.696954 | − | 0.717116i | \(-0.745462\pi\) | ||||
−0.696954 | + | 0.717116i | \(0.745462\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.97925 | 0.416403 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 26.6386 | 1.23269 | 0.616343 | − | 0.787478i | \(-0.288614\pi\) | ||||
0.616343 | + | 0.787478i | \(0.288614\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −33.8859 | −1.56470 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −3.76196 | −0.173342 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.70787 | −0.0785279 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.255044 | 0.0117022 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 1.26409 | 0.0578786 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −34.6774 | −1.58445 | −0.792225 | − | 0.610229i | \(-0.791078\pi\) | ||||
−0.792225 | + | 0.610229i | \(0.791078\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −19.8578 | −0.905437 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −17.0151 | −0.774215 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −15.8445 | −0.719461 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 15.7054 | 0.711678 | 0.355839 | − | 0.934547i | \(-0.384195\pi\) | ||||
0.355839 | + | 0.934547i | \(0.384195\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 18.3629 | 0.830399 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −16.0372 | −0.723751 | −0.361875 | − | 0.932226i | \(-0.617863\pi\) | ||||
−0.361875 | + | 0.932226i | \(0.617863\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.214811 | −0.00967459 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −0.290366 | −0.0130510 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −21.0471 | −0.944090 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.7331 | 0.570011 | 0.285005 | − | 0.958526i | \(-0.408005\pi\) | ||||
0.285005 | + | 0.958526i | \(0.408005\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.00000 | 0.0446767 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −3.14474 | −0.140217 | −0.0701086 | − | 0.997539i | \(-0.522335\pi\) | ||||
−0.0701086 | + | 0.997539i | \(0.522335\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −21.9073 | −0.974863 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.6343 | −0.561107 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −4.63793 | −0.205572 | −0.102786 | − | 0.994703i | \(-0.532776\pi\) | ||||
−0.102786 | + | 0.994703i | \(0.532776\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −43.2698 | −1.91414 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.432187 | 0.0190815 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 26.1806 | 1.15365 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.27623 | 0.0561286 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 24.3625 | 1.06940 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 37.2557 | 1.63220 | 0.816102 | − | 0.577908i | \(-0.196131\pi\) | ||||
0.816102 | + | 0.577908i | \(0.196131\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.9630 | 1.22274 | 0.611369 | − | 0.791346i | \(-0.290619\pi\) | ||||
0.611369 | + | 0.791346i | \(0.290619\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1.75512 | −0.0765999 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.27907 | 0.0557172 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.72967 | 0.423029 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.01296 | −0.130751 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 38.3733 | 1.66213 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −12.2773 | −0.530796 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −0.719729 | −0.0310586 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0.255197 | 0.0109921 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −22.7551 | −0.978316 | −0.489158 | − | 0.872195i | \(-0.662696\pi\) | ||||
−0.489158 | + | 0.872195i | \(0.662696\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.81586 | 0.163754 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −23.9739 | −1.02693 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.58788 | −0.281677 | −0.140839 | − | 0.990033i | \(-0.544980\pi\) | ||||
−0.140839 | + | 0.990033i | \(0.544980\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.98537 | 0.127412 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 0.310356 | 0.0132216 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 40.9452 | 1.74117 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.23633 | −0.349613 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 16.1334 | 0.683594 | 0.341797 | − | 0.939774i | \(-0.388964\pi\) | ||||
0.341797 | + | 0.939774i | \(0.388964\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −62.5362 | −2.64500 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.0413619 | −0.00174630 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −11.2526 | −0.474240 | −0.237120 | − | 0.971480i | \(-0.576203\pi\) | ||||
−0.237120 | + | 0.971480i | \(0.576203\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −37.1989 | −1.56497 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −2.97416 | −0.124903 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 19.1087 | 0.801079 | 0.400539 | − | 0.916280i | \(-0.368823\pi\) | ||||
0.400539 | + | 0.916280i | \(0.368823\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.7499 | 1.11945 | 0.559725 | − | 0.828679i | \(-0.310907\pi\) | ||||
0.559725 | + | 0.828679i | \(0.310907\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 17.9273 | 0.748922 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.37609 | 0.140793 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.62594 | 0.109319 | 0.0546596 | − | 0.998505i | \(-0.482593\pi\) | ||||
0.0546596 | + | 0.998505i | \(0.482593\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.31831 | 0.262580 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −46.9214 | −1.94663 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.174787 | 0.00723895 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −10.6322 | −0.439588 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 24.6288 | 1.01654 | 0.508269 | − | 0.861198i | \(-0.330286\pi\) | ||||
0.508269 | + | 0.861198i | \(0.330286\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.84799 | −0.0761450 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.17097 | 0.0893016 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 12.2107 | 0.501433 | 0.250716 | − | 0.968061i | \(-0.419334\pi\) | ||||
0.250716 | + | 0.968061i | \(0.419334\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.86829 | 0.0765925 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 12.0022 | 0.491219 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 21.7233 | 0.887591 | 0.443796 | − | 0.896128i | \(-0.353632\pi\) | ||||
0.443796 | + | 0.896128i | \(0.353632\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.7575 | −1.17304 | −0.586521 | − | 0.809934i | \(-0.699503\pi\) | ||||
−0.586521 | + | 0.809934i | \(0.699503\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 11.3934 | 0.463976 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 23.0595 | 0.937503 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 22.9370 | 0.930985 | 0.465493 | − | 0.885052i | \(-0.345877\pi\) | ||||
0.465493 | + | 0.885052i | \(0.345877\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −2.13576 | −0.0865455 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 46.7312 | 1.89054 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −39.7699 | −1.60629 | −0.803145 | − | 0.595784i | \(-0.796842\pi\) | ||||
−0.803145 | + | 0.595784i | \(0.796842\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 15.9159 | 0.641792 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −16.6341 | −0.669663 | −0.334832 | − | 0.942278i | \(-0.608679\pi\) | ||||
−0.334832 | + | 0.942278i | \(0.608679\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 20.5361 | 0.825416 | 0.412708 | − | 0.910863i | \(-0.364583\pi\) | ||||
0.412708 | + | 0.910863i | \(0.364583\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.72098 | 0.229575 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 37.1717 | 1.48925 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −21.7011 | −0.868045 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.0597592 | 0.00238655 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.17324 | −0.0467802 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −26.0602 | −1.03744 | −0.518721 | − | 0.854944i | \(-0.673592\pi\) | ||||
−0.518721 | + | 0.854944i | \(0.673592\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.4126 | 0.493358 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 17.8385 | 0.707898 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 9.34443 | 0.370240 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.07665 | 0.279948 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −17.1851 | −0.678771 | −0.339386 | − | 0.940647i | \(-0.610219\pi\) | ||||
−0.339386 | + | 0.940647i | \(0.610219\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 39.0699 | 1.54077 | 0.770383 | − | 0.637582i | \(-0.220065\pi\) | ||||
0.770383 | + | 0.637582i | \(0.220065\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −25.9379 | −1.02130 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.31198 | 0.0515794 | 0.0257897 | − | 0.999667i | \(-0.491790\pi\) | ||||
0.0257897 | + | 0.999667i | \(0.491790\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.416606 | −0.0163532 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 12.7172 | 0.498426 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 36.2903 | 1.42015 | 0.710074 | − | 0.704127i | \(-0.248661\pi\) | ||||
0.710074 | + | 0.704127i | \(0.248661\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.99676 | −0.234313 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 14.5486 | 0.567594 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −7.04958 | −0.274613 | −0.137306 | − | 0.990529i | \(-0.543844\pi\) | ||||
−0.137306 | + | 0.990529i | \(0.543844\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 21.4844 | 0.835648 | 0.417824 | − | 0.908528i | \(-0.362793\pi\) | ||||
0.417824 | + | 0.908528i | \(0.362793\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −1.51453 | −0.0588194 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −2.69929 | −0.104674 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 4.10827 | 0.159073 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 16.6831 | 0.645008 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 0.412792 | 0.0159356 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6.31641 | −0.243480 | −0.121740 | − | 0.992562i | \(-0.538847\pi\) | ||||
−0.121740 | + | 0.992562i | \(0.538847\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0.590124 | 0.0227139 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 21.2225 | 0.815648 | 0.407824 | − | 0.913061i | \(-0.366288\pi\) | ||||
0.407824 | + | 0.913061i | \(0.366288\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −22.4403 | −0.861181 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −7.20014 | −0.275910 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −40.0609 | −1.53289 | −0.766443 | − | 0.642312i | \(-0.777975\pi\) | ||||
−0.766443 | + | 0.642312i | \(0.777975\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −3.45514 | −0.132014 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.3304 | −0.623044 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.40011 | 0.243825 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −41.3269 | −1.57215 | −0.786075 | − | 0.618131i | \(-0.787890\pi\) | ||||
−0.786075 | + | 0.618131i | \(0.787890\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −0.411242 | −0.0156218 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 25.5494 | 0.969146 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.26718 | 0.0858756 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −16.8678 | −0.637997 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −26.1035 | −0.985916 | −0.492958 | − | 0.870053i | \(-0.664084\pi\) | ||||
−0.492958 | + | 0.870053i | \(0.664084\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.69509 | 0.0639314 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 19.3825 | 0.729987 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −31.0270 | −1.16689 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.259309 | −0.00973854 | −0.00486927 | − | 0.999988i | \(-0.501550\pi\) | ||||
−0.00486927 | + | 0.999988i | \(0.501550\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −13.7670 | −0.516303 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −24.4623 | −0.916122 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.47013 | −0.0549799 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 24.1014 | 0.900082 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 44.6788 | 1.66624 | 0.833120 | − | 0.553093i | \(-0.186553\pi\) | ||||
0.833120 | + | 0.553093i | \(0.186553\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 37.0792 | 1.38090 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.37146 | 0.0510051 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0.423772 | 0.0157385 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.9819 | −0.444384 | −0.222192 | − | 0.975003i | \(-0.571321\pi\) | ||||
−0.222192 | + | 0.975003i | \(0.571321\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −3.69478 | −0.136656 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −18.2924 | −0.675645 | −0.337822 | − | 0.941210i | \(-0.609690\pi\) | ||||
−0.337822 | + | 0.941210i | \(0.609690\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 3.87575 | 0.142959 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.57539 | 0.0580302 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 11.5860 | 0.426197 | 0.213099 | − | 0.977031i | \(-0.431644\pi\) | ||||
0.213099 | + | 0.977031i | \(0.431644\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.18818 | 0.0803846 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 14.2882 | 0.524183 | 0.262092 | − | 0.965043i | \(-0.415588\pi\) | ||||
0.262092 | + | 0.965043i | \(0.415588\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 27.2562 | 0.998589 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 15.7764 | 0.577226 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17.3882 | −0.635352 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.28638 | −0.0469407 | −0.0234703 | − | 0.999725i | \(-0.507472\pi\) | ||||
−0.0234703 | + | 0.999725i | \(0.507472\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.57248 | 0.0937465 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −43.2043 | −1.57237 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 15.5228 | 0.564185 | 0.282092 | − | 0.959387i | \(-0.408972\pi\) | ||||
0.282092 | + | 0.959387i | \(0.408972\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0.791050 | 0.0287133 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −1.55417 | −0.0563385 | −0.0281693 | − | 0.999603i | \(-0.508968\pi\) | ||||
−0.0281693 | + | 0.999603i | \(0.508968\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −33.9539 | −1.22921 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.628175 | −0.0227117 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15.2547 | −0.550815 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −45.1817 | −1.62929 | −0.814647 | − | 0.579957i | \(-0.803069\pi\) | ||||
−0.814647 | + | 0.579957i | \(0.803069\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.87895 | −0.247739 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −53.9167 | −1.93925 | −0.969625 | − | 0.244597i | \(-0.921344\pi\) | ||||
−0.969625 | + | 0.244597i | \(0.921344\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.52331 | −0.0906399 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −11.6650 | −0.418479 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −3.27560 | −0.117361 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.978500 | 0.0350135 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0.718106 | 0.0256630 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.90001 | −0.281963 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.43062 | −0.300519 | −0.150260 | − | 0.988647i | \(-0.548011\pi\) | ||||
−0.150260 | + | 0.988647i | \(0.548011\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 30.1737 | 1.07421 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −52.6843 | −1.87324 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 15.1150 | 0.536749 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.65454 | 0.0941470 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.7547 | 0.876856 | 0.438428 | − | 0.898766i | \(-0.355535\pi\) | ||||
0.438428 | + | 0.898766i | \(0.355535\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.76098 | 0.0976766 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −12.4982 | −0.441603 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.01166 | 0.0709899 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −35.7312 | −1.25936 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.26235 | −0.290849 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −27.3604 | −0.961941 | −0.480970 | − | 0.876737i | \(-0.659716\pi\) | ||||
−0.480970 | + | 0.876737i | \(0.659716\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.45887 | 0.0863426 | 0.0431713 | − | 0.999068i | \(-0.486254\pi\) | ||||
0.0431713 | + | 0.999068i | \(0.486254\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 23.3323 | 0.818300 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 38.5616 | 1.35075 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.33818 | 0.186759 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −15.0583 | −0.526178 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 6.86656 | 0.239645 | 0.119822 | − | 0.992795i | \(-0.461768\pi\) | ||||
0.119822 | + | 0.992795i | \(0.461768\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −19.4606 | −0.678355 | −0.339178 | − | 0.940722i | \(-0.610149\pi\) | ||||
−0.339178 | + | 0.940722i | \(0.610149\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.0815975 | 0.00284086 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −8.19257 | −0.284884 | −0.142442 | − | 0.989803i | \(-0.545495\pi\) | ||||
−0.142442 | + | 0.989803i | \(0.545495\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −46.2894 | −1.60770 | −0.803849 | − | 0.594833i | \(-0.797218\pi\) | ||||
−0.803849 | + | 0.594833i | \(0.797218\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 2.10722 | 0.0730986 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0.552090 | 0.0191288 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.09997 | 0.0726725 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −4.27590 | −0.147797 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.64299 | −0.160294 | −0.0801468 | − | 0.996783i | \(-0.525539\pi\) | ||||
−0.0801468 | + | 0.996783i | \(0.525539\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.4843 | −0.982218 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 7.06113 | 0.243198 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −26.5316 | −0.912713 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 32.6589 | 1.12217 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.3953 | −0.356766 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 22.4384 | 0.769177 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.12150 | 0.312314 | 0.156157 | − | 0.987732i | \(-0.450089\pi\) | ||||
0.156157 | + | 0.987732i | \(0.450089\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.907580 | 0.0310386 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7.34645 | −0.250950 | −0.125475 | − | 0.992097i | \(-0.540046\pi\) | ||||
−0.125475 | + | 0.992097i | \(0.540046\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 37.2638 | 1.27142 | 0.635712 | − | 0.771927i | \(-0.280707\pi\) | ||||
0.635712 | + | 0.771927i | \(0.280707\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 22.5415 | 0.768213 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 17.3469 | 0.590496 | 0.295248 | − | 0.955421i | \(-0.404598\pi\) | ||||
0.295248 | + | 0.955421i | \(0.404598\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 51.1606 | 1.73951 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 16.9105 | 0.574311 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1.90359 | −0.0645747 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 57.6852 | 1.95459 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 7.54510 | 0.255363 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −34.9139 | −1.18031 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.09836 | 0.307230 | 0.153615 | − | 0.988131i | \(-0.450908\pi\) | ||||
0.153615 | + | 0.988131i | \(0.450908\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 24.7202 | 0.833793 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.1065 | −0.879550 | −0.439775 | − | 0.898108i | \(-0.644942\pi\) | ||||
−0.439775 | + | 0.898108i | \(0.644942\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.3088 | −0.750750 | −0.375375 | − | 0.926873i | \(-0.622486\pi\) | ||||
−0.375375 | + | 0.926873i | \(0.622486\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −6.32712 | −0.212684 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 34.3987 | 1.15500 | 0.577498 | − | 0.816392i | \(-0.304029\pi\) | ||||
0.577498 | + | 0.816392i | \(0.304029\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 25.2644 | 0.847340 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0.138272 | 0.00463228 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.98904 | −0.133488 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.51141 | −0.0505208 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 28.9655 | 0.967130 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.07055 | −0.102408 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0.378133 | 0.0125974 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −36.7355 | −1.22248 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 8.01318 | 0.266367 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −18.7791 | −0.623551 | −0.311776 | − | 0.950156i | \(-0.600924\pi\) | ||||
−0.311776 | + | 0.950156i | \(0.600924\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 10.4322 | 0.346014 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −42.3954 | −1.40462 | −0.702311 | − | 0.711870i | \(-0.747849\pi\) | ||||
−0.702311 | + | 0.711870i | \(0.747849\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.18142 | 0.0721945 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 6.26918 | 0.207253 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −8.49313 | −0.280468 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.3230 | −0.703379 | −0.351690 | − | 0.936117i | \(-0.614393\pi\) | ||||
−0.351690 | + | 0.936117i | \(0.614393\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −31.2025 | −1.02816 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 35.8293 | 1.17933 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.31454 | 0.0761015 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −12.4671 | −0.409474 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 44.9861 | 1.47595 | 0.737973 | − | 0.674830i | \(-0.235783\pi\) | ||||
0.737973 | + | 0.674830i | \(0.235783\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.797654 | −0.0261420 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 33.4235 | 1.09424 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.0868588 | −0.00284059 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.2610 | −1.11926 | −0.559629 | − | 0.828743i | \(-0.689056\pi\) | ||||
−0.559629 | + | 0.828743i | \(0.689056\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 18.4281 | 0.601377 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −18.7215 | −0.610303 | −0.305152 | − | 0.952304i | \(-0.598707\pi\) | ||||
−0.305152 | + | 0.952304i | \(0.598707\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −43.3600 | −1.41200 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −6.24565 | −0.203171 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −33.2088 | −1.07914 | −0.539570 | − | 0.841941i | \(-0.681413\pi\) | ||||
−0.539570 | + | 0.841941i | \(0.681413\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 73.6599 | 2.39110 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 23.6150 | 0.765770 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −29.9705 | −0.970838 | −0.485419 | − | 0.874282i | \(-0.661333\pi\) | ||||
−0.485419 | + | 0.874282i | \(0.661333\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 37.6467 | 1.21822 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0.0992938 | 0.00320971 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −4.89347 | −0.158018 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −12.7167 | −0.410217 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.84644 | 0.188399 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 13.2683 | 0.427121 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 14.7207 | 0.473387 | 0.236693 | − | 0.971584i | \(-0.423936\pi\) | ||||
0.236693 | + | 0.971584i | \(0.423936\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.129282 | 0.00415315 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −11.0754 | −0.355428 | −0.177714 | − | 0.984082i | \(-0.556870\pi\) | ||||
−0.177714 | + | 0.984082i | \(0.556870\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 36.1853 | 1.16005 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.98782 | 0.0956867 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −24.1829 | −0.773681 | −0.386840 | − | 0.922147i | \(-0.626434\pi\) | ||||
−0.386840 | + | 0.922147i | \(0.626434\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.72815 | −0.0552319 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 11.4163 | 0.364494 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 21.5383 | 0.686964 | 0.343482 | − | 0.939159i | \(-0.388393\pi\) | ||||
0.343482 | + | 0.939159i | \(0.388393\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4.55897 | 0.145261 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 27.4512 | 0.873780 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 70.6630 | 2.24695 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −31.2346 | −0.992199 | −0.496099 | − | 0.868266i | \(-0.665235\pi\) | ||||
−0.496099 | + | 0.868266i | \(0.665235\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0.822383 | 0.0260975 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 25.2043 | 0.799032 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 50.4341 | 1.59726 | 0.798632 | − | 0.601820i | \(-0.205557\pi\) | ||||
0.798632 | + | 0.601820i | \(0.205557\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.92212 | 0.124090 |
(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 | 8016.2.a.bf.1.3 | 12 | ||
4.3 | odd | 2 | 4008.2.a.l.1.3 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4008.2.a.l.1.3 | ✓ | 12 | 4.3 | odd | 2 | ||
8016.2.a.bf.1.3 | 12 | 1.1 | even | 1 | trivial |