Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [6028,2,Mod(1,6028)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(6028, 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("6028.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 6028 = 2^{2} \cdot 11 \cdot 137 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 6028.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: | \(48.1338223384\) |
Analytic rank: | \(0\) |
Dimension: | \(29\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Character | \(\chi\) | \(=\) | 6028.1 |
$q$-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 | ||||||||
\(3\) | −2.90851 | −1.67923 | −0.839614 | − | 0.543183i | \(-0.817219\pi\) | ||||
−0.839614 | + | 0.543183i | \(0.817219\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.776599 | 0.347305 | 0.173653 | − | 0.984807i | \(-0.444443\pi\) | ||||
0.173653 | + | 0.984807i | \(0.444443\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.27589 | −0.860206 | −0.430103 | − | 0.902780i | \(-0.641523\pi\) | ||||
−0.430103 | + | 0.902780i | \(0.641523\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 5.45943 | 1.81981 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.00000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.17535 | −0.603332 | −0.301666 | − | 0.953414i | \(-0.597543\pi\) | ||||
−0.301666 | + | 0.953414i | \(0.597543\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.25874 | −0.583205 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.46266 | 1.32489 | 0.662445 | − | 0.749111i | \(-0.269519\pi\) | ||||
0.662445 | + | 0.749111i | \(0.269519\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.46623 | 1.94229 | 0.971143 | − | 0.238499i | \(-0.0766555\pi\) | ||||
0.971143 | + | 0.238499i | \(0.0766555\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 6.61945 | 1.44448 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 8.47742 | 1.76766 | 0.883832 | − | 0.467804i | \(-0.154955\pi\) | ||||
0.883832 | + | 0.467804i | \(0.154955\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.39689 | −0.879379 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −7.15327 | −1.37665 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −7.09951 | −1.31835 | −0.659173 | − | 0.751991i | \(-0.729094\pi\) | ||||
−0.659173 | + | 0.751991i | \(0.729094\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.35214 | 0.242851 | 0.121426 | − | 0.992601i | \(-0.461253\pi\) | ||||
0.121426 | + | 0.992601i | \(0.461253\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.90851 | −0.506307 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −1.76745 | −0.298754 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.08994 | −0.179185 | −0.0895927 | − | 0.995978i | \(-0.528557\pi\) | ||||
−0.0895927 | + | 0.995978i | \(0.528557\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 6.32701 | 1.01313 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.64877 | 0.569842 | 0.284921 | − | 0.958551i | \(-0.408033\pi\) | ||||
0.284921 | + | 0.958551i | \(0.408033\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.94036 | 0.753398 | 0.376699 | − | 0.926336i | \(-0.377059\pi\) | ||||
0.376699 | + | 0.926336i | \(0.377059\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 4.23978 | 0.632030 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.962432 | 0.140385 | 0.0701926 | − | 0.997533i | \(-0.477639\pi\) | ||||
0.0701926 | + | 0.997533i | \(0.477639\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.82032 | −0.260046 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −15.8882 | −2.22479 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.67850 | 0.230559 | 0.115280 | − | 0.993333i | \(-0.463224\pi\) | ||||
0.115280 | + | 0.993333i | \(0.463224\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.776599 | 0.104717 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −24.6241 | −3.26154 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −3.04816 | −0.396837 | −0.198418 | − | 0.980117i | \(-0.563580\pi\) | ||||
−0.198418 | + | 0.980117i | \(0.563580\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.49641 | −0.447669 | −0.223835 | − | 0.974627i | \(-0.571858\pi\) | ||||
−0.223835 | + | 0.974627i | \(0.571858\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −12.4251 | −1.56541 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.68937 | −0.209541 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 6.77072 | 0.827175 | 0.413588 | − | 0.910464i | \(-0.364276\pi\) | ||||
0.413588 | + | 0.910464i | \(0.364276\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −24.6567 | −2.96831 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.61897 | −0.904206 | −0.452103 | − | 0.891966i | \(-0.649326\pi\) | ||||
−0.452103 | + | 0.891966i | \(0.649326\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.9447 | −1.28098 | −0.640491 | − | 0.767965i | \(-0.721269\pi\) | ||||
−0.640491 | + | 0.767965i | \(0.721269\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 12.7884 | 1.47668 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −2.27589 | −0.259362 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 8.86549 | 0.997446 | 0.498723 | − | 0.866761i | \(-0.333803\pi\) | ||||
0.498723 | + | 0.866761i | \(0.333803\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.42707 | 0.491897 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.91904 | 0.320407 | 0.160203 | − | 0.987084i | \(-0.448785\pi\) | ||||
0.160203 | + | 0.987084i | \(0.448785\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 4.24229 | 0.460141 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 20.6490 | 2.21381 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −0.376105 | −0.0398670 | −0.0199335 | − | 0.999801i | \(-0.506345\pi\) | ||||
−0.0199335 | + | 0.999801i | \(0.506345\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.95085 | 0.518990 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.93271 | −0.407803 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 6.57486 | 0.674566 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 2.23944 | 0.227381 | 0.113690 | − | 0.993516i | \(-0.463733\pi\) | ||||
0.113690 | + | 0.993516i | \(0.463733\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 5.45943 | 0.548693 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −11.3690 | −1.13126 | −0.565630 | − | 0.824659i | \(-0.691367\pi\) | ||||
−0.565630 | + | 0.824659i | \(0.691367\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.95094 | 0.684896 | 0.342448 | − | 0.939537i | \(-0.388744\pi\) | ||||
0.342448 | + | 0.939537i | \(0.388744\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 5.14066 | 0.501677 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −2.23638 | −0.216199 | −0.108099 | − | 0.994140i | \(-0.534476\pi\) | ||||
−0.108099 | + | 0.994140i | \(0.534476\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 6.25227 | 0.598859 | 0.299430 | − | 0.954118i | \(-0.403204\pi\) | ||||
0.299430 | + | 0.954118i | \(0.403204\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.17011 | 0.300893 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 9.29764 | 0.874648 | 0.437324 | − | 0.899304i | \(-0.355926\pi\) | ||||
0.437324 | + | 0.899304i | \(0.355926\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 6.58355 | 0.613920 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −11.8761 | −1.09795 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −12.4324 | −1.13968 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 1.00000 | 0.0909091 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.6125 | −0.956896 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.29761 | −0.652718 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 9.88726 | 0.877352 | 0.438676 | − | 0.898645i | \(-0.355448\pi\) | ||||
0.438676 | + | 0.898645i | \(0.355448\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −14.3691 | −1.26513 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.3171 | −1.68774 | −0.843870 | − | 0.536548i | \(-0.819728\pi\) | ||||
−0.843870 | + | 0.536548i | \(0.819728\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −19.2682 | −1.67077 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −5.55522 | −0.478117 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.00000 | 0.0854358 | ||||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.13447 | −0.435500 | −0.217750 | − | 0.976005i | \(-0.569872\pi\) | ||||
−0.217750 | + | 0.976005i | \(0.569872\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.79924 | −0.235739 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.17535 | −0.181912 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −5.51347 | −0.457869 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 5.29442 | 0.436676 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12.0520 | −0.987339 | −0.493669 | − | 0.869650i | \(-0.664345\pi\) | ||||
−0.493669 | + | 0.869650i | \(0.664345\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 20.4687 | 1.66572 | 0.832861 | − | 0.553482i | \(-0.186701\pi\) | ||||
0.832861 | + | 0.553482i | \(0.186701\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 29.8230 | 2.41105 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1.05007 | 0.0843436 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 18.0882 | 1.44360 | 0.721799 | − | 0.692103i | \(-0.243316\pi\) | ||||
0.721799 | + | 0.692103i | \(0.243316\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −4.88192 | −0.387162 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −19.2937 | −1.52056 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −11.7760 | −0.922366 | −0.461183 | − | 0.887305i | \(-0.652575\pi\) | ||||
−0.461183 | + | 0.887305i | \(0.652575\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.25874 | −0.175843 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.0879 | −0.858004 | −0.429002 | − | 0.903304i | \(-0.641135\pi\) | ||||
−0.429002 | + | 0.903304i | \(0.641135\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −8.26787 | −0.635990 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 46.2208 | 3.53459 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 25.2206 | 1.91748 | 0.958742 | − | 0.284278i | \(-0.0917539\pi\) | ||||
0.958742 | + | 0.284278i | \(0.0917539\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 10.0069 | 0.756447 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 8.86560 | 0.666379 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −15.7112 | −1.17431 | −0.587154 | − | 0.809475i | \(-0.699752\pi\) | ||||
−0.587154 | + | 0.809475i | \(0.699752\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.4428 | −0.776207 | −0.388104 | − | 0.921616i | \(-0.626870\pi\) | ||||
−0.388104 | + | 0.921616i | \(0.626870\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.1693 | 0.751739 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.846447 | −0.0622320 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.46266 | 0.399469 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 16.2801 | 1.18420 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.16004 | 0.518082 | 0.259041 | − | 0.965866i | \(-0.416593\pi\) | ||||
0.259041 | + | 0.965866i | \(0.416593\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.34321 | 0.600558 | 0.300279 | − | 0.953851i | \(-0.402920\pi\) | ||||
0.300279 | + | 0.953851i | \(0.402920\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 4.91355 | 0.351867 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.7561 | 0.980079 | 0.490040 | − | 0.871700i | \(-0.336982\pi\) | ||||
0.490040 | + | 0.871700i | \(0.336982\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.56292 | 0.677897 | 0.338949 | − | 0.940805i | \(-0.389929\pi\) | ||||
0.338949 | + | 0.940805i | \(0.389929\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −19.6927 | −1.38902 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 16.1577 | 1.13405 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.83363 | 0.197909 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 46.2819 | 3.21681 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 8.46623 | 0.585621 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5.71044 | 0.393123 | 0.196561 | − | 0.980492i | \(-0.437023\pi\) | ||||
0.196561 | + | 0.980492i | \(0.437023\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 22.1599 | 1.51837 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 3.83668 | 0.261659 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.07732 | −0.208902 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 31.8328 | 2.15106 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −11.8832 | −0.799349 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −24.5661 | −1.64507 | −0.822535 | − | 0.568714i | \(-0.807441\pi\) | ||||
−0.822535 | + | 0.568714i | \(0.807441\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −24.0045 | −1.60030 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 24.6377 | 1.63526 | 0.817631 | − | 0.575743i | \(-0.195287\pi\) | ||||
0.817631 | + | 0.575743i | \(0.195287\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −11.8100 | −0.780429 | −0.390214 | − | 0.920724i | \(-0.627599\pi\) | ||||
−0.390214 | + | 0.920724i | \(0.627599\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.61945 | 0.435528 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 23.5551 | 1.54314 | 0.771572 | − | 0.636142i | \(-0.219471\pi\) | ||||
0.771572 | + | 0.636142i | \(0.219471\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.747423 | 0.0487565 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −25.7854 | −1.67494 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −13.1792 | −0.852493 | −0.426246 | − | 0.904607i | \(-0.640164\pi\) | ||||
−0.426246 | + | 0.904607i | \(0.640164\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −12.4210 | −0.800109 | −0.400055 | − | 0.916491i | \(-0.631009\pi\) | ||||
−0.400055 | + | 0.916491i | \(0.631009\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 8.58363 | 0.550640 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.41366 | −0.0903153 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −18.4170 | −1.17184 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −8.49007 | −0.538036 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.5751 | 0.730611 | 0.365305 | − | 0.930888i | \(-0.380965\pi\) | ||||
0.365305 | + | 0.930888i | \(0.380965\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.47742 | 0.532971 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −12.3388 | −0.772683 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.616266 | 0.0384416 | 0.0192208 | − | 0.999815i | \(-0.493881\pi\) | ||||
0.0192208 | + | 0.999815i | \(0.493881\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.48059 | 0.154136 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −38.7593 | −2.39914 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 15.0318 | 0.926901 | 0.463450 | − | 0.886123i | \(-0.346611\pi\) | ||||
0.463450 | + | 0.886123i | \(0.346611\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.30352 | 0.0800745 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.09390 | 0.0669459 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 23.0401 | 1.40478 | 0.702390 | − | 0.711792i | \(-0.252116\pi\) | ||||
0.702390 | + | 0.711792i | \(0.252116\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 6.48764 | 0.394096 | 0.197048 | − | 0.980394i | \(-0.436864\pi\) | ||||
0.197048 | + | 0.980394i | \(0.436864\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −14.3996 | −0.871503 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.39689 | −0.265143 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.5551 | −0.634193 | −0.317096 | − | 0.948393i | \(-0.602708\pi\) | ||||
−0.317096 | + | 0.948393i | \(0.602708\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 7.38191 | 0.441943 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −30.2747 | −1.80604 | −0.903019 | − | 0.429600i | \(-0.858655\pi\) | ||||
−0.903019 | + | 0.429600i | \(0.858655\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 19.0442 | 1.13206 | 0.566029 | − | 0.824385i | \(-0.308479\pi\) | ||||
0.566029 | + | 0.824385i | \(0.308479\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −19.1230 | −1.13275 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.30421 | −0.490182 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 12.8407 | 0.755334 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −6.51343 | −0.381824 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 4.85669 | 0.283731 | 0.141865 | − | 0.989886i | \(-0.454690\pi\) | ||||
0.141865 | + | 0.989886i | \(0.454690\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.36720 | −0.137823 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −7.15327 | −0.415075 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −18.4413 | −1.06649 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −11.2437 | −0.648077 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 33.0669 | 1.89964 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.71530 | −0.155478 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −24.4403 | −1.39488 | −0.697440 | − | 0.716643i | \(-0.745678\pi\) | ||||
−0.697440 | + | 0.716643i | \(0.745678\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −20.2169 | −1.15010 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.30450 | 0.414200 | 0.207100 | − | 0.978320i | \(-0.433597\pi\) | ||||
0.207100 | + | 0.978320i | \(0.433597\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 33.3926 | 1.88746 | 0.943729 | − | 0.330719i | \(-0.107291\pi\) | ||||
0.943729 | + | 0.330719i | \(0.107291\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.64929 | −0.543676 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −26.9814 | −1.51543 | −0.757713 | − | 0.652587i | \(-0.773684\pi\) | ||||
−0.757713 | + | 0.652587i | \(0.773684\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.09951 | −0.397496 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.50452 | 0.363047 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 46.2481 | 2.57331 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.56477 | 0.530558 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −18.1848 | −1.00562 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.19039 | −0.120760 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 29.2312 | 1.60669 | 0.803346 | − | 0.595513i | \(-0.203051\pi\) | ||||
0.803346 | + | 0.595513i | \(0.203051\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.95046 | −0.326083 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.25813 | 0.287282 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.23610 | 0.448649 | 0.224324 | − | 0.974515i | \(-0.427982\pi\) | ||||
0.224324 | + | 0.974515i | \(0.427982\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −27.0423 | −1.46873 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.35214 | 0.0732225 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0741 | 1.08390 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −19.1483 | −1.03091 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −18.6655 | −1.00202 | −0.501008 | − | 0.865443i | \(-0.667037\pi\) | ||||
−0.501008 | + | 0.865443i | \(0.667037\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.14780 | 0.114969 | 0.0574844 | − | 0.998346i | \(-0.481692\pi\) | ||||
0.0574844 | + | 0.998346i | \(0.481692\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 15.5608 | 0.830576 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −24.4143 | −1.29944 | −0.649722 | − | 0.760172i | \(-0.725115\pi\) | ||||
−0.649722 | + | 0.760172i | \(0.725115\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.91688 | −0.314036 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 36.1598 | 1.91378 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −28.1105 | −1.48362 | −0.741808 | − | 0.670613i | \(-0.766031\pi\) | ||||
−0.741808 | + | 0.670613i | \(0.766031\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 52.6770 | 2.77247 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2.90851 | −0.152657 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.49965 | −0.444892 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.1869 | 0.583952 | 0.291976 | − | 0.956426i | \(-0.405687\pi\) | ||||
0.291976 | + | 0.956426i | \(0.405687\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 19.9202 | 1.03700 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −3.82008 | −0.198328 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.6708 | −0.759623 | −0.379812 | − | 0.925064i | \(-0.624011\pi\) | ||||
−0.379812 | + | 0.925064i | \(0.624011\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 21.2252 | 1.09606 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 15.4439 | 0.795401 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.21465 | 0.421958 | 0.210979 | − | 0.977491i | \(-0.432335\pi\) | ||||
0.210979 | + | 0.977491i | \(0.432335\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −28.7572 | −1.47328 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 16.5081 | 0.843526 | 0.421763 | − | 0.906706i | \(-0.361412\pi\) | ||||
0.421763 | + | 0.906706i | \(0.361412\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.76745 | −0.0900778 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 26.9715 | 1.37104 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 4.68802 | 0.237692 | 0.118846 | − | 0.992913i | \(-0.462081\pi\) | ||||
0.118846 | + | 0.992913i | \(0.462081\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 46.3093 | 2.34196 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 56.1839 | 2.83410 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 6.88493 | 0.346418 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9.83885 | −0.493798 | −0.246899 | − | 0.969041i | \(-0.579412\pi\) | ||||
−0.246899 | + | 0.969041i | \(0.579412\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 56.0418 | 2.80560 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 26.0445 | 1.30060 | 0.650301 | − | 0.759677i | \(-0.274643\pi\) | ||||
0.650301 | + | 0.759677i | \(0.274643\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.94137 | −0.146520 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 3.43806 | 0.170838 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.08994 | −0.0540264 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 34.7729 | 1.71941 | 0.859704 | − | 0.510793i | \(-0.170648\pi\) | ||||
0.859704 | + | 0.510793i | \(0.170648\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −2.90851 | −0.143466 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 6.93728 | 0.341361 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.26693 | 0.111279 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 14.9337 | 0.731305 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.1538 | 0.496045 | 0.248023 | − | 0.968754i | \(-0.420219\pi\) | ||||
0.248023 | + | 0.968754i | \(0.420219\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 14.4245 | 0.703009 | 0.351504 | − | 0.936186i | \(-0.385670\pi\) | ||||
0.351504 | + | 0.936186i | \(0.385670\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5.25433 | 0.255474 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −24.0187 | −1.16508 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 7.95744 | 0.385088 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.32701 | 0.305471 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 18.1177 | 0.872700 | 0.436350 | − | 0.899777i | \(-0.356271\pi\) | ||||
0.436350 | + | 0.899777i | \(0.356271\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 23.0489 | 1.10766 | 0.553830 | − | 0.832630i | \(-0.313166\pi\) | ||||
0.553830 | + | 0.832630i | \(0.313166\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 16.0360 | 0.768867 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 71.7718 | 3.43331 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −39.0897 | −1.86565 | −0.932826 | − | 0.360328i | \(-0.882665\pi\) | ||||
−0.932826 | + | 0.360328i | \(0.882665\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −9.93791 | −0.473234 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −16.1318 | −0.766446 | −0.383223 | − | 0.923656i | \(-0.625186\pi\) | ||||
−0.383223 | + | 0.923656i | \(0.625186\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.292083 | −0.0138460 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 35.0534 | 1.65797 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 13.2046 | 0.623165 | 0.311583 | − | 0.950219i | \(-0.399141\pi\) | ||||
0.311583 | + | 0.950219i | \(0.399141\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.64877 | 0.171814 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −59.5335 | −2.79713 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.84482 | 0.180248 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 33.9227 | 1.58684 | 0.793418 | − | 0.608677i | \(-0.208299\pi\) | ||||
0.793418 | + | 0.608677i | \(0.208299\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −39.0759 | −1.82391 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 16.2397 | 0.756359 | 0.378180 | − | 0.925732i | \(-0.376550\pi\) | ||||
0.378180 | + | 0.925732i | \(0.376550\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.8427 | −1.29396 | −0.646981 | − | 0.762506i | \(-0.723969\pi\) | ||||
−0.646981 | + | 0.762506i | \(0.723969\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.05414 | −0.141632 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 37.8361 | 1.75084 | 0.875422 | − | 0.483359i | \(-0.160583\pi\) | ||||
0.875422 | + | 0.483359i | \(0.160583\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −15.4094 | −0.711541 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −52.6098 | −2.42413 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 4.94036 | 0.227158 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −37.2251 | −1.70800 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.16363 | 0.419574 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 26.3140 | 1.20232 | 0.601158 | − | 0.799130i | \(-0.294706\pi\) | ||||
0.601158 | + | 0.799130i | \(0.294706\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.37100 | 0.108108 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 56.1159 | 2.55336 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.73915 | 0.0789706 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2.33102 | 0.105629 | 0.0528144 | − | 0.998604i | \(-0.483181\pi\) | ||||
0.0528144 | + | 0.998604i | \(0.483181\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 34.2506 | 1.54886 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 8.33436 | 0.376125 | 0.188062 | − | 0.982157i | \(-0.439779\pi\) | ||||
0.188062 | + | 0.982157i | \(0.439779\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −38.7822 | −1.74666 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 4.23978 | 0.190564 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 17.3400 | 0.777803 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 0.356854 | 0.0159750 | 0.00798749 | − | 0.999968i | \(-0.497457\pi\) | ||||
0.00798749 | + | 0.999968i | \(0.497457\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 32.2491 | 1.44078 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.2880 | 0.458718 | 0.229359 | − | 0.973342i | \(-0.426337\pi\) | ||||
0.229359 | + | 0.973342i | \(0.426337\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.82917 | −0.392893 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 24.0472 | 1.06797 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.63489 | 0.338410 | 0.169205 | − | 0.985581i | \(-0.445880\pi\) | ||||
0.169205 | + | 0.985581i | \(0.445880\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 24.9090 | 1.10191 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −60.5612 | −2.67384 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.39809 | 0.237868 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.962432 | 0.0423277 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −73.3542 | −3.21989 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 28.6936 | 1.25709 | 0.628544 | − | 0.777774i | \(-0.283651\pi\) | ||||
0.628544 | + | 0.777774i | \(0.283651\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.69936 | −0.249215 | −0.124608 | − | 0.992206i | \(-0.539767\pi\) | ||||
−0.124608 | + | 0.992206i | \(0.539767\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −29.1050 | −1.27025 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 7.38628 | 0.321752 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 48.8667 | 2.12464 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −16.6412 | −0.722167 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −7.93734 | −0.343804 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −1.73677 | −0.0750870 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 45.6961 | 1.97193 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.82032 | −0.0784067 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 5.97793 | 0.257011 | 0.128506 | − | 0.991709i | \(-0.458982\pi\) | ||||
0.128506 | + | 0.991709i | \(0.458982\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 30.3730 | 1.30343 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4.85551 | 0.207987 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 35.4291 | 1.51484 | 0.757419 | − | 0.652929i | \(-0.226460\pi\) | ||||
0.757419 | + | 0.652929i | \(0.226460\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −19.0884 | −0.814672 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −60.1061 | −2.56060 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −20.1769 | −0.858009 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 2.46190 | 0.104502 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −13.6464 | −0.578218 | −0.289109 | − | 0.957296i | \(-0.593359\pi\) | ||||
−0.289109 | + | 0.957296i | \(0.593359\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −10.7470 | −0.454549 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −15.8882 | −0.670800 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 18.2209 | 0.767918 | 0.383959 | − | 0.923350i | \(-0.374560\pi\) | ||||
0.383959 | + | 0.923350i | \(0.374560\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.22053 | 0.303770 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −10.0755 | −0.423133 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.96094 | −0.0822071 | −0.0411035 | − | 0.999155i | \(-0.513087\pi\) | ||||
−0.0411035 | + | 0.999155i | \(0.513087\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 26.7693 | 1.12026 | 0.560130 | − | 0.828405i | \(-0.310751\pi\) | ||||
0.560130 | + | 0.828405i | \(0.310751\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −20.8250 | −0.869979 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −37.2743 | −1.55445 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 0.224688 | 0.00935390 | 0.00467695 | − | 0.999989i | \(-0.498511\pi\) | ||||
0.00467695 | + | 0.999989i | \(0.498511\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −24.2663 | −1.00847 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.64343 | −0.275616 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1.67850 | 0.0695162 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −9.22300 | −0.381324 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −31.7122 | −1.30890 | −0.654451 | − | 0.756104i | \(-0.727100\pi\) | ||||
−0.654451 | + | 0.756104i | \(0.727100\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.4475 | 0.471687 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −40.0096 | −1.64578 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.0417 | 0.453429 | 0.226715 | − | 0.973961i | \(-0.427202\pi\) | ||||
0.226715 | + | 0.973961i | \(0.427202\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −9.65500 | −0.395816 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −27.8138 | −1.13834 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.9202 | 0.936494 | 0.468247 | − | 0.883598i | \(-0.344886\pi\) | ||||
0.468247 | + | 0.883598i | \(0.344886\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.97492 | −0.325304 | −0.162652 | − | 0.986684i | \(-0.552005\pi\) | ||||
−0.162652 | + | 0.986684i | \(0.552005\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 36.9643 | 1.50530 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.776599 | 0.0315732 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.7978 | 0.641215 | 0.320607 | − | 0.947212i | \(-0.396113\pi\) | ||||
0.320607 | + | 0.947212i | \(0.396113\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −46.9949 | −1.90433 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −2.09362 | −0.0846989 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −35.2948 | −1.42554 | −0.712772 | − | 0.701396i | \(-0.752561\pi\) | ||||
−0.712772 | + | 0.701396i | \(0.752561\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −8.24164 | −0.332335 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 33.2245 | 1.33757 | 0.668785 | − | 0.743456i | \(-0.266815\pi\) | ||||
0.668785 | + | 0.743456i | \(0.266815\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.19969 | 0.0884130 | 0.0442065 | − | 0.999022i | \(-0.485924\pi\) | ||||
0.0442065 | + | 0.999022i | \(0.485924\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −60.6413 | −2.43345 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.855974 | 0.0342939 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 16.3172 | 0.652686 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −24.6241 | −0.983392 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −5.95398 | −0.237401 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −41.7539 | −1.66220 | −0.831099 | − | 0.556125i | \(-0.812288\pi\) | ||||
−0.831099 | + | 0.556125i | \(0.812288\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16.6089 | −0.660143 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 7.67843 | 0.304709 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.95983 | 0.156894 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −41.5952 | −1.64548 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −10.2230 | −0.403782 | −0.201891 | − | 0.979408i | \(-0.564709\pi\) | ||||
−0.201891 | + | 0.979408i | \(0.564709\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 28.6883 | 1.13136 | 0.565678 | − | 0.824626i | \(-0.308614\pi\) | ||||
0.565678 | + | 0.824626i | \(0.308614\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −11.1590 | −0.439386 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −11.1728 | −0.439248 | −0.219624 | − | 0.975585i | \(-0.570483\pi\) | ||||
−0.219624 | + | 0.975585i | \(0.570483\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.04816 | −0.119651 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.95042 | 0.350795 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 17.3511 | 0.679002 | 0.339501 | − | 0.940606i | \(-0.389742\pi\) | ||||
0.339501 | + | 0.940606i | \(0.389742\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −15.0016 | −0.586161 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −59.7519 | −2.33114 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −23.3534 | −0.909718 | −0.454859 | − | 0.890563i | \(-0.650310\pi\) | ||||
−0.454859 | + | 0.890563i | \(0.650310\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −11.6916 | −0.454751 | −0.227375 | − | 0.973807i | \(-0.573014\pi\) | ||||
−0.227375 | + | 0.973807i | \(0.573014\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 34.5623 | 1.34229 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −14.9637 | −0.580266 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −60.1856 | −2.33039 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 71.4509 | 2.76245 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.49641 | −0.134977 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.04115 | −0.271416 | −0.135708 | − | 0.990749i | \(-0.543331\pi\) | ||||
−0.135708 | + | 0.990749i | \(0.543331\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 31.4522 | 1.21059 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −25.4862 | −0.979515 | −0.489757 | − | 0.871859i | \(-0.662915\pi\) | ||||
−0.489757 | + | 0.871859i | \(0.662915\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.09672 | −0.195594 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −71.6590 | −2.74598 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 12.7209 | 0.486751 | 0.243375 | − | 0.969932i | \(-0.421745\pi\) | ||||
0.243375 | + | 0.969932i | \(0.421745\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0.776599 | 0.0296723 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 34.3496 | 1.31052 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.65131 | −0.139104 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.14120 | −0.271664 | −0.135832 | − | 0.990732i | \(-0.543371\pi\) | ||||
−0.135832 | + | 0.990732i | \(0.543371\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −12.4251 | −0.471989 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3.98743 | −0.151252 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.9320 | 0.754978 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −68.5101 | −2.59129 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −13.5998 | −0.513657 | −0.256829 | − | 0.966457i | \(-0.582678\pi\) | ||||
−0.256829 | + | 0.966457i | \(0.582678\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.22769 | −0.348029 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −2.17389 | −0.0818734 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 25.8747 | 0.973117 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.11325 | −0.192032 | −0.0960160 | − | 0.995380i | \(-0.530610\pi\) | ||||
−0.0960160 | + | 0.995380i | \(0.530610\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 48.4005 | 1.81516 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.4627 | 0.429280 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.68937 | −0.0631789 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 38.3319 | 1.43153 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −7.61492 | −0.283989 | −0.141994 | − | 0.989867i | \(-0.545351\pi\) | ||||
−0.141994 | + | 0.989867i | \(0.545351\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −15.8196 | −0.589152 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 36.1267 | 1.34357 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 31.2158 | 1.15933 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 24.7138 | 0.916582 | 0.458291 | − | 0.888802i | \(-0.348462\pi\) | ||||
0.458291 | + | 0.888802i | \(0.348462\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −38.2468 | −1.41655 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 26.9875 | 0.998169 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −22.0377 | −0.813981 | −0.406991 | − | 0.913432i | \(-0.633422\pi\) | ||||
−0.406991 | + | 0.913432i | \(0.633422\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.11164 | 0.151660 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.77072 | 0.249403 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −2.57064 | −0.0945624 | −0.0472812 | − | 0.998882i | \(-0.515056\pi\) | ||||
−0.0472812 | + | 0.998882i | \(0.515056\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 53.5659 | 1.96779 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −8.96476 | −0.328885 | −0.164443 | − | 0.986387i | \(-0.552583\pi\) | ||||
−0.164443 | + | 0.986387i | \(0.552583\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −9.35957 | −0.342908 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 15.9363 | 0.583079 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.08975 | 0.185975 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 51.9137 | 1.89436 | 0.947179 | − | 0.320705i | \(-0.103920\pi\) | ||||
0.947179 | + | 0.320705i | \(0.103920\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −33.6662 | −1.22686 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 15.8960 | 0.578514 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.7842 | −1.40963 | −0.704817 | − | 0.709389i | \(-0.748971\pi\) | ||||
−0.704817 | + | 0.709389i | \(0.748971\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −24.6567 | −0.894980 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −10.2193 | −0.370450 | −0.185225 | − | 0.982696i | \(-0.559301\pi\) | ||||
−0.185225 | + | 0.982696i | \(0.559301\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −14.2295 | −0.515142 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 23.1605 | 0.837370 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6.63080 | 0.239424 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 34.9017 | 1.25859 | 0.629294 | − | 0.777167i | \(-0.283344\pi\) | ||||
0.629294 | + | 0.777167i | \(0.283344\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −1.79242 | −0.0645523 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19.3308 | −0.695280 | −0.347640 | − | 0.937628i | \(-0.613017\pi\) | ||||
−0.347640 | + | 0.937628i | \(0.613017\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.94522 | −0.213558 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −7.21482 | −0.258830 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 30.8913 | 1.10680 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.61897 | −0.272628 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 50.7847 | 1.81490 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.0473 | 0.501369 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.15418 | −0.0767884 | −0.0383942 | − | 0.999263i | \(-0.512224\pi\) | ||||
−0.0383942 | + | 0.999263i | \(0.512224\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −43.7201 | −1.55648 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −21.1604 | −0.752378 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.60589 | 0.270093 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.79130 | −0.134463 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 54.3976 | 1.92686 | 0.963431 | − | 0.267957i | \(-0.0863486\pi\) | ||||
0.963431 | + | 0.267957i | \(0.0863486\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.25744 | 0.185995 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.05332 | −0.0725504 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −10.9447 | −0.386231 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −14.9835 | −0.528097 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −67.0124 | −2.35895 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 27.0473 | 0.950931 | 0.475466 | − | 0.879734i | \(-0.342280\pi\) | ||||
0.475466 | + | 0.879734i | \(0.342280\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.5444 | −1.42371 | −0.711853 | − | 0.702329i | \(-0.752144\pi\) | ||||
−0.711853 | + | 0.702329i | \(0.752144\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −18.8694 | −0.661778 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −9.14521 | −0.320343 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 41.8262 | 1.46331 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 27.0288 | 0.944463 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −23.0882 | −0.805785 | −0.402892 | − | 0.915247i | \(-0.631995\pi\) | ||||
−0.402892 | + | 0.915247i | \(0.631995\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −22.7946 | −0.794571 | −0.397286 | − | 0.917695i | \(-0.630048\pi\) | ||||
−0.397286 | + | 0.917695i | \(0.630048\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12.7884 | 0.445235 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −36.6264 | −1.27362 | −0.636812 | − | 0.771019i | \(-0.719747\pi\) | ||||
−0.636812 | + | 0.771019i | \(0.719747\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 10.0786 | 0.350043 | 0.175021 | − | 0.984565i | \(-0.444001\pi\) | ||||
0.175021 | + | 0.984565i | \(0.444001\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 30.6995 | 1.06496 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −9.94379 | −0.344532 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8.61081 | −0.297989 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −9.67222 | −0.334321 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.33726 | 0.322358 | 0.161179 | − | 0.986925i | \(-0.448470\pi\) | ||||
0.161179 | + | 0.986925i | \(0.448470\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.4031 | 0.738037 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 88.0543 | 3.03275 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −6.42082 | −0.220883 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.27589 | −0.0782005 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −55.3902 | −1.90099 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −9.23990 | −0.316740 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −10.1668 | −0.348106 | −0.174053 | − | 0.984736i | \(-0.555686\pi\) | ||||
−0.174053 | + | 0.984736i | \(0.555686\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 35.8950 | 1.22758 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.6146 | −0.533385 | −0.266693 | − | 0.963782i | \(-0.585931\pi\) | ||||
−0.266693 | + | 0.963782i | \(0.585931\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −24.7718 | −0.845202 | −0.422601 | − | 0.906316i | \(-0.638883\pi\) | ||||
−0.422601 | + | 0.906316i | \(0.638883\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 24.1529 | 0.823127 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −37.9548 | −1.29200 | −0.645999 | − | 0.763338i | \(-0.723559\pi\) | ||||
−0.645999 | + | 0.763338i | \(0.723559\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 19.5863 | 0.665952 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −37.3472 | −1.26838 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8.86549 | 0.300741 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.7287 | −0.499062 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 12.2261 | 0.413790 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 16.6086 | 0.561472 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.18673 | 0.0738405 | 0.0369203 | − | 0.999318i | \(-0.488245\pi\) | ||||
0.0369203 | + | 0.999318i | \(0.488245\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −14.1257 | −0.476449 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −15.7981 | −0.532253 | −0.266126 | − | 0.963938i | \(-0.585744\pi\) | ||||
−0.266126 | + | 0.963938i | \(0.585744\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −40.9074 | −1.37664 | −0.688322 | − | 0.725405i | \(-0.741652\pi\) | ||||
−0.688322 | + | 0.725405i | \(0.741652\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.88501 | 0.231437 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −36.5981 | −1.22884 | −0.614421 | − | 0.788978i | \(-0.710611\pi\) | ||||
−0.614421 | + | 0.788978i | \(0.710611\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −22.5023 | −0.754704 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.42707 | 0.148313 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 8.14817 | 0.272668 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −12.2013 | −0.407844 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 53.6368 | 1.79088 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.59953 | −0.320162 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.16906 | 0.305466 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 32.7025 | 1.08827 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.10986 | −0.269581 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 20.8110 | 0.691018 | 0.345509 | − | 0.938415i | \(-0.387706\pi\) | ||||
0.345509 | + | 0.938415i | \(0.387706\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −62.0684 | −2.05868 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 45.5177 | 1.50807 | 0.754035 | − | 0.656834i | \(-0.228105\pi\) | ||||
0.754035 | + | 0.656834i | \(0.228105\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.91904 | 0.0966063 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.89749 | 0.261083 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 43.9635 | 1.45180 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −27.5488 | −0.908750 | −0.454375 | − | 0.890811i | \(-0.650137\pi\) | ||||
−0.454375 | + | 0.890811i | \(0.650137\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 71.0848 | 2.34232 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 16.5739 | 0.545537 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.79236 | 0.157572 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 37.9481 | 1.24638 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 13.1293 | 0.430759 | 0.215380 | − | 0.976530i | \(-0.430901\pi\) | ||||
0.215380 | + | 0.976530i | \(0.430901\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.4112 | −0.505083 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −21.2452 | −0.695537 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.24229 | 0.138738 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.563467 | 0.0184077 | 0.00920383 | − | 0.999958i | \(-0.497070\pi\) | ||||
0.00920383 | + | 0.999958i | \(0.497070\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −97.1226 | −3.16948 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −26.6323 | −0.868188 | −0.434094 | − | 0.900868i | \(-0.642931\pi\) | ||||
−0.434094 | + | 0.900868i | \(0.642931\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 30.9322 | 1.00729 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 12.6431 | 0.411279 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 43.3481 | 1.40862 | 0.704311 | − | 0.709891i | \(-0.251256\pi\) | ||||
0.704311 | + | 0.709891i | \(0.251256\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 23.8086 | 0.772858 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 78.4757 | 2.54475 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.34467 | −0.140738 | −0.0703689 | − | 0.997521i | \(-0.522418\pi\) | ||||
−0.0703689 | + | 0.997521i | \(0.522418\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.56048 | 0.179933 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 20.6490 | 0.667487 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.27589 | −0.0734924 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29.1717 | −0.941023 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −12.2093 | −0.393440 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.47933 | 0.208577 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 52.7645 | 1.69679 | 0.848396 | − | 0.529362i | \(-0.177569\pi\) | ||||
0.848396 | + | 0.529362i | \(0.177569\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −134.513 | −4.32118 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 21.4278 | 0.687650 | 0.343825 | − | 0.939034i | \(-0.388277\pi\) | ||||
0.343825 | + | 0.939034i | \(0.388277\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.6855 | 0.374620 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −27.8192 | −0.890928 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 45.0915 | 1.44260 | 0.721302 | − | 0.692621i | \(-0.243544\pi\) | ||||
0.721302 | + | 0.692621i | \(0.243544\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −0.376105 | −0.0120204 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 34.1338 | 1.08981 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −4.68626 | −0.149468 | −0.0747342 | − | 0.997203i | \(-0.523811\pi\) | ||||
−0.0747342 | + | 0.997203i | \(0.523811\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10.6829 | 0.340387 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 6.37077 | 0.202784 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 41.8815 | 1.33175 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −55.3514 | −1.75829 | −0.879147 | − | 0.476551i | \(-0.841887\pi\) | ||||
−0.879147 | + | 0.476551i | \(0.841887\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −85.0192 | −2.69800 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.42655 | 0.235437 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −22.0342 | −0.697830 | −0.348915 | − | 0.937154i | \(-0.613450\pi\) | ||||
−0.348915 | + | 0.937154i | \(0.613450\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.79665 | 0.246675 |
(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 | 6028.2.a.f.1.2 | ✓ | 29 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
6028.2.a.f.1.2 | ✓ | 29 | 1.1 | even | 1 | trivial |