Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4028,2,Mod(1,4028)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4028, 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("4028.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4028 = 2^{2} \cdot 19 \cdot 53 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4028.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(32.1637419342\) |
Analytic rank: | \(1\) |
Dimension: | \(19\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{19} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{19} - 4 x^{18} - 30 x^{17} + 132 x^{16} + 332 x^{15} - 1714 x^{14} - 1598 x^{13} + 11179 x^{12} + \cdots - 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.19 | ||
Root | \(-3.17454\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4028.1 |
$q$-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 | ||||||||
\(3\) | 3.17454 | 1.83282 | 0.916412 | − | 0.400236i | \(-0.131072\pi\) | ||||
0.916412 | + | 0.400236i | \(0.131072\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.27638 | −1.91246 | −0.956228 | − | 0.292623i | \(-0.905472\pi\) | ||||
−0.956228 | + | 0.292623i | \(0.905472\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4.73492 | −1.78963 | −0.894815 | − | 0.446436i | \(-0.852693\pi\) | ||||
−0.894815 | + | 0.446436i | \(0.852693\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 7.07773 | 2.35924 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 3.63629 | 1.09638 | 0.548192 | − | 0.836352i | \(-0.315316\pi\) | ||||
0.548192 | + | 0.836352i | \(0.315316\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.74027 | 1.03736 | 0.518682 | − | 0.854967i | \(-0.326423\pi\) | ||||
0.518682 | + | 0.854967i | \(0.326423\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −13.5756 | −3.50519 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.80496 | −0.437768 | −0.218884 | − | 0.975751i | \(-0.570242\pi\) | ||||
−0.218884 | + | 0.975751i | \(0.570242\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | ||||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −15.0312 | −3.28008 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.48625 | −0.518419 | −0.259210 | − | 0.965821i | \(-0.583462\pi\) | ||||
−0.259210 | + | 0.965821i | \(0.583462\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 13.2874 | 2.65749 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 12.9449 | 2.49126 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.417081 | 0.0774499 | 0.0387250 | − | 0.999250i | \(-0.487670\pi\) | ||||
0.0387250 | + | 0.999250i | \(0.487670\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.42779 | −1.15447 | −0.577233 | − | 0.816580i | \(-0.695867\pi\) | ||||
−0.577233 | + | 0.816580i | \(0.695867\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 11.5436 | 2.00948 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 20.2483 | 3.42259 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4.97711 | −0.818231 | −0.409116 | − | 0.912483i | \(-0.634163\pi\) | ||||
−0.409116 | + | 0.912483i | \(0.634163\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 11.8737 | 1.90131 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.0129771 | −0.00202668 | −0.00101334 | − | 0.999999i | \(-0.500323\pi\) | ||||
−0.00101334 | + | 0.999999i | \(0.500323\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −11.1876 | −1.70609 | −0.853044 | − | 0.521839i | \(-0.825246\pi\) | ||||
−0.853044 | + | 0.521839i | \(0.825246\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −30.2671 | −4.51195 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −6.11779 | −0.892372 | −0.446186 | − | 0.894940i | \(-0.647218\pi\) | ||||
−0.446186 | + | 0.894940i | \(0.647218\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 15.4195 | 2.20278 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −5.72994 | −0.802352 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.00000 | 0.137361 | ||||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −15.5502 | −2.09679 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.17454 | −0.420479 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −12.4760 | −1.62424 | −0.812120 | − | 0.583491i | \(-0.801686\pi\) | ||||
−0.812120 | + | 0.583491i | \(0.801686\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.40643 | 0.564186 | 0.282093 | − | 0.959387i | \(-0.408971\pi\) | ||||
0.282093 | + | 0.959387i | \(0.408971\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −33.5125 | −4.22218 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −15.9948 | −1.98391 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −14.2338 | −1.73894 | −0.869470 | − | 0.493986i | \(-0.835539\pi\) | ||||
−0.869470 | + | 0.493986i | \(0.835539\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −7.89271 | −0.950171 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.24339 | 0.503597 | 0.251799 | − | 0.967780i | \(-0.418978\pi\) | ||||
0.251799 | + | 0.967780i | \(0.418978\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −10.7983 | −1.26384 | −0.631921 | − | 0.775033i | \(-0.717733\pi\) | ||||
−0.631921 | + | 0.775033i | \(0.717733\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 42.1815 | 4.87071 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −17.2176 | −1.96212 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.93332 | −0.442533 | −0.221267 | − | 0.975213i | \(-0.571019\pi\) | ||||
−0.221267 | + | 0.975213i | \(0.571019\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 19.8611 | 2.20679 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −11.0579 | −1.21376 | −0.606882 | − | 0.794792i | \(-0.707580\pi\) | ||||
−0.606882 | + | 0.794792i | \(0.707580\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.71872 | 0.837212 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.32404 | 0.141952 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 3.91713 | 0.415215 | 0.207608 | − | 0.978212i | \(-0.433432\pi\) | ||||
0.207608 | + | 0.978212i | \(0.433432\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −17.7099 | −1.85650 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −20.4053 | −2.11593 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 4.27638 | 0.438747 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.08577 | 0.719451 | 0.359726 | − | 0.933058i | \(-0.382870\pi\) | ||||
0.359726 | + | 0.933058i | \(0.382870\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 25.7367 | 2.58664 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 6.28317 | 0.625199 | 0.312600 | − | 0.949885i | \(-0.398800\pi\) | ||||
0.312600 | + | 0.949885i | \(0.398800\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.36553 | −0.134550 | −0.0672750 | − | 0.997734i | \(-0.521430\pi\) | ||||
−0.0672750 | + | 0.997734i | \(0.521430\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 64.2792 | 6.27301 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −14.7230 | −1.42333 | −0.711664 | − | 0.702520i | \(-0.752058\pi\) | ||||
−0.711664 | + | 0.702520i | \(0.752058\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 17.0448 | 1.63260 | 0.816299 | − | 0.577630i | \(-0.196022\pi\) | ||||
0.816299 | + | 0.577630i | \(0.196022\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −15.8000 | −1.49967 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −5.32408 | −0.500847 | −0.250424 | − | 0.968136i | \(-0.580570\pi\) | ||||
−0.250424 | + | 0.968136i | \(0.580570\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 10.6322 | 0.991453 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 26.4726 | 2.44740 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.54636 | 0.783444 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.22264 | 0.202058 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −0.0411964 | −0.00371455 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −35.4402 | −3.16987 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −11.2335 | −0.996814 | −0.498407 | − | 0.866943i | \(-0.666081\pi\) | ||||
−0.498407 | + | 0.866943i | \(0.666081\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −35.5154 | −3.12696 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.46946 | −0.215758 | −0.107879 | − | 0.994164i | \(-0.534406\pi\) | ||||
−0.107879 | + | 0.994164i | \(0.534406\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.73492 | 0.410570 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −55.3575 | −4.76442 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.84634 | 0.755794 | 0.377897 | − | 0.925848i | \(-0.376647\pi\) | ||||
0.377897 | + | 0.925848i | \(0.376647\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 15.0915 | 1.28004 | 0.640021 | − | 0.768358i | \(-0.278926\pi\) | ||||
0.640021 | + | 0.768358i | \(0.278926\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −19.4212 | −1.63556 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 13.6007 | 1.13735 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.78360 | −0.148120 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 48.9497 | 4.03731 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 3.63193 | 0.297540 | 0.148770 | − | 0.988872i | \(-0.452469\pi\) | ||||
0.148770 | + | 0.988872i | \(0.452469\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.70641 | 0.464381 | 0.232190 | − | 0.972670i | \(-0.425411\pi\) | ||||
0.232190 | + | 0.972670i | \(0.425411\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −12.7751 | −1.03280 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 27.4877 | 2.20786 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −16.8079 | −1.34142 | −0.670709 | − | 0.741721i | \(-0.734010\pi\) | ||||
−0.670709 | + | 0.741721i | \(0.734010\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.17454 | 0.251758 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.7722 | 0.927779 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −22.2051 | −1.73924 | −0.869619 | − | 0.493724i | \(-0.835635\pi\) | ||||
−0.869619 | + | 0.493724i | \(0.835635\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −49.3647 | −3.84304 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 10.4987 | 0.812417 | 0.406208 | − | 0.913780i | \(-0.366851\pi\) | ||||
0.406208 | + | 0.913780i | \(0.366851\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.989635 | 0.0761258 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.07773 | −0.541248 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.0826 | −0.994649 | −0.497324 | − | 0.867565i | \(-0.665684\pi\) | ||||
−0.497324 | + | 0.867565i | \(0.665684\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −62.9149 | −4.75592 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −39.6057 | −2.97695 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 18.7498 | 1.40142 | 0.700712 | − | 0.713444i | \(-0.252866\pi\) | ||||
0.700712 | + | 0.713444i | \(0.252866\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 17.9054 | 1.33090 | 0.665449 | − | 0.746443i | \(-0.268240\pi\) | ||||
0.665449 | + | 0.746443i | \(0.268240\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 13.9884 | 1.03405 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 21.2840 | 1.56483 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −6.56338 | −0.479962 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −61.2933 | −4.45843 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −24.2695 | −1.75608 | −0.878039 | − | 0.478588i | \(-0.841149\pi\) | ||||
−0.878039 | + | 0.478588i | \(0.841149\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −27.6589 | −1.99093 | −0.995467 | − | 0.0951104i | \(-0.969680\pi\) | ||||
−0.995467 | + | 0.0951104i | \(0.969680\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −50.7763 | −3.63617 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 17.5481 | 1.25025 | 0.625126 | − | 0.780524i | \(-0.285047\pi\) | ||||
0.625126 | + | 0.780524i | \(0.285047\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −7.03326 | −0.498575 | −0.249287 | − | 0.968430i | \(-0.580196\pi\) | ||||
−0.249287 | + | 0.968430i | \(0.580196\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −45.1859 | −3.18717 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.97484 | −0.138607 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.0554950 | 0.00387594 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −17.5970 | −1.22308 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.63629 | −0.251528 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.66387 | −0.665288 | −0.332644 | − | 0.943052i | \(-0.607941\pi\) | ||||
−0.332644 | + | 0.943052i | \(0.607941\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 13.4708 | 0.923005 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 47.8423 | 3.26282 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 30.4351 | 2.06607 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −34.2796 | −2.31640 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −6.75106 | −0.454125 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 12.1280 | 0.812151 | 0.406075 | − | 0.913840i | \(-0.366897\pi\) | ||||
0.406075 | + | 0.913840i | \(0.366897\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 94.0449 | 6.26966 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 18.5331 | 1.23009 | 0.615043 | − | 0.788493i | \(-0.289139\pi\) | ||||
0.615043 | + | 0.788493i | \(0.289139\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −21.6898 | −1.43330 | −0.716650 | − | 0.697433i | \(-0.754326\pi\) | ||||
−0.716650 | + | 0.697433i | \(0.754326\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −54.6579 | −3.59623 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −6.77239 | −0.443674 | −0.221837 | − | 0.975084i | \(-0.571205\pi\) | ||||
−0.221837 | + | 0.975084i | \(0.571205\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 26.1620 | 1.70662 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −12.4865 | −0.811086 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.16525 | 0.463481 | 0.231741 | − | 0.972778i | \(-0.425558\pi\) | ||||
0.231741 | + | 0.972778i | \(0.425558\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.06497 | −0.133017 | −0.0665083 | − | 0.997786i | \(-0.521186\pi\) | ||||
−0.0665083 | + | 0.997786i | \(0.521186\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 24.2151 | 1.55340 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −65.9395 | −4.21272 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.74027 | −0.237988 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −35.1038 | −2.22462 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.87980 | 0.497369 | 0.248684 | − | 0.968585i | \(-0.420002\pi\) | ||||
0.248684 | + | 0.968585i | \(0.420002\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.04074 | −0.568386 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 24.5034 | 1.53446 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 24.1450 | 1.50613 | 0.753063 | − | 0.657948i | \(-0.228575\pi\) | ||||
0.753063 | + | 0.657948i | \(0.228575\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 23.5662 | 1.46433 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.95199 | 0.182723 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.62011 | −0.593202 | −0.296601 | − | 0.955002i | \(-0.595853\pi\) | ||||
−0.296601 | + | 0.955002i | \(0.595853\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.27638 | −0.262696 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.4351 | 0.761017 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.6103 | 1.25663 | 0.628316 | − | 0.777958i | \(-0.283745\pi\) | ||||
0.628316 | + | 0.777958i | \(0.283745\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −14.7013 | −0.893040 | −0.446520 | − | 0.894774i | \(-0.647337\pi\) | ||||
−0.446520 | + | 0.894774i | \(0.647337\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −56.2208 | −3.40264 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 48.3170 | 2.91363 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 3.43234 | 0.206229 | 0.103115 | − | 0.994669i | \(-0.467119\pi\) | ||||
0.103115 | + | 0.994669i | \(0.467119\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −45.4942 | −2.72367 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −28.8272 | −1.71968 | −0.859842 | − | 0.510560i | \(-0.829438\pi\) | ||||
−0.859842 | + | 0.510560i | \(0.829438\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 31.7392 | 1.88670 | 0.943349 | − | 0.331802i | \(-0.107657\pi\) | ||||
0.943349 | + | 0.331802i | \(0.107657\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 13.5756 | 0.804147 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0.0614455 | 0.00362701 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.7421 | −0.808359 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 22.4941 | 1.31863 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.61913 | −0.503535 | −0.251767 | − | 0.967788i | \(-0.581012\pi\) | ||||
−0.251767 | + | 0.967788i | \(0.581012\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 53.3522 | 3.10629 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 47.0716 | 2.73137 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −9.29925 | −0.537790 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 52.9722 | 3.05327 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 19.9462 | 1.14588 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −18.8436 | −1.07898 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 16.1844 | 0.923694 | 0.461847 | − | 0.886960i | \(-0.347187\pi\) | ||||
0.461847 | + | 0.886960i | \(0.347187\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.33495 | −0.246607 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.62784 | −0.262421 | −0.131210 | − | 0.991355i | \(-0.541886\pi\) | ||||
−0.131210 | + | 0.991355i | \(0.541886\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.99505 | −0.451907 | −0.225953 | − | 0.974138i | \(-0.572550\pi\) | ||||
−0.225953 | + | 0.974138i | \(0.572550\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 143.312 | 8.07473 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 23.0306 | 1.29353 | 0.646763 | − | 0.762691i | \(-0.276122\pi\) | ||||
0.646763 | + | 0.762691i | \(0.276122\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.51663 | 0.0849149 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −46.7389 | −2.60871 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.80496 | 0.100431 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 49.6986 | 2.75678 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 54.1095 | 2.99226 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 28.9672 | 1.59702 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.06911 | 0.498484 | 0.249242 | − | 0.968441i | \(-0.419819\pi\) | ||||
0.249242 | + | 0.968441i | \(0.419819\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −35.2266 | −1.93041 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 60.8693 | 3.32564 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.6223 | −0.633108 | −0.316554 | − | 0.948575i | \(-0.602526\pi\) | ||||
−0.316554 | + | 0.948575i | \(0.602526\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −16.9015 | −0.917965 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −23.3733 | −1.26574 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −39.8654 | −2.15253 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 33.7522 | 1.81716 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.64973 | 0.518024 | 0.259012 | − | 0.965874i | \(-0.416603\pi\) | ||||
0.259012 | + | 0.965874i | \(0.416603\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 12.8659 | 0.688695 | 0.344347 | − | 0.938842i | \(-0.388100\pi\) | ||||
0.344347 | + | 0.938842i | \(0.388100\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 48.4176 | 2.58434 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.3810 | −1.35089 | −0.675446 | − | 0.737410i | \(-0.736049\pi\) | ||||
−0.675446 | + | 0.737410i | \(0.736049\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −18.1463 | −0.963108 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 27.1308 | 1.43591 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.73670 | −0.461106 | −0.230553 | − | 0.973060i | \(-0.574053\pi\) | ||||
−0.230553 | + | 0.973060i | \(0.574053\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.00000 | 0.0526316 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 7.05587 | 0.370337 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 46.1775 | 2.41704 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.8751 | 0.567675 | 0.283838 | − | 0.958872i | \(-0.408392\pi\) | ||||
0.283838 | + | 0.958872i | \(0.408392\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −0.0918484 | −0.00478144 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.73492 | −0.245825 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −0.610842 | −0.0316282 | −0.0158141 | − | 0.999875i | \(-0.505034\pi\) | ||||
−0.0158141 | + | 0.999875i | \(0.505034\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −112.507 | −5.80981 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.56000 | 0.0803438 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.22331 | −0.0628374 | −0.0314187 | − | 0.999506i | \(-0.510003\pi\) | ||||
−0.0314187 | + | 0.999506i | \(0.510003\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −35.6613 | −1.82698 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.17965 | −0.213570 | −0.106785 | − | 0.994282i | \(-0.534056\pi\) | ||||
−0.106785 | + | 0.994282i | \(0.534056\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 73.6288 | 3.75247 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −79.1826 | −4.02508 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 11.6166 | 0.588984 | 0.294492 | − | 0.955654i | \(-0.404850\pi\) | ||||
0.294492 | + | 0.955654i | \(0.404850\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.48759 | 0.226947 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −7.83941 | −0.395446 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 16.8204 | 0.846325 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −17.0512 | −0.855776 | −0.427888 | − | 0.903832i | \(-0.640742\pi\) | ||||
−0.427888 | + | 0.903832i | \(0.640742\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 15.0312 | 0.752502 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 7.21698 | 0.360399 | 0.180199 | − | 0.983630i | \(-0.442326\pi\) | ||||
0.180199 | + | 0.983630i | \(0.442326\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −24.0417 | −1.19760 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −84.9337 | −4.22039 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −18.0982 | −0.897096 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 31.7986 | 1.57234 | 0.786170 | − | 0.618010i | \(-0.212061\pi\) | ||||
0.786170 | + | 0.618010i | \(0.212061\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 28.0831 | 1.38524 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 59.0729 | 2.90679 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 47.2879 | 2.32127 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 47.9085 | 2.34609 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 28.4319 | 1.38899 | 0.694494 | − | 0.719499i | \(-0.255628\pi\) | ||||
0.694494 | + | 0.719499i | \(0.255628\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.8992 | −1.11604 | −0.558019 | − | 0.829828i | \(-0.688438\pi\) | ||||
−0.558019 | + | 0.829828i | \(0.688438\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −43.3001 | −2.10532 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −23.9834 | −1.16336 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −20.8641 | −1.00968 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 43.1761 | 2.08456 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 12.3161 | 0.593247 | 0.296623 | − | 0.954995i | \(-0.404139\pi\) | ||||
0.296623 | + | 0.954995i | \(0.404139\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −0.236191 | −0.0113506 | −0.00567530 | − | 0.999984i | \(-0.501807\pi\) | ||||
−0.00567530 | + | 0.999984i | \(0.501807\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −5.66210 | −0.271477 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.48625 | 0.118933 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.88355 | −0.233079 | −0.116540 | − | 0.993186i | \(-0.537180\pi\) | ||||
−0.116540 | + | 0.993186i | \(0.537180\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 109.135 | 5.19689 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 26.2317 | 1.24630 | 0.623152 | − | 0.782101i | \(-0.285852\pi\) | ||||
0.623152 | + | 0.782101i | \(0.285852\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −16.7512 | −0.794081 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.5297 | 0.545338 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2.34028 | 0.110445 | 0.0552224 | − | 0.998474i | \(-0.482413\pi\) | ||||
0.0552224 | + | 0.998474i | \(0.482413\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.0471885 | −0.00222202 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 18.1152 | 0.851128 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 75.7342 | 3.55047 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8.04674 | 0.376410 | 0.188205 | − | 0.982130i | \(-0.439733\pi\) | ||||
0.188205 | + | 0.982130i | \(0.439733\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −23.3652 | −1.09059 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 37.6901 | 1.75540 | 0.877702 | − | 0.479206i | \(-0.159075\pi\) | ||||
0.877702 | + | 0.479206i | \(0.159075\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.57700 | 0.259185 | 0.129592 | − | 0.991567i | \(-0.458633\pi\) | ||||
0.129592 | + | 0.991567i | \(0.458633\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 87.2609 | 4.04663 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −30.5446 | −1.41343 | −0.706717 | − | 0.707496i | \(-0.749825\pi\) | ||||
−0.706717 | + | 0.707496i | \(0.749825\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 67.3960 | 3.11206 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −53.3575 | −2.45858 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −40.6813 | −1.87053 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.2874 | −0.609669 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.07773 | 0.324067 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.63999 | 0.0749330 | 0.0374665 | − | 0.999298i | \(-0.488071\pi\) | ||||
0.0374665 | + | 0.999298i | \(0.488071\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −18.6157 | −0.848804 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 37.3714 | 1.70046 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −30.3015 | −1.37592 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −10.3716 | −0.469983 | −0.234991 | − | 0.971997i | \(-0.575506\pi\) | ||||
−0.234991 | + | 0.971997i | \(0.575506\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −70.4911 | −3.18772 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −38.0504 | −1.71719 | −0.858595 | − | 0.512654i | \(-0.828662\pi\) | ||||
−0.858595 | + | 0.512654i | \(0.828662\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −0.752816 | −0.0339051 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −110.060 | −4.94683 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −20.0921 | −0.901253 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −33.9758 | −1.52097 | −0.760483 | − | 0.649358i | \(-0.775038\pi\) | ||||
−0.760483 | + | 0.649358i | \(0.775038\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 33.3287 | 1.48902 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 13.4820 | 0.601132 | 0.300566 | − | 0.953761i | \(-0.402824\pi\) | ||||
0.300566 | + | 0.953761i | \(0.402824\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −26.8692 | −1.19567 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 3.14164 | 0.139525 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 13.3229 | 0.590529 | 0.295264 | − | 0.955416i | \(-0.404592\pi\) | ||||
0.295264 | + | 0.955416i | \(0.404592\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 51.1289 | 2.26181 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −12.9449 | −0.571533 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 5.83954 | 0.257321 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −22.2461 | −0.978382 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −41.5312 | −1.82302 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −6.51367 | −0.285369 | −0.142685 | − | 0.989768i | \(-0.545573\pi\) | ||||
−0.142685 | + | 0.989768i | \(0.545573\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −9.38391 | −0.410330 | −0.205165 | − | 0.978727i | \(-0.565773\pi\) | ||||
−0.205165 | + | 0.978727i | \(0.565773\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −199.726 | −8.71677 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 11.6019 | 0.505388 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.8186 | −0.731242 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −88.3019 | −3.83198 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.0485379 | −0.00210241 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 62.9612 | 2.72205 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 59.5220 | 2.56856 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 56.0697 | 2.41509 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.62461 | −0.112841 | −0.0564203 | − | 0.998407i | \(-0.517969\pi\) | ||||
−0.0564203 | + | 0.998407i | \(0.517969\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 56.8415 | 2.43930 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −72.8901 | −3.12227 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.94741 | −0.0832651 | −0.0416325 | − | 0.999133i | \(-0.513256\pi\) | ||||
−0.0416325 | + | 0.999133i | \(0.513256\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 31.1876 | 1.33105 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.417081 | −0.0177682 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 18.6240 | 0.791971 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 67.5670 | 2.86806 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 20.9226 | 0.886518 | 0.443259 | − | 0.896393i | \(-0.353822\pi\) | ||||
0.443259 | + | 0.896393i | \(0.353822\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −41.8445 | −1.76984 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −20.8358 | −0.879686 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.8069 | −0.834762 | −0.417381 | − | 0.908732i | \(-0.637052\pi\) | ||||
−0.417381 | + | 0.908732i | \(0.637052\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 22.7678 | 0.957848 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −94.0407 | −3.94934 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9.47854 | 0.397361 | 0.198680 | − | 0.980064i | \(-0.436334\pi\) | ||||
0.198680 | + | 0.980064i | \(0.436334\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 20.5826 | 0.861356 | 0.430678 | − | 0.902506i | \(-0.358275\pi\) | ||||
0.430678 | + | 0.902506i | \(0.358275\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −77.0446 | −3.21858 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −33.0359 | −1.37769 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.18773 | 0.132707 | 0.0663534 | − | 0.997796i | \(-0.478864\pi\) | ||||
0.0663534 | + | 0.997796i | \(0.478864\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −87.8045 | −3.64903 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 52.3583 | 2.17219 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.63629 | 0.150600 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −113.207 | −4.68054 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 40.7227 | 1.68081 | 0.840403 | − | 0.541962i | \(-0.182318\pi\) | ||||
0.840403 | + | 0.541962i | \(0.182318\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.42779 | 0.264852 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 55.7073 | 2.29149 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −0.612310 | −0.0251446 | −0.0125723 | − | 0.999921i | \(-0.504002\pi\) | ||||
−0.0125723 | + | 0.999921i | \(0.504002\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −36.5475 | −1.49830 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −22.3274 | −0.913800 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −29.7994 | −1.21757 | −0.608785 | − | 0.793335i | \(-0.708343\pi\) | ||||
−0.608785 | + | 0.793335i | \(0.708343\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 13.3764 | 0.545635 | 0.272818 | − | 0.962066i | \(-0.412044\pi\) | ||||
0.272818 | + | 0.962066i | \(0.412044\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −100.743 | −4.10258 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −9.50485 | −0.386427 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24.9370 | −1.01216 | −0.506080 | − | 0.862486i | \(-0.668906\pi\) | ||||
−0.506080 | + | 0.862486i | \(0.668906\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.26923 | −0.254042 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22.8822 | −0.925715 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.02600 | 0.283778 | 0.141889 | − | 0.989883i | \(-0.454682\pi\) | ||||
0.141889 | + | 0.989883i | \(0.454682\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.176171 | 0.00710391 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 36.7738 | 1.48046 | 0.740229 | − | 0.672355i | \(-0.234717\pi\) | ||||
0.740229 | + | 0.672355i | \(0.234717\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −17.6301 | −0.708613 | −0.354306 | − | 0.935129i | \(-0.615283\pi\) | ||||
−0.354306 | + | 0.935129i | \(0.615283\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −32.1844 | −1.29151 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −18.5473 | −0.743082 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 85.1187 | 3.40475 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −11.5436 | −0.461006 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 8.98350 | 0.358196 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 32.4321 | 1.29110 | 0.645551 | − | 0.763717i | \(-0.276628\pi\) | ||||
0.645551 | + | 0.763717i | \(0.276628\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −30.6784 | −1.21936 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 48.0388 | 1.90636 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 57.6729 | 2.28509 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 30.0336 | 1.18811 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −33.5398 | −1.32474 | −0.662371 | − | 0.749176i | \(-0.730450\pi\) | ||||
−0.662371 | + | 0.749176i | \(0.730450\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 36.7000 | 1.44731 | 0.723654 | − | 0.690163i | \(-0.242461\pi\) | ||||
0.723654 | + | 0.690163i | \(0.242461\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 151.877 | 5.98017 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 18.3697 | 0.722186 | 0.361093 | − | 0.932530i | \(-0.382404\pi\) | ||||
0.361093 | + | 0.932530i | \(0.382404\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −45.3665 | −1.78079 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 96.6175 | 3.78674 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −43.9517 | −1.71996 | −0.859982 | − | 0.510324i | \(-0.829526\pi\) | ||||
−0.859982 | + | 0.510324i | \(0.829526\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 10.5604 | 0.412627 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −76.4273 | −2.98171 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15.3575 | 0.598245 | 0.299122 | − | 0.954215i | \(-0.403306\pi\) | ||||
0.299122 | + | 0.954215i | \(0.403306\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −37.3749 | −1.45372 | −0.726858 | − | 0.686787i | \(-0.759020\pi\) | ||||
−0.726858 | + | 0.686787i | \(0.759020\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −21.4315 | −0.832332 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −20.2483 | −0.785196 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.03697 | −0.0401515 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 38.5009 | 1.48853 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 16.0231 | 0.618565 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.34765 | 0.0519481 | 0.0259741 | − | 0.999663i | \(-0.491731\pi\) | ||||
0.0259741 | + | 0.999663i | \(0.491731\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 172.005 | 6.62048 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 42.4717 | 1.63232 | 0.816160 | − | 0.577825i | \(-0.196099\pi\) | ||||
0.816160 | + | 0.577825i | \(0.196099\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −33.5505 | −1.28755 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 58.8342 | 2.25453 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −16.6167 | −0.635820 | −0.317910 | − | 0.948121i | \(-0.602981\pi\) | ||||
−0.317910 | + | 0.948121i | \(0.602981\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −37.8303 | −1.44542 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −68.8552 | −2.62699 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.74027 | 0.142493 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 36.2051 | 1.37731 | 0.688654 | − | 0.725090i | \(-0.258202\pi\) | ||||
0.688654 | + | 0.725090i | \(0.258202\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −121.861 | −4.62913 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −64.5368 | −2.44802 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.0234232 | 0.000887217 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −21.4993 | −0.813177 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.01274 | 0.302637 | 0.151319 | − | 0.988485i | \(-0.451648\pi\) | ||||
0.151319 | + | 0.988485i | \(0.451648\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.97711 | 0.187715 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 83.0525 | 3.12794 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −29.7503 | −1.11888 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −26.0454 | −0.978155 | −0.489077 | − | 0.872240i | \(-0.662666\pi\) | ||||
−0.489077 | + | 0.872240i | \(0.662666\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −27.8390 | −1.04404 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 15.9811 | 0.598497 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −58.1619 | −2.17513 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 22.7464 | 0.849480 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.8824 | 0.927959 | 0.463979 | − | 0.885846i | \(-0.346421\pi\) | ||||
0.463979 | + | 0.885846i | \(0.346421\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.46569 | 0.240795 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.55535 | −0.243796 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5.54193 | 0.205822 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 7.24276 | 0.268619 | 0.134309 | − | 0.990939i | \(-0.457118\pi\) | ||||
0.134309 | + | 0.990939i | \(0.457118\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 17.2887 | 0.640322 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 20.1932 | 0.746871 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.98752 | 0.0734107 | 0.0367053 | − | 0.999326i | \(-0.488314\pi\) | ||||
0.0367053 | + | 0.999326i | \(0.488314\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −209.328 | −7.72117 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −51.7584 | −1.90655 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29.7505 | −1.09439 | −0.547195 | − | 0.837005i | \(-0.684305\pi\) | ||||
−0.547195 | + | 0.837005i | \(0.684305\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −11.8737 | −0.436190 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.9921 | −0.696752 | −0.348376 | − | 0.937355i | \(-0.613267\pi\) | ||||
−0.348376 | + | 0.937355i | \(0.613267\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −15.5315 | −0.569031 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −78.2650 | −2.86357 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 69.7123 | 2.54723 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 37.1163 | 1.35439 | 0.677196 | − | 0.735802i | \(-0.263195\pi\) | ||||
0.677196 | + | 0.735802i | \(0.263195\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 25.0148 | 0.911589 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −24.4028 | −0.888108 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.1729 | 0.478776 | 0.239388 | − | 0.970924i | \(-0.423053\pi\) | ||||
0.239388 | + | 0.970924i | \(0.423053\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −28.7002 | −1.04175 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 54.5440 | 1.97722 | 0.988610 | − | 0.150503i | \(-0.0480893\pi\) | ||||
0.988610 | + | 0.150503i | \(0.0480893\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −80.7058 | −2.92175 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 54.6310 | 1.97519 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −46.6637 | −1.68493 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −33.6028 | −1.21175 | −0.605873 | − | 0.795561i | \(-0.707176\pi\) | ||||
−0.605873 | + | 0.795561i | \(0.707176\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 76.6495 | 2.76046 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.50565 | −0.126090 | −0.0630448 | − | 0.998011i | \(-0.520081\pi\) | ||||
−0.0630448 | + | 0.998011i | \(0.520081\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −85.4088 | −3.06798 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 74.8119 | 2.68386 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.0129771 | 0.000464953 0 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 15.4302 | 0.552136 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 5.39909 | 0.192948 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 71.8771 | 2.56540 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −20.7607 | −0.740041 | −0.370020 | − | 0.929024i | \(-0.620649\pi\) | ||||
−0.370020 | + | 0.929024i | \(0.620649\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −30.5395 | −1.08723 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 25.2091 | 0.896332 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.4813 | 0.585267 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −13.5756 | −0.481476 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −16.5479 | −0.586156 | −0.293078 | − | 0.956088i | \(-0.594680\pi\) | ||||
−0.293078 | + | 0.956088i | \(0.594680\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 11.0424 | 0.390652 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 27.7244 | 0.979595 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −39.2657 | −1.38566 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −50.3424 | −1.77434 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 65.4283 | 2.30319 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 49.4756 | 1.73947 | 0.869735 | − | 0.493519i | \(-0.164290\pi\) | ||||
0.869735 | + | 0.493519i | \(0.164290\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −37.7298 | −1.32487 | −0.662436 | − | 0.749119i | \(-0.730477\pi\) | ||||
−0.662436 | + | 0.749119i | \(0.730477\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −46.6699 | −1.63679 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 94.9574 | 3.32621 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.1876 | 0.391403 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −125.346 | −4.37994 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3.71452 | 0.129638 | 0.0648188 | − | 0.997897i | \(-0.479353\pi\) | ||||
0.0648188 | + | 0.997897i | \(0.479353\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 45.1834 | 1.57500 | 0.787498 | − | 0.616317i | \(-0.211376\pi\) | ||||
0.787498 | + | 0.616317i | \(0.211376\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 153.385 | 5.34016 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −11.7935 | −0.410099 | −0.205050 | − | 0.978752i | \(-0.565736\pi\) | ||||
−0.205050 | + | 0.978752i | \(0.565736\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.8515 | −0.585276 | −0.292638 | − | 0.956223i | \(-0.594533\pi\) | ||||
−0.292638 | + | 0.956223i | \(0.594533\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.8961 | 0.377982 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −27.8316 | −0.964307 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −44.8966 | −1.55371 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −83.2074 | −2.87607 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −4.25734 | −0.146980 | −0.0734898 | − | 0.997296i | \(-0.523414\pi\) | ||||
−0.0734898 | + | 0.997296i | \(0.523414\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.8260 | −0.994002 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −91.5131 | −3.15188 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −4.23206 | −0.145587 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.5240 | −0.361609 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 100.757 | 3.45799 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 12.3743 | 0.424187 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 0.607038 | 0.0207846 | 0.0103923 | − | 0.999946i | \(-0.496692\pi\) | ||||
0.0103923 | + | 0.999946i | \(0.496692\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 30.2671 | 1.03511 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 0.617490 | 0.0210931 | 0.0105465 | − | 0.999944i | \(-0.496643\pi\) | ||||
0.0105465 | + | 0.999944i | \(0.496643\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 15.0494 | 0.513478 | 0.256739 | − | 0.966481i | \(-0.417352\pi\) | ||||
0.256739 | + | 0.966481i | \(0.417352\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.195061 | 0.00664767 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −11.0514 | −0.376195 | −0.188097 | − | 0.982150i | \(-0.560232\pi\) | ||||
−0.188097 | + | 0.982150i | \(0.560232\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 55.9460 | 1.90222 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −43.6249 | −1.48158 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −14.3027 | −0.485187 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −53.2384 | −1.80391 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 50.1512 | 1.69736 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 167.807 | 5.67290 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −27.4907 | −0.928294 | −0.464147 | − | 0.885758i | \(-0.653639\pi\) | ||||
−0.464147 | + | 0.885758i | \(0.653639\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −27.3618 | −0.922891 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −8.63410 | −0.290890 | −0.145445 | − | 0.989366i | \(-0.546461\pi\) | ||||
−0.145445 | + | 0.989366i | \(0.546461\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33.3515 | −1.12237 | −0.561183 | − | 0.827691i | \(-0.689654\pi\) | ||||
−0.561183 | + | 0.827691i | \(0.689654\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 169.369 | 5.69328 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.0868 | 0.405834 | 0.202917 | − | 0.979196i | \(-0.434958\pi\) | ||||
0.202917 | + | 0.979196i | \(0.434958\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 53.1898 | 1.78393 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 72.2208 | 2.41949 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.11779 | 0.204724 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −80.1812 | −2.68016 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −29.5209 | −0.985674 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −2.68091 | −0.0894132 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.80496 | −0.0601321 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 168.163 | 5.59610 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −76.5703 | −2.54528 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −10.4689 | −0.347615 | −0.173807 | − | 0.984780i | \(-0.555607\pi\) | ||||
−0.173807 | + | 0.984780i | \(0.555607\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 44.4706 | 1.47500 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 35.2074 | 1.16647 | 0.583236 | − | 0.812303i | \(-0.301786\pi\) | ||||
0.583236 | + | 0.812303i | \(0.301786\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −40.2098 | −1.33075 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −59.8198 | −1.97758 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 11.6927 | 0.386127 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −11.4368 | −0.377266 | −0.188633 | − | 0.982048i | \(-0.560406\pi\) | ||||
−0.188633 | + | 0.982048i | \(0.560406\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 51.3782 | 1.69297 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 15.8714 | 0.522414 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −66.1330 | −2.17444 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −9.66489 | −0.317436 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −28.3131 | −0.928921 | −0.464461 | − | 0.885594i | \(-0.653752\pi\) | ||||
−0.464461 | + | 0.885594i | \(0.653752\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −15.4195 | −0.505352 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −14.6913 | −0.480971 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 28.0675 | 0.917906 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −8.47783 | −0.276959 | −0.138479 | − | 0.990365i | \(-0.544221\pi\) | ||||
−0.138479 | + | 0.990365i | \(0.544221\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −25.3806 | −0.828266 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 17.6707 | 0.576049 | 0.288025 | − | 0.957623i | \(-0.407001\pi\) | ||||
0.288025 | + | 0.957623i | \(0.407001\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 0.0322643 | 0.00105067 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 262.113 | 8.52655 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13.9249 | −0.452500 | −0.226250 | − | 0.974069i | \(-0.572647\pi\) | ||||
−0.226250 | + | 0.974069i | \(0.572647\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −40.3885 | −1.31107 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 73.1116 | 2.37080 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 54.2582 | 1.75760 | 0.878798 | − | 0.477193i | \(-0.158346\pi\) | ||||
0.878798 | + | 0.477193i | \(0.158346\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 103.786 | 3.35842 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.81460 | 0.155634 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −41.8867 | −1.35259 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.3165 | 0.332790 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −104.206 | −3.35798 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 118.280 | 3.80757 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −55.5567 | −1.78658 | −0.893292 | − | 0.449476i | \(-0.851611\pi\) | ||||
−0.893292 | + | 0.449476i | \(0.851611\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 5.72994 | 0.184072 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −38.6461 | −1.24021 | −0.620106 | − | 0.784518i | \(-0.712910\pi\) | ||||
−0.620106 | + | 0.784518i | \(0.712910\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −71.4569 | −2.29080 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 157.770 | 5.05270 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 39.0149 | 1.24820 | 0.624099 | − | 0.781345i | \(-0.285466\pi\) | ||||
0.624099 | + | 0.781345i | \(0.285466\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.2439 | 0.455236 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 120.639 | 3.85170 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.0682 | 0.416811 | 0.208406 | − | 0.978042i | \(-0.433173\pi\) | ||||
0.208406 | + | 0.978042i | \(0.433173\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −75.0425 | −2.39105 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 91.9578 | 2.92705 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 27.8151 | 0.884468 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −42.5907 | −1.35294 | −0.676468 | − | 0.736472i | \(-0.736490\pi\) | ||||
−0.676468 | + | 0.736472i | \(0.736490\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 28.7903 | 0.913633 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 30.0769 | 0.953502 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 34.2479 | 1.08464 | 0.542321 | − | 0.840171i | \(-0.317546\pi\) | ||||
0.542321 | + | 0.840171i | \(0.317546\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −64.4284 | −2.03842 |
(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 | 4028.2.a.d.1.19 | ✓ | 19 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4028.2.a.d.1.19 | ✓ | 19 | 1.1 | even | 1 | trivial |