Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4016,2,Mod(1,4016)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4016, 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("4016.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4016 = 2^{4} \cdot 251 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4016.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: | \(32.0679214517\) |
Analytic rank: | \(1\) |
Dimension: | \(14\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 3 x^{13} - 27 x^{12} + 79 x^{11} + 274 x^{10} - 747 x^{9} - 1422 x^{8} + 3287 x^{7} + 4161 x^{6} - 6861 x^{5} - 6676 x^{4} + 5599 x^{3} + 4627 x^{2} - 359 x - 196 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 1004) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.7 | ||
Root | \(0.224635\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4016.1 |
$q$-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 | ||||||||
\(3\) | −0.224635 | −0.129693 | −0.0648465 | − | 0.997895i | \(-0.520656\pi\) | ||||
−0.0648465 | + | 0.997895i | \(0.520656\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −2.42875 | −1.08617 | −0.543085 | − | 0.839678i | \(-0.682744\pi\) | ||||
−0.543085 | + | 0.839678i | \(0.682744\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.24830 | 0.849778 | 0.424889 | − | 0.905245i | \(-0.360313\pi\) | ||||
0.424889 | + | 0.905245i | \(0.360313\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.94954 | −0.983180 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.64215 | −0.495125 | −0.247563 | − | 0.968872i | \(-0.579630\pi\) | ||||
−0.247563 | + | 0.968872i | \(0.579630\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.22381 | 1.72617 | 0.863087 | − | 0.505055i | \(-0.168528\pi\) | ||||
0.863087 | + | 0.505055i | \(0.168528\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.545582 | 0.140869 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.62535 | −0.394206 | −0.197103 | − | 0.980383i | \(-0.563153\pi\) | ||||
−0.197103 | + | 0.980383i | \(0.563153\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −7.83395 | −1.79723 | −0.898615 | − | 0.438738i | \(-0.855426\pi\) | ||||
−0.898615 | + | 0.438738i | \(0.855426\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.505047 | −0.110210 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 6.98629 | 1.45674 | 0.728371 | − | 0.685183i | \(-0.240278\pi\) | ||||
0.728371 | + | 0.685183i | \(0.240278\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0.898832 | 0.179766 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1.33647 | 0.257204 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.44758 | 1.56868 | 0.784338 | − | 0.620334i | \(-0.213003\pi\) | ||||
0.784338 | + | 0.620334i | \(0.213003\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7.71452 | −1.38557 | −0.692785 | − | 0.721145i | \(-0.743616\pi\) | ||||
−0.692785 | + | 0.721145i | \(0.743616\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.368883 | 0.0642143 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −5.46056 | −0.923004 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 9.24659 | 1.52013 | 0.760065 | − | 0.649847i | \(-0.225167\pi\) | ||||
0.760065 | + | 0.649847i | \(0.225167\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.39808 | −0.223873 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 8.41207 | 1.31375 | 0.656873 | − | 0.754002i | \(-0.271879\pi\) | ||||
0.656873 | + | 0.754002i | \(0.271879\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.97586 | −0.606313 | −0.303157 | − | 0.952941i | \(-0.598041\pi\) | ||||
−0.303157 | + | 0.952941i | \(0.598041\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.16370 | 1.06790 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0.735589 | 0.107297 | 0.0536484 | − | 0.998560i | \(-0.482915\pi\) | ||||
0.0536484 | + | 0.998560i | \(0.482915\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.94514 | −0.277877 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.365111 | 0.0511258 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.9903 | −1.50963 | −0.754817 | − | 0.655936i | \(-0.772274\pi\) | ||||
−0.754817 | + | 0.655936i | \(0.772274\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.98836 | 0.537791 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 1.75978 | 0.233088 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −8.63639 | −1.12436 | −0.562181 | − | 0.827014i | \(-0.690038\pi\) | ||||
−0.562181 | + | 0.827014i | \(0.690038\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −8.71829 | −1.11626 | −0.558131 | − | 0.829753i | \(-0.688481\pi\) | ||||
−0.558131 | + | 0.829753i | \(0.688481\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.63145 | −0.835485 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −15.1161 | −1.87492 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −4.17803 | −0.510428 | −0.255214 | − | 0.966885i | \(-0.582146\pi\) | ||||
−0.255214 | + | 0.966885i | \(0.582146\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.56936 | −0.188929 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 4.49162 | 0.533058 | 0.266529 | − | 0.963827i | \(-0.414123\pi\) | ||||
0.266529 | + | 0.963827i | \(0.414123\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.2570 | −1.43458 | −0.717288 | − | 0.696777i | \(-0.754617\pi\) | ||||
−0.717288 | + | 0.696777i | \(0.754617\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.201909 | −0.0233144 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −3.69204 | −0.420747 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.66788 | −0.412669 | −0.206334 | − | 0.978482i | \(-0.566153\pi\) | ||||
−0.206334 | + | 0.978482i | \(0.566153\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 8.54840 | 0.949822 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −1.17546 | −0.129023 | −0.0645116 | − | 0.997917i | \(-0.520549\pi\) | ||||
−0.0645116 | + | 0.997917i | \(0.520549\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.94758 | 0.428175 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.89762 | −0.203446 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 17.2264 | 1.82599 | 0.912996 | − | 0.407968i | \(-0.133762\pi\) | ||||
0.912996 | + | 0.407968i | \(0.133762\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.9930 | 1.46687 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.73295 | 0.179699 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 19.0267 | 1.95210 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 9.08104 | 0.922040 | 0.461020 | − | 0.887390i | \(-0.347484\pi\) | ||||
0.461020 | + | 0.887390i | \(0.347484\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.84357 | 0.486797 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.31035 | 0.130385 | 0.0651924 | − | 0.997873i | \(-0.479234\pi\) | ||||
0.0651924 | + | 0.997873i | \(0.479234\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.17455 | 0.509863 | 0.254932 | − | 0.966959i | \(-0.417947\pi\) | ||||
0.254932 | + | 0.966959i | \(0.417947\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 1.22663 | 0.119707 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −15.5548 | −1.50374 | −0.751869 | − | 0.659313i | \(-0.770847\pi\) | ||||
−0.751869 | + | 0.659313i | \(0.770847\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.94967 | −0.761441 | −0.380720 | − | 0.924690i | \(-0.624324\pi\) | ||||
−0.380720 | + | 0.924690i | \(0.624324\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.07710 | −0.197150 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −4.80047 | −0.451590 | −0.225795 | − | 0.974175i | \(-0.572498\pi\) | ||||
−0.225795 | + | 0.974175i | \(0.572498\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −16.9680 | −1.58227 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −18.3574 | −1.69714 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.65429 | −0.334988 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.30336 | −0.754851 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.88964 | −0.170383 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.96072 | 0.890914 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −17.1925 | −1.52559 | −0.762795 | − | 0.646641i | \(-0.776173\pi\) | ||||
−0.762795 | + | 0.646641i | \(0.776173\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.893117 | 0.0786345 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.30291 | 0.375947 | 0.187974 | − | 0.982174i | \(-0.439808\pi\) | ||||
0.187974 | + | 0.982174i | \(0.439808\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −17.6131 | −1.52725 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −3.24596 | −0.279368 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 0.00645063 | 0.000551114 0 | 0.000275557 | − | 1.00000i | \(-0.499912\pi\) | ||||
0.000275557 | 1.00000i | \(0.499912\pi\) | ||||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.181781 | 0.0154185 | 0.00770923 | − | 0.999970i | \(-0.497546\pi\) | ||||
0.00770923 | + | 0.999970i | \(0.497546\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −0.165239 | −0.0139156 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −10.2204 | −0.854673 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −20.5171 | −1.70385 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.436946 | 0.0360387 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −23.6239 | −1.93535 | −0.967673 | − | 0.252209i | \(-0.918843\pi\) | ||||
−0.967673 | + | 0.252209i | \(0.918843\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2.45736 | −0.199977 | −0.0999886 | − | 0.994989i | \(-0.531881\pi\) | ||||
−0.0999886 | + | 0.994989i | \(0.531881\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 4.79405 | 0.387576 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 18.7367 | 1.50496 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 12.7494 | 1.01751 | 0.508755 | − | 0.860912i | \(-0.330106\pi\) | ||||
0.508755 | + | 0.860912i | \(0.330106\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.46880 | 0.195789 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.7073 | 1.23791 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −18.8119 | −1.47346 | −0.736730 | − | 0.676187i | \(-0.763631\pi\) | ||||
−0.736730 | + | 0.676187i | \(0.763631\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −0.895925 | −0.0697476 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.91688 | −0.457862 | −0.228931 | − | 0.973443i | \(-0.573523\pi\) | ||||
−0.228931 | + | 0.973443i | \(0.573523\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 25.7358 | 1.97968 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 23.1065 | 1.76700 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.0221 | −0.990053 | −0.495027 | − | 0.868878i | \(-0.664842\pi\) | ||||
−0.495027 | + | 0.868878i | \(0.664842\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.02085 | 0.152762 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.94003 | 0.145822 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.3014 | −0.844710 | −0.422355 | − | 0.906431i | \(-0.638796\pi\) | ||||
−0.422355 | + | 0.906431i | \(0.638796\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −10.6066 | −0.788379 | −0.394190 | − | 0.919029i | \(-0.628975\pi\) | ||||
−0.394190 | + | 0.919029i | \(0.628975\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.95843 | 0.144771 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −22.4577 | −1.65112 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.66907 | 0.195182 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 3.00479 | 0.218567 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 10.1524 | 0.734599 | 0.367300 | − | 0.930103i | \(-0.380282\pi\) | ||||
0.367300 | + | 0.930103i | \(0.380282\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.19678 | −0.661999 | −0.330999 | − | 0.943631i | \(-0.607386\pi\) | ||||
−0.330999 | + | 0.943631i | \(0.607386\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 3.39560 | 0.243164 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −20.1222 | −1.43365 | −0.716825 | − | 0.697253i | \(-0.754405\pi\) | ||||
−0.716825 | + | 0.697253i | \(0.754405\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.2239 | 0.866531 | 0.433266 | − | 0.901266i | \(-0.357361\pi\) | ||||
0.433266 | + | 0.901266i | \(0.357361\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.938532 | 0.0661989 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 18.9927 | 1.33303 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −20.4308 | −1.42695 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −20.6063 | −1.43224 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 12.8645 | 0.889854 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −24.4289 | −1.68175 | −0.840877 | − | 0.541227i | \(-0.817960\pi\) | ||||
−0.840877 | + | 0.541227i | \(0.817960\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.00897 | −0.0691338 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 9.65638 | 0.658560 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −17.3446 | −1.17743 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.75335 | 0.186054 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −10.1159 | −0.680469 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.9845 | −1.33826 | −0.669130 | − | 0.743145i | \(-0.733333\pi\) | ||||
−0.669130 | + | 0.743145i | \(0.733333\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2.65114 | −0.176743 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.68676 | −0.244699 | −0.122349 | − | 0.992487i | \(-0.539043\pi\) | ||||
−0.122349 | + | 0.992487i | \(0.539043\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.96570 | 0.129897 | 0.0649485 | − | 0.997889i | \(-0.479312\pi\) | ||||
0.0649485 | + | 0.997889i | \(0.479312\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.829360 | 0.0545679 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −7.53560 | −0.493674 | −0.246837 | − | 0.969057i | \(-0.579391\pi\) | ||||
−0.246837 | + | 0.969057i | \(0.579391\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.78656 | −0.116543 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.823933 | 0.0535202 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 7.87974 | 0.509698 | 0.254849 | − | 0.966981i | \(-0.417974\pi\) | ||||
0.254849 | + | 0.966981i | \(0.417974\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.20915 | 0.464382 | 0.232191 | − | 0.972670i | \(-0.425411\pi\) | ||||
0.232191 | + | 0.972670i | \(0.425411\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −5.92969 | −0.380390 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 4.72426 | 0.301822 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −48.7570 | −3.10233 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.264049 | 0.0167334 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.00000 | 0.0631194 | ||||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −11.4725 | −0.721270 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.886764 | −0.0555313 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 25.9988 | 1.62176 | 0.810879 | − | 0.585213i | \(-0.198989\pi\) | ||||
0.810879 | + | 0.585213i | \(0.198989\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 20.7891 | 1.29177 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −24.9165 | −1.54229 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 31.1491 | 1.92074 | 0.960369 | − | 0.278731i | \(-0.0899139\pi\) | ||||
0.960369 | + | 0.278731i | \(0.0899139\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 26.6927 | 1.63972 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.86964 | −0.236818 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 3.41438 | 0.208178 | 0.104089 | − | 0.994568i | \(-0.466807\pi\) | ||||
0.104089 | + | 0.994568i | \(0.466807\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −22.8379 | −1.38730 | −0.693652 | − | 0.720310i | \(-0.743999\pi\) | ||||
−0.693652 | + | 0.720310i | \(0.743999\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −3.14331 | −0.190242 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.47601 | −0.0890069 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.04269 | −0.242902 | −0.121451 | − | 0.992597i | \(-0.538755\pi\) | ||||
−0.121451 | + | 0.992597i | \(0.538755\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 22.7543 | 1.36226 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.35718 | −0.140618 | −0.0703088 | − | 0.997525i | \(-0.522398\pi\) | ||||
−0.0703088 | + | 0.997525i | \(0.522398\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −20.1634 | −1.19859 | −0.599296 | − | 0.800528i | \(-0.704553\pi\) | ||||
−0.599296 | + | 0.800528i | \(0.704553\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −4.27406 | −0.253173 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 18.9129 | 1.11639 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −14.3582 | −0.844601 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.03992 | −0.119582 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −12.9511 | −0.756610 | −0.378305 | − | 0.925681i | \(-0.623493\pi\) | ||||
−0.378305 | + | 0.925681i | \(0.623493\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 20.9757 | 1.22125 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −2.19468 | −0.127348 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 43.4814 | 2.51459 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −8.93894 | −0.515232 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.294350 | −0.0169100 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 21.1746 | 1.21245 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −6.71716 | −0.383369 | −0.191684 | − | 0.981457i | \(-0.561395\pi\) | ||||
−0.191684 | + | 0.981457i | \(0.561395\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.16238 | −0.0661257 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −15.8087 | −0.896429 | −0.448214 | − | 0.893926i | \(-0.647940\pi\) | ||||
−0.448214 | + | 0.893926i | \(0.647940\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −27.6720 | −1.56411 | −0.782057 | − | 0.623207i | \(-0.785830\pi\) | ||||
−0.782057 | + | 0.623207i | \(0.785830\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 16.1061 | 0.907479 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.14088 | −0.120244 | −0.0601218 | − | 0.998191i | \(-0.519149\pi\) | ||||
−0.0601218 | + | 0.998191i | \(0.519149\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −13.8721 | −0.776691 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 3.49414 | 0.195024 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 12.7329 | 0.708479 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.59416 | 0.310308 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1.78577 | 0.0987535 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 1.65383 | 0.0911784 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.0310 | 0.716246 | 0.358123 | − | 0.933674i | \(-0.383417\pi\) | ||||
0.358123 | + | 0.933674i | \(0.383417\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −27.2732 | −1.49456 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 10.1474 | 0.554412 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.70826 | −0.147528 | −0.0737642 | − | 0.997276i | \(-0.523501\pi\) | ||||
−0.0737642 | + | 0.997276i | \(0.523501\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.07835 | 0.0585680 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 12.6684 | 0.686030 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −20.1114 | −1.08591 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 3.81159 | 0.205209 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 26.4326 | 1.41898 | 0.709489 | − | 0.704716i | \(-0.248926\pi\) | ||||
0.709489 | + | 0.704716i | \(0.248926\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.6941 | −0.786559 | −0.393280 | − | 0.919419i | \(-0.628660\pi\) | ||||
−0.393280 | + | 0.919419i | \(0.628660\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 8.31796 | 0.443980 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −12.0164 | −0.639566 | −0.319783 | − | 0.947491i | \(-0.603610\pi\) | ||||
−0.319783 | + | 0.947491i | \(0.603610\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −10.9090 | −0.578992 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0.820879 | 0.0434455 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −32.2776 | −1.70354 | −0.851772 | − | 0.523912i | \(-0.824472\pi\) | ||||
−0.851772 | + | 0.523912i | \(0.824472\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 42.3707 | 2.23004 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 1.86522 | 0.0978988 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 29.7693 | 1.55819 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.7888 | 1.45056 | 0.725282 | − | 0.688452i | \(-0.241709\pi\) | ||||
0.725282 | + | 0.688452i | \(0.241709\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −24.8117 | −1.29165 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −24.7095 | −1.28285 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 23.2716 | 1.20496 | 0.602478 | − | 0.798135i | \(-0.294180\pi\) | ||||
0.602478 | + | 0.798135i | \(0.294180\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.23752 | −0.115545 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 52.5761 | 2.70781 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −21.4700 | −1.10284 | −0.551420 | − | 0.834228i | \(-0.685914\pi\) | ||||
−0.551420 | + | 0.834228i | \(0.685914\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.86204 | 0.197858 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 27.7055 | 1.41569 | 0.707843 | − | 0.706370i | \(-0.249669\pi\) | ||||
0.707843 | + | 0.706370i | \(0.249669\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.96704 | 0.457003 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.7270 | 0.596115 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 22.2832 | 1.12980 | 0.564901 | − | 0.825158i | \(-0.308914\pi\) | ||||
0.564901 | + | 0.825158i | \(0.308914\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.3552 | −0.574257 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −0.966584 | −0.0487577 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.90837 | 0.448229 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.54049 | −0.127504 | −0.0637518 | − | 0.997966i | \(-0.520307\pi\) | ||||
−0.0637518 | + | 0.997966i | \(0.520307\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3.95651 | 0.198073 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.42313 | 0.0710676 | 0.0355338 | − | 0.999368i | \(-0.488687\pi\) | ||||
0.0355338 | + | 0.999368i | \(0.488687\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −48.0137 | −2.39173 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −20.7619 | −1.03167 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −15.1842 | −0.752655 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.83345 | 0.436786 | 0.218393 | − | 0.975861i | \(-0.429919\pi\) | ||||
0.218393 | + | 0.975861i | \(0.429919\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −0.00144903 | −7.14756e−5 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −19.4172 | −0.955459 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.85490 | 0.140141 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −0.0408343 | −0.00199967 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −34.0729 | −1.66457 | −0.832286 | − | 0.554346i | \(-0.812968\pi\) | ||||
−0.832286 | + | 0.554346i | \(0.812968\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 29.2308 | 1.42462 | 0.712311 | − | 0.701864i | \(-0.247649\pi\) | ||||
0.712311 | + | 0.701864i | \(0.247649\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.16965 | −0.105492 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.46092 | −0.0708650 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −19.6013 | −0.948576 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 2.29586 | 0.110845 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.82572 | 0.232447 | 0.116223 | − | 0.993223i | \(-0.462921\pi\) | ||||
0.116223 | + | 0.993223i | \(0.462921\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −23.7354 | −1.14065 | −0.570326 | − | 0.821418i | \(-0.693183\pi\) | ||||
−0.570326 | + | 0.821418i | \(0.693183\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.60884 | 0.220977 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −54.7302 | −2.61810 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 30.8566 | 1.47271 | 0.736354 | − | 0.676597i | \(-0.236546\pi\) | ||||
0.736354 | + | 0.676597i | \(0.236546\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 5.73727 | 0.273203 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −37.8298 | −1.79735 | −0.898674 | − | 0.438616i | \(-0.855469\pi\) | ||||
−0.898674 | + | 0.438616i | \(0.855469\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −41.8386 | −1.98334 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 5.30675 | 0.251001 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 38.1436 | 1.80011 | 0.900054 | − | 0.435779i | \(-0.143527\pi\) | ||||
0.900054 | + | 0.435779i | \(0.143527\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −13.8138 | −0.650469 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0.552009 | 0.0259356 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −33.9855 | −1.59327 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −20.1481 | −0.942489 | −0.471244 | − | 0.882003i | \(-0.656195\pi\) | ||||
−0.471244 | + | 0.882003i | \(0.656195\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2.17224 | −0.101392 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −0.500312 | −0.0233019 | −0.0116509 | − | 0.999932i | \(-0.503709\pi\) | ||||
−0.0116509 | + | 0.999932i | \(0.503709\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −4.86536 | −0.226113 | −0.113056 | − | 0.993589i | \(-0.536064\pi\) | ||||
−0.113056 | + | 0.993589i | \(0.536064\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.20890 | −0.195183 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.56899 | 0.165153 | 0.0825765 | − | 0.996585i | \(-0.473685\pi\) | ||||
0.0825765 | + | 0.996585i | \(0.473685\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −9.39348 | −0.433751 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.86395 | −0.131964 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.52894 | 0.300201 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.04140 | −0.323082 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 32.4163 | 1.48424 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −0.936786 | −0.0428028 | −0.0214014 | − | 0.999771i | \(-0.506813\pi\) | ||||
−0.0214014 | + | 0.999771i | \(0.506813\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 57.5490 | 2.62401 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.52840 | −0.160548 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −22.0556 | −1.00149 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 19.2487 | 0.872242 | 0.436121 | − | 0.899888i | \(-0.356352\pi\) | ||||
0.436121 | + | 0.899888i | \(0.356352\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.22580 | 0.191097 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 15.5938 | 0.703739 | 0.351870 | − | 0.936049i | \(-0.385546\pi\) | ||||
0.351870 | + | 0.936049i | \(0.385546\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −13.7303 | −0.618382 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −11.7638 | −0.528745 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 10.0985 | 0.452981 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.3922 | 1.62914 | 0.814570 | − | 0.580066i | \(-0.196973\pi\) | ||||
0.814570 | + | 0.580066i | \(0.196973\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 1.32914 | 0.0593814 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −9.65241 | −0.430380 | −0.215190 | − | 0.976572i | \(-0.569037\pi\) | ||||
−0.215190 | + | 0.976572i | \(0.569037\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.18252 | −0.141620 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5.78116 | −0.256750 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 16.1978 | 0.717955 | 0.358977 | − | 0.933346i | \(-0.383126\pi\) | ||||
0.358977 | + | 0.933346i | \(0.383126\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.5575 | −1.21907 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −10.4699 | −0.462256 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −12.5677 | −0.553799 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.20794 | −0.0531253 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.92522 | 0.128403 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.2198 | −0.622981 | −0.311491 | − | 0.950249i | \(-0.600828\pi\) | ||||
−0.311491 | + | 0.950249i | \(0.600828\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.66535 | −0.160275 | −0.0801373 | − | 0.996784i | \(-0.525536\pi\) | ||||
−0.0801373 | + | 0.996784i | \(0.525536\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −0.453952 | −0.0198121 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 12.5388 | 0.546200 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 25.8083 | 1.12210 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 25.4734 | 1.10545 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 52.3552 | 2.26775 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 37.7787 | 1.63332 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.53870 | 0.109553 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 3.19420 | 0.137584 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −17.4901 | −0.751959 | −0.375980 | − | 0.926628i | \(-0.622694\pi\) | ||||
−0.375980 | + | 0.926628i | \(0.622694\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 2.38260 | 0.102247 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.3078 | 0.827054 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.1597 | −1.11851 | −0.559254 | − | 0.828996i | \(-0.688912\pi\) | ||||
−0.559254 | + | 0.828996i | \(0.688912\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 25.7149 | 1.09749 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −66.1778 | −2.81927 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.24650 | −0.350677 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 5.04477 | 0.214139 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.8690 | −0.841879 | −0.420939 | − | 0.907089i | \(-0.638299\pi\) | ||||
−0.420939 | + | 0.907089i | \(0.638299\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −24.7450 | −1.04660 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.599565 | −0.0253137 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 26.1613 | 1.10257 | 0.551284 | − | 0.834318i | \(-0.314138\pi\) | ||||
0.551284 | + | 0.834318i | \(0.314138\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.6591 | 0.490504 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 19.2194 | 0.807138 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −20.8786 | −0.875277 | −0.437638 | − | 0.899151i | \(-0.644185\pi\) | ||||
−0.437638 | + | 0.899151i | \(0.644185\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −43.1297 | −1.80492 | −0.902461 | − | 0.430772i | \(-0.858241\pi\) | ||||
−0.902461 | + | 0.430772i | \(0.858241\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2.28057 | −0.0952723 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.27950 | 0.261873 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −17.6062 | −0.732958 | −0.366479 | − | 0.930426i | \(-0.619437\pi\) | ||||
−0.366479 | + | 0.930426i | \(0.619437\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 2.06592 | 0.0858566 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −2.64278 | −0.109641 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.0477 | 0.747458 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 44.5855 | 1.84338 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 45.5328 | 1.87934 | 0.939670 | − | 0.342083i | \(-0.111132\pi\) | ||||
0.939670 | + | 0.342083i | \(0.111132\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 60.4351 | 2.49019 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 4.52015 | 0.185934 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.18374 | 0.130741 | 0.0653703 | − | 0.997861i | \(-0.479177\pi\) | ||||
0.0653703 | + | 0.997861i | \(0.479177\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 8.87535 | 0.363854 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.74592 | −0.112383 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.93843 | −0.406073 | −0.203037 | − | 0.979171i | \(-0.565081\pi\) | ||||
−0.203037 | + | 0.979171i | \(0.565081\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11.1826 | 0.456147 | 0.228074 | − | 0.973644i | \(-0.426757\pi\) | ||||
0.228074 | + | 0.973644i | \(0.426757\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 12.3233 | 0.501843 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 20.1668 | 0.819897 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18.8713 | 0.765961 | 0.382981 | − | 0.923756i | \(-0.374898\pi\) | ||||
0.382981 | + | 0.923756i | \(0.374898\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −4.26642 | −0.172884 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.57817 | 0.185213 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 42.1894 | 1.70401 | 0.852007 | − | 0.523531i | \(-0.175386\pi\) | ||||
0.852007 | + | 0.523531i | \(0.175386\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 4.58948 | 0.185065 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 16.7840 | 0.675696 | 0.337848 | − | 0.941201i | \(-0.390301\pi\) | ||||
0.337848 | + | 0.941201i | \(0.390301\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 31.7125 | 1.27463 | 0.637317 | − | 0.770602i | \(-0.280044\pi\) | ||||
0.637317 | + | 0.770602i | \(0.280044\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 9.33699 | 0.374681 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 38.7301 | 1.55169 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −28.6863 | −1.14745 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.88981 | −0.115408 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −15.0290 | −0.599245 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6.58208 | 0.262028 | 0.131014 | − | 0.991381i | \(-0.458177\pi\) | ||||
0.131014 | + | 0.991381i | \(0.458177\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.48757 | 0.218112 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 41.7564 | 1.65705 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −12.1062 | −0.479665 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −13.2482 | −0.524092 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −40.0105 | −1.58032 | −0.790161 | − | 0.612900i | \(-0.790003\pi\) | ||||
−0.790161 | + | 0.612900i | \(0.790003\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 24.1750 | 0.953370 | 0.476685 | − | 0.879074i | \(-0.341838\pi\) | ||||
0.476685 | + | 0.879074i | \(0.341838\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.16916 | −0.0854105 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 12.5910 | 0.495004 | 0.247502 | − | 0.968887i | \(-0.420390\pi\) | ||||
0.247502 | + | 0.968887i | \(0.420390\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14.1822 | 0.556701 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.89619 | 0.152704 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 34.6001 | 1.35401 | 0.677003 | − | 0.735981i | \(-0.263279\pi\) | ||||
0.677003 | + | 0.735981i | \(0.263279\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.4507 | −0.408343 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 36.1526 | 1.41045 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −31.6427 | −1.23263 | −0.616313 | − | 0.787502i | \(-0.711374\pi\) | ||||
−0.616313 | + | 0.787502i | \(0.711374\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.5221 | 0.564843 | 0.282422 | − | 0.959290i | \(-0.408862\pi\) | ||||
0.282422 | + | 0.959290i | \(0.408862\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.27238 | 0.0882520 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 42.7778 | 1.65885 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 59.0172 | 2.28516 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.48921 | 0.173563 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.3167 | 0.552690 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11.7338 | −0.452304 | −0.226152 | − | 0.974092i | \(-0.572615\pi\) | ||||
−0.226152 | + | 0.974092i | \(0.572615\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.20126 | 0.0462367 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 2.50545 | 0.0962923 | 0.0481461 | − | 0.998840i | \(-0.484669\pi\) | ||||
0.0481461 | + | 0.998840i | \(0.484669\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.4169 | 0.783529 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0.828175 | 0.0317357 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −14.4053 | −0.551203 | −0.275602 | − | 0.961272i | \(-0.588877\pi\) | ||||
−0.275602 | + | 0.961272i | \(0.588877\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.0156670 | −0.000598604 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.441564 | −0.0168467 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −68.4015 | −2.60589 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.1265 | −0.423271 | −0.211635 | − | 0.977349i | \(-0.567879\pi\) | ||||
−0.211635 | + | 0.977349i | \(0.567879\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 10.8898 | 0.413670 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.441501 | −0.0167471 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −13.6726 | −0.517887 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.69276 | 0.0640260 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 14.5012 | 0.547704 | 0.273852 | − | 0.961772i | \(-0.411702\pi\) | ||||
0.273852 | + | 0.961772i | \(0.411702\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −72.4373 | −2.73202 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.401324 | 0.0151147 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.94606 | 0.110798 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 19.8600 | 0.745859 | 0.372929 | − | 0.927860i | \(-0.378353\pi\) | ||||
0.372929 | + | 0.927860i | \(0.378353\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 10.8186 | 0.405728 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −53.8959 | −2.01842 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 24.8228 | 0.928320 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −1.77006 | −0.0661042 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −6.68379 | −0.249263 | −0.124632 | − | 0.992203i | \(-0.539775\pi\) | ||||
−0.124632 | + | 0.992203i | \(0.539775\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 11.6339 | 0.433271 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.61943 | −0.0602271 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 7.59295 | 0.281995 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.6007 | 0.504421 | 0.252210 | − | 0.967672i | \(-0.418842\pi\) | ||||
0.252210 | + | 0.967672i | \(0.418842\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −24.3132 | −0.900488 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.46218 | 0.239012 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.562255 | 0.0207674 | 0.0103837 | − | 0.999946i | \(-0.496695\pi\) | ||||
0.0103837 | + | 0.999946i | \(0.496695\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1.06123 | −0.0391442 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6.86094 | 0.252726 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −30.9406 | −1.13817 | −0.569085 | − | 0.822279i | \(-0.692702\pi\) | ||||
−0.569085 | + | 0.822279i | \(0.692702\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 10.9525 | 0.402351 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −10.2863 | −0.377369 | −0.188685 | − | 0.982038i | \(-0.560422\pi\) | ||||
−0.188685 | + | 0.982038i | \(0.560422\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 57.3766 | 2.10212 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.46706 | 0.126853 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −34.9718 | −1.27784 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.1131 | 0.843410 | 0.421705 | − | 0.906733i | \(-0.361432\pi\) | ||||
0.421705 | + | 0.906733i | \(0.361432\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −0.224635 | −0.00818615 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 5.96832 | 0.217209 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40.0512 | 1.45569 | 0.727843 | − | 0.685743i | \(-0.240523\pi\) | ||||
0.727843 | + | 0.685743i | \(0.240523\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.57712 | 0.0935436 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 31.9526 | 1.15828 | 0.579141 | − | 0.815228i | \(-0.303388\pi\) | ||||
0.579141 | + | 0.815228i | \(0.303388\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −17.8733 | −0.647055 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −11.6435 | −0.420973 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −53.7513 | −1.94085 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.2993 | −0.407463 | −0.203732 | − | 0.979027i | \(-0.565307\pi\) | ||||
−0.203732 | + | 0.979027i | \(0.565307\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5.84023 | −0.210331 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 4.44963 | 0.160042 | 0.0800210 | − | 0.996793i | \(-0.474501\pi\) | ||||
0.0800210 | + | 0.996793i | \(0.474501\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.93406 | −0.249079 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.66996 | −0.167534 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −65.8997 | −2.36110 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.37590 | −0.263930 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 11.2900 | 0.403470 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −30.9650 | −1.10519 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 12.2070 | 0.435133 | 0.217566 | − | 0.976046i | \(-0.430188\pi\) | ||||
0.217566 | + | 0.976046i | \(0.430188\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −6.99718 | −0.249106 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −10.7929 | −0.383751 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −54.2610 | −1.92686 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −5.99611 | −0.212660 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −27.5856 | −0.977131 | −0.488565 | − | 0.872527i | \(-0.662480\pi\) | ||||
−0.488565 | + | 0.872527i | \(0.662480\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.19559 | −0.0422970 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −50.8099 | −1.79528 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 20.1278 | 0.710295 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −38.1491 | −1.34458 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −0.766988 | −0.0269993 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −17.3522 | −0.610071 | −0.305036 | − | 0.952341i | \(-0.598668\pi\) | ||||
−0.305036 | + | 0.952341i | \(0.598668\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 22.4430 | 0.788081 | 0.394041 | − | 0.919093i | \(-0.371077\pi\) | ||||
0.394041 | + | 0.919093i | \(0.371077\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.13019 | 0.179924 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 45.6894 | 1.60043 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 31.1467 | 1.08968 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −41.2729 | −1.44219 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 2.18088 | 0.0761133 | 0.0380567 | − | 0.999276i | \(-0.487883\pi\) | ||||
0.0380567 | + | 0.999276i | \(0.487883\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.22243 | 0.216900 | 0.108450 | − | 0.994102i | \(-0.465411\pi\) | ||||
0.108450 | + | 0.994102i | \(0.465411\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.331564 | 0.0115436 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −17.5574 | −0.610530 | −0.305265 | − | 0.952267i | \(-0.598745\pi\) | ||||
−0.305265 | + | 0.952267i | \(0.598745\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −0.230530 | −0.00800664 | −0.00400332 | − | 0.999992i | \(-0.501274\pi\) | ||||
−0.00400332 | + | 0.999992i | \(0.501274\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0.908130 | 0.0315027 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.16154 | 0.109541 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 14.3706 | 0.497316 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −10.3103 | −0.356374 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 42.3974 | 1.46372 | 0.731860 | − | 0.681455i | \(-0.238652\pi\) | ||||
0.731860 | + | 0.681455i | \(0.238652\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 42.3615 | 1.46074 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0.529504 | 0.0182371 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −62.5059 | −2.15027 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.6685 | −0.641456 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 4.52941 | 0.155449 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 64.5994 | 2.21444 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −27.0749 | −0.927026 | −0.463513 | − | 0.886090i | \(-0.653411\pi\) | ||||
−0.463513 | + | 0.886090i | \(0.653411\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −56.1200 | −1.91926 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 10.5979 | 0.362017 | 0.181008 | − | 0.983482i | \(-0.442064\pi\) | ||||
0.181008 | + | 0.983482i | \(0.442064\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 57.4152 | 1.95898 | 0.979491 | − | 0.201489i | \(-0.0645781\pi\) | ||||
0.979491 | + | 0.201489i | \(0.0645781\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.24849 | −0.144788 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −31.6763 | −1.07827 | −0.539136 | − | 0.842219i | \(-0.681249\pi\) | ||||
−0.539136 | + | 0.842219i | \(0.681249\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 31.6275 | 1.07537 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.22536 | 0.109539 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 6.02319 | 0.204323 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −26.0033 | −0.881088 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −26.7849 | −0.906531 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 22.3947 | 0.757079 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 23.1500 | 0.781719 | 0.390860 | − | 0.920450i | \(-0.372178\pi\) | ||||
0.390860 | + | 0.920450i | \(0.372178\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2.90926 | 0.0981270 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 9.26056 | 0.311996 | 0.155998 | − | 0.987757i | \(-0.450141\pi\) | ||||
0.155998 | + | 0.987757i | \(0.450141\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 34.1105 | 1.14791 | 0.573954 | − | 0.818887i | \(-0.305409\pi\) | ||||
0.573954 | + | 0.818887i | \(0.305409\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.71186 | −0.158387 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −36.0360 | −1.20997 | −0.604986 | − | 0.796236i | \(-0.706821\pi\) | ||||
−0.604986 | + | 0.796236i | \(0.706821\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −38.6540 | −1.29641 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −14.0377 | −0.470281 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.76257 | −0.192837 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 27.4484 | 0.917499 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −9.76742 | −0.326125 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −65.1690 | −2.17351 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.8631 | 0.595107 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.00800 | 0.0668219 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 25.7607 | 0.856314 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −41.7267 | −1.38551 | −0.692756 | − | 0.721172i | \(-0.743604\pi\) | ||||
−0.692756 | + | 0.721172i | \(0.743604\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −3.86493 | −0.128192 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 32.2971 | 1.07005 | 0.535026 | − | 0.844836i | \(-0.320302\pi\) | ||||
0.535026 | + | 0.844836i | \(0.320302\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.93027 | 0.0638827 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.75654 | −0.157246 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 9.67425 | 0.319472 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −37.3668 | −1.23262 | −0.616308 | − | 0.787505i | \(-0.711372\pi\) | ||||
−0.616308 | + | 0.787505i | \(0.711372\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1.50891 | 0.0497202 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 27.9550 | 0.920151 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.31113 | 0.273268 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −15.2625 | −0.501287 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.07810 | 0.0681804 | 0.0340902 | − | 0.999419i | \(-0.489147\pi\) | ||||
0.0340902 | + | 0.999419i | \(0.489147\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 15.2381 | 0.499410 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 3.55118 | 0.116260 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −6.48250 | −0.212000 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.54512 | −0.148483 | −0.0742413 | − | 0.997240i | \(-0.523654\pi\) | ||||
−0.0742413 | + | 0.997240i | \(0.523654\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 6.21610 | 0.202855 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.5658 | −0.898620 | −0.449310 | − | 0.893376i | \(-0.648330\pi\) | ||||
−0.449310 | + | 0.893376i | \(0.648330\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 58.7692 | 1.91379 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −7.29790 | −0.237401 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 40.4811 | 1.31546 | 0.657729 | − | 0.753255i | \(-0.271517\pi\) | ||||
0.657729 | + | 0.753255i | \(0.271517\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −76.2854 | −2.47633 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0.480915 | 0.0155948 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −33.9206 | −1.09880 | −0.549398 | − | 0.835561i | \(-0.685143\pi\) | ||||
−0.549398 | + | 0.835561i | \(0.685143\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −24.6576 | −0.797900 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.11617 | 0.100731 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.0145030 | 0.000468325 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 28.5139 | 0.919802 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 45.8794 | 1.47844 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 22.3367 | 0.719044 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −15.0645 | −0.484441 | −0.242221 | − | 0.970221i | \(-0.577876\pi\) | ||||
−0.242221 | + | 0.970221i | \(0.577876\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.86026 | −0.0918848 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.61438 | 0.115991 | 0.0579956 | − | 0.998317i | \(-0.481529\pi\) | ||||
0.0579956 | + | 0.998317i | \(0.481529\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.408699 | 0.0131023 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.25664 | −0.0402448 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 40.6929 | 1.30188 | 0.650940 | − | 0.759129i | \(-0.274375\pi\) | ||||
0.650940 | + | 0.759129i | \(0.274375\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −28.2882 | −0.904095 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 23.4479 | 0.748633 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 17.5420 | 0.559504 | 0.279752 | − | 0.960072i | \(-0.409748\pi\) | ||||
0.279752 | + | 0.960072i | \(0.409748\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 48.8719 | 1.55719 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.371507 | −0.0118252 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −27.7765 | −0.883242 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 47.1532 | 1.49787 | 0.748936 | − | 0.662643i | \(-0.230565\pi\) | ||||
0.748936 | + | 0.662643i | \(0.230565\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −2.92721 | −0.0928920 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −29.6889 | −0.941201 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −53.5944 | −1.69735 | −0.848676 | − | 0.528912i | \(-0.822600\pi\) | ||||
−0.848676 | + | 0.528912i | \(0.822600\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 12.3578 | 0.390984 |
(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 | 4016.2.a.j.1.7 | 14 | ||
4.3 | odd | 2 | 1004.2.a.b.1.8 | ✓ | 14 | ||
12.11 | even | 2 | 9036.2.a.m.1.11 | 14 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1004.2.a.b.1.8 | ✓ | 14 | 4.3 | odd | 2 | ||
4016.2.a.j.1.7 | 14 | 1.1 | even | 1 | trivial | ||
9036.2.a.m.1.11 | 14 | 12.11 | even | 2 |