Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [8024,2,Mod(1,8024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(8024, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("8024.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 8024 = 2^{3} \cdot 17 \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 8024.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(64.0719625819\) |
Analytic rank: | \(1\) |
Dimension: | \(23\) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.20 | ||
Character | \(\chi\) | \(=\) | 8024.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.41453 | 1.39403 | 0.697014 | − | 0.717057i | \(-0.254511\pi\) | ||||
0.697014 | + | 0.717057i | \(0.254511\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.0537401 | 0.0240333 | 0.0120167 | − | 0.999928i | \(-0.496175\pi\) | ||||
0.0120167 | + | 0.999928i | \(0.496175\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.349134 | 0.131960 | 0.0659801 | − | 0.997821i | \(-0.478983\pi\) | ||||
0.0659801 | + | 0.997821i | \(0.478983\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.82994 | 0.943315 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.73444 | 0.522952 | 0.261476 | − | 0.965210i | \(-0.415791\pi\) | ||||
0.261476 | + | 0.965210i | \(0.415791\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −5.19703 | −1.44140 | −0.720698 | − | 0.693249i | \(-0.756179\pi\) | ||||
−0.720698 | + | 0.693249i | \(0.756179\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.129757 | 0.0335031 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.00000 | −0.242536 | ||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.66321 | 1.52864 | 0.764322 | − | 0.644834i | \(-0.223074\pi\) | ||||
0.764322 | + | 0.644834i | \(0.223074\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0.842993 | 0.183956 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −8.08544 | −1.68593 | −0.842966 | − | 0.537967i | \(-0.819192\pi\) | ||||
−0.842966 | + | 0.537967i | \(0.819192\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.99711 | −0.999422 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −0.410603 | −0.0790206 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.27135 | −0.793170 | −0.396585 | − | 0.917998i | \(-0.629805\pi\) | ||||
−0.396585 | + | 0.917998i | \(0.629805\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.11085 | −1.63636 | −0.818179 | − | 0.574964i | \(-0.805016\pi\) | ||||
−0.818179 | + | 0.574964i | \(0.805016\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.18784 | 0.729010 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.0187625 | 0.00317144 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.81775 | −0.298837 | −0.149418 | − | 0.988774i | \(-0.547740\pi\) | ||||
−0.149418 | + | 0.988774i | \(0.547740\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −12.5484 | −2.00935 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.44082 | −0.849713 | −0.424857 | − | 0.905261i | \(-0.639676\pi\) | ||||
−0.424857 | + | 0.905261i | \(0.639676\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.67981 | 0.713665 | 0.356832 | − | 0.934168i | \(-0.383857\pi\) | ||||
0.356832 | + | 0.934168i | \(0.383857\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.152082 | 0.0226710 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.77792 | 0.988661 | 0.494331 | − | 0.869274i | \(-0.335413\pi\) | ||||
0.494331 | + | 0.869274i | \(0.335413\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.87811 | −0.982587 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.41453 | −0.338102 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −4.55286 | −0.625383 | −0.312692 | − | 0.949855i | \(-0.601231\pi\) | ||||
−0.312692 | + | 0.949855i | \(0.601231\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.0932088 | 0.0125683 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 16.0885 | 2.13097 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.00000 | −0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −5.51837 | −0.706554 | −0.353277 | − | 0.935519i | \(-0.614933\pi\) | ||||
−0.353277 | + | 0.935519i | \(0.614933\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0.988029 | 0.124480 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.279289 | −0.0346415 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.57074 | −0.191896 | −0.0959481 | − | 0.995386i | \(-0.530588\pi\) | ||||
−0.0959481 | + | 0.995386i | \(0.530588\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −19.5225 | −2.35024 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −9.26340 | −1.09936 | −0.549681 | − | 0.835374i | \(-0.685251\pi\) | ||||
−0.549681 | + | 0.835374i | \(0.685251\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.8838 | −1.50793 | −0.753966 | − | 0.656914i | \(-0.771861\pi\) | ||||
−0.753966 | + | 0.656914i | \(0.771861\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −12.0657 | −1.39322 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.605550 | 0.0690088 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.61283 | 0.181457 | 0.0907285 | − | 0.995876i | \(-0.471080\pi\) | ||||
0.0907285 | + | 0.995876i | \(0.471080\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −9.48125 | −1.05347 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 13.9676 | 1.53314 | 0.766571 | − | 0.642159i | \(-0.221961\pi\) | ||||
0.766571 | + | 0.642159i | \(0.221961\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.0537401 | −0.00582894 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −10.3133 | −1.10570 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 4.80452 | 0.509278 | 0.254639 | − | 0.967036i | \(-0.418043\pi\) | ||||
0.254639 | + | 0.967036i | \(0.418043\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.81446 | −0.190207 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −21.9984 | −2.28113 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.358082 | 0.0367384 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.1429 | 1.74060 | 0.870301 | − | 0.492521i | \(-0.163924\pi\) | ||||
0.870301 | + | 0.492521i | \(0.163924\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.90836 | 0.493309 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.13439 | −0.212380 | −0.106190 | − | 0.994346i | \(-0.533865\pi\) | ||||
−0.106190 | + | 0.994346i | \(0.533865\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.99359 | 0.492033 | 0.246017 | − | 0.969266i | \(-0.420878\pi\) | ||||
0.246017 | + | 0.969266i | \(0.420878\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.0453026 | 0.00442108 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.9023 | 1.15064 | 0.575321 | − | 0.817928i | \(-0.304877\pi\) | ||||
0.575321 | + | 0.817928i | \(0.304877\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 12.1250 | 1.16136 | 0.580680 | − | 0.814132i | \(-0.302787\pi\) | ||||
0.580680 | + | 0.814132i | \(0.302787\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −4.38902 | −0.416587 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −15.6906 | −1.47604 | −0.738022 | − | 0.674777i | \(-0.764240\pi\) | ||||
−0.738022 | + | 0.674777i | \(0.764240\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.434513 | −0.0405185 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −14.7073 | −1.35969 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −0.349134 | −0.0320050 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −7.99173 | −0.726521 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −13.1370 | −1.18452 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −0.537246 | −0.0480527 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.8016 | −1.13596 | −0.567981 | − | 0.823042i | \(-0.692275\pi\) | ||||
−0.567981 | + | 0.823042i | \(0.692275\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 11.2995 | 0.994869 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 5.79213 | 0.506060 | 0.253030 | − | 0.967458i | \(-0.418573\pi\) | ||||
0.253030 | + | 0.967458i | \(0.418573\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.32635 | 0.201720 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −0.0220658 | −0.00189913 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −7.90806 | −0.675632 | −0.337816 | − | 0.941212i | \(-0.609688\pi\) | ||||
−0.337816 | + | 0.941212i | \(0.609688\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 20.1594 | 1.70990 | 0.854950 | − | 0.518710i | \(-0.173588\pi\) | ||||
0.854950 | + | 0.518710i | \(0.173588\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 16.3655 | 1.37822 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −9.01391 | −0.753781 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.229543 | −0.0190625 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −16.6074 | −1.36975 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −13.8859 | −1.13758 | −0.568790 | − | 0.822483i | \(-0.692588\pi\) | ||||
−0.568790 | + | 0.822483i | \(0.692588\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.03667 | 0.409878 | 0.204939 | − | 0.978775i | \(-0.434300\pi\) | ||||
0.204939 | + | 0.978775i | \(0.434300\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.82994 | −0.228787 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.489618 | −0.0393271 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.43483 | 0.433747 | 0.216873 | − | 0.976200i | \(-0.430414\pi\) | ||||
0.216873 | + | 0.976200i | \(0.430414\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.9930 | −0.871802 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −2.82290 | −0.222476 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 10.4295 | 0.816900 | 0.408450 | − | 0.912781i | \(-0.366069\pi\) | ||||
0.408450 | + | 0.912781i | \(0.366069\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.225055 | 0.0175205 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.73934 | −0.211976 | −0.105988 | − | 0.994367i | \(-0.533801\pi\) | ||||
−0.105988 | + | 0.994367i | \(0.533801\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 14.0091 | 1.07762 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 18.8565 | 1.44199 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 12.2123 | 0.928485 | 0.464243 | − | 0.885708i | \(-0.346327\pi\) | ||||
0.464243 | + | 0.885708i | \(0.346327\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.74466 | −0.131884 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −2.41453 | −0.181487 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 22.6154 | 1.69035 | 0.845177 | − | 0.534486i | \(-0.179495\pi\) | ||||
0.845177 | + | 0.534486i | \(0.179495\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.8215 | 1.25033 | 0.625166 | − | 0.780491i | \(-0.285031\pi\) | ||||
0.625166 | + | 0.780491i | \(0.285031\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −13.3242 | −0.984957 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.0976863 | −0.00718204 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.73444 | −0.126835 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.143355 | −0.0104276 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −8.02871 | −0.580937 | −0.290469 | − | 0.956885i | \(-0.593811\pi\) | ||||
−0.290469 | + | 0.956885i | \(0.593811\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.3011 | −0.741491 | −0.370745 | − | 0.928735i | \(-0.620898\pi\) | ||||
−0.370745 | + | 0.928735i | \(0.620898\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.674351 | −0.0482913 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.56841 | −0.325486 | −0.162743 | − | 0.986669i | \(-0.552034\pi\) | ||||
−0.162743 | + | 0.986669i | \(0.552034\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.2585 | 0.798094 | 0.399047 | − | 0.916930i | \(-0.369341\pi\) | ||||
0.399047 | + | 0.916930i | \(0.369341\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.79259 | −0.267509 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.49127 | −0.104667 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.292390 | −0.0204214 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −22.8814 | −1.59036 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 11.5569 | 0.799408 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.4911 | −1.27298 | −0.636490 | − | 0.771285i | \(-0.719614\pi\) | ||||
−0.636490 | + | 0.771285i | \(0.719614\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −22.3667 | −1.53254 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.251494 | 0.0171517 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.18091 | −0.215934 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −31.1082 | −2.10210 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 5.19703 | 0.349590 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −19.5691 | −1.31044 | −0.655221 | − | 0.755437i | \(-0.727425\pi\) | ||||
−0.655221 | + | 0.755437i | \(0.727425\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −14.1416 | −0.942770 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −10.9587 | −0.727352 | −0.363676 | − | 0.931526i | \(-0.618478\pi\) | ||||
−0.363676 | + | 0.931526i | \(0.618478\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −25.0556 | −1.65572 | −0.827862 | − | 0.560933i | \(-0.810443\pi\) | ||||
−0.827862 | + | 0.560933i | \(0.810443\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1.46212 | 0.0962003 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 0.405513 | 0.0265661 | 0.0132830 | − | 0.999912i | \(-0.495772\pi\) | ||||
0.0132830 | + | 0.999912i | \(0.495772\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.364246 | 0.0237608 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.89421 | 0.252956 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 27.0527 | 1.74989 | 0.874945 | − | 0.484222i | \(-0.160897\pi\) | ||||
0.874945 | + | 0.484222i | \(0.160897\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.764113 | 0.0492209 | 0.0246104 | − | 0.999697i | \(-0.492165\pi\) | ||||
0.0246104 | + | 0.999697i | \(0.492165\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −21.6609 | −1.38955 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.369630 | −0.0236148 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −34.6289 | −2.20338 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 33.7251 | 2.13724 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.10180 | 0.132664 | 0.0663321 | − | 0.997798i | \(-0.478870\pi\) | ||||
0.0663321 | + | 0.997798i | \(0.478870\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −14.0237 | −0.881661 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.129757 | −0.00812570 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −6.37208 | −0.397480 | −0.198740 | − | 0.980052i | \(-0.563685\pi\) | ||||
−0.198740 | + | 0.980052i | \(0.563685\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −0.634639 | −0.0394345 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −12.0877 | −0.748209 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 12.0398 | 0.742408 | 0.371204 | − | 0.928551i | \(-0.378945\pi\) | ||||
0.371204 | + | 0.928551i | \(0.378945\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.244671 | −0.0150300 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 11.6006 | 0.709948 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 20.0423 | 1.22200 | 0.611002 | − | 0.791629i | \(-0.290767\pi\) | ||||
0.611002 | + | 0.791629i | \(0.290767\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −23.0256 | −1.39871 | −0.699354 | − | 0.714776i | \(-0.746529\pi\) | ||||
−0.699354 | + | 0.714776i | \(0.746529\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −4.38106 | −0.265154 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −8.66717 | −0.522650 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.41713 | −0.385568 | −0.192784 | − | 0.981241i | \(-0.561752\pi\) | ||||
−0.192784 | + | 0.981241i | \(0.561752\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −25.7832 | −1.54360 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −21.4305 | −1.27844 | −0.639219 | − | 0.769025i | \(-0.720742\pi\) | ||||
−0.639219 | + | 0.769025i | \(0.720742\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.2515 | 1.20383 | 0.601914 | − | 0.798561i | \(-0.294405\pi\) | ||||
0.601914 | + | 0.798561i | \(0.294405\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.864598 | 0.0512144 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −1.89957 | −0.112128 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.00000 | 0.0588235 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 41.3921 | 2.42645 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.64095 | 0.0958652 | 0.0479326 | − | 0.998851i | \(-0.484737\pi\) | ||||
0.0479326 | + | 0.998851i | \(0.484737\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.0537401 | −0.00312887 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.712164 | −0.0413240 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 42.0203 | 2.43010 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.63388 | 0.0941753 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.15354 | −0.296063 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −0.296558 | −0.0169808 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −22.1243 | −1.26270 | −0.631350 | − | 0.775498i | \(-0.717499\pi\) | ||||
−0.631350 | + | 0.775498i | \(0.717499\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 12.0572 | 0.685909 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.57081 | 0.372596 | 0.186298 | − | 0.982493i | \(-0.440351\pi\) | ||||
0.186298 | + | 0.982493i | \(0.440351\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.06102 | −0.173019 | −0.0865096 | − | 0.996251i | \(-0.527571\pi\) | ||||
−0.0865096 | + | 0.996251i | \(0.527571\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0.0530968 | 0.00299167 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 10.4983 | 0.589643 | 0.294822 | − | 0.955552i | \(-0.404740\pi\) | ||||
0.294822 | + | 0.955552i | \(0.404740\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −7.40839 | −0.414790 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 28.7385 | 1.60403 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −6.66321 | −0.370751 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 25.9701 | 1.44056 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 29.2761 | 1.61897 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.36640 | 0.130464 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −20.7618 | −1.14117 | −0.570586 | − | 0.821238i | \(-0.693284\pi\) | ||||
−0.570586 | + | 0.821238i | \(0.693284\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −5.14414 | −0.281897 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.0844116 | −0.00461190 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.14981 | 0.226055 | 0.113027 | − | 0.993592i | \(-0.463945\pi\) | ||||
0.113027 | + | 0.993592i | \(0.463945\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −37.8853 | −2.05765 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −15.8022 | −0.855737 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4.84531 | −0.261622 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.04914 | −0.0564840 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −5.64556 | −0.303069 | −0.151535 | − | 0.988452i | \(-0.548422\pi\) | ||||
−0.151535 | + | 0.988452i | \(0.548422\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.08264 | −0.165010 | −0.0825050 | − | 0.996591i | \(-0.526292\pi\) | ||||
−0.0825050 | + | 0.996591i | \(0.526292\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 2.13391 | 0.113900 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 17.8925 | 0.952319 | 0.476160 | − | 0.879359i | \(-0.342028\pi\) | ||||
0.476160 | + | 0.879359i | \(0.342028\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.497816 | −0.0264213 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.842993 | −0.0446159 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 9.36247 | 0.494132 | 0.247066 | − | 0.968999i | \(-0.420534\pi\) | ||||
0.247066 | + | 0.968999i | \(0.420534\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 25.3983 | 1.33675 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −19.2963 | −1.01279 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −0.692375 | −0.0362406 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 22.6479 | 1.18221 | 0.591105 | − | 0.806594i | \(-0.298692\pi\) | ||||
0.591105 | + | 0.806594i | \(0.298692\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −15.3972 | −0.801547 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.58956 | −0.0825257 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −17.9109 | −0.927394 | −0.463697 | − | 0.885994i | \(-0.653477\pi\) | ||||
−0.463697 | + | 0.885994i | \(0.653477\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.29720 | −0.0669869 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 22.1983 | 1.14327 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 22.5349 | 1.15754 | 0.578771 | − | 0.815490i | \(-0.303532\pi\) | ||||
0.578771 | + | 0.815490i | \(0.303532\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −30.9099 | −1.58356 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −30.1045 | −1.53827 | −0.769134 | − | 0.639088i | \(-0.779312\pi\) | ||||
−0.769134 | + | 0.639088i | \(0.779312\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.0325423 | 0.00165851 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 13.2436 | 0.673210 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −27.7088 | −1.40489 | −0.702445 | − | 0.711738i | \(-0.747908\pi\) | ||||
−0.702445 | + | 0.711738i | \(0.747908\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.08544 | 0.408898 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.9852 | 0.705463 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0.0866735 | 0.00436102 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 31.6917 | 1.59056 | 0.795282 | − | 0.606240i | \(-0.207323\pi\) | ||||
0.795282 | + | 0.606240i | \(0.207323\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.61704 | 0.281204 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.5677 | −1.12698 | −0.563490 | − | 0.826123i | \(-0.690542\pi\) | ||||
−0.563490 | + | 0.826123i | \(0.690542\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 47.3494 | 2.35864 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −0.509523 | −0.0253184 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.15278 | −0.156277 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.18714 | 0.108147 | 0.0540735 | − | 0.998537i | \(-0.482779\pi\) | ||||
0.0540735 | + | 0.998537i | \(0.482779\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −19.0942 | −0.941850 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.349134 | −0.0171797 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.750620 | 0.0368465 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 48.6755 | 2.38365 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −34.4929 | −1.68509 | −0.842544 | − | 0.538628i | \(-0.818943\pi\) | ||||
−0.842544 | + | 0.538628i | \(0.818943\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −35.6128 | −1.73566 | −0.867831 | − | 0.496859i | \(-0.834487\pi\) | ||||
−0.867831 | + | 0.496859i | \(0.834487\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 19.1811 | 0.932619 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.99711 | 0.242396 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.92665 | −0.0932370 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −21.7643 | −1.05079 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14.0728 | 0.677864 | 0.338932 | − | 0.940811i | \(-0.389934\pi\) | ||||
0.338932 | + | 0.940811i | \(0.389934\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −10.0740 | −0.484126 | −0.242063 | − | 0.970260i | \(-0.577824\pi\) | ||||
−0.242063 | + | 0.970260i | \(0.577824\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.554238 | −0.0265737 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −53.8750 | −2.57719 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.47384 | 0.404434 | 0.202217 | − | 0.979341i | \(-0.435185\pi\) | ||||
0.202217 | + | 0.979341i | \(0.435185\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −19.4647 | −0.926889 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −20.8634 | −0.991252 | −0.495626 | − | 0.868536i | \(-0.665061\pi\) | ||||
−0.495626 | + | 0.868536i | \(0.665061\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.258195 | 0.0122396 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −33.5279 | −1.58582 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −33.8575 | −1.59783 | −0.798917 | − | 0.601441i | \(-0.794594\pi\) | ||||
−0.798917 | + | 0.601441i | \(0.794594\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −9.43675 | −0.444359 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 12.1612 | 0.571382 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −0.0975092 | −0.00457130 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −11.9766 | −0.560242 | −0.280121 | − | 0.959965i | \(-0.590375\pi\) | ||||
−0.280121 | + | 0.959965i | \(0.590375\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.410603 | 0.0191653 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 35.0328 | 1.63164 | 0.815820 | − | 0.578305i | \(-0.196286\pi\) | ||||
0.815820 | + | 0.578305i | \(0.196286\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 37.1208 | 1.72515 | 0.862575 | − | 0.505928i | \(-0.168850\pi\) | ||||
0.862575 | + | 0.505928i | \(0.168850\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.18220 | −0.0548231 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 7.96690 | 0.368664 | 0.184332 | − | 0.982864i | \(-0.440988\pi\) | ||||
0.184332 | + | 0.982864i | \(0.440988\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −0.548397 | −0.0253226 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 13.1226 | 0.604655 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.11683 | 0.373212 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −33.2968 | −1.52776 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −12.8843 | −0.589933 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −16.3586 | −0.747442 | −0.373721 | − | 0.927541i | \(-0.621918\pi\) | ||||
−0.373721 | + | 0.927541i | \(0.621918\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9.44692 | 0.430742 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −6.81597 | −0.310137 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0.921264 | 0.0418324 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.15399 | −0.0976064 | −0.0488032 | − | 0.998808i | \(-0.515541\pi\) | ||||
−0.0488032 | + | 0.998808i | \(0.515541\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 25.1823 | 1.13878 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.4834 | 1.28544 | 0.642719 | − | 0.766102i | \(-0.277806\pi\) | ||||
0.642719 | + | 0.766102i | \(0.277806\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.27135 | 0.192372 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.263776 | 0.0118558 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.23416 | −0.145072 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −25.9575 | −1.16202 | −0.581008 | − | 0.813898i | \(-0.697342\pi\) | ||||
−0.581008 | + | 0.813898i | \(0.697342\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −6.61421 | −0.295501 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.9092 | 0.575592 | 0.287796 | − | 0.957692i | \(-0.407078\pi\) | ||||
0.287796 | + | 0.957692i | \(0.407078\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.114702 | −0.00510418 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 33.8254 | 1.50224 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −18.1021 | −0.802362 | −0.401181 | − | 0.915999i | \(-0.631400\pi\) | ||||
−0.401181 | + | 0.915999i | \(0.631400\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.49816 | −0.198987 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −2.73593 | −0.120794 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.268356 | 0.0118252 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 11.7559 | 0.517022 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 29.4870 | 1.29433 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.5318 | −0.592838 | −0.296419 | − | 0.955058i | \(-0.595792\pi\) | ||||
−0.296419 | + | 0.955058i | \(0.595792\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 11.9232 | 0.521363 | 0.260681 | − | 0.965425i | \(-0.416053\pi\) | ||||
0.260681 | + | 0.965425i | \(0.416053\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −4.21253 | −0.183850 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 9.11085 | 0.396875 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 42.3744 | 1.84236 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.82994 | −0.122809 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 28.2761 | 1.22477 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.639633 | 0.0276537 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 54.6055 | 2.35640 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −11.9296 | −0.513846 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.59963 | 0.154760 | 0.0773800 | − | 0.997002i | \(-0.475345\pi\) | ||||
0.0773800 | + | 0.997002i | \(0.475345\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 40.6160 | 1.74300 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0.651597 | 0.0279113 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −11.5984 | −0.495912 | −0.247956 | − | 0.968771i | \(-0.579759\pi\) | ||||
−0.247956 | + | 0.968771i | \(0.579759\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −15.6167 | −0.666503 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −28.4609 | −1.21248 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.563092 | 0.0239451 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −0.235866 | −0.0100120 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −26.9875 | −1.14350 | −0.571748 | − | 0.820429i | \(-0.693734\pi\) | ||||
−0.571748 | + | 0.820429i | \(0.693734\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −24.3211 | −1.02867 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −4.18784 | −0.176811 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 32.5175 | 1.37045 | 0.685226 | − | 0.728331i | \(-0.259704\pi\) | ||||
0.685226 | + | 0.728331i | \(0.259704\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −0.843213 | −0.0354742 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −3.31022 | −0.139016 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −12.2343 | −0.512887 | −0.256444 | − | 0.966559i | \(-0.582551\pi\) | ||||
−0.256444 | + | 0.966559i | \(0.582551\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.43087 | −0.143577 | −0.0717887 | − | 0.997420i | \(-0.522871\pi\) | ||||
−0.0717887 | + | 0.997420i | \(0.522871\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −19.3856 | −0.809843 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 40.4039 | 1.68496 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −44.1741 | −1.83899 | −0.919496 | − | 0.393099i | \(-0.871403\pi\) | ||||
−0.919496 | + | 0.393099i | \(0.871403\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −24.8723 | −1.03366 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.87656 | 0.202314 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −7.89664 | −0.327046 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.790372 | −0.0326779 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 18.4762 | 0.762595 | 0.381298 | − | 0.924452i | \(-0.375477\pi\) | ||||
0.381298 | + | 0.924452i | \(0.375477\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −60.7075 | −2.50141 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −11.0305 | −0.453736 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11.3726 | 0.467017 | 0.233509 | − | 0.972355i | \(-0.424979\pi\) | ||||
0.233509 | + | 0.972355i | \(0.424979\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.0187625 | −0.000769187 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 27.1840 | 1.11257 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −20.3972 | −0.833408 | −0.416704 | − | 0.909042i | \(-0.636815\pi\) | ||||
−0.416704 | + | 0.909042i | \(0.636815\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.04262 | −0.287274 | −0.143637 | − | 0.989630i | \(-0.545880\pi\) | ||||
−0.143637 | + | 0.989630i | \(0.545880\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.44510 | −0.181018 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −0.429477 | −0.0174607 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −17.3165 | −0.702855 | −0.351427 | − | 0.936215i | \(-0.614304\pi\) | ||||
−0.351427 | + | 0.936215i | \(0.614304\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.60072 | −0.145909 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −35.2250 | −1.42505 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 34.5167 | 1.39412 | 0.697058 | − | 0.717015i | \(-0.254492\pi\) | ||||
0.697058 | + | 0.717015i | \(0.254492\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.705985 | −0.0284681 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15.1052 | −0.608114 | −0.304057 | − | 0.952654i | \(-0.598341\pi\) | ||||
−0.304057 | + | 0.952654i | \(0.598341\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.359586 | −0.0144530 | −0.00722648 | − | 0.999974i | \(-0.502300\pi\) | ||||
−0.00722648 | + | 0.999974i | \(0.502300\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.31991 | 0.133223 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.67742 | 0.0672044 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.9567 | 0.998268 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 27.9045 | 1.11440 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.81775 | 0.0724786 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 9.43418 | 0.375569 | 0.187784 | − | 0.982210i | \(-0.439869\pi\) | ||||
0.187784 | + | 0.982210i | \(0.439869\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −44.6473 | −1.77457 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.687962 | −0.0273009 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 35.7457 | 1.41630 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −26.2149 | −1.03705 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.44665 | 0.254627 | 0.127314 | − | 0.991863i | \(-0.459365\pi\) | ||||
0.127314 | + | 0.991863i | \(0.459365\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.7865 | −0.938047 | −0.469024 | − | 0.883186i | \(-0.655394\pi\) | ||||
−0.469024 | + | 0.883186i | \(0.655394\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.607238 | 0.0239100 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −5.81776 | −0.228720 | −0.114360 | − | 0.993439i | \(-0.536482\pi\) | ||||
−0.114360 | + | 0.993439i | \(0.536482\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.73444 | −0.0680826 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.68039 | −0.301018 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 22.1633 | 0.867317 | 0.433658 | − | 0.901077i | \(-0.357222\pi\) | ||||
0.433658 | + | 0.901077i | \(0.357222\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.311270 | 0.0121623 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −36.4604 | −1.42245 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −19.8457 | −0.773077 | −0.386539 | − | 0.922273i | \(-0.626329\pi\) | ||||
−0.386539 | + | 0.922273i | \(0.626329\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 20.1704 | 0.784538 | 0.392269 | − | 0.919851i | \(-0.371690\pi\) | ||||
0.392269 | + | 0.919851i | \(0.371690\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 12.5484 | 0.487338 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.125018 | 0.00484800 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 34.5358 | 1.33723 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −47.2501 | −1.82679 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9.57125 | −0.369494 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 18.1562 | 0.699870 | 0.349935 | − | 0.936774i | \(-0.386204\pi\) | ||||
0.349935 | + | 0.936774i | \(0.386204\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.05183 | 0.0789749 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 10.7326 | 0.412489 | 0.206244 | − | 0.978501i | \(-0.433876\pi\) | ||||
0.206244 | + | 0.978501i | \(0.433876\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 5.98518 | 0.229690 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −26.4600 | −1.01395 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −23.2790 | −0.890746 | −0.445373 | − | 0.895345i | \(-0.646929\pi\) | ||||
−0.445373 | + | 0.895345i | \(0.646929\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.424980 | −0.0162377 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −60.4975 | −2.30812 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 23.6613 | 0.901425 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.80026 | 0.372820 | 0.186410 | − | 0.982472i | \(-0.440315\pi\) | ||||
0.186410 | + | 0.982472i | \(0.440315\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.71367 | 0.0650971 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.08337 | 0.0410946 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.44082 | 0.206086 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0.979124 | 0.0370339 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.9483 | 1.01782 | 0.508912 | − | 0.860819i | \(-0.330048\pi\) | ||||
0.508912 | + | 0.860819i | \(0.330048\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −12.1121 | −0.456815 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0.879483 | 0.0331232 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.745187 | −0.0280256 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −32.0476 | −1.20357 | −0.601787 | − | 0.798657i | \(-0.705544\pi\) | ||||
−0.601787 | + | 0.798657i | \(0.705544\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 4.56421 | 0.171171 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 73.6653 | 2.75879 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.484409 | −0.0181159 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 65.3194 | 2.43940 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 15.6089 | 0.582114 | 0.291057 | − | 0.956706i | \(-0.405993\pi\) | ||||
0.291057 | + | 0.956706i | \(0.405993\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.74343 | 0.0649288 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.84497 | 0.0686153 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 21.3444 | 0.792712 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.51700 | 0.204614 | 0.102307 | − | 0.994753i | \(-0.467378\pi\) | ||||
0.102307 | + | 0.994753i | \(0.467378\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.8572 | −0.883599 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.67981 | −0.173089 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 34.1749 | 1.26228 | 0.631139 | − | 0.775670i | \(-0.282588\pi\) | ||||
0.631139 | + | 0.775670i | \(0.282588\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −0.892483 | −0.0329197 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −2.72434 | −0.100352 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.66078 | 0.318592 | 0.159296 | − | 0.987231i | \(-0.449078\pi\) | ||||
0.159296 | + | 0.987231i | \(0.449078\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −83.6124 | −3.07158 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −26.9103 | −0.987244 | −0.493622 | − | 0.869676i | \(-0.664327\pi\) | ||||
−0.493622 | + | 0.869676i | \(0.664327\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.746231 | −0.0273398 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 39.5275 | 1.44624 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.15550 | 0.151839 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −24.6401 | −0.899130 | −0.449565 | − | 0.893248i | \(-0.648421\pi\) | ||||
−0.449565 | + | 0.893248i | \(0.648421\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 5.07485 | 0.184938 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0.270671 | 0.00985073 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −11.2517 | −0.408950 | −0.204475 | − | 0.978872i | \(-0.565549\pi\) | ||||
−0.204475 | + | 0.978872i | \(0.565549\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −33.8606 | −1.22906 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 13.3883 | 0.485325 | 0.242663 | − | 0.970111i | \(-0.421979\pi\) | ||||
0.242663 | + | 0.970111i | \(0.421979\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 4.23323 | 0.153253 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −0.152082 | −0.00549852 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 5.19703 | 0.187654 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −15.3465 | −0.553407 | −0.276704 | − | 0.960955i | \(-0.589242\pi\) | ||||
−0.276704 | + | 0.960955i | \(0.589242\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −15.3856 | −0.554098 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.93963 | −0.285569 | −0.142784 | − | 0.989754i | \(-0.545606\pi\) | ||||
−0.142784 | + | 0.989754i | \(0.545606\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 45.5280 | 1.63541 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.53235 | −0.0549729 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −36.2533 | −1.29891 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −16.0668 | −0.574914 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.75383 | 0.0626767 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.292069 | 0.0104244 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −21.2545 | −0.757640 | −0.378820 | − | 0.925470i | \(-0.623670\pi\) | ||||
−0.378820 | + | 0.925470i | \(0.623670\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 29.0705 | 1.03494 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −5.47810 | −0.194779 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 28.6791 | 1.01842 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.590765 | −0.0209523 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 42.2136 | 1.49528 | 0.747641 | − | 0.664103i | \(-0.231187\pi\) | ||||
0.747641 | + | 0.664103i | \(0.231187\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.77792 | −0.239786 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 13.5965 | 0.480409 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −22.3461 | −0.788576 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.151703 | −0.00534683 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 48.3928 | 1.70351 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 49.0752 | 1.72539 | 0.862695 | − | 0.505724i | \(-0.168775\pi\) | ||||
0.862695 | + | 0.505724i | \(0.168775\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11.0126 | 0.386705 | 0.193353 | − | 0.981129i | \(-0.438064\pi\) | ||||
0.193353 | + | 0.981129i | \(0.438064\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −55.5960 | −1.94984 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0.560482 | 0.0196328 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 31.1826 | 1.09094 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −5.13482 | −0.179425 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 40.5380 | 1.41479 | 0.707394 | − | 0.706820i | \(-0.249871\pi\) | ||||
0.707394 | + | 0.706820i | \(0.249871\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −0.946740 | −0.0330013 | −0.0165006 | − | 0.999864i | \(-0.505253\pi\) | ||||
−0.0165006 | + | 0.999864i | \(0.505253\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −20.9271 | −0.728589 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.5194 | 0.678758 | 0.339379 | − | 0.940650i | \(-0.389783\pi\) | ||||
0.339379 | + | 0.940650i | \(0.389783\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 43.9129 | 1.52516 | 0.762579 | − | 0.646895i | \(-0.223933\pi\) | ||||
0.762579 | + | 0.646895i | \(0.223933\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15.4943 | −0.537492 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 6.87811 | 0.238312 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −0.147212 | −0.00509450 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 3.74094 | 0.129306 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.04587 | 0.208727 | 0.104363 | − | 0.994539i | \(-0.466720\pi\) | ||||
0.104363 | + | 0.994539i | \(0.466720\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −10.7556 | −0.370881 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −51.7446 | −1.78218 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0.752851 | 0.0258989 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2.79018 | −0.0958718 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 48.8979 | 1.67817 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.6973 | 0.503818 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 28.8950 | 0.989347 | 0.494673 | − | 0.869079i | \(-0.335288\pi\) | ||||
0.494673 | + | 0.869079i | \(0.335288\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 1.01335 | 0.0346559 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −3.69170 | −0.126106 | −0.0630531 | − | 0.998010i | \(-0.520084\pi\) | ||||
−0.0630531 | + | 0.998010i | \(0.520084\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −37.9888 | −1.29616 | −0.648080 | − | 0.761572i | \(-0.724428\pi\) | ||||
−0.648080 | + | 0.761572i | \(0.724428\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.58657 | −0.156310 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −36.3211 | −1.23638 | −0.618192 | − | 0.786027i | \(-0.712135\pi\) | ||||
−0.618192 | + | 0.786027i | \(0.712135\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.656292 | 0.0223146 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.41453 | 0.0820017 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.79734 | 0.0948934 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.16317 | 0.276598 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 48.5136 | 1.64194 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.187571 | −0.00634105 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −34.0447 | −1.14961 | −0.574804 | − | 0.818291i | \(-0.694922\pi\) | ||||
−0.574804 | + | 0.818291i | \(0.694922\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 3.96211 | 0.133639 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.05354 | −0.0691855 | −0.0345927 | − | 0.999401i | \(-0.511013\pi\) | ||||
−0.0345927 | + | 0.999401i | \(0.511013\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.4374 | 0.586816 | 0.293408 | − | 0.955987i | \(-0.405211\pi\) | ||||
0.293408 | + | 0.955987i | \(0.405211\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.129757 | −0.00436174 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16.0174 | −0.537812 | −0.268906 | − | 0.963166i | \(-0.586662\pi\) | ||||
−0.268906 | + | 0.963166i | \(0.586662\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −4.46948 | −0.149902 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −16.4446 | −0.550915 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 45.1627 | 1.51131 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.21535 | 0.0406248 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 101.459 | 3.38762 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 38.9157 | 1.29791 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.55286 | 0.151678 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 3.94505 | 0.131283 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.903990 | 0.0300496 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 24.6182 | 0.817435 | 0.408718 | − | 0.912661i | \(-0.365976\pi\) | ||||
0.408718 | + | 0.912661i | \(0.365976\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −6.04020 | −0.200341 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 20.9391 | 0.693742 | 0.346871 | − | 0.937913i | \(-0.387244\pi\) | ||||
0.346871 | + | 0.937913i | \(0.387244\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.2259 | 0.801760 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −0.716047 | −0.0236718 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 2.02223 | 0.0667798 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −41.5753 | −1.37144 | −0.685721 | − | 0.727864i | \(-0.740513\pi\) | ||||
−0.685721 | + | 0.727864i | \(0.740513\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −53.4197 | −1.76024 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 48.1421 | 1.58462 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.08352 | 0.298664 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 14.1316 | 0.464143 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 35.5445 | 1.16618 | 0.583088 | − | 0.812409i | \(-0.301844\pi\) | ||||
0.583088 | + | 0.812409i | \(0.301844\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −45.8302 | −1.50203 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 15.8654 | 0.519410 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.0932088 | −0.00304825 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.27771 | 0.270421 | 0.135210 | − | 0.990817i | \(-0.456829\pi\) | ||||
0.135210 | + | 0.990817i | \(0.456829\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −7.39092 | −0.241194 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.50491 | −0.146856 | −0.0734279 | − | 0.997301i | \(-0.523394\pi\) | ||||
−0.0734279 | + | 0.997301i | \(0.523394\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 43.9914 | 1.43256 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −0.00770393 | −0.000250609 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 34.0978 | 1.10803 | 0.554015 | − | 0.832507i | \(-0.313095\pi\) | ||||
0.554015 | + | 0.832507i | \(0.313095\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 66.9573 | 2.17353 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 25.3484 | 0.821979 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −18.9888 | −0.615106 | −0.307553 | − | 0.951531i | \(-0.599510\pi\) | ||||
−0.307553 | + | 0.951531i | \(0.599510\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −0.431464 | −0.0139618 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −17.8878 | −0.578229 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.76097 | −0.0891564 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 52.0076 | 1.67767 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 33.6829 | 1.08542 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −0.553583 | −0.0178205 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.3110 | −0.910421 | −0.455211 | − | 0.890384i | \(-0.650436\pi\) | ||||
−0.455211 | + | 0.890384i | \(0.650436\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −16.0885 | −0.516837 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.06717 | 0.162613 | 0.0813066 | − | 0.996689i | \(-0.474091\pi\) | ||||
0.0813066 | + | 0.996689i | \(0.474091\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 7.03834 | 0.225639 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 62.7056 | 2.00819 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 8.89827 | 0.284681 | 0.142340 | − | 0.989818i | \(-0.454537\pi\) | ||||
0.142340 | + | 0.989818i | \(0.454537\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.33313 | 0.266328 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 34.3130 | 1.09553 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −24.9256 | −0.795003 | −0.397501 | − | 0.917602i | \(-0.630123\pi\) | ||||
−0.397501 | + | 0.917602i | \(0.630123\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.245507 | −0.00782250 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 5.71374 | 0.181870 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −37.8383 | −1.20319 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −21.5978 | −0.686076 | −0.343038 | − | 0.939321i | \(-0.611456\pi\) | ||||
−0.343038 | + | 0.939321i | \(0.611456\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −50.1300 | −1.59083 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0.605033 | 0.0191808 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.14487 | −0.131269 | −0.0656346 | − | 0.997844i | \(-0.520907\pi\) | ||||
−0.0656346 | + | 0.997844i | \(0.520907\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0.746375 | 0.0236143 |
(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 | 8024.2.a.y.1.20 | ✓ | 23 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
8024.2.a.y.1.20 | ✓ | 23 | 1.1 | even | 1 | trivial |