Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4023,2,Mod(1,4023)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4023, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("4023.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4023 = 3^{3} \cdot 149 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4023.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: | \(32.1238167332\) |
Analytic rank: | \(0\) |
Dimension: | \(25\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.9 | ||
Character | \(\chi\) | \(=\) | 4023.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.599558 | −0.423952 | −0.211976 | − | 0.977275i | \(-0.567990\pi\) | ||||
−0.211976 | + | 0.977275i | \(0.567990\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.64053 | −0.820265 | ||||||||
\(5\) | −0.261228 | −0.116825 | −0.0584125 | − | 0.998293i | \(-0.518604\pi\) | ||||
−0.0584125 | + | 0.998293i | \(0.518604\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.444015 | −0.167822 | −0.0839109 | − | 0.996473i | \(-0.526741\pi\) | ||||
−0.0839109 | + | 0.996473i | \(0.526741\pi\) | |||||||
\(8\) | 2.18271 | 0.771705 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0.156622 | 0.0495281 | ||||||||
\(11\) | 3.27284 | 0.986800 | 0.493400 | − | 0.869803i | \(-0.335754\pi\) | ||||
0.493400 | + | 0.869803i | \(0.335754\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.82387 | 1.33790 | 0.668951 | − | 0.743307i | \(-0.266744\pi\) | ||||
0.668951 | + | 0.743307i | \(0.266744\pi\) | |||||||
\(14\) | 0.266213 | 0.0711483 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.97240 | 0.493099 | ||||||||
\(17\) | −0.628330 | −0.152392 | −0.0761962 | − | 0.997093i | \(-0.524278\pi\) | ||||
−0.0761962 | + | 0.997093i | \(0.524278\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.37907 | 1.46346 | 0.731730 | − | 0.681595i | \(-0.238713\pi\) | ||||
0.731730 | + | 0.681595i | \(0.238713\pi\) | |||||||
\(20\) | 0.428553 | 0.0958274 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.96226 | −0.418356 | ||||||||
\(23\) | 6.91056 | 1.44095 | 0.720476 | − | 0.693480i | \(-0.243923\pi\) | ||||
0.720476 | + | 0.693480i | \(0.243923\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.93176 | −0.986352 | ||||||||
\(26\) | −2.89219 | −0.567206 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.728419 | 0.137658 | ||||||||
\(29\) | 3.92656 | 0.729144 | 0.364572 | − | 0.931175i | \(-0.381215\pi\) | ||||
0.364572 | + | 0.931175i | \(0.381215\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.84367 | 0.690344 | 0.345172 | − | 0.938539i | \(-0.387821\pi\) | ||||
0.345172 | + | 0.938539i | \(0.387821\pi\) | |||||||
\(32\) | −5.54799 | −0.980755 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.376720 | 0.0646070 | ||||||||
\(35\) | 0.115989 | 0.0196058 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.74015 | −1.27247 | −0.636236 | − | 0.771494i | \(-0.719510\pi\) | ||||
−0.636236 | + | 0.771494i | \(0.719510\pi\) | |||||||
\(38\) | −3.82463 | −0.620436 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.570186 | −0.0901543 | ||||||||
\(41\) | −12.1523 | −1.89786 | −0.948932 | − | 0.315479i | \(-0.897835\pi\) | ||||
−0.948932 | + | 0.315479i | \(0.897835\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.58602 | 0.546863 | 0.273432 | − | 0.961891i | \(-0.411841\pi\) | ||||
0.273432 | + | 0.961891i | \(0.411841\pi\) | |||||||
\(44\) | −5.36920 | −0.809437 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.14329 | −0.610894 | ||||||||
\(47\) | 6.18985 | 0.902882 | 0.451441 | − | 0.892301i | \(-0.350910\pi\) | ||||
0.451441 | + | 0.892301i | \(0.350910\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.80285 | −0.971836 | ||||||||
\(50\) | 2.95688 | 0.418166 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −7.91370 | −1.09743 | ||||||||
\(53\) | 2.50738 | 0.344415 | 0.172207 | − | 0.985061i | \(-0.444910\pi\) | ||||
0.172207 | + | 0.985061i | \(0.444910\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.854960 | −0.115283 | ||||||||
\(56\) | −0.969155 | −0.129509 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.35420 | −0.309122 | ||||||||
\(59\) | −8.32542 | −1.08388 | −0.541939 | − | 0.840418i | \(-0.682309\pi\) | ||||
−0.541939 | + | 0.840418i | \(0.682309\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.21416 | 0.283494 | 0.141747 | − | 0.989903i | \(-0.454728\pi\) | ||||
0.141747 | + | 0.989903i | \(0.454728\pi\) | |||||||
\(62\) | −2.30451 | −0.292673 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −0.618452 | −0.0773065 | ||||||||
\(65\) | −1.26013 | −0.156300 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 3.22654 | 0.394184 | 0.197092 | − | 0.980385i | \(-0.436850\pi\) | ||||
0.197092 | + | 0.980385i | \(0.436850\pi\) | |||||||
\(68\) | 1.03079 | 0.125002 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −0.0695423 | −0.00831190 | ||||||||
\(71\) | 9.85495 | 1.16957 | 0.584783 | − | 0.811189i | \(-0.301179\pi\) | ||||
0.584783 | + | 0.811189i | \(0.301179\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.8578 | −1.50489 | −0.752446 | − | 0.658654i | \(-0.771126\pi\) | ||||
−0.752446 | + | 0.658654i | \(0.771126\pi\) | |||||||
\(74\) | 4.64067 | 0.539467 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −10.4651 | −1.20042 | ||||||||
\(77\) | −1.45319 | −0.165606 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 9.04869 | 1.01806 | 0.509028 | − | 0.860750i | \(-0.330005\pi\) | ||||
0.509028 | + | 0.860750i | \(0.330005\pi\) | |||||||
\(80\) | −0.515246 | −0.0576063 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 7.28599 | 0.804603 | ||||||||
\(83\) | 5.99942 | 0.658522 | 0.329261 | − | 0.944239i | \(-0.393200\pi\) | ||||
0.329261 | + | 0.944239i | \(0.393200\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0.164138 | 0.0178032 | ||||||||
\(86\) | −2.15003 | −0.231844 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 7.14367 | 0.761518 | ||||||||
\(89\) | 4.41461 | 0.467948 | 0.233974 | − | 0.972243i | \(-0.424827\pi\) | ||||
0.233974 | + | 0.972243i | \(0.424827\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.14187 | −0.224529 | ||||||||
\(92\) | −11.3370 | −1.18196 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −3.71118 | −0.382778 | ||||||||
\(95\) | −1.66639 | −0.170968 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −5.55167 | −0.563687 | −0.281844 | − | 0.959460i | \(-0.590946\pi\) | ||||
−0.281844 | + | 0.959460i | \(0.590946\pi\) | |||||||
\(98\) | 4.07871 | 0.412012 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.09070 | 0.809070 | ||||||||
\(101\) | 1.04054 | 0.103537 | 0.0517687 | − | 0.998659i | \(-0.483514\pi\) | ||||
0.0517687 | + | 0.998659i | \(0.483514\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −7.72271 | −0.760942 | −0.380471 | − | 0.924793i | \(-0.624238\pi\) | ||||
−0.380471 | + | 0.924793i | \(0.624238\pi\) | |||||||
\(104\) | 10.5291 | 1.03246 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.50332 | −0.146015 | ||||||||
\(107\) | 20.4149 | 1.97358 | 0.986790 | − | 0.162003i | \(-0.0517955\pi\) | ||||
0.986790 | + | 0.162003i | \(0.0517955\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 8.94231 | 0.856518 | 0.428259 | − | 0.903656i | \(-0.359127\pi\) | ||||
0.428259 | + | 0.903656i | \(0.359127\pi\) | |||||||
\(110\) | 0.512598 | 0.0488743 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.875773 | −0.0827528 | ||||||||
\(113\) | 5.51469 | 0.518778 | 0.259389 | − | 0.965773i | \(-0.416479\pi\) | ||||
0.259389 | + | 0.965773i | \(0.416479\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.80524 | −0.168339 | ||||||||
\(116\) | −6.44164 | −0.598091 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 4.99157 | 0.459512 | ||||||||
\(119\) | 0.278988 | 0.0255748 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −0.288490 | −0.0262263 | ||||||||
\(122\) | −1.32752 | −0.120188 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.30566 | −0.566265 | ||||||||
\(125\) | 2.59446 | 0.232055 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.17707 | −0.814333 | −0.407166 | − | 0.913354i | \(-0.633483\pi\) | ||||
−0.407166 | + | 0.913354i | \(0.633483\pi\) | |||||||
\(128\) | 11.4668 | 1.01353 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0.755523 | 0.0662637 | ||||||||
\(131\) | 12.1510 | 1.06164 | 0.530818 | − | 0.847486i | \(-0.321885\pi\) | ||||
0.530818 | + | 0.847486i | \(0.321885\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −2.83240 | −0.245600 | ||||||||
\(134\) | −1.93450 | −0.167115 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.37146 | −0.117602 | ||||||||
\(137\) | 2.81072 | 0.240136 | 0.120068 | − | 0.992766i | \(-0.461689\pi\) | ||||
0.120068 | + | 0.992766i | \(0.461689\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −11.6351 | −0.986879 | −0.493440 | − | 0.869780i | \(-0.664261\pi\) | ||||
−0.493440 | + | 0.869780i | \(0.664261\pi\) | |||||||
\(140\) | −0.190284 | −0.0160819 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.90862 | −0.495840 | ||||||||
\(143\) | 15.7878 | 1.32024 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −1.02573 | −0.0851821 | ||||||||
\(146\) | 7.70901 | 0.638002 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 12.6979 | 1.04376 | ||||||||
\(149\) | 1.00000 | 0.0819232 | ||||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 12.5969 | 1.02512 | 0.512561 | − | 0.858651i | \(-0.328697\pi\) | ||||
0.512561 | + | 0.858651i | \(0.328697\pi\) | |||||||
\(152\) | 13.9237 | 1.12936 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.871273 | 0.0702092 | ||||||||
\(155\) | −1.00408 | −0.0806494 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −21.5713 | −1.72157 | −0.860787 | − | 0.508965i | \(-0.830028\pi\) | ||||
−0.860787 | + | 0.508965i | \(0.830028\pi\) | |||||||
\(158\) | −5.42522 | −0.431607 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.44929 | 0.114577 | ||||||||
\(161\) | −3.06839 | −0.241823 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.17715 | −0.483832 | −0.241916 | − | 0.970297i | \(-0.577776\pi\) | ||||
−0.241916 | + | 0.970297i | \(0.577776\pi\) | |||||||
\(164\) | 19.9362 | 1.55675 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −3.59700 | −0.279181 | ||||||||
\(167\) | −9.65140 | −0.746848 | −0.373424 | − | 0.927661i | \(-0.621816\pi\) | ||||
−0.373424 | + | 0.927661i | \(0.621816\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.2697 | 0.789980 | ||||||||
\(170\) | −0.0984101 | −0.00754771 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −5.88297 | −0.448573 | ||||||||
\(173\) | 19.0109 | 1.44537 | 0.722685 | − | 0.691178i | \(-0.242908\pi\) | ||||
0.722685 | + | 0.691178i | \(0.242908\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.18977 | 0.165531 | ||||||||
\(176\) | 6.45535 | 0.486590 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2.64682 | −0.198387 | ||||||||
\(179\) | 16.8228 | 1.25739 | 0.628696 | − | 0.777651i | \(-0.283589\pi\) | ||||
0.628696 | + | 0.777651i | \(0.283589\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −4.57424 | −0.340000 | −0.170000 | − | 0.985444i | \(-0.554377\pi\) | ||||
−0.170000 | + | 0.985444i | \(0.554377\pi\) | |||||||
\(182\) | 1.28418 | 0.0951894 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 15.0838 | 1.11199 | ||||||||
\(185\) | 2.02195 | 0.148656 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −2.05643 | −0.150381 | ||||||||
\(188\) | −10.1546 | −0.740602 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.999101 | 0.0724824 | ||||||||
\(191\) | −10.9470 | −0.792099 | −0.396049 | − | 0.918229i | \(-0.629619\pi\) | ||||
−0.396049 | + | 0.918229i | \(0.629619\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.22630 | 0.0882713 | 0.0441357 | − | 0.999026i | \(-0.485947\pi\) | ||||
0.0441357 | + | 0.999026i | \(0.485947\pi\) | |||||||
\(194\) | 3.32855 | 0.238976 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 11.1603 | 0.797163 | ||||||||
\(197\) | 23.0036 | 1.63894 | 0.819471 | − | 0.573121i | \(-0.194268\pi\) | ||||
0.819471 | + | 0.573121i | \(0.194268\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.64001 | 0.328922 | 0.164461 | − | 0.986384i | \(-0.447412\pi\) | ||||
0.164461 | + | 0.986384i | \(0.447412\pi\) | |||||||
\(200\) | −10.7646 | −0.761172 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −0.623863 | −0.0438949 | ||||||||
\(203\) | −1.74345 | −0.122366 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.17452 | 0.221718 | ||||||||
\(206\) | 4.63022 | 0.322603 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 9.51459 | 0.659718 | ||||||||
\(209\) | 20.8777 | 1.44414 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.989304 | −0.0681065 | −0.0340532 | − | 0.999420i | \(-0.510842\pi\) | ||||
−0.0340532 | + | 0.999420i | \(0.510842\pi\) | |||||||
\(212\) | −4.11343 | −0.282511 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −12.2399 | −0.836703 | ||||||||
\(215\) | −0.936770 | −0.0638872 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.70665 | −0.115855 | ||||||||
\(218\) | −5.36144 | −0.363122 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.40259 | 0.0945624 | ||||||||
\(221\) | −3.03098 | −0.203886 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 17.9115 | 1.19944 | 0.599721 | − | 0.800209i | \(-0.295278\pi\) | ||||
0.599721 | + | 0.800209i | \(0.295278\pi\) | |||||||
\(224\) | 2.46339 | 0.164592 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3.30638 | −0.219937 | ||||||||
\(227\) | −11.8155 | −0.784220 | −0.392110 | − | 0.919918i | \(-0.628255\pi\) | ||||
−0.392110 | + | 0.919918i | \(0.628255\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 7.12495 | 0.470830 | 0.235415 | − | 0.971895i | \(-0.424355\pi\) | ||||
0.235415 | + | 0.971895i | \(0.424355\pi\) | |||||||
\(230\) | 1.08234 | 0.0713677 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 8.57054 | 0.562683 | ||||||||
\(233\) | 6.65663 | 0.436091 | 0.218045 | − | 0.975939i | \(-0.430032\pi\) | ||||
0.218045 | + | 0.975939i | \(0.430032\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.61696 | −0.105479 | ||||||||
\(236\) | 13.6581 | 0.889066 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.167269 | −0.0108425 | ||||||||
\(239\) | −25.9173 | −1.67645 | −0.838226 | − | 0.545323i | \(-0.816407\pi\) | ||||
−0.838226 | + | 0.545323i | \(0.816407\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 3.81308 | 0.245622 | 0.122811 | − | 0.992430i | \(-0.460809\pi\) | ||||
0.122811 | + | 0.992430i | \(0.460809\pi\) | |||||||
\(242\) | 0.172967 | 0.0111187 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.63240 | −0.232540 | ||||||||
\(245\) | 1.77710 | 0.113535 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 30.7718 | 1.95796 | ||||||||
\(248\) | 8.38963 | 0.532742 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.55553 | −0.0983803 | ||||||||
\(251\) | −9.02429 | −0.569608 | −0.284804 | − | 0.958586i | \(-0.591929\pi\) | ||||
−0.284804 | + | 0.958586i | \(0.591929\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 22.6172 | 1.42193 | ||||||||
\(254\) | 5.50219 | 0.345238 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −5.63810 | −0.352381 | ||||||||
\(257\) | −17.5684 | −1.09589 | −0.547944 | − | 0.836515i | \(-0.684589\pi\) | ||||
−0.547944 | + | 0.836515i | \(0.684589\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.43674 | 0.213549 | ||||||||
\(260\) | 2.06728 | 0.128208 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −7.28522 | −0.450082 | ||||||||
\(263\) | 9.80603 | 0.604665 | 0.302333 | − | 0.953202i | \(-0.402235\pi\) | ||||
0.302333 | + | 0.953202i | \(0.402235\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −0.654998 | −0.0402362 | ||||||||
\(266\) | 1.69819 | 0.104123 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5.29323 | −0.323336 | ||||||||
\(269\) | 3.16294 | 0.192848 | 0.0964238 | − | 0.995340i | \(-0.469260\pi\) | ||||
0.0964238 | + | 0.995340i | \(0.469260\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −9.46191 | −0.574770 | −0.287385 | − | 0.957815i | \(-0.592786\pi\) | ||||
−0.287385 | + | 0.957815i | \(0.592786\pi\) | |||||||
\(272\) | −1.23932 | −0.0751446 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.68519 | −0.101806 | ||||||||
\(275\) | −16.1409 | −0.973332 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 18.4411 | 1.10802 | 0.554009 | − | 0.832511i | \(-0.313097\pi\) | ||||
0.554009 | + | 0.832511i | \(0.313097\pi\) | |||||||
\(278\) | 6.97594 | 0.418389 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.253171 | 0.0151299 | ||||||||
\(281\) | 0.316081 | 0.0188558 | 0.00942791 | − | 0.999956i | \(-0.496999\pi\) | ||||
0.00942791 | + | 0.999956i | \(0.496999\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 20.5665 | 1.22255 | 0.611276 | − | 0.791418i | \(-0.290657\pi\) | ||||
0.611276 | + | 0.791418i | \(0.290657\pi\) | |||||||
\(284\) | −16.1673 | −0.959355 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −9.46570 | −0.559718 | ||||||||
\(287\) | 5.39578 | 0.318503 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −16.6052 | −0.976777 | ||||||||
\(290\) | 0.614984 | 0.0361131 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 21.0936 | 1.23441 | ||||||||
\(293\) | 24.2034 | 1.41398 | 0.706989 | − | 0.707224i | \(-0.250053\pi\) | ||||
0.706989 | + | 0.707224i | \(0.250053\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2.17484 | 0.126624 | ||||||||
\(296\) | −16.8945 | −0.981973 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −0.599558 | −0.0347315 | ||||||||
\(299\) | 33.3357 | 1.92785 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.59225 | −0.0917755 | ||||||||
\(302\) | −7.55259 | −0.434603 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 12.5821 | 0.721631 | ||||||||
\(305\) | −0.578402 | −0.0331192 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −28.2176 | −1.61046 | −0.805232 | − | 0.592960i | \(-0.797959\pi\) | ||||
−0.805232 | + | 0.592960i | \(0.797959\pi\) | |||||||
\(308\) | 2.38400 | 0.135841 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0.602003 | 0.0341915 | ||||||||
\(311\) | −23.0808 | −1.30879 | −0.654396 | − | 0.756152i | \(-0.727077\pi\) | ||||
−0.654396 | + | 0.756152i | \(0.727077\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −29.4823 | −1.66644 | −0.833219 | − | 0.552943i | \(-0.813505\pi\) | ||||
−0.833219 | + | 0.552943i | \(0.813505\pi\) | |||||||
\(314\) | 12.9332 | 0.729865 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −14.8446 | −0.835076 | ||||||||
\(317\) | 22.9025 | 1.28633 | 0.643165 | − | 0.765728i | \(-0.277621\pi\) | ||||
0.643165 | + | 0.765728i | \(0.277621\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.8510 | 0.719519 | ||||||||
\(320\) | 0.161557 | 0.00903132 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.83968 | 0.102521 | ||||||||
\(323\) | −4.00816 | −0.223020 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −23.7902 | −1.31964 | ||||||||
\(326\) | 3.70356 | 0.205121 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −26.5249 | −1.46459 | ||||||||
\(329\) | −2.74838 | −0.151523 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.8813 | 1.09277 | 0.546387 | − | 0.837533i | \(-0.316003\pi\) | ||||
0.546387 | + | 0.837533i | \(0.316003\pi\) | |||||||
\(332\) | −9.84222 | −0.540162 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 5.78658 | 0.316627 | ||||||||
\(335\) | −0.842863 | −0.0460505 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.1256 | −0.660526 | −0.330263 | − | 0.943889i | \(-0.607137\pi\) | ||||
−0.330263 | + | 0.943889i | \(0.607137\pi\) | |||||||
\(338\) | −6.15731 | −0.334913 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −0.269273 | −0.0146034 | ||||||||
\(341\) | 12.5797 | 0.681231 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.12867 | 0.330917 | ||||||||
\(344\) | 7.82724 | 0.422017 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −11.3981 | −0.612767 | ||||||||
\(347\) | −12.1614 | −0.652858 | −0.326429 | − | 0.945222i | \(-0.605845\pi\) | ||||
−0.326429 | + | 0.945222i | \(0.605845\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.3827 | −0.609304 | −0.304652 | − | 0.952464i | \(-0.598540\pi\) | ||||
−0.304652 | + | 0.952464i | \(0.598540\pi\) | |||||||
\(350\) | −1.31290 | −0.0701773 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −18.1577 | −0.967809 | ||||||||
\(353\) | 30.1093 | 1.60255 | 0.801277 | − | 0.598293i | \(-0.204154\pi\) | ||||
0.801277 | + | 0.598293i | \(0.204154\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.57439 | −0.136635 | ||||||||
\(356\) | −7.24230 | −0.383841 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −10.0862 | −0.533074 | ||||||||
\(359\) | 14.2687 | 0.753074 | 0.376537 | − | 0.926402i | \(-0.377115\pi\) | ||||
0.376537 | + | 0.926402i | \(0.377115\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 21.6925 | 1.14171 | ||||||||
\(362\) | 2.74252 | 0.144144 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3.51380 | 0.184173 | ||||||||
\(365\) | 3.35883 | 0.175809 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.1200 | −0.945858 | −0.472929 | − | 0.881101i | \(-0.656803\pi\) | ||||
−0.472929 | + | 0.881101i | \(0.656803\pi\) | |||||||
\(368\) | 13.6304 | 0.710533 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.21228 | −0.0630232 | ||||||||
\(371\) | −1.11331 | −0.0578003 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 34.0027 | 1.76059 | 0.880296 | − | 0.474425i | \(-0.157344\pi\) | ||||
0.880296 | + | 0.474425i | \(0.157344\pi\) | |||||||
\(374\) | 1.23295 | 0.0637542 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 13.5106 | 0.696758 | ||||||||
\(377\) | 18.9412 | 0.975522 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.110504 | 0.00567621 | 0.00283810 | − | 0.999996i | \(-0.499097\pi\) | ||||
0.00283810 | + | 0.999996i | \(0.499097\pi\) | |||||||
\(380\) | 2.73377 | 0.140239 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 6.56338 | 0.335812 | ||||||||
\(383\) | 4.21011 | 0.215126 | 0.107563 | − | 0.994198i | \(-0.465695\pi\) | ||||
0.107563 | + | 0.994198i | \(0.465695\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.379615 | 0.0193470 | ||||||||
\(386\) | −0.735241 | −0.0374228 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9.10769 | 0.462373 | ||||||||
\(389\) | −8.13526 | −0.412474 | −0.206237 | − | 0.978502i | \(-0.566122\pi\) | ||||
−0.206237 | + | 0.978502i | \(0.566122\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.34211 | −0.219590 | ||||||||
\(392\) | −14.8487 | −0.749970 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −13.7920 | −0.694832 | ||||||||
\(395\) | −2.36377 | −0.118934 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 16.2733 | 0.816734 | 0.408367 | − | 0.912818i | \(-0.366098\pi\) | ||||
0.408367 | + | 0.912818i | \(0.366098\pi\) | |||||||
\(398\) | −2.78196 | −0.139447 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −9.72739 | −0.486369 | ||||||||
\(401\) | −15.3552 | −0.766801 | −0.383400 | − | 0.923582i | \(-0.625247\pi\) | ||||
−0.383400 | + | 0.923582i | \(0.625247\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.5414 | 0.923612 | ||||||||
\(404\) | −1.70703 | −0.0849281 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.04530 | 0.0518774 | ||||||||
\(407\) | −25.3323 | −1.25568 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.8831 | 0.735920 | 0.367960 | − | 0.929842i | \(-0.380056\pi\) | ||||
0.367960 | + | 0.929842i | \(0.380056\pi\) | |||||||
\(410\) | −1.90331 | −0.0939977 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 12.6693 | 0.624174 | ||||||||
\(413\) | 3.69661 | 0.181898 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.56722 | −0.0769317 | ||||||||
\(416\) | −26.7628 | −1.31215 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −12.5174 | −0.612246 | ||||||||
\(419\) | 30.4137 | 1.48580 | 0.742902 | − | 0.669400i | \(-0.233449\pi\) | ||||
0.742902 | + | 0.669400i | \(0.233449\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 22.4259 | 1.09297 | 0.546485 | − | 0.837469i | \(-0.315966\pi\) | ||||
0.546485 | + | 0.837469i | \(0.315966\pi\) | |||||||
\(422\) | 0.593145 | 0.0288739 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.47288 | 0.265786 | ||||||||
\(425\) | 3.09877 | 0.150313 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −0.983119 | −0.0475765 | ||||||||
\(428\) | −33.4912 | −1.61886 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.561649 | 0.0270851 | ||||||||
\(431\) | −21.9702 | −1.05827 | −0.529134 | − | 0.848539i | \(-0.677483\pi\) | ||||
−0.529134 | + | 0.848539i | \(0.677483\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.6950 | 0.850367 | 0.425183 | − | 0.905107i | \(-0.360210\pi\) | ||||
0.425183 | + | 0.905107i | \(0.360210\pi\) | |||||||
\(434\) | 1.02323 | 0.0491168 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −14.6701 | −0.702572 | ||||||||
\(437\) | 44.0830 | 2.10878 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −3.03826 | −0.145008 | −0.0725040 | − | 0.997368i | \(-0.523099\pi\) | ||||
−0.0725040 | + | 0.997368i | \(0.523099\pi\) | |||||||
\(440\) | −1.86613 | −0.0889642 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.81725 | 0.0864378 | ||||||||
\(443\) | −8.37147 | −0.397741 | −0.198870 | − | 0.980026i | \(-0.563727\pi\) | ||||
−0.198870 | + | 0.980026i | \(0.563727\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.15322 | −0.0546680 | ||||||||
\(446\) | −10.7390 | −0.508506 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0.274602 | 0.0129737 | ||||||||
\(449\) | −40.5209 | −1.91230 | −0.956149 | − | 0.292881i | \(-0.905386\pi\) | ||||
−0.956149 | + | 0.292881i | \(0.905386\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −39.7725 | −1.87281 | ||||||||
\(452\) | −9.04701 | −0.425536 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 7.08406 | 0.332472 | ||||||||
\(455\) | 0.559517 | 0.0262306 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −34.8252 | −1.62905 | −0.814527 | − | 0.580126i | \(-0.803003\pi\) | ||||
−0.814527 | + | 0.580126i | \(0.803003\pi\) | |||||||
\(458\) | −4.27183 | −0.199609 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.96154 | 0.138083 | ||||||||
\(461\) | 38.7754 | 1.80595 | 0.902976 | − | 0.429691i | \(-0.141377\pi\) | ||||
0.902976 | + | 0.429691i | \(0.141377\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 9.24148 | 0.429488 | 0.214744 | − | 0.976670i | \(-0.431108\pi\) | ||||
0.214744 | + | 0.976670i | \(0.431108\pi\) | |||||||
\(464\) | 7.74473 | 0.359540 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3.99104 | −0.184881 | ||||||||
\(467\) | 29.2041 | 1.35140 | 0.675701 | − | 0.737175i | \(-0.263841\pi\) | ||||
0.675701 | + | 0.737175i | \(0.263841\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.43263 | −0.0661527 | ||||||||
\(470\) | 0.969464 | 0.0447181 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −18.1720 | −0.836433 | ||||||||
\(473\) | 11.7365 | 0.539644 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −31.4600 | −1.44349 | ||||||||
\(476\) | −0.457688 | −0.0209781 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 15.5389 | 0.710735 | ||||||||
\(479\) | −13.5808 | −0.620521 | −0.310261 | − | 0.950652i | \(-0.600416\pi\) | ||||
−0.310261 | + | 0.950652i | \(0.600416\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −37.3375 | −1.70244 | ||||||||
\(482\) | −2.28616 | −0.104132 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.473276 | 0.0215126 | ||||||||
\(485\) | 1.45026 | 0.0658527 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 20.2699 | 0.918515 | 0.459258 | − | 0.888303i | \(-0.348115\pi\) | ||||
0.459258 | + | 0.888303i | \(0.348115\pi\) | |||||||
\(488\) | 4.83287 | 0.218774 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.06547 | −0.0481332 | ||||||||
\(491\) | 0.396394 | 0.0178890 | 0.00894451 | − | 0.999960i | \(-0.497153\pi\) | ||||
0.00894451 | + | 0.999960i | \(0.497153\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.46717 | −0.111116 | ||||||||
\(494\) | −18.4495 | −0.830082 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.58125 | 0.340408 | ||||||||
\(497\) | −4.37574 | −0.196279 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.61548 | 0.296149 | 0.148075 | − | 0.988976i | \(-0.452692\pi\) | ||||
0.148075 | + | 0.988976i | \(0.452692\pi\) | |||||||
\(500\) | −4.25629 | −0.190347 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 5.41059 | 0.241486 | ||||||||
\(503\) | −20.0664 | −0.894715 | −0.447358 | − | 0.894355i | \(-0.647635\pi\) | ||||
−0.447358 | + | 0.894355i | \(0.647635\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −0.271818 | −0.0120957 | ||||||||
\(506\) | −13.5603 | −0.602830 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 15.0552 | 0.667969 | ||||||||
\(509\) | 32.9530 | 1.46061 | 0.730307 | − | 0.683119i | \(-0.239377\pi\) | ||||
0.730307 | + | 0.683119i | \(0.239377\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.70905 | 0.252554 | ||||||||
\(512\) | −19.5532 | −0.864137 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10.5333 | 0.464604 | ||||||||
\(515\) | 2.01739 | 0.0888969 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 20.2584 | 0.890964 | ||||||||
\(518\) | −2.06053 | −0.0905343 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −2.75050 | −0.120618 | ||||||||
\(521\) | 10.7886 | 0.472659 | 0.236329 | − | 0.971673i | \(-0.424056\pi\) | ||||
0.236329 | + | 0.971673i | \(0.424056\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.19598 | −0.139750 | −0.0698751 | − | 0.997556i | \(-0.522260\pi\) | ||||
−0.0698751 | + | 0.997556i | \(0.522260\pi\) | |||||||
\(524\) | −19.9340 | −0.870822 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.87929 | −0.256349 | ||||||||
\(527\) | −2.41510 | −0.105203 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 24.7559 | 1.07634 | ||||||||
\(530\) | 0.392710 | 0.0170582 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.64664 | 0.201457 | ||||||||
\(533\) | −58.6210 | −2.53916 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.33295 | −0.230563 | ||||||||
\(536\) | 7.04260 | 0.304194 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.89637 | −0.0817581 | ||||||||
\(539\) | −22.2647 | −0.959007 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.540896 | 0.0232549 | 0.0116275 | − | 0.999932i | \(-0.496299\pi\) | ||||
0.0116275 | + | 0.999932i | \(0.496299\pi\) | |||||||
\(542\) | 5.67297 | 0.243675 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.48597 | 0.149460 | ||||||||
\(545\) | −2.33599 | −0.100063 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.20203 | −0.136909 | −0.0684545 | − | 0.997654i | \(-0.521807\pi\) | ||||
−0.0684545 | + | 0.997654i | \(0.521807\pi\) | |||||||
\(548\) | −4.61107 | −0.196975 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 9.67740 | 0.412646 | ||||||||
\(551\) | 25.0478 | 1.06707 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.01775 | −0.170852 | ||||||||
\(554\) | −11.0565 | −0.469746 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 19.0878 | 0.809502 | ||||||||
\(557\) | −27.5147 | −1.16583 | −0.582917 | − | 0.812532i | \(-0.698089\pi\) | ||||
−0.582917 | + | 0.812532i | \(0.698089\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 17.2985 | 0.731649 | ||||||||
\(560\) | 0.228777 | 0.00966759 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.189509 | −0.00799396 | ||||||||
\(563\) | −23.7576 | −1.00126 | −0.500631 | − | 0.865661i | \(-0.666899\pi\) | ||||
−0.500631 | + | 0.865661i | \(0.666899\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.44059 | −0.0606062 | ||||||||
\(566\) | −12.3308 | −0.518303 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 21.5105 | 0.902560 | ||||||||
\(569\) | 27.3845 | 1.14802 | 0.574009 | − | 0.818849i | \(-0.305387\pi\) | ||||
0.574009 | + | 0.818849i | \(0.305387\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.1732 | −1.13716 | −0.568582 | − | 0.822627i | \(-0.692508\pi\) | ||||
−0.568582 | + | 0.822627i | \(0.692508\pi\) | |||||||
\(572\) | −25.9003 | −1.08295 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.23509 | −0.135030 | ||||||||
\(575\) | −34.0812 | −1.42129 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 37.6523 | 1.56748 | 0.783742 | − | 0.621086i | \(-0.213308\pi\) | ||||
0.783742 | + | 0.621086i | \(0.213308\pi\) | |||||||
\(578\) | 9.95579 | 0.414106 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.68274 | 0.0698719 | ||||||||
\(581\) | −2.66383 | −0.110514 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.20625 | 0.339868 | ||||||||
\(584\) | −28.0649 | −1.16133 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −14.5114 | −0.599459 | ||||||||
\(587\) | −13.3155 | −0.549591 | −0.274795 | − | 0.961503i | \(-0.588610\pi\) | ||||
−0.274795 | + | 0.961503i | \(0.588610\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 24.5191 | 1.01029 | ||||||||
\(590\) | −1.30394 | −0.0536824 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −15.2666 | −0.627455 | ||||||||
\(593\) | −14.2693 | −0.585969 | −0.292984 | − | 0.956117i | \(-0.594648\pi\) | ||||
−0.292984 | + | 0.956117i | \(0.594648\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.0728795 | −0.00298777 | ||||||||
\(596\) | −1.64053 | −0.0671987 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −19.9867 | −0.817316 | ||||||||
\(599\) | 17.4816 | 0.714278 | 0.357139 | − | 0.934051i | \(-0.383752\pi\) | ||||
0.357139 | + | 0.934051i | \(0.383752\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 15.4975 | 0.632157 | 0.316079 | − | 0.948733i | \(-0.397634\pi\) | ||||
0.316079 | + | 0.948733i | \(0.397634\pi\) | |||||||
\(602\) | 0.954644 | 0.0389084 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −20.6656 | −0.840872 | ||||||||
\(605\) | 0.0753617 | 0.00306389 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.01090 | 0.162797 | 0.0813987 | − | 0.996682i | \(-0.474061\pi\) | ||||
0.0813987 | + | 0.996682i | \(0.474061\pi\) | |||||||
\(608\) | −35.3910 | −1.43529 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.346786 | 0.0140409 | ||||||||
\(611\) | 29.8590 | 1.20797 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −12.5165 | −0.505535 | −0.252767 | − | 0.967527i | \(-0.581341\pi\) | ||||
−0.252767 | + | 0.967527i | \(0.581341\pi\) | |||||||
\(614\) | 16.9181 | 0.682759 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.17189 | −0.127799 | ||||||||
\(617\) | 5.54908 | 0.223398 | 0.111699 | − | 0.993742i | \(-0.464371\pi\) | ||||
0.111699 | + | 0.993742i | \(0.464371\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 43.4692 | 1.74717 | 0.873587 | − | 0.486668i | \(-0.161788\pi\) | ||||
0.873587 | + | 0.486668i | \(0.161788\pi\) | |||||||
\(620\) | 1.64722 | 0.0661539 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 13.8383 | 0.554865 | ||||||||
\(623\) | −1.96015 | −0.0785319 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 23.9811 | 0.959242 | ||||||||
\(626\) | 17.6764 | 0.706490 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 35.3883 | 1.41215 | ||||||||
\(629\) | 4.86337 | 0.193915 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.42040 | −0.215783 | −0.107891 | − | 0.994163i | \(-0.534410\pi\) | ||||
−0.107891 | + | 0.994163i | \(0.534410\pi\) | |||||||
\(632\) | 19.7507 | 0.785639 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −13.7314 | −0.545342 | ||||||||
\(635\) | 2.39731 | 0.0951344 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −32.8161 | −1.30022 | ||||||||
\(638\) | −7.70493 | −0.305041 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.99545 | −0.118405 | ||||||||
\(641\) | 25.5927 | 1.01085 | 0.505425 | − | 0.862871i | \(-0.331336\pi\) | ||||
0.505425 | + | 0.862871i | \(0.331336\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 0.497333 | 0.0196129 | 0.00980646 | − | 0.999952i | \(-0.496878\pi\) | ||||
0.00980646 | + | 0.999952i | \(0.496878\pi\) | |||||||
\(644\) | 5.03379 | 0.198359 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 2.40313 | 0.0945498 | ||||||||
\(647\) | 29.8394 | 1.17311 | 0.586554 | − | 0.809910i | \(-0.300484\pi\) | ||||
0.586554 | + | 0.809910i | \(0.300484\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −27.2478 | −1.06957 | ||||||||
\(650\) | 14.2636 | 0.559464 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 10.1338 | 0.396870 | ||||||||
\(653\) | −34.4463 | −1.34799 | −0.673995 | − | 0.738736i | \(-0.735423\pi\) | ||||
−0.673995 | + | 0.738736i | \(0.735423\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.17418 | −0.124025 | ||||||||
\(656\) | −23.9691 | −0.935836 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.64782 | 0.0642386 | ||||||||
\(659\) | 5.25578 | 0.204736 | 0.102368 | − | 0.994747i | \(-0.467358\pi\) | ||||
0.102368 | + | 0.994747i | \(0.467358\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.37505 | 0.0923786 | 0.0461893 | − | 0.998933i | \(-0.485292\pi\) | ||||
0.0461893 | + | 0.998933i | \(0.485292\pi\) | |||||||
\(662\) | −11.9200 | −0.463284 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 13.0950 | 0.508184 | ||||||||
\(665\) | 0.739904 | 0.0286922 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 27.1347 | 1.05066 | ||||||||
\(668\) | 15.8334 | 0.612613 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0.505346 | 0.0195232 | ||||||||
\(671\) | 7.24660 | 0.279752 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −25.2096 | −0.971757 | −0.485879 | − | 0.874026i | \(-0.661500\pi\) | ||||
−0.485879 | + | 0.874026i | \(0.661500\pi\) | |||||||
\(674\) | 7.27003 | 0.280031 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −16.8478 | −0.647992 | ||||||||
\(677\) | 11.2836 | 0.433662 | 0.216831 | − | 0.976209i | \(-0.430428\pi\) | ||||
0.216831 | + | 0.976209i | \(0.430428\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.46502 | 0.0945989 | ||||||||
\(680\) | 0.358265 | 0.0137388 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.54229 | −0.288809 | ||||||||
\(683\) | −25.0490 | −0.958473 | −0.479237 | − | 0.877686i | \(-0.659086\pi\) | ||||
−0.479237 | + | 0.877686i | \(0.659086\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −0.734239 | −0.0280538 | ||||||||
\(686\) | −3.67449 | −0.140293 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 7.07306 | 0.269658 | ||||||||
\(689\) | 12.0953 | 0.460793 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −29.1571 | −1.10919 | −0.554594 | − | 0.832121i | \(-0.687126\pi\) | ||||
−0.554594 | + | 0.832121i | \(0.687126\pi\) | |||||||
\(692\) | −31.1879 | −1.18559 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.29147 | 0.276780 | ||||||||
\(695\) | 3.03943 | 0.115292 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 7.63563 | 0.289220 | ||||||||
\(698\) | 6.82462 | 0.258316 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −3.59239 | −0.135780 | ||||||||
\(701\) | 19.8243 | 0.748753 | 0.374377 | − | 0.927277i | \(-0.377857\pi\) | ||||
0.374377 | + | 0.927277i | \(0.377857\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −49.3750 | −1.86221 | ||||||||
\(704\) | −2.02410 | −0.0762860 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −18.0523 | −0.679406 | ||||||||
\(707\) | −0.462014 | −0.0173758 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −48.3680 | −1.81650 | −0.908250 | − | 0.418428i | \(-0.862581\pi\) | ||||
−0.908250 | + | 0.418428i | \(0.862581\pi\) | |||||||
\(710\) | 1.54350 | 0.0579265 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 9.63582 | 0.361118 | ||||||||
\(713\) | 26.5620 | 0.994753 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −4.12422 | −0.154237 | ||||||||
\(716\) | −27.5983 | −1.03140 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −8.55493 | −0.319267 | ||||||||
\(719\) | −19.4064 | −0.723736 | −0.361868 | − | 0.932229i | \(-0.617861\pi\) | ||||
−0.361868 | + | 0.932229i | \(0.617861\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3.42900 | 0.127703 | ||||||||
\(722\) | −13.0060 | −0.484031 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 7.50417 | 0.278890 | ||||||||
\(725\) | −19.3648 | −0.719192 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 17.8775 | 0.663041 | 0.331521 | − | 0.943448i | \(-0.392438\pi\) | ||||
0.331521 | + | 0.943448i | \(0.392438\pi\) | |||||||
\(728\) | −4.67508 | −0.173270 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.01381 | −0.0745345 | ||||||||
\(731\) | −2.25320 | −0.0833378 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 37.9664 | 1.40232 | 0.701161 | − | 0.713003i | \(-0.252666\pi\) | ||||
0.701161 | + | 0.713003i | \(0.252666\pi\) | |||||||
\(734\) | 10.8640 | 0.400998 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −38.3397 | −1.41322 | ||||||||
\(737\) | 10.5600 | 0.388981 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 45.1250 | 1.65995 | 0.829976 | − | 0.557800i | \(-0.188354\pi\) | ||||
0.829976 | + | 0.557800i | \(0.188354\pi\) | |||||||
\(740\) | −3.31706 | −0.121938 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0.667495 | 0.0245045 | ||||||||
\(743\) | 3.12372 | 0.114598 | 0.0572990 | − | 0.998357i | \(-0.481751\pi\) | ||||
0.0572990 | + | 0.998357i | \(0.481751\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.261228 | −0.00957067 | ||||||||
\(746\) | −20.3866 | −0.746406 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.37363 | 0.123352 | ||||||||
\(749\) | −9.06450 | −0.331210 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −0.918626 | −0.0335211 | −0.0167606 | − | 0.999860i | \(-0.505335\pi\) | ||||
−0.0167606 | + | 0.999860i | \(0.505335\pi\) | |||||||
\(752\) | 12.2088 | 0.445210 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −11.3564 | −0.413574 | ||||||||
\(755\) | −3.29067 | −0.119760 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −49.7475 | −1.80810 | −0.904051 | − | 0.427424i | \(-0.859421\pi\) | ||||
−0.904051 | + | 0.427424i | \(0.859421\pi\) | |||||||
\(758\) | −0.0662536 | −0.00240644 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −3.63726 | −0.131937 | ||||||||
\(761\) | −29.8519 | −1.08213 | −0.541065 | − | 0.840981i | \(-0.681979\pi\) | ||||
−0.541065 | + | 0.840981i | \(0.681979\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.97052 | −0.143742 | ||||||||
\(764\) | 17.9589 | 0.649731 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −2.52420 | −0.0912032 | ||||||||
\(767\) | −40.1607 | −1.45012 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −40.8013 | −1.47133 | −0.735666 | − | 0.677345i | \(-0.763131\pi\) | ||||
−0.735666 | + | 0.677345i | \(0.763131\pi\) | |||||||
\(770\) | −0.227601 | −0.00820218 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.01179 | −0.0724059 | ||||||||
\(773\) | −23.0022 | −0.827330 | −0.413665 | − | 0.910429i | \(-0.635752\pi\) | ||||
−0.413665 | + | 0.910429i | \(0.635752\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18.9561 | −0.680922 | ||||||||
\(776\) | −12.1177 | −0.435000 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 4.87756 | 0.174869 | ||||||||
\(779\) | −77.5202 | −2.77745 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 32.2537 | 1.15413 | ||||||||
\(782\) | 2.60335 | 0.0930956 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −13.4179 | −0.479212 | ||||||||
\(785\) | 5.63503 | 0.201123 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 44.6790 | 1.59263 | 0.796317 | − | 0.604880i | \(-0.206779\pi\) | ||||
0.796317 | + | 0.604880i | \(0.206779\pi\) | |||||||
\(788\) | −37.7382 | −1.34437 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 1.41722 | 0.0504224 | ||||||||
\(791\) | −2.44860 | −0.0870623 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.6808 | 0.379287 | ||||||||
\(794\) | −9.75679 | −0.346256 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.61207 | −0.269803 | ||||||||
\(797\) | −29.5661 | −1.04728 | −0.523642 | − | 0.851939i | \(-0.675427\pi\) | ||||
−0.523642 | + | 0.851939i | \(0.675427\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.88927 | −0.137592 | ||||||||
\(800\) | 27.3613 | 0.967370 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 9.20632 | 0.325087 | ||||||||
\(803\) | −42.0816 | −1.48503 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0.801551 | 0.0282510 | ||||||||
\(806\) | −11.1166 | −0.391567 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.27119 | 0.0799003 | ||||||||
\(809\) | 39.7260 | 1.39669 | 0.698346 | − | 0.715760i | \(-0.253920\pi\) | ||||
0.698346 | + | 0.715760i | \(0.253920\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17.2842 | 0.606930 | 0.303465 | − | 0.952843i | \(-0.401857\pi\) | ||||
0.303465 | + | 0.952843i | \(0.401857\pi\) | |||||||
\(812\) | 2.86018 | 0.100373 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 15.1882 | 0.532346 | ||||||||
\(815\) | 1.61365 | 0.0565236 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 22.8755 | 0.800312 | ||||||||
\(818\) | −8.92327 | −0.311995 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −5.20789 | −0.181867 | ||||||||
\(821\) | 44.8857 | 1.56652 | 0.783261 | − | 0.621694i | \(-0.213555\pi\) | ||||
0.783261 | + | 0.621694i | \(0.213555\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −30.2619 | −1.05486 | −0.527431 | − | 0.849598i | \(-0.676845\pi\) | ||||
−0.527431 | + | 0.849598i | \(0.676845\pi\) | |||||||
\(824\) | −16.8564 | −0.587222 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2.21633 | −0.0771160 | ||||||||
\(827\) | 38.7434 | 1.34724 | 0.673620 | − | 0.739077i | \(-0.264738\pi\) | ||||
0.673620 | + | 0.739077i | \(0.264738\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 27.5153 | 0.955645 | 0.477823 | − | 0.878456i | \(-0.341426\pi\) | ||||
0.477823 | + | 0.878456i | \(0.341426\pi\) | |||||||
\(830\) | 0.939639 | 0.0326153 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.98333 | −0.103428 | ||||||||
\(833\) | 4.27443 | 0.148100 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.52122 | 0.0872504 | ||||||||
\(836\) | −34.2505 | −1.18458 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −18.2348 | −0.629910 | ||||||||
\(839\) | 4.74016 | 0.163648 | 0.0818242 | − | 0.996647i | \(-0.473925\pi\) | ||||
0.0818242 | + | 0.996647i | \(0.473925\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.5821 | −0.468350 | ||||||||
\(842\) | −13.4456 | −0.463367 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.62298 | 0.0558654 | ||||||||
\(845\) | −2.68275 | −0.0922893 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0.128094 | 0.00440135 | ||||||||
\(848\) | 4.94554 | 0.169831 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.85789 | −0.0637253 | ||||||||
\(851\) | −53.4888 | −1.83357 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 52.6087 | 1.80129 | 0.900643 | − | 0.434559i | \(-0.143096\pi\) | ||||
0.900643 | + | 0.434559i | \(0.143096\pi\) | |||||||
\(854\) | 0.589438 | 0.0201701 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 44.5598 | 1.52302 | ||||||||
\(857\) | −2.38074 | −0.0813244 | −0.0406622 | − | 0.999173i | \(-0.512947\pi\) | ||||
−0.0406622 | + | 0.999173i | \(0.512947\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 4.31177 | 0.147116 | 0.0735578 | − | 0.997291i | \(-0.476565\pi\) | ||||
0.0735578 | + | 0.997291i | \(0.476565\pi\) | |||||||
\(860\) | 1.53680 | 0.0524044 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13.1724 | 0.448654 | ||||||||
\(863\) | −33.2810 | −1.13290 | −0.566449 | − | 0.824097i | \(-0.691683\pi\) | ||||
−0.566449 | + | 0.824097i | \(0.691683\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −4.96618 | −0.168855 | ||||||||
\(866\) | −10.6092 | −0.360514 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2.79981 | 0.0950316 | ||||||||
\(869\) | 29.6149 | 1.00462 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 15.5644 | 0.527380 | ||||||||
\(872\) | 19.5185 | 0.660979 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −26.4303 | −0.894019 | ||||||||
\(875\) | −1.15198 | −0.0389439 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.71046 | 0.125293 | 0.0626467 | − | 0.998036i | \(-0.480046\pi\) | ||||
0.0626467 | + | 0.998036i | \(0.480046\pi\) | |||||||
\(878\) | 1.82161 | 0.0614764 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.68632 | −0.0568459 | ||||||||
\(881\) | −31.9505 | −1.07644 | −0.538219 | − | 0.842805i | \(-0.680903\pi\) | ||||
−0.538219 | + | 0.842805i | \(0.680903\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.05315 | −0.0354412 | −0.0177206 | − | 0.999843i | \(-0.505641\pi\) | ||||
−0.0177206 | + | 0.999843i | \(0.505641\pi\) | |||||||
\(884\) | 4.97242 | 0.167240 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 5.01919 | 0.168623 | ||||||||
\(887\) | 45.8752 | 1.54034 | 0.770169 | − | 0.637840i | \(-0.220172\pi\) | ||||
0.770169 | + | 0.637840i | \(0.220172\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 4.07475 | 0.136663 | ||||||||
\(890\) | 0.691424 | 0.0231766 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −29.3843 | −0.983860 | ||||||||
\(893\) | 39.4855 | 1.32133 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.39459 | −0.146895 | ||||||||
\(896\) | −5.09141 | −0.170092 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 24.2946 | 0.810722 | ||||||||
\(899\) | 15.0924 | 0.503360 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1.57546 | −0.0524862 | ||||||||
\(902\) | 23.8459 | 0.793982 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 12.0370 | 0.400344 | ||||||||
\(905\) | 1.19492 | 0.0397205 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 32.5597 | 1.08113 | 0.540563 | − | 0.841304i | \(-0.318211\pi\) | ||||
0.540563 | + | 0.841304i | \(0.318211\pi\) | |||||||
\(908\) | 19.3836 | 0.643268 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −0.335463 | −0.0111205 | ||||||||
\(911\) | −43.9638 | −1.45658 | −0.728292 | − | 0.685267i | \(-0.759686\pi\) | ||||
−0.728292 | + | 0.685267i | \(0.759686\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 19.6352 | 0.649829 | ||||||||
\(914\) | 20.8797 | 0.690640 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11.6887 | −0.386205 | ||||||||
\(917\) | −5.39521 | −0.178165 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4.69180 | 0.154768 | 0.0773840 | − | 0.997001i | \(-0.475343\pi\) | ||||
0.0773840 | + | 0.997001i | \(0.475343\pi\) | |||||||
\(920\) | −3.94031 | −0.129908 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −23.2481 | −0.765637 | ||||||||
\(923\) | 47.5390 | 1.56476 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 38.1726 | 1.25511 | ||||||||
\(926\) | −5.54081 | −0.182082 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −21.7845 | −0.715111 | ||||||||
\(929\) | −34.3079 | −1.12561 | −0.562803 | − | 0.826591i | \(-0.690277\pi\) | ||||
−0.562803 | + | 0.826591i | \(0.690277\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −43.3959 | −1.42224 | ||||||||
\(932\) | −10.9204 | −0.357710 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −17.5095 | −0.572930 | ||||||||
\(935\) | 0.537197 | 0.0175682 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −23.3932 | −0.764223 | −0.382111 | − | 0.924116i | \(-0.624803\pi\) | ||||
−0.382111 | + | 0.924116i | \(0.624803\pi\) | |||||||
\(938\) | 0.858945 | 0.0280456 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.65268 | 0.0865208 | ||||||||
\(941\) | −52.0248 | −1.69596 | −0.847979 | − | 0.530029i | \(-0.822181\pi\) | ||||
−0.847979 | + | 0.530029i | \(0.822181\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −83.9790 | −2.73473 | ||||||||
\(944\) | −16.4210 | −0.534459 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −7.03671 | −0.228783 | ||||||||
\(947\) | 49.5994 | 1.61176 | 0.805882 | − | 0.592076i | \(-0.201692\pi\) | ||||
0.805882 | + | 0.592076i | \(0.201692\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −62.0244 | −2.01340 | ||||||||
\(950\) | 18.8621 | 0.611968 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0.608949 | 0.0197362 | ||||||||
\(953\) | 22.6710 | 0.734384 | 0.367192 | − | 0.930145i | \(-0.380319\pi\) | ||||
0.367192 | + | 0.930145i | \(0.380319\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 2.85967 | 0.0925369 | ||||||||
\(956\) | 42.5181 | 1.37513 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8.14246 | 0.263071 | ||||||||
\(959\) | −1.24800 | −0.0403000 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −16.2262 | −0.523425 | ||||||||
\(962\) | 22.3860 | 0.721754 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −6.25547 | −0.201475 | ||||||||
\(965\) | −0.320346 | −0.0103123 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.82815 | 0.219579 | 0.109789 | − | 0.993955i | \(-0.464982\pi\) | ||||
0.109789 | + | 0.993955i | \(0.464982\pi\) | |||||||
\(968\) | −0.629690 | −0.0202390 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.869513 | −0.0279184 | ||||||||
\(971\) | 21.5753 | 0.692383 | 0.346191 | − | 0.938164i | \(-0.387475\pi\) | ||||
0.346191 | + | 0.938164i | \(0.387475\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.16617 | 0.165620 | ||||||||
\(974\) | −12.1530 | −0.389406 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.36720 | 0.139791 | ||||||||
\(977\) | −42.6020 | −1.36296 | −0.681480 | − | 0.731837i | \(-0.738663\pi\) | ||||
−0.681480 | + | 0.731837i | \(0.738663\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.4483 | 0.461771 | ||||||||
\(980\) | −2.91538 | −0.0931285 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −0.237661 | −0.00758408 | ||||||||
\(983\) | −41.6211 | −1.32751 | −0.663753 | − | 0.747952i | \(-0.731038\pi\) | ||||
−0.663753 | + | 0.747952i | \(0.731038\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −6.00920 | −0.191469 | ||||||||
\(986\) | 1.47921 | 0.0471078 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −50.4821 | −1.60605 | ||||||||
\(989\) | 24.7814 | 0.788004 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.1346 | −0.417233 | −0.208616 | − | 0.977998i | \(-0.566896\pi\) | ||||
−0.208616 | + | 0.977998i | \(0.566896\pi\) | |||||||
\(992\) | −21.3247 | −0.677058 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 2.62351 | 0.0832127 | ||||||||
\(995\) | −1.21210 | −0.0384262 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 30.3719 | 0.961887 | 0.480943 | − | 0.876752i | \(-0.340294\pi\) | ||||
0.480943 | + | 0.876752i | \(0.340294\pi\) | |||||||
\(998\) | −3.96636 | −0.125553 | ||||||||
\(999\) | 0 | 0 |
(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 | 4023.2.a.f.1.9 | yes | 25 | |
3.2 | odd | 2 | 4023.2.a.e.1.17 | ✓ | 25 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
4023.2.a.e.1.17 | ✓ | 25 | 3.2 | odd | 2 | ||
4023.2.a.f.1.9 | yes | 25 | 1.1 | even | 1 | trivial |