Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [588,3,Mod(197,588)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(588, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("588.197");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 588 = 2^{2} \cdot 3 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 588.c (of order \(2\), degree \(1\), minimal) |
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: | no |
Analytic conductor: | \(16.0218395444\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.6018425749504.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 18x^{6} + 123x^{4} + 304x^{2} + 441 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{2} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 197.4 | ||
Root | \(0.707107 + 2.83573i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 588.197 |
Dual form | 588.3.c.j.197.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/588\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(295\) | \(493\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | −1.79703 | + | 2.40223i | −0.599009 | + | 0.800742i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 0.867013i | − | 0.173403i | −0.996234 | − | 0.0867013i | \(-0.972367\pi\) | ||
0.996234 | − | 0.0867013i | \(-0.0276326\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.54138 | − | 8.63374i | −0.282376 | − | 0.959304i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.45228i | − | 0.222935i | −0.993768 | − | 0.111467i | \(-0.964445\pi\) | ||
0.993768 | − | 0.111467i | \(-0.0355551\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6.53953 | 0.503041 | 0.251520 | − | 0.967852i | \(-0.419069\pi\) | ||||
0.251520 | + | 0.967852i | \(0.419069\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.08276 | + | 1.55805i | 0.138851 | + | 0.103870i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 18.7484i | 1.10285i | 0.834225 | + | 0.551424i | \(0.185915\pi\) | ||||
−0.834225 | + | 0.551424i | \(0.814085\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 13.6106 | 0.716347 | 0.358174 | − | 0.933655i | \(-0.383400\pi\) | ||||
0.358174 | + | 0.933655i | \(0.383400\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 41.9933i | − | 1.82579i | −0.408189 | − | 0.912897i | \(-0.633840\pi\) | ||
0.408189 | − | 0.912897i | \(-0.366160\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.2483 | 0.969932 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 25.3071 | + | 9.41009i | 0.937301 | + | 0.348522i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 22.8358i | 0.787443i | 0.919230 | + | 0.393722i | \(0.128813\pi\) | ||||
−0.919230 | + | 0.393722i | \(0.871187\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.48528 | 0.273719 | 0.136859 | − | 0.990590i | \(-0.456299\pi\) | ||||
0.136859 | + | 0.990590i | \(0.456299\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 5.89094 | + | 4.40682i | 0.178513 | + | 0.133540i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −41.7449 | −1.12824 | −0.564120 | − | 0.825693i | \(-0.690784\pi\) | ||||
−0.564120 | + | 0.825693i | \(0.690784\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −11.7517 | + | 15.7094i | −0.301326 | + | 0.402806i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 71.1998i | 1.73658i | 0.496057 | + | 0.868290i | \(0.334781\pi\) | ||||
−0.496057 | + | 0.868290i | \(0.665219\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 59.7449 | 1.38942 | 0.694708 | − | 0.719292i | \(-0.255534\pi\) | ||||
0.694708 | + | 0.719292i | \(0.255534\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.48556 | + | 2.20341i | −0.166346 | + | 0.0489647i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 69.7916i | 1.48493i | 0.669886 | + | 0.742464i | \(0.266343\pi\) | ||||
−0.669886 | + | 0.742464i | \(0.733657\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −45.0380 | − | 33.6914i | −0.883097 | − | 0.660617i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 62.3768i | 1.17692i | 0.808526 | + | 0.588461i | \(0.200266\pi\) | ||||
−0.808526 | + | 0.588461i | \(0.799734\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.12616 | −0.0386575 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −24.4586 | + | 32.6957i | −0.429099 | + | 0.573609i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 57.1123i | − | 0.968005i | −0.875067 | − | 0.484002i | \(-0.839183\pi\) | ||
0.875067 | − | 0.484002i | \(-0.160817\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 59.2166 | 0.970763 | 0.485382 | − | 0.874302i | \(-0.338681\pi\) | ||||
0.485382 | + | 0.874302i | \(0.338681\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 5.66986i | − | 0.0872286i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 66.0000 | 0.985075 | 0.492537 | − | 0.870291i | \(-0.336070\pi\) | ||||
0.492537 | + | 0.870291i | \(0.336070\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 100.877 | + | 75.4631i | 1.46199 | + | 1.09367i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 53.7938i | 0.757660i | 0.925466 | + | 0.378830i | \(0.123673\pi\) | ||||
−0.925466 | + | 0.378830i | \(0.876327\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 95.4546 | 1.30760 | 0.653798 | − | 0.756669i | \(-0.273174\pi\) | ||||
0.653798 | + | 0.756669i | \(0.273174\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −43.5748 | + | 58.2499i | −0.580998 | + | 0.776665i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −40.9932 | −0.518901 | −0.259450 | − | 0.965756i | \(-0.583541\pi\) | ||||
−0.259450 | + | 0.965756i | \(0.583541\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −68.0828 | + | 43.8832i | −0.840528 | + | 0.541768i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 23.0835i | 0.278114i | 0.990284 | + | 0.139057i | \(0.0444072\pi\) | ||||
−0.990284 | + | 0.139057i | \(0.955593\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 16.2551 | 0.191237 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −54.8569 | − | 41.0367i | −0.630539 | − | 0.471686i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 5.52795i | − | 0.0621118i | −0.999518 | − | 0.0310559i | \(-0.990113\pi\) | ||
0.999518 | − | 0.0310559i | \(-0.00988700\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −15.2483 | + | 20.3836i | −0.163960 | + | 0.219178i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 11.8006i | − | 0.124217i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −85.5648 | −0.882111 | −0.441055 | − | 0.897480i | \(-0.645396\pi\) | ||||
−0.441055 | + | 0.897480i | \(0.645396\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −21.1724 | + | 6.23219i | −0.213862 | + | 0.0629514i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 89.0812i | 0.881992i | 0.897509 | + | 0.440996i | \(0.145375\pi\) | ||||
−0.897509 | + | 0.440996i | \(0.854625\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 35.0042 | 0.339847 | 0.169923 | − | 0.985457i | \(-0.445648\pi\) | ||||
0.169923 | + | 0.985457i | \(0.445648\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 88.1258i | − | 0.823606i | −0.911273 | − | 0.411803i | \(-0.864899\pi\) | ||
0.911273 | − | 0.411803i | \(-0.135101\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 133.745 | 1.22702 | 0.613509 | − | 0.789688i | \(-0.289758\pi\) | ||||
0.613509 | + | 0.789688i | \(0.289758\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 75.0167 | − | 100.281i | 0.675826 | − | 0.903429i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 70.4990i | − | 0.623885i | −0.950101 | − | 0.311942i | \(-0.899020\pi\) | ||
0.950101 | − | 0.311942i | \(-0.100980\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −36.4087 | −0.316598 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −16.6194 | − | 56.4605i | −0.142046 | − | 0.482569i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 114.986 | 0.950300 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −171.038 | − | 127.948i | −1.39055 | − | 1.04023i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 42.6989i | − | 0.341591i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 142.993 | 1.12593 | 0.562965 | − | 0.826481i | \(-0.309661\pi\) | ||||
0.562965 | + | 0.826481i | \(0.309661\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −107.363 | + | 143.521i | −0.832273 | + | 1.11256i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 116.500i | − | 0.889311i | −0.895702 | − | 0.444656i | \(-0.853326\pi\) | ||
0.895702 | − | 0.444656i | \(-0.146674\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.15868 | − | 21.9416i | 0.0604346 | − | 0.162530i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 57.4723i | − | 0.419506i | −0.977754 | − | 0.209753i | \(-0.932734\pi\) | ||
0.977754 | − | 0.209753i | \(-0.0672659\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −252.242 | −1.81469 | −0.907346 | − | 0.420385i | \(-0.861895\pi\) | ||||
−0.907346 | + | 0.420385i | \(0.861895\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −167.655 | − | 125.417i | −1.18904 | − | 0.889486i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 16.0368i | − | 0.112145i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 19.7990 | 0.136545 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 129.197i | 0.867097i | 0.901130 | + | 0.433548i | \(0.142739\pi\) | ||||
−0.901130 | + | 0.433548i | \(0.857261\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 54.5103 | 0.360995 | 0.180498 | − | 0.983575i | \(-0.442229\pi\) | ||||
0.180498 | + | 0.983575i | \(0.442229\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 161.869 | − | 47.6469i | 1.05797 | − | 0.311418i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 7.35685i | − | 0.0474636i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 170.588 | 1.08655 | 0.543275 | − | 0.839555i | \(-0.317184\pi\) | ||||
0.543275 | + | 0.839555i | \(0.317184\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −149.843 | − | 112.093i | −0.942411 | − | 0.704987i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 182.241 | 1.11805 | 0.559023 | − | 0.829152i | \(-0.311176\pi\) | ||||
0.559023 | + | 0.829152i | \(0.311176\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 3.82078 | − | 5.10753i | 0.0231562 | − | 0.0309547i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 305.607i | − | 1.82998i | −0.403471 | − | 0.914992i | \(-0.632197\pi\) | ||
0.403471 | − | 0.914992i | \(-0.367803\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −126.235 | −0.746950 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −34.5897 | − | 117.510i | −0.202279 | − | 0.687195i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 102.302i | − | 0.591339i | −0.955290 | − | 0.295670i | \(-0.904457\pi\) | ||
0.955290 | − | 0.295670i | \(-0.0955427\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 137.197 | + | 102.632i | 0.775122 | + | 0.579844i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 190.809i | − | 1.06597i | −0.846124 | − | 0.532986i | \(-0.821070\pi\) | ||
0.846124 | − | 0.532986i | \(-0.178930\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −227.859 | −1.25889 | −0.629445 | − | 0.777045i | \(-0.716718\pi\) | ||||
−0.629445 | + | 0.777045i | \(0.716718\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −106.414 | + | 142.252i | −0.581496 | + | 0.777331i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 36.1934i | 0.195640i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 45.9765 | 0.245863 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 248.742i | 1.30231i | 0.758943 | + | 0.651157i | \(0.225716\pi\) | ||||
−0.758943 | + | 0.651157i | \(0.774284\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 27.7586 | 0.143827 | 0.0719134 | − | 0.997411i | \(-0.477089\pi\) | ||||
0.0719134 | + | 0.997411i | \(0.477089\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 13.6203 | + | 10.1889i | 0.0698476 | + | 0.0522507i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 351.121i | − | 1.78234i | −0.453671 | − | 0.891169i | \(-0.649886\pi\) | ||
0.453671 | − | 0.891169i | \(-0.350114\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −129.386 | −0.650181 | −0.325090 | − | 0.945683i | \(-0.605395\pi\) | ||||
−0.325090 | + | 0.945683i | \(0.605395\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −118.604 | + | 158.547i | −0.590069 | + | 0.788791i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 61.7312 | 0.301128 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −362.559 | + | 106.721i | −1.75149 | + | 0.515560i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 33.3771i | − | 0.159699i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 143.503 | 0.680111 | 0.340056 | − | 0.940405i | \(-0.389554\pi\) | ||||
0.340056 | + | 0.940405i | \(0.389554\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −129.225 | − | 96.6690i | −0.606690 | − | 0.453845i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − | 51.7996i | − | 0.240928i | ||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −171.535 | + | 229.303i | −0.783263 | + | 1.04705i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 122.606i | 0.554777i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −303.685 | −1.36182 | −0.680909 | − | 0.732368i | \(-0.738415\pi\) | ||||
−0.680909 | + | 0.732368i | \(0.738415\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −61.6241 | − | 209.353i | −0.273885 | − | 0.930459i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 357.518i | − | 1.57497i | −0.616335 | − | 0.787484i | \(-0.711383\pi\) | ||
0.616335 | − | 0.787484i | \(-0.288617\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −207.699 | −0.906984 | −0.453492 | − | 0.891260i | \(-0.649822\pi\) | ||||
−0.453492 | + | 0.891260i | \(0.649822\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 346.216i | 1.48591i | 0.669343 | + | 0.742953i | \(0.266576\pi\) | ||||
−0.669343 | + | 0.742953i | \(0.733424\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 60.5103 | 0.257491 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 73.6658 | − | 98.4748i | 0.310826 | − | 0.415506i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 377.331i | 1.57879i | 0.613886 | + | 0.789395i | \(0.289605\pi\) | ||||
−0.613886 | + | 0.789395i | \(0.710395\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 356.353 | 1.47864 | 0.739321 | − | 0.673353i | \(-0.235147\pi\) | ||||
0.739321 | + | 0.673353i | \(0.235147\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 16.9292 | − | 242.410i | 0.0696675 | − | 0.997570i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 89.0068 | 0.360352 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −55.4518 | − | 41.4817i | −0.222698 | − | 0.166593i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 98.7289i | 0.393342i | 0.980470 | + | 0.196671i | \(0.0630131\pi\) | ||||
−0.980470 | + | 0.196671i | \(0.936987\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −102.979 | −0.407033 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −29.2109 | + | 39.0485i | −0.114553 | + | 0.153131i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 323.274i | 1.25787i | 0.777456 | + | 0.628937i | \(0.216510\pi\) | ||||
−0.777456 | + | 0.628937i | \(0.783490\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 197.159 | − | 58.0346i | 0.755397 | − | 0.222355i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 71.8815i | 0.273314i | 0.990618 | + | 0.136657i | \(0.0436358\pi\) | ||||
−0.990618 | + | 0.136657i | \(0.956364\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 54.0816 | 0.204081 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 13.2794 | + | 9.93389i | 0.0497356 | + | 0.0372056i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 42.4837i | 0.157932i | 0.996877 | + | 0.0789659i | \(0.0251618\pi\) | ||||
−0.996877 | + | 0.0789659i | \(0.974838\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 88.3835 | 0.326138 | 0.163069 | − | 0.986615i | \(-0.447861\pi\) | ||||
0.163069 | + | 0.986615i | \(0.447861\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 59.4637i | − | 0.216232i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 84.9795 | 0.306785 | 0.153393 | − | 0.988165i | \(-0.450980\pi\) | ||||
0.153393 | + | 0.988165i | \(0.450980\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −21.5643 | − | 73.2597i | −0.0772915 | − | 0.262579i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 237.707i | − | 0.845932i | −0.906146 | − | 0.422966i | \(-0.860989\pi\) | ||
0.906146 | − | 0.422966i | \(-0.139011\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −184.721 | −0.652723 | −0.326362 | − | 0.945245i | \(-0.605823\pi\) | ||||
−0.326362 | + | 0.945245i | \(0.605823\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 28.3476 | + | 21.2060i | 0.0994654 | + | 0.0744069i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −62.5034 | −0.216275 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 153.762 | − | 205.546i | 0.528393 | − | 0.706343i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 103.384i | 0.352846i | 0.984314 | + | 0.176423i | \(0.0564527\pi\) | ||||
−0.984314 | + | 0.176423i | \(0.943547\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −49.5171 | −0.167855 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 23.0762 | − | 62.0603i | 0.0776977 | − | 0.208957i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 274.616i | − | 0.918449i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −213.993 | − | 160.081i | −0.706248 | − | 0.528321i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 51.3416i | − | 0.168333i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 138.422 | 0.450887 | 0.225443 | − | 0.974256i | \(-0.427617\pi\) | ||||
0.225443 | + | 0.974256i | \(0.427617\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −62.9035 | + | 84.0880i | −0.203571 | + | 0.272130i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 231.265i | 0.743619i | 0.928309 | + | 0.371809i | \(0.121263\pi\) | ||||
−0.928309 | + | 0.371809i | \(0.878737\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 312.522 | 0.998472 | 0.499236 | − | 0.866466i | \(-0.333614\pi\) | ||||
0.499236 | + | 0.866466i | \(0.333614\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 541.164i | − | 1.70714i | −0.520976 | − | 0.853572i | \(-0.674432\pi\) | ||
0.520976 | − | 0.853572i | \(-0.325568\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 56.0000 | 0.175549 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 211.698 | + | 158.365i | 0.659496 | + | 0.493348i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 255.177i | 0.790022i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 158.572 | 0.487915 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −240.343 | + | 321.285i | −0.734995 | + | 0.982524i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −108.738 | −0.328514 | −0.164257 | − | 0.986418i | \(-0.552523\pi\) | ||||
−0.164257 | + | 0.986418i | \(0.552523\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 106.090 | + | 360.414i | 0.318587 | + | 1.08232i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 57.2229i | − | 0.170815i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 327.717 | 0.972455 | 0.486228 | − | 0.873832i | \(-0.338373\pi\) | ||||
0.486228 | + | 0.873832i | \(0.338373\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 169.354 | + | 126.689i | 0.499571 | + | 0.373713i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 20.8083i | − | 0.0610215i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 65.4275 | − | 87.4620i | 0.189645 | − | 0.253513i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 306.832i | − | 0.884241i | −0.896956 | − | 0.442120i | \(-0.854226\pi\) | ||
0.896956 | − | 0.442120i | \(-0.145774\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 85.7161 | 0.245605 | 0.122802 | − | 0.992431i | \(-0.460812\pi\) | ||||
0.122802 | + | 0.992431i | \(0.460812\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 165.497 | + | 61.5375i | 0.471500 | + | 0.175321i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 450.719i | 1.27682i | 0.769695 | + | 0.638412i | \(0.220408\pi\) | ||||
−0.769695 | + | 0.638412i | \(0.779592\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 46.6400 | 0.131380 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 432.499i | − | 1.20473i | −0.798220 | − | 0.602366i | \(-0.794225\pi\) | ||
0.798220 | − | 0.602366i | \(-0.205775\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −175.752 | −0.486847 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −206.634 | + | 276.223i | −0.569239 | + | 0.760945i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 82.7604i | − | 0.226741i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −595.716 | −1.62320 | −0.811602 | − | 0.584211i | \(-0.801404\pi\) | ||||
−0.811602 | + | 0.584211i | \(0.801404\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 614.720 | − | 180.946i | 1.66591 | − | 0.490368i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −428.952 | −1.15001 | −0.575003 | − | 0.818151i | \(-0.694999\pi\) | ||||
−0.575003 | + | 0.818151i | \(0.694999\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 102.572 | + | 76.7312i | 0.273527 | + | 0.204616i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 149.336i | 0.396116i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 304.228 | 0.802712 | 0.401356 | − | 0.915922i | \(-0.368539\pi\) | ||||
0.401356 | + | 0.915922i | \(0.368539\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −256.963 | + | 343.502i | −0.674443 | + | 0.901580i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 100.783i | 0.263141i | 0.991307 | + | 0.131570i | \(0.0420019\pi\) | ||||
−0.991307 | + | 0.131570i | \(0.957998\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −151.834 | − | 515.821i | −0.392337 | − | 1.33287i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 411.811i | 1.05864i | 0.848423 | + | 0.529320i | \(0.177553\pi\) | ||||
−0.848423 | + | 0.529320i | \(0.822447\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 787.308 | 2.01357 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 279.859 | + | 209.353i | 0.712109 | + | 0.532706i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 35.5416i | 0.0899788i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −481.696 | −1.21334 | −0.606670 | − | 0.794954i | \(-0.707495\pi\) | ||||
−0.606670 | + | 0.794954i | \(0.707495\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 245.681i | − | 0.612671i | −0.951924 | − | 0.306335i | \(-0.900897\pi\) | ||
0.951924 | − | 0.306335i | \(-0.0991029\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 55.4897 | 0.137692 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 38.0473 | + | 59.0287i | 0.0939441 | + | 0.145750i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 102.370i | 0.251524i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 272.582 | 0.666461 | 0.333230 | − | 0.942845i | \(-0.391861\pi\) | ||||
0.333230 | + | 0.942845i | \(0.391861\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 138.061 | + | 103.279i | 0.335916 | + | 0.251288i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 20.0137 | 0.0482258 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 453.286 | − | 605.943i | 1.08702 | − | 1.45310i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 477.375i | 1.13932i | 0.821881 | + | 0.569660i | \(0.192925\pi\) | ||||
−0.821881 | + | 0.569660i | \(0.807075\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −711.476 | −1.68997 | −0.844983 | − | 0.534793i | \(-0.820390\pi\) | ||||
−0.844983 | + | 0.534793i | \(0.820390\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 602.562 | − | 177.367i | 1.42450 | − | 0.419308i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 454.617i | 1.06969i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 38.5240 | + | 28.8185i | 0.0897995 | + | 0.0671761i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 581.166i | 1.34841i | 0.738543 | + | 0.674207i | \(0.235514\pi\) | ||||
−0.738543 | + | 0.674207i | \(0.764486\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 358.137 | 0.827107 | 0.413554 | − | 0.910480i | \(-0.364287\pi\) | ||||
0.413554 | + | 0.910480i | \(0.364287\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −35.5793 | + | 47.5617i | −0.0817916 | + | 0.109337i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 571.553i | − | 1.30790i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 620.830 | 1.41419 | 0.707096 | − | 0.707118i | \(-0.250005\pi\) | ||||
0.707096 | + | 0.707118i | \(0.250005\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 162.303i | − | 0.366373i | −0.983078 | − | 0.183186i | \(-0.941359\pi\) | ||
0.983078 | − | 0.183186i | \(-0.0586412\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −4.79281 | −0.0107704 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −310.361 | − | 232.171i | −0.694321 | − | 0.519399i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 800.020i | 1.78178i | 0.454217 | + | 0.890891i | \(0.349919\pi\) | ||||
−0.454217 | + | 0.890891i | \(0.650081\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 174.602 | 0.387144 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −97.9565 | + | 130.946i | −0.216239 | + | 0.289064i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −682.738 | −1.49396 | −0.746978 | − | 0.664849i | \(-0.768496\pi\) | ||||
−0.746978 | + | 0.664849i | \(0.768496\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −176.424 | + | 474.469i | −0.384367 | + | 1.03370i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 443.241i | 0.961478i | 0.876864 | + | 0.480739i | \(0.159632\pi\) | ||||
−0.876864 | + | 0.480739i | \(0.840368\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 21.5034 | 0.0464437 | 0.0232218 | − | 0.999730i | \(-0.492608\pi\) | ||||
0.0232218 | + | 0.999730i | \(0.492608\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 17.6728 | + | 13.2205i | 0.0380061 | + | 0.0284311i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 610.243i | 1.30673i | 0.757043 | + | 0.653365i | \(0.226643\pi\) | ||||
−0.757043 | + | 0.653365i | \(0.773357\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −306.552 | + | 409.792i | −0.650853 | + | 0.870046i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 146.511i | − | 0.309749i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 330.034 | 0.694808 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 538.545 | − | 158.523i | 1.12903 | − | 0.332334i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 126.793i | − | 0.264704i | −0.991203 | − | 0.132352i | \(-0.957747\pi\) | ||
0.991203 | − | 0.132352i | \(-0.0422530\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −272.992 | −0.567550 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 74.1858i | 0.152960i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −240.497 | −0.493833 | −0.246916 | − | 0.969037i | \(-0.579417\pi\) | ||||
−0.246916 | + | 0.969037i | \(0.579417\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −327.493 | + | 437.785i | −0.669720 | + | 0.895266i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 602.463i | − | 1.22701i | −0.789690 | − | 0.613506i | \(-0.789759\pi\) | ||
0.789690 | − | 0.613506i | \(-0.210241\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −428.136 | −0.868430 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.40339 | + | 18.3567i | 0.0109159 | + | 0.0370843i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 341.517 | 0.684403 | 0.342202 | − | 0.939627i | \(-0.388827\pi\) | ||||
0.342202 | + | 0.939627i | \(0.388827\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 734.138 | + | 549.185i | 1.46535 | + | 1.09618i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 42.6989i | 0.0848885i | 0.999099 | + | 0.0424443i | \(0.0135145\pi\) | ||||
−0.999099 | + | 0.0424443i | \(0.986486\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 77.2346 | 0.152940 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 226.847 | − | 303.244i | 0.447430 | − | 0.598114i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 777.024i | − | 1.52657i | −0.646062 | − | 0.763285i | \(-0.723585\pi\) | ||
0.646062 | − | 0.763285i | \(-0.276415\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 344.445 | + | 128.077i | 0.671433 | + | 0.249663i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 30.3491i | − | 0.0589303i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 171.149 | 0.331042 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 245.752 | + | 183.839i | 0.473510 | + | 0.354218i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 105.659i | 0.202801i | 0.994846 | + | 0.101400i | \(0.0323323\pi\) | ||||
−0.994846 | + | 0.101400i | \(0.967668\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −415.589 | −0.794625 | −0.397312 | − | 0.917683i | \(-0.630057\pi\) | ||||
−0.397312 | + | 0.917683i | \(0.630057\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 159.086i | 0.301870i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1234.43 | −2.33353 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −493.092 | + | 145.144i | −0.928611 | + | 0.273341i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 465.613i | 0.873570i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −76.4063 | −0.142815 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 458.366 | + | 342.889i | 0.853568 | + | 0.638527i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −283.503 | −0.524036 | −0.262018 | − | 0.965063i | \(-0.584388\pi\) | ||||
−0.262018 | + | 0.965063i | \(0.584388\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 409.469 | − | 547.369i | 0.754087 | − | 1.00805i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 115.959i | − | 0.212768i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −398.269 | −0.728097 | −0.364048 | − | 0.931380i | \(-0.618606\pi\) | ||||
−0.364048 | + | 0.931380i | \(0.618606\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −150.492 | − | 511.260i | −0.274120 | − | 0.931257i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 310.809i | 0.564083i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −86.9446 | − | 65.0405i | −0.156657 | − | 0.117190i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 60.8463i | 0.109239i | 0.998507 | + | 0.0546196i | \(0.0173946\pi\) | ||||
−0.998507 | + | 0.0546196i | \(0.982605\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 390.703 | 0.698932 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −82.6210 | + | 110.446i | −0.147275 | + | 0.196873i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.92691i | 0.00519878i | 0.999997 | + | 0.00259939i | \(0.000827412\pi\) | ||||
−0.999997 | + | 0.00259939i | \(0.999173\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −61.1236 | −0.108183 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 751.131i | 1.32009i | 0.751226 | + | 0.660045i | \(0.229463\pi\) | ||||
−0.751226 | + | 0.660045i | \(0.770537\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 166.724 | 0.291987 | 0.145993 | − | 0.989286i | \(-0.453362\pi\) | ||||
0.145993 | + | 0.989286i | \(0.453362\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −597.535 | − | 446.996i | −1.04282 | − | 0.780098i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 1018.26i | − | 1.77090i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −117.682 | −0.203956 | −0.101978 | − | 0.994787i | \(-0.532517\pi\) | ||||
−0.101978 | + | 0.994787i | \(0.532517\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −49.8829 | + | 66.6823i | −0.0861536 | + | 0.115168i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 152.966 | 0.262377 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −48.9521 | + | 14.4093i | −0.0836787 | + | 0.0246312i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 650.556i | − | 1.10827i | −0.832426 | − | 0.554137i | \(-0.813049\pi\) | ||
0.832426 | − | 0.554137i | \(-0.186951\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 115.490 | 0.196078 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 843.471 | + | 630.974i | 1.42719 | + | 1.06764i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 377.459i | − | 0.636524i | −0.948003 | − | 0.318262i | \(-0.896901\pi\) | ||
0.948003 | − | 0.318262i | \(-0.103099\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 232.510 | − | 310.814i | 0.389464 | − | 0.520627i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 76.7861i | − | 0.128190i | −0.997944 | − | 0.0640952i | \(-0.979584\pi\) | ||
0.997944 | − | 0.0640952i | \(-0.0204161\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −436.612 | −0.726476 | −0.363238 | − | 0.931696i | \(-0.618329\pi\) | ||||
−0.363238 | + | 0.931696i | \(0.618329\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −167.731 | − | 569.827i | −0.278161 | − | 0.944986i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 99.6947i | − | 0.164785i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −751.240 | −1.23763 | −0.618814 | − | 0.785537i | \(-0.712387\pi\) | ||||
−0.618814 | + | 0.785537i | \(0.712387\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 456.404i | 0.746979i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −188.752 | −0.307915 | −0.153957 | − | 0.988077i | \(-0.549202\pi\) | ||||
−0.153957 | + | 0.988077i | \(0.549202\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −110.933 | + | 148.292i | −0.180378 | + | 0.241126i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 548.513i | 0.889000i | 0.895779 | + | 0.444500i | \(0.146619\pi\) | ||||
−0.895779 | + | 0.444500i | \(0.853381\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −907.716 | −1.46642 | −0.733211 | − | 0.680001i | \(-0.761979\pi\) | ||||
−0.733211 | + | 0.680001i | \(0.761979\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 395.160 | − | 1062.73i | 0.636329 | − | 1.71132i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 569.187 | 0.910699 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 80.1792 | + | 59.9795i | 0.127878 | + | 0.0956611i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 782.650i | − | 1.24428i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1032.40 | −1.63613 | −0.818067 | − | 0.575123i | \(-0.804954\pi\) | ||||
−0.818067 | + | 0.575123i | \(0.804954\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −257.880 | + | 344.728i | −0.407393 | + | 0.544593i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 123.977i | − | 0.195239i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 464.442 | − | 136.711i | 0.726826 | − | 0.213945i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 1183.64i | − | 1.84655i | −0.384141 | − | 0.923274i | \(-0.625502\pi\) | ||
0.384141 | − | 0.923274i | \(-0.374498\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 810.525 | 1.26054 | 0.630268 | − | 0.776378i | \(-0.282945\pi\) | ||||
0.630268 | + | 0.776378i | \(0.282945\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 124.434 | + | 93.0853i | 0.192921 | + | 0.144318i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 122.895i | 0.189945i | 0.995480 | + | 0.0949727i | \(0.0302764\pi\) | ||||
−0.995480 | + | 0.0949727i | \(0.969724\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −140.056 | −0.215802 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 442.160i | − | 0.677121i | −0.940945 | − | 0.338560i | \(-0.890060\pi\) | ||
0.940945 | − | 0.338560i | \(-0.109940\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −101.007 | −0.154209 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −242.586 | − | 824.129i | −0.369234 | − | 1.25438i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 219.158i | − | 0.332562i | −0.986078 | − | 0.166281i | \(-0.946824\pi\) | ||
0.986078 | − | 0.166281i | \(-0.0531758\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 135.984 | 0.205724 | 0.102862 | − | 0.994696i | \(-0.467200\pi\) | ||||
0.102862 | + | 0.994696i | \(0.467200\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −294.527 | − | 220.326i | −0.444234 | − | 0.332317i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 958.952 | 1.43771 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 545.731 | − | 729.521i | 0.815742 | − | 1.09046i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 145.216i | − | 0.216417i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −553.531 | −0.822483 | −0.411241 | − | 0.911527i | \(-0.634905\pi\) | ||||
−0.411241 | + | 0.911527i | \(0.634905\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 613.654 | + | 228.179i | 0.909117 | + | 0.338042i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 676.881i | − | 0.999824i | −0.866076 | − | 0.499912i | \(-0.833366\pi\) | ||
0.866076 | − | 0.499912i | \(-0.166634\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 858.838 | + | 642.469i | 1.26114 | + | 0.943420i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 257.021i | − | 0.376311i | −0.982139 | − | 0.188156i | \(-0.939749\pi\) | ||
0.982139 | − | 0.188156i | \(-0.0602509\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −49.8292 | −0.0727434 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 373.241 | − | 498.941i | 0.543292 | − | 0.726260i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 407.915i | 0.592039i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 493.039 | 0.713515 | 0.356757 | − | 0.934197i | \(-0.383882\pi\) | ||||
0.356757 | + | 0.934197i | \(0.383882\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 218.697i | 0.314672i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1334.88 | −1.91518 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −831.690 | − | 622.160i | −1.18983 | − | 0.890072i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 891.207i | − | 1.27134i | −0.771962 | − | 0.635668i | \(-0.780725\pi\) | ||
0.771962 | − | 0.635668i | \(-0.219275\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −568.172 | −0.808211 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −108.739 | + | 145.359i | −0.154239 | + | 0.206183i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −972.241 | −1.37129 | −0.685643 | − | 0.727938i | \(-0.740479\pi\) | ||||
−0.685643 | + | 0.727938i | \(0.740479\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 104.179 | + | 353.924i | 0.146525 | + | 0.497783i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 356.325i | − | 0.499754i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −13.9041 | −0.0194463 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −906.433 | − | 678.074i | −1.26420 | − | 0.945709i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 708.530i | − | 0.985438i | −0.870189 | − | 0.492719i | \(-0.836003\pi\) | ||
0.870189 | − | 0.492719i | \(-0.163997\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −640.376 | + | 856.040i | −0.885720 | + | 1.18401i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 553.730i | 0.763766i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −855.912 | −1.17732 | −0.588660 | − | 0.808381i | \(-0.700344\pi\) | ||||
−0.588660 | + | 0.808381i | \(0.700344\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 551.900 | + | 476.285i | 0.757065 | + | 0.653340i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1120.12i | 1.53231i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1272.19 | −1.73560 | −0.867799 | − | 0.496916i | \(-0.834466\pi\) | ||||
−0.867799 | + | 0.496916i | \(0.834466\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 161.851i | − | 0.219608i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 84.2277 | 0.113975 | 0.0569876 | − | 0.998375i | \(-0.481850\pi\) | ||||
0.0569876 | + | 0.998375i | \(0.481850\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −159.948 | + | 213.815i | −0.215854 | + | 0.288549i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 236.020i | − | 0.317658i | −0.987306 | − | 0.158829i | \(-0.949228\pi\) | ||
0.987306 | − | 0.158829i | \(-0.0507718\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 112.016 | 0.150357 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 199.297 | − | 58.6640i | 0.266796 | − | 0.0785327i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1068.39 | 1.42262 | 0.711310 | − | 0.702879i | \(-0.248102\pi\) | ||||
0.711310 | + | 0.702879i | \(0.248102\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −237.169 | − | 177.419i | −0.314966 | − | 0.235616i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 47.2611i | − | 0.0625975i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 800.187 | 1.05705 | 0.528525 | − | 0.848918i | \(-0.322745\pi\) | ||||
0.528525 | + | 0.848918i | \(0.322745\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 185.057 | − | 247.380i | 0.243817 | − | 0.325929i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 801.190i | 1.05281i | 0.850234 | + | 0.526406i | \(0.176461\pi\) | ||||
−0.850234 | + | 0.526406i | \(0.823539\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −41.3105 | − | 140.343i | −0.0540007 | − | 0.183454i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 373.487i | − | 0.486946i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −236.096 | −0.307017 | −0.153509 | − | 0.988147i | \(-0.549057\pi\) | ||||
−0.153509 | + | 0.988147i | \(0.549057\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −776.576 | − | 580.932i | −1.00723 | − | 0.753478i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 1387.16i | − | 1.79451i | −0.441513 | − | 0.897255i | \(-0.645558\pi\) | ||
0.441513 | − | 0.897255i | \(-0.354442\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 205.754 | 0.265488 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 969.071i | 1.24399i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 131.918 | 0.168909 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −214.887 | + | 577.910i | −0.274441 | + | 0.738071i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 147.902i | − | 0.188411i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 374.225 | 0.475509 | 0.237754 | − | 0.971325i | \(-0.423589\pi\) | ||||
0.237754 | + | 0.971325i | \(0.423589\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −172.676 | − | 129.173i | −0.218854 | − | 0.163718i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 387.248 | 0.488333 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −97.1861 | + | 129.916i | −0.122247 | + | 0.163417i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 1150.47i | − | 1.44350i | −0.692155 | − | 0.721749i | \(-0.743339\pi\) | ||
0.692155 | − | 0.721749i | \(-0.256661\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1308.48 | −1.63765 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −47.7269 | + | 14.0486i | −0.0595841 | + | 0.0175389i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 234.082i | − | 0.291509i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −102.055 | − | 76.3443i | −0.126463 | − | 0.0946026i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 983.620i | − | 1.21585i | −0.793996 | − | 0.607923i | \(-0.792003\pi\) | ||
0.793996 | − | 0.607923i | \(-0.207997\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1159.05 | 1.42916 | 0.714578 | − | 0.699555i | \(-0.246619\pi\) | ||||
0.714578 | + | 0.699555i | \(0.246619\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −158.828 | + | 212.317i | −0.195360 | + | 0.261153i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 158.006i | − | 0.193872i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 813.163 | 0.995304 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 563.548i | 0.686416i | 0.939259 | + | 0.343208i | \(0.111514\pi\) | ||||
−0.939259 | + | 0.343208i | \(0.888486\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 429.503 | 0.521875 | 0.260938 | − | 0.965356i | \(-0.415968\pi\) | ||||
0.260938 | + | 0.965356i | \(0.415968\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 142.845 | + | 106.858i | 0.173146 | + | 0.129525i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 911.451i | 1.10212i | 0.834467 | + | 0.551059i | \(0.185776\pi\) | ||||
−0.834467 | + | 0.551059i | \(0.814224\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 59.9769 | 0.0723485 | 0.0361743 | − | 0.999345i | \(-0.488483\pi\) | ||||
0.0361743 | + | 0.999345i | \(0.488483\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −152.710 | + | 204.140i | −0.183767 | + | 0.245656i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −264.966 | −0.317324 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 214.738 | + | 79.8473i | 0.256557 | + | 0.0953970i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1124.25i | 1.33999i | 0.742364 | + | 0.669996i | \(0.233704\pi\) | ||||
−0.742364 | + | 0.669996i | \(0.766296\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 319.524 | 0.379933 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 571.025 | + | 427.166i | 0.677373 | + | 0.506721i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 109.447i | 0.129523i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 331.948 | − | 443.741i | 0.390987 | − | 0.522663i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1753.00i | 2.05993i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −776.915 | −0.910804 | −0.455402 | − | 0.890286i | \(-0.650504\pi\) | ||||
−0.455402 | + | 0.890286i | \(0.650504\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −101.883 | + | 29.9897i | −0.119161 | + | 0.0350757i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1691.79i | − | 1.97409i | −0.160455 | − | 0.987043i | \(-0.551296\pi\) | ||
0.160455 | − | 0.987043i | \(-0.448704\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −671.951 | −0.782248 | −0.391124 | − | 0.920338i | \(-0.627914\pi\) | ||||
−0.391124 | + | 0.920338i | \(0.627914\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 674.501i | 0.781577i | 0.920480 | + | 0.390789i | \(0.127798\pi\) | ||||
−0.920480 | + | 0.390789i | \(0.872202\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −88.6969 | −0.102540 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 112.320 | − | 150.147i | 0.129551 | − | 0.173180i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 100.527i | 0.115681i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 431.609 | 0.495532 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 217.453 | + | 738.744i | 0.249087 | + | 0.846212i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −824.159 | −0.939748 | −0.469874 | − | 0.882733i | \(-0.655701\pi\) | ||||
−0.469874 | + | 0.882733i | \(0.655701\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −248.352 | − | 185.784i | −0.282539 | − | 0.211358i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 911.504i | 1.03462i | 0.855797 | + | 0.517312i | \(0.173067\pi\) | ||||
−0.855797 | + | 0.517312i | \(0.826933\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 917.973 | 1.03961 | 0.519803 | − | 0.854286i | \(-0.326005\pi\) | ||||
0.519803 | + | 0.854286i | \(0.326005\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 88.9837 | − | 118.951i | 0.100547 | − | 0.134408i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 95.8020i | − | 0.108007i | −0.998541 | − | 0.0540034i | \(-0.982802\pi\) | ||
0.998541 | − | 0.0540034i | \(-0.0171982\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 107.614 | + | 166.958i | 0.120779 | + | 0.187383i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 949.905i | 1.06372i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −165.434 | −0.184842 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 659.690 | + | 493.493i | 0.735440 | + | 0.550159i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 193.769i | 0.215538i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −1169.47 | −1.29797 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 197.557i | 0.218295i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −26.4555 | −0.0291681 | −0.0145841 | − | 0.999894i | \(-0.504642\pi\) | ||||
−0.0145841 | + | 0.999894i | \(0.504642\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 769.103 | − | 226.389i | 0.846098 | − | 0.249053i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 713.573i | − | 0.783285i | −0.920117 | − | 0.391643i | \(-0.871907\pi\) | ||
0.920117 | − | 0.391643i | \(-0.128093\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 56.6073 | 0.0620014 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 123.334 | + | 92.2622i | 0.134791 | + | 0.100833i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −675.408 | −0.734937 | −0.367469 | − | 0.930036i | \(-0.619776\pi\) | ||||
−0.367469 | + | 0.930036i | \(0.619776\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −248.749 | + | 332.521i | −0.270085 | + | 0.361044i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 351.786i | 0.381134i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1012.24 | −1.09432 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −88.9590 | − | 302.217i | −0.0959644 | − | 0.326016i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 1151.01i | 1.23898i | 0.785006 | + | 0.619488i | \(0.212660\pi\) | ||||
−0.785006 | + | 0.619488i | \(0.787340\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −555.552 | − | 415.590i | −0.595447 | − | 0.445435i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 39.8622i | − | 0.0426334i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −344.395 | −0.367551 | −0.183775 | − | 0.982968i | \(-0.558832\pi\) | ||||
−0.183775 | + | 0.982968i | \(0.558832\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −561.610 | + | 750.748i | −0.598094 | + | 0.799519i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 667.780i | 0.709649i | 0.934933 | + | 0.354825i | \(0.115459\pi\) | ||||
−0.934933 | + | 0.354825i | \(0.884541\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 2989.91 | 3.17064 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 1436.97i | − | 1.51739i | −0.651444 | − | 0.758697i | \(-0.725836\pi\) | ||
0.651444 | − | 0.758697i | \(-0.274164\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 624.228 | 0.657774 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 1300.00 | + | 972.488i | 1.36698 | + | 1.02259i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 1005.39i | 1.05497i | 0.849564 | + | 0.527485i | \(0.176865\pi\) | ||||
−0.849564 | + | 0.527485i | \(0.823135\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 215.663 | 0.225825 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −100.634 | + | 134.525i | −0.105155 | + | 0.140569i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −889.000 | −0.925078 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −760.855 | + | 223.961i | −0.790088 | + | 0.232566i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 24.0670i | − | 0.0249399i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1695.39 | 1.75325 | 0.876626 | − | 0.481173i | \(-0.159789\pi\) | ||||
0.876626 | + | 0.481173i | \(0.159789\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −612.993 | − | 458.561i | −0.632604 | − | 0.473231i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 268.430i | 0.276447i | 0.990401 | + | 0.138224i | \(0.0441393\pi\) | ||||
−0.990401 | + | 0.138224i | \(0.955861\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −284.959 | + | 380.927i | −0.292266 | + | 0.390694i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1321.25i | − | 1.35236i | −0.736738 | − | 0.676179i | \(-0.763635\pi\) | ||
0.736738 | − | 0.676179i | \(-0.236365\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −13.5561 | −0.0138469 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −339.897 | − | 1154.72i | −0.346480 | − | 1.17708i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 628.543i | 0.639413i | 0.947517 | + | 0.319707i | \(0.103584\pi\) | ||||
−0.947517 | + | 0.319707i | \(0.896416\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −304.426 | −0.309062 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 2508.88i | − | 2.53679i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 908.911 | 0.917165 | 0.458583 | − | 0.888652i | \(-0.348357\pi\) | ||||
0.458583 | + | 0.888652i | \(0.348357\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 195.405 | − | 261.213i | 0.196783 | − | 0.263055i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 112.179i | 0.112743i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −962.792 | −0.965690 | −0.482845 | − | 0.875706i | \(-0.660396\pi\) | ||||
−0.482845 | + | 0.875706i | \(0.660396\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −1056.44 | − | 392.823i | −1.05750 | − | 0.393216i |
(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 | 588.3.c.j.197.4 | yes | 8 | |
3.2 | odd | 2 | inner | 588.3.c.j.197.3 | ✓ | 8 | |
7.2 | even | 3 | 588.3.p.i.557.3 | 16 | |||
7.3 | odd | 6 | 588.3.p.i.569.1 | 16 | |||
7.4 | even | 3 | 588.3.p.i.569.8 | 16 | |||
7.5 | odd | 6 | 588.3.p.i.557.6 | 16 | |||
7.6 | odd | 2 | inner | 588.3.c.j.197.5 | yes | 8 | |
21.2 | odd | 6 | 588.3.p.i.557.8 | 16 | |||
21.5 | even | 6 | 588.3.p.i.557.1 | 16 | |||
21.11 | odd | 6 | 588.3.p.i.569.3 | 16 | |||
21.17 | even | 6 | 588.3.p.i.569.6 | 16 | |||
21.20 | even | 2 | inner | 588.3.c.j.197.6 | yes | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
588.3.c.j.197.3 | ✓ | 8 | 3.2 | odd | 2 | inner | |
588.3.c.j.197.4 | yes | 8 | 1.1 | even | 1 | trivial | |
588.3.c.j.197.5 | yes | 8 | 7.6 | odd | 2 | inner | |
588.3.c.j.197.6 | yes | 8 | 21.20 | even | 2 | inner | |
588.3.p.i.557.1 | 16 | 21.5 | even | 6 | |||
588.3.p.i.557.3 | 16 | 7.2 | even | 3 | |||
588.3.p.i.557.6 | 16 | 7.5 | odd | 6 | |||
588.3.p.i.557.8 | 16 | 21.2 | odd | 6 | |||
588.3.p.i.569.1 | 16 | 7.3 | odd | 6 | |||
588.3.p.i.569.3 | 16 | 21.11 | odd | 6 | |||
588.3.p.i.569.6 | 16 | 21.17 | even | 6 | |||
588.3.p.i.569.8 | 16 | 7.4 | even | 3 |