Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1143,3,Mod(890,1143)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1143, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("1143.890");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1143 = 3^{2} \cdot 127 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1143.b (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: | \(31.1444942164\) |
Analytic rank: | \(0\) |
Dimension: | \(84\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 890.15 | ||
Character | \(\chi\) | \(=\) | 1143.890 |
Dual form | 1143.3.b.a.890.70 |
$q$-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 \(\left(\mathbb{Z}/1143\mathbb{Z}\right)^\times\).
\(n\) | \(128\) | \(892\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 2.89430i | − 1.44715i | −0.690246 | − | 0.723574i | \(-0.742498\pi\) | ||||
0.690246 | − | 0.723574i | \(-0.257502\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −4.37696 | −1.09424 | ||||||||
\(5\) | 0.368899i | 0.0737798i | 0.999319 | + | 0.0368899i | \(0.0117451\pi\) | ||||
−0.999319 | + | 0.0368899i | \(0.988255\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −11.4242 | −1.63203 | −0.816016 | − | 0.578029i | \(-0.803822\pi\) | ||||
−0.816016 | + | 0.578029i | \(0.803822\pi\) | |||||||
\(8\) | 1.09103i | 0.136379i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.06770 | 0.106770 | ||||||||
\(11\) | 12.4660i | 1.13327i | 0.823969 | + | 0.566635i | \(0.191755\pi\) | ||||
−0.823969 | + | 0.566635i | \(0.808245\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −14.3568 | −1.10437 | −0.552185 | − | 0.833722i | \(-0.686206\pi\) | ||||
−0.552185 | + | 0.833722i | \(0.686206\pi\) | |||||||
\(14\) | 33.0651i | 2.36179i | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −14.3501 | −0.896879 | ||||||||
\(17\) | 4.03686i | 0.237463i | 0.992926 | + | 0.118731i | \(0.0378827\pi\) | ||||
−0.992926 | + | 0.118731i | \(0.962117\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.50638 | 0.237178 | 0.118589 | − | 0.992943i | \(-0.462163\pi\) | ||||
0.118589 | + | 0.992943i | \(0.462163\pi\) | |||||||
\(20\) | − 1.61466i | − 0.0807328i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 36.0802 | 1.64001 | ||||||||
\(23\) | − 24.7854i | − 1.07763i | −0.842425 | − | 0.538813i | \(-0.818873\pi\) | ||||
0.842425 | − | 0.538813i | \(-0.181127\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.8639 | 0.994557 | ||||||||
\(26\) | 41.5529i | 1.59819i | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 50.0034 | 1.78583 | ||||||||
\(29\) | − 40.2521i | − 1.38800i | −0.719974 | − | 0.694001i | \(-0.755846\pi\) | ||||
0.719974 | − | 0.694001i | \(-0.244154\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.142872 | −0.00460879 | −0.00230439 | − | 0.999997i | \(-0.500734\pi\) | ||||
−0.00230439 | + | 0.999997i | \(0.500734\pi\) | |||||||
\(32\) | 45.8975i | 1.43430i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 11.6839 | 0.343644 | ||||||||
\(35\) | − 4.21439i | − 0.120411i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 70.5507 | 1.90678 | 0.953388 | − | 0.301747i | \(-0.0975699\pi\) | ||||
0.953388 | + | 0.301747i | \(0.0975699\pi\) | |||||||
\(38\) | − 13.0428i | − 0.343232i | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.402480 | −0.0100620 | ||||||||
\(41\) | 72.7348i | 1.77402i | 0.461751 | + | 0.887009i | \(0.347221\pi\) | ||||
−0.461751 | + | 0.887009i | \(0.652779\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 32.2116 | 0.749108 | 0.374554 | − | 0.927205i | \(-0.377796\pi\) | ||||
0.374554 | + | 0.927205i | \(0.377796\pi\) | |||||||
\(44\) | − 54.5630i | − 1.24007i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −71.7363 | −1.55949 | ||||||||
\(47\) | 29.8941i | 0.636044i | 0.948083 | + | 0.318022i | \(0.103019\pi\) | ||||
−0.948083 | + | 0.318022i | \(0.896981\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 81.5130 | 1.66353 | ||||||||
\(50\) | − 71.9636i | − 1.43927i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 62.8392 | 1.20845 | ||||||||
\(53\) | − 46.0232i | − 0.868362i | −0.900826 | − | 0.434181i | \(-0.857038\pi\) | ||||
0.900826 | − | 0.434181i | \(-0.142962\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.59868 | −0.0836124 | ||||||||
\(56\) | − 12.4642i | − 0.222575i | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −116.501 | −2.00865 | ||||||||
\(59\) | 67.6830i | 1.14717i | 0.819146 | + | 0.573585i | \(0.194448\pi\) | ||||
−0.819146 | + | 0.573585i | \(0.805552\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −40.9491 | −0.671297 | −0.335648 | − | 0.941987i | \(-0.608955\pi\) | ||||
−0.335648 | + | 0.941987i | \(0.608955\pi\) | |||||||
\(62\) | 0.413515i | 0.00666960i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 75.4407 | 1.17876 | ||||||||
\(65\) | − 5.29621i | − 0.0814802i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13.7399 | −0.205073 | −0.102536 | − | 0.994729i | \(-0.532696\pi\) | ||||
−0.102536 | + | 0.994729i | \(0.532696\pi\) | |||||||
\(68\) | − 17.6692i | − 0.259841i | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −12.1977 | −0.174253 | ||||||||
\(71\) | − 14.7337i | − 0.207517i | −0.994603 | − | 0.103759i | \(-0.966913\pi\) | ||||
0.994603 | − | 0.103759i | \(-0.0330870\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 131.028 | 1.79491 | 0.897454 | − | 0.441109i | \(-0.145415\pi\) | ||||
0.897454 | + | 0.441109i | \(0.145415\pi\) | |||||||
\(74\) | − 204.195i | − 2.75939i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −19.7242 | −0.259530 | ||||||||
\(77\) | − 142.414i | − 1.84953i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 86.0968 | 1.08983 | 0.544916 | − | 0.838490i | \(-0.316561\pi\) | ||||
0.544916 | + | 0.838490i | \(0.316561\pi\) | |||||||
\(80\) | − 5.29373i | − 0.0661716i | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 210.516 | 2.56727 | ||||||||
\(83\) | 141.334i | 1.70281i | 0.524505 | + | 0.851407i | \(0.324250\pi\) | ||||
−0.524505 | + | 0.851407i | \(0.675750\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.48920 | −0.0175199 | ||||||||
\(86\) | − 93.2301i | − 1.08407i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −13.6007 | −0.154554 | ||||||||
\(89\) | 136.262i | 1.53104i | 0.643413 | + | 0.765519i | \(0.277518\pi\) | ||||
−0.643413 | + | 0.765519i | \(0.722482\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 164.016 | 1.80237 | ||||||||
\(92\) | 108.485i | 1.17918i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 86.5224 | 0.920451 | ||||||||
\(95\) | 1.66240i | 0.0174989i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 22.3537 | 0.230450 | 0.115225 | − | 0.993339i | \(-0.463241\pi\) | ||||
0.115225 | + | 0.993339i | \(0.463241\pi\) | |||||||
\(98\) | − 235.923i | − 2.40738i | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −108.828 | −1.08828 | ||||||||
\(101\) | − 143.434i | − 1.42014i | −0.704131 | − | 0.710070i | \(-0.748663\pi\) | ||||
0.704131 | − | 0.710070i | \(-0.251337\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 48.6766 | 0.472588 | 0.236294 | − | 0.971682i | \(-0.424067\pi\) | ||||
0.236294 | + | 0.971682i | \(0.424067\pi\) | |||||||
\(104\) | − 15.6637i | − 0.150613i | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −133.205 | −1.25665 | ||||||||
\(107\) | − 59.3338i | − 0.554522i | −0.960795 | − | 0.277261i | \(-0.910573\pi\) | ||||
0.960795 | − | 0.277261i | \(-0.0894266\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −170.051 | −1.56010 | −0.780050 | − | 0.625717i | \(-0.784806\pi\) | ||||
−0.780050 | + | 0.625717i | \(0.784806\pi\) | |||||||
\(110\) | 13.3100i | 0.121000i | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 163.938 | 1.46374 | ||||||||
\(113\) | 75.6100i | 0.669115i | 0.942375 | + | 0.334558i | \(0.108587\pi\) | ||||
−0.942375 | + | 0.334558i | \(0.891413\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.14331 | 0.0795071 | ||||||||
\(116\) | 176.182i | 1.51881i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 195.895 | 1.66012 | ||||||||
\(119\) | − 46.1181i | − 0.387547i | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −34.4002 | −0.284299 | ||||||||
\(122\) | 118.519i | 0.971466i | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0.625347 | 0.00504312 | ||||||||
\(125\) | 18.3948i | 0.147158i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.2694 | 0.0887357 | ||||||||
\(128\) | − 34.7579i | − 0.271546i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −15.3288 | −0.117914 | ||||||||
\(131\) | − 155.996i | − 1.19081i | −0.803425 | − | 0.595406i | \(-0.796991\pi\) | ||||
0.803425 | − | 0.595406i | \(-0.203009\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −51.4819 | −0.387082 | ||||||||
\(134\) | 39.7672i | 0.296770i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −4.40434 | −0.0323848 | ||||||||
\(137\) | 73.9267i | 0.539611i | 0.962915 | + | 0.269806i | \(0.0869594\pi\) | ||||
−0.962915 | + | 0.269806i | \(0.913041\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −264.466 | −1.90264 | −0.951318 | − | 0.308212i | \(-0.900269\pi\) | ||||
−0.951318 | + | 0.308212i | \(0.900269\pi\) | |||||||
\(140\) | 18.4462i | 0.131759i | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −42.6438 | −0.300308 | ||||||||
\(143\) | − 178.971i | − 1.25155i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.8489 | 0.102407 | ||||||||
\(146\) | − 379.235i | − 2.59750i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −308.798 | −2.08647 | ||||||||
\(149\) | 81.6878i | 0.548240i | 0.961695 | + | 0.274120i | \(0.0883866\pi\) | ||||
−0.961695 | + | 0.274120i | \(0.911613\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −245.937 | −1.62872 | −0.814360 | − | 0.580360i | \(-0.802912\pi\) | ||||
−0.814360 | + | 0.580360i | \(0.802912\pi\) | |||||||
\(152\) | 4.91660i | 0.0323460i | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −412.188 | −2.67655 | ||||||||
\(155\) | − 0.0527055i | 0 0.000340035i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 231.778 | 1.47629 | 0.738147 | − | 0.674640i | \(-0.235701\pi\) | ||||
0.738147 | + | 0.674640i | \(0.235701\pi\) | |||||||
\(158\) | − 249.190i | − 1.57715i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −16.9315 | −0.105822 | ||||||||
\(161\) | 283.154i | 1.75872i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 124.426 | 0.763347 | 0.381673 | − | 0.924297i | \(-0.375348\pi\) | ||||
0.381673 | + | 0.924297i | \(0.375348\pi\) | |||||||
\(164\) | − 318.357i | − 1.94120i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 409.062 | 2.46423 | ||||||||
\(167\) | 47.4894i | 0.284368i | 0.989840 | + | 0.142184i | \(0.0454124\pi\) | ||||
−0.989840 | + | 0.142184i | \(0.954588\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 37.1181 | 0.219634 | ||||||||
\(170\) | 4.31017i | 0.0253540i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −140.989 | −0.819704 | ||||||||
\(173\) | 220.614i | 1.27522i | 0.770357 | + | 0.637612i | \(0.220078\pi\) | ||||
−0.770357 | + | 0.637612i | \(0.779922\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −284.051 | −1.62315 | ||||||||
\(176\) | − 178.887i | − 1.01641i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 394.384 | 2.21564 | ||||||||
\(179\) | 94.0577i | 0.525462i | 0.964869 | + | 0.262731i | \(0.0846232\pi\) | ||||
−0.964869 | + | 0.262731i | \(0.915377\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 115.413 | 0.637642 | 0.318821 | − | 0.947815i | \(-0.396713\pi\) | ||||
0.318821 | + | 0.947815i | \(0.396713\pi\) | |||||||
\(182\) | − 474.710i | − 2.60830i | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 27.0416 | 0.146965 | ||||||||
\(185\) | 26.0261i | 0.140682i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −50.3234 | −0.269109 | ||||||||
\(188\) | − 130.845i | − 0.695985i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.81148 | 0.0253236 | ||||||||
\(191\) | 74.0418i | 0.387654i | 0.981036 | + | 0.193827i | \(0.0620900\pi\) | ||||
−0.981036 | + | 0.193827i | \(0.937910\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.0989 | −0.0730514 | −0.0365257 | − | 0.999333i | \(-0.511629\pi\) | ||||
−0.0365257 | + | 0.999333i | \(0.511629\pi\) | |||||||
\(194\) | − 64.6983i | − 0.333496i | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −356.779 | −1.82030 | ||||||||
\(197\) | − 312.804i | − 1.58784i | −0.608024 | − | 0.793919i | \(-0.708038\pi\) | ||||
0.608024 | − | 0.793919i | \(-0.291962\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 69.5241 | 0.349367 | 0.174684 | − | 0.984625i | \(-0.444110\pi\) | ||||
0.174684 | + | 0.984625i | \(0.444110\pi\) | |||||||
\(200\) | 27.1273i | 0.135636i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −415.141 | −2.05515 | ||||||||
\(203\) | 459.849i | 2.26526i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −26.8318 | −0.130887 | ||||||||
\(206\) | − 140.885i | − 0.683906i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 206.021 | 0.990487 | ||||||||
\(209\) | 56.1764i | 0.268787i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 211.824 | 1.00390 | 0.501952 | − | 0.864896i | \(-0.332615\pi\) | ||||
0.501952 | + | 0.864896i | \(0.332615\pi\) | |||||||
\(212\) | 201.442i | 0.950196i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −171.730 | −0.802476 | ||||||||
\(215\) | 11.8828i | 0.0552691i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.63221 | 0.00752169 | ||||||||
\(218\) | 492.178i | 2.25770i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 20.1282 | 0.0914920 | ||||||||
\(221\) | − 57.9565i | − 0.262247i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −264.549 | −1.18632 | −0.593159 | − | 0.805085i | \(-0.702120\pi\) | ||||
−0.593159 | + | 0.805085i | \(0.702120\pi\) | |||||||
\(224\) | − 524.343i | − 2.34082i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 218.838 | 0.968309 | ||||||||
\(227\) | 390.263i | 1.71922i | 0.510949 | + | 0.859611i | \(0.329294\pi\) | ||||
−0.510949 | + | 0.859611i | \(0.670706\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −156.112 | −0.681714 | −0.340857 | − | 0.940115i | \(-0.610717\pi\) | ||||
−0.340857 | + | 0.940115i | \(0.610717\pi\) | |||||||
\(230\) | − 26.4635i | − 0.115059i | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 43.9162 | 0.189294 | ||||||||
\(233\) | − 327.852i | − 1.40709i | −0.710650 | − | 0.703545i | \(-0.751599\pi\) | ||||
0.710650 | − | 0.703545i | \(-0.248401\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −11.0279 | −0.0469272 | ||||||||
\(236\) | − 296.246i | − 1.25528i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −133.479 | −0.560838 | ||||||||
\(239\) | 218.750i | 0.915274i | 0.889139 | + | 0.457637i | \(0.151304\pi\) | ||||
−0.889139 | + | 0.457637i | \(0.848696\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −145.126 | −0.602182 | −0.301091 | − | 0.953595i | \(-0.597351\pi\) | ||||
−0.301091 | + | 0.953595i | \(0.597351\pi\) | |||||||
\(242\) | 99.5643i | 0.411423i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 179.232 | 0.734559 | ||||||||
\(245\) | 30.0701i | 0.122735i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −64.6973 | −0.261932 | ||||||||
\(248\) | − 0.155878i | 0 0.000628540i | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 53.2399 | 0.212960 | ||||||||
\(251\) | − 347.366i | − 1.38393i | −0.721933 | − | 0.691963i | \(-0.756746\pi\) | ||||
0.721933 | − | 0.691963i | \(-0.243254\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 308.974 | 1.22124 | ||||||||
\(254\) | − 32.6171i | − 0.128414i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 201.163 | 0.785793 | ||||||||
\(257\) | 121.233i | 0.471722i | 0.971787 | + | 0.235861i | \(0.0757910\pi\) | ||||
−0.971787 | + | 0.235861i | \(0.924209\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −805.987 | −3.11192 | ||||||||
\(260\) | 23.1813i | 0.0891589i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −451.500 | −1.72328 | ||||||||
\(263\) | 288.631i | 1.09746i | 0.836000 | + | 0.548729i | \(0.184888\pi\) | ||||
−0.836000 | + | 0.548729i | \(0.815112\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 16.9779 | 0.0640676 | ||||||||
\(266\) | 149.004i | 0.560166i | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 60.1388 | 0.224398 | ||||||||
\(269\) | 67.7121i | 0.251718i | 0.992048 | + | 0.125859i | \(0.0401687\pi\) | ||||
−0.992048 | + | 0.125859i | \(0.959831\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 396.016 | 1.46131 | 0.730657 | − | 0.682745i | \(-0.239214\pi\) | ||||
0.730657 | + | 0.682745i | \(0.239214\pi\) | |||||||
\(272\) | − 57.9293i | − 0.212975i | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 213.966 | 0.780898 | ||||||||
\(275\) | 309.953i | 1.12710i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −215.982 | −0.779718 | −0.389859 | − | 0.920875i | \(-0.627476\pi\) | ||||
−0.389859 | + | 0.920875i | \(0.627476\pi\) | |||||||
\(278\) | 765.444i | 2.75340i | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 4.59802 | 0.0164215 | ||||||||
\(281\) | − 170.535i | − 0.606886i | −0.952850 | − | 0.303443i | \(-0.901864\pi\) | ||||
0.952850 | − | 0.303443i | \(-0.0981362\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −0.946273 | −0.00334372 | −0.00167186 | − | 0.999999i | \(-0.500532\pi\) | ||||
−0.00167186 | + | 0.999999i | \(0.500532\pi\) | |||||||
\(284\) | 64.4889i | 0.227074i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −517.997 | −1.81118 | ||||||||
\(287\) | − 830.939i | − 2.89526i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 272.704 | 0.943612 | ||||||||
\(290\) | − 42.9773i | − 0.148197i | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −573.505 | −1.96406 | ||||||||
\(293\) | 308.048i | 1.05136i | 0.850683 | + | 0.525679i | \(0.176189\pi\) | ||||
−0.850683 | + | 0.525679i | \(0.823811\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −24.9682 | −0.0846380 | ||||||||
\(296\) | 76.9729i | 0.260044i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 236.429 | 0.793385 | ||||||||
\(299\) | 355.839i | 1.19010i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −367.993 | −1.22257 | ||||||||
\(302\) | 711.814i | 2.35700i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −64.6669 | −0.212720 | ||||||||
\(305\) | − 15.1061i | − 0.0495281i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −226.372 | −0.737369 | −0.368685 | − | 0.929555i | \(-0.620192\pi\) | ||||
−0.368685 | + | 0.929555i | \(0.620192\pi\) | |||||||
\(308\) | 623.340i | 2.02383i | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.152545 | −0.000492082 0 | ||||||||
\(311\) | 286.254i | 0.920431i | 0.887807 | + | 0.460215i | \(0.152228\pi\) | ||||
−0.887807 | + | 0.460215i | \(0.847772\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 403.280 | 1.28844 | 0.644218 | − | 0.764842i | \(-0.277183\pi\) | ||||
0.644218 | + | 0.764842i | \(0.277183\pi\) | |||||||
\(314\) | − 670.835i | − 2.13642i | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −376.842 | −1.19254 | ||||||||
\(317\) | 252.786i | 0.797431i | 0.917075 | + | 0.398715i | \(0.130544\pi\) | ||||
−0.917075 | + | 0.398715i | \(0.869456\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 501.780 | 1.57298 | ||||||||
\(320\) | 27.8300i | 0.0869688i | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 819.532 | 2.54513 | ||||||||
\(323\) | 18.1917i | 0.0563209i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −356.967 | −1.09836 | ||||||||
\(326\) | − 360.125i | − 1.10468i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −79.3558 | −0.241938 | ||||||||
\(329\) | − 341.517i | − 1.03804i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 493.284 | 1.49028 | 0.745142 | − | 0.666906i | \(-0.232382\pi\) | ||||
0.745142 | + | 0.666906i | \(0.232382\pi\) | |||||||
\(332\) | − 618.611i | − 1.86329i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 137.448 | 0.411522 | ||||||||
\(335\) | − 5.06862i | − 0.0151302i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 437.426 | 1.29800 | 0.649000 | − | 0.760789i | \(-0.275188\pi\) | ||||
0.649000 | + | 0.760789i | \(0.275188\pi\) | |||||||
\(338\) | − 107.431i | − 0.317843i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.51815 | 0.0191710 | ||||||||
\(341\) | − 1.78104i | − 0.00522300i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −371.436 | −1.08290 | ||||||||
\(344\) | 35.1439i | 0.102162i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 638.522 | 1.84544 | ||||||||
\(347\) | 585.153i | 1.68632i | 0.537663 | + | 0.843160i | \(0.319307\pi\) | ||||
−0.537663 | + | 0.843160i | \(0.680693\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 526.031 | 1.50725 | 0.753626 | − | 0.657304i | \(-0.228303\pi\) | ||||
0.753626 | + | 0.657304i | \(0.228303\pi\) | |||||||
\(350\) | 822.128i | 2.34894i | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −572.156 | −1.62544 | ||||||||
\(353\) | 50.5781i | 0.143281i | 0.997431 | + | 0.0716404i | \(0.0228234\pi\) | ||||
−0.997431 | + | 0.0716404i | \(0.977177\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 5.43526 | 0.0153106 | ||||||||
\(356\) | − 596.415i | − 1.67532i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 272.231 | 0.760422 | ||||||||
\(359\) | 141.833i | 0.395078i | 0.980295 | + | 0.197539i | \(0.0632949\pi\) | ||||
−0.980295 | + | 0.197539i | \(0.936705\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −340.693 | −0.943747 | ||||||||
\(362\) | − 334.040i | − 0.922763i | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −717.889 | −1.97222 | ||||||||
\(365\) | 48.3362i | 0.132428i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −158.951 | −0.433110 | −0.216555 | − | 0.976270i | \(-0.569482\pi\) | ||||
−0.216555 | + | 0.976270i | \(0.569482\pi\) | |||||||
\(368\) | 355.672i | 0.966501i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 75.3272 | 0.203587 | ||||||||
\(371\) | 525.779i | 1.41719i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 530.611 | 1.42255 | 0.711275 | − | 0.702914i | \(-0.248118\pi\) | ||||
0.711275 | + | 0.702914i | \(0.248118\pi\) | |||||||
\(374\) | 145.651i | 0.389441i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −32.6153 | −0.0867429 | ||||||||
\(377\) | 577.891i | 1.53287i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 244.663 | 0.645548 | 0.322774 | − | 0.946476i | \(-0.395385\pi\) | ||||
0.322774 | + | 0.946476i | \(0.395385\pi\) | |||||||
\(380\) | − 7.27626i | − 0.0191480i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 214.299 | 0.560992 | ||||||||
\(383\) | − 167.289i | − 0.436786i | −0.975861 | − | 0.218393i | \(-0.929919\pi\) | ||||
0.975861 | − | 0.218393i | \(-0.0700814\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 52.5364 | 0.136458 | ||||||||
\(386\) | 40.8065i | 0.105716i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −97.8412 | −0.252168 | ||||||||
\(389\) | − 412.946i | − 1.06156i | −0.847511 | − | 0.530779i | \(-0.821900\pi\) | ||||
0.847511 | − | 0.530779i | \(-0.178100\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 100.055 | 0.255896 | ||||||||
\(392\) | 88.9331i | 0.226870i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −905.348 | −2.29784 | ||||||||
\(395\) | 31.7610i | 0.0804077i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 536.080 | 1.35033 | 0.675164 | − | 0.737668i | \(-0.264073\pi\) | ||||
0.675164 | + | 0.737668i | \(0.264073\pi\) | |||||||
\(398\) | − 201.223i | − 0.505587i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −356.799 | −0.891997 | ||||||||
\(401\) | − 535.852i | − 1.33629i | −0.744032 | − | 0.668144i | \(-0.767089\pi\) | ||||
0.744032 | − | 0.668144i | \(-0.232911\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 2.05119 | 0.00508981 | ||||||||
\(404\) | 627.805i | 1.55397i | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1330.94 | 3.27817 | ||||||||
\(407\) | 879.482i | 2.16089i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −357.786 | −0.874783 | −0.437391 | − | 0.899271i | \(-0.644098\pi\) | ||||
−0.437391 | + | 0.899271i | \(0.644098\pi\) | |||||||
\(410\) | 77.6592i | 0.189413i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −213.056 | −0.517125 | ||||||||
\(413\) | − 773.226i | − 1.87222i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −52.1378 | −0.125633 | ||||||||
\(416\) | − 658.942i | − 1.58399i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 162.591 | 0.388974 | ||||||||
\(419\) | 613.475i | 1.46414i | 0.681229 | + | 0.732070i | \(0.261446\pi\) | ||||
−0.681229 | + | 0.732070i | \(0.738554\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 569.239 | 1.35211 | 0.676056 | − | 0.736850i | \(-0.263688\pi\) | ||||
0.676056 | + | 0.736850i | \(0.263688\pi\) | |||||||
\(422\) | − 613.081i | − 1.45280i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 50.2127 | 0.118426 | ||||||||
\(425\) | 100.372i | 0.236170i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 467.812 | 1.09558 | ||||||||
\(428\) | 259.702i | 0.606780i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 34.3925 | 0.0799826 | ||||||||
\(431\) | 269.812i | 0.626014i | 0.949751 | + | 0.313007i | \(0.101336\pi\) | ||||
−0.949751 | + | 0.313007i | \(0.898664\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 151.221 | 0.349241 | 0.174620 | − | 0.984636i | \(-0.444130\pi\) | ||||
0.174620 | + | 0.984636i | \(0.444130\pi\) | |||||||
\(434\) | − 4.72409i | − 0.0108850i | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 744.306 | 1.70712 | ||||||||
\(437\) | − 111.692i | − 0.255589i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 272.925 | 0.621698 | 0.310849 | − | 0.950459i | \(-0.399387\pi\) | ||||
0.310849 | + | 0.950459i | \(0.399387\pi\) | |||||||
\(440\) | − 5.01730i | − 0.0114029i | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −167.743 | −0.379510 | ||||||||
\(443\) | − 173.360i | − 0.391331i | −0.980671 | − | 0.195666i | \(-0.937313\pi\) | ||||
0.980671 | − | 0.195666i | \(-0.0626867\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −50.2671 | −0.112960 | ||||||||
\(446\) | 765.684i | 1.71678i | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −861.852 | −1.92378 | ||||||||
\(449\) | 97.2936i | 0.216690i | 0.994113 | + | 0.108345i | \(0.0345550\pi\) | ||||
−0.994113 | + | 0.108345i | \(0.965445\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −906.709 | −2.01044 | ||||||||
\(452\) | − 330.942i | − 0.732172i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1129.54 | 2.48797 | ||||||||
\(455\) | 60.5052i | 0.132978i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 30.5417 | 0.0668310 | 0.0334155 | − | 0.999442i | \(-0.489362\pi\) | ||||
0.0334155 | + | 0.999442i | \(0.489362\pi\) | |||||||
\(458\) | 451.836i | 0.986541i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −40.0199 | −0.0869998 | ||||||||
\(461\) | 88.1669i | 0.191251i | 0.995417 | + | 0.0956257i | \(0.0304852\pi\) | ||||
−0.995417 | + | 0.0956257i | \(0.969515\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −794.001 | −1.71491 | −0.857453 | − | 0.514563i | \(-0.827954\pi\) | ||||
−0.857453 | + | 0.514563i | \(0.827954\pi\) | |||||||
\(464\) | 577.620i | 1.24487i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −948.902 | −2.03627 | ||||||||
\(467\) | − 142.933i | − 0.306066i | −0.988221 | − | 0.153033i | \(-0.951096\pi\) | ||||
0.988221 | − | 0.153033i | \(-0.0489041\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 156.967 | 0.334685 | ||||||||
\(470\) | 31.9180i | 0.0679107i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −73.8442 | −0.156450 | ||||||||
\(473\) | 401.549i | 0.848941i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 112.046 | 0.235887 | ||||||||
\(476\) | 201.857i | 0.424069i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 633.129 | 1.32454 | ||||||||
\(479\) | − 555.490i | − 1.15969i | −0.814728 | − | 0.579843i | \(-0.803114\pi\) | ||||
0.814728 | − | 0.579843i | \(-0.196886\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1012.88 | −2.10579 | ||||||||
\(482\) | 420.037i | 0.871447i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 150.568 | 0.311091 | ||||||||
\(485\) | 8.24626i | 0.0170026i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 456.287 | 0.936934 | 0.468467 | − | 0.883481i | \(-0.344807\pi\) | ||||
0.468467 | + | 0.883481i | \(0.344807\pi\) | |||||||
\(488\) | − 44.6767i | − 0.0915506i | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 87.0317 | 0.177616 | ||||||||
\(491\) | − 428.089i | − 0.871872i | −0.899978 | − | 0.435936i | \(-0.856417\pi\) | ||||
0.899978 | − | 0.435936i | \(-0.143583\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 162.492 | 0.329598 | ||||||||
\(494\) | 187.253i | 0.379055i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.05023 | 0.00413353 | ||||||||
\(497\) | 168.321i | 0.338675i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −216.198 | −0.433263 | −0.216632 | − | 0.976253i | \(-0.569507\pi\) | ||||
−0.216632 | + | 0.976253i | \(0.569507\pi\) | |||||||
\(500\) | − 80.5131i | − 0.161026i | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1005.38 | −2.00275 | ||||||||
\(503\) | 484.500i | 0.963220i | 0.876386 | + | 0.481610i | \(0.159948\pi\) | ||||
−0.876386 | + | 0.481610i | \(0.840052\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 52.9127 | 0.104778 | ||||||||
\(506\) | − 894.262i | − 1.76732i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −49.3258 | −0.0970981 | ||||||||
\(509\) | 618.428i | 1.21499i | 0.794325 | + | 0.607493i | \(0.207825\pi\) | ||||
−0.794325 | + | 0.607493i | \(0.792175\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1496.90 | −2.92935 | ||||||||
\(512\) | − 721.258i | − 1.40871i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 350.883 | 0.682652 | ||||||||
\(515\) | 17.9568i | 0.0348675i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −372.658 | −0.720809 | ||||||||
\(518\) | 2332.77i | 4.50341i | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 5.77833 | 0.0111122 | ||||||||
\(521\) | 15.6085i | 0.0299587i | 0.999888 | + | 0.0149793i | \(0.00476825\pi\) | ||||
−0.999888 | + | 0.0149793i | \(0.995232\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −422.072 | −0.807022 | −0.403511 | − | 0.914975i | \(-0.632210\pi\) | ||||
−0.403511 | + | 0.914975i | \(0.632210\pi\) | |||||||
\(524\) | 682.789i | 1.30303i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 835.385 | 1.58818 | ||||||||
\(527\) | − 0.576756i | − 0.00109441i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −85.3161 | −0.161278 | ||||||||
\(530\) | − 49.1391i | − 0.0927153i | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 225.334 | 0.423561 | ||||||||
\(533\) | − 1044.24i | − 1.95917i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 21.8882 | 0.0409125 | ||||||||
\(536\) | − 14.9906i | − 0.0279675i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 195.979 | 0.364273 | ||||||||
\(539\) | 1016.14i | 1.88523i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −797.374 | −1.47389 | −0.736944 | − | 0.675953i | \(-0.763732\pi\) | ||||
−0.736944 | + | 0.675953i | \(0.763732\pi\) | |||||||
\(542\) | − 1146.19i | − 2.11474i | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −185.282 | −0.340592 | ||||||||
\(545\) | − 62.7316i | − 0.115104i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 607.308 | 1.11025 | 0.555126 | − | 0.831766i | \(-0.312670\pi\) | ||||
0.555126 | + | 0.831766i | \(0.312670\pi\) | |||||||
\(548\) | − 323.574i | − 0.590464i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 897.095 | 1.63108 | ||||||||
\(551\) | − 181.391i | − 0.329204i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −983.589 | −1.77864 | ||||||||
\(554\) | 625.116i | 1.12837i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1157.56 | 2.08194 | ||||||||
\(557\) | 763.344i | 1.37046i | 0.728329 | + | 0.685228i | \(0.240297\pi\) | ||||
−0.728329 | + | 0.685228i | \(0.759703\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −462.457 | −0.827293 | ||||||||
\(560\) | 60.4767i | 0.107994i | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −493.579 | −0.878254 | ||||||||
\(563\) | 911.688i | 1.61934i | 0.586886 | + | 0.809670i | \(0.300354\pi\) | ||||
−0.586886 | + | 0.809670i | \(0.699646\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −27.8925 | −0.0493672 | ||||||||
\(566\) | 2.73880i | 0.00483886i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 16.0749 | 0.0283009 | ||||||||
\(569\) | 680.350i | 1.19569i | 0.801610 | + | 0.597847i | \(0.203977\pi\) | ||||
−0.801610 | + | 0.597847i | \(0.796023\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 74.3734 | 0.130251 | 0.0651256 | − | 0.997877i | \(-0.479255\pi\) | ||||
0.0651256 | + | 0.997877i | \(0.479255\pi\) | |||||||
\(572\) | 783.351i | 1.36949i | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −2404.98 | −4.18987 | ||||||||
\(575\) | − 616.262i | − 1.07176i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 234.061 | 0.405652 | 0.202826 | − | 0.979215i | \(-0.434987\pi\) | ||||
0.202826 | + | 0.979215i | \(0.434987\pi\) | |||||||
\(578\) | − 789.286i | − 1.36555i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −64.9932 | −0.112057 | ||||||||
\(581\) | − 1614.63i | − 2.77905i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 573.723 | 0.984088 | ||||||||
\(584\) | 142.956i | 0.244787i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 891.583 | 1.52147 | ||||||||
\(587\) | − 547.257i | − 0.932295i | −0.884707 | − | 0.466147i | \(-0.845642\pi\) | ||||
0.884707 | − | 0.466147i | \(-0.154358\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.643838 | −0.00109310 | ||||||||
\(590\) | 72.2654i | 0.122484i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1012.41 | −1.71015 | ||||||||
\(593\) | − 453.958i | − 0.765528i | −0.923846 | − | 0.382764i | \(-0.874972\pi\) | ||||
0.923846 | − | 0.382764i | \(-0.125028\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 17.0129 | 0.0285931 | ||||||||
\(596\) | − 357.544i | − 0.599906i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 1029.90 | 1.72225 | ||||||||
\(599\) | 852.190i | 1.42269i | 0.702844 | + | 0.711344i | \(0.251913\pi\) | ||||
−0.702844 | + | 0.711344i | \(0.748087\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 70.0421 | 0.116543 | 0.0582713 | − | 0.998301i | \(-0.481441\pi\) | ||||
0.0582713 | + | 0.998301i | \(0.481441\pi\) | |||||||
\(602\) | 1065.08i | 1.76924i | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 1076.45 | 1.78221 | ||||||||
\(605\) | − 12.6902i | − 0.0209755i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 569.835 | 0.938773 | 0.469387 | − | 0.882993i | \(-0.344475\pi\) | ||||
0.469387 | + | 0.882993i | \(0.344475\pi\) | |||||||
\(608\) | 206.832i | 0.340184i | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −43.7215 | −0.0716746 | ||||||||
\(611\) | − 429.184i | − 0.702428i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 477.707 | 0.779294 | 0.389647 | − | 0.920964i | \(-0.372597\pi\) | ||||
0.389647 | + | 0.920964i | \(0.372597\pi\) | |||||||
\(614\) | 655.189i | 1.06708i | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 155.378 | 0.252237 | ||||||||
\(617\) | − 1014.71i | − 1.64459i | −0.569061 | − | 0.822295i | \(-0.692693\pi\) | ||||
0.569061 | − | 0.822295i | \(-0.307307\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −401.464 | −0.648569 | −0.324284 | − | 0.945960i | \(-0.605123\pi\) | ||||
−0.324284 | + | 0.945960i | \(0.605123\pi\) | |||||||
\(620\) | 0.230690i | 0 0.000372080i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 828.504 | 1.33200 | ||||||||
\(623\) | − 1556.69i | − 2.49871i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 614.812 | 0.983699 | ||||||||
\(626\) | − 1167.21i | − 1.86456i | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1014.48 | −1.61542 | ||||||||
\(629\) | 284.804i | 0.452788i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −807.950 | −1.28043 | −0.640214 | − | 0.768197i | \(-0.721154\pi\) | ||||
−0.640214 | + | 0.768197i | \(0.721154\pi\) | |||||||
\(632\) | 93.9342i | 0.148630i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 731.637 | 1.15400 | ||||||||
\(635\) | 4.15728i | 0.00654690i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1170.27 | −1.83715 | ||||||||
\(638\) | − 1452.30i | − 2.27634i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 12.8222 | 0.0200346 | ||||||||
\(641\) | 225.405i | 0.351646i | 0.984422 | + | 0.175823i | \(0.0562587\pi\) | ||||
−0.984422 | + | 0.175823i | \(0.943741\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −282.242 | −0.438946 | −0.219473 | − | 0.975619i | \(-0.570434\pi\) | ||||
−0.219473 | + | 0.975619i | \(0.570434\pi\) | |||||||
\(644\) | − 1239.35i | − 1.92446i | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 52.6521 | 0.0815047 | ||||||||
\(647\) | − 927.159i | − 1.43301i | −0.697581 | − | 0.716506i | \(-0.745740\pi\) | ||||
0.697581 | − | 0.716506i | \(-0.254260\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −843.734 | −1.30005 | ||||||||
\(650\) | 1033.17i | 1.58949i | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −544.605 | −0.835284 | ||||||||
\(653\) | 91.8009i | 0.140583i | 0.997526 | + | 0.0702916i | \(0.0223930\pi\) | ||||
−0.997526 | + | 0.0702916i | \(0.977607\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 57.5469 | 0.0878578 | ||||||||
\(656\) | − 1043.75i | − 1.59108i | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −988.451 | −1.50221 | ||||||||
\(659\) | 201.283i | 0.305437i | 0.988270 | + | 0.152718i | \(0.0488027\pi\) | ||||
−0.988270 | + | 0.152718i | \(0.951197\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1000.56 | −1.51371 | −0.756856 | − | 0.653582i | \(-0.773266\pi\) | ||||
−0.756856 | + | 0.653582i | \(0.773266\pi\) | |||||||
\(662\) | − 1427.71i | − 2.15666i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −154.199 | −0.232228 | ||||||||
\(665\) | − 18.9916i | − 0.0285589i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −997.663 | −1.49575 | ||||||||
\(668\) | − 207.859i | − 0.311166i | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −14.6701 | −0.0218957 | ||||||||
\(671\) | − 510.470i | − 0.760760i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −787.143 | −1.16960 | −0.584801 | − | 0.811177i | \(-0.698828\pi\) | ||||
−0.584801 | + | 0.811177i | \(0.698828\pi\) | |||||||
\(674\) | − 1266.04i | − 1.87840i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −162.464 | −0.240332 | ||||||||
\(677\) | − 846.014i | − 1.24965i | −0.780764 | − | 0.624825i | \(-0.785170\pi\) | ||||
0.780764 | − | 0.624825i | \(-0.214830\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −255.374 | −0.376103 | ||||||||
\(680\) | − 1.62476i | − 0.00238935i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5.15486 | −0.00755845 | ||||||||
\(683\) | 24.7020i | 0.0361669i | 0.999836 | + | 0.0180834i | \(0.00575645\pi\) | ||||
−0.999836 | + | 0.0180834i | \(0.994244\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −27.2715 | −0.0398124 | ||||||||
\(686\) | 1075.05i | 1.56712i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −462.239 | −0.671860 | ||||||||
\(689\) | 660.746i | 0.958993i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1031.11 | 1.49219 | 0.746097 | − | 0.665838i | \(-0.231926\pi\) | ||||
0.746097 | + | 0.665838i | \(0.231926\pi\) | |||||||
\(692\) | − 965.618i | − 1.39540i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 1693.61 | 2.44036 | ||||||||
\(695\) | − 97.5614i | − 0.140376i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −293.620 | −0.421263 | ||||||||
\(698\) | − 1522.49i | − 2.18122i | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1243.28 | 1.77611 | ||||||||
\(701\) | − 131.146i | − 0.187085i | −0.995615 | − | 0.0935424i | \(-0.970181\pi\) | ||||
0.995615 | − | 0.0935424i | \(-0.0298191\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 317.928 | 0.452245 | ||||||||
\(704\) | 940.441i | 1.33585i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 146.388 | 0.207349 | ||||||||
\(707\) | 1638.62i | 2.31772i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 488.183 | 0.688552 | 0.344276 | − | 0.938869i | \(-0.388124\pi\) | ||||
0.344276 | + | 0.938869i | \(0.388124\pi\) | |||||||
\(710\) | − 15.7313i | − 0.0221567i | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −148.666 | −0.208801 | ||||||||
\(713\) | 3.54115i | 0.00496655i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 66.0224 | 0.0923390 | ||||||||
\(716\) | − 411.687i | − 0.574982i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 410.507 | 0.571737 | ||||||||
\(719\) | − 14.8164i | − 0.0206069i | −0.999947 | − | 0.0103035i | \(-0.996720\pi\) | ||||
0.999947 | − | 0.0103035i | \(-0.00327975\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −556.093 | −0.771280 | ||||||||
\(722\) | 986.066i | 1.36574i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −505.159 | −0.697733 | ||||||||
\(725\) | − 1000.82i | − 1.38045i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 288.303 | 0.396565 | 0.198282 | − | 0.980145i | \(-0.436464\pi\) | ||||
0.198282 | + | 0.980145i | \(0.436464\pi\) | |||||||
\(728\) | 178.946i | 0.245805i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 139.899 | 0.191643 | ||||||||
\(731\) | 130.034i | 0.177885i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1127.93 | 1.53879 | 0.769393 | − | 0.638776i | \(-0.220559\pi\) | ||||
0.769393 | + | 0.638776i | \(0.220559\pi\) | |||||||
\(734\) | 460.053i | 0.626775i | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1137.59 | 1.54564 | ||||||||
\(737\) | − 171.281i | − 0.232402i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 289.034 | 0.391115 | 0.195557 | − | 0.980692i | \(-0.437348\pi\) | ||||
0.195557 | + | 0.980692i | \(0.437348\pi\) | |||||||
\(740\) | − 113.915i | − 0.153939i | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1521.76 | 2.05089 | ||||||||
\(743\) | − 1057.13i | − 1.42279i | −0.702793 | − | 0.711395i | \(-0.748064\pi\) | ||||
0.702793 | − | 0.711395i | \(-0.251936\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −30.1345 | −0.0404491 | ||||||||
\(746\) | − 1535.75i | − 2.05864i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 220.263 | 0.294470 | ||||||||
\(749\) | 677.843i | 0.904998i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 528.864 | 0.704214 | 0.352107 | − | 0.935960i | \(-0.385465\pi\) | ||||
0.352107 | + | 0.935960i | \(0.385465\pi\) | |||||||
\(752\) | − 428.982i | − 0.570455i | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 1672.59 | 2.21829 | ||||||||
\(755\) | − 90.7258i | − 0.120167i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1351.92 | 1.78589 | 0.892943 | − | 0.450170i | \(-0.148637\pi\) | ||||
0.892943 | + | 0.450170i | \(0.148637\pi\) | |||||||
\(758\) | − 708.126i | − 0.934203i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.81373 | −0.00238648 | ||||||||
\(761\) | − 615.698i | − 0.809064i | −0.914524 | − | 0.404532i | \(-0.867434\pi\) | ||||
0.914524 | − | 0.404532i | \(-0.132566\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1942.70 | 2.54613 | ||||||||
\(764\) | − 324.078i | − 0.424186i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −484.184 | −0.632094 | ||||||||
\(767\) | − 971.712i | − 1.26690i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1291.47 | −1.67942 | −0.839711 | − | 0.543034i | \(-0.817275\pi\) | ||||
−0.839711 | + | 0.543034i | \(0.817275\pi\) | |||||||
\(770\) | − 152.056i | − 0.197475i | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 61.7104 | 0.0799357 | ||||||||
\(773\) | − 354.437i | − 0.458521i | −0.973365 | − | 0.229261i | \(-0.926369\pi\) | ||||
0.973365 | − | 0.229261i | \(-0.0736308\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.55237 | −0.00458370 | ||||||||
\(776\) | 24.3885i | 0.0314285i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1195.19 | −1.53623 | ||||||||
\(779\) | 327.771i | 0.420758i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 183.670 | 0.235173 | ||||||||
\(782\) | − 289.590i | − 0.370319i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1169.72 | −1.49199 | ||||||||
\(785\) | 85.5027i | 0.108921i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1040.99 | −1.32273 | −0.661363 | − | 0.750066i | \(-0.730022\pi\) | ||||
−0.661363 | + | 0.750066i | \(0.730022\pi\) | |||||||
\(788\) | 1369.13i | 1.73747i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 91.9259 | 0.116362 | ||||||||
\(791\) | − 863.786i | − 1.09202i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 587.898 | 0.741360 | ||||||||
\(794\) | − 1551.58i | − 1.95413i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −304.304 | −0.382292 | ||||||||
\(797\) | − 423.595i | − 0.531486i | −0.964044 | − | 0.265743i | \(-0.914383\pi\) | ||||
0.964044 | − | 0.265743i | \(-0.0856173\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −120.678 | −0.151037 | ||||||||
\(800\) | 1141.19i | 1.42649i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1550.91 | −1.93381 | ||||||||
\(803\) | 1633.39i | 2.03411i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −104.455 | −0.129758 | ||||||||
\(806\) | − 5.93676i | − 0.00736571i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 156.491 | 0.193677 | ||||||||
\(809\) | 643.837i | 0.795843i | 0.917419 | + | 0.397922i | \(0.130268\pi\) | ||||
−0.917419 | + | 0.397922i | \(0.869732\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42.7687 | 0.0527357 | 0.0263679 | − | 0.999652i | \(-0.491606\pi\) | ||||
0.0263679 | + | 0.999652i | \(0.491606\pi\) | |||||||
\(812\) | − 2012.74i | − 2.47874i | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 2545.48 | 3.12713 | ||||||||
\(815\) | 45.9005i | 0.0563196i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 145.158 | 0.177672 | ||||||||
\(818\) | 1035.54i | 1.26594i | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 117.442 | 0.143221 | ||||||||
\(821\) | − 155.646i | − 0.189581i | −0.995497 | − | 0.0947906i | \(-0.969782\pi\) | ||||
0.995497 | − | 0.0947906i | \(-0.0302182\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −835.537 | −1.01523 | −0.507617 | − | 0.861583i | \(-0.669473\pi\) | ||||
−0.507617 | + | 0.861583i | \(0.669473\pi\) | |||||||
\(824\) | 53.1076i | 0.0644510i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −2237.95 | −2.70938 | ||||||||
\(827\) | − 319.635i | − 0.386499i | −0.981150 | − | 0.193250i | \(-0.938097\pi\) | ||||
0.981150 | − | 0.193250i | \(-0.0619027\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −745.509 | −0.899288 | −0.449644 | − | 0.893208i | \(-0.648449\pi\) | ||||
−0.449644 | + | 0.893208i | \(0.648449\pi\) | |||||||
\(830\) | 150.902i | 0.181810i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1083.09 | −1.30179 | ||||||||
\(833\) | 329.057i | 0.395026i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −17.5188 | −0.0209806 | ||||||||
\(836\) | − 245.882i | − 0.294117i | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1775.58 | 2.11883 | ||||||||
\(839\) | 1295.12i | 1.54365i | 0.635838 | + | 0.771823i | \(0.280655\pi\) | ||||
−0.635838 | + | 0.771823i | \(0.719345\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −779.228 | −0.926549 | ||||||||
\(842\) | − 1647.55i | − 1.95671i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −927.143 | −1.09851 | ||||||||
\(845\) | 13.6928i | 0.0162045i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 392.995 | 0.463985 | ||||||||
\(848\) | 660.436i | 0.778816i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 290.507 | 0.341773 | ||||||||
\(851\) | − 1748.63i | − 2.05479i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 30.6295 | 0.0359080 | 0.0179540 | − | 0.999839i | \(-0.494285\pi\) | ||||
0.0179540 | + | 0.999839i | \(0.494285\pi\) | |||||||
\(854\) | − 1353.99i | − 1.58546i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 64.7350 | 0.0756250 | ||||||||
\(857\) | − 446.511i | − 0.521016i | −0.965472 | − | 0.260508i | \(-0.916110\pi\) | ||||
0.965472 | − | 0.260508i | \(-0.0838901\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1409.65 | −1.64103 | −0.820516 | − | 0.571624i | \(-0.806314\pi\) | ||||
−0.820516 | + | 0.571624i | \(0.806314\pi\) | |||||||
\(860\) | − 52.0107i | − 0.0604776i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 780.916 | 0.905935 | ||||||||
\(863\) | 1037.85i | 1.20260i | 0.799022 | + | 0.601301i | \(0.205351\pi\) | ||||
−0.799022 | + | 0.601301i | \(0.794649\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −81.3842 | −0.0940858 | ||||||||
\(866\) | − 437.679i | − 0.505403i | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.14410 | −0.00823053 | ||||||||
\(869\) | 1073.28i | 1.23507i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 197.261 | 0.226476 | ||||||||
\(872\) | − 185.531i | − 0.212764i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −323.271 | −0.369876 | ||||||||
\(875\) | − 210.146i | − 0.240167i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 74.7317 | 0.0852129 | 0.0426065 | − | 0.999092i | \(-0.486434\pi\) | ||||
0.0426065 | + | 0.999092i | \(0.486434\pi\) | |||||||
\(878\) | − 789.927i | − 0.899689i | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 65.9914 | 0.0749902 | ||||||||
\(881\) | 278.915i | 0.316589i | 0.987392 | + | 0.158294i | \(0.0505995\pi\) | ||||
−0.987392 | + | 0.158294i | \(0.949400\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 172.659 | 0.195537 | 0.0977686 | − | 0.995209i | \(-0.468829\pi\) | ||||
0.0977686 | + | 0.995209i | \(0.468829\pi\) | |||||||
\(884\) | 253.673i | 0.286961i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −501.755 | −0.566314 | ||||||||
\(887\) | 221.858i | 0.250122i | 0.992149 | + | 0.125061i | \(0.0399127\pi\) | ||||
−0.992149 | + | 0.125061i | \(0.960087\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −128.745 | −0.144819 | ||||||||
\(890\) | 145.488i | 0.163470i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1157.92 | 1.29812 | ||||||||
\(893\) | 134.714i | 0.150856i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −34.6978 | −0.0387685 | ||||||||
\(896\) | 397.082i | 0.443172i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 281.597 | 0.313582 | ||||||||
\(899\) | 5.75091i | 0.00639700i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 185.789 | 0.206203 | ||||||||
\(902\) | 2624.28i | 2.90941i | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −82.4928 | −0.0912531 | ||||||||
\(905\) | 42.5758i | 0.0470451i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 680.121 | 0.749858 | 0.374929 | − | 0.927054i | \(-0.377667\pi\) | ||||
0.374929 | + | 0.927054i | \(0.377667\pi\) | |||||||
\(908\) | − 1708.17i | − 1.88124i | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 175.120 | 0.192440 | ||||||||
\(911\) | 1046.68i | 1.14894i | 0.818527 | + | 0.574469i | \(0.194791\pi\) | ||||
−0.818527 | + | 0.574469i | \(0.805209\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1761.86 | −1.92975 | ||||||||
\(914\) | − 88.3969i | − 0.0967143i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 683.298 | 0.745958 | ||||||||
\(917\) | 1782.14i | 1.94344i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −244.736 | −0.266306 | −0.133153 | − | 0.991095i | \(-0.542510\pi\) | ||||
−0.133153 | + | 0.991095i | \(0.542510\pi\) | |||||||
\(920\) | 9.97562i | 0.0108431i | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 255.181 | 0.276769 | ||||||||
\(923\) | 211.529i | 0.229176i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1754.17 | 1.89640 | ||||||||
\(926\) | 2298.08i | 2.48172i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1847.47 | 1.99081 | ||||||||
\(929\) | 120.321i | 0.129516i | 0.997901 | + | 0.0647582i | \(0.0206276\pi\) | ||||
−0.997901 | + | 0.0647582i | \(0.979372\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 367.329 | 0.394553 | ||||||||
\(932\) | 1435.00i | 1.53969i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −413.690 | −0.442923 | ||||||||
\(935\) | − 18.5642i | − 0.0198548i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 412.610 | 0.440353 | 0.220176 | − | 0.975460i | \(-0.429337\pi\) | ||||
0.220176 | + | 0.975460i | \(0.429337\pi\) | |||||||
\(938\) | − 454.310i | − 0.484339i | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 48.2687 | 0.0513496 | ||||||||
\(941\) | 288.520i | 0.306610i | 0.988179 | + | 0.153305i | \(0.0489917\pi\) | ||||
−0.988179 | + | 0.153305i | \(0.951008\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1802.76 | 1.91173 | ||||||||
\(944\) | − 971.256i | − 1.02887i | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1162.20 | 1.22854 | ||||||||
\(947\) | 301.186i | 0.318042i | 0.987275 | + | 0.159021i | \(0.0508338\pi\) | ||||
−0.987275 | + | 0.159021i | \(0.949166\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1881.15 | −1.98224 | ||||||||
\(950\) | − 324.295i | − 0.341364i | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 50.3162 | 0.0528531 | ||||||||
\(953\) | − 791.241i | − 0.830263i | −0.909761 | − | 0.415132i | \(-0.863735\pi\) | ||||
0.909761 | − | 0.415132i | \(-0.136265\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −27.3140 | −0.0286010 | ||||||||
\(956\) | − 957.462i | − 1.00153i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1607.75 | −1.67824 | ||||||||
\(959\) | − 844.556i | − 0.880663i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −960.980 | −0.999979 | ||||||||
\(962\) | 2931.59i | 3.04739i | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 635.210 | 0.658931 | ||||||||
\(965\) | − 5.20108i | − 0.00538972i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 110.779 | 0.114560 | 0.0572798 | − | 0.998358i | \(-0.481757\pi\) | ||||
0.0572798 | + | 0.998358i | \(0.481757\pi\) | |||||||
\(968\) | − 37.5316i | − 0.0387723i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 23.8671 | 0.0246053 | ||||||||
\(971\) | − 1479.69i | − 1.52388i | −0.647648 | − | 0.761940i | \(-0.724247\pi\) | ||||
0.647648 | − | 0.761940i | \(-0.275753\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3021.32 | 3.10516 | ||||||||
\(974\) | − 1320.63i | − 1.35588i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 587.622 | 0.602072 | ||||||||
\(977\) | − 565.276i | − 0.578584i | −0.957241 | − | 0.289292i | \(-0.906580\pi\) | ||||
0.957241 | − | 0.289292i | \(-0.0934198\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1698.64 | −1.73508 | ||||||||
\(980\) | − 131.615i | − 0.134301i | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1239.02 | −1.26173 | ||||||||
\(983\) | 1189.08i | 1.20965i | 0.796360 | + | 0.604823i | \(0.206756\pi\) | ||||
−0.796360 | + | 0.604823i | \(0.793244\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 115.393 | 0.117150 | ||||||||
\(986\) | − 470.300i | − 0.476978i | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 283.177 | 0.286617 | ||||||||
\(989\) | − 798.379i | − 0.807258i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1580.49 | −1.59484 | −0.797421 | − | 0.603424i | \(-0.793803\pi\) | ||||
−0.797421 | + | 0.603424i | \(0.793803\pi\) | |||||||
\(992\) | − 6.55748i | − 0.00661037i | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 487.172 | 0.490113 | ||||||||
\(995\) | 25.6474i | 0.0257763i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1820.34 | −1.82582 | −0.912908 | − | 0.408166i | \(-0.866168\pi\) | ||||
−0.912908 | + | 0.408166i | \(0.866168\pi\) | |||||||
\(998\) | 625.742i | 0.626996i | ||||||||
\(999\) | 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 | 1143.3.b.a.890.15 | ✓ | 84 | |
3.2 | odd | 2 | inner | 1143.3.b.a.890.70 | yes | 84 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1143.3.b.a.890.15 | ✓ | 84 | 1.1 | even | 1 | trivial | |
1143.3.b.a.890.70 | yes | 84 | 3.2 | odd | 2 | inner |