Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(509,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.509");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.w (of order \(6\), degree \(2\), not 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: | \(14.0856109166\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3x^{14} - 9x^{12} - 9x^{10} + 225x^{8} - 81x^{6} - 729x^{4} - 2187x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1109.6 | ||
Root | \(-0.744857 + 1.56371i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.1109 |
Dual form | 1764.2.w.a.509.6 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0.981784 | − | 1.42692i | 0.566833 | − | 0.823833i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.276914 | + | 0.479629i | −0.123840 | + | 0.214496i | −0.921279 | − | 0.388903i | \(-0.872854\pi\) |
0.797439 | + | 0.603399i | \(0.206187\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.07220 | − | 2.80185i | −0.357400 | − | 0.933951i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.03478 | + | 2.32948i | −1.21653 | + | 0.702365i | −0.964174 | − | 0.265270i | \(-0.914539\pi\) |
−0.252357 | + | 0.967634i | \(0.581206\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3.58265 | + | 2.06844i | −0.993648 | + | 0.573683i | −0.906363 | − | 0.422500i | \(-0.861153\pi\) |
−0.0872856 | + | 0.996183i | \(0.527819\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.412522 | + | 0.866025i | 0.106513 | + | 0.223607i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3.62264 | + | 6.27459i | −0.878619 | + | 1.52181i | −0.0257612 | + | 0.999668i | \(0.508201\pi\) |
−0.852857 | + | 0.522144i | \(0.825132\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.81722 | − | 3.35857i | 1.33456 | − | 0.770510i | 0.348567 | − | 0.937284i | \(-0.386668\pi\) |
0.985995 | + | 0.166774i | \(0.0533351\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.85295 | + | 2.80185i | 1.01191 | + | 0.584227i | 0.911751 | − | 0.410744i | \(-0.134731\pi\) |
0.100160 | + | 0.994971i | \(0.468064\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.34664 | + | 4.06450i | 0.469328 | + | 0.812899i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.05069 | − | 1.22087i | −0.972006 | − | 0.234957i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.16599 | + | 0.673187i | 0.216520 | + | 0.125008i | 0.604338 | − | 0.796728i | \(-0.293438\pi\) |
−0.387818 | + | 0.921736i | \(0.626771\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.959257i | 0.172288i | 0.996283 | + | 0.0861438i | \(0.0274545\pi\) | ||||
−0.996283 | + | 0.0861438i | \(0.972546\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.637299 | + | 8.04435i | −0.110939 | + | 1.40034i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 3.53478 | + | 6.12241i | 0.581114 | + | 1.00652i | 0.995348 | + | 0.0963482i | \(0.0307162\pi\) |
−0.414234 | + | 0.910170i | \(0.635950\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.565885 | + | 7.14292i | −0.0906141 | + | 1.14378i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.39152 | + | 4.14224i | 0.373493 | + | 0.646909i | 0.990100 | − | 0.140362i | \(-0.0448265\pi\) |
−0.616607 | + | 0.787271i | \(0.711493\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.02846 | + | 1.78135i | −0.156839 | + | 0.271653i | −0.933727 | − | 0.357986i | \(-0.883464\pi\) |
0.776888 | + | 0.629639i | \(0.216797\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 1.64076 | + | 0.261614i | 0.244590 | + | 0.0389991i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −9.80602 | −1.43035 | −0.715177 | − | 0.698943i | \(-0.753654\pi\) | ||||
−0.715177 | + | 0.698943i | \(0.753654\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 5.39669 | + | 11.3295i | 0.755688 | + | 1.58645i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.30235 | + | 4.21601i | 1.00305 | + | 0.579114i | 0.909151 | − | 0.416468i | \(-0.136732\pi\) |
0.0939038 | + | 0.995581i | \(0.470065\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 2.58026i | − | 0.347922i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.918838 | − | 11.5981i | 0.121703 | − | 1.53621i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.79910 | 1.01536 | 0.507678 | − | 0.861547i | \(-0.330504\pi\) | ||||
0.507678 | + | 0.861547i | \(0.330504\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 6.20463i | − | 0.794421i | −0.917728 | − | 0.397211i | \(-0.869978\pi\) | ||
0.917728 | − | 0.397211i | \(-0.130022\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 2.29112i | − | 0.284179i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.37628 | −0.412478 | −0.206239 | − | 0.978502i | \(-0.566122\pi\) | ||||
−0.206239 | + | 0.978502i | \(0.566122\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.76257 | − | 4.17396i | 1.05489 | − | 0.502486i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 0.407556i | − | 0.0483680i | −0.999708 | − | 0.0241840i | \(-0.992301\pi\) | ||
0.999708 | − | 0.0241840i | \(-0.00769875\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −7.47870 | − | 4.31783i | −0.875316 | − | 0.505364i | −0.00620487 | − | 0.999981i | \(-0.501975\pi\) |
−0.869111 | + | 0.494617i | \(0.835308\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 8.10360 | + | 0.641993i | 0.935723 | + | 0.0741309i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.636352 | 0.0715952 | 0.0357976 | − | 0.999359i | \(-0.488603\pi\) | ||||
0.0357976 | + | 0.999359i | \(0.488603\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −6.70077 | + | 6.00830i | −0.744530 | + | 0.667589i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −2.78840 | + | 4.82965i | −0.306066 | + | 0.530123i | −0.977498 | − | 0.210944i | \(-0.932346\pi\) |
0.671432 | + | 0.741066i | \(0.265680\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.00632 | − | 3.47504i | −0.217616 | − | 0.376921i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.10534 | − | 1.00286i | 0.225716 | − | 0.107517i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.46568 | − | 6.00274i | −0.367362 | − | 0.636289i | 0.621790 | − | 0.783184i | \(-0.286406\pi\) |
−0.989152 | + | 0.146895i | \(0.953072\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.36878 | + | 0.941783i | 0.141936 | + | 0.0976584i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 3.72014i | 0.381678i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.48798 | − | 4.32318i | −0.760289 | − | 0.438953i | 0.0691107 | − | 0.997609i | \(-0.477984\pi\) |
−0.829399 | + | 0.558656i | \(0.811317\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 10.8530 | + | 8.80719i | 1.09076 | + | 0.885156i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −2.34227 | − | 4.05692i | −0.233064 | − | 0.403679i | 0.725644 | − | 0.688070i | \(-0.241542\pi\) |
−0.958708 | + | 0.284391i | \(0.908209\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.40804 | − | 3.69969i | −0.631403 | − | 0.364541i | 0.149892 | − | 0.988702i | \(-0.452107\pi\) |
−0.781295 | + | 0.624162i | \(0.785441\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.38260 | + | 2.53029i | −0.423682 | + | 0.244613i | −0.696651 | − | 0.717410i | \(-0.745327\pi\) |
0.272970 | + | 0.962023i | \(0.411994\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.88142 | + | 10.1869i | −0.563337 | + | 0.975729i | 0.433865 | + | 0.900978i | \(0.357150\pi\) |
−0.997202 | + | 0.0747510i | \(0.976184\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.2066 | + | 0.967044i | 1.15860 | + | 0.0917877i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.51895 | + | 0.876965i | −0.142891 | + | 0.0824979i | −0.569741 | − | 0.821824i | \(-0.692956\pi\) |
0.426850 | + | 0.904322i | \(0.359623\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −2.68770 | + | 1.55174i | −0.250629 | + | 0.144701i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 9.63680 | + | 7.82028i | 0.890922 | + | 0.722985i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.35295 | − | 9.27159i | 0.486632 | − | 0.842872i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 8.25861 | + | 0.654273i | 0.744654 | + | 0.0589938i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.36840 | −0.480164 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 11.0822 | 0.983385 | 0.491693 | − | 0.870769i | \(-0.336378\pi\) | ||||
0.491693 | + | 0.870769i | \(0.336378\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.53211 | + | 3.21643i | 0.134895 | + | 0.283191i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −9.23643 | + | 15.9980i | −0.806990 | + | 1.39775i | 0.107949 | + | 0.994156i | \(0.465572\pi\) |
−0.914939 | + | 0.403592i | \(0.867762\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.98417 | − | 2.08438i | 0.170770 | − | 0.179395i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −19.0537 | + | 11.0007i | −1.62787 | + | 0.939851i | −0.643142 | + | 0.765747i | \(0.722370\pi\) |
−0.984727 | + | 0.174104i | \(0.944297\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.55986 | − | 4.94204i | 0.726038 | − | 0.419178i | −0.0909332 | − | 0.995857i | \(-0.528985\pi\) |
0.816971 | + | 0.576679i | \(0.195652\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.62739 | + | 13.9924i | −0.810773 | + | 1.17837i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 9.63680 | − | 16.6914i | 0.805870 | − | 1.39581i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.645760 | + | 0.372830i | −0.0536274 | + | 0.0309618i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 6.36677 | + | 3.67585i | 0.521586 | + | 0.301138i | 0.737583 | − | 0.675256i | \(-0.235967\pi\) |
−0.215997 | + | 0.976394i | \(0.569300\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.16599 | + | 3.75161i | 0.176266 | + | 0.305302i | 0.940599 | − | 0.339520i | \(-0.110265\pi\) |
−0.764333 | + | 0.644822i | \(0.776931\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 21.4647 | + | 3.42248i | 1.73532 | + | 0.276691i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.460087 | − | 0.265632i | −0.0369551 | − | 0.0213360i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1.78000i | 0.142059i | 0.997474 | + | 0.0710296i | \(0.0226285\pi\) | ||||
−0.997474 | + | 0.0710296i | \(0.977372\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 13.1852 | − | 6.28065i | 1.04566 | − | 0.498088i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.81818 | + | 4.88122i | 0.220737 | + | 0.382327i | 0.955032 | − | 0.296503i | \(-0.0958206\pi\) |
−0.734295 | + | 0.678830i | \(0.762487\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −3.68182 | − | 2.53326i | −0.286630 | − | 0.197214i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 2.38803 | + | 4.13618i | 0.184791 | + | 0.320067i | 0.943506 | − | 0.331355i | \(-0.107506\pi\) |
−0.758715 | + | 0.651423i | \(0.774173\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.05692 | − | 3.56270i | 0.158225 | − | 0.274054i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −15.6475 | − | 12.6979i | −1.19659 | − | 0.971036i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −5.67531 | −0.431486 | −0.215743 | − | 0.976450i | \(-0.569217\pi\) | ||||
−0.215743 | + | 0.976450i | \(0.569217\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 7.65703 | − | 11.1287i | 0.575538 | − | 0.836484i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 10.9383 | + | 6.31525i | 0.817570 | + | 0.472024i | 0.849578 | − | 0.527463i | \(-0.176857\pi\) |
−0.0320079 | + | 0.999488i | \(0.510190\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 22.7424i | − | 1.69043i | −0.534426 | − | 0.845215i | \(-0.679472\pi\) | ||
0.534426 | − | 0.845215i | \(-0.320528\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −8.85351 | − | 6.09160i | −0.654470 | − | 0.450304i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.91531 | −0.287860 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 33.7554i | − | 2.46844i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 11.6090i | 0.840001i | 0.907524 | + | 0.420000i | \(0.137970\pi\) | ||||
−0.907524 | + | 0.420000i | \(0.862030\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.33199 | 0.455787 | 0.227893 | − | 0.973686i | \(-0.426816\pi\) | ||||
0.227893 | + | 0.973686i | \(0.426816\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.26925 | − | 2.24939i | −0.234116 | − | 0.161082i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 3.10030i | − | 0.220888i | −0.993882 | − | 0.110444i | \(-0.964773\pi\) | ||
0.993882 | − | 0.110444i | \(-0.0352272\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 13.6198 | + | 7.86341i | 0.965484 | + | 0.557422i | 0.897856 | − | 0.440288i | \(-0.145124\pi\) |
0.0676272 | + | 0.997711i | \(0.478457\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −3.31478 | + | 4.81768i | −0.233806 | + | 0.339813i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.64898 | −0.185013 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 2.64705 | − | 16.6014i | 0.183982 | − | 1.15388i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −15.6475 | + | 27.1022i | −1.08236 | + | 1.87470i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.51263 | + | 6.08406i | 0.241820 | + | 0.418844i | 0.961233 | − | 0.275739i | \(-0.0889225\pi\) |
−0.719413 | + | 0.694582i | \(0.755589\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −0.581549 | − | 0.400132i | −0.0398471 | − | 0.0274166i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.569590 | − | 0.986559i | −0.0388457 | − | 0.0672828i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −13.5037 | + | 6.43233i | −0.912493 | + | 0.434657i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 29.9729i | − | 2.01619i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.3477 | − | 12.3251i | −1.42955 | − | 0.825350i | −0.432464 | − | 0.901651i | \(-0.642356\pi\) |
−0.997085 | + | 0.0763008i | \(0.975689\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 8.87206 | − | 10.9329i | 0.591470 | − | 0.728859i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 10.0372 | + | 17.3849i | 0.666190 | + | 1.15388i | 0.978961 | + | 0.204047i | \(0.0654095\pi\) |
−0.312771 | + | 0.949829i | \(0.601257\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.75865 | + | 3.90211i | 0.446624 | + | 0.257859i | 0.706403 | − | 0.707809i | \(-0.250316\pi\) |
−0.259779 | + | 0.965668i | \(0.583650\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 6.89843 | − | 3.98281i | 0.451931 | − | 0.260922i | −0.256714 | − | 0.966487i | \(-0.582640\pi\) |
0.708645 | + | 0.705565i | \(0.249307\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.71542 | − | 4.70325i | 0.177135 | − | 0.306806i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0.624760 | − | 0.908023i | 0.0405825 | − | 0.0589824i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 23.2059 | − | 13.3979i | 1.50107 | − | 0.866640i | 0.501066 | − | 0.865409i | \(-0.332941\pi\) |
0.999999 | − | 0.00123146i | \(-0.000391987\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 0.757259 | − | 0.437203i | 0.0487793 | − | 0.0281628i | −0.475412 | − | 0.879763i | \(-0.657701\pi\) |
0.524191 | + | 0.851601i | \(0.324368\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.99465 | + | 15.4603i | 0.127957 | + | 0.991780i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.8940 | + | 24.0652i | −0.884057 | + | 1.53123i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.15391 | + | 8.72049i | 0.263244 | + | 0.552639i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.32082 | 0.146489 | 0.0732445 | − | 0.997314i | \(-0.476665\pi\) | ||||
0.0732445 | + | 0.997314i | \(0.476665\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −26.1075 | −1.64136 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.92837 | − | 0.548888i | −0.433872 | − | 0.0343727i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −12.3017 | + | 21.3072i | −0.767361 | + | 1.32911i | 0.171628 | + | 0.985162i | \(0.445097\pi\) |
−0.938989 | + | 0.343947i | \(0.888236\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0.635992 | − | 3.98874i | 0.0393669 | − | 0.246897i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 20.5268 | − | 11.8512i | 1.26574 | − | 0.730775i | 0.291560 | − | 0.956552i | \(-0.405826\pi\) |
0.974179 | + | 0.225778i | \(0.0724922\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.04424 | + | 2.33494i | −0.248436 | + | 0.143434i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −11.9680 | − | 0.948141i | −0.732429 | − | 0.0580253i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −10.3106 | + | 17.8585i | −0.628648 | + | 1.08885i | 0.359176 | + | 0.933270i | \(0.383058\pi\) |
−0.987823 | + | 0.155580i | \(0.950275\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 12.0771 | − | 6.97270i | 0.733630 | − | 0.423562i | −0.0861186 | − | 0.996285i | \(-0.527446\pi\) |
0.819749 | + | 0.572723i | \(0.194113\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −18.9363 | − | 10.9329i | −1.14190 | − | 0.659278i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −10.3940 | − | 18.0030i | −0.624518 | − | 1.08170i | −0.988634 | − | 0.150343i | \(-0.951962\pi\) |
0.364116 | − | 0.931354i | \(-0.381371\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.68770 | − | 1.02852i | 0.160908 | − | 0.0615757i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −20.3371 | − | 11.7416i | −1.21321 | − | 0.700448i | −0.249754 | − | 0.968309i | \(-0.580350\pi\) |
−0.963457 | + | 0.267862i | \(0.913683\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 12.9218i | 0.768120i | 0.923308 | + | 0.384060i | \(0.125474\pi\) | ||||
−0.923308 | + | 0.384060i | \(0.874526\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5.30834 | + | 3.65237i | 0.314439 | + | 0.216348i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −17.7470 | − | 30.7387i | −1.04394 | − | 1.80816i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −13.5204 | + | 6.44031i | −0.792581 | + | 0.377538i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.99115 | + | 3.44878i | 0.116324 | + | 0.201480i | 0.918308 | − | 0.395866i | \(-0.129555\pi\) |
−0.801984 | + | 0.597346i | \(0.796222\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.15968 | + | 3.74067i | −0.125741 | + | 0.217790i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 23.2224 | − | 6.83954i | 1.34750 | − | 0.396870i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −23.1819 | −1.34064 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −8.08850 | − | 0.640797i | −0.464672 | − | 0.0368128i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.97592 | + | 1.71815i | 0.170401 | + | 0.0983808i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 22.3162i | 1.27365i | 0.771008 | + | 0.636825i | \(0.219753\pi\) | ||||
−0.771008 | + | 0.636825i | \(0.780247\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −11.5705 | + | 5.51147i | −0.658221 | + | 0.313537i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −16.3674 | −0.928111 | −0.464056 | − | 0.885806i | \(-0.653606\pi\) | ||||
−0.464056 | + | 0.885806i | \(0.653606\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 19.1157i | − | 1.08048i | −0.841510 | − | 0.540242i | \(-0.818333\pi\) | ||
0.841510 | − | 0.540242i | \(-0.181667\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 24.1099i | − | 1.35415i | −0.735915 | − | 0.677074i | \(-0.763248\pi\) | ||
0.735915 | − | 0.677074i | \(-0.236752\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −6.27270 | −0.351204 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −0.692237 | + | 8.73781i | −0.0386369 | + | 0.487697i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 48.6676i | 2.70794i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.8144 | − | 9.70778i | −0.932693 | − | 0.538491i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 8.76163 | + | 18.3937i | 0.484519 | + | 1.01717i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 11.4015 | 0.626686 | 0.313343 | − | 0.949640i | \(-0.398551\pi\) | ||||
0.313343 | + | 0.949640i | \(0.398551\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 13.3641 | − | 16.4684i | 0.732349 | − | 0.902462i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0.934938 | − | 1.61936i | 0.0510811 | − | 0.0884751i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.16599 | + | 3.75161i | 0.117989 | + | 0.204363i | 0.918971 | − | 0.394326i | \(-0.129022\pi\) |
−0.800981 | + | 0.598689i | \(0.795689\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.239920 | + | 3.02841i | −0.0130307 | + | 0.164480i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.23457 | − | 3.87039i | −0.121009 | − | 0.209593i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −0.424526 | + | 5.35861i | −0.0228557 | + | 0.288498i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 5.33765i | − | 0.286540i | −0.989684 | − | 0.143270i | \(-0.954238\pi\) | ||
0.989684 | − | 0.143270i | \(-0.0457617\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −8.78031 | − | 5.06931i | −0.469999 | − | 0.271354i | 0.246240 | − | 0.969209i | \(-0.420805\pi\) |
−0.716239 | + | 0.697855i | \(0.754138\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 20.6202 | − | 6.07312i | 1.10062 | − | 0.324159i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.67564 | + | 13.2946i | 0.408533 | + | 0.707600i | 0.994726 | − | 0.102571i | \(-0.0327070\pi\) |
−0.586192 | + | 0.810172i | \(0.699374\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0.195475 | + | 0.112858i | 0.0103748 | + | 0.00598987i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.51381 | − | 0.874000i | 0.0798960 | − | 0.0461280i | −0.459520 | − | 0.888168i | \(-0.651978\pi\) |
0.539416 | + | 0.842040i | \(0.318645\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 13.0600 | − | 22.6207i | 0.687371 | − | 1.19056i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −7.97437 | − | 16.7409i | −0.418546 | − | 0.878671i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.14191 | − | 2.39133i | 0.216798 | − | 0.125168i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −11.1720 | + | 6.45018i | −0.583176 | + | 0.336697i | −0.762394 | − | 0.647113i | \(-0.775976\pi\) |
0.179219 | + | 0.983809i | \(0.442643\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 9.04176 | − | 11.1420i | 0.470695 | − | 0.580030i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5.34782 | − | 9.26269i | 0.276900 | − | 0.479604i | −0.693713 | − | 0.720251i | \(-0.744026\pi\) |
0.970613 | + | 0.240647i | \(0.0773597\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.27061 | + | 7.66028i | −0.272173 | + | 0.395575i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −5.56980 | −0.286859 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.566797 | 0.0291144 | 0.0145572 | − | 0.999894i | \(-0.495366\pi\) | ||||
0.0145572 | + | 0.999894i | \(0.495366\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 10.8803 | − | 15.8134i | 0.557415 | − | 0.810145i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 9.43059 | − | 16.3343i | 0.481880 | − | 0.834641i | −0.517903 | − | 0.855439i | \(-0.673287\pi\) |
0.999784 | + | 0.0207978i | \(0.00662061\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 6.09379 | + | 0.971637i | 0.309765 | + | 0.0493911i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −14.3182 | + | 8.26660i | −0.725960 | + | 0.419133i | −0.816943 | − | 0.576719i | \(-0.804333\pi\) |
0.0909822 | + | 0.995853i | \(0.470999\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −35.1610 | + | 20.3002i | −1.77817 | + | 1.02663i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 13.7596 | + | 28.8862i | 0.694082 | + | 1.45712i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.176215 | + | 0.305213i | −0.00886632 | + | 0.0153569i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 29.5384 | − | 17.0540i | 1.48249 | − | 0.855917i | 0.482688 | − | 0.875792i | \(-0.339660\pi\) |
0.999802 | + | 0.0198756i | \(0.00632700\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −18.6395 | − | 10.7615i | −0.930811 | − | 0.537404i | −0.0437428 | − | 0.999043i | \(-0.513928\pi\) |
−0.887068 | + | 0.461639i | \(0.847262\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.98417 | − | 3.43668i | −0.0988386 | − | 0.171193i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.02622 | − | 4.87766i | −0.0509931 | − | 0.242373i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −28.5241 | − | 16.4684i | −1.41389 | − | 0.816308i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 22.2299i | − | 1.09920i | −0.835429 | − | 0.549599i | \(-0.814781\pi\) | ||
0.835429 | − | 0.549599i | \(-0.185219\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.00956 | + | 37.9884i | −0.148451 | + | 1.87383i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.54429 | − | 2.67479i | −0.0758063 | − | 0.131300i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.35204 | − | 17.0662i | 0.0662098 | − | 0.835738i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.81490 | + | 11.8038i | 0.332930 | + | 0.576651i | 0.983085 | − | 0.183150i | \(-0.0586294\pi\) |
−0.650155 | + | 0.759802i | \(0.725296\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.7071 | − | 23.7414i | 0.668043 | − | 1.15708i | −0.310408 | − | 0.950603i | \(-0.600466\pi\) |
0.978451 | − | 0.206480i | \(-0.0662009\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 10.5140 | + | 27.4750i | 0.511209 | + | 1.33588i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −34.0041 | −1.64944 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −14.3561 | − | 30.1383i | −0.693118 | − | 1.45509i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −30.1663 | − | 17.4165i | −1.45306 | − | 0.838925i | −0.454406 | − | 0.890795i | \(-0.650149\pi\) |
−0.998654 | + | 0.0518699i | \(0.983482\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 19.5648i | − | 0.940223i | −0.882607 | − | 0.470112i | \(-0.844214\pi\) | ||
0.882607 | − | 0.470112i | \(-0.155786\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −0.101999 | + | 1.28749i | −0.00489046 | + | 0.0617302i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 37.6409 | 1.80061 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.5628i | 1.36323i | 0.731712 | + | 0.681614i | \(0.238722\pi\) | ||||
−0.731712 | + | 0.681614i | \(0.761278\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 25.2431i | 1.19934i | 0.800248 | + | 0.599669i | \(0.204701\pi\) | ||||
−0.800248 | + | 0.599669i | \(0.795299\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 3.83878 | 0.181976 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 11.4959 | − | 5.47597i | 0.543739 | − | 0.259005i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15.1042i | 0.712811i | 0.934331 | + | 0.356405i | \(0.115998\pi\) | ||||
−0.934331 | + | 0.356405i | \(0.884002\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −19.2985 | − | 11.1420i | −0.908733 | − | 0.524657i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7.47979 | + | 0.592572i | 0.351431 | + | 0.0278415i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.50276 | 0.163852 | 0.0819261 | − | 0.996638i | \(-0.473893\pi\) | ||||
0.0819261 | + | 0.996638i | \(0.473893\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 25.9573 | − | 27.2682i | 1.21158 | − | 1.27277i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.98765 | + | 3.44272i | −0.0925743 | + | 0.160343i | −0.908594 | − | 0.417681i | \(-0.862843\pi\) |
0.816019 | + | 0.578025i | \(0.196176\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −5.18494 | − | 8.98058i | −0.240965 | − | 0.417363i | 0.720025 | − | 0.693948i | \(-0.244130\pi\) |
−0.960989 | + | 0.276585i | \(0.910797\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −0.830741 | + | 0.395715i | −0.0385247 | + | 0.0183508i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −9.80952 | − | 16.9906i | −0.453930 | − | 0.786230i | 0.544696 | − | 0.838634i | \(-0.316645\pi\) |
−0.998626 | + | 0.0524035i | \(0.983312\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 2.53991 | + | 1.74757i | 0.117033 | + | 0.0805239i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | − | 9.58312i | − | 0.440632i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 27.3018 | + | 15.7627i | 1.25269 | + | 0.723243i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 3.98307 | − | 24.9805i | 0.182372 | − | 1.14378i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −15.8237 | − | 27.4074i | −0.723002 | − | 1.25228i | −0.959791 | − | 0.280715i | \(-0.909428\pi\) |
0.236789 | − | 0.971561i | \(-0.423905\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −25.3277 | − | 14.6230i | −1.15485 | − | 0.666751i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.14705 | − | 2.39430i | 0.188308 | − | 0.108719i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.72923 | − | 16.8515i | 0.440874 | − | 0.763616i | −0.556881 | − | 0.830592i | \(-0.688002\pi\) |
0.997755 | + | 0.0669768i | \(0.0213353\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 9.73196 | + | 0.770996i | 0.440094 | + | 0.0348656i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 23.9525 | − | 13.8290i | 1.08096 | − | 0.624094i | 0.149806 | − | 0.988715i | \(-0.452135\pi\) |
0.931156 | + | 0.364622i | \(0.118802\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.44795 | + | 4.87743i | −0.380476 | + | 0.219668i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.22951 | + | 2.76656i | −0.324942 | + | 0.124347i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.50632 | − | 7.80517i | 0.201730 | − | 0.349407i | −0.747356 | − | 0.664424i | \(-0.768677\pi\) |
0.949086 | + | 0.315017i | \(0.102010\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 8.24653 | + | 0.653316i | 0.368428 | + | 0.0291880i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.1572 | 1.21088 | 0.605440 | − | 0.795891i | \(-0.292997\pi\) | ||||
0.605440 | + | 0.795891i | \(0.292997\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.59442 | 0.115450 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.06423 | − | 6.43286i | −0.136087 | − | 0.285693i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.56799 | − | 11.3761i | 0.291121 | − | 0.504236i | −0.682954 | − | 0.730461i | \(-0.739305\pi\) |
0.974075 | + | 0.226225i | \(0.0726384\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −33.4814 | + | 9.86104i | −1.47824 | + | 0.435376i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.54895 | − | 2.04899i | 0.156385 | − | 0.0902892i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 39.5651 | − | 22.8429i | 1.74007 | − | 1.00463i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.57193 | + | 8.09822i | −0.244581 | + | 0.355472i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.01609 | − | 3.49198i | 0.0883266 | − | 0.152986i | −0.818477 | − | 0.574539i | \(-0.805181\pi\) |
0.906804 | + | 0.421553i | \(0.138515\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 0.516117 | − | 0.297980i | 0.0225682 | − | 0.0130298i | −0.488673 | − | 0.872467i | \(-0.662519\pi\) |
0.511242 | + | 0.859437i | \(0.329186\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −6.01895 | − | 3.47504i | −0.262189 | − | 0.151375i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 4.20077 | + | 7.27595i | 0.182642 | + | 0.316346i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.36220 | − | 21.8519i | −0.362889 | − | 0.948294i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −17.1360 | − | 9.89347i | −0.742242 | − | 0.428534i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 2.80269i | − | 0.121171i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 19.7504 | − | 9.40792i | 0.852295 | − | 0.405982i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.05061 | + | 12.2120i | 0.303129 | + | 0.525035i | 0.976843 | − | 0.213957i | \(-0.0686353\pi\) |
−0.673714 | + | 0.738992i | \(0.735302\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −32.4516 | − | 22.3281i | −1.39263 | − | 0.958192i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.25729 | − | 5.64179i | −0.139527 | − | 0.241668i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −18.9921 | + | 32.8952i | −0.812042 | + | 1.40650i | 0.0993905 | + | 0.995049i | \(0.468311\pi\) |
−0.911433 | + | 0.411450i | \(0.865023\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −17.3845 | + | 6.65260i | −0.741951 | + | 0.283926i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 9.04380 | 0.385279 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −3.84399 | + | 5.58684i | −0.163168 | + | 0.237148i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 36.1181 | + | 20.8528i | 1.53037 | + | 0.883562i | 0.999344 | + | 0.0362098i | \(0.0115285\pi\) |
0.531031 | + | 0.847353i | \(0.321805\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 8.50926i | − | 0.359903i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −48.1663 | − | 33.1406i | −2.03358 | − | 1.39920i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −1.87687 | −0.0791007 | −0.0395504 | − | 0.999218i | \(-0.512593\pi\) | ||||
−0.0395504 | + | 0.999218i | \(0.512593\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 0.971375i | − | 0.0408660i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 23.8320i | 0.999089i | 0.866288 | + | 0.499545i | \(0.166499\pi\) | ||||
−0.866288 | + | 0.499545i | \(0.833501\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.7438 | 1.24474 | 0.622370 | − | 0.782723i | \(-0.286170\pi\) | ||||
0.622370 | + | 0.782723i | \(0.286170\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 16.5652 | + | 11.3976i | 0.692020 | + | 0.476140i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 26.2997i | 1.09678i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.6950 | + | 7.32947i | 0.528501 | + | 0.305130i | 0.740406 | − | 0.672160i | \(-0.234633\pi\) |
−0.211905 | + | 0.977290i | \(0.567967\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.21664 | − | 9.03524i | 0.258355 | − | 0.375492i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −39.2845 | −1.62700 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −6.41939 | + | 2.45654i | −0.265409 | + | 0.101566i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 22.2189 | − | 38.4843i | 0.917074 | − | 1.58842i | 0.113238 | − | 0.993568i | \(-0.463878\pi\) |
0.803836 | − | 0.594851i | \(-0.202789\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.22174 | + | 5.58021i | 0.132749 | + | 0.229929i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −4.42389 | − | 3.04383i | −0.181974 | − | 0.125206i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.5593 | + | 32.1457i | 0.762140 | + | 1.32006i | 0.941746 | + | 0.336326i | \(0.109184\pi\) |
−0.179606 | + | 0.983739i | \(0.557482\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 24.5922 | − | 11.7142i | 1.00649 | − | 0.479431i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 13.9180i | − | 0.568675i | −0.958724 | − | 0.284338i | \(-0.908226\pi\) | ||
0.958724 | − | 0.284338i | \(-0.0917737\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.377613 | − | 0.218015i | −0.0154032 | − | 0.00889301i | 0.492279 | − | 0.870438i | \(-0.336164\pi\) |
−0.507682 | + | 0.861545i | \(0.669497\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.62005 | + | 9.45984i | 0.147420 | + | 0.385235i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 2.96461 | + | 5.13486i | 0.120529 | + | 0.208762i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.92117 | + | 1.10919i | 0.0779778 | + | 0.0450205i | 0.538482 | − | 0.842637i | \(-0.318998\pi\) |
−0.460504 | + | 0.887658i | \(0.652331\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 35.1315 | − | 20.2832i | 1.42127 | − | 0.820570i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −19.1011 | + | 33.0841i | −0.771488 | + | 1.33626i | 0.165260 | + | 0.986250i | \(0.447154\pi\) |
−0.936748 | + | 0.350006i | \(0.886180\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.60073 | + | 3.77989i | −0.104872 | + | 0.152420i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 21.1043 | − | 12.1846i | 0.849628 | − | 0.490533i | −0.0108970 | − | 0.999941i | \(-0.503469\pi\) |
0.860525 | + | 0.509407i | \(0.170135\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.4477 | − | 14.6922i | 1.02283 | − | 0.590531i | 0.107907 | − | 0.994161i | \(-0.465585\pi\) |
0.914922 | + | 0.403630i | \(0.132252\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −21.0901 | − | 20.0761i | −0.846315 | − | 0.805627i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −10.2466 | + | 17.7476i | −0.409864 | + | 0.709906i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 23.3102 | + | 48.9362i | 0.930921 | + | 1.95432i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −51.2209 | −2.04231 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.17077 | 0.205845 | 0.102923 | − | 0.994689i | \(-0.467181\pi\) | ||||
0.102923 | + | 0.994689i | \(0.467181\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 12.1301 | + | 0.960985i | 0.482128 | + | 0.0381957i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.06881 | + | 5.31533i | −0.121782 | + | 0.210933i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1.14191 | + | 0.436981i | −0.0451733 | + | 0.0172867i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.32405 | − | 3.07384i | 0.210287 | − | 0.121410i | −0.391158 | − | 0.920324i | \(-0.627925\pi\) |
0.601445 | + | 0.798914i | \(0.294592\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −23.9599 | + | 13.8333i | −0.944886 | + | 0.545530i | −0.891489 | − | 0.453043i | \(-0.850338\pi\) |
−0.0533976 | + | 0.998573i | \(0.517005\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.96696 | − | 0.155828i | −0.0774488 | − | 0.00613574i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 2.40729 | − | 4.16954i | 0.0946402 | − | 0.163922i | −0.814818 | − | 0.579717i | \(-0.803163\pi\) |
0.909458 | + | 0.415795i | \(0.136497\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −31.4676 | + | 18.1679i | −1.23521 | + | 0.713151i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −21.1759 | − | 12.2259i | −0.828677 | − | 0.478437i | 0.0247223 | − | 0.999694i | \(-0.492130\pi\) |
−0.853400 | + | 0.521257i | \(0.825463\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.11539 | − | 8.86011i | −0.199875 | − | 0.346193i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −4.07926 | + | 25.5838i | −0.159147 | + | 0.998120i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −20.7514 | − | 11.9808i | −0.808359 | − | 0.466706i | 0.0380267 | − | 0.999277i | \(-0.487893\pi\) |
−0.846386 | + | 0.532570i | \(0.821226\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.77431i | 0.302386i | 0.988504 | + | 0.151193i | \(0.0483114\pi\) | ||||
−0.988504 | + | 0.151193i | \(0.951689\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −42.7689 | − | 29.4269i | −1.66101 | − | 1.14285i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.77234 | + | 6.53389i | 0.146066 | + | 0.252993i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −38.5458 | + | 18.3609i | −1.49027 | + | 0.709873i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 14.4536 | + | 25.0343i | 0.557973 | + | 0.966438i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −14.7281 | + | 25.5097i | −0.567725 | + | 0.983328i | 0.429066 | + | 0.903273i | \(0.358843\pi\) |
−0.996790 | + | 0.0800548i | \(0.974490\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.88992 | − | 23.3935i | −0.265193 | − | 0.900414i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 35.6586 | 1.37047 | 0.685235 | − | 0.728322i | \(-0.259700\pi\) | ||||
0.685235 | + | 0.728322i | \(0.259700\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 34.6612 | + | 2.74597i | 1.32822 | + | 0.105226i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 11.3423 | + | 6.54846i | 0.433999 | + | 0.250570i | 0.701049 | − | 0.713113i | \(-0.252715\pi\) |
−0.267050 | + | 0.963683i | \(0.586049\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 12.1850i | − | 0.465563i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 12.2035 | − | 5.81302i | 0.465594 | − | 0.221781i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −34.8823 | −1.32891 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9.02967i | 0.343505i | 0.985140 | + | 0.171752i | \(0.0549429\pi\) | ||||
−0.985140 | + | 0.171752i | \(0.945057\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5.47407i | 0.207643i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −34.6545 | −1.31263 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.08962 | − | 13.7538i | 0.0412131 | − | 0.520215i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 0.259274i | 0.00979264i | 0.999988 | + | 0.00489632i | \(0.00155855\pi\) | ||||
−0.999988 | + | 0.00489632i | \(0.998441\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 41.1252 | + | 23.7436i | 1.55107 | + | 0.895508i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.04520 | − | 8.49226i | −0.152351 | − | 0.319837i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.17149 | 0.231775 | 0.115888 | − | 0.993262i | \(-0.463029\pi\) | ||||
0.115888 | + | 0.993262i | \(0.463029\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.682297 | − | 1.78296i | −0.0255881 | − | 0.0668664i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.68770 | + | 4.65523i | −0.100655 | + | 0.174340i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 5.33712 | + | 9.24417i | 0.199597 | + | 0.345712i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 3.66541 | − | 46.2668i | 0.136887 | − | 1.72787i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 9.76375 | + | 16.9113i | 0.364127 | + | 0.630686i | 0.988636 | − | 0.150332i | \(-0.0480342\pi\) |
−0.624509 | + | 0.781018i | \(0.714701\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0.119610 | − | 1.50979i | 0.00444835 | − | 0.0561496i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 6.31890i | 0.234678i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.425312 | − | 0.245554i | −0.0157740 | − | 0.00910710i | 0.492092 | − | 0.870543i | \(-0.336232\pi\) |
−0.507866 | + | 0.861436i | \(0.669566\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 24.0189 | + | 12.3325i | 0.889591 | + | 0.456759i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −7.45149 | − | 12.9064i | −0.275603 | − | 0.477359i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.68424 | + | 3.85915i | 0.246888 | + | 0.142541i | 0.618338 | − | 0.785912i | \(-0.287806\pi\) |
−0.371450 | + | 0.928453i | \(0.621139\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 13.6225 | − | 7.86498i | 0.501793 | − | 0.289710i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −5.45417 | + | 9.44690i | −0.200635 | + | 0.347510i | −0.948733 | − | 0.316078i | \(-0.897634\pi\) |
0.748098 | + | 0.663588i | \(0.230967\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 20.6982 | + | 43.4525i | 0.760366 | + | 1.59627i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 27.0051 | − | 15.5914i | 0.990722 | − | 0.571994i | 0.0852322 | − | 0.996361i | \(-0.472837\pi\) |
0.905490 | + | 0.424367i | \(0.139503\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −3.52609 | + | 2.03579i | −0.129186 | + | 0.0745855i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 16.5217 | + | 2.63433i | 0.604497 | + | 0.0963852i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 23.0367 | − | 39.9008i | 0.840622 | − | 1.45600i | −0.0487482 | − | 0.998811i | \(-0.515523\pi\) |
0.889370 | − | 0.457188i | \(-0.151143\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.27855 | − | 3.31163i | 0.0830349 | − | 0.120682i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −2.39917 | −0.0873149 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40.6419 | 1.47715 | 0.738577 | − | 0.674169i | \(-0.235498\pi\) | ||||
0.738577 | + | 0.674169i | \(0.235498\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −25.6319 | + | 37.2532i | −0.930378 | + | 1.35221i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.64190 | + | 6.30795i | −0.132019 | + | 0.228663i | −0.924455 | − | 0.381292i | \(-0.875479\pi\) |
0.792436 | + | 0.609955i | \(0.208813\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.58538 | + | 9.34735i | −0.274250 | + | 0.337954i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −27.9415 | + | 16.1320i | −1.00891 | + | 0.582493i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 35.8261 | − | 20.6842i | 1.29192 | − | 0.745892i | 0.312927 | − | 0.949777i | \(-0.398690\pi\) |
0.978995 | + | 0.203886i | \(0.0653570\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.3261 | + | 38.4727i | 0.659997 | + | 1.38556i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 8.55914 | − | 14.8249i | 0.307851 | − | 0.533213i | −0.670041 | − | 0.742324i | \(-0.733724\pi\) |
0.977892 | + | 0.209111i | \(0.0670569\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.89890 | + | 2.25103i | −0.140053 | + | 0.0808594i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 27.8241 | + | 16.0642i | 0.996900 | + | 0.575561i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.949393 | + | 1.64440i | 0.0339719 | + | 0.0588411i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −5.06720 | − | 4.82359i | −0.181087 | − | 0.172381i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −0.853737 | − | 0.492906i | −0.0304712 | − | 0.0175926i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 29.7250i | 1.05958i | 0.848129 | + | 0.529790i | \(0.177729\pi\) | ||||
−0.848129 | + | 0.529790i | \(0.822271\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3.24224 | − | 40.9255i | 0.115427 | − | 1.45698i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.8339 | + | 22.2290i | 0.455746 | + | 0.789375i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −0.638793 | + | 8.06322i | −0.0226557 | + | 0.285973i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −20.6019 | − | 35.6836i | −0.729757 | − | 1.26398i | −0.956986 | − | 0.290135i | \(-0.906300\pi\) |
0.227229 | − | 0.973841i | \(-0.427034\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 35.5236 | − | 61.5288i | 1.25674 | − | 2.17673i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13.1029 | + | 16.1465i | −0.462968 | + | 0.570508i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 40.2332 | 1.41980 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 15.3598 | + | 32.2455i | 0.540691 | + | 1.13510i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 10.7589 | + | 6.21165i | 0.378262 | + | 0.218390i | 0.677062 | − | 0.735926i | \(-0.263253\pi\) |
−0.298800 | + | 0.954316i | \(0.596586\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 32.8713i | 1.15427i | 0.816650 | + | 0.577133i | \(0.195829\pi\) | ||||
−0.816650 | + | 0.577133i | \(0.804171\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.90759 | − | 24.0787i | 0.0669021 | − | 0.844477i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.12157 | −0.109344 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13.8167i | 0.483384i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 13.5575i | 0.473159i | 0.971612 | + | 0.236579i | \(0.0760263\pi\) | ||||
−0.971612 | + | 0.236579i | \(0.923974\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.5130 | −0.854470 | −0.427235 | − | 0.904141i | \(-0.640512\pi\) | ||||
−0.427235 | + | 0.904141i | \(0.640512\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −34.1917 | + | 16.2869i | −1.19040 | + | 0.567036i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 14.7323i | 0.512292i | 0.966638 | + | 0.256146i | \(0.0824527\pi\) | ||||
−0.966638 | + | 0.256146i | \(0.917547\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 11.7079 | + | 6.75957i | 0.406633 | + | 0.234770i | 0.689342 | − | 0.724436i | \(-0.257900\pi\) |
−0.282709 | + | 0.959206i | \(0.591233\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −35.8936 | − | 2.84360i | −1.24513 | − | 0.0986434i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.64511 | −0.0915378 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.17113 | − | 4.84491i | 0.0404802 | − | 0.167465i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 0.511154 | − | 0.885345i | 0.0176470 | − | 0.0305655i | −0.857067 | − | 0.515205i | \(-0.827716\pi\) |
0.874714 | + | 0.484639i | \(0.161049\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.5936 | − | 23.5449i | −0.468746 | − | 0.811892i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −36.7210 | + | 17.4917i | −1.26474 | + | 0.602446i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.13918 | + | 1.97312i | 0.0391890 | + | 0.0678773i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 18.4383 | + | 12.6864i | 0.632802 | + | 0.435396i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 39.6157i | 1.35801i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.70682 | − | 5.02689i | −0.298116 | − | 0.172117i | 0.343480 | − | 0.939160i | \(-0.388394\pi\) |
−0.641596 | + | 0.767043i | \(0.721727\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 10.4233 | − | 3.98874i | 0.356469 | − | 0.136412i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 14.1272 | + | 24.4690i | 0.482575 | + | 0.835844i | 0.999800 | − | 0.0200052i | \(-0.00636826\pi\) |
−0.517225 | + | 0.855850i | \(0.673035\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 26.9800 | + | 15.5769i | 0.920544 | + | 0.531476i | 0.883809 | − | 0.467849i | \(-0.154971\pi\) |
0.0367356 | + | 0.999325i | \(0.488304\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −49.4703 | + | 28.5617i | −1.68399 | + | 0.972252i | −0.725026 | + | 0.688722i | \(0.758172\pi\) |
−0.958963 | + | 0.283530i | \(0.908495\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.57157 | − | 2.72204i | 0.0534351 | − | 0.0925522i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −61.2854 | − | 4.85522i | −2.08136 | − | 0.164892i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −2.56754 | + | 1.48237i | −0.0870978 | + | 0.0502859i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 12.0960 | − | 6.98365i | 0.409858 | − | 0.236632i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −4.08432 | + | 25.6155i | −0.138233 | + | 0.866955i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 15.6691 | − | 27.1397i | 0.529108 | − | 0.916443i | −0.470315 | − | 0.882498i | \(-0.655860\pi\) |
0.999424 | − | 0.0339441i | \(-0.0108068\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6.87601 | + | 0.544739i | 0.231922 | + | 0.0183736i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.2822 | −0.413799 | −0.206900 | − | 0.978362i | \(-0.566337\pi\) | ||||
−0.206900 | + | 0.978362i | \(0.566337\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 3.61496 | 0.121653 | 0.0608266 | − | 0.998148i | \(-0.480626\pi\) | ||||
0.0608266 | + | 0.998148i | \(0.480626\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 3.21730 | + | 6.75422i | 0.108148 | + | 0.227041i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 9.44264 | − | 16.3551i | 0.317053 | − | 0.549152i | −0.662819 | − | 0.748780i | \(-0.730640\pi\) |
0.979872 | + | 0.199628i | \(0.0639734\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 13.0399 | − | 39.8515i | 0.436854 | − | 1.33507i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −57.0438 | + | 32.9342i | −1.90890 | + | 1.10210i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −6.05795 | + | 3.49756i | −0.202495 | + | 0.116911i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −22.7596 | + | 33.0787i | −0.759922 | + | 1.10447i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −0.645760 | + | 1.11849i | −0.0215373 | + | 0.0373037i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −52.9075 | + | 30.5462i | −1.76260 | + | 1.01764i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.9079 | + | 6.29769i | 0.362591 | + | 0.209342i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 28.8802 | + | 50.0219i | 0.958950 | + | 1.66095i | 0.725059 | + | 0.688687i | \(0.241813\pi\) |
0.233891 | + | 0.972263i | \(0.424854\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.85553 | + | 10.9125i | −0.293719 | + | 0.361945i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −33.7810 | − | 19.5034i | −1.11921 | − | 0.646178i | −0.178013 | − | 0.984028i | \(-0.556967\pi\) |
−0.941200 | + | 0.337850i | \(0.890300\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 25.9821i | − | 0.859881i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 5.37336 | − | 2.55955i | 0.177638 | − | 0.0846160i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 15.9047 | + | 27.5478i | 0.524649 | + | 0.908719i | 0.999588 | + | 0.0287001i | \(0.00913677\pi\) |
−0.474939 | + | 0.880019i | \(0.657530\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 31.8434 | + | 21.9096i | 1.04927 | + | 0.721947i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.843006 | + | 1.46013i | 0.0277479 | + | 0.0480607i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −16.5897 | + | 28.7342i | −0.545465 | + | 0.944774i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.49527 | + | 21.9212i | −0.114800 | + | 0.719987i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 38.0849 | 1.24952 | 0.624762 | − | 0.780815i | \(-0.285196\pi\) | ||||
0.624762 | + | 0.780815i | \(0.285196\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −16.0693 | + | 23.3550i | −0.526084 | + | 0.764608i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16.1901 | + | 9.34735i | 0.529472 | + | 0.305691i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 37.6261i | 1.22919i | 0.788842 | + | 0.614596i | \(0.210681\pi\) | ||||
−0.788842 | + | 0.614596i | \(0.789319\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −27.2766 | − | 18.7675i | −0.890137 | − | 0.612454i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −1.67547 | −0.0546189 | −0.0273094 | − | 0.999627i | \(-0.508694\pi\) | ||||
−0.0273094 | + | 0.999627i | \(0.508694\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 26.8028i | 0.872820i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 22.2085i | − | 0.721679i | −0.932628 | − | 0.360839i | \(-0.882490\pi\) | ||
0.932628 | − | 0.360839i | \(-0.117510\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 35.7248 | 1.15968 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −34.4029 | − | 23.6707i | −1.11559 | − | 0.767576i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.1505i | 0.879491i | 0.898122 | + | 0.439746i | \(0.144931\pi\) | ||||
−0.898122 | + | 0.439746i | \(0.855069\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.56803 | − | 3.21470i | −0.180177 | − | 0.104025i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.15844 | + | 8.95065i | −0.199074 | + | 0.289333i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.0798 | 0.970317 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 11.7885 | + | 9.56641i | 0.379880 | + | 0.308273i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.75341 | + | 3.03700i | −0.0564444 | + | 0.0977646i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −16.7553 | − | 29.0211i | −0.538815 | − | 0.933255i | −0.998968 | − | 0.0454157i | \(-0.985539\pi\) |
0.460153 | − | 0.887840i | \(-0.347795\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 69.4447 | + | 47.7811i | 2.23089 | + | 1.53495i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −17.8733 | − | 30.9574i | −0.573580 | − | 0.993470i | −0.996194 | − | 0.0871606i | \(-0.972221\pi\) |
0.422614 | − | 0.906310i | \(-0.361113\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −30.3603 | + | 14.4618i | −0.972308 | + | 0.463149i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 45.6910i | − | 1.46178i | −0.682493 | − | 0.730892i | \(-0.739104\pi\) | ||
0.682493 | − | 0.730892i | \(-0.260896\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 27.9665 | + | 16.1465i | 0.893814 | + | 0.516044i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 34.8483 | + | 5.55646i | 1.11262 | + | 0.177404i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −9.33713 | − | 16.1724i | −0.297808 | − | 0.515819i | 0.677826 | − | 0.735222i | \(-0.262922\pi\) |
−0.975634 | + | 0.219404i | \(0.929589\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.48699 | + | 0.858517i | 0.0473796 | + | 0.0273546i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.98215 | + | 5.76320i | −0.317414 | + | 0.183259i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −24.2806 | + | 42.0552i | −0.771299 | + | 1.33593i | 0.165553 | + | 0.986201i | \(0.447059\pi\) |
−0.936851 | + | 0.349727i | \(0.886274\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 11.1939 | − | 16.2691i | 0.355226 | − | 0.516284i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.54303 | + | 4.35497i | −0.239130 | + | 0.138062i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −45.1982 | + | 26.0952i | −1.43144 | + | 0.826442i | −0.997231 | − | 0.0743700i | \(-0.976305\pi\) |
−0.434209 | + | 0.900812i | \(0.642972\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −10.3784 | − | 35.2379i | −0.328358 | − | 1.11488i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))