Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,2,Mod(25,252)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(252, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.25");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.i (of order \(3\), degree \(2\), 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: | \(2.01223013094\) |
Analytic rank: | \(0\) |
Dimension: | \(14\) |
Relative dimension: | \(7\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{14} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{14} - 5x^{12} - 3x^{11} + 7x^{10} + 30x^{9} - 117x^{7} + 270x^{5} + 189x^{4} - 243x^{3} - 1215x^{2} + 2187 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3^{4} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 121.6 | ||
Root | \(-1.58203 - 0.705117i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.121 |
Dual form | 252.2.i.b.25.6 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.40166 | − | 1.01752i | 0.809251 | − | 0.587464i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.26013 | + | 2.18261i | 0.563548 | + | 0.976094i | 0.997183 | + | 0.0750053i | \(0.0238974\pi\) |
−0.433635 | + | 0.901089i | \(0.642769\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.527655 | + | 2.59260i | 0.199435 | + | 0.979911i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.929318 | − | 2.85243i | 0.309773 | − | 0.950811i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.687041 | − | 1.18999i | 0.207151 | − | 0.358796i | −0.743665 | − | 0.668552i | \(-0.766914\pi\) |
0.950816 | + | 0.309757i | \(0.100248\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.80008 | + | 4.84989i | −0.776603 | + | 1.34512i | 0.157285 | + | 0.987553i | \(0.449726\pi\) |
−0.933889 | + | 0.357563i | \(0.883608\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.98712 | + | 1.77708i | 1.02947 | + | 0.458840i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.69613 | − | 4.66983i | −0.653907 | − | 1.13260i | −0.982167 | − | 0.188013i | \(-0.939795\pi\) |
0.328260 | − | 0.944588i | \(-0.393538\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.44717 | − | 4.23863i | 0.561420 | − | 0.972408i | −0.435953 | − | 0.899969i | \(-0.643589\pi\) |
0.997373 | − | 0.0724385i | \(-0.0230781\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.37761 | + | 3.09705i | 0.737055 | + | 0.675833i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.08765 | − | 3.61591i | −0.435304 | − | 0.753969i | 0.562016 | − | 0.827126i | \(-0.310026\pi\) |
−0.997320 | + | 0.0731570i | \(0.976693\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −0.675864 | + | 1.17063i | −0.135173 | + | 0.234126i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.59981 | − | 4.94375i | −0.307883 | − | 0.951424i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1.56761 | − | 2.71518i | −0.291097 | − | 0.504195i | 0.682972 | − | 0.730444i | \(-0.260687\pi\) |
−0.974069 | + | 0.226249i | \(0.927354\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 4.80121 | 0.862323 | 0.431161 | − | 0.902275i | \(-0.358104\pi\) | ||||
0.431161 | + | 0.902275i | \(0.358104\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.247835 | − | 2.36704i | −0.0431426 | − | 0.412049i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −4.99373 | + | 4.41869i | −0.844094 | + | 0.746894i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.69839 | + | 4.67374i | −0.443612 | + | 0.768359i | −0.997954 | − | 0.0639302i | \(-0.979637\pi\) |
0.554342 | + | 0.832289i | \(0.312970\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.01007 | + | 9.64704i | 0.161740 | + | 1.54476i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.02991 | + | 5.24797i | −0.473193 | + | 0.819595i | −0.999529 | − | 0.0306820i | \(-0.990232\pi\) |
0.526336 | + | 0.850277i | \(0.323565\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.44717 | + | 4.23863i | 0.373190 | + | 0.646385i | 0.990054 | − | 0.140685i | \(-0.0449305\pi\) |
−0.616864 | + | 0.787070i | \(0.711597\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 7.39682 | − | 1.56610i | 1.10265 | − | 0.233460i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −5.65548 | −0.824936 | −0.412468 | − | 0.910972i | \(-0.635333\pi\) | ||||
−0.412468 | + | 0.910972i | \(0.635333\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.44316 | + | 2.73600i | −0.920451 | + | 0.390857i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8.53069 | − | 3.80217i | −1.19454 | − | 0.532411i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −7.00281 | − | 12.1292i | −0.961910 | − | 1.66608i | −0.717696 | − | 0.696356i | \(-0.754803\pi\) |
−0.244214 | − | 0.969721i | \(-0.578530\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.46305 | 0.466958 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −0.882764 | − | 8.43117i | −0.116925 | − | 1.11674i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14.2688 | 1.85765 | 0.928823 | − | 0.370524i | \(-0.120822\pi\) | ||||
0.928823 | + | 0.370524i | \(0.120822\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −6.85721 | −0.877975 | −0.438988 | − | 0.898493i | \(-0.644663\pi\) | ||||
−0.438988 | + | 0.898493i | \(0.644663\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 7.88558 | + | 0.904251i | 0.993489 | + | 0.113925i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −14.1139 | −1.75061 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.11356 | −0.991229 | −0.495615 | − | 0.868543i | \(-0.665057\pi\) | ||||
−0.495615 | + | 0.868543i | \(0.665057\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −6.60543 | − | 2.94407i | −0.795200 | − | 0.354424i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −2.25704 | −0.267861 | −0.133931 | − | 0.990991i | \(-0.542760\pi\) | ||||
−0.133931 | + | 0.990991i | \(0.542760\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.51456 | + | 6.08739i | 0.411348 | + | 0.712475i | 0.995037 | − | 0.0995017i | \(-0.0317249\pi\) |
−0.583690 | + | 0.811977i | \(0.698392\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0.243803 | + | 2.32853i | 0.0281520 | + | 0.268876i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 3.44769 | + | 1.15332i | 0.392901 | + | 0.131433i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.75685 | 0.310170 | 0.155085 | − | 0.987901i | \(-0.450435\pi\) | ||||
0.155085 | + | 0.987901i | \(0.450435\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.27273 | − | 5.30163i | −0.808082 | − | 0.589070i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 7.48876 | + | 12.9709i | 0.821998 | + | 1.42374i | 0.904192 | + | 0.427127i | \(0.140474\pi\) |
−0.0821933 | + | 0.996616i | \(0.526192\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 6.79495 | − | 11.7692i | 0.737016 | − | 1.27655i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −4.95999 | − | 2.21069i | −0.531767 | − | 0.237011i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 2.75804 | − | 4.77707i | 0.292352 | − | 0.506368i | −0.682014 | − | 0.731339i | \(-0.738896\pi\) |
0.974365 | + | 0.224971i | \(0.0722289\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −14.0513 | − | 4.70043i | −1.47298 | − | 0.492739i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 6.72968 | − | 4.88531i | 0.697835 | − | 0.506583i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 12.3350 | 1.26555 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 0.894003 | + | 1.54846i | 0.0907722 | + | 0.157222i | 0.907836 | − | 0.419325i | \(-0.137733\pi\) |
−0.817064 | + | 0.576547i | \(0.804400\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.75589 | − | 3.06562i | −0.276977 | − | 0.308106i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −6.69534 | + | 11.5967i | −0.666211 | + | 1.15391i | 0.312744 | + | 0.949837i | \(0.398752\pi\) |
−0.978955 | + | 0.204074i | \(0.934582\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.10164 | − | 1.90810i | −0.108548 | − | 0.188010i | 0.806634 | − | 0.591051i | \(-0.201287\pi\) |
−0.915182 | + | 0.403040i | \(0.867953\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.50343 | + | 11.2747i | −0.244310 | + | 1.10030i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 4.93284 | − | 8.54392i | 0.476875 | − | 0.825972i | −0.522774 | − | 0.852472i | \(-0.675103\pi\) |
0.999649 | + | 0.0264995i | \(0.00843603\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.54340 | + | 2.67325i | 0.147831 | + | 0.256051i | 0.930426 | − | 0.366481i | \(-0.119438\pi\) |
−0.782595 | + | 0.622532i | \(0.786104\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0.973384 | + | 9.29667i | 0.0923895 | + | 0.882401i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 0.218815 | − | 0.378999i | 0.0205844 | − | 0.0356532i | −0.855550 | − | 0.517721i | \(-0.826781\pi\) |
0.876134 | + | 0.482067i | \(0.160114\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 5.26142 | − | 9.11304i | 0.490630 | − | 0.849796i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 11.2318 | + | 12.4941i | 1.03838 | + | 1.15508i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 10.6844 | − | 9.45404i | 0.979435 | − | 0.866651i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 4.55595 | + | 7.89113i | 0.414177 | + | 0.717376i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.09298 | + | 10.4389i | 0.0985503 | + | 0.941241i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 9.19461 | 0.822391 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −5.75958 | −0.511080 | −0.255540 | − | 0.966798i | \(-0.582253\pi\) | ||||
−0.255540 | + | 0.966798i | \(0.582253\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 7.74299 | + | 3.45109i | 0.681732 | + | 0.303851i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.714865 | + | 1.23818i | 0.0624580 | + | 0.108180i | 0.895564 | − | 0.444934i | \(-0.146773\pi\) |
−0.833106 | + | 0.553114i | \(0.813439\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 12.2803 | + | 4.10801i | 1.06484 | + | 0.356210i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.77431 | − | 9.72153i | 0.755172 | − | 0.836696i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −5.59335 | + | 9.68796i | −0.477872 | + | 0.827698i | −0.999678 | − | 0.0253656i | \(-0.991925\pi\) |
0.521806 | + | 0.853064i | \(0.325258\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 7.87024 | − | 13.6317i | 0.667545 | − | 1.15622i | −0.311044 | − | 0.950396i | \(-0.600679\pi\) |
0.978589 | − | 0.205826i | \(-0.0659881\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −7.92707 | + | 5.75454i | −0.667580 | + | 0.484620i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.84755 | + | 6.66415i | 0.321748 | + | 0.557284i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.95078 | − | 6.84296i | 0.328095 | − | 0.568277i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −6.24721 | + | 10.3910i | −0.515261 | + | 0.857033i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −3.96513 | − | 6.86780i | −0.324836 | − | 0.562632i | 0.656643 | − | 0.754201i | \(-0.271976\pi\) |
−0.981479 | + | 0.191569i | \(0.938642\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 5.39683 | − | 9.34758i | 0.439188 | − | 0.760696i | −0.558439 | − | 0.829545i | \(-0.688600\pi\) |
0.997627 | + | 0.0688499i | \(0.0219329\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −15.8259 | + | 3.35076i | −1.27945 | + | 0.270893i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.05016 | + | 10.4792i | 0.485960 | + | 0.841708i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 21.1768 | 1.69009 | 0.845045 | − | 0.534695i | \(-0.179574\pi\) | ||||
0.845045 | + | 0.534695i | \(0.179574\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −22.1573 | − | 9.87561i | −1.75719 | − | 0.783187i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 8.27305 | − | 7.32039i | 0.652008 | − | 0.576927i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 0.536552 | − | 0.929336i | 0.0420260 | − | 0.0727912i | −0.844247 | − | 0.535954i | \(-0.819952\pi\) |
0.886273 | + | 0.463163i | \(0.153285\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.85403 | − | 3.52371i | 0.377886 | − | 0.274321i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −7.71638 | + | 13.3652i | −0.597112 | + | 1.03423i | 0.396133 | + | 0.918193i | \(0.370352\pi\) |
−0.993245 | + | 0.116035i | \(0.962982\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.18094 | − | 15.9018i | −0.706226 | − | 1.22322i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −9.81620 | − | 10.9194i | −0.750663 | − | 0.835030i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 20.3620 | 1.54809 | 0.774046 | − | 0.633129i | \(-0.218230\pi\) | ||||
0.774046 | + | 0.633129i | \(0.218230\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.39160 | − | 1.13456i | −0.256381 | − | 0.0857644i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 20.0001 | − | 14.5188i | 1.50330 | − | 1.09130i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 3.04960 | + | 5.28206i | 0.227938 | + | 0.394800i | 0.957197 | − | 0.289438i | \(-0.0934684\pi\) |
−0.729259 | + | 0.684238i | \(0.760135\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.0056 | 0.743714 | 0.371857 | − | 0.928290i | \(-0.378721\pi\) | ||||
0.371857 | + | 0.928290i | \(0.378721\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.61149 | + | 6.97733i | −0.710502 | + | 0.515779i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −13.6013 | −0.999987 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −7.40940 | −0.541829 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 11.9730 | − | 6.75625i | 0.870909 | − | 0.491445i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −22.1987 | −1.60624 | −0.803120 | − | 0.595818i | \(-0.796828\pi\) | ||||
−0.803120 | + | 0.595818i | \(0.796828\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −26.6160 | −1.91586 | −0.957930 | − | 0.287002i | \(-0.907342\pi\) | ||||
−0.957930 | + | 0.287002i | \(0.907342\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −19.7829 | + | 14.3611i | −1.41668 | + | 1.02842i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 10.1696 | 0.724551 | 0.362276 | − | 0.932071i | \(-0.382000\pi\) | ||||
0.362276 | + | 0.932071i | \(0.382000\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.66243 | − | 2.87941i | −0.117846 | − | 0.204116i | 0.801068 | − | 0.598574i | \(-0.204266\pi\) |
−0.918914 | + | 0.394458i | \(0.870932\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −11.3725 | + | 8.25569i | −0.802153 | + | 0.582311i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.21221 | − | 5.49686i | 0.436012 | − | 0.385804i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −15.2724 | −1.06667 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −12.2542 | + | 2.59454i | −0.851727 | + | 0.180333i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −3.36262 | − | 5.82423i | −0.232597 | − | 0.402870i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.29535 | + | 2.24361i | −0.0891755 | + | 0.154456i | −0.907163 | − | 0.420780i | \(-0.861757\pi\) |
0.817987 | + | 0.575236i | \(0.195090\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.16361 | + | 2.29658i | −0.216767 | + | 0.157359i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −6.16752 | + | 10.6825i | −0.420621 | + | 0.728538i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.53338 | + | 12.4476i | 0.171977 | + | 0.845000i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 11.1202 | + | 4.95635i | 0.751437 | + | 0.334919i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 30.1975 | 2.03131 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −12.4029 | − | 21.4824i | −0.830556 | − | 1.43857i | −0.897598 | − | 0.440816i | \(-0.854689\pi\) |
0.0670411 | − | 0.997750i | \(-0.478644\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 2.71105 | + | 3.01574i | 0.180737 | + | 0.201050i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.55125 | + | 6.15095i | −0.235705 | + | 0.408253i | −0.959477 | − | 0.281786i | \(-0.909073\pi\) |
0.723772 | + | 0.690039i | \(0.242407\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3.23252 | + | 5.59889i | 0.213611 | + | 0.369985i | 0.952842 | − | 0.303467i | \(-0.0981442\pi\) |
−0.739231 | + | 0.673452i | \(0.764811\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 6.00602 | − | 1.89152i | 0.395167 | − | 0.124453i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −4.42950 | + | 7.67212i | −0.290186 | + | 0.502617i | −0.973854 | − | 0.227177i | \(-0.927051\pi\) |
0.683667 | + | 0.729794i | \(0.260384\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −7.12665 | − | 12.3437i | −0.464891 | − | 0.805215i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 3.86418 | − | 2.80514i | 0.251005 | − | 0.182214i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 8.60836 | − | 14.9101i | 0.556828 | − | 0.964455i | −0.440930 | − | 0.897541i | \(-0.645351\pi\) |
0.997759 | − | 0.0669138i | \(-0.0213152\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.1106 | + | 17.5120i | −0.651279 | + | 1.12805i | 0.331534 | + | 0.943443i | \(0.392434\pi\) |
−0.982813 | + | 0.184604i | \(0.940900\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5884 | − | 0.0309734i | −0.999998 | − | 0.00198694i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −14.0909 | − | 10.6152i | −0.900232 | − | 0.678180i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 13.7046 | + | 23.7370i | 0.872001 | + | 1.51035i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 23.6949 | + | 10.5609i | 1.50160 | + | 0.669271i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.32214 | 0.462169 | 0.231085 | − | 0.972934i | \(-0.425773\pi\) | ||||
0.231085 | + | 0.972934i | \(0.425773\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.73720 | −0.360695 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.45113 | − | 23.4104i | −0.153496 | − | 1.46602i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −3.07308 | − | 5.32274i | −0.191694 | − | 0.332023i | 0.754118 | − | 0.656739i | \(-0.228065\pi\) |
−0.945812 | + | 0.324716i | \(0.894731\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −13.5410 | − | 4.52971i | −0.841395 | − | 0.281463i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.20166 | + | 1.94823i | −0.569568 | + | 0.120592i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.0824634 | − | 0.142831i | 0.00508491 | − | 0.00880732i | −0.863472 | − | 0.504397i | \(-0.831715\pi\) |
0.868557 | + | 0.495590i | \(0.165048\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 17.6489 | − | 30.5689i | 1.08417 | − | 1.87783i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.994903 | − | 9.50219i | −0.0608871 | − | 0.581525i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.86477 | − | 3.22988i | −0.113697 | − | 0.196929i | 0.803561 | − | 0.595222i | \(-0.202936\pi\) |
−0.917258 | + | 0.398293i | \(0.869603\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −0.393652 | + | 0.681825i | −0.0239127 | + | 0.0414179i | −0.877734 | − | 0.479148i | \(-0.840946\pi\) |
0.853821 | + | 0.520566i | \(0.174279\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −24.4780 | + | 7.70902i | −1.48147 | + | 0.466571i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.928693 | + | 1.60854i | 0.0560023 | + | 0.0969988i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.62954 | − | 2.82245i | 0.0979096 | − | 0.169584i | −0.812910 | − | 0.582390i | \(-0.802118\pi\) |
0.910819 | + | 0.412805i | \(0.135451\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 4.46185 | − | 13.6951i | 0.267124 | − | 0.819906i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.39147 | + | 16.2665i | 0.560248 | + | 0.970379i | 0.997474 | + | 0.0710269i | \(0.0226276\pi\) |
−0.437226 | + | 0.899352i | \(0.644039\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.8370 | −0.763078 | −0.381539 | − | 0.924353i | \(-0.624606\pi\) | ||||
−0.381539 | + | 0.924353i | \(0.624606\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 17.2896 | − | 12.5511i | 1.02415 | − | 0.743464i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −15.2046 | − | 5.08624i | −0.897501 | − | 0.300231i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −6.03821 | + | 10.4585i | −0.355189 | + | 0.615205i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.82867 | + | 1.26075i | 0.165820 | + | 0.0739067i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.6293 | + | 23.6066i | −0.796230 | + | 1.37911i | 0.125825 | + | 0.992052i | \(0.459842\pi\) |
−0.922055 | + | 0.387058i | \(0.873491\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 17.9806 | + | 31.1434i | 1.04687 | + | 1.81324i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −6.98214 | − | 1.49280i | −0.405145 | − | 0.0866212i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 23.3823 | 1.35224 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −9.69781 | + | 8.58108i | −0.558972 | + | 0.494605i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.41520 | + | 23.0672i | 0.138749 | + | 1.32518i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −8.64098 | − | 14.9666i | −0.494781 | − | 0.856986i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 24.4623 | 1.39614 | 0.698069 | − | 0.716030i | \(-0.254043\pi\) | ||||
0.698069 | + | 0.716030i | \(0.254043\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.48565 | − | 1.55357i | −0.198292 | − | 0.0883796i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.1783 | −0.974094 | −0.487047 | − | 0.873376i | \(-0.661926\pi\) | ||||
−0.487047 | + | 0.873376i | \(0.661926\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 15.8645 | 0.896715 | 0.448358 | − | 0.893854i | \(-0.352009\pi\) | ||||
0.448358 | + | 0.893854i | \(0.352009\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 7.96324 | + | 18.3506i | 0.448678 | + | 1.03394i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −22.7252 | −1.27638 | −0.638188 | − | 0.769880i | \(-0.720316\pi\) | ||||
−0.638188 | + | 0.769880i | \(0.720316\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −4.30804 | −0.241204 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.77941 | − | 16.9949i | −0.0993171 | − | 0.948565i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −26.3916 | −1.46847 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.78495 | − | 6.55573i | −0.209951 | − | 0.363646i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 4.88340 | + | 2.17656i | 0.270053 | + | 0.120364i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.98414 | − | 14.6624i | −0.164521 | − | 0.808364i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 24.2281 | 1.33170 | 0.665848 | − | 0.746088i | \(-0.268070\pi\) | ||||
0.665848 | + | 0.746088i | \(0.268070\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.8239 | + | 12.0404i | 0.593145 | + | 0.659808i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −10.2242 | − | 17.7088i | −0.558605 | − | 0.967533i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.20181 | + | 3.81365i | −0.119940 | + | 0.207743i | −0.919744 | − | 0.392519i | \(-0.871604\pi\) |
0.799803 | + | 0.600262i | \(0.204937\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −0.0789328 | − | 0.753877i | −0.00428704 | − | 0.0409450i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 3.29863 | − | 5.71339i | 0.178631 | − | 0.309398i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −10.4931 | − | 15.2609i | −0.566575 | − | 0.824010i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.89794 | − | 18.1270i | −0.102182 | − | 0.975925i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −12.2506 | −0.657645 | −0.328823 | − | 0.944392i | \(-0.606652\pi\) | ||||
−0.328823 | + | 0.944392i | \(0.606652\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 7.19444 | + | 12.4611i | 0.385110 | + | 0.667030i | 0.991784 | − | 0.127921i | \(-0.0408303\pi\) |
−0.606675 | + | 0.794950i | \(0.707497\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 28.4562 | + | 6.08402i | 1.51888 | + | 0.324741i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.40835 | − | 7.63549i | 0.234633 | − | 0.406396i | −0.724533 | − | 0.689240i | \(-0.757945\pi\) |
0.959166 | + | 0.282844i | \(0.0912779\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2.84417 | − | 4.92624i | −0.150953 | − | 0.261458i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 5.35625 | − | 24.1229i | 0.283483 | − | 1.27672i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.04909 | + | 5.28118i | −0.160925 | + | 0.278730i | −0.935201 | − | 0.354118i | \(-0.884781\pi\) |
0.774276 | + | 0.632848i | \(0.218114\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.47731 | − | 4.29083i | −0.130385 | − | 0.225833i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 14.4153 | + | 6.42496i | 0.756605 | + | 0.337223i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −8.85761 | + | 15.3418i | −0.463628 | + | 0.803028i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3.45814 | − | 5.98967i | 0.180513 | − | 0.312658i | −0.761542 | − | 0.648115i | \(-0.775557\pi\) |
0.942055 | + | 0.335457i | \(0.108891\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 12.1537 | + | 13.5197i | 0.632697 | + | 0.703805i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 27.7512 | − | 24.5556i | 1.44077 | − | 1.27486i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 11.9489 | + | 20.6961i | 0.618691 | + | 1.07160i | 0.989725 | + | 0.142985i | \(0.0456701\pi\) |
−0.371034 | + | 0.928619i | \(0.620997\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.8877 | − | 9.35567i | 0.665520 | − | 0.483125i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 17.5577 | 0.904269 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 34.6719 | 1.78097 | 0.890487 | − | 0.455008i | \(-0.150364\pi\) | ||||
0.890487 | + | 0.455008i | \(0.150364\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −8.07299 | + | 5.86047i | −0.413592 | + | 0.300241i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −9.71507 | − | 16.8270i | −0.496417 | − | 0.859820i | 0.503574 | − | 0.863952i | \(-0.332018\pi\) |
−0.999991 | + | 0.00413220i | \(0.998685\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.82730 | + | 8.97831i | 0.0931277 | + | 0.457577i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 14.3646 | − | 3.04136i | 0.730194 | − | 0.154601i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 16.3172 | − | 28.2623i | 0.827317 | − | 1.43295i | −0.0728190 | − | 0.997345i | \(-0.523200\pi\) |
0.900136 | − | 0.435610i | \(-0.143467\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.2571 | + | 19.4979i | −0.569297 | + | 0.986051i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 2.26187 | + | 1.00813i | 0.114096 | + | 0.0508533i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.47400 | + | 6.01714i | 0.174796 | + | 0.302755i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.11807 | + | 5.40065i | −0.156491 | + | 0.271051i | −0.933601 | − | 0.358314i | \(-0.883352\pi\) |
0.777110 | + | 0.629365i | \(0.216685\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 21.3929 | − | 6.73741i | 1.07098 | − | 0.337292i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 12.3672 | + | 21.4207i | 0.617591 | + | 1.06970i | 0.989924 | + | 0.141599i | \(0.0452245\pi\) |
−0.372333 | + | 0.928099i | \(0.621442\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −13.4438 | + | 23.2853i | −0.669683 | + | 1.15992i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.40681 | − | 22.5543i | 0.119595 | − | 1.12073i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.70781 | + | 6.42211i | 0.183789 | + | 0.318332i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −23.1499 | −1.14469 | −0.572344 | − | 0.820014i | \(-0.693966\pi\) | ||||
−0.572344 | + | 0.820014i | \(0.693966\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.01768 | + | 19.2706i | 0.0995247 | + | 0.950548i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 7.52903 | + | 36.9934i | 0.370480 | + | 1.82033i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −18.8737 | + | 32.6901i | −0.926471 | + | 1.60470i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −2.83902 | − | 27.1151i | −0.139027 | − | 1.32783i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −0.703260 | + | 1.21808i | −0.0343565 | + | 0.0595072i | −0.882692 | − | 0.469951i | \(-0.844271\pi\) |
0.848336 | + | 0.529458i | \(0.177605\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.663904 | − | 1.14992i | −0.0323567 | − | 0.0560435i | 0.849394 | − | 0.527760i | \(-0.176968\pi\) |
−0.881750 | + | 0.471716i | \(0.843635\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −5.25574 | + | 16.1319i | −0.255543 | + | 0.784358i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.28886 | 0.353562 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.61824 | − | 17.7780i | −0.175099 | − | 0.860338i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 12.1738 | + | 5.42594i | 0.587759 | + | 0.261967i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.83378 | − | 4.90825i | −0.136498 | − | 0.236422i | 0.789670 | − | 0.613531i | \(-0.210252\pi\) |
−0.926169 | + | 0.377109i | \(0.876918\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.60371 | 0.0770696 | 0.0385348 | − | 0.999257i | \(-0.487731\pi\) | ||||
0.0385348 | + | 0.999257i | \(0.487731\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.42516 | − | 13.6115i | −0.0683311 | − | 0.652622i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −20.4353 | −0.977554 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −0.454645 | −0.0216990 | −0.0108495 | − | 0.999941i | \(-0.503454\pi\) | ||||
−0.0108495 | + | 0.999941i | \(0.503454\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1.81651 | + | 20.9213i | 0.0865003 | + | 0.996252i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 18.6288 | 0.885083 | 0.442542 | − | 0.896748i | \(-0.354077\pi\) | ||||
0.442542 | + | 0.896748i | \(0.354077\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.9020 | 0.659017 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −12.5459 | − | 5.59176i | −0.593400 | − | 0.264481i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −14.2330 | −0.671696 | −0.335848 | − | 0.941916i | \(-0.609023\pi\) | ||||
−0.335848 | + | 0.941916i | \(0.609023\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 4.16335 | + | 7.21114i | 0.196045 | + | 0.339559i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −1.94679 | − | 18.5935i | −0.0914681 | − | 0.873600i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −7.44727 | − | 36.5917i | −0.349134 | − | 1.71545i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 29.3458 | 1.37274 | 0.686370 | − | 0.727252i | \(-0.259203\pi\) | ||||
0.686370 | + | 0.727252i | \(0.259203\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −18.7732 | + | 20.7998i | −0.876256 | + | 0.970851i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.6587 | − | 21.9254i | −0.589572 | − | 1.02117i | −0.994288 | − | 0.106727i | \(-0.965963\pi\) |
0.404716 | − | 0.914442i | \(-0.367370\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −11.6503 | + | 20.1789i | −0.541435 | + | 0.937793i | 0.457387 | + | 0.889268i | \(0.348785\pi\) |
−0.998822 | + | 0.0485250i | \(0.984548\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 19.1430 | + | 8.53214i | 0.887736 | + | 0.395669i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −20.8409 | + | 36.0976i | −0.964403 | + | 1.67040i | −0.253194 | + | 0.967416i | \(0.581481\pi\) |
−0.711210 | + | 0.702980i | \(0.751852\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.28116 | − | 21.0352i | −0.197686 | − | 0.971316i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 29.6827 | − | 21.5477i | 1.36771 | − | 0.992866i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.72524 | 0.309227 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 3.30791 | + | 5.72947i | 0.151777 | + | 0.262886i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −41.1056 | + | 8.70313i | −1.88210 | + | 0.398489i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.76946 | + | 4.79684i | −0.126540 | + | 0.219173i | −0.922334 | − | 0.386394i | \(-0.873720\pi\) |
0.795794 | + | 0.605567i | \(0.207054\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15.1114 | − | 26.1737i | −0.689021 | − | 1.19342i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 4.14741 | − | 18.6787i | 0.188714 | − | 0.849910i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2.25312 | + | 3.90252i | −0.102309 | + | 0.177204i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 12.3357 | + | 21.3661i | 0.558985 | + | 0.968190i | 0.997582 | + | 0.0695061i | \(0.0221423\pi\) |
−0.438597 | + | 0.898684i | \(0.644524\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −0.193549 | − | 1.84857i | −0.00875261 | − | 0.0835951i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.0509 | + | 17.4087i | −0.453590 | + | 0.785642i | −0.998606 | − | 0.0527842i | \(-0.983190\pi\) |
0.545015 | + | 0.838426i | \(0.316524\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.45294 | + | 14.6409i | −0.380701 | + | 0.659394i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.21828 | − | 9.87812i | 0.144651 | − | 0.443988i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.19094 | − | 5.85160i | −0.0534209 | − | 0.262480i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −17.7587 | − | 30.7589i | −0.794987 | − | 1.37696i | −0.922848 | − | 0.385166i | \(-0.874144\pi\) |
0.127861 | − | 0.991792i | \(-0.459189\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2.78352 | + | 26.5850i | 0.124358 | + | 1.18773i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 24.2236 | 1.08008 | 0.540039 | − | 0.841640i | \(-0.318410\pi\) | ||||
0.540039 | + | 0.841640i | \(0.318410\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −33.7480 | −1.50177 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −29.0490 | − | 12.9473i | −1.29011 | − | 0.575009i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 3.86723 | + | 6.69824i | 0.171412 | + | 0.296894i | 0.938914 | − | 0.344153i | \(-0.111834\pi\) |
−0.767502 | + | 0.641047i | \(0.778500\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13.9277 | + | 12.3239i | −0.616125 | + | 0.545177i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −24.8697 | − | 5.31721i | −1.09802 | − | 0.234761i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.77642 | − | 4.80891i | 0.122344 | − | 0.211906i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −3.88555 | + | 6.72997i | −0.170886 | + | 0.295984i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 28.5406 | − | 20.7187i | 1.25279 | − | 0.909448i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −14.9050 | − | 25.8161i | −0.652998 | − | 1.13103i | −0.982392 | − | 0.186833i | \(-0.940178\pi\) |
0.329394 | − | 0.944193i | \(-0.393156\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −1.76218 | + | 3.05219i | −0.0770547 | + | 0.133463i | −0.901978 | − | 0.431782i | \(-0.857885\pi\) |
0.824923 | + | 0.565245i | \(0.191218\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −5.90831 | + | 1.86075i | −0.257860 | + | 0.0812097i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12.9447 | − | 22.4208i | −0.563879 | − | 0.976667i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.78347 | − | 4.82110i | 0.121020 | − | 0.209613i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 13.2603 | − | 40.7009i | 0.575448 | − | 1.76627i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −16.9680 | − | 29.3895i | −0.734967 | − | 1.27300i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 24.8641 | 1.07497 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 9.64910 | + | 4.30065i | 0.416389 | + | 0.185587i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1.17090 | + | 9.54704i | −0.0504344 | + | 0.411220i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 13.8435 | − | 23.9777i | 0.595180 | − | 1.03088i | −0.398342 | − | 0.917237i | \(-0.630414\pi\) |
0.993521 | − | 0.113645i | \(-0.0362525\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 14.0245 | − | 10.1809i | 0.601851 | − | 0.436905i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.88977 | + | 6.73729i | −0.166620 | + | 0.288594i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −16.6136 | − | 28.7756i | −0.710347 | − | 1.23036i | −0.964727 | − | 0.263253i | \(-0.915205\pi\) |
0.254380 | − | 0.967104i | \(-0.418129\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.37253 | + | 19.5597i | −0.271973 | + | 0.834788i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −15.3448 | −0.653712 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.45467 | + | 7.14741i | 0.0618587 | + | 0.303939i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −19.0644 | + | 13.8395i | −0.809240 | + | 0.587456i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 7.80873 | + | 13.5251i | 0.330866 | + | 0.573078i | 0.982682 | − | 0.185300i | \(-0.0593257\pi\) |
−0.651816 | + | 0.758378i | \(0.725992\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −27.4092 | −1.15928 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −10.3855 | + | 7.53919i | −0.438476 | + | 0.318305i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19.5118 | −0.822326 | −0.411163 | − | 0.911562i | \(-0.634877\pi\) | ||||
−0.411163 | + | 0.911562i | \(0.634877\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.10294 | 0.0464012 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9.90753 | − | 21.6527i | 0.416077 | − | 0.909329i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 7.18361 | 0.301153 | 0.150576 | − | 0.988598i | \(-0.451887\pi\) | ||||
0.150576 | + | 0.988598i | \(0.451887\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 29.5773 | 1.23777 | 0.618886 | − | 0.785481i | \(-0.287584\pi\) | ||||
0.618886 | + | 0.785481i | \(0.287584\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −31.1151 | + | 22.5875i | −1.29985 | + | 0.943607i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 5.64386 | 0.235365 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 5.18911 | + | 8.98780i | 0.216025 | + | 0.374167i | 0.953589 | − | 0.301110i | \(-0.0973573\pi\) |
−0.737564 | + | 0.675277i | \(0.764024\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −37.3066 | + | 27.0822i | −1.55041 | + | 1.12550i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −29.6769 | + | 26.2595i | −1.23121 | + | 1.08943i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −19.2449 | −0.797042 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −13.1163 | + | 40.2589i | −0.542292 | + | 1.66450i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 14.4563 | + | 25.0391i | 0.596677 | + | 1.03348i | 0.993308 | + | 0.115497i | \(0.0368461\pi\) |
−0.396630 | + | 0.917978i | \(0.629821\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 11.7494 | − | 20.3505i | 0.484125 | − | 0.838530i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.2543 | − | 10.3477i | 0.586343 | − | 0.425647i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −10.2645 | + | 17.7786i | −0.421512 | + | 0.730080i | −0.996088 | − | 0.0883714i | \(-0.971834\pi\) |
0.574576 | + | 0.818451i | \(0.305167\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 34.0982 | + | 11.4065i | 1.39789 | + | 0.467622i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5.26001 | − | 2.34441i | −0.215278 | − | 0.0959504i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 7.83304 | 0.320049 | 0.160025 | − | 0.987113i | \(-0.448843\pi\) | ||||
0.160025 | + | 0.987113i | \(0.448843\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.27021 | − | 12.5924i | −0.296558 | − | 0.513654i | 0.678788 | − | 0.734334i | \(-0.262505\pi\) |
−0.975346 | + | 0.220681i | \(0.929172\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.54008 | + | 23.1434i | −0.307056 | + | 0.942471i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −11.4822 | + | 19.8877i | −0.466817 | + | 0.808551i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 15.2755 | + | 26.4579i | 0.620013 | + | 1.07389i | 0.989483 | + | 0.144651i | \(0.0462060\pi\) |
−0.369470 | + | 0.929243i | \(0.620461\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 3.11428 | − | 14.0258i | 0.126197 | − | 0.568353i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15.8358 | − | 27.4284i | 0.640648 | − | 1.10964i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −14.4646 | − | 25.0534i | −0.584220 | − | 1.01190i | −0.994972 | − | 0.100152i | \(-0.968067\pi\) |
0.410752 | − | 0.911747i | \(-0.365266\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −21.4067 | + | 15.5399i | −0.863202 | + | 0.626629i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.2106 | − | 35.0059i | 0.813650 | − | 1.40928i | −0.0966430 | − | 0.995319i | \(-0.530811\pi\) |
0.910293 | − | 0.413964i | \(-0.135856\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 9.05857 | − | 15.6899i | 0.364095 | − | 0.630631i | −0.624536 | − | 0.780996i | \(-0.714712\pi\) |
0.988630 | + | 0.150366i | \(0.0480451\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14.5363 | + | 16.1055i | −0.583322 | + | 0.646293i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13.8403 | + | 4.62985i | 0.554501 | + | 0.185491i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.9657 | + | 25.9214i | 0.598629 | + | 1.03686i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10.6395 | − | 4.74208i | −0.424901 | − | 0.189380i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 29.1008 | 1.16032 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 8.50373 | 0.338528 | 0.169264 | − | 0.985571i | \(-0.445861\pi\) | ||||
0.169264 | + | 0.985571i | \(0.445861\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0.467269 | + | 4.46282i | 0.0185723 | + | 0.177381i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.25783 | − | 12.5709i | −0.288018 | − | 0.498862i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 4.77210 | − | 38.9096i | 0.189077 | − | 1.54166i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.09751 | + | 6.43805i | −0.0829762 | + | 0.254685i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −11.0020 | + | 19.0561i | −0.434554 | + | 0.752669i | −0.997259 | − | 0.0739883i | \(-0.976427\pi\) |
0.562705 | + | 0.826658i | \(0.309761\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.1156 | − | 22.7170i | 0.517230 | − | 0.895869i | −0.482569 | − | 0.875858i | \(-0.660296\pi\) |
0.999800 | − | 0.0200115i | \(-0.00637029\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 2.22480 | + | 21.2488i | 0.0876013 | + | 0.836669i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 19.5845 | + | 33.9214i | 0.769946 | + | 1.33359i | 0.937591 | + | 0.347739i | \(0.113050\pi\) |
−0.167645 | + | 0.985847i | \(0.553616\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 9.80329 | − | 16.9798i | 0.384813 | − | 0.666515i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 16.2166 | + | 14.8696i | 0.635579 | + | 0.582786i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −6.83467 | − | 11.8380i | −0.267461 | − | 0.463257i | 0.700744 | − | 0.713413i | \(-0.252851\pi\) |
−0.968206 | + | 0.250156i | \(0.919518\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.80165 | + | 3.12054i | −0.0703962 | + | 0.121930i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 20.6300 | − | 4.36791i | 0.804853 | − | 0.170408i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.06683 | − | 5.31191i | −0.119467 | − | 0.206923i | 0.800090 | − | 0.599880i | \(-0.204785\pi\) |
−0.919557 | + | 0.392958i | \(0.871452\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −44.6236 | −1.73566 | −0.867828 | − | 0.496865i | \(-0.834484\pi\) | ||||
−0.867828 | + | 0.496865i | \(0.834484\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 42.3268 | − | 30.7265i | 1.64384 | − | 1.19332i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 6.50865 | + | 31.9798i | 0.252395 | + | 1.24013i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.54522 | + | 11.3367i | −0.253432 | + | 0.438957i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −39.2433 | − | 17.4909i | −1.51723 | − | 0.676238i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.71119 | + | 8.16001i | −0.181873 | + | 0.315014i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −16.3833 | − | 28.3767i | −0.631531 | − | 1.09384i | −0.987239 | − | 0.159246i | \(-0.949094\pi\) |
0.355708 | − | 0.934597i | \(-0.384240\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 6.86855 | + | 1.46852i | 0.264371 | + | 0.0565232i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 27.1527 | 1.04356 | 0.521782 | − | 0.853079i | \(-0.325267\pi\) | ||||
0.521782 | + | 0.853079i | \(0.325267\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.54281 | + | 3.13484i | −0.135961 | + | 0.120304i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.28104 | + | 12.2350i | 0.0490895 | + | 0.468847i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −19.0334 | − | 32.9668i | −0.728293 | − | 1.26144i | −0.957604 | − | 0.288087i | \(-0.906981\pi\) |
0.229312 | − | 0.973353i | \(-0.426353\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −28.1934 | −1.07721 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 10.2279 | + | 4.55861i | 0.390217 | + | 0.173922i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 78.4338 | 2.98809 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.7570 | −0.485297 | −0.242649 | − | 0.970114i | \(-0.578016\pi\) | ||||
−0.242649 | + | 0.970114i | \(0.578016\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 6.49377 | − | 8.76250i | 0.246678 | − | 0.332860i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 39.6701 | 1.50477 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 32.6761 | 1.23770 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.59784 | + | 15.2608i | 0.0604360 | + | 0.577217i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 40.6428 | 1.53506 | 0.767528 | − | 0.641015i | \(-0.221486\pi\) | ||||
0.767528 | + | 0.641015i | \(0.221486\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 13.2068 | + | 22.8749i | 0.498105 | + | 0.862744i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −22.5491 | − | 10.0502i | −0.849248 | − | 0.378514i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −33.5984 | − | 11.2393i | −1.26360 | − | 0.422697i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.49104 | −0.281332 | −0.140666 | − | 0.990057i | \(-0.544924\pi\) | ||||
−0.140666 | + | 0.990057i | \(0.544924\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 2.56199 | − | 7.86373i | 0.0960822 | − | 0.294913i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −10.0232 | − | 17.3607i | −0.375373 | − | 0.650165i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −9.69683 | + | 16.7954i | −0.362641 | + | 0.628112i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.10528 | − | 29.6581i | −0.115969 | − | 1.10760i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.64056 | + | 2.84154i | −0.0611827 | + | 0.105972i | −0.894994 | − | 0.446078i | \(-0.852821\pi\) |
0.833812 | + | 0.552049i | \(0.186154\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 4.36565 | − | 3.86293i | 0.162585 | − | 0.143863i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.64716 | + | 34.8336i | 0.135639 | + | 1.29548i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.23796 | 0.157394 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 8.01088 | + | 13.8753i | 0.297107 | + | 0.514605i | 0.975473 | − | 0.220120i | \(-0.0706448\pi\) |
−0.678366 | + | 0.734724i | \(0.737311\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −21.8812 | + | 15.8181i | −0.810416 | + | 0.585855i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 13.1958 | − | 22.8558i | 0.488064 | − | 0.845351i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −14.8123 | − | 25.6556i | −0.547104 | − | 0.947611i | −0.998471 | − | 0.0552733i | \(-0.982397\pi\) |
0.451368 | − | 0.892338i | \(-0.350936\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −30.5518 | − | 0.541247i | −1.12692 | − | 0.0199642i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5.57435 | + | 9.65506i | −0.205334 | + | 0.355649i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22.2867 | − | 38.6017i | −0.819829 | − | 1.41998i | −0.905808 | − | 0.423688i | \(-0.860735\pi\) |
0.0859797 | − | 0.996297i | \(-0.472598\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 43.3620 | + | 19.3267i | 1.59294 | + | 0.709983i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.67364 | + | 9.82704i | −0.208146 | + | 0.360519i | −0.951130 | − | 0.308789i | \(-0.900076\pi\) |
0.742985 | + | 0.669308i | \(0.233410\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 9.99317 | − | 17.3087i | 0.366121 | − | 0.634141i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 43.9581 | − | 9.30707i | 1.60834 | − | 0.340528i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 24.7538 | + | 8.28063i | 0.904485 | + | 0.302568i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −17.5928 | − | 30.4716i | −0.641970 | − | 1.11192i | −0.984992 | − | 0.172597i | \(-0.944784\pi\) |
0.343023 | − | 0.939327i | \(-0.388549\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 10.2632 | − | 7.45040i | 0.374011 | − | 0.271508i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 27.2029 | 0.990014 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 40.9186 | 1.48721 | 0.743605 | − | 0.668619i | \(-0.233114\pi\) | ||||
0.743605 | + | 0.668619i | \(0.233114\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −8.04162 | + | 5.83770i | −0.291892 | + | 0.211895i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −5.72243 | − | 9.91155i | −0.207438 | − | 0.359293i | 0.743469 | − | 0.668771i | \(-0.233179\pi\) |
−0.950907 | + | 0.309477i | \(0.899846\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.11628 | + | 5.41197i | −0.221424 | + | 0.195927i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −27.2562 | − | 30.3195i | −0.985449 | − | 1.09620i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −39.9540 | + | 69.2023i | −1.44265 | + | 2.49875i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −14.9723 | + | 25.9328i | −0.539916 | + | 0.935162i | 0.458992 | + | 0.888440i | \(0.348211\pi\) |
−0.998908 | + | 0.0467217i | \(0.985123\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.72340 | − | 4.33377i | −0.350180 | − | 0.156077i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −3.96578 | − | 6.86893i | −0.142639 | − | 0.247058i | 0.785851 | − | 0.618416i | \(-0.212225\pi\) |
−0.928490 | + | 0.371358i | \(0.878892\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.24496 | + | 5.62044i | −0.116563 | + | 0.201892i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −23.5889 | + | 7.42903i | −0.846248 | + | 0.266515i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 14.8295 | + | 25.6854i | 0.531320 | + | 0.920274i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.55068 | + | 2.68586i | −0.0554877 | + | 0.0961075i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10.9153 | + | 12.0936i | −0.390080 | + | 0.432190i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 26.6855 | + | 46.2207i | 0.952447 | + | 1.64969i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 43.2074 | 1.54018 | 0.770089 | − | 0.637936i | \(-0.220212\pi\) | ||||
0.770089 | + | 0.637936i | \(0.220212\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −0.0297469 | − | 0.284108i | −0.00105902 | − | 0.0101145i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.09805 | + | 0.367320i | 0.0390422 | + | 0.0130604i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 19.2008 | − | 33.2567i | 0.681839 | − | 1.18098i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6.36647 | − | 60.8053i | −0.225795 | − | 2.15654i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −8.34385 | + | 14.4520i | −0.295554 | + | 0.511915i | −0.975114 | − | 0.221706i | \(-0.928838\pi\) |
0.679559 | + | 0.733620i | \(0.262171\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.2479 | + | 26.4101i | 0.539432 | + | 0.934323i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −11.0632 | − | 12.3065i | −0.390897 | − | 0.434830i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.65858 | 0.340844 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 26.4027 | + | 8.83221i | 0.930573 | + | 0.311295i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.90024 | − | 2.62977i | −0.207698 | − | 0.0925722i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.54846 | − | 4.41407i | −0.0895992 | − | 0.155190i | 0.817743 | − | 0.575584i | \(-0.195225\pi\) |
−0.907342 | + | 0.420394i | \(0.861892\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 10.2996 | 0.361666 | 0.180833 | − | 0.983514i | \(-0.442121\pi\) | ||||
0.180833 | + | 0.983514i | \(0.442121\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0.142001 | + | 1.35624i | 0.00498021 | + | 0.0475653i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 2.70451 | 0.0947347 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 23.9546 | 0.838066 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −26.4658 | + | 35.7122i | −0.924790 | + | 1.24788i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −25.2738 | −0.882063 | −0.441031 | − | 0.897492i | \(-0.645387\pi\) | ||||
−0.441031 | + | 0.897492i | \(0.645387\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 8.88782 | 0.309810 | 0.154905 | − | 0.987929i | \(-0.450493\pi\) | ||||
0.154905 | + | 0.987929i | \(0.450493\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.93843 | + | 1.30967i | 0.102303 | + | 0.0455970i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −13.1680 | −0.457895 | −0.228947 | − | 0.973439i | \(-0.573528\pi\) | ||||
−0.228947 | + | 0.973439i | \(0.573528\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.3459 | − | 19.6516i | −0.394058 | − | 0.682529i | 0.598922 | − | 0.800807i | \(-0.295596\pi\) |
−0.992981 | + | 0.118278i | \(0.962263\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −0.587821 | − | 5.61421i | −0.0203913 | − | 0.194755i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 30.1482 | + | 22.7119i | 1.04457 | + | 0.786919i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −38.8946 | −1.34600 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −7.68101 | − | 23.7360i | −0.265494 | − | 0.820435i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −14.9632 | − | 25.9171i | −0.516588 | − | 0.894757i | −0.999814 | − | 0.0192618i | \(-0.993868\pi\) |
0.483226 | − | 0.875496i | \(-0.339465\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9.58522 | − | 16.6021i | 0.330525 | − | 0.572486i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 29.7151 | + | 13.2442i | 1.02344 | + | 0.456154i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 23.1384 | − | 40.0768i | 0.795984 | − | 1.37869i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −18.0546 | + | 15.9756i | −0.620363 | + | 0.548927i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −17.9931 | + | 13.0618i | −0.617522 | + | 0.448281i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 22.5331 | 0.772425 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6.46929 | + | 11.2051i | 0.221504 | + | 0.383657i | 0.955265 | − | 0.295751i | \(-0.0955699\pi\) |
−0.733761 | + | 0.679408i | \(0.762237\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 11.4632 | − | 35.1849i | 0.392032 | − | 1.20330i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.12252 | − | 7.14042i | 0.140823 | − | 0.243912i | −0.786984 | − | 0.616973i | \(-0.788359\pi\) |
0.927807 | + | 0.373061i | \(0.121692\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1.73399 | − | 3.00336i | −0.0591630 | − | 0.102473i | 0.834927 | − | 0.550361i | \(-0.185510\pi\) |
−0.894090 | + | 0.447888i | \(0.852177\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −26.4871 | + | 8.34177i | −0.902678 | + | 0.284287i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −0.256394 | + | 0.444087i | −0.00872775 | + | 0.0151169i | −0.870356 | − | 0.492423i | \(-0.836111\pi\) |
0.861629 | + | 0.507539i | \(0.169445\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 25.6588 | + | 44.4423i | 0.872424 | + | 1.51108i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.17815 | + | 20.8032i | 0.0739739 | + | 0.706515i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.89407 | − | 3.28063i | 0.0642519 | − | 0.111288i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 22.7186 | − | 39.3499i | 0.769792 | − | 1.33332i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5.24768 | − | 1.11107i | 0.177607 | − | 0.0376041i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.85158 | + | 23.8379i | 0.164013 | + | 0.805870i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.1880 | − | 31.5026i | −0.614166 | − | 1.06377i | −0.990530 | − | 0.137295i | \(-0.956159\pi\) |
0.376365 | − | 0.926472i | \(-0.377174\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 4.91646 | + | 46.9565i | 0.165828 | + | 1.58380i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −23.3999 | −0.788363 | −0.394181 | − | 0.919033i | \(-0.628972\pi\) | ||||
−0.394181 | + | 0.919033i | \(0.628972\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.8345 | −0.768442 | −0.384221 | − | 0.923241i | \(-0.625530\pi\) | ||||
−0.384221 | + | 0.923241i | \(0.625530\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 56.8917 | + | 25.3569i | 1.91239 | + | 0.852363i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −22.0791 | − | 38.2421i | −0.741344 | − | 1.28405i | −0.951883 | − | 0.306460i | \(-0.900855\pi\) |
0.210539 | − | 0.977585i | \(-0.432478\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.03907 | − | 14.9323i | −0.101927 | − | 0.500813i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −11.3056 | + | 5.01204i | −0.378751 | + | 0.167910i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −13.8399 | + | 23.9715i | −0.463136 | + | 0.802175i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.68579 | + | 13.3122i | −0.256908 | + | 0.444977i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 32.7742 | − | 23.7919i | 1.09430 | − | 0.794389i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −7.52641 | − | 13.0361i | −0.251020 | − | 0.434779i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −37.7610 | + | 65.4039i | −1.25800 | + | 2.17892i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −4.86167 | + | 21.8955i | −0.161786 | + | 0.728635i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 12.6084 | + | 21.8384i | 0.419118 | + | 0.725934i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.53884 | + | 6.12946i | −0.117505 | + | 0.203525i | −0.918778 | − | 0.394773i | \(-0.870823\pi\) |
0.801273 | + | 0.598299i | \(0.204156\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 26.8566 | + | 29.8750i | 0.890777 | + | 0.990891i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −23.6764 | − | 41.0088i | −0.784435 | − | 1.35868i | −0.929336 | − | 0.369235i | \(-0.879620\pi\) |
0.144901 | − | 0.989446i | \(-0.453714\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20.5804 | 0.681110 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −27.3405 | − | 12.1858i | −0.903850 | − | 0.402851i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.83291 | + | 2.50669i | −0.0935509 | + | 0.0827783i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 12.9752 | − | 22.4736i | 0.428011 | − | 0.741337i | −0.568685 | − | 0.822555i | \(-0.692548\pi\) |
0.996696 | + | 0.0812182i | \(0.0258811\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 34.2879 | − | 24.8908i | 1.12983 | − | 0.820181i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.31990 | − | 10.9464i | 0.208022 | − | 0.360305i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3.64748 | − | 6.31763i | −0.119929 | − | 0.207722i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −6.46649 | + | 1.36912i | −0.212387 | + | 0.0449680i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −5.32221 | −0.174616 | −0.0873080 | − | 0.996181i | \(-0.527826\pi\) | ||||
−0.0873080 | + | 0.996181i | \(0.527826\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −4.17064 | + | 34.0056i | −0.136687 | + | 1.11449i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −24.0782 | + | 17.4792i | −0.788286 | + | 0.572245i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −9.33682 | − | 16.1719i | −0.305347 | − | 0.528876i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.4266 | −0.993994 | −0.496997 | − | 0.867752i | \(-0.665564\pi\) | ||||
−0.496997 | + | 0.867752i | \(0.665564\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 22.2367 | − | 16.1424i | 0.725667 | − | 0.526788i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 21.7637 | 0.709476 | 0.354738 | − | 0.934966i | \(-0.384570\pi\) | ||||
0.354738 | + | 0.934966i | \(0.384570\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 25.3016 | 0.823932 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 29.8339 | + | 17.6187i | 0.970495 | + | 0.573135i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −34.8784 | −1.13339 | −0.566697 | − | 0.823926i | \(-0.691779\pi\) | ||||
−0.566697 | + | 0.823926i | \(0.691779\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −39.3642 | −1.27782 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −31.8531 | + | 23.1233i | −1.03291 | + | 0.749825i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 27.3744 | 0.886742 | 0.443371 | − | 0.896338i | \(-0.353782\pi\) | ||||
0.443371 | + | 0.896338i | \(0.353782\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −27.9732 | − | 48.4511i | −0.905193 | − | 1.56784i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.03843 | + | 4.38351i | −0.195195 | + | 0.141699i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −28.0684 | − | 9.38941i | −0.906375 | − | 0.303200i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −7.94838 | −0.256399 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −19.7868 | − | 22.0106i | −0.637620 | − | 0.709282i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −33.5396 | − | 58.0924i | −1.07968 | − | 1.87006i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.21327 | − | 12.4937i | 0.231963 | − | 0.401772i | −0.726423 | − | 0.687248i | \(-0.758819\pi\) |
0.958386 | + | 0.285476i | \(0.0921518\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −36.9921 | + | 26.8539i | −1.18836 | + | 0.862670i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −13.2592 | + | 22.9657i | −0.425509 | + | 0.737004i | −0.996468 | − | 0.0839752i | \(-0.973238\pi\) |
0.570959 | + | 0.820979i | \(0.306572\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 39.4942 | + | 13.2116i | 1.26613 | + | 0.423544i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −11.9758 | − | 5.33767i | −0.383532 | − | 0.170942i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −40.3733 | −1.29166 | −0.645829 | − | 0.763482i | \(-0.723488\pi\) | ||||
−0.645829 | + | 0.763482i | \(0.723488\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.78978 | − | 6.56408i | −0.121122 | − | 0.209789i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 9.05957 | − | 1.91815i | 0.289250 | − | 0.0612417i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 10.7299 | − | 18.5847i | 0.342230 | − | 0.592759i | −0.642617 | − | 0.766188i | \(-0.722151\pi\) |
0.984846 | + | 0.173429i | \(0.0554846\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.8150 | + | 22.1962i | 0.408319 | + | 0.707230i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −19.1020 | − | 17.5153i | −0.608023 | − | 0.557519i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 10.2177 | − | 17.6975i | 0.324903 | − | 0.562748i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 7.25341 | + | 12.5633i | 0.230412 | + | 0.399085i | 0.957929 | − | 0.287004i | \(-0.0926593\pi\) |
−0.727517 | + | 0.686089i | \(0.759326\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 33.9596 | − | 24.6525i | 1.07768 | − | 0.782323i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4.18975 | − | 7.25687i | 0.132824 | − | 0.230058i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.2204 | + | 31.5587i | −0.577047 | + | 0.999475i | 0.418769 | + | 0.908093i | \(0.362462\pi\) |
−0.995816 | + | 0.0913822i | \(0.970871\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 27.4227 | + | 5.86305i | 0.867616 | + | 0.185499i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))