Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [567,2,Mod(566,567)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(567, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("567.566");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 567 = 3^{4} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 567.c (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(4.52751779461\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 7x^{10} + 37x^{8} - 78x^{6} + 123x^{4} - 36x^{2} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 63) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 566.9 | ||
Root | \(-1.82904 + 1.05600i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 567.566 |
Dual form | 567.2.c.c.566.3 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/567\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(407\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.18593i | 0.838576i | 0.907853 | + | 0.419288i | \(0.137720\pi\) | ||||
−0.907853 | + | 0.419288i | \(0.862280\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.593579 | 0.296790 | ||||||||
\(5\) | −2.83797 | −1.26918 | −0.634590 | − | 0.772849i | \(-0.718831\pi\) | ||||
−0.634590 | + | 0.772849i | \(0.718831\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.46050 | − | 0.972582i | 0.929983 | − | 0.367601i | ||||
\(8\) | 3.07579i | 1.08746i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − | 3.36562i | − | 1.06430i | ||||||
\(11\) | 0.157816i | 0.0475835i | 0.999717 | + | 0.0237917i | \(0.00757386\pi\) | ||||
−0.999717 | + | 0.0237917i | \(0.992426\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.94293i | 1.09357i | 0.837272 | + | 0.546786i | \(0.184149\pi\) | ||||
−0.837272 | + | 0.546786i | \(0.815851\pi\) | |||||||
\(14\) | 1.15341 | + | 2.91798i | 0.308262 | + | 0.779862i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.46050 | −0.615126 | ||||||||
\(17\) | 4.14487 | 1.00528 | 0.502640 | − | 0.864496i | \(-0.332362\pi\) | ||||
0.502640 | + | 0.864496i | \(0.332362\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.33597i | 1.45357i | 0.686864 | + | 0.726786i | \(0.258987\pi\) | ||||
−0.686864 | + | 0.726786i | \(0.741013\pi\) | |||||||
\(20\) | −1.68456 | −0.376679 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.187159 | −0.0399024 | ||||||||
\(23\) | − | 0.546125i | − | 0.113875i | −0.998378 | − | 0.0569374i | \(-0.981866\pi\) | ||
0.998378 | − | 0.0569374i | \(-0.0181336\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 3.05408 | 0.610817 | ||||||||
\(26\) | −4.67602 | −0.917044 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.46050 | − | 0.577305i | 0.276009 | − | 0.109100i | ||||
\(29\) | 4.65003i | 0.863488i | 0.901996 | + | 0.431744i | \(0.142102\pi\) | ||||
−0.901996 | + | 0.431744i | \(0.857898\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 0.129426i | − | 0.0232456i | −0.999932 | − | 0.0116228i | \(-0.996300\pi\) | ||
0.999932 | − | 0.0116228i | \(-0.00369973\pi\) | |||||||
\(32\) | 3.23361i | 0.571627i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 4.91551i | 0.843003i | ||||||||
\(35\) | −6.98284 | + | 2.76016i | −1.18032 | + | 0.466552i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.46050 | −0.404505 | −0.202252 | − | 0.979333i | \(-0.564826\pi\) | ||||
−0.202252 | + | 0.979333i | \(0.564826\pi\) | |||||||
\(38\) | −7.51399 | −1.21893 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 8.72902i | − | 1.38018i | ||||||
\(41\) | 3.99138 | 0.623349 | 0.311675 | − | 0.950189i | \(-0.399110\pi\) | ||||
0.311675 | + | 0.950189i | \(0.399110\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −6.56867 | −1.00171 | −0.500857 | − | 0.865530i | \(-0.666982\pi\) | ||||
−0.500857 | + | 0.865530i | \(0.666982\pi\) | |||||||
\(44\) | 0.0936766i | 0.0141223i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.647664 | 0.0954928 | ||||||||
\(47\) | 8.66741 | 1.26427 | 0.632135 | − | 0.774858i | \(-0.282179\pi\) | ||||
0.632135 | + | 0.774858i | \(0.282179\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.10817 | − | 4.78609i | 0.729738 | − | 0.683727i | ||||
\(50\) | 3.62192i | 0.512217i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.34044i | 0.324561i | ||||||||
\(53\) | − | 2.60234i | − | 0.357459i | −0.983898 | − | 0.178730i | \(-0.942801\pi\) | ||
0.983898 | − | 0.178730i | \(-0.0571988\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.447879i | − | 0.0603920i | ||||||
\(56\) | 2.99146 | + | 7.56800i | 0.399751 | + | 1.01132i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −5.51459 | −0.724101 | ||||||||
\(59\) | −3.61372 | −0.470466 | −0.235233 | − | 0.971939i | \(-0.575585\pi\) | ||||
−0.235233 | + | 0.971939i | \(0.575585\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 3.36562i | − | 0.430924i | −0.976512 | − | 0.215462i | \(-0.930874\pi\) | ||
0.976512 | − | 0.215462i | \(-0.0691258\pi\) | |||||||
\(62\) | 0.153489 | 0.0194932 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −8.75583 | −1.09448 | ||||||||
\(65\) | − | 11.1899i | − | 1.38794i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.32743 | 0.162171 | 0.0810857 | − | 0.996707i | \(-0.474161\pi\) | ||||
0.0810857 | + | 0.996707i | \(0.474161\pi\) | |||||||
\(68\) | 2.46031 | 0.298356 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.27335 | − | 8.28114i | −0.391240 | − | 0.989785i | ||||
\(71\) | − | 0.409310i | − | 0.0485761i | −0.999705 | − | 0.0242881i | \(-0.992268\pi\) | ||
0.999705 | − | 0.0242881i | \(-0.00773189\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 15.0124i | − | 1.75707i | −0.477681 | − | 0.878533i | \(-0.658522\pi\) | ||
0.477681 | − | 0.878533i | \(-0.341478\pi\) | |||||||
\(74\) | − | 2.91798i | − | 0.339208i | ||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.76090i | 0.431405i | ||||||||
\(77\) | 0.153489 | + | 0.388308i | 0.0174917 | + | 0.0442518i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.32743 | 0.486874 | 0.243437 | − | 0.969917i | \(-0.421725\pi\) | ||||
0.243437 | + | 0.969917i | \(0.421725\pi\) | |||||||
\(80\) | 6.98284 | 0.780706 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.73348i | 0.522726i | ||||||||
\(83\) | −6.45169 | −0.708165 | −0.354083 | − | 0.935214i | \(-0.615207\pi\) | ||||
−0.354083 | + | 0.935214i | \(0.615207\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.7630 | −1.27588 | ||||||||
\(86\) | − | 7.78996i | − | 0.840013i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.485411 | −0.0517450 | ||||||||
\(89\) | 5.05368 | 0.535689 | 0.267845 | − | 0.963462i | \(-0.413689\pi\) | ||||
0.267845 | + | 0.963462i | \(0.413689\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.83482 | + | 9.70160i | 0.401999 | + | 1.01700i | ||||
\(92\) | − | 0.324168i | − | 0.0337969i | ||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 10.2789i | 1.06019i | ||||||||
\(95\) | − | 17.9813i | − | 1.84484i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 2.52247i | − | 0.256118i | −0.991767 | − | 0.128059i | \(-0.959125\pi\) | ||
0.991767 | − | 0.128059i | \(-0.0408747\pi\) | |||||||
\(98\) | 5.67594 | + | 6.05791i | 0.573357 | + | 0.611941i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.81284 | 0.181284 | ||||||||
\(101\) | −2.99146 | −0.297662 | −0.148831 | − | 0.988863i | \(-0.547551\pi\) | ||||
−0.148831 | + | 0.988863i | \(0.547551\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 13.1966i | 1.30030i | 0.759804 | + | 0.650152i | \(0.225295\pi\) | ||||
−0.759804 | + | 0.650152i | \(0.774705\pi\) | |||||||
\(104\) | −12.1276 | −1.18921 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.08619 | 0.299757 | ||||||||
\(107\) | − | 19.5555i | − | 1.89051i | −0.326339 | − | 0.945253i | \(-0.605815\pi\) | ||
0.326339 | − | 0.945253i | \(-0.394185\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 13.2484 | 1.26897 | 0.634485 | − | 0.772935i | \(-0.281212\pi\) | ||||
0.634485 | + | 0.772935i | \(0.281212\pi\) | |||||||
\(110\) | 0.531151 | 0.0506433 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −6.05408 | + | 2.39304i | −0.572057 | + | 0.226121i | ||||
\(113\) | 10.0767i | 0.947934i | 0.880543 | + | 0.473967i | \(0.157178\pi\) | ||||
−0.880543 | + | 0.473967i | \(0.842822\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.54989i | 0.144528i | ||||||||
\(116\) | 2.76016i | 0.256274i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | − | 4.28561i | − | 0.394522i | ||||||
\(119\) | 10.1985 | − | 4.03123i | 0.934893 | − | 0.369542i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 10.9751 | 0.997736 | ||||||||
\(122\) | 3.99138 | 0.361363 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 0.0768245i | − | 0.00689904i | ||||||
\(125\) | 5.52245 | 0.493943 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −12.4897 | −1.10828 | −0.554140 | − | 0.832423i | \(-0.686953\pi\) | ||||
−0.554140 | + | 0.832423i | \(0.686953\pi\) | |||||||
\(128\) | − | 3.91655i | − | 0.346177i | ||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 13.2704 | 1.16389 | ||||||||
\(131\) | 10.0450 | 0.877635 | 0.438817 | − | 0.898576i | \(-0.355398\pi\) | ||||
0.438817 | + | 0.898576i | \(0.355398\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.16225 | + | 15.5897i | 0.534335 | + | 1.35180i | ||||
\(134\) | 1.57423i | 0.135993i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 12.7488i | 1.09320i | ||||||||
\(137\) | − | 8.04145i | − | 0.687028i | −0.939148 | − | 0.343514i | \(-0.888383\pi\) | ||
0.939148 | − | 0.343514i | \(-0.111617\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 18.9027i | − | 1.60331i | −0.597789 | − | 0.801654i | \(-0.703954\pi\) | ||
0.597789 | − | 0.801654i | \(-0.296046\pi\) | |||||||
\(140\) | −4.14487 | + | 1.63837i | −0.350306 | + | 0.138468i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0.485411 | 0.0407348 | ||||||||
\(143\) | −0.622259 | −0.0520359 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 13.1966i | − | 1.09592i | ||||||
\(146\) | 17.8036 | 1.47343 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.46050 | −0.120053 | ||||||||
\(149\) | − | 19.4063i | − | 1.58982i | −0.606725 | − | 0.794912i | \(-0.707517\pi\) | ||
0.606725 | − | 0.794912i | \(-0.292483\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1.78794 | −0.145500 | −0.0727501 | − | 0.997350i | \(-0.523178\pi\) | ||||
−0.0727501 | + | 0.997350i | \(0.523178\pi\) | |||||||
\(152\) | −19.4881 | −1.58070 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.460505 | + | 0.182027i | −0.0371085 | + | 0.0146682i | ||||
\(155\) | 0.367307i | 0.0295028i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 4.39081i | − | 0.350425i | −0.984531 | − | 0.175212i | \(-0.943939\pi\) | ||
0.984531 | − | 0.175212i | \(-0.0560612\pi\) | |||||||
\(158\) | 5.13201i | 0.408281i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − | 9.17689i | − | 0.725497i | ||||||
\(161\) | −0.531151 | − | 1.34374i | −0.0418606 | − | 0.105902i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.43560 | 0.425749 | 0.212874 | − | 0.977080i | \(-0.431717\pi\) | ||||
0.212874 | + | 0.977080i | \(0.431717\pi\) | |||||||
\(164\) | 2.36920 | 0.185004 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 7.65123i | − | 0.593851i | ||||||
\(167\) | 10.5055 | 0.812937 | 0.406468 | − | 0.913665i | \(-0.366760\pi\) | ||||
0.406468 | + | 0.913665i | \(0.366760\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.54669 | −0.195899 | ||||||||
\(170\) | − | 13.9501i | − | 1.06992i | ||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.89903 | −0.297298 | ||||||||
\(173\) | −17.5590 | −1.33498 | −0.667492 | − | 0.744617i | \(-0.732632\pi\) | ||||
−0.667492 | + | 0.744617i | \(0.732632\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 7.51459 | − | 2.97035i | 0.568050 | − | 0.224537i | ||||
\(176\) | − | 0.388308i | − | 0.0292698i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 5.99330i | 0.449217i | ||||||||
\(179\) | − | 18.2033i | − | 1.36058i | −0.732945 | − | 0.680288i | \(-0.761855\pi\) | ||
0.732945 | − | 0.680288i | \(-0.238145\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.60182i | 0.490710i | 0.969433 | + | 0.245355i | \(0.0789045\pi\) | ||||
−0.969433 | + | 0.245355i | \(0.921096\pi\) | |||||||
\(182\) | −11.5054 | + | 4.54782i | −0.852835 | + | 0.337107i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.67977 | 0.123834 | ||||||||
\(185\) | 6.98284 | 0.513389 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.654129i | 0.0478347i | ||||||||
\(188\) | 5.14479 | 0.375223 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 21.3245 | 1.54704 | ||||||||
\(191\) | − | 14.2101i | − | 1.02821i | −0.857728 | − | 0.514104i | \(-0.828125\pi\) | ||
0.857728 | − | 0.514104i | \(-0.171875\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −10.0043 | −0.720123 | −0.360062 | − | 0.932929i | \(-0.617244\pi\) | ||||
−0.360062 | + | 0.932929i | \(0.617244\pi\) | |||||||
\(194\) | 2.99146 | 0.214774 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 3.03210 | − | 2.84092i | 0.216579 | − | 0.202923i | ||||
\(197\) | 20.1017i | 1.43218i | 0.698006 | + | 0.716092i | \(0.254071\pi\) | ||||
−0.698006 | + | 0.716092i | \(0.745929\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 12.9378i | 0.917136i | 0.888659 | + | 0.458568i | \(0.151637\pi\) | ||||
−0.888659 | + | 0.458568i | \(0.848363\pi\) | |||||||
\(200\) | 9.39373i | 0.664237i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − | 3.54765i | − | 0.249612i | ||||||
\(203\) | 4.52253 | + | 11.4414i | 0.317420 | + | 0.803030i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −11.3274 | −0.791142 | ||||||||
\(206\) | −15.6502 | −1.09040 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | − | 9.70160i | − | 0.672685i | ||||||
\(209\) | −0.999921 | −0.0691660 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.01439 | 0.620577 | 0.310288 | − | 0.950643i | \(-0.399574\pi\) | ||||
0.310288 | + | 0.950643i | \(0.399574\pi\) | |||||||
\(212\) | − | 1.54470i | − | 0.106090i | ||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 23.1914 | 1.58533 | ||||||||
\(215\) | 18.6417 | 1.27135 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.125877 | − | 0.318453i | −0.00854510 | − | 0.0216180i | ||||
\(218\) | 15.7117i | 1.06413i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | − | 0.265852i | − | 0.0179237i | ||||||
\(221\) | 16.3429i | 1.09934i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 2.25662i | − | 0.151114i | −0.997141 | − | 0.0755571i | \(-0.975926\pi\) | ||
0.997141 | − | 0.0755571i | \(-0.0240735\pi\) | |||||||
\(224\) | 3.14495 | + | 7.95631i | 0.210131 | + | 0.531604i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −11.9502 | −0.794915 | ||||||||
\(227\) | 18.6417 | 1.23729 | 0.618647 | − | 0.785669i | \(-0.287681\pi\) | ||||
0.618647 | + | 0.785669i | \(0.287681\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 14.3057i | 0.945344i | 0.881238 | + | 0.472672i | \(0.156711\pi\) | ||||
−0.881238 | + | 0.472672i | \(0.843289\pi\) | |||||||
\(230\) | −1.83805 | −0.121197 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −14.3025 | −0.939007 | ||||||||
\(233\) | 17.0679i | 1.11815i | 0.829116 | + | 0.559077i | \(0.188844\pi\) | ||||
−0.829116 | + | 0.559077i | \(0.811156\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −24.5979 | −1.60459 | ||||||||
\(236\) | −2.14503 | −0.139630 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.78074 | + | 12.0946i | 0.309889 | + | 0.783979i | ||||
\(239\) | − | 2.23504i | − | 0.144573i | −0.997384 | − | 0.0722863i | \(-0.976970\pi\) | ||
0.997384 | − | 0.0722863i | \(-0.0230295\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 4.52023i | − | 0.291174i | −0.989345 | − | 0.145587i | \(-0.953493\pi\) | ||
0.989345 | − | 0.145587i | \(-0.0465070\pi\) | |||||||
\(242\) | 13.0157i | 0.836678i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − | 1.99777i | − | 0.127894i | ||||||
\(245\) | −14.4968 | + | 13.5828i | −0.926169 | + | 0.867772i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −24.9823 | −1.58959 | ||||||||
\(248\) | 0.398087 | 0.0252786 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 6.54922i | 0.414209i | ||||||||
\(251\) | −21.1727 | −1.33641 | −0.668205 | − | 0.743978i | \(-0.732937\pi\) | ||||
−0.668205 | + | 0.743978i | \(0.732937\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.0861875 | 0.00541856 | ||||||||
\(254\) | − | 14.8118i | − | 0.929378i | ||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −12.8669 | −0.804183 | ||||||||
\(257\) | −31.3005 | −1.95247 | −0.976236 | − | 0.216712i | \(-0.930467\pi\) | ||||
−0.976236 | + | 0.216712i | \(0.930467\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −6.05408 | + | 2.39304i | −0.376182 | + | 0.148696i | ||||
\(260\) | − | 6.64211i | − | 0.411926i | ||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 11.9126i | 0.735964i | ||||||||
\(263\) | − | 6.67671i | − | 0.411704i | −0.978583 | − | 0.205852i | \(-0.934004\pi\) | ||
0.978583 | − | 0.205852i | \(-0.0659965\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.38538i | 0.453680i | ||||||||
\(266\) | −18.4882 | + | 7.30798i | −1.13359 | + | 0.448081i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0.787935 | 0.0481308 | ||||||||
\(269\) | −10.6589 | −0.649887 | −0.324944 | − | 0.945733i | \(-0.605345\pi\) | ||||
−0.324944 | + | 0.945733i | \(0.605345\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 7.44498i | − | 0.452250i | −0.974098 | − | 0.226125i | \(-0.927394\pi\) | ||
0.974098 | − | 0.226125i | \(-0.0726058\pi\) | |||||||
\(272\) | −10.1985 | −0.618373 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 9.53657 | 0.576125 | ||||||||
\(275\) | 0.481985i | 0.0290648i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −26.5586 | −1.59575 | −0.797874 | − | 0.602824i | \(-0.794042\pi\) | ||||
−0.797874 | + | 0.602824i | \(0.794042\pi\) | |||||||
\(278\) | 22.4172 | 1.34450 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −8.48968 | − | 21.4778i | −0.507356 | − | 1.28354i | ||||
\(281\) | 24.3634i | 1.45340i | 0.686956 | + | 0.726699i | \(0.258946\pi\) | ||||
−0.686956 | + | 0.726699i | \(0.741054\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 8.65219i | − | 0.514319i | −0.966369 | − | 0.257160i | \(-0.917213\pi\) | ||
0.966369 | − | 0.257160i | \(-0.0827866\pi\) | |||||||
\(284\) | − | 0.242958i | − | 0.0144169i | ||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | − | 0.737954i | − | 0.0436361i | ||||||
\(287\) | 9.82082 | − | 3.88195i | 0.579704 | − | 0.229144i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 0.179961 | 0.0105860 | ||||||||
\(290\) | 15.6502 | 0.919014 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − | 8.91104i | − | 0.521479i | ||||||
\(293\) | −8.80047 | −0.514129 | −0.257064 | − | 0.966394i | \(-0.582755\pi\) | ||||
−0.257064 | + | 0.966394i | \(0.582755\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 10.2556 | 0.597106 | ||||||||
\(296\) | − | 7.56800i | − | 0.439881i | ||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 23.0144 | 1.33319 | ||||||||
\(299\) | 2.15333 | 0.124530 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −16.1623 | + | 6.38857i | −0.931577 | + | 0.368231i | ||||
\(302\) | − | 2.12036i | − | 0.122013i | ||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 15.5897i | − | 0.894130i | ||||||
\(305\) | 9.55155i | 0.546920i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 11.1747i | − | 0.637771i | −0.947793 | − | 0.318886i | \(-0.896691\pi\) | ||
0.947793 | − | 0.318886i | \(-0.103309\pi\) | |||||||
\(308\) | 0.0911082 | + | 0.230492i | 0.00519137 | + | 0.0131335i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.435599 | −0.0247404 | ||||||||
\(311\) | −16.4056 | −0.930275 | −0.465137 | − | 0.885239i | \(-0.653995\pi\) | ||||
−0.465137 | + | 0.885239i | \(0.653995\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 8.20431i | − | 0.463735i | −0.972747 | − | 0.231868i | \(-0.925516\pi\) | ||
0.972747 | − | 0.231868i | \(-0.0744836\pi\) | |||||||
\(314\) | 5.20717 | 0.293858 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.56867 | 0.144499 | ||||||||
\(317\) | 22.9124i | 1.28689i | 0.765494 | + | 0.643443i | \(0.222495\pi\) | ||||
−0.765494 | + | 0.643443i | \(0.777505\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.733851 | −0.0410878 | ||||||||
\(320\) | 24.8488 | 1.38909 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1.59358 | − | 0.629906i | 0.0888067 | − | 0.0351033i | ||||
\(323\) | 26.2618i | 1.46125i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 12.0420i | 0.667972i | ||||||||
\(326\) | 6.44622i | 0.357023i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 12.2767i | 0.677866i | ||||||||
\(329\) | 21.3262 | − | 8.42976i | 1.17575 | − | 0.464748i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 19.2632 | 1.05880 | 0.529401 | − | 0.848372i | \(-0.322417\pi\) | ||||
0.529401 | + | 0.848372i | \(0.322417\pi\) | |||||||
\(332\) | −3.82959 | −0.210176 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 12.4587i | 0.681709i | ||||||||
\(335\) | −3.76721 | −0.205825 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4.53657 | 0.247123 | 0.123561 | − | 0.992337i | \(-0.460568\pi\) | ||||
0.123561 | + | 0.992337i | \(0.460568\pi\) | |||||||
\(338\) | − | 3.02019i | − | 0.164277i | ||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.98229 | −0.378668 | ||||||||
\(341\) | 0.0204255 | 0.00110610 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.91381 | − | 16.7443i | 0.427306 | − | 0.904107i | ||||
\(344\) | − | 20.2039i | − | 1.08932i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − | 20.8237i | − | 1.11949i | ||||||
\(347\) | − | 8.73293i | − | 0.468808i | −0.972139 | − | 0.234404i | \(-0.924686\pi\) | ||
0.972139 | − | 0.234404i | \(-0.0753139\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.04047i | 0.483925i | 0.970286 | + | 0.241963i | \(0.0777911\pi\) | ||||
−0.970286 | + | 0.241963i | \(0.922209\pi\) | |||||||
\(350\) | 3.52261 | + | 8.91175i | 0.188292 | + | 0.476353i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.510317 | −0.0272000 | ||||||||
\(353\) | −1.21579 | −0.0647101 | −0.0323550 | − | 0.999476i | \(-0.510301\pi\) | ||||
−0.0323550 | + | 0.999476i | \(0.510301\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.16161i | 0.0616518i | ||||||||
\(356\) | 2.99976 | 0.158987 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 21.5877 | 1.14095 | ||||||||
\(359\) | − | 17.3069i | − | 0.913424i | −0.889615 | − | 0.456712i | \(-0.849027\pi\) | ||
0.889615 | − | 0.456712i | \(-0.150973\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −21.1445 | −1.11287 | ||||||||
\(362\) | −7.82927 | −0.411498 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.27627 | + | 5.75867i | 0.119309 | + | 0.301836i | ||||
\(365\) | 42.6047i | 2.23003i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 28.2090i | − | 1.47250i | −0.676710 | − | 0.736250i | \(-0.736595\pi\) | ||
0.676710 | − | 0.736250i | \(-0.263405\pi\) | |||||||
\(368\) | 1.34374i | 0.0700474i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8.28114i | 0.430516i | ||||||||
\(371\) | −2.53099 | − | 6.40308i | −0.131403 | − | 0.332431i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 28.2527 | 1.46287 | 0.731435 | − | 0.681911i | \(-0.238851\pi\) | ||||
0.731435 | + | 0.681911i | \(0.238851\pi\) | |||||||
\(374\) | −0.775749 | −0.0401130 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 26.6591i | 1.37484i | ||||||||
\(377\) | −18.3347 | −0.944287 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.6447 | 0.752250 | 0.376125 | − | 0.926569i | \(-0.377256\pi\) | ||||
0.376125 | + | 0.926569i | \(0.377256\pi\) | |||||||
\(380\) | − | 10.6733i | − | 0.547531i | ||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 16.8521 | 0.862231 | ||||||||
\(383\) | −24.7864 | −1.26653 | −0.633264 | − | 0.773936i | \(-0.718285\pi\) | ||||
−0.633264 | + | 0.773936i | \(0.718285\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.435599 | − | 1.10201i | −0.0222002 | − | 0.0561635i | ||||
\(386\) | − | 11.8643i | − | 0.603878i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − | 1.49729i | − | 0.0760131i | ||||||
\(389\) | 5.12348i | 0.259771i | 0.991529 | + | 0.129885i | \(0.0414609\pi\) | ||||
−0.991529 | + | 0.129885i | \(0.958539\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 2.26362i | − | 0.114476i | ||||||
\(392\) | 14.7210 | + | 15.7117i | 0.743523 | + | 0.793559i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −23.8391 | −1.20100 | ||||||||
\(395\) | −12.2811 | −0.617930 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.92094i | 0.0964093i | 0.998837 | + | 0.0482046i | \(0.0153500\pi\) | ||||
−0.998837 | + | 0.0482046i | \(0.984650\pi\) | |||||||
\(398\) | −15.3433 | −0.769089 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −7.51459 | −0.375729 | ||||||||
\(401\) | 14.3889i | 0.718549i | 0.933232 | + | 0.359274i | \(0.116976\pi\) | ||||
−0.933232 | + | 0.359274i | \(0.883024\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.510317 | 0.0254207 | ||||||||
\(404\) | −1.77567 | −0.0883429 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −13.5687 | + | 5.36339i | −0.673402 | + | 0.266181i | ||||
\(407\) | − | 0.388308i | − | 0.0192477i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 9.72582i | − | 0.480911i | −0.970660 | − | 0.240455i | \(-0.922703\pi\) | ||
0.970660 | − | 0.240455i | \(-0.0772968\pi\) | |||||||
\(410\) | − | 13.4335i | − | 0.663433i | ||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 7.83326i | 0.385917i | ||||||||
\(413\) | −8.89158 | + | 3.51464i | −0.437526 | + | 0.172944i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 18.3097 | 0.898789 | ||||||||
\(416\) | −12.7499 | −0.625115 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | − | 1.18583i | − | 0.0580010i | ||||||
\(419\) | 29.9025 | 1.46083 | 0.730416 | − | 0.683002i | \(-0.239326\pi\) | ||||
0.730416 | + | 0.683002i | \(0.239326\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 25.0905 | 1.22283 | 0.611417 | − | 0.791309i | \(-0.290600\pi\) | ||||
0.611417 | + | 0.791309i | \(0.290600\pi\) | |||||||
\(422\) | 10.6904i | 0.520401i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.00427 | 0.388722 | ||||||||
\(425\) | 12.6588 | 0.614041 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −3.27335 | − | 8.28114i | −0.158408 | − | 0.400752i | ||||
\(428\) | − | 11.6078i | − | 0.561083i | ||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 22.1077i | 1.06613i | ||||||||
\(431\) | − | 6.39061i | − | 0.307825i | −0.988084 | − | 0.153913i | \(-0.950813\pi\) | ||
0.988084 | − | 0.153913i | \(-0.0491874\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 33.1771i | 1.59439i | 0.603721 | + | 0.797196i | \(0.293684\pi\) | ||||
−0.603721 | + | 0.797196i | \(0.706316\pi\) | |||||||
\(434\) | 0.377662 | − | 0.149281i | 0.0181283 | − | 0.00716572i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 7.86400 | 0.376617 | ||||||||
\(437\) | 3.46023 | 0.165525 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.46316i | 0.403925i | 0.979393 | + | 0.201962i | \(0.0647319\pi\) | ||||
−0.979393 | + | 0.201962i | \(0.935268\pi\) | |||||||
\(440\) | 1.37758 | 0.0656737 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −19.3815 | −0.921885 | ||||||||
\(443\) | 18.6001i | 0.883718i | 0.897085 | + | 0.441859i | \(0.145681\pi\) | ||||
−0.897085 | + | 0.441859i | \(0.854319\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −14.3422 | −0.679886 | ||||||||
\(446\) | 2.67618 | 0.126721 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −21.5438 | + | 8.51576i | −1.01785 | + | 0.402332i | ||||
\(449\) | − | 20.3100i | − | 0.958489i | −0.877681 | − | 0.479245i | \(-0.840911\pi\) | ||
0.877681 | − | 0.479245i | \(-0.159089\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0.629906i | 0.0296611i | ||||||||
\(452\) | 5.98130i | 0.281337i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 22.1077i | 1.03757i | ||||||||
\(455\) | −10.8831 | − | 27.5329i | −0.510208 | − | 1.29076i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11.3566 | 0.531240 | 0.265620 | − | 0.964078i | \(-0.414423\pi\) | ||||
0.265620 | + | 0.964078i | \(0.414423\pi\) | |||||||
\(458\) | −16.9654 | −0.792743 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.919981i | 0.0428943i | ||||||||
\(461\) | 38.9967 | 1.81626 | 0.908129 | − | 0.418691i | \(-0.137511\pi\) | ||||
0.908129 | + | 0.418691i | \(0.137511\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.0689 | 0.467940 | 0.233970 | − | 0.972244i | \(-0.424828\pi\) | ||||
0.233970 | + | 0.972244i | \(0.424828\pi\) | |||||||
\(464\) | − | 11.4414i | − | 0.531154i | ||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −20.2412 | −0.937657 | ||||||||
\(467\) | 3.59330 | 0.166278 | 0.0831389 | − | 0.996538i | \(-0.473505\pi\) | ||||
0.0831389 | + | 0.996538i | \(0.473505\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.26615 | − | 1.29103i | 0.150817 | − | 0.0596145i | ||||
\(470\) | − | 29.1712i | − | 1.34557i | ||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | − | 11.1151i | − | 0.511612i | ||||||
\(473\) | − | 1.03664i | − | 0.0476650i | ||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 19.3506i | 0.887866i | ||||||||
\(476\) | 6.05361 | − | 2.39285i | 0.277467 | − | 0.109676i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.65059 | 0.121235 | ||||||||
\(479\) | −1.62218 | −0.0741193 | −0.0370597 | − | 0.999313i | \(-0.511799\pi\) | ||||
−0.0370597 | + | 0.999313i | \(0.511799\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 9.70160i | − | 0.442355i | ||||||
\(482\) | 5.36066 | 0.244172 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 6.51459 | 0.296118 | ||||||||
\(485\) | 7.15869i | 0.325060i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 7.99573 | 0.362321 | 0.181161 | − | 0.983454i | \(-0.442015\pi\) | ||||
0.181161 | + | 0.983454i | \(0.442015\pi\) | |||||||
\(488\) | 10.3520 | 0.468612 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −16.1082 | − | 17.1922i | −0.727693 | − | 0.776663i | ||||
\(491\) | − | 10.7460i | − | 0.484961i | −0.970156 | − | 0.242480i | \(-0.922039\pi\) | ||
0.970156 | − | 0.242480i | \(-0.0779610\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.2738i | 0.868047i | ||||||||
\(494\) | − | 29.6272i | − | 1.33299i | ||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0.318453i | 0.0142990i | ||||||||
\(497\) | −0.398087 | − | 1.00711i | −0.0178566 | − | 0.0451750i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 16.9210 | 0.757488 | 0.378744 | − | 0.925501i | \(-0.376356\pi\) | ||||
0.378744 | + | 0.925501i | \(0.376356\pi\) | |||||||
\(500\) | 3.27801 | 0.146597 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | − | 25.1093i | − | 1.12068i | ||||||
\(503\) | 33.9226 | 1.51253 | 0.756267 | − | 0.654263i | \(-0.227021\pi\) | ||||
0.756267 | + | 0.654263i | \(0.227021\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 8.48968 | 0.377786 | ||||||||
\(506\) | 0.102212i | 0.00454388i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −7.41362 | −0.328926 | ||||||||
\(509\) | 10.1361 | 0.449275 | 0.224637 | − | 0.974442i | \(-0.427880\pi\) | ||||
0.224637 | + | 0.974442i | \(0.427880\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −14.6008 | − | 36.9380i | −0.645900 | − | 1.63404i | ||||
\(512\) | − | 23.0923i | − | 1.02055i | ||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | − | 37.1201i | − | 1.63730i | ||||||
\(515\) | − | 37.4517i | − | 1.65032i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.36786i | 0.0601584i | ||||||||
\(518\) | −2.83797 | − | 7.17970i | −0.124693 | − | 0.315458i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 34.4179 | 1.50932 | ||||||||
\(521\) | 31.6986 | 1.38874 | 0.694370 | − | 0.719618i | \(-0.255683\pi\) | ||||
0.694370 | + | 0.719618i | \(0.255683\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8.09911i | 0.354149i | 0.984197 | + | 0.177075i | \(0.0566634\pi\) | ||||
−0.984197 | + | 0.177075i | \(0.943337\pi\) | |||||||
\(524\) | 5.96250 | 0.260473 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.91808 | 0.345245 | ||||||||
\(527\) | − | 0.536454i | − | 0.0233683i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 22.7017 | 0.987033 | ||||||||
\(530\) | −8.75851 | −0.380446 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.65779 | + | 9.25372i | 0.158585 | + | 0.401200i | ||||
\(533\) | 15.7377i | 0.681677i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 55.4981i | 2.39939i | ||||||||
\(536\) | 4.08290i | 0.176354i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − | 12.6407i | − | 0.544980i | ||||||
\(539\) | 0.755323 | + | 0.806153i | 0.0325341 | + | 0.0347235i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.21634 | 0.0522944 | 0.0261472 | − | 0.999658i | \(-0.491676\pi\) | ||||
0.0261472 | + | 0.999658i | \(0.491676\pi\) | |||||||
\(542\) | 8.82920 | 0.379246 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 13.4029i | 0.574645i | ||||||||
\(545\) | −37.5987 | −1.61055 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −26.2556 | −1.12261 | −0.561305 | − | 0.827609i | \(-0.689701\pi\) | ||||
−0.561305 | + | 0.827609i | \(0.689701\pi\) | |||||||
\(548\) | − | 4.77324i | − | 0.203903i | ||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −0.571598 | −0.0243730 | ||||||||
\(551\) | −29.4624 | −1.25514 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 10.6477 | − | 4.20878i | 0.452785 | − | 0.178976i | ||||
\(554\) | − | 31.4965i | − | 1.33816i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − | 11.2203i | − | 0.475845i | ||||||
\(557\) | 27.2172i | 1.15323i | 0.817016 | + | 0.576615i | \(0.195627\pi\) | ||||
−0.817016 | + | 0.576615i | \(0.804373\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 25.8998i | − | 1.09545i | ||||||
\(560\) | 17.1813 | − | 6.79139i | 0.726043 | − | 0.286989i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −28.8932 | −1.21879 | ||||||||
\(563\) | 9.36035 | 0.394492 | 0.197246 | − | 0.980354i | \(-0.436800\pi\) | ||||
0.197246 | + | 0.980354i | \(0.436800\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 28.5973i | − | 1.20310i | ||||||
\(566\) | 10.2609 | 0.431296 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.25895 | 0.0528244 | ||||||||
\(569\) | − | 34.9209i | − | 1.46396i | −0.681326 | − | 0.731980i | \(-0.738596\pi\) | ||
0.681326 | − | 0.731980i | \(-0.261404\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.47197 | −0.0616002 | −0.0308001 | − | 0.999526i | \(-0.509806\pi\) | ||||
−0.0308001 | + | 0.999526i | \(0.509806\pi\) | |||||||
\(572\) | −0.369360 | −0.0154437 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.60370 | + | 11.6468i | 0.192155 | + | 0.486126i | ||||
\(575\) | − | 1.66791i | − | 0.0695567i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 18.6196i | − | 0.775146i | −0.921839 | − | 0.387573i | \(-0.873314\pi\) | ||
0.921839 | − | 0.387573i | \(-0.126686\pi\) | |||||||
\(578\) | 0.213421i | 0.00887714i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | − | 7.83326i | − | 0.325258i | ||||||
\(581\) | −15.8744 | + | 6.27480i | −0.658582 | + | 0.260323i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0.410693 | 0.0170092 | ||||||||
\(584\) | 46.1750 | 1.91073 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − | 10.4367i | − | 0.431136i | ||||||
\(587\) | −18.5710 | −0.766508 | −0.383254 | − | 0.923643i | \(-0.625197\pi\) | ||||
−0.383254 | + | 0.923643i | \(0.625197\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.820039 | 0.0337891 | ||||||||
\(590\) | 12.1624i | 0.500719i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 6.05408 | 0.248821 | ||||||||
\(593\) | −30.9228 | −1.26985 | −0.634924 | − | 0.772574i | \(-0.718969\pi\) | ||||
−0.634924 | + | 0.772574i | \(0.718969\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −28.9430 | + | 11.4405i | −1.18655 | + | 0.469015i | ||||
\(596\) | − | 11.5192i | − | 0.471843i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.55369i | 0.104428i | ||||||||
\(599\) | − | 13.7111i | − | 0.560219i | −0.959968 | − | 0.280109i | \(-0.909629\pi\) | ||
0.959968 | − | 0.280109i | \(-0.0903707\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 19.7529i | − | 0.805736i | −0.915258 | − | 0.402868i | \(-0.868013\pi\) | ||
0.915258 | − | 0.402868i | \(-0.131987\pi\) | |||||||
\(602\) | −7.57638 | − | 19.1672i | −0.308790 | − | 0.781198i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.06128 | −0.0431829 | ||||||||
\(605\) | −31.1470 | −1.26631 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 17.9231i | 0.727477i | 0.931501 | + | 0.363739i | \(0.118500\pi\) | ||||
−0.931501 | + | 0.363739i | \(0.881500\pi\) | |||||||
\(608\) | −20.4881 | −0.830901 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −11.3274 | −0.458634 | ||||||||
\(611\) | 34.1750i | 1.38257i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −41.4327 | −1.67345 | −0.836725 | − | 0.547623i | \(-0.815533\pi\) | ||||
−0.836725 | + | 0.547623i | \(0.815533\pi\) | |||||||
\(614\) | 13.2523 | 0.534820 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1.19436 | + | 0.472102i | −0.0481220 | + | 0.0190215i | ||||
\(617\) | − | 23.0577i | − | 0.928269i | −0.885765 | − | 0.464134i | \(-0.846365\pi\) | ||
0.885765 | − | 0.464134i | \(-0.153635\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 1.93816i | 0.0779014i | 0.999241 | + | 0.0389507i | \(0.0124015\pi\) | ||||
−0.999241 | + | 0.0389507i | \(0.987598\pi\) | |||||||
\(620\) | 0.218026i | 0.00875613i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | − | 19.4558i | − | 0.780106i | ||||||
\(623\) | 12.4346 | − | 4.91512i | 0.498182 | − | 0.196920i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −30.9430 | −1.23772 | ||||||||
\(626\) | 9.72971 | 0.388877 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − | 2.60629i | − | 0.104002i | ||||||
\(629\) | −10.1985 | −0.406640 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.5831 | 0.938827 | 0.469414 | − | 0.882978i | \(-0.344465\pi\) | ||||
0.469414 | + | 0.882978i | \(0.344465\pi\) | |||||||
\(632\) | 13.3103i | 0.529455i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −27.1724 | −1.07915 | ||||||||
\(635\) | 35.4454 | 1.40661 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 18.8712 | + | 20.1411i | 0.747704 | + | 0.798021i | ||||
\(638\) | − | 0.870293i | − | 0.0344552i | ||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 11.1151i | 0.439361i | ||||||||
\(641\) | 24.8368i | 0.980996i | 0.871442 | + | 0.490498i | \(0.163185\pi\) | ||||
−0.871442 | + | 0.490498i | \(0.836815\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 43.7917i | − | 1.72698i | −0.504369 | − | 0.863489i | \(-0.668275\pi\) | ||
0.504369 | − | 0.863489i | \(-0.331725\pi\) | |||||||
\(644\) | −0.315280 | − | 0.797618i | −0.0124238 | − | 0.0314305i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −31.1445 | −1.22537 | ||||||||
\(647\) | 29.3713 | 1.15471 | 0.577353 | − | 0.816494i | \(-0.304086\pi\) | ||||
0.577353 | + | 0.816494i | \(0.304086\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 0.570305i | − | 0.0223864i | ||||||
\(650\) | −14.2810 | −0.560146 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.22646 | 0.126358 | ||||||||
\(653\) | 32.4258i | 1.26892i | 0.772955 | + | 0.634461i | \(0.218778\pi\) | ||||
−0.772955 | + | 0.634461i | \(0.781222\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −28.5074 | −1.11388 | ||||||||
\(656\) | −9.82082 | −0.383438 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 9.99707 | + | 25.2913i | 0.389727 | + | 0.985957i | ||||
\(659\) | − | 0.234422i | − | 0.00913180i | −0.999990 | − | 0.00456590i | \(-0.998547\pi\) | ||
0.999990 | − | 0.00456590i | \(-0.00145338\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 3.52343i | 0.137045i | 0.997650 | + | 0.0685227i | \(0.0218286\pi\) | ||||
−0.997650 | + | 0.0685227i | \(0.978171\pi\) | |||||||
\(662\) | 22.8448i | 0.887887i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 19.8441i | − | 0.770099i | ||||||
\(665\) | −17.4883 | − | 44.2431i | −0.678167 | − | 1.71567i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.53950 | 0.0983296 | ||||||||
\(668\) | 6.23582 | 0.241271 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − | 4.46763i | − | 0.172600i | ||||||
\(671\) | 0.531151 | 0.0205049 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −18.3317 | −0.706635 | −0.353318 | − | 0.935503i | \(-0.614946\pi\) | ||||
−0.353318 | + | 0.935503i | \(0.614946\pi\) | |||||||
\(674\) | 5.38004i | 0.207231i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.51166 | −0.0581409 | ||||||||
\(677\) | 33.8519 | 1.30103 | 0.650517 | − | 0.759491i | \(-0.274552\pi\) | ||||
0.650517 | + | 0.759491i | \(0.274552\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.45331 | − | 6.20655i | −0.0941493 | − | 0.238185i | ||||
\(680\) | − | 36.1806i | − | 1.38746i | ||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0.0242232i | 0.000927553i | ||||||||
\(683\) | − | 28.0284i | − | 1.07248i | −0.844066 | − | 0.536239i | \(-0.819844\pi\) | ||
0.844066 | − | 0.536239i | \(-0.180156\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 22.8214i | 0.871962i | ||||||||
\(686\) | 19.8575 | + | 9.38520i | 0.758163 | + | 0.358328i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 16.1623 | 0.616180 | ||||||||
\(689\) | 10.2609 | 0.390908 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 49.3511i | 1.87741i | 0.344727 | + | 0.938703i | \(0.387971\pi\) | ||||
−0.344727 | + | 0.938703i | \(0.612029\pi\) | |||||||
\(692\) | −10.4226 | −0.396210 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 10.3566 | 0.393131 | ||||||||
\(695\) | 53.6454i | 2.03488i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16.5438 | 0.626640 | ||||||||
\(698\) | −10.7213 | −0.405808 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 4.46050 | − | 1.76314i | 0.168591 | − | 0.0666403i | ||||
\(701\) | 26.3889i | 0.996696i | 0.866977 | + | 0.498348i | \(0.166060\pi\) | ||||
−0.866977 | + | 0.498348i | \(0.833940\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 15.5897i | − | 0.587976i | ||||||
\(704\) | − | 1.38181i | − | 0.0520791i | ||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 1.44184i | − | 0.0542643i | ||||||
\(707\) | −7.36051 | + | 2.90944i | −0.276820 | + | 0.109421i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −10.7132 | −0.402343 | −0.201172 | − | 0.979556i | \(-0.564475\pi\) | ||||
−0.201172 | + | 0.979556i | \(0.564475\pi\) | |||||||
\(710\) | −1.37758 | −0.0516998 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 15.5441i | 0.582539i | ||||||||
\(713\) | −0.0706827 | −0.00264709 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.76595 | 0.0660429 | ||||||||
\(716\) | − | 10.8051i | − | 0.403805i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 20.5247 | 0.765975 | ||||||||
\(719\) | −17.5794 | −0.655601 | −0.327801 | − | 0.944747i | \(-0.606307\pi\) | ||||
−0.327801 | + | 0.944747i | \(0.606307\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 12.8348 | + | 32.4704i | 0.477994 | + | 1.20926i | ||||
\(722\) | − | 25.0759i | − | 0.933227i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 3.91871i | 0.145638i | ||||||||
\(725\) | 14.2016i | 0.527433i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 50.1943i | 1.86160i | 0.365524 | + | 0.930802i | \(0.380890\pi\) | ||||
−0.365524 | + | 0.930802i | \(0.619110\pi\) | |||||||
\(728\) | −29.8401 | + | 11.7951i | −1.10595 | + | 0.437156i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −50.5261 | −1.87005 | ||||||||
\(731\) | −27.2263 | −1.00700 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 39.9084i | − | 1.47405i | −0.675865 | − | 0.737025i | \(-0.736230\pi\) | ||
0.675865 | − | 0.737025i | \(-0.263770\pi\) | |||||||
\(734\) | 33.4538 | 1.23480 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.76595 | 0.0650939 | ||||||||
\(737\) | 0.209490i | 0.00771668i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 30.3432 | 1.11619 | 0.558096 | − | 0.829777i | \(-0.311532\pi\) | ||||
0.558096 | + | 0.829777i | \(0.311532\pi\) | |||||||
\(740\) | 4.14487 | 0.152369 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 7.59358 | − | 3.00157i | 0.278769 | − | 0.110191i | ||||
\(743\) | 45.7101i | 1.67694i | 0.544948 | + | 0.838470i | \(0.316549\pi\) | ||||
−0.544948 | + | 0.838470i | \(0.683451\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 55.0744i | 2.01777i | ||||||||
\(746\) | 33.5056i | 1.22673i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.388278i | 0.0141968i | ||||||||
\(749\) | −19.0194 | − | 48.1165i | −0.694953 | − | 1.75814i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 12.1551 | 0.443544 | 0.221772 | − | 0.975099i | \(-0.428816\pi\) | ||||
0.221772 | + | 0.975099i | \(0.428816\pi\) | |||||||
\(752\) | −21.3262 | −0.777686 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | − | 21.7436i | − | 0.791857i | ||||||
\(755\) | 5.07411 | 0.184666 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.71614 | −0.353139 | −0.176570 | − | 0.984288i | \(-0.556500\pi\) | ||||
−0.176570 | + | 0.984288i | \(0.556500\pi\) | |||||||
\(758\) | 17.3676i | 0.630819i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 55.3068 | 2.00619 | ||||||||
\(761\) | 38.8349 | 1.40776 | 0.703882 | − | 0.710317i | \(-0.251448\pi\) | ||||
0.703882 | + | 0.710317i | \(0.251448\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 32.5979 | − | 12.8852i | 1.18012 | − | 0.466475i | ||||
\(764\) | − | 8.43483i | − | 0.305161i | ||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − | 29.3949i | − | 1.06208i | ||||||
\(767\) | − | 14.2486i | − | 0.514489i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 10.8874i | 0.392611i | 0.980543 | + | 0.196305i | \(0.0628944\pi\) | ||||
−0.980543 | + | 0.196305i | \(0.937106\pi\) | |||||||
\(770\) | 1.30690 | − | 0.516588i | 0.0470974 | − | 0.0186165i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −5.93833 | −0.213725 | ||||||||
\(773\) | −37.3337 | −1.34280 | −0.671400 | − | 0.741096i | \(-0.734307\pi\) | ||||
−0.671400 | + | 0.741096i | \(0.734307\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 0.395277i | − | 0.0141988i | ||||||
\(776\) | 7.75859 | 0.278517 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6.07607 | −0.217837 | ||||||||
\(779\) | 25.2893i | 0.906083i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0.0645958 | 0.00231142 | ||||||||
\(782\) | 2.68448 | 0.0959969 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −12.5687 | + | 11.7762i | −0.448881 | + | 0.420578i | ||||
\(785\) | 12.4610i | 0.444752i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17.8463i | 0.636152i | 0.948065 | + | 0.318076i | \(0.103037\pi\) | ||||
−0.948065 | + | 0.318076i | \(0.896963\pi\) | |||||||
\(788\) | 11.9319i | 0.425058i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | − | 14.5645i | − | 0.518182i | ||||||
\(791\) | 9.80039 | + | 24.7937i | 0.348462 | + | 0.881562i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 13.2704 | 0.471246 | ||||||||
\(794\) | −2.27809 | −0.0808465 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 7.67961i | 0.272197i | ||||||||
\(797\) | −11.4971 | −0.407247 | −0.203624 | − | 0.979049i | \(-0.565272\pi\) | ||||
−0.203624 | + | 0.979049i | \(0.565272\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 35.9253 | 1.27095 | ||||||||
\(800\) | 9.87572i | 0.349159i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −17.0642 | −0.602558 | ||||||||
\(803\) | 2.36920 | 0.0836073 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.50739 | + | 3.81350i | 0.0531286 | + | 0.134408i | ||||
\(806\) | 0.605198i | 0.0213172i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − | 9.20112i | − | 0.323694i | ||||||
\(809\) | − | 13.1945i | − | 0.463893i | −0.972729 | − | 0.231946i | \(-0.925491\pi\) | ||
0.972729 | − | 0.231946i | \(-0.0745094\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 46.5800i | − | 1.63565i | −0.575469 | − | 0.817823i | \(-0.695181\pi\) | ||
0.575469 | − | 0.817823i | \(-0.304819\pi\) | |||||||
\(812\) | 2.68448 | + | 6.79139i | 0.0942069 | + | 0.238331i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.460505 | 0.0161407 | ||||||||
\(815\) | −15.4261 | −0.540352 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 41.6189i | − | 1.45606i | ||||||
\(818\) | 11.5341 | 0.403280 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −6.72373 | −0.234803 | ||||||||
\(821\) | 39.6782i | 1.38478i | 0.721524 | + | 0.692390i | \(0.243442\pi\) | ||||
−0.721524 | + | 0.692390i | \(0.756558\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −39.2311 | −1.36751 | −0.683755 | − | 0.729711i | \(-0.739654\pi\) | ||||
−0.683755 | + | 0.729711i | \(0.739654\pi\) | |||||||
\(824\) | −40.5902 | −1.41403 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.16810 | − | 10.5448i | −0.145027 | − | 0.366899i | ||||
\(827\) | − | 21.0827i | − | 0.733118i | −0.930395 | − | 0.366559i | \(-0.880536\pi\) | ||
0.930395 | − | 0.366559i | \(-0.119464\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.3261i | 0.462834i | 0.972855 | + | 0.231417i | \(0.0743361\pi\) | ||||
−0.972855 | + | 0.231417i | \(0.925664\pi\) | |||||||
\(830\) | 21.7140i | 0.753703i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | − | 34.5236i | − | 1.19689i | ||||||
\(833\) | 21.1727 | − | 19.8377i | 0.733591 | − | 0.687336i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −29.8142 | −1.03176 | ||||||||
\(836\) | −0.593532 | −0.0205277 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 35.4621i | 1.22502i | ||||||||
\(839\) | −16.7954 | −0.579840 | −0.289920 | − | 0.957051i | \(-0.593629\pi\) | ||||
−0.289920 | + | 0.957051i | \(0.593629\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.37724 | 0.254388 | ||||||||
\(842\) | 29.7554i | 1.02544i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.35076 | 0.184181 | ||||||||
\(845\) | 7.22744 | 0.248632 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 27.0043 | − | 10.6742i | 0.927878 | − | 0.366769i | ||||
\(848\) | 6.40308i | 0.219883i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 15.0124i | 0.514921i | ||||||||
\(851\) | 1.34374i | 0.0460629i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 40.9932i | − | 1.40358i | −0.712384 | − | 0.701790i | \(-0.752385\pi\) | ||
0.712384 | − | 0.701790i | \(-0.247615\pi\) | |||||||
\(854\) | 9.82082 | − | 3.88195i | 0.336061 | − | 0.132837i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 60.1488 | 2.05584 | ||||||||
\(857\) | −41.7436 | −1.42593 | −0.712967 | − | 0.701198i | \(-0.752649\pi\) | ||||
−0.712967 | + | 0.701198i | \(0.752649\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 27.7682i | − | 0.947437i | −0.880676 | − | 0.473719i | \(-0.842911\pi\) | ||
0.880676 | − | 0.473719i | \(-0.157089\pi\) | |||||||
\(860\) | 11.0653 | 0.377325 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 7.57880 | 0.258135 | ||||||||
\(863\) | 45.6090i | 1.55255i | 0.630396 | + | 0.776274i | \(0.282893\pi\) | ||||
−0.630396 | + | 0.776274i | \(0.717107\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 49.8319 | 1.69434 | ||||||||
\(866\) | −39.3456 | −1.33702 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.0747181 | − | 0.189027i | −0.00253610 | − | 0.00641600i | ||||
\(869\) | 0.682940i | 0.0231671i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 5.23396i | 0.177346i | ||||||||
\(872\) | 40.7495i | 1.37995i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.10358i | 0.138806i | ||||||||
\(875\) | 13.5880 | − | 5.37104i | 0.459359 | − | 0.181574i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 17.6874 | 0.597259 | 0.298630 | − | 0.954369i | \(-0.403470\pi\) | ||||
0.298630 | + | 0.954369i | \(0.403470\pi\) | |||||||
\(878\) | −10.0367 | −0.338722 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 1.10201i | 0.0371487i | ||||||||
\(881\) | −11.6169 | −0.391384 | −0.195692 | − | 0.980665i | \(-0.562695\pi\) | ||||
−0.195692 | + | 0.980665i | \(0.562695\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.5480 | −1.19629 | −0.598143 | − | 0.801389i | \(-0.704095\pi\) | ||||
−0.598143 | + | 0.801389i | \(0.704095\pi\) | |||||||
\(884\) | 9.70083i | 0.326274i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −22.0584 | −0.741065 | ||||||||
\(887\) | −24.5501 | −0.824313 | −0.412156 | − | 0.911113i | \(-0.635224\pi\) | ||||
−0.412156 | + | 0.911113i | \(0.635224\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −30.7309 | + | 12.1472i | −1.03068 | + | 0.407405i | ||||
\(890\) | − | 17.0088i | − | 0.570136i | ||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 1.33948i | − | 0.0448492i | ||||||
\(893\) | 54.9164i | 1.83771i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 51.6604i | 1.72682i | ||||||||
\(896\) | −3.80917 | − | 9.63669i | −0.127255 | − | 0.321939i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 24.0862 | 0.803766 | ||||||||
\(899\) | 0.601834 | 0.0200723 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 10.7864i | − | 0.359346i | ||||||
\(902\) | −0.747022 | −0.0248731 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −30.9938 | −1.03084 | ||||||||
\(905\) | − | 18.7358i | − | 0.622799i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 36.9004 | 1.22526 | 0.612628 | − | 0.790371i | \(-0.290112\pi\) | ||||
0.612628 | + | 0.790371i | \(0.290112\pi\) | |||||||
\(908\) | 11.0653 | 0.367216 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 32.6519 | − | 12.9066i | 1.08240 | − | 0.427849i | ||||
\(911\) | − | 39.8111i | − | 1.31900i | −0.751704 | − | 0.659500i | \(-0.770768\pi\) | ||
0.751704 | − | 0.659500i | \(-0.229232\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 1.01818i | − | 0.0336970i | ||||||
\(914\) | 13.4681i | 0.445485i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 8.49154i | 0.280568i | ||||||||
\(917\) | 24.7157 | − | 9.76957i | 0.816186 | − | 0.322620i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −56.8725 | −1.87605 | −0.938026 | − | 0.346565i | \(-0.887348\pi\) | ||||
−0.938026 | + | 0.346565i | \(0.887348\pi\) | |||||||
\(920\) | −4.76713 | −0.157168 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 46.2472i | 1.52307i | ||||||||
\(923\) | 1.61388 | 0.0531215 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.51459 | −0.247078 | ||||||||
\(926\) | 11.9409i | 0.392403i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −15.0364 | −0.493593 | ||||||||
\(929\) | 45.7769 | 1.50189 | 0.750946 | − | 0.660364i | \(-0.229598\pi\) | ||||
0.750946 | + | 0.660364i | \(0.229598\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 30.3245 | + | 32.3652i | 0.993846 | + | 1.06073i | ||||
\(932\) | 10.1311i | 0.331857i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.26138i | 0.139437i | ||||||||
\(935\) | − | 1.85640i | − | 0.0607108i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 24.0003i | − | 0.784054i | −0.919954 | − | 0.392027i | \(-0.871774\pi\) | ||
0.919954 | − | 0.392027i | \(-0.128226\pi\) | |||||||
\(938\) | 1.53107 | + | 3.87341i | 0.0499913 | + | 0.126471i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −14.6008 | −0.476225 | ||||||||
\(941\) | −3.28632 | −0.107131 | −0.0535654 | − | 0.998564i | \(-0.517059\pi\) | ||||
−0.0535654 | + | 0.998564i | \(0.517059\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 2.17979i | − | 0.0709838i | ||||||
\(944\) | 8.89158 | 0.289396 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.22938 | 0.0399707 | ||||||||
\(947\) | − | 29.9552i | − | 0.973415i | −0.873565 | − | 0.486707i | \(-0.838198\pi\) | ||
0.873565 | − | 0.486707i | \(-0.161802\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 59.1928 | 1.92148 | ||||||||
\(950\) | −22.9484 | −0.744544 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 12.3992 | + | 31.3684i | 0.401861 | + | 1.01666i | ||||
\(953\) | 16.0580i | 0.520169i | 0.965586 | + | 0.260084i | \(0.0837504\pi\) | ||||
−0.965586 | + | 0.260084i | \(0.916250\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 40.3279i | 1.30498i | ||||||||
\(956\) | − | 1.32667i | − | 0.0429076i | ||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − | 1.92379i | − | 0.0621547i | ||||||
\(959\) | −7.82097 | − | 19.7860i | −0.252552 | − | 0.638924i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.9832 | 0.999460 | ||||||||
\(962\) | 11.5054 | 0.370948 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − | 2.68312i | − | 0.0864174i | ||||||
\(965\) | 28.3918 | 0.913966 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −50.0550 | −1.60966 | −0.804831 | − | 0.593504i | \(-0.797744\pi\) | ||||
−0.804831 | + | 0.593504i | \(0.797744\pi\) | |||||||
\(968\) | 33.7571i | 1.08499i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −8.48968 | −0.272587 | ||||||||
\(971\) | −1.04188 | −0.0334354 | −0.0167177 | − | 0.999860i | \(-0.505322\pi\) | ||||
−0.0167177 | + | 0.999860i | \(0.505322\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −18.3844 | − | 46.5102i | −0.589378 | − | 1.49105i | ||||
\(974\) | 9.48234i | 0.303834i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8.28114i | 0.265073i | ||||||||
\(977\) | − | 24.4525i | − | 0.782304i | −0.920326 | − | 0.391152i | \(-0.872077\pi\) | ||
0.920326 | − | 0.391152i | \(-0.127923\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0.797555i | 0.0254900i | ||||||||
\(980\) | −8.60502 | + | 8.06246i | −0.274877 | + | 0.257546i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 12.7440 | 0.406677 | ||||||||
\(983\) | 56.1576 | 1.79115 | 0.895575 | − | 0.444911i | \(-0.146765\pi\) | ||||
0.895575 | + | 0.444911i | \(0.146765\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 57.0480i | − | 1.81770i | ||||||
\(986\) | −22.8573 | −0.727924 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −14.8290 | −0.471772 | ||||||||
\(989\) | 3.58731i | 0.114070i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.2278 | 0.579025 | 0.289513 | − | 0.957174i | \(-0.406507\pi\) | ||||
0.289513 | + | 0.957174i | \(0.406507\pi\) | |||||||
\(992\) | 0.418513 | 0.0132878 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.19436 | − | 0.472102i | 0.0378827 | − | 0.0149742i | ||||
\(995\) | − | 36.7171i | − | 1.16401i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 34.4328i | − | 1.09050i | −0.838274 | − | 0.545249i | \(-0.816435\pi\) | ||
0.838274 | − | 0.545249i | \(-0.183565\pi\) | |||||||
\(998\) | 20.0671i | 0.635212i | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))