Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [252,2,Mod(193,252)]
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, 2, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("252.193");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 252 = 2^{2} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 252.l (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 | 193.3 | ||
Root | \(-0.674693 - 1.59524i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 252.193 |
Dual form | 252.2.l.b.205.3 |
$q$-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 \(\left(\mathbb{Z}/252\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(73\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −0.674693 | − | 1.59524i | −0.389534 | − | 0.921012i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 4.14520 | 1.85379 | 0.926894 | − | 0.375322i | \(-0.122468\pi\) | ||||
0.926894 | + | 0.375322i | \(0.122468\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.190437 | + | 2.63889i | 0.0719784 | + | 0.997406i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.08958 | + | 2.15260i | −0.696526 | + | 0.717532i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.868858 | 0.261971 | 0.130985 | − | 0.991384i | \(-0.458186\pi\) | ||||
0.130985 | + | 0.991384i | \(0.458186\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.86231 | − | 4.95766i | 0.793861 | − | 1.37501i | −0.129698 | − | 0.991554i | \(-0.541401\pi\) |
0.923560 | − | 0.383455i | \(-0.125266\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.79674 | − | 6.61258i | −0.722115 | − | 1.70736i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.44613 | + | 2.50478i | −0.350739 | + | 0.607498i | −0.986379 | − | 0.164488i | \(-0.947403\pi\) |
0.635640 | + | 0.771986i | \(0.280736\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.00703 | − | 3.47627i | −0.460444 | − | 0.797512i | 0.538539 | − | 0.842600i | \(-0.318976\pi\) |
−0.998983 | + | 0.0450884i | \(0.985643\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.08117 | − | 2.08423i | 0.890585 | − | 0.454817i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.82977 | −1.21559 | −0.607795 | − | 0.794094i | \(-0.707946\pi\) | ||||
−0.607795 | + | 0.794094i | \(0.707946\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 12.1827 | 2.43653 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.84373 | + | 1.88104i | 0.932176 | + | 0.362005i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.900417 | − | 1.55957i | −0.167203 | − | 0.289604i | 0.770232 | − | 0.637763i | \(-0.220140\pi\) |
−0.937435 | + | 0.348159i | \(0.886807\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.48046 | + | 2.56422i | 0.265898 | + | 0.460548i | 0.967798 | − | 0.251727i | \(-0.0809984\pi\) |
−0.701901 | + | 0.712275i | \(0.747665\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −0.586213 | − | 1.38604i | −0.102047 | − | 0.241278i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.789399 | + | 10.9387i | 0.133433 | + | 1.84898i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.64925 | − | 4.58864i | −0.435535 | − | 0.754368i | 0.561804 | − | 0.827270i | \(-0.310107\pi\) |
−0.997339 | + | 0.0729017i | \(0.976774\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −9.83984 | − | 1.22116i | −1.57564 | − | 0.195543i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −5.89325 | + | 10.2074i | −0.920371 | + | 1.59413i | −0.121528 | + | 0.992588i | \(0.538780\pi\) |
−0.798842 | + | 0.601541i | \(0.794554\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −2.00703 | − | 3.47627i | −0.306069 | − | 0.530127i | 0.671430 | − | 0.741068i | \(-0.265680\pi\) |
−0.977499 | + | 0.210941i | \(0.932347\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −8.66171 | + | 8.92293i | −1.29121 | + | 1.33015i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.17218 | + | 2.03028i | −0.170980 | + | 0.296147i | −0.938763 | − | 0.344564i | \(-0.888027\pi\) |
0.767783 | + | 0.640711i | \(0.221360\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.92747 | + | 1.00508i | −0.989638 | + | 0.143583i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.97142 | + | 0.616973i | 0.696138 | + | 0.0863935i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.09116 | + | 1.88995i | −0.149883 | + | 0.259605i | −0.931184 | − | 0.364549i | \(-0.881223\pi\) |
0.781301 | + | 0.624154i | \(0.214556\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.60159 | 0.485638 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −4.19136 | + | 5.54711i | −0.555159 | + | 0.734733i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 1.52715 | + | 2.64510i | 0.198818 | + | 0.344363i | 0.948146 | − | 0.317837i | \(-0.102956\pi\) |
−0.749327 | + | 0.662200i | \(0.769623\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.81659 | + | 4.87848i | −0.360628 | + | 0.624625i | −0.988064 | − | 0.154042i | \(-0.950771\pi\) |
0.627437 | + | 0.778668i | \(0.284104\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.07839 | − | 5.10423i | −0.765805 | − | 0.643072i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 11.8648 | − | 20.5505i | 1.47165 | − | 2.54898i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 1.25539 | + | 2.17440i | 0.153370 | + | 0.265645i | 0.932464 | − | 0.361262i | \(-0.117654\pi\) |
−0.779094 | + | 0.626907i | \(0.784321\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 3.93331 | + | 9.29988i | 0.473514 | + | 1.11957i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.09143 | −0.129529 | −0.0647647 | − | 0.997901i | \(-0.520630\pi\) | ||||
−0.0647647 | + | 0.997901i | \(0.520630\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.723285 | − | 1.25277i | 0.0846541 | − | 0.146625i | −0.820590 | − | 0.571518i | \(-0.806355\pi\) |
0.905244 | + | 0.424893i | \(0.139688\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.21956 | − | 19.4343i | −0.949113 | − | 2.24408i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0.165463 | + | 2.29282i | 0.0188562 | + | 0.261291i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.06464 | − | 1.84401i | 0.119781 | − | 0.207468i | −0.799900 | − | 0.600134i | \(-0.795114\pi\) |
0.919681 | + | 0.392666i | \(0.128447\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.267330 | − | 8.99603i | −0.0297034 | − | 0.999559i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.18784 | + | 3.78946i | 0.240147 | + | 0.415947i | 0.960756 | − | 0.277395i | \(-0.0894710\pi\) |
−0.720609 | + | 0.693342i | \(0.756138\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.99451 | + | 10.3828i | −0.650196 | + | 1.12617i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.88038 | + | 2.48861i | −0.201598 | + | 0.266807i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.83373 | + | 10.1043i | 0.618374 | + | 1.07105i | 0.989783 | + | 0.142585i | \(0.0455415\pi\) |
−0.371409 | + | 0.928469i | \(0.621125\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.6278 | + | 6.60919i | 1.42858 | + | 0.692831i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.09170 | − | 4.09174i | 0.320594 | − | 0.424294i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −8.31953 | − | 14.4098i | −0.853566 | − | 1.47842i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −3.98779 | − | 6.90706i | −0.404899 | − | 0.701306i | 0.589411 | − | 0.807834i | \(-0.299360\pi\) |
−0.994310 | + | 0.106528i | \(0.966027\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −1.81555 | + | 1.87030i | −0.182469 | + | 0.187972i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.76370 | −0.374502 | −0.187251 | − | 0.982312i | \(-0.559958\pi\) | ||||
−0.187251 | + | 0.982312i | \(0.559958\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.8556 | 1.06963 | 0.534815 | − | 0.844969i | \(-0.320381\pi\) | ||||
0.534815 | + | 0.844969i | \(0.320381\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 16.9173 | − | 8.63956i | 1.65096 | − | 0.843135i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −4.82343 | − | 8.35442i | −0.466298 | − | 0.807653i | 0.532961 | − | 0.846140i | \(-0.321079\pi\) |
−0.999259 | + | 0.0384875i | \(0.987746\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −5.86131 | + | 10.1521i | −0.561412 | + | 0.972394i | 0.435962 | + | 0.899965i | \(0.356408\pi\) |
−0.997374 | + | 0.0724288i | \(0.976925\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −5.53255 | + | 7.32212i | −0.525127 | + | 0.694985i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.88981 | − | 5.00530i | 0.271851 | − | 0.470859i | −0.697485 | − | 0.716599i | \(-0.745698\pi\) |
0.969336 | + | 0.245740i | \(0.0790310\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −24.1655 | −2.25345 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.69083 | + | 16.5208i | 0.433667 | + | 1.52735i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −6.88523 | − | 3.33918i | −0.631168 | − | 0.306103i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.2451 | −0.931371 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 20.2594 | + | 2.51427i | 1.82673 | + | 0.226704i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 29.7736 | 2.66303 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 6.47468 | 0.574535 | 0.287268 | − | 0.957850i | \(-0.407253\pi\) | ||||
0.287268 | + | 0.957850i | \(0.407253\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −4.19136 | + | 5.54711i | −0.369029 | + | 0.488396i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −17.7303 | −1.54910 | −0.774551 | − | 0.632511i | \(-0.782024\pi\) | ||||
−0.774551 | + | 0.632511i | \(0.782024\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 8.79129 | − | 5.95833i | 0.762301 | − | 0.516653i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 20.0782 | + | 7.79726i | 1.72806 | + | 0.671081i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.72232 | 0.232583 | 0.116292 | − | 0.993215i | \(-0.462899\pi\) | ||||
0.116292 | + | 0.993215i | \(0.462899\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.65431 | − | 14.9897i | 0.734049 | − | 1.27141i | −0.221090 | − | 0.975253i | \(-0.570962\pi\) |
0.955139 | − | 0.296157i | \(-0.0957051\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 4.02964 | + | 0.500095i | 0.339357 | + | 0.0421156i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 2.48694 | − | 4.30751i | 0.207968 | − | 0.360212i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.73241 | − | 6.46472i | −0.309959 | − | 0.536865i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 6.27727 | + | 10.3728i | 0.517740 | + | 0.855538i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.84685 | −0.560916 | −0.280458 | − | 0.959866i | \(-0.590486\pi\) | ||||
−0.280458 | + | 0.959866i | \(0.590486\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.28166 | 0.755331 | 0.377666 | − | 0.925942i | \(-0.376727\pi\) | ||||
0.377666 | + | 0.925942i | \(0.376727\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −2.36996 | − | 8.34687i | −0.191600 | − | 0.674804i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 6.13678 | + | 10.6292i | 0.492918 | + | 0.853759i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.83840 | − | 11.8445i | −0.545764 | − | 0.945291i | −0.998558 | − | 0.0536759i | \(-0.982906\pi\) |
0.452795 | − | 0.891615i | \(-0.350427\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 3.75113 | + | 0.465530i | 0.297484 | + | 0.0369189i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −1.11020 | − | 15.3841i | −0.0874963 | − | 1.21244i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.65003 | − | 2.85793i | −0.129240 | − | 0.223850i | 0.794142 | − | 0.607732i | \(-0.207920\pi\) |
−0.923382 | + | 0.383882i | \(0.874587\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −2.42997 | − | 5.74540i | −0.189173 | − | 0.447279i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 5.96228 | − | 10.3270i | 0.461375 | − | 0.799125i | −0.537655 | − | 0.843165i | \(-0.680690\pi\) |
0.999030 | + | 0.0440399i | \(0.0140229\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.88562 | − | 17.1224i | −0.760432 | − | 1.31711i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.6769 | + | 2.94363i | 0.892951 | + | 0.225105i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.81694 | − | 8.34319i | 0.366225 | − | 0.634321i | −0.622747 | − | 0.782424i | \(-0.713983\pi\) |
0.988972 | + | 0.148103i | \(0.0473166\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.32003 | + | 32.1487i | 0.175378 | + | 2.43021i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.18922 | − | 4.22081i | 0.239716 | − | 0.317255i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.5285 | + | 19.9680i | −0.861682 | + | 1.49248i | 0.00862183 | + | 0.999963i | \(0.497256\pi\) |
−0.870304 | + | 0.492515i | \(0.836078\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −11.8325 | −0.879504 | −0.439752 | − | 0.898119i | \(-0.644934\pi\) | ||||
−0.439752 | + | 0.898119i | \(0.644934\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 9.68268 | + | 1.20166i | 0.715764 | + | 0.0888292i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −10.9817 | − | 19.0208i | −0.807390 | − | 1.39844i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.25649 | + | 2.17630i | −0.0918833 | + | 0.159147i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −4.04142 | + | 13.1403i | −0.293970 | + | 0.955815i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.14254 | − | 5.44303i | 0.227386 | − | 0.393844i | −0.729647 | − | 0.683824i | \(-0.760315\pi\) |
0.957033 | + | 0.289980i | \(0.0936487\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −6.86559 | − | 11.8915i | −0.494196 | − | 0.855972i | 0.505782 | − | 0.862661i | \(-0.331204\pi\) |
−0.999978 | + | 0.00668919i | \(0.997871\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −40.7881 | − | 5.06197i | −2.92090 | − | 0.362495i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.161495 | −0.0115061 | −0.00575303 | − | 0.999983i | \(-0.501831\pi\) | ||||
−0.00575303 | + | 0.999983i | \(0.501831\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −12.4140 | + | 21.5016i | −0.880003 | + | 1.52421i | −0.0286672 | + | 0.999589i | \(0.509126\pi\) |
−0.851336 | + | 0.524621i | \(0.824207\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.62168 | − | 3.46970i | 0.184919 | − | 0.244733i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 3.94405 | − | 2.67310i | 0.276818 | − | 0.187615i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −24.4287 | + | 42.3117i | −1.70617 | + | 2.95518i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.1818 | − | 12.5491i | 0.846690 | − | 0.872225i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.74382 | − | 3.02039i | −0.120623 | − | 0.208925i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.44607 | − | 16.3611i | 0.650295 | − | 1.12634i | −0.332757 | − | 0.943013i | \(-0.607979\pi\) |
0.983051 | − | 0.183331i | \(-0.0586879\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0.736384 | + | 1.74110i | 0.0504562 | + | 0.119298i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −8.31953 | − | 14.4098i | −0.567387 | − | 0.982743i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.48477 | + | 4.39508i | −0.440215 | + | 0.298357i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −2.48646 | − | 0.308580i | −0.168019 | − | 0.0208519i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.27856 | + | 14.3389i | 0.556876 | + | 0.964538i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 7.04717 | + | 12.2061i | 0.471914 | + | 0.817378i | 0.999484 | − | 0.0321333i | \(-0.0102301\pi\) |
−0.527570 | + | 0.849512i | \(0.676897\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −25.4566 | + | 26.2243i | −1.69711 | + | 1.74829i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 25.9782 | 1.72424 | 0.862118 | − | 0.506708i | \(-0.169138\pi\) | ||||
0.862118 | + | 0.506708i | \(0.169138\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 24.9157 | 1.64648 | 0.823239 | − | 0.567695i | \(-0.192165\pi\) | ||||
0.823239 | + | 0.567695i | \(0.192165\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 3.54596 | − | 1.81090i | 0.233307 | − | 0.119149i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.05923 | − | 5.29874i | −0.200417 | − | 0.347132i | 0.748246 | − | 0.663421i | \(-0.230896\pi\) |
−0.948663 | + | 0.316289i | \(0.897563\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −4.85893 | + | 8.41591i | −0.316961 | + | 0.548993i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.65995 | − | 0.454214i | −0.237739 | − | 0.0295044i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −7.71988 | + | 13.3712i | −0.499357 | + | 0.864912i | −1.00000 | 0.000742080i | \(-0.999764\pi\) | |
0.500643 | + | 0.865654i | \(0.333097\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 9.84518 | 0.634183 | 0.317092 | − | 0.948395i | \(-0.397294\pi\) | ||||
0.317092 | + | 0.948395i | \(0.397294\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −14.1705 | + | 6.49602i | −0.909035 | + | 0.416720i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −28.7157 | + | 4.16627i | −1.83458 | + | 0.266173i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −22.9789 | −1.46211 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.56897 | − | 6.04685i | 0.289546 | − | 0.383204i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 26.8843 | 1.69692 | 0.848461 | − | 0.529258i | \(-0.177530\pi\) | ||||
0.848461 | + | 0.529258i | \(0.177530\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −5.06524 | −0.318449 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 20.6075 | + | 2.55748i | 1.29049 | + | 0.160155i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 11.0127 | 0.686954 | 0.343477 | − | 0.939161i | \(-0.388395\pi\) | ||||
0.343477 | + | 0.939161i | \(0.388395\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 11.6044 | − | 7.86494i | 0.721063 | − | 0.488703i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 5.23861 | + | 1.32060i | 0.324262 | + | 0.0817434i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −7.31095 | −0.450812 | −0.225406 | − | 0.974265i | \(-0.572371\pi\) | ||||
−0.225406 | + | 0.974265i | \(0.572371\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.52309 | + | 7.83423i | −0.277851 | + | 0.481253i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 12.1828 | − | 16.1235i | 0.745576 | − | 0.986742i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2.08048 | + | 3.60349i | −0.126849 | + | 0.219709i | −0.922454 | − | 0.386107i | \(-0.873820\pi\) |
0.795605 | + | 0.605815i | \(0.207153\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −4.18300 | − | 7.24516i | −0.254099 | − | 0.440112i | 0.710551 | − | 0.703645i | \(-0.248446\pi\) |
−0.964650 | + | 0.263533i | \(0.915112\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.34865 | − | 26.1988i | 0.0816239 | − | 1.58562i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 10.5850 | 0.638300 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.79856 | −0.168149 | −0.0840745 | − | 0.996459i | \(-0.526793\pi\) | ||||
−0.0840745 | + | 0.996459i | \(0.526793\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −8.61326 | − | 2.17132i | −0.515662 | − | 0.129994i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −5.44314 | − | 9.42779i | −0.324710 | − | 0.562415i | 0.656743 | − | 0.754114i | \(-0.271933\pi\) |
−0.981454 | + | 0.191699i | \(0.938600\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.01212 | + | 1.75304i | 0.0601642 | + | 0.104207i | 0.894539 | − | 0.446990i | \(-0.147504\pi\) |
−0.834374 | + | 0.551198i | \(0.814171\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −17.3740 | + | 22.9939i | −1.02915 | + | 1.36204i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −28.0585 | − | 13.6078i | −1.65624 | − | 0.803241i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4.31739 | + | 7.47794i | 0.253964 | + | 0.439879i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −8.32788 | + | 11.0216i | −0.488189 | + | 0.646100i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −9.65448 | + | 16.7220i | −0.564021 | + | 0.976912i | 0.433120 | + | 0.901336i | \(0.357413\pi\) |
−0.997140 | + | 0.0755757i | \(0.975921\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.33035 | + | 10.9645i | 0.368567 | + | 0.638377i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.20851 | + | 1.63435i | 0.244203 | + | 0.0948348i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −16.6866 | + | 28.9020i | −0.965011 | + | 1.67145i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 8.79129 | − | 5.95833i | 0.506721 | − | 0.343433i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.53935 | + | 6.00401i | 0.145882 | + | 0.344921i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −11.6753 | + | 20.2223i | −0.668527 | + | 1.15792i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −13.1378 | −0.749813 | −0.374907 | − | 0.927063i | \(-0.622325\pi\) | ||||
−0.374907 | + | 0.927063i | \(0.622325\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −7.32417 | − | 17.3172i | −0.416658 | − | 0.985142i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.76606 | + | 11.7192i | 0.383668 | + | 0.664533i | 0.991583 | − | 0.129469i | \(-0.0413273\pi\) |
−0.607915 | + | 0.794002i | \(0.707994\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 12.6000 | − | 21.8238i | 0.712194 | − | 1.23356i | −0.251838 | − | 0.967770i | \(-0.581035\pi\) |
0.964032 | − | 0.265787i | \(-0.0856318\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −25.1961 | − | 21.1580i | −1.41964 | − | 1.19212i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6.14888 | − | 10.6502i | 0.345356 | − | 0.598173i | −0.640063 | − | 0.768323i | \(-0.721092\pi\) |
0.985418 | + | 0.170149i | \(0.0544250\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.782335 | − | 1.35504i | −0.0438023 | − | 0.0758679i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.0730 | + | 13.3312i | −0.562218 | + | 0.744075i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 11.6097 | 0.645982 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 34.8705 | − | 60.3975i | 1.93427 | − | 3.35025i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 20.1496 | + | 2.50065i | 1.11428 | + | 0.138286i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −5.58091 | − | 2.70662i | −0.307685 | − | 0.149221i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9.96285 | − | 17.2562i | 0.547608 | − | 0.948484i | −0.450830 | − | 0.892610i | \(-0.648872\pi\) |
0.998438 | − | 0.0558745i | \(-0.0177947\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 15.4133 | + | 3.88556i | 0.844645 | + | 0.212927i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.20383 | + | 9.01330i | 0.284316 | + | 0.492449i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.966380 | + | 1.67382i | −0.0526421 | + | 0.0911788i | −0.891146 | − | 0.453717i | \(-0.850098\pi\) |
0.838504 | + | 0.544896i | \(0.183431\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −9.93439 | − | 1.23290i | −0.539562 | − | 0.0669618i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.28631 | + | 2.22795i | 0.0696574 | + | 0.120650i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3.97155 | − | 18.0894i | −0.214444 | − | 0.976736i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 16.3043 | + | 38.5498i | 0.877796 | + | 2.07545i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −8.48241 | − | 14.6920i | −0.455360 | − | 0.788706i | 0.543349 | − | 0.839507i | \(-0.317156\pi\) |
−0.998709 | + | 0.0508006i | \(0.983823\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.25767 | − | 10.8386i | −0.334966 | − | 0.580177i | 0.648513 | − | 0.761204i | \(-0.275391\pi\) |
−0.983478 | + | 0.181027i | \(0.942058\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 23.1898 | − | 18.6295i | 1.23778 | − | 0.994368i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 32.3857 | 1.72372 | 0.861859 | − | 0.507149i | \(-0.169300\pi\) | ||||
0.861859 | + | 0.507149i | \(0.169300\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.52421 | −0.240120 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −0.681382 | + | 13.2365i | −0.0360626 | + | 0.700550i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.98559 | + | 15.5635i | 0.474242 | + | 0.821410i | 0.999565 | − | 0.0294922i | \(-0.00938902\pi\) |
−0.525323 | + | 0.850903i | \(0.676056\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.44368 | − | 2.50052i | 0.0759830 | − | 0.131606i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 6.91229 | + | 16.3434i | 0.362801 | + | 0.857804i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.99816 | − | 5.19297i | 0.156931 | − | 0.271812i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.16840 | 0.426387 | 0.213194 | − | 0.977010i | \(-0.431614\pi\) | ||||
0.213194 | + | 0.977010i | \(0.431614\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −9.65801 | − | 34.0149i | −0.502776 | − | 1.77075i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.19517 | − | 2.51954i | −0.269720 | − | 0.130808i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.16161 | −0.267258 | −0.133629 | − | 0.991031i | \(-0.542663\pi\) | ||||
−0.133629 | + | 0.991031i | \(0.542663\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −20.0880 | − | 47.4960i | −1.03734 | − | 2.45268i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.3091 | −0.530945 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.0017 | 1.07878 | 0.539392 | − | 0.842055i | \(-0.318654\pi\) | ||||
0.539392 | + | 0.842055i | \(0.318654\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −4.36843 | − | 10.3287i | −0.223801 | − | 0.529154i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 29.5589 | 1.51039 | 0.755194 | − | 0.655501i | \(-0.227542\pi\) | ||||
0.755194 | + | 0.655501i | \(0.227542\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.685876 | + | 9.50419i | 0.0349555 | + | 0.484379i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 11.6769 | + | 2.94363i | 0.593568 | + | 0.149633i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −16.5379 | −0.838505 | −0.419252 | − | 0.907870i | \(-0.637708\pi\) | ||||
−0.419252 | + | 0.907870i | \(0.637708\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.43063 | − | 14.6023i | 0.426355 | − | 0.738469i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.9625 | + | 28.2840i | 0.603429 | + | 1.42674i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 4.41315 | − | 7.64379i | 0.222049 | − | 0.384601i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 15.4394 | + | 26.7418i | 0.774881 | + | 1.34213i | 0.934861 | + | 0.355014i | \(0.115524\pi\) |
−0.159980 | + | 0.987120i | \(0.551143\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −15.4364 | − | 10.0042i | −0.772786 | − | 0.500835i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.6323 | 0.530951 | 0.265475 | − | 0.964118i | \(-0.414471\pi\) | ||||
0.265475 | + | 0.964118i | \(0.414471\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 16.9501 | 0.844343 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1.10814 | − | 37.2903i | −0.0550638 | − | 1.85297i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −2.30183 | − | 3.98688i | −0.114097 | − | 0.197622i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.39782 | + | 12.8134i | 0.365799 | + | 0.633582i | 0.988904 | − | 0.148556i | \(-0.0474625\pi\) |
−0.623105 | + | 0.782138i | \(0.714129\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −1.83673 | − | 4.34275i | −0.0905993 | − | 0.214212i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.68931 | + | 4.53371i | −0.329159 | + | 0.223089i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.06904 | + | 15.7080i | 0.445182 | + | 0.771078i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −29.7512 | − | 3.69224i | −1.45692 | − | 0.180810i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.56134 | + | 2.70432i | −0.0762765 | + | 0.132115i | −0.901641 | − | 0.432486i | \(-0.857637\pi\) |
0.825364 | + | 0.564601i | \(0.190970\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −0.644580 | − | 1.11645i | −0.0314149 | − | 0.0544122i | 0.849891 | − | 0.526959i | \(-0.176668\pi\) |
−0.881305 | + | 0.472547i | \(0.843335\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −1.92100 | − | 6.76566i | −0.0934023 | − | 0.328958i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −17.6178 | + | 30.5149i | −0.854587 | + | 1.48019i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −13.4101 | − | 6.50363i | −0.648962 | − | 0.314733i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.54943 | − | 1.06102i | −0.412770 | − | 0.0512265i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11.5916 | + | 20.0773i | −0.558350 | + | 0.967090i | 0.439285 | + | 0.898348i | \(0.355232\pi\) |
−0.997634 | + | 0.0687421i | \(0.978101\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 35.6437 | 1.71293 | 0.856464 | − | 0.516207i | \(-0.172657\pi\) | ||||
0.856464 | + | 0.516207i | \(0.172657\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −7.79454 | + | 10.3158i | −0.373720 | + | 0.494604i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 11.7005 | + | 20.2659i | 0.559711 | + | 0.969448i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8.00620 | + | 13.8671i | −0.382115 | + | 0.661843i | −0.991364 | − | 0.131136i | \(-0.958138\pi\) |
0.609249 | + | 0.792979i | \(0.291471\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 12.3119 | − | 17.0122i | 0.586283 | − | 0.810106i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.17778 | + | 12.4323i | −0.341027 | + | 0.590676i | −0.984624 | − | 0.174689i | \(-0.944108\pi\) |
0.643597 | + | 0.765365i | \(0.277441\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 24.1819 | + | 41.8844i | 1.14633 | + | 1.98551i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 4.61953 | + | 10.9224i | 0.218496 | + | 0.516610i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.72475 | 0.270168 | 0.135084 | − | 0.990834i | \(-0.456870\pi\) | ||||
0.135084 | + | 0.990834i | \(0.456870\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −5.12040 | + | 8.86879i | −0.241110 | + | 0.417615i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −6.26228 | − | 14.8065i | −0.294227 | − | 0.695669i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 56.4900 | + | 27.3964i | 2.64829 | + | 1.28436i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.33175 | + | 12.6990i | −0.342965 | + | 0.594033i | −0.984982 | − | 0.172658i | \(-0.944765\pi\) |
0.642017 | + | 0.766690i | \(0.278098\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −11.7163 | + | 9.41223i | −0.546868 | + | 0.439325i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −12.9720 | − | 22.4681i | −0.604164 | − | 1.04644i | −0.992183 | − | 0.124792i | \(-0.960174\pi\) |
0.388018 | − | 0.921652i | \(-0.373160\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.46277 | + | 11.1939i | −0.300351 | + | 0.520223i | −0.976215 | − | 0.216803i | \(-0.930437\pi\) |
0.675865 | + | 0.737026i | \(0.263770\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 12.8157 | − | 16.9611i | 0.594314 | − | 0.786552i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −16.3104 | − | 28.2504i | −0.754755 | − | 1.30727i | −0.945496 | − | 0.325633i | \(-0.894423\pi\) |
0.190741 | − | 0.981640i | \(-0.438911\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5.49892 | + | 3.72692i | −0.253916 | + | 0.172093i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −14.2809 | + | 18.9003i | −0.658030 | + | 0.870878i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.74382 | − | 3.02039i | −0.0801811 | − | 0.138878i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −24.4509 | − | 42.3503i | −1.12189 | − | 1.94316i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.78823 | − | 6.29804i | −0.0818774 | − | 0.288367i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −25.3478 | −1.15817 | −0.579084 | − | 0.815268i | \(-0.696590\pi\) | ||||
−0.579084 | + | 0.815268i | \(0.696590\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −30.3319 | −1.38302 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −23.7923 | + | 12.1506i | −1.08259 | + | 0.552871i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −16.5302 | − | 28.6311i | −0.750597 | − | 1.30007i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 17.7383 | − | 30.7236i | 0.803799 | − | 1.39222i | −0.113299 | − | 0.993561i | \(-0.536142\pi\) |
0.917099 | − | 0.398660i | \(-0.130525\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −3.44582 | + | 4.56041i | −0.155825 | + | 0.206229i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 13.2554 | − | 22.9590i | 0.598208 | − | 1.03613i | −0.394877 | − | 0.918734i | \(-0.629213\pi\) |
0.993085 | − | 0.117393i | \(-0.0374538\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 5.20849 | 0.234579 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −7.52580 | + | 7.75276i | −0.338260 | + | 0.348461i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −0.207849 | − | 2.88017i | −0.00932332 | − | 0.129193i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −6.00261 | −0.268714 | −0.134357 | − | 0.990933i | \(-0.542897\pi\) | ||||
−0.134357 | + | 0.990933i | \(0.542897\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −20.4967 | − | 2.54373i | −0.915725 | − | 0.113645i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −22.9460 | −1.02311 | −0.511556 | − | 0.859250i | \(-0.670931\pi\) | ||||
−0.511556 | + | 0.859250i | \(0.670931\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −15.6013 | −0.694248 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −20.6446 | + | 27.3223i | −0.916857 | + | 1.21343i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 29.8697 | 1.32395 | 0.661975 | − | 0.749526i | \(-0.269719\pi\) | ||||
0.661975 | + | 0.749526i | \(0.269719\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 3.44365 | + | 1.67010i | 0.152338 | + | 0.0738807i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −3.18250 | − | 20.6134i | −0.140511 | − | 0.910105i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 44.9984 | 1.98287 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.01846 | + | 1.76402i | −0.0447918 | + | 0.0775817i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −16.5593 | − | 2.05508i | −0.726875 | − | 0.0902081i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.5980 | − | 27.0166i | 0.683362 | − | 1.18362i | −0.290587 | − | 0.956849i | \(-0.593851\pi\) |
0.973949 | − | 0.226769i | \(-0.0728162\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.07911 | − | 5.33318i | −0.134640 | − | 0.233203i | 0.790820 | − | 0.612049i | \(-0.209654\pi\) |
−0.925460 | + | 0.378846i | \(0.876321\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 49.7196 | − | 25.3915i | 2.16994 | − | 1.10818i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −8.56375 | −0.373043 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 10.9862 | 0.477661 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −8.88494 | − | 2.23981i | −0.385574 | − | 0.0971995i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 33.7366 | + | 58.4335i | 1.46129 | + | 2.53103i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −19.9941 | − | 34.6307i | −0.864419 | − | 1.49722i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 39.6319 | + | 4.91849i | 1.71024 | + | 0.212248i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −6.01899 | + | 0.873275i | −0.259256 | + | 0.0376146i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −13.5137 | − | 23.4064i | −0.580999 | − | 1.00632i | −0.995361 | − | 0.0962083i | \(-0.969329\pi\) |
0.414362 | − | 0.910112i | \(-0.364005\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 7.98332 | + | 18.8757i | 0.342597 | + | 0.810033i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −24.2963 | + | 42.0824i | −1.04074 | + | 1.80261i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 14.9426 | + | 25.8814i | 0.638900 | + | 1.10661i | 0.985675 | + | 0.168658i | \(0.0539434\pi\) |
−0.346775 | + | 0.937948i | \(0.612723\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −4.61590 | − | 16.2569i | −0.197002 | − | 0.693829i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.61432 | + | 6.26019i | −0.153975 | + | 0.266693i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 5.06889 | + | 2.45830i | 0.215551 | + | 0.104538i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −22.9335 | + | 30.3517i | −0.973474 | + | 1.28836i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 10.6650 | − | 18.4722i | 0.451889 | − | 0.782694i | −0.546615 | − | 0.837384i | \(-0.684084\pi\) |
0.998503 | + | 0.0546900i | \(0.0174171\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −22.9789 | −0.971905 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 4.31946 | + | 0.536062i | 0.182368 | + | 0.0226326i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −15.7317 | − | 27.2482i | −0.663014 | − | 1.14837i | −0.979820 | − | 0.199884i | \(-0.935944\pi\) |
0.316805 | − | 0.948491i | \(-0.397390\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 11.9788 | − | 20.7480i | 0.503954 | − | 0.872873i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 23.6886 | − | 2.41863i | 0.994828 | − | 0.101573i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −14.6696 | + | 25.4084i | −0.614980 | + | 1.06518i | 0.375408 | + | 0.926860i | \(0.377503\pi\) |
−0.990388 | + | 0.138317i | \(0.955831\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 13.7473 | + | 23.8111i | 0.575308 | + | 0.996463i | 0.996008 | + | 0.0892631i | \(0.0284512\pi\) |
−0.420700 | + | 0.907200i | \(0.638215\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −10.8032 | − | 1.34072i | −0.451310 | − | 0.0560094i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −71.0221 | −2.96183 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −20.2293 | + | 35.0381i | −0.842156 | + | 1.45866i | 0.0459122 | + | 0.998945i | \(0.485381\pi\) |
−0.888068 | + | 0.459712i | \(0.847953\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −14.3377 | + | 18.9754i | −0.595854 | + | 0.788591i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −9.58331 | + | 6.49513i | −0.397583 | + | 0.269463i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.948067 | + | 1.64210i | −0.0392649 | + | 0.0680089i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 19.4444 | + | 68.4820i | 0.803927 | + | 2.83138i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −13.6559 | − | 23.6528i | −0.563641 | − | 0.976255i | −0.997175 | − | 0.0751177i | \(-0.976067\pi\) |
0.433533 | − | 0.901137i | \(-0.357267\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 5.94263 | − | 10.2929i | 0.244862 | − | 0.424113i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.108960 | + | 0.257624i | 0.00448201 | + | 0.0105972i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 14.2898 | + | 24.7507i | 0.586813 | + | 1.01639i | 0.994647 | + | 0.103334i | \(0.0329512\pi\) |
−0.407833 | + | 0.913056i | \(0.633716\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −28.5406 | − | 13.8416i | −1.17005 | − | 0.567449i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 42.6759 | + | 5.29625i | 1.74661 | + | 0.216761i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −19.9919 | − | 34.6270i | −0.816848 | − | 1.41482i | −0.907994 | − | 0.418984i | \(-0.862386\pi\) |
0.0911461 | − | 0.995838i | \(-0.470947\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.6948 | − | 21.9880i | −0.517831 | − | 0.896910i | −0.999785 | − | 0.0207133i | \(-0.993406\pi\) |
0.481954 | − | 0.876196i | \(-0.339927\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.30383 | − | 1.84123i | −0.297435 | − | 0.0749806i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −42.4679 | −1.72657 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −37.2939 | −1.51371 | −0.756856 | − | 0.653581i | \(-0.773266\pi\) | ||||
−0.756856 | + | 0.653581i | \(0.773266\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −6.92526 | − | 4.48819i | −0.280626 | − | 0.181870i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 6.71029 | + | 11.6226i | 0.271469 | + | 0.470199i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −11.7319 | + | 20.3203i | −0.473848 | + | 0.820729i | −0.999552 | − | 0.0299390i | \(-0.990469\pi\) |
0.525704 | + | 0.850668i | \(0.323802\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 83.9792 | + | 10.4222i | 3.38637 | + | 0.420262i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.56888 | − | 11.3776i | 0.264453 | − | 0.458047i | −0.702967 | − | 0.711223i | \(-0.748142\pi\) |
0.967420 | + | 0.253176i | \(0.0814752\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 21.5553 | 0.866380 | 0.433190 | − | 0.901303i | \(-0.357388\pi\) | ||||
0.433190 | + | 0.901303i | \(0.357388\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −28.2378 | − | 10.9660i | −1.13314 | − | 0.440050i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −25.5532 | + | 17.3188i | −1.02377 | + | 0.693862i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 62.5040 | 2.50016 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −3.64170 | + | 4.81965i | −0.145435 | + | 0.192478i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 15.3247 | 0.611036 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −6.15223 | −0.244916 | −0.122458 | − | 0.992474i | \(-0.539078\pi\) | ||||
−0.122458 | + | 0.992474i | \(0.539078\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −32.4730 | − | 4.03004i | −1.29069 | − | 0.160180i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 26.8388 | 1.06507 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −14.8457 | + | 37.2209i | −0.588207 | + | 1.47475i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.28064 | − | 2.34942i | 0.0902206 | − | 0.0929415i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.47364 | −0.176698 | −0.0883491 | − | 0.996090i | \(-0.528159\pi\) | ||||
−0.0883491 | + | 0.996090i | \(0.528159\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.98009 | − | 15.5540i | 0.354140 | − | 0.613389i | −0.632830 | − | 0.774291i | \(-0.718107\pi\) |
0.986970 | + | 0.160902i | \(0.0514402\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −17.3740 | + | 22.9939i | −0.684101 | + | 0.905383i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6.02992 | − | 10.4441i | 0.237061 | − | 0.410601i | −0.722809 | − | 0.691048i | \(-0.757149\pi\) |
0.959870 | + | 0.280447i | \(0.0904826\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.32688 | + | 2.29822i | 0.0520845 | + | 0.0902131i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 11.3864 | + | 7.37943i | 0.446269 | + | 0.289222i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −48.2733 | −1.88908 | −0.944540 | − | 0.328397i | \(-0.893492\pi\) | ||||
−0.944540 | + | 0.328397i | \(0.893492\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −73.4955 | −2.87171 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.18534 | + | 4.17469i | 0.0462445 | + | 0.162870i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.5795 | + | 25.2525i | 0.567937 | + | 0.983696i | 0.996770 | + | 0.0803122i | \(0.0255917\pi\) |
−0.428832 | + | 0.903384i | \(0.641075\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 7.27428 | + | 12.5994i | 0.282937 | + | 0.490061i | 0.972107 | − | 0.234539i | \(-0.0753581\pi\) |
−0.689170 | + | 0.724600i | \(0.742025\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 17.2885 | − | 22.8806i | 0.671429 | − | 0.888611i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 36.4416 | − | 24.6985i | 1.41315 | − | 0.957766i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.24922 | + | 9.09192i | 0.203251 | + | 0.352040i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 14.7169 | − | 19.4773i | 0.568989 | − | 0.753035i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.44722 | + | 4.23871i | −0.0944738 | + | 0.163633i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11.6825 | + | 20.2348i | 0.450329 | + | 0.779993i | 0.998406 | − | 0.0564349i | \(-0.0179733\pi\) |
−0.548077 | + | 0.836428i | \(0.684640\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 59.0095 | + | 22.9160i | 2.27128 | + | 0.882038i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.85875 | − | 15.3438i | 0.340469 | − | 0.589710i | −0.644051 | − | 0.764983i | \(-0.722747\pi\) |
0.984520 | + | 0.175273i | \(0.0560807\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 17.4675 | − | 11.8387i | 0.670343 | − | 0.454328i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17.5273 | − | 41.4415i | −0.671649 | − | 1.58804i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.7769 | − | 37.7186i | 0.833269 | − | 1.44326i | −0.0621637 | − | 0.998066i | \(-0.519800\pi\) |
0.895432 | − | 0.445198i | \(-0.146867\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11.2846 | 0.431161 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −16.8105 | − | 39.7466i | −0.641360 | − | 1.51643i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 6.24650 | + | 10.8193i | 0.237973 | + | 0.412181i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −11.7672 | + | 20.3814i | −0.447645 | + | 0.775345i | −0.998232 | − | 0.0594333i | \(-0.981071\pi\) |
0.550587 | + | 0.834778i | \(0.314404\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −5.28126 | − | 4.43485i | −0.200619 | − | 0.168466i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 35.8738 | − | 62.1353i | 1.36077 | − | 2.35693i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −17.0449 | − | 29.5225i | −0.645620 | − | 1.11825i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −6.38872 | + | 8.45523i | −0.241644 | + | 0.319806i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 45.1804 | 1.70644 | 0.853219 | − | 0.521552i | \(-0.174647\pi\) | ||||
0.853219 | + | 0.521552i | \(0.174647\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −10.6343 | + | 18.4191i | −0.401079 | + | 0.694689i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 16.7037 | + | 2.07299i | 0.629097 | + | 0.0780735i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −0.716748 | − | 9.93199i | −0.0269561 | − | 0.373531i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 13.5064 | − | 23.3937i | 0.507242 | − | 0.878568i | −0.492723 | − | 0.870186i | \(-0.663998\pi\) |
0.999965 | − | 0.00838223i | \(-0.00266818\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 1.74476 | + | 6.14495i | 0.0654337 | + | 0.230453i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −8.63071 | − | 14.9488i | −0.323223 | − | 0.559838i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.3089 | − | 17.8555i | 0.385529 | − | 0.667757i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 26.5388 | + | 3.29358i | 0.991111 | + | 0.123001i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −11.2096 | − | 19.4156i | −0.418048 | − | 0.724080i | 0.577695 | − | 0.816253i | \(-0.303952\pi\) |
−0.995743 | + | 0.0921724i | \(0.970619\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.06730 | + | 28.6466i | 0.0769902 | + | 1.06686i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.64247 | − | 15.7054i | −0.247036 | − | 0.584091i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −10.9695 | − | 18.9997i | −0.407396 | − | 0.705631i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 21.9820 | + | 38.0740i | 0.815268 | + | 1.41208i | 0.909136 | + | 0.416500i | \(0.136744\pi\) |
−0.0938680 | + | 0.995585i | \(0.529923\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 19.9234 | + | 18.2224i | 0.737904 | + | 0.674905i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 11.6097 | 0.429401 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 0.866772 | 0.0320149 | 0.0160075 | − | 0.999872i | \(-0.494904\pi\) | ||||
0.0160075 | + | 0.999872i | \(0.494904\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 26.0205 | + | 42.9975i | 0.959781 | + | 1.58599i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.09075 | + | 1.88924i | 0.0401785 | + | 0.0695911i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 13.0442 | − | 22.5932i | 0.479838 | − | 0.831103i | −0.519895 | − | 0.854230i | \(-0.674029\pi\) |
0.999733 | + | 0.0231270i | \(0.00736222\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.5037 | + | 36.6569i | 0.569544 | + | 1.34662i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 22.5842 | − | 39.1170i | 0.828533 | − | 1.43506i | −0.0706551 | − | 0.997501i | \(-0.522509\pi\) |
0.899189 | − | 0.437561i | \(-0.144158\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −28.3816 | −1.03982 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −12.7288 | − | 3.20882i | −0.465724 | − | 0.117405i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 21.1278 | − | 14.3195i | 0.771994 | − | 0.523222i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −20.5988 | −0.751662 | −0.375831 | − | 0.926688i | \(-0.622643\pi\) | ||||
−0.375831 | + | 0.926688i | \(0.622643\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −18.1387 | − | 42.8869i | −0.661009 | − | 1.56288i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 38.4743 | 1.40022 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −39.0856 | −1.42059 | −0.710294 | − | 0.703905i | \(-0.751438\pi\) | ||||
−0.710294 | + | 0.703905i | \(0.751438\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.41749 | + | 8.08028i | 0.124047 | + | 0.293295i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −28.8872 | −1.04716 | −0.523581 | − | 0.851976i | \(-0.675404\pi\) | ||||
−0.523581 | + | 0.851976i | \(0.675404\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −27.9065 | − | 13.5340i | −1.01028 | − | 0.489964i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.82396 | − | 34.5994i | −0.355186 | − | 1.25094i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 17.4847 | 0.631336 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.1407 | + | 19.2962i | −0.401742 | + | 0.695838i | −0.993936 | − | 0.109957i | \(-0.964929\pi\) |
0.592194 | + | 0.805796i | \(0.298262\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −7.43021 | − | 17.5679i | −0.267592 | − | 0.632693i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −21.3593 | + | 36.9955i | −0.768242 | + | 1.33063i | 0.170273 | + | 0.985397i | \(0.445535\pi\) |
−0.938515 | + | 0.345238i | \(0.887798\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 18.0359 | + | 31.2391i | 0.647868 | + | 1.12214i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −20.3759 | − | 13.2054i | −0.730980 | − | 0.473741i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 47.3116 | 1.69512 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −0.948302 | −0.0339329 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.42777 | − | 9.24784i | −0.0510245 | − | 0.330491i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −28.3465 | − | 49.0976i | −1.01173 | − | 1.75237i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.143384 | + | 0.248349i | 0.00511110 | + | 0.00885268i | 0.868570 | − | 0.495567i | \(-0.165040\pi\) |
−0.863459 | + | 0.504420i | \(0.831706\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.93265 | + | 11.6627i | 0.175607 | + | 0.415203i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.7588 | + | 6.67270i | 0.489205 | + | 0.237254i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 16.1239 | + | 27.9274i | 0.572577 | + | 0.991732i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 15.5492 | + | 1.92971i | 0.551472 | + | 0.0684399i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.457746 | + | 0.792840i | −0.0162142 | + | 0.0280838i | −0.874019 | − | 0.485892i | \(-0.838495\pi\) |
0.857804 | + | 0.513976i | \(0.171828\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −3.39026 | − | 5.87211i | −0.119939 | − | 0.207740i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −33.9405 | − | 8.55609i | −1.19923 | − | 0.302315i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 0.628433 | − | 1.08848i | 0.0221769 | − | 0.0384115i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −4.60201 | − | 63.7702i | −0.162200 | − | 2.24760i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 7.15211 | + | 0.887606i | 0.251766 | + | 0.0312452i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −14.3721 | + | 24.8932i | −0.505297 | + | 0.875199i | 0.494685 | + | 0.869073i | \(0.335284\pi\) |
−0.999981 | + | 0.00612685i | \(0.998050\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.3005 | 0.502157 | 0.251079 | − | 0.967967i | \(-0.419215\pi\) | ||||
0.251079 | + | 0.967967i | \(0.419215\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.73553 | + | 11.5611i | −0.306368 | + | 0.405467i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.83969 | − | 11.8467i | −0.239584 | − | 0.414971i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −8.05632 | + | 13.9540i | −0.281855 | + | 0.488187i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −42.7033 | + | 15.5247i | −1.49217 | + | 0.542478i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −17.8125 | + | 30.8521i | −0.621660 | + | 1.07675i | 0.367516 | + | 0.930017i | \(0.380208\pi\) |
−0.989177 | + | 0.146730i | \(0.953125\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.2157 | + | 19.4261i | 0.390953 | + | 0.677151i | 0.992576 | − | 0.121630i | \(-0.0388121\pi\) |
−0.601622 | + | 0.798781i | \(0.705479\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −7.14164 | − | 16.8856i | −0.248640 | − | 0.587882i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −26.6728 | −0.927505 | −0.463753 | − | 0.885965i | \(-0.653497\pi\) | ||||
−0.463753 | + | 0.885965i | \(0.653497\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −16.0078 | + | 27.7263i | −0.555973 | + | 0.962973i | 0.441854 | + | 0.897087i | \(0.354321\pi\) |
−0.997827 | + | 0.0658866i | \(0.979012\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.88817 | + | 4.46437i | 0.0654998 | + | 0.154867i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 7.50053 | − | 18.8053i | 0.259878 | − | 0.651563i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 24.7148 | − | 42.8074i | 0.855292 | − | 1.48141i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 2.34753 | + | 15.2052i | 0.0811425 | + | 0.525568i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 9.10375 | + | 15.7682i | 0.314296 | + | 0.544377i | 0.979288 | − | 0.202474i | \(-0.0648982\pi\) |
−0.664991 | + | 0.746851i | \(0.731565\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 12.8785 | − | 22.3062i | 0.444086 | − | 0.769180i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −11.3671 | + | 15.0440i | −0.391505 | + | 0.518142i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −40.9778 | − | 70.9757i | −1.40968 | − | 2.44164i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.95104 | − | 27.0356i | −0.0670386 | − | 0.928956i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 2.11365 | − | 2.79734i | 0.0725403 | − | 0.0960044i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 15.4445 | + | 26.7507i | 0.529432 | + | 0.917003i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 20.9242 | + | 36.2419i | 0.716432 | + | 1.24090i | 0.962404 | + | 0.271621i | \(0.0875596\pi\) |
−0.245972 | + | 0.969277i | \(0.579107\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 48.4029 | + | 12.2019i | 1.65534 | + | 0.417297i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 15.7141 | 0.536783 | 0.268391 | − | 0.963310i | \(-0.413508\pi\) | ||||
0.268391 | + | 0.963310i | \(0.413508\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 24.2046 | 0.825849 | 0.412924 | − | 0.910765i | \(-0.364507\pi\) | ||||
0.412924 | + | 0.910765i | \(0.364507\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −2.77675 | + | 53.9411i | −0.0946314 | + | 1.83831i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 26.0542 | + | 45.1272i | 0.886896 | + | 1.53615i | 0.843525 | + | 0.537090i | \(0.180477\pi\) |
0.0433714 | + | 0.999059i | \(0.486190\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 19.9672 | − | 34.5842i | 0.678904 | − | 1.17590i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 9.01619 | − | 11.9326i | 0.306206 | − | 0.405252i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0.925022 | − | 1.60219i | 0.0313792 | − | 0.0543504i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 14.3732 | 0.487018 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 23.2009 | + | 5.84874i | 0.785232 | + | 0.197950i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 5.66999 | + | 78.5691i | 0.191680 | + | 2.65612i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −13.9768 | −0.471964 | −0.235982 | − | 0.971757i | \(-0.575831\pi\) | ||||
−0.235982 | + | 0.971757i | \(0.575831\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 33.1895 | + | 4.11895i | 1.11945 | + | 0.138929i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 28.1210 | 0.947421 | 0.473710 | − | 0.880681i | \(-0.342914\pi\) | ||||
0.473710 | + | 0.880681i | \(0.342914\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −35.1633 | −1.18334 | −0.591670 | − | 0.806180i | \(-0.701531\pi\) | ||||
−0.591670 | + | 0.806180i | \(0.701531\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.2199 | − | 17.4961i | 0.444383 | − | 0.588124i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −26.9219 | −0.903950 | −0.451975 | − | 0.892031i | \(-0.649280\pi\) | ||||
−0.451975 | + | 0.892031i | \(0.649280\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.23302 | + | 17.0860i | 0.0413541 | + | 0.573045i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.232272 | − | 7.81627i | −0.00778142 | − | 0.261855i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 9.41041 | 0.314907 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −47.7880 | + | 82.7713i | −1.59738 | + | 2.76674i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 57.3640 | + | 7.11911i | 1.91533 | + | 0.237700i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2.66605 | − | 4.61774i | 0.0889179 | − | 0.154010i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.15594 | − | 5.46625i | −0.105140 | − | 0.182107i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −15.4364 | − | 10.0042i | −0.513691 | − | 0.332918i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −49.0481 | −1.63041 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −44.7142 | −1.48471 | −0.742355 | − | 0.670007i | \(-0.766291\pi\) | ||||
−0.742355 | + | 0.670007i | \(0.766291\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.86455 | − | 8.10173i | 0.260851 | − | 0.268717i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −13.7822 | − | 23.8715i | −0.456626 | − | 0.790899i | 0.542154 | − | 0.840279i | \(-0.317609\pi\) |
−0.998780 | + | 0.0493800i | \(0.984275\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.90093 | + | 3.29250i | 0.0629115 | + | 0.108966i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 40.1366 | + | 4.98112i | 1.32688 | + | 0.164671i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −3.37650 | − | 46.7882i | −0.111502 | − | 1.54508i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −21.3836 | − | 37.0376i | −0.705381 | − | 1.22176i | −0.966554 | − | 0.256464i | \(-0.917442\pi\) |
0.261173 | − | 0.965292i | \(-0.415891\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.86398 | + | 20.9579i | 0.292078 | + | 0.690587i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.12402 | + | 5.41096i | −0.102828 | + | 0.178104i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −32.2750 | − | 55.9019i | −1.06119 | − | 1.83804i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −22.6835 | + | 23.3676i | −0.745025 | + | 0.767493i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −23.9748 | + | 41.5256i | −0.786589 | + | 1.36241i | 0.141456 | + | 0.989945i | \(0.454822\pi\) |
−0.928045 | + | 0.372468i | \(0.878512\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 17.3976 | + | 22.0645i | 0.570182 | + | 0.723136i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 14.1299 | − | 18.7003i | 0.462591 | − | 0.612221i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5.20838 | + | 9.02118i | −0.170332 | + | 0.295024i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.9136 | 1.10791 | 0.553955 | − | 0.832547i | \(-0.313118\pi\) | ||||
0.553955 | + | 0.832547i | \(0.313118\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −43.3154 | − | 5.37562i | −1.41354 | − | 0.175427i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 4.27395 | + | 7.40270i | 0.139327 | + | 0.241321i | 0.927242 | − | 0.374463i | \(-0.122173\pi\) |
−0.787915 | + | 0.615784i | \(0.788839\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 34.3563 | − | 59.5068i | 1.11879 | − | 1.93781i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −16.7525 | + | 54.4691i | −0.544958 | + | 1.77188i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −0.411563 | + | 0.712848i | −0.0133740 | + | 0.0231645i | −0.872635 | − | 0.488373i | \(-0.837591\pi\) |
0.859261 | + | 0.511538i | \(0.170924\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.14053 | − | 7.17161i | −0.134407 | − | 0.232800i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −21.1382 | − | 2.62334i | −0.685453 | − | 0.0850675i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −44.6726 | −1.44709 | −0.723544 | − | 0.690278i | \(-0.757488\pi\) | ||||
−0.723544 | + | 0.690278i | \(0.757488\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 13.0264 | − | 22.5625i | 0.421526 | − | 0.730104i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −1.63378 | + | 2.16225i | −0.0528127 | + | 0.0698956i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.518430 | + | 7.18390i | 0.0167410 | + | 0.231980i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 11.1165 | − | 19.2544i | 0.358597 | − | 0.621108i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 28.0626 | + | 7.07433i | 0.904305 | + | 0.227967i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −28.4592 | − | 49.2928i | −0.916135 | − | 1.58679i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −18.2289 | + | 31.5735i | −0.586203 | + | 1.01533i | 0.408521 | + | 0.912749i | \(0.366045\pi\) |
−0.994724 | + | 0.102585i | \(0.967289\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.83301 | − | 18.5203i | −0.251632 | − | 0.594957i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.63674 | + | 14.9593i | 0.277166 | + | 0.480066i | 0.970679 | − | 0.240378i | \(-0.0772714\pi\) |
−0.693513 | + | 0.720444i | \(0.743938\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 41.2043 | + | 19.9832i | 1.32095 | + | 0.640631i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −119.875 | − | 14.8770i | −3.83909 | − | 0.476446i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −4.51775 | − | 7.82497i | −0.144536 | − | 0.250343i | 0.784664 | − | 0.619921i | \(-0.212835\pi\) |
−0.929200 | + | 0.369578i | \(0.879502\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.06868 | + | 8.77921i | 0.161996 | + | 0.280585i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.60567 | − | 33.8306i | −0.306686 | − | 1.08013i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −22.8573 | −0.729034 | −0.364517 | − | 0.931197i | \(-0.618766\pi\) | ||||
−0.364517 | + | 0.931197i | \(0.618766\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −0.669430 | −0.0213298 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −0.552303 | + | 10.7290i | −0.0175800 | + | 0.341508i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 11.7005 | + | 20.2659i | 0.372055 | + | 0.644417i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.37884 | + | 7.58437i | −0.139098 | + | 0.240925i | −0.927156 | − | 0.374677i | \(-0.877754\pi\) |
0.788057 | + | 0.615602i | \(0.211087\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −34.2496 | − | 4.25051i | −1.08688 | − | 0.134886i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −51.4584 | + | 89.1285i | −1.63134 | + | 2.82556i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 6.93070 | 0.219498 | 0.109749 | − | 0.993959i | \(-0.464995\pi\) | ||||
0.109749 | + | 0.993959i | \(0.464995\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −4.20087 | − | 27.2095i | −0.132910 | − | 0.860870i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))