Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [450,2,Mod(91,450)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(450, base_ring=CyclotomicField(10))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("450.91");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 450 = 2 \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 450.h (of order \(5\), degree \(4\), 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: | \(3.59326809096\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{5})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - x^{11} + 6 x^{10} - 26 x^{9} + 61 x^{8} - 120 x^{7} + 465 x^{6} - 600 x^{5} + 1525 x^{4} + \cdots + 15625 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{5}]$ |
Embedding invariants
Embedding label | 271.3 | ||
Root | \(-1.24741 + 1.85579i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 450.271 |
Dual form | 450.2.h.g.181.3 |
$q$-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 \(\left(\mathbb{Z}/450\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{3}{5}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.309017 | + | 0.951057i | −0.218508 | + | 0.672499i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.809017 | − | 0.587785i | −0.404508 | − | 0.293893i | ||||
\(5\) | 1.24741 | − | 1.85579i | 0.557858 | − | 0.829936i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.68284 | −1.01402 | −0.507008 | − | 0.861941i | \(-0.669249\pi\) | ||||
−0.507008 | + | 0.861941i | \(0.669249\pi\) | |||||||
\(8\) | 0.809017 | − | 0.587785i | 0.286031 | − | 0.207813i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.37949 | + | 1.75983i | 0.436234 | + | 0.556507i | ||||
\(11\) | 0.167451 | − | 0.515361i | 0.0504884 | − | 0.155387i | −0.922634 | − | 0.385678i | \(-0.873968\pi\) |
0.973122 | + | 0.230291i | \(0.0739677\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.55643 | − | 4.79019i | −0.431675 | − | 1.32856i | −0.896456 | − | 0.443133i | \(-0.853867\pi\) |
0.464781 | − | 0.885426i | \(-0.346133\pi\) | |||||||
\(14\) | 0.829042 | − | 2.55153i | 0.221571 | − | 0.681925i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.309017 | + | 0.951057i | 0.0772542 | + | 0.237764i | ||||
\(17\) | 6.22521 | − | 4.52288i | 1.50984 | − | 1.09696i | 0.543586 | − | 0.839354i | \(-0.317066\pi\) |
0.966250 | − | 0.257606i | \(-0.0829337\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −5.05944 | + | 3.67590i | −1.16071 | + | 0.843308i | −0.989868 | − | 0.141990i | \(-0.954650\pi\) |
−0.170846 | + | 0.985298i | \(0.554650\pi\) | |||||||
\(20\) | −2.09998 | + | 0.768160i | −0.469571 | + | 0.171766i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.438392 | + | 0.318511i | 0.0934655 | + | 0.0679067i | ||||
\(23\) | 1.50887 | − | 4.64382i | 0.314621 | − | 0.968304i | −0.661289 | − | 0.750131i | \(-0.729990\pi\) |
0.975910 | − | 0.218173i | \(-0.0700096\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.88794 | − | 4.62987i | −0.377588 | − | 0.925974i | ||||
\(26\) | 5.03670 | 0.987778 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 2.17046 | + | 1.57693i | 0.410178 | + | 0.298012i | ||||
\(29\) | −4.62991 | − | 3.36383i | −0.859753 | − | 0.624647i | 0.0680646 | − | 0.997681i | \(-0.478318\pi\) |
−0.927818 | + | 0.373034i | \(0.878318\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.53838 | − | 1.84424i | 0.455906 | − | 0.331235i | −0.336017 | − | 0.941856i | \(-0.609080\pi\) |
0.791923 | + | 0.610621i | \(0.209080\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 2.37782 | + | 7.31818i | 0.407793 | + | 1.25506i | ||||
\(35\) | −3.34660 | + | 4.97879i | −0.565678 | + | 0.841569i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.07737 | − | 3.31581i | −0.177119 | − | 0.545116i | 0.822605 | − | 0.568613i | \(-0.192520\pi\) |
−0.999724 | + | 0.0234975i | \(0.992520\pi\) | |||||||
\(38\) | −1.93253 | − | 5.94772i | −0.313498 | − | 0.964848i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.0816329 | − | 2.23458i | −0.0129073 | − | 0.353318i | ||||
\(41\) | 1.70564 | + | 5.24942i | 0.266376 | + | 0.819822i | 0.991373 | + | 0.131070i | \(0.0418413\pi\) |
−0.724997 | + | 0.688752i | \(0.758159\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 12.9002 | 1.96726 | 0.983629 | − | 0.180206i | \(-0.0576765\pi\) | ||||
0.983629 | + | 0.180206i | \(0.0576765\pi\) | |||||||
\(44\) | −0.438392 | + | 0.318511i | −0.0660901 | + | 0.0480173i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 3.95027 | + | 2.87004i | 0.582436 | + | 0.423164i | ||||
\(47\) | 1.41338 | + | 1.02688i | 0.206163 | + | 0.149786i | 0.686076 | − | 0.727530i | \(-0.259332\pi\) |
−0.479913 | + | 0.877316i | \(0.659332\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0.197613 | 0.0282304 | ||||||||
\(50\) | 4.98667 | − | 0.364830i | 0.705222 | − | 0.0515947i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.55643 | + | 4.79019i | −0.215837 | + | 0.664279i | ||||
\(53\) | 8.24147 | + | 5.98778i | 1.13205 | + | 0.822485i | 0.985992 | − | 0.166790i | \(-0.0533403\pi\) |
0.146061 | + | 0.989276i | \(0.453340\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −0.747524 | − | 0.953620i | −0.100796 | − | 0.128586i | ||||
\(56\) | −2.17046 | + | 1.57693i | −0.290040 | + | 0.210726i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.62991 | − | 3.36383i | 0.607937 | − | 0.441692i | ||||
\(59\) | 0.245881 | + | 0.756745i | 0.0320110 | + | 0.0985199i | 0.965785 | − | 0.259342i | \(-0.0835058\pi\) |
−0.933774 | + | 0.357862i | \(0.883506\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −0.530688 | + | 1.63329i | −0.0679477 | + | 0.209121i | −0.979265 | − | 0.202583i | \(-0.935066\pi\) |
0.911317 | + | 0.411704i | \(0.135066\pi\) | |||||||
\(62\) | 0.969573 | + | 2.98404i | 0.123136 | + | 0.378973i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0.309017 | − | 0.951057i | 0.0386271 | − | 0.118882i | ||||
\(65\) | −10.8311 | − | 3.08692i | −1.34343 | − | 0.382885i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −11.0177 | + | 8.00483i | −1.34603 | + | 0.977946i | −0.346828 | + | 0.937929i | \(0.612741\pi\) |
−0.999199 | + | 0.0400172i | \(0.987259\pi\) | |||||||
\(68\) | −7.69479 | −0.933130 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −3.70096 | − | 4.72133i | −0.442349 | − | 0.564307i | ||||
\(71\) | −6.99463 | − | 5.08190i | −0.830110 | − | 0.603110i | 0.0894803 | − | 0.995989i | \(-0.471479\pi\) |
−0.919591 | + | 0.392878i | \(0.871479\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 0.402106 | − | 1.23755i | 0.0470629 | − | 0.144845i | −0.924764 | − | 0.380542i | \(-0.875737\pi\) |
0.971827 | + | 0.235697i | \(0.0757374\pi\) | |||||||
\(74\) | 3.48645 | 0.405291 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 6.25381 | 0.717361 | ||||||||
\(77\) | −0.449244 | + | 1.38263i | −0.0511961 | + | 0.157565i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 2.61562 | + | 1.90036i | 0.294281 | + | 0.213807i | 0.725122 | − | 0.688620i | \(-0.241783\pi\) |
−0.430842 | + | 0.902428i | \(0.641783\pi\) | |||||||
\(80\) | 2.15044 | + | 0.612885i | 0.240426 | + | 0.0685226i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −5.51957 | −0.609535 | ||||||||
\(83\) | −0.617229 | + | 0.448443i | −0.0677497 | + | 0.0492230i | −0.621145 | − | 0.783696i | \(-0.713332\pi\) |
0.553395 | + | 0.832919i | \(0.313332\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.628147 | − | 17.1946i | −0.0681322 | − | 1.86502i | ||||
\(86\) | −3.98637 | + | 12.2688i | −0.429862 | + | 1.32298i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.167451 | − | 0.515361i | −0.0178503 | − | 0.0549377i | ||||
\(89\) | −2.26290 | + | 6.96448i | −0.239867 | + | 0.738234i | 0.756572 | + | 0.653911i | \(0.226873\pi\) |
−0.996438 | + | 0.0843230i | \(0.973127\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.17564 | + | 12.8513i | 0.437726 | + | 1.34718i | ||||
\(92\) | −3.95027 | + | 2.87004i | −0.411844 | + | 0.299222i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.41338 | + | 1.02688i | −0.145779 | + | 0.105915i | ||||
\(95\) | 0.510516 | + | 13.9746i | 0.0523779 | + | 1.43377i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.24177 | − | 6.71454i | −0.938360 | − | 0.681759i | 0.00966528 | − | 0.999953i | \(-0.496923\pi\) |
−0.948025 | + | 0.318195i | \(0.896923\pi\) | |||||||
\(98\) | −0.0610656 | + | 0.187941i | −0.00616856 | + | 0.0189849i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.19399 | + | 4.85535i | −0.119399 | + | 0.485535i | ||||
\(101\) | −2.23667 | −0.222557 | −0.111278 | − | 0.993789i | \(-0.535495\pi\) | ||||
−0.111278 | + | 0.993789i | \(0.535495\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −8.45660 | − | 6.14408i | −0.833253 | − | 0.605394i | 0.0872247 | − | 0.996189i | \(-0.472200\pi\) |
−0.920478 | + | 0.390795i | \(0.872200\pi\) | |||||||
\(104\) | −4.07478 | − | 2.96050i | −0.399565 | − | 0.290301i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.24147 | + | 5.98778i | −0.800483 | + | 0.581585i | ||||
\(107\) | 5.92492 | 0.572784 | 0.286392 | − | 0.958113i | \(-0.407544\pi\) | ||||
0.286392 | + | 0.958113i | \(0.407544\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 2.65733 | + | 8.17842i | 0.254526 | + | 0.783351i | 0.993923 | + | 0.110081i | \(0.0351109\pi\) |
−0.739397 | + | 0.673270i | \(0.764889\pi\) | |||||||
\(110\) | 1.13794 | − | 0.416252i | 0.108499 | − | 0.0396881i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −0.829042 | − | 2.55153i | −0.0783371 | − | 0.241097i | ||||
\(113\) | −0.748822 | − | 2.30464i | −0.0704433 | − | 0.216802i | 0.909637 | − | 0.415404i | \(-0.136360\pi\) |
−0.980080 | + | 0.198602i | \(0.936360\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −6.73580 | − | 8.59290i | −0.628116 | − | 0.801292i | ||||
\(116\) | 1.76847 | + | 5.44279i | 0.164198 | + | 0.505350i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.795689 | −0.0732491 | ||||||||
\(119\) | −16.7012 | + | 12.1342i | −1.53100 | + | 1.11234i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.66163 | + | 6.29304i | 0.787421 | + | 0.572095i | ||||
\(122\) | −1.38936 | − | 1.00943i | −0.125787 | − | 0.0913894i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.13760 | −0.281765 | ||||||||
\(125\) | −10.9471 | − | 2.27171i | −0.979140 | − | 0.203188i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.451862 | − | 1.39069i | 0.0400963 | − | 0.123404i | −0.929005 | − | 0.370068i | \(-0.879334\pi\) |
0.969101 | + | 0.246664i | \(0.0793344\pi\) | |||||||
\(128\) | 0.809017 | + | 0.587785i | 0.0715077 | + | 0.0519534i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 6.28283 | − | 9.34708i | 0.551040 | − | 0.819793i | ||||
\(131\) | 15.9222 | − | 11.5682i | 1.39113 | − | 1.01072i | 0.395391 | − | 0.918513i | \(-0.370609\pi\) |
0.995740 | − | 0.0922028i | \(-0.0293908\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.5736 | − | 9.86183i | 1.17698 | − | 0.855129i | ||||
\(134\) | −4.20839 | − | 12.9521i | −0.363549 | − | 1.11889i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.37782 | − | 7.31818i | 0.203896 | − | 0.627528i | ||||
\(137\) | −1.82551 | − | 5.61833i | −0.155964 | − | 0.480007i | 0.842294 | − | 0.539019i | \(-0.181205\pi\) |
−0.998257 | + | 0.0590123i | \(0.981205\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −5.38071 | + | 16.5601i | −0.456386 | + | 1.40461i | 0.413115 | + | 0.910679i | \(0.364441\pi\) |
−0.869500 | + | 0.493932i | \(0.835559\pi\) | |||||||
\(140\) | 5.63391 | − | 2.06085i | 0.476153 | − | 0.174173i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.99463 | − | 5.08190i | 0.586977 | − | 0.426463i | ||||
\(143\) | −2.72930 | −0.228236 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −12.0180 | + | 4.39609i | −0.998038 | + | 0.365076i | ||||
\(146\) | 1.05273 | + | 0.764851i | 0.0871243 | + | 0.0632995i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1.07737 | + | 3.31581i | −0.0885594 | + | 0.272558i | ||||
\(149\) | 16.1584 | 1.32375 | 0.661874 | − | 0.749615i | \(-0.269761\pi\) | ||||
0.661874 | + | 0.749615i | \(0.269761\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.1900 | 0.829248 | 0.414624 | − | 0.909993i | \(-0.363913\pi\) | ||||
0.414624 | + | 0.909993i | \(0.363913\pi\) | |||||||
\(152\) | −1.93253 | + | 5.94772i | −0.156749 | + | 0.482424i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.17613 | − | 0.854512i | −0.0947756 | − | 0.0688585i | ||||
\(155\) | −0.256132 | − | 7.01122i | −0.0205730 | − | 0.563155i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 0.868121 | 0.0692836 | 0.0346418 | − | 0.999400i | \(-0.488971\pi\) | ||||
0.0346418 | + | 0.999400i | \(0.488971\pi\) | |||||||
\(158\) | −2.61562 | + | 1.90036i | −0.208088 | + | 0.151185i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −1.24741 | + | 1.85579i | −0.0986164 | + | 0.146713i | ||||
\(161\) | −4.04805 | + | 12.4586i | −0.319031 | + | 0.981877i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.51983 | + | 7.75525i | 0.197368 | + | 0.607438i | 0.999941 | + | 0.0108829i | \(0.00346420\pi\) |
−0.802572 | + | 0.596555i | \(0.796536\pi\) | |||||||
\(164\) | 1.70564 | − | 5.24942i | 0.133188 | − | 0.409911i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −0.235761 | − | 0.725596i | −0.0182986 | − | 0.0563172i | ||||
\(167\) | −4.15450 | + | 3.01842i | −0.321485 | + | 0.233572i | −0.736809 | − | 0.676101i | \(-0.763668\pi\) |
0.415324 | + | 0.909674i | \(0.363668\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −10.0062 | + | 7.26994i | −0.769709 | + | 0.559226i | ||||
\(170\) | 16.5471 | + | 4.71602i | 1.26911 | + | 0.361702i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −10.4365 | − | 7.58253i | −0.795772 | − | 0.578163i | ||||
\(173\) | −5.45037 | + | 16.7745i | −0.414384 | + | 1.27534i | 0.498417 | + | 0.866937i | \(0.333915\pi\) |
−0.912801 | + | 0.408405i | \(0.866085\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.06504 | + | 12.4212i | 0.382881 | + | 0.938953i | ||||
\(176\) | 0.541883 | 0.0408459 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −5.92434 | − | 4.30429i | −0.444048 | − | 0.322620i | ||||
\(179\) | 13.3621 | + | 9.70812i | 0.998729 | + | 0.725619i | 0.961815 | − | 0.273699i | \(-0.0882474\pi\) |
0.0369136 | + | 0.999318i | \(0.488247\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 15.6169 | − | 11.3463i | 1.16079 | − | 0.843366i | 0.170916 | − | 0.985286i | \(-0.445327\pi\) |
0.989878 | + | 0.141920i | \(0.0453274\pi\) | |||||||
\(182\) | −13.5126 | −1.00162 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.50887 | − | 4.64382i | −0.111235 | − | 0.342347i | ||||
\(185\) | −7.49738 | − | 2.13679i | −0.551218 | − | 0.157100i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.28850 | − | 3.96559i | −0.0942244 | − | 0.289993i | ||||
\(188\) | −0.539865 | − | 1.66153i | −0.0393737 | − | 0.121180i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −13.4484 | − | 3.83286i | −0.975650 | − | 0.278065i | ||||
\(191\) | −7.94718 | − | 24.4589i | −0.575038 | − | 1.76978i | −0.636050 | − | 0.771648i | \(-0.719433\pi\) |
0.0610119 | − | 0.998137i | \(-0.480567\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.93834 | 0.643396 | 0.321698 | − | 0.946842i | \(-0.395746\pi\) | ||||
0.321698 | + | 0.946842i | \(0.395746\pi\) | |||||||
\(194\) | 9.24177 | − | 6.71454i | 0.663521 | − | 0.482076i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.159872 | − | 0.116154i | −0.0114194 | − | 0.00829670i | ||||
\(197\) | 10.4272 | + | 7.57581i | 0.742908 | + | 0.539754i | 0.893620 | − | 0.448824i | \(-0.148157\pi\) |
−0.150713 | + | 0.988578i | \(0.548157\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 16.5675 | 1.17444 | 0.587218 | − | 0.809428i | \(-0.300223\pi\) | ||||
0.587218 | + | 0.809428i | \(0.300223\pi\) | |||||||
\(200\) | −4.24874 | − | 2.63594i | −0.300432 | − | 0.186389i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0.691168 | − | 2.12720i | 0.0486304 | − | 0.149669i | ||||
\(203\) | 12.4213 | + | 9.02460i | 0.871804 | + | 0.633403i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 11.8695 | + | 3.38286i | 0.829000 | + | 0.236269i | ||||
\(206\) | 8.45660 | − | 6.14408i | 0.589199 | − | 0.428078i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.07478 | − | 2.96050i | 0.282535 | − | 0.205274i | ||||
\(209\) | 1.04721 | + | 3.22297i | 0.0724367 | + | 0.222937i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −7.07675 | + | 21.7800i | −0.487184 | + | 1.49940i | 0.341609 | + | 0.939842i | \(0.389028\pi\) |
−0.828793 | + | 0.559555i | \(0.810972\pi\) | |||||||
\(212\) | −3.14796 | − | 9.68843i | −0.216203 | − | 0.665404i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.83090 | + | 5.63494i | −0.125158 | + | 0.385196i | ||||
\(215\) | 16.0918 | − | 23.9401i | 1.09745 | − | 1.63270i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −6.81005 | + | 4.94779i | −0.462296 | + | 0.335878i | ||||
\(218\) | −8.59930 | −0.582418 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.0442354 | + | 1.21088i | 0.00298235 | + | 0.0816374i | ||||
\(221\) | −31.3545 | − | 22.7804i | −2.10913 | − | 1.53238i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2.79582 | + | 8.60464i | −0.187222 | + | 0.576209i | −0.999980 | − | 0.00639253i | \(-0.997965\pi\) |
0.812758 | + | 0.582602i | \(0.197965\pi\) | |||||||
\(224\) | 2.68284 | 0.179255 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.42324 | 0.161192 | ||||||||
\(227\) | 6.66088 | − | 20.5001i | 0.442098 | − | 1.36064i | −0.443536 | − | 0.896256i | \(-0.646276\pi\) |
0.885635 | − | 0.464383i | \(-0.153724\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.95698 | − | 7.23417i | −0.657976 | − | 0.478047i | 0.208003 | − | 0.978128i | \(-0.433304\pi\) |
−0.865979 | + | 0.500081i | \(0.833304\pi\) | |||||||
\(230\) | 10.2538 | − | 3.75077i | 0.676116 | − | 0.247319i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.72289 | −0.375726 | ||||||||
\(233\) | 23.4944 | − | 17.0697i | 1.53917 | − | 1.11827i | 0.588319 | − | 0.808629i | \(-0.299790\pi\) |
0.950852 | − | 0.309645i | \(-0.100210\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.66875 | − | 1.34201i | 0.239323 | − | 0.0875428i | ||||
\(236\) | 0.245881 | − | 0.756745i | 0.0160055 | − | 0.0492599i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −6.37930 | − | 19.6335i | −0.413509 | − | 1.27265i | ||||
\(239\) | −3.16021 | + | 9.72613i | −0.204417 | + | 0.629131i | 0.795320 | + | 0.606190i | \(0.207303\pi\) |
−0.999737 | + | 0.0229408i | \(0.992697\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.55006 | − | 7.84827i | −0.164264 | − | 0.505551i | 0.834718 | − | 0.550678i | \(-0.185631\pi\) |
−0.998981 | + | 0.0451268i | \(0.985631\pi\) | |||||||
\(242\) | −8.66163 | + | 6.29304i | −0.556791 | + | 0.404532i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.38936 | − | 1.00943i | 0.0889446 | − | 0.0646221i | ||||
\(245\) | 0.246504 | − | 0.366728i | 0.0157485 | − | 0.0234294i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 25.4829 | + | 18.5144i | 1.62144 | + | 1.17804i | ||||
\(248\) | 0.969573 | − | 2.98404i | 0.0615680 | − | 0.189487i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5.54337 | − | 9.70933i | 0.350594 | − | 0.614072i | ||||
\(251\) | 20.2355 | 1.27726 | 0.638628 | − | 0.769515i | \(-0.279502\pi\) | ||||
0.638628 | + | 0.769515i | \(0.279502\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.14058 | − | 1.55522i | −0.134577 | − | 0.0977761i | ||||
\(254\) | 1.18299 | + | 0.859493i | 0.0742274 | + | 0.0539294i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.809017 | + | 0.587785i | −0.0505636 | + | 0.0367366i | ||||
\(257\) | −3.26629 | −0.203745 | −0.101873 | − | 0.994797i | \(-0.532483\pi\) | ||||
−0.101873 | + | 0.994797i | \(0.532483\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.89041 | + | 8.89577i | 0.179601 | + | 0.552757i | ||||
\(260\) | 6.94810 | + | 8.86373i | 0.430903 | + | 0.549705i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.08175 | + | 18.7177i | 0.375732 | + | 1.15638i | ||||
\(263\) | −1.72720 | − | 5.31577i | −0.106504 | − | 0.327784i | 0.883577 | − | 0.468286i | \(-0.155128\pi\) |
−0.990080 | + | 0.140502i | \(0.955128\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 21.3926 | − | 7.82526i | 1.31414 | − | 0.480702i | ||||
\(266\) | 5.18467 | + | 15.9568i | 0.317892 | + | 0.978372i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 13.6186 | 0.831890 | ||||||||
\(269\) | 19.4406 | − | 14.1244i | 1.18531 | − | 0.861181i | 0.192553 | − | 0.981287i | \(-0.438323\pi\) |
0.992761 | + | 0.120105i | \(0.0383232\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.32203 | − | 5.31977i | −0.444782 | − | 0.323153i | 0.342750 | − | 0.939427i | \(-0.388642\pi\) |
−0.787532 | + | 0.616274i | \(0.788642\pi\) | |||||||
\(272\) | 6.22521 | + | 4.52288i | 0.377459 | + | 0.274240i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 5.90747 | 0.356883 | ||||||||
\(275\) | −2.70219 | + | 0.197695i | −0.162948 | + | 0.0119215i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.765152 | − | 2.35490i | 0.0459736 | − | 0.141492i | −0.925435 | − | 0.378907i | \(-0.876300\pi\) |
0.971408 | + | 0.237415i | \(0.0763001\pi\) | |||||||
\(278\) | −14.0869 | − | 10.2347i | −0.844875 | − | 0.613838i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.219008 | + | 5.99501i | 0.0130882 | + | 0.358270i | ||||
\(281\) | 14.5421 | − | 10.5654i | 0.867506 | − | 0.630280i | −0.0624105 | − | 0.998051i | \(-0.519879\pi\) |
0.929917 | + | 0.367770i | \(0.119879\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −12.9783 | + | 9.42925i | −0.771477 | + | 0.560511i | −0.902409 | − | 0.430880i | \(-0.858203\pi\) |
0.130932 | + | 0.991391i | \(0.458203\pi\) | |||||||
\(284\) | 2.67171 | + | 8.22268i | 0.158537 | + | 0.487927i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.843400 | − | 2.59572i | 0.0498713 | − | 0.153488i | ||||
\(287\) | −4.57596 | − | 14.0833i | −0.270110 | − | 0.831314i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 13.0435 | − | 40.1438i | 0.767266 | − | 2.36140i | ||||
\(290\) | −0.467176 | − | 12.7882i | −0.0274335 | − | 0.750951i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1.05273 | + | 0.764851i | −0.0616062 | + | 0.0447595i | ||||
\(293\) | −4.97078 | −0.290396 | −0.145198 | − | 0.989403i | \(-0.546382\pi\) | ||||
−0.145198 | + | 0.989403i | \(0.546382\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.71108 | + | 0.487666i | 0.0996228 | + | 0.0283930i | ||||
\(296\) | −2.82060 | − | 2.04928i | −0.163944 | − | 0.119112i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −4.99322 | + | 15.3676i | −0.289249 | + | 0.890218i | ||||
\(299\) | −24.5932 | −1.42226 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −34.6091 | −1.99483 | ||||||||
\(302\) | −3.14888 | + | 9.69124i | −0.181197 | + | 0.557668i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −5.05944 | − | 3.67590i | −0.290179 | − | 0.210827i | ||||
\(305\) | 2.36906 | + | 3.02223i | 0.135652 | + | 0.173052i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −12.0074 | −0.685297 | −0.342649 | − | 0.939464i | \(-0.611324\pi\) | ||||
−0.342649 | + | 0.939464i | \(0.611324\pi\) | |||||||
\(308\) | 1.17613 | − | 0.854512i | 0.0670165 | − | 0.0486903i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 6.74722 | + | 1.92299i | 0.383216 | + | 0.109219i | ||||
\(311\) | −5.84196 | + | 17.9797i | −0.331267 | + | 1.01954i | 0.637265 | + | 0.770645i | \(0.280066\pi\) |
−0.968532 | + | 0.248890i | \(0.919934\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.68893 | − | 8.27568i | −0.151987 | − | 0.467769i | 0.845856 | − | 0.533412i | \(-0.179090\pi\) |
−0.997843 | + | 0.0656426i | \(0.979090\pi\) | |||||||
\(314\) | −0.268264 | + | 0.825632i | −0.0151390 | + | 0.0465931i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −0.999080 | − | 3.07485i | −0.0562026 | − | 0.172974i | ||||
\(317\) | 10.3238 | − | 7.50070i | 0.579844 | − | 0.421281i | −0.258824 | − | 0.965925i | \(-0.583335\pi\) |
0.838668 | + | 0.544643i | \(0.183335\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.50887 | + | 1.82280i | −0.140470 | + | 0.102057i | ||||
\(320\) | −1.37949 | − | 1.75983i | −0.0771161 | − | 0.0983774i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −10.5979 | − | 7.69985i | −0.590600 | − | 0.429096i | ||||
\(323\) | −14.8704 | + | 45.7665i | −0.827412 | + | 2.54651i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −19.2395 | + | 16.2496i | −1.06722 | + | 0.901368i | ||||
\(326\) | −8.15435 | −0.451628 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4.46543 | + | 3.24432i | 0.246562 | + | 0.179138i | ||||
\(329\) | −3.79188 | − | 2.75496i | −0.209053 | − | 0.151886i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −3.10477 | + | 2.25575i | −0.170654 | + | 0.123987i | −0.669834 | − | 0.742511i | \(-0.733635\pi\) |
0.499180 | + | 0.866498i | \(0.333635\pi\) | |||||||
\(332\) | 0.762937 | 0.0418716 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.58688 | − | 4.88390i | −0.0868300 | − | 0.267235i | ||||
\(335\) | 1.11173 | + | 30.4319i | 0.0607402 | + | 1.66267i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0.525700 | + | 1.61794i | 0.0286367 | + | 0.0881348i | 0.964353 | − | 0.264618i | \(-0.0852458\pi\) |
−0.935717 | + | 0.352752i | \(0.885246\pi\) | |||||||
\(338\) | −3.82203 | − | 11.7630i | −0.207891 | − | 0.639823i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −9.59855 | + | 14.2799i | −0.520554 | + | 0.774438i | ||||
\(341\) | −0.525395 | − | 1.61700i | −0.0284517 | − | 0.0875654i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 18.2497 | 0.985391 | ||||||||
\(344\) | 10.4365 | − | 7.58253i | 0.562696 | − | 0.408823i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −14.2692 | − | 10.3672i | −0.767119 | − | 0.557345i | ||||
\(347\) | −21.5469 | − | 15.6547i | −1.15670 | − | 0.840390i | −0.167341 | − | 0.985899i | \(-0.553518\pi\) |
−0.989357 | + | 0.145509i | \(0.953518\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −6.45413 | −0.345482 | −0.172741 | − | 0.984967i | \(-0.555262\pi\) | ||||
−0.172741 | + | 0.984967i | \(0.555262\pi\) | |||||||
\(350\) | −13.3784 | + | 0.978779i | −0.715107 | + | 0.0523179i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −0.167451 | + | 0.515361i | −0.00892517 | + | 0.0274688i | ||||
\(353\) | 19.3743 | + | 14.0762i | 1.03119 | + | 0.749203i | 0.968546 | − | 0.248833i | \(-0.0800471\pi\) |
0.0626429 | + | 0.998036i | \(0.480047\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −18.1561 | + | 6.64139i | −0.963627 | + | 0.352488i | ||||
\(356\) | 5.92434 | − | 4.30429i | 0.313989 | − | 0.228127i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −13.3621 | + | 9.70812i | −0.706208 | + | 0.513090i | ||||
\(359\) | 4.84566 | + | 14.9134i | 0.255744 | + | 0.787100i | 0.993682 | + | 0.112231i | \(0.0357997\pi\) |
−0.737938 | + | 0.674868i | \(0.764200\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.21436 | − | 19.1258i | 0.327072 | − | 1.00662i | ||||
\(362\) | 5.96512 | + | 18.3587i | 0.313520 | + | 0.964914i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 4.17564 | − | 12.8513i | 0.218863 | − | 0.673591i | ||||
\(365\) | −1.79505 | − | 2.28996i | −0.0939575 | − | 0.119862i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 11.5852 | − | 8.41711i | 0.604740 | − | 0.439369i | −0.242818 | − | 0.970072i | \(-0.578072\pi\) |
0.847558 | + | 0.530702i | \(0.178072\pi\) | |||||||
\(368\) | 4.88280 | 0.254534 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 4.34903 | − | 6.47013i | 0.226095 | − | 0.336366i | ||||
\(371\) | −22.1105 | − | 16.0642i | −1.14792 | − | 0.834014i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.67003 | + | 17.4506i | −0.293583 | + | 0.903556i | 0.690110 | + | 0.723704i | \(0.257562\pi\) |
−0.983694 | + | 0.179852i | \(0.942438\pi\) | |||||||
\(374\) | 4.16967 | 0.215609 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.74704 | 0.0900967 | ||||||||
\(377\) | −8.90725 | + | 27.4137i | −0.458747 | + | 1.41188i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −17.8579 | − | 12.9745i | −0.917298 | − | 0.666456i | 0.0255521 | − | 0.999673i | \(-0.491866\pi\) |
−0.942850 | + | 0.333218i | \(0.891866\pi\) | |||||||
\(380\) | 7.80106 | − | 11.6058i | 0.400186 | − | 0.595364i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 25.7176 | 1.31583 | ||||||||
\(383\) | 10.9364 | − | 7.94573i | 0.558822 | − | 0.406008i | −0.272206 | − | 0.962239i | \(-0.587753\pi\) |
0.831028 | + | 0.556231i | \(0.187753\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.00548 | + | 2.55841i | 0.102209 | + | 0.130389i | ||||
\(386\) | −2.76210 | + | 8.50087i | −0.140587 | + | 0.432683i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 3.53004 | + | 10.8644i | 0.179211 | + | 0.551554i | ||||
\(389\) | −2.16552 | + | 6.66479i | −0.109796 | + | 0.337918i | −0.990826 | − | 0.135142i | \(-0.956851\pi\) |
0.881030 | + | 0.473061i | \(0.156851\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −11.6104 | − | 35.7332i | −0.587164 | − | 1.80711i | ||||
\(392\) | 0.159872 | − | 0.116154i | 0.00807475 | − | 0.00586665i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −10.4272 | + | 7.57581i | −0.525315 | + | 0.381664i | ||||
\(395\) | 6.78943 | − | 2.48353i | 0.341614 | − | 0.124960i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.29448 | + | 5.29975i | 0.366099 | + | 0.265987i | 0.755592 | − | 0.655043i | \(-0.227349\pi\) |
−0.389492 | + | 0.921030i | \(0.627349\pi\) | |||||||
\(398\) | −5.11963 | + | 15.7566i | −0.256624 | + | 0.789807i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 3.81986 | − | 3.22625i | 0.190993 | − | 0.161312i | ||||
\(401\) | 5.60409 | 0.279855 | 0.139927 | − | 0.990162i | \(-0.455313\pi\) | ||||
0.139927 | + | 0.990162i | \(0.455313\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −12.7850 | − | 9.28888i | −0.636868 | − | 0.462712i | ||||
\(404\) | 1.80950 | + | 1.31468i | 0.0900261 | + | 0.0654078i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −12.4213 | + | 9.02460i | −0.616459 | + | 0.447884i | ||||
\(407\) | −1.88925 | −0.0936464 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.25729 | + | 22.3357i | 0.358850 | + | 1.10443i | 0.953743 | + | 0.300622i | \(0.0971943\pi\) |
−0.594893 | + | 0.803805i | \(0.702806\pi\) | |||||||
\(410\) | −6.88516 | + | 10.2432i | −0.340034 | + | 0.505875i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 3.23013 | + | 9.94132i | 0.159137 | + | 0.489774i | ||||
\(413\) | −0.659660 | − | 2.03022i | −0.0324597 | − | 0.0999008i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.0622808 | + | 1.70484i | 0.00305724 | + | 0.0836874i | ||||
\(416\) | 1.55643 | + | 4.79019i | 0.0763101 | + | 0.234858i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −3.38883 | −0.165753 | ||||||||
\(419\) | −8.60618 | + | 6.25276i | −0.420439 | + | 0.305467i | −0.777815 | − | 0.628494i | \(-0.783672\pi\) |
0.357375 | + | 0.933961i | \(0.383672\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 5.58833 | + | 4.06016i | 0.272359 | + | 0.197880i | 0.715578 | − | 0.698533i | \(-0.246164\pi\) |
−0.443219 | + | 0.896413i | \(0.646164\pi\) | |||||||
\(422\) | −18.5272 | − | 13.4608i | −0.901889 | − | 0.655261i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 10.1870 | 0.494726 | ||||||||
\(425\) | −32.6932 | − | 20.2830i | −1.58585 | − | 0.983869i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.42375 | − | 4.38185i | 0.0689001 | − | 0.212053i | ||||
\(428\) | −4.79336 | − | 3.48258i | −0.231696 | − | 0.168337i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 17.7957 | + | 22.7021i | 0.858185 | + | 1.09479i | ||||
\(431\) | 2.79764 | − | 2.03261i | 0.134758 | − | 0.0979073i | −0.518364 | − | 0.855160i | \(-0.673459\pi\) |
0.653122 | + | 0.757253i | \(0.273459\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −17.9929 | + | 13.0726i | −0.864681 | + | 0.628228i | −0.929155 | − | 0.369692i | \(-0.879463\pi\) |
0.0644731 | + | 0.997919i | \(0.479463\pi\) | |||||||
\(434\) | −2.60121 | − | 8.00569i | −0.124862 | − | 0.384285i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 2.65733 | − | 8.17842i | 0.127263 | − | 0.391675i | ||||
\(437\) | 9.43618 | + | 29.0416i | 0.451394 | + | 1.38925i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 7.73905 | − | 23.8184i | 0.369365 | − | 1.13679i | −0.577838 | − | 0.816152i | \(-0.696103\pi\) |
0.947202 | − | 0.320636i | \(-0.103897\pi\) | |||||||
\(440\) | −1.16528 | − | 0.332112i | −0.0555527 | − | 0.0158328i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 31.3545 | − | 22.7804i | 1.49138 | − | 1.08355i | ||||
\(443\) | −32.7481 | −1.55591 | −0.777955 | − | 0.628320i | \(-0.783743\pi\) | ||||
−0.777955 | + | 0.628320i | \(0.783743\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.1019 | + | 12.8870i | 0.478875 | + | 0.610904i | ||||
\(446\) | −7.31954 | − | 5.31796i | −0.346590 | − | 0.251813i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −0.829042 | + | 2.55153i | −0.0391686 | + | 0.120548i | ||||
\(449\) | −20.5341 | −0.969064 | −0.484532 | − | 0.874774i | \(-0.661010\pi\) | ||||
−0.484532 | + | 0.874774i | \(0.661010\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.99096 | 0.140839 | ||||||||
\(452\) | −0.748822 | + | 2.30464i | −0.0352216 | + | 0.108401i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 17.4384 | + | 12.6698i | 0.818426 | + | 0.594621i | ||||
\(455\) | 29.0581 | + | 8.28170i | 1.36226 | + | 0.388252i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 37.1312 | 1.73693 | 0.868463 | − | 0.495755i | \(-0.165108\pi\) | ||||
0.868463 | + | 0.495755i | \(0.165108\pi\) | |||||||
\(458\) | 9.95698 | − | 7.23417i | 0.465259 | − | 0.338031i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0.398597 | + | 10.9110i | 0.0185847 | + | 0.508728i | ||||
\(461\) | −11.3976 | + | 35.0781i | −0.530838 | + | 1.63375i | 0.221637 | + | 0.975129i | \(0.428860\pi\) |
−0.752475 | + | 0.658621i | \(0.771140\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.57829 | − | 23.3236i | −0.352193 | − | 1.08394i | −0.957619 | − | 0.288037i | \(-0.906997\pi\) |
0.605426 | − | 0.795901i | \(-0.293003\pi\) | |||||||
\(464\) | 1.76847 | − | 5.44279i | 0.0820991 | − | 0.252675i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.97408 | + | 27.6194i | 0.415716 | + | 1.27944i | ||||
\(467\) | 14.0385 | − | 10.1995i | 0.649622 | − | 0.471978i | −0.213520 | − | 0.976939i | \(-0.568493\pi\) |
0.863142 | + | 0.504960i | \(0.168493\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 29.5587 | − | 21.4757i | 1.36489 | − | 0.991654i | ||||
\(470\) | 0.142616 | + | 3.90389i | 0.00657838 | + | 0.180073i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0.643726 | + | 0.467694i | 0.0296299 | + | 0.0215274i | ||||
\(473\) | 2.16015 | − | 6.64825i | 0.0993236 | − | 0.305687i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 26.5708 | + | 16.4847i | 1.21915 | + | 0.756368i | ||||
\(476\) | 20.6439 | 0.946209 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.27354 | − | 6.01108i | −0.378423 | − | 0.274940i | ||||
\(479\) | 12.4299 | + | 9.03087i | 0.567938 | + | 0.412631i | 0.834356 | − | 0.551227i | \(-0.185840\pi\) |
−0.266418 | + | 0.963858i | \(0.585840\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −14.2065 | + | 10.3216i | −0.647761 | + | 0.470626i | ||||
\(482\) | 8.25216 | 0.375875 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −3.30845 | − | 10.1824i | −0.150384 | − | 0.462834i | ||||
\(485\) | −23.9891 | + | 8.77505i | −1.08929 | + | 0.398454i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −11.9390 | − | 36.7445i | −0.541009 | − | 1.66505i | −0.730295 | − | 0.683132i | \(-0.760618\pi\) |
0.189287 | − | 0.981922i | \(-0.439382\pi\) | |||||||
\(488\) | 0.530688 | + | 1.63329i | 0.0240231 | + | 0.0739356i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0.272605 | + | 0.347764i | 0.0123151 | + | 0.0157104i | ||||
\(491\) | 12.9351 | + | 39.8103i | 0.583755 | + | 1.79661i | 0.604214 | + | 0.796822i | \(0.293487\pi\) |
−0.0204596 | + | 0.999791i | \(0.506513\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −44.0364 | −1.98330 | ||||||||
\(494\) | −25.4829 | + | 18.5144i | −1.14653 | + | 0.833002i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 2.53838 | + | 1.84424i | 0.113976 | + | 0.0828087i | ||||
\(497\) | 18.7655 | + | 13.6339i | 0.841746 | + | 0.611564i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −5.05384 | −0.226241 | −0.113120 | − | 0.993581i | \(-0.536085\pi\) | ||||
−0.113120 | + | 0.993581i | \(0.536085\pi\) | |||||||
\(500\) | 7.52112 | + | 8.27241i | 0.336355 | + | 0.369953i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6.25313 | + | 19.2451i | −0.279091 | + | 0.858953i | ||||
\(503\) | −18.2724 | − | 13.2757i | −0.814725 | − | 0.591932i | 0.100472 | − | 0.994940i | \(-0.467965\pi\) |
−0.915197 | + | 0.403008i | \(0.867965\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2.79004 | + | 4.15079i | −0.124155 | + | 0.184708i | ||||
\(506\) | 2.14058 | − | 1.55522i | 0.0951605 | − | 0.0691382i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.18299 | + | 0.859493i | −0.0524867 | + | 0.0381338i | ||||
\(509\) | −10.9142 | − | 33.5905i | −0.483765 | − | 1.48887i | −0.833762 | − | 0.552124i | \(-0.813818\pi\) |
0.349997 | − | 0.936751i | \(-0.386182\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.07878 | + | 3.32016i | −0.0477226 | + | 0.146875i | ||||
\(512\) | −0.309017 | − | 0.951057i | −0.0136568 | − | 0.0420312i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.00934 | − | 3.10642i | 0.0445200 | − | 0.137018i | ||||
\(515\) | −21.9510 | + | 8.02952i | −0.967276 | + | 0.353823i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0.765889 | − | 0.556451i | 0.0336837 | − | 0.0244727i | ||||
\(518\) | −9.35357 | −0.410972 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −10.5770 | + | 3.86899i | −0.463832 | + | 0.169667i | ||||
\(521\) | −22.7441 | − | 16.5245i | −0.996437 | − | 0.723954i | −0.0351154 | − | 0.999383i | \(-0.511180\pi\) |
−0.961321 | + | 0.275430i | \(0.911180\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.2019 | + | 31.3982i | −0.446098 | + | 1.37295i | 0.435177 | + | 0.900345i | \(0.356686\pi\) |
−0.881275 | + | 0.472603i | \(0.843314\pi\) | |||||||
\(524\) | −19.6809 | −0.859766 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 5.58933 | 0.243706 | ||||||||
\(527\) | 7.46066 | − | 22.9615i | 0.324991 | − | 1.00022i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −0.681006 | − | 0.494780i | −0.0296090 | − | 0.0215122i | ||||
\(530\) | 0.831596 | + | 22.7637i | 0.0361222 | + | 0.988792i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −16.7779 | −0.727416 | ||||||||
\(533\) | 22.4910 | − | 16.3407i | 0.974194 | − | 0.707794i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.39080 | − | 10.9954i | 0.319532 | − | 0.475374i | ||||
\(536\) | −4.20839 | + | 12.9521i | −0.181775 | + | 0.559445i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7.42565 | + | 22.8538i | 0.320142 | + | 0.985297i | ||||
\(539\) | 0.0330904 | − | 0.101842i | 0.00142530 | − | 0.00438664i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −0.101192 | − | 0.311437i | −0.00435058 | − | 0.0133897i | 0.948858 | − | 0.315704i | \(-0.102241\pi\) |
−0.953208 | + | 0.302314i | \(0.902241\pi\) | |||||||
\(542\) | 7.32203 | − | 5.31977i | 0.314508 | − | 0.228504i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −6.22521 | + | 4.52288i | −0.266904 | + | 0.193917i | ||||
\(545\) | 18.4922 | + | 5.27038i | 0.792121 | + | 0.225758i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.5274 | + | 16.3671i | 0.963201 | + | 0.699806i | 0.953892 | − | 0.300151i | \(-0.0970369\pi\) |
0.00930869 | + | 0.999957i | \(0.497037\pi\) | |||||||
\(548\) | −1.82551 | + | 5.61833i | −0.0779818 | + | 0.240003i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.647004 | − | 2.63103i | 0.0275883 | − | 0.112187i | ||||
\(551\) | 35.7898 | 1.52470 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.01729 | − | 5.09836i | −0.298406 | − | 0.216804i | ||||
\(554\) | 2.00319 | + | 1.45541i | 0.0851076 | + | 0.0618343i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 14.0869 | − | 10.2347i | 0.597417 | − | 0.434049i | ||||
\(557\) | 20.5761 | 0.871836 | 0.435918 | − | 0.899986i | \(-0.356424\pi\) | ||||
0.435918 | + | 0.899986i | \(0.356424\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20.0782 | − | 61.7942i | −0.849216 | − | 2.61362i | ||||
\(560\) | −5.76927 | − | 1.64427i | −0.243796 | − | 0.0694831i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 5.55457 | + | 17.0952i | 0.234305 | + | 0.721118i | ||||
\(563\) | −13.6583 | − | 42.0358i | −0.575627 | − | 1.77160i | −0.634033 | − | 0.773306i | \(-0.718602\pi\) |
0.0584058 | − | 0.998293i | \(-0.481398\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.21102 | − | 1.48517i | −0.219229 | − | 0.0624815i | ||||
\(566\) | −4.95725 | − | 15.2569i | −0.208369 | − | 0.641293i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −8.64584 | −0.362771 | ||||||||
\(569\) | 1.91682 | − | 1.39265i | 0.0803571 | − | 0.0583829i | −0.546881 | − | 0.837210i | \(-0.684185\pi\) |
0.627239 | + | 0.778827i | \(0.284185\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.0097 | − | 11.6317i | −0.669985 | − | 0.486773i | 0.200035 | − | 0.979789i | \(-0.435894\pi\) |
−0.870020 | + | 0.493016i | \(0.835894\pi\) | |||||||
\(572\) | 2.20805 | + | 1.60424i | 0.0923232 | + | 0.0670768i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 14.8081 | 0.618078 | ||||||||
\(575\) | −24.3489 | + | 1.78139i | −1.01542 | + | 0.0742892i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.16650 | − | 28.2116i | 0.381607 | − | 1.17446i | −0.557306 | − | 0.830307i | \(-0.688165\pi\) |
0.938912 | − | 0.344157i | \(-0.111835\pi\) | |||||||
\(578\) | 34.1484 | + | 24.8103i | 1.42039 | + | 1.03197i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 12.3067 | + | 3.50747i | 0.511008 | + | 0.145640i | ||||
\(581\) | 1.65592 | − | 1.20310i | 0.0686993 | − | 0.0499130i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.46591 | − | 3.24468i | 0.184959 | − | 0.134381i | ||||
\(584\) | −0.402106 | − | 1.23755i | −0.0166393 | − | 0.0512104i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 1.53605 | − | 4.72749i | 0.0634538 | − | 0.195291i | ||||
\(587\) | 0.933553 | + | 2.87318i | 0.0385318 | + | 0.118589i | 0.968472 | − | 0.249121i | \(-0.0801418\pi\) |
−0.929940 | + | 0.367710i | \(0.880142\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.06352 | + | 18.6616i | −0.249843 | + | 0.768938i | ||||
\(590\) | −0.992550 | + | 1.47663i | −0.0408626 | + | 0.0607921i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.82060 | − | 2.04928i | 0.115926 | − | 0.0842250i | ||||
\(593\) | 23.6709 | 0.972046 | 0.486023 | − | 0.873946i | \(-0.338447\pi\) | ||||
0.486023 | + | 0.873946i | \(0.338447\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.68522 | + | 46.1303i | 0.0690872 | + | 1.89116i | ||||
\(596\) | −13.0724 | − | 9.49767i | −0.535467 | − | 0.389040i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 7.59972 | − | 23.3895i | 0.310776 | − | 0.956470i | ||||
\(599\) | 33.2245 | 1.35752 | 0.678759 | − | 0.734361i | \(-0.262518\pi\) | ||||
0.678759 | + | 0.734361i | \(0.262518\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −34.9169 | −1.42429 | −0.712146 | − | 0.702032i | \(-0.752277\pi\) | ||||
−0.712146 | + | 0.702032i | \(0.752277\pi\) | |||||||
\(602\) | 10.6948 | − | 32.9152i | 0.435887 | − | 1.34152i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.24386 | − | 5.98952i | −0.335438 | − | 0.243710i | ||||
\(605\) | 22.4832 | − | 8.22420i | 0.914071 | − | 0.334361i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 14.1488 | 0.574282 | 0.287141 | − | 0.957888i | \(-0.407295\pi\) | ||||
0.287141 | + | 0.957888i | \(0.407295\pi\) | |||||||
\(608\) | 5.05944 | − | 3.67590i | 0.205187 | − | 0.149077i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.60639 | + | 1.31919i | −0.146019 | + | 0.0534126i | ||||
\(611\) | 2.71914 | − | 8.36865i | 0.110005 | − | 0.338559i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 12.9536 | + | 39.8671i | 0.523191 | + | 1.61022i | 0.767866 | + | 0.640611i | \(0.221319\pi\) |
−0.244675 | + | 0.969605i | \(0.578681\pi\) | |||||||
\(614\) | 3.71048 | − | 11.4197i | 0.149743 | − | 0.460861i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.449244 | + | 1.38263i | 0.0181005 | + | 0.0557077i | ||||
\(617\) | −32.5377 | + | 23.6400i | −1.30992 | + | 0.951712i | −0.309919 | + | 0.950763i | \(0.600302\pi\) |
−1.00000 | 0.000948881i | \(0.999698\pi\) | ||||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.0988 | − | 13.8761i | 0.767644 | − | 0.557726i | −0.133601 | − | 0.991035i | \(-0.542654\pi\) |
0.901245 | + | 0.433309i | \(0.142654\pi\) | |||||||
\(620\) | −3.91388 | + | 5.82275i | −0.157185 | + | 0.233847i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −15.2944 | − | 11.1121i | −0.613252 | − | 0.445553i | ||||
\(623\) | 6.07098 | − | 18.6846i | 0.243229 | − | 0.748581i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −17.8714 | + | 17.4818i | −0.714854 | + | 0.699273i | ||||
\(626\) | 8.70156 | 0.347784 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −0.702324 | − | 0.510268i | −0.0280258 | − | 0.0203619i | ||||
\(629\) | −21.7039 | − | 15.7688i | −0.865390 | − | 0.628743i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 14.0785 | − | 10.2286i | 0.560455 | − | 0.407195i | −0.271170 | − | 0.962531i | \(-0.587411\pi\) |
0.831626 | + | 0.555337i | \(0.187411\pi\) | |||||||
\(632\) | 3.23309 | 0.128605 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 3.94335 | + | 12.1364i | 0.156610 | + | 0.481998i | ||||
\(635\) | −2.01717 | − | 2.57332i | −0.0800491 | − | 0.102119i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −0.307569 | − | 0.946601i | −0.0121863 | − | 0.0375057i | ||||
\(638\) | −0.958303 | − | 2.94935i | −0.0379396 | − | 0.116766i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.09998 | − | 0.768160i | 0.0830091 | − | 0.0303642i | ||||
\(641\) | 6.36332 | + | 19.5843i | 0.251336 | + | 0.773533i | 0.994529 | + | 0.104456i | \(0.0333102\pi\) |
−0.743194 | + | 0.669077i | \(0.766690\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −13.1725 | −0.519473 | −0.259736 | − | 0.965680i | \(-0.583636\pi\) | ||||
−0.259736 | + | 0.965680i | \(0.583636\pi\) | |||||||
\(644\) | 10.5979 | − | 7.69985i | 0.417617 | − | 0.303417i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −38.9313 | − | 28.2852i | −1.53173 | − | 1.11287i | ||||
\(647\) | −17.8760 | − | 12.9877i | −0.702780 | − | 0.510599i | 0.178057 | − | 0.984020i | \(-0.443019\pi\) |
−0.880836 | + | 0.473421i | \(0.843019\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0.431170 | 0.0169249 | ||||||||
\(650\) | −9.50899 | − | 23.3193i | −0.372973 | − | 0.914657i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 2.51983 | − | 7.75525i | 0.0986842 | − | 0.303719i | ||||
\(653\) | 16.1998 | + | 11.7698i | 0.633947 | + | 0.460589i | 0.857765 | − | 0.514042i | \(-0.171852\pi\) |
−0.223818 | + | 0.974631i | \(0.571852\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.60661 | − | 43.9786i | −0.0627755 | − | 1.71839i | ||||
\(656\) | −4.46543 | + | 3.24432i | −0.174346 | + | 0.126670i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.79188 | − | 2.75496i | 0.147823 | − | 0.107400i | ||||
\(659\) | 7.56699 | + | 23.2888i | 0.294768 | + | 0.907203i | 0.983299 | + | 0.181996i | \(0.0582558\pi\) |
−0.688531 | + | 0.725207i | \(0.741744\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.65040 | + | 17.3901i | −0.219775 | + | 0.676398i | 0.779005 | + | 0.627018i | \(0.215725\pi\) |
−0.998780 | + | 0.0493804i | \(0.984275\pi\) | |||||||
\(662\) | −1.18592 | − | 3.64987i | −0.0460919 | − | 0.141856i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −0.235761 | + | 0.725596i | −0.00914928 | + | 0.0281586i | ||||
\(665\) | −1.36963 | − | 37.4916i | −0.0531120 | − | 1.45386i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −22.6070 | + | 16.4249i | −0.875345 | + | 0.635975i | ||||
\(668\) | 5.13524 | 0.198688 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −29.2860 | − | 8.34666i | −1.13142 | − | 0.322459i | ||||
\(671\) | 0.752870 | + | 0.546992i | 0.0290642 | + | 0.0211164i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.28629 | + | 7.03648i | −0.0881301 | + | 0.271236i | −0.985402 | − | 0.170241i | \(-0.945545\pi\) |
0.897272 | + | 0.441477i | \(0.145545\pi\) | |||||||
\(674\) | −1.70120 | −0.0655279 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 12.3684 | 0.475706 | ||||||||
\(677\) | 4.06460 | − | 12.5096i | 0.156215 | − | 0.480782i | −0.842067 | − | 0.539374i | \(-0.818661\pi\) |
0.998282 | + | 0.0585919i | \(0.0186611\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 24.7942 | + | 18.0140i | 0.951513 | + | 0.691315i | ||||
\(680\) | −10.6149 | − | 13.5415i | −0.407063 | − | 0.519293i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.70021 | 0.0651045 | ||||||||
\(683\) | −17.3035 | + | 12.5717i | −0.662099 | + | 0.481043i | −0.867371 | − | 0.497662i | \(-0.834192\pi\) |
0.205272 | + | 0.978705i | \(0.434192\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.7036 | − | 3.62060i | −0.485381 | − | 0.138336i | ||||
\(686\) | −5.63947 | + | 17.3565i | −0.215316 | + | 0.662674i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.98637 | + | 12.2688i | 0.151979 | + | 0.467743i | ||||
\(689\) | 15.8554 | − | 48.7978i | 0.604041 | − | 1.85905i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.5117 | − | 38.5071i | −0.475968 | − | 1.46488i | −0.844648 | − | 0.535321i | \(-0.820190\pi\) |
0.368681 | − | 0.929556i | \(-0.379810\pi\) | |||||||
\(692\) | 14.2692 | − | 10.3672i | 0.542435 | − | 0.394102i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 21.5469 | − | 15.6547i | 0.817909 | − | 0.594246i | ||||
\(695\) | 24.0202 | + | 30.6427i | 0.911139 | + | 1.16235i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 34.3605 | + | 24.9644i | 1.30150 | + | 0.945593i | ||||
\(698\) | 1.99444 | − | 6.13824i | 0.0754905 | − | 0.232336i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 3.20329 | − | 13.0261i | 0.121073 | − | 0.492340i | ||||
\(701\) | −21.5704 | −0.814704 | −0.407352 | − | 0.913271i | \(-0.633548\pi\) | ||||
−0.407352 | + | 0.913271i | \(0.633548\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 17.6395 | + | 12.8158i | 0.665285 | + | 0.483358i | ||||
\(704\) | −0.438392 | − | 0.318511i | −0.0165225 | − | 0.0120043i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −19.3743 | + | 14.0762i | −0.729161 | + | 0.529766i | ||||
\(707\) | 6.00061 | 0.225676 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.59709 | − | 4.91534i | −0.0599800 | − | 0.184600i | 0.916577 | − | 0.399858i | \(-0.130941\pi\) |
−0.976557 | + | 0.215259i | \(0.930941\pi\) | |||||||
\(710\) | −0.705785 | − | 19.3198i | −0.0264876 | − | 0.725059i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 2.26290 | + | 6.96448i | 0.0848057 | + | 0.261005i | ||||
\(713\) | −4.73424 | − | 14.5705i | −0.177299 | − | 0.545669i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.40456 | + | 5.06502i | −0.127323 | + | 0.189421i | ||||
\(716\) | −5.10386 | − | 15.7081i | −0.190740 | − | 0.587038i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −15.6809 | −0.585205 | ||||||||
\(719\) | 14.8280 | − | 10.7732i | 0.552991 | − | 0.401771i | −0.275896 | − | 0.961187i | \(-0.588975\pi\) |
0.828887 | + | 0.559416i | \(0.188975\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.6877 | + | 16.4836i | 0.844933 | + | 0.613880i | ||||
\(722\) | 16.2694 | + | 11.8204i | 0.605485 | + | 0.439910i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −19.3035 | −0.717410 | ||||||||
\(725\) | −6.83308 | + | 27.7866i | −0.253774 | + | 1.03197i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.14016 | + | 3.50905i | −0.0422862 | + | 0.130144i | −0.969971 | − | 0.243221i | \(-0.921796\pi\) |
0.927685 | + | 0.373365i | \(0.121796\pi\) | |||||||
\(728\) | 10.9320 | + | 7.94253i | 0.405165 | + | 0.294370i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.73259 | − | 0.999561i | 0.101138 | − | 0.0369954i | ||||
\(731\) | 80.3063 | − | 58.3459i | 2.97024 | − | 2.15800i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 25.4477 | − | 18.4888i | 0.939932 | − | 0.682901i | −0.00847226 | − | 0.999964i | \(-0.502697\pi\) |
0.948404 | + | 0.317064i | \(0.102697\pi\) | |||||||
\(734\) | 4.42514 | + | 13.6192i | 0.163335 | + | 0.502693i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.50887 | + | 4.64382i | −0.0556177 | + | 0.171174i | ||||
\(737\) | 2.28045 | + | 7.01851i | 0.0840016 | + | 0.258530i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6.57476 | + | 20.2350i | −0.241856 | + | 0.744357i | 0.754281 | + | 0.656551i | \(0.227986\pi\) |
−0.996138 | + | 0.0878059i | \(0.972014\pi\) | |||||||
\(740\) | 4.80953 | + | 6.13555i | 0.176802 | + | 0.225547i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 22.1105 | − | 16.0642i | 0.811703 | − | 0.589737i | ||||
\(743\) | −41.2006 | −1.51150 | −0.755751 | − | 0.654859i | \(-0.772728\pi\) | ||||
−0.755751 | + | 0.654859i | \(0.772728\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 20.1561 | − | 29.9867i | 0.738464 | − | 1.09863i | ||||
\(746\) | −14.8443 | − | 10.7850i | −0.543490 | − | 0.394868i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.28850 | + | 3.96559i | −0.0471122 | + | 0.144996i | ||||
\(749\) | −15.8956 | −0.580813 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.6837 | −0.791251 | −0.395625 | − | 0.918412i | \(-0.629472\pi\) | ||||
−0.395625 | + | 0.918412i | \(0.629472\pi\) | |||||||
\(752\) | −0.539865 | + | 1.66153i | −0.0196868 | + | 0.0605899i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −23.3195 | − | 16.9426i | −0.849246 | − | 0.617013i | ||||
\(755\) | 12.7111 | − | 18.9105i | 0.462603 | − | 0.688223i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −9.12978 | −0.331828 | −0.165914 | − | 0.986140i | \(-0.553057\pi\) | ||||
−0.165914 | + | 0.986140i | \(0.553057\pi\) | |||||||
\(758\) | 17.8579 | − | 12.9745i | 0.648628 | − | 0.471255i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 8.62709 | + | 11.0056i | 0.312937 | + | 0.399216i | ||||
\(761\) | −15.0615 | + | 46.3546i | −0.545979 | + | 1.68035i | 0.172670 | + | 0.984980i | \(0.444760\pi\) |
−0.718650 | + | 0.695372i | \(0.755240\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.12918 | − | 21.9414i | −0.258094 | − | 0.794331i | ||||
\(764\) | −7.94718 | + | 24.4589i | −0.287519 | + | 0.884892i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 4.17732 | + | 12.8565i | 0.150933 | + | 0.464523i | ||||
\(767\) | 3.24226 | − | 2.35564i | 0.117071 | − | 0.0850571i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −22.9587 | + | 16.6805i | −0.827911 | + | 0.601513i | −0.918968 | − | 0.394333i | \(-0.870976\pi\) |
0.0910564 | + | 0.995846i | \(0.470976\pi\) | |||||||
\(770\) | −3.05292 | + | 1.11674i | −0.110020 | + | 0.0402444i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −7.23127 | − | 5.25383i | −0.260259 | − | 0.189089i | ||||
\(773\) | 7.90525 | − | 24.3299i | 0.284332 | − | 0.875084i | −0.702266 | − | 0.711915i | \(-0.747828\pi\) |
0.986598 | − | 0.163170i | \(-0.0521718\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −13.3309 | − | 8.27053i | −0.478859 | − | 0.297086i | ||||
\(776\) | −11.4235 | −0.410078 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5.66941 | − | 4.11906i | −0.203258 | − | 0.147676i | ||||
\(779\) | −27.9259 | − | 20.2894i | −1.00055 | − | 0.726942i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.79027 | + | 2.75379i | −0.135627 | + | 0.0985384i | ||||
\(782\) | 37.5721 | 1.34358 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0.0610656 | + | 0.187941i | 0.00218092 | + | 0.00671217i | ||||
\(785\) | 1.08290 | − | 1.61105i | 0.0386504 | − | 0.0575009i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.64111 | + | 8.12849i | 0.0941453 | + | 0.289749i | 0.987030 | − | 0.160536i | \(-0.0513222\pi\) |
−0.892885 | + | 0.450285i | \(0.851322\pi\) | |||||||
\(788\) | −3.98284 | − | 12.2579i | −0.141883 | − | 0.436670i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0.263926 | + | 7.22459i | 0.00939008 | + | 0.257039i | ||||
\(791\) | 2.00897 | + | 6.18297i | 0.0714307 | + | 0.219841i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.64974 | 0.307161 | ||||||||
\(794\) | −7.29448 | + | 5.29975i | −0.258871 | + | 0.188081i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −13.4034 | − | 9.73812i | −0.475070 | − | 0.345158i | ||||
\(797\) | 4.31303 | + | 3.13360i | 0.152775 | + | 0.110998i | 0.661547 | − | 0.749904i | \(-0.269900\pi\) |
−0.508772 | + | 0.860902i | \(0.669900\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.4431 | 0.475582 | ||||||||
\(800\) | 1.88794 | + | 4.62987i | 0.0667488 | + | 0.163691i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.73176 | + | 5.32981i | −0.0611505 | + | 0.188202i | ||||
\(803\) | −0.570454 | − | 0.414459i | −0.0201309 | − | 0.0146259i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 18.0710 | + | 23.0533i | 0.636921 | + | 0.812523i | ||||
\(806\) | 12.7850 | − | 9.28888i | 0.450334 | − | 0.327187i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −1.80950 | + | 1.31468i | −0.0636581 | + | 0.0462503i | ||||
\(809\) | 2.71203 | + | 8.34677i | 0.0953499 | + | 0.293457i | 0.987345 | − | 0.158589i | \(-0.0506944\pi\) |
−0.891995 | + | 0.452046i | \(0.850694\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.35490 | − | 7.24763i | 0.0826916 | − | 0.254499i | −0.901159 | − | 0.433488i | \(-0.857283\pi\) |
0.983851 | + | 0.178989i | \(0.0572827\pi\) | |||||||
\(812\) | −4.74451 | − | 14.6021i | −0.166500 | − | 0.512434i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.583809 | − | 1.79678i | 0.0204625 | − | 0.0629771i | ||||
\(815\) | 17.5354 | + | 4.99768i | 0.614238 | + | 0.175061i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −65.2676 | + | 47.4197i | −2.28342 | + | 1.65900i | ||||
\(818\) | −23.4851 | −0.821137 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.61422 | − | 9.71350i | −0.265900 | − | 0.339210i | ||||
\(821\) | 19.5644 | + | 14.2143i | 0.682801 | + | 0.496084i | 0.874286 | − | 0.485412i | \(-0.161330\pi\) |
−0.191485 | + | 0.981496i | \(0.561330\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 11.4452 | − | 35.2248i | 0.398955 | − | 1.22786i | −0.526883 | − | 0.849938i | \(-0.676639\pi\) |
0.925838 | − | 0.377920i | \(-0.123361\pi\) | |||||||
\(824\) | −10.4529 | −0.364145 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2.13470 | 0.0742759 | ||||||||
\(827\) | −10.3423 | + | 31.8302i | −0.359635 | + | 1.10684i | 0.593637 | + | 0.804733i | \(0.297691\pi\) |
−0.953273 | + | 0.302111i | \(0.902309\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.26918 | + | 5.28137i | 0.252469 | + | 0.183430i | 0.706820 | − | 0.707393i | \(-0.250129\pi\) |
−0.454351 | + | 0.890823i | \(0.650129\pi\) | |||||||
\(830\) | −1.64065 | − | 0.467593i | −0.0569477 | − | 0.0162304i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.03670 | −0.174616 | ||||||||
\(833\) | 1.23018 | − | 0.893778i | 0.0426232 | − | 0.0309676i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.419205 | + | 11.4751i | 0.0145072 | + | 0.397112i | ||||
\(836\) | 1.04721 | − | 3.22297i | 0.0362184 | − | 0.111469i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3.28727 | − | 10.1172i | −0.113557 | − | 0.349492i | ||||
\(839\) | 3.32934 | − | 10.2467i | 0.114942 | − | 0.353754i | −0.876993 | − | 0.480503i | \(-0.840454\pi\) |
0.991935 | + | 0.126749i | \(0.0404542\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.15926 | + | 3.56783i | 0.0399744 | + | 0.123028i | ||||
\(842\) | −5.58833 | + | 4.06016i | −0.192587 | + | 0.139922i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 18.5272 | − | 13.4608i | 0.637732 | − | 0.463339i | ||||
\(845\) | 1.00966 | + | 27.6381i | 0.0347335 | + | 0.950778i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −23.2377 | − | 16.8832i | −0.798458 | − | 0.580114i | ||||
\(848\) | −3.14796 | + | 9.68843i | −0.108102 | + | 0.332702i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 29.3930 | − | 24.8253i | 1.00817 | − | 0.851500i | ||||
\(851\) | −17.0236 | −0.583563 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 25.6142 | + | 18.6098i | 0.877012 | + | 0.637187i | 0.932459 | − | 0.361275i | \(-0.117658\pi\) |
−0.0554472 | + | 0.998462i | \(0.517658\pi\) | |||||||
\(854\) | 3.72742 | + | 2.70813i | 0.127550 | + | 0.0926704i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 4.79336 | − | 3.48258i | 0.163834 | − | 0.119032i | ||||
\(857\) | −19.3605 | −0.661343 | −0.330671 | − | 0.943746i | \(-0.607275\pi\) | ||||
−0.330671 | + | 0.943746i | \(0.607275\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −0.0770598 | − | 0.237166i | −0.00262925 | − | 0.00809199i | 0.949733 | − | 0.313060i | \(-0.101354\pi\) |
−0.952363 | + | 0.304968i | \(0.901354\pi\) | |||||||
\(860\) | −27.0901 | + | 9.90939i | −0.923766 | + | 0.337908i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.06861 | + | 3.28883i | 0.0363968 | + | 0.112018i | ||||
\(863\) | 1.65408 | + | 5.09074i | 0.0563056 | + | 0.173291i | 0.975254 | − | 0.221086i | \(-0.0709603\pi\) |
−0.918949 | + | 0.394377i | \(0.870960\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 24.3312 | + | 31.0394i | 0.827285 | + | 1.05537i | ||||
\(866\) | −6.87266 | − | 21.1519i | −0.233542 | − | 0.718770i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 8.41768 | 0.285715 | ||||||||
\(869\) | 1.41736 | − | 1.02977i | 0.0480807 | − | 0.0349327i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 55.4929 | + | 40.3179i | 1.88030 | + | 1.36612i | ||||
\(872\) | 6.95698 | + | 5.05454i | 0.235593 | + | 0.171168i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −30.5361 | −1.03290 | ||||||||
\(875\) | 29.3693 | + | 6.09463i | 0.992864 | + | 0.206036i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.678510 | − | 2.08824i | 0.0229116 | − | 0.0705148i | −0.938947 | − | 0.344062i | \(-0.888197\pi\) |
0.961859 | + | 0.273547i | \(0.0881970\pi\) | |||||||
\(878\) | 20.2611 | + | 14.7206i | 0.683779 | + | 0.496795i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.675949 | − | 1.00562i | 0.0227862 | − | 0.0338995i | ||||
\(881\) | −37.9834 | + | 27.5966i | −1.27969 | + | 0.929751i | −0.999544 | − | 0.0302050i | \(-0.990384\pi\) |
−0.280149 | + | 0.959956i | \(0.590384\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −19.6566 | + | 14.2814i | −0.661498 | + | 0.480606i | −0.867168 | − | 0.498015i | \(-0.834062\pi\) |
0.205671 | + | 0.978621i | \(0.434062\pi\) | |||||||
\(884\) | 11.9764 | + | 36.8595i | 0.402809 | + | 1.23972i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10.1197 | − | 31.1453i | 0.339979 | − | 1.04635i | ||||
\(887\) | −11.3071 | − | 34.7995i | −0.379654 | − | 1.16845i | −0.940285 | − | 0.340388i | \(-0.889442\pi\) |
0.560631 | − | 0.828065i | \(-0.310558\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.21227 | + | 3.73099i | −0.0406583 | + | 0.125133i | ||||
\(890\) | −15.3779 | + | 5.62515i | −0.515470 | + | 0.188555i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.31954 | − | 5.31796i | 0.245076 | − | 0.178058i | ||||
\(893\) | −10.9256 | −0.365613 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 34.6843 | − | 12.6873i | 1.15937 | − | 0.424089i | ||||
\(896\) | −2.17046 | − | 1.57693i | −0.0725100 | − | 0.0526816i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 6.34538 | − | 19.5291i | 0.211748 | − | 0.651694i | ||||
\(899\) | −17.9562 | −0.598871 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 78.3870 | 2.61145 | ||||||||
\(902\) | −0.924257 | + | 2.84457i | −0.0307744 | + | 0.0947139i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1.96044 | − | 1.42434i | −0.0652034 | − | 0.0473730i | ||||
\(905\) | −1.57580 | − | 43.1352i | −0.0523815 | − | 1.43386i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 30.1732 | 1.00189 | 0.500943 | − | 0.865481i | \(-0.332987\pi\) | ||||
0.500943 | + | 0.865481i | \(0.332987\pi\) | |||||||
\(908\) | −17.4384 | + | 12.6698i | −0.578714 | + | 0.420461i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −16.8558 | + | 25.0767i | −0.558764 | + | 0.831284i | ||||
\(911\) | −8.21882 | + | 25.2949i | −0.272302 | + | 0.838059i | 0.717619 | + | 0.696436i | \(0.245232\pi\) |
−0.989921 | + | 0.141623i | \(0.954768\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.127755 | + | 0.393188i | 0.00422806 | + | 0.0130126i | ||||
\(914\) | −11.4742 | + | 35.3139i | −0.379532 | + | 1.16808i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.80323 | + | 11.7051i | 0.125662 | + | 0.386748i | ||||
\(917\) | −42.7167 | + | 31.0355i | −1.41063 | + | 1.02488i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.9718 | + | 15.2369i | −0.691796 | + | 0.502619i | −0.877250 | − | 0.480034i | \(-0.840624\pi\) |
0.185454 | + | 0.982653i | \(0.440624\pi\) | |||||||
\(920\) | −10.5002 | − | 2.99260i | −0.346180 | − | 0.0986630i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −29.8392 | − | 21.6795i | −0.982702 | − | 0.713975i | ||||
\(923\) | −13.4566 | + | 41.4152i | −0.442930 | + | 1.36320i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −13.3177 | + | 11.2481i | −0.437885 | + | 0.369837i | ||||
\(926\) | 24.5239 | 0.805904 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.62991 | + | 3.36383i | 0.151984 | + | 0.110423i | ||||
\(929\) | 30.0226 | + | 21.8127i | 0.985009 | + | 0.715651i | 0.958822 | − | 0.284006i | \(-0.0916637\pi\) |
0.0261864 | + | 0.999657i | \(0.491664\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.999808 | + | 0.726403i | −0.0327674 | + | 0.0238069i | ||||
\(932\) | −29.0407 | −0.951260 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5.36221 | + | 16.5032i | 0.175457 | + | 0.540001i | ||||
\(935\) | −8.96661 | − | 2.55553i | −0.293239 | − | 0.0835747i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.56078 | − | 7.88126i | −0.0836569 | − | 0.257470i | 0.900475 | − | 0.434908i | \(-0.143219\pi\) |
−0.984132 | + | 0.177438i | \(0.943219\pi\) | |||||||
\(938\) | 11.2904 | + | 34.7483i | 0.368645 | + | 1.13457i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.75690 | − | 1.07073i | −0.122536 | − | 0.0349235i | ||||
\(941\) | −3.57339 | − | 10.9978i | −0.116489 | − | 0.358517i | 0.875766 | − | 0.482737i | \(-0.160357\pi\) |
−0.992255 | + | 0.124220i | \(0.960357\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 26.9510 | 0.877645 | ||||||||
\(944\) | −0.643726 | + | 0.467694i | −0.0209515 | + | 0.0152222i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.65534 | + | 4.10884i | 0.183871 | + | 0.133590i | ||||
\(947\) | 25.6584 | + | 18.6420i | 0.833787 | + | 0.605782i | 0.920628 | − | 0.390440i | \(-0.127677\pi\) |
−0.0868408 | + | 0.996222i | \(0.527677\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.55396 | −0.212751 | ||||||||
\(950\) | −23.8887 | + | 20.1763i | −0.775051 | + | 0.654606i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −6.37930 | + | 19.6335i | −0.206754 | + | 0.636324i | ||||
\(953\) | 21.7191 | + | 15.7799i | 0.703551 | + | 0.511160i | 0.881087 | − | 0.472954i | \(-0.156812\pi\) |
−0.177535 | + | 0.984114i | \(0.556812\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −55.3041 | − | 15.7619i | −1.78960 | − | 0.510045i | ||||
\(956\) | 8.27354 | − | 6.01108i | 0.267585 | − | 0.194412i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −12.4299 | + | 9.03087i | −0.401593 | + | 0.291774i | ||||
\(959\) | 4.89754 | + | 15.0731i | 0.158150 | + | 0.486735i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −6.53739 | + | 20.1200i | −0.210884 | + | 0.649033i | ||||
\(962\) | −5.42640 | − | 16.7007i | −0.174954 | − | 0.538453i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.55006 | + | 7.84827i | −0.0821318 | + | 0.252776i | ||||
\(965\) | 11.1498 | − | 16.5877i | 0.358924 | − | 0.533978i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.0325 | − | 15.2810i | 0.676361 | − | 0.491405i | −0.195787 | − | 0.980646i | \(-0.562726\pi\) |
0.872148 | + | 0.489241i | \(0.162726\pi\) | |||||||
\(968\) | 10.7064 | 0.344116 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.932530 | − | 25.5266i | −0.0299417 | − | 0.819610i | ||||
\(971\) | −23.0178 | − | 16.7234i | −0.738678 | − | 0.536681i | 0.153619 | − | 0.988130i | \(-0.450907\pi\) |
−0.892297 | + | 0.451449i | \(0.850907\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 14.4356 | − | 44.4281i | 0.462783 | − | 1.42430i | ||||
\(974\) | 38.6355 | 1.23796 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.71734 | −0.0549708 | ||||||||
\(977\) | −3.45996 | + | 10.6487i | −0.110694 | + | 0.340681i | −0.991025 | − | 0.133680i | \(-0.957321\pi\) |
0.880331 | + | 0.474361i | \(0.157321\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.21030 | + | 2.33242i | 0.102602 | + | 0.0745444i | ||||
\(980\) | −0.414983 | + | 0.151798i | −0.0132561 | + | 0.00484901i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −41.8590 | −1.33577 | ||||||||
\(983\) | −32.2607 | + | 23.4388i | −1.02896 | + | 0.747580i | −0.968099 | − | 0.250566i | \(-0.919383\pi\) |
−0.0608564 | + | 0.998147i | \(0.519383\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 27.0661 | − | 9.90061i | 0.862398 | − | 0.315460i | ||||
\(986\) | 13.6080 | − | 41.8811i | 0.433367 | − | 1.33377i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9.73359 | − | 29.9569i | −0.309667 | − | 0.953056i | ||||
\(989\) | 19.4647 | − | 59.9061i | 0.618941 | − | 1.90490i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 9.09055 | + | 27.9778i | 0.288771 | + | 0.888745i | 0.985243 | + | 0.171161i | \(0.0547519\pi\) |
−0.696472 | + | 0.717584i | \(0.745248\pi\) | |||||||
\(992\) | −2.53838 | + | 1.84424i | −0.0805935 | + | 0.0585546i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −18.7655 | + | 13.6339i | −0.595204 | + | 0.432441i | ||||
\(995\) | 20.6664 | − | 30.7458i | 0.655169 | − | 0.974708i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.81998 | + | 5.68155i | 0.247661 | + | 0.179936i | 0.704690 | − | 0.709516i | \(-0.251086\pi\) |
−0.457028 | + | 0.889452i | \(0.651086\pi\) | |||||||
\(998\) | 1.56172 | − | 4.80648i | 0.0494354 | − | 0.152147i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 450.2.h.g.271.3 | yes | 12 | |
3.2 | odd | 2 | 450.2.h.f.271.1 | yes | 12 | ||
25.6 | even | 5 | inner | 450.2.h.g.181.3 | yes | 12 | |
75.56 | odd | 10 | 450.2.h.f.181.1 | ✓ | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
450.2.h.f.181.1 | ✓ | 12 | 75.56 | odd | 10 | ||
450.2.h.f.271.1 | yes | 12 | 3.2 | odd | 2 | ||
450.2.h.g.181.3 | yes | 12 | 25.6 | even | 5 | inner | |
450.2.h.g.271.3 | yes | 12 | 1.1 | even | 1 | trivial |