Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1040,2,Mod(289,1040)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1040, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1040.289");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1040 = 2^{4} \cdot 5 \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1040.dh (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.30444181021\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{6})\) |
Coefficient field: | 12.0.89539436150784.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2x^{11} + 2x^{10} - 8x^{9} + 4x^{8} + 16x^{7} - 8x^{6} + 20x^{5} + 20x^{4} - 24x^{3} + 8x^{2} - 8x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 130) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 289.3 | ||
Root | \(0.312819 - 1.16746i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1040.289 |
Dual form | 1040.2.dh.b.529.3 |
$q$-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 \(\left(\mathbb{Z}/1040\mathbb{Z}\right)^\times\).
\(n\) | \(261\) | \(417\) | \(561\) | \(911\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −0.466951 | + | 0.269594i | −0.269594 | + | 0.155650i | −0.628703 | − | 0.777645i | \(-0.716414\pi\) |
0.359109 | + | 0.933296i | \(0.383081\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.539189 | − | 2.17009i | −0.241133 | − | 0.970492i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.614250 | + | 0.354638i | 0.232165 | + | 0.134040i | 0.611570 | − | 0.791190i | \(-0.290538\pi\) |
−0.379406 | + | 0.925230i | \(0.623871\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.35464 | + | 2.34630i | −0.451546 | + | 0.782100i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.25513 | − | 3.90600i | −0.679947 | − | 1.17770i | −0.974996 | − | 0.222221i | \(-0.928669\pi\) |
0.295049 | − | 0.955482i | \(-0.404664\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.35963 | + | 1.30878i | 0.931793 | + | 0.362991i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.836818 | + | 0.867962i | 0.216066 | + | 0.224107i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.74538 | − | 1.58504i | −0.665851 | − | 0.384429i | 0.128652 | − | 0.991690i | \(-0.458935\pi\) |
−0.794503 | + | 0.607260i | \(0.792268\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 0.0603191 | − | 0.104476i | 0.0138381 | − | 0.0239684i | −0.859023 | − | 0.511936i | \(-0.828928\pi\) |
0.872862 | + | 0.487968i | \(0.162262\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −0.382433 | −0.0834538 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.30507 | − | 2.48554i | 0.897670 | − | 0.518270i | 0.0212264 | − | 0.999775i | \(-0.493243\pi\) |
0.876443 | + | 0.481505i | \(0.159910\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.41855 | + | 2.34017i | −0.883710 | + | 0.468035i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 3.07838i | − | 0.592434i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −3.63090 | − | 6.28890i | −0.674241 | − | 1.16782i | −0.976690 | − | 0.214654i | \(-0.931138\pi\) |
0.302449 | − | 0.953165i | \(-0.402196\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9.66701 | −1.73625 | −0.868124 | − | 0.496348i | \(-0.834674\pi\) | ||||
−0.868124 | + | 0.496348i | \(0.834674\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 2.10607 | + | 1.21594i | 0.366620 | + | 0.211668i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.438397 | − | 1.52419i | 0.0741027 | − | 0.257636i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.02558 | + | 3.47887i | −0.990599 | + | 0.571923i | −0.905453 | − | 0.424446i | \(-0.860469\pi\) |
−0.0851458 | + | 0.996369i | \(0.527136\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.92162 | + | 0.294598i | −0.307706 | + | 0.0471735i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.223740 | − | 0.387529i | −0.0349423 | − | 0.0605219i | 0.848025 | − | 0.529956i | \(-0.177791\pi\) |
−0.882968 | + | 0.469434i | \(0.844458\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.73205 | − | 1.00000i | −0.264135 | − | 0.152499i | 0.362084 | − | 0.932145i | \(-0.382065\pi\) |
−0.626219 | + | 0.779647i | \(0.715399\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 5.82208 | + | 1.67458i | 0.867905 | + | 0.249632i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 4.70928i | 0.686918i | 0.939168 | + | 0.343459i | \(0.111599\pi\) | ||||
−0.939168 | + | 0.343459i | \(0.888401\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.24846 | − | 5.62651i | −0.464066 | − | 0.803786i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 1.70928 | 0.239346 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 9.58864i | − | 1.31710i | −0.752537 | − | 0.658550i | \(-0.771170\pi\) | ||
0.752537 | − | 0.658550i | \(-0.228830\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −7.26042 | + | 6.99990i | −0.978994 | + | 0.943866i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0.0650468i | 0.00861565i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 2.87936 | − | 4.98720i | 0.374861 | − | 0.649278i | −0.615445 | − | 0.788180i | \(-0.711024\pi\) |
0.990306 | + | 0.138901i | \(0.0443571\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.53139 | + | 6.11655i | −0.452148 | + | 0.783144i | −0.998519 | − | 0.0543997i | \(-0.982675\pi\) |
0.546371 | + | 0.837543i | \(0.316009\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.66417 | + | 0.960811i | −0.209666 | + | 0.121051i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.02870 | − | 7.99636i | 0.127595 | − | 0.991826i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.53020 | − | 1.46081i | 0.309113 | − | 0.178466i | −0.337416 | − | 0.941355i | \(-0.609553\pi\) |
0.646530 | + | 0.762889i | \(0.276220\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.34017 | + | 2.32125i | −0.161338 | + | 0.279445i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −4.09171 | + | 7.08705i | −0.485596 | + | 0.841078i | −0.999863 | − | 0.0165526i | \(-0.994731\pi\) |
0.514267 | + | 0.857630i | \(0.328064\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 6.74539i | − | 0.789488i | −0.918791 | − | 0.394744i | \(-0.870833\pi\) | ||
0.918791 | − | 0.394744i | \(-0.129167\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.43235 | − | 2.28396i | 0.165394 | − | 0.263729i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 3.19902i | − | 0.364562i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −16.0072 | −1.80095 | −0.900475 | − | 0.434908i | \(-0.856781\pi\) | ||||
−0.900475 | + | 0.434908i | \(0.856781\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.23400 | − | 5.60145i | −0.359333 | − | 0.622383i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − | 0.355771i | − | 0.0390510i | −0.999809 | − | 0.0195255i | \(-0.993784\pi\) | ||
0.999809 | − | 0.0195255i | \(-0.00621555\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.95941 | + | 6.81234i | −0.212527 | + | 0.738902i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 3.39090 | + | 1.95774i | 0.363543 | + | 0.209892i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.81545 | + | 3.14445i | 0.192437 | + | 0.333311i | 0.946057 | − | 0.323999i | \(-0.105027\pi\) |
−0.753620 | + | 0.657310i | \(0.771694\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.59951 | + | 1.99537i | 0.167674 | + | 0.209172i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 4.51402 | − | 2.60617i | 0.468083 | − | 0.270248i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.259245 | − | 0.0745655i | −0.0265979 | − | 0.00765026i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.84878 | + | 3.95415i | 0.695388 | + | 0.401483i | 0.805627 | − | 0.592422i | \(-0.201828\pi\) |
−0.110239 | + | 0.993905i | \(0.535162\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 12.2195 | 1.22811 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −3.07058 | − | 5.31840i | −0.305534 | − | 0.529200i | 0.671846 | − | 0.740691i | \(-0.265502\pi\) |
−0.977380 | + | 0.211490i | \(0.932168\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 17.6803i | − | 1.74210i | −0.491198 | − | 0.871048i | \(-0.663441\pi\) | ||
0.491198 | − | 0.871048i | \(-0.336559\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0.206204 | + | 0.829914i | 0.0201234 | + | 0.0809913i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −0.466951 | + | 0.269594i | −0.0451419 | + | 0.0260627i | −0.522401 | − | 0.852700i | \(-0.674964\pi\) |
0.477259 | + | 0.878763i | \(0.341630\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 11.0205 | 1.05557 | 0.527787 | − | 0.849377i | \(-0.323022\pi\) | ||||
0.527787 | + | 0.849377i | \(0.323022\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1.87577 | − | 3.24893i | 0.178040 | − | 0.308374i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −12.1244 | − | 7.00000i | −1.14056 | − | 0.658505i | −0.193993 | − | 0.981003i | \(-0.562144\pi\) |
−0.946570 | + | 0.322498i | \(0.895477\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −7.71507 | − | 8.00221i | −0.719434 | − | 0.746210i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −7.62188 | + | 6.10977i | −0.704643 | + | 0.564848i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.12423 | − | 1.94723i | −0.103058 | − | 0.178502i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.67122 | + | 8.09079i | −0.424656 | + | 0.735526i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.208951 | + | 0.120638i | 0.0188405 | + | 0.0108776i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 7.46081 | + | 8.32684i | 0.667315 | + | 0.744775i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.5458 | − | 6.08864i | 0.935791 | − | 0.540279i | 0.0471526 | − | 0.998888i | \(-0.484985\pi\) |
0.888638 | + | 0.458609i | \(0.151652\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 1.07838 | 0.0949459 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 17.4547 | 1.52502 | 0.762511 | − | 0.646976i | \(-0.223966\pi\) | ||||
0.762511 | + | 0.646976i | \(0.223966\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0.0741020 | − | 0.0427828i | 0.00642546 | − | 0.00370974i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −6.68035 | + | 1.65983i | −0.574953 | + | 0.142855i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 8.10037 | + | 4.67675i | 0.692061 | + | 0.399562i | 0.804384 | − | 0.594110i | \(-0.202496\pi\) |
−0.112322 | + | 0.993672i | \(0.535829\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1.32211 | − | 2.28997i | 0.112140 | − | 0.194233i | −0.804493 | − | 0.593963i | \(-0.797563\pi\) |
0.916633 | + | 0.399730i | \(0.130896\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.26959 | − | 2.19900i | −0.106919 | − | 0.185189i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.46429 | − | 16.0742i | −0.206074 | − | 1.34419i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −11.6897 | + | 11.2703i | −0.970778 | + | 0.935945i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.03375 | + | 1.75154i | 0.250219 | + | 0.144464i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.61757 | + | 7.99786i | −0.378286 | + | 0.655210i | −0.990813 | − | 0.135239i | \(-0.956820\pi\) |
0.612527 | + | 0.790450i | \(0.290153\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 9.42574 | 0.767056 | 0.383528 | − | 0.923529i | \(-0.374709\pi\) | ||||
0.383528 | + | 0.923529i | \(0.374709\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.43798 | − | 4.29432i | 0.601325 | − | 0.347175i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.21235 | + | 20.9783i | 0.418666 | + | 1.68501i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 5.77205i | − | 0.460660i | −0.973113 | − | 0.230330i | \(-0.926019\pi\) | ||
0.973113 | − | 0.230330i | \(-0.0739806\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2.58504 | + | 4.47743i | 0.205007 | + | 0.355083i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.52586 | 0.277877 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 14.5678 | + | 8.41075i | 1.14104 | + | 0.658781i | 0.946688 | − | 0.322151i | \(-0.104406\pi\) |
0.194354 | + | 0.980932i | \(0.437739\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.50313 | − | 5.22598i | 0.117018 | − | 0.406842i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −15.6919 | + | 9.05971i | −1.21427 | + | 0.701061i | −0.963687 | − | 0.267033i | \(-0.913957\pi\) |
−0.250586 | + | 0.968094i | \(0.580623\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 9.57417 | + | 8.79404i | 0.736475 | + | 0.676465i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.163421 | + | 0.283053i | 0.0124971 | + | 0.0216456i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 8.92357 | + | 5.15203i | 0.678447 | + | 0.391701i | 0.799270 | − | 0.600973i | \(-0.205220\pi\) |
−0.120823 | + | 0.992674i | \(0.538553\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.54401 | − | 0.129532i | −0.267902 | − | 0.00979171i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3.10504i | 0.233389i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −0.630898 | − | 1.09275i | −0.0471555 | − | 0.0816757i | 0.841484 | − | 0.540282i | \(-0.181682\pi\) |
−0.888640 | + | 0.458606i | \(0.848349\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.38243 | 0.177085 | 0.0885424 | − | 0.996072i | \(-0.471779\pi\) | ||||
0.0885424 | + | 0.996072i | \(0.471779\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 3.80817i | − | 0.281508i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.7984 | + | 11.2003i | 0.793912 | + | 0.823460i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 14.2979i | 1.04557i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.09171 | − | 1.89090i | 0.0794101 | − | 0.137542i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −5.54278 | + | 9.60038i | −0.401062 | + | 0.694659i | −0.993854 | − | 0.110696i | \(-0.964692\pi\) |
0.592793 | + | 0.805355i | \(0.298025\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 12.1244 | − | 7.00000i | 0.872730 | − | 0.503871i | 0.00447566 | − | 0.999990i | \(-0.498575\pi\) |
0.868255 | + | 0.496119i | \(0.165242\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 1.67542 | + | 4.01124i | 0.119979 | + | 0.287251i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.52895 | + | 4.34684i | −0.536415 | + | 0.309699i | −0.743625 | − | 0.668597i | \(-0.766895\pi\) |
0.207210 | + | 0.978297i | \(0.433562\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −10.7587 | + | 18.6347i | −0.762666 | + | 1.32098i | 0.178806 | + | 0.983884i | \(0.442776\pi\) |
−0.941472 | + | 0.337091i | \(0.890557\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.787653 | + | 1.36426i | −0.0555568 | + | 0.0962271i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 5.15061i | − | 0.361502i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.720334 | + | 0.694487i | −0.0503103 | + | 0.0485051i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 13.4680i | 0.936091i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.544109 | −0.0376368 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.79432 | − | 4.83990i | −0.192369 | − | 0.333193i | 0.753666 | − | 0.657258i | \(-0.228284\pi\) |
−0.946035 | + | 0.324065i | \(0.894950\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 4.41241i | − | 0.302333i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −1.23618 | + | 4.29789i | −0.0843070 | + | 0.293114i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.93797 | − | 3.42829i | −0.403096 | − | 0.232727i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.81852 | + | 3.14977i | 0.122884 | + | 0.212842i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.14896 | − | 8.91825i | −0.480891 | − | 0.599907i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −21.3989 | + | 12.3546i | −1.43297 | + | 0.827328i | −0.997347 | − | 0.0727995i | \(-0.976807\pi\) |
−0.435627 | + | 0.900127i | \(0.643473\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0.494784 | − | 13.5373i | 0.0329856 | − | 0.902489i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −24.8504 | − | 14.3474i | −1.64938 | − | 0.952268i | −0.977320 | − | 0.211768i | \(-0.932078\pi\) |
−0.672056 | − | 0.740500i | \(-0.734589\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.89988 | 0.125548 | 0.0627738 | − | 0.998028i | \(-0.480005\pi\) | ||||
0.0627738 | + | 0.998028i | \(0.480005\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.862437 | + | 1.49378i | 0.0567442 | + | 0.0982838i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 22.2485i | 1.45755i | 0.684756 | + | 0.728773i | \(0.259909\pi\) | ||||
−0.684756 | + | 0.728773i | \(0.740091\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 10.2195 | − | 2.53919i | 0.666649 | − | 0.165638i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.47458 | − | 4.31545i | 0.485526 | − | 0.280319i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.8710 | 1.60877 | 0.804384 | − | 0.594110i | \(-0.202495\pi\) | ||||
0.804384 | + | 0.594110i | \(0.202495\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.47528 | − | 2.55525i | 0.0950309 | − | 0.164598i | −0.814591 | − | 0.580036i | \(-0.803038\pi\) |
0.909621 | + | 0.415438i | \(0.136372\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 11.0181 | + | 6.36130i | 0.706811 | + | 0.408078i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −10.4585 | + | 10.0832i | −0.668167 | + | 0.644192i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 0.339386 | − | 0.272055i | 0.0215946 | − | 0.0173104i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0.0959140 | + | 0.166128i | 0.00607830 | + | 0.0105279i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.27985 | − | 14.3411i | 0.522620 | − | 0.905204i | −0.477034 | − | 0.878885i | \(-0.658288\pi\) |
0.999654 | − | 0.0263190i | \(-0.00837857\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −19.4170 | − | 11.2104i | −1.22074 | − | 0.704792i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −0.921622 | − | 3.70928i | −0.0577142 | − | 0.232284i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 0.453443 | − | 0.261795i | 0.0282850 | − | 0.0163303i | −0.485791 | − | 0.874075i | \(-0.661468\pi\) |
0.514076 | + | 0.857745i | \(0.328135\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.93495 | −0.306643 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 19.6742 | 1.21780 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 24.9255 | − | 14.3908i | 1.53697 | − | 0.887372i | 0.537960 | − | 0.842971i | \(-0.319195\pi\) |
0.999014 | − | 0.0444013i | \(-0.0141380\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −20.8082 | + | 5.17009i | −1.27824 | + | 0.317596i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.69545 | − | 0.978870i | −0.103760 | − | 0.0599059i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 5.02832 | − | 8.70930i | 0.306582 | − | 0.531016i | −0.671030 | − | 0.741430i | \(-0.734148\pi\) |
0.977612 | + | 0.210414i | \(0.0674813\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.06278 | + | 15.6972i | 0.550525 | + | 0.953537i | 0.998237 | + | 0.0593589i | \(0.0189056\pi\) |
−0.447712 | + | 0.894178i | \(0.647761\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.28483 | − | 0.500522i | −0.0777616 | − | 0.0302930i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 19.1051 | + | 11.9815i | 1.15208 | + | 0.722509i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 21.4051 | + | 12.3582i | 1.28611 | + | 0.742534i | 0.977958 | − | 0.208804i | \(-0.0669570\pi\) |
0.308149 | + | 0.951338i | \(0.400290\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 13.0953 | − | 22.6817i | 0.783995 | − | 1.35792i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 22.9854 | 1.37120 | 0.685598 | − | 0.727980i | \(-0.259541\pi\) | ||||
0.685598 | + | 0.727980i | \(0.259541\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 15.6741 | − | 9.04945i | 0.931729 | − | 0.537934i | 0.0443709 | − | 0.999015i | \(-0.485872\pi\) |
0.887358 | + | 0.461081i | \(0.152538\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.141157 | − | 0.0350725i | 0.00836142 | − | 0.00207751i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 0.317387i | − | 0.0187347i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.47528 | − | 6.01935i | −0.204428 | − | 0.354080i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −4.26406 | −0.249964 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 15.4536 | + | 8.92214i | 0.902809 | + | 0.521237i | 0.878111 | − | 0.478458i | \(-0.158804\pi\) |
0.0246988 | + | 0.999695i | \(0.492137\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −12.3752 | − | 3.55942i | −0.720511 | − | 0.207237i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −12.0241 | + | 6.94214i | −0.697711 | + | 0.402824i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 17.7165 | − | 2.71606i | 1.02457 | − | 0.157074i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.709275 | − | 1.22850i | −0.0408820 | − | 0.0708096i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 2.86762 | + | 1.65562i | 0.164741 | + | 0.0951130i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 15.1775 | + | 4.36545i | 0.869062 | + | 0.249965i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 3.44521i | − | 0.196629i | −0.995155 | − | 0.0983143i | \(-0.968655\pi\) | ||
0.995155 | − | 0.0983143i | \(-0.0313451\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.76652 | + | 8.25586i | 0.271158 | + | 0.469659i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −17.8238 | −1.01069 | −0.505347 | − | 0.862916i | \(-0.668635\pi\) | ||||
−0.505347 | + | 0.862916i | \(0.668635\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 32.2245i | − | 1.82143i | −0.413031 | − | 0.910717i | \(-0.635530\pi\) | ||
0.413031 | − | 0.910717i | \(-0.364470\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.98235 | + | 3.09334i | 0.168036 | + | 0.174290i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.90602i | 0.107053i | 0.998566 | + | 0.0535265i | \(0.0170462\pi\) | ||||
−0.998566 | + | 0.0535265i | \(0.982954\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −16.3763 | + | 28.3646i | −0.916896 | + | 1.58811i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0.145362 | − | 0.251775i | 0.00811333 | − | 0.0140527i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −0.331197 | + | 0.191217i | −0.0184283 | + | 0.0106396i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −17.9075 | + | 2.07918i | −0.993327 | + | 0.115332i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −5.14605 | + | 2.97107i | −0.284577 | + | 0.164301i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −1.67009 | + | 2.89267i | −0.0920748 | + | 0.159478i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −0.355771 | + | 0.616214i | −0.0195550 | + | 0.0338702i | −0.875637 | − | 0.482969i | \(-0.839558\pi\) |
0.856082 | + | 0.516839i | \(0.172892\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 18.8504i | − | 1.03300i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −4.53434 | − | 4.70310i | −0.247738 | − | 0.256958i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.85043i | 0.536587i | 0.963337 | + | 0.268294i | \(0.0864597\pi\) | ||||
−0.963337 | + | 0.268294i | \(0.913540\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7.54864 | 0.409986 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 21.8004 | + | 37.7594i | 1.18056 | + | 2.04478i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 9.57304i | − | 0.516896i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 5.75991 | + | 1.65670i | 0.310103 | + | 0.0891937i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −22.1123 | − | 12.7665i | −1.18705 | − | 0.685343i | −0.229414 | − | 0.973329i | \(-0.573681\pi\) |
−0.957635 | + | 0.287986i | \(0.907014\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −9.02832 | − | 15.6375i | −0.483275 | − | 0.837056i | 0.516541 | − | 0.856263i | \(-0.327219\pi\) |
−0.999816 | + | 0.0192061i | \(0.993886\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 4.02893 | − | 10.3422i | 0.215048 | − | 0.552026i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 12.6842 | − | 7.32325i | 0.675114 | − | 0.389777i | −0.122898 | − | 0.992419i | \(-0.539219\pi\) |
0.798012 | + | 0.602642i | \(0.205885\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 17.5857 | + | 5.05810i | 0.933353 | + | 0.268456i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.04992 | + | 0.606173i | 0.0555678 | + | 0.0320821i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −13.4186 | −0.708204 | −0.354102 | − | 0.935207i | \(-0.615213\pi\) | ||||
−0.354102 | + | 0.935207i | \(0.615213\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.49272 | + | 16.4419i | 0.499617 | + | 0.865362i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 5.03734i | − | 0.264392i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −14.6381 | + | 3.63704i | −0.766192 | + | 0.190371i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −18.6577 | + | 10.7721i | −0.973926 | + | 0.562297i | −0.900431 | − | 0.434999i | \(-0.856749\pi\) |
−0.0734954 | + | 0.997296i | \(0.523415\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 1.21235 | 0.0631123 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.40049 | − | 5.88983i | 0.176545 | − | 0.305784i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −18.4758 | − | 10.6670i | −0.956641 | − | 0.552317i | −0.0615036 | − | 0.998107i | \(-0.519590\pi\) |
−0.895138 | + | 0.445790i | \(0.852923\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.72871 | − | 1.87684i | −0.295829 | − | 0.0969194i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.96765 | − | 25.8804i | −0.204344 | − | 1.33291i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.05611 | − | 7.02540i | −0.208349 | − | 0.360870i | 0.742846 | − | 0.669462i | \(-0.233476\pi\) |
−0.951194 | + | 0.308592i | \(0.900142\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3.28293 | + | 5.68619i | −0.168189 | + | 0.291313i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 21.5986 | + | 12.4699i | 1.10364 | + | 0.637184i | 0.937173 | − | 0.348864i | \(-0.113432\pi\) |
0.166462 | + | 0.986048i | \(0.446766\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −6.94214 | + | 1.72487i | −0.353804 | + | 0.0879077i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 4.69260 | − | 2.70928i | 0.238538 | − | 0.137720i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −13.5330 | −0.686153 | −0.343076 | − | 0.939308i | \(-0.611469\pi\) | ||||
−0.343076 | + | 0.939308i | \(0.611469\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −15.7587 | −0.796953 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −8.15048 | + | 4.70568i | −0.411137 | + | 0.237370i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 8.63090 | + | 34.7370i | 0.434268 | + | 1.74781i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.97920 | − | 2.29739i | −0.199710 | − | 0.115303i | 0.396810 | − | 0.917901i | \(-0.370117\pi\) |
−0.596520 | + | 0.802598i | \(0.703450\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −0.0230680 | + | 0.0399550i | −0.00115485 | + | 0.00200025i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −14.8516 | − | 25.7237i | −0.741652 | − | 1.28458i | −0.951743 | − | 0.306897i | \(-0.900709\pi\) |
0.210091 | − | 0.977682i | \(-0.432624\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −32.4776 | − | 12.6520i | −1.61782 | − | 0.630242i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −10.4119 | + | 10.0383i | −0.517371 | + | 0.498807i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 27.1769 | + | 15.6906i | 1.34711 | + | 0.777754i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.15562 | + | 8.92980i | −0.254929 | + | 0.441550i | −0.964876 | − | 0.262705i | \(-0.915385\pi\) |
0.709947 | + | 0.704255i | \(0.248719\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −5.04331 | −0.248768 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 3.53730 | − | 2.04226i | 0.174059 | − | 0.100493i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −0.772055 | + | 0.191828i | −0.0378987 | + | 0.00941646i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.42574i | 0.0698187i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −19.0452 | − | 32.9873i | −0.930421 | − | 1.61154i | −0.782602 | − | 0.622522i | \(-0.786108\pi\) |
−0.147819 | − | 0.989014i | \(-0.547225\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −26.7103 | −1.30178 | −0.650891 | − | 0.759171i | \(-0.725604\pi\) | ||||
−0.650891 | + | 0.759171i | \(0.725604\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11.0494 | − | 6.37936i | −0.537239 | − | 0.310175i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15.8399 | + | 0.578941i | 0.768346 | + | 0.0280827i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.33832 | + | 2.50473i | −0.209946 | + | 0.121212i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 5.48421 | + | 6.84150i | 0.264780 | + | 0.330311i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −10.3594 | − | 17.9429i | −0.498993 | − | 0.864281i | 0.501006 | − | 0.865444i | \(-0.332963\pi\) |
−0.999999 | + | 0.00116231i | \(0.999630\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13.7331 | + | 7.92881i | 0.659971 | + | 0.381034i | 0.792266 | − | 0.610176i | \(-0.208901\pi\) |
−0.132295 | + | 0.991210i | \(0.542235\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2.42013 | − | 8.41415i | 0.116036 | − | 0.403427i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − | 0.599701i | − | 0.0286876i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.86962 | + | 8.43444i | 0.232415 | + | 0.402554i | 0.958518 | − | 0.285032i | \(-0.0920041\pi\) |
−0.726104 | + | 0.687585i | \(0.758671\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 17.6020 | 0.838189 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 9.23060i | − | 0.438559i | −0.975662 | − | 0.219279i | \(-0.929629\pi\) | ||
0.975662 | − | 0.219279i | \(-0.0703707\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.84486 | − | 5.63513i | 0.277073 | − | 0.267131i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 4.97948i | − | 0.235521i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.46194 | + | 2.53216i | −0.0689934 | + | 0.119500i | −0.898458 | − | 0.439058i | \(-0.855312\pi\) |
0.829465 | + | 0.558559i | \(0.188645\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.00913 | + | 1.74786i | −0.0475179 | + | 0.0823034i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −4.40136 | + | 2.54113i | −0.206794 | + | 0.119393i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.46769 | − | 4.54695i | 0.162568 | − | 0.213164i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.0915 | + | 5.82632i | −0.472060 | + | 0.272544i | −0.717101 | − | 0.696969i | \(-0.754532\pi\) |
0.245042 | + | 0.969512i | \(0.421198\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −4.87936 | + | 8.45130i | −0.227749 | + | 0.394473i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.1490 | − | 26.2388i | 0.705557 | − | 1.22206i | −0.260933 | − | 0.965357i | \(-0.584030\pi\) |
0.966490 | − | 0.256704i | \(-0.0826366\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 7.04331i | − | 0.327330i | −0.986516 | − | 0.163665i | \(-0.947668\pi\) | ||
0.986516 | − | 0.163665i | \(-0.0523316\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −8.08953 | − | 8.39060i | −0.375143 | − | 0.389105i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.90110i | 0.180522i | 0.995918 | + | 0.0902608i | \(0.0287700\pi\) | ||||
−0.995918 | + | 0.0902608i | \(0.971230\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.07223 | 0.0956869 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.55611 | + | 2.69527i | 0.0717019 | + | 0.124191i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 9.02052i | 0.414764i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −0.0220317 | + | 0.602788i | −0.00101088 | + | 0.0276578i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 22.4978 | + | 12.9891i | 1.03010 | + | 0.594731i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.75513 | − | 15.1643i | −0.400032 | − | 0.692876i | 0.593697 | − | 0.804689i | \(-0.297668\pi\) |
−0.993729 | + | 0.111813i | \(0.964334\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −24.7968 | + | 3.80152i | −1.13064 | + | 0.173335i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.64640 | + | 0.950552i | −0.0749140 | + | 0.0432516i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4.88805 | − | 16.9945i | 0.221955 | − | 0.771680i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 33.3695 | + | 19.2659i | 1.51212 | + | 0.873022i | 0.999900 | + | 0.0141666i | \(0.00450951\pi\) |
0.512218 | + | 0.858855i | \(0.328824\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.06997 | −0.410158 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.41189 | + | 5.90956i | 0.153976 | + | 0.266695i | 0.932686 | − | 0.360690i | \(-0.117459\pi\) |
−0.778710 | + | 0.627385i | \(0.784125\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 23.0205i | 1.03679i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −6.58864 | − | 26.5174i | −0.296137 | − | 1.19187i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −5.02667 | + | 2.90215i | −0.225477 | + | 0.130179i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.57918 | 0.428823 | 0.214412 | − | 0.976743i | \(-0.431217\pi\) | ||||
0.214412 | + | 0.976743i | \(0.431217\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.88489 | − | 8.46088i | 0.218241 | − | 0.378004i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −14.4403 | − | 8.33710i | −0.643860 | − | 0.371733i | 0.142240 | − | 0.989832i | \(-0.454570\pi\) |
−0.786100 | + | 0.618099i | \(0.787903\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −9.88576 | + | 9.53104i | −0.439911 | + | 0.424126i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −6.84150 | − | 1.52525i | −0.303842 | − | 0.0677386i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.8299 | − | 20.4900i | −0.524352 | − | 0.908204i | −0.999598 | − | 0.0283510i | \(-0.990974\pi\) |
0.475246 | − | 0.879853i | \(-0.342359\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.39217 | − | 4.14336i | 0.105823 | − | 0.183291i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −0.321616 | − | 0.185685i | −0.0141997 | − | 0.00819819i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −38.3679 | + | 9.53305i | −1.69069 | + | 0.420076i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 18.3944 | − | 10.6200i | 0.808986 | − | 0.467068i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.55583 | −0.243874 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −24.0472 | −1.05353 | −0.526763 | − | 0.850012i | \(-0.676594\pi\) | ||||
−0.526763 | + | 0.850012i | \(0.676594\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 20.2079 | − | 11.6670i | 0.883628 | − | 0.510163i | 0.0117752 | − | 0.999931i | \(-0.496252\pi\) |
0.871853 | + | 0.489768i | \(0.162918\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.68980 | − | 0.894960i | 0.0737490 | − | 0.0390593i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 26.5396 | + | 15.3226i | 1.15608 | + | 0.667465i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.855771 | − | 1.48224i | 0.0372075 | − | 0.0644452i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.80098 | + | 13.5117i | 0.338534 | + | 0.586358i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −0.244491 | − | 1.59478i | −0.0105901 | − | 0.0690776i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.836818 | + | 0.867962i | 0.0361788 | + | 0.0375253i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0.589197 | + | 0.340173i | 0.0254257 | + | 0.0146795i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −14.6514 | + | 25.3770i | −0.631081 | + | 1.09306i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −33.1494 | −1.42520 | −0.712602 | − | 0.701569i | \(-0.752483\pi\) | ||||
−0.712602 | + | 0.701569i | \(0.752483\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.11248 | + | 0.642291i | −0.0477411 | + | 0.0275633i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −5.94214 | − | 23.9155i | −0.254533 | − | 1.02443i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 43.6742i | − | 1.86737i | −0.358090 | − | 0.933687i | \(-0.616572\pi\) | ||
0.358090 | − | 0.933687i | \(-0.383428\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −9.56751 | − | 16.5714i | −0.408331 | − | 0.707250i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.876050 | −0.0373210 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −9.83242 | − | 5.67675i | −0.418117 | − | 0.241400i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −8.06184 | − | 2.31879i | −0.342206 | − | 0.0984273i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −19.3982 | + | 11.1995i | −0.821927 | + | 0.474540i | −0.851080 | − | 0.525035i | \(-0.824052\pi\) |
0.0291537 | + | 0.999575i | \(0.490719\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −4.51026 | − | 5.62651i | −0.190764 | − | 0.237976i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.85464 | − | 6.67643i | −0.162743 | − | 0.281879i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −0.208951 | − | 0.120638i | −0.00880625 | − | 0.00508429i | 0.495590 | − | 0.868556i | \(-0.334952\pi\) |
−0.504397 | + | 0.863472i | \(0.668285\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −8.65329 | + | 30.0852i | −0.364047 | + | 1.26569i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | − | 4.58759i | − | 0.192661i | ||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 13.5856 | + | 23.5309i | 0.569537 | + | 0.986466i | 0.996612 | + | 0.0822501i | \(0.0262106\pi\) |
−0.427075 | + | 0.904216i | \(0.640456\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.25461 | −0.0943524 | −0.0471762 | − | 0.998887i | \(-0.515022\pi\) | ||||
−0.0471762 | + | 0.998887i | \(0.515022\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 5.97721i | − | 0.249702i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −13.2056 | + | 21.0571i | −0.550712 | + | 0.878141i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.86481i | 0.327416i | 0.986509 | + | 0.163708i | \(0.0523455\pi\) | ||||
−0.986509 | + | 0.163708i | \(0.947654\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.77432 | + | 6.53732i | −0.156855 | + | 0.271682i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.126170 | − | 0.218533i | 0.00523441 | − | 0.00906627i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −37.4532 | + | 21.6236i | −1.55115 | + | 0.895559i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 17.3684 | + | 13.2458i | 0.718093 | + | 0.547647i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 9.70289 | − | 5.60197i | 0.400481 | − | 0.231218i | −0.286210 | − | 0.958167i | \(-0.592396\pi\) |
0.686692 | + | 0.726949i | \(0.259062\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.583105 | + | 1.00997i | −0.0240264 | + | 0.0416150i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.34377 | − | 4.05952i | 0.0964097 | − | 0.166986i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 13.4186i | − | 0.551034i | −0.961296 | − | 0.275517i | \(-0.911151\pi\) | ||
0.961296 | − | 0.275517i | \(-0.0888490\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.61948 | + | 3.48960i | −0.148384 | + | 0.143060i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 11.6020i | − | 0.474837i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 29.5753 | 1.20841 | 0.604207 | − | 0.796827i | \(-0.293490\pi\) | ||||
0.604207 | + | 0.796827i | \(0.293490\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.4916 | − | 21.6361i | −0.509543 | − | 0.882554i | −0.999939 | − | 0.0110541i | \(-0.996481\pi\) |
0.490396 | − | 0.871500i | \(-0.336852\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 7.91548i | 0.322343i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 20.0764 | + | 5.77449i | 0.816221 | + | 0.234766i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.99964 | + | 5.19594i | 0.365284 | + | 0.210897i | 0.671396 | − | 0.741099i | \(-0.265695\pi\) |
−0.306112 | + | 0.951995i | \(0.599028\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.38858 | + | 2.40508i | 0.0562680 | + | 0.0974590i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −6.16342 | + | 15.8214i | −0.249345 | + | 0.640065i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 26.4385 | − | 15.2643i | 1.06784 | − | 0.616517i | 0.140249 | − | 0.990116i | \(-0.455210\pi\) |
0.927590 | + | 0.373599i | \(0.121876\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0.149131 | − | 0.518489i | 0.00601354 | − | 0.0209075i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −6.32444 | − | 3.65142i | −0.254612 | − | 0.147000i | 0.367262 | − | 0.930118i | \(-0.380295\pi\) |
−0.621874 | + | 0.783117i | \(0.713629\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −24.5103 | −0.985151 | −0.492575 | − | 0.870270i | \(-0.663944\pi\) | ||||
−0.492575 | + | 0.870270i | \(0.663944\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.65142 | − | 13.2526i | −0.307041 | − | 0.531810i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.57531i | 0.103177i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 14.0472 | − | 20.6803i | 0.561887 | − | 0.827214i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.254073 | − | 0.146689i | 0.0101467 | − | 0.00585819i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 22.0566 | 0.879456 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.53919 | + | 2.66595i | −0.0612741 | + | 0.106130i | −0.895035 | − | 0.445996i | \(-0.852850\pi\) |
0.833761 | + | 0.552125i | \(0.186183\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.60962 | + | 1.50667i | 0.103723 | + | 0.0598846i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −18.8991 | − | 19.6024i | −0.749986 | − | 0.777899i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.54975 | − | 23.1545i | −0.140646 | − | 0.917414i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −11.0856 | − | 19.2008i | −0.438538 | − | 0.759570i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.23400 | − | 2.13735i | 0.0487401 | − | 0.0844202i | −0.840626 | − | 0.541616i | \(-0.817813\pi\) |
0.889366 | + | 0.457196i | \(0.151146\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 16.2999 | + | 9.41075i | 0.642805 | + | 0.371124i | 0.785694 | − | 0.618615i | \(-0.212306\pi\) |
−0.142889 | + | 0.989739i | \(0.545639\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −0.581449 | − | 2.34017i | −0.0228945 | − | 0.0921442i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 10.1352 | − | 5.85157i | 0.398456 | − | 0.230049i | −0.287361 | − | 0.957822i | \(-0.592778\pi\) |
0.685818 | + | 0.727773i | \(0.259445\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −25.9733 | −1.01954 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.69699 | 0.144896 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −12.7251 | + | 7.34684i | −0.497972 | + | 0.287504i | −0.727875 | − | 0.685709i | \(-0.759492\pi\) |
0.229904 | + | 0.973213i | \(0.426159\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −9.41136 | − | 37.8781i | −0.367732 | − | 1.48002i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 15.8267 | + | 9.13756i | 0.617459 | + | 0.356490i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −9.39383 | + | 16.2706i | −0.365932 | + | 0.633812i | −0.988925 | − | 0.148415i | \(-0.952583\pi\) |
0.622994 | + | 0.782227i | \(0.285916\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.92101 | + | 5.05934i | 0.113614 | + | 0.196785i | 0.917225 | − | 0.398370i | \(-0.130424\pi\) |
−0.803611 | + | 0.595155i | \(0.797091\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 5.74253 | + | 2.23707i | 0.223021 | + | 0.0868806i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.132797 | − | 0.137740i | −0.00514966 | − | 0.00534132i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −31.2626 | − | 18.0494i | −1.21049 | − | 0.698877i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.66148 | − | 11.5380i | 0.257548 | − | 0.446086i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 31.8550 | 1.22975 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 35.4140 | − | 20.4463i | 1.36511 | − | 0.788145i | 0.374809 | − | 0.927102i | \(-0.377708\pi\) |
0.990298 | + | 0.138957i | \(0.0443749\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 7.20394 | + | 13.6020i | 0.277280 | + | 0.523540i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 28.2700i | − | 1.08651i | −0.839569 | − | 0.543253i | \(-0.817193\pi\) | ||
0.839569 | − | 0.543253i | \(-0.182807\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.80458 | + | 4.85767i | 0.107630 | + | 0.186420i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 15.4719 | 0.592884 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 35.9445 | + | 20.7526i | 1.37538 | + | 0.794075i | 0.991599 | − | 0.129349i | \(-0.0412888\pi\) |
0.383780 | + | 0.923425i | \(0.374622\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.78133 | − | 20.1002i | 0.220893 | − | 0.767988i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.887152 | + | 0.512197i | −0.0338469 | + | 0.0195415i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 12.5494 | − | 32.2142i | 0.478096 | − | 1.22726i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −12.0542 | − | 20.8784i | −0.458562 | − | 0.794253i | 0.540323 | − | 0.841458i | \(-0.318302\pi\) |
−0.998885 | + | 0.0472043i | \(0.984969\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 7.50586 | + | 4.33351i | 0.285124 | + | 0.164616i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −5.68230 | − | 1.63438i | −0.215542 | − | 0.0619954i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.41855i | 0.0537314i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.99806 | − | 10.3889i | −0.226868 | − | 0.392946i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −14.1822 | −0.535654 | −0.267827 | − | 0.963467i | \(-0.586306\pi\) | ||||
−0.267827 | + | 0.963467i | \(0.586306\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.839369i | 0.0316574i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4.08747 | + | 3.94081i | −0.153943 | + | 0.148419i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | − | 4.35577i | − | 0.163816i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −23.2479 | + | 40.2665i | −0.873091 | + | 1.51224i | −0.0143094 | + | 0.999898i | \(0.504555\pi\) |
−0.858782 | + | 0.512341i | \(0.828778\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 21.6839 | − | 37.5577i | 0.813211 | − | 1.40852i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −41.6172 | + | 24.0277i | −1.55858 | + | 0.899845i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −33.5536 | + | 14.0147i | −1.25483 | + | 0.524121i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −11.6135 | + | 6.70507i | −0.433715 | + | 0.250405i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6.36069 | − | 11.0170i | 0.237214 | − | 0.410866i | −0.722700 | − | 0.691162i | \(-0.757099\pi\) |
0.959914 | + | 0.280296i | \(0.0904325\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 6.27012 | − | 10.8602i | 0.233511 | − | 0.404454i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1.59090i | 0.0591664i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 30.7604 | + | 19.2909i | 1.14241 | + | 0.716446i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 13.2595i | 0.491769i | 0.969299 | + | 0.245884i | \(0.0790783\pi\) | ||||
−0.969299 | + | 0.245884i | \(0.920922\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 12.5441 | 0.464597 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.17009 | + | 5.49075i | 0.117250 | + | 0.203083i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 31.5848i | 1.16661i | 0.812253 | + | 0.583305i | \(0.198241\pi\) | ||||
−0.812253 | + | 0.583305i | \(0.801759\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 2.16522 | − | 7.52791i | 0.0798654 | − | 0.277671i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −11.4119 | − | 6.58864i | −0.420361 | − | 0.242696i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.41609 | − | 2.45274i | −0.0520917 | − | 0.0902255i | 0.838804 | − | 0.544434i | \(-0.183255\pi\) |
−0.890895 | + | 0.454208i | \(0.849922\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −0.0851321 | + | 0.218533i | −0.00312741 | + | 0.00802800i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −18.0151 | + | 10.4010i | −0.660909 | + | 0.381576i | −0.792623 | − | 0.609712i | \(-0.791285\pi\) |
0.131714 | + | 0.991288i | \(0.457952\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 19.8458 | + | 5.70816i | 0.727093 | + | 0.209131i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0.834747 | + | 0.481941i | 0.0305418 | + | 0.0176333i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −0.382433 | −0.0139738 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 18.1412 | + | 31.4214i | 0.661980 | + | 1.14658i | 0.980095 | + | 0.198531i | \(0.0636171\pi\) |
−0.318114 | + | 0.948052i | \(0.603050\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 8.92881i | 0.325384i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −5.08225 | − | 20.4547i | −0.184962 | − | 0.744422i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −35.3933 | + | 20.4343i | −1.28639 | + | 0.742699i | −0.978009 | − | 0.208563i | \(-0.933121\pi\) |
−0.308383 | + | 0.951262i | \(0.599788\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 12.0891 | 0.438805 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −17.8112 | + | 30.8500i | −0.645657 | + | 1.11831i | 0.338492 | + | 0.940969i | \(0.390083\pi\) |
−0.984149 | + | 0.177342i | \(0.943250\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 6.76936 | + | 3.90829i | 0.245067 | + | 0.141490i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −13.3295 | − | 13.8256i | −0.481930 | − | 0.499866i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 16.2007 | − | 12.9867i | 0.584975 | − | 0.468921i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.68455 | + | 2.91773i | 0.0607465 | + | 0.105216i | 0.894799 | − | 0.446469i | \(-0.147319\pi\) |
−0.834053 | + | 0.551685i | \(0.813985\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −0.141157 | + | 0.244491i | −0.00508365 | + | 0.00880514i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 9.59506 | + | 5.53971i | 0.345110 | + | 0.199250i | 0.662530 | − | 0.749036i | \(-0.269483\pi\) |
−0.317419 | + | 0.948285i | \(0.602816\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 42.7142 | − | 22.6225i | 1.53434 | − | 0.812624i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 2.30438 | − | 1.33044i | 0.0826693 | − | 0.0477291i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −0.0539832 | −0.00193415 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 36.9093 | 1.32072 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −19.3596 | + | 11.1773i | −0.691856 | + | 0.399443i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −12.5259 | + | 3.11223i | −0.447067 | + | 0.111080i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 4.91114 | + | 2.83545i | 0.175063 | + | 0.101073i | 0.584971 | − | 0.811054i | \(-0.301106\pi\) |
−0.409908 | + | 0.912127i | \(0.634439\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −7.75933 | + | 13.4396i | −0.276240 | + | 0.478461i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −4.96493 | − | 8.59951i | −0.176532 | − | 0.305763i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19.8694 | + | 15.9275i | −0.705582 | + | 0.565602i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 8.32258 | − | 8.02395i | 0.295171 | − | 0.284580i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −23.6792 | − | 13.6712i | −0.838762 | − | 0.484259i | 0.0180812 | − | 0.999837i | \(-0.494244\pi\) |
−0.856843 | + | 0.515577i | \(0.827578\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.46441 | − | 12.9287i | 0.264072 | − | 0.457386i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −9.83710 | −0.347577 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −26.3475 | + | 15.2117i | −0.929783 | + | 0.536810i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1.90110 | − | 7.65142i | −0.0670051 | − | 0.269677i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 5.42243i | 0.190878i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −2.51446 | − | 4.35518i | −0.0884039 | − | 0.153120i | 0.818433 | − | 0.574602i | \(-0.194843\pi\) |
−0.906837 | + | 0.421482i | \(0.861510\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −47.3390 | −1.66230 | −0.831148 | − | 0.556052i | \(-0.812316\pi\) | ||||
−0.831148 | + | 0.556052i | \(0.812316\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −8.46375 | − | 4.88655i | −0.296837 | − | 0.171379i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 10.3972 | − | 36.1485i | 0.364199 | − | 1.26623i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −0.208951 | + | 0.120638i | −0.00731028 | + | 0.00422059i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.84849 | + | 1.04992i | −0.239306 | + | 0.0366873i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 10.3408 | + | 17.9108i | 0.360896 | + | 0.625090i | 0.988109 | − | 0.153758i | \(-0.0491376\pi\) |
−0.627213 | + | 0.778848i | \(0.715804\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 17.1794 | + | 9.91855i | 0.598837 | + | 0.345739i | 0.768584 | − | 0.639749i | \(-0.220962\pi\) |
−0.169747 | + | 0.985488i | \(0.554295\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −12.1513 | − | 0.444125i | −0.423054 | − | 0.0154625i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 39.6730i | − | 1.37956i | −0.724017 | − | 0.689782i | \(-0.757706\pi\) | ||
0.724017 | − | 0.689782i | \(-0.242294\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −12.6937 | − | 21.9861i | −0.440870 | − | 0.763609i | 0.556885 | − | 0.830590i | \(-0.311997\pi\) |
−0.997754 | + | 0.0669813i | \(0.978663\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −13.3268 | −0.462303 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 20.5958i | 0.713603i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 28.1212 | + | 29.1678i | 0.973175 | + | 1.00939i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 29.7587i | 1.02861i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 11.5139 | − | 19.9426i | 0.397502 | − | 0.688494i | −0.595915 | − | 0.803048i | \(-0.703210\pi\) |
0.993417 | + | 0.114553i | \(0.0365437\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −11.8668 | + | 20.5540i | −0.409201 | + | 0.708757i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.7331 | + | 6.19675i | −0.369667 | + | 0.213427i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 13.9216 | − | 25.5184i | 0.478916 | − | 0.877861i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.73860 | + | 3.31318i | −0.197181 | + | 0.113842i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −4.87936 | + | 8.45130i | −0.167459 | + | 0.290048i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −17.2937 | + | 29.9536i | −0.592821 | + | 1.02680i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.7047i | 0.469241i | 0.972087 | + | 0.234621i | \(0.0753848\pi\) | ||||
−0.972087 | + | 0.234621i | \(0.924615\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.526136 | − | 0.507257i | 0.0179935 | − | 0.0173478i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 17.8648i | − | 0.610250i | −0.952312 | − | 0.305125i | \(-0.901302\pi\) | ||
0.952312 | − | 0.305125i | \(-0.0986983\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 13.7187 | 0.468077 | 0.234039 | − | 0.972227i | \(-0.424806\pi\) | ||||
0.234039 | + | 0.972227i | \(0.424806\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0.0855657 | + | 0.148204i | 0.00291607 | + | 0.00505078i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 19.9383i | − | 0.678706i | −0.940659 | − | 0.339353i | \(-0.889792\pi\) | ||
0.940659 | − | 0.339353i | \(-0.110208\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 6.36885 | − | 22.1428i | 0.216548 | − | 0.752879i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 3.24557 | + | 1.87383i | 0.110225 | + | 0.0636386i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 36.0983 | + | 62.5241i | 1.22455 | + | 2.12098i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 10.4124 | − | 1.59630i | 0.352811 | − | 0.0540884i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −18.5552 | + | 10.7129i | −0.628000 | + | 0.362576i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.62979 | + | 7.76065i | 0.0550971 | + | 0.262358i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 18.7203 | + | 10.8082i | 0.632140 | + | 0.364966i | 0.781580 | − | 0.623805i | \(-0.214414\pi\) |
−0.149441 | + | 0.988771i | \(0.547747\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.62144 | −0.324523 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.99693 | + | 6.92288i | 0.134660 | + | 0.233238i | 0.925468 | − | 0.378827i | \(-0.123672\pi\) |
−0.790808 | + | 0.612065i | \(0.790339\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.2713i | 0.884098i | 0.896991 | + | 0.442049i | \(0.145748\pi\) | ||||
−0.896991 | + | 0.442049i | \(0.854252\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 6.73820 | − | 1.67420i | 0.226502 | − | 0.0562777i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −14.8634 | + | 8.58136i | −0.499063 | + | 0.288134i | −0.728326 | − | 0.685230i | \(-0.759701\pi\) |
0.229264 | + | 0.973364i | \(0.426368\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.63704 | 0.289677 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −14.5862 | + | 25.2640i | −0.488655 | + | 0.846376i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0.492005 | + | 0.284059i | 0.0164643 | + | 0.00950568i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −2.03118 | + | 1.95830i | −0.0678949 | + | 0.0654587i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.54049 | + | 6.04453i | −0.251770 | + | 0.201821i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 35.0999 | + | 60.7949i | 1.17065 | + | 2.02762i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −15.1984 | + | 26.3244i | −0.506332 | + | 0.876993i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0.662394 | + | 0.382433i | 0.0220431 | + | 0.0127266i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1.28458 | − | 5.17009i | −0.0427009 | − | 0.171859i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −14.2146 | + | 8.20682i | −0.471989 | + | 0.272503i | −0.717072 | − | 0.696999i | \(-0.754518\pi\) |
0.245083 | + | 0.969502i | \(0.421185\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 16.6381 | 0.551850 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4.52359 | 0.149873 | 0.0749366 | − | 0.997188i | \(-0.476125\pi\) | ||||
0.0749366 | + | 0.997188i | \(0.476125\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.38964 | + | 0.802311i | −0.0459905 | + | 0.0265526i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −8.26406 | + | 2.05332i | −0.273201 | + | 0.0678808i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 10.7215 | + | 6.19008i | 0.354056 | + | 0.204415i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.82150 | − | 6.61904i | 0.126060 | − | 0.218342i | −0.796087 | − | 0.605182i | \(-0.793100\pi\) |
0.922147 | + | 0.386840i | \(0.126434\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0.928810 | + | 1.60875i | 0.0306053 | + | 0.0530100i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −23.0220 | + | 18.4547i | −0.757779 | + | 0.607443i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.4832 | − | 29.4725i | 0.607723 | − | 0.969049i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 41.4834 | + | 23.9505i | 1.36249 | + | 0.786636i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 29.6647 | − | 51.3808i | 0.973269 | − | 1.68575i | 0.287735 | − | 0.957710i | \(-0.407098\pi\) |
0.685534 | − | 0.728041i | \(-0.259569\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −0.783777 | −0.0256873 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.32283 | − | 4.80519i | 0.272477 | − | 0.157315i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 31.0277 | − | 7.70928i | 1.01471 | − | 0.252120i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 1.75872i | 0.0574550i | 0.999587 | + | 0.0287275i | \(0.00914551\pi\) | ||||
−0.999587 | + | 0.0287275i | \(0.990854\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 8.68753 | + | 15.0473i | 0.283507 | + | 0.491048i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 42.2967 | 1.37883 | 0.689416 | − | 0.724365i | \(-0.257867\pi\) | ||||
0.689416 | + | 0.724365i | \(0.257867\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.92643 | − | 1.11223i | −0.0627333 | − | 0.0362191i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −4.69204 | − | 1.34955i | −0.152632 | − | 0.0439010i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.19011 | + | 2.41916i | −0.136160 | + | 0.0786122i | −0.566533 | − | 0.824039i | \(-0.691716\pi\) |
0.430372 | + | 0.902651i | \(0.358382\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.82826 | − | 22.6620i | 0.286577 | − | 0.735640i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.513853 | − | 0.890020i | −0.0166628 | − | 0.0288609i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 22.4767 | + | 12.9769i | 0.728092 | + | 0.420364i | 0.817724 | − | 0.575611i | \(-0.195236\pi\) |
−0.0896318 | + | 0.995975i | \(0.528569\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 23.8223 | + | 6.85190i | 0.770870 | + | 0.221722i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 17.6598i | − | 0.570861i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 3.31710 | + | 5.74539i | 0.107115 | + | 0.185528i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 62.4512 | 2.01455 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 1.46081i | − | 0.0470740i | ||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −21.7279 | − | 22.5366i | −0.699447 | − | 0.725478i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.9939i | 0.964537i | 0.876023 | + | 0.482269i | \(0.160187\pi\) | ||||
−0.876023 | + | 0.482269i | \(0.839813\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0.103102 | − | 0.178578i | 0.00331211 | − | 0.00573674i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.86429 | − | 13.6213i | 0.252377 | − | 0.437130i | −0.711803 | − | 0.702379i | \(-0.752121\pi\) |
0.964180 | + | 0.265250i | \(0.0854544\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.62422 | − | 0.937743i | 0.0520701 | − | 0.0300627i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.80137 | − | 5.79863i | 0.249844 | − | 0.185705i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.8539 | − | 13.7721i | 0.763154 | − | 0.440607i | −0.0672731 | − | 0.997735i | \(-0.521430\pi\) |
0.830427 | + | 0.557128i | \(0.188097\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.18815 | − | 14.1823i | 0.261694 | − | 0.453268i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −14.9288 | + | 25.8575i | −0.476640 | + | 0.825565i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 18.0289i | − | 0.575034i | −0.957776 | − | 0.287517i | \(-0.907170\pi\) | ||
0.957776 | − | 0.287517i | \(-0.0928297\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.4925 | + | 13.9947i | 0.429908 | + | 0.445908i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | − | 1.80098i | − | 0.0573260i | ||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −9.94214 | −0.316142 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 5.81658 | + | 10.0746i | 0.184770 | + | 0.320031i | 0.943499 | − | 0.331376i | \(-0.107513\pi\) |
−0.758729 | + | 0.651406i | \(0.774179\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 0.383656i | − | 0.0121750i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 46.2398 | + | 13.2998i | 1.46590 | + | 0.421631i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −24.9977 | − | 14.4324i | −0.791684 | − | 0.457079i | 0.0488712 | − | 0.998805i | \(-0.484438\pi\) |
−0.840555 | + | 0.541726i | \(0.817771\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 10.7093 | + | 18.5490i | 0.338826 | + | 0.586865i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))