Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1008,2,Mod(337,1008)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1008, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1008.337");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1008 = 2^{4} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1008.r (of order \(3\), 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: | \(8.04892052375\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.309123.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 337.3 | ||
Root | \(0.500000 - 1.41036i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1008.337 |
Dual form | 1008.2.r.g.673.3 |
$q$-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 \(\left(\mathbb{Z}/1008\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(577\) | \(757\) | \(785\) |
\(\chi(n)\) | \(1\) | \(1\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 | 0 | ||||||||
\(3\) | 1.09097 | − | 1.34528i | 0.629873 | − | 0.776698i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.97141 | − | 3.41458i | 0.881641 | − | 1.52705i | 0.0321260 | − | 0.999484i | \(-0.489772\pi\) |
0.849515 | − | 0.527564i | \(-0.176894\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.500000 | + | 0.866025i | 0.188982 | + | 0.327327i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.619562 | − | 2.93533i | −0.206521 | − | 0.978442i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.471410 | + | 0.816506i | 0.142135 | + | 0.246186i | 0.928301 | − | 0.371831i | \(-0.121270\pi\) |
−0.786165 | + | 0.618017i | \(0.787936\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.500000 | − | 0.866025i | 0.138675 | − | 0.240192i | −0.788320 | − | 0.615265i | \(-0.789049\pi\) |
0.926995 | + | 0.375073i | \(0.122382\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.44282 | − | 6.37731i | −0.630733 | − | 1.64662i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 5.60301 | 1.35893 | 0.679465 | − | 0.733708i | \(-0.262212\pi\) | ||||
0.679465 | + | 0.733708i | \(0.262212\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.28263 | −0.294256 | −0.147128 | − | 0.989117i | \(-0.547003\pi\) | ||||
−0.147128 | + | 0.989117i | \(0.547003\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.71053 | + | 0.272169i | 0.373269 | + | 0.0593921i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.33009 | + | 4.03584i | −0.485858 | + | 0.841531i | −0.999868 | − | 0.0162531i | \(-0.994826\pi\) |
0.514010 | + | 0.857784i | \(0.328160\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −5.27292 | − | 9.13296i | −1.05458 | − | 1.82659i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −4.62476 | − | 2.36887i | −0.890036 | − | 0.455890i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.83009 | + | 6.63392i | 0.711231 | + | 1.23189i | 0.964395 | + | 0.264465i | \(0.0851952\pi\) |
−0.253165 | + | 0.967423i | \(0.581471\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 3.91423 | − | 6.77965i | 0.703016 | − | 1.21766i | −0.264386 | − | 0.964417i | \(-0.585169\pi\) |
0.967403 | − | 0.253243i | \(-0.0814973\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.61273 | + | 0.256606i | 0.280739 | + | 0.0446694i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 3.94282 | 0.666458 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.82846 | −1.61579 | −0.807894 | − | 0.589327i | \(-0.799393\pi\) | ||||
−0.807894 | + | 0.589327i | \(0.799393\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −0.619562 | − | 1.61745i | −0.0992093 | − | 0.258999i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −0.471410 | + | 0.816506i | −0.0736219 | + | 0.127517i | −0.900486 | − | 0.434885i | \(-0.856789\pi\) |
0.826864 | + | 0.562402i | \(0.190122\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 4.63160 | + | 8.02217i | 0.706312 | + | 1.22337i | 0.966216 | + | 0.257734i | \(0.0829759\pi\) |
−0.259903 | + | 0.965635i | \(0.583691\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −11.2443 | − | 3.67119i | −1.67621 | − | 0.547268i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −2.64132 | − | 4.57489i | −0.385275 | − | 0.667317i | 0.606532 | − | 0.795059i | \(-0.292560\pi\) |
−0.991807 | + | 0.127743i | \(0.959227\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −0.500000 | + | 0.866025i | −0.0714286 | + | 0.123718i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.11273 | − | 7.53762i | 0.855953 | − | 1.05548i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −9.22545 | −1.26721 | −0.633607 | − | 0.773655i | \(-0.718426\pi\) | ||||
−0.633607 | + | 0.773655i | \(0.718426\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.71737 | 0.501250 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.39931 | + | 1.72550i | −0.185344 | + | 0.228548i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.77292 | + | 8.26693i | −0.621381 | + | 1.07626i | 0.367848 | + | 0.929886i | \(0.380095\pi\) |
−0.989229 | + | 0.146377i | \(0.953239\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.27292 | + | 9.13296i | 0.675128 | + | 1.16936i | 0.976432 | + | 0.215827i | \(0.0692448\pi\) |
−0.301304 | + | 0.953528i | \(0.597422\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 2.23229 | − | 2.00422i | 0.281242 | − | 0.252508i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.97141 | − | 3.41458i | −0.244523 | − | 0.423527i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.858685 | + | 1.48729i | −0.104905 | + | 0.181701i | −0.913699 | − | 0.406391i | \(-0.866787\pi\) |
0.808794 | + | 0.588092i | \(0.200121\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 2.88727 | + | 7.53762i | 0.347587 | + | 0.907423i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.54583 | −0.420813 | −0.210406 | − | 0.977614i | \(-0.567479\pi\) | ||||
−0.210406 | + | 0.977614i | \(0.567479\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.71737 | 0.318044 | 0.159022 | − | 0.987275i | \(-0.449166\pi\) | ||||
0.159022 | + | 0.987275i | \(0.449166\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −18.0390 | − | 2.87024i | −2.08296 | − | 0.331427i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.471410 | + | 0.816506i | −0.0537222 | + | 0.0930495i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.18715 | − | 14.1806i | −0.921126 | − | 1.59544i | −0.797676 | − | 0.603086i | \(-0.793938\pi\) |
−0.123449 | − | 0.992351i | \(-0.539396\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −8.23229 | + | 3.63723i | −0.914699 | + | 0.404137i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.198495 | − | 0.343803i | −0.0217877 | − | 0.0377373i | 0.854926 | − | 0.518750i | \(-0.173602\pi\) |
−0.876714 | + | 0.481013i | \(0.840269\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 11.0458 | − | 19.1319i | 1.19809 | − | 2.07515i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 13.1030 | + | 2.08486i | 1.40479 | + | 0.223521i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 5.50808 | 0.583855 | 0.291928 | − | 0.956440i | \(-0.405703\pi\) | ||||
0.291928 | + | 0.956440i | \(0.405703\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.00000 | 0.104828 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −4.85021 | − | 12.6621i | −0.502944 | − | 1.31300i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2.52859 | + | 4.37965i | −0.259428 | + | 0.449342i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.77292 | + | 11.7310i | 0.687685 | + | 1.19111i | 0.972585 | + | 0.232549i | \(0.0747064\pi\) |
−0.284899 | + | 0.958557i | \(0.591960\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 2.10464 | − | 1.88962i | 0.211525 | − | 0.189914i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.30150 | + | 2.25427i | 0.129505 | + | 0.224309i | 0.923485 | − | 0.383635i | \(-0.125328\pi\) |
−0.793980 | + | 0.607944i | \(0.791995\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.99028 | − | 13.8396i | 0.787306 | − | 1.36365i | −0.140305 | − | 0.990108i | \(-0.544808\pi\) |
0.927612 | − | 0.373546i | \(-0.121858\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 4.30150 | − | 5.30420i | 0.419784 | − | 0.517637i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 10.8856 | 1.05235 | 0.526177 | − | 0.850375i | \(-0.323625\pi\) | ||||
0.526177 | + | 0.850375i | \(0.323625\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −3.28263 | −0.314419 | −0.157209 | − | 0.987565i | \(-0.550250\pi\) | ||||
−0.157209 | + | 0.987565i | \(0.550250\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −10.7226 | + | 13.2220i | −1.01774 | + | 1.25498i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 3.22545 | − | 5.58664i | 0.303425 | − | 0.525547i | −0.673485 | − | 0.739201i | \(-0.735203\pi\) |
0.976909 | + | 0.213654i | \(0.0685365\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 9.18715 | + | 15.9126i | 0.856706 | + | 1.48386i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.85185 | − | 0.931107i | −0.263653 | − | 0.0860809i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.80150 | + | 4.85235i | 0.256814 | + | 0.444814i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.05555 | − | 8.75646i | 0.459595 | − | 0.796042i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0.584135 | + | 1.52496i | 0.0526697 | + | 0.137501i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −21.8662 | −1.95577 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.828460 | 0.0735140 | 0.0367570 | − | 0.999324i | \(-0.488297\pi\) | ||||
0.0367570 | + | 0.999324i | \(0.488297\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 15.8450 | + | 2.52115i | 1.39508 | + | 0.221975i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.71574 | − | 4.70379i | 0.237275 | − | 0.410972i | −0.722656 | − | 0.691207i | \(-0.757079\pi\) |
0.959931 | + | 0.280235i | \(0.0904125\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.641315 | − | 1.11079i | −0.0556091 | − | 0.0963177i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −17.2060 | + | 11.1216i | −1.48086 | + | 0.957196i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 10.5744 | + | 18.3154i | 0.903434 | + | 1.56479i | 0.823006 | + | 0.568033i | \(0.192295\pi\) |
0.0804276 | + | 0.996760i | \(0.474371\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −0.923945 | + | 1.60032i | −0.0783680 | + | 0.135737i | −0.902546 | − | 0.430594i | \(-0.858304\pi\) |
0.824178 | + | 0.566331i | \(0.191638\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −9.03611 | − | 1.43777i | −0.760978 | − | 0.121082i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.942820 | 0.0788426 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 30.2028 | 2.50820 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0.619562 | + | 1.61745i | 0.0511006 | + | 0.133405i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.07442 | + | 10.5212i | −0.497636 | + | 0.861931i | −0.999996 | − | 0.00272771i | \(-0.999132\pi\) |
0.502360 | + | 0.864658i | \(0.332465\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.49028 | − | 7.77740i | −0.365414 | − | 0.632916i | 0.623428 | − | 0.781880i | \(-0.285739\pi\) |
−0.988843 | + | 0.148965i | \(0.952406\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −3.47141 | − | 16.4467i | −0.280647 | − | 1.32963i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −15.4331 | − | 26.7309i | −1.23962 | − | 2.14708i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.90451 | − | 10.2269i | 0.471232 | − | 0.816197i | −0.528227 | − | 0.849103i | \(-0.677143\pi\) |
0.999458 | + | 0.0329062i | \(0.0104763\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −10.0647 | + | 12.4108i | −0.798183 | + | 0.984242i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −4.66019 | −0.367274 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 12.2826 | 0.962050 | 0.481025 | − | 0.876707i | \(-0.340265\pi\) | ||||
0.481025 | + | 0.876707i | \(0.340265\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 4.05555 | − | 5.00091i | 0.315724 | − | 0.389320i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −11.4428 | + | 19.8195i | −0.885472 | + | 1.53368i | −0.0403003 | + | 0.999188i | \(0.512831\pi\) |
−0.845172 | + | 0.534495i | \(0.820502\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.00000 | + | 10.3923i | 0.461538 | + | 0.799408i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.794668 | + | 3.76494i | 0.0607698 | + | 0.287912i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −9.63160 | − | 16.6824i | −0.732277 | − | 1.26834i | −0.955908 | − | 0.293667i | \(-0.905124\pi\) |
0.223631 | − | 0.974674i | \(-0.428209\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.27292 | − | 9.13296i | 0.398595 | − | 0.690387i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 5.91423 | + | 15.4399i | 0.444541 | + | 1.16053i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 4.83173 | 0.361140 | 0.180570 | − | 0.983562i | \(-0.442206\pi\) | ||||
0.180570 | + | 0.983562i | \(0.442206\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.26320 | 0.242552 | 0.121276 | − | 0.992619i | \(-0.461301\pi\) | ||||
0.121276 | + | 0.992619i | \(0.461301\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 18.0390 | + | 2.87024i | 1.33348 | + | 0.212175i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −19.3759 | + | 33.5601i | −1.42455 | + | 2.46739i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.64132 | + | 4.57489i | 0.193152 | + | 0.334549i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −0.260877 | − | 5.18960i | −0.0189760 | − | 0.377488i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.34897 | + | 12.7288i | 0.531753 | + | 0.921023i | 0.999313 | + | 0.0370616i | \(0.0117998\pi\) |
−0.467560 | + | 0.883961i | \(0.654867\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −5.05555 | + | 8.75646i | −0.363906 | + | 0.630304i | −0.988600 | − | 0.150566i | \(-0.951890\pi\) |
0.624694 | + | 0.780870i | \(0.285224\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −6.74433 | − | 1.07311i | −0.482971 | − | 0.0768472i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 16.6375 | 1.18537 | 0.592686 | − | 0.805434i | \(-0.298067\pi\) | ||||
0.592686 | + | 0.805434i | \(0.298067\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −13.1111 | −0.929421 | −0.464710 | − | 0.885463i | \(-0.653842\pi\) | ||||
−0.464710 | + | 0.885463i | \(0.653842\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.06402 | + | 2.77776i | 0.0750499 | + | 0.195928i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −3.83009 | + | 6.63392i | −0.268820 | + | 0.465610i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.85868 | + | 3.21934i | 0.129816 | + | 0.224848i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 13.2902 | + | 4.33914i | 0.923730 | + | 0.301591i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −0.604645 | − | 1.04728i | −0.0418242 | − | 0.0724416i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.06526 | − | 1.84509i | 0.0733355 | − | 0.127021i | −0.827026 | − | 0.562164i | \(-0.809969\pi\) |
0.900361 | + | 0.435143i | \(0.143302\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −3.86840 | + | 4.77014i | −0.265058 | + | 0.326844i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 36.5231 | 2.49086 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.82846 | 0.531431 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 2.96457 | − | 3.65563i | 0.200327 | − | 0.247024i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 2.80150 | − | 4.85235i | 0.188450 | − | 0.326404i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.04583 | − | 12.2037i | −0.471824 | − | 0.817223i | 0.527657 | − | 0.849458i | \(-0.323071\pi\) |
−0.999480 | + | 0.0322352i | \(0.989737\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −23.5413 | + | 21.1362i | −1.56942 | + | 1.40908i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.39536 | + | 4.14888i | 0.158985 | + | 0.275371i | 0.934503 | − | 0.355955i | \(-0.115844\pi\) |
−0.775518 | + | 0.631326i | \(0.782511\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.04583 | + | 15.6678i | −0.597765 | + | 1.03536i | 0.395385 | + | 0.918516i | \(0.370611\pi\) |
−0.993150 | + | 0.116844i | \(0.962722\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.584135 | + | 1.52496i | 0.0384333 | + | 0.100335i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.14884 | −0.206287 | −0.103144 | − | 0.994666i | \(-0.532890\pi\) | ||||
−0.103144 | + | 0.994666i | \(0.532890\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −20.8285 | −1.35870 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −28.0088 | − | 4.45657i | −1.81937 | − | 0.289485i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6.16019 | + | 10.6698i | −0.398470 | + | 0.690170i | −0.993537 | − | 0.113506i | \(-0.963792\pi\) |
0.595068 | + | 0.803676i | \(0.297125\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.27292 | − | 12.5971i | −0.468490 | − | 0.811448i | 0.530862 | − | 0.847458i | \(-0.321868\pi\) |
−0.999351 | + | 0.0360106i | \(0.988535\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −4.08809 | + | 15.0429i | −0.262251 | + | 0.965000i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.97141 | + | 3.41458i | 0.125949 | + | 0.218150i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.641315 | + | 1.11079i | −0.0408059 | + | 0.0706779i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −0.679065 | − | 0.108048i | −0.0430340 | − | 0.00684728i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.28263 | 0.144078 | 0.0720392 | − | 0.997402i | \(-0.477049\pi\) | ||||
0.0720392 | + | 0.997402i | \(0.477049\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −4.39372 | −0.276231 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −13.6871 | − | 35.7321i | −0.857122 | − | 2.23763i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −0.396990 | + | 0.687607i | −0.0247636 | + | 0.0428917i | −0.878142 | − | 0.478401i | \(-0.841217\pi\) |
0.853378 | + | 0.521293i | \(0.174550\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.91423 | − | 8.51170i | −0.305355 | − | 0.528891i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 17.0997 | − | 15.3527i | 1.05845 | − | 0.950308i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 5.24433 | + | 9.08344i | 0.323379 | + | 0.560109i | 0.981183 | − | 0.193080i | \(-0.0618478\pi\) |
−0.657804 | + | 0.753189i | \(0.728514\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −18.1871 | + | 31.5011i | −1.11723 | + | 1.93509i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 6.00916 | − | 7.40992i | 0.367755 | − | 0.453479i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 10.3398 | 0.630429 | 0.315215 | − | 0.949020i | \(-0.397923\pi\) | ||||
0.315215 | + | 0.949020i | \(0.397923\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 30.8285 | 1.87270 | 0.936348 | − | 0.351074i | \(-0.114183\pi\) | ||||
0.936348 | + | 0.351074i | \(0.114183\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.09097 | − | 1.34528i | 0.0660286 | − | 0.0814201i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 4.97141 | − | 8.61073i | 0.299787 | − | 0.519247i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.12188 | − | 12.3355i | −0.427913 | − | 0.741166i | 0.568775 | − | 0.822493i | \(-0.307418\pi\) |
−0.996687 | + | 0.0813269i | \(0.974084\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −22.3256 | − | 7.28914i | −1.33660 | − | 0.436389i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 4.46169 | + | 7.72788i | 0.266162 | + | 0.461007i | 0.967868 | − | 0.251461i | \(-0.0809109\pi\) |
−0.701705 | + | 0.712468i | \(0.747578\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −11.6316 | + | 20.1465i | −0.691427 | + | 1.19759i | 0.279944 | + | 0.960016i | \(0.409684\pi\) |
−0.971370 | + | 0.237570i | \(0.923649\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.13323 | + | 8.17973i | 0.185597 | + | 0.484526i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −0.942820 | −0.0556529 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 14.3937 | 0.846689 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 23.1706 | + | 3.68675i | 1.35828 | + | 0.216121i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −11.9412 | + | 20.6827i | −0.697611 | + | 1.20830i | 0.271681 | + | 0.962387i | \(0.412420\pi\) |
−0.969292 | + | 0.245911i | \(0.920913\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 18.8187 | + | 32.5950i | 1.09567 | + | 1.89776i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −0.245960 | − | 4.89286i | −0.0142720 | − | 0.283912i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.33009 | + | 4.03584i | 0.134753 | + | 0.233399i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.63160 | + | 8.02217i | −0.266961 | + | 0.462390i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4.45254 | + | 0.708458i | 0.255791 | + | 0.0406998i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 41.5803 | 2.38088 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.37429 | 0.420873 | 0.210436 | − | 0.977608i | \(-0.432511\pi\) | ||||
0.210436 | + | 0.977608i | \(0.432511\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.90095 | − | 25.8478i | −0.563245 | − | 1.47043i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.58577 | − | 7.94279i | 0.260035 | − | 0.450394i | −0.706216 | − | 0.707997i | \(-0.749599\pi\) |
0.966251 | + | 0.257603i | \(0.0829325\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −8.05555 | − | 13.9526i | −0.455326 | − | 0.788648i | 0.543381 | − | 0.839486i | \(-0.317144\pi\) |
−0.998707 | + | 0.0508381i | \(0.983811\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2.44282 | − | 11.5735i | −0.137637 | − | 0.652091i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.13160 | + | 3.69204i | 0.119723 | + | 0.207366i | 0.919658 | − | 0.392721i | \(-0.128466\pi\) |
−0.799935 | + | 0.600086i | \(0.795133\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.61109 | + | 6.25459i | −0.202182 | + | 0.350190i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 11.8759 | − | 14.6442i | 0.662849 | − | 0.817362i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −7.18659 | −0.399873 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.5458 | −0.584977 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3.58126 | + | 4.41606i | −0.198044 | + | 0.244209i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 2.64132 | − | 4.57489i | 0.145620 | − | 0.252222i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.14132 | − | 10.6371i | −0.337557 | − | 0.584666i | 0.646415 | − | 0.762986i | \(-0.276267\pi\) |
−0.983973 | + | 0.178319i | \(0.942934\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 6.08934 | + | 28.8497i | 0.333694 | + | 1.58096i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.38564 | + | 5.86410i | 0.184977 | + | 0.320390i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.4903 | − | 23.3659i | 0.734863 | − | 1.27282i | −0.219921 | − | 0.975518i | \(-0.570580\pi\) |
0.954784 | − | 0.297302i | \(-0.0960867\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.99673 | − | 10.4340i | −0.217073 | − | 0.566697i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.38083 | 0.399694 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 31.4298 | + | 5.00091i | 1.69213 | + | 0.269240i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −10.7524 | + | 18.6237i | −0.577219 | + | 0.999773i | 0.418577 | + | 0.908181i | \(0.362529\pi\) |
−0.995797 | + | 0.0915921i | \(0.970804\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.54583 | + | 4.40951i | 0.136275 | + | 0.236035i | 0.926084 | − | 0.377318i | \(-0.123154\pi\) |
−0.789809 | + | 0.613353i | \(0.789820\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.36389 | + | 2.82073i | −0.232927 | + | 0.150559i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.78426 | − | 8.28659i | −0.254641 | − | 0.441051i | 0.710157 | − | 0.704043i | \(-0.248624\pi\) |
−0.964798 | + | 0.262993i | \(0.915291\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.99028 | + | 12.1075i | −0.371006 | + | 0.642601i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 9.58414 | + | 1.52496i | 0.507246 | + | 0.0807097i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −10.9623 | −0.578565 | −0.289283 | − | 0.957244i | \(-0.593417\pi\) | ||||
−0.289283 | + | 0.957244i | \(0.593417\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.3549 | −0.913414 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.26444 | − | 16.3542i | −0.328798 | − | 0.858372i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.35705 | − | 9.27868i | 0.280401 | − | 0.485668i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.34897 | + | 4.06853i | 0.122615 | + | 0.212376i | 0.920798 | − | 0.390039i | \(-0.127539\pi\) |
−0.798183 | + | 0.602415i | \(0.794205\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.68878 | + | 0.877867i | 0.139972 | + | 0.0456999i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.61273 | − | 7.98947i | −0.239481 | − | 0.414793i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.63160 | + | 8.02217i | −0.239815 | + | 0.415372i | −0.960661 | − | 0.277723i | \(-0.910420\pi\) |
0.720846 | + | 0.693095i | \(0.243754\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −23.8554 | + | 29.4162i | −1.23189 | + | 1.51905i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 7.66019 | 0.394520 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 13.5458 | 0.695803 | 0.347901 | − | 0.937531i | \(-0.386894\pi\) | ||||
0.347901 | + | 0.937531i | \(0.386894\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0.903827 | − | 1.11451i | 0.0463044 | − | 0.0570982i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 6.13968 | − | 10.6342i | 0.313723 | − | 0.543384i | −0.665442 | − | 0.746449i | \(-0.731757\pi\) |
0.979165 | + | 0.203065i | \(0.0650903\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.85868 | + | 3.21934i | 0.0947274 | + | 0.164073i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 20.6781 | − | 18.5655i | 1.05113 | − | 0.943737i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 3.75567 | + | 6.50502i | 0.190420 | + | 0.329818i | 0.945390 | − | 0.325943i | \(-0.105682\pi\) |
−0.754969 | + | 0.655760i | \(0.772348\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −13.0555 | + | 22.6129i | −0.660247 | + | 1.14358i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.36513 | − | 8.78513i | −0.169748 | − | 0.443151i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −64.5609 | −3.24841 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −22.9201 | −1.15033 | −0.575164 | − | 0.818038i | \(-0.695062\pi\) | ||||
−0.575164 | + | 0.818038i | \(0.695062\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −2.19398 | − | 0.349092i | −0.109836 | − | 0.0174764i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 10.5631 | − | 18.2958i | 0.527495 | − | 0.913647i | −0.471992 | − | 0.881603i | \(-0.656465\pi\) |
0.999486 | − | 0.0320445i | \(-0.0102018\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.91423 | − | 6.77965i | −0.194982 | − | 0.337718i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −3.80959 | + | 35.2803i | −0.189300 | + | 1.75309i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.63323 | − | 8.02500i | −0.229661 | − | 0.397784i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.71737 | + | 2.97457i | −0.0849185 | + | 0.147083i | −0.905356 | − | 0.424652i | \(-0.860396\pi\) |
0.820438 | + | 0.571736i | \(0.193730\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 36.1758 | + | 5.75605i | 1.78442 | + | 0.283925i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −9.54583 | −0.469720 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.56526 | −0.0768356 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.14488 | + | 2.98887i | 0.0560651 | + | 0.146366i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −10.2157 | + | 17.6942i | −0.499071 | + | 0.864417i | −0.999999 | − | 0.00107202i | \(-0.999659\pi\) |
0.500928 | + | 0.865489i | \(0.332992\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −7.90451 | − | 13.6910i | −0.385242 | − | 0.667260i | 0.606560 | − | 0.795037i | \(-0.292549\pi\) |
−0.991803 | + | 0.127778i | \(0.959216\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11.7923 | + | 10.5876i | −0.573363 | + | 0.514784i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −29.5442 | − | 51.1720i | −1.43310 | − | 2.48221i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.27292 | + | 9.13296i | −0.255174 | + | 0.441975i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.02859 | − | 1.26836i | 0.0496608 | − | 0.0612369i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 26.7518 | 1.28859 | 0.644296 | − | 0.764777i | \(-0.277151\pi\) | ||||
0.644296 | + | 0.764777i | \(0.277151\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −14.4347 | −0.693689 | −0.346845 | − | 0.937923i | \(-0.612747\pi\) | ||||
−0.346845 | + | 0.937923i | \(0.612747\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 32.9503 | − | 40.6312i | 1.57985 | − | 1.94812i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2.98865 | − | 5.17649i | 0.142967 | − | 0.247625i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −19.3187 | − | 33.4610i | −0.922033 | − | 1.59701i | −0.796264 | − | 0.604949i | \(-0.793193\pi\) |
−0.125769 | − | 0.992060i | \(-0.540140\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 2.85185 | + | 0.931107i | 0.135802 | + | 0.0443384i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.28263 | + | 9.14978i | 0.250985 | + | 0.434719i | 0.963797 | − | 0.266636i | \(-0.0859121\pi\) |
−0.712812 | + | 0.701355i | \(0.752579\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 10.8587 | − | 18.8078i | 0.514751 | − | 0.891575i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 7.52696 | + | 19.6501i | 0.356013 | + | 0.929420i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −9.37429 | −0.442400 | −0.221200 | − | 0.975228i | \(-0.570997\pi\) | ||||
−0.221200 | + | 0.975228i | \(0.570997\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −0.888910 | −0.0418571 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −15.3616 | − | 2.44423i | −0.721749 | − | 0.114840i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.97141 | − | 3.41458i | 0.0924211 | − | 0.160078i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −10.3587 | − | 17.9418i | −0.484559 | − | 0.839281i | 0.515284 | − | 0.857020i | \(-0.327687\pi\) |
−0.999843 | + | 0.0177391i | \(0.994353\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −25.9126 | − | 13.2728i | −1.20950 | − | 0.619522i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17.6300 | − | 30.5360i | −0.821109 | − | 1.42220i | −0.904857 | − | 0.425716i | \(-0.860022\pi\) |
0.0837475 | − | 0.996487i | \(-0.473311\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.55555 | − | 6.15838i | 0.165240 | − | 0.286204i | −0.771500 | − | 0.636229i | \(-0.780493\pi\) |
0.936741 | + | 0.350024i | \(0.113827\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −52.7977 | − | 8.40082i | −2.44843 | − | 0.389579i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.03448 | −0.232968 | −0.116484 | − | 0.993193i | \(-0.537162\pi\) | ||||
−0.116484 | + | 0.993193i | \(0.537162\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.71737 | −0.0793008 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.31642 | − | 19.1005i | −0.337123 | − | 0.880105i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −4.36677 | + | 7.56346i | −0.200784 | + | 0.347768i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.76320 | + | 11.7142i | 0.310317 | + | 0.537485i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.71574 | + | 27.0797i | 0.261706 | + | 1.23989i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.13323 | + | 5.42692i | 0.143161 | + | 0.247962i | 0.928685 | − | 0.370869i | \(-0.120940\pi\) |
−0.785524 | + | 0.618831i | \(0.787607\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.91423 | + | 8.51170i | −0.224070 | + | 0.388100i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.08414 | + | 6.26926i | −0.231336 | + | 0.285261i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 53.4088 | 2.42517 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −14.0722 | −0.637674 | −0.318837 | − | 0.947810i | \(-0.603292\pi\) | ||||
−0.318837 | + | 0.947810i | \(0.603292\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 13.4000 | − | 16.5236i | 0.605969 | − | 0.747222i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.97141 | − | 3.41458i | 0.0889685 | − | 0.154098i | −0.818107 | − | 0.575066i | \(-0.804976\pi\) |
0.907075 | + | 0.420968i | \(0.138310\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 21.4601 | + | 37.1699i | 0.966512 | + | 1.67405i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.30314 | − | 10.9117i | −0.103518 | − | 0.490444i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.77292 | − | 3.07078i | −0.0795261 | − | 0.137743i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.82846 | − | 17.0234i | 0.439982 | − | 0.762072i | −0.557705 | − | 0.830039i | \(-0.688318\pi\) |
0.997688 | + | 0.0679674i | \(0.0216514\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 14.1791 | + | 37.0164i | 0.633474 | + | 1.65377i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 10.2632 | 0.457613 | 0.228807 | − | 0.973472i | \(-0.426518\pi\) | ||||
0.228807 | + | 0.973472i | \(0.426518\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.2632 | 0.456706 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.5264 | + | 3.26602i | 0.911609 | + | 0.145049i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −0.669905 | + | 1.16031i | −0.0296930 | + | 0.0514298i | −0.880490 | − | 0.474065i | \(-0.842786\pi\) |
0.850797 | + | 0.525494i | \(0.176120\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1.35868 | + | 2.35331i | 0.0601047 | + | 0.104104i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 5.93186 | + | 3.03839i | 0.261898 | + | 0.134148i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −31.5043 | − | 54.5670i | −1.38824 | − | 2.40451i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.49028 | − | 4.31330i | 0.109523 | − | 0.189699i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −32.9503 | − | 5.24284i | −1.44636 | − | 0.230135i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15.7940 | 0.691947 | 0.345973 | − | 0.938244i | \(-0.387549\pi\) | ||||
0.345973 | + | 0.938244i | \(0.387549\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.6764 | 0.466844 | 0.233422 | − | 0.972376i | \(-0.425008\pi\) | ||||
0.233422 | + | 0.972376i | \(0.425008\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.53379 | − | 17.0573i | −0.285158 | − | 0.744444i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 21.9315 | − | 37.9864i | 0.955350 | − | 1.65471i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.641315 | + | 1.11079i | 0.0278833 | + | 0.0482952i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 27.2233 | + | 8.88819i | 1.18139 | + | 0.385715i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.471410 | + | 0.816506i | 0.0204190 | + | 0.0353668i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 21.4601 | − | 37.1699i | 0.927799 | − | 1.60700i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 5.27128 | − | 6.50003i | 0.227473 | − | 0.280497i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.942820 | −0.0406101 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16.6569 | 0.716137 | 0.358068 | − | 0.933695i | \(-0.383435\pi\) | ||||
0.358068 | + | 0.933695i | \(0.383435\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.56006 | − | 4.38992i | 0.152777 | − | 0.188390i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.47141 | + | 11.2088i | −0.277205 | + | 0.480133i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 7.81875 | + | 13.5425i | 0.334305 | + | 0.579034i | 0.983351 | − | 0.181715i | \(-0.0581650\pi\) |
−0.649046 | + | 0.760749i | \(0.724832\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 23.5413 | − | 21.1362i | 1.00472 | − | 0.902069i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −4.91260 | − | 8.50886i | −0.209284 | − | 0.362490i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.18715 | − | 14.1806i | 0.348153 | − | 0.603018i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 24.0092 | + | 62.6792i | 1.01913 | + | 2.66058i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −16.7907 | −0.711445 | −0.355723 | − | 0.934592i | \(-0.615765\pi\) | ||||
−0.355723 | + | 0.934592i | \(0.615765\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.26320 | 0.391792 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.03611 | + | 1.43777i | 0.381505 | + | 0.0607026i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 7.58577 | − | 13.1389i | 0.319702 | − | 0.553740i | −0.660724 | − | 0.750629i | \(-0.729751\pi\) |
0.980426 | + | 0.196889i | \(0.0630838\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −12.7174 | − | 22.0271i | −0.535024 | − | 0.926688i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.26608 | − | 5.31075i | −0.305147 | − | 0.223031i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −17.7632 | − | 30.7668i | −0.744672 | − | 1.28981i | −0.950348 | − | 0.311190i | \(-0.899273\pi\) |
0.205676 | − | 0.978620i | \(-0.434061\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −0.772915 | + | 1.33873i | −0.0323455 | + | 0.0560240i | −0.881745 | − | 0.471726i | \(-0.843631\pi\) |
0.849400 | + | 0.527750i | \(0.176964\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 25.1413 | + | 4.00032i | 1.05029 | + | 0.167116i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 49.1456 | 2.04951 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.67635 | −0.0697874 | −0.0348937 | − | 0.999391i | \(-0.511109\pi\) | ||||
−0.0348937 | + | 0.999391i | \(0.511109\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 6.26444 | + | 16.3542i | 0.260341 | + | 0.679657i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0.198495 | − | 0.343803i | 0.00823496 | − | 0.0142634i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.34897 | − | 7.53264i | −0.180116 | − | 0.311970i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.80150 | + | 7.90228i | −0.363897 | + | 0.326719i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −19.7346 | − | 34.1813i | −0.814535 | − | 1.41082i | −0.909662 | − | 0.415350i | \(-0.863659\pi\) |
0.0951271 | − | 0.995465i | \(-0.469674\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.02051 | + | 8.69578i | −0.206866 | + | 0.358303i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 18.1510 | − | 22.3821i | 0.746634 | − | 0.920677i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 22.8317 | 0.937587 | 0.468793 | − | 0.883308i | \(-0.344689\pi\) | ||||
0.468793 | + | 0.883308i | \(0.344689\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 22.0917 | 0.905670 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −14.3038 | + | 17.6381i | −0.585417 | + | 0.721879i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 22.6375 | − | 39.2093i | 0.924943 | − | 1.60205i | 0.133290 | − | 0.991077i | \(-0.457446\pi\) |
0.791653 | − | 0.610971i | \(-0.209221\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.5253 | − | 23.4265i | −0.551709 | − | 0.955589i | −0.998151 | − | 0.0607761i | \(-0.980642\pi\) |
0.446442 | − | 0.894813i | \(-0.352691\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 4.89768 | + | 1.59906i | 0.199449 | + | 0.0651186i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −19.9331 | − | 34.5252i | −0.810396 | − | 1.40365i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9.32846 | + | 16.1574i | −0.378631 | + | 0.655807i | −0.990863 | − | 0.134870i | \(-0.956938\pi\) |
0.612233 | + | 0.790678i | \(0.290272\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 4.74596 | + | 12.3900i | 0.192316 | + | 0.502067i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −5.28263 | −0.213712 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −28.9611 | −1.16973 | −0.584865 | − | 0.811131i | \(-0.698852\pi\) | ||||
−0.584865 | + | 0.811131i | \(0.698852\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 6.35868 | + | 1.01175i | 0.256407 | + | 0.0407978i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −18.8457 | + | 32.6417i | −0.758699 | + | 1.31411i | 0.184815 | + | 0.982773i | \(0.440831\pi\) |
−0.943514 | + | 0.331332i | \(0.892502\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.00971516 | + | 0.0168272i | 0.000390485 | + | 0.000676340i | 0.866221 | − | 0.499662i | \(-0.166542\pi\) |
−0.865830 | + | 0.500338i | \(0.833209\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 20.3365 | − | 13.1451i | 0.816077 | − | 0.527495i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.75404 | + | 4.77014i | 0.110338 | + | 0.191112i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −16.7427 | + | 28.9992i | −0.669708 | + | 1.15997i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −2.06853 | − | 0.329131i | −0.0826091 | − | 0.0131442i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −55.0690 | −2.19574 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −28.4854 | −1.13399 | −0.566993 | − | 0.823723i | \(-0.691893\pi\) | ||||
−0.566993 | + | 0.823723i | \(0.691893\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.31999 | − | 3.44601i | −0.0524648 | − | 0.136967i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.63323 | − | 2.82885i | 0.0648129 | − | 0.112259i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0.500000 | + | 0.866025i | 0.0198107 | + | 0.0343132i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.19686 | + | 10.4082i | 0.0869064 | + | 0.411741i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22.2696 | − | 38.5722i | −0.879598 | − | 1.52351i | −0.851783 | − | 0.523896i | \(-0.824478\pi\) |
−0.0278156 | − | 0.999613i | \(-0.508855\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.50972 | − | 7.81106i | 0.177846 | − | 0.308038i | −0.763297 | − | 0.646048i | \(-0.776421\pi\) |
0.941142 | + | 0.338010i | \(0.109754\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 39.8457 | − | 49.1339i | 1.56892 | − | 1.93464i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −42.8252 | −1.68363 | −0.841816 | − | 0.539765i | \(-0.818513\pi\) | ||||
−0.841816 | + | 0.539765i | \(0.818513\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −9.00000 | −0.353281 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 8.54063 | − | 10.5315i | 0.334734 | − | 0.412761i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.80150 | + | 4.85235i | −0.109631 | + | 0.189887i | −0.915621 | − | 0.402043i | \(-0.868300\pi\) |
0.805990 | + | 0.591930i | \(0.201634\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −10.7077 | − | 18.5462i | −0.418383 | − | 0.724660i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.68358 | − | 7.97637i | −0.0656826 | − | 0.311188i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −3.26376 | − | 5.65299i | −0.127138 | − | 0.220209i | 0.795429 | − | 0.606047i | \(-0.207246\pi\) |
−0.922567 | + | 0.385838i | \(0.873912\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.50972 | − | 9.54311i | 0.214303 | − | 0.371184i | −0.738754 | − | 0.673976i | \(-0.764585\pi\) |
0.953057 | + | 0.302792i | \(0.0979186\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.47141 | − | 9.06259i | −0.134818 | − | 0.351962i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.05718 | −0.196109 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −35.6979 | −1.38223 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −24.1043 | − | 3.83531i | −0.931924 | − | 0.148282i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −4.97141 | + | 8.61073i | −0.191919 | + | 0.332414i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.67743 | + | 2.90539i | 0.0646602 | + | 0.111995i | 0.896543 | − | 0.442956i | \(-0.146070\pi\) |
−0.831883 | + | 0.554951i | \(0.812737\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 2.75116 | + | 54.7286i | 0.105892 | + | 2.10651i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 20.3187 | + | 35.1931i | 0.780913 | + | 1.35258i | 0.931411 | + | 0.363970i | \(0.118579\pi\) |
−0.150498 | + | 0.988610i | \(0.548088\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −6.77292 | + | 11.7310i | −0.259921 | + | 0.450196i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 8.19467 | + | 1.30388i | 0.314020 | + | 0.0499648i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 14.0755 | 0.538584 | 0.269292 | − | 0.963059i | \(-0.413210\pi\) | ||||
0.269292 | + | 0.963059i | \(0.413210\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 83.3861 | 3.18602 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 11.2089 | + | 29.2623i | 0.427646 | + | 1.11643i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −4.61273 | + | 7.98947i | −0.175731 | + | 0.304375i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.9601 | − | 38.0359i | −0.835400 | − | 1.44696i | −0.893704 | − | 0.448656i | \(-0.851903\pi\) |
0.0583042 | − | 0.998299i | \(-0.481431\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.68878 | + | 0.877867i | 0.102138 | + | 0.0333474i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 3.64295 | + | 6.30977i | 0.138185 | + | 0.239343i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.64132 | + | 4.57489i | −0.100047 | + | 0.173286i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −3.43530 | + | 4.23607i | −0.129935 | + | 0.160223i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7.69578 | 0.290666 | 0.145333 | − | 0.989383i | \(-0.453575\pi\) | ||||
0.145333 | + | 0.989383i | \(0.453575\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 12.6063 | 0.475455 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −22.7233 | + | 28.0201i | −0.855807 | + | 1.05530i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −1.30150 | + | 2.25427i | −0.0489481 | + | 0.0847807i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −0.111090 | − | 0.192414i | −0.00417209 | − | 0.00722626i | 0.863932 | − | 0.503609i | \(-0.167995\pi\) |
−0.868104 | + | 0.496383i | \(0.834661\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −36.5521 | + | 32.8177i | −1.37081 | + | 1.23076i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 18.2411 | + | 31.5944i | 0.683133 | + | 1.18322i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.85868 | − | 3.21934i | 0.0695109 | − | 0.120396i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 7.63323 | + | 19.9276i | 0.285068 | + | 0.744210i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.64403 | 0.0986056 | 0.0493028 | − | 0.998784i | \(-0.484300\pi\) | ||||
0.0493028 | + | 0.998784i | \(0.484300\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 15.9806 | 0.595148 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −24.8811 | − | 3.95892i | −0.925339 | − | 0.147234i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 40.3915 | − | 69.9602i | 1.50010 | − | 2.59826i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 12.7427 | + | 22.0710i | 0.472600 | + | 0.818568i | 0.999508 | − | 0.0313547i | \(-0.00998214\pi\) |
−0.526908 | + | 0.849922i | \(0.676649\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 15.7769 | + | 21.9110i | 0.584329 | + | 0.811517i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 25.9509 | + | 44.9483i | 0.959829 | + | 1.66247i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −0.934740 | + | 1.61902i | −0.0345254 | + | 0.0597997i | −0.882772 | − | 0.469802i | \(-0.844325\pi\) |
0.848246 | + | 0.529602i | \(0.177659\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 6.74433 | + | 1.07311i | 0.248768 | + | 0.0395823i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.61917 | −0.0596429 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −51.1639 | −1.88209 | −0.941047 | − | 0.338276i | \(-0.890156\pi\) | ||||
−0.941047 | + | 0.338276i | \(0.890156\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0.794668 | + | 2.07459i | 0.0291929 | + | 0.0762120i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −19.3668 | + | 33.5442i | −0.710498 | + | 1.23062i | 0.254173 | + | 0.967159i | \(0.418197\pi\) |
−0.964671 | + | 0.263459i | \(0.915137\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 23.9503 | + | 41.4832i | 0.877473 | + | 1.51983i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −0.886196 | + | 0.795655i | −0.0324242 | + | 0.0291115i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 5.44282 | + | 9.42724i | 0.198876 | + | 0.344464i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 3.09549 | − | 5.36154i | 0.112956 | − | 0.195645i | −0.804005 | − | 0.594623i | \(-0.797301\pi\) |
0.916961 | + | 0.398977i | \(0.130635\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.49028 | − | 3.07078i | 0.0907510 | − | 0.111905i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −35.4088 | −1.28866 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −13.7174 | −0.498566 | −0.249283 | − | 0.968431i | \(-0.580195\pi\) | ||||
−0.249283 | + | 0.968431i | \(0.580195\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −4.79342 | + | 5.91079i | −0.173990 | + | 0.214548i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −19.6602 | + | 34.0524i | −0.712681 | + | 1.23440i | 0.251166 | + | 0.967944i | \(0.419186\pi\) |
−0.963847 | + | 0.266456i | \(0.914147\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.64132 | − | 2.84284i | −0.0594196 | − | 0.102918i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −63.0021 | − | 20.5697i | −2.27784 | − | 0.743699i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 4.77292 | + | 8.26693i | 0.172340 | + | 0.298502i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −11.3646 | + | 19.6840i | −0.409817 | + | 0.709824i | −0.994869 | − | 0.101172i | \(-0.967741\pi\) |
0.585052 | + | 0.810996i | \(0.301074\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0.491920 | + | 1.28422i | 0.0177161 | + | 0.0462502i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −28.7324 | −1.03343 | −0.516717 | − | 0.856156i | \(-0.672846\pi\) | ||||
−0.516717 | + | 0.856156i | \(0.672846\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −82.5576 | −2.96556 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −16.8119 | − | 2.67500i | −0.603124 | − | 0.0959651i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 0.604645 | − | 1.04728i | 0.0216636 | − | 0.0375225i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.67154 | − | 2.89519i | −0.0598124 | − | 0.103598i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.99837 | − | 39.7533i | −0.0714157 | − | 1.42067i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −23.2804 | − | 40.3229i | −0.830915 | − | 1.43919i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −27.0059 | + | 46.7756i | −0.962656 | + | 1.66737i | −0.246871 | + | 0.969048i | \(0.579402\pi\) |
−0.715785 | + | 0.698321i | \(0.753931\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 17.9412 | + | 2.85468i | 0.638723 | + | 0.101629i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 6.45090 | 0.229368 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 10.5458 | 0.374493 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 22.5361 | + | 58.8336i | 0.799274 | + | 2.08661i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 0.103565 | − | 0.179381i | 0.00366848 | − | 0.00635399i | −0.864185 | − | 0.503174i | \(-0.832166\pi\) |
0.867854 | + | 0.496820i | \(0.165499\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −14.7993 | − | 25.6332i | −0.523562 | − | 0.906836i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.41260 | − | 16.1680i | −0.120578 | − | 0.571269i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.28100 | + | 2.21875i | 0.0452053 | + | 0.0782980i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9.18715 | + | 15.9126i | −0.323804 | + | 0.560846i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 11.2804 | − | 13.9099i | 0.397090 | − | 0.489653i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −36.0539 | −1.26759 | −0.633794 | − | 0.773502i | \(-0.718503\pi\) | ||||
−0.633794 | + | 0.773502i | \(0.718503\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2.01943 | 0.0709118 | 0.0354559 | − | 0.999371i | \(-0.488712\pi\) | ||||
0.0354559 | + | 0.999371i | \(0.488712\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 33.6330 | − | 41.4729i | 1.17956 | − | 1.45452i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 24.2141 | − | 41.9401i | 0.848183 | − | 1.46910i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.94063 | − | 10.2895i | −0.207836 | − | 0.359983i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −0.619562 | − | 2.93533i | −0.0216492 | − | 0.102569i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 15.1871 | + | 26.3049i | 0.530035 | + | 0.918048i | 0.999386 | + | 0.0350359i | \(0.0111546\pi\) |
−0.469351 | + | 0.883012i | \(0.655512\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.56526 | + | 11.3714i | −0.228851 | + | 0.396381i | −0.957468 | − | 0.288540i | \(-0.906830\pi\) |
0.728617 | + | 0.684921i | \(0.240163\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.16019 | − | 16.0820i | −0.214470 | − | 0.559904i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 11.3236 | 0.393762 | 0.196881 | − | 0.980427i | \(-0.436919\pi\) | ||||
0.196881 | + | 0.980427i | \(0.436919\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11.0604 | −0.384145 | −0.192073 | − | 0.981381i | \(-0.561521\pi\) | ||||
−0.192073 | + | 0.981381i | \(0.561521\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −24.3644 | − | 3.87671i | −0.845193 | − | 0.134482i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −2.80150 | + | 4.85235i | −0.0970664 | + | 0.168124i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 45.1170 | + | 78.1449i | 1.56134 | + | 2.70432i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −34.1625 | + | 22.0819i | −1.18083 | + | 0.763263i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 5.27128 | + | 9.13013i | 0.181985 | + | 0.315207i | 0.942556 | − | 0.334047i | \(-0.108414\pi\) |
−0.760572 | + | 0.649254i | \(0.775081\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.8393 | + | 25.7023i | −0.511698 | + | 0.886288i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 15.2638 | + | 2.42867i | 0.525712 | + | 0.0836478i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 47.3138 | 1.62765 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 10.1111 | 0.347421 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 14.4130 | + | 37.6271i | 0.494652 | + | 1.29136i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 22.9012 | − | 39.6661i | 0.785045 | − | 1.35974i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 13.6413 | + | 23.6275i | 0.467070 | + | 0.808989i | 0.999292 | − | 0.0376160i | \(-0.0119764\pi\) |
−0.532223 | + | 0.846604i | \(0.678643\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 14.4223 | + | 4.70878i | 0.493233 | + | 0.161037i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.21574 | + | 2.10571i | 0.0415287 | + | 0.0719299i | 0.886043 | − | 0.463604i | \(-0.153444\pi\) |
−0.844514 | + | 0.535534i | \(0.820111\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −15.8743 | + | 27.4951i | −0.541624 | + | 0.938120i | 0.457187 | + | 0.889370i | \(0.348857\pi\) |
−0.998811 | + | 0.0487495i | \(0.984476\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.02859 | + | 1.26836i | −0.0350543 | + | 0.0432255i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 27.8252 | 0.947181 | 0.473590 | − | 0.880745i | \(-0.342958\pi\) | ||||
0.473590 | + | 0.880745i | \(0.342958\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −75.9513 | −2.58242 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 15.7031 | − | 19.3636i | 0.533307 | − | 0.657622i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 7.71900 | − | 13.3697i | 0.261849 | − | 0.453536i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0.858685 | + | 1.48729i | 0.0290954 | + | 0.0503948i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 30.2382 | − | 27.1488i | 1.02341 | − | 0.918848i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −10.9331 | − | 18.9367i | −0.369606 | − | 0.640177i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.29342 | − | 3.97233i | 0.0774434 | − | 0.134136i | −0.824703 | − | 0.565566i | \(-0.808658\pi\) |
0.902146 | + | 0.431430i | \(0.141991\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 14.7966 | + | 38.6285i | 0.499077 | + | 1.30291i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 57.4465 | 1.93542 | 0.967711 | − | 0.252062i | \(-0.0811085\pi\) | ||||
0.967711 | + | 0.252062i | \(0.0811085\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −36.3937 | −1.22475 | −0.612373 | − | 0.790569i | \(-0.709785\pi\) | ||||
−0.612373 | + | 0.790569i | \(0.709785\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 64.3802 | + | 10.2437i | 2.16412 | + | 0.344340i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21.7238 | + | 37.6268i | −0.729414 | + | 1.26338i | 0.227717 | + | 0.973727i | \(0.426874\pi\) |
−0.957131 | + | 0.289655i | \(0.906459\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.414230 | + | 0.717468i | 0.0138928 | + | 0.0240631i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6.85060 | − | 5.00708i | −0.229504 | − | 0.167744i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3.38783 | + | 5.86789i | 0.113369 | + | 0.196362i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 9.52532 | − | 16.4983i | 0.318396 | − | 0.551479i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 7.97141 | + | 1.26836i | 0.266158 | + | 0.0423492i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 59.9675 | 2.00003 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −51.6903 | −1.72205 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.73912 | + | 14.9828i | 0.190986 | + | 0.498595i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.43310 | − | 11.1425i | 0.213844 | − | 0.370388i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 11.1569 | + | 19.3244i | 0.370459 | + | 0.641655i | 0.989636 | − | 0.143597i | \(-0.0458669\pi\) |
−0.619177 | + | 0.785252i | \(0.712534\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 5.81066 | − | 5.21700i | 0.192728 | − | 0.173037i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.67799 | − | 13.2987i | −0.254383 | − | 0.440604i | 0.710345 | − | 0.703854i | \(-0.248539\pi\) |
−0.964728 | + | 0.263250i | \(0.915206\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0.187145 | − | 0.324145i | 0.00619360 | − | 0.0107276i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 45.3629 | − | 55.9372i | 1.49965 | − | 1.84923i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5.43147 | 0.179363 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 36.8285 | 1.21486 | 0.607429 | − | 0.794374i | \(-0.292201\pi\) | ||||
0.607429 | + | 0.794374i | \(0.292201\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 8.04514 | − | 9.92049i | 0.265096 | − | 0.326891i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −1.77292 | + | 3.07078i | −0.0583562 | + | 0.101076i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 51.8246 | + | 89.7629i | 1.70398 | + | 2.95139i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −45.5742 | − | 14.8796i | −1.49685 | − | 0.488711i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 20.8646 | + | 36.1385i | 0.684545 | + | 1.18567i | 0.973580 | + | 0.228347i | \(0.0733322\pi\) |
−0.289035 | + | 0.957318i | \(0.593334\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.641315 | − | 1.11079i | 0.0210183 | − | 0.0364047i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −5.68233 | − | 14.8345i | −0.186031 | − | 0.485660i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 20.8285 | 0.681163 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −25.3743 | −0.828942 | −0.414471 | − | 0.910063i | \(-0.636033\pi\) | ||||
−0.414471 | + | 0.910063i | \(0.636033\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −27.5586 | − | 4.38493i | −0.899340 | − | 0.143097i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23.5712 | + | 40.8264i | −0.768398 | + | 1.33090i | 0.170034 | + | 0.985438i | \(0.445612\pi\) |
−0.938431 | + | 0.345465i | \(0.887721\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.19686 | − | 3.80507i | −0.0715396 | − | 0.123910i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −18.2346 | − | 9.34004i | −0.593172 | − | 0.303832i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17.2535 | − | 29.8839i | −0.560663 | − | 0.971097i | −0.997439 | − | 0.0715263i | \(-0.977213\pi\) |
0.436776 | − | 0.899570i | \(-0.356120\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.35868 | − | 2.35331i | 0.0441048 | − | 0.0763917i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.29235 | + | 1.16031i | 0.236470 | + | 0.0376256i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −44.1833 | −1.43124 | −0.715619 | − | 0.698491i | \(-0.753855\pi\) | ||||
−0.715619 | + | 0.698491i | \(0.753855\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 57.9513 | 1.87526 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 4.47459 | + | 11.6815i | 0.144643 | + | 0.377610i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −10.5744 | + | 18.3154i | −0.341466 | + | 0.591436i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −15.1424 | − | 26.2274i | −0.488464 | − | 0.846045i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −6.74433 | − | 31.9529i | −0.217333 | − | 1.02967i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 19.9331 | + | 34.5252i | 0.641669 | + | 1.11140i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 21.2330 | − | 36.7766i | 0.682806 | − | 1.18266i | −0.291314 | − | 0.956627i | \(-0.594093\pi\) |
0.974121 | − | 0.226028i | \(-0.0725741\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −7.84037 | + | 9.66798i | −0.251869 | + | 0.310580i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −6.05391 | −0.194279 | −0.0971396 | − | 0.995271i | \(-0.530969\pi\) | ||||
−0.0971396 | + | 0.995271i | \(0.530969\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.84789 | −0.0592406 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −11.5052 | + | 14.1871i | −0.368461 | + | 0.454351i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 22.0264 | − | 38.1508i | 0.704687 | − | 1.22055i | −0.262117 | − | 0.965036i | \(-0.584421\pi\) |
0.966804 | − | 0.255518i | \(-0.0822459\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.59656 | + | 4.49738i | 0.0829866 | + | 0.143737i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.03379 | + | 9.63559i | 0.0649340 | + | 0.307641i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.23517 | − | 3.87142i | −0.0712907 | − | 0.123479i | 0.828177 | − | 0.560467i | \(-0.189378\pi\) |
−0.899467 | + | 0.436988i | \(0.856045\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 32.7993 | − | 56.8101i | 1.04507 | − | 1.81012i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −3.27292 | − | 8.54439i | −0.104178 | − | 0.271971i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −43.1683 | −1.37267 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 31.5048 | 1.00078 | 0.500392 | − | 0.865799i | \(-0.333189\pi\) | ||||
0.500392 | + | 0.865799i | \(0.333189\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −21.0098 | − | 3.34295i | −0.666727 | − | 0.106085i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −25.8473 | + | 44.7689i | −0.819416 | + | 1.41927i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −13.0000 | − | 22.5167i | −0.411714 | − | 0.713110i | 0.583363 | − | 0.812211i | \(-0.301736\pi\) |
−0.995077 | + | 0.0991016i | \(0.968403\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 45.4543 | + | 23.2824i | 1.43811 | + | 0.736622i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))