Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [448,2,Mod(255,448)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(448, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("448.255");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 448 = 2^{6} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 448.p (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: | \(3.57729801055\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\Q(\zeta_{12})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 28) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 255.2 | ||
Root | \(-0.866025 + 0.500000i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 448.255 |
Dual form | 448.2.p.d.383.2 |
$q$-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 \(\left(\mathbb{Z}/448\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 | ||||||||
\(3\) | 0.866025 | − | 1.50000i | 0.500000 | − | 0.866025i | −0.500000 | − | 0.866025i | \(-0.666667\pi\) |
1.00000 | \(0\) | |||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.50000 | − | 0.866025i | 0.670820 | − | 0.387298i | −0.125567 | − | 0.992085i | \(-0.540075\pi\) |
0.796387 | + | 0.604787i | \(0.206742\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.73205 | − | 2.00000i | 0.654654 | − | 0.755929i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.866025 | + | 0.500000i | 0.261116 | + | 0.150756i | 0.624844 | − | 0.780750i | \(-0.285163\pi\) |
−0.363727 | + | 0.931505i | \(0.618496\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 3.46410i | 0.960769i | 0.877058 | + | 0.480384i | \(0.159503\pi\) | ||||
−0.877058 | + | 0.480384i | \(0.840497\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 3.00000i | − | 0.774597i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.50000 | − | 0.866025i | −0.363803 | − | 0.210042i | 0.306944 | − | 0.951727i | \(-0.400693\pi\) |
−0.670748 | + | 0.741685i | \(0.734027\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.59808 | − | 4.50000i | −0.596040 | − | 1.03237i | −0.993399 | − | 0.114708i | \(-0.963407\pi\) |
0.397360 | − | 0.917663i | \(-0.369927\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.50000 | − | 4.33013i | −0.327327 | − | 0.944911i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.866025 | + | 0.500000i | −0.180579 | + | 0.104257i | −0.587565 | − | 0.809177i | \(-0.699913\pi\) |
0.406986 | + | 0.913434i | \(0.366580\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | + | 1.73205i | −0.200000 | + | 0.346410i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 5.19615 | 1.00000 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4.00000 | −0.742781 | −0.371391 | − | 0.928477i | \(-0.621119\pi\) | ||||
−0.371391 | + | 0.928477i | \(0.621119\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.866025 | − | 1.50000i | 0.155543 | − | 0.269408i | −0.777714 | − | 0.628619i | \(-0.783621\pi\) |
0.933257 | + | 0.359211i | \(0.116954\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1.50000 | − | 0.866025i | 0.261116 | − | 0.150756i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.866025 | − | 4.50000i | 0.146385 | − | 0.760639i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.50000 | + | 2.59808i | 0.246598 | + | 0.427121i | 0.962580 | − | 0.270998i | \(-0.0873538\pi\) |
−0.715981 | + | 0.698119i | \(0.754020\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.19615 | + | 3.00000i | 0.832050 | + | 0.480384i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 3.46410i | 0.541002i | 0.962720 | + | 0.270501i | \(0.0871893\pi\) | ||||
−0.962720 | + | 0.270501i | \(0.912811\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.00000i | 0.304997i | 0.988304 | + | 0.152499i | \(0.0487319\pi\) | ||||
−0.988304 | + | 0.152499i | \(0.951268\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −4.33013 | − | 7.50000i | −0.631614 | − | 1.09399i | −0.987222 | − | 0.159352i | \(-0.949059\pi\) |
0.355608 | − | 0.934635i | \(-0.384274\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −1.00000 | − | 6.92820i | −0.142857 | − | 0.989743i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −2.59808 | + | 1.50000i | −0.363803 | + | 0.210042i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −0.500000 | + | 0.866025i | −0.0686803 | + | 0.118958i | −0.898321 | − | 0.439340i | \(-0.855212\pi\) |
0.829640 | + | 0.558298i | \(0.188546\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1.73205 | 0.233550 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.00000 | −1.19208 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.59808 | + | 4.50000i | −0.338241 | + | 0.585850i | −0.984102 | − | 0.177605i | \(-0.943165\pi\) |
0.645861 | + | 0.763455i | \(0.276498\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 4.50000 | − | 2.59808i | 0.576166 | − | 0.332650i | −0.183442 | − | 0.983030i | \(-0.558724\pi\) |
0.759608 | + | 0.650381i | \(0.225391\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 3.00000 | + | 5.19615i | 0.372104 | + | 0.644503i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.59808 | + | 1.50000i | 0.317406 | + | 0.183254i | 0.650236 | − | 0.759733i | \(-0.274670\pi\) |
−0.332830 | + | 0.942987i | \(0.608004\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.73205i | 0.208514i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 14.0000i | 1.66149i | 0.556650 | + | 0.830747i | \(0.312086\pi\) | ||||
−0.556650 | + | 0.830747i | \(0.687914\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 7.50000 | + | 4.33013i | 0.877809 | + | 0.506803i | 0.869935 | − | 0.493166i | \(-0.164160\pi\) |
0.00787336 | + | 0.999969i | \(0.497494\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.73205 | + | 3.00000i | 0.200000 | + | 0.346410i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 2.50000 | − | 0.866025i | 0.284901 | − | 0.0986928i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −7.79423 | + | 4.50000i | −0.876919 | + | 0.506290i | −0.869641 | − | 0.493684i | \(-0.835650\pi\) |
−0.00727784 | + | 0.999974i | \(0.502317\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 4.50000 | − | 7.79423i | 0.500000 | − | 0.866025i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −13.8564 | −1.52094 | −0.760469 | − | 0.649374i | \(-0.775031\pi\) | ||||
−0.760469 | + | 0.649374i | \(0.775031\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −3.00000 | −0.325396 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −3.46410 | + | 6.00000i | −0.371391 | + | 0.643268i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 13.5000 | − | 7.79423i | 1.43100 | − | 0.826187i | 0.433800 | − | 0.901009i | \(-0.357172\pi\) |
0.997197 | + | 0.0748225i | \(0.0238390\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.92820 | + | 6.00000i | 0.726273 | + | 0.628971i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −1.50000 | − | 2.59808i | −0.155543 | − | 0.269408i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −7.79423 | − | 4.50000i | −0.799671 | − | 0.461690i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 17.3205i | 1.75863i | 0.476240 | + | 0.879316i | \(0.342000\pi\) | ||||
−0.476240 | + | 0.879316i | \(0.658000\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 7.50000 | + | 4.33013i | 0.746278 | + | 0.430864i | 0.824347 | − | 0.566084i | \(-0.191542\pi\) |
−0.0780696 | + | 0.996948i | \(0.524876\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.33013 | + | 7.50000i | 0.426660 | + | 0.738997i | 0.996574 | − | 0.0827075i | \(-0.0263567\pi\) |
−0.569914 | + | 0.821705i | \(0.693023\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −6.00000 | − | 5.19615i | −0.585540 | − | 0.507093i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −11.2583 | + | 6.50000i | −1.08838 | + | 0.628379i | −0.933146 | − | 0.359498i | \(-0.882948\pi\) |
−0.155238 | + | 0.987877i | \(0.549614\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.50000 | − | 7.79423i | 0.431022 | − | 0.746552i | −0.565940 | − | 0.824447i | \(-0.691487\pi\) |
0.996962 | + | 0.0778949i | \(0.0248199\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 5.19615 | 0.493197 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −16.0000 | −1.50515 | −0.752577 | − | 0.658505i | \(-0.771189\pi\) | ||||
−0.752577 | + | 0.658505i | \(0.771189\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.866025 | + | 1.50000i | −0.0807573 | + | 0.139876i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −4.33013 | + | 1.50000i | −0.396942 | + | 0.137505i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.00000 | − | 8.66025i | −0.454545 | − | 0.787296i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.19615 | + | 3.00000i | 0.468521 | + | 0.270501i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.1244i | 1.08444i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 6.00000i | − | 0.532414i | −0.963916 | − | 0.266207i | \(-0.914230\pi\) | ||
0.963916 | − | 0.266207i | \(-0.0857705\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 3.00000 | + | 1.73205i | 0.264135 | + | 0.152499i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 2.59808 | + | 4.50000i | 0.226995 | + | 0.393167i | 0.956916 | − | 0.290365i | \(-0.0937766\pi\) |
−0.729921 | + | 0.683531i | \(0.760443\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −13.5000 | − | 2.59808i | −1.17060 | − | 0.225282i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.79423 | − | 4.50000i | 0.670820 | − | 0.387298i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −0.500000 | + | 0.866025i | −0.0427179 | + | 0.0739895i | −0.886594 | − | 0.462549i | \(-0.846935\pi\) |
0.843876 | + | 0.536538i | \(0.180268\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.92820 | 0.587643 | 0.293821 | − | 0.955860i | \(-0.405073\pi\) | ||||
0.293821 | + | 0.955860i | \(0.405073\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −15.0000 | −1.26323 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.73205 | + | 3.00000i | −0.144841 | + | 0.250873i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −6.00000 | + | 3.46410i | −0.498273 | + | 0.287678i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −11.2583 | − | 4.50000i | −0.928571 | − | 0.371154i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 0.500000 | + | 0.866025i | 0.0409616 | + | 0.0709476i | 0.885779 | − | 0.464107i | \(-0.153625\pi\) |
−0.844818 | + | 0.535054i | \(0.820291\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.06218 | + | 3.50000i | 0.493333 | + | 0.284826i | 0.725956 | − | 0.687741i | \(-0.241398\pi\) |
−0.232623 | + | 0.972567i | \(0.574731\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − | 3.00000i | − | 0.240966i | ||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1.50000 | − | 0.866025i | −0.119713 | − | 0.0691164i | 0.438948 | − | 0.898513i | \(-0.355351\pi\) |
−0.558661 | + | 0.829396i | \(0.688685\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0.866025 | + | 1.50000i | 0.0686803 | + | 0.118958i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −0.500000 | + | 2.59808i | −0.0394055 | + | 0.204757i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 18.1865 | − | 10.5000i | 1.42448 | − | 0.822423i | 0.427802 | − | 0.903873i | \(-0.359288\pi\) |
0.996678 | + | 0.0814491i | \(0.0259548\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 1.50000 | − | 2.59808i | 0.116775 | − | 0.202260i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −17.3205 | −1.34030 | −0.670151 | − | 0.742225i | \(-0.733770\pi\) | ||||
−0.670151 | + | 0.742225i | \(0.733770\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.00000 | 0.0769231 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 10.5000 | − | 6.06218i | 0.798300 | − | 0.460899i | −0.0445762 | − | 0.999006i | \(-0.514194\pi\) |
0.842876 | + | 0.538107i | \(0.180860\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.73205 | + | 5.00000i | 0.130931 | + | 0.377964i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.50000 | + | 7.79423i | 0.338241 | + | 0.585850i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −16.4545 | − | 9.50000i | −1.22987 | − | 0.710063i | −0.262864 | − | 0.964833i | \(-0.584667\pi\) |
−0.967002 | + | 0.254770i | \(0.918000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.92820i | 0.514969i | 0.966282 | + | 0.257485i | \(0.0828937\pi\) | ||||
−0.966282 | + | 0.257485i | \(0.917106\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 9.00000i | − | 0.665299i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.50000 | + | 2.59808i | 0.330847 | + | 0.191014i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −0.866025 | − | 1.50000i | −0.0633300 | − | 0.109691i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 9.00000 | − | 10.3923i | 0.654654 | − | 0.755929i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.866025 | − | 0.500000i | 0.0626634 | − | 0.0361787i | −0.468341 | − | 0.883548i | \(-0.655148\pi\) |
0.531004 | + | 0.847369i | \(0.321815\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.50000 | − | 12.9904i | 0.539862 | − | 0.935068i | −0.459049 | − | 0.888411i | \(-0.651810\pi\) |
0.998911 | − | 0.0466572i | \(-0.0148568\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 10.3923 | 0.744208 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −16.0000 | −1.13995 | −0.569976 | − | 0.821661i | \(-0.693048\pi\) | ||||
−0.569976 | + | 0.821661i | \(0.693048\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 11.2583 | − | 19.5000i | 0.798082 | − | 1.38232i | −0.122782 | − | 0.992434i | \(-0.539182\pi\) |
0.920864 | − | 0.389885i | \(-0.127485\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.50000 | − | 2.59808i | 0.317406 | − | 0.183254i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −6.92820 | + | 8.00000i | −0.486265 | + | 0.561490i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 3.00000 | + | 5.19615i | 0.209529 | + | 0.362915i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 5.19615i | − | 0.359425i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 10.0000i | 0.688428i | 0.938891 | + | 0.344214i | \(0.111855\pi\) | ||||
−0.938891 | + | 0.344214i | \(0.888145\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 21.0000 | + | 12.1244i | 1.43890 | + | 0.830747i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.73205 | + | 3.00000i | 0.118125 | + | 0.204598i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.50000 | − | 4.33013i | −0.101827 | − | 0.293948i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 12.9904 | − | 7.50000i | 0.877809 | − | 0.506803i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3.00000 | − | 5.19615i | 0.201802 | − | 0.349531i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.92820 | 0.463947 | 0.231973 | − | 0.972722i | \(-0.425482\pi\) | ||||
0.231973 | + | 0.972722i | \(0.425482\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.52628 | − | 16.5000i | 0.632281 | − | 1.09514i | −0.354803 | − | 0.934941i | \(-0.615452\pi\) |
0.987084 | − | 0.160202i | \(-0.0512147\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.5000 | − | 7.79423i | 0.892105 | − | 0.515057i | 0.0174746 | − | 0.999847i | \(-0.494437\pi\) |
0.874630 | + | 0.484790i | \(0.161104\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0.866025 | − | 4.50000i | 0.0569803 | − | 0.296078i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.50000 | + | 6.06218i | 0.229293 | + | 0.397146i | 0.957599 | − | 0.288106i | \(-0.0930254\pi\) |
−0.728306 | + | 0.685252i | \(0.759692\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −12.9904 | − | 7.50000i | −0.847399 | − | 0.489246i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 15.5885i | 1.01258i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 20.0000i | − | 1.29369i | −0.762620 | − | 0.646846i | \(-0.776088\pi\) | ||
0.762620 | − | 0.646846i | \(-0.223912\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.50000 | − | 2.59808i | −0.289870 | − | 0.167357i | 0.348013 | − | 0.937490i | \(-0.386857\pi\) |
−0.637883 | + | 0.770133i | \(0.720190\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −7.50000 | − | 9.52628i | −0.479157 | − | 0.608612i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 15.5885 | − | 9.00000i | 0.991870 | − | 0.572656i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −12.0000 | + | 20.7846i | −0.760469 | + | 1.31717i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.46410 | 0.218652 | 0.109326 | − | 0.994006i | \(-0.465131\pi\) | ||||
0.109326 | + | 0.994006i | \(0.465131\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.00000 | −0.0628695 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2.59808 | + | 4.50000i | −0.162698 | + | 0.281801i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.50000 | − | 2.59808i | 0.280702 | − | 0.162064i | −0.353039 | − | 0.935609i | \(-0.614852\pi\) |
0.633741 | + | 0.773545i | \(0.281518\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7.79423 | + | 1.50000i | 0.484310 | + | 0.0932055i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −19.9186 | − | 11.5000i | −1.22823 | − | 0.709120i | −0.261573 | − | 0.965184i | \(-0.584241\pi\) |
−0.966660 | + | 0.256063i | \(0.917574\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 1.73205i | 0.106399i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 27.0000i | − | 1.65237i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −19.5000 | − | 11.2583i | −1.18894 | − | 0.686433i | −0.230871 | − | 0.972984i | \(-0.574158\pi\) |
−0.958065 | + | 0.286552i | \(0.907491\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7.79423 | + | 13.5000i | 0.473466 | + | 0.820067i | 0.999539 | − | 0.0303728i | \(-0.00966946\pi\) |
−0.526073 | + | 0.850439i | \(0.676336\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 15.0000 | − | 5.19615i | 0.907841 | − | 0.314485i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.73205 | + | 1.00000i | −0.104447 | + | 0.0603023i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −6.50000 | + | 11.2583i | −0.390547 | + | 0.676448i | −0.992522 | − | 0.122068i | \(-0.961047\pi\) |
0.601975 | + | 0.798515i | \(0.294381\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −4.00000 | −0.238620 | −0.119310 | − | 0.992857i | \(-0.538068\pi\) | ||||
−0.119310 | + | 0.992857i | \(0.538068\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.06218 | − | 10.5000i | 0.360359 | − | 0.624160i | −0.627661 | − | 0.778487i | \(-0.715988\pi\) |
0.988020 | + | 0.154327i | \(0.0493208\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −13.5000 | + | 7.79423i | −0.799671 | + | 0.461690i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 6.92820 | + | 6.00000i | 0.408959 | + | 0.354169i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.00000 | − | 12.1244i | −0.411765 | − | 0.713197i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 25.9808 | + | 15.0000i | 1.52302 | + | 0.879316i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 20.7846i | − | 1.21425i | −0.794606 | − | 0.607125i | \(-0.792323\pi\) | ||
0.794606 | − | 0.607125i | \(-0.207677\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 9.00000i | 0.524000i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.50000 | + | 2.59808i | 0.261116 | + | 0.150756i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.73205 | − | 3.00000i | −0.100167 | − | 0.173494i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.00000 | + | 3.46410i | 0.230556 | + | 0.199667i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 12.9904 | − | 7.50000i | 0.746278 | − | 0.430864i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.50000 | − | 7.79423i | 0.257669 | − | 0.446296i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −20.7846 | −1.18624 | −0.593120 | − | 0.805114i | \(-0.702104\pi\) | ||||
−0.593120 | + | 0.805114i | \(0.702104\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 15.0000 | 0.853320 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.33013 | + | 7.50000i | −0.245539 | + | 0.425286i | −0.962283 | − | 0.272050i | \(-0.912298\pi\) |
0.716744 | + | 0.697336i | \(0.245632\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.50000 | − | 0.866025i | 0.0847850 | − | 0.0489506i | −0.457008 | − | 0.889463i | \(-0.651079\pi\) |
0.541793 | + | 0.840512i | \(0.317746\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.50000 | + | 9.52628i | 0.308911 | + | 0.535049i | 0.978124 | − | 0.208021i | \(-0.0667022\pi\) |
−0.669214 | + | 0.743070i | \(0.733369\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.46410 | − | 2.00000i | −0.193952 | − | 0.111979i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 22.5167i | 1.25676i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 9.00000i | 0.500773i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.00000 | − | 3.46410i | −0.332820 | − | 0.192154i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −7.79423 | − | 13.5000i | −0.431022 | − | 0.746552i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −22.5000 | − | 4.33013i | −1.24047 | − | 0.238728i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.06218 | + | 3.50000i | −0.333207 | + | 0.192377i | −0.657264 | − | 0.753660i | \(-0.728286\pi\) |
0.324057 | + | 0.946038i | \(0.394953\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 5.19615 | 0.283896 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −13.8564 | + | 24.0000i | −0.752577 | + | 1.30350i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.50000 | − | 0.866025i | 0.0812296 | − | 0.0468979i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −15.5885 | − | 10.0000i | −0.841698 | − | 0.539949i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.50000 | + | 2.59808i | 0.0807573 | + | 0.139876i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −11.2583 | − | 6.50000i | −0.604379 | − | 0.348938i | 0.166383 | − | 0.986061i | \(-0.446791\pi\) |
−0.770762 | + | 0.637123i | \(0.780124\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.3923i | 0.556287i | 0.960539 | + | 0.278144i | \(0.0897191\pi\) | ||||
−0.960539 | + | 0.278144i | \(0.910281\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 18.0000i | 0.960769i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −25.5000 | − | 14.7224i | −1.35723 | − | 0.783596i | −0.367979 | − | 0.929834i | \(-0.619950\pi\) |
−0.989249 | + | 0.146238i | \(0.953283\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12.1244 | + | 21.0000i | 0.643494 | + | 1.11456i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.50000 | + | 7.79423i | −0.0793884 | + | 0.412514i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −19.9186 | + | 11.5000i | −1.05126 | + | 0.606947i | −0.923003 | − | 0.384794i | \(-0.874273\pi\) |
−0.128260 | + | 0.991741i | \(0.540939\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4.00000 | + | 6.92820i | −0.210526 | + | 0.364642i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −17.3205 | −0.909091 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 15.0000 | 0.785136 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −0.866025 | + | 1.50000i | −0.0452062 | + | 0.0782994i | −0.887743 | − | 0.460339i | \(-0.847728\pi\) |
0.842537 | + | 0.538639i | \(0.181061\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.866025 | + | 2.50000i | 0.0449618 | + | 0.129794i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −14.5000 | − | 25.1147i | −0.750782 | − | 1.30039i | −0.947444 | − | 0.319921i | \(-0.896344\pi\) |
0.196663 | − | 0.980471i | \(-0.436990\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 18.1865 | + | 10.5000i | 0.939149 | + | 0.542218i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 13.8564i | − | 0.713641i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 8.00000i | − | 0.410932i | −0.978664 | − | 0.205466i | \(-0.934129\pi\) | ||
0.978664 | − | 0.205466i | \(-0.0658711\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −9.00000 | − | 5.19615i | −0.461084 | − | 0.266207i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 2.59808 | + | 4.50000i | 0.132755 | + | 0.229939i | 0.924738 | − | 0.380605i | \(-0.124284\pi\) |
−0.791982 | + | 0.610544i | \(0.790951\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.00000 | − | 3.46410i | 0.152894 | − | 0.176547i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.50000 | + | 16.4545i | −0.481669 | + | 0.834275i | −0.999779 | − | 0.0210389i | \(-0.993303\pi\) |
0.518110 | + | 0.855314i | \(0.326636\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.73205 | 0.0875936 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 9.00000 | 0.453990 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7.79423 | + | 13.5000i | −0.392170 | + | 0.679259i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −16.5000 | + | 9.52628i | −0.828111 | + | 0.478110i | −0.853206 | − | 0.521575i | \(-0.825345\pi\) |
0.0250943 | + | 0.999685i | \(0.492011\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −15.5885 | + | 18.0000i | −0.780399 | + | 0.901127i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.5000 | + | 19.9186i | 0.574283 | + | 0.994687i | 0.996119 | + | 0.0880147i | \(0.0280523\pi\) |
−0.421837 | + | 0.906672i | \(0.638614\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 5.19615 | + | 3.00000i | 0.258839 | + | 0.149441i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | − | 15.5885i | − | 0.774597i | ||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.00000i | 0.148704i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 22.5000 | + | 12.9904i | 1.11255 | + | 0.642333i | 0.939490 | − | 0.342578i | \(-0.111300\pi\) |
0.173064 | + | 0.984911i | \(0.444633\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0.866025 | + | 1.50000i | 0.0427179 | + | 0.0739895i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.50000 | + | 12.9904i | 0.221431 | + | 0.639215i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −20.7846 | + | 12.0000i | −1.02028 | + | 0.589057i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 6.00000 | − | 10.3923i | 0.293821 | − | 0.508913i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 20.7846 | 1.01539 | 0.507697 | − | 0.861536i | \(-0.330497\pi\) | ||||
0.507697 | + | 0.861536i | \(0.330497\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 20.0000 | 0.974740 | 0.487370 | − | 0.873195i | \(-0.337956\pi\) | ||||
0.487370 | + | 0.873195i | \(0.337956\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.00000 | − | 1.73205i | 0.145521 | − | 0.0840168i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.59808 | − | 13.5000i | 0.125730 | − | 0.653311i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.00000 | + | 5.19615i | 0.144841 | + | 0.250873i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 19.9186 | + | 11.5000i | 0.959444 | + | 0.553936i | 0.896002 | − | 0.444050i | \(-0.146459\pi\) |
0.0634424 | + | 0.997985i | \(0.479792\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 10.3923i | 0.499422i | 0.968320 | + | 0.249711i | \(0.0803357\pi\) | ||||
−0.968320 | + | 0.249711i | \(0.919664\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 12.0000i | 0.575356i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 4.50000 | + | 2.59808i | 0.215264 | + | 0.124283i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −11.2583 | − | 19.5000i | −0.537331 | − | 0.930684i | −0.999047 | − | 0.0436563i | \(-0.986099\pi\) |
0.461716 | − | 0.887028i | \(-0.347234\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.7224 | + | 8.50000i | −0.699484 | + | 0.403847i | −0.807155 | − | 0.590339i | \(-0.798994\pi\) |
0.107671 | + | 0.994187i | \(0.465661\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 13.5000 | − | 23.3827i | 0.639961 | − | 1.10845i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.73205 | 0.0819232 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.00000 | 0.377543 | 0.188772 | − | 0.982021i | \(-0.439549\pi\) | ||||
0.188772 | + | 0.982021i | \(0.439549\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.73205 | + | 3.00000i | −0.0815591 | + | 0.141264i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 10.5000 | − | 6.06218i | 0.493333 | − | 0.284826i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 15.5885 | + | 3.00000i | 0.730798 | + | 0.140642i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −7.50000 | − | 12.9904i | −0.350835 | − | 0.607664i | 0.635561 | − | 0.772051i | \(-0.280769\pi\) |
−0.986396 | + | 0.164386i | \(0.947436\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.79423 | − | 4.50000i | −0.363803 | − | 0.210042i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 17.3205i | − | 0.806696i | −0.915047 | − | 0.403348i | \(-0.867846\pi\) | ||
0.915047 | − | 0.403348i | \(-0.132154\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.0000i | 1.39422i | 0.716965 | + | 0.697109i | \(0.245531\pi\) | ||||
−0.716965 | + | 0.697109i | \(0.754469\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −4.50000 | − | 2.59808i | −0.208683 | − | 0.120483i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4.33013 | − | 7.50000i | −0.200374 | − | 0.347059i | 0.748275 | − | 0.663389i | \(-0.230883\pi\) |
−0.948649 | + | 0.316330i | \(0.897549\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 7.50000 | − | 2.59808i | 0.346318 | − | 0.119968i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.59808 | + | 1.50000i | −0.119713 | + | 0.0691164i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.00000 | + | 1.73205i | −0.0459800 | + | 0.0796398i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 10.3923 | 0.476832 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 6.06218 | − | 10.5000i | 0.276988 | − | 0.479757i | −0.693647 | − | 0.720315i | \(-0.743997\pi\) |
0.970635 | + | 0.240558i | \(0.0773304\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −9.00000 | + | 5.19615i | −0.410365 | + | 0.236924i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3.46410 | + | 3.00000i | 0.157622 | + | 0.136505i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 15.0000 | + | 25.9808i | 0.681115 | + | 1.17973i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −26.8468 | − | 15.5000i | −1.21654 | − | 0.702372i | −0.252367 | − | 0.967632i | \(-0.581209\pi\) |
−0.964177 | + | 0.265260i | \(0.914542\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 36.3731i | − | 1.64485i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.0000i | 1.44414i | 0.691820 | + | 0.722070i | \(0.256809\pi\) | ||||
−0.691820 | + | 0.722070i | \(0.743191\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.00000 | + | 3.46410i | 0.270226 | + | 0.156015i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 28.0000 | + | 24.2487i | 1.25597 | + | 1.08770i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −30.3109 | + | 17.5000i | −1.35690 | + | 0.783408i | −0.989205 | − | 0.146538i | \(-0.953187\pi\) |
−0.367697 | + | 0.929946i | \(0.619854\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −15.0000 | + | 25.9808i | −0.670151 | + | 1.16073i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −6.92820 | −0.308913 | −0.154457 | − | 0.988000i | \(-0.549363\pi\) | ||||
−0.154457 | + | 0.988000i | \(0.549363\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 15.0000 | 0.667491 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0.866025 | − | 1.50000i | 0.0384615 | − | 0.0666173i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −10.5000 | + | 6.06218i | −0.465404 | + | 0.268701i | −0.714314 | − | 0.699825i | \(-0.753261\pi\) |
0.248910 | + | 0.968527i | \(0.419928\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.6506 | − | 7.50000i | 0.957768 | − | 0.331780i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −13.5000 | − | 23.3827i | −0.596040 | − | 1.03237i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 12.9904 | + | 7.50000i | 0.572425 | + | 0.330489i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 8.66025i | − | 0.380878i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 21.0000i | − | 0.921798i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.50000 | + | 0.866025i | 0.0657162 | + | 0.0379413i | 0.532498 | − | 0.846431i | \(-0.321253\pi\) |
−0.466782 | + | 0.884372i | \(0.654587\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −12.9904 | − | 22.5000i | −0.568030 | − | 0.983856i | −0.996761 | − | 0.0804241i | \(-0.974373\pi\) |
0.428731 | − | 0.903432i | \(-0.358961\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 9.00000 | + | 1.73205i | 0.392792 | + | 0.0755929i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.59808 | + | 1.50000i | −0.113174 | + | 0.0653410i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −11.0000 | + | 19.0526i | −0.478261 | + | 0.828372i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −12.0000 | −0.519778 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −11.2583 | + | 19.5000i | −0.486740 | + | 0.843059i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −28.5000 | + | 16.4545i | −1.22987 | + | 0.710063i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.59808 | − | 6.50000i | 0.111907 | − | 0.279975i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.50000 | − | 16.4545i | −0.408437 | − | 0.707433i | 0.586278 | − | 0.810110i | \(-0.300593\pi\) |
−0.994715 | + | 0.102677i | \(0.967259\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10.3923 | + | 6.00000i | 0.445976 | + | 0.257485i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 15.5885i | − | 0.667736i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10.3923 | + | 18.0000i | 0.442727 | + | 0.766826i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.50000 | + | 23.3827i | −0.191359 | + | 0.994333i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 7.79423 | − | 4.50000i | 0.330847 | − | 0.191014i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 18.5000 | − | 32.0429i | 0.783870 | − | 1.35770i | −0.145802 | − | 0.989314i | \(-0.546576\pi\) |
0.929672 | − | 0.368389i | \(-0.120091\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.92820 | −0.293032 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.00000 | −0.126660 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 11.2583 | − | 19.5000i | 0.474482 | − | 0.821827i | −0.525091 | − | 0.851046i | \(-0.675969\pi\) |
0.999573 | + | 0.0292191i | \(0.00930205\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −24.0000 | + | 13.8564i | −1.00969 | + | 0.582943i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −7.79423 | − | 22.5000i | −0.327327 | − | 0.944911i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 6.50000 | + | 11.2583i | 0.272494 | + | 0.471974i | 0.969500 | − | 0.245092i | \(-0.0788181\pi\) |
−0.697006 | + | 0.717066i | \(0.745485\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 18.1865 | + | 10.5000i | 0.761083 | + | 0.439411i | 0.829684 | − | 0.558233i | \(-0.188520\pi\) |
−0.0686016 | + | 0.997644i | \(0.521854\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 1.73205i | − | 0.0723575i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 2.00000i | − | 0.0834058i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −28.5000 | − | 16.4545i | −1.18647 | − | 0.685009i | −0.228968 | − | 0.973434i | \(-0.573535\pi\) |
−0.957503 | + | 0.288425i | \(0.906868\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −12.9904 | − | 22.5000i | −0.539862 | − | 0.935068i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −24.0000 | + | 27.7128i | −0.995688 | + | 1.14972i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −0.866025 | + | 0.500000i | −0.0358671 | + | 0.0207079i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6.92820 | −0.285958 | −0.142979 | − | 0.989726i | \(-0.545668\pi\) | ||||
−0.142979 | + | 0.989726i | \(0.545668\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.00000 | −0.370839 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −13.8564 | + | 24.0000i | −0.569976 | + | 0.987228i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13.5000 | + | 7.79423i | −0.554379 | + | 0.320071i | −0.750886 | − | 0.660432i | \(-0.770373\pi\) |
0.196508 | + | 0.980502i | \(0.437040\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −5.19615 | + | 6.00000i | −0.213021 | + | 0.245976i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −19.5000 | − | 33.7750i | −0.798082 | − | 1.38232i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 14.7224 | + | 8.50000i | 0.601542 | + | 0.347301i | 0.769648 | − | 0.638468i | \(-0.220432\pi\) |
−0.168106 | + | 0.985769i | \(0.553765\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 38.1051i | − | 1.55434i | −0.629291 | − | 0.777170i | \(-0.716654\pi\) | ||
0.629291 | − | 0.777170i | \(-0.283346\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −15.0000 | − | 8.66025i | −0.609837 | − | 0.352089i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −7.79423 | − | 13.5000i | −0.316358 | − | 0.547948i | 0.663367 | − | 0.748294i | \(-0.269127\pi\) |
−0.979725 | + | 0.200346i | \(0.935793\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 6.00000 | + | 17.3205i | 0.243132 | + | 0.701862i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 25.9808 | − | 15.0000i | 1.05107 | − | 0.606835i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15.5000 | + | 26.8468i | −0.626039 | + | 1.08433i | 0.362300 | + | 0.932062i | \(0.381992\pi\) |
−0.988339 | + | 0.152270i | \(0.951342\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 10.3923 | 0.419058 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.0000 | 0.805170 | 0.402585 | − | 0.915383i | \(-0.368112\pi\) | ||||
0.402585 | + | 0.915383i | \(0.368112\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.79423 | − | 13.5000i | 0.313276 | − | 0.542611i | −0.665793 | − | 0.746136i | \(-0.731907\pi\) |
0.979070 | + | 0.203526i | \(0.0652400\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −4.50000 | + | 2.59808i | −0.180579 | + | 0.104257i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.79423 | − | 40.5000i | 0.312269 | − | 1.62260i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.50000 | + | 9.52628i | 0.220000 | + | 0.381051i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −7.79423 | − | 4.50000i | −0.311272 | − | 0.179713i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 5.19615i | − | 0.207184i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 30.0000i | − | 1.19428i | −0.802137 | − | 0.597141i | \(-0.796303\pi\) | ||
0.802137 | − | 0.597141i | \(-0.203697\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 15.0000 | + | 8.66025i | 0.596196 | + | 0.344214i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −5.19615 | − | 9.00000i | −0.206203 | − | 0.357154i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 24.0000 | − | 3.46410i | 0.950915 | − | 0.137253i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 6.50000 | − | 11.2583i | 0.256735 | − | 0.444677i | −0.708631 | − | 0.705580i | \(-0.750687\pi\) |
0.965365 | + | 0.260902i | \(0.0840201\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 13.8564 | 0.546443 | 0.273222 | − | 0.961951i | \(-0.411911\pi\) | ||||
0.273222 | + | 0.961951i | \(0.411911\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.00000 | 0.236250 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.4545 | − | 28.5000i | 0.646892 | − | 1.12045i | −0.336968 | − | 0.941516i | \(-0.609402\pi\) |
0.983861 | − | 0.178935i | \(-0.0572651\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.50000 | + | 2.59808i | −0.176640 | + | 0.101983i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −7.79423 | − | 1.50000i | −0.305480 | − | 0.0587896i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 15.5000 | + | 26.8468i | 0.606562 | + | 1.05060i | 0.991803 | + | 0.127780i | \(0.0407851\pi\) |
−0.385241 | + | 0.922816i | \(0.625882\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.79423 | + | 4.50000i | 0.304546 | + | 0.175830i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 38.0000i | − | 1.48027i | −0.672458 | − | 0.740135i | \(-0.734762\pi\) | ||
0.672458 | − | 0.740135i | \(-0.265238\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 34.5000 | + | 19.9186i | 1.34189 | + | 0.774743i | 0.987085 | − | 0.160196i | \(-0.0512125\pi\) |
0.354809 | + | 0.934939i | \(0.384546\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −5.19615 | − | 9.00000i | −0.201802 | − | 0.349531i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −22.5000 | + | 7.79423i | −0.872513 | + | 0.302247i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.46410 | − | 2.00000i | 0.134131 | − | 0.0774403i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6.00000 | − | 10.3923i | 0.231973 | − | 0.401790i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.19615 | 0.200595 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 24.0000 | 0.925132 | 0.462566 | − | 0.886585i | \(-0.346929\pi\) | ||||
0.462566 | + | 0.886585i | \(0.346929\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5.19615 | + | 9.00000i | −0.200000 | + | 0.346410i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 37.5000 | − | 21.6506i | 1.44124 | − | 0.832102i | 0.443309 | − | 0.896369i | \(-0.353804\pi\) |
0.997933 | + | 0.0642672i | \(0.0204710\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 34.6410 | + | 30.0000i | 1.32940 | + | 1.15129i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −16.5000 | − | 28.5788i | −0.632281 | − | 1.09514i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 21.6506 | + | 12.5000i | 0.828439 | + | 0.478299i | 0.853318 | − | 0.521391i | \(-0.174587\pi\) |
−0.0248792 | + | 0.999690i | \(0.507920\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.73205i | 0.0661783i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 27.0000i | − | 1.03011i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.00000 | − | 1.73205i | −0.114291 | − | 0.0659859i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6.06218 | + | 10.5000i | 0.230616 | + | 0.399439i | 0.957990 | − | 0.286803i | \(-0.0925925\pi\) |
−0.727373 | + | 0.686242i | \(0.759259\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 10.3923 | − | 6.00000i | 0.394203 | − | 0.227593i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.00000 | − | 5.19615i | 0.113633 | − | 0.196818i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 12.1244 | 0.458585 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 26.0000 | 0.982006 | 0.491003 | − | 0.871158i | \(-0.336630\pi\) | ||||
0.491003 | + | 0.871158i | \(0.336630\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 7.79423 | − | 13.5000i | 0.293965 | − | 0.509162i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −22.5000 | + | 12.9904i | −0.847399 | + | 0.489246i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 21.6506 | − | 7.50000i | 0.814256 | − | 0.282067i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −4.50000 | − | 7.79423i | −0.169001 | − | 0.292718i | 0.769068 | − | 0.639167i | \(-0.220721\pi\) |
−0.938069 | + | 0.346449i | \(0.887387\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.73205i | 0.0648658i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.00000i | 0.224387i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −30.0000 | − | 17.3205i | −1.12037 | − | 0.646846i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −12.9904 | − | 22.5000i | −0.484459 | − | 0.839108i | 0.515381 | − | 0.856961i | \(-0.327650\pi\) |
−0.999841 | + | 0.0178527i | \(0.994317\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.5000 | + | 4.33013i | 0.837944 | + | 0.161262i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.79423 | + | 4.50000i | −0.289870 | + | 0.167357i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.00000 | − | 6.92820i | 0.148556 | − | 0.257307i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 27.0000 | 1.00000 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.73205 | − | 3.00000i | 0.0640622 | − | 0.110959i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −37.5000 | + | 21.6506i | −1.38509 | + | 0.799684i | −0.992757 | − | 0.120137i | \(-0.961667\pi\) |
−0.392337 | + | 0.919822i | \(0.628333\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −20.7846 | + | 3.00000i | −0.766652 | + | 0.110657i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.50000 | + | 2.59808i | 0.0552532 | + | 0.0957014i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −44.1673 | − | 25.5000i | −1.62472 | − | 0.938033i | −0.985634 | − | 0.168898i | \(-0.945979\pi\) |
−0.639087 | − | 0.769135i | \(-0.720687\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 31.1769i | − | 1.14531i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 34.0000i | 1.24734i | 0.781688 | + | 0.623670i | \(0.214359\pi\) | ||||
−0.781688 | + | 0.623670i | \(0.785641\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.50000 | + | 0.866025i | 0.0549557 | + | 0.0317287i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.50000 | + | 33.7750i | −0.237505 | + | 1.23411i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.6506 | − | 12.5000i | 0.790043 | − | 0.456131i | −0.0499348 | − | 0.998752i | \(-0.515901\pi\) |
0.839978 | + | 0.542621i | \(0.182568\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 3.00000 | − | 5.19615i | 0.109326 | − | 0.189358i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 12.1244 | 0.441250 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 48.0000 | 1.74459 | 0.872295 | − | 0.488980i | \(-0.162631\pi\) | ||||
0.872295 | + | 0.488980i | \(0.162631\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −0.866025 | + | 1.50000i | −0.0314347 | + | 0.0544466i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 16.5000 | − | 9.52628i | 0.598125 | − | 0.345327i | −0.170179 | − | 0.985413i | \(-0.554435\pi\) |
0.768303 | + | 0.640086i | \(0.221101\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −7.79423 | − | 22.5000i | −0.282170 | − | 0.814555i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −15.5885 | − | 9.00000i | −0.562867 | − | 0.324971i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.46410i | 0.124919i | 0.998048 | + | 0.0624593i | \(0.0198944\pi\) | ||||
−0.998048 | + | 0.0624593i | \(0.980106\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 9.00000i | − | 0.324127i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −22.5000 | − | 12.9904i | −0.809269 | − | 0.467232i | 0.0374331 | − | 0.999299i | \(-0.488082\pi\) |
−0.846702 | + | 0.532068i | \(0.821415\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.73205 | + | 3.00000i | 0.0622171 | + | 0.107763i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 9.00000 | − | 10.3923i | 0.322873 | − | 0.372822i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 15.5885 | − | 9.00000i | 0.558514 | − | 0.322458i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.00000 | + | 12.1244i | −0.250480 | + | 0.433844i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −20.7846 | −0.742781 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3.00000 | −0.107075 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.59808 | + | 4.50000i | −0.0926114 | + | 0.160408i | −0.908609 | − | 0.417647i | \(-0.862855\pi\) |
0.815998 | + | 0.578055i | \(0.196188\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −34.5000 | + | 19.9186i | −1.22823 | + | 0.709120i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −27.7128 | + | 32.0000i | −0.985354 | + | 1.13779i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 9.00000 | + | 15.5885i | 0.319599 | + | 0.553562i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.59808 | + | 1.50000i | 0.0921443 | + | 0.0531995i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 10.3923i | − | 0.368114i | −0.982916 | − | 0.184057i | \(-0.941077\pi\) | ||
0.982916 | − | 0.184057i | \(-0.0589232\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15.0000i | 0.530662i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.33013 | + | 7.50000i | 0.152807 | + | 0.264669i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.50000 | + | 4.33013i | 0.0528681 | + | 0.152617i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −33.7750 | + | 19.5000i | −1.18894 | + | 0.686433i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −21.5000 | + | 37.2391i | −0.755900 | + | 1.30926i | 0.189026 | + | 0.981972i | \(0.439467\pi\) |
−0.944926 | + | 0.327285i | \(0.893866\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −13.8564 | −0.486564 | −0.243282 | − | 0.969956i | \(-0.578224\pi\) | ||||
−0.243282 | + | 0.969956i | \(0.578224\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 27.0000 | 0.946931 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 18.1865 | − | 31.5000i | 0.637046 | − | 1.10340i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.00000 | − | 5.19615i | 0.314870 | − | 0.181790i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.50000 | − | 9.52628i | −0.191951 | − | 0.332469i | 0.753946 | − | 0.656937i | \(-0.228148\pi\) |
−0.945897 | + | 0.324468i | \(0.894815\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 7.79423 | + | 4.50000i | 0.271690 | + | 0.156860i | 0.629655 | − | 0.776875i | \(-0.283196\pi\) |
−0.357966 | + | 0.933735i | \(0.616529\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.46410i | 0.120605i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22.0000i | 0.765015i | 0.923952 | + | 0.382507i | \(0.124939\pi\) | ||||
−0.923952 | + | 0.382507i | \(0.875061\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 7.50000 | + | 4.33013i | 0.260486 | + | 0.150392i | 0.624556 | − | 0.780980i | \(-0.285280\pi\) |
−0.364070 | + | 0.931371i | \(0.618613\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 11.2583 | + | 19.5000i | 0.390547 | + | 0.676448i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.50000 | + | 11.2583i | −0.155916 | + | 0.390078i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −25.9808 | + | 15.0000i | −0.899101 | + | 0.519096i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.50000 | − | 7.79423i | 0.155543 | − | 0.269408i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 48.4974 | 1.67432 | 0.837158 | − | 0.546960i | \(-0.184215\pi\) | ||||
0.837158 | + | 0.546960i | \(0.184215\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.0000 | −0.448276 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −3.46410 | + | 6.00000i | −0.119310 | + | 0.206651i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.50000 | − | 0.866025i | 0.0516016 | − | 0.0297922i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −25.9808 | − | 5.00000i | −0.892710 | − | 0.171802i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.5000 | − | 18.1865i | −0.360359 | − | 0.624160i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.59808 | − | 1.50000i | −0.0890609 | − | 0.0514193i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 24.2487i | − | 0.830260i | −0.909762 | − | 0.415130i | \(-0.863736\pi\) | ||
0.909762 | − | 0.415130i | \(-0.136264\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −22.5000 | − | 12.9904i | −0.768585 | − | 0.443743i | 0.0637844 | − | 0.997964i | \(-0.479683\pi\) |
−0.832370 | + | 0.554221i | \(0.813016\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 25.1147 | + | 43.5000i | 0.856904 | + | 1.48420i | 0.874868 | + | 0.484362i | \(0.160948\pi\) |
−0.0179638 | + | 0.999839i | \(0.505718\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 15.0000 | − | 5.19615i | 0.511199 | − | 0.177084i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 30.3109 | − | 17.5000i | 1.03179 | − | 0.595707i | 0.114296 | − | 0.993447i | \(-0.463539\pi\) |
0.917498 | + | 0.397740i | \(0.130205\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 10.5000 | − | 18.1865i | 0.357011 | − | 0.618361i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −24.2487 | −0.823529 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −9.00000 | −0.305304 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −5.19615 | + | 9.00000i | −0.176065 | + | 0.304953i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 24.2487 | + | 21.0000i | 0.819756 | + | 0.709930i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.500000 | + | 0.866025i | 0.0168838 | + | 0.0292436i | 0.874344 | − | 0.485307i | \(-0.161292\pi\) |
−0.857460 | + | 0.514551i | \(0.827959\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −31.1769 | − | 18.0000i | −1.05157 | − | 0.607125i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 13.8564i | − | 0.466834i | −0.972377 | − | 0.233417i | \(-0.925009\pi\) | ||
0.972377 | − | 0.233417i | \(-0.0749907\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 10.0000i | − | 0.336527i | −0.985742 | − | 0.168263i | \(-0.946184\pi\) | ||
0.985742 | − | 0.168263i | \(-0.0538159\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 13.5000 | + | 7.79423i | 0.453798 | + | 0.262000i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 12.9904 | + | 22.5000i | 0.436174 | + | 0.755476i | 0.997391 | − | 0.0721931i | \(-0.0229998\pi\) |
−0.561216 | + | 0.827669i | \(0.689666\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12.0000 | − | 10.3923i | −0.402467 | − | 0.348547i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 7.79423 | − | 4.50000i | 0.261116 | − | 0.150756i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −22.5000 | + | 38.9711i | −0.752934 | + | 1.30412i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −32.9090 | −1.10003 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −6.00000 | −0.200334 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −3.46410 | + | 6.00000i | −0.115534 | + | 0.200111i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.50000 | − | 0.866025i | 0.0499722 | − | 0.0288515i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 8.66025 | − | 3.00000i | 0.288195 | − | 0.0998337i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 6.00000 | + | 10.3923i | 0.199447 | + | 0.345452i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.06218 | + | 3.50000i | 0.201291 | + | 0.116216i | 0.597258 | − | 0.802049i | \(-0.296257\pi\) |
−0.395966 | + | 0.918265i | \(0.629590\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.0000i | 0.861418i | 0.902491 | + | 0.430709i | \(0.141737\pi\) | ||||
−0.902491 | + | 0.430709i | \(0.858263\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −12.0000 | − | 6.92820i | −0.397142 | − | 0.229290i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −7.79423 | − | 13.5000i | −0.257669 | − | 0.446296i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 13.5000 | + | 2.59808i | 0.445809 | + | 0.0857960i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 0.866025 | − | 0.500000i | 0.0285675 | − | 0.0164935i | −0.485648 | − | 0.874154i | \(-0.661416\pi\) |
0.514216 | + | 0.857661i | \(0.328083\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −18.0000 | + | 31.1769i | −0.593120 | + | 1.02731i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −48.4974 | −1.59631 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.00000 | −0.197279 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.50000 | − | 4.33013i | 0.246067 | − | 0.142067i | −0.371895 | − | 0.928275i | \(-0.621292\pi\) |
0.617962 | + | 0.786208i | \(0.287959\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −28.5788 | + | 22.5000i | −0.936634 | + | 0.737408i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 7.50000 | + | 12.9904i | 0.245539 | + | 0.425286i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.59808 | − | 1.50000i | −0.0849662 | − | 0.0490552i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 3.00000i | − | 0.0979013i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −49.5000 | − | 28.5788i | −1.61365 | − | 0.931644i | −0.988514 | − | 0.151131i | \(-0.951708\pi\) |
−0.625140 | − | 0.780513i | \(-0.714958\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.73205 | − | 3.00000i | −0.0564033 | − | 0.0976934i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 4.50000 | − | 23.3827i | 0.146385 | − | 0.760639i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 25.1147 | − | 14.5000i | 0.816119 | − | 0.471187i | −0.0329571 | − | 0.999457i | \(-0.510492\pi\) |
0.849076 | + | 0.528270i | \(0.177159\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −15.0000 | + | 25.9808i | −0.486921 | + | 0.843371i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 19.0526 | 0.617822 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −8.00000 | −0.259145 | −0.129573 | − | 0.991570i | \(-0.541361\pi\) | ||||
−0.129573 | + | 0.991570i | \(0.541361\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.866025 | − | 1.50000i | 0.0280239 | − | 0.0485389i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −6.00000 | + | 3.46410i | −0.193952 | + | 0.111979i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0.866025 | + | 2.50000i | 0.0279654 | + | 0.0807292i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14.0000 | + | 24.2487i | 0.451613 | + | 0.782216i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 25.9808i | − | 0.836350i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 6.00000i | 0.192947i | 0.995336 | + | 0.0964735i | \(0.0307563\pi\) | ||||
−0.995336 | + | 0.0964735i | \(0.969244\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 13.5000 | + | 7.79423i | 0.433682 | + | 0.250387i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 30.3109 | + | 52.5000i | 0.972723 | + | 1.68481i | 0.687254 | + | 0.726417i | \(0.258816\pi\) |
0.285469 | + | 0.958388i | \(0.407851\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 12.0000 | − | 13.8564i | 0.384702 | − | 0.444216i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −10.3923 | + | 6.00000i | −0.332820 | + | 0.192154i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 15.5000 | − | 26.8468i | 0.495889 | − | 0.858905i | −0.504100 | − | 0.863645i | \(-0.668176\pi\) |
0.999989 | + | 0.00474056i | \(0.00150897\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 15.5885 | 0.498209 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −30.3109 | + | 52.5000i | −0.966767 | + | 1.67449i | −0.261977 | + | 0.965074i | \(0.584374\pi\) |
−0.704790 | + | 0.709416i | \(0.748959\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −24.0000 | + | 13.8564i | −0.764704 | + | 0.441502i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −25.9808 | + | 30.0000i | −0.826977 | + | 0.954911i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.00000 | − | 1.73205i | −0.0317982 | − | 0.0550760i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −19.9186 | − | 11.5000i | −0.632735 | − | 0.365310i | 0.149076 | − | 0.988826i | \(-0.452370\pi\) |
−0.781810 | + | 0.623516i | \(0.785704\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 12.1244i | 0.384755i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | − | 39.0000i | − | 1.23638i | ||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19.5000 | − | 11.2583i | −0.617571 | − | 0.356555i | 0.158352 | − | 0.987383i | \(-0.449382\pi\) |
−0.775923 | + | 0.630828i | \(0.782715\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7.79423 | + | 13.5000i | 0.246598 | + | 0.427121i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))