Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(341,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.341");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.w (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: | \(6.03669039281\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} - 156 x^{7} + 558 x^{6} - 837 x^{5} + 1782 x^{4} - 4131 x^{3} + 3645 x^{2} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 3^{6} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 521.4 | ||
Root | \(1.68124 + 0.416458i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 756.521 |
Dual form | 756.2.w.a.341.4 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
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 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.349828 | + | 0.605920i | −0.156448 | + | 0.270975i | −0.933585 | − | 0.358355i | \(-0.883338\pi\) |
0.777137 | + | 0.629331i | \(0.216671\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.48683 | − | 0.903137i | 0.939935 | − | 0.341354i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.229685 | + | 0.132608i | −0.0692525 | + | 0.0399829i | −0.534226 | − | 0.845341i | \(-0.679397\pi\) |
0.464974 | + | 0.885324i | \(0.346064\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.13823 | − | 0.657156i | 0.315688 | − | 0.182262i | −0.333781 | − | 0.942651i | \(-0.608325\pi\) |
0.649469 | + | 0.760388i | \(0.274991\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.86392 | − | 3.22840i | 0.452067 | − | 0.783003i | −0.546447 | − | 0.837493i | \(-0.684020\pi\) |
0.998514 | + | 0.0544906i | \(0.0173535\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.382449 | + | 0.220807i | −0.0877398 | + | 0.0506566i | −0.543228 | − | 0.839585i | \(-0.682798\pi\) |
0.455488 | + | 0.890242i | \(0.349465\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4.29949 | + | 2.48231i | 0.896507 | + | 0.517598i | 0.876065 | − | 0.482193i | \(-0.160160\pi\) |
0.0204414 | + | 0.999791i | \(0.493493\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.25524 | + | 3.90619i | 0.451048 | + | 0.781238i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 0.273287 | + | 0.157782i | 0.0507480 | + | 0.0292994i | 0.525159 | − | 0.851004i | \(-0.324006\pi\) |
−0.474411 | + | 0.880303i | \(0.657339\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 5.60632i | − | 1.00692i | −0.864017 | − | 0.503462i | \(-0.832059\pi\) | ||
0.864017 | − | 0.503462i | \(-0.167941\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.322736 | + | 1.82276i | −0.0545523 | + | 0.308103i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −0.351124 | − | 0.608164i | −0.0577244 | − | 0.0999816i | 0.835719 | − | 0.549157i | \(-0.185051\pi\) |
−0.893444 | + | 0.449175i | \(0.851718\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.39354 | + | 9.34189i | 0.842330 | + | 1.45896i | 0.887920 | + | 0.459998i | \(0.152150\pi\) |
−0.0455900 | + | 0.998960i | \(0.514517\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.73131 | − | 6.46283i | 0.569020 | − | 0.985572i | −0.427643 | − | 0.903948i | \(-0.640656\pi\) |
0.996663 | − | 0.0816240i | \(-0.0260106\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 7.00570 | 1.02189 | 0.510943 | − | 0.859614i | \(-0.329296\pi\) | ||||
0.510943 | + | 0.859614i | \(0.329296\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 5.36869 | − | 4.49190i | 0.766955 | − | 0.641700i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8.51919 | − | 4.91856i | −1.17020 | − | 0.675616i | −0.216474 | − | 0.976288i | \(-0.569456\pi\) |
−0.953727 | + | 0.300672i | \(0.902789\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.185561i | − | 0.0250210i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 13.4636 | 1.75282 | 0.876408 | − | 0.481570i | \(-0.159933\pi\) | ||||
0.876408 | + | 0.481570i | \(0.159933\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.65207i | 0.723674i | 0.932241 | + | 0.361837i | \(0.117850\pi\) | ||||
−0.932241 | + | 0.361837i | \(0.882150\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.919566i | 0.114058i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5.94120 | −0.725833 | −0.362916 | − | 0.931822i | \(-0.618219\pi\) | ||||
−0.362916 | + | 0.931822i | \(0.618219\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 13.4323i | 1.59412i | 0.603900 | + | 0.797060i | \(0.293613\pi\) | ||||
−0.603900 | + | 0.797060i | \(0.706387\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.66182 | − | 3.84620i | −0.779707 | − | 0.450164i | 0.0566194 | − | 0.998396i | \(-0.481968\pi\) |
−0.836326 | + | 0.548232i | \(0.815301\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.451424 | + | 0.537212i | −0.0514445 | + | 0.0612210i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.39672 | 0.157143 | 0.0785716 | − | 0.996908i | \(-0.474964\pi\) | ||||
0.0785716 | + | 0.996908i | \(0.474964\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 3.72399 | − | 6.45014i | 0.408761 | − | 0.707995i | −0.585990 | − | 0.810318i | \(-0.699294\pi\) |
0.994751 | + | 0.102323i | \(0.0326276\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.30410 | + | 2.25877i | 0.141450 | + | 0.244998i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −5.59261 | − | 9.68668i | −0.592815 | − | 1.02679i | −0.993851 | − | 0.110724i | \(-0.964683\pi\) |
0.401036 | − | 0.916062i | \(-0.368650\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.23708 | − | 2.66221i | 0.234510 | − | 0.279076i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 0.308978i | − | 0.0317004i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −9.18225 | − | 5.30138i | −0.932316 | − | 0.538273i | −0.0447729 | − | 0.998997i | \(-0.514256\pi\) |
−0.887543 | + | 0.460724i | \(0.847590\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.75357 | − | 15.1616i | −0.871013 | − | 1.50864i | −0.860950 | − | 0.508690i | \(-0.830130\pi\) |
−0.0100634 | − | 0.999949i | \(-0.503203\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 7.39775 | + | 4.27110i | 0.728922 | + | 0.420844i | 0.818028 | − | 0.575179i | \(-0.195067\pi\) |
−0.0891054 | + | 0.996022i | \(0.528401\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.09489 | + | 5.25093i | −0.879236 | + | 0.507627i | −0.870406 | − | 0.492334i | \(-0.836144\pi\) |
−0.00882940 | + | 0.999961i | \(0.502811\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −7.12110 | + | 12.3341i | −0.682078 | + | 1.18139i | 0.292268 | + | 0.956337i | \(0.405590\pi\) |
−0.974346 | + | 0.225057i | \(0.927743\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −13.3783 | + | 7.72396i | −1.25852 | + | 0.726609i | −0.972788 | − | 0.231699i | \(-0.925572\pi\) |
−0.285737 | + | 0.958308i | \(0.592238\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.00817 | + | 1.73677i | −0.280513 | + | 0.161954i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 1.71957 | − | 9.71188i | 0.157633 | − | 0.890286i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −5.46483 | + | 9.46536i | −0.496803 | + | 0.860488i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −6.65406 | −0.595157 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 21.8304 | 1.93713 | 0.968566 | − | 0.248758i | \(-0.0800225\pi\) | ||||
0.968566 | + | 0.248758i | \(0.0800225\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.60461 | + | 4.51132i | −0.227566 | + | 0.394156i | −0.957086 | − | 0.289803i | \(-0.906410\pi\) |
0.729520 | + | 0.683959i | \(0.239743\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −0.751668 | + | 0.894514i | −0.0651779 | + | 0.0775642i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 2.33589 | − | 1.34863i | 0.199568 | − | 0.115221i | −0.396886 | − | 0.917868i | \(-0.629909\pi\) |
0.596454 | + | 0.802647i | \(0.296576\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −10.1448 | + | 5.85710i | −0.860470 | + | 0.496793i | −0.864170 | − | 0.503200i | \(-0.832156\pi\) |
0.00369951 | + | 0.999993i | \(0.498822\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −0.174289 | + | 0.301877i | −0.0145748 | + | 0.0252442i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −0.191206 | + | 0.110393i | −0.0158788 | + | 0.00916765i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −16.3055 | − | 9.41399i | −1.33580 | − | 0.771224i | −0.349618 | − | 0.936892i | \(-0.613689\pi\) |
−0.986182 | + | 0.165668i | \(0.947022\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −5.00143 | − | 8.66273i | −0.407010 | − | 0.704963i | 0.587543 | − | 0.809193i | \(-0.300095\pi\) |
−0.994553 | + | 0.104230i | \(0.966762\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.39698 | + | 1.96125i | 0.272852 | + | 0.157531i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 0.252063i | − | 0.0201168i | −0.999949 | − | 0.0100584i | \(-0.996798\pi\) | ||
0.999949 | − | 0.0100584i | \(-0.00320175\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 12.9340 | + | 2.29007i | 1.01934 | + | 0.180483i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 4.29780 | + | 7.44400i | 0.336629 | + | 0.583059i | 0.983796 | − | 0.179289i | \(-0.0573797\pi\) |
−0.647167 | + | 0.762348i | \(0.724046\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −2.24437 | − | 3.88736i | −0.173674 | − | 0.300813i | 0.766027 | − | 0.642808i | \(-0.222231\pi\) |
−0.939702 | + | 0.341995i | \(0.888897\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.63629 | + | 9.76234i | −0.433561 | + | 0.750949i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 7.12145 | 0.541434 | 0.270717 | − | 0.962659i | \(-0.412739\pi\) | ||||
0.270717 | + | 0.962659i | \(0.412739\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.13624 | + | 7.67726i | 0.690634 | + | 0.580346i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −22.1270 | − | 12.7750i | −1.65385 | − | 0.954848i | −0.975470 | − | 0.220134i | \(-0.929351\pi\) |
−0.678376 | − | 0.734715i | \(-0.737316\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 0.943175i | − | 0.0701057i | −0.999385 | − | 0.0350528i | \(-0.988840\pi\) | ||
0.999385 | − | 0.0350528i | \(-0.0111599\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0.491332 | 0.0361234 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.988686i | 0.0722999i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2.97235i | 0.215072i | 0.994201 | + | 0.107536i | \(0.0342960\pi\) | ||||
−0.994201 | + | 0.107536i | \(0.965704\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −18.5144 | −1.33270 | −0.666348 | − | 0.745641i | \(-0.732144\pi\) | ||||
−0.666348 | + | 0.745641i | \(0.732144\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 14.1774i | 1.01010i | 0.863091 | + | 0.505048i | \(0.168525\pi\) | ||||
−0.863091 | + | 0.505048i | \(0.831475\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −20.5293 | − | 11.8526i | −1.45529 | − | 0.840209i | −0.456512 | − | 0.889717i | \(-0.650901\pi\) |
−0.998774 | + | 0.0495081i | \(0.984235\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0.822117 | + | 0.145563i | 0.0577013 | + | 0.0102165i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.54725 | −0.527123 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.0585617 | − | 0.101432i | 0.00405080 | − | 0.00701619i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.04004 | + | 5.26550i | 0.209285 | + | 0.362492i | 0.951489 | − | 0.307681i | \(-0.0995531\pi\) |
−0.742205 | + | 0.670173i | \(0.766220\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.61063 | + | 4.52175i | 0.178044 | + | 0.308381i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −5.06327 | − | 13.9420i | −0.343717 | − | 0.946444i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 4.89954i | − | 0.329579i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.796137 | + | 0.459650i | 0.0533133 | + | 0.0307804i | 0.526420 | − | 0.850225i | \(-0.323534\pi\) |
−0.473106 | + | 0.881005i | \(0.656867\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −5.00297 | − | 8.66540i | −0.332059 | − | 0.575143i | 0.650857 | − | 0.759201i | \(-0.274410\pi\) |
−0.982915 | + | 0.184058i | \(0.941077\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2.38179 | − | 1.37513i | −0.157393 | − | 0.0908710i | 0.419235 | − | 0.907878i | \(-0.362298\pi\) |
−0.576628 | + | 0.817007i | \(0.695632\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5.55513 | − | 3.20725i | 0.363928 | − | 0.210114i | −0.306874 | − | 0.951750i | \(-0.599283\pi\) |
0.670803 | + | 0.741636i | \(0.265950\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −2.45079 | + | 4.24489i | −0.159872 | + | 0.276906i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 11.4288 | − | 6.59844i | 0.739270 | − | 0.426818i | −0.0825337 | − | 0.996588i | \(-0.526301\pi\) |
0.821804 | + | 0.569770i | \(0.192968\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2.20722 | + | 1.27434i | −0.142180 | + | 0.0820874i | −0.569402 | − | 0.822059i | \(-0.692825\pi\) |
0.427223 | + | 0.904146i | \(0.359492\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.843615 | + | 4.82439i | 0.0538966 | + | 0.308219i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −0.290209 | + | 0.502657i | −0.0184656 | + | 0.0319833i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −18.7893 | −1.18597 | −0.592986 | − | 0.805213i | \(-0.702051\pi\) | ||||
−0.592986 | + | 0.805213i | \(0.702051\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.31670 | −0.0827804 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −7.19727 | + | 12.4660i | −0.448953 | + | 0.777610i | −0.998318 | − | 0.0579725i | \(-0.981536\pi\) |
0.549365 | + | 0.835583i | \(0.314870\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.42244 | − | 1.19529i | −0.0883863 | − | 0.0742718i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.79810 | + | 3.92488i | −0.419189 | + | 0.242019i | −0.694730 | − | 0.719271i | \(-0.744476\pi\) |
0.275542 | + | 0.961289i | \(0.411143\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.96050 | − | 3.44130i | 0.366151 | − | 0.211397i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.72267 | − | 13.3760i | 0.470859 | − | 0.815552i | −0.528585 | − | 0.848880i | \(-0.677277\pi\) |
0.999444 | + | 0.0333281i | \(0.0106106\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.9476 | − | 6.32057i | 0.665016 | − | 0.383947i | −0.129169 | − | 0.991623i | \(-0.541231\pi\) |
0.794186 | + | 0.607675i | \(0.207898\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.03599 | − | 0.598128i | −0.0624724 | − | 0.0360685i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.94531 | + | 10.2976i | 0.357219 | + | 0.618722i | 0.987495 | − | 0.157649i | \(-0.0503915\pi\) |
−0.630276 | + | 0.776371i | \(0.717058\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.75411 | + | 1.59009i | 0.164297 | + | 0.0948568i | 0.579894 | − | 0.814692i | \(-0.303094\pi\) |
−0.415597 | + | 0.909549i | \(0.636427\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 18.4978i | − | 1.09958i | −0.835303 | − | 0.549789i | \(-0.814708\pi\) | ||
0.835303 | − | 0.549789i | \(-0.185292\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 21.8499 | + | 18.3606i | 1.28976 | + | 1.08379i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.55161 | + | 2.68746i | 0.0912711 | + | 0.158086i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.42975 | + | 2.47639i | 0.0835266 | + | 0.144672i | 0.904762 | − | 0.425917i | \(-0.140048\pi\) |
−0.821236 | + | 0.570589i | \(0.806715\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.70995 | + | 8.15788i | −0.274224 | + | 0.474970i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 6.52507 | 0.377355 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.44234 | − | 19.4419i | 0.198413 | − | 1.12061i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.42470 | − | 1.97725i | −0.196098 | − | 0.113217i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.6746i | 1.23704i | 0.785771 | + | 0.618518i | \(0.212266\pi\) | ||||
−0.785771 | + | 0.618518i | \(0.787734\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 23.6925 | 1.34348 | 0.671738 | − | 0.740789i | \(-0.265548\pi\) | ||||
0.671738 | + | 0.740789i | \(0.265548\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 27.2836i | − | 1.54216i | −0.636737 | − | 0.771081i | \(-0.719716\pi\) | ||
0.636737 | − | 0.771081i | \(-0.280284\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 24.5544i | 1.37911i | 0.724232 | + | 0.689556i | \(0.242194\pi\) | ||||
−0.724232 | + | 0.689556i | \(0.757806\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.0836929 | −0.00468590 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.64626i | 0.0916006i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 5.13396 | + | 2.96409i | 0.284781 | + | 0.164418i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 17.4220 | − | 6.32711i | 0.960507 | − | 0.348825i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.3116 | 0.896566 | 0.448283 | − | 0.893892i | \(-0.352036\pi\) | ||||
0.448283 | + | 0.893892i | \(0.352036\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2.07840 | − | 3.59989i | 0.113555 | − | 0.196683i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 13.6580 | + | 23.6563i | 0.743998 | + | 1.28864i | 0.950661 | + | 0.310230i | \(0.100406\pi\) |
−0.206663 | + | 0.978412i | \(0.566261\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.743445 | + | 1.28768i | 0.0402598 | + | 0.0697320i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 9.29424 | − | 16.0193i | 0.501842 | − | 0.864960i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 6.21213i | − | 0.333485i | −0.986001 | − | 0.166742i | \(-0.946675\pi\) | ||
0.986001 | − | 0.166742i | \(-0.0533248\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 24.6529 | + | 14.2334i | 1.31964 | + | 0.761896i | 0.983671 | − | 0.179977i | \(-0.0576023\pi\) |
0.335971 | + | 0.941872i | \(0.390936\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −1.49346 | − | 2.58674i | −0.0794887 | − | 0.137678i | 0.823541 | − | 0.567257i | \(-0.191995\pi\) |
−0.903029 | + | 0.429579i | \(0.858662\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.13889 | − | 4.69899i | −0.431968 | − | 0.249397i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 26.5977 | − | 15.3562i | 1.40377 | − | 0.810468i | 0.408994 | − | 0.912537i | \(-0.365880\pi\) |
0.994777 | + | 0.102070i | \(0.0325465\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.40249 | + | 16.2856i | −0.494868 | + | 0.857136i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.66098 | − | 2.69102i | 0.243967 | − | 0.140854i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 16.4877 | − | 9.51918i | 0.860651 | − | 0.496897i | −0.00357920 | − | 0.999994i | \(-0.501139\pi\) |
0.864230 | + | 0.503096i | \(0.167806\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −25.6280 | − | 4.53764i | −1.33054 | − | 0.235583i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.05869 | + | 3.56576i | −0.106595 | + | 0.184628i | −0.914389 | − | 0.404837i | \(-0.867328\pi\) |
0.807794 | + | 0.589465i | \(0.200661\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.414750 | 0.0213607 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −11.2436 | −0.577546 | −0.288773 | − | 0.957398i | \(-0.593247\pi\) | ||||
−0.288773 | + | 0.957398i | \(0.593247\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −15.8046 | + | 27.3745i | −0.807580 | + | 1.39877i | 0.106956 | + | 0.994264i | \(0.465890\pi\) |
−0.914536 | + | 0.404505i | \(0.867444\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.167586 | − | 0.461458i | −0.00854100 | − | 0.0235181i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −18.4018 | + | 10.6243i | −0.933007 | + | 0.538672i | −0.887761 | − | 0.460304i | \(-0.847740\pi\) |
−0.0452458 | + | 0.998976i | \(0.514407\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 16.0278 | − | 9.25367i | 0.810562 | − | 0.467978i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.488611 | + | 0.846300i | −0.0245847 | + | 0.0425820i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.6927 | − | 11.9469i | 1.03854 | − | 0.599599i | 0.119118 | − | 0.992880i | \(-0.461993\pi\) |
0.919419 | + | 0.393281i | \(0.128660\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −22.0121 | − | 12.7087i | −1.09923 | − | 0.634642i | −0.163213 | − | 0.986591i | \(-0.552186\pi\) |
−0.936019 | + | 0.351948i | \(0.885519\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.68423 | − | 6.38127i | −0.183524 | − | 0.317874i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 0.161295 | + | 0.0931240i | 0.00799512 | + | 0.00461598i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 22.3817i | − | 1.10670i | −0.832948 | − | 0.553351i | \(-0.813349\pi\) | ||
0.832948 | − | 0.553351i | \(-0.186651\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 33.4818 | − | 12.1595i | 1.64753 | − | 0.598330i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2.60551 | + | 4.51288i | 0.127900 | + | 0.221528i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.04181 | − | 12.1968i | −0.344015 | − | 0.595851i | 0.641159 | − | 0.767408i | \(-0.278454\pi\) |
−0.985174 | + | 0.171556i | \(0.945120\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 8.07639 | − | 13.9887i | 0.393619 | − | 0.681768i | −0.599305 | − | 0.800521i | \(-0.704556\pi\) |
0.992924 | + | 0.118753i | \(0.0378896\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 16.8143 | 0.815616 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.10459 | + | 14.0558i | 0.247029 | + | 0.680206i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.16179 | + | 4.13486i | 0.344971 | + | 0.199169i | 0.662468 | − | 0.749090i | \(-0.269509\pi\) |
−0.317497 | + | 0.948259i | \(0.602842\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 4.35102i | − | 0.209097i | −0.994520 | − | 0.104548i | \(-0.966660\pi\) | ||
0.994520 | − | 0.104548i | \(-0.0333397\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.19245 | −0.104879 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 20.8077i | 0.993098i | 0.868009 | + | 0.496549i | \(0.165400\pi\) | ||||
−0.868009 | + | 0.496549i | \(0.834600\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 30.9376i | 1.46989i | 0.678127 | + | 0.734945i | \(0.262792\pi\) | ||||
−0.678127 | + | 0.734945i | \(0.737208\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.82580 | 0.370978 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 20.9215i | − | 0.987346i | −0.869648 | − | 0.493673i | \(-0.835654\pi\) | ||
0.869648 | − | 0.493673i | \(-0.164346\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −2.47763 | − | 1.43046i | −0.116667 | − | 0.0673577i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.830494 | + | 2.28681i | 0.0389342 | + | 0.107207i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.30115 | 0.107643 | 0.0538217 | − | 0.998551i | \(-0.482860\pi\) | ||||
0.0538217 | + | 0.998551i | \(0.482860\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −8.92497 | + | 15.4585i | −0.415677 | + | 0.719974i | −0.995499 | − | 0.0947688i | \(-0.969789\pi\) |
0.579822 | + | 0.814743i | \(0.303122\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −6.24034 | − | 10.8086i | −0.290013 | − | 0.502318i | 0.683799 | − | 0.729670i | \(-0.260326\pi\) |
−0.973813 | + | 0.227353i | \(0.926993\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 2.42799 | + | 4.20541i | 0.112354 | + | 0.194603i | 0.916719 | − | 0.399533i | \(-0.130828\pi\) |
−0.804365 | + | 0.594136i | \(0.797494\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −14.7748 | + | 5.36571i | −0.682236 | + | 0.247766i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.97921i | 0.0910044i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.72503 | − | 0.995945i | −0.0791497 | − | 0.0456971i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −4.40542 | − | 7.63041i | −0.201289 | − | 0.348642i | 0.747655 | − | 0.664087i | \(-0.231180\pi\) |
−0.948944 | + | 0.315445i | \(0.897846\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −0.799318 | − | 0.461486i | −0.0364458 | − | 0.0210420i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.42441 | − | 3.70914i | 0.291718 | − | 0.168423i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.66185 | − | 8.07456i | 0.211249 | − | 0.365893i | −0.740857 | − | 0.671663i | \(-0.765580\pi\) |
0.952106 | + | 0.305770i | \(0.0989137\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 26.9192 | − | 15.5418i | 1.21485 | − | 0.701391i | 0.251034 | − | 0.967978i | \(-0.419229\pi\) |
0.963811 | + | 0.266587i | \(0.0858960\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.01877 | − | 0.588186i | 0.0458830 | − | 0.0264906i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 12.1312 | + | 33.4039i | 0.544159 | + | 1.49837i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 11.1694 | − | 19.3459i | 0.500010 | − | 0.866043i | −0.499990 | − | 0.866031i | \(-0.666663\pi\) |
1.00000 | 1.16519e-5i | \(-3.70891e-6\pi\) | ||||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 12.2396 | 0.545738 | 0.272869 | − | 0.962051i | \(-0.412027\pi\) | ||||
0.272869 | + | 0.962051i | \(0.412027\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 12.2490 | 0.545072 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 7.05496 | − | 12.2195i | 0.312706 | − | 0.541622i | −0.666242 | − | 0.745736i | \(-0.732098\pi\) |
0.978947 | + | 0.204114i | \(0.0654314\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20.0405 | − | 3.54834i | −0.886539 | − | 0.156969i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −5.17588 | + | 2.98830i | −0.228077 | + | 0.131680i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.60910 | + | 0.929015i | −0.0707682 | + | 0.0408580i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2.81632 | + | 4.87800i | −0.123385 | + | 0.213709i | −0.921101 | − | 0.389325i | \(-0.872708\pi\) |
0.797715 | + | 0.603034i | \(0.206042\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −33.2293 | + | 19.1849i | −1.45302 | + | 0.838899i | −0.998651 | − | 0.0519176i | \(-0.983467\pi\) |
−0.454364 | + | 0.890816i | \(0.650133\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.0995 | − | 10.4497i | −0.788425 | − | 0.455197i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 0.823769 | + | 1.42681i | 0.0358161 | + | 0.0620352i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.2782 | + | 7.08880i | 0.531826 | + | 0.307050i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 7.34769i | − | 0.317668i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −0.637441 | + | 1.74365i | −0.0274565 | + | 0.0751045i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.21673 | − | 5.57154i | −0.138298 | − | 0.239539i | 0.788555 | − | 0.614965i | \(-0.210830\pi\) |
−0.926852 | + | 0.375426i | \(0.877496\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −4.98232 | − | 8.62963i | −0.213419 | − | 0.369653i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −6.52889 | + | 11.3084i | −0.279155 | + | 0.483511i | −0.971175 | − | 0.238368i | \(-0.923388\pi\) |
0.692020 | + | 0.721878i | \(0.256721\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −0.139357 | −0.00593683 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.47341 | − | 1.26143i | 0.147704 | − | 0.0536414i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 25.5409 | + | 14.7460i | 1.08220 | + | 0.624809i | 0.931489 | − | 0.363769i | \(-0.118510\pi\) |
0.150712 | + | 0.988578i | \(0.451843\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 9.80822i | − | 0.414844i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.5187 | 0.443310 | 0.221655 | − | 0.975125i | \(-0.428854\pi\) | ||||
0.221655 | + | 0.975125i | \(0.428854\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 10.8082i | − | 0.454706i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26.3334i | 1.10395i | 0.833859 | + | 0.551977i | \(0.186126\pi\) | ||||
−0.833859 | + | 0.551977i | \(0.813874\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −44.0590 | −1.84381 | −0.921906 | − | 0.387413i | \(-0.873369\pi\) | ||||
−0.921906 | + | 0.387413i | \(0.873369\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 22.3929i | 0.933847i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.1535 | + | 7.01684i | 0.505957 | + | 0.292115i | 0.731170 | − | 0.682195i | \(-0.238974\pi\) |
−0.225213 | + | 0.974310i | \(0.572308\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 3.43559 | − | 19.4037i | 0.142532 | − | 0.805001i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 2.60897 | 0.108052 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.52469 | + | 2.64085i | −0.0629308 | + | 0.108999i | −0.895774 | − | 0.444509i | \(-0.853378\pi\) |
0.832843 | + | 0.553509i | \(0.186711\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.23791 | + | 2.14413i | 0.0510073 | + | 0.0883473i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −13.3041 | − | 23.0434i | −0.546334 | − | 0.946278i | −0.998522 | − | 0.0543552i | \(-0.982690\pi\) |
0.452188 | − | 0.891923i | \(-0.350644\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.28306 | + | 4.43941i | 0.216585 | + | 0.181998i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 4.46099i | − | 0.182271i | −0.995838 | − | 0.0911356i | \(-0.970950\pi\) | ||
0.995838 | − | 0.0911356i | \(-0.0290497\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.25019 | + | 3.03120i | 0.214160 | + | 0.123645i | 0.603243 | − | 0.797557i | \(-0.293875\pi\) |
−0.389083 | + | 0.921203i | \(0.627208\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.82350 | − | 6.62250i | −0.155447 | − | 0.269243i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 39.2581 | + | 22.6657i | 1.59344 | + | 0.919971i | 0.992711 | + | 0.120516i | \(0.0384548\pi\) |
0.600725 | + | 0.799455i | \(0.294879\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 7.97409 | − | 4.60384i | 0.322597 | − | 0.186251i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 16.6294 | − | 28.8029i | 0.671654 | − | 1.16334i | −0.305781 | − | 0.952102i | \(-0.598917\pi\) |
0.977435 | − | 0.211237i | \(-0.0677492\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −31.3001 | + | 18.0711i | −1.26010 | + | 0.727516i | −0.973093 | − | 0.230414i | \(-0.925992\pi\) |
−0.287002 | + | 0.957930i | \(0.592659\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −22.9031 | + | 13.2231i | −0.920554 | + | 0.531482i | −0.883812 | − | 0.467843i | \(-0.845031\pi\) |
−0.0367423 | + | 0.999325i | \(0.511698\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −22.6563 | − | 19.0383i | −0.907705 | − | 0.762752i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −8.94843 | + | 15.4991i | −0.357937 | + | 0.619965i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.61787 | −0.104381 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −32.0484 | −1.27583 | −0.637914 | − | 0.770107i | \(-0.720203\pi\) | ||||
−0.637914 | + | 0.770107i | \(0.720203\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −7.63687 | + | 13.2274i | −0.303060 | + | 0.524915i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3.15891 | − | 8.64088i | 0.125161 | − | 0.342364i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21.1444 | − | 12.2077i | 0.835153 | − | 0.482176i | −0.0204610 | − | 0.999791i | \(-0.506513\pi\) |
0.855614 | + | 0.517615i | \(0.173180\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31.9014 | + | 18.4183i | −1.25807 | + | 0.726346i | −0.972699 | − | 0.232071i | \(-0.925450\pi\) |
−0.285370 | + | 0.958418i | \(0.592116\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −13.2847 | + | 23.0098i | −0.522276 | + | 0.904608i | 0.477389 | + | 0.878692i | \(0.341583\pi\) |
−0.999664 | + | 0.0259155i | \(0.991750\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.09239 | + | 1.78539i | −0.121387 | + | 0.0700827i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −26.2767 | − | 15.1709i | −1.02829 | − | 0.593683i | −0.111794 | − | 0.993731i | \(-0.535660\pi\) |
−0.916494 | + | 0.400049i | \(0.868993\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.82233 | − | 3.15637i | −0.0712044 | − | 0.123330i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −40.9873 | − | 23.6640i | −1.59664 | − | 0.921820i | −0.992129 | − | 0.125223i | \(-0.960035\pi\) |
−0.604511 | − | 0.796597i | \(-0.706631\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 35.1245i | 1.36618i | 0.730332 | + | 0.683092i | \(0.239365\pi\) | ||||
−0.730332 | + | 0.683092i | \(0.760635\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −0.279049 | − | 0.768376i | −0.0108211 | − | 0.0297963i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 0.783329 | + | 1.35677i | 0.0303306 | + | 0.0525342i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −0.749513 | − | 1.29819i | −0.0289346 | − | 0.0501162i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.54758 | + | 4.41254i | −0.0982020 | + | 0.170091i | −0.910940 | − | 0.412538i | \(-0.864642\pi\) |
0.812738 | + | 0.582629i | \(0.197976\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 16.8414 | 0.647269 | 0.323635 | − | 0.946182i | \(-0.395095\pi\) | ||||
0.323635 | + | 0.946182i | \(0.395095\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −27.6226 | − | 4.89081i | −1.06006 | − | 0.187692i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −15.7555 | − | 9.09645i | −0.602868 | − | 0.348066i | 0.167301 | − | 0.985906i | \(-0.446495\pi\) |
−0.770169 | + | 0.637840i | \(0.779828\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.88715i | 0.0721042i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −12.9290 | −0.492557 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.52652i | 0.134155i | 0.997748 | + | 0.0670775i | \(0.0213675\pi\) | ||||
−0.997748 | + | 0.0670775i | \(0.978633\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 8.19591i | − | 0.310888i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 40.2125 | 1.52316 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.3502i | 0.504229i | 0.967697 | + | 0.252114i | \(0.0811259\pi\) | ||||
−0.967697 | + | 0.252114i | \(0.918874\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 0.268574 | + | 0.155061i | 0.0101295 | + | 0.00584824i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −35.4617 | − | 29.7988i | −1.33368 | − | 1.12070i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −42.2894 | −1.58821 | −0.794107 | − | 0.607779i | \(-0.792061\pi\) | ||||
−0.794107 | + | 0.607779i | \(0.792061\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.9166 | − | 24.1043i | 0.521182 | − | 0.902715i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.121942 | − | 0.211210i | −0.00456038 | − | 0.00789881i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −15.2035 | − | 26.3332i | −0.566994 | − | 0.982062i | −0.996861 | − | 0.0791697i | \(-0.974773\pi\) |
0.429868 | − | 0.902892i | \(-0.358560\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 22.2544 | + | 3.94032i | 0.828796 | + | 0.146745i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 1.42335i | 0.0528617i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −11.3671 | − | 6.56280i | −0.421583 | − | 0.243401i | 0.274171 | − | 0.961681i | \(-0.411596\pi\) |
−0.695754 | + | 0.718280i | \(0.744930\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −13.9097 | − | 24.0924i | −0.514470 | − | 0.891089i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −32.7001 | − | 18.8794i | −1.20781 | − | 0.697327i | −0.245527 | − | 0.969390i | \(-0.578961\pi\) |
−0.962280 | + | 0.272063i | \(0.912294\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.36460 | − | 0.787853i | 0.0502657 | − | 0.0290209i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −13.1215 | + | 22.7271i | −0.482683 | + | 0.836031i | −0.999802 | − | 0.0198820i | \(-0.993671\pi\) |
0.517119 | + | 0.855913i | \(0.327004\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 8.78379 | − | 5.07132i | 0.322246 | − | 0.186049i | −0.330147 | − | 0.943929i | \(-0.607098\pi\) |
0.652393 | + | 0.757881i | \(0.273765\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 11.4082 | − | 6.58655i | 0.417966 | − | 0.241313i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −17.8752 | + | 21.2721i | −0.653144 | + | 0.777267i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.95369 | + | 6.84798i | −0.144272 | + | 0.249886i | −0.929101 | − | 0.369826i | \(-0.879417\pi\) |
0.784829 | + | 0.619712i | \(0.212751\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6.99855 | 0.254703 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.8903 | 1.08638 | 0.543191 | − | 0.839609i | \(-0.317216\pi\) | ||||
0.543191 | + | 0.839609i | \(0.317216\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.05687 | − | 5.29465i | 0.110811 | − | 0.191931i | −0.805286 | − | 0.592886i | \(-0.797988\pi\) |
0.916098 | + | 0.400955i | \(0.131322\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.56961 | + | 37.1042i | −0.237836 | + | 1.34326i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 15.3247 | − | 8.84771i | 0.553342 | − | 0.319472i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −9.79863 | + | 5.65724i | −0.353348 | + | 0.204005i | −0.666159 | − | 0.745810i | \(-0.732063\pi\) |
0.312811 | + | 0.949815i | \(0.398729\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −19.2106 | + | 33.2737i | −0.690956 | + | 1.19677i | 0.280569 | + | 0.959834i | \(0.409477\pi\) |
−0.971525 | + | 0.236937i | \(0.923856\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.8994 | − | 12.6436i | 0.786648 | − | 0.454172i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −4.12551 | − | 2.38186i | −0.147812 | − | 0.0853391i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.78124 | − | 3.08519i | −0.0637376 | − | 0.110397i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.152730 | + | 0.0881788i | 0.00545117 | + | 0.00314723i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 47.6600i | 1.69889i | 0.527674 | + | 0.849447i | \(0.323064\pi\) | ||||
−0.527674 | + | 0.849447i | \(0.676936\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −26.2938 | + | 31.2906i | −0.934900 | + | 1.11257i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.71430 | + | 6.43335i | 0.131898 | + | 0.228455i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15.1359 | + | 26.2161i | 0.536139 | + | 0.928621i | 0.999107 | + | 0.0422457i | \(0.0134512\pi\) |
−0.462968 | + | 0.886375i | \(0.653215\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 13.0581 | − | 22.6172i | 0.461961 | − | 0.800140i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 2.04016 | 0.0719955 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.91227 | + | 7.03583i | −0.208380 | + | 0.247981i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.219373 | − | 0.126655i | −0.00771273 | − | 0.00445295i | 0.496139 | − | 0.868243i | \(-0.334751\pi\) |
−0.503851 | + | 0.863790i | \(0.668084\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 22.0629i | − | 0.774735i | −0.921925 | − | 0.387367i | \(-0.873385\pi\) | ||
0.921925 | − | 0.387367i | \(-0.126615\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.01395 | −0.210660 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.29560i | 0.115298i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 27.9976i | − | 0.977124i | −0.872529 | − | 0.488562i | \(-0.837522\pi\) | ||
0.872529 | − | 0.488562i | \(-0.162478\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 48.9542 | 1.70643 | 0.853217 | − | 0.521556i | \(-0.174648\pi\) | ||||
0.853217 | + | 0.521556i | \(0.174648\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 0.641658i | − | 0.0223126i | −0.999938 | − | 0.0111563i | \(-0.996449\pi\) | ||
0.999938 | − | 0.0111563i | \(-0.00355124\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.57180 | + | 5.52628i | 0.332442 | + | 0.191936i | 0.656925 | − | 0.753956i | \(-0.271857\pi\) |
−0.324483 | + | 0.945892i | \(0.605190\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −4.49487 | − | 25.7048i | −0.155738 | − | 0.890620i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.14057 | 0.108684 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.62330 | − | 8.00780i | 0.159614 | − | 0.276460i | −0.775115 | − | 0.631820i | \(-0.782308\pi\) |
0.934730 | + | 0.355360i | \(0.115642\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −14.4502 | − | 25.0285i | −0.498283 | − | 0.863052i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −3.94346 | − | 6.83028i | −0.135659 | − | 0.234969i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −5.04161 | + | 28.4743i | −0.173232 | + | 0.978388i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 3.48640i | − | 0.119512i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −34.3256 | − | 19.8179i | −1.17529 | − | 0.678551i | −0.220366 | − | 0.975417i | \(-0.570725\pi\) |
−0.954919 | + | 0.296866i | \(0.904059\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 11.9260 | + | 20.6565i | 0.407385 | + | 0.705612i | 0.994596 | − | 0.103822i | \(-0.0331074\pi\) |
−0.587211 | + | 0.809434i | \(0.699774\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −9.62480 | − | 5.55688i | −0.328394 | − | 0.189598i | 0.326734 | − | 0.945116i | \(-0.394052\pi\) |
−0.655128 | + | 0.755518i | \(0.727385\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 38.7780 | − | 22.3885i | 1.32002 | − | 0.762113i | 0.336287 | − | 0.941759i | \(-0.390829\pi\) |
0.983731 | + | 0.179646i | \(0.0574954\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.49128 | + | 4.31503i | −0.0847061 | + | 0.146715i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.320805 | + | 0.185217i | −0.0108826 | + | 0.00628305i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −6.76244 | + | 3.90429i | −0.229136 | + | 0.132292i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −16.5476 | + | 6.00953i | −0.559409 | + | 0.203159i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.84096 | + | 3.18863i | −0.0621647 | + | 0.107672i | −0.895433 | − | 0.445197i | \(-0.853134\pi\) |
0.833268 | + | 0.552869i | \(0.186467\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −17.3992 | −0.586194 | −0.293097 | − | 0.956083i | \(-0.594686\pi\) | ||||
−0.293097 | + | 0.956083i | \(0.594686\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.02834 | −0.0682592 | −0.0341296 | − | 0.999417i | \(-0.510866\pi\) | ||||
−0.0341296 | + | 0.999417i | \(0.510866\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −23.1890 | + | 40.1645i | −0.778610 | + | 1.34859i | 0.154132 | + | 0.988050i | \(0.450742\pi\) |
−0.932743 | + | 0.360542i | \(0.882592\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 54.2885 | − | 19.7158i | 1.82078 | − | 0.661247i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.67932 | + | 1.54691i | −0.0896601 | + | 0.0517653i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 15.4812 | − | 8.93810i | 0.517481 | − | 0.298768i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.884576 | − | 1.53213i | 0.0295023 | − | 0.0510994i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −31.7582 | + | 18.3356i | −1.05802 | + | 0.610847i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0.571488 | + | 0.329949i | 0.0189969 | + | 0.0109679i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.01957 | − | 13.8903i | −0.266285 | − | 0.461220i | 0.701614 | − | 0.712557i | \(-0.252463\pi\) |
−0.967900 | + | 0.251337i | \(0.919130\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −17.7833 | − | 10.2672i | −0.589187 | − | 0.340167i | 0.175589 | − | 0.984464i | \(-0.443817\pi\) |
−0.764776 | + | 0.644296i | \(0.777150\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.97533i | 0.0653739i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.40290 | + | 13.5712i | −0.0793507 | + | 0.448161i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −17.7069 | − | 30.6693i | −0.584097 | − | 1.01169i | −0.994987 | − | 0.100001i | \(-0.968115\pi\) |
0.410890 | − | 0.911685i | \(-0.365218\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.82712 | + | 15.2890i | 0.290548 | + | 0.503244i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.58374 | − | 2.74311i | 0.0520730 | − | 0.0901930i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 39.7251 | 1.30334 | 0.651670 | − | 0.758503i | \(-0.274069\pi\) | ||||
0.651670 | + | 0.758503i | \(0.274069\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.06141 | + | 2.90337i | −0.0347861 | + | 0.0951540i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −0.599064 | − | 0.345870i | −0.0195915 | − | 0.0113112i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 23.2142i | − | 0.758376i | −0.925320 | − | 0.379188i | \(-0.876203\pi\) | ||
0.925320 | − | 0.379188i | \(-0.123797\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 35.9232 | 1.17106 | 0.585531 | − | 0.810650i | \(-0.300886\pi\) | ||||
0.585531 | + | 0.810650i | \(0.300886\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 53.5539i | 1.74395i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 30.8726i | 1.00322i | 0.865093 | + | 0.501612i | \(0.167260\pi\) | ||||
−0.865093 | + | 0.501612i | \(0.832740\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10.1102 | −0.328192 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 30.4640i | − | 0.986826i | −0.869795 | − | 0.493413i | \(-0.835749\pi\) | ||
0.869795 | − | 0.493413i | \(-0.164251\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.80100 | − | 1.03981i | −0.0582791 | − | 0.0336475i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.59098 | − | 5.46344i | 0.148250 | − | 0.176424i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −0.430813 | −0.0138972 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 6.47686 | − | 11.2182i | 0.208497 | − | 0.361128i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −6.75865 | − | 11.7063i | −0.217343 | − | 0.376450i | 0.736652 | − | 0.676272i | \(-0.236406\pi\) |
−0.953995 | + | 0.299823i | \(0.903072\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −16.6428 | − | 28.8261i | −0.534092 | − | 0.925074i | −0.999207 | − | 0.0398238i | \(-0.987320\pi\) |
0.465115 | − | 0.885250i | \(-0.346013\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −19.9387 | + | 23.7278i | −0.639204 | + | 0.760677i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 44.9325i | 1.43752i | 0.695260 | + | 0.718758i | \(0.255289\pi\) | ||||
−0.695260 | + | 0.718758i | \(0.744711\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.56907 | + | 1.48325i | 0.0821079 | + | 0.0474050i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 13.4474 | + | 23.2916i | 0.428907 | + | 0.742888i | 0.996776 | − | 0.0802305i | \(-0.0255656\pi\) |
−0.567870 | + | 0.823118i | \(0.692232\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.59035 | − | 4.95964i | −0.273711 | − | 0.158027i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 32.0855 | − | 18.5246i | 1.02026 | − | 0.589048i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17.7201 | − | 30.6920i | 0.562896 | − | 0.974965i | −0.434346 | − | 0.900746i | \(-0.643020\pi\) |
0.997242 | − | 0.0742186i | \(-0.0236463\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 14.3635 | − | 8.29275i | 0.455352 | − | 0.262898i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −28.1418 | + | 16.2477i | −0.891259 | + | 0.514568i | −0.874354 | − | 0.485289i | \(-0.838714\pi\) |
−0.0169046 | + | 0.999857i | \(0.505381\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))