Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [867,2,Mod(577,867)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(867, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("867.577");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 867 = 3 \cdot 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 867.d (of order \(2\), degree \(1\), 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: | \(6.92302985525\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{17})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 51) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 577.2 | ||
Root | \(1.56155i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 867.577 |
Dual form | 867.2.d.c.577.1 |
$q$-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 \(\left(\mathbb{Z}/867\mathbb{Z}\right)^\times\).
\(n\) | \(290\) | \(292\) |
\(\chi(n)\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.56155 | −1.10418 | −0.552092 | − | 0.833783i | \(-0.686170\pi\) | ||||
−0.552092 | + | 0.833783i | \(0.686170\pi\) | |||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0.438447 | 0.219224 | ||||||||
\(5\) | 0.561553i | 0.251134i | 0.992085 | + | 0.125567i | \(0.0400750\pi\) | ||||
−0.992085 | + | 0.125567i | \(0.959925\pi\) | |||||||
\(6\) | − 1.56155i | − 0.637501i | ||||||||
\(7\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(8\) | 2.43845 | 0.862121 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | − 0.876894i | − 0.277298i | ||||||||
\(11\) | − 2.56155i | − 0.772337i | −0.922428 | − | 0.386169i | \(-0.873798\pi\) | ||||
0.922428 | − | 0.386169i | \(-0.126202\pi\) | |||||||
\(12\) | 0.438447i | 0.126569i | ||||||||
\(13\) | 4.56155 | 1.26515 | 0.632574 | − | 0.774500i | \(-0.281999\pi\) | ||||
0.632574 | + | 0.774500i | \(0.281999\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.561553 | −0.144992 | ||||||||
\(16\) | −4.68466 | −1.17116 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | 1.56155 | 0.368062 | ||||||||
\(19\) | −7.68466 | −1.76298 | −0.881491 | − | 0.472201i | \(-0.843460\pi\) | ||||
−0.881491 | + | 0.472201i | \(0.843460\pi\) | |||||||
\(20\) | 0.246211i | 0.0550545i | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.00000i | 0.852803i | ||||||||
\(23\) | − 6.56155i | − 1.36818i | −0.729398 | − | 0.684089i | \(-0.760200\pi\) | ||||
0.729398 | − | 0.684089i | \(-0.239800\pi\) | |||||||
\(24\) | 2.43845i | 0.497746i | ||||||||
\(25\) | 4.68466 | 0.936932 | ||||||||
\(26\) | −7.12311 | −1.39696 | ||||||||
\(27\) | − 1.00000i | − 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 8.24621i | − 1.53128i | −0.643268 | − | 0.765641i | \(-0.722422\pi\) | ||||
0.643268 | − | 0.765641i | \(-0.277578\pi\) | |||||||
\(30\) | 0.876894 | 0.160098 | ||||||||
\(31\) | 5.12311i | 0.920137i | 0.887883 | + | 0.460068i | \(0.152175\pi\) | ||||
−0.887883 | + | 0.460068i | \(0.847825\pi\) | |||||||
\(32\) | 2.43845 | 0.431061 | ||||||||
\(33\) | 2.56155 | 0.445909 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.438447 | −0.0730745 | ||||||||
\(37\) | − 3.12311i | − 0.513435i | −0.966486 | − | 0.256718i | \(-0.917359\pi\) | ||||
0.966486 | − | 0.256718i | \(-0.0826411\pi\) | |||||||
\(38\) | 12.0000 | 1.94666 | ||||||||
\(39\) | 4.56155i | 0.730433i | ||||||||
\(40\) | 1.36932i | 0.216508i | ||||||||
\(41\) | 0.561553i | 0.0876998i | 0.999038 | + | 0.0438499i | \(0.0139623\pi\) | ||||
−0.999038 | + | 0.0438499i | \(0.986038\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 7.68466 | 1.17190 | 0.585950 | − | 0.810347i | \(-0.300722\pi\) | ||||
0.585950 | + | 0.810347i | \(0.300722\pi\) | |||||||
\(44\) | − 1.12311i | − 0.169315i | ||||||||
\(45\) | − 0.561553i | − 0.0837114i | ||||||||
\(46\) | 10.2462i | 1.51072i | ||||||||
\(47\) | −2.87689 | −0.419638 | −0.209819 | − | 0.977740i | \(-0.567288\pi\) | ||||
−0.209819 | + | 0.977740i | \(0.567288\pi\) | |||||||
\(48\) | − 4.68466i | − 0.676172i | ||||||||
\(49\) | 7.00000 | 1.00000 | ||||||||
\(50\) | −7.31534 | −1.03455 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.00000 | 0.277350 | ||||||||
\(53\) | 4.24621 | 0.583262 | 0.291631 | − | 0.956531i | \(-0.405802\pi\) | ||||
0.291631 | + | 0.956531i | \(0.405802\pi\) | |||||||
\(54\) | 1.56155i | 0.212500i | ||||||||
\(55\) | 1.43845 | 0.193960 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − 7.68466i | − 1.01786i | ||||||||
\(58\) | 12.8769i | 1.69082i | ||||||||
\(59\) | 1.12311 | 0.146216 | 0.0731079 | − | 0.997324i | \(-0.476708\pi\) | ||||
0.0731079 | + | 0.997324i | \(0.476708\pi\) | |||||||
\(60\) | −0.246211 | −0.0317857 | ||||||||
\(61\) | 0.876894i | 0.112275i | 0.998423 | + | 0.0561374i | \(0.0178785\pi\) | ||||
−0.998423 | + | 0.0561374i | \(0.982122\pi\) | |||||||
\(62\) | − 8.00000i | − 1.01600i | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 5.56155 | 0.695194 | ||||||||
\(65\) | 2.56155i | 0.317722i | ||||||||
\(66\) | −4.00000 | −0.492366 | ||||||||
\(67\) | 4.00000 | 0.488678 | 0.244339 | − | 0.969690i | \(-0.421429\pi\) | ||||
0.244339 | + | 0.969690i | \(0.421429\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 6.56155 | 0.789918 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 10.2462i | − 1.21600i | −0.793936 | − | 0.608001i | \(-0.791972\pi\) | ||||
0.793936 | − | 0.608001i | \(-0.208028\pi\) | |||||||
\(72\) | −2.43845 | −0.287374 | ||||||||
\(73\) | − 4.24621i | − 0.496981i | −0.968634 | − | 0.248491i | \(-0.920065\pi\) | ||||
0.968634 | − | 0.248491i | \(-0.0799345\pi\) | |||||||
\(74\) | 4.87689i | 0.566927i | ||||||||
\(75\) | 4.68466i | 0.540938i | ||||||||
\(76\) | −3.36932 | −0.386487 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | − 7.12311i | − 0.806533i | ||||||||
\(79\) | 15.3693i | 1.72918i | 0.502475 | + | 0.864592i | \(0.332423\pi\) | ||||
−0.502475 | + | 0.864592i | \(0.667577\pi\) | |||||||
\(80\) | − 2.63068i | − 0.294119i | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | − 0.876894i | − 0.0968368i | ||||||||
\(83\) | 9.12311 | 1.00139 | 0.500695 | − | 0.865624i | \(-0.333078\pi\) | ||||
0.500695 | + | 0.865624i | \(0.333078\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −12.0000 | −1.29399 | ||||||||
\(87\) | 8.24621 | 0.884087 | ||||||||
\(88\) | − 6.24621i | − 0.665848i | ||||||||
\(89\) | 7.12311 | 0.755048 | 0.377524 | − | 0.926000i | \(-0.376776\pi\) | ||||
0.377524 | + | 0.926000i | \(0.376776\pi\) | |||||||
\(90\) | 0.876894i | 0.0924328i | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − 2.87689i | − 0.299937i | ||||||||
\(93\) | −5.12311 | −0.531241 | ||||||||
\(94\) | 4.49242 | 0.463358 | ||||||||
\(95\) | − 4.31534i | − 0.442745i | ||||||||
\(96\) | 2.43845i | 0.248873i | ||||||||
\(97\) | 11.1231i | 1.12938i | 0.825303 | + | 0.564690i | \(0.191004\pi\) | ||||
−0.825303 | + | 0.564690i | \(0.808996\pi\) | |||||||
\(98\) | −10.9309 | −1.10418 | ||||||||
\(99\) | 2.56155i | 0.257446i | ||||||||
\(100\) | 2.05398 | 0.205398 | ||||||||
\(101\) | 19.1231 | 1.90282 | 0.951410 | − | 0.307927i | \(-0.0996352\pi\) | ||||
0.951410 | + | 0.307927i | \(0.0996352\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 4.31534 | 0.425203 | 0.212602 | − | 0.977139i | \(-0.431806\pi\) | ||||
0.212602 | + | 0.977139i | \(0.431806\pi\) | |||||||
\(104\) | 11.1231 | 1.09071 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −6.63068 | −0.644029 | ||||||||
\(107\) | − 7.68466i | − 0.742904i | −0.928452 | − | 0.371452i | \(-0.878860\pi\) | ||||
0.928452 | − | 0.371452i | \(-0.121140\pi\) | |||||||
\(108\) | − 0.438447i | − 0.0421896i | ||||||||
\(109\) | − 15.1231i | − 1.44853i | −0.689521 | − | 0.724265i | \(-0.742179\pi\) | ||||
0.689521 | − | 0.724265i | \(-0.257821\pi\) | |||||||
\(110\) | −2.24621 | −0.214168 | ||||||||
\(111\) | 3.12311 | 0.296432 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − 4.56155i | − 0.429115i | −0.976711 | − | 0.214557i | \(-0.931169\pi\) | ||||
0.976711 | − | 0.214557i | \(-0.0688309\pi\) | |||||||
\(114\) | 12.0000i | 1.12390i | ||||||||
\(115\) | 3.68466 | 0.343596 | ||||||||
\(116\) | − 3.61553i | − 0.335693i | ||||||||
\(117\) | −4.56155 | −0.421716 | ||||||||
\(118\) | −1.75379 | −0.161449 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −1.36932 | −0.125001 | ||||||||
\(121\) | 4.43845 | 0.403495 | ||||||||
\(122\) | − 1.36932i | − 0.123972i | ||||||||
\(123\) | −0.561553 | −0.0506335 | ||||||||
\(124\) | 2.24621i | 0.201716i | ||||||||
\(125\) | 5.43845i | 0.486430i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.807764 | 0.0716775 | 0.0358387 | − | 0.999358i | \(-0.488590\pi\) | ||||
0.0358387 | + | 0.999358i | \(0.488590\pi\) | |||||||
\(128\) | −13.5616 | −1.19868 | ||||||||
\(129\) | 7.68466i | 0.676596i | ||||||||
\(130\) | − 4.00000i | − 0.350823i | ||||||||
\(131\) | − 18.5616i | − 1.62173i | −0.585233 | − | 0.810865i | \(-0.698997\pi\) | ||||
0.585233 | − | 0.810865i | \(-0.301003\pi\) | |||||||
\(132\) | 1.12311 | 0.0977538 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −6.24621 | −0.539590 | ||||||||
\(135\) | 0.561553 | 0.0483308 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.2462 | −1.38801 | −0.694004 | − | 0.719971i | \(-0.744155\pi\) | ||||
−0.694004 | + | 0.719971i | \(0.744155\pi\) | |||||||
\(138\) | −10.2462 | −0.872215 | ||||||||
\(139\) | 9.12311i | 0.773812i | 0.922119 | + | 0.386906i | \(0.126456\pi\) | ||||
−0.922119 | + | 0.386906i | \(0.873544\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 2.87689i | − 0.242278i | ||||||||
\(142\) | 16.0000i | 1.34269i | ||||||||
\(143\) | − 11.6847i | − 0.977120i | ||||||||
\(144\) | 4.68466 | 0.390388 | ||||||||
\(145\) | 4.63068 | 0.384557 | ||||||||
\(146\) | 6.63068i | 0.548759i | ||||||||
\(147\) | 7.00000i | 0.577350i | ||||||||
\(148\) | − 1.36932i | − 0.112557i | ||||||||
\(149\) | −4.24621 | −0.347863 | −0.173932 | − | 0.984758i | \(-0.555647\pi\) | ||||
−0.173932 | + | 0.984758i | \(0.555647\pi\) | |||||||
\(150\) | − 7.31534i | − 0.597295i | ||||||||
\(151\) | −8.00000 | −0.651031 | −0.325515 | − | 0.945537i | \(-0.605538\pi\) | ||||
−0.325515 | + | 0.945537i | \(0.605538\pi\) | |||||||
\(152\) | −18.7386 | −1.51990 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2.87689 | −0.231078 | ||||||||
\(156\) | 2.00000i | 0.160128i | ||||||||
\(157\) | −5.68466 | −0.453685 | −0.226843 | − | 0.973931i | \(-0.572840\pi\) | ||||
−0.226843 | + | 0.973931i | \(0.572840\pi\) | |||||||
\(158\) | − 24.0000i | − 1.90934i | ||||||||
\(159\) | 4.24621i | 0.336746i | ||||||||
\(160\) | 1.36932i | 0.108254i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.56155 | −0.122687 | ||||||||
\(163\) | − 6.87689i | − 0.538640i | −0.963051 | − | 0.269320i | \(-0.913201\pi\) | ||||
0.963051 | − | 0.269320i | \(-0.0867989\pi\) | |||||||
\(164\) | 0.246211i | 0.0192259i | ||||||||
\(165\) | 1.43845i | 0.111983i | ||||||||
\(166\) | −14.2462 | −1.10572 | ||||||||
\(167\) | 0.807764i | 0.0625067i | 0.999511 | + | 0.0312533i | \(0.00994986\pi\) | ||||
−0.999511 | + | 0.0312533i | \(0.990050\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.80776 | 0.600597 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 7.68466 | 0.587661 | ||||||||
\(172\) | 3.36932 | 0.256908 | ||||||||
\(173\) | 18.8078i | 1.42993i | 0.699161 | + | 0.714964i | \(0.253557\pi\) | ||||
−0.699161 | + | 0.714964i | \(0.746443\pi\) | |||||||
\(174\) | −12.8769 | −0.976195 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 12.0000i | 0.904534i | ||||||||
\(177\) | 1.12311i | 0.0844178i | ||||||||
\(178\) | −11.1231 | −0.833712 | ||||||||
\(179\) | 9.12311 | 0.681893 | 0.340946 | − | 0.940083i | \(-0.389253\pi\) | ||||
0.340946 | + | 0.940083i | \(0.389253\pi\) | |||||||
\(180\) | − 0.246211i | − 0.0183515i | ||||||||
\(181\) | 6.00000i | 0.445976i | 0.974821 | + | 0.222988i | \(0.0715812\pi\) | ||||
−0.974821 | + | 0.222988i | \(0.928419\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −0.876894 | −0.0648219 | ||||||||
\(184\) | − 16.0000i | − 1.17954i | ||||||||
\(185\) | 1.75379 | 0.128941 | ||||||||
\(186\) | 8.00000 | 0.586588 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −1.26137 | −0.0919946 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 6.73863i | 0.488872i | ||||||||
\(191\) | −13.1231 | −0.949555 | −0.474777 | − | 0.880106i | \(-0.657471\pi\) | ||||
−0.474777 | + | 0.880106i | \(0.657471\pi\) | |||||||
\(192\) | 5.56155i | 0.401371i | ||||||||
\(193\) | − 24.2462i | − 1.74528i | −0.488364 | − | 0.872640i | \(-0.662406\pi\) | ||||
0.488364 | − | 0.872640i | \(-0.337594\pi\) | |||||||
\(194\) | − 17.3693i | − 1.24704i | ||||||||
\(195\) | −2.56155 | −0.183437 | ||||||||
\(196\) | 3.06913 | 0.219224 | ||||||||
\(197\) | 19.9309i | 1.42002i | 0.704194 | + | 0.710008i | \(0.251309\pi\) | ||||
−0.704194 | + | 0.710008i | \(0.748691\pi\) | |||||||
\(198\) | − 4.00000i | − 0.284268i | ||||||||
\(199\) | − 16.0000i | − 1.13421i | −0.823646 | − | 0.567105i | \(-0.808063\pi\) | ||||
0.823646 | − | 0.567105i | \(-0.191937\pi\) | |||||||
\(200\) | 11.4233 | 0.807749 | ||||||||
\(201\) | 4.00000i | 0.282138i | ||||||||
\(202\) | −29.8617 | −2.10106 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.315342 | −0.0220244 | ||||||||
\(206\) | −6.73863 | −0.469503 | ||||||||
\(207\) | 6.56155i | 0.456059i | ||||||||
\(208\) | −21.3693 | −1.48170 | ||||||||
\(209\) | 19.6847i | 1.36162i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 11.3693i | − 0.782696i | −0.920243 | − | 0.391348i | \(-0.872009\pi\) | ||||
0.920243 | − | 0.391348i | \(-0.127991\pi\) | |||||||
\(212\) | 1.86174 | 0.127865 | ||||||||
\(213\) | 10.2462 | 0.702059 | ||||||||
\(214\) | 12.0000i | 0.820303i | ||||||||
\(215\) | 4.31534i | 0.294304i | ||||||||
\(216\) | − 2.43845i | − 0.165915i | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 23.6155i | 1.59945i | ||||||||
\(219\) | 4.24621 | 0.286932 | ||||||||
\(220\) | 0.630683 | 0.0425206 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −4.87689 | −0.327316 | ||||||||
\(223\) | −13.9309 | −0.932880 | −0.466440 | − | 0.884553i | \(-0.654464\pi\) | ||||
−0.466440 | + | 0.884553i | \(0.654464\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −4.68466 | −0.312311 | ||||||||
\(226\) | 7.12311i | 0.473822i | ||||||||
\(227\) | 23.0540i | 1.53015i | 0.643944 | + | 0.765073i | \(0.277297\pi\) | ||||
−0.643944 | + | 0.765073i | \(0.722703\pi\) | |||||||
\(228\) | − 3.36932i | − 0.223138i | ||||||||
\(229\) | −6.00000 | −0.396491 | −0.198246 | − | 0.980152i | \(-0.563524\pi\) | ||||
−0.198246 | + | 0.980152i | \(0.563524\pi\) | |||||||
\(230\) | −5.75379 | −0.379394 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | − 20.1080i | − 1.32015i | ||||||||
\(233\) | − 0.561553i | − 0.0367885i | −0.999831 | − | 0.0183943i | \(-0.994145\pi\) | ||||
0.999831 | − | 0.0183943i | \(-0.00585541\pi\) | |||||||
\(234\) | 7.12311 | 0.465652 | ||||||||
\(235\) | − 1.61553i | − 0.105385i | ||||||||
\(236\) | 0.492423 | 0.0320540 | ||||||||
\(237\) | −15.3693 | −0.998344 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.2462 | 0.662772 | 0.331386 | − | 0.943495i | \(-0.392484\pi\) | ||||
0.331386 | + | 0.943495i | \(0.392484\pi\) | |||||||
\(240\) | 2.63068 | 0.169810 | ||||||||
\(241\) | 21.3693i | 1.37652i | 0.725465 | + | 0.688259i | \(0.241625\pi\) | ||||
−0.725465 | + | 0.688259i | \(0.758375\pi\) | |||||||
\(242\) | −6.93087 | −0.445533 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0.384472i | 0.0246133i | ||||||||
\(245\) | 3.93087i | 0.251134i | ||||||||
\(246\) | 0.876894 | 0.0559087 | ||||||||
\(247\) | −35.0540 | −2.23043 | ||||||||
\(248\) | 12.4924i | 0.793270i | ||||||||
\(249\) | 9.12311i | 0.578153i | ||||||||
\(250\) | − 8.49242i | − 0.537108i | ||||||||
\(251\) | −24.4924 | −1.54595 | −0.772974 | − | 0.634438i | \(-0.781232\pi\) | ||||
−0.772974 | + | 0.634438i | \(0.781232\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.8078 | −1.05670 | ||||||||
\(254\) | −1.26137 | −0.0791452 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 10.0540 | 0.628373 | ||||||||
\(257\) | −9.36932 | −0.584442 | −0.292221 | − | 0.956351i | \(-0.594394\pi\) | ||||
−0.292221 | + | 0.956351i | \(0.594394\pi\) | |||||||
\(258\) | − 12.0000i | − 0.747087i | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 1.12311i | 0.0696521i | ||||||||
\(261\) | 8.24621i | 0.510428i | ||||||||
\(262\) | 28.9848i | 1.79069i | ||||||||
\(263\) | −12.4924 | −0.770316 | −0.385158 | − | 0.922851i | \(-0.625853\pi\) | ||||
−0.385158 | + | 0.922851i | \(0.625853\pi\) | |||||||
\(264\) | 6.24621 | 0.384428 | ||||||||
\(265\) | 2.38447i | 0.146477i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 7.12311i | 0.435927i | ||||||||
\(268\) | 1.75379 | 0.107130 | ||||||||
\(269\) | − 20.5616i | − 1.25366i | −0.779156 | − | 0.626830i | \(-0.784352\pi\) | ||||
0.779156 | − | 0.626830i | \(-0.215648\pi\) | |||||||
\(270\) | −0.876894 | −0.0533661 | ||||||||
\(271\) | −0.807764 | −0.0490682 | −0.0245341 | − | 0.999699i | \(-0.507810\pi\) | ||||
−0.0245341 | + | 0.999699i | \(0.507810\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 25.3693 | 1.53262 | ||||||||
\(275\) | − 12.0000i | − 0.723627i | ||||||||
\(276\) | 2.87689 | 0.173169 | ||||||||
\(277\) | − 6.00000i | − 0.360505i | −0.983620 | − | 0.180253i | \(-0.942309\pi\) | ||||
0.983620 | − | 0.180253i | \(-0.0576915\pi\) | |||||||
\(278\) | − 14.2462i | − 0.854431i | ||||||||
\(279\) | − 5.12311i | − 0.306712i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 19.1231 | 1.14079 | 0.570394 | − | 0.821371i | \(-0.306790\pi\) | ||||
0.570394 | + | 0.821371i | \(0.306790\pi\) | |||||||
\(282\) | 4.49242i | 0.267520i | ||||||||
\(283\) | − 3.36932i | − 0.200285i | −0.994973 | − | 0.100143i | \(-0.968070\pi\) | ||||
0.994973 | − | 0.100143i | \(-0.0319299\pi\) | |||||||
\(284\) | − 4.49242i | − 0.266576i | ||||||||
\(285\) | 4.31534 | 0.255619 | ||||||||
\(286\) | 18.2462i | 1.07892i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | −2.43845 | −0.143687 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −7.23106 | −0.424622 | ||||||||
\(291\) | −11.1231 | −0.652048 | ||||||||
\(292\) | − 1.86174i | − 0.108950i | ||||||||
\(293\) | −7.12311 | −0.416136 | −0.208068 | − | 0.978114i | \(-0.566718\pi\) | ||||
−0.208068 | + | 0.978114i | \(0.566718\pi\) | |||||||
\(294\) | − 10.9309i | − 0.637501i | ||||||||
\(295\) | 0.630683i | 0.0367198i | ||||||||
\(296\) | − 7.61553i | − 0.442644i | ||||||||
\(297\) | −2.56155 | −0.148636 | ||||||||
\(298\) | 6.63068 | 0.384105 | ||||||||
\(299\) | − 29.9309i | − 1.73095i | ||||||||
\(300\) | 2.05398i | 0.118586i | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 12.4924 | 0.718858 | ||||||||
\(303\) | 19.1231i | 1.09859i | ||||||||
\(304\) | 36.0000 | 2.06474 | ||||||||
\(305\) | −0.492423 | −0.0281960 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −0.492423 | −0.0281040 | −0.0140520 | − | 0.999901i | \(-0.504473\pi\) | ||||
−0.0140520 | + | 0.999901i | \(0.504473\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.31534i | 0.245491i | ||||||||
\(310\) | 4.49242 | 0.255152 | ||||||||
\(311\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(312\) | 11.1231i | 0.629722i | ||||||||
\(313\) | − 7.61553i | − 0.430455i | −0.976564 | − | 0.215228i | \(-0.930951\pi\) | ||||
0.976564 | − | 0.215228i | \(-0.0690493\pi\) | |||||||
\(314\) | 8.87689 | 0.500952 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.73863i | 0.379078i | ||||||||
\(317\) | − 18.0000i | − 1.01098i | −0.862832 | − | 0.505490i | \(-0.831312\pi\) | ||||
0.862832 | − | 0.505490i | \(-0.168688\pi\) | |||||||
\(318\) | − 6.63068i | − 0.371830i | ||||||||
\(319\) | −21.1231 | −1.18267 | ||||||||
\(320\) | 3.12311i | 0.174587i | ||||||||
\(321\) | 7.68466 | 0.428916 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0.438447 | 0.0243582 | ||||||||
\(325\) | 21.3693 | 1.18536 | ||||||||
\(326\) | 10.7386i | 0.594758i | ||||||||
\(327\) | 15.1231 | 0.836310 | ||||||||
\(328\) | 1.36932i | 0.0756079i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | − 2.24621i | − 0.123650i | ||||||||
\(331\) | 6.06913 | 0.333590 | 0.166795 | − | 0.985992i | \(-0.446658\pi\) | ||||
0.166795 | + | 0.985992i | \(0.446658\pi\) | |||||||
\(332\) | 4.00000 | 0.219529 | ||||||||
\(333\) | 3.12311i | 0.171145i | ||||||||
\(334\) | − 1.26137i | − 0.0690189i | ||||||||
\(335\) | 2.24621i | 0.122724i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − 32.7386i | − 1.78339i | −0.452640 | − | 0.891694i | \(-0.649518\pi\) | ||||
0.452640 | − | 0.891694i | \(-0.350482\pi\) | |||||||
\(338\) | −12.1922 | −0.663170 | ||||||||
\(339\) | 4.56155 | 0.247750 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 13.1231 | 0.710656 | ||||||||
\(342\) | −12.0000 | −0.648886 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 18.7386 | 1.01032 | ||||||||
\(345\) | 3.68466i | 0.198375i | ||||||||
\(346\) | − 29.3693i | − 1.57890i | ||||||||
\(347\) | 24.4924i | 1.31482i | 0.753532 | + | 0.657411i | \(0.228348\pi\) | ||||
−0.753532 | + | 0.657411i | \(0.771652\pi\) | |||||||
\(348\) | 3.61553 | 0.193813 | ||||||||
\(349\) | −7.43845 | −0.398171 | −0.199085 | − | 0.979982i | \(-0.563797\pi\) | ||||
−0.199085 | + | 0.979982i | \(0.563797\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − 4.56155i | − 0.243478i | ||||||||
\(352\) | − 6.24621i | − 0.332924i | ||||||||
\(353\) | 22.4924 | 1.19715 | 0.598575 | − | 0.801066i | \(-0.295734\pi\) | ||||
0.598575 | + | 0.801066i | \(0.295734\pi\) | |||||||
\(354\) | − 1.75379i | − 0.0932128i | ||||||||
\(355\) | 5.75379 | 0.305379 | ||||||||
\(356\) | 3.12311 | 0.165524 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −14.2462 | −0.752936 | ||||||||
\(359\) | 2.24621 | 0.118550 | 0.0592752 | − | 0.998242i | \(-0.481121\pi\) | ||||
0.0592752 | + | 0.998242i | \(0.481121\pi\) | |||||||
\(360\) | − 1.36932i | − 0.0721693i | ||||||||
\(361\) | 40.0540 | 2.10810 | ||||||||
\(362\) | − 9.36932i | − 0.492440i | ||||||||
\(363\) | 4.43845i | 0.232958i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.38447 | 0.124809 | ||||||||
\(366\) | 1.36932 | 0.0715753 | ||||||||
\(367\) | − 18.2462i | − 0.952444i | −0.879325 | − | 0.476222i | \(-0.842006\pi\) | ||||
0.879325 | − | 0.476222i | \(-0.157994\pi\) | |||||||
\(368\) | 30.7386i | 1.60236i | ||||||||
\(369\) | − 0.561553i | − 0.0292333i | ||||||||
\(370\) | −2.73863 | −0.142375 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −2.24621 | −0.116461 | ||||||||
\(373\) | 16.2462 | 0.841197 | 0.420598 | − | 0.907247i | \(-0.361820\pi\) | ||||
0.420598 | + | 0.907247i | \(0.361820\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.43845 | −0.280840 | ||||||||
\(376\) | −7.01515 | −0.361779 | ||||||||
\(377\) | − 37.6155i | − 1.93730i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 12.0000i | 0.616399i | 0.951322 | + | 0.308199i | \(0.0997264\pi\) | ||||
−0.951322 | + | 0.308199i | \(0.900274\pi\) | |||||||
\(380\) | − 1.89205i | − 0.0970601i | ||||||||
\(381\) | 0.807764i | 0.0413830i | ||||||||
\(382\) | 20.4924 | 1.04848 | ||||||||
\(383\) | 10.2462 | 0.523557 | 0.261778 | − | 0.965128i | \(-0.415691\pi\) | ||||
0.261778 | + | 0.965128i | \(0.415691\pi\) | |||||||
\(384\) | − 13.5616i | − 0.692060i | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 37.8617i | 1.92711i | ||||||||
\(387\) | −7.68466 | −0.390633 | ||||||||
\(388\) | 4.87689i | 0.247587i | ||||||||
\(389\) | 21.8617 | 1.10843 | 0.554217 | − | 0.832372i | \(-0.313018\pi\) | ||||
0.554217 | + | 0.832372i | \(0.313018\pi\) | |||||||
\(390\) | 4.00000 | 0.202548 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 17.0691 | 0.862121 | ||||||||
\(393\) | 18.5616 | 0.936306 | ||||||||
\(394\) | − 31.1231i | − 1.56796i | ||||||||
\(395\) | −8.63068 | −0.434257 | ||||||||
\(396\) | 1.12311i | 0.0564382i | ||||||||
\(397\) | 5.36932i | 0.269478i | 0.990881 | + | 0.134739i | \(0.0430196\pi\) | ||||
−0.990881 | + | 0.134739i | \(0.956980\pi\) | |||||||
\(398\) | 24.9848i | 1.25238i | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −21.9460 | −1.09730 | ||||||||
\(401\) | − 6.17708i | − 0.308469i | −0.988034 | − | 0.154234i | \(-0.950709\pi\) | ||||
0.988034 | − | 0.154234i | \(-0.0492911\pi\) | |||||||
\(402\) | − 6.24621i | − 0.311533i | ||||||||
\(403\) | 23.3693i | 1.16411i | ||||||||
\(404\) | 8.38447 | 0.417143 | ||||||||
\(405\) | 0.561553i | 0.0279038i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.00000 | −0.396545 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.31534 | −0.114486 | −0.0572431 | − | 0.998360i | \(-0.518231\pi\) | ||||
−0.0572431 | + | 0.998360i | \(0.518231\pi\) | |||||||
\(410\) | 0.492423 | 0.0243190 | ||||||||
\(411\) | − 16.2462i | − 0.801367i | ||||||||
\(412\) | 1.89205 | 0.0932146 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | − 10.2462i | − 0.503574i | ||||||||
\(415\) | 5.12311i | 0.251483i | ||||||||
\(416\) | 11.1231 | 0.545355 | ||||||||
\(417\) | −9.12311 | −0.446760 | ||||||||
\(418\) | − 30.7386i | − 1.50348i | ||||||||
\(419\) | 32.4924i | 1.58736i | 0.608336 | + | 0.793679i | \(0.291837\pi\) | ||||
−0.608336 | + | 0.793679i | \(0.708163\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 28.5616 | 1.39200 | 0.696002 | − | 0.718039i | \(-0.254960\pi\) | ||||
0.696002 | + | 0.718039i | \(0.254960\pi\) | |||||||
\(422\) | 17.7538i | 0.864241i | ||||||||
\(423\) | 2.87689 | 0.139879 | ||||||||
\(424\) | 10.3542 | 0.502843 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −16.0000 | −0.775203 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − 3.36932i | − 0.162862i | ||||||||
\(429\) | 11.6847 | 0.564141 | ||||||||
\(430\) | − 6.73863i | − 0.324966i | ||||||||
\(431\) | − 24.0000i | − 1.15604i | −0.816023 | − | 0.578020i | \(-0.803826\pi\) | ||||
0.816023 | − | 0.578020i | \(-0.196174\pi\) | |||||||
\(432\) | 4.68466i | 0.225391i | ||||||||
\(433\) | −14.3153 | −0.687951 | −0.343976 | − | 0.938979i | \(-0.611774\pi\) | ||||
−0.343976 | + | 0.938979i | \(0.611774\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.63068i | 0.222024i | ||||||||
\(436\) | − 6.63068i | − 0.317552i | ||||||||
\(437\) | 50.4233i | 2.41207i | ||||||||
\(438\) | −6.63068 | −0.316826 | ||||||||
\(439\) | 5.75379i | 0.274613i | 0.990529 | + | 0.137307i | \(0.0438446\pi\) | ||||
−0.990529 | + | 0.137307i | \(0.956155\pi\) | |||||||
\(440\) | 3.50758 | 0.167217 | ||||||||
\(441\) | −7.00000 | −0.333333 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −22.8769 | −1.08691 | −0.543457 | − | 0.839437i | \(-0.682885\pi\) | ||||
−0.543457 | + | 0.839437i | \(0.682885\pi\) | |||||||
\(444\) | 1.36932 | 0.0649849 | ||||||||
\(445\) | 4.00000i | 0.189618i | ||||||||
\(446\) | 21.7538 | 1.03007 | ||||||||
\(447\) | − 4.24621i | − 0.200839i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − 12.7386i | − 0.601173i | −0.953755 | − | 0.300587i | \(-0.902818\pi\) | ||||
0.953755 | − | 0.300587i | \(-0.0971825\pi\) | |||||||
\(450\) | 7.31534 | 0.344849 | ||||||||
\(451\) | 1.43845 | 0.0677338 | ||||||||
\(452\) | − 2.00000i | − 0.0940721i | ||||||||
\(453\) | − 8.00000i | − 0.375873i | ||||||||
\(454\) | − 36.0000i | − 1.68956i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | − 18.7386i | − 0.877517i | ||||||||
\(457\) | 6.80776 | 0.318454 | 0.159227 | − | 0.987242i | \(-0.449100\pi\) | ||||
0.159227 | + | 0.987242i | \(0.449100\pi\) | |||||||
\(458\) | 9.36932 | 0.437799 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.61553 | 0.0753244 | ||||||||
\(461\) | −8.24621 | −0.384064 | −0.192032 | − | 0.981389i | \(-0.561508\pi\) | ||||
−0.192032 | + | 0.981389i | \(0.561508\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 24.9848 | 1.16114 | 0.580572 | − | 0.814209i | \(-0.302829\pi\) | ||||
0.580572 | + | 0.814209i | \(0.302829\pi\) | |||||||
\(464\) | 38.6307i | 1.79338i | ||||||||
\(465\) | − 2.87689i | − 0.133413i | ||||||||
\(466\) | 0.876894i | 0.0406213i | ||||||||
\(467\) | 3.36932 | 0.155913 | 0.0779567 | − | 0.996957i | \(-0.475160\pi\) | ||||
0.0779567 | + | 0.996957i | \(0.475160\pi\) | |||||||
\(468\) | −2.00000 | −0.0924500 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 2.52273i | 0.116365i | ||||||||
\(471\) | − 5.68466i | − 0.261935i | ||||||||
\(472\) | 2.73863 | 0.126056 | ||||||||
\(473\) | − 19.6847i | − 0.905102i | ||||||||
\(474\) | 24.0000 | 1.10236 | ||||||||
\(475\) | −36.0000 | −1.65179 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −4.24621 | −0.194421 | ||||||||
\(478\) | −16.0000 | −0.731823 | ||||||||
\(479\) | 29.3002i | 1.33876i | 0.742920 | + | 0.669380i | \(0.233440\pi\) | ||||
−0.742920 | + | 0.669380i | \(0.766560\pi\) | |||||||
\(480\) | −1.36932 | −0.0625005 | ||||||||
\(481\) | − 14.2462i | − 0.649571i | ||||||||
\(482\) | − 33.3693i | − 1.51993i | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.94602 | 0.0884557 | ||||||||
\(485\) | −6.24621 | −0.283626 | ||||||||
\(486\) | − 1.56155i | − 0.0708335i | ||||||||
\(487\) | − 7.36932i | − 0.333936i | −0.985962 | − | 0.166968i | \(-0.946602\pi\) | ||||
0.985962 | − | 0.166968i | \(-0.0533976\pi\) | |||||||
\(488\) | 2.13826i | 0.0967945i | ||||||||
\(489\) | 6.87689 | 0.310984 | ||||||||
\(490\) | − 6.13826i | − 0.277298i | ||||||||
\(491\) | −3.36932 | −0.152055 | −0.0760276 | − | 0.997106i | \(-0.524224\pi\) | ||||
−0.0760276 | + | 0.997106i | \(0.524224\pi\) | |||||||
\(492\) | −0.246211 | −0.0111001 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 54.7386 | 2.46281 | ||||||||
\(495\) | −1.43845 | −0.0646534 | ||||||||
\(496\) | − 24.0000i | − 1.07763i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | − 14.2462i | − 0.638388i | ||||||||
\(499\) | − 11.3693i | − 0.508961i | −0.967078 | − | 0.254480i | \(-0.918096\pi\) | ||||
0.967078 | − | 0.254480i | \(-0.0819044\pi\) | |||||||
\(500\) | 2.38447i | 0.106637i | ||||||||
\(501\) | −0.807764 | −0.0360882 | ||||||||
\(502\) | 38.2462 | 1.70701 | ||||||||
\(503\) | − 25.4384i | − 1.13424i | −0.823634 | − | 0.567122i | \(-0.808057\pi\) | ||||
0.823634 | − | 0.567122i | \(-0.191943\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10.7386i | 0.477863i | ||||||||
\(506\) | 26.2462 | 1.16679 | ||||||||
\(507\) | 7.80776i | 0.346755i | ||||||||
\(508\) | 0.354162 | 0.0157134 | ||||||||
\(509\) | 16.8769 | 0.748055 | 0.374028 | − | 0.927418i | \(-0.377977\pi\) | ||||
0.374028 | + | 0.927418i | \(0.377977\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 11.4233 | 0.504843 | ||||||||
\(513\) | 7.68466i | 0.339286i | ||||||||
\(514\) | 14.6307 | 0.645332 | ||||||||
\(515\) | 2.42329i | 0.106783i | ||||||||
\(516\) | 3.36932i | 0.148326i | ||||||||
\(517\) | 7.36932i | 0.324102i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −18.8078 | −0.825569 | ||||||||
\(520\) | 6.24621i | 0.273914i | ||||||||
\(521\) | − 31.4384i | − 1.37734i | −0.725073 | − | 0.688672i | \(-0.758194\pi\) | ||||
0.725073 | − | 0.688672i | \(-0.241806\pi\) | |||||||
\(522\) | − 12.8769i | − 0.563606i | ||||||||
\(523\) | −20.0000 | −0.874539 | −0.437269 | − | 0.899331i | \(-0.644054\pi\) | ||||
−0.437269 | + | 0.899331i | \(0.644054\pi\) | |||||||
\(524\) | − 8.13826i | − 0.355522i | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 19.5076 | 0.850571 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −12.0000 | −0.522233 | ||||||||
\(529\) | −20.0540 | −0.871912 | ||||||||
\(530\) | − 3.72348i | − 0.161738i | ||||||||
\(531\) | −1.12311 | −0.0487386 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.56155i | 0.110953i | ||||||||
\(534\) | − 11.1231i | − 0.481344i | ||||||||
\(535\) | 4.31534 | 0.186568 | ||||||||
\(536\) | 9.75379 | 0.421300 | ||||||||
\(537\) | 9.12311i | 0.393691i | ||||||||
\(538\) | 32.1080i | 1.38427i | ||||||||
\(539\) | − 17.9309i | − 0.772337i | ||||||||
\(540\) | 0.246211 | 0.0105952 | ||||||||
\(541\) | 40.1080i | 1.72438i | 0.506589 | + | 0.862188i | \(0.330906\pi\) | ||||
−0.506589 | + | 0.862188i | \(0.669094\pi\) | |||||||
\(542\) | 1.26137 | 0.0541803 | ||||||||
\(543\) | −6.00000 | −0.257485 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 8.49242 | 0.363775 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 28.0000i | − 1.19719i | −0.801050 | − | 0.598597i | \(-0.795725\pi\) | ||||
0.801050 | − | 0.598597i | \(-0.204275\pi\) | |||||||
\(548\) | −7.12311 | −0.304284 | ||||||||
\(549\) | − 0.876894i | − 0.0374249i | ||||||||
\(550\) | 18.7386i | 0.799018i | ||||||||
\(551\) | 63.3693i | 2.69962i | ||||||||
\(552\) | 16.0000 | 0.681005 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 9.36932i | 0.398064i | ||||||||
\(555\) | 1.75379i | 0.0744442i | ||||||||
\(556\) | 4.00000i | 0.169638i | ||||||||
\(557\) | −6.49242 | −0.275093 | −0.137546 | − | 0.990495i | \(-0.543922\pi\) | ||||
−0.137546 | + | 0.990495i | \(0.543922\pi\) | |||||||
\(558\) | 8.00000i | 0.338667i | ||||||||
\(559\) | 35.0540 | 1.48263 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −29.8617 | −1.25964 | ||||||||
\(563\) | −22.8769 | −0.964146 | −0.482073 | − | 0.876131i | \(-0.660116\pi\) | ||||
−0.482073 | + | 0.876131i | \(0.660116\pi\) | |||||||
\(564\) | − 1.26137i | − 0.0531131i | ||||||||
\(565\) | 2.56155 | 0.107765 | ||||||||
\(566\) | 5.26137i | 0.221152i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | − 24.9848i | − 1.04834i | ||||||||
\(569\) | −12.8769 | −0.539827 | −0.269914 | − | 0.962885i | \(-0.586995\pi\) | ||||
−0.269914 | + | 0.962885i | \(0.586995\pi\) | |||||||
\(570\) | −6.73863 | −0.282250 | ||||||||
\(571\) | 18.7386i | 0.784187i | 0.919925 | + | 0.392094i | \(0.128249\pi\) | ||||
−0.919925 | + | 0.392094i | \(0.871751\pi\) | |||||||
\(572\) | − 5.12311i | − 0.214208i | ||||||||
\(573\) | − 13.1231i | − 0.548226i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 30.7386i | − 1.28189i | ||||||||
\(576\) | −5.56155 | −0.231731 | ||||||||
\(577\) | −41.0540 | −1.70910 | −0.854550 | − | 0.519370i | \(-0.826167\pi\) | ||||
−0.854550 | + | 0.519370i | \(0.826167\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 24.2462 | 1.00764 | ||||||||
\(580\) | 2.03031 | 0.0843040 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 17.3693 | 0.719981 | ||||||||
\(583\) | − 10.8769i | − 0.450475i | ||||||||
\(584\) | − 10.3542i | − 0.428458i | ||||||||
\(585\) | − 2.56155i | − 0.105907i | ||||||||
\(586\) | 11.1231 | 0.459491 | ||||||||
\(587\) | −36.9848 | −1.52653 | −0.763264 | − | 0.646087i | \(-0.776404\pi\) | ||||
−0.763264 | + | 0.646087i | \(0.776404\pi\) | |||||||
\(588\) | 3.06913i | 0.126569i | ||||||||
\(589\) | − 39.3693i | − 1.62218i | ||||||||
\(590\) | − 0.984845i | − 0.0405454i | ||||||||
\(591\) | −19.9309 | −0.819846 | ||||||||
\(592\) | 14.6307i | 0.601317i | ||||||||
\(593\) | −44.2462 | −1.81697 | −0.908487 | − | 0.417913i | \(-0.862762\pi\) | ||||
−0.908487 | + | 0.417913i | \(0.862762\pi\) | |||||||
\(594\) | 4.00000 | 0.164122 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1.86174 | −0.0762598 | ||||||||
\(597\) | 16.0000 | 0.654836 | ||||||||
\(598\) | 46.7386i | 1.91128i | ||||||||
\(599\) | −41.6155 | −1.70036 | −0.850182 | − | 0.526489i | \(-0.823508\pi\) | ||||
−0.850182 | + | 0.526489i | \(0.823508\pi\) | |||||||
\(600\) | 11.4233i | 0.466354i | ||||||||
\(601\) | 34.9848i | 1.42706i | 0.700624 | + | 0.713531i | \(0.252905\pi\) | ||||
−0.700624 | + | 0.713531i | \(0.747095\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.00000 | −0.162893 | ||||||||
\(604\) | −3.50758 | −0.142721 | ||||||||
\(605\) | 2.49242i | 0.101331i | ||||||||
\(606\) | − 29.8617i | − 1.21305i | ||||||||
\(607\) | − 15.3693i | − 0.623821i | −0.950111 | − | 0.311911i | \(-0.899031\pi\) | ||||
0.950111 | − | 0.311911i | \(-0.100969\pi\) | |||||||
\(608\) | −18.7386 | −0.759952 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.768944 | 0.0311336 | ||||||||
\(611\) | −13.1231 | −0.530904 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.31534 | 0.0935158 | 0.0467579 | − | 0.998906i | \(-0.485111\pi\) | ||||
0.0467579 | + | 0.998906i | \(0.485111\pi\) | |||||||
\(614\) | 0.768944 | 0.0310320 | ||||||||
\(615\) | − 0.315342i | − 0.0127158i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 27.7538i | 1.11733i | 0.829395 | + | 0.558663i | \(0.188685\pi\) | ||||
−0.829395 | + | 0.558663i | \(0.811315\pi\) | |||||||
\(618\) | − 6.73863i | − 0.271068i | ||||||||
\(619\) | − 19.3693i | − 0.778519i | −0.921128 | − | 0.389259i | \(-0.872731\pi\) | ||||
0.921128 | − | 0.389259i | \(-0.127269\pi\) | |||||||
\(620\) | −1.26137 | −0.0506577 | ||||||||
\(621\) | −6.56155 | −0.263306 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | − 21.3693i | − 0.855457i | ||||||||
\(625\) | 20.3693 | 0.814773 | ||||||||
\(626\) | 11.8920i | 0.475302i | ||||||||
\(627\) | −19.6847 | −0.786130 | ||||||||
\(628\) | −2.49242 | −0.0994585 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.6847 | −0.465159 | −0.232579 | − | 0.972577i | \(-0.574717\pi\) | ||||
−0.232579 | + | 0.972577i | \(0.574717\pi\) | |||||||
\(632\) | 37.4773i | 1.49077i | ||||||||
\(633\) | 11.3693 | 0.451890 | ||||||||
\(634\) | 28.1080i | 1.11631i | ||||||||
\(635\) | 0.453602i | 0.0180007i | ||||||||
\(636\) | 1.86174i | 0.0738228i | ||||||||
\(637\) | 31.9309 | 1.26515 | ||||||||
\(638\) | 32.9848 | 1.30588 | ||||||||
\(639\) | 10.2462i | 0.405334i | ||||||||
\(640\) | − 7.61553i | − 0.301030i | ||||||||
\(641\) | 0.0691303i | 0.00273048i | 0.999999 | + | 0.00136524i | \(0.000434570\pi\) | ||||
−0.999999 | + | 0.00136524i | \(0.999565\pi\) | |||||||
\(642\) | −12.0000 | −0.473602 | ||||||||
\(643\) | 30.2462i | 1.19279i | 0.802690 | + | 0.596397i | \(0.203402\pi\) | ||||
−0.802690 | + | 0.596397i | \(0.796598\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −4.31534 | −0.169916 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 15.3693 | 0.604230 | 0.302115 | − | 0.953271i | \(-0.402307\pi\) | ||||
0.302115 | + | 0.953271i | \(0.402307\pi\) | |||||||
\(648\) | 2.43845 | 0.0957913 | ||||||||
\(649\) | − 2.87689i | − 0.112928i | ||||||||
\(650\) | −33.3693 | −1.30885 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | − 3.01515i | − 0.118083i | ||||||||
\(653\) | − 4.06913i | − 0.159237i | −0.996825 | − | 0.0796187i | \(-0.974630\pi\) | ||||
0.996825 | − | 0.0796187i | \(-0.0253703\pi\) | |||||||
\(654\) | −23.6155 | −0.923440 | ||||||||
\(655\) | 10.4233 | 0.407272 | ||||||||
\(656\) | − 2.63068i | − 0.102711i | ||||||||
\(657\) | 4.24621i | 0.165660i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 47.8617 | 1.86443 | 0.932214 | − | 0.361907i | \(-0.117874\pi\) | ||||
0.932214 | + | 0.361907i | \(0.117874\pi\) | |||||||
\(660\) | 0.630683i | 0.0245493i | ||||||||
\(661\) | −25.6847 | −0.999017 | −0.499509 | − | 0.866309i | \(-0.666486\pi\) | ||||
−0.499509 | + | 0.866309i | \(0.666486\pi\) | |||||||
\(662\) | −9.47727 | −0.368344 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 22.2462 | 0.863320 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | − 4.87689i | − 0.188976i | ||||||||
\(667\) | −54.1080 | −2.09507 | ||||||||
\(668\) | 0.354162i | 0.0137029i | ||||||||
\(669\) | − 13.9309i | − 0.538599i | ||||||||
\(670\) | − 3.50758i | − 0.135510i | ||||||||
\(671\) | 2.24621 | 0.0867140 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 48.7386i | 1.87874i | 0.342910 | + | 0.939368i | \(0.388587\pi\) | ||||
−0.342910 | + | 0.939368i | \(0.611413\pi\) | |||||||
\(674\) | 51.1231i | 1.96919i | ||||||||
\(675\) | − 4.68466i | − 0.180313i | ||||||||
\(676\) | 3.42329 | 0.131665 | ||||||||
\(677\) | 13.6847i | 0.525944i | 0.964803 | + | 0.262972i | \(0.0847027\pi\) | ||||
−0.964803 | + | 0.262972i | \(0.915297\pi\) | |||||||
\(678\) | −7.12311 | −0.273561 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −23.0540 | −0.883430 | ||||||||
\(682\) | −20.4924 | −0.784695 | ||||||||
\(683\) | 5.43845i | 0.208096i | 0.994572 | + | 0.104048i | \(0.0331796\pi\) | ||||
−0.994572 | + | 0.104048i | \(0.966820\pi\) | |||||||
\(684\) | 3.36932 | 0.128829 | ||||||||
\(685\) | − 9.12311i | − 0.348576i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − 6.00000i | − 0.228914i | ||||||||
\(688\) | −36.0000 | −1.37249 | ||||||||
\(689\) | 19.3693 | 0.737912 | ||||||||
\(690\) | − 5.75379i | − 0.219043i | ||||||||
\(691\) | 36.9848i | 1.40697i | 0.710710 | + | 0.703485i | \(0.248374\pi\) | ||||
−0.710710 | + | 0.703485i | \(0.751626\pi\) | |||||||
\(692\) | 8.24621i | 0.313474i | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − 38.2462i | − 1.45181i | ||||||||
\(695\) | −5.12311 | −0.194330 | ||||||||
\(696\) | 20.1080 | 0.762190 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 11.6155 | 0.439654 | ||||||||
\(699\) | 0.561553 | 0.0212399 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.36932 | −0.353874 | −0.176937 | − | 0.984222i | \(-0.556619\pi\) | ||||
−0.176937 | + | 0.984222i | \(0.556619\pi\) | |||||||
\(702\) | 7.12311i | 0.268844i | ||||||||
\(703\) | 24.0000i | 0.905177i | ||||||||
\(704\) | − 14.2462i | − 0.536924i | ||||||||
\(705\) | 1.61553 | 0.0608443 | ||||||||
\(706\) | −35.1231 | −1.32188 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0.492423i | 0.0185064i | ||||||||
\(709\) | − 4.73863i | − 0.177963i | −0.996033 | − | 0.0889816i | \(-0.971639\pi\) | ||||
0.996033 | − | 0.0889816i | \(-0.0283612\pi\) | |||||||
\(710\) | −8.98485 | −0.337195 | ||||||||
\(711\) | − 15.3693i | − 0.576394i | ||||||||
\(712\) | 17.3693 | 0.650943 | ||||||||
\(713\) | 33.6155 | 1.25891 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.56155 | 0.245388 | ||||||||
\(716\) | 4.00000 | 0.149487 | ||||||||
\(717\) | 10.2462i | 0.382652i | ||||||||
\(718\) | −3.50758 | −0.130902 | ||||||||
\(719\) | − 8.80776i | − 0.328474i | −0.986421 | − | 0.164237i | \(-0.947484\pi\) | ||||
0.986421 | − | 0.164237i | \(-0.0525162\pi\) | |||||||
\(720\) | 2.63068i | 0.0980398i | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −62.5464 | −2.32774 | ||||||||
\(723\) | −21.3693 | −0.794733 | ||||||||
\(724\) | 2.63068i | 0.0977686i | ||||||||
\(725\) | − 38.6307i | − 1.43471i | ||||||||
\(726\) | − 6.93087i | − 0.257229i | ||||||||
\(727\) | −8.00000 | −0.296704 | −0.148352 | − | 0.988935i | \(-0.547397\pi\) | ||||
−0.148352 | + | 0.988935i | \(0.547397\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | −3.72348 | −0.137812 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −0.384472 | −0.0142105 | ||||||||
\(733\) | 28.2462 | 1.04330 | 0.521649 | − | 0.853160i | \(-0.325317\pi\) | ||||
0.521649 | + | 0.853160i | \(0.325317\pi\) | |||||||
\(734\) | 28.4924i | 1.05167i | ||||||||
\(735\) | −3.93087 | −0.144992 | ||||||||
\(736\) | − 16.0000i | − 0.589768i | ||||||||
\(737\) | − 10.2462i | − 0.377424i | ||||||||
\(738\) | 0.876894i | 0.0322789i | ||||||||
\(739\) | 8.31534 | 0.305885 | 0.152942 | − | 0.988235i | \(-0.451125\pi\) | ||||
0.152942 | + | 0.988235i | \(0.451125\pi\) | |||||||
\(740\) | 0.768944 | 0.0282669 | ||||||||
\(741\) | − 35.0540i | − 1.28774i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.49242i | 0.164811i | 0.996599 | + | 0.0824055i | \(0.0262603\pi\) | ||||
−0.996599 | + | 0.0824055i | \(0.973740\pi\) | |||||||
\(744\) | −12.4924 | −0.457994 | ||||||||
\(745\) | − 2.38447i | − 0.0873603i | ||||||||
\(746\) | −25.3693 | −0.928837 | ||||||||
\(747\) | −9.12311 | −0.333797 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 8.49242 | 0.310099 | ||||||||
\(751\) | 0.630683i | 0.0230140i | 0.999934 | + | 0.0115070i | \(0.00366287\pi\) | ||||
−0.999934 | + | 0.0115070i | \(0.996337\pi\) | |||||||
\(752\) | 13.4773 | 0.491465 | ||||||||
\(753\) | − 24.4924i | − 0.892553i | ||||||||
\(754\) | 58.7386i | 2.13913i | ||||||||
\(755\) | − 4.49242i | − 0.163496i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21.0540 | 0.765220 | 0.382610 | − | 0.923910i | \(-0.375025\pi\) | ||||
0.382610 | + | 0.923910i | \(0.375025\pi\) | |||||||
\(758\) | − 18.7386i | − 0.680618i | ||||||||
\(759\) | − 16.8078i | − 0.610083i | ||||||||
\(760\) | − 10.5227i | − 0.381700i | ||||||||
\(761\) | −32.2462 | −1.16892 | −0.584462 | − | 0.811421i | \(-0.698694\pi\) | ||||
−0.584462 | + | 0.811421i | \(0.698694\pi\) | |||||||
\(762\) | − 1.26137i | − 0.0456945i | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −5.75379 | −0.208165 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −16.0000 | −0.578103 | ||||||||
\(767\) | 5.12311 | 0.184985 | ||||||||
\(768\) | 10.0540i | 0.362792i | ||||||||
\(769\) | −29.5464 | −1.06547 | −0.532735 | − | 0.846282i | \(-0.678836\pi\) | ||||
−0.532735 | + | 0.846282i | \(0.678836\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 9.36932i | − 0.337428i | ||||||||
\(772\) | − 10.6307i | − 0.382607i | ||||||||
\(773\) | 33.3693 | 1.20021 | 0.600105 | − | 0.799921i | \(-0.295125\pi\) | ||||
0.600105 | + | 0.799921i | \(0.295125\pi\) | |||||||
\(774\) | 12.0000 | 0.431331 | ||||||||
\(775\) | 24.0000i | 0.862105i | ||||||||
\(776\) | 27.1231i | 0.973663i | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −34.1383 | −1.22392 | ||||||||
\(779\) | − 4.31534i | − 0.154613i | ||||||||
\(780\) | −1.12311 | −0.0402136 | ||||||||
\(781\) | −26.2462 | −0.939163 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −8.24621 | −0.294696 | ||||||||
\(784\) | −32.7926 | −1.17116 | ||||||||
\(785\) | − 3.19224i | − 0.113936i | ||||||||
\(786\) | −28.9848 | −1.03386 | ||||||||
\(787\) | − 6.24621i | − 0.222653i | −0.993784 | − | 0.111327i | \(-0.964490\pi\) | ||||
0.993784 | − | 0.111327i | \(-0.0355100\pi\) | |||||||
\(788\) | 8.73863i | 0.311301i | ||||||||
\(789\) | − 12.4924i | − 0.444742i | ||||||||
\(790\) | 13.4773 | 0.479500 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 6.24621i | 0.221949i | ||||||||
\(793\) | 4.00000i | 0.142044i | ||||||||
\(794\) | − 8.38447i | − 0.297554i | ||||||||
\(795\) | −2.38447 | −0.0845685 | ||||||||
\(796\) | − 7.01515i | − 0.248646i | ||||||||
\(797\) | −31.6155 | −1.11988 | −0.559940 | − | 0.828533i | \(-0.689176\pi\) | ||||
−0.559940 | + | 0.828533i | \(0.689176\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 11.4233 | 0.403874 | ||||||||
\(801\) | −7.12311 | −0.251683 | ||||||||
\(802\) | 9.64584i | 0.340606i | ||||||||
\(803\) | −10.8769 | −0.383837 | ||||||||
\(804\) | 1.75379i | 0.0618514i | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − 36.4924i | − 1.28539i | ||||||||
\(807\) | 20.5616 | 0.723801 | ||||||||
\(808\) | 46.6307 | 1.64046 | ||||||||
\(809\) | 53.0540i | 1.86528i | 0.360810 | + | 0.932639i | \(0.382500\pi\) | ||||
−0.360810 | + | 0.932639i | \(0.617500\pi\) | |||||||
\(810\) | − 0.876894i | − 0.0308109i | ||||||||
\(811\) | 20.6307i | 0.724441i | 0.932092 | + | 0.362221i | \(0.117981\pi\) | ||||
−0.932092 | + | 0.362221i | \(0.882019\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 0.807764i | − 0.0283295i | ||||||||
\(814\) | 12.4924 | 0.437859 | ||||||||
\(815\) | 3.86174 | 0.135271 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −59.0540 | −2.06604 | ||||||||
\(818\) | 3.61553 | 0.126414 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −0.138261 | −0.00482827 | ||||||||
\(821\) | 16.5616i | 0.578002i | 0.957329 | + | 0.289001i | \(0.0933231\pi\) | ||||
−0.957329 | + | 0.289001i | \(0.906677\pi\) | |||||||
\(822\) | 25.3693i | 0.884857i | ||||||||
\(823\) | 36.4924i | 1.27205i | 0.771670 | + | 0.636023i | \(0.219422\pi\) | ||||
−0.771670 | + | 0.636023i | \(0.780578\pi\) | |||||||
\(824\) | 10.5227 | 0.366577 | ||||||||
\(825\) | 12.0000 | 0.417786 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 14.4233i | − 0.501547i | −0.968046 | − | 0.250774i | \(-0.919315\pi\) | ||||
0.968046 | − | 0.250774i | \(-0.0806849\pi\) | |||||||
\(828\) | 2.87689i | 0.0999790i | ||||||||
\(829\) | 50.4924 | 1.75367 | 0.876837 | − | 0.480787i | \(-0.159649\pi\) | ||||
0.876837 | + | 0.480787i | \(0.159649\pi\) | |||||||
\(830\) | − 8.00000i | − 0.277684i | ||||||||
\(831\) | 6.00000 | 0.208138 | ||||||||
\(832\) | 25.3693 | 0.879523 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 14.2462 | 0.493306 | ||||||||
\(835\) | −0.453602 | −0.0156976 | ||||||||
\(836\) | 8.63068i | 0.298498i | ||||||||
\(837\) | 5.12311 | 0.177080 | ||||||||
\(838\) | − 50.7386i | − 1.75274i | ||||||||
\(839\) | 11.0540i | 0.381626i | 0.981626 | + | 0.190813i | \(0.0611123\pi\) | ||||
−0.981626 | + | 0.190813i | \(0.938888\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −39.0000 | −1.34483 | ||||||||
\(842\) | −44.6004 | −1.53703 | ||||||||
\(843\) | 19.1231i | 0.658635i | ||||||||
\(844\) | − 4.98485i | − 0.171585i | ||||||||
\(845\) | 4.38447i | 0.150830i | ||||||||
\(846\) | −4.49242 | −0.154453 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −19.8920 | −0.683096 | ||||||||
\(849\) | 3.36932 | 0.115635 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −20.4924 | −0.702471 | ||||||||
\(852\) | 4.49242 | 0.153908 | ||||||||
\(853\) | − 20.7386i | − 0.710077i | −0.934852 | − | 0.355039i | \(-0.884468\pi\) | ||||
0.934852 | − | 0.355039i | \(-0.115532\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 4.31534i | 0.147582i | ||||||||
\(856\) | − 18.7386i | − 0.640473i | ||||||||
\(857\) | − 6.00000i | − 0.204956i | −0.994735 | − | 0.102478i | \(-0.967323\pi\) | ||||
0.994735 | − | 0.102478i | \(-0.0326771\pi\) | |||||||
\(858\) | −18.2462 | −0.622915 | ||||||||
\(859\) | −12.0000 | −0.409435 | −0.204717 | − | 0.978821i | \(-0.565628\pi\) | ||||
−0.204717 | + | 0.978821i | \(0.565628\pi\) | |||||||
\(860\) | 1.89205i | 0.0645183i | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 37.4773i | 1.27648i | ||||||||
\(863\) | −26.2462 | −0.893431 | −0.446716 | − | 0.894676i | \(-0.647406\pi\) | ||||
−0.446716 | + | 0.894676i | \(0.647406\pi\) | |||||||
\(864\) | − 2.43845i | − 0.0829577i | ||||||||
\(865\) | −10.5616 | −0.359104 | ||||||||
\(866\) | 22.3542 | 0.759625 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 39.3693 | 1.33551 | ||||||||
\(870\) | − 7.23106i | − 0.245156i | ||||||||
\(871\) | 18.2462 | 0.618249 | ||||||||
\(872\) | − 36.8769i | − 1.24881i | ||||||||
\(873\) | − 11.1231i | − 0.376460i | ||||||||
\(874\) | − 78.7386i | − 2.66337i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 1.86174 | 0.0629023 | ||||||||
\(877\) | − 34.0000i | − 1.14810i | −0.818821 | − | 0.574049i | \(-0.805372\pi\) | ||||
0.818821 | − | 0.574049i | \(-0.194628\pi\) | |||||||
\(878\) | − 8.98485i | − 0.303224i | ||||||||
\(879\) | − 7.12311i | − 0.240256i | ||||||||
\(880\) | −6.73863 | −0.227159 | ||||||||
\(881\) | − 23.7538i | − 0.800285i | −0.916453 | − | 0.400143i | \(-0.868961\pi\) | ||||
0.916453 | − | 0.400143i | \(-0.131039\pi\) | |||||||
\(882\) | 10.9309 | 0.368062 | ||||||||
\(883\) | 38.4233 | 1.29305 | 0.646523 | − | 0.762894i | \(-0.276222\pi\) | ||||
0.646523 | + | 0.762894i | \(0.276222\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −0.630683 | −0.0212002 | ||||||||
\(886\) | 35.7235 | 1.20015 | ||||||||
\(887\) | − 22.5616i | − 0.757543i | −0.925490 | − | 0.378771i | \(-0.876347\pi\) | ||||
0.925490 | − | 0.378771i | \(-0.123653\pi\) | |||||||
\(888\) | 7.61553 | 0.255560 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − 6.24621i | − 0.209373i | ||||||||
\(891\) | − 2.56155i | − 0.0858152i | ||||||||
\(892\) | −6.10795 | −0.204509 | ||||||||
\(893\) | 22.1080 | 0.739814 | ||||||||
\(894\) | 6.63068i | 0.221763i | ||||||||
\(895\) | 5.12311i | 0.171247i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 29.9309 | 0.999363 | ||||||||
\(898\) | 19.8920i | 0.663806i | ||||||||
\(899\) | 42.2462 | 1.40899 | ||||||||
\(900\) | −2.05398 | −0.0684658 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | −2.24621 | −0.0747907 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − 11.1231i | − 0.369949i | ||||||||
\(905\) | −3.36932 | −0.112000 | ||||||||
\(906\) | 12.4924i | 0.415033i | ||||||||
\(907\) | 47.8617i | 1.58922i | 0.607118 | + | 0.794611i | \(0.292325\pi\) | ||||
−0.607118 | + | 0.794611i | \(0.707675\pi\) | |||||||
\(908\) | 10.1080i | 0.335444i | ||||||||
\(909\) | −19.1231 | −0.634273 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − 29.3002i | − 0.970758i | −0.874304 | − | 0.485379i | \(-0.838682\pi\) | ||||
0.874304 | − | 0.485379i | \(-0.161318\pi\) | |||||||
\(912\) | 36.0000i | 1.19208i | ||||||||
\(913\) | − 23.3693i | − 0.773412i | ||||||||
\(914\) | −10.6307 | −0.351632 | ||||||||
\(915\) | − 0.492423i | − 0.0162790i | ||||||||
\(916\) | −2.63068 | −0.0869202 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.31534 | −0.142350 | −0.0711750 | − | 0.997464i | \(-0.522675\pi\) | ||||
−0.0711750 | + | 0.997464i | \(0.522675\pi\) | |||||||
\(920\) | 8.98485 | 0.296222 | ||||||||
\(921\) | − 0.492423i | − 0.0162259i | ||||||||
\(922\) | 12.8769 | 0.424078 | ||||||||
\(923\) | − 46.7386i | − 1.53842i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 14.6307i | − 0.481054i | ||||||||
\(926\) | −39.0152 | −1.28212 | ||||||||
\(927\) | −4.31534 | −0.141734 | ||||||||
\(928\) | − 20.1080i | − 0.660076i | ||||||||
\(929\) | 31.9309i | 1.04762i | 0.851836 | + | 0.523809i | \(0.175489\pi\) | ||||
−0.851836 | + | 0.523809i | \(0.824511\pi\) | |||||||
\(930\) | 4.49242i | 0.147312i | ||||||||
\(931\) | −53.7926 | −1.76298 | ||||||||
\(932\) | − 0.246211i | − 0.00806492i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −5.26137 | −0.172157 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −11.1231 | −0.363570 | ||||||||
\(937\) | 22.0000 | 0.718709 | 0.359354 | − | 0.933201i | \(-0.382997\pi\) | ||||
0.359354 | + | 0.933201i | \(0.382997\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 7.61553 | 0.248523 | ||||||||
\(940\) | − 0.708324i | − 0.0231030i | ||||||||
\(941\) | 30.0000i | 0.977972i | 0.872292 | + | 0.488986i | \(0.162633\pi\) | ||||
−0.872292 | + | 0.488986i | \(0.837367\pi\) | |||||||
\(942\) | 8.87689i | 0.289225i | ||||||||
\(943\) | 3.68466 | 0.119989 | ||||||||
\(944\) | −5.26137 | −0.171243 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 30.7386i | 0.999399i | ||||||||
\(947\) | − 12.0000i | − 0.389948i | −0.980808 | − | 0.194974i | \(-0.937538\pi\) | ||||
0.980808 | − | 0.194974i | \(-0.0624622\pi\) | |||||||
\(948\) | −6.73863 | −0.218861 | ||||||||
\(949\) | − 19.3693i | − 0.628755i | ||||||||
\(950\) | 56.2159 | 1.82388 | ||||||||
\(951\) | 18.0000 | 0.583690 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −54.3542 | −1.76070 | −0.880352 | − | 0.474321i | \(-0.842694\pi\) | ||||
−0.880352 | + | 0.474321i | \(0.842694\pi\) | |||||||
\(954\) | 6.63068 | 0.214676 | ||||||||
\(955\) | − 7.36932i | − 0.238465i | ||||||||
\(956\) | 4.49242 | 0.145295 | ||||||||
\(957\) | − 21.1231i | − 0.682813i | ||||||||
\(958\) | − 45.7538i | − 1.47824i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −3.12311 | −0.100798 | ||||||||
\(961\) | 4.75379 | 0.153348 | ||||||||
\(962\) | 22.2462i | 0.717247i | ||||||||
\(963\) | 7.68466i | 0.247635i | ||||||||
\(964\) | 9.36932i | 0.301765i | ||||||||
\(965\) | 13.6155 | 0.438299 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −46.5616 | −1.49732 | −0.748659 | − | 0.662955i | \(-0.769302\pi\) | ||||
−0.748659 | + | 0.662955i | \(0.769302\pi\) | |||||||
\(968\) | 10.8229 | 0.347862 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 9.75379 | 0.313175 | ||||||||
\(971\) | 2.38447 | 0.0765213 | 0.0382607 | − | 0.999268i | \(-0.487818\pi\) | ||||
0.0382607 | + | 0.999268i | \(0.487818\pi\) | |||||||
\(972\) | 0.438447i | 0.0140632i | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 11.5076i | 0.368727i | ||||||||
\(975\) | 21.3693i | 0.684366i | ||||||||
\(976\) | − 4.10795i | − 0.131492i | ||||||||
\(977\) | 8.24621 | 0.263820 | 0.131910 | − | 0.991262i | \(-0.457889\pi\) | ||||
0.131910 | + | 0.991262i | \(0.457889\pi\) | |||||||
\(978\) | −10.7386 | −0.343384 | ||||||||
\(979\) | − 18.2462i | − 0.583151i | ||||||||
\(980\) | 1.72348i | 0.0550545i | ||||||||
\(981\) | 15.1231i | 0.482844i | ||||||||
\(982\) | 5.26137 | 0.167897 | ||||||||
\(983\) | − 2.06913i | − 0.0659950i | −0.999455 | − | 0.0329975i | \(-0.989495\pi\) | ||||
0.999455 | − | 0.0329975i | \(-0.0105053\pi\) | |||||||
\(984\) | −1.36932 | −0.0436522 | ||||||||
\(985\) | −11.1922 | −0.356614 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −15.3693 | −0.488963 | ||||||||
\(989\) | − 50.4233i | − 1.60337i | ||||||||
\(990\) | 2.24621 | 0.0713893 | ||||||||
\(991\) | 6.73863i | 0.214060i | 0.994256 | + | 0.107030i | \(0.0341341\pi\) | ||||
−0.994256 | + | 0.107030i | \(0.965866\pi\) | |||||||
\(992\) | 12.4924i | 0.396635i | ||||||||
\(993\) | 6.06913i | 0.192598i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 8.98485 | 0.284839 | ||||||||
\(996\) | 4.00000i | 0.126745i | ||||||||
\(997\) | − 10.0000i | − 0.316703i | −0.987383 | − | 0.158352i | \(-0.949382\pi\) | ||||
0.987383 | − | 0.158352i | \(-0.0506179\pi\) | |||||||
\(998\) | 17.7538i | 0.561986i | ||||||||
\(999\) | −3.12311 | −0.0988107 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))