Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [224,2,Mod(113,224)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(224, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("224.113");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 224 = 2^{5} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 224.b (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: | \(1.78864900528\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | 4.0.2312.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 2x + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 113.4 | ||
Root | \(-0.780776 + 1.17915i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 224.113 |
Dual form | 224.2.b.b.113.1 |
$q$-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 \(\left(\mathbb{Z}/224\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(129\) | \(197\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 3.02045i | 1.74386i | 0.489634 | + | 0.871928i | \(0.337130\pi\) | ||||
−0.489634 | + | 0.871928i | \(0.662870\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.69614i | 0.758537i | 0.925287 | + | 0.379269i | \(0.123824\pi\) | ||||
−0.925287 | + | 0.379269i | \(0.876176\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −6.12311 | −2.04104 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − 1.32431i | − 0.399294i | −0.979868 | − | 0.199647i | \(-0.936021\pi\) | ||||
0.979868 | − | 0.199647i | \(-0.0639795\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 1.69614i | − 0.470425i | −0.971944 | − | 0.235212i | \(-0.924421\pi\) | ||||
0.971944 | − | 0.235212i | \(-0.0755786\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −5.12311 | −1.32278 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.00000 | 0.485071 | 0.242536 | − | 0.970143i | \(-0.422021\pi\) | ||||
0.242536 | + | 0.970143i | \(0.422021\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.02045i | 0.692938i | 0.938061 | + | 0.346469i | \(0.112619\pi\) | ||||
−0.938061 | + | 0.346469i | \(0.887381\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 3.02045i | 0.659116i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −5.12311 | −1.06824 | −0.534121 | − | 0.845408i | \(-0.679357\pi\) | ||||
−0.534121 | + | 0.845408i | \(0.679357\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.12311 | 0.424621 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 9.43318i | − 1.81542i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 6.04090i | 1.12177i | 0.827895 | + | 0.560883i | \(0.189538\pi\) | ||||
−0.827895 | + | 0.560883i | \(0.810462\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10.2462 | 1.84027 | 0.920137 | − | 0.391597i | \(-0.128077\pi\) | ||||
0.920137 | + | 0.391597i | \(0.128077\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 4.00000 | 0.696311 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.69614i | 0.286700i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − 6.04090i | − 0.993117i | −0.868003 | − | 0.496559i | \(-0.834597\pi\) | ||||
0.868003 | − | 0.496559i | \(-0.165403\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 5.12311 | 0.820353 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4.24621 | 0.663147 | 0.331573 | − | 0.943429i | \(-0.392421\pi\) | ||||
0.331573 | + | 0.943429i | \(0.392421\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − 1.32431i | − 0.201955i | −0.994889 | − | 0.100977i | \(-0.967803\pi\) | ||||
0.994889 | − | 0.100977i | \(-0.0321970\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − 10.3857i | − 1.54820i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 6.04090i | 0.845895i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 2.64861i | 0.363815i | 0.983316 | + | 0.181908i | \(0.0582272\pi\) | ||||
−0.983316 | + | 0.181908i | \(0.941773\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.24621 | 0.302879 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −9.12311 | −1.20838 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 0.371834i | − 0.0484087i | −0.999707 | − | 0.0242043i | \(-0.992295\pi\) | ||||
0.999707 | − | 0.0242043i | \(-0.00770523\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 1.69614i | − 0.217169i | −0.994087 | − | 0.108584i | \(-0.965368\pi\) | ||||
0.994087 | − | 0.108584i | \(-0.0346317\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −6.12311 | −0.771439 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 2.87689 | 0.356835 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 11.5012i | − 1.40509i | −0.711640 | − | 0.702545i | \(-0.752047\pi\) | ||||
0.711640 | − | 0.702545i | \(-0.247953\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 15.4741i | − 1.86286i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.00000 | 0.949425 | 0.474713 | − | 0.880141i | \(-0.342552\pi\) | ||||
0.474713 | + | 0.880141i | \(0.342552\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.00000 | −0.702247 | −0.351123 | − | 0.936329i | \(-0.614200\pi\) | ||||
−0.351123 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 6.41273i | 0.740478i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − 1.32431i | − 0.150919i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 10.1231 | 1.12479 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 5.66906i | − 0.622260i | −0.950367 | − | 0.311130i | \(-0.899292\pi\) | ||||
0.950367 | − | 0.311130i | \(-0.100708\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.39228i | 0.367945i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −18.2462 | −1.95620 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −16.2462 | −1.72209 | −0.861047 | − | 0.508525i | \(-0.830191\pi\) | ||||
−0.861047 | + | 0.508525i | \(0.830191\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − 1.69614i | − 0.177804i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 30.9481i | 3.20917i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.12311 | −0.525620 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 12.2462 | 1.24341 | 0.621707 | − | 0.783250i | \(-0.286439\pi\) | ||||
0.621707 | + | 0.783250i | \(0.286439\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 8.10887i | 0.814972i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 10.3857i | 1.03341i | 0.856163 | + | 0.516705i | \(0.172842\pi\) | ||||
−0.856163 | + | 0.516705i | \(0.827158\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.24621 | −0.221326 | −0.110663 | − | 0.993858i | \(-0.535297\pi\) | ||||
−0.110663 | + | 0.993858i | \(0.535297\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −5.12311 | −0.499964 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 14.1498i | 1.36791i | 0.729524 | + | 0.683955i | \(0.239741\pi\) | ||||
−0.729524 | + | 0.683955i | \(0.760259\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 18.1227i | − 1.73584i | −0.496705 | − | 0.867919i | \(-0.665457\pi\) | ||||
0.496705 | − | 0.867919i | \(-0.334543\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 18.2462 | 1.73185 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 4.87689 | 0.458780 | 0.229390 | − | 0.973335i | \(-0.426327\pi\) | ||||
0.229390 | + | 0.973335i | \(0.426327\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 8.68951i | − 0.810301i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 10.3857i | 0.960154i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2.00000 | 0.183340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.24621 | 0.840565 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 12.8255i | 1.15643i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 12.0818i | 1.08063i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −13.1231 | −1.16449 | −0.582244 | − | 0.813014i | \(-0.697825\pi\) | ||||
−0.582244 | + | 0.813014i | \(0.697825\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 4.00000 | 0.352180 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − 12.4536i | − 1.08808i | −0.839060 | − | 0.544039i | \(-0.816894\pi\) | ||||
0.839060 | − | 0.544039i | \(-0.183106\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 3.02045i | 0.261906i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 16.0000 | 1.37706 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −16.2462 | −1.38801 | −0.694004 | − | 0.719971i | \(-0.744155\pi\) | ||||
−0.694004 | + | 0.719971i | \(0.744155\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.31768i | 0.705496i | 0.935718 | + | 0.352748i | \(0.114753\pi\) | ||||
−0.935718 | + | 0.352748i | \(0.885247\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.24621 | −0.187838 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.2462 | −0.850902 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 3.02045i | 0.249122i | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 14.7304i | − 1.20676i | −0.797453 | − | 0.603381i | \(-0.793820\pi\) | ||||
0.797453 | − | 0.603381i | \(-0.206180\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.8769 | −0.885149 | −0.442575 | − | 0.896732i | \(-0.645935\pi\) | ||||
−0.442575 | + | 0.896732i | \(0.645935\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −12.2462 | −0.990048 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 17.3790i | 1.39592i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 8.48071i | − 0.676834i | −0.940996 | − | 0.338417i | \(-0.890109\pi\) | ||||
0.940996 | − | 0.338417i | \(-0.109891\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −8.00000 | −0.634441 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −5.12311 | −0.403757 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − 13.4061i | − 1.05005i | −0.851088 | − | 0.525023i | \(-0.824057\pi\) | ||||
0.851088 | − | 0.525023i | \(-0.175943\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 6.78456i | 0.528178i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −8.00000 | −0.619059 | −0.309529 | − | 0.950890i | \(-0.600171\pi\) | ||||
−0.309529 | + | 0.950890i | \(0.600171\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 10.1231 | 0.778700 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 18.4945i | − 1.41431i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 19.0752i | − 1.45026i | −0.688613 | − | 0.725129i | \(-0.741780\pi\) | ||||
0.688613 | − | 0.725129i | \(-0.258220\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2.12311 | 0.160492 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 1.12311 | 0.0844178 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − 4.71659i | − 0.352534i | −0.984342 | − | 0.176267i | \(-0.943598\pi\) | ||||
0.984342 | − | 0.176267i | \(-0.0564023\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − 6.99337i | − 0.519813i | −0.965634 | − | 0.259906i | \(-0.916308\pi\) | ||||
0.965634 | − | 0.259906i | \(-0.0836917\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.12311 | 0.378711 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 10.2462 | 0.753316 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 2.64861i | − 0.193686i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − 9.43318i | − 0.686163i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.0000 | −1.15772 | −0.578860 | − | 0.815427i | \(-0.696502\pi\) | ||||
−0.578860 | + | 0.815427i | \(0.696502\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −11.1231 | −0.800659 | −0.400329 | − | 0.916371i | \(-0.631104\pi\) | ||||
−0.400329 | + | 0.916371i | \(0.631104\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 8.68951i | 0.622269i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 21.5150i | − 1.53288i | −0.642317 | − | 0.766439i | \(-0.722027\pi\) | ||||
0.642317 | − | 0.766439i | \(-0.277973\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 18.2462 | 1.29344 | 0.646720 | − | 0.762728i | \(-0.276140\pi\) | ||||
0.646720 | + | 0.762728i | \(0.276140\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 34.7386 | 2.45027 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 6.04090i | 0.423988i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.20217i | 0.503022i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 31.3693 | 2.18032 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 4.00000 | 0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 4.71659i | − 0.324703i | −0.986733 | − | 0.162352i | \(-0.948092\pi\) | ||||
0.986733 | − | 0.162352i | \(-0.0519079\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 24.1636i | 1.65566i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.24621 | 0.153190 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.2462 | 0.695558 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − 18.1227i | − 1.22462i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − 3.39228i | − 0.228190i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 5.75379 | 0.385302 | 0.192651 | − | 0.981267i | \(-0.438291\pi\) | ||||
0.192651 | + | 0.981267i | \(0.438291\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −13.0000 | −0.866667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.80501i | 0.650782i | 0.945580 | + | 0.325391i | \(0.105496\pi\) | ||||
−0.945580 | + | 0.325391i | \(0.894504\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 25.8597i | 1.70886i | 0.519568 | + | 0.854429i | \(0.326093\pi\) | ||||
−0.519568 | + | 0.854429i | \(0.673907\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 4.00000 | 0.263181 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −16.2462 | −1.06432 | −0.532162 | − | 0.846642i | \(-0.678620\pi\) | ||||
−0.532162 | + | 0.846642i | \(0.678620\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 17.6155 | 1.13945 | 0.569727 | − | 0.821834i | \(-0.307049\pi\) | ||||
0.569727 | + | 0.821834i | \(0.307049\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −3.75379 | −0.241803 | −0.120901 | − | 0.992665i | \(-0.538578\pi\) | ||||
−0.120901 | + | 0.992665i | \(0.538578\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 2.27678i | 0.146055i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.69614i | 0.108362i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5.12311 | 0.325975 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 17.1231 | 1.08513 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 10.9663i | − 0.692186i | −0.938200 | − | 0.346093i | \(-0.887508\pi\) | ||||
0.938200 | − | 0.346093i | \(-0.112492\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.78456i | 0.426542i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −10.2462 | −0.641643 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 22.4924 | 1.40304 | 0.701519 | − | 0.712650i | \(-0.252505\pi\) | ||||
0.701519 | + | 0.712650i | \(0.252505\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − 6.04090i | − 0.375363i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − 36.9890i | − 2.28956i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −12.4924 | −0.770316 | −0.385158 | − | 0.922851i | \(-0.625853\pi\) | ||||
−0.385158 | + | 0.922851i | \(0.625853\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4.49242 | −0.275967 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 49.0708i | − 3.00309i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 11.8730i | 0.723909i | 0.932196 | + | 0.361954i | \(0.117890\pi\) | ||||
−0.932196 | + | 0.361954i | \(0.882110\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −10.2462 | −0.622413 | −0.311207 | − | 0.950342i | \(-0.600733\pi\) | ||||
−0.311207 | + | 0.950342i | \(0.600733\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.12311 | 0.310064 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − 2.81164i | − 0.169548i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.64861i | 0.159140i | 0.996829 | + | 0.0795699i | \(0.0253547\pi\) | ||||
−0.996829 | + | 0.0795699i | \(0.974645\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −62.7386 | −3.75606 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −6.00000 | −0.357930 | −0.178965 | − | 0.983855i | \(-0.557275\pi\) | ||||
−0.178965 | + | 0.983855i | \(0.557275\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 21.8868i | 1.30104i | 0.759491 | + | 0.650518i | \(0.225448\pi\) | ||||
−0.759491 | + | 0.650518i | \(0.774552\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − 15.4741i | − 0.916605i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4.24621 | 0.250646 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 36.9890i | 2.16834i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 10.3857i | 0.606736i | 0.952873 | + | 0.303368i | \(0.0981112\pi\) | ||||
−0.952873 | + | 0.303368i | \(0.901889\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.630683 | 0.0367198 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −12.4924 | −0.724884 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 8.68951i | 0.502527i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − 1.32431i | − 0.0763318i | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −31.3693 | −1.80212 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.87689 | 0.164730 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 25.2791i | 1.44275i | 0.692543 | + | 0.721377i | \(0.256490\pi\) | ||||
−0.692543 | + | 0.721377i | \(0.743510\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 6.78456i | − 0.385960i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.4924 | 0.708380 | 0.354190 | − | 0.935173i | \(-0.384757\pi\) | ||||
0.354190 | + | 0.935173i | \(0.384757\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −20.7386 | −1.17222 | −0.586108 | − | 0.810233i | \(-0.699341\pi\) | ||||
−0.586108 | + | 0.810233i | \(0.699341\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − 10.3857i | − 0.585165i | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 4.13595i | 0.232298i | 0.993232 | + | 0.116149i | \(0.0370550\pi\) | ||||
−0.993232 | + | 0.116149i | \(0.962945\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.00000 | 0.447914 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −42.7386 | −2.38544 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.04090i | 0.336124i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 3.60109i | − 0.199752i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 54.7386 | 3.02705 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 14.8934i | − 0.818617i | −0.912396 | − | 0.409309i | \(-0.865770\pi\) | ||||
0.912396 | − | 0.409309i | \(-0.134230\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 36.9890i | 2.02699i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 19.5076 | 1.06581 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.876894 | −0.0477675 | −0.0238837 | − | 0.999715i | \(-0.507603\pi\) | ||||
−0.0238837 | + | 0.999715i | \(0.507603\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 14.7304i | 0.800046i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 13.5691i | − 0.734809i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.00000 | 0.0539949 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 26.2462 | 1.41305 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 8.10887i | − 0.435307i | −0.976026 | − | 0.217654i | \(-0.930160\pi\) | ||||
0.976026 | − | 0.217654i | \(-0.0698403\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 27.3471i | 1.46385i | 0.681383 | + | 0.731927i | \(0.261379\pi\) | ||||
−0.681383 | + | 0.731927i | \(0.738621\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −16.0000 | −0.854017 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7.75379 | 0.412693 | 0.206346 | − | 0.978479i | \(-0.433843\pi\) | ||||
0.206346 | + | 0.978479i | \(0.433843\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 13.5691i | 0.720175i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 6.04090i | 0.319718i | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 31.3693 | 1.65561 | 0.827805 | − | 0.561017i | \(-0.189590\pi\) | ||||
0.827805 | + | 0.561017i | \(0.189590\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.87689 | 0.519837 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 27.9277i | 1.46582i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 10.1768i | − 0.532680i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −10.2462 | −0.534848 | −0.267424 | − | 0.963579i | \(-0.586172\pi\) | ||||
−0.267424 | + | 0.963579i | \(0.586172\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −26.0000 | −1.35351 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 2.64861i | 0.137509i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 14.7304i | − 0.762711i | −0.924428 | − | 0.381356i | \(-0.875457\pi\) | ||||
0.924428 | − | 0.381356i | \(-0.124543\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −36.4924 | −1.88446 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 10.2462 | 0.527707 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 36.4084i | 1.87017i | 0.354418 | + | 0.935087i | \(0.384679\pi\) | ||||
−0.354418 | + | 0.935087i | \(0.615321\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 39.6377i | − 2.03070i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 4.49242 | 0.229552 | 0.114776 | − | 0.993391i | \(-0.463385\pi\) | ||||
0.114776 | + | 0.993391i | \(0.463385\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.24621 | 0.114478 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 8.10887i | 0.412197i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 24.9073i | 1.26285i | 0.775438 | + | 0.631424i | \(0.217529\pi\) | ||||
−0.775438 | + | 0.631424i | \(0.782471\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −10.2462 | −0.518173 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 37.6155 | 1.89745 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.5625i | 1.03200i | 0.856588 | + | 0.516001i | \(0.172580\pi\) | ||||
−0.856588 | + | 0.516001i | \(0.827420\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −9.12311 | −0.456727 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −0.876894 | −0.0437900 | −0.0218950 | − | 0.999760i | \(-0.506970\pi\) | ||||
−0.0218950 | + | 0.999760i | \(0.506970\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − 17.3790i | − 0.865711i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 17.1702i | 0.853195i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −8.00000 | −0.396545 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.0000 | 1.28562 | 0.642809 | − | 0.766027i | \(-0.277769\pi\) | ||||
0.642809 | + | 0.766027i | \(0.277769\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 49.0708i | − 2.42049i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − 0.371834i | − 0.0182968i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.61553 | 0.472008 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −25.1231 | −1.23028 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | − 27.9277i | − 1.36436i | −0.731185 | − | 0.682179i | \(-0.761033\pi\) | ||||
0.731185 | − | 0.682179i | \(-0.238967\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.8122i | 1.30675i | 0.757036 | + | 0.653373i | \(0.226647\pi\) | ||||
−0.757036 | + | 0.653373i | \(0.773353\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.24621 | 0.205971 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − 1.69614i | − 0.0820820i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − 6.78456i | − 0.327562i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −17.6155 | −0.848510 | −0.424255 | − | 0.905543i | \(-0.639464\pi\) | ||||
−0.424255 | + | 0.905543i | \(0.639464\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −18.4924 | −0.888689 | −0.444345 | − | 0.895856i | \(-0.646563\pi\) | ||||
−0.444345 | + | 0.895856i | \(0.646563\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 30.9481i | − 1.48385i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 15.4741i | − 0.740225i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −22.7386 | −1.08526 | −0.542628 | − | 0.839973i | \(-0.682571\pi\) | ||||
−0.542628 | + | 0.839973i | \(0.682571\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −6.12311 | −0.291576 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 7.36520i | 0.349931i | 0.984575 | + | 0.174966i | \(0.0559814\pi\) | ||||
−0.984575 | + | 0.174966i | \(0.944019\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 27.5559i | − 1.30627i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 44.4924 | 2.10442 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 16.7386 | 0.789945 | 0.394972 | − | 0.918693i | \(-0.370754\pi\) | ||||
0.394972 | + | 0.918693i | \(0.370754\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 5.62329i | − 0.264790i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 32.8531i | − 1.54357i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 2.87689 | 0.134871 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.3693 | 0.812502 | 0.406251 | − | 0.913761i | \(-0.366836\pi\) | ||||
0.406251 | + | 0.913761i | \(0.366836\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 18.8664i | − 0.880606i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 24.3724i | 1.13514i | 0.823327 | + | 0.567568i | \(0.192115\pi\) | ||||
−0.823327 | + | 0.567568i | \(0.807885\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −52.4924 | −2.43428 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 3.02045i | 0.139770i | 0.997555 | + | 0.0698848i | \(0.0222632\pi\) | ||||
−0.997555 | + | 0.0698848i | \(0.977737\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − 11.5012i | − 0.531074i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 25.6155 | 1.18030 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.75379 | −0.0806393 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.41273i | 0.294236i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 16.2177i | − 0.742559i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −10.2462 | −0.468161 | −0.234081 | − | 0.972217i | \(-0.575208\pi\) | ||||
−0.234081 | + | 0.972217i | \(0.575208\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −10.2462 | −0.467187 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − 15.4741i | − 0.704095i | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 20.7713i | 0.943176i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −0.630683 | −0.0285790 | −0.0142895 | − | 0.999898i | \(-0.504549\pi\) | ||||
−0.0142895 | + | 0.999898i | \(0.504549\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 40.4924 | 1.83113 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 34.1774i | − 1.54240i | −0.636590 | − | 0.771202i | \(-0.719656\pi\) | ||||
0.636590 | − | 0.771202i | \(-0.280344\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 12.0818i | 0.544137i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −13.7538 | −0.618187 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8.00000 | 0.358849 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 8.85254i | 0.396294i | 0.980172 | + | 0.198147i | \(0.0634924\pi\) | ||||
−0.980172 | + | 0.198147i | \(0.936508\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 24.1636i | − 1.07955i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −13.7538 | −0.613251 | −0.306626 | − | 0.951830i | \(-0.599200\pi\) | ||||
−0.306626 | + | 0.951830i | \(0.599200\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −17.6155 | −0.783881 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 30.5763i | 1.35794i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − 30.7393i | − 1.36250i | −0.732052 | − | 0.681249i | \(-0.761437\pi\) | ||||
0.732052 | − | 0.681249i | \(-0.238563\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6.00000 | −0.265424 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 28.4924 | 1.25797 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 3.80989i | − 0.167884i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 57.6155 | 2.52904 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −22.0000 | −0.963837 | −0.481919 | − | 0.876216i | \(-0.660060\pi\) | ||||
−0.481919 | + | 0.876216i | \(0.660060\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 41.1708i | 1.80027i | 0.435609 | + | 0.900136i | \(0.356533\pi\) | ||||
−0.435609 | + | 0.900136i | \(0.643467\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 6.41273i | 0.279874i | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 20.4924 | 0.892664 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.24621 | 0.141140 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 2.27678i | 0.0988038i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 7.20217i | − 0.311961i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −24.0000 | −1.03761 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 14.2462 | 0.614769 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | − 1.32431i | − 0.0570419i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 13.2431i | − 0.569364i | −0.958622 | − | 0.284682i | \(-0.908112\pi\) | ||||
0.958622 | − | 0.284682i | \(-0.0918880\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 21.1231 | 0.906479 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 30.7386 | 1.31670 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 9.59621i | − 0.410304i | −0.978730 | − | 0.205152i | \(-0.934231\pi\) | ||||
0.978730 | − | 0.205152i | \(-0.0657689\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 10.3857i | 0.443249i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −18.2462 | −0.777315 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 30.9481i | 1.31368i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − 2.64861i | − 0.112225i | −0.998424 | − | 0.0561127i | \(-0.982129\pi\) | ||||
0.998424 | − | 0.0561127i | \(-0.0178706\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.24621 | −0.0950046 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 8.00000 | 0.337760 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − 29.8326i | − 1.25730i | −0.777690 | − | 0.628648i | \(-0.783609\pi\) | ||||
0.777690 | − | 0.628648i | \(-0.216391\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 8.27190i | 0.348001i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 10.1231 | 0.425130 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −13.3693 | −0.560471 | −0.280235 | − | 0.959931i | \(-0.590413\pi\) | ||||
−0.280235 | + | 0.959931i | \(0.590413\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.27015i | 0.387944i | 0.981007 | + | 0.193972i | \(0.0621370\pi\) | ||||
−0.981007 | + | 0.193972i | \(0.937863\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − 48.3272i | − 2.01890i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −10.8769 | −0.453598 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.75379 | 0.322794 | 0.161397 | − | 0.986890i | \(-0.448400\pi\) | ||||
0.161397 | + | 0.986890i | \(0.448400\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | − 33.5968i | − 1.39623i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − 5.66906i | − 0.235192i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.50758 | 0.145269 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −17.6155 | −0.728312 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 21.8868i | 0.903365i | 0.892179 | + | 0.451683i | \(0.149176\pi\) | ||||
−0.892179 | + | 0.451683i | \(0.850824\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 30.9481i | 1.27520i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 64.9848 | 2.67312 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18.0000 | 0.739171 | 0.369586 | − | 0.929197i | \(-0.379500\pi\) | ||||
0.369586 | + | 0.929197i | \(0.379500\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3.39228i | 0.139070i | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 55.1117i | 2.25557i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 12.4924 | 0.510427 | 0.255213 | − | 0.966885i | \(-0.417854\pi\) | ||||
0.255213 | + | 0.966885i | \(0.417854\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −16.2462 | −0.662697 | −0.331348 | − | 0.943508i | \(-0.607504\pi\) | ||||
−0.331348 | + | 0.943508i | \(0.607504\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 70.4228i | 2.86784i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 15.6829i | 0.637600i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −40.9848 | −1.66352 | −0.831762 | − | 0.555133i | \(-0.812667\pi\) | ||||
−0.831762 | + | 0.555133i | \(0.812667\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −18.2462 | −0.739374 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 2.23100i | − 0.0901094i | −0.998985 | − | 0.0450547i | \(-0.985654\pi\) | ||||
0.998985 | − | 0.0450547i | \(-0.0143462\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −21.7538 | −0.877197 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −29.3693 | −1.18236 | −0.591182 | − | 0.806538i | \(-0.701339\pi\) | ||||
−0.591182 | + | 0.806538i | \(0.701339\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − 19.6558i | − 0.790033i | −0.918674 | − | 0.395017i | \(-0.870739\pi\) | ||||
0.918674 | − | 0.395017i | \(-0.129261\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 48.3272i | 1.93930i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −16.2462 | −0.650891 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.87689 | −0.395076 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 12.0818i | 0.482500i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − 12.0818i | − 0.481733i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.50758 | 0.139634 | 0.0698172 | − | 0.997560i | \(-0.477758\pi\) | ||||
0.0698172 | + | 0.997560i | \(0.477758\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 14.2462 | 0.566236 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − 22.2586i | − 0.883307i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − 1.69614i | − 0.0672036i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −48.9848 | −1.93781 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5.36932 | −0.212075 | −0.106038 | − | 0.994362i | \(-0.533816\pi\) | ||||
−0.106038 | + | 0.994362i | \(0.533816\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − 5.66906i | − 0.223566i | −0.993733 | − | 0.111783i | \(-0.964344\pi\) | ||||
0.993733 | − | 0.111783i | \(-0.0356562\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 6.78456i | 0.267142i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −43.2311 | −1.69959 | −0.849794 | − | 0.527115i | \(-0.823274\pi\) | ||||
−0.849794 | + | 0.527115i | \(0.823274\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.492423 | −0.0193293 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 30.9481i | 1.21295i | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 31.6918i | − 1.24020i | −0.784524 | − | 0.620098i | \(-0.787093\pi\) | ||||
0.784524 | − | 0.620098i | \(-0.212907\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 21.1231 | 0.825348 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 36.7386 | 1.43331 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 6.62153i | − 0.257938i | −0.991649 | − | 0.128969i | \(-0.958833\pi\) | ||||
0.991649 | − | 0.128969i | \(-0.0411668\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 44.7261i | − 1.73964i | −0.493367 | − | 0.869821i | \(-0.664234\pi\) | ||||
0.493367 | − | 0.869821i | \(-0.335766\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10.2462 | 0.397930 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −5.12311 | −0.198666 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − 30.9481i | − 1.19832i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 17.3790i | 0.671912i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.24621 | −0.0867140 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −38.9848 | −1.50276 | −0.751378 | − | 0.659872i | \(-0.770610\pi\) | ||||
−0.751378 | + | 0.659872i | \(0.770610\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 20.0276i | − 0.770864i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 17.1702i | 0.659905i | 0.943998 | + | 0.329952i | \(0.107033\pi\) | ||||
−0.943998 | + | 0.329952i | \(0.892967\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12.2462 | 0.469966 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −29.6155 | −1.13487 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 0.580639i | 0.0222175i | 0.999938 | + | 0.0111088i | \(0.00353610\pi\) | ||||
−0.999938 | + | 0.0111088i | \(0.996464\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 27.5559i | − 1.05286i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −78.1080 | −2.98000 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.49242 | 0.171148 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 38.8482i | 1.47786i | 0.673785 | + | 0.738928i | \(0.264668\pi\) | ||||
−0.673785 | + | 0.738928i | \(0.735332\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.10887i | 0.308031i | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.1080 | −0.535145 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.49242 | 0.321673 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | − 49.0708i | − 1.85603i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 2.23100i | 0.0842639i | 0.999112 | + | 0.0421319i | \(0.0134150\pi\) | ||||
−0.999112 | + | 0.0421319i | \(0.986585\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 18.2462 | 0.688169 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 10.3857i | 0.390593i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.7171i | 1.07849i | 0.842147 | + | 0.539247i | \(0.181291\pi\) | ||||
−0.842147 | + | 0.539247i | \(0.818709\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −52.4924 | −1.96586 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − 3.80989i | − 0.142482i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 53.2068i | 1.98704i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 52.4924 | 1.95764 | 0.978819 | − | 0.204730i | \(-0.0656316\pi\) | ||||
0.978819 | + | 0.204730i | \(0.0656316\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.24621 | −0.0836533 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 11.3381i | − 0.421669i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 12.8255i | 0.476326i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16.9848 | 0.629933 | 0.314967 | − | 0.949103i | \(-0.398007\pi\) | ||||
0.314967 | + | 0.949103i | \(0.398007\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 23.4924 | 0.870090 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − 2.64861i | − 0.0979625i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.2520i | 1.08045i | 0.841521 | + | 0.540224i | \(0.181660\pi\) | ||||
−0.841521 | + | 0.540224i | \(0.818340\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.12311 | −0.188969 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −15.2311 | −0.561043 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 21.3519i | 0.785444i | 0.919657 | + | 0.392722i | \(0.128467\pi\) | ||||
−0.919657 | + | 0.392722i | \(0.871533\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15.4741i | 0.568454i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −0.630683 | −0.0231375 | −0.0115688 | − | 0.999933i | \(-0.503683\pi\) | ||||
−0.0115688 | + | 0.999933i | \(0.503683\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 24.9848 | 0.915374 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 34.7123i | 1.27006i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 14.1498i | 0.517021i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.63068 | −0.314938 | −0.157469 | − | 0.987524i | \(-0.550333\pi\) | ||||
−0.157469 | + | 0.987524i | \(0.550333\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 33.1231 | 1.20707 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − 18.4487i | − 0.671419i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − 26.3946i | − 0.959328i | −0.877452 | − | 0.479664i | \(-0.840759\pi\) | ||||
0.877452 | − | 0.479664i | \(-0.159241\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −20.4924 | −0.743828 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 8.73863 | 0.316775 | 0.158388 | − | 0.987377i | \(-0.449370\pi\) | ||||
0.158388 | + | 0.987377i | \(0.449370\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − 18.1227i | − 0.656085i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 20.7713i | − 0.750988i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −0.630683 | −0.0227726 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −40.2462 | −1.45132 | −0.725658 | − | 0.688056i | \(-0.758464\pi\) | ||||
−0.725658 | + | 0.688056i | \(0.758464\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 67.9372i | 2.44670i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.69614i | 0.0610060i | 0.999535 | + | 0.0305030i | \(0.00971091\pi\) | ||||
−0.999535 | + | 0.0305030i | \(0.990289\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.7538 | 0.781419 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 18.2462 | 0.654579 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 12.8255i | 0.459520i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 10.5945i | − 0.379099i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 56.9848 | 2.03647 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 14.3845 | 0.513404 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − 10.5487i | − 0.376020i | −0.982167 | − | 0.188010i | \(-0.939796\pi\) | ||||
0.982167 | − | 0.188010i | \(-0.0602037\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − 37.7327i | − 1.34332i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.87689 | 0.173402 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.87689 | −0.102162 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | − 13.5691i | − 0.481247i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 25.8597i | − 0.915998i | −0.888953 | − | 0.457999i | \(-0.848566\pi\) | ||||
0.888953 | − | 0.457999i | \(-0.151434\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 99.4773 | 3.51486 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 7.94584i | 0.280403i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − 8.68951i | − 0.306265i | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −35.8617 | −1.26239 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 37.8617 | 1.33115 | 0.665574 | − | 0.746332i | \(-0.268187\pi\) | ||||
0.665574 | + | 0.746332i | \(0.268187\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − 15.8459i | − 0.556425i | −0.960520 | − | 0.278213i | \(-0.910258\pi\) | ||||
0.960520 | − | 0.278213i | \(-0.0897420\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | − 30.9481i | − 1.08540i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 22.7386 | 0.796500 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.00000 | 0.139942 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 10.3857i | 0.362904i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33.5968i | 1.17254i | 0.810118 | + | 0.586268i | \(0.199403\pi\) | ||||
−0.810118 | + | 0.586268i | \(0.800597\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 32.9848 | 1.14978 | 0.574890 | − | 0.818231i | \(-0.305045\pi\) | ||||
0.574890 | + | 0.818231i | \(0.305045\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 8.49242 | 0.295668 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 6.20393i | − 0.215732i | −0.994165 | − | 0.107866i | \(-0.965598\pi\) | ||||
0.994165 | − | 0.107866i | \(-0.0344017\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 46.6310i | 1.61956i | 0.586732 | + | 0.809781i | \(0.300414\pi\) | ||||
−0.586732 | + | 0.809781i | \(0.699586\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.00000 | −0.277517 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 2.00000 | 0.0692959 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 13.5691i | − 0.469579i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 96.6543i | − 3.34086i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.73863 | 0.232643 | 0.116322 | − | 0.993212i | \(-0.462890\pi\) | ||||
0.116322 | + | 0.993212i | \(0.462890\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.49242 | −0.258359 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 18.1227i | − 0.624179i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 17.1702i | 0.590673i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.24621 | 0.317704 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −66.1080 | −2.26882 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 30.9481i | 1.06089i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 25.4421i | − 0.871121i | −0.900159 | − | 0.435561i | \(-0.856550\pi\) | ||||
0.900159 | − | 0.435561i | \(-0.143450\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 31.3693 | 1.07281 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −46.9848 | −1.60497 | −0.802486 | − | 0.596671i | \(-0.796490\pi\) | ||||
−0.802486 | + | 0.596671i | \(0.796490\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − 28.3453i | − 0.967129i | −0.875309 | − | 0.483565i | \(-0.839342\pi\) | ||||
0.875309 | − | 0.483565i | \(-0.160658\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 12.8255i | 0.437091i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −36.4924 | −1.24222 | −0.621108 | − | 0.783725i | \(-0.713317\pi\) | ||||
−0.621108 | + | 0.783725i | \(0.713317\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 32.3542 | 1.10007 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 39.2658i | − 1.33354i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −19.5076 | −0.660989 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −74.9848 | −2.53785 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 12.0818i | 0.408439i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − 35.5017i | − 1.19881i | −0.800447 | − | 0.599404i | \(-0.795404\pi\) | ||||
0.800447 | − | 0.599404i | \(-0.204596\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −31.3693 | −1.05806 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 44.2462 | 1.49069 | 0.745346 | − | 0.666677i | \(-0.232284\pi\) | ||||
0.745346 | + | 0.666677i | \(0.232284\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − 4.71659i | − 0.158726i | −0.996846 | − | 0.0793629i | \(-0.974711\pi\) | ||||
0.996846 | − | 0.0793629i | \(-0.0252886\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 1.90495i | 0.0640340i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 28.4924 | 0.956682 | 0.478341 | − | 0.878174i | \(-0.341238\pi\) | ||||
0.478341 | + | 0.878174i | \(0.341238\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −13.1231 | −0.440135 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − 13.4061i | − 0.449121i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8.00000 | 0.267411 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −26.2462 | −0.876335 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 61.8963i | 2.06436i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.29723i | 0.176476i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.00000 | 0.133112 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 11.8617 | 0.394298 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − 51.5564i | − 1.71190i | −0.517056 | − | 0.855951i | \(-0.672972\pi\) | ||||
0.517056 | − | 0.855951i | \(-0.327028\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 63.5924i | − 2.10923i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.8617 | −0.392997 | −0.196498 | − | 0.980504i | \(-0.562957\pi\) | ||||
−0.196498 | + | 0.980504i | \(0.562957\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.50758 | −0.248465 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 8.68951i | 0.287266i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − 12.4536i | − 0.411255i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.00000 | −0.263896 | −0.131948 | − | 0.991257i | \(-0.542123\pi\) | ||||
−0.131948 | + | 0.991257i | \(0.542123\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −76.3542 | −2.51596 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 13.5691i | − 0.446633i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − 12.8255i | − 0.421699i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 13.7538 | 0.451734 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −2.49242 | −0.0817737 | −0.0408869 | − | 0.999164i | \(-0.513018\pi\) | ||||
−0.0408869 | + | 0.999164i | \(0.513018\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 3.02045i | 0.0989912i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 37.7327i | 1.23531i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4.49242 | 0.146918 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.9848 | 1.14291 | 0.571453 | − | 0.820635i | \(-0.306380\pi\) | ||||
0.571453 | + | 0.820635i | \(0.306380\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 62.6400i | − 2.04418i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 30.7393i | − 1.00207i | −0.865426 | − | 0.501037i | \(-0.832952\pi\) | ||||
0.865426 | − | 0.501037i | \(-0.167048\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −21.7538 | −0.708401 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 16.0000 | 0.520480 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 41.7056i | 1.35525i | 0.735407 | + | 0.677625i | \(0.236991\pi\) | ||||
−0.735407 | + | 0.677625i | \(0.763009\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 10.1768i | 0.330354i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −12.4924 | −0.405095 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −17.5076 | −0.567126 | −0.283563 | − | 0.958954i | \(-0.591517\pi\) | ||||
−0.283563 | + | 0.958954i | \(0.591517\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 27.1383i | − 0.878173i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 24.1636i | 0.781098i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −16.2462 | −0.524618 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 73.9848 | 2.38661 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − 86.6405i | − 2.79195i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 18.8664i | − 0.607329i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.8769 | 0.349777 | 0.174889 | − | 0.984588i | \(-0.444043\pi\) | ||||
0.174889 | + | 0.984588i | \(0.444043\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −18.2462 | −0.586153 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − 10.9663i | − 0.351925i | −0.984397 | − | 0.175962i | \(-0.943696\pi\) | ||||
0.984397 | − | 0.175962i | \(-0.0563037\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8.31768i | 0.266652i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 10.8769 | 0.348339 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.7538 | 0.759951 | 0.379976 | − | 0.924997i | \(-0.375932\pi\) | ||||
0.379976 | + | 0.924997i | \(0.375932\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 21.5150i | 0.687621i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 110.967i | 3.54291i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 34.2462 | 1.09228 | 0.546142 | − | 0.837692i | \(-0.316096\pi\) | ||||
0.546142 | + | 0.837692i | \(0.316096\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 36.4924 | 1.16275 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.78456i | 0.215737i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 36.4924 | 1.15922 | 0.579610 | − | 0.814894i | \(-0.303205\pi\) | ||||
0.579610 | + | 0.814894i | \(0.303205\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 44.9848 | 1.42755 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 30.9481i | 0.981122i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 33.0619i | − 1.04708i | −0.852001 | − | 0.523540i | \(-0.824611\pi\) | ||||
0.852001 | − | 0.523540i | \(-0.175389\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −56.9848 | −1.80292 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))