Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [504,2,Mod(253,504)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(504, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("504.253");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 504 = 2^{3} \cdot 3^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 504.c (of order \(2\), degree \(1\), 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: | \(4.02446026187\) |
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: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 253.1 | ||
Root | \(-0.780776 - 1.17915i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 504.253 |
Dual form | 504.2.c.d.253.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/504\mathbb{Z}\right)^\times\).
\(n\) | \(73\) | \(127\) | \(253\) | \(281\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.780776 | − | 1.17915i | −0.552092 | − | 0.833783i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −0.780776 | + | 1.84130i | −0.390388 | + | 0.920650i | ||||
\(5\) | − | 1.69614i | − | 0.758537i | −0.925287 | − | 0.379269i | \(-0.876176\pi\) | ||
0.925287 | − | 0.379269i | \(-0.123824\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1.00000 | −0.377964 | ||||||||
\(8\) | 2.78078 | − | 0.516994i | 0.983153 | − | 0.182785i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −2.00000 | + | 1.32431i | −0.632456 | + | 0.418783i | ||||
\(11\) | − | 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 | \(-0.0755786\pi\) | |||||||
\(14\) | 0.780776 | + | 1.17915i | 0.208671 | + | 0.315140i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.78078 | − | 2.87529i | −0.695194 | − | 0.718822i | ||||
\(17\) | −2.00000 | −0.485071 | −0.242536 | − | 0.970143i | \(-0.577979\pi\) | ||||
−0.242536 | + | 0.970143i | \(0.577979\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 3.02045i | − | 0.692938i | −0.938061 | − | 0.346469i | \(-0.887381\pi\) | ||
0.938061 | − | 0.346469i | \(-0.112619\pi\) | |||||||
\(20\) | 3.12311 | + | 1.32431i | 0.698348 | + | 0.296124i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.56155 | + | 1.03399i | −0.332924 | + | 0.220447i | ||||
\(23\) | −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 | ||||||||
\(26\) | −2.00000 | + | 1.32431i | −0.392232 | + | 0.259718i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0.780776 | − | 1.84130i | 0.147553 | − | 0.347973i | ||||
\(29\) | − | 6.04090i | − | 1.12177i | −0.827895 | − | 0.560883i | \(-0.810462\pi\) | ||
0.827895 | − | 0.560883i | \(-0.189538\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −10.2462 | −1.84027 | −0.920137 | − | 0.391597i | \(-0.871923\pi\) | ||||
−0.920137 | + | 0.391597i | \(0.871923\pi\) | |||||||
\(32\) | −1.21922 | + | 5.52390i | −0.215530 | + | 0.976497i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.56155 | + | 2.35829i | 0.267804 | + | 0.404444i | ||||
\(35\) | 1.69614i | 0.286700i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 6.04090i | − | 0.993117i | −0.868003 | − | 0.496559i | \(-0.834597\pi\) | ||
0.868003 | − | 0.496559i | \(-0.165403\pi\) | |||||||
\(38\) | −3.56155 | + | 2.35829i | −0.577760 | + | 0.382566i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −0.876894 | − | 4.71659i | −0.138649 | − | 0.745758i | ||||
\(41\) | −4.24621 | −0.663147 | −0.331573 | − | 0.943429i | \(-0.607579\pi\) | ||||
−0.331573 | + | 0.943429i | \(0.607579\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.32431i | 0.201955i | 0.994889 | + | 0.100977i | \(0.0321970\pi\) | ||||
−0.994889 | + | 0.100977i | \(0.967803\pi\) | |||||||
\(44\) | 2.43845 | + | 1.03399i | 0.367610 | + | 0.155879i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 4.00000 | + | 6.04090i | 0.589768 | + | 0.890681i | ||||
\(47\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.00000 | 0.142857 | ||||||||
\(50\) | −1.65767 | − | 2.50345i | −0.234430 | − | 0.354042i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.12311 | + | 1.32431i | 0.433097 | + | 0.183648i | ||||
\(53\) | − | 2.64861i | − | 0.363815i | −0.983316 | − | 0.181908i | \(-0.941773\pi\) | ||
0.983316 | − | 0.181908i | \(-0.0582272\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −2.24621 | −0.302879 | ||||||||
\(56\) | −2.78078 | + | 0.516994i | −0.371597 | + | 0.0690862i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −7.12311 | + | 4.71659i | −0.935310 | + | 0.619318i | ||||
\(59\) | − | 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 | \(-0.0346317\pi\) | |||||||
\(62\) | 8.00000 | + | 12.0818i | 1.01600 | + | 1.53439i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 7.46543 | − | 2.87529i | 0.933179 | − | 0.359411i | ||||
\(65\) | −2.87689 | −0.356835 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 11.5012i | 1.40509i | 0.711640 | + | 0.702545i | \(0.247953\pi\) | ||||
−0.711640 | + | 0.702545i | \(0.752047\pi\) | |||||||
\(68\) | 1.56155 | − | 3.68260i | 0.189366 | − | 0.446581i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 2.00000 | − | 1.32431i | 0.239046 | − | 0.158285i | ||||
\(71\) | 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 | \(0.614200\pi\) | |||||||
\(74\) | −7.12311 | + | 4.71659i | −0.828044 | + | 0.548292i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 5.56155 | + | 2.35829i | 0.637954 | + | 0.270515i | ||||
\(77\) | 1.32431i | 0.150919i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(80\) | −4.87689 | + | 4.71659i | −0.545253 | + | 0.527331i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.31534 | + | 5.00691i | 0.366118 | + | 0.552921i | ||||
\(83\) | − | 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 | ||||||||
\(86\) | 1.56155 | − | 1.03399i | 0.168387 | − | 0.111498i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −0.684658 | − | 3.68260i | −0.0729848 | − | 0.392567i | ||||
\(89\) | 16.2462 | 1.72209 | 0.861047 | − | 0.508525i | \(-0.169809\pi\) | ||||
0.861047 | + | 0.508525i | \(0.169809\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.69614i | 0.177804i | ||||||||
\(92\) | 4.00000 | − | 9.43318i | 0.417029 | − | 0.983477i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 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 | \(0.286439\pi\) | |||||||
\(98\) | −0.780776 | − | 1.17915i | −0.0788703 | − | 0.119112i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.65767 | + | 3.90928i | −0.165767 | + | 0.390928i | ||||
\(101\) | − | 10.3857i | − | 1.03341i | −0.856163 | − | 0.516705i | \(-0.827158\pi\) | ||
0.856163 | − | 0.516705i | \(-0.172842\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.24621 | 0.221326 | 0.110663 | − | 0.993858i | \(-0.464703\pi\) | ||||
0.110663 | + | 0.993858i | \(0.464703\pi\) | |||||||
\(104\) | −0.876894 | − | 4.71659i | −0.0859866 | − | 0.462500i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.12311 | + | 2.06798i | −0.303343 | + | 0.200860i | ||||
\(107\) | 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 | \(-0.334543\pi\) | |||||||
\(110\) | 1.75379 | + | 2.64861i | 0.167217 | + | 0.252535i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.78078 | + | 2.87529i | 0.262759 | + | 0.271689i | ||||
\(113\) | −4.87689 | −0.458780 | −0.229390 | − | 0.973335i | \(-0.573673\pi\) | ||||
−0.229390 | + | 0.973335i | \(0.573673\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.68951i | 0.810301i | ||||||||
\(116\) | 11.1231 | + | 4.71659i | 1.03275 | + | 0.437924i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −0.438447 | + | 0.290319i | −0.0403623 | + | 0.0267261i | ||||
\(119\) | 2.00000 | 0.183340 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 9.24621 | 0.840565 | ||||||||
\(122\) | −2.00000 | + | 1.32431i | −0.181071 | + | 0.119897i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 8.00000 | − | 18.8664i | 0.718421 | − | 1.69425i | ||||
\(125\) | − | 12.0818i | − | 1.08063i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.1231 | 1.16449 | 0.582244 | − | 0.813014i | \(-0.302175\pi\) | ||||
0.582244 | + | 0.813014i | \(0.302175\pi\) | |||||||
\(128\) | −9.21922 | − | 6.55789i | −0.814872 | − | 0.579641i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.24621 | + | 3.39228i | 0.197006 | + | 0.297523i | ||||
\(131\) | − | 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 | ||||||||
\(134\) | 13.5616 | − | 8.97983i | 1.17154 | − | 0.775739i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −5.56155 | + | 1.03399i | −0.476899 | + | 0.0886637i | ||||
\(137\) | 16.2462 | 1.38801 | 0.694004 | − | 0.719971i | \(-0.255845\pi\) | ||||
0.694004 | + | 0.719971i | \(0.255845\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 8.31768i | − | 0.705496i | −0.935718 | − | 0.352748i | \(-0.885247\pi\) | ||
0.935718 | − | 0.352748i | \(-0.114753\pi\) | |||||||
\(140\) | −3.12311 | − | 1.32431i | −0.263951 | − | 0.111924i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −6.24621 | − | 9.43318i | −0.524170 | − | 0.791615i | ||||
\(143\) | −2.24621 | −0.187838 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −10.2462 | −0.850902 | ||||||||
\(146\) | 4.68466 | + | 7.07488i | 0.387705 | + | 0.585522i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 11.1231 | + | 4.71659i | 0.914314 | + | 0.387701i | ||||
\(149\) | 14.7304i | 1.20676i | 0.797453 | + | 0.603381i | \(0.206180\pi\) | ||||
−0.797453 | + | 0.603381i | \(0.793820\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.8769 | 0.885149 | 0.442575 | − | 0.896732i | \(-0.354065\pi\) | ||||
0.442575 | + | 0.896732i | \(0.354065\pi\) | |||||||
\(152\) | −1.56155 | − | 8.39919i | −0.126659 | − | 0.681264i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.56155 | − | 1.03399i | 0.125834 | − | 0.0833211i | ||||
\(155\) | 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 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 9.36932 | + | 2.06798i | 0.740710 | + | 0.163488i | ||||
\(161\) | 5.12311 | 0.403757 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.4061i | 1.05005i | 0.851088 | + | 0.525023i | \(0.175943\pi\) | ||||
−0.851088 | + | 0.525023i | \(0.824057\pi\) | |||||||
\(164\) | 3.31534 | − | 7.81855i | 0.258885 | − | 0.610526i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −6.68466 | + | 4.42627i | −0.518830 | + | 0.343545i | ||||
\(167\) | −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 | ||||||||
\(170\) | 4.00000 | − | 2.64861i | 0.306786 | − | 0.203139i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −2.43845 | − | 1.03399i | −0.185930 | − | 0.0788408i | ||||
\(173\) | 19.0752i | 1.45026i | 0.688613 | + | 0.725129i | \(0.258220\pi\) | ||||
−0.688613 | + | 0.725129i | \(0.741780\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.12311 | −0.160492 | ||||||||
\(176\) | −3.80776 | + | 3.68260i | −0.287021 | + | 0.277587i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −12.6847 | − | 19.1567i | −0.950755 | − | 1.43585i | ||||
\(179\) | − | 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 | \(-0.0836917\pi\) | |||||||
\(182\) | 2.00000 | − | 1.32431i | 0.148250 | − | 0.0981642i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −14.2462 | + | 2.64861i | −1.05024 | + | 0.195258i | ||||
\(185\) | −10.2462 | −0.753316 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.64861i | 0.193686i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 4.00000 | + | 6.04090i | 0.290191 | + | 0.438253i | ||||
\(191\) | −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 | \(0.631104\pi\) | |||||||
\(194\) | −9.56155 | − | 14.4401i | −0.686479 | − | 1.03674i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.780776 | + | 1.84130i | −0.0557697 | + | 0.131521i | ||||
\(197\) | 21.5150i | 1.53288i | 0.642317 | + | 0.766439i | \(0.277973\pi\) | ||||
−0.642317 | + | 0.766439i | \(0.722027\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −18.2462 | −1.29344 | −0.646720 | − | 0.762728i | \(-0.723860\pi\) | ||||
−0.646720 | + | 0.762728i | \(0.723860\pi\) | |||||||
\(200\) | 5.90388 | − | 1.09763i | 0.417468 | − | 0.0776143i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −12.2462 | + | 8.10887i | −0.861640 | + | 0.570538i | ||||
\(203\) | 6.04090i | 0.423988i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 7.20217i | 0.503022i | ||||||||
\(206\) | −1.75379 | − | 2.64861i | −0.122192 | − | 0.184538i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.87689 | + | 4.71659i | −0.338152 | + | 0.327037i | ||||
\(209\) | −4.00000 | −0.276686 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.71659i | 0.324703i | 0.986733 | + | 0.162352i | \(0.0519079\pi\) | ||||
−0.986733 | + | 0.162352i | \(0.948092\pi\) | |||||||
\(212\) | 4.87689 | + | 2.06798i | 0.334946 | + | 0.142029i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 16.6847 | − | 11.0478i | 1.14054 | − | 0.755212i | ||||
\(215\) | 2.24621 | 0.153190 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 10.2462 | 0.695558 | ||||||||
\(218\) | −21.3693 | + | 14.1498i | −1.44731 | + | 0.958343i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1.75379 | − | 4.13595i | 0.118240 | − | 0.278846i | ||||
\(221\) | 3.39228i | 0.228190i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.75379 | −0.385302 | −0.192651 | − | 0.981267i | \(-0.561709\pi\) | ||||
−0.192651 | + | 0.981267i | \(0.561709\pi\) | |||||||
\(224\) | 1.21922 | − | 5.52390i | 0.0814628 | − | 0.369081i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.80776 | + | 5.75058i | 0.253289 | + | 0.382523i | ||||
\(227\) | 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 | \(0.673907\pi\) | |||||||
\(230\) | 10.2462 | − | 6.78456i | 0.675615 | − | 0.447361i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.12311 | − | 16.7984i | −0.205042 | − | 1.10287i | ||||
\(233\) | 16.2462 | 1.06432 | 0.532162 | − | 0.846642i | \(-0.321380\pi\) | ||||
0.532162 | + | 0.846642i | \(0.321380\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0.684658 | + | 0.290319i | 0.0445675 | + | 0.0188982i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1.56155 | − | 2.35829i | −0.101220 | − | 0.152866i | ||||
\(239\) | 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 | \(0.538578\pi\) | |||||||
\(242\) | −7.21922 | − | 10.9026i | −0.464069 | − | 0.700849i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.12311 | + | 1.32431i | 0.199936 | + | 0.0847801i | ||||
\(245\) | − | 1.69614i | − | 0.108362i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −5.12311 | −0.325975 | ||||||||
\(248\) | −28.4924 | + | 5.29723i | −1.80927 | + | 0.336374i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −14.2462 | + | 9.43318i | −0.901010 | + | 0.596607i | ||||
\(251\) | − | 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 | ||||||||
\(254\) | −10.2462 | − | 15.4741i | −0.642904 | − | 0.970930i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.534565 | + | 15.9911i | −0.0334103 | + | 0.999442i | ||||
\(257\) | −22.4924 | −1.40304 | −0.701519 | − | 0.712650i | \(-0.747495\pi\) | ||||
−0.701519 | + | 0.712650i | \(0.747495\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 6.04090i | 0.375363i | ||||||||
\(260\) | 2.24621 | − | 5.29723i | 0.139304 | − | 0.328520i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −14.6847 | + | 9.72350i | −0.907221 | + | 0.600720i | ||||
\(263\) | −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 | ||||||||
\(266\) | 3.56155 | − | 2.35829i | 0.218373 | − | 0.144596i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −21.1771 | − | 8.97983i | −1.29360 | − | 0.548530i | ||||
\(269\) | − | 11.8730i | − | 0.723909i | −0.932196 | − | 0.361954i | \(-0.882110\pi\) | ||
0.932196 | − | 0.361954i | \(-0.117890\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 10.2462 | 0.622413 | 0.311207 | − | 0.950342i | \(-0.399267\pi\) | ||||
0.311207 | + | 0.950342i | \(0.399267\pi\) | |||||||
\(272\) | 5.56155 | + | 5.75058i | 0.337219 | + | 0.348680i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −12.6847 | − | 19.1567i | −0.766308 | − | 1.15730i | ||||
\(275\) | − | 2.81164i | − | 0.169548i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.64861i | 0.159140i | 0.996829 | + | 0.0795699i | \(0.0253547\pi\) | ||||
−0.996829 | + | 0.0795699i | \(0.974645\pi\) | |||||||
\(278\) | −9.80776 | + | 6.49424i | −0.588231 | + | 0.389499i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0.876894 | + | 4.71659i | 0.0524045 | + | 0.281870i | ||||
\(281\) | 6.00000 | 0.357930 | 0.178965 | − | 0.983855i | \(-0.442725\pi\) | ||||
0.178965 | + | 0.983855i | \(0.442725\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 21.8868i | − | 1.30104i | −0.759491 | − | 0.650518i | \(-0.774552\pi\) | ||
0.759491 | − | 0.650518i | \(-0.225448\pi\) | |||||||
\(284\) | −6.24621 | + | 14.7304i | −0.370644 | + | 0.874089i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.75379 | + | 2.64861i | 0.103704 | + | 0.156616i | ||||
\(287\) | 4.24621 | 0.250646 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −13.0000 | −0.764706 | ||||||||
\(290\) | 8.00000 | + | 12.0818i | 0.469776 | + | 0.709467i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.68466 | − | 11.0478i | 0.274149 | − | 0.646524i | ||||
\(293\) | − | 10.3857i | − | 0.606736i | −0.952873 | − | 0.303368i | \(-0.901889\pi\) | ||
0.952873 | − | 0.303368i | \(-0.0981112\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.630683 | −0.0367198 | ||||||||
\(296\) | −3.12311 | − | 16.7984i | −0.181527 | − | 0.976386i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 17.3693 | − | 11.5012i | 1.00618 | − | 0.666244i | ||||
\(299\) | 8.68951i | 0.502527i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 1.32431i | − | 0.0763318i | ||||||
\(302\) | −8.49242 | − | 12.8255i | −0.488684 | − | 0.738022i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −8.68466 | + | 8.39919i | −0.498099 | + | 0.481727i | ||||
\(305\) | −2.87689 | −0.164730 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 25.2791i | − | 1.44275i | −0.692543 | − | 0.721377i | \(-0.743510\pi\) | ||
0.692543 | − | 0.721377i | \(-0.256490\pi\) | |||||||
\(308\) | −2.43845 | − | 1.03399i | −0.138943 | − | 0.0589169i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 20.4924 | − | 13.5691i | 1.16389 | − | 0.770675i | ||||
\(311\) | 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 | \(0.699341\pi\) | |||||||
\(314\) | −10.0000 | + | 6.62153i | −0.564333 | + | 0.373675i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 4.13595i | − | 0.232298i | −0.993232 | − | 0.116149i | \(-0.962945\pi\) | ||
0.993232 | − | 0.116149i | \(-0.0370550\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −8.00000 | −0.447914 | ||||||||
\(320\) | −4.87689 | − | 12.6624i | −0.272627 | − | 0.707851i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.00000 | − | 6.04090i | −0.222911 | − | 0.336646i | ||||
\(323\) | 6.04090i | 0.336124i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 3.60109i | − | 0.199752i | ||||||
\(326\) | 15.8078 | − | 10.4672i | 0.875511 | − | 0.579723i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −11.8078 | + | 2.19526i | −0.651975 | + | 0.121213i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 14.8934i | 0.818617i | 0.912396 | + | 0.409309i | \(0.134230\pi\) | ||||
−0.912396 | + | 0.409309i | \(0.865770\pi\) | |||||||
\(332\) | 10.4384 | + | 4.42627i | 0.572884 | + | 0.242923i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 6.24621 | + | 9.43318i | 0.341777 | + | 0.516161i | ||||
\(335\) | 19.5076 | 1.06581 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.876894 | −0.0477675 | −0.0238837 | − | 0.999715i | \(-0.507603\pi\) | ||||
−0.0238837 | + | 0.999715i | \(0.507603\pi\) | |||||||
\(338\) | −7.90388 | − | 11.9366i | −0.429915 | − | 0.649267i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −6.24621 | − | 2.64861i | −0.338748 | − | 0.143641i | ||||
\(341\) | 13.5691i | 0.734809i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.00000 | −0.0539949 | ||||||||
\(344\) | 0.684658 | + | 3.68260i | 0.0369143 | + | 0.198553i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 22.4924 | − | 14.8934i | 1.20920 | − | 0.800676i | ||||
\(347\) | − | 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 | \(0.738621\pi\) | |||||||
\(350\) | 1.65767 | + | 2.50345i | 0.0886062 | + | 0.133815i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 7.31534 | + | 1.61463i | 0.389909 | + | 0.0860599i | ||||
\(353\) | −7.75379 | −0.412693 | −0.206346 | − | 0.978479i | \(-0.566157\pi\) | ||||
−0.206346 | + | 0.978479i | \(0.566157\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 13.5691i | − | 0.720175i | ||||||
\(356\) | −12.6847 | + | 29.9142i | −0.672286 | + | 1.58545i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.56155 | + | 3.68260i | −0.293937 | + | 0.194632i | ||||
\(359\) | 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 | ||||||||
\(362\) | −8.24621 | + | 5.46026i | −0.433411 | + | 0.286985i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −3.12311 | − | 1.32431i | −0.163695 | − | 0.0694125i | ||||
\(365\) | 10.1768i | 0.532680i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.2462 | 0.534848 | 0.267424 | − | 0.963579i | \(-0.413828\pi\) | ||||
0.267424 | + | 0.963579i | \(0.413828\pi\) | |||||||
\(368\) | 14.2462 | + | 14.7304i | 0.742635 | + | 0.767875i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 8.00000 | + | 12.0818i | 0.415900 | + | 0.628102i | ||||
\(371\) | 2.64861i | 0.137509i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 14.7304i | − | 0.762711i | −0.924428 | − | 0.381356i | \(-0.875457\pi\) | ||
0.924428 | − | 0.381356i | \(-0.124543\pi\) | |||||||
\(374\) | 3.12311 | − | 2.06798i | 0.161492 | − | 0.106932i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −10.2462 | −0.527707 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 36.4084i | − | 1.87017i | −0.354418 | − | 0.935087i | \(-0.615321\pi\) | ||
0.354418 | − | 0.935087i | \(-0.384679\pi\) | |||||||
\(380\) | 4.00000 | − | 9.43318i | 0.205196 | − | 0.483912i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 12.4924 | + | 18.8664i | 0.639168 | + | 0.965287i | ||||
\(383\) | 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 | ||||||||
\(386\) | 8.68466 | + | 13.1158i | 0.442037 | + | 0.667576i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −9.56155 | + | 22.5490i | −0.485414 | + | 1.14475i | ||||
\(389\) | − | 24.9073i | − | 1.26285i | −0.775438 | − | 0.631424i | \(-0.782471\pi\) | ||
0.775438 | − | 0.631424i | \(-0.217529\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 10.2462 | 0.518173 | ||||||||
\(392\) | 2.78078 | − | 0.516994i | 0.140450 | − | 0.0261121i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 25.3693 | − | 16.7984i | 1.27809 | − | 0.846290i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.5625i | 1.03200i | 0.856588 | + | 0.516001i | \(0.172580\pi\) | ||||
−0.856588 | + | 0.516001i | \(0.827420\pi\) | |||||||
\(398\) | 14.2462 | + | 21.5150i | 0.714098 | + | 1.07845i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −5.90388 | − | 6.10454i | −0.295194 | − | 0.305227i | ||||
\(401\) | 0.876894 | 0.0437900 | 0.0218950 | − | 0.999760i | \(-0.493030\pi\) | ||||
0.0218950 | + | 0.999760i | \(0.493030\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17.3790i | 0.865711i | ||||||||
\(404\) | 19.1231 | + | 8.10887i | 0.951410 | + | 0.403431i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.12311 | − | 4.71659i | 0.353514 | − | 0.234080i | ||||
\(407\) | −8.00000 | −0.396545 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.0000 | 1.28562 | 0.642809 | − | 0.766027i | \(-0.277769\pi\) | ||||
0.642809 | + | 0.766027i | \(0.277769\pi\) | |||||||
\(410\) | 8.49242 | − | 5.62329i | 0.419411 | − | 0.277714i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.75379 | + | 4.13595i | −0.0864030 | + | 0.203764i | ||||
\(413\) | 0.371834i | 0.0182968i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −9.61553 | −0.472008 | ||||||||
\(416\) | 9.36932 | + | 2.06798i | 0.459369 | + | 0.101391i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.12311 | + | 4.71659i | 0.152756 | + | 0.230696i | ||||
\(419\) | − | 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 | \(0.773353\pi\) | |||||||
\(422\) | 5.56155 | − | 3.68260i | 0.270732 | − | 0.179266i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.36932 | − | 7.36520i | −0.0664999 | − | 0.357686i | ||||
\(425\) | −4.24621 | −0.205971 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.69614i | 0.0820820i | ||||||||
\(428\) | −26.0540 | − | 11.0478i | −1.25937 | − | 0.534016i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.75379 | − | 2.64861i | −0.0845752 | − | 0.127727i | ||||
\(431\) | −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 | \(0.646563\pi\) | |||||||
\(434\) | −8.00000 | − | 12.0818i | −0.384012 | − | 0.579945i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 33.3693 | + | 14.1498i | 1.59810 | + | 0.677651i | ||||
\(437\) | 15.4741i | 0.740225i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 22.7386 | 1.08526 | 0.542628 | − | 0.839973i | \(-0.317429\pi\) | ||||
0.542628 | + | 0.839973i | \(0.317429\pi\) | |||||||
\(440\) | −6.24621 | + | 1.16128i | −0.297776 | + | 0.0553617i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 4.00000 | − | 2.64861i | 0.190261 | − | 0.125982i | ||||
\(443\) | 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 | ||||||
\(446\) | 4.49242 | + | 6.78456i | 0.212722 | + | 0.321258i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −7.46543 | + | 2.87529i | −0.352709 | + | 0.135845i | ||||
\(449\) | −16.7386 | −0.789945 | −0.394972 | − | 0.918693i | \(-0.629246\pi\) | ||||
−0.394972 | + | 0.918693i | \(0.629246\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.62329i | 0.264790i | ||||||||
\(452\) | 3.80776 | − | 8.97983i | 0.179102 | − | 0.422376i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 11.5616 | − | 7.65552i | 0.542611 | − | 0.359291i | ||||
\(455\) | 2.87689 | 0.134871 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 17.3693 | 0.812502 | 0.406251 | − | 0.913761i | \(-0.366836\pi\) | ||||
0.406251 | + | 0.913761i | \(0.366836\pi\) | |||||||
\(458\) | 30.4924 | − | 20.1907i | 1.42482 | − | 0.943448i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −16.0000 | − | 6.78456i | −0.746004 | − | 0.316332i | ||||
\(461\) | − | 24.3724i | − | 1.13514i | −0.823327 | − | 0.567568i | \(-0.807885\pi\) | ||
0.823327 | − | 0.567568i | \(-0.192115\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(464\) | −17.3693 | + | 16.7984i | −0.806350 | + | 0.779845i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −12.6847 | − | 19.1567i | −0.587605 | − | 0.887416i | ||||
\(467\) | 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 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −0.192236 | − | 1.03399i | −0.00884838 | − | 0.0475931i | ||||
\(473\) | 1.75379 | 0.0806393 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 6.41273i | − | 0.294236i | ||||||
\(476\) | −1.56155 | + | 3.68260i | −0.0715737 | + | 0.168792i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −13.7538 | − | 20.7713i | −0.629084 | − | 0.950057i | ||||
\(479\) | −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 | ||||||||
\(482\) | 2.93087 | + | 4.42627i | 0.133497 | + | 0.201611i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −7.21922 | + | 17.0251i | −0.328147 | + | 0.773866i | ||||
\(485\) | − | 20.7713i | − | 0.943176i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 0.630683 | 0.0285790 | 0.0142895 | − | 0.999898i | \(-0.495451\pi\) | ||||
0.0142895 | + | 0.999898i | \(0.495451\pi\) | |||||||
\(488\) | −0.876894 | − | 4.71659i | −0.0396951 | − | 0.213510i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2.00000 | + | 1.32431i | −0.0903508 | + | 0.0598261i | ||||
\(491\) | − | 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 | ||||||||
\(494\) | 4.00000 | + | 6.04090i | 0.179969 | + | 0.271793i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 28.4924 | + | 29.4608i | 1.27935 | + | 1.32283i | ||||
\(497\) | −8.00000 | −0.358849 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 8.85254i | − | 0.396294i | −0.980172 | − | 0.198147i | \(-0.936508\pi\) | ||
0.980172 | − | 0.198147i | \(-0.0634924\pi\) | |||||||
\(500\) | 22.2462 | + | 9.43318i | 0.994881 | + | 0.421865i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −12.9309 | + | 8.56222i | −0.577133 | + | 0.382151i | ||||
\(503\) | −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 | ||||||||
\(506\) | 8.00000 | − | 5.29723i | 0.355643 | − | 0.235490i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −10.2462 | + | 24.1636i | −0.454602 | + | 1.07209i | ||||
\(509\) | 30.7393i | 1.36250i | 0.732052 | + | 0.681249i | \(0.238563\pi\) | ||||
−0.732052 | + | 0.681249i | \(0.761437\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 6.00000 | 0.265424 | ||||||||
\(512\) | 19.2732 | − | 11.8551i | 0.851763 | − | 0.523927i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 17.5616 | + | 26.5219i | 0.774607 | + | 1.16983i | ||||
\(515\) | − | 3.80989i | − | 0.167884i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 7.12311 | − | 4.71659i | 0.312971 | − | 0.207235i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −8.00000 | + | 1.48734i | −0.350823 | + | 0.0652240i | ||||
\(521\) | 22.0000 | 0.963837 | 0.481919 | − | 0.876216i | \(-0.339940\pi\) | ||||
0.481919 | + | 0.876216i | \(0.339940\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 41.1708i | − | 1.80027i | −0.435609 | − | 0.900136i | \(-0.643467\pi\) | ||
0.435609 | − | 0.900136i | \(-0.356533\pi\) | |||||||
\(524\) | 22.9309 | + | 9.72350i | 1.00174 | + | 0.424773i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 9.75379 | + | 14.7304i | 0.425285 | + | 0.642276i | ||||
\(527\) | 20.4924 | 0.892664 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3.24621 | 0.141140 | ||||||||
\(530\) | 3.50758 | + | 5.29723i | 0.152359 | + | 0.230097i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5.56155 | − | 2.35829i | −0.241124 | − | 0.102245i | ||||
\(533\) | 7.20217i | 0.311961i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 24.0000 | 1.03761 | ||||||||
\(536\) | 5.94602 | + | 31.9821i | 0.256829 | + | 1.38142i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −14.0000 | + | 9.27015i | −0.603583 | + | 0.399664i | ||||
\(539\) | − | 1.32431i | − | 0.0570419i | ||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 13.2431i | − | 0.569364i | −0.958622 | − | 0.284682i | \(-0.908112\pi\) | ||
0.958622 | − | 0.284682i | \(-0.0918880\pi\) | |||||||
\(542\) | −8.00000 | − | 12.0818i | −0.343629 | − | 0.518957i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.43845 | − | 11.0478i | 0.104548 | − | 0.473671i | ||||
\(545\) | −30.7386 | −1.31670 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.59621i | 0.410304i | 0.978730 | + | 0.205152i | \(0.0657689\pi\) | ||||
−0.978730 | + | 0.205152i | \(0.934231\pi\) | |||||||
\(548\) | −12.6847 | + | 29.9142i | −0.541862 | + | 1.27787i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.31534 | + | 2.19526i | −0.141367 | + | 0.0936064i | ||||
\(551\) | −18.2462 | −0.777315 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 3.12311 | − | 2.06798i | 0.132688 | − | 0.0878598i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 15.3153 | + | 6.49424i | 0.649515 | + | 0.275417i | ||||
\(557\) | 2.64861i | 0.112225i | 0.998424 | + | 0.0561127i | \(0.0178706\pi\) | ||||
−0.998424 | + | 0.0561127i | \(0.982129\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.24621 | 0.0950046 | ||||||||
\(560\) | 4.87689 | − | 4.71659i | 0.206086 | − | 0.199312i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −4.68466 | − | 7.07488i | −0.197610 | − | 0.298436i | ||||
\(563\) | − | 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 | ||||||||
\(566\) | −25.8078 | + | 17.0887i | −1.08478 | + | 0.718292i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 22.2462 | − | 4.13595i | 0.933430 | − | 0.173541i | ||||
\(569\) | 13.3693 | 0.560471 | 0.280235 | − | 0.959931i | \(-0.409587\pi\) | ||||
0.280235 | + | 0.959931i | \(0.409587\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 9.27015i | − | 0.387944i | −0.981007 | − | 0.193972i | \(-0.937863\pi\) | ||
0.981007 | − | 0.193972i | \(-0.0621370\pi\) | |||||||
\(572\) | 1.75379 | − | 4.13595i | 0.0733296 | − | 0.172933i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.31534 | − | 5.00691i | −0.138380 | − | 0.208984i | ||||
\(575\) | −10.8769 | −0.453598 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.75379 | 0.322794 | 0.161397 | − | 0.986890i | \(-0.448400\pi\) | ||||
0.161397 | + | 0.986890i | \(0.448400\pi\) | |||||||
\(578\) | 10.1501 | + | 15.3289i | 0.422188 | + | 0.637599i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 8.00000 | − | 18.8664i | 0.332182 | − | 0.783383i | ||||
\(581\) | 5.66906i | 0.235192i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.50758 | −0.145269 | ||||||||
\(584\) | −16.6847 | + | 3.10196i | −0.690416 | + | 0.128360i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −12.2462 | + | 8.10887i | −0.505886 | + | 0.334974i | ||||
\(587\) | 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 | ||||||||
\(590\) | 0.492423 | + | 0.743668i | 0.0202727 | + | 0.0306163i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −17.3693 | + | 16.7984i | −0.713875 | + | 0.690409i | ||||
\(593\) | −18.0000 | −0.739171 | −0.369586 | − | 0.929197i | \(-0.620500\pi\) | ||||
−0.369586 | + | 0.929197i | \(0.620500\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 3.39228i | − | 0.139070i | ||||||
\(596\) | −27.1231 | − | 11.5012i | −1.11101 | − | 0.471106i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 10.2462 | − | 6.78456i | 0.418999 | − | 0.277441i | ||||
\(599\) | 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 | \(0.607504\pi\) | |||||||
\(602\) | −1.56155 | + | 1.03399i | −0.0636441 | + | 0.0421422i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −8.49242 | + | 20.0276i | −0.345552 | + | 0.814913i | ||||
\(605\) | − | 15.6829i | − | 0.637600i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 40.9848 | 1.66352 | 0.831762 | − | 0.555133i | \(-0.187333\pi\) | ||||
0.831762 | + | 0.555133i | \(0.187333\pi\) | |||||||
\(608\) | 16.6847 | + | 3.68260i | 0.676652 | + | 0.149349i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.24621 | + | 3.39228i | 0.0909464 | + | 0.137349i | ||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 2.23100i | − | 0.0901094i | −0.998985 | − | 0.0450547i | \(-0.985654\pi\) | ||
0.998985 | − | 0.0450547i | \(-0.0143462\pi\) | |||||||
\(614\) | −29.8078 | + | 19.7373i | −1.20294 | + | 0.796533i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.684658 | + | 3.68260i | 0.0275857 | + | 0.148376i | ||||
\(617\) | 29.3693 | 1.18236 | 0.591182 | − | 0.806538i | \(-0.298661\pi\) | ||||
0.591182 | + | 0.806538i | \(0.298661\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 19.6558i | 0.790033i | 0.918674 | + | 0.395017i | \(0.129261\pi\) | ||||
−0.918674 | + | 0.395017i | \(0.870739\pi\) | |||||||
\(620\) | −32.0000 | − | 13.5691i | −1.28515 | − | 0.544949i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −9.75379 | − | 14.7304i | −0.391091 | − | 0.590635i | ||||
\(623\) | −16.2462 | −0.650891 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.87689 | −0.395076 | ||||||||
\(626\) | 16.1922 | + | 24.4539i | 0.647172 | + | 0.977375i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 15.6155 | + | 6.62153i | 0.623127 | + | 0.264228i | ||||
\(629\) | 12.0818i | 0.481733i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.50758 | −0.139634 | −0.0698172 | − | 0.997560i | \(-0.522242\pi\) | ||||
−0.0698172 | + | 0.997560i | \(0.522242\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −4.87689 | + | 3.22925i | −0.193686 | + | 0.128250i | ||||
\(635\) | − | 22.2586i | − | 0.883307i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 1.69614i | − | 0.0672036i | ||||||
\(638\) | 6.24621 | + | 9.43318i | 0.247290 | + | 0.373463i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −11.1231 | + | 15.6371i | −0.439679 | + | 0.618111i | ||||
\(641\) | 5.36932 | 0.212075 | 0.106038 | − | 0.994362i | \(-0.466184\pi\) | ||||
0.106038 | + | 0.994362i | \(0.466184\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.66906i | 0.223566i | 0.993733 | + | 0.111783i | \(0.0356562\pi\) | ||||
−0.993733 | + | 0.111783i | \(0.964344\pi\) | |||||||
\(644\) | −4.00000 | + | 9.43318i | −0.157622 | + | 0.371719i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.12311 | − | 4.71659i | 0.280255 | − | 0.185572i | ||||
\(647\) | −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 | ||||||||
\(650\) | −4.24621 | + | 2.81164i | −0.166550 | + | 0.110282i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −24.6847 | − | 10.4672i | −0.966726 | − | 0.409926i | ||||
\(653\) | 31.6918i | 1.24020i | 0.784524 | + | 0.620098i | \(0.212907\pi\) | ||||
−0.784524 | + | 0.620098i | \(0.787093\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −21.1231 | −0.825348 | ||||||||
\(656\) | 11.8078 | + | 12.2091i | 0.461016 | + | 0.476685i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 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 | \(-0.335766\pi\) | |||||||
\(662\) | 17.5616 | − | 11.6284i | 0.682549 | − | 0.451952i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.93087 | − | 15.7644i | −0.113740 | − | 0.611777i | ||||
\(665\) | 5.12311 | 0.198666 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 30.9481i | 1.19832i | ||||||||
\(668\) | 6.24621 | − | 14.7304i | 0.241673 | − | 0.569936i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −15.2311 | − | 23.0023i | −0.588427 | − | 0.888657i | ||||
\(671\) | −2.24621 | −0.0867140 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −38.9848 | −1.50276 | −0.751378 | − | 0.659872i | \(-0.770610\pi\) | ||||
−0.751378 | + | 0.659872i | \(0.770610\pi\) | |||||||
\(674\) | 0.684658 | + | 1.03399i | 0.0263721 | + | 0.0398277i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −7.90388 | + | 18.6397i | −0.303995 | + | 0.716911i | ||||
\(677\) | − | 17.1702i | − | 0.659905i | −0.943998 | − | 0.329952i | \(-0.892967\pi\) | ||
0.943998 | − | 0.329952i | \(-0.107033\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −12.2462 | −0.469966 | ||||||||
\(680\) | 1.75379 | + | 9.43318i | 0.0672547 | + | 0.361746i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 16.0000 | − | 10.5945i | 0.612672 | − | 0.405683i | ||||
\(683\) | 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 | ||||||
\(686\) | 0.780776 | + | 1.17915i | 0.0298102 | + | 0.0450201i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 3.80776 | − | 3.68260i | 0.145170 | − | 0.140398i | ||||
\(689\) | −4.49242 | −0.171148 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 38.8482i | − | 1.47786i | −0.673785 | − | 0.738928i | \(-0.735332\pi\) | ||
0.673785 | − | 0.738928i | \(-0.264668\pi\) | |||||||
\(692\) | −35.1231 | − | 14.8934i | −1.33518 | − | 0.566163i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.56155 | + | 6.33122i | −0.362952 | + | 0.240330i | ||||
\(695\) | −14.1080 | −0.535145 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.49242 | 0.321673 | ||||||||
\(698\) | 32.2462 | − | 21.3519i | 1.22054 | − | 0.808183i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.65767 | − | 3.90928i | 0.0626541 | − | 0.147757i | ||||
\(701\) | − | 2.23100i | − | 0.0842639i | −0.999112 | − | 0.0421319i | \(-0.986585\pi\) | ||
0.999112 | − | 0.0421319i | \(-0.0134150\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −18.2462 | −0.688169 | ||||||||
\(704\) | −3.80776 | − | 9.88653i | −0.143511 | − | 0.372612i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.05398 | + | 9.14286i | 0.227844 | + | 0.344096i | ||||
\(707\) | 10.3857i | 0.390593i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28.7171i | 1.07849i | 0.842147 | + | 0.539247i | \(0.181291\pi\) | ||||
−0.842147 | + | 0.539247i | \(0.818709\pi\) | |||||||
\(710\) | −16.0000 | + | 10.5945i | −0.600469 | + | 0.397603i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 45.1771 | − | 8.39919i | 1.69308 | − | 0.314773i | ||||
\(713\) | 52.4924 | 1.96586 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.80989i | 0.142482i | ||||||||
\(716\) | 8.68466 | + | 3.68260i | 0.324561 | + | 0.137625i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −24.4924 | − | 36.9890i | −0.914049 | − | 1.38042i | ||||
\(719\) | 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 | ||||||||
\(722\) | −7.71165 | − | 11.6463i | −0.286998 | − | 0.433431i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 12.8769 | + | 5.46026i | 0.478566 | + | 0.202929i | ||||
\(725\) | − | 12.8255i | − | 0.476326i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −16.9848 | −0.629933 | −0.314967 | − | 0.949103i | \(-0.601993\pi\) | ||||
−0.314967 | + | 0.949103i | \(0.601993\pi\) | |||||||
\(728\) | 0.876894 | + | 4.71659i | 0.0324999 | + | 0.174808i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 12.0000 | − | 7.94584i | 0.444140 | − | 0.294089i | ||||
\(731\) | − | 2.64861i | − | 0.0979625i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.2520i | 1.08045i | 0.841521 | + | 0.540224i | \(0.181660\pi\) | ||||
−0.841521 | + | 0.540224i | \(0.818340\pi\) | |||||||
\(734\) | −8.00000 | − | 12.0818i | −0.295285 | − | 0.445947i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.24621 | − | 28.2995i | 0.230238 | − | 1.04313i | ||||
\(737\) | 15.2311 | 0.561043 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 21.3519i | − | 0.785444i | −0.919657 | − | 0.392722i | \(-0.871533\pi\) | ||
0.919657 | − | 0.392722i | \(-0.128467\pi\) | |||||||
\(740\) | 8.00000 | − | 18.8664i | 0.294086 | − | 0.693541i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.12311 | − | 2.06798i | 0.114653 | − | 0.0759178i | ||||
\(743\) | −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 | ||||||||
\(746\) | −17.3693 | + | 11.5012i | −0.635936 | + | 0.421087i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −4.87689 | − | 2.06798i | −0.178317 | − | 0.0756127i | ||||
\(749\) | − | 14.1498i | − | 0.517021i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.63068 | 0.314938 | 0.157469 | − | 0.987524i | \(-0.449667\pi\) | ||||
0.157469 | + | 0.987524i | \(0.449667\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.00000 | + | 12.0818i | 0.291343 | + | 0.439993i | ||||
\(755\) | − | 18.4487i | − | 0.671419i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 26.3946i | − | 0.959328i | −0.877452 | − | 0.479664i | \(-0.840759\pi\) | ||
0.877452 | − | 0.479664i | \(-0.159241\pi\) | |||||||
\(758\) | −42.9309 | + | 28.4268i | −1.55932 | + | 1.03251i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −14.2462 | + | 2.64861i | −0.516764 | + | 0.0960753i | ||||
\(761\) | −8.73863 | −0.316775 | −0.158388 | − | 0.987377i | \(-0.550630\pi\) | ||||
−0.158388 | + | 0.987377i | \(0.550630\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 18.1227i | 0.656085i | ||||||||
\(764\) | 12.4924 | − | 29.4608i | 0.451960 | − | 1.06585i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3.50758 | − | 5.29723i | −0.126734 | − | 0.191397i | ||||
\(767\) | −0.630683 | −0.0227726 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −40.2462 | −1.45132 | −0.725658 | − | 0.688056i | \(-0.758464\pi\) | ||||
−0.725658 | + | 0.688056i | \(0.758464\pi\) | |||||||
\(770\) | −1.75379 | − | 2.64861i | −0.0632022 | − | 0.0954494i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8.68466 | − | 20.4810i | 0.312568 | − | 0.737127i | ||||
\(773\) | − | 1.69614i | − | 0.0610060i | −0.999535 | − | 0.0305030i | \(-0.990289\pi\) | ||
0.999535 | − | 0.0305030i | \(-0.00971091\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −21.7538 | −0.781419 | ||||||||
\(776\) | 34.0540 | − | 6.33122i | 1.22247 | − | 0.227277i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −29.3693 | + | 19.4470i | −1.05294 | + | 0.697209i | ||||
\(779\) | 12.8255i | 0.459520i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 10.5945i | − | 0.379099i | ||||||
\(782\) | −8.00000 | − | 12.0818i | −0.286079 | − | 0.432044i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.78078 | − | 2.87529i | −0.0993134 | − | 0.102689i | ||||
\(785\) | −14.3845 | −0.513404 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 10.5487i | 0.376020i | 0.982167 | + | 0.188010i | \(0.0602037\pi\) | ||||
−0.982167 | + | 0.188010i | \(0.939796\pi\) | |||||||
\(788\) | −39.6155 | − | 16.7984i | −1.41124 | − | 0.598418i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4.87689 | 0.173402 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −2.87689 | −0.102162 | ||||||||
\(794\) | 24.2462 | − | 16.0547i | 0.860466 | − | 0.569760i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 14.2462 | − | 33.5968i | 0.504944 | − | 1.19081i | ||||
\(797\) | 25.8597i | 0.915998i | 0.888953 | + | 0.457999i | \(0.151434\pi\) | ||||
−0.888953 | + | 0.457999i | \(0.848566\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −2.58854 | + | 11.7278i | −0.0915187 | + | 0.414641i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −0.684658 | − | 1.03399i | −0.0241761 | − | 0.0365114i | ||||
\(803\) | 7.94584i | 0.280403i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | − | 8.68951i | − | 0.306265i | ||||||
\(806\) | 20.4924 | − | 13.5691i | 0.721815 | − | 0.477952i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.36932 | − | 28.8802i | −0.188892 | − | 1.01600i | ||||
\(809\) | −37.8617 | −1.33115 | −0.665574 | − | 0.746332i | \(-0.731813\pi\) | ||||
−0.665574 | + | 0.746332i | \(0.731813\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 15.8459i | 0.556425i | 0.960520 | + | 0.278213i | \(0.0897420\pi\) | ||||
−0.960520 | + | 0.278213i | \(0.910258\pi\) | |||||||
\(812\) | −11.1231 | − | 4.71659i | −0.390344 | − | 0.165520i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 6.24621 | + | 9.43318i | 0.218930 | + | 0.330633i | ||||
\(815\) | 22.7386 | 0.796500 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.00000 | 0.139942 | ||||||||
\(818\) | −20.3002 | − | 30.6578i | −0.709779 | − | 1.07193i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −13.2614 | − | 5.62329i | −0.463107 | − | 0.196374i | ||||
\(821\) | − | 33.5968i | − | 1.17254i | −0.810118 | − | 0.586268i | \(-0.800597\pi\) | ||
0.810118 | − | 0.586268i | \(-0.199403\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −32.9848 | −1.14978 | −0.574890 | − | 0.818231i | \(-0.694955\pi\) | ||||
−0.574890 | + | 0.818231i | \(0.694955\pi\) | |||||||
\(824\) | 6.24621 | − | 1.16128i | 0.217597 | − | 0.0404550i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0.438447 | − | 0.290319i | 0.0152555 | − | 0.0101015i | ||||
\(827\) | − | 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 | \(0.699586\pi\) | |||||||
\(830\) | 7.50758 | + | 11.3381i | 0.260592 | + | 0.393552i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.87689 | − | 12.6624i | −0.169076 | − | 0.438991i | ||||
\(833\) | −2.00000 | −0.0692959 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.5691i | 0.469579i | ||||||||
\(836\) | 3.12311 | − | 7.36520i | 0.108015 | − | 0.254731i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −32.9309 | + | 21.8053i | −1.13758 | + | 0.753251i | ||||
\(839\) | 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 | ||||||||
\(842\) | 31.6155 | − | 20.9343i | 1.08954 | − | 0.721445i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −8.68466 | − | 3.68260i | −0.298938 | − | 0.126760i | ||||
\(845\) | − | 17.1702i | − | 0.590673i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −9.24621 | −0.317704 | ||||||||
\(848\) | −7.61553 | + | 7.36520i | −0.261518 | + | 0.252922i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 3.31534 | + | 5.00691i | 0.113715 | + | 0.171736i | ||||
\(851\) | 30.9481i | 1.06089i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 25.4421i | − | 0.871121i | −0.900159 | − | 0.435561i | \(-0.856550\pi\) | ||
0.900159 | − | 0.435561i | \(-0.143450\pi\) | |||||||
\(854\) | 2.00000 | − | 1.32431i | 0.0684386 | − | 0.0453168i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 7.31534 | + | 39.3473i | 0.250033 | + | 1.34486i | ||||
\(857\) | 46.9848 | 1.60497 | 0.802486 | − | 0.596671i | \(-0.203510\pi\) | ||||
0.802486 | + | 0.596671i | \(0.203510\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 28.3453i | 0.967129i | 0.875309 | + | 0.483565i | \(0.160658\pi\) | ||||
−0.875309 | + | 0.483565i | \(0.839342\pi\) | |||||||
\(860\) | −1.75379 | + | 4.13595i | −0.0598037 | + | 0.141035i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 13.7538 | + | 20.7713i | 0.468456 | + | 0.707473i | ||||
\(863\) | −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 | ||||||||
\(866\) | 14.4384 | + | 21.8053i | 0.490638 | + | 0.740974i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −8.00000 | + | 18.8664i | −0.271538 | + | 0.640366i | ||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 19.5076 | 0.660989 | ||||||||
\(872\) | −9.36932 | − | 50.3951i | −0.317285 | − | 1.70659i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 18.2462 | − | 12.0818i | 0.617187 | − | 0.408673i | ||||
\(875\) | 12.0818i | 0.408439i | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 35.5017i | − | 1.19881i | −0.800447 | − | 0.599404i | \(-0.795404\pi\) | ||
0.800447 | − | 0.599404i | \(-0.204596\pi\) | |||||||
\(878\) | −17.7538 | − | 26.8122i | −0.599161 | − | 0.904868i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 6.24621 | + | 6.45850i | 0.210560 | + | 0.217716i | ||||
\(881\) | −44.2462 | −1.49069 | −0.745346 | − | 0.666677i | \(-0.767716\pi\) | ||||
−0.745346 | + | 0.666677i | \(0.767716\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 4.71659i | 0.158726i | 0.996846 | + | 0.0793629i | \(0.0252886\pi\) | ||||
−0.996846 | + | 0.0793629i | \(0.974711\pi\) | |||||||
\(884\) | −6.24621 | − | 2.64861i | −0.210083 | − | 0.0890825i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 8.68466 | − | 5.75058i | 0.291767 | − | 0.193194i | ||||
\(887\) | 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 | ||||||||
\(890\) | −32.4924 | + | 21.5150i | −1.08915 | + | 0.721183i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.49242 | − | 10.5945i | 0.150417 | − | 0.354729i | ||||
\(893\) | 0 | 0 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −8.00000 | −0.267411 | ||||||||
\(896\) | 9.21922 | + | 6.55789i | 0.307993 | + | 0.219084i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 13.0691 | + | 19.7373i | 0.436123 | + | 0.658643i | ||||
\(899\) | 61.8963i | 2.06436i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 5.29723i | 0.176476i | ||||||||
\(902\) | 6.63068 | − | 4.39053i | 0.220778 | − | 0.146189i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −13.5616 | + | 2.52132i | −0.451051 | + | 0.0838580i | ||||
\(905\) | −11.8617 | −0.394298 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 51.5564i | 1.71190i | 0.517056 | + | 0.855951i | \(0.327028\pi\) | ||||
−0.517056 | + | 0.855951i | \(0.672972\pi\) | |||||||
\(908\) | −18.0540 | − | 7.65552i | −0.599142 | − | 0.254057i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −2.24621 | − | 3.39228i | −0.0744612 | − | 0.112453i | ||||
\(911\) | −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 | ||||||||
\(914\) | −13.5616 | − | 20.4810i | −0.448576 | − | 0.677451i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −47.6155 | − | 20.1907i | −1.57326 | − | 0.667118i | ||||
\(917\) | 12.4536i | 0.411255i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 8.00000 | 0.263896 | 0.131948 | − | 0.991257i | \(-0.457877\pi\) | ||||
0.131948 | + | 0.991257i | \(0.457877\pi\) | |||||||
\(920\) | 4.49242 | + | 24.1636i | 0.148111 | + | 0.796650i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −28.7386 | + | 19.0294i | −0.946456 | + | 0.626699i | ||||
\(923\) | − | 13.5691i | − | 0.446633i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 12.8255i | − | 0.421699i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 33.3693 | + | 7.36520i | 1.09540 | + | 0.241775i | ||||
\(929\) | 2.49242 | 0.0817737 | 0.0408869 | − | 0.999164i | \(-0.486982\pi\) | ||||
0.0408869 | + | 0.999164i | \(0.486982\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 3.02045i | − | 0.0989912i | ||||||
\(932\) | −12.6847 | + | 29.9142i | −0.415500 | + | 0.979871i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 3.56155 | − | 2.35829i | 0.116538 | − | 0.0771658i | ||||
\(935\) | 4.49242 | 0.146918 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 34.9848 | 1.14291 | 0.571453 | − | 0.820635i | \(-0.306380\pi\) | ||||
0.571453 | + | 0.820635i | \(0.306380\pi\) | |||||||
\(938\) | −13.5616 | + | 8.97983i | −0.442800 | + | 0.293202i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 30.7393i | 1.00207i | 0.865426 | + | 0.501037i | \(0.167048\pi\) | ||||
−0.865426 | + | 0.501037i | \(0.832952\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 21.7538 | 0.708401 | ||||||||
\(944\) | −1.06913 | + | 1.03399i | −0.0347972 | + | 0.0336534i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.36932 | − | 2.06798i | −0.0445203 | − | 0.0672357i | ||||
\(947\) | 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 | ||||||||
\(950\) | −7.56155 | + | 5.00691i | −0.245329 | + | 0.162446i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 5.56155 | − | 1.03399i | 0.180251 | − | 0.0335117i | ||||
\(953\) | 17.5076 | 0.567126 | 0.283563 | − | 0.958954i | \(-0.408483\pi\) | ||||
0.283563 | + | 0.958954i | \(0.408483\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 27.1383i | 0.878173i | ||||||||
\(956\) | −13.7538 | + | 32.4355i | −0.444829 | + | 1.04904i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 8.00000 | + | 12.0818i | 0.258468 | + | 0.390345i | ||||
\(959\) | −16.2462 | −0.524618 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 73.9848 | 2.38661 | ||||||||
\(962\) | 8.00000 | + | 12.0818i | 0.257930 | + | 0.389533i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.93087 | − | 6.91185i | 0.0943970 | − | 0.222616i | ||||
\(965\) | 18.8664i | 0.607329i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.8769 | −0.349777 | −0.174889 | − | 0.984588i | \(-0.555957\pi\) | ||||
−0.174889 | + | 0.984588i | \(0.555957\pi\) | |||||||
\(968\) | 25.7116 | − | 4.78023i | 0.826404 | − | 0.153643i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −24.4924 | + | 16.2177i | −0.786404 | + | 0.520720i | ||||
\(971\) | − | 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 | ||||||||
\(974\) | −0.492423 | − | 0.743668i | −0.0157782 | − | 0.0238287i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.87689 | + | 4.71659i | −0.156106 | + | 0.150974i | ||||
\(977\) | −23.7538 | −0.759951 | −0.379976 | − | 0.924997i | \(-0.624068\pi\) | ||||
−0.379976 | + | 0.924997i | \(0.624068\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 21.5150i | − | 0.687621i | ||||||
\(980\) | 3.12311 | + | 1.32431i | 0.0997639 | + | 0.0423034i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −40.3002 | + | 26.6849i | −1.28603 | + | 0.851550i | ||||
\(983\) | 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 | ||||||||
\(986\) | 14.2462 | − | 9.43318i | 0.453692 | − | 0.300414i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.00000 | − | 9.43318i | 0.127257 | − | 0.300109i | ||||
\(989\) | − | 6.78456i | − | 0.215737i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −36.4924 | −1.15922 | −0.579610 | − | 0.814894i | \(-0.696795\pi\) | ||||
−0.579610 | + | 0.814894i | \(0.696795\pi\) | |||||||
\(992\) | 12.4924 | − | 56.5991i | 0.396635 | − | 1.79702i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 6.24621 | + | 9.43318i | 0.198118 | + | 0.299202i | ||||
\(995\) | 30.9481i | 0.981122i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 33.0619i | − | 1.04708i | −0.852001 | − | 0.523540i | \(-0.824611\pi\) | ||
0.852001 | − | 0.523540i | \(-0.175389\pi\) | |||||||
\(998\) | −10.4384 | + | 6.91185i | −0.330423 | + | 0.218791i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))