Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3024,2,Mod(17,3024)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3024, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 0, 5, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("3024.17");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3024 = 2^{4} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3024.df (of order \(6\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(24.1467615712\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 3^{6} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 17.5 | ||
Root | \(1.08696 - 1.34852i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3024.17 |
Dual form | 3024.2.df.d.1601.5 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.0764245 | −0.0341781 | −0.0170890 | − | 0.999854i | \(-0.505440\pi\) | ||||
−0.0170890 | + | 0.999854i | \(0.505440\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.39886 | + | 1.11601i | 0.906683 | + | 0.421812i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 5.38437i | − | 1.62345i | −0.584040 | − | 0.811725i | \(-0.698529\pi\) | ||
0.584040 | − | 0.811725i | \(-0.301471\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.60313 | − | 2.65762i | −1.27668 | − | 0.737091i | −0.300442 | − | 0.953800i | \(-0.597134\pi\) |
−0.976236 | + | 0.216709i | \(0.930468\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.89092 | − | 3.27516i | 0.458615 | − | 0.794344i | −0.540273 | − | 0.841490i | \(-0.681679\pi\) |
0.998888 | + | 0.0471458i | \(0.0150125\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.33939 | − | 2.50535i | 0.995525 | − | 0.574767i | 0.0886040 | − | 0.996067i | \(-0.471759\pi\) |
0.906921 | + | 0.421300i | \(0.138426\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 2.33784i | − | 0.487473i | −0.969841 | − | 0.243737i | \(-0.921627\pi\) | ||
0.969841 | − | 0.243737i | \(-0.0783732\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −4.99416 | −0.998832 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −8.84430 | + | 5.10626i | −1.64235 | + | 0.948209i | −0.662349 | + | 0.749196i | \(0.730440\pi\) |
−0.979997 | + | 0.199013i | \(0.936226\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.97636 | + | 2.87310i | −0.893780 | + | 0.516024i | −0.875177 | − | 0.483803i | \(-0.839255\pi\) |
−0.0186031 | + | 0.999827i | \(0.505922\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −0.183331 | − | 0.0852905i | −0.0309887 | − | 0.0144167i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 0.354486 | + | 0.613988i | 0.0582771 | + | 0.100939i | 0.893692 | − | 0.448681i | \(-0.148106\pi\) |
−0.835415 | + | 0.549620i | \(0.814773\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.29910 | + | 5.71422i | −0.515234 | + | 0.892411i | 0.484610 | + | 0.874730i | \(0.338961\pi\) |
−0.999844 | + | 0.0176805i | \(0.994372\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.716520 | − | 1.24105i | −0.109268 | − | 0.189258i | 0.806206 | − | 0.591635i | \(-0.201517\pi\) |
−0.915474 | + | 0.402377i | \(0.868184\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.46192 | + | 2.53213i | −0.213244 | + | 0.369349i | −0.952728 | − | 0.303825i | \(-0.901736\pi\) |
0.739484 | + | 0.673174i | \(0.235069\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.50904 | + | 5.35430i | 0.644148 | + | 0.764900i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.4835 | − | 6.05264i | −1.44002 | − | 0.831394i | −0.442167 | − | 0.896933i | \(-0.645790\pi\) |
−0.997850 | + | 0.0655390i | \(0.979123\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.411498i | 0.0554863i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.289951 | − | 0.502210i | −0.0377484 | − | 0.0653822i | 0.846534 | − | 0.532335i | \(-0.178685\pi\) |
−0.884282 | + | 0.466953i | \(0.845352\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.40641 | − | 1.38934i | −0.308109 | − | 0.177887i | 0.337971 | − | 0.941156i | \(-0.390259\pi\) |
−0.646080 | + | 0.763270i | \(0.723593\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.351792 | + | 0.203107i | 0.0436344 | + | 0.0251923i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.63593 | + | 4.56556i | 0.322030 | + | 0.557771i | 0.980907 | − | 0.194479i | \(-0.0623016\pi\) |
−0.658877 | + | 0.752251i | \(0.728968\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.32103i | 0.394134i | 0.980390 | + | 0.197067i | \(0.0631416\pi\) | ||||
−0.980390 | + | 0.197067i | \(0.936858\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.17326 | − | 3.56413i | −0.722525 | − | 0.417150i | 0.0931564 | − | 0.995651i | \(-0.470304\pi\) |
−0.815681 | + | 0.578502i | \(0.803638\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 6.00902 | − | 12.9163i | 0.684791 | − | 1.47195i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.469123 | − | 0.812544i | 0.0527804 | − | 0.0914184i | −0.838428 | − | 0.545012i | \(-0.816525\pi\) |
0.891208 | + | 0.453594i | \(0.149858\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.49790 | − | 11.2547i | −0.713238 | − | 1.23536i | −0.963635 | − | 0.267221i | \(-0.913895\pi\) |
0.250398 | − | 0.968143i | \(-0.419439\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.144512 | + | 0.250303i | −0.0156746 | + | 0.0271491i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.51794 | + | 2.62915i | 0.160901 | + | 0.278689i | 0.935192 | − | 0.354141i | \(-0.115227\pi\) |
−0.774291 | + | 0.632830i | \(0.781893\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −8.07632 | − | 11.5124i | −0.846629 | − | 1.20683i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −0.331636 | + | 0.191470i | −0.0340251 | + | 0.0196444i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.18183 | − | 3.56908i | 0.627670 | − | 0.362385i | −0.152179 | − | 0.988353i | \(-0.548629\pi\) |
0.779849 | + | 0.625967i | \(0.215296\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.17257 | −0.813201 | −0.406600 | − | 0.913606i | \(-0.633286\pi\) | ||||
−0.406600 | + | 0.913606i | \(0.633286\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 7.46628i | − | 0.735675i | −0.929890 | − | 0.367837i | \(-0.880098\pi\) | ||
0.929890 | − | 0.367837i | \(-0.119902\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.99991 | − | 2.30935i | 0.386686 | − | 0.223253i | −0.294037 | − | 0.955794i | \(-0.594999\pi\) |
0.680723 | + | 0.732541i | \(0.261666\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.22792 | − | 9.05503i | 0.500744 | − | 0.867314i | −0.499256 | − | 0.866455i | \(-0.666393\pi\) |
1.00000 | 0.000859385i | \(-0.000273551\pi\) | ||||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.6379 | + | 9.60591i | 1.56516 | + | 0.903648i | 0.996720 | + | 0.0809270i | \(0.0257881\pi\) |
0.568445 | + | 0.822721i | \(0.307545\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.178668i | 0.0166609i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 8.19116 | − | 5.74637i | 0.750882 | − | 0.526769i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −17.9915 | −1.63559 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0.763798 | 0.0683162 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.26488 | −0.112240 | −0.0561198 | − | 0.998424i | \(-0.517873\pi\) | ||||
−0.0561198 | + | 0.998424i | \(0.517873\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −14.4879 | −1.26581 | −0.632906 | − | 0.774229i | \(-0.718138\pi\) | ||||
−0.632906 | + | 0.774229i | \(0.718138\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 13.2056 | − | 1.16717i | 1.14507 | − | 0.101206i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | − | 15.4053i | − | 1.31616i | −0.752947 | − | 0.658081i | \(-0.771368\pi\) | ||
0.752947 | − | 0.658081i | \(-0.228632\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.374701 | + | 0.216333i | 0.0317817 | + | 0.0183492i | 0.515807 | − | 0.856705i | \(-0.327492\pi\) |
−0.484025 | + | 0.875054i | \(0.660826\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −14.3096 | + | 24.7850i | −1.19663 | + | 2.07262i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0.675921 | − | 0.390243i | 0.0561322 | − | 0.0324079i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.67117i | 0.382677i | 0.981524 | + | 0.191338i | \(0.0612828\pi\) | ||||
−0.981524 | + | 0.191338i | \(0.938717\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.24552 | 0.671011 | 0.335506 | − | 0.942038i | \(-0.391093\pi\) | ||||
0.335506 | + | 0.942038i | \(0.391093\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0.380316 | − | 0.219575i | 0.0305477 | − | 0.0176367i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 15.2334 | − | 8.79500i | 1.21576 | − | 0.701917i | 0.251749 | − | 0.967793i | \(-0.418994\pi\) |
0.964007 | + | 0.265875i | \(0.0856609\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2.60905 | − | 5.60814i | 0.205622 | − | 0.441984i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.27097 | + | 9.12959i | 0.412854 | + | 0.715085i | 0.995201 | − | 0.0978563i | \(-0.0311985\pi\) |
−0.582346 | + | 0.812941i | \(0.697865\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.59146 | + | 7.95265i | −0.355298 | + | 0.615395i | −0.987169 | − | 0.159679i | \(-0.948954\pi\) |
0.631871 | + | 0.775074i | \(0.282287\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 7.62587 | + | 13.2084i | 0.586605 | + | 1.01603i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1.22358 | − | 2.11931i | 0.0930274 | − | 0.161128i | −0.815756 | − | 0.578396i | \(-0.803679\pi\) |
0.908784 | + | 0.417268i | \(0.137012\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −11.9803 | − | 5.57354i | −0.905624 | − | 0.421320i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 5.05509 | + | 2.91856i | 0.377835 | + | 0.218143i | 0.676876 | − | 0.736097i | \(-0.263333\pi\) |
−0.299041 | + | 0.954240i | \(0.596667\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 16.0704i | − | 1.19451i | −0.802053 | − | 0.597253i | \(-0.796259\pi\) | ||
0.802053 | − | 0.597253i | \(-0.203741\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −0.0270914 | − | 0.0469237i | −0.00199180 | − | 0.00344990i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −17.6347 | − | 10.1814i | −1.28958 | − | 0.744537i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.90415 | − | 3.98611i | −0.499567 | − | 0.288425i | 0.228968 | − | 0.973434i | \(-0.426465\pi\) |
−0.728535 | + | 0.685009i | \(0.759798\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.359027 | − | 0.621853i | −0.0258433 | − | 0.0447620i | 0.852814 | − | 0.522214i | \(-0.174894\pi\) |
−0.878658 | + | 0.477452i | \(0.841560\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 13.5035i | 0.962083i | 0.876698 | + | 0.481042i | \(0.159741\pi\) | ||||
−0.876698 | + | 0.481042i | \(0.840259\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.2568 | − | 12.2726i | −1.50685 | − | 0.869983i | −0.999968 | − | 0.00796947i | \(-0.997463\pi\) |
−0.506886 | − | 0.862013i | \(-0.669203\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −26.9149 | + | 2.37886i | −1.88905 | + | 0.166963i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0.252132 | − | 0.436706i | 0.0176097 | − | 0.0305009i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −13.4897 | − | 23.3649i | −0.933105 | − | 1.61618i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.7838 | − | 20.4101i | 0.811227 | − | 1.40509i | −0.100778 | − | 0.994909i | \(-0.532133\pi\) |
0.912005 | − | 0.410178i | \(-0.134533\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.0547597 | + | 0.0948465i | 0.00373458 | + | 0.00646848i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −15.1440 | + | 1.33849i | −1.02804 | + | 0.0908628i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −17.4083 | + | 10.0507i | −1.17101 | + | 0.676081i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 6.47489 | − | 3.73828i | 0.433590 | − | 0.250334i | −0.267285 | − | 0.963618i | \(-0.586126\pi\) |
0.700875 | + | 0.713284i | \(0.252793\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 0.637402 | 0.0423058 | 0.0211529 | − | 0.999776i | \(-0.493266\pi\) | ||||
0.0211529 | + | 0.999776i | \(0.493266\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.82848i | 0.120829i | 0.998173 | + | 0.0604146i | \(0.0192423\pi\) | ||||
−0.998173 | + | 0.0604146i | \(0.980758\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −17.4232 | + | 10.0593i | −1.14143 | + | 0.659007i | −0.946785 | − | 0.321866i | \(-0.895690\pi\) |
−0.194649 | + | 0.980873i | \(0.562357\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.111727 | − | 0.193516i | 0.00728825 | − | 0.0126236i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −2.41455 | − | 1.39404i | −0.156184 | − | 0.0901730i | 0.419871 | − | 0.907584i | \(-0.362075\pi\) |
−0.576055 | + | 0.817411i | \(0.695409\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 23.1291i | − | 1.48988i | −0.667134 | − | 0.744938i | \(-0.732479\pi\) | ||
0.667134 | − | 0.744938i | \(-0.267521\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −0.344601 | − | 0.409200i | −0.0220157 | − | 0.0261428i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −26.6331 | −1.69462 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 18.6541 | 1.17743 | 0.588717 | − | 0.808339i | \(-0.299633\pi\) | ||||
0.588717 | + | 0.808339i | \(0.299633\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −12.5878 | −0.791388 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −10.8737 | −0.678286 | −0.339143 | − | 0.940735i | \(-0.610137\pi\) | ||||
−0.339143 | + | 0.940735i | \(0.610137\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0.165144 | + | 1.86848i | 0.0102616 | + | 0.116102i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 18.9970i | − | 1.17141i | −0.810525 | − | 0.585704i | \(-0.800818\pi\) | ||
0.810525 | − | 0.585704i | \(-0.199182\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.801194 | + | 0.462570i | 0.0492170 | + | 0.0284154i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 4.29788 | − | 7.44415i | 0.262046 | − | 0.453878i | −0.704739 | − | 0.709467i | \(-0.748936\pi\) |
0.966786 | + | 0.255589i | \(0.0822693\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.58706 | + | 0.916292i | −0.0964073 | + | 0.0556608i | −0.547429 | − | 0.836852i | \(-0.684393\pi\) |
0.451021 | + | 0.892513i | \(0.351060\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 26.8904i | 1.62155i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 15.8186 | 0.950449 | 0.475224 | − | 0.879865i | \(-0.342367\pi\) | ||||
0.475224 | + | 0.879865i | \(0.342367\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 9.95916 | − | 5.74992i | 0.594114 | − | 0.343012i | −0.172609 | − | 0.984990i | \(-0.555220\pi\) |
0.766722 | + | 0.641979i | \(0.221886\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.59806 | − | 4.96409i | 0.511101 | − | 0.295085i | −0.222185 | − | 0.975005i | \(-0.571319\pi\) |
0.733286 | + | 0.679920i | \(0.237986\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −14.2912 | + | 10.0258i | −0.843584 | + | 0.591802i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 1.34887 | + | 2.33631i | 0.0793454 | + | 0.137430i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −8.63598 | + | 14.9580i | −0.504520 | + | 0.873854i | 0.495467 | + | 0.868627i | \(0.334997\pi\) |
−0.999986 | + | 0.00522664i | \(0.998336\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0.0221594 | + | 0.0383812i | 0.00129017 | + | 0.00223464i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.21308 | + | 10.7614i | −0.359312 | + | 0.622346i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.333806 | − | 3.77675i | −0.0192402 | − | 0.217688i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0.183908 | + | 0.106180i | 0.0105306 | + | 0.00607982i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 21.6425i | − | 1.23520i | −0.786490 | − | 0.617602i | \(-0.788104\pi\) | ||
0.786490 | − | 0.617602i | \(-0.211896\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.1016 | + | 17.4964i | 0.572808 | + | 0.992133i | 0.996276 | + | 0.0862215i | \(0.0274793\pi\) |
−0.423468 | + | 0.905911i | \(0.639187\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.9146 | − | 10.9203i | −1.06911 | − | 0.617254i | −0.141175 | − | 0.989985i | \(-0.545088\pi\) |
−0.927939 | + | 0.372731i | \(0.878421\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.5288 | + | 12.4297i | 1.20918 | + | 0.698120i | 0.962580 | − | 0.270997i | \(-0.0873535\pi\) |
0.246599 | + | 0.969117i | \(0.420687\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 27.4940 | + | 47.6210i | 1.53937 | + | 2.66626i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 18.9496i | − | 1.05439i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 22.9888 | + | 13.2726i | 1.27519 | + | 0.736230i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −6.33283 | + | 4.44269i | −0.349140 | + | 0.244933i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.07219 | − | 13.9814i | 0.443688 | − | 0.768490i | −0.554272 | − | 0.832336i | \(-0.687003\pi\) |
0.997960 | + | 0.0638459i | \(0.0203366\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −0.201449 | − | 0.348920i | −0.0110063 | − | 0.0190635i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −7.81522 | + | 13.5364i | −0.425722 | + | 0.737372i | −0.996488 | − | 0.0837408i | \(-0.973313\pi\) |
0.570765 | + | 0.821113i | \(0.306647\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 15.4698 | + | 26.7946i | 0.837739 | + | 1.45101i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4.84108 | + | 17.8764i | 0.261394 | + | 0.965232i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 28.0445 | − | 16.1915i | 1.50551 | − | 0.869206i | 0.505529 | − | 0.862810i | \(-0.331297\pi\) |
0.999980 | − | 0.00639573i | \(-0.00203584\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.0421 | + | 15.0354i | −1.39400 | + | 0.804827i | −0.993755 | − | 0.111581i | \(-0.964409\pi\) |
−0.400246 | + | 0.916408i | \(0.631075\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −17.0121 | −0.905465 | −0.452733 | − | 0.891646i | \(-0.649551\pi\) | ||||
−0.452733 | + | 0.891646i | \(0.649551\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − | 0.253808i | − | 0.0134707i | ||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 25.2692 | − | 14.5892i | 1.33366 | − | 0.769987i | 0.347798 | − | 0.937570i | \(-0.386930\pi\) |
0.985858 | + | 0.167583i | \(0.0535962\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.05356 | − | 5.28892i | 0.160714 | − | 0.278364i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.471788 | + | 0.272387i | 0.0246945 | + | 0.0142574i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 18.1266i | 0.946200i | 0.881009 | + | 0.473100i | \(0.156865\pi\) | ||||
−0.881009 | + | 0.473100i | \(0.843135\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −18.3936 | − | 26.2191i | −0.954946 | − | 1.36123i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −20.3646 | −1.05444 | −0.527219 | − | 0.849730i | \(-0.676765\pi\) | ||||
−0.527219 | + | 0.849730i | \(0.676765\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 54.2820 | 2.79566 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 21.9961 | 1.12986 | 0.564931 | − | 0.825138i | \(-0.308903\pi\) | ||||
0.564931 | + | 0.825138i | \(0.308903\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 32.6253 | 1.66708 | 0.833538 | − | 0.552462i | \(-0.186312\pi\) | ||||
0.833538 | + | 0.552462i | \(0.186312\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −0.459236 | + | 0.987125i | −0.0234048 | + | 0.0503085i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 15.7501i | − | 0.798560i | −0.916829 | − | 0.399280i | \(-0.869260\pi\) | ||
0.916829 | − | 0.399280i | \(-0.130740\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.65680 | − | 4.42066i | −0.387221 | − | 0.223562i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −0.0358524 | + | 0.0620983i | −0.00180393 | + | 0.00312450i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.95864 | + | 1.70817i | −0.148490 | + | 0.0857308i | −0.572404 | − | 0.819972i | \(-0.693989\pi\) |
0.423914 | + | 0.905702i | \(0.360656\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 0.983052i | 0.0490913i | 0.999699 | + | 0.0245456i | \(0.00781390\pi\) | ||||
−0.999699 | + | 0.0245456i | \(0.992186\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 30.5424 | 1.52143 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.30594 | − | 1.90868i | 0.163869 | − | 0.0946099i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 25.0195 | − | 14.4450i | 1.23714 | − | 0.714260i | 0.268627 | − | 0.963244i | \(-0.413430\pi\) |
0.968508 | + | 0.248984i | \(0.0800966\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −0.135080 | − | 1.52832i | −0.00664684 | − | 0.0752037i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0.496599 | + | 0.860135i | 0.0243771 | + | 0.0422223i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 6.28926 | − | 10.8933i | 0.307251 | − | 0.532174i | −0.670509 | − | 0.741901i | \(-0.733924\pi\) |
0.977760 | + | 0.209727i | \(0.0672577\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.0232 | − | 22.5568i | −0.634710 | − | 1.09935i | −0.986576 | − | 0.163300i | \(-0.947786\pi\) |
0.351866 | − | 0.936050i | \(-0.385547\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −9.44354 | + | 16.3567i | −0.458079 | + | 0.793416i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.22211 | − | 6.01840i | −0.204322 | − | 0.291251i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 6.28454 | + | 3.62838i | 0.302716 | + | 0.174773i | 0.643662 | − | 0.765310i | \(-0.277414\pi\) |
−0.340947 | + | 0.940083i | \(0.610748\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.29113i | 0.398446i | 0.979954 | + | 0.199223i | \(0.0638419\pi\) | ||||
−0.979954 | + | 0.199223i | \(0.936158\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.85710 | − | 10.1448i | −0.280183 | − | 0.485292i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.83357 | + | 1.63596i | 0.135239 | + | 0.0780802i | 0.566093 | − | 0.824341i | \(-0.308454\pi\) |
−0.430854 | + | 0.902422i | \(0.641788\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.46737 | + | 1.42454i | 0.117228 | + | 0.0676817i | 0.557468 | − | 0.830199i | \(-0.311773\pi\) |
−0.440239 | + | 0.897880i | \(0.645106\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −0.116008 | − | 0.200931i | −0.00549929 | − | 0.00952505i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 19.9802i | − | 0.942925i | −0.881886 | − | 0.471463i | \(-0.843726\pi\) | ||
0.881886 | − | 0.471463i | \(-0.156274\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 30.7675 | + | 17.7636i | 1.44878 | + | 0.836455i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0.617229 | + | 0.879828i | 0.0289361 | + | 0.0412470i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −9.15008 | + | 15.8484i | −0.428023 | + | 0.741357i | −0.996697 | − | 0.0812053i | \(-0.974123\pi\) |
0.568675 | + | 0.822563i | \(0.307456\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.52954 | − | 7.84539i | −0.210962 | − | 0.365396i | 0.741054 | − | 0.671445i | \(-0.234326\pi\) |
−0.952016 | + | 0.306049i | \(0.900993\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.8227 | + | 18.7455i | −0.502974 | + | 0.871176i | 0.497021 | + | 0.867739i | \(0.334427\pi\) |
−0.999994 | + | 0.00343694i | \(0.998906\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.7761 | − | 23.8610i | −0.637484 | − | 1.10415i | −0.985983 | − | 0.166845i | \(-0.946642\pi\) |
0.348500 | − | 0.937309i | \(-0.386691\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.22800 | + | 13.8938i | 0.0567038 | + | 0.641558i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −6.68227 | + | 3.85801i | −0.307251 | + | 0.177392i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −21.6716 | + | 12.5121i | −0.994362 | + | 0.574095i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4.94651 | 0.226012 | 0.113006 | − | 0.993594i | \(-0.463952\pi\) | ||||
0.113006 | + | 0.993594i | \(0.463952\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 3.76835i | − | 0.171822i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −0.472443 | + | 0.272765i | −0.0214525 | + | 0.0123856i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 4.78573 | − | 8.28913i | 0.216862 | − | 0.375616i | −0.736985 | − | 0.675909i | \(-0.763751\pi\) |
0.953847 | + | 0.300293i | \(0.0970845\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −33.0010 | − | 19.0531i | −1.48931 | − | 0.859855i | −0.489387 | − | 0.872067i | \(-0.662779\pi\) |
−0.999925 | + | 0.0122119i | \(0.996113\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 38.6220i | 1.73945i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −3.70631 | + | 7.96668i | −0.166251 | + | 0.357355i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 24.8384 | 1.11192 | 0.555960 | − | 0.831209i | \(-0.312351\pi\) | ||||
0.555960 | + | 0.831209i | \(0.312351\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 27.2820 | 1.21645 | 0.608223 | − | 0.793766i | \(-0.291883\pi\) | ||||
0.608223 | + | 0.793766i | \(0.291883\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0.624584 | 0.0277936 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −41.7721 | −1.85152 | −0.925758 | − | 0.378117i | \(-0.876572\pi\) | ||||
−0.925758 | + | 0.378117i | \(0.876572\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −10.8312 | − | 15.4393i | −0.479142 | − | 0.682993i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.570607i | 0.0251439i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 13.6339 | + | 7.87154i | 0.599619 | + | 0.346190i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 2.02629 | − | 3.50963i | 0.0887732 | − | 0.153760i | −0.818220 | − | 0.574906i | \(-0.805039\pi\) |
0.906993 | + | 0.421146i | \(0.138372\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.2429 | + | 15.1514i | −1.14752 | + | 0.662523i | −0.948282 | − | 0.317428i | \(-0.897181\pi\) |
−0.199241 | + | 0.979951i | \(0.563848\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 21.7312i | 0.946625i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 17.5345 | 0.762370 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 30.3724 | − | 17.5355i | 1.31558 | − | 0.759548i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.305691 | + | 0.176491i | −0.0132162 | + | 0.00763037i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 28.8296 | − | 24.2783i | 1.24178 | − | 1.04574i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 8.82681 | + | 15.2885i | 0.379494 | + | 0.657303i | 0.990989 | − | 0.133946i | \(-0.0427647\pi\) |
−0.611495 | + | 0.791249i | \(0.709431\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −0.399541 | + | 0.692026i | −0.0171145 | + | 0.0296431i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.18319 | + | 3.78140i | 0.0933466 | + | 0.161681i | 0.908917 | − | 0.416976i | \(-0.136910\pi\) |
−0.815571 | + | 0.578657i | \(0.803577\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −25.5859 | + | 44.3161i | −1.09000 | + | 1.88793i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.03217 | − | 1.42563i | 0.0864165 | − | 0.0606240i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 14.7527 | + | 8.51750i | 0.625094 | + | 0.360898i | 0.778849 | − | 0.627211i | \(-0.215804\pi\) |
−0.153756 | + | 0.988109i | \(0.549137\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 7.61695i | 0.322163i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.45992 | − | 11.1889i | −0.272253 | − | 0.471556i | 0.697185 | − | 0.716891i | \(-0.254436\pi\) |
−0.969438 | + | 0.245335i | \(0.921102\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.27155 | − | 0.734127i | −0.0534943 | − | 0.0308850i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 18.8280 | + | 10.8704i | 0.789313 | + | 0.455710i | 0.839720 | − | 0.543019i | \(-0.182719\pi\) |
−0.0504079 | + | 0.998729i | \(0.516052\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.8254 | − | 29.1425i | −0.704122 | − | 1.21958i | −0.967007 | − | 0.254748i | \(-0.918007\pi\) |
0.262885 | − | 0.964827i | \(-0.415326\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11.6755i | 0.486904i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 12.5598 | + | 7.25141i | 0.522871 | + | 0.301880i | 0.738109 | − | 0.674682i | \(-0.235719\pi\) |
−0.215237 | + | 0.976562i | \(0.569052\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.02718 | − | 34.2502i | −0.125589 | − | 1.42094i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −32.5897 | + | 56.4469i | −1.34973 | + | 2.33779i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 15.8417 | + | 27.4386i | 0.653857 | + | 1.13251i | 0.982179 | + | 0.187948i | \(0.0601837\pi\) |
−0.328322 | + | 0.944566i | \(0.606483\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −14.3963 | + | 24.9350i | −0.593187 | + | 1.02743i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.54101 | + | 6.13320i | 0.145412 | + | 0.251860i | 0.929526 | − | 0.368755i | \(-0.120216\pi\) |
−0.784115 | + | 0.620616i | \(0.786883\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −0.626005 | + | 0.439163i | −0.0256637 | + | 0.0180039i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −5.20178 | + | 3.00325i | −0.212539 | + | 0.122709i | −0.602491 | − | 0.798126i | \(-0.705825\pi\) |
0.389952 | + | 0.920835i | \(0.372492\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.530083 | + | 0.306043i | −0.0216225 | + | 0.0124838i | −0.510772 | − | 0.859716i | \(-0.670640\pi\) |
0.489150 | + | 0.872200i | \(0.337307\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 1.37499 | 0.0559012 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.04959i | 0.0831904i | 0.999135 | + | 0.0415952i | \(0.0132440\pi\) | ||||
−0.999135 | + | 0.0415952i | \(0.986756\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 13.4588 | − | 7.77047i | 0.544487 | − | 0.314360i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −4.93166 | + | 8.54189i | −0.199188 | + | 0.345003i | −0.948265 | − | 0.317479i | \(-0.897164\pi\) |
0.749077 | + | 0.662482i | \(0.230497\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.2143 | − | 13.4028i | −0.934571 | − | 0.539575i | −0.0463170 | − | 0.998927i | \(-0.514748\pi\) |
−0.888254 | + | 0.459352i | \(0.848082\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 0.0696297i | − | 0.00279865i | −0.999999 | − | 0.00139933i | \(-0.999555\pi\) | ||
0.999999 | − | 0.00139933i | \(-0.000445420\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0.707163 | + | 8.00098i | 0.0283319 | + | 0.320553i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 24.9124 | 0.996497 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 2.68121 | 0.106907 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −11.8214 | −0.470603 | −0.235301 | − | 0.971922i | \(-0.575608\pi\) | ||||
−0.235301 | + | 0.971922i | \(0.575608\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0.0966675 | 0.00383613 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.52600 | − | 36.6299i | −0.258569 | − | 1.45133i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 20.5159i | − | 0.810330i | −0.914244 | − | 0.405165i | \(-0.867214\pi\) | ||
0.914244 | − | 0.405165i | \(-0.132786\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.6081 | + | 9.01132i | 0.615522 | + | 0.355372i | 0.775123 | − | 0.631810i | \(-0.217688\pi\) |
−0.159602 | + | 0.987182i | \(0.551021\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.11827 | + | 15.7933i | −0.358476 | + | 0.620899i | −0.987706 | − | 0.156320i | \(-0.950037\pi\) |
0.629230 | + | 0.777219i | \(0.283370\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.70409 | + | 1.56121i | −0.106145 | + | 0.0612827i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 9.00158i | 0.352259i | 0.984367 | + | 0.176129i | \(0.0563577\pi\) | ||||
−0.984367 | + | 0.176129i | \(0.943642\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.10723 | 0.0432630 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 30.4806 | − | 17.5980i | 1.18735 | − | 0.685519i | 0.229650 | − | 0.973273i | \(-0.426242\pi\) |
0.957704 | + | 0.287754i | \(0.0929086\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.8797 | + | 6.28141i | −0.423172 | + | 0.244318i | −0.696433 | − | 0.717621i | \(-0.745231\pi\) |
0.273262 | + | 0.961940i | \(0.411898\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −1.00923 | + | 0.0892002i | −0.0391363 | + | 0.00345904i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.9376 | + | 20.6765i | 0.462226 | + | 0.800599i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.48072 | + | 12.9570i | −0.288790 | + | 0.500199i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 23.8913 | + | 41.3810i | 0.920942 | + | 1.59512i | 0.797960 | + | 0.602710i | \(0.205913\pi\) |
0.122982 | + | 0.992409i | \(0.460754\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.5235 | − | 32.0837i | 0.711918 | − | 1.23308i | −0.252219 | − | 0.967670i | \(-0.581160\pi\) |
0.964136 | − | 0.265407i | \(-0.0855064\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 18.8125 | − | 1.66273i | 0.721956 | − | 0.0638097i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21.6844 | − | 12.5195i | −0.829732 | − | 0.479046i | 0.0240289 | − | 0.999711i | \(-0.492351\pi\) |
−0.853761 | + | 0.520665i | \(0.825684\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.17734i | 0.0449839i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 32.1712 | + | 55.7222i | 1.22563 | + | 2.12285i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −40.2655 | − | 23.2473i | −1.53177 | − | 0.884370i | −0.999280 | − | 0.0379352i | \(-0.987922\pi\) |
−0.532493 | − | 0.846434i | \(-0.678745\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.0286363 | − | 0.0165332i | −0.00108624 | − | 0.000627139i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 12.4767 | + | 21.6102i | 0.472587 | + | 0.818545i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 36.0041i | 1.35986i | 0.733279 | + | 0.679928i | \(0.237989\pi\) | ||||
−0.733279 | + | 0.679928i | \(0.762011\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 3.07651 | + | 1.77622i | 0.116033 | + | 0.0669915i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −19.6048 | − | 9.12067i | −0.737315 | − | 0.343018i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −15.9158 | + | 27.5670i | −0.597731 | + | 1.03530i | 0.395424 | + | 0.918499i | \(0.370598\pi\) |
−0.993155 | + | 0.116802i | \(0.962736\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 6.71685 | + | 11.6339i | 0.251548 | + | 0.435694i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.09360 | − | 1.89418i | 0.0408985 | − | 0.0708382i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −20.0271 | − | 34.6879i | −0.746883 | − | 1.29364i | −0.949310 | − | 0.314342i | \(-0.898216\pi\) |
0.202427 | − | 0.979297i | \(-0.435117\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.33245 | − | 17.9106i | 0.310317 | − | 0.667024i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 44.1699 | − | 25.5015i | 1.64043 | − | 0.947101i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.39242 | − | 1.95862i | 0.125818 | − | 0.0726411i | −0.435770 | − | 0.900058i | \(-0.643524\pi\) |
0.561588 | + | 0.827417i | \(0.310191\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.41952 | −0.200448 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 23.5835i | − | 0.871078i | −0.900170 | − | 0.435539i | \(-0.856558\pi\) | ||
0.900170 | − | 0.435539i | \(-0.143442\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 24.5827 | − | 14.1928i | 0.905514 | − | 0.522798i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −16.8641 | + | 29.2094i | −0.620355 | + | 1.07449i | 0.369065 | + | 0.929404i | \(0.379678\pi\) |
−0.989420 | + | 0.145083i | \(0.953655\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29.4003 | + | 16.9743i | 1.07859 | + | 0.622725i | 0.930516 | − | 0.366251i | \(-0.119359\pi\) |
0.148076 | + | 0.988976i | \(0.452692\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 0.356991i | − | 0.0130792i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 12.1725 | − | 1.07586i | 0.444773 | − | 0.0393110i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.39663 | −0.123945 | −0.0619724 | − | 0.998078i | \(-0.519739\pi\) | ||||
−0.0619724 | + | 0.998078i | \(0.519739\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −0.630160 | −0.0229339 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 29.1344 | 1.05891 | 0.529454 | − | 0.848339i | \(-0.322397\pi\) | ||||
0.529454 | + | 0.848339i | \(0.322397\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −16.7258 | −0.606309 | −0.303154 | − | 0.952941i | \(-0.598040\pi\) | ||||
−0.303154 | + | 0.952941i | \(0.598040\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 22.6465 | − | 15.8873i | 0.819860 | − | 0.575159i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 3.08232i | 0.111296i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −24.0816 | − | 13.9035i | −0.868404 | − | 0.501373i | −0.00158643 | − | 0.999999i | \(-0.500505\pi\) |
−0.866818 | + | 0.498625i | \(0.833838\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.42238 | − | 11.1239i | 0.230997 | − | 0.400098i | −0.727105 | − | 0.686526i | \(-0.759135\pi\) |
0.958102 | + | 0.286428i | \(0.0924679\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 24.8527 | − | 14.3487i | 0.892736 | − | 0.515421i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 33.0617i | 1.18456i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 17.8817 | 0.639856 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.16420 | + | 0.672153i | −0.0415522 | + | 0.0239902i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.55243 | + | 3.78305i | −0.233569 | + | 0.134851i | −0.612217 | − | 0.790689i | \(-0.709722\pi\) |
0.378648 | + | 0.925541i | \(0.376389\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 29.1917 | + | 41.6113i | 1.03794 | + | 1.47953i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 7.38467 | + | 12.7906i | 0.262237 | + | 0.454208i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 4.03362 | − | 6.98643i | 0.142878 | − | 0.247472i | −0.785701 | − | 0.618606i | \(-0.787698\pi\) |
0.928579 | + | 0.371134i | \(0.121031\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 5.52875 | + | 9.57608i | 0.195593 | + | 0.338777i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −19.1906 | + | 33.2391i | −0.677222 | + | 1.17298i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.199396 | + | 0.428599i | −0.00702777 | + | 0.0151061i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 0.0849492 | + | 0.0490454i | 0.00298665 | + | 0.00172435i | 0.501493 | − | 0.865162i | \(-0.332784\pi\) |
−0.498506 | + | 0.866886i | \(0.666118\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.3085i | 1.06428i | 0.846658 | + | 0.532138i | \(0.178611\pi\) | ||||
−0.846658 | + | 0.532138i | \(0.821389\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −0.402831 | − | 0.697724i | −0.0141106 | − | 0.0244402i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.21853 | − | 3.59027i | −0.217559 | − | 0.125608i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 19.5499 | + | 11.2871i | 0.682295 | + | 0.393923i | 0.800719 | − | 0.599040i | \(-0.204451\pi\) |
−0.118424 | + | 0.992963i | \(0.537784\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.2655 | − | 21.2445i | −0.427549 | − | 0.740536i | 0.569106 | − | 0.822264i | \(-0.307289\pi\) |
−0.996655 | + | 0.0817282i | \(0.973956\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 40.3057i | 1.40157i | 0.713375 | + | 0.700783i | \(0.247166\pi\) | ||||
−0.713375 | + | 0.700783i | \(0.752834\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −46.8081 | − | 27.0247i | −1.62571 | − | 0.938605i | −0.985353 | − | 0.170529i | \(-0.945452\pi\) |
−0.640359 | − | 0.768076i | \(-0.721214\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 26.0624 | − | 4.64330i | 0.903010 | − | 0.160881i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.350900 | − | 0.607777i | 0.0121434 | − | 0.0210330i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −11.8650 | − | 20.5507i | −0.409624 | − | 0.709489i | 0.585224 | − | 0.810872i | \(-0.301007\pi\) |
−0.994847 | + | 0.101383i | \(0.967673\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 37.6478 | − | 65.2079i | 1.29820 | − | 2.24855i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −0.582803 | − | 1.00944i | −0.0200490 | − | 0.0347259i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −43.1589 | − | 20.0787i | −1.48296 | − | 0.689911i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.43540 | − | 0.828731i | 0.0492050 | − | 0.0284085i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 48.0748 | − | 27.7560i | 1.64605 | − | 0.950347i | 0.667429 | − | 0.744673i | \(-0.267395\pi\) |
0.978621 | − | 0.205674i | \(-0.0659387\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −30.6097 | −1.04561 | −0.522803 | − | 0.852453i | \(-0.675114\pi\) | ||||
−0.522803 | + | 0.852453i | \(0.675114\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 42.1401i | − | 1.43780i | −0.695113 | − | 0.718900i | \(-0.744646\pi\) | ||
0.695113 | − | 0.718900i | \(-0.255354\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22.7782 | − | 13.1510i | 0.775379 | − | 0.447665i | −0.0594112 | − | 0.998234i | \(-0.518922\pi\) |
0.834790 | + | 0.550568i | \(0.185589\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −0.0935118 | + | 0.161967i | −0.00317950 | + | 0.00550705i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −4.37504 | − | 2.52593i | −0.148413 | − | 0.0856863i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 28.0211i | − | 0.949460i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.83224 | + | 0.852407i | 0.0619411 | + | 0.0288166i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 35.7066 | 1.20573 | 0.602863 | − | 0.797845i | \(-0.294027\pi\) | ||||
0.602863 | + | 0.797845i | \(0.294027\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 12.4482 | 0.419392 | 0.209696 | − | 0.977767i | \(-0.432753\pi\) | ||||
0.209696 | + | 0.977767i | \(0.432753\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −2.35637 | −0.0792982 | −0.0396491 | − | 0.999214i | \(-0.512624\pi\) | ||||
−0.0396491 | + | 0.999214i | \(0.512624\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −33.4597 | −1.12347 | −0.561734 | − | 0.827318i | \(-0.689866\pi\) | ||||
−0.561734 | + | 0.827318i | \(0.689866\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −3.03426 | − | 1.41162i | −0.101766 | − | 0.0473441i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 14.6505i | 0.490261i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −0.386333 | − | 0.223049i | −0.0129137 | − | 0.00745572i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 29.3416 | − | 50.8212i | 0.978597 | − | 1.69498i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −39.6468 | + | 22.8901i | −1.32083 | + | 0.762579i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 1.22817i | 0.0408259i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.935925 | 0.0310769 | 0.0155384 | − | 0.999879i | \(-0.495054\pi\) | ||||
0.0155384 | + | 0.999879i | \(0.495054\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 28.8739 | − | 16.6703i | 0.956634 | − | 0.552313i | 0.0614988 | − | 0.998107i | \(-0.480412\pi\) |
0.895136 | + | 0.445794i | \(0.147079\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −60.5995 | + | 34.9871i | −2.00555 | + | 1.15791i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −34.7544 | − | 16.1686i | −1.14769 | − | 0.533935i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.73484 | + | 3.00483i | 0.0572270 | + | 0.0991200i | 0.893220 | − | 0.449621i | \(-0.148441\pi\) |
−0.835993 | + | 0.548741i | \(0.815107\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 8.82603 | − | 15.2871i | 0.290512 | − | 0.503182i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.77036 | − | 3.06635i | −0.0582090 | − | 0.100821i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −7.57680 | + | 13.1234i | −0.248587 | + | 0.430565i | −0.963134 | − | 0.269022i | \(-0.913299\pi\) |
0.714547 | + | 0.699587i | \(0.246633\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 32.9809 | + | 11.9377i | 1.08091 | + | 0.391243i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.34772 | + | 0.778108i | 0.0440752 | + | 0.0254468i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 33.6651i | 1.09979i | 0.835233 | + | 0.549896i | \(0.185333\pi\) | ||||
−0.835233 | + | 0.549896i | \(0.814667\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.8980 | + | 32.7323i | 0.616058 | + | 1.06704i | 0.990198 | + | 0.139671i | \(0.0446045\pi\) |
−0.374140 | + | 0.927372i | \(0.622062\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 13.3589 | + | 7.71277i | 0.435026 | + | 0.251162i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 9.47426 | + | 5.46997i | 0.307872 | + | 0.177750i | 0.645974 | − | 0.763360i | \(-0.276452\pi\) |
−0.338102 | + | 0.941110i | \(0.609785\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 18.9442 | + | 32.8123i | 0.614955 | + | 1.06513i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 11.0914i | − | 0.359284i | −0.983732 | − | 0.179642i | \(-0.942506\pi\) | ||
0.983732 | − | 0.179642i | \(-0.0574939\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.527646 | + | 0.304637i | 0.0170742 | + | 0.00985781i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.1925 | − | 36.9551i | 0.555174 | − | 1.19334i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.00942 | − | 1.74838i | 0.0325621 | − | 0.0563992i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.0274384 | + | 0.0475248i | 0.000883275 | + | 0.00152988i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −20.1446 | + | 34.8915i | −0.647807 | + | 1.12203i | 0.335839 | + | 0.941920i | \(0.390980\pi\) |
−0.983646 | + | 0.180115i | \(0.942353\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.8458 | + | 41.3021i | 0.765248 | + | 1.32545i | 0.940115 | + | 0.340856i | \(0.110717\pi\) |
−0.174867 | + | 0.984592i | \(0.555950\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0.657423 | + | 0.937123i | 0.0210760 | + | 0.0300428i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 14.4540 | − | 8.34504i | 0.462426 | − | 0.266982i | −0.250638 | − | 0.968081i | \(-0.580640\pi\) |
0.713064 | + | 0.701099i | \(0.247307\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.1563 | − | 8.17314i | 0.452437 | − | 0.261215i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 33.8509 | 1.07968 | 0.539838 | − | 0.841769i | \(-0.318485\pi\) | ||||
0.539838 | + | 0.841769i | \(0.318485\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 1.03200i | − | 0.0328821i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −2.90137 | + | 1.67511i | −0.0922583 | + | 0.0532653i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.09775 | − | 7.09751i | 0.130169 | − | 0.225460i | −0.793572 | − | 0.608476i | \(-0.791781\pi\) |
0.923742 | + | 0.383016i | \(0.125115\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 1.62454 | + | 0.937928i | 0.0515014 | + | 0.0297343i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 21.6380i | − | 0.685282i | −0.939466 | − | 0.342641i | \(-0.888679\pi\) | ||
0.939466 | − | 0.342641i | \(-0.111321\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))