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 | 1601.5 | ||
Root | \(1.08696 + 1.34852i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3024.1601 |
Dual form | 3024.2.df.d.17.5 |
$q$-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 \(\left(\mathbb{Z}/3024\mathbb{Z}\right)^\times\).
\(n\) | \(757\) | \(785\) | \(1135\) | \(2593\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{6}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
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 | \(0.301471\pi\) | ||||
−0.584040 | + | 0.811725i | \(0.698529\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −4.60313 | + | 2.65762i | −1.27668 | + | 0.737091i | −0.976236 | − | 0.216709i | \(-0.930468\pi\) |
−0.300442 | + | 0.953800i | \(0.597134\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 1.89092 | + | 3.27516i | 0.458615 | + | 0.794344i | 0.998888 | − | 0.0471458i | \(-0.0150125\pi\) |
−0.540273 | + | 0.841490i | \(0.681679\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.33939 | + | 2.50535i | 0.995525 | + | 0.574767i | 0.906921 | − | 0.421300i | \(-0.138426\pi\) |
0.0886040 | + | 0.996067i | \(0.471759\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.33784i | 0.487473i | 0.969841 | + | 0.243737i | \(0.0783732\pi\) | ||||
−0.969841 | + | 0.243737i | \(0.921627\pi\) | |||||||
\(24\) | 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 | −0.979997 | − | 0.199013i | \(-0.936226\pi\) |
−0.662349 | − | 0.749196i | \(-0.730440\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −4.97636 | − | 2.87310i | −0.893780 | − | 0.516024i | −0.0186031 | − | 0.999827i | \(-0.505922\pi\) |
−0.875177 | + | 0.483803i | \(0.839255\pi\) | |||||||
\(32\) | 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 | −0.835415 | − | 0.549620i | \(-0.814773\pi\) |
0.893692 | + | 0.448681i | \(0.148106\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −3.29910 | − | 5.71422i | −0.515234 | − | 0.892411i | −0.999844 | − | 0.0176805i | \(-0.994372\pi\) |
0.484610 | − | 0.874730i | \(-0.338961\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.716520 | + | 1.24105i | −0.109268 | + | 0.189258i | −0.915474 | − | 0.402377i | \(-0.868184\pi\) |
0.806206 | + | 0.591635i | \(0.201517\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −1.46192 | − | 2.53213i | −0.213244 | − | 0.369349i | 0.739484 | − | 0.673174i | \(-0.235069\pi\) |
−0.952728 | + | 0.303825i | \(0.901736\pi\) | |||||||
\(48\) | 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 | −0.997850 | − | 0.0655390i | \(-0.979123\pi\) |
−0.442167 | + | 0.896933i | \(0.645790\pi\) | |||||||
\(54\) | 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 | −0.884282 | − | 0.466953i | \(-0.845352\pi\) |
0.846534 | + | 0.532335i | \(0.178685\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.40641 | + | 1.38934i | −0.308109 | + | 0.177887i | −0.646080 | − | 0.763270i | \(-0.723593\pi\) |
0.337971 | + | 0.941156i | \(0.390259\pi\) | |||||||
\(62\) | 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 | −0.658877 | − | 0.752251i | \(-0.728968\pi\) |
0.980907 | + | 0.194479i | \(0.0623016\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 3.32103i | − | 0.394134i | −0.980390 | − | 0.197067i | \(-0.936858\pi\) | ||
0.980390 | − | 0.197067i | \(-0.0631416\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.17326 | + | 3.56413i | −0.722525 | + | 0.417150i | −0.815681 | − | 0.578502i | \(-0.803638\pi\) |
0.0931564 | + | 0.995651i | \(0.470304\pi\) | |||||||
\(74\) | 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 | 0.891208 | − | 0.453594i | \(-0.149858\pi\) |
−0.838428 | + | 0.545012i | \(0.816525\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −6.49790 | + | 11.2547i | −0.713238 | + | 1.23536i | 0.250398 | + | 0.968143i | \(0.419439\pi\) |
−0.963635 | + | 0.267221i | \(0.913895\pi\) | |||||||
\(84\) | 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 | −0.774291 | − | 0.632830i | \(-0.781893\pi\) |
0.935192 | + | 0.354141i | \(0.115227\pi\) | |||||||
\(90\) | 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 | 0.779849 | − | 0.625967i | \(-0.215296\pi\) |
−0.152179 | + | 0.988353i | \(0.548629\pi\) | |||||||
\(98\) | 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 | \(0.119902\pi\) | ||||
−0.929890 | + | 0.367837i | \(0.880098\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.99991 | + | 2.30935i | 0.386686 | + | 0.223253i | 0.680723 | − | 0.732541i | \(-0.261666\pi\) |
−0.294037 | + | 0.955794i | \(0.594999\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 5.22792 | + | 9.05503i | 0.500744 | + | 0.867314i | 1.00000 | 0.000859385i | \(0.000273551\pi\) | |
−0.499256 | + | 0.866455i | \(0.666393\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 16.6379 | − | 9.60591i | 1.56516 | − | 0.903648i | 0.568445 | − | 0.822721i | \(-0.307545\pi\) |
0.996720 | − | 0.0809270i | \(-0.0257881\pi\) | |||||||
\(114\) | 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 | \(0.228632\pi\) | ||||
−0.752947 | + | 0.658081i | \(0.771368\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 0.374701 | − | 0.216333i | 0.0317817 | − | 0.0183492i | −0.484025 | − | 0.875054i | \(-0.660826\pi\) |
0.515807 | + | 0.856705i | \(0.327492\pi\) | |||||||
\(140\) | 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 | \(-0.938717\pi\) | ||
0.981524 | − | 0.191338i | \(-0.0612828\pi\) | |||||||
\(150\) | 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 | 0.964007 | − | 0.265875i | \(-0.0856609\pi\) |
0.251749 | + | 0.967793i | \(0.418994\pi\) | |||||||
\(158\) | 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 | −0.582346 | − | 0.812941i | \(-0.697865\pi\) |
0.995201 | + | 0.0978563i | \(0.0311985\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.59146 | − | 7.95265i | −0.355298 | − | 0.615395i | 0.631871 | − | 0.775074i | \(-0.282287\pi\) |
−0.987169 | + | 0.159679i | \(0.948954\pi\) | |||||||
\(168\) | 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 | 0.908784 | − | 0.417268i | \(-0.137012\pi\) |
−0.815756 | + | 0.578396i | \(0.803679\pi\) | |||||||
\(174\) | 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 | −0.299041 | − | 0.954240i | \(-0.596667\pi\) |
0.676876 | + | 0.736097i | \(0.263333\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 16.0704i | 1.19451i | 0.802053 | + | 0.597253i | \(0.203741\pi\) | ||||
−0.802053 | + | 0.597253i | \(0.796259\pi\) | |||||||
\(182\) | 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 | −0.728535 | − | 0.685009i | \(-0.759798\pi\) |
0.228968 | + | 0.973434i | \(0.426465\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −0.359027 | + | 0.621853i | −0.0258433 | + | 0.0447620i | −0.878658 | − | 0.477452i | \(-0.841560\pi\) |
0.852814 | + | 0.522214i | \(0.174894\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 13.5035i | − | 0.962083i | −0.876698 | − | 0.481042i | \(-0.840259\pi\) | ||
0.876698 | − | 0.481042i | \(-0.159741\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −21.2568 | + | 12.2726i | −1.50685 | + | 0.869983i | −0.506886 | + | 0.862013i | \(0.669203\pi\) |
−0.999968 | + | 0.00796947i | \(0.997463\pi\) | |||||||
\(200\) | 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 | 0.912005 | + | 0.410178i | \(0.134533\pi\) |
−0.100778 | + | 0.994909i | \(0.532133\pi\) | |||||||
\(212\) | 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 | 0.700875 | − | 0.713284i | \(-0.252793\pi\) |
−0.267285 | + | 0.963618i | \(0.586126\pi\) | |||||||
\(224\) | 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 | \(-0.980758\pi\) | ||
0.998173 | − | 0.0604146i | \(-0.0192423\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −17.4232 | − | 10.0593i | −1.14143 | − | 0.659007i | −0.194649 | − | 0.980873i | \(-0.562357\pi\) |
−0.946785 | + | 0.321866i | \(0.895690\pi\) | |||||||
\(234\) | 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 | −0.576055 | − | 0.817411i | \(-0.695409\pi\) |
0.419871 | + | 0.907584i | \(0.362075\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 23.1291i | 1.48988i | 0.667134 | + | 0.744938i | \(0.267521\pi\) | ||||
−0.667134 | + | 0.744938i | \(0.732479\pi\) | |||||||
\(242\) | 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 | \(0.199182\pi\) | ||||
−0.810525 | + | 0.585704i | \(0.800818\pi\) | |||||||
\(264\) | 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 | 0.966786 | − | 0.255589i | \(-0.0822693\pi\) |
−0.704739 | + | 0.709467i | \(0.748936\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.58706 | − | 0.916292i | −0.0964073 | − | 0.0556608i | 0.451021 | − | 0.892513i | \(-0.351060\pi\) |
−0.547429 | + | 0.836852i | \(0.684393\pi\) | |||||||
\(272\) | 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 | 0.766722 | − | 0.641979i | \(-0.221886\pi\) |
−0.172609 | + | 0.984990i | \(0.555220\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.59806 | + | 4.96409i | 0.511101 | + | 0.295085i | 0.733286 | − | 0.679920i | \(-0.237986\pi\) |
−0.222185 | + | 0.975005i | \(0.571319\pi\) | |||||||
\(284\) | 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 | −0.999986 | − | 0.00522664i | \(-0.998336\pi\) |
0.495467 | − | 0.868627i | \(-0.334997\pi\) | |||||||
\(294\) | 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 | \(0.211896\pi\) | ||||
−0.786490 | + | 0.617602i | \(0.788104\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 10.1016 | − | 17.4964i | 0.572808 | − | 0.992133i | −0.423468 | − | 0.905911i | \(-0.639187\pi\) |
0.996276 | − | 0.0862215i | \(-0.0274793\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −18.9146 | + | 10.9203i | −1.06911 | + | 0.617254i | −0.927939 | − | 0.372731i | \(-0.878421\pi\) |
−0.141175 | + | 0.989985i | \(0.545088\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 21.5288 | − | 12.4297i | 1.20918 | − | 0.698120i | 0.246599 | − | 0.969117i | \(-0.420687\pi\) |
0.962580 | + | 0.270997i | \(0.0873535\pi\) | |||||||
\(318\) | 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 | 0.997960 | − | 0.0638459i | \(-0.0203366\pi\) |
−0.554272 | + | 0.832336i | \(0.687003\pi\) | |||||||
\(332\) | 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 | 0.570765 | − | 0.821113i | \(-0.306647\pi\) |
−0.996488 | + | 0.0837408i | \(0.973313\pi\) | |||||||
\(338\) | 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 | 0.999980 | + | 0.00639573i | \(0.00203584\pi\) |
0.505529 | + | 0.862810i | \(0.331297\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −26.0421 | − | 15.0354i | −1.39400 | − | 0.804827i | −0.400246 | − | 0.916408i | \(-0.631075\pi\) |
−0.993755 | + | 0.111581i | \(0.964409\pi\) | |||||||
\(350\) | 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 | 0.985858 | − | 0.167583i | \(-0.0535962\pi\) |
0.347798 | + | 0.937570i | \(0.386930\pi\) | |||||||
\(360\) | 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 | \(-0.843135\pi\) | ||
0.881009 | − | 0.473100i | \(-0.156865\pi\) | |||||||
\(368\) | 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 | \(0.130740\pi\) | ||||
−0.916829 | + | 0.399280i | \(0.869260\pi\) | |||||||
\(390\) | 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 | 0.423914 | − | 0.905702i | \(-0.360656\pi\) |
−0.572404 | + | 0.819972i | \(0.693989\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 0.983052i | − | 0.0490913i | −0.999699 | − | 0.0245456i | \(-0.992186\pi\) | ||
0.999699 | − | 0.0245456i | \(-0.00781390\pi\) | |||||||
\(402\) | 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 | 0.968508 | − | 0.248984i | \(-0.0800966\pi\) |
0.268627 | + | 0.963244i | \(0.413430\pi\) | |||||||
\(410\) | 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 | 0.977760 | − | 0.209727i | \(-0.0672577\pi\) |
−0.670509 | + | 0.741901i | \(0.733924\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −13.0232 | + | 22.5568i | −0.634710 | + | 1.09935i | 0.351866 | + | 0.936050i | \(0.385547\pi\) |
−0.986576 | + | 0.163300i | \(0.947786\pi\) | |||||||
\(422\) | 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 | −0.340947 | − | 0.940083i | \(-0.610748\pi\) |
0.643662 | + | 0.765310i | \(0.277414\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 8.29113i | − | 0.398446i | −0.979954 | − | 0.199223i | \(-0.936158\pi\) | ||
0.979954 | − | 0.199223i | \(-0.0638419\pi\) | |||||||
\(434\) | 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 | −0.430854 | − | 0.902422i | \(-0.641788\pi\) |
0.566093 | + | 0.824341i | \(0.308454\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.46737 | − | 1.42454i | 0.117228 | − | 0.0676817i | −0.440239 | − | 0.897880i | \(-0.645106\pi\) |
0.557468 | + | 0.830199i | \(0.311773\pi\) | |||||||
\(444\) | 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 | \(0.156274\pi\) | ||||
−0.881886 | + | 0.471463i | \(0.843726\pi\) | |||||||
\(450\) | 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 | 0.568675 | − | 0.822563i | \(-0.307456\pi\) |
−0.996697 | + | 0.0812053i | \(0.974123\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.52954 | + | 7.84539i | −0.210962 | + | 0.365396i | −0.952016 | − | 0.306049i | \(-0.900993\pi\) |
0.741054 | + | 0.671445i | \(0.234326\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −10.8227 | − | 18.7455i | −0.502974 | − | 0.871176i | −0.999994 | − | 0.00343694i | \(-0.998906\pi\) |
0.497021 | − | 0.867739i | \(-0.334427\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.7761 | + | 23.8610i | −0.637484 | + | 1.10415i | 0.348500 | + | 0.937309i | \(0.386691\pi\) |
−0.985983 | + | 0.166845i | \(0.946642\pi\) | |||||||
\(468\) | 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 | 0.953847 | − | 0.300293i | \(-0.0970845\pi\) |
−0.736985 | + | 0.675909i | \(0.763751\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −33.0010 | + | 19.0531i | −1.48931 | + | 0.859855i | −0.999925 | − | 0.0122119i | \(-0.996113\pi\) |
−0.489387 | + | 0.872067i | \(0.662779\pi\) | |||||||
\(492\) | 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 | 0.906993 | − | 0.421146i | \(-0.138372\pi\) |
−0.818220 | + | 0.574906i | \(0.805039\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −26.2429 | − | 15.1514i | −1.14752 | − | 0.662523i | −0.199241 | − | 0.979951i | \(-0.563848\pi\) |
−0.948282 | + | 0.317428i | \(0.897181\pi\) | |||||||
\(524\) | 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 | −0.611495 | − | 0.791249i | \(-0.709431\pi\) |
0.990989 | + | 0.133946i | \(0.0427647\pi\) | |||||||
\(542\) | 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 | −0.815571 | − | 0.578657i | \(-0.803577\pi\) |
0.908917 | + | 0.416976i | \(0.136910\pi\) | |||||||
\(548\) | 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 | −0.153756 | − | 0.988109i | \(-0.549137\pi\) |
0.778849 | + | 0.627211i | \(0.215804\pi\) | |||||||
\(558\) | 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 | −0.969438 | − | 0.245335i | \(-0.921102\pi\) |
0.697185 | + | 0.716891i | \(0.254436\pi\) | |||||||
\(564\) | 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 | −0.0504079 | − | 0.998729i | \(-0.516052\pi\) |
0.839720 | + | 0.543019i | \(0.182719\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −16.8254 | + | 29.1425i | −0.704122 | + | 1.21958i | 0.262885 | + | 0.964827i | \(0.415326\pi\) |
−0.967007 | + | 0.254748i | \(0.918007\pi\) | |||||||
\(572\) | 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 | −0.215237 | − | 0.976562i | \(-0.569052\pi\) |
0.738109 | + | 0.674682i | \(0.235719\pi\) | |||||||
\(578\) | 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 | −0.328322 | − | 0.944566i | \(-0.606483\pi\) |
0.982179 | − | 0.187948i | \(-0.0601837\pi\) | |||||||
\(588\) | 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 | −0.784115 | − | 0.620616i | \(-0.786883\pi\) |
0.929526 | + | 0.368755i | \(0.120216\pi\) | |||||||
\(594\) | 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 | 0.389952 | − | 0.920835i | \(-0.372492\pi\) |
−0.602491 | + | 0.798126i | \(0.705825\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −0.530083 | − | 0.306043i | −0.0216225 | − | 0.0124838i | 0.489150 | − | 0.872200i | \(-0.337307\pi\) |
−0.510772 | + | 0.859716i | \(0.670640\pi\) | |||||||
\(602\) | 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 | \(-0.986756\pi\) | ||
0.999135 | − | 0.0415952i | \(-0.0132440\pi\) | |||||||
\(608\) | 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 | 0.749077 | − | 0.662482i | \(-0.230497\pi\) |
−0.948265 | + | 0.317479i | \(0.897164\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −23.2143 | + | 13.4028i | −0.934571 | + | 0.539575i | −0.888254 | − | 0.459352i | \(-0.848082\pi\) |
−0.0463170 | + | 0.998927i | \(0.514748\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.0696297i | 0.00279865i | 0.999999 | + | 0.00139933i | \(0.000445420\pi\) | ||||
−0.999999 | + | 0.00139933i | \(0.999555\pi\) | |||||||
\(620\) | 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 | \(0.132786\pi\) | ||||
−0.914244 | + | 0.405165i | \(0.867214\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15.6081 | − | 9.01132i | 0.615522 | − | 0.355372i | −0.159602 | − | 0.987182i | \(-0.551021\pi\) |
0.775123 | + | 0.631810i | \(0.217688\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9.11827 | − | 15.7933i | −0.358476 | − | 0.620899i | 0.629230 | − | 0.777219i | \(-0.283370\pi\) |
−0.987706 | + | 0.156320i | \(0.950037\pi\) | |||||||
\(648\) | 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 | \(-0.943642\pi\) | ||
0.984367 | − | 0.176129i | \(-0.0563577\pi\) | |||||||
\(654\) | 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 | 0.957704 | − | 0.287754i | \(-0.0929086\pi\) |
0.229650 | + | 0.973273i | \(0.426242\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −10.8797 | − | 6.28141i | −0.423172 | − | 0.244318i | 0.273262 | − | 0.961940i | \(-0.411898\pi\) |
−0.696433 | + | 0.717621i | \(0.745231\pi\) | |||||||
\(662\) | 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 | 0.122982 | − | 0.992409i | \(-0.460754\pi\) |
0.797960 | − | 0.602710i | \(-0.205913\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 18.5235 | + | 32.0837i | 0.711918 | + | 1.23308i | 0.964136 | + | 0.265407i | \(0.0855064\pi\) |
−0.252219 | + | 0.967670i | \(0.581160\pi\) | |||||||
\(678\) | 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 | −0.853761 | − | 0.520665i | \(-0.825684\pi\) |
0.0240289 | + | 0.999711i | \(0.492351\pi\) | |||||||
\(684\) | 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 | −0.532493 | + | 0.846434i | \(0.678745\pi\) |
−0.999280 | + | 0.0379352i | \(0.987922\pi\) | |||||||
\(692\) | 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 | \(-0.762011\pi\) | ||
0.733279 | − | 0.679928i | \(-0.237989\pi\) | |||||||
\(702\) | 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 | −0.993155 | − | 0.116802i | \(-0.962736\pi\) |
0.395424 | − | 0.918499i | \(-0.370598\pi\) | |||||||
\(710\) | 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 | 0.202427 | + | 0.979297i | \(0.435117\pi\) |
−0.949310 | + | 0.314342i | \(0.898216\pi\) | |||||||
\(720\) | 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 | 0.561588 | − | 0.827417i | \(-0.310191\pi\) |
−0.435770 | + | 0.900058i | \(0.643524\pi\) | |||||||
\(728\) | 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 | \(0.143442\pi\) | ||||
−0.900170 | + | 0.435539i | \(0.856558\pi\) | |||||||
\(734\) | 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 | −0.989420 | − | 0.145083i | \(-0.953655\pi\) |
0.369065 | − | 0.929404i | \(-0.379678\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 29.4003 | − | 16.9743i | 1.07859 | − | 0.622725i | 0.148076 | − | 0.988976i | \(-0.452692\pi\) |
0.930516 | + | 0.366251i | \(0.119359\pi\) | |||||||
\(744\) | 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 | −0.866818 | − | 0.498625i | \(-0.833838\pi\) |
−0.00158643 | + | 0.999999i | \(0.500505\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 6.42238 | + | 11.1239i | 0.230997 | + | 0.400098i | 0.958102 | − | 0.286428i | \(-0.0924679\pi\) |
−0.727105 | + | 0.686526i | \(0.759135\pi\) | |||||||
\(774\) | 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 | 0.378648 | − | 0.925541i | \(-0.376389\pi\) |
−0.612217 | + | 0.790689i | \(0.709722\pi\) | |||||||
\(788\) | 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 | 0.928579 | − | 0.371134i | \(-0.121031\pi\) |
−0.785701 | + | 0.618606i | \(0.787698\pi\) | |||||||
\(798\) | 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 | −0.498506 | − | 0.866886i | \(-0.666118\pi\) |
0.501493 | + | 0.865162i | \(0.332784\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 30.3085i | − | 1.06428i | −0.846658 | − | 0.532138i | \(-0.821389\pi\) | ||
0.846658 | − | 0.532138i | \(-0.178611\pi\) | |||||||
\(812\) | 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 | −0.118424 | − | 0.992963i | \(-0.537784\pi\) |
0.800719 | + | 0.599040i | \(0.204451\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −12.2655 | + | 21.2445i | −0.427549 | + | 0.740536i | −0.996655 | − | 0.0817282i | \(-0.973956\pi\) |
0.569106 | + | 0.822264i | \(0.307289\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 40.3057i | − | 1.40157i | −0.713375 | − | 0.700783i | \(-0.752834\pi\) | ||
0.713375 | − | 0.700783i | \(-0.247166\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −46.8081 | + | 27.0247i | −1.62571 | + | 0.938605i | −0.640359 | + | 0.768076i | \(0.721214\pi\) |
−0.985353 | + | 0.170529i | \(0.945452\pi\) | |||||||
\(830\) | 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 | −0.994847 | − | 0.101383i | \(-0.967673\pi\) |
0.585224 | + | 0.810872i | \(0.301007\pi\) | |||||||
\(840\) | 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 | 0.978621 | + | 0.205674i | \(0.0659387\pi\) |
0.667429 | + | 0.744673i | \(0.267395\pi\) | |||||||
\(854\) | 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 | \(0.255354\pi\) | ||||
−0.695113 | + | 0.718900i | \(0.744646\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 22.7782 | + | 13.1510i | 0.775379 | + | 0.447665i | 0.834790 | − | 0.550568i | \(-0.185589\pi\) |
−0.0594112 | + | 0.998234i | \(0.518922\pi\) | |||||||
\(864\) | 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 | 0.895136 | − | 0.445794i | \(-0.147079\pi\) |
0.0614988 | + | 0.998107i | \(0.480412\pi\) | |||||||
\(912\) | 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 | −0.835993 | − | 0.548741i | \(-0.815107\pi\) |
0.893220 | + | 0.449621i | \(0.148441\pi\) | |||||||
\(920\) | 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 | 0.714547 | − | 0.699587i | \(-0.246633\pi\) |
−0.963134 | + | 0.269022i | \(0.913299\pi\) | |||||||
\(930\) | 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 | \(-0.814667\pi\) | ||
0.835233 | − | 0.549896i | \(-0.185333\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 18.8980 | − | 32.7323i | 0.616058 | − | 1.06704i | −0.374140 | − | 0.927372i | \(-0.622062\pi\) |
0.990198 | − | 0.139671i | \(-0.0446045\pi\) | |||||||
\(942\) | 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 | −0.338102 | − | 0.941110i | \(-0.609785\pi\) |
0.645974 | + | 0.763360i | \(0.276452\pi\) | |||||||
\(948\) | 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 | \(0.0574939\pi\) | ||||
−0.983732 | + | 0.179642i | \(0.942506\pi\) | |||||||
\(954\) | 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 | −0.983646 | − | 0.180115i | \(-0.942353\pi\) |
0.335839 | − | 0.941920i | \(-0.390980\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 23.8458 | − | 41.3021i | 0.765248 | − | 1.32545i | −0.174867 | − | 0.984592i | \(-0.555950\pi\) |
0.940115 | − | 0.340856i | \(-0.110717\pi\) | |||||||
\(972\) | 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 | 0.713064 | − | 0.701099i | \(-0.247307\pi\) |
−0.250638 | + | 0.968081i | \(0.580640\pi\) | |||||||
\(978\) | 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 | 0.923742 | − | 0.383016i | \(-0.125115\pi\) |
−0.793572 | + | 0.608476i | \(0.791781\pi\) | |||||||
\(992\) | 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 | \(0.111321\pi\) | ||||
−0.939466 | + | 0.342641i | \(0.888679\pi\) | |||||||
\(998\) | 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 \(a_p\))