Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [756,2,Mod(341,756)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(756, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 5, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("756.341");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 756 = 2^{2} \cdot 3^{3} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 756.w (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: | \(6.03669039281\) |
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: | \( x^{16} - 2 x^{15} + 5 x^{14} - 17 x^{13} + 22 x^{12} - 31 x^{11} + 62 x^{10} - 52 x^{9} + 52 x^{8} - 156 x^{7} + 558 x^{6} - 837 x^{5} + 1782 x^{4} - 4131 x^{3} + 3645 x^{2} + \cdots + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
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 | 521.5 | ||
Root | \(1.08696 - 1.34852i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 756.521 |
Dual form | 756.2.w.a.341.5 |
$q$-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 \(\left(\mathbb{Z}/756\mathbb{Z}\right)^\times\).
\(n\) | \(29\) | \(325\) | \(379\) |
\(\chi(n)\) | \(e\left(\frac{1}{6}\right)\) | \(e\left(\frac{1}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.0382122 | + | 0.0661855i | −0.0170890 | + | 0.0295991i | −0.874443 | − | 0.485127i | \(-0.838773\pi\) |
0.857354 | + | 0.514727i | \(0.172107\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0.232935 | + | 2.63548i | 0.0880412 | + | 0.996117i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −4.66300 | + | 2.69219i | −1.40595 | + | 0.811725i | −0.994994 | − | 0.0999316i | \(-0.968138\pi\) |
−0.410954 | + | 0.911656i | \(0.634804\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.60313 | − | 2.65762i | 1.27668 | − | 0.737091i | 0.300442 | − | 0.953800i | \(-0.402866\pi\) |
0.976236 | + | 0.216709i | \(0.0695324\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −1.89092 | + | 3.27516i | −0.458615 | + | 0.794344i | −0.998888 | − | 0.0471458i | \(-0.984987\pi\) |
0.540273 | + | 0.841490i | \(0.318321\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.33939 | + | 2.50535i | −0.995525 | + | 0.574767i | −0.906921 | − | 0.421300i | \(-0.861574\pi\) |
−0.0886040 | + | 0.996067i | \(0.528241\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.02463 | + | 1.16892i | 0.422164 | + | 0.243737i | 0.696003 | − | 0.718039i | \(-0.254960\pi\) |
−0.273839 | + | 0.961776i | \(0.588293\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 2.49708 | + | 4.32507i | 0.499416 | + | 0.865014i | ||||
\(26\) | 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 | ||||||||
\(31\) | 5.74620i | 1.03205i | 0.856574 | + | 0.516024i | \(0.172589\pi\) | ||||
−0.856574 | + | 0.516024i | \(0.827411\pi\) | |||||||
\(32\) | 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 | 0.999844 | + | 0.0176805i | \(0.00562816\pi\) |
−0.484610 | + | 0.874730i | \(0.661039\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.716520 | − | 1.24105i | 0.109268 | − | 0.189258i | −0.806206 | − | 0.591635i | \(-0.798483\pi\) |
0.915474 | + | 0.402377i | \(0.131816\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.92385 | 0.426487 | 0.213244 | − | 0.976999i | \(-0.431597\pi\) | ||||
0.213244 | + | 0.976999i | \(0.431597\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.89148 | + | 1.22779i | −0.984497 | + | 0.175399i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 10.4835 | + | 6.05264i | 1.44002 | + | 0.831394i | 0.997850 | − | 0.0655390i | \(-0.0208767\pi\) |
0.442167 | + | 0.896933i | \(0.354210\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.411498i | − | 0.0554863i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 0.579903 | 0.0754969 | 0.0377484 | − | 0.999287i | \(-0.487981\pi\) | ||||
0.0377484 | + | 0.999287i | \(0.487981\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.77868i | 0.355773i | 0.984051 | + | 0.177887i | \(0.0569261\pi\) | ||||
−0.984051 | + | 0.177887i | \(0.943074\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.406214i | 0.0503847i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 5.27185 | 0.644059 | 0.322030 | − | 0.946730i | \(-0.395635\pi\) | ||||
0.322030 | + | 0.946730i | \(0.395635\pi\) | |||||||
\(68\) | 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 | ||||||||
\(77\) | −8.18137 | − | 11.6621i | −0.932354 | − | 1.32902i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 0.938245 | 0.105561 | 0.0527804 | − | 0.998606i | \(-0.483192\pi\) | ||||
0.0527804 | + | 0.998606i | \(0.483192\pi\) | |||||||
\(80\) | 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 | \(-0.218107\pi\) |
−0.935192 | + | 0.354141i | \(0.884773\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 8.07632 | + | 11.5124i | 0.846629 | + | 1.20683i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 0.382940i | − | 0.0392888i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −6.18183 | − | 3.56908i | −0.627670 | − | 0.362385i | 0.152179 | − | 0.988353i | \(-0.451371\pi\) |
−0.779849 | + | 0.625967i | \(0.784704\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −4.08628 | − | 7.07765i | −0.406600 | − | 0.704252i | 0.587906 | − | 0.808929i | \(-0.299952\pi\) |
−0.994506 | + | 0.104677i | \(0.966619\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −6.46599 | − | 3.73314i | −0.637113 | − | 0.367837i | 0.146389 | − | 0.989227i | \(-0.453235\pi\) |
−0.783502 | + | 0.621390i | \(0.786568\pi\) | |||||||
\(104\) | 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 | 0.568445 | − | 0.822721i | \(-0.307545\pi\) |
0.996720 | − | 0.0809270i | \(-0.0257881\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.154731 | + | 0.0893340i | −0.0144287 | + | 0.00833044i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −9.07208 | − | 4.22057i | −0.831636 | − | 0.386899i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.99573 | − | 15.5811i | 0.817793 | − | 1.41646i | ||||
\(122\) | 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 | \(-0.482127\pi\) | ||||
0.0561198 | + | 0.998424i | \(0.482127\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 7.24394 | − | 12.5469i | 0.632906 | − | 1.09623i | −0.354049 | − | 0.935227i | \(-0.615195\pi\) |
0.986955 | − | 0.160998i | \(-0.0514714\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −7.61359 | − | 10.8528i | −0.660182 | − | 0.941056i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 13.3414 | − | 7.70264i | 1.13983 | − | 0.658081i | 0.193442 | − | 0.981112i | \(-0.438035\pi\) |
0.946389 | + | 0.323030i | \(0.104702\pi\) | |||||||
\(138\) | 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 | ||||||||
\(149\) | 4.04535 | + | 2.33558i | 0.331408 | + | 0.191338i | 0.656466 | − | 0.754356i | \(-0.272051\pi\) |
−0.325058 | + | 0.945694i | \(0.605384\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.12276 | + | 7.14083i | 0.335506 | + | 0.581113i | 0.983582 | − | 0.180463i | \(-0.0577595\pi\) |
−0.648076 | + | 0.761575i | \(0.724426\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.380316 | − | 0.219575i | −0.0305477 | − | 0.0176367i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 17.5900i | 1.40383i | 0.712258 | + | 0.701917i | \(0.247672\pi\) | ||||
−0.712258 | + | 0.701917i | \(0.752328\pi\) | |||||||
\(158\) | 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 | \(-0.302135\pi\) |
−0.995201 | + | 0.0978563i | \(0.968801\pi\) | |||||||
\(164\) | 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 | ||||||||
\(173\) | 2.44717 | 0.186055 | 0.0930274 | − | 0.995664i | \(-0.470346\pi\) | ||||
0.0930274 | + | 0.995664i | \(0.470346\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −10.8170 | + | 7.58846i | −0.817686 | + | 0.573633i | ||||
\(176\) | 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 | ||||||||
\(185\) | −0.0541828 | −0.00398360 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 20.3628i | − | 1.48907i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 7.97223i | 0.576850i | 0.957502 | + | 0.288425i | \(0.0931316\pi\) | ||||
−0.957502 | + | 0.288425i | \(0.906868\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 0.718054 | 0.0516867 | 0.0258433 | − | 0.999666i | \(-0.491773\pi\) | ||||
0.0258433 | + | 0.999666i | \(0.491773\pi\) | |||||||
\(194\) | 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 | 0.999968 | + | 0.00796947i | \(0.00253679\pi\) |
0.506886 | + | 0.862013i | \(0.330797\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 11.3973 | − | 24.4984i | 0.799932 | − | 1.71945i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.504265 | −0.0352194 | ||||||||
\(206\) | 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 | \(-0.865467\pi\) |
0.100778 | − | 0.994909i | \(-0.467867\pi\) | |||||||
\(212\) | 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 | ||||||||
\(221\) | 20.1013i | 1.35216i | ||||||||
\(222\) | 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 | ||||||||
\(227\) | −0.318701 | − | 0.552006i | −0.0211529 | − | 0.0366379i | 0.855255 | − | 0.518207i | \(-0.173400\pi\) |
−0.876408 | + | 0.481569i | \(0.840067\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.58351 | − | 0.914239i | −0.104641 | − | 0.0604146i | 0.446766 | − | 0.894651i | \(-0.352576\pi\) |
−0.551407 | + | 0.834236i | \(0.685909\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 17.4232 | − | 10.0593i | 1.14143 | − | 0.659007i | 0.194649 | − | 0.980873i | \(-0.437643\pi\) |
0.946785 | + | 0.321866i | \(0.104310\pi\) | |||||||
\(234\) | 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 | \(-0.637925\pi\) |
0.576055 | + | 0.817411i | \(0.304591\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −20.0304 | + | 11.5645i | −1.29027 | + | 0.744938i | −0.978702 | − | 0.205286i | \(-0.934187\pi\) |
−0.311568 | + | 0.950224i | \(0.600854\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0.182077 | − | 0.503033i | 0.0116325 | − | 0.0321376i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −13.3165 | + | 23.0649i | −0.847310 | + | 1.46758i | ||||
\(248\) | 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 | ||||||||
\(257\) | −5.43687 | + | 9.41694i | −0.339143 | + | 0.587413i | −0.984272 | − | 0.176661i | \(-0.943470\pi\) |
0.645129 | + | 0.764074i | \(0.276804\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1.53558 | + | 1.07726i | −0.0954162 | + | 0.0669376i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −16.4519 | + | 9.49852i | −1.01447 | + | 0.585704i | −0.912497 | − | 0.409083i | \(-0.865849\pi\) |
−0.101972 | + | 0.994787i | \(0.532515\pi\) | |||||||
\(264\) | 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 | \(-0.917731\pi\) |
0.704739 | + | 0.709467i | \(0.251064\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.58706 | − | 0.916292i | 0.0964073 | − | 0.0556608i | −0.451021 | − | 0.892513i | \(-0.648940\pi\) |
0.547429 | + | 0.836852i | \(0.315607\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −23.2878 | − | 13.4452i | −1.40431 | − | 0.810776i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.90931 | − | 13.6993i | −0.475224 | − | 0.823113i | 0.524373 | − | 0.851489i | \(-0.324300\pi\) |
−0.999597 | + | 0.0283760i | \(0.990966\pi\) | |||||||
\(278\) | 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 | ||||||||
\(283\) | − | 9.92818i | − | 0.590169i | −0.955471 | − | 0.295085i | \(-0.904652\pi\) | ||
0.955471 | − | 0.295085i | \(-0.0953478\pi\) | |||||||
\(284\) | 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 | \(0.00166370\pi\) |
−0.495467 | + | 0.868627i | \(0.665003\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.0221594 | + | 0.0383812i | −0.00129017 | + | 0.00223464i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.4262 | 0.718624 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.43766 | + | 1.59929i | 0.198143 | + | 0.0921815i | ||||
\(302\) | 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 | ||||||||
\(311\) | −20.2032 | −1.14562 | −0.572808 | − | 0.819690i | \(-0.694146\pi\) | ||||
−0.572808 | + | 0.819690i | \(0.694146\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 21.8407i | 1.23451i | 0.786764 | + | 0.617254i | \(0.211755\pi\) | ||||
−0.786764 | + | 0.617254i | \(0.788245\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 24.8594i | 1.39624i | 0.715981 | + | 0.698120i | \(0.245980\pi\) | ||||
−0.715981 | + | 0.698120i | \(0.754020\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 54.9880 | 3.07874 | ||||||||
\(320\) | 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 | ||||||||
\(329\) | 0.681067 | + | 7.70574i | 0.0375484 | + | 0.424831i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 16.1444 | 0.887375 | 0.443688 | − | 0.896181i | \(-0.353670\pi\) | ||||
0.443688 | + | 0.896181i | \(0.353670\pi\) | |||||||
\(332\) | 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 | ||||||||
\(347\) | 32.3830i | 1.73841i | 0.494451 | + | 0.869206i | \(0.335369\pi\) | ||||
−0.494451 | + | 0.869206i | \(0.664631\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.0421 | + | 15.0354i | 1.39400 | + | 0.804827i | 0.993755 | − | 0.111581i | \(-0.0355915\pi\) |
0.400246 | + | 0.916408i | \(0.368925\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −8.50607 | − | 14.7329i | −0.452733 | − | 0.784156i | 0.545822 | − | 0.837901i | \(-0.316217\pi\) |
−0.998555 | + | 0.0537453i | \(0.982884\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −0.219804 | − | 0.126904i | −0.0116660 | − | 0.00673537i | ||||
\(356\) | 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 | ||||||||
\(367\) | −15.6981 | + | 9.06329i | −0.819433 | + | 0.473100i | −0.850221 | − | 0.526426i | \(-0.823532\pi\) |
0.0307880 | + | 0.999526i | \(0.490198\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.5096 | + | 29.0388i | −0.701385 | + | 1.50762i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.1823 | − | 17.6362i | 0.527219 | − | 0.913170i | −0.472278 | − | 0.881450i | \(-0.656568\pi\) |
0.999497 | − | 0.0317200i | \(-0.0100985\pi\) | |||||||
\(374\) | 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 | \(-0.691097\pi\) | ||||
−0.564931 | + | 0.825138i | \(0.691097\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −16.3127 | + | 28.2544i | −0.833538 | + | 1.44373i | 0.0616774 | + | 0.998096i | \(0.480355\pi\) |
−0.895215 | + | 0.445634i | \(0.852978\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.08449 | − | 0.0958523i | 0.0552709 | − | 0.00488509i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 13.6400 | − | 7.87504i | 0.691574 | − | 0.399280i | −0.112628 | − | 0.993637i | \(-0.535927\pi\) |
0.804201 | + | 0.594357i | \(0.202593\pi\) | |||||||
\(390\) | 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 | ||||||||
\(401\) | 0.851348 | + | 0.491526i | 0.0425143 | + | 0.0245456i | 0.521106 | − | 0.853492i | \(-0.325519\pi\) |
−0.478592 | + | 0.878037i | \(0.658853\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 15.2712 | + | 26.4505i | 0.760713 | + | 1.31759i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −3.30594 | − | 1.90868i | −0.163869 | − | 0.0946099i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.8900i | 1.42852i | 0.699880 | + | 0.714260i | \(0.253237\pi\) | ||||
−0.699880 | + | 0.714260i | \(0.746763\pi\) | |||||||
\(410\) | 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 | ||||||||
\(425\) | −18.8871 | −0.916158 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −7.32315 | + | 0.647252i | −0.354392 | + | 0.0313227i | ||||
\(428\) | 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 | ||||||||
\(437\) | −11.7142 | −0.560367 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.27192i | 0.156160i | 0.996947 | + | 0.0780802i | \(0.0248790\pi\) | ||||
−0.996947 | + | 0.0780802i | \(0.975121\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − | 2.84907i | − | 0.135363i | −0.997707 | − | 0.0676817i | \(-0.978440\pi\) | ||
0.997707 | − | 0.0676817i | \(-0.0215602\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0.232015 | 0.0109986 | ||||||||
\(446\) | 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 | ||||||||
\(455\) | −1.07057 | + | 0.0946216i | −0.0501890 | + | 0.00443593i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 18.3002 | 0.856046 | 0.428023 | − | 0.903768i | \(-0.359210\pi\) | ||||
0.428023 | + | 0.903768i | \(0.359210\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 4.52954 | − | 7.84539i | 0.210962 | − | 0.365396i | −0.741054 | − | 0.671445i | \(-0.765674\pi\) |
0.952016 | + | 0.306049i | \(0.0990071\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 10.8227 | + | 18.7455i | 0.502974 | + | 0.871176i | 0.999994 | + | 0.00343694i | \(0.00109401\pi\) |
−0.497021 | + | 0.867739i | \(0.665573\pi\) | |||||||
\(464\) | 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 | ||||||||
\(473\) | 7.71602i | 0.354783i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −21.6716 | − | 12.5121i | −0.994362 | − | 0.574095i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −2.47325 | − | 4.28380i | −0.113006 | − | 0.195732i | 0.803975 | − | 0.594663i | \(-0.202715\pi\) |
−0.916981 | + | 0.398931i | \(0.869381\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.26349 | + | 1.88418i | 0.148802 | + | 0.0859110i | ||||
\(482\) | 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 | \(-0.902916\pi\) |
0.736985 | + | 0.675909i | \(0.236249\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 33.0010 | − | 19.0531i | 1.48931 | − | 0.859855i | 0.489387 | − | 0.872067i | \(-0.337221\pi\) |
0.999925 | + | 0.0122119i | \(0.00388725\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 33.4477 | − | 19.3110i | 1.50641 | − | 0.869725i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8.75250 | + | 0.773585i | −0.392603 | + | 0.0347000i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 12.4192 | − | 21.5107i | 0.555960 | − | 0.962951i | −0.441868 | − | 0.897080i | \(-0.645684\pi\) |
0.997828 | − | 0.0658709i | \(-0.0209825\pi\) | |||||||
\(500\) | 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 | ||||||||
\(509\) | −20.8860 | + | 36.1757i | −0.925758 | + | 1.60346i | −0.135420 | + | 0.990788i | \(0.543238\pi\) |
−0.790338 | + | 0.612671i | \(0.790095\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.95522 | − | 17.0997i | 0.351918 | − | 0.756446i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0.494160 | − | 0.285303i | 0.0217753 | − | 0.0125720i | ||||
\(516\) | 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 | \(-0.861628\pi\) |
0.818220 | + | 0.574906i | \(0.194961\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 26.2429 | − | 15.1514i | 1.14752 | − | 0.662523i | 0.199241 | − | 0.979951i | \(-0.436152\pi\) |
0.948282 | + | 0.317428i | \(0.102819\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −18.8198 | − | 10.8656i | −0.819801 | − | 0.473312i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.76726 | − | 15.1853i | −0.381185 | − | 0.660232i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 30.3724 | + | 17.5355i | 1.31558 | + | 0.759548i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0.352982i | 0.0152607i | ||||||||
\(536\) | 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 | \(-0.863090\pi\) |
0.815571 | + | 0.578657i | \(0.196423\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 51.1719 | 2.18000 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0.218550 | + | 2.47272i | 0.00929371 | + | 0.105151i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −14.7527 | − | 8.51750i | −0.625094 | − | 0.360898i | 0.153756 | − | 0.988109i | \(-0.450863\pi\) |
−0.778849 | + | 0.627211i | \(0.784196\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 7.61695i | − | 0.322163i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 12.9198 | 0.544507 | 0.272253 | − | 0.962226i | \(-0.412231\pi\) | ||||
0.272253 | + | 0.962226i | \(0.412231\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.46825i | 0.0617699i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 21.7408i | 0.911420i | 0.890128 | + | 0.455710i | \(0.150615\pi\) | ||||
−0.890128 | + | 0.455710i | \(0.849385\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −33.6508 | −1.40824 | −0.704122 | − | 0.710079i | \(-0.748659\pi\) | ||||
−0.704122 | + | 0.710079i | \(0.748659\pi\) | |||||||
\(572\) | 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 | ||||||||
\(581\) | −31.1751 | − | 14.5035i | −1.29336 | − | 0.601705i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −65.1793 | −2.69945 | ||||||||
\(584\) | 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 | \(-0.213117\pi\) |
−0.929526 | + | 0.368755i | \(0.879784\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0.626005 | − | 0.439163i | 0.0256637 | − | 0.0180039i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 6.00650i | − | 0.245419i | −0.992443 | − | 0.122709i | \(-0.960842\pi\) | ||
0.992443 | − | 0.122709i | \(-0.0391583\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 0.530083 | + | 0.306043i | 0.0216225 | + | 0.0124838i | 0.510772 | − | 0.859716i | \(-0.329360\pi\) |
−0.489150 | + | 0.872200i | \(0.662693\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0.687494 | + | 1.19077i | 0.0279506 | + | 0.0484119i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.77500 | + | 1.02480i | 0.0720450 | + | 0.0415952i | 0.535590 | − | 0.844478i | \(-0.320089\pi\) |
−0.463545 | + | 0.886073i | \(0.653423\pi\) | |||||||
\(608\) | 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 | −0.888254 | − | 0.459352i | \(-0.848082\pi\) |
−0.0463170 | + | 0.998927i | \(0.514748\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.0603011 | − | 0.0348148i | 0.00242370 | − | 0.00139933i | −0.498788 | − | 0.866724i | \(-0.666221\pi\) |
0.501211 | + | 0.865325i | \(0.332888\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6.57547 | − | 4.61291i | 0.263441 | − | 0.184812i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −12.4562 | + | 21.5748i | −0.498248 | + | 0.862992i | ||||
\(626\) | 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 | \(-0.424392\pi\) | ||||
0.235301 | + | 0.971922i | \(0.424392\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −0.0483338 | + | 0.0837165i | −0.00191807 | + | 0.00332219i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −28.4594 | + | 23.9666i | −1.12760 | + | 0.949592i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 17.7673 | − | 10.2580i | 0.701766 | − | 0.405165i | −0.106239 | − | 0.994341i | \(-0.533881\pi\) |
0.808005 | + | 0.589176i | \(0.200547\pi\) | |||||||
\(642\) | 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 | −0.987706 | − | 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 | ||||||||
\(653\) | 7.79559 | + | 4.50079i | 0.305065 | + | 0.176129i | 0.644716 | − | 0.764422i | \(-0.276976\pi\) |
−0.339651 | + | 0.940552i | \(0.610309\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.553614 | + | 0.958888i | 0.0216315 | + | 0.0374669i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −30.4806 | − | 17.5980i | −1.18735 | − | 0.685519i | −0.229650 | − | 0.973273i | \(-0.573758\pi\) |
−0.957704 | + | 0.287754i | \(0.907091\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 12.5628i | − | 0.488637i | −0.969695 | − | 0.244318i | \(-0.921436\pi\) | ||
0.969695 | − | 0.244318i | \(-0.0785642\pi\) | |||||||
\(662\) | 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 | ||||||||
\(677\) | 37.0471 | 1.42384 | 0.711918 | − | 0.702263i | \(-0.247827\pi\) | ||||
0.711918 | + | 0.702263i | \(0.247827\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.96627 | − | 17.1234i | 0.305717 | − | 0.657137i | ||||
\(680\) | 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 | ||||||||
\(689\) | 64.3424 | 2.45125 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 46.4946i | − | 1.76874i | −0.466787 | − | 0.884370i | \(-0.654589\pi\) | ||
0.466787 | − | 0.884370i | \(-0.345411\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0.0330663i | 0.00125428i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −24.9533 | −0.945174 | ||||||||
\(698\) | 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 | ||||||||
\(707\) | 17.7011 | − | 12.4179i | 0.665720 | − | 0.467025i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 31.8316 | 1.19546 | 0.597731 | − | 0.801697i | \(-0.296069\pi\) | ||||
0.597731 | + | 0.801697i | \(0.296069\pi\) | |||||||
\(710\) | 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 | ||||||||
\(725\) | − | 51.0030i | − | 1.89420i | ||||||
\(726\) | 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 | ||||||||
\(731\) | 2.70976 | + | 4.69344i | 0.100224 | + | 0.173593i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 20.4239 | + | 11.7918i | 0.754376 | + | 0.435539i | 0.827273 | − | 0.561800i | \(-0.189891\pi\) |
−0.0728971 | + | 0.997339i | \(0.523224\pi\) | |||||||
\(734\) | 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 | \(-0.620322\pi\) |
0.989420 | − | 0.145083i | \(-0.0463448\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −29.4003 | + | 16.9743i | −1.07859 | + | 0.622725i | −0.930516 | − | 0.366251i | \(-0.880641\pi\) |
−0.148076 | + | 0.988976i | \(0.547308\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −0.309164 | + | 0.178496i | −0.0113269 | + | 0.00653958i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 7.01796 | + | 10.0038i | 0.256431 | + | 0.365529i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.69831 | + | 2.94157i | −0.0619724 | + | 0.107339i | −0.895347 | − | 0.445369i | \(-0.853072\pi\) |
0.833375 | + | 0.552709i | \(0.186406\pi\) | |||||||
\(752\) | 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 | ||||||||
\(761\) | −8.36288 | + | 14.4849i | −0.303154 | + | 0.525079i | −0.976849 | − | 0.213931i | \(-0.931373\pi\) |
0.673694 | + | 0.739010i | \(0.264706\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 25.0821 | + | 11.6688i | 0.908032 | + | 0.422440i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 2.66937 | − | 1.54116i | 0.0963852 | − | 0.0556480i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 24.0816 | − | 13.9035i | 0.868404 | − | 0.501373i | 0.00158643 | − | 0.999999i | \(-0.499495\pi\) |
0.866818 | + | 0.498625i | \(0.166162\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −6.42238 | + | 11.1239i | −0.230997 | + | 0.400098i | −0.958102 | − | 0.286428i | \(-0.907532\pi\) |
0.727105 | + | 0.686526i | \(0.240865\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −24.8527 | + | 14.3487i | −0.892736 | + | 0.515421i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −28.6322 | − | 16.5308i | −1.02586 | − | 0.592278i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.94083 | − | 15.4860i | −0.319928 | − | 0.554132i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.16420 | − | 0.672153i | −0.0415522 | − | 0.0239902i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.56610i | 0.269702i | 0.990866 | + | 0.134851i | \(0.0430556\pi\) | ||||
−0.990866 | + | 0.134851i | \(0.956944\pi\) | |||||||
\(788\) | 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 | \(-0.212302\pi\) |
−0.928579 | + | 0.371134i | \(0.878969\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.52875 | + | 9.57608i | −0.195593 | + | 0.338777i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 38.3812 | 1.35444 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −0.271480 | − | 0.386981i | −0.00956842 | − | 0.0136393i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −0.0849492 | − | 0.0490454i | −0.00298665 | − | 0.00172435i | 0.498506 | − | 0.866886i | \(-0.333882\pi\) |
−0.501493 | + | 0.865162i | \(0.667216\pi\) | |||||||
\(810\) | 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 | ||||||||
\(815\) | 0.805662 | 0.0282211 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.18054i | 0.251215i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 22.5742i | 0.787846i | 0.919143 | + | 0.393923i | \(0.128882\pi\) | ||||
−0.919143 | + | 0.393923i | \(0.871118\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −24.5310 | −0.855097 | −0.427549 | − | 0.903992i | \(-0.640623\pi\) | ||||
−0.427549 | + | 0.903992i | \(0.640623\pi\) | |||||||
\(824\) | 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 | ||||||||
\(833\) | 9.01000 | − | 24.8924i | 0.312178 | − | 0.862470i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.701801 | 0.0242868 | ||||||||
\(836\) | 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 | ||||||||
\(851\) | 1.65746i | 0.0568170i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −48.0748 | − | 27.7560i | −1.64605 | − | 0.950347i | −0.978621 | − | 0.205674i | \(-0.934061\pi\) |
−0.667429 | − | 0.744673i | \(-0.732605\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −15.3048 | − | 26.5088i | −0.522803 | − | 0.905522i | −0.999648 | − | 0.0265343i | \(-0.991553\pi\) |
0.476845 | − | 0.878988i | \(-0.341780\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −36.4944 | − | 21.0700i | −1.24517 | − | 0.718900i | −0.275030 | − | 0.961436i | \(-0.588688\pi\) |
−0.970143 | + | 0.242535i | \(0.922021\pi\) | |||||||
\(860\) | 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 | ||||||||
\(871\) | 24.2670 | − | 14.0106i | 0.822256 | − | 0.474730i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −0.177916 | − | 2.01297i | −0.00601464 | − | 0.0680509i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17.8533 | + | 30.9228i | −0.602863 | + | 1.04419i | 0.389522 | + | 0.921017i | \(0.372640\pi\) |
−0.992385 | + | 0.123172i | \(0.960693\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −12.4482 | −0.419392 | −0.209696 | − | 0.977767i | \(-0.567247\pi\) | ||||
−0.209696 | + | 0.977767i | \(0.567247\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.35637 | 0.0792982 | 0.0396491 | − | 0.999214i | \(-0.487376\pi\) | ||||
0.0396491 | + | 0.999214i | \(0.487376\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 16.7299 | − | 28.9770i | 0.561734 | − | 0.972952i | −0.435611 | − | 0.900135i | \(-0.643468\pi\) |
0.997345 | − | 0.0728170i | \(-0.0231989\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0.294634 | + | 3.33355i | 0.00988172 | + | 0.111804i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −12.6877 | + | 7.32526i | −0.424579 | + | 0.245131i | ||||
\(894\) | 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 | ||||||||
\(905\) | 1.06363 | + | 0.614087i | 0.0353563 | + | 0.0204130i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 0.467962 | + | 0.810535i | 0.0155384 | + | 0.0269134i | 0.873690 | − | 0.486483i | \(-0.161720\pi\) |
−0.858152 | + | 0.513396i | \(0.828387\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −28.8739 | − | 16.6703i | −0.956634 | − | 0.552313i | −0.0614988 | − | 0.998107i | \(-0.519588\pi\) |
−0.895136 | + | 0.445794i | \(0.852921\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 69.9743i | − | 2.31581i | ||||||
\(914\) | 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 | \(-0.184893\pi\) |
−0.893220 | + | 0.449621i | \(0.851559\pi\) | |||||||
\(920\) | 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 | ||||||||
\(929\) | −15.1536 | −0.497174 | −0.248587 | − | 0.968610i | \(-0.579966\pi\) | ||||
−0.248587 | + | 0.968610i | \(0.579966\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 26.8288 | − | 22.5934i | 0.879279 | − | 0.740470i | ||||
\(932\) | 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 | ||||||||
\(941\) | 37.7960 | 1.23212 | 0.616058 | − | 0.787701i | \(-0.288729\pi\) | ||||
0.616058 | + | 0.787701i | \(0.288729\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 15.4255i | 0.502325i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 10.9399i | − | 0.355500i | −0.984076 | − | 0.177750i | \(-0.943118\pi\) | ||
0.984076 | − | 0.177750i | \(-0.0568818\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −37.8884 | −1.22991 | ||||||||
\(950\) | 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 | ||||||||
\(959\) | 23.4078 | + | 33.3667i | 0.755878 | + | 1.07747i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.01885 | −0.0651242 | ||||||||
\(962\) | 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 | \(0.0576470\pi\) |
−0.335839 | + | 0.941920i | \(0.609020\pi\) | |||||||
\(968\) | 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 | ||||||||
\(977\) | − | 16.6901i | − | 0.533963i | −0.963702 | − | 0.266982i | \(-0.913974\pi\) | ||
0.963702 | − | 0.266982i | \(-0.0860263\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.1563 | + | 8.17314i | 0.452437 | + | 0.261215i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −16.9255 | − | 29.3157i | −0.539838 | − | 0.935027i | −0.998912 | − | 0.0466291i | \(-0.985152\pi\) |
0.459074 | − | 0.888398i | \(-0.348181\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0.893735 | + | 0.515998i | 0.0284768 | + | 0.0164411i | ||||
\(986\) | 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 | \(-0.874885\pi\) |
0.793572 | + | 0.608476i | \(0.208219\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.62454 | + | 0.937928i | −0.0515014 | + | 0.0297343i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −18.7391 | + | 10.8190i | −0.593472 | + | 0.342641i | −0.766469 | − | 0.642281i | \(-0.777988\pi\) |
0.172997 | + | 0.984922i | \(0.444655\pi\) | |||||||
\(998\) | 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 \(a_p\))