Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1800,2,Mod(901,1800)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1800, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1800.901");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1800 = 2^{3} \cdot 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1800.k (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(14.3730723638\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | 8.0.214798336.3 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 2x^{5} + 9x^{4} - 4x^{3} - 16x + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | no (minimal twist has level 600) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 901.4 | ||
Root | \(-1.08003 + 0.912978i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1800.901 |
Dual form | 1800.2.k.t.901.3 |
$q$-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 \(\left(\mathbb{Z}/1800\mathbb{Z}\right)^\times\).
\(n\) | \(577\) | \(901\) | \(1001\) | \(1351\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.0591148 | + | 1.41298i | −0.0418005 | + | 0.999126i | ||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −1.99301 | − | 0.167056i | −0.996505 | − | 0.0835279i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.33411 | 0.504247 | 0.252123 | − | 0.967695i | \(-0.418871\pi\) | ||||
0.252123 | + | 0.967695i | \(0.418871\pi\) | |||||||
\(8\) | 0.353863 | − | 2.80620i | 0.125109 | − | 0.992143i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 2.94418i | − | 0.887705i | −0.896100 | − | 0.443853i | \(-0.853611\pi\) | ||
0.896100 | − | 0.443853i | \(-0.146389\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − | 2.04184i | − | 0.566304i | −0.959075 | − | 0.283152i | \(-0.908620\pi\) | ||
0.959075 | − | 0.283152i | \(-0.0913800\pi\) | |||||||
\(14\) | −0.0788658 | + | 1.88507i | −0.0210778 | + | 0.503806i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 3.94418 | + | 0.665888i | 0.986046 | + | 0.166472i | ||||
\(17\) | −3.61241 | −0.876138 | −0.438069 | − | 0.898941i | \(-0.644337\pi\) | ||||
−0.438069 | + | 0.898941i | \(0.644337\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.35964i | 1.22958i | 0.788689 | + | 0.614792i | \(0.210760\pi\) | ||||
−0.788689 | + | 0.614792i | \(0.789240\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4.16007 | + | 0.174045i | 0.886929 | + | 0.0371065i | ||||
\(23\) | −8.59609 | −1.79241 | −0.896205 | − | 0.443641i | \(-0.853687\pi\) | ||||
−0.896205 | + | 0.443641i | \(0.853687\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.88507 | + | 0.120703i | 0.565809 | + | 0.0236718i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −2.65890 | − | 0.222871i | −0.502485 | − | 0.0421187i | ||||
\(29\) | − | 5.26432i | − | 0.977559i | −0.872407 | − | 0.488780i | \(-0.837442\pi\) | ||
0.872407 | − | 0.488780i | \(-0.162558\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.08134 | −0.373820 | −0.186910 | − | 0.982377i | \(-0.559847\pi\) | ||||
−0.186910 | + | 0.982377i | \(0.559847\pi\) | |||||||
\(32\) | −1.17404 | + | 5.53368i | −0.207544 | + | 0.978226i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.213547 | − | 5.10425i | 0.0366230 | − | 0.875372i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 6.55659i | 1.07790i | 0.842339 | + | 0.538949i | \(0.181178\pi\) | ||||
−0.842339 | + | 0.538949i | \(0.818822\pi\) | |||||||
\(38\) | −7.57304 | − | 0.316834i | −1.22851 | − | 0.0513973i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −7.02786 | −1.09757 | −0.548784 | − | 0.835964i | \(-0.684909\pi\) | ||||
−0.548784 | + | 0.835964i | \(0.684909\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 8.50078i | − | 1.29636i | −0.761489 | − | 0.648178i | \(-0.775531\pi\) | ||
0.761489 | − | 0.648178i | \(-0.224469\pi\) | |||||||
\(44\) | −0.491843 | + | 5.86779i | −0.0741482 | + | 0.884603i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.508157 | − | 12.1461i | 0.0749236 | − | 1.79084i | ||||
\(47\) | −9.97204 | −1.45457 | −0.727286 | − | 0.686334i | \(-0.759219\pi\) | ||||
−0.727286 | + | 0.686334i | \(0.759219\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5.22015 | −0.745735 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −0.341101 | + | 4.06940i | −0.0473022 | + | 0.564325i | ||||
\(53\) | 6.12318i | 0.841083i | 0.907273 | + | 0.420541i | \(0.138160\pi\) | ||||
−0.907273 | + | 0.420541i | \(0.861840\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0.472092 | − | 3.74379i | 0.0630860 | − | 0.500285i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 7.43836 | + | 0.311199i | 0.976705 | + | 0.0408625i | ||||
\(59\) | − | 4.75190i | − | 0.618644i | −0.950957 | − | 0.309322i | \(-0.899898\pi\) | ||
0.950957 | − | 0.309322i | \(-0.100102\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 8.51476i | − | 1.09020i | −0.838370 | − | 0.545101i | \(-0.816491\pi\) | ||
0.838370 | − | 0.545101i | \(-0.183509\pi\) | |||||||
\(62\) | 0.123038 | − | 2.94089i | 0.0156258 | − | 0.373493i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −7.74956 | − | 1.98602i | −0.968695 | − | 0.248253i | ||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 10.6961i | 1.30673i | 0.757041 | + | 0.653367i | \(0.226644\pi\) | ||||
−0.757041 | + | 0.653367i | \(0.773356\pi\) | |||||||
\(68\) | 7.19957 | + | 0.603474i | 0.873076 | + | 0.0731820i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.62405 | 0.311418 | 0.155709 | − | 0.987803i | \(-0.450234\pi\) | ||||
0.155709 | + | 0.987803i | \(0.450234\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −15.3875 | −1.80097 | −0.900485 | − | 0.434887i | \(-0.856788\pi\) | ||||
−0.900485 | + | 0.434887i | \(0.856788\pi\) | |||||||
\(74\) | −9.26432 | − | 0.387592i | −1.07696 | − | 0.0450566i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0.895358 | − | 10.6818i | 0.102705 | − | 1.22529i | ||||
\(77\) | − | 3.92787i | − | 0.447622i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 10.4450 | 1.17515 | 0.587575 | − | 0.809170i | \(-0.300083\pi\) | ||||
0.587575 | + | 0.809170i | \(0.300083\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0.415451 | − | 9.93021i | 0.0458789 | − | 1.09661i | ||||
\(83\) | − | 1.52708i | − | 0.167619i | −0.996482 | − | 0.0838095i | \(-0.973291\pi\) | ||
0.996482 | − | 0.0838095i | \(-0.0267087\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 12.0114 | + | 0.502522i | 1.29522 | + | 0.0541883i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −8.26198 | − | 1.04184i | −0.880730 | − | 0.111060i | ||||
\(89\) | 12.7193 | 1.34824 | 0.674120 | − | 0.738622i | \(-0.264523\pi\) | ||||
0.674120 | + | 0.738622i | \(0.264523\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 2.72404i | − | 0.285557i | ||||||
\(92\) | 17.1321 | + | 1.43603i | 1.78615 | + | 0.149716i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0.589496 | − | 14.0903i | 0.0608018 | − | 1.45330i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.4450 | −1.36513 | −0.682565 | − | 0.730825i | \(-0.739135\pi\) | ||||
−0.682565 | + | 0.730825i | \(0.739135\pi\) | |||||||
\(98\) | 0.308588 | − | 7.37595i | 0.0311721 | − | 0.745083i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 10.1232i | − | 1.00729i | −0.863910 | − | 0.503647i | \(-0.831991\pi\) | ||
0.863910 | − | 0.503647i | \(-0.168009\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 10.7472 | 1.05896 | 0.529478 | − | 0.848324i | \(-0.322388\pi\) | ||||
0.529478 | + | 0.848324i | \(0.322388\pi\) | |||||||
\(104\) | −5.72981 | − | 0.722530i | −0.561854 | − | 0.0708499i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −8.65191 | − | 0.361971i | −0.840348 | − | 0.0351577i | ||||
\(107\) | 4.86518i | 0.470335i | 0.971955 | + | 0.235167i | \(0.0755638\pi\) | ||||
−0.971955 | + | 0.235167i | \(0.924436\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 15.4573i | − | 1.48054i | −0.672310 | − | 0.740270i | \(-0.734698\pi\) | ||
0.672310 | − | 0.740270i | \(-0.265302\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 5.26198 | + | 0.888369i | 0.497211 | + | 0.0839430i | ||||
\(113\) | 9.88837 | 0.930220 | 0.465110 | − | 0.885253i | \(-0.346015\pi\) | ||||
0.465110 | + | 0.885253i | \(0.346015\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −0.879435 | + | 10.4918i | −0.0816535 | + | 0.974143i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.71432 | + | 0.280908i | 0.618104 | + | 0.0258596i | ||||
\(119\) | −4.81936 | −0.441790 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.33178 | 0.211980 | ||||||||
\(122\) | 12.0312 | + | 0.503348i | 1.08925 | + | 0.0455710i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 4.14813 | + | 0.347700i | 0.372513 | + | 0.0312244i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −8.75190 | −0.776605 | −0.388303 | − | 0.921532i | \(-0.626938\pi\) | ||||
−0.388303 | + | 0.921532i | \(0.626938\pi\) | |||||||
\(128\) | 3.26432 | − | 10.8326i | 0.288528 | − | 0.957472i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 0.471266i | 0.0411747i | 0.999788 | + | 0.0205874i | \(0.00655362\pi\) | ||||
−0.999788 | + | 0.0205874i | \(0.993446\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 7.15035i | 0.620014i | ||||||||
\(134\) | −15.1133 | − | 0.632297i | −1.30559 | − | 0.0546222i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.27830 | + | 10.1372i | −0.109613 | + | 0.869254i | ||||
\(137\) | −1.30382 | −0.111393 | −0.0556964 | − | 0.998448i | \(-0.517738\pi\) | ||||
−0.0556964 | + | 0.998448i | \(0.517738\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 8.74723i | 0.741930i | 0.928647 | + | 0.370965i | \(0.120973\pi\) | ||||
−0.928647 | + | 0.370965i | \(0.879027\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.155120 | + | 3.70773i | −0.0130174 | + | 0.311145i | ||||
\(143\) | −6.01155 | −0.502711 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0.909629 | − | 21.7422i | 0.0752814 | − | 1.79940i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.09532 | − | 13.0674i | 0.0900345 | − | 1.07413i | ||||
\(149\) | − | 15.1411i | − | 1.24041i | −0.784439 | − | 0.620205i | \(-0.787049\pi\) | ||
0.784439 | − | 0.620205i | \(-0.212951\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −23.2782 | −1.89435 | −0.947176 | − | 0.320713i | \(-0.896078\pi\) | ||||
−0.947176 | + | 0.320713i | \(0.896078\pi\) | |||||||
\(152\) | 15.0402 | + | 1.89657i | 1.21992 | + | 0.153833i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 5.54999 | + | 0.232195i | 0.447231 | + | 0.0187108i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 21.8976i | − | 1.74762i | −0.486270 | − | 0.873809i | \(-0.661643\pi\) | ||
0.486270 | − | 0.873809i | \(-0.338357\pi\) | |||||||
\(158\) | −0.617452 | + | 14.7585i | −0.0491219 | + | 1.17412i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −11.4682 | −0.903817 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 11.1643i | − | 0.874458i | −0.899350 | − | 0.437229i | \(-0.855960\pi\) | ||
0.899350 | − | 0.437229i | \(-0.144040\pi\) | |||||||
\(164\) | 14.0066 | + | 1.17404i | 1.09373 | + | 0.0916775i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.15773 | + | 0.0902732i | 0.167472 | + | 0.00700656i | ||||
\(167\) | −10.0952 | −0.781192 | −0.390596 | − | 0.920562i | \(-0.627731\pi\) | ||||
−0.390596 | + | 0.920562i | \(0.627731\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 8.83090 | 0.679300 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.42010 | + | 16.9421i | −0.108282 | + | 1.29183i | ||||
\(173\) | − | 13.8162i | − | 1.05043i | −0.850970 | − | 0.525215i | \(-0.823985\pi\) | ||
0.850970 | − | 0.525215i | \(-0.176015\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.96050 | − | 11.6124i | 0.147778 | − | 0.875318i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −0.751898 | + | 17.9720i | −0.0563571 | + | 1.34706i | ||||
\(179\) | 21.9441i | 1.64018i | 0.572236 | + | 0.820089i | \(0.306076\pi\) | ||||
−0.572236 | + | 0.820089i | \(0.693924\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 1.93021i | − | 0.143471i | −0.997424 | − | 0.0717356i | \(-0.977146\pi\) | ||
0.997424 | − | 0.0717356i | \(-0.0228538\pi\) | |||||||
\(182\) | 3.84901 | + | 0.161031i | 0.285307 | + | 0.0119364i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −3.04184 | + | 24.1224i | −0.224247 | + | 1.77833i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 10.6356i | 0.777752i | ||||||||
\(188\) | 19.8744 | + | 1.66589i | 1.44949 | + | 0.121497i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −12.1232 | −0.877202 | −0.438601 | − | 0.898682i | \(-0.644526\pi\) | ||||
−0.438601 | + | 0.898682i | \(0.644526\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.27431 | −0.0917267 | −0.0458634 | − | 0.998948i | \(-0.514604\pi\) | ||||
−0.0458634 | + | 0.998948i | \(0.514604\pi\) | |||||||
\(194\) | 0.794797 | − | 18.9974i | 0.0570631 | − | 1.36394i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 10.4038 | + | 0.872056i | 0.743129 | + | 0.0622897i | ||||
\(197\) | 3.30849i | 0.235720i | 0.993030 | + | 0.117860i | \(0.0376034\pi\) | ||||
−0.993030 | + | 0.117860i | \(0.962397\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 9.02718 | 0.639920 | 0.319960 | − | 0.947431i | \(-0.396331\pi\) | ||||
0.319960 | + | 0.947431i | \(0.396331\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 14.3038 | + | 0.598430i | 1.00641 | + | 0.0421054i | ||||
\(203\) | − | 7.02319i | − | 0.492931i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −0.635321 | + | 15.1856i | −0.0442649 | + | 1.05803i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.35964 | − | 8.05338i | 0.0942738 | − | 0.558402i | ||||
\(209\) | 15.7798 | 1.09151 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 6.61241i | 0.455217i | 0.973753 | + | 0.227608i | \(0.0730906\pi\) | ||||
−0.973753 | + | 0.227608i | \(0.926909\pi\) | |||||||
\(212\) | 1.02291 | − | 12.2036i | 0.0702539 | − | 0.838144i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −6.87439 | − | 0.287604i | −0.469924 | − | 0.0196602i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −2.77674 | −0.188497 | ||||||||
\(218\) | 21.8408 | + | 0.913755i | 1.47925 | + | 0.0618873i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.37595i | 0.496160i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 0.833237 | 0.0557976 | 0.0278988 | − | 0.999611i | \(-0.491118\pi\) | ||||
0.0278988 | + | 0.999611i | \(0.491118\pi\) | |||||||
\(224\) | −1.56631 | + | 7.38255i | −0.104653 | + | 0.493267i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −0.584549 | + | 13.9720i | −0.0388836 | + | 0.929407i | ||||
\(227\) | 10.9999i | 0.730089i | 0.930990 | + | 0.365045i | \(0.118946\pi\) | ||||
−0.930990 | + | 0.365045i | \(0.881054\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 15.2061i | − | 1.00485i | −0.864622 | − | 0.502423i | \(-0.832442\pi\) | ||
0.864622 | − | 0.502423i | \(-0.167558\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −14.7728 | − | 1.86285i | −0.969879 | − | 0.122302i | ||||
\(233\) | −2.47594 | −0.162204 | −0.0811020 | − | 0.996706i | \(-0.525844\pi\) | ||||
−0.0811020 | + | 0.996706i | \(0.525844\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −0.793832 | + | 9.47058i | −0.0516741 | + | 0.616482i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0.284895 | − | 6.80964i | 0.0184670 | − | 0.441404i | ||||
\(239\) | 21.0737 | 1.36314 | 0.681572 | − | 0.731751i | \(-0.261297\pi\) | ||||
0.681572 | + | 0.731751i | \(0.261297\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −6.10852 | −0.393484 | −0.196742 | − | 0.980455i | \(-0.563036\pi\) | ||||
−0.196742 | + | 0.980455i | \(0.563036\pi\) | |||||||
\(242\) | −0.137843 | + | 3.29475i | −0.00886086 | + | 0.211794i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −1.42244 | + | 16.9700i | −0.0910624 | + | 1.08639i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 10.9435 | 0.696318 | ||||||||
\(248\) | −0.736508 | + | 5.84066i | −0.0467683 | + | 0.370882i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 22.5286i | 1.42199i | 0.703195 | + | 0.710997i | \(0.251756\pi\) | ||||
−0.703195 | + | 0.710997i | \(0.748244\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 25.3085i | 1.59113i | ||||||||
\(254\) | 0.517367 | − | 12.3662i | 0.0324625 | − | 0.775927i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 15.1132 | + | 5.25277i | 0.944574 | + | 0.328298i | ||||
\(257\) | −14.5286 | −0.906271 | −0.453136 | − | 0.891442i | \(-0.649695\pi\) | ||||
−0.453136 | + | 0.891442i | \(0.649695\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.74723i | 0.543526i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.665888 | − | 0.0278588i | −0.0411387 | − | 0.00172112i | ||||
\(263\) | −5.29694 | −0.326624 | −0.163312 | − | 0.986575i | \(-0.552218\pi\) | ||||
−0.163312 | + | 0.986575i | \(0.552218\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −10.1033 | − | 0.422692i | −0.619472 | − | 0.0259169i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 1.78684 | − | 21.3174i | 0.109149 | − | 1.30217i | ||||
\(269\) | 27.0737i | 1.65071i | 0.564613 | + | 0.825356i | \(0.309025\pi\) | ||||
−0.564613 | + | 0.825356i | \(0.690975\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 15.8604 | 0.963451 | 0.481726 | − | 0.876322i | \(-0.340010\pi\) | ||||
0.481726 | + | 0.876322i | \(0.340010\pi\) | |||||||
\(272\) | −14.2480 | − | 2.40546i | −0.863912 | − | 0.145852i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0.0770751 | − | 1.84227i | 0.00465628 | − | 0.111296i | ||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − | 9.98592i | − | 0.599996i | −0.953940 | − | 0.299998i | \(-0.903014\pi\) | ||
0.953940 | − | 0.299998i | \(-0.0969860\pi\) | |||||||
\(278\) | −12.3596 | − | 0.517091i | −0.741282 | − | 0.0310130i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −13.4218 | −0.800676 | −0.400338 | − | 0.916368i | \(-0.631107\pi\) | ||||
−0.400338 | + | 0.916368i | \(0.631107\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.83722i | 0.228099i | 0.993475 | + | 0.114050i | \(0.0363823\pi\) | ||||
−0.993475 | + | 0.114050i | \(0.963618\pi\) | |||||||
\(284\) | −5.22976 | − | 0.438363i | −0.310329 | − | 0.0260121i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0.355372 | − | 8.49418i | 0.0210136 | − | 0.502271i | ||||
\(287\) | −9.37595 | −0.553445 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.95051 | −0.232383 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 30.6674 | + | 2.57057i | 1.79468 | + | 0.150431i | ||||
\(293\) | 26.4450i | 1.54493i | 0.635057 | + | 0.772466i | \(0.280977\pi\) | ||||
−0.635057 | + | 0.772466i | \(0.719023\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 18.3991 | + | 2.32013i | 1.06943 | + | 0.134855i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 21.3941 | + | 0.895066i | 1.23933 | + | 0.0518498i | ||||
\(299\) | 17.5518i | 1.01505i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | − | 11.3410i | − | 0.653684i | ||||||
\(302\) | 1.37609 | − | 32.8916i | 0.0791849 | − | 1.89270i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.56892 | + | 21.1394i | −0.204692 | + | 1.21243i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.27596i | 0.0728230i | 0.999337 | + | 0.0364115i | \(0.0115927\pi\) | ||||
−0.999337 | + | 0.0364115i | \(0.988407\pi\) | |||||||
\(308\) | −0.656174 | + | 7.82829i | −0.0373890 | + | 0.446058i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2.44496 | −0.138641 | −0.0693205 | − | 0.997594i | \(-0.522083\pi\) | ||||
−0.0693205 | + | 0.997594i | \(0.522083\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 22.8325 | 1.29057 | 0.645283 | − | 0.763943i | \(-0.276739\pi\) | ||||
0.645283 | + | 0.763943i | \(0.276739\pi\) | |||||||
\(314\) | 30.9408 | + | 1.29447i | 1.74609 | + | 0.0730513i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −20.8169 | − | 1.74489i | −1.17104 | − | 0.0981579i | ||||
\(317\) | 2.11163i | 0.118601i | 0.998240 | + | 0.0593005i | \(0.0188870\pi\) | ||||
−0.998240 | + | 0.0593005i | \(0.981113\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −15.4991 | −0.867784 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0.677938 | − | 16.2042i | 0.0377800 | − | 0.903027i | ||||
\(323\) | − | 19.3612i | − | 1.07729i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 15.7749 | + | 0.659978i | 0.873694 | + | 0.0365528i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −2.48690 | + | 19.7216i | −0.137316 | + | 1.08894i | ||||
\(329\) | −13.3038 | −0.733463 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 23.2248i | 1.27655i | 0.769808 | + | 0.638276i | \(0.220352\pi\) | ||||
−0.769808 | + | 0.638276i | \(0.779648\pi\) | |||||||
\(332\) | −0.255108 | + | 3.04349i | −0.0140009 | + | 0.167033i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0.596777 | − | 14.2643i | 0.0326542 | − | 0.780509i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 12.8884 | 0.702074 | 0.351037 | − | 0.936362i | \(-0.385829\pi\) | ||||
0.351037 | + | 0.936362i | \(0.385829\pi\) | |||||||
\(338\) | −0.522037 | + | 12.4779i | −0.0283951 | + | 0.678706i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.12785i | 0.331841i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −16.3030 | −0.880281 | ||||||||
\(344\) | −23.8549 | − | 3.00811i | −1.28617 | − | 0.162186i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 19.5220 | + | 0.816745i | 1.04951 | + | 0.0439085i | ||||
\(347\) | 6.79827i | 0.364951i | 0.983210 | + | 0.182475i | \(0.0584109\pi\) | ||||
−0.983210 | + | 0.182475i | \(0.941589\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 34.6076i | − | 1.85250i | −0.376904 | − | 0.926252i | \(-0.623011\pi\) | ||
0.376904 | − | 0.926252i | \(-0.376989\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 16.2922 | + | 3.45661i | 0.868376 | + | 0.184238i | ||||
\(353\) | −12.2433 | −0.651647 | −0.325823 | − | 0.945431i | \(-0.605642\pi\) | ||||
−0.325823 | + | 0.945431i | \(0.605642\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −25.3496 | − | 2.12483i | −1.34353 | − | 0.112616i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −31.0065 | − | 1.29722i | −1.63874 | − | 0.0685603i | ||||
\(359\) | 2.01622 | 0.106412 | 0.0532059 | − | 0.998584i | \(-0.483056\pi\) | ||||
0.0532059 | + | 0.998584i | \(0.483056\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9.72569 | −0.511878 | ||||||||
\(362\) | 2.72734 | + | 0.114104i | 0.143346 | + | 0.00599716i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −0.455067 | + | 5.42904i | −0.0238520 | + | 0.284559i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −13.4131 | −0.700159 | −0.350079 | − | 0.936720i | \(-0.613845\pi\) | ||||
−0.350079 | + | 0.936720i | \(0.613845\pi\) | |||||||
\(368\) | −33.9046 | − | 5.72404i | −1.76740 | − | 0.298386i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 8.16900i | 0.424113i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 10.0976i | 0.522832i | 0.965226 | + | 0.261416i | \(0.0841894\pi\) | ||||
−0.965226 | + | 0.261416i | \(0.915811\pi\) | |||||||
\(374\) | −15.0279 | − | 0.628722i | −0.777072 | − | 0.0325104i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.52873 | + | 27.9836i | −0.181981 | + | 1.44314i | ||||
\(377\) | −10.7489 | −0.553595 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 18.2775i | 0.938853i | 0.882972 | + | 0.469426i | \(0.155539\pi\) | ||||
−0.882972 | + | 0.469426i | \(0.844461\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0.716660 | − | 17.1298i | 0.0366675 | − | 0.876436i | ||||
\(383\) | 11.7734 | 0.601594 | 0.300797 | − | 0.953688i | \(-0.402747\pi\) | ||||
0.300797 | + | 0.953688i | \(0.402747\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.0753305 | − | 1.80057i | 0.00383422 | − | 0.0916466i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 26.7960 | + | 2.24606i | 1.36036 | + | 0.114026i | ||||
\(389\) | − | 33.4270i | − | 1.69482i | −0.530942 | − | 0.847408i | \(-0.678162\pi\) | ||
0.530942 | − | 0.847408i | \(-0.321838\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 31.0526 | 1.57040 | ||||||||
\(392\) | −1.84721 | + | 14.6488i | −0.0932984 | + | 0.739876i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −4.67482 | − | 0.195581i | −0.235514 | − | 0.00985322i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 39.0434i | − | 1.95953i | −0.200147 | − | 0.979766i | \(-0.564142\pi\) | ||
0.200147 | − | 0.979766i | \(-0.435858\pi\) | |||||||
\(398\) | −0.533640 | + | 12.7552i | −0.0267490 | + | 0.639360i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 24.6140 | 1.22916 | 0.614581 | − | 0.788853i | \(-0.289325\pi\) | ||||
0.614581 | + | 0.788853i | \(0.289325\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.24976i | 0.211695i | ||||||||
\(404\) | −1.69114 | + | 20.1756i | −0.0841372 | + | 1.00377i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 9.92361 | + | 0.415175i | 0.492500 | + | 0.0206048i | ||||
\(407\) | 19.3038 | 0.956855 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −14.5024 | −0.717099 | −0.358550 | − | 0.933511i | \(-0.616729\pi\) | ||||
−0.358550 | + | 0.933511i | \(0.616729\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −21.4193 | − | 1.79539i | −1.05526 | − | 0.0884524i | ||||
\(413\) | − | 6.33956i | − | 0.311949i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 11.2989 | + | 2.39721i | 0.553973 | + | 0.117533i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.932818 | + | 22.2964i | −0.0456256 | + | 1.09055i | ||||
\(419\) | − | 12.6419i | − | 0.617598i | −0.951127 | − | 0.308799i | \(-0.900073\pi\) | ||
0.951127 | − | 0.308799i | \(-0.0999271\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 16.8389i | 0.820677i | 0.911933 | + | 0.410338i | \(0.134589\pi\) | ||||
−0.911933 | + | 0.410338i | \(0.865411\pi\) | |||||||
\(422\) | −9.34318 | − | 0.390891i | −0.454819 | − | 0.0190283i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 17.1829 | + | 2.16676i | 0.834474 | + | 0.105227i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | − | 11.3596i | − | 0.549731i | ||||||
\(428\) | 0.812757 | − | 9.69636i | 0.0392861 | − | 0.468691i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.98845 | −0.288454 | −0.144227 | − | 0.989545i | \(-0.546070\pi\) | ||||
−0.144227 | + | 0.989545i | \(0.546070\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.22482 | −0.106918 | −0.0534589 | − | 0.998570i | \(-0.517025\pi\) | ||||
−0.0534589 | + | 0.998570i | \(0.517025\pi\) | |||||||
\(434\) | 0.164146 | − | 3.92347i | 0.00787928 | − | 0.188333i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −2.58223 | + | 30.8065i | −0.123666 | + | 1.47537i | ||||
\(437\) | − | 46.0719i | − | 2.20392i | ||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.30460 | −0.109993 | −0.0549963 | − | 0.998487i | \(-0.517515\pi\) | ||||
−0.0549963 | + | 0.998487i | \(0.517515\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −10.4220 | − | 0.436028i | −0.495726 | − | 0.0207397i | ||||
\(443\) | 22.1347i | 1.05165i | 0.850592 | + | 0.525826i | \(0.176244\pi\) | ||||
−0.850592 | + | 0.525826i | \(0.823756\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −0.0492566 | + | 1.17734i | −0.00233237 | + | 0.0557489i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −10.3388 | − | 2.64957i | −0.488462 | − | 0.125181i | ||||
\(449\) | −21.5861 | −1.01871 | −0.509356 | − | 0.860556i | \(-0.670116\pi\) | ||||
−0.509356 | + | 0.860556i | \(0.670116\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 20.6913i | 0.974316i | ||||||||
\(452\) | −19.7076 | − | 1.65191i | −0.926969 | − | 0.0776993i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −15.5426 | − | 0.650257i | −0.729451 | − | 0.0305181i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.50088 | −0.116986 | −0.0584930 | − | 0.998288i | \(-0.518630\pi\) | ||||
−0.0584930 | + | 0.998288i | \(0.518630\pi\) | |||||||
\(458\) | 21.4858 | + | 0.898904i | 1.00397 | + | 0.0420030i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 2.59609i | − | 0.120912i | −0.998171 | − | 0.0604561i | \(-0.980744\pi\) | ||
0.998171 | − | 0.0604561i | \(-0.0192555\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −27.8604 | −1.29478 | −0.647392 | − | 0.762158i | \(-0.724140\pi\) | ||||
−0.647392 | + | 0.762158i | \(0.724140\pi\) | |||||||
\(464\) | 3.50545 | − | 20.7634i | 0.162736 | − | 0.963919i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.146365 | − | 3.49844i | 0.00678021 | − | 0.162062i | ||||
\(467\) | 5.75200i | 0.266171i | 0.991105 | + | 0.133085i | \(0.0424884\pi\) | ||||
−0.991105 | + | 0.133085i | \(0.957512\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 14.2698i | 0.658917i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −13.3348 | − | 1.68152i | −0.613784 | − | 0.0773982i | ||||
\(473\) | −25.0279 | −1.15078 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 9.60503 | + | 0.805102i | 0.440246 | + | 0.0369018i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.24577 | + | 29.7766i | −0.0569801 | + | 1.36195i | ||||
\(479\) | 12.5473 | 0.573299 | 0.286649 | − | 0.958036i | \(-0.407459\pi\) | ||||
0.286649 | + | 0.958036i | \(0.407459\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 13.3875 | 0.610417 | ||||||||
\(482\) | 0.361104 | − | 8.63119i | 0.0164478 | − | 0.393140i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −4.64726 | − | 0.389537i | −0.211239 | − | 0.0177062i | ||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8.60530 | −0.389944 | −0.194972 | − | 0.980809i | \(-0.562462\pi\) | ||||
−0.194972 | + | 0.980809i | \(0.562462\pi\) | |||||||
\(488\) | −23.8941 | − | 3.01305i | −1.08164 | − | 0.136395i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 36.8866i | − | 1.66467i | −0.554273 | − | 0.832335i | \(-0.687004\pi\) | ||
0.554273 | − | 0.832335i | \(-0.312996\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 19.0169i | 0.856477i | ||||||||
\(494\) | −0.646923 | + | 15.4629i | −0.0291065 | + | 0.695710i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.20919 | − | 1.38594i | −0.368603 | − | 0.0622305i | ||||
\(497\) | 3.50078 | 0.157031 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 36.2496i | 1.62275i | 0.584524 | + | 0.811377i | \(0.301281\pi\) | ||||
−0.584524 | + | 0.811377i | \(0.698719\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −31.8325 | − | 1.33178i | −1.42075 | − | 0.0594401i | ||||
\(503\) | 23.3527 | 1.04124 | 0.520622 | − | 0.853787i | \(-0.325700\pi\) | ||||
0.520622 | + | 0.853787i | \(0.325700\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −35.7603 | − | 1.49611i | −1.58974 | − | 0.0665101i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 17.4426 | + | 1.46206i | 0.773891 | + | 0.0648682i | ||||
\(509\) | 3.35506i | 0.148711i | 0.997232 | + | 0.0743553i | \(0.0236899\pi\) | ||||
−0.997232 | + | 0.0743553i | \(0.976310\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −20.5286 | −0.908133 | ||||||||
\(512\) | −8.31546 | + | 21.0441i | −0.367495 | + | 0.930025i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0.858858 | − | 20.5286i | 0.0378826 | − | 0.905479i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 29.3595i | 1.29123i | ||||||||
\(518\) | −12.3596 | − | 0.517091i | −0.543051 | − | 0.0227197i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 33.6029 | 1.47217 | 0.736084 | − | 0.676890i | \(-0.236673\pi\) | ||||
0.736084 | + | 0.676890i | \(0.236673\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 0.965721i | − | 0.0422280i | −0.999777 | − | 0.0211140i | \(-0.993279\pi\) | ||
0.999777 | − | 0.0211140i | \(-0.00672130\pi\) | |||||||
\(524\) | 0.0787277 | − | 0.939238i | 0.00343924 | − | 0.0410308i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.313128 | − | 7.48446i | 0.0136530 | − | 0.326338i | ||||
\(527\) | 7.51865 | 0.327517 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 50.8928 | 2.21273 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 1.19451 | − | 14.2507i | 0.0517885 | − | 0.617848i | ||||
\(533\) | 14.3497i | 0.621556i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 30.0154 | + | 3.78494i | 1.29647 | + | 0.163485i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −38.2545 | − | 1.60046i | −1.64927 | − | 0.0690006i | ||||
\(539\) | 15.3691i | 0.661993i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 6.34877i | − | 0.272955i | −0.990643 | − | 0.136478i | \(-0.956422\pi\) | ||
0.990643 | − | 0.136478i | \(-0.0435781\pi\) | |||||||
\(542\) | −0.937586 | + | 22.4104i | −0.0402728 | + | 0.962609i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.24113 | − | 19.9899i | 0.181837 | − | 0.857060i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.07433i | 0.0886921i | 0.999016 | + | 0.0443460i | \(0.0141204\pi\) | ||||
−0.999016 | + | 0.0443460i | \(0.985880\pi\) | |||||||
\(548\) | 2.59853 | + | 0.217811i | 0.111004 | + | 0.00930442i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 28.2148 | 1.20199 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 13.9347 | 0.592566 | ||||||||
\(554\) | 14.1099 | + | 0.590316i | 0.599472 | + | 0.0250801i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.46128 | − | 17.4333i | 0.0619719 | − | 0.739337i | ||||
\(557\) | 27.6931i | 1.17339i | 0.809807 | + | 0.586696i | \(0.199572\pi\) | ||||
−0.809807 | + | 0.586696i | \(0.800428\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −17.3572 | −0.734131 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0.793426 | − | 18.9647i | 0.0334687 | − | 0.799976i | ||||
\(563\) | 3.80771i | 0.160476i | 0.996776 | + | 0.0802380i | \(0.0255680\pi\) | ||||
−0.996776 | + | 0.0802380i | \(0.974432\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −5.42191 | − | 0.226837i | −0.227900 | − | 0.00953467i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0.928554 | − | 7.36362i | 0.0389613 | − | 0.308971i | ||||
\(569\) | −38.6371 | −1.61975 | −0.809875 | − | 0.586603i | \(-0.800465\pi\) | ||||
−0.809875 | + | 0.586603i | \(0.800465\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 6.24976i | − | 0.261544i | −0.991412 | − | 0.130772i | \(-0.958254\pi\) | ||
0.991412 | − | 0.130772i | \(-0.0417456\pi\) | |||||||
\(572\) | 11.9811 | + | 1.00426i | 0.500954 | + | 0.0419904i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0.554258 | − | 13.2480i | 0.0231343 | − | 0.552961i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.17377 | −0.0904952 | −0.0452476 | − | 0.998976i | \(-0.514408\pi\) | ||||
−0.0452476 | + | 0.998976i | \(0.514408\pi\) | |||||||
\(578\) | 0.233534 | − | 5.58198i | 0.00971372 | − | 0.232180i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 2.03730i | − | 0.0845213i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 18.0278 | 0.746634 | ||||||||
\(584\) | −5.44506 | + | 43.1804i | −0.225318 | + | 1.78682i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −37.3661 | − | 1.56329i | −1.54358 | − | 0.0645789i | ||||
\(587\) | − | 34.1688i | − | 1.41030i | −0.709059 | − | 0.705149i | \(-0.750880\pi\) | ||
0.709059 | − | 0.705149i | \(-0.249120\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 11.1552i | − | 0.459643i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4.36596 | + | 25.8604i | −0.179440 | + | 1.06286i | ||||
\(593\) | −12.9952 | −0.533650 | −0.266825 | − | 0.963745i | \(-0.585975\pi\) | ||||
−0.266825 | + | 0.963745i | \(0.585975\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.52942 | + | 30.1765i | −0.103609 | + | 1.23608i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −24.8003 | − | 1.03757i | −1.01416 | − | 0.0424295i | ||||
\(599\) | −47.2572 | −1.93088 | −0.965439 | − | 0.260628i | \(-0.916071\pi\) | ||||
−0.965439 | + | 0.260628i | \(0.916071\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23.5007 | −0.958613 | −0.479306 | − | 0.877648i | \(-0.659112\pi\) | ||||
−0.479306 | + | 0.877648i | \(0.659112\pi\) | |||||||
\(602\) | 16.0246 | + | 0.670421i | 0.653112 | + | 0.0273243i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 46.3937 | + | 3.88876i | 1.88773 | + | 0.158231i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −0.218591 | −0.00887233 | −0.00443617 | − | 0.999990i | \(-0.501412\pi\) | ||||
−0.00443617 | + | 0.999990i | \(0.501412\pi\) | |||||||
\(608\) | −29.6585 | − | 6.29245i | −1.20281 | − | 0.255193i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 20.3613i | 0.823730i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 35.7488i | − | 1.44388i | −0.691956 | − | 0.721940i | \(-0.743251\pi\) | ||
0.691956 | − | 0.721940i | \(-0.256749\pi\) | |||||||
\(614\) | −1.80290 | − | 0.0754282i | −0.0727593 | − | 0.00304404i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −11.0224 | − | 1.38993i | −0.444105 | − | 0.0560018i | ||||
\(617\) | 33.0836 | 1.33189 | 0.665947 | − | 0.745999i | \(-0.268028\pi\) | ||||
0.665947 | + | 0.745999i | \(0.268028\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25.1084i | 1.00919i | 0.863355 | + | 0.504596i | \(0.168359\pi\) | ||||
−0.863355 | + | 0.504596i | \(0.831641\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0.144534 | − | 3.45468i | 0.00579527 | − | 0.138520i | ||||
\(623\) | 16.9689 | 0.679846 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −1.34974 | + | 32.2617i | −0.0539463 | + | 1.28944i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.65812 | + | 43.6421i | −0.145975 | + | 1.74151i | ||||
\(629\) | − | 23.6851i | − | 0.944386i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 23.2829 | 0.926876 | 0.463438 | − | 0.886129i | \(-0.346616\pi\) | ||||
0.463438 | + | 0.886129i | \(0.346616\pi\) | |||||||
\(632\) | 3.69608 | − | 29.3107i | 0.147022 | − | 1.16592i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −2.98369 | − | 0.124829i | −0.118497 | − | 0.00495758i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.6587i | 0.422313i | ||||||||
\(638\) | 0.916228 | − | 21.8999i | 0.0362738 | − | 0.867026i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 38.3021 | 1.51284 | 0.756420 | − | 0.654086i | \(-0.226946\pi\) | ||||
0.756420 | + | 0.654086i | \(0.226946\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 45.8045i | − | 1.80635i | −0.429269 | − | 0.903177i | \(-0.641229\pi\) | ||
0.429269 | − | 0.903177i | \(-0.358771\pi\) | |||||||
\(644\) | 22.8561 | + | 1.91582i | 0.900658 | + | 0.0754940i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 27.3569 | + | 1.14453i | 1.07634 | + | 0.0450311i | ||||
\(647\) | 48.1114 | 1.89146 | 0.945728 | − | 0.324960i | \(-0.105351\pi\) | ||||
0.945728 | + | 0.324960i | \(0.105351\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −13.9905 | −0.549174 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.86507 | + | 22.2506i | −0.0730417 | + | 0.871402i | ||||
\(653\) | 38.3331i | 1.50009i | 0.661386 | + | 0.750046i | \(0.269969\pi\) | ||||
−0.661386 | + | 0.750046i | \(0.730031\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −27.7192 | − | 4.67977i | −1.08225 | − | 0.182714i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0.786453 | − | 18.7980i | 0.0306591 | − | 0.732822i | ||||
\(659\) | − | 5.03253i | − | 0.196040i | −0.995184 | − | 0.0980198i | \(-0.968749\pi\) | ||
0.995184 | − | 0.0980198i | \(-0.0312508\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 17.4665i | 0.679368i | 0.940540 | + | 0.339684i | \(0.110320\pi\) | ||||
−0.940540 | + | 0.339684i | \(0.889680\pi\) | |||||||
\(662\) | −32.8161 | − | 1.37293i | −1.27544 | − | 0.0533605i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −4.28530 | − | 0.540377i | −0.166302 | − | 0.0209707i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 45.2526i | 1.75219i | ||||||||
\(668\) | 20.1199 | + | 1.68647i | 0.778462 | + | 0.0652513i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −25.0690 | −0.967779 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 32.4448 | 1.25065 | 0.625327 | − | 0.780363i | \(-0.284966\pi\) | ||||
0.625327 | + | 0.780363i | \(0.284966\pi\) | |||||||
\(674\) | −0.761894 | + | 18.2110i | −0.0293471 | + | 0.701461i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −17.6001 | − | 1.47525i | −0.676926 | − | 0.0567405i | ||||
\(677\) | − | 8.07213i | − | 0.310237i | −0.987896 | − | 0.155119i | \(-0.950424\pi\) | ||
0.987896 | − | 0.155119i | \(-0.0495760\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −17.9371 | −0.688362 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −8.65851 | − | 0.362247i | −0.331551 | − | 0.0138711i | ||||
\(683\) | − | 36.3380i | − | 1.39043i | −0.718799 | − | 0.695217i | \(-0.755308\pi\) | ||
0.718799 | − | 0.695217i | \(-0.244692\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0.963751 | − | 23.0358i | 0.0367962 | − | 0.879512i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.66057 | − | 33.5286i | 0.215807 | − | 1.27827i | ||||
\(689\) | 12.5025 | 0.476308 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 15.0016i | − | 0.570686i | −0.958425 | − | 0.285343i | \(-0.907892\pi\) | ||
0.958425 | − | 0.285343i | \(-0.0921075\pi\) | |||||||
\(692\) | −2.30808 | + | 27.5359i | −0.0877402 | + | 1.04676i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −9.60581 | − | 0.401879i | −0.364632 | − | 0.0152551i | ||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 25.3875 | 0.961620 | ||||||||
\(698\) | 48.8998 | + | 2.04582i | 1.85089 | + | 0.0774356i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 13.2874i | − | 0.501859i | −0.968005 | − | 0.250929i | \(-0.919264\pi\) | ||
0.968005 | − | 0.250929i | \(-0.0807362\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −35.1409 | −1.32537 | ||||||||
\(704\) | −5.84721 | + | 22.8161i | −0.220375 | + | 0.859916i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.723763 | − | 17.2996i | 0.0272392 | − | 0.651077i | ||||
\(707\) | − | 13.5054i | − | 0.507925i | ||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 37.8976i | 1.42327i | 0.702548 | + | 0.711637i | \(0.252046\pi\) | ||||
−0.702548 | + | 0.711637i | \(0.747954\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.50088 | − | 35.6929i | 0.168677 | − | 1.33765i | ||||
\(713\) | 17.8914 | 0.670038 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 3.66589 | − | 43.7348i | 0.137001 | − | 1.63445i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −0.119188 | + | 2.84887i | −0.00444807 | + | 0.106319i | ||||
\(719\) | 4.17909 | 0.155854 | 0.0779269 | − | 0.996959i | \(-0.475170\pi\) | ||||
0.0779269 | + | 0.996959i | \(0.475170\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 14.3380 | 0.533975 | ||||||||
\(722\) | 0.574933 | − | 13.7422i | 0.0213968 | − | 0.511431i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −0.322452 | + | 3.84692i | −0.0119838 | + | 0.142970i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 26.7727 | 0.992943 | 0.496471 | − | 0.868053i | \(-0.334629\pi\) | ||||
0.496471 | + | 0.868053i | \(0.334629\pi\) | |||||||
\(728\) | −7.64421 | − | 0.963936i | −0.283313 | − | 0.0357258i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 30.7083i | 1.13579i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 21.3364i | 0.788080i | 0.919093 | + | 0.394040i | \(0.128923\pi\) | ||||
−0.919093 | + | 0.394040i | \(0.871077\pi\) | |||||||
\(734\) | 0.792914 | − | 18.9524i | 0.0292670 | − | 0.699547i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 10.0922 | − | 47.5680i | 0.372003 | − | 1.75338i | ||||
\(737\) | 31.4912 | 1.15999 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 13.1038i | − | 0.482033i | −0.970521 | − | 0.241016i | \(-0.922519\pi\) | ||
0.970521 | − | 0.241016i | \(-0.0774807\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −11.5426 | − | 0.482909i | −0.423743 | − | 0.0177282i | ||||
\(743\) | 33.3595 | 1.22384 | 0.611921 | − | 0.790919i | \(-0.290397\pi\) | ||||
0.611921 | + | 0.790919i | \(0.290397\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −14.2676 | − | 0.596915i | −0.522375 | − | 0.0218546i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 1.77674 | − | 21.1969i | 0.0649640 | − | 0.775034i | ||||
\(749\) | 6.49069i | 0.237165i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.92100 | −0.0700981 | −0.0350491 | − | 0.999386i | \(-0.511159\pi\) | ||||
−0.0350491 | + | 0.999386i | \(0.511159\pi\) | |||||||
\(752\) | −39.3316 | − | 6.64027i | −1.43428 | − | 0.242146i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0.635418 | − | 15.1879i | 0.0231406 | − | 0.553112i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 13.9908i | 0.508504i | 0.967138 | + | 0.254252i | \(0.0818292\pi\) | ||||
−0.967138 | + | 0.254252i | \(0.918171\pi\) | |||||||
\(758\) | −25.8257 | − | 1.08047i | −0.938032 | − | 0.0392445i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −25.6618 | −0.930240 | −0.465120 | − | 0.885248i | \(-0.653989\pi\) | ||||
−0.465120 | + | 0.885248i | \(0.653989\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 20.6217i | − | 0.746557i | ||||||
\(764\) | 24.1616 | + | 2.02525i | 0.874137 | + | 0.0732709i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −0.695985 | + | 16.6356i | −0.0251469 | + | 0.601069i | ||||
\(767\) | −9.70260 | −0.350341 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12.3922 | −0.446873 | −0.223436 | − | 0.974719i | \(-0.571728\pi\) | ||||
−0.223436 | + | 0.974719i | \(0.571728\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.53971 | + | 0.212881i | 0.0914062 | + | 0.00766174i | ||||
\(773\) | − | 38.4843i | − | 1.38418i | −0.721810 | − | 0.692091i | \(-0.756689\pi\) | ||
0.721810 | − | 0.692091i | \(-0.243311\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −4.75767 | + | 37.7293i | −0.170790 | + | 1.35440i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 47.2316 | + | 1.97603i | 1.69333 | + | 0.0708442i | ||||
\(779\) | − | 37.6668i | − | 1.34955i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 7.72569i | − | 0.276447i | ||||||
\(782\) | −1.83567 | + | 43.8766i | −0.0656434 | + | 1.56903i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −20.5892 | − | 3.47603i | −0.735329 | − | 0.124144i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 0.389147i | 0.0138716i | 0.999976 | + | 0.00693579i | \(0.00220775\pi\) | ||||
−0.999976 | + | 0.00693579i | \(0.997792\pi\) | |||||||
\(788\) | 0.552703 | − | 6.59386i | 0.0196892 | − | 0.234896i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 13.1922 | 0.469060 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −17.3857 | −0.617386 | ||||||||
\(794\) | 55.1674 | + | 2.30804i | 1.95782 | + | 0.0819094i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −17.9913 | − | 1.50804i | −0.637683 | − | 0.0534512i | ||||
\(797\) | 0.854188i | 0.0302569i | 0.999886 | + | 0.0151284i | \(0.00481572\pi\) | ||||
−0.999886 | + | 0.0151284i | \(0.995184\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 36.0231 | 1.27441 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.45505 | + | 34.7790i | −0.0513796 | + | 1.22809i | ||||
\(803\) | 45.3036i | 1.59873i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −6.00481 | − | 0.251224i | −0.211510 | − | 0.00884897i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −28.4077 | − | 3.58221i | −0.999379 | − | 0.126022i | ||||
\(809\) | 10.4107 | 0.366020 | 0.183010 | − | 0.983111i | \(-0.441416\pi\) | ||||
0.183010 | + | 0.983111i | \(0.441416\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 6.08825i | − | 0.213787i | −0.994270 | − | 0.106894i | \(-0.965910\pi\) | ||
0.994270 | − | 0.106894i | \(-0.0340904\pi\) | |||||||
\(812\) | −1.17326 | + | 13.9973i | −0.0411735 | + | 0.491209i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.14114 | + | 27.2759i | −0.0399970 | + | 0.956019i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 45.5611 | 1.59398 | ||||||||
\(818\) | 0.857309 | − | 20.4916i | 0.0299751 | − | 0.716472i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 35.3908i | − | 1.23515i | −0.786513 | − | 0.617574i | \(-0.788116\pi\) | ||
0.786513 | − | 0.617574i | \(-0.211884\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 16.2846 | 0.567646 | 0.283823 | − | 0.958877i | \(-0.408397\pi\) | ||||
0.283823 | + | 0.958877i | \(0.408397\pi\) | |||||||
\(824\) | 3.80304 | − | 30.1589i | 0.132485 | − | 1.05064i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 8.95766 | + | 0.374762i | 0.311677 | + | 0.0130396i | ||||
\(827\) | 32.1362i | 1.11748i | 0.829341 | + | 0.558742i | \(0.188716\pi\) | ||||
−0.829341 | + | 0.558742i | \(0.811284\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − | 22.4682i | − | 0.780355i | −0.920740 | − | 0.390177i | \(-0.872414\pi\) | ||
0.920740 | − | 0.390177i | \(-0.127586\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.05513 | + | 15.8233i | −0.140586 | + | 0.548576i | ||||
\(833\) | 18.8573 | 0.653367 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −31.4492 | − | 2.63610i | −1.08769 | − | 0.0911715i | ||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 17.8627 | + | 0.747325i | 0.617058 | + | 0.0258159i | ||||
\(839\) | 16.1358 | 0.557070 | 0.278535 | − | 0.960426i | \(-0.410151\pi\) | ||||
0.278535 | + | 0.960426i | \(0.410151\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.28695 | 0.0443777 | ||||||||
\(842\) | −23.7930 | − | 0.995427i | −0.819959 | − | 0.0343047i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.10464 | − | 13.1786i | 0.0380233 | − | 0.453626i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 3.11085 | 0.106890 | ||||||||
\(848\) | −4.07735 | + | 24.1509i | −0.140017 | + | 0.829347i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 56.3611i | − | 1.93203i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 44.6262i | − | 1.52797i | −0.645233 | − | 0.763986i | \(-0.723240\pi\) | ||
0.645233 | − | 0.763986i | \(-0.276760\pi\) | |||||||
\(854\) | 16.0509 | + | 0.671523i | 0.549251 | + | 0.0229790i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13.6527 | + | 1.72161i | 0.466639 | + | 0.0588433i | ||||
\(857\) | −4.52553 | −0.154589 | −0.0772945 | − | 0.997008i | \(-0.524628\pi\) | ||||
−0.0772945 | + | 0.997008i | \(0.524628\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 42.7783i | − | 1.45958i | −0.683673 | − | 0.729788i | \(-0.739619\pi\) | ||
0.683673 | − | 0.729788i | \(-0.260381\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0.354006 | − | 8.46155i | 0.0120575 | − | 0.288202i | ||||
\(863\) | −23.7734 | −0.809257 | −0.404629 | − | 0.914481i | \(-0.632599\pi\) | ||||
−0.404629 | + | 0.914481i | \(0.632599\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0.131520 | − | 3.14362i | 0.00446922 | − | 0.106824i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 5.53407 | + | 0.463870i | 0.187839 | + | 0.0157448i | ||||
\(869\) | − | 30.7519i | − | 1.04319i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 21.8397 | 0.740009 | ||||||||
\(872\) | −43.3763 | − | 5.46976i | −1.46891 | − | 0.185229i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 65.0986 | + | 2.72353i | 2.20199 | + | 0.0921249i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 13.1470i | − | 0.443944i | −0.975053 | − | 0.221972i | \(-0.928751\pi\) | ||
0.975053 | − | 0.221972i | \(-0.0712494\pi\) | |||||||
\(878\) | 0.136236 | − | 3.25635i | 0.00459774 | − | 0.109896i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −38.9132 | −1.31102 | −0.655510 | − | 0.755187i | \(-0.727546\pi\) | ||||
−0.655510 | + | 0.755187i | \(0.727546\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 44.5843i | 1.50038i | 0.661223 | + | 0.750190i | \(0.270038\pi\) | ||||
−0.661223 | + | 0.750190i | \(0.729962\pi\) | |||||||
\(884\) | 1.23220 | − | 14.7003i | 0.0414432 | − | 0.494426i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −31.2759 | − | 1.30849i | −1.05073 | − | 0.0439596i | ||||
\(887\) | 32.3240 | 1.08533 | 0.542667 | − | 0.839948i | \(-0.317415\pi\) | ||||
0.542667 | + | 0.839948i | \(0.317415\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −11.6760 | −0.391601 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.66065 | − | 0.139197i | −0.0556027 | − | 0.00466066i | ||||
\(893\) | − | 53.4465i | − | 1.78852i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 4.35497 | − | 14.4518i | 0.145489 | − | 0.482802i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.27606 | − | 30.5007i | 0.0425826 | − | 1.01782i | ||||
\(899\) | 10.9568i | 0.365431i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 22.1194i | − | 0.736904i | ||||||
\(902\) | −29.2364 | − | 1.22316i | −0.973464 | − | 0.0407269i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.49912 | − | 27.7488i | 0.116379 | − | 0.922911i | ||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 14.8309i | − | 0.492452i | −0.969212 | − | 0.246226i | \(-0.920809\pi\) | ||
0.969212 | − | 0.246226i | \(-0.0791905\pi\) | |||||||
\(908\) | 1.83760 | − | 21.9229i | 0.0609828 | − | 0.727538i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −11.6108 | −0.384681 | −0.192341 | − | 0.981328i | \(-0.561608\pi\) | ||||
−0.192341 | + | 0.981328i | \(0.561608\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −4.49601 | −0.148796 | ||||||||
\(914\) | 0.147839 | − | 3.53368i | 0.00489007 | − | 0.116884i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.54026 | + | 30.3059i | −0.0839327 | + | 1.00133i | ||||
\(917\) | 0.628722i | 0.0207622i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −58.2518 | −1.92155 | −0.960775 | − | 0.277330i | \(-0.910550\pi\) | ||||
−0.960775 | + | 0.277330i | \(0.910550\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 3.66822 | + | 0.153468i | 0.120807 | + | 0.00505419i | ||||
\(923\) | − | 5.35789i | − | 0.176357i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1.64696 | − | 39.3661i | 0.0541226 | − | 1.29365i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 29.1311 | + | 6.18055i | 0.956274 | + | 0.202886i | ||||
\(929\) | −18.4433 | −0.605105 | −0.302553 | − | 0.953133i | \(-0.597839\pi\) | ||||
−0.302553 | + | 0.953133i | \(0.597839\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | − | 27.9781i | − | 0.916944i | ||||||
\(932\) | 4.93457 | + | 0.413620i | 0.161637 | + | 0.0135486i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −8.12744 | − | 0.340028i | −0.265938 | − | 0.0111261i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −16.1005 | −0.525982 | −0.262991 | − | 0.964798i | \(-0.584709\pi\) | ||||
−0.262991 | + | 0.964798i | \(0.584709\pi\) | |||||||
\(938\) | −20.1629 | − | 0.843555i | −0.658341 | − | 0.0275430i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 32.0974i | 1.04635i | 0.852226 | + | 0.523173i | \(0.175252\pi\) | ||||
−0.852226 | + | 0.523173i | \(0.824748\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 60.4121 | 1.96729 | ||||||||
\(944\) | 3.16423 | − | 18.7424i | 0.102987 | − | 0.610012i | ||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 1.47952 | − | 35.3638i | 0.0481033 | − | 1.14978i | ||||
\(947\) | − | 4.10998i | − | 0.133556i | −0.997768 | − | 0.0667782i | \(-0.978728\pi\) | ||
0.997768 | − | 0.0667782i | \(-0.0212720\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 31.4188i | 1.01990i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −1.70539 | + | 13.5241i | −0.0552720 | + | 0.438318i | ||||
\(953\) | 31.7208 | 1.02754 | 0.513769 | − | 0.857928i | \(-0.328249\pi\) | ||||
0.513769 | + | 0.857928i | \(0.328249\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −42.0001 | − | 3.52048i | −1.35838 | − | 0.113861i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −0.741729 | + | 17.7290i | −0.0239642 | + | 0.572798i | ||||
\(959\) | −1.73944 | −0.0561695 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −26.6680 | −0.860259 | ||||||||
\(962\) | −0.791399 | + | 18.9162i | −0.0255157 | + | 0.609884i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 12.1743 | + | 1.02046i | 0.392109 | + | 0.0328669i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 26.9936 | 0.868055 | 0.434027 | − | 0.900900i | \(-0.357092\pi\) | ||||
0.434027 | + | 0.900900i | \(0.357092\pi\) | |||||||
\(968\) | 0.825129 | − | 6.54344i | 0.0265206 | − | 0.210314i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 14.0559i | − | 0.451076i | −0.974234 | − | 0.225538i | \(-0.927586\pi\) | ||
0.974234 | − | 0.225538i | \(-0.0724139\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 11.6698i | 0.374116i | ||||||||
\(974\) | 0.508701 | − | 12.1591i | 0.0162998 | − | 0.389603i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.66988 | − | 33.5838i | 0.181488 | − | 1.07499i | ||||
\(977\) | 1.14251 | 0.0365520 | 0.0182760 | − | 0.999833i | \(-0.494182\pi\) | ||||
0.0182760 | + | 0.999833i | \(0.494182\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 37.4479i | − | 1.19684i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 52.1200 | + | 2.18055i | 1.66321 | + | 0.0695840i | ||||
\(983\) | 6.41720 | 0.204677 | 0.102338 | − | 0.994750i | \(-0.467368\pi\) | ||||
0.102338 | + | 0.994750i | \(0.467368\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −26.8704 | − | 1.12418i | −0.855728 | − | 0.0358011i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −21.8105 | − | 1.82818i | −0.693885 | − | 0.0581620i | ||||
\(989\) | 73.0735i | 2.32360i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −7.39470 | −0.234900 | −0.117450 | − | 0.993079i | \(-0.537472\pi\) | ||||
−0.117450 | + | 0.993079i | \(0.537472\pi\) | |||||||
\(992\) | 2.44359 | − | 11.5175i | 0.0775839 | − | 0.365680i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −0.206948 | + | 4.94652i | −0.00656399 | + | 0.156894i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − | 31.6649i | − | 1.00284i | −0.865205 | − | 0.501419i | \(-0.832812\pi\) | ||
0.865205 | − | 0.501419i | \(-0.167188\pi\) | |||||||
\(998\) | −51.2198 | − | 2.14289i | −1.62133 | − | 0.0678319i | ||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))