Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,4,Mod(136,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.136");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.e (of order \(3\), 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: | \(23.8957735523\) |
Analytic rank: | \(0\) |
Dimension: | \(12\) |
Relative dimension: | \(6\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{12} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{12} - 2 x^{11} + 2 x^{10} + 32 x^{9} + 583 x^{8} - 624 x^{7} + 594 x^{6} + 9450 x^{5} + 90513 x^{4} - 20304 x^{3} + 10368 x^{2} + 124416 x + 746496 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{9} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 271.3 | ||
Root | \(-2.82176 + 2.82176i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 405.271 |
Dual form | 405.4.e.w.136.3 |
$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.03663 | − | 1.79550i | −0.366504 | − | 0.634804i | 0.622512 | − | 0.782610i | \(-0.286112\pi\) |
−0.989016 | + | 0.147806i | \(0.952779\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.85079 | − | 3.20567i | 0.231349 | − | 0.400709i | ||||
\(5\) | −2.50000 | + | 4.33013i | −0.223607 | + | 0.387298i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.33056 | + | 4.03665i | 0.125838 | + | 0.217959i | 0.922060 | − | 0.387046i | \(-0.126505\pi\) |
−0.796222 | + | 0.605005i | \(0.793171\pi\) | |||||||
\(8\) | −24.2604 | −1.07217 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 10.3663 | 0.327811 | ||||||||
\(11\) | −4.44705 | − | 7.70252i | −0.121894 | − | 0.211127i | 0.798620 | − | 0.601835i | \(-0.205564\pi\) |
−0.920515 | + | 0.390708i | \(0.872230\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −17.3086 | + | 29.9793i | −0.369272 | + | 0.639598i | −0.989452 | − | 0.144862i | \(-0.953726\pi\) |
0.620180 | + | 0.784460i | \(0.287060\pi\) | |||||||
\(14\) | 4.83186 | − | 8.36903i | 0.0922407 | − | 0.159766i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 10.3428 | + | 17.9142i | 0.161606 | + | 0.279910i | ||||
\(17\) | 2.66659 | 0.0380437 | 0.0190218 | − | 0.999819i | \(-0.493945\pi\) | ||||
0.0190218 | + | 0.999819i | \(0.493945\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 125.599 | 1.51655 | 0.758273 | − | 0.651937i | \(-0.226043\pi\) | ||||
0.758273 | + | 0.651937i | \(0.226043\pi\) | |||||||
\(20\) | 9.25397 | + | 16.0283i | 0.103463 | + | 0.179202i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −9.21990 | + | 15.9693i | −0.0893495 | + | 0.154758i | ||||
\(23\) | −65.9874 | + | 114.294i | −0.598231 | + | 1.03617i | 0.394851 | + | 0.918745i | \(0.370796\pi\) |
−0.993082 | + | 0.117422i | \(0.962537\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −12.5000 | − | 21.6506i | −0.100000 | − | 0.173205i | ||||
\(26\) | 71.7704 | 0.541359 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 17.2535 | 0.116451 | ||||||||
\(29\) | 35.6053 | + | 61.6702i | 0.227991 | + | 0.394892i | 0.957213 | − | 0.289386i | \(-0.0934510\pi\) |
−0.729222 | + | 0.684278i | \(0.760118\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.71252 | + | 11.6264i | −0.0388905 | + | 0.0673603i | −0.884815 | − | 0.465942i | \(-0.845716\pi\) |
0.845925 | + | 0.533302i | \(0.179049\pi\) | |||||||
\(32\) | −75.5985 | + | 130.940i | −0.417627 | + | 0.723351i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −2.76427 | − | 4.78785i | −0.0139432 | − | 0.0241503i | ||||
\(35\) | −23.3056 | −0.112553 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 283.849 | 1.26120 | 0.630600 | − | 0.776108i | \(-0.282809\pi\) | ||||
0.630600 | + | 0.776108i | \(0.282809\pi\) | |||||||
\(38\) | −130.200 | − | 225.513i | −0.555821 | − | 0.962710i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 60.6511 | − | 105.051i | 0.239745 | − | 0.415250i | ||||
\(41\) | −191.726 | + | 332.079i | −0.730307 | + | 1.26493i | 0.226445 | + | 0.974024i | \(0.427289\pi\) |
−0.956752 | + | 0.290904i | \(0.906044\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 169.588 | + | 293.734i | 0.601438 | + | 1.04172i | 0.992604 | + | 0.121401i | \(0.0387388\pi\) |
−0.391165 | + | 0.920321i | \(0.627928\pi\) | |||||||
\(44\) | −32.9223 | −0.112801 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 273.618 | 0.877018 | ||||||||
\(47\) | −39.1434 | − | 67.7983i | −0.121482 | − | 0.210413i | 0.798870 | − | 0.601503i | \(-0.205431\pi\) |
−0.920352 | + | 0.391090i | \(0.872098\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 160.637 | − | 278.231i | 0.468329 | − | 0.811170i | ||||
\(50\) | −25.9158 | + | 44.8874i | −0.0733009 | + | 0.126961i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 64.0692 | + | 110.971i | 0.170862 | + | 0.295941i | ||||
\(53\) | 254.626 | 0.659915 | 0.329958 | − | 0.943996i | \(-0.392966\pi\) | ||||
0.329958 | + | 0.943996i | \(0.392966\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 44.4705 | 0.109026 | ||||||||
\(56\) | −56.5404 | − | 97.9309i | −0.134920 | − | 0.233689i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 73.8191 | − | 127.858i | 0.167119 | − | 0.289459i | ||||
\(59\) | 16.4098 | − | 28.4226i | 0.0362097 | − | 0.0627171i | −0.847353 | − | 0.531031i | \(-0.821805\pi\) |
0.883562 | + | 0.468314i | \(0.155138\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −93.4914 | − | 161.932i | −0.196235 | − | 0.339889i | 0.751070 | − | 0.660223i | \(-0.229538\pi\) |
−0.947305 | + | 0.320334i | \(0.896205\pi\) | |||||||
\(62\) | 27.8336 | 0.0570141 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 478.955 | 0.935460 | ||||||||
\(65\) | −86.5429 | − | 149.897i | −0.165143 | − | 0.286037i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −203.307 | + | 352.138i | −0.370715 | + | 0.642097i | −0.989676 | − | 0.143325i | \(-0.954221\pi\) |
0.618961 | + | 0.785422i | \(0.287554\pi\) | |||||||
\(68\) | 4.93530 | − | 8.54819i | 0.00880137 | − | 0.0152444i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 24.1593 | + | 41.8451i | 0.0412513 | + | 0.0714493i | ||||
\(71\) | 966.124 | 1.61490 | 0.807450 | − | 0.589936i | \(-0.200847\pi\) | ||||
0.807450 | + | 0.589936i | \(0.200847\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 276.177 | 0.442796 | 0.221398 | − | 0.975184i | \(-0.428938\pi\) | ||||
0.221398 | + | 0.975184i | \(0.428938\pi\) | |||||||
\(74\) | −294.246 | − | 509.649i | −0.462235 | − | 0.800615i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 232.458 | − | 402.629i | 0.350852 | − | 0.607693i | ||||
\(77\) | 20.7282 | − | 35.9024i | 0.0306780 | − | 0.0531358i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 573.426 | + | 993.204i | 0.816652 | + | 1.41448i | 0.908136 | + | 0.418676i | \(0.137506\pi\) |
−0.0914836 | + | 0.995807i | \(0.529161\pi\) | |||||||
\(80\) | −103.428 | −0.144545 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 794.996 | 1.07064 | ||||||||
\(83\) | −89.0225 | − | 154.191i | −0.117729 | − | 0.203912i | 0.801139 | − | 0.598479i | \(-0.204228\pi\) |
−0.918867 | + | 0.394567i | \(0.870895\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6.66647 | + | 11.5467i | −0.00850682 | + | 0.0147342i | ||||
\(86\) | 351.599 | − | 608.988i | 0.440860 | − | 0.763591i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 107.887 | + | 186.867i | 0.130691 | + | 0.226364i | ||||
\(89\) | 806.486 | 0.960532 | 0.480266 | − | 0.877123i | \(-0.340540\pi\) | ||||
0.480266 | + | 0.877123i | \(0.340540\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −161.355 | −0.185874 | ||||||||
\(92\) | 244.258 | + | 423.068i | 0.276801 | + | 0.479433i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −81.1544 | + | 140.564i | −0.0890472 | + | 0.154234i | ||||
\(95\) | −313.998 | + | 543.860i | −0.339110 | + | 0.587356i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 619.023 | + | 1072.18i | 0.647961 | + | 1.12230i | 0.983609 | + | 0.180314i | \(0.0577115\pi\) |
−0.335648 | + | 0.941988i | \(0.608955\pi\) | |||||||
\(98\) | −666.085 | −0.686579 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −92.5397 | −0.0925397 | ||||||||
\(101\) | −283.428 | − | 490.912i | −0.279229 | − | 0.483639i | 0.691964 | − | 0.721932i | \(-0.256746\pi\) |
−0.971193 | + | 0.238293i | \(0.923412\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 409.509 | − | 709.290i | 0.391748 | − | 0.678528i | −0.600932 | − | 0.799300i | \(-0.705204\pi\) |
0.992680 | + | 0.120772i | \(0.0385371\pi\) | |||||||
\(104\) | 419.914 | − | 727.312i | 0.395923 | − | 0.685758i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −263.953 | − | 457.179i | −0.241862 | − | 0.418917i | ||||
\(107\) | −543.772 | −0.491293 | −0.245647 | − | 0.969359i | \(-0.579000\pi\) | ||||
−0.245647 | + | 0.969359i | \(0.579000\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1636.54 | −1.43809 | −0.719046 | − | 0.694963i | \(-0.755421\pi\) | ||||
−0.719046 | + | 0.694963i | \(0.755421\pi\) | |||||||
\(110\) | −46.0995 | − | 79.8467i | −0.0399583 | − | 0.0692098i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −48.2089 | + | 83.5003i | −0.0406725 | + | 0.0704468i | ||||
\(113\) | 272.899 | − | 472.675i | 0.227188 | − | 0.393500i | −0.729786 | − | 0.683676i | \(-0.760380\pi\) |
0.956974 | + | 0.290175i | \(0.0937136\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −329.937 | − | 571.468i | −0.267537 | − | 0.463388i | ||||
\(116\) | 263.592 | 0.210982 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −68.0436 | −0.0530841 | ||||||||
\(119\) | 6.21464 | + | 10.7641i | 0.00478736 | + | 0.00829194i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 625.947 | − | 1084.17i | 0.470284 | − | 0.814555i | ||||
\(122\) | −193.832 | + | 335.727i | −0.143842 | + | 0.249142i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 24.8470 | + | 43.0363i | 0.0179946 | + | 0.0311675i | ||||
\(125\) | 125.000 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 36.0480 | 0.0251869 | 0.0125935 | − | 0.999921i | \(-0.495991\pi\) | ||||
0.0125935 | + | 0.999921i | \(0.495991\pi\) | |||||||
\(128\) | 108.288 | + | 187.561i | 0.0747768 | + | 0.129517i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −179.426 | + | 310.775i | −0.121052 | + | 0.209667i | ||||
\(131\) | −655.075 | + | 1134.62i | −0.436902 | + | 0.756737i | −0.997449 | − | 0.0713860i | \(-0.977258\pi\) |
0.560547 | + | 0.828123i | \(0.310591\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 292.716 | + | 506.999i | 0.190840 | + | 0.330544i | ||||
\(134\) | 843.016 | 0.543474 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −64.6926 | −0.0407893 | ||||||||
\(137\) | 1098.60 | + | 1902.83i | 0.685109 | + | 1.18664i | 0.973403 | + | 0.229101i | \(0.0735786\pi\) |
−0.288294 | + | 0.957542i | \(0.593088\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −863.005 | + | 1494.77i | −0.526612 | + | 0.912119i | 0.472907 | + | 0.881112i | \(0.343205\pi\) |
−0.999519 | + | 0.0310067i | \(0.990129\pi\) | |||||||
\(140\) | −43.1339 | + | 74.7101i | −0.0260391 | + | 0.0451011i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1001.51 | − | 1734.67i | −0.591868 | − | 1.02514i | ||||
\(143\) | 307.889 | 0.180049 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −356.053 | −0.203921 | ||||||||
\(146\) | −286.294 | − | 495.875i | −0.162286 | − | 0.281088i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 525.345 | − | 909.925i | 0.291778 | − | 0.505374i | ||||
\(149\) | 900.699 | − | 1560.06i | 0.495222 | − | 0.857750i | −0.504763 | − | 0.863258i | \(-0.668420\pi\) |
0.999985 | + | 0.00550809i | \(0.00175329\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −1664.09 | − | 2882.30i | −0.896835 | − | 1.55336i | −0.831517 | − | 0.555500i | \(-0.812527\pi\) |
−0.0653185 | − | 0.997864i | \(-0.520806\pi\) | |||||||
\(152\) | −3047.09 | −1.62600 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −85.9501 | −0.0449744 | ||||||||
\(155\) | −33.5626 | − | 58.1322i | −0.0173924 | − | 0.0301244i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1915.09 | + | 3317.04i | −0.973510 | + | 1.68617i | −0.288745 | + | 0.957406i | \(0.593238\pi\) |
−0.684766 | + | 0.728763i | \(0.740096\pi\) | |||||||
\(158\) | 1188.86 | − | 2059.17i | 0.598613 | − | 1.03683i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −377.993 | − | 654.702i | −0.186768 | − | 0.323492i | ||||
\(161\) | −615.151 | −0.301122 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2404.51 | −1.15543 | −0.577717 | − | 0.816237i | \(-0.696056\pi\) | ||||
−0.577717 | + | 0.816237i | \(0.696056\pi\) | |||||||
\(164\) | 709.691 | + | 1229.22i | 0.337912 | + | 0.585280i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −184.567 | + | 319.679i | −0.0862962 | + | 0.149469i | ||||
\(167\) | −1785.48 | + | 3092.53i | −0.827331 | + | 1.43298i | 0.0727941 | + | 0.997347i | \(0.476808\pi\) |
−0.900125 | + | 0.435632i | \(0.856525\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 499.326 | + | 864.859i | 0.227276 | + | 0.393654i | ||||
\(170\) | 27.6427 | 0.0124711 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1255.49 | 0.556569 | ||||||||
\(173\) | 79.9681 | + | 138.509i | 0.0351437 | + | 0.0608707i | 0.883062 | − | 0.469256i | \(-0.155478\pi\) |
−0.847919 | + | 0.530126i | \(0.822144\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 58.2640 | − | 100.916i | 0.0251677 | − | 0.0435917i | ||||
\(176\) | 91.9897 | − | 159.331i | 0.0393976 | − | 0.0682387i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −836.028 | − | 1448.04i | −0.352039 | − | 0.609750i | ||||
\(179\) | −1120.87 | −0.468030 | −0.234015 | − | 0.972233i | \(-0.575187\pi\) | ||||
−0.234015 | + | 0.972233i | \(0.575187\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3856.65 | −1.58377 | −0.791886 | − | 0.610669i | \(-0.790901\pi\) | ||||
−0.791886 | + | 0.610669i | \(0.790901\pi\) | |||||||
\(182\) | 167.265 | + | 289.712i | 0.0681238 | + | 0.117994i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1600.88 | − | 2772.81i | 0.641406 | − | 1.11095i | ||||
\(185\) | −709.621 | + | 1229.10i | −0.282013 | + | 0.488461i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −11.8584 | − | 20.5394i | −0.00463730 | − | 0.00803204i | ||||
\(188\) | −289.785 | −0.112419 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1302.00 | 0.497141 | ||||||||
\(191\) | 39.5050 | + | 68.4246i | 0.0149659 | + | 0.0259216i | 0.873411 | − | 0.486983i | \(-0.161903\pi\) |
−0.858445 | + | 0.512905i | \(0.828569\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −2285.75 | + | 3959.03i | −0.852496 | + | 1.47657i | 0.0264535 | + | 0.999650i | \(0.491579\pi\) |
−0.878949 | + | 0.476916i | \(0.841755\pi\) | |||||||
\(194\) | 1283.40 | − | 2222.91i | 0.474961 | − | 0.822657i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −594.612 | − | 1029.90i | −0.216695 | − | 0.375327i | ||||
\(197\) | −4081.61 | −1.47615 | −0.738077 | − | 0.674717i | \(-0.764266\pi\) | ||||
−0.738077 | + | 0.674717i | \(0.764266\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −2518.98 | −0.897316 | −0.448658 | − | 0.893703i | \(-0.648098\pi\) | ||||
−0.448658 | + | 0.893703i | \(0.648098\pi\) | |||||||
\(200\) | 303.256 | + | 525.254i | 0.107217 | + | 0.185705i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −587.620 | + | 1017.79i | −0.204677 | + | 0.354512i | ||||
\(203\) | −165.961 | + | 287.452i | −0.0573801 | + | 0.0993852i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −958.630 | − | 1660.40i | −0.326603 | − | 0.565693i | ||||
\(206\) | −1698.04 | −0.574310 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −716.075 | −0.238706 | ||||||||
\(209\) | −558.545 | − | 967.429i | −0.184858 | − | 0.320184i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −113.622 | + | 196.799i | −0.0370714 | + | 0.0642095i | −0.883966 | − | 0.467552i | \(-0.845136\pi\) |
0.846894 | + | 0.531761i | \(0.178470\pi\) | |||||||
\(212\) | 471.259 | − | 816.245i | 0.152671 | − | 0.264434i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 563.690 | + | 976.340i | 0.180061 | + | 0.311875i | ||||
\(215\) | −1695.88 | −0.537943 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −62.5758 | −0.0195757 | ||||||||
\(218\) | 1696.49 | + | 2938.40i | 0.527067 | + | 0.912906i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 82.3058 | − | 142.558i | 0.0252230 | − | 0.0436875i | ||||
\(221\) | −46.1548 | + | 79.9425i | −0.0140485 | + | 0.0243326i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 257.612 | + | 446.196i | 0.0773585 | + | 0.133989i | 0.902109 | − | 0.431507i | \(-0.142018\pi\) |
−0.824751 | + | 0.565496i | \(0.808685\pi\) | |||||||
\(224\) | −704.748 | −0.210214 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1131.58 | −0.333061 | ||||||||
\(227\) | 1978.02 | + | 3426.03i | 0.578352 | + | 1.00173i | 0.995669 | + | 0.0929736i | \(0.0296372\pi\) |
−0.417317 | + | 0.908761i | \(0.637029\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 838.285 | − | 1451.95i | 0.241901 | − | 0.418985i | −0.719355 | − | 0.694643i | \(-0.755562\pi\) |
0.961256 | + | 0.275658i | \(0.0888956\pi\) | |||||||
\(230\) | −684.046 | + | 1184.80i | −0.196107 | + | 0.339667i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −863.801 | − | 1496.15i | −0.244445 | − | 0.423392i | ||||
\(233\) | 4610.01 | 1.29619 | 0.648095 | − | 0.761560i | \(-0.275566\pi\) | ||||
0.648095 | + | 0.761560i | \(0.275566\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 391.434 | 0.108657 | ||||||||
\(236\) | −60.7423 | − | 105.209i | −0.0167542 | − | 0.0290191i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 12.8846 | − | 22.3167i | 0.00350917 | − | 0.00607806i | ||||
\(239\) | 3454.12 | − | 5982.71i | 0.934846 | − | 1.61920i | 0.159939 | − | 0.987127i | \(-0.448870\pi\) |
0.774907 | − | 0.632075i | \(-0.217796\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1490.48 | + | 2581.59i | 0.398383 | + | 0.690019i | 0.993527 | − | 0.113600i | \(-0.0362383\pi\) |
−0.595144 | + | 0.803619i | \(0.702905\pi\) | |||||||
\(242\) | −2595.51 | −0.689444 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −692.133 | −0.181595 | ||||||||
\(245\) | 803.185 | + | 1391.16i | 0.209443 | + | 0.362766i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −2173.94 | + | 3765.37i | −0.560018 | + | 0.969980i | ||||
\(248\) | 162.849 | − | 282.062i | 0.0416972 | − | 0.0722217i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −129.579 | − | 224.437i | −0.0327811 | − | 0.0567786i | ||||
\(251\) | 7132.90 | 1.79372 | 0.896862 | − | 0.442310i | \(-0.145841\pi\) | ||||
0.896862 | + | 0.442310i | \(0.145841\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1173.80 | 0.291684 | ||||||||
\(254\) | −37.3684 | − | 64.7240i | −0.00923112 | − | 0.0159888i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2140.33 | − | 3707.16i | 0.522542 | − | 0.905069i | ||||
\(257\) | −3281.28 | + | 5683.35i | −0.796423 | + | 1.37945i | 0.125509 | + | 0.992093i | \(0.459944\pi\) |
−0.921932 | + | 0.387353i | \(0.873390\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 661.526 | + | 1145.80i | 0.158708 | + | 0.274889i | ||||
\(260\) | −640.692 | −0.152823 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2716.28 | 0.640506 | ||||||||
\(263\) | −2831.75 | − | 4904.73i | −0.663928 | − | 1.14996i | −0.979575 | − | 0.201080i | \(-0.935555\pi\) |
0.315647 | − | 0.948877i | \(-0.397779\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −636.564 | + | 1102.56i | −0.147562 | + | 0.255584i | ||||
\(266\) | 606.877 | − | 1051.14i | 0.139887 | − | 0.242292i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 752.558 | + | 1303.47i | 0.171529 | + | 0.297097i | ||||
\(269\) | 4018.43 | 0.910811 | 0.455406 | − | 0.890284i | \(-0.349494\pi\) | ||||
0.455406 | + | 0.890284i | \(0.349494\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1518.33 | −0.340340 | −0.170170 | − | 0.985415i | \(-0.554432\pi\) | ||||
−0.170170 | + | 0.985415i | \(0.554432\pi\) | |||||||
\(272\) | 27.5799 | + | 47.7698i | 0.00614808 | + | 0.0106488i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 2277.69 | − | 3945.07i | 0.502190 | − | 0.869819i | ||||
\(275\) | −111.176 | + | 192.563i | −0.0243788 | + | 0.0422254i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1091.22 | − | 1890.05i | −0.236697 | − | 0.409971i | 0.723068 | − | 0.690777i | \(-0.242731\pi\) |
−0.959764 | + | 0.280806i | \(0.909398\pi\) | |||||||
\(278\) | 3578.47 | 0.772022 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 565.404 | 0.120676 | ||||||||
\(281\) | −2551.28 | − | 4418.95i | −0.541626 | − | 0.938123i | −0.998811 | − | 0.0487518i | \(-0.984476\pi\) |
0.457185 | − | 0.889372i | \(-0.348858\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1288.97 | − | 2232.56i | 0.270747 | − | 0.468947i | −0.698307 | − | 0.715799i | \(-0.746063\pi\) |
0.969053 | + | 0.246852i | \(0.0793961\pi\) | |||||||
\(284\) | 1788.10 | − | 3097.08i | 0.373606 | − | 0.647104i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −319.167 | − | 552.813i | −0.0659885 | − | 0.114296i | ||||
\(287\) | −1787.32 | −0.367603 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4905.89 | −0.998553 | ||||||||
\(290\) | 369.095 | + | 639.292i | 0.0747380 | + | 0.129450i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 511.147 | − | 885.332i | 0.102440 | − | 0.177432i | ||||
\(293\) | 4169.93 | − | 7222.52i | 0.831432 | − | 1.44008i | −0.0654699 | − | 0.997855i | \(-0.520855\pi\) |
0.896902 | − | 0.442229i | \(-0.145812\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 82.0490 | + | 142.113i | 0.0161935 | + | 0.0280479i | ||||
\(296\) | −6886.29 | −1.35222 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −3734.77 | −0.726004 | ||||||||
\(299\) | −2284.30 | − | 3956.52i | −0.441820 | − | 0.765255i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −790.468 | + | 1369.13i | −0.151368 | + | 0.262177i | ||||
\(302\) | −3450.10 | + | 5975.75i | −0.657388 | + | 1.13863i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1299.04 | + | 2250.01i | 0.245083 | + | 0.424496i | ||||
\(305\) | 934.914 | 0.175518 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7042.31 | 1.30921 | 0.654603 | − | 0.755973i | \(-0.272836\pi\) | ||||
0.654603 | + | 0.755973i | \(0.272836\pi\) | |||||||
\(308\) | −76.7274 | − | 132.896i | −0.0141946 | − | 0.0245858i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −69.5841 | + | 120.523i | −0.0127487 | + | 0.0220815i | ||||
\(311\) | −1171.46 | + | 2029.03i | −0.213593 | + | 0.369954i | −0.952836 | − | 0.303485i | \(-0.901850\pi\) |
0.739243 | + | 0.673438i | \(0.235183\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1916.73 | + | 3319.88i | 0.346135 | + | 0.599523i | 0.985559 | − | 0.169331i | \(-0.0541607\pi\) |
−0.639425 | + | 0.768854i | \(0.720827\pi\) | |||||||
\(314\) | 7940.98 | 1.42718 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 4245.18 | 0.755727 | ||||||||
\(317\) | −2944.99 | − | 5100.87i | −0.521789 | − | 0.903765i | −0.999679 | − | 0.0253451i | \(-0.991932\pi\) |
0.477890 | − | 0.878420i | \(-0.341402\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 316.677 | − | 548.501i | 0.0555816 | − | 0.0962701i | ||||
\(320\) | −1197.39 | + | 2073.94i | −0.209175 | + | 0.362302i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 637.684 | + | 1104.50i | 0.110363 | + | 0.191154i | ||||
\(323\) | 334.921 | 0.0576950 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 865.429 | 0.147709 | ||||||||
\(326\) | 2492.59 | + | 4317.29i | 0.423472 | + | 0.733474i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 4651.36 | − | 8056.39i | 0.783013 | − | 1.35622i | ||||
\(329\) | 182.452 | − | 316.016i | 0.0305742 | − | 0.0529560i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3169.48 | + | 5489.69i | 0.526315 | + | 0.911604i | 0.999530 | + | 0.0306570i | \(0.00975997\pi\) |
−0.473215 | + | 0.880947i | \(0.656907\pi\) | |||||||
\(332\) | −659.049 | −0.108946 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 7403.51 | 1.21288 | ||||||||
\(335\) | −1016.53 | − | 1760.69i | −0.165789 | − | 0.287154i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −484.171 | + | 838.609i | −0.0782625 | + | 0.135555i | −0.902500 | − | 0.430689i | \(-0.858271\pi\) |
0.824238 | + | 0.566244i | \(0.191604\pi\) | |||||||
\(338\) | 1035.23 | − | 1793.08i | 0.166596 | − | 0.288552i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 24.6765 | + | 42.7410i | 0.00393609 | + | 0.00681751i | ||||
\(341\) | 119.404 | 0.0189621 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3096.26 | 0.487412 | ||||||||
\(344\) | −4114.27 | − | 7126.12i | −0.644845 | − | 1.11690i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 165.795 | − | 287.165i | 0.0257606 | − | 0.0446188i | ||||
\(347\) | −3228.85 | + | 5592.54i | −0.499521 | + | 0.865196i | −1.00000 | 0.000552683i | \(-0.999824\pi\) | |
0.500479 | + | 0.865749i | \(0.333157\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 3077.59 | + | 5330.54i | 0.472033 | + | 0.817586i | 0.999488 | − | 0.0319976i | \(-0.0101869\pi\) |
−0.527455 | + | 0.849583i | \(0.676854\pi\) | |||||||
\(350\) | −241.593 | −0.0368963 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1344.76 | 0.203625 | ||||||||
\(353\) | −1831.77 | − | 3172.71i | −0.276190 | − | 0.478375i | 0.694245 | − | 0.719739i | \(-0.255739\pi\) |
−0.970435 | + | 0.241364i | \(0.922405\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −2415.31 | + | 4183.44i | −0.361103 | + | 0.625448i | ||||
\(356\) | 1492.64 | − | 2585.33i | 0.222218 | − | 0.384894i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1161.92 | + | 2012.51i | 0.171535 | + | 0.297107i | ||||
\(359\) | 12112.6 | 1.78073 | 0.890364 | − | 0.455250i | \(-0.150450\pi\) | ||||
0.890364 | + | 0.455250i | \(0.150450\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8916.11 | 1.29991 | ||||||||
\(362\) | 3997.92 | + | 6924.61i | 0.580459 | + | 1.00538i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −298.634 | + | 517.250i | −0.0430019 | + | 0.0744815i | ||||
\(365\) | −690.443 | + | 1195.88i | −0.0990121 | + | 0.171494i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −5808.08 | − | 10059.9i | −0.826101 | − | 1.43085i | −0.901075 | − | 0.433664i | \(-0.857221\pi\) |
0.0749736 | − | 0.997186i | \(-0.476113\pi\) | |||||||
\(368\) | −2729.97 | −0.386711 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2942.46 | 0.413436 | ||||||||
\(371\) | 593.420 | + | 1027.83i | 0.0830427 | + | 0.143834i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1107.86 | − | 1918.87i | 0.153788 | − | 0.266369i | −0.778829 | − | 0.627236i | \(-0.784186\pi\) |
0.932617 | + | 0.360868i | \(0.117519\pi\) | |||||||
\(374\) | −24.5857 | + | 42.5836i | −0.00339918 | + | 0.00588756i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 949.636 | + | 1644.82i | 0.130249 | + | 0.225598i | ||||
\(377\) | −2465.11 | −0.336763 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −6539.83 | −0.886354 | −0.443177 | − | 0.896434i | \(-0.646149\pi\) | ||||
−0.443177 | + | 0.896434i | \(0.646149\pi\) | |||||||
\(380\) | 1162.29 | + | 2013.14i | 0.156906 | + | 0.271769i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 81.9041 | − | 141.862i | 0.0109701 | − | 0.0190008i | ||||
\(383\) | −4247.63 | + | 7357.12i | −0.566694 | + | 0.981543i | 0.430196 | + | 0.902736i | \(0.358445\pi\) |
−0.996890 | + | 0.0788075i | \(0.974889\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 103.641 | + | 179.512i | 0.0137196 | + | 0.0237630i | ||||
\(386\) | 9477.90 | 1.24977 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 4582.74 | 0.599621 | ||||||||
\(389\) | 1768.42 | + | 3062.99i | 0.230494 | + | 0.399228i | 0.957954 | − | 0.286923i | \(-0.0926323\pi\) |
−0.727459 | + | 0.686151i | \(0.759299\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −175.961 | + | 304.774i | −0.0227589 | + | 0.0394196i | ||||
\(392\) | −3897.13 | + | 6750.02i | −0.502129 | + | 0.869713i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 4231.12 | + | 7328.51i | 0.541017 | + | 0.937068i | ||||
\(395\) | −5734.26 | −0.730436 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 8586.22 | 1.08547 | 0.542733 | − | 0.839905i | \(-0.317390\pi\) | ||||
0.542733 | + | 0.839905i | \(0.317390\pi\) | |||||||
\(398\) | 2611.25 | + | 4522.82i | 0.328870 | + | 0.569620i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 258.569 | − | 447.855i | 0.0323212 | − | 0.0559819i | ||||
\(401\) | 3616.39 | − | 6263.78i | 0.450359 | − | 0.780045i | −0.548049 | − | 0.836446i | \(-0.684629\pi\) |
0.998408 | + | 0.0564010i | \(0.0179625\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −232.369 | − | 402.474i | −0.0287223 | − | 0.0497485i | ||||
\(404\) | −2098.27 | −0.258398 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 688.160 | 0.0841202 | ||||||||
\(407\) | −1262.29 | − | 2186.35i | −0.153733 | − | 0.266274i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −615.480 | + | 1066.04i | −0.0744096 | + | 0.128881i | −0.900829 | − | 0.434173i | \(-0.857041\pi\) |
0.826420 | + | 0.563054i | \(0.190374\pi\) | |||||||
\(410\) | −1987.49 | + | 3442.43i | −0.239403 | + | 0.414658i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1515.83 | − | 2625.50i | −0.181261 | − | 0.313954i | ||||
\(413\) | 152.976 | 0.0182263 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 890.225 | 0.105300 | ||||||||
\(416\) | −2617.01 | − | 4532.79i | −0.308436 | − | 0.534226i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −1158.01 | + | 2005.73i | −0.135503 | + | 0.234698i | ||||
\(419\) | 291.219 | − | 504.407i | 0.0339547 | − | 0.0588112i | −0.848549 | − | 0.529117i | \(-0.822523\pi\) |
0.882503 | + | 0.470306i | \(0.155856\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6281.14 | + | 10879.3i | 0.727135 | + | 1.25944i | 0.958089 | + | 0.286471i | \(0.0924821\pi\) |
−0.230954 | + | 0.972965i | \(0.574185\pi\) | |||||||
\(422\) | 471.136 | 0.0543473 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −6177.33 | −0.707542 | ||||||||
\(425\) | −33.3323 | − | 57.7333i | −0.00380437 | − | 0.00658936i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 435.775 | − | 754.784i | 0.0493878 | − | 0.0855422i | ||||
\(428\) | −1006.41 | + | 1743.15i | −0.113660 | + | 0.196865i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1758.00 | + | 3044.94i | 0.197158 | + | 0.341488i | ||||
\(431\) | −9612.85 | −1.07433 | −0.537163 | − | 0.843478i | \(-0.680504\pi\) | ||||
−0.537163 | + | 0.843478i | \(0.680504\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8285.20 | 0.919541 | 0.459771 | − | 0.888038i | \(-0.347932\pi\) | ||||
0.459771 | + | 0.888038i | \(0.347932\pi\) | |||||||
\(434\) | 64.8680 | + | 112.355i | 0.00717457 | + | 0.0124267i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −3028.90 | + | 5246.20i | −0.332701 | + | 0.576256i | ||||
\(437\) | −8287.95 | + | 14355.2i | −0.907246 | + | 1.57140i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −5384.48 | − | 9326.20i | −0.585393 | − | 1.01393i | −0.994826 | − | 0.101590i | \(-0.967607\pi\) |
0.409434 | − | 0.912340i | \(-0.365726\pi\) | |||||||
\(440\) | −1078.87 | −0.116894 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 191.382 | 0.0205953 | ||||||||
\(443\) | −4404.96 | − | 7629.62i | −0.472429 | − | 0.818271i | 0.527073 | − | 0.849820i | \(-0.323289\pi\) |
−0.999502 | + | 0.0315487i | \(0.989956\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2016.22 | + | 3492.19i | −0.214782 | + | 0.372013i | ||||
\(446\) | 534.096 | − | 925.082i | 0.0567045 | − | 0.0982150i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1116.23 | + | 1933.37i | 0.117717 | + | 0.203891i | ||||
\(449\) | −9060.10 | −0.952277 | −0.476139 | − | 0.879370i | \(-0.657964\pi\) | ||||
−0.476139 | + | 0.879370i | \(0.657964\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3410.46 | 0.356081 | ||||||||
\(452\) | −1010.16 | − | 1749.65i | −0.105119 | − | 0.182072i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4100.95 | − | 7103.06i | 0.423937 | − | 0.734280i | ||||
\(455\) | 403.387 | − | 698.687i | 0.0415628 | − | 0.0719889i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1238.78 | − | 2145.62i | −0.126800 | − | 0.219624i | 0.795635 | − | 0.605776i | \(-0.207137\pi\) |
−0.922435 | + | 0.386152i | \(0.873804\pi\) | |||||||
\(458\) | −3475.97 | −0.354631 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2442.58 | −0.247578 | ||||||||
\(461\) | 7650.77 | + | 13251.5i | 0.772954 | + | 1.33880i | 0.935937 | + | 0.352167i | \(0.114555\pi\) |
−0.162983 | + | 0.986629i | \(0.552112\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 341.506 | − | 591.506i | 0.0342789 | − | 0.0593728i | −0.848377 | − | 0.529393i | \(-0.822420\pi\) |
0.882656 | + | 0.470020i | \(0.155753\pi\) | |||||||
\(464\) | −736.515 | + | 1275.68i | −0.0736894 | + | 0.127634i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4778.88 | − | 8277.27i | −0.475059 | − | 0.822826i | ||||
\(467\) | 6569.32 | 0.650946 | 0.325473 | − | 0.945551i | \(-0.394477\pi\) | ||||
0.325473 | + | 0.945551i | \(0.394477\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1895.28 | −0.186601 | ||||||||
\(470\) | −405.772 | − | 702.818i | −0.0398231 | − | 0.0689757i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −398.109 | + | 689.545i | −0.0388230 | + | 0.0672434i | ||||
\(473\) | 1508.33 | − | 2612.50i | 0.146624 | − | 0.253960i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1569.99 | − | 2719.30i | −0.151655 | − | 0.262674i | ||||
\(476\) | 46.0081 | 0.00443020 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −14322.6 | −1.37050 | ||||||||
\(479\) | −5644.33 | − | 9776.26i | −0.538405 | − | 0.932544i | −0.998990 | − | 0.0449289i | \(-0.985694\pi\) |
0.460585 | − | 0.887615i | \(-0.347639\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4913.02 | + | 8509.59i | −0.465726 | + | 0.806661i | ||||
\(482\) | 3090.15 | − | 5352.30i | 0.292018 | − | 0.505790i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2317.00 | − | 4013.16i | −0.217599 | − | 0.376893i | ||||
\(485\) | −6190.23 | −0.579554 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −8937.53 | −0.831618 | −0.415809 | − | 0.909452i | \(-0.636502\pi\) | ||||
−0.415809 | + | 0.909452i | \(0.636502\pi\) | |||||||
\(488\) | 2268.14 | + | 3928.54i | 0.210397 | + | 0.364419i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 1665.21 | − | 2884.23i | 0.153524 | − | 0.265911i | ||||
\(491\) | −1846.57 | + | 3198.35i | −0.169724 | + | 0.293971i | −0.938323 | − | 0.345760i | \(-0.887621\pi\) |
0.768599 | + | 0.639731i | \(0.220954\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 94.9446 | + | 164.449i | 0.00867361 | + | 0.0150231i | ||||
\(494\) | 9014.29 | 0.820996 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −277.705 | −0.0251397 | ||||||||
\(497\) | 2251.61 | + | 3899.91i | 0.203216 | + | 0.351981i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5593.22 | − | 9687.74i | 0.501777 | − | 0.869104i | −0.498220 | − | 0.867050i | \(-0.666013\pi\) |
0.999998 | − | 0.00205364i | \(-0.000653694\pi\) | |||||||
\(500\) | 231.349 | − | 400.709i | 0.0206925 | − | 0.0358405i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −7394.19 | − | 12807.1i | −0.657408 | − | 1.13866i | ||||
\(503\) | 6553.81 | 0.580954 | 0.290477 | − | 0.956882i | \(-0.406186\pi\) | ||||
0.290477 | + | 0.956882i | \(0.406186\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2834.28 | 0.249750 | ||||||||
\(506\) | −1216.79 | − | 2107.55i | −0.106903 | − | 0.185162i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 66.7174 | − | 115.558i | 0.00582698 | − | 0.0100926i | ||||
\(509\) | 7513.86 | − | 13014.4i | 0.654314 | − | 1.13331i | −0.327751 | − | 0.944764i | \(-0.606291\pi\) |
0.982065 | − | 0.188542i | \(-0.0603760\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 643.647 | + | 1114.83i | 0.0557207 | + | 0.0965111i | ||||
\(512\) | −7142.32 | −0.616502 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 13605.9 | 1.16757 | ||||||||
\(515\) | 2047.54 | + | 3546.45i | 0.175195 | + | 0.303447i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −348.145 | + | 603.005i | −0.0296159 | + | 0.0512962i | ||||
\(518\) | 1371.52 | − | 2375.54i | 0.116334 | − | 0.201496i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2099.57 | + | 3636.56i | 0.177062 | + | 0.306680i | ||||
\(521\) | −835.969 | −0.0702965 | −0.0351483 | − | 0.999382i | \(-0.511190\pi\) | ||||
−0.0351483 | + | 0.999382i | \(0.511190\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −13032.4 | −1.08961 | −0.544805 | − | 0.838563i | \(-0.683396\pi\) | ||||
−0.544805 | + | 0.838563i | \(0.683396\pi\) | |||||||
\(524\) | 2424.82 | + | 4199.91i | 0.202154 | + | 0.350141i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5870.95 | + | 10168.8i | −0.486665 | + | 0.842928i | ||||
\(527\) | −17.8995 | + | 31.0029i | −0.00147954 | + | 0.00256263i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −2625.17 | − | 4546.93i | −0.215762 | − | 0.373710i | ||||
\(530\) | 2639.53 | 0.216328 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2167.03 | 0.176603 | ||||||||
\(533\) | −6637.01 | − | 11495.6i | −0.539364 | − | 0.934205i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1359.43 | − | 2354.60i | 0.109857 | − | 0.190277i | ||||
\(536\) | 4932.32 | − | 8543.02i | 0.397469 | − | 0.688437i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −4165.63 | − | 7215.09i | −0.333816 | − | 0.578187i | ||||
\(539\) | −2857.44 | −0.228347 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4182.33 | −0.332370 | −0.166185 | − | 0.986095i | \(-0.553145\pi\) | ||||
−0.166185 | + | 0.986095i | \(0.553145\pi\) | |||||||
\(542\) | 1573.95 | + | 2726.16i | 0.124736 | + | 0.216049i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −201.590 | + | 349.164i | −0.0158881 | + | 0.0275189i | ||||
\(545\) | 4091.35 | − | 7086.42i | 0.321567 | − | 0.556970i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2506.95 | − | 4342.17i | −0.195959 | − | 0.339411i | 0.751256 | − | 0.660011i | \(-0.229449\pi\) |
−0.947214 | + | 0.320601i | \(0.896115\pi\) | |||||||
\(548\) | 8133.14 | 0.633997 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 460.995 | 0.0357398 | ||||||||
\(551\) | 4471.99 | + | 7745.72i | 0.345759 | + | 0.598872i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2672.81 | + | 4629.44i | −0.205532 | + | 0.355993i | ||||
\(554\) | −2262.38 | + | 3918.56i | −0.173501 | + | 0.300512i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3194.49 | + | 5533.01i | 0.243663 | + | 0.422036i | ||||
\(557\) | −2611.86 | −0.198686 | −0.0993430 | − | 0.995053i | \(-0.531674\pi\) | ||||
−0.0993430 | + | 0.995053i | \(0.531674\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −11741.3 | −0.888377 | ||||||||
\(560\) | −241.045 | − | 417.502i | −0.0181893 | − | 0.0315048i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5289.48 | + | 9161.64i | −0.397016 | + | 0.687652i | ||||
\(563\) | 9337.00 | − | 16172.2i | 0.698948 | − | 1.21061i | −0.269884 | − | 0.962893i | \(-0.586985\pi\) |
0.968832 | − | 0.247720i | \(-0.0796813\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1364.50 | + | 2363.38i | 0.101601 | + | 0.175979i | ||||
\(566\) | −5344.74 | −0.396919 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −23438.6 | −1.73145 | ||||||||
\(569\) | 11835.5 | + | 20499.7i | 0.872004 | + | 1.51036i | 0.859920 | + | 0.510429i | \(0.170513\pi\) |
0.0120843 | + | 0.999927i | \(0.496153\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4677.77 | − | 8102.14i | 0.342835 | − | 0.593807i | −0.642123 | − | 0.766601i | \(-0.721946\pi\) |
0.984958 | + | 0.172794i | \(0.0552796\pi\) | |||||||
\(572\) | 569.838 | − | 986.989i | 0.0416541 | − | 0.0721470i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1852.79 | + | 3209.12i | 0.134728 | + | 0.233356i | ||||
\(575\) | 3299.37 | 0.239293 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −21695.2 | −1.56531 | −0.782653 | − | 0.622459i | \(-0.786134\pi\) | ||||
−0.782653 | + | 0.622459i | \(0.786134\pi\) | |||||||
\(578\) | 5085.60 | + | 8808.51i | 0.365974 | + | 0.633885i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −658.981 | + | 1141.39i | −0.0471770 | + | 0.0817130i | ||||
\(581\) | 414.944 | − | 718.705i | 0.0296296 | − | 0.0513200i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1132.33 | − | 1961.26i | −0.0804399 | − | 0.139326i | ||||
\(584\) | −6700.18 | −0.474752 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −17290.7 | −1.21889 | ||||||||
\(587\) | −368.574 | − | 638.389i | −0.0259160 | − | 0.0448878i | 0.852777 | − | 0.522276i | \(-0.174917\pi\) |
−0.878693 | + | 0.477388i | \(0.841584\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −843.086 | + | 1460.27i | −0.0589792 | + | 0.102155i | ||||
\(590\) | 170.109 | − | 294.637i | 0.0118700 | − | 0.0205594i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2935.78 | + | 5084.92i | 0.203817 | + | 0.353022i | ||||
\(593\) | −21908.1 | −1.51713 | −0.758565 | − | 0.651597i | \(-0.774099\pi\) | ||||
−0.758565 | + | 0.651597i | \(0.774099\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −62.1464 | −0.00428194 | ||||||||
\(596\) | −3334.02 | − | 5774.68i | −0.229139 | − | 0.396880i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −4735.94 | + | 8202.89i | −0.323858 | + | 0.560939i | ||||
\(599\) | 3797.92 | − | 6578.19i | 0.259063 | − | 0.448710i | −0.706928 | − | 0.707285i | \(-0.749920\pi\) |
0.965991 | + | 0.258575i | \(0.0832529\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3251.26 | + | 5631.35i | 0.220668 | + | 0.382209i | 0.955011 | − | 0.296570i | \(-0.0958428\pi\) |
−0.734343 | + | 0.678779i | \(0.762509\pi\) | |||||||
\(602\) | 3277.69 | 0.221908 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −12319.6 | −0.829929 | ||||||||
\(605\) | 3129.74 | + | 5420.86i | 0.210317 | + | 0.364280i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 13078.4 | − | 22652.5i | 0.874524 | − | 1.51472i | 0.0172560 | − | 0.999851i | \(-0.494507\pi\) |
0.857268 | − | 0.514870i | \(-0.172160\pi\) | |||||||
\(608\) | −9495.10 | + | 16446.0i | −0.633351 | + | 1.09700i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −969.160 | − | 1678.63i | −0.0643281 | − | 0.111420i | ||||
\(611\) | 2710.06 | 0.179439 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 18172.8 | 1.19738 | 0.598690 | − | 0.800981i | \(-0.295688\pi\) | ||||
0.598690 | + | 0.800981i | \(0.295688\pi\) | |||||||
\(614\) | −7300.28 | − | 12644.4i | −0.479829 | − | 0.831089i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −502.877 | + | 871.008i | −0.0328920 | + | 0.0569706i | ||||
\(617\) | 13292.4 | − | 23023.1i | 0.867312 | − | 1.50223i | 0.00257822 | − | 0.999997i | \(-0.499179\pi\) |
0.864733 | − | 0.502231i | \(-0.167487\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −10843.9 | − | 18782.2i | −0.704124 | − | 1.21958i | −0.967007 | − | 0.254751i | \(-0.918006\pi\) |
0.262882 | − | 0.964828i | \(-0.415327\pi\) | |||||||
\(620\) | −248.470 | −0.0160948 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 4857.48 | 0.313131 | ||||||||
\(623\) | 1879.57 | + | 3255.50i | 0.120872 | + | 0.209356i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −312.500 | + | 541.266i | −0.0200000 | + | 0.0346410i | ||||
\(626\) | 3973.89 | − | 6882.98i | 0.253720 | − | 0.439455i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 7088.89 | + | 12278.3i | 0.450442 | + | 0.780188i | ||||
\(629\) | 756.907 | 0.0479807 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −7685.15 | −0.484851 | −0.242426 | − | 0.970170i | \(-0.577943\pi\) | ||||
−0.242426 | + | 0.970170i | \(0.577943\pi\) | |||||||
\(632\) | −13911.6 | − | 24095.6i | −0.875590 | − | 1.51657i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6105.73 | + | 10575.4i | −0.382476 | + | 0.662467i | ||||
\(635\) | −90.1199 | + | 156.092i | −0.00563197 | + | 0.00975486i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5560.79 | + | 9631.58i | 0.345882 | + | 0.599085i | ||||
\(638\) | −1313.11 | −0.0814835 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1082.88 | −0.0668824 | ||||||||
\(641\) | 4027.84 | + | 6976.43i | 0.248191 | + | 0.429879i | 0.963024 | − | 0.269416i | \(-0.0868307\pi\) |
−0.714833 | + | 0.699295i | \(0.753497\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 3561.01 | − | 6167.85i | 0.218402 | − | 0.378283i | −0.735918 | − | 0.677071i | \(-0.763249\pi\) |
0.954320 | + | 0.298788i | \(0.0965823\pi\) | |||||||
\(644\) | −1138.52 | + | 1971.97i | −0.0696644 | + | 0.120662i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −347.189 | − | 601.349i | −0.0211455 | − | 0.0366250i | ||||
\(647\) | 10280.7 | 0.624692 | 0.312346 | − | 0.949968i | \(-0.398885\pi\) | ||||
0.312346 | + | 0.949968i | \(0.398885\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −291.901 | −0.0176550 | ||||||||
\(650\) | −897.130 | − | 1553.87i | −0.0541359 | − | 0.0937661i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −4450.25 | + | 7708.06i | −0.267309 | + | 0.462992i | ||||
\(653\) | −4492.52 | + | 7781.27i | −0.269228 | + | 0.466316i | −0.968663 | − | 0.248380i | \(-0.920102\pi\) |
0.699435 | + | 0.714696i | \(0.253435\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3275.38 | − | 5673.12i | −0.195389 | − | 0.338423i | ||||
\(656\) | −7931.92 | −0.472087 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −756.541 | −0.0448223 | ||||||||
\(659\) | 6269.36 | + | 10858.9i | 0.370591 | + | 0.641883i | 0.989657 | − | 0.143457i | \(-0.0458217\pi\) |
−0.619065 | + | 0.785340i | \(0.712488\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6239.95 | − | 10807.9i | 0.367180 | − | 0.635974i | −0.621944 | − | 0.783062i | \(-0.713657\pi\) |
0.989123 | + | 0.147088i | \(0.0469900\pi\) | |||||||
\(662\) | 6571.15 | − | 11381.6i | 0.385793 | − | 0.668213i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2159.72 | + | 3740.75i | 0.126225 | + | 0.218629i | ||||
\(665\) | −2927.16 | −0.170692 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −9398.01 | −0.545566 | ||||||||
\(668\) | 6609.09 | + | 11447.3i | 0.382805 | + | 0.663037i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −2107.54 | + | 3650.37i | −0.121524 | + | 0.210487i | ||||
\(671\) | −831.522 | + | 1440.24i | −0.0478399 | + | 0.0828611i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −6592.82 | − | 11419.1i | −0.377614 | − | 0.654047i | 0.613100 | − | 0.790005i | \(-0.289922\pi\) |
−0.990715 | + | 0.135958i | \(0.956589\pi\) | |||||||
\(674\) | 2007.63 | 0.114734 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 3696.60 | 0.210321 | ||||||||
\(677\) | 13284.1 | + | 23008.8i | 0.754136 | + | 1.30620i | 0.945802 | + | 0.324742i | \(0.105278\pi\) |
−0.191666 | + | 0.981460i | \(0.561389\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2885.34 | + | 4997.56i | −0.163077 | + | 0.282457i | ||||
\(680\) | 161.731 | − | 280.127i | 0.00912076 | − | 0.0157976i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −123.778 | − | 214.389i | −0.00694969 | − | 0.0120372i | ||||
\(683\) | 7602.40 | 0.425912 | 0.212956 | − | 0.977062i | \(-0.431691\pi\) | ||||
0.212956 | + | 0.977062i | \(0.431691\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −10986.0 | −0.612780 | ||||||||
\(686\) | −3209.68 | − | 5559.33i | −0.178639 | − | 0.309411i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3508.01 | + | 6076.05i | −0.194392 | + | 0.336697i | ||||
\(689\) | −4407.21 | + | 7633.51i | −0.243688 | + | 0.422080i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −3128.66 | − | 5418.99i | −0.172243 | − | 0.298333i | 0.766961 | − | 0.641694i | \(-0.221768\pi\) |
−0.939204 | + | 0.343361i | \(0.888435\pi\) | |||||||
\(692\) | 592.018 | 0.0325219 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 13388.5 | 0.732307 | ||||||||
\(695\) | −4315.02 | − | 7473.84i | −0.235508 | − | 0.407912i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −511.254 | + | 885.518i | −0.0277835 | + | 0.0481225i | ||||
\(698\) | 6380.65 | − | 11051.6i | 0.346004 | − | 0.599297i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −215.669 | − | 373.550i | −0.0116451 | − | 0.0201698i | ||||
\(701\) | −769.271 | −0.0414479 | −0.0207239 | − | 0.999785i | \(-0.506597\pi\) | ||||
−0.0207239 | + | 0.999785i | \(0.506597\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 35651.1 | 1.91267 | ||||||||
\(704\) | −2129.94 | − | 3689.16i | −0.114027 | − | 0.197501i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3797.73 | + | 6577.87i | −0.202450 | + | 0.350653i | ||||
\(707\) | 1321.09 | − | 2288.20i | 0.0702755 | − | 0.121721i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4225.16 | + | 7318.19i | 0.223807 | + | 0.387645i | 0.955961 | − | 0.293494i | \(-0.0948181\pi\) |
−0.732154 | + | 0.681139i | \(0.761485\pi\) | |||||||
\(710\) | 10015.1 | 0.529383 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −19565.7 | −1.02985 | ||||||||
\(713\) | −885.884 | − | 1534.40i | −0.0465310 | − | 0.0805941i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −769.721 | + | 1333.20i | −0.0402601 | + | 0.0697325i | ||||
\(716\) | −2074.49 | + | 3593.12i | −0.108278 | + | 0.187544i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −12556.3 | − | 21748.2i | −0.652644 | − | 1.13041i | ||||
\(719\) | −25350.0 | −1.31488 | −0.657438 | − | 0.753508i | \(-0.728360\pi\) | ||||
−0.657438 | + | 0.753508i | \(0.728360\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 3817.54 | 0.197188 | ||||||||
\(722\) | −9242.71 | − | 16008.9i | −0.476424 | − | 0.825191i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −7137.87 | + | 12363.2i | −0.366404 | + | 0.634631i | ||||
\(725\) | 890.133 | − | 1541.75i | 0.0455982 | − | 0.0789784i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1912.57 | + | 3312.68i | 0.0975701 | + | 0.168996i | 0.910678 | − | 0.413116i | \(-0.135560\pi\) |
−0.813108 | + | 0.582113i | \(0.802226\pi\) | |||||||
\(728\) | 3914.54 | 0.199289 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2862.94 | 0.145153 | ||||||||
\(731\) | 452.220 | + | 783.268i | 0.0228809 | + | 0.0396309i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1846.41 | − | 3198.08i | 0.0930407 | − | 0.161151i | −0.815749 | − | 0.578407i | \(-0.803675\pi\) |
0.908789 | + | 0.417256i | \(0.137008\pi\) | |||||||
\(734\) | −12041.7 | + | 20856.8i | −0.605539 | + | 1.04882i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −9977.10 | − | 17280.8i | −0.499675 | − | 0.865462i | ||||
\(737\) | 3616.46 | 0.180752 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 4181.32 | 0.208136 | 0.104068 | − | 0.994570i | \(-0.466814\pi\) | ||||
0.104068 | + | 0.994570i | \(0.466814\pi\) | |||||||
\(740\) | 2626.73 | + | 4549.62i | 0.130487 | + | 0.226010i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 1230.32 | − | 2130.97i | 0.0608710 | − | 0.105432i | ||||
\(743\) | 463.991 | − | 803.656i | 0.0229101 | − | 0.0396814i | −0.854343 | − | 0.519709i | \(-0.826040\pi\) |
0.877253 | + | 0.480028i | \(0.159374\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4503.49 | + | 7800.28i | 0.221470 | + | 0.383598i | ||||
\(746\) | −4593.78 | −0.225456 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −87.7902 | −0.00429135 | ||||||||
\(749\) | −1267.29 | − | 2195.02i | −0.0618236 | − | 0.107082i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 11184.7 | − | 19372.5i | 0.543458 | − | 0.941297i | −0.455244 | − | 0.890367i | \(-0.650448\pi\) |
0.998702 | − | 0.0509306i | \(-0.0162187\pi\) | |||||||
\(752\) | 809.702 | − | 1402.45i | 0.0392644 | − | 0.0680079i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2555.41 | + | 4426.09i | 0.123425 | + | 0.213778i | ||||
\(755\) | 16640.9 | 0.802154 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 35390.0 | 1.69917 | 0.849586 | − | 0.527451i | \(-0.176852\pi\) | ||||
0.849586 | + | 0.527451i | \(0.176852\pi\) | |||||||
\(758\) | 6779.38 | + | 11742.2i | 0.324853 | + | 0.562661i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7617.72 | − | 13194.3i | 0.363584 | − | 0.629746i | ||||
\(761\) | −16717.3 | + | 28955.2i | −0.796323 | + | 1.37927i | 0.125673 | + | 0.992072i | \(0.459891\pi\) |
−0.921996 | + | 0.387200i | \(0.873442\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3814.05 | − | 6606.13i | −0.180967 | − | 0.313444i | ||||
\(764\) | 292.462 | 0.0138494 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 17612.9 | 0.830783 | ||||||||
\(767\) | 568.060 | + | 983.909i | 0.0267425 | + | 0.0463193i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −12510.7 | + | 21669.2i | −0.586668 | + | 1.01614i | 0.407998 | + | 0.912983i | \(0.366227\pi\) |
−0.994665 | + | 0.103155i | \(0.967106\pi\) | |||||||
\(770\) | 214.875 | − | 372.175i | 0.0100566 | − | 0.0174185i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 8460.89 | + | 14654.7i | 0.394448 | + | 0.683205i | ||||
\(773\) | −3065.27 | −0.142626 | −0.0713132 | − | 0.997454i | \(-0.522719\pi\) | ||||
−0.0713132 | + | 0.997454i | \(0.522719\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 335.626 | 0.0155562 | ||||||||
\(776\) | −15017.8 | − | 26011.5i | −0.694725 | − | 1.20330i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 3666.39 | − | 6350.38i | 0.168954 | − | 0.292638i | ||||
\(779\) | −24080.6 | + | 41708.8i | −1.10754 | + | 1.91832i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4296.41 | − | 7441.59i | −0.196847 | − | 0.340949i | ||||
\(782\) | 729.627 | 0.0333650 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 6645.73 | 0.302739 | ||||||||
\(785\) | −9575.47 | − | 16585.2i | −0.435367 | − | 0.754078i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 17841.6 | − | 30902.5i | 0.808111 | − | 1.39969i | −0.106060 | − | 0.994360i | \(-0.533824\pi\) |
0.914171 | − | 0.405329i | \(-0.132843\pi\) | |||||||
\(788\) | −7554.21 | + | 13084.3i | −0.341507 | + | 0.591508i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 5944.31 | + | 10295.9i | 0.267708 | + | 0.463684i | ||||
\(791\) | 2544.03 | 0.114356 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6472.81 | 0.289856 | ||||||||
\(794\) | −8900.73 | − | 15416.5i | −0.397828 | − | 0.689058i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −4662.12 | + | 8075.02i | −0.207593 | + | 0.359562i | ||||
\(797\) | 2262.54 | − | 3918.83i | 0.100556 | − | 0.174168i | −0.811358 | − | 0.584550i | \(-0.801271\pi\) |
0.911914 | + | 0.410382i | \(0.134604\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −104.379 | − | 180.790i | −0.00462162 | − | 0.00800487i | ||||
\(800\) | 3779.93 | 0.167051 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −14995.5 | −0.660235 | ||||||||
\(803\) | −1228.17 | − | 2127.26i | −0.0539742 | − | 0.0934861i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1537.88 | − | 2663.68i | 0.0673329 | − | 0.116624i | ||||
\(806\) | −481.761 | + | 834.434i | −0.0210537 | + | 0.0364661i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 6876.09 | + | 11909.7i | 0.299381 | + | 0.518544i | ||||
\(809\) | −16234.6 | −0.705535 | −0.352767 | − | 0.935711i | \(-0.614759\pi\) | ||||
−0.352767 | + | 0.935711i | \(0.614759\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 2197.06 | 0.0951286 | 0.0475643 | − | 0.998868i | \(-0.484854\pi\) | ||||
0.0475643 | + | 0.998868i | \(0.484854\pi\) | |||||||
\(812\) | 614.318 | + | 1064.03i | 0.0265497 | + | 0.0459854i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −2617.06 | + | 4532.87i | −0.112688 | + | 0.195181i | ||||
\(815\) | 6011.28 | − | 10411.8i | 0.258363 | − | 0.447498i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 21300.0 | + | 36892.7i | 0.912109 | + | 1.57982i | ||||
\(818\) | 2552.10 | 0.109086 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7096.91 | −0.302237 | ||||||||
\(821\) | 10070.8 | + | 17443.1i | 0.428104 | + | 0.741498i | 0.996705 | − | 0.0811157i | \(-0.0258483\pi\) |
−0.568601 | + | 0.822614i | \(0.692515\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −7758.51 | + | 13438.1i | −0.328608 | + | 0.569166i | −0.982236 | − | 0.187650i | \(-0.939913\pi\) |
0.653628 | + | 0.756816i | \(0.273246\pi\) | |||||||
\(824\) | −9934.86 | + | 17207.7i | −0.420021 | + | 0.727498i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −158.580 | − | 274.668i | −0.00668002 | − | 0.0115701i | ||||
\(827\) | 5582.51 | 0.234732 | 0.117366 | − | 0.993089i | \(-0.462555\pi\) | ||||
0.117366 | + | 0.993089i | \(0.462555\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 26037.6 | 1.09086 | 0.545430 | − | 0.838157i | \(-0.316367\pi\) | ||||
0.545430 | + | 0.838157i | \(0.316367\pi\) | |||||||
\(830\) | −922.834 | − | 1598.40i | −0.0385928 | − | 0.0668447i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −8290.04 | + | 14358.8i | −0.345439 | + | 0.598318i | ||||
\(833\) | 428.352 | − | 741.928i | 0.0178170 | − | 0.0308599i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −8927.38 | − | 15462.7i | −0.369994 | − | 0.640848i | ||||
\(836\) | −4135.01 | −0.171067 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1207.55 | −0.0497781 | ||||||||
\(839\) | 9043.99 | + | 15664.6i | 0.372149 | + | 0.644581i | 0.989896 | − | 0.141796i | \(-0.0452877\pi\) |
−0.617747 | + | 0.786377i | \(0.711954\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 9659.02 | − | 16729.9i | 0.396040 | − | 0.685962i | ||||
\(842\) | 13022.4 | − | 22555.5i | 0.532996 | − | 0.923177i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 420.582 | + | 728.469i | 0.0171529 | + | 0.0297096i | ||||
\(845\) | −4993.26 | −0.203282 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 5835.23 | 0.236719 | ||||||||
\(848\) | 2633.53 | + | 4561.42i | 0.106646 | + | 0.184717i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −69.1066 | + | 119.696i | −0.00278863 | + | 0.00483005i | ||||
\(851\) | −18730.4 | + | 32442.1i | −0.754490 | + | 1.30681i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 12674.5 | + | 21952.9i | 0.508753 | + | 0.881187i | 0.999949 | + | 0.0101371i | \(0.00322680\pi\) |
−0.491195 | + | 0.871049i | \(0.663440\pi\) | |||||||
\(854\) | −1806.95 | −0.0724034 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 13192.1 | 0.526750 | ||||||||
\(857\) | 281.899 | + | 488.263i | 0.0112363 | + | 0.0194618i | 0.871589 | − | 0.490238i | \(-0.163090\pi\) |
−0.860353 | + | 0.509699i | \(0.829757\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 10279.4 | − | 17804.5i | 0.408300 | − | 0.707197i | −0.586399 | − | 0.810022i | \(-0.699455\pi\) |
0.994699 | + | 0.102826i | \(0.0327884\pi\) | |||||||
\(860\) | −3138.71 | + | 5436.41i | −0.124453 | + | 0.215558i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9964.97 | + | 17259.8i | 0.393745 | + | 0.681987i | ||||
\(863\) | −7056.31 | −0.278331 | −0.139166 | − | 0.990269i | \(-0.544442\pi\) | ||||
−0.139166 | + | 0.990269i | \(0.544442\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −799.681 | −0.0314335 | ||||||||
\(866\) | −8588.70 | − | 14876.1i | −0.337016 | − | 0.583729i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −115.815 | + | 200.597i | −0.00452882 | + | 0.00784414i | ||||
\(869\) | 5100.11 | − | 8833.66i | 0.199090 | − | 0.344835i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −7037.90 | − | 12190.0i | −0.273789 | − | 0.474217i | ||||
\(872\) | 39703.2 | 1.54188 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 34366.2 | 1.33004 | ||||||||
\(875\) | 291.320 | + | 504.581i | 0.0112553 | + | 0.0194948i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1258.15 | + | 2179.18i | −0.0484432 | + | 0.0839061i | −0.889230 | − | 0.457460i | \(-0.848759\pi\) |
0.840787 | + | 0.541366i | \(0.182093\pi\) | |||||||
\(878\) | −11163.4 | + | 19335.6i | −0.429098 | + | 0.743219i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 459.949 | + | 796.654i | 0.0176192 | + | 0.0305173i | ||||
\(881\) | 31571.2 | 1.20733 | 0.603666 | − | 0.797237i | \(-0.293706\pi\) | ||||
0.603666 | + | 0.797237i | \(0.293706\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 47743.5 | 1.81959 | 0.909794 | − | 0.415059i | \(-0.136239\pi\) | ||||
0.909794 | + | 0.415059i | \(0.136239\pi\) | |||||||
\(884\) | 170.846 | + | 295.914i | 0.00650020 | + | 0.0112587i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9132.64 | + | 15818.2i | −0.346295 | + | 0.599800i | ||||
\(887\) | 16514.4 | − | 28603.8i | 0.625141 | − | 1.08278i | −0.363372 | − | 0.931644i | \(-0.618375\pi\) |
0.988514 | − | 0.151132i | \(-0.0482919\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 84.0120 | + | 145.513i | 0.00316948 | + | 0.00548971i | ||||
\(890\) | 8360.28 | 0.314873 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1907.14 | 0.0715873 | ||||||||
\(893\) | −4916.37 | − | 8515.40i | −0.184233 | − | 0.319101i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 2802.16 | − | 4853.49i | 0.104655 | − | 0.181267i | ||||
\(896\) | −504.745 | + | 874.244i | −0.0188196 | + | 0.0325965i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 9391.98 | + | 16267.4i | 0.349014 | + | 0.604510i | ||||
\(899\) | −956.006 | −0.0354667 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 678.981 | 0.0251056 | ||||||||
\(902\) | −3535.39 | − | 6123.47i | −0.130505 | − | 0.226041i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −6620.66 | + | 11467.3i | −0.243584 | + | 0.421900i | ||||
\(905\) | 9641.63 | − | 16699.8i | 0.354142 | − | 0.613392i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 21665.3 | + | 37525.3i | 0.793146 | + | 1.37377i | 0.924010 | + | 0.382369i | \(0.124892\pi\) |
−0.130864 | + | 0.991400i | \(0.541775\pi\) | |||||||
\(908\) | 14643.6 | 0.535205 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1672.65 | −0.0609318 | ||||||||
\(911\) | −11177.2 | − | 19359.5i | −0.406496 | − | 0.704071i | 0.587999 | − | 0.808862i | \(-0.299916\pi\) |
−0.994494 | + | 0.104791i | \(0.966583\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −791.775 | + | 1371.39i | −0.0287009 | + | 0.0497114i | ||||
\(914\) | −2568.31 | + | 4448.44i | −0.0929454 | + | 0.160986i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −3102.98 | − | 5374.53i | −0.111927 | − | 0.193864i | ||||
\(917\) | −6106.77 | −0.219916 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1306.08 | 0.0468811 | 0.0234406 | − | 0.999725i | \(-0.492538\pi\) | ||||
0.0234406 | + | 0.999725i | \(0.492538\pi\) | |||||||
\(920\) | 8004.42 | + | 13864.1i | 0.286846 | + | 0.496831i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 15862.0 | − | 27473.9i | 0.566582 | − | 0.981349i | ||||
\(923\) | −16722.2 | + | 28963.8i | −0.596337 | + | 1.03289i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −3548.11 | − | 6145.50i | −0.126120 | − | 0.218446i | ||||
\(926\) | −1416.06 | −0.0502535 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −10766.8 | −0.380861 | ||||||||
\(929\) | 25331.9 | + | 43876.2i | 0.894633 | + | 1.54955i | 0.834258 | + | 0.551374i | \(0.185896\pi\) |
0.0603743 | + | 0.998176i | \(0.480771\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 20175.8 | − | 34945.6i | 0.710243 | − | 1.23018i | ||||
\(932\) | 8532.18 | − | 14778.2i | 0.299872 | − | 0.519394i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −6809.95 | − | 11795.2i | −0.238574 | − | 0.413223i | ||||
\(935\) | 118.584 | 0.00414773 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −12652.4 | −0.441126 | −0.220563 | − | 0.975373i | \(-0.570789\pi\) | ||||
−0.220563 | + | 0.975373i | \(0.570789\pi\) | |||||||
\(938\) | 1964.70 | + | 3402.96i | 0.0683899 | + | 0.118455i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 724.463 | − | 1254.81i | 0.0251376 | − | 0.0435397i | ||||
\(941\) | 20338.7 | − | 35227.7i | 0.704594 | − | 1.22039i | −0.262243 | − | 0.965002i | \(-0.584462\pi\) |
0.966838 | − | 0.255392i | \(-0.0822044\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −25303.0 | − | 43826.1i | −0.873785 | − | 1.51344i | ||||
\(944\) | 678.891 | 0.0234068 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −6254.32 | −0.214953 | ||||||||
\(947\) | −13458.4 | − | 23310.6i | −0.461816 | − | 0.799888i | 0.537236 | − | 0.843432i | \(-0.319468\pi\) |
−0.999052 | + | 0.0435439i | \(0.986135\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4780.23 | + | 8279.60i | −0.163512 | + | 0.283211i | ||||
\(950\) | −3254.99 | + | 5637.82i | −0.111164 | + | 0.192542i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −150.770 | − | 261.141i | −0.00513286 | − | 0.00889038i | ||||
\(953\) | −29644.9 | −1.00765 | −0.503827 | − | 0.863805i | \(-0.668075\pi\) | ||||
−0.503827 | + | 0.863805i | \(0.668075\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −395.050 | −0.0133859 | ||||||||
\(956\) | −12785.7 | − | 22145.5i | −0.432552 | − | 0.749202i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −11702.2 | + | 20268.7i | −0.394655 | + | 0.683563i | ||||
\(959\) | −5120.72 | + | 8869.34i | −0.172426 | + | 0.298651i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 14805.4 | + | 25643.7i | 0.496975 | + | 0.860786i | ||||
\(962\) | 20371.9 | 0.682762 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 11034.3 | 0.368662 | ||||||||
\(965\) | −11428.7 | − | 19795.1i | −0.381248 | − | 0.660340i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10726.0 | + | 18578.1i | −0.356697 | + | 0.617818i | −0.987407 | − | 0.158201i | \(-0.949431\pi\) |
0.630710 | + | 0.776019i | \(0.282764\pi\) | |||||||
\(968\) | −15185.8 | + | 26302.5i | −0.504224 | + | 0.873342i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 6416.98 | + | 11114.5i | 0.212409 | + | 0.367903i | ||||
\(971\) | 42684.6 | 1.41073 | 0.705363 | − | 0.708846i | \(-0.250784\pi\) | ||||
0.705363 | + | 0.708846i | \(0.250784\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8045.14 | −0.265072 | ||||||||
\(974\) | 9264.91 | + | 16047.3i | 0.304792 | + | 0.527914i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1933.92 | − | 3349.65i | 0.0634255 | − | 0.109856i | ||||
\(977\) | 30193.1 | − | 52296.0i | 0.988704 | − | 1.71248i | 0.364548 | − | 0.931184i | \(-0.381223\pi\) |
0.624155 | − | 0.781300i | \(-0.285443\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3586.49 | − | 6211.98i | −0.117083 | − | 0.202794i | ||||
\(980\) | 5946.12 | 0.193818 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7656.85 | 0.248818 | ||||||||
\(983\) | −29504.6 | − | 51103.4i | −0.957325 | − | 1.65814i | −0.728956 | − | 0.684560i | \(-0.759994\pi\) |
−0.228369 | − | 0.973575i | \(-0.573339\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 10204.0 | − | 17673.9i | 0.330078 | − | 0.571712i | ||||
\(986\) | 196.845 | − | 340.946i | 0.00635783 | − | 0.0110121i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8047.03 | + | 13937.9i | 0.259120 | + | 0.448808i | ||||
\(989\) | −44762.6 | −1.43920 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −30899.0 | −0.990454 | −0.495227 | − | 0.868764i | \(-0.664915\pi\) | ||||
−0.495227 | + | 0.868764i | \(0.664915\pi\) | |||||||
\(992\) | −1014.91 | − | 1757.88i | −0.0324834 | − | 0.0562629i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 4668.18 | − | 8085.52i | 0.148959 | − | 0.258005i | ||||
\(995\) | 6297.46 | − | 10907.5i | 0.200646 | − | 0.347529i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 16933.4 | + | 29329.6i | 0.537901 | + | 0.931671i | 0.999017 | + | 0.0443315i | \(0.0141158\pi\) |
−0.461116 | + | 0.887340i | \(0.652551\pi\) | |||||||
\(998\) | −23192.4 | −0.735614 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 405.4.e.w.271.3 | 12 | ||
3.2 | odd | 2 | 405.4.e.x.271.4 | 12 | |||
9.2 | odd | 6 | 405.4.e.x.136.4 | 12 | |||
9.4 | even | 3 | 405.4.a.l.1.4 | yes | 6 | ||
9.5 | odd | 6 | 405.4.a.k.1.3 | ✓ | 6 | ||
9.7 | even | 3 | inner | 405.4.e.w.136.3 | 12 | ||
45.4 | even | 6 | 2025.4.a.y.1.3 | 6 | |||
45.14 | odd | 6 | 2025.4.a.z.1.4 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
405.4.a.k.1.3 | ✓ | 6 | 9.5 | odd | 6 | ||
405.4.a.l.1.4 | yes | 6 | 9.4 | even | 3 | ||
405.4.e.w.136.3 | 12 | 9.7 | even | 3 | inner | ||
405.4.e.w.271.3 | 12 | 1.1 | even | 1 | trivial | ||
405.4.e.x.136.4 | 12 | 9.2 | odd | 6 | |||
405.4.e.x.271.4 | 12 | 3.2 | odd | 2 | |||
2025.4.a.y.1.3 | 6 | 45.4 | even | 6 | |||
2025.4.a.z.1.4 | 6 | 45.14 | odd | 6 |