Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [825,4,Mod(199,825)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(825, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("825.199");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 825 = 3 \cdot 5^{2} \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 825.c (of order \(2\), degree \(1\), 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: | \(48.6765757547\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Coefficient field: | 6.0.36142572544.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} + 53x^{4} + 632x^{2} + 484 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2 \) |
Twist minimal: | no (minimal twist has level 165) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 199.4 | ||
Root | \(0.906392i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 825.199 |
Dual form | 825.4.c.k.199.3 |
$q$-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 \(\left(\mathbb{Z}/825\mathbb{Z}\right)^\times\).
\(n\) | \(376\) | \(551\) | \(727\) |
\(\chi(n)\) | \(1\) | \(1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.90639i | 0.674011i | 0.941503 | + | 0.337006i | \(0.109414\pi\) | ||||
−0.941503 | + | 0.337006i | \(0.890586\pi\) | |||||||
\(3\) | 3.00000i | 0.577350i | ||||||||
\(4\) | 4.36567 | 0.545709 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −5.71918 | −0.389141 | ||||||||
\(7\) | 22.9186i | 1.23749i | 0.785594 | + | 0.618743i | \(0.212358\pi\) | ||||
−0.785594 | + | 0.618743i | \(0.787642\pi\) | |||||||
\(8\) | 23.5738i | 1.04183i | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | 13.0970i | 0.315065i | ||||||||
\(13\) | 66.7313i | 1.42369i | 0.702338 | + | 0.711844i | \(0.252140\pi\) | ||||
−0.702338 | + | 0.711844i | \(0.747860\pi\) | |||||||
\(14\) | −43.6917 | −0.834079 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −10.0156 | −0.156493 | ||||||||
\(17\) | 3.45588i | 0.0493043i | 0.999696 | + | 0.0246522i | \(0.00784782\pi\) | ||||
−0.999696 | + | 0.0246522i | \(0.992152\pi\) | |||||||
\(18\) | − 17.1575i | − 0.224670i | ||||||||
\(19\) | −78.2359 | −0.944660 | −0.472330 | − | 0.881422i | \(-0.656587\pi\) | ||||
−0.472330 | + | 0.881422i | \(0.656587\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −68.7557 | −0.714463 | ||||||||
\(22\) | 20.9703i | 0.203222i | ||||||||
\(23\) | 12.2907i | 0.111426i | 0.998447 | + | 0.0557129i | \(0.0177432\pi\) | ||||
−0.998447 | + | 0.0557129i | \(0.982257\pi\) | |||||||
\(24\) | −70.7214 | −0.601498 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −127.216 | −0.959582 | ||||||||
\(27\) | − 27.0000i | − 0.192450i | ||||||||
\(28\) | 100.055i | 0.675307i | ||||||||
\(29\) | 31.1827 | 0.199672 | 0.0998358 | − | 0.995004i | \(-0.468168\pi\) | ||||
0.0998358 | + | 0.995004i | \(0.468168\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 247.181 | 1.43210 | 0.716049 | − | 0.698050i | \(-0.245949\pi\) | ||||
0.716049 | + | 0.698050i | \(0.245949\pi\) | |||||||
\(32\) | 169.497i | 0.936347i | ||||||||
\(33\) | 33.0000i | 0.174078i | ||||||||
\(34\) | −6.58825 | −0.0332317 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −39.2910 | −0.181903 | ||||||||
\(37\) | − 304.128i | − 1.35131i | −0.737220 | − | 0.675653i | \(-0.763862\pi\) | ||||
0.737220 | − | 0.675653i | \(-0.236138\pi\) | |||||||
\(38\) | − 149.148i | − 0.636712i | ||||||||
\(39\) | −200.194 | −0.821967 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −29.8219 | −0.113595 | −0.0567975 | − | 0.998386i | \(-0.518089\pi\) | ||||
−0.0567975 | + | 0.998386i | \(0.518089\pi\) | |||||||
\(42\) | − 131.075i | − 0.481556i | ||||||||
\(43\) | 269.060i | 0.954215i | 0.878845 | + | 0.477108i | \(0.158315\pi\) | ||||
−0.878845 | + | 0.477108i | \(0.841685\pi\) | |||||||
\(44\) | 48.0224 | 0.164537 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −23.4309 | −0.0751023 | ||||||||
\(47\) | − 225.463i | − 0.699726i | −0.936801 | − | 0.349863i | \(-0.886228\pi\) | ||||
0.936801 | − | 0.349863i | \(-0.113772\pi\) | |||||||
\(48\) | − 30.0467i | − 0.0903514i | ||||||||
\(49\) | −182.260 | −0.531371 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −10.3676 | −0.0284659 | ||||||||
\(52\) | 291.327i | 0.776919i | ||||||||
\(53\) | − 16.8371i | − 0.0436369i | −0.999762 | − | 0.0218184i | \(-0.993054\pi\) | ||||
0.999762 | − | 0.0218184i | \(-0.00694557\pi\) | |||||||
\(54\) | 51.4726 | 0.129714 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −540.278 | −1.28924 | ||||||||
\(57\) | − 234.708i | − 0.545400i | ||||||||
\(58\) | 59.4464i | 0.134581i | ||||||||
\(59\) | −28.0701 | −0.0619392 | −0.0309696 | − | 0.999520i | \(-0.509860\pi\) | ||||
−0.0309696 | + | 0.999520i | \(0.509860\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −853.742 | −1.79198 | −0.895988 | − | 0.444079i | \(-0.853531\pi\) | ||||
−0.895988 | + | 0.444079i | \(0.853531\pi\) | |||||||
\(62\) | 471.224i | 0.965250i | ||||||||
\(63\) | − 206.267i | − 0.412495i | ||||||||
\(64\) | −403.252 | −0.787602 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −62.9109 | −0.117330 | ||||||||
\(67\) | 36.7885i | 0.0670810i | 0.999437 | + | 0.0335405i | \(0.0106783\pi\) | ||||
−0.999437 | + | 0.0335405i | \(0.989322\pi\) | |||||||
\(68\) | 15.0872i | 0.0269058i | ||||||||
\(69\) | −36.8722 | −0.0643317 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 23.8552 | 0.0398746 | 0.0199373 | − | 0.999801i | \(-0.493653\pi\) | ||||
0.0199373 | + | 0.999801i | \(0.493653\pi\) | |||||||
\(72\) | − 212.164i | − 0.347275i | ||||||||
\(73\) | 707.265i | 1.13396i | 0.823731 | + | 0.566980i | \(0.191889\pi\) | ||||
−0.823731 | + | 0.566980i | \(0.808111\pi\) | |||||||
\(74\) | 579.787 | 0.910795 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −341.552 | −0.515509 | ||||||||
\(77\) | 252.104i | 0.373116i | ||||||||
\(78\) | − 381.648i | − 0.554015i | ||||||||
\(79\) | 412.126 | 0.586934 | 0.293467 | − | 0.955969i | \(-0.405191\pi\) | ||||
0.293467 | + | 0.955969i | \(0.405191\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | − 56.8522i | − 0.0765643i | ||||||||
\(83\) | − 552.596i | − 0.730786i | −0.930853 | − | 0.365393i | \(-0.880935\pi\) | ||||
0.930853 | − | 0.365393i | \(-0.119065\pi\) | |||||||
\(84\) | −300.165 | −0.389889 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −512.934 | −0.643152 | ||||||||
\(87\) | 93.5480i | 0.115280i | ||||||||
\(88\) | 259.312i | 0.314122i | ||||||||
\(89\) | 1495.26 | 1.78087 | 0.890434 | − | 0.455113i | \(-0.150401\pi\) | ||||
0.890434 | + | 0.455113i | \(0.150401\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1529.39 | −1.76179 | ||||||||
\(92\) | 53.6573i | 0.0608060i | ||||||||
\(93\) | 741.543i | 0.826822i | ||||||||
\(94\) | 429.820 | 0.471623 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −508.491 | −0.540600 | ||||||||
\(97\) | − 1199.45i | − 1.25552i | −0.778406 | − | 0.627761i | \(-0.783971\pi\) | ||||
0.778406 | − | 0.627761i | \(-0.216029\pi\) | |||||||
\(98\) | − 347.459i | − 0.358150i | ||||||||
\(99\) | −99.0000 | −0.100504 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1009.66 | −0.994701 | −0.497351 | − | 0.867550i | \(-0.665694\pi\) | ||||
−0.497351 | + | 0.867550i | \(0.665694\pi\) | |||||||
\(102\) | − 19.7648i | − 0.0191863i | ||||||||
\(103\) | 1156.70i | 1.10653i | 0.833004 | + | 0.553266i | \(0.186619\pi\) | ||||
−0.833004 | + | 0.553266i | \(0.813381\pi\) | |||||||
\(104\) | −1573.11 | −1.48323 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 32.0981 | 0.0294117 | ||||||||
\(107\) | − 491.857i | − 0.444389i | −0.975002 | − | 0.222194i | \(-0.928678\pi\) | ||||
0.975002 | − | 0.222194i | \(-0.0713220\pi\) | |||||||
\(108\) | − 117.873i | − 0.105022i | ||||||||
\(109\) | −1340.77 | −1.17819 | −0.589093 | − | 0.808066i | \(-0.700515\pi\) | ||||
−0.589093 | + | 0.808066i | \(0.700515\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 912.384 | 0.780177 | ||||||||
\(112\) | − 229.542i | − 0.193658i | ||||||||
\(113\) | 1849.21i | 1.53946i | 0.638371 | + | 0.769729i | \(0.279609\pi\) | ||||
−0.638371 | + | 0.769729i | \(0.720391\pi\) | |||||||
\(114\) | 447.445 | 0.367606 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 136.133 | 0.108963 | ||||||||
\(117\) | − 600.582i | − 0.474563i | ||||||||
\(118\) | − 53.5126i | − 0.0417478i | ||||||||
\(119\) | −79.2037 | −0.0610134 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | − 1627.57i | − 1.20781i | ||||||||
\(123\) | − 89.4656i | − 0.0655841i | ||||||||
\(124\) | 1079.11 | 0.781508 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 393.226 | 0.278026 | ||||||||
\(127\) | 1020.24i | 0.712850i | 0.934324 | + | 0.356425i | \(0.116005\pi\) | ||||
−0.934324 | + | 0.356425i | \(0.883995\pi\) | |||||||
\(128\) | 587.219i | 0.405495i | ||||||||
\(129\) | −807.180 | −0.550917 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1003.30 | 0.669147 | 0.334574 | − | 0.942370i | \(-0.391408\pi\) | ||||
0.334574 | + | 0.942370i | \(0.391408\pi\) | |||||||
\(132\) | 144.067i | 0.0949957i | ||||||||
\(133\) | − 1793.05i | − 1.16900i | ||||||||
\(134\) | −70.1332 | −0.0452134 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −81.4682 | −0.0513665 | ||||||||
\(137\) | − 2665.14i | − 1.66203i | −0.556249 | − | 0.831016i | \(-0.687760\pi\) | ||||
0.556249 | − | 0.831016i | \(-0.312240\pi\) | |||||||
\(138\) | − 70.2928i | − 0.0433603i | ||||||||
\(139\) | −2557.64 | −1.56069 | −0.780347 | − | 0.625347i | \(-0.784957\pi\) | ||||
−0.780347 | + | 0.625347i | \(0.784957\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 676.388 | 0.403987 | ||||||||
\(142\) | 45.4774i | 0.0268759i | ||||||||
\(143\) | 734.045i | 0.429258i | ||||||||
\(144\) | 90.1401 | 0.0521644 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | −1348.32 | −0.764303 | ||||||||
\(147\) | − 546.781i | − 0.306787i | ||||||||
\(148\) | − 1327.72i | − 0.737419i | ||||||||
\(149\) | 2644.66 | 1.45409 | 0.727044 | − | 0.686591i | \(-0.240894\pi\) | ||||
0.727044 | + | 0.686591i | \(0.240894\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2871.44 | −1.54751 | −0.773757 | − | 0.633482i | \(-0.781625\pi\) | ||||
−0.773757 | + | 0.633482i | \(0.781625\pi\) | |||||||
\(152\) | − 1844.32i | − 0.984171i | ||||||||
\(153\) | − 31.1029i | − 0.0164348i | ||||||||
\(154\) | −480.609 | −0.251484 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −873.981 | −0.448554 | ||||||||
\(157\) | − 1048.51i | − 0.532996i | −0.963835 | − | 0.266498i | \(-0.914133\pi\) | ||||
0.963835 | − | 0.266498i | \(-0.0858666\pi\) | |||||||
\(158\) | 785.674i | 0.395600i | ||||||||
\(159\) | 50.5113 | 0.0251937 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −281.686 | −0.137888 | ||||||||
\(162\) | 154.418i | 0.0748901i | ||||||||
\(163\) | − 1953.90i | − 0.938905i | −0.882958 | − | 0.469452i | \(-0.844451\pi\) | ||||
0.882958 | − | 0.469452i | \(-0.155549\pi\) | |||||||
\(164\) | −130.192 | −0.0619898 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1053.46 | 0.492558 | ||||||||
\(167\) | − 2085.79i | − 0.966488i | −0.875486 | − | 0.483244i | \(-0.839458\pi\) | ||||
0.875486 | − | 0.483244i | \(-0.160542\pi\) | |||||||
\(168\) | − 1620.83i | − 0.744345i | ||||||||
\(169\) | −2256.07 | −1.02689 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 704.123 | 0.314887 | ||||||||
\(172\) | 1174.63i | 0.520724i | ||||||||
\(173\) | − 3999.28i | − 1.75757i | −0.477218 | − | 0.878785i | \(-0.658355\pi\) | ||||
0.477218 | − | 0.878785i | \(-0.341645\pi\) | |||||||
\(174\) | −178.339 | −0.0777003 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −110.171 | −0.0471845 | ||||||||
\(177\) | − 84.2103i | − 0.0357606i | ||||||||
\(178\) | 2850.55i | 1.20032i | ||||||||
\(179\) | −2046.60 | −0.854580 | −0.427290 | − | 0.904115i | \(-0.640532\pi\) | ||||
−0.427290 | + | 0.904115i | \(0.640532\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 64.2973 | 0.0264043 | 0.0132022 | − | 0.999913i | \(-0.495797\pi\) | ||||
0.0132022 | + | 0.999913i | \(0.495797\pi\) | |||||||
\(182\) | − 2915.61i | − 1.18747i | ||||||||
\(183\) | − 2561.23i | − 1.03460i | ||||||||
\(184\) | −289.739 | −0.116086 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −1413.67 | −0.557287 | ||||||||
\(187\) | 38.0146i | 0.0148658i | ||||||||
\(188\) | − 984.296i | − 0.381846i | ||||||||
\(189\) | 618.801 | 0.238154 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 4816.60 | 1.82470 | 0.912348 | − | 0.409416i | \(-0.134268\pi\) | ||||
0.912348 | + | 0.409416i | \(0.134268\pi\) | |||||||
\(192\) | − 1209.76i | − 0.454722i | ||||||||
\(193\) | − 295.804i | − 0.110323i | −0.998477 | − | 0.0551617i | \(-0.982433\pi\) | ||||
0.998477 | − | 0.0551617i | \(-0.0175674\pi\) | |||||||
\(194\) | 2286.62 | 0.846237 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −795.688 | −0.289974 | ||||||||
\(197\) | 2147.97i | 0.776835i | 0.921483 | + | 0.388418i | \(0.126978\pi\) | ||||
−0.921483 | + | 0.388418i | \(0.873022\pi\) | |||||||
\(198\) | − 188.733i | − 0.0677407i | ||||||||
\(199\) | 876.260 | 0.312143 | 0.156071 | − | 0.987746i | \(-0.450117\pi\) | ||||
0.156071 | + | 0.987746i | \(0.450117\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −110.365 | −0.0387292 | ||||||||
\(202\) | − 1924.81i | − 0.670440i | ||||||||
\(203\) | 714.662i | 0.247091i | ||||||||
\(204\) | −45.2616 | −0.0155341 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −2205.12 | −0.745815 | ||||||||
\(207\) | − 110.617i | − 0.0371419i | ||||||||
\(208\) | − 668.352i | − 0.222798i | ||||||||
\(209\) | −860.595 | −0.284826 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1413.99 | 0.461341 | 0.230670 | − | 0.973032i | \(-0.425908\pi\) | ||||
0.230670 | + | 0.973032i | \(0.425908\pi\) | |||||||
\(212\) | − 73.5052i | − 0.0238130i | ||||||||
\(213\) | 71.5657i | 0.0230216i | ||||||||
\(214\) | 937.672 | 0.299523 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 636.493 | 0.200499 | ||||||||
\(217\) | 5665.03i | 1.77220i | ||||||||
\(218\) | − 2556.03i | − 0.794110i | ||||||||
\(219\) | −2121.80 | −0.654693 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −230.615 | −0.0701939 | ||||||||
\(222\) | 1739.36i | 0.525848i | ||||||||
\(223\) | 3365.53i | 1.01064i | 0.862932 | + | 0.505320i | \(0.168626\pi\) | ||||
−0.862932 | + | 0.505320i | \(0.831374\pi\) | |||||||
\(224\) | −3884.62 | −1.15872 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −3525.31 | −1.03761 | ||||||||
\(227\) | 5724.31i | 1.67373i | 0.547411 | + | 0.836864i | \(0.315613\pi\) | ||||
−0.547411 | + | 0.836864i | \(0.684387\pi\) | |||||||
\(228\) | − 1024.66i | − 0.297629i | ||||||||
\(229\) | −2586.74 | −0.746447 | −0.373224 | − | 0.927741i | \(-0.621748\pi\) | ||||
−0.373224 | + | 0.927741i | \(0.621748\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −756.312 | −0.215419 | ||||||||
\(232\) | 735.095i | 0.208023i | ||||||||
\(233\) | 5571.63i | 1.56656i | 0.621666 | + | 0.783282i | \(0.286456\pi\) | ||||
−0.621666 | + | 0.783282i | \(0.713544\pi\) | |||||||
\(234\) | 1144.94 | 0.319861 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −122.545 | −0.0338008 | ||||||||
\(237\) | 1236.38i | 0.338867i | ||||||||
\(238\) | − 150.993i | − 0.0411237i | ||||||||
\(239\) | 1822.92 | 0.493369 | 0.246685 | − | 0.969096i | \(-0.420659\pi\) | ||||
0.246685 | + | 0.969096i | \(0.420659\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2226.66 | −0.595152 | −0.297576 | − | 0.954698i | \(-0.596178\pi\) | ||||
−0.297576 | + | 0.954698i | \(0.596178\pi\) | |||||||
\(242\) | 230.673i | 0.0612738i | ||||||||
\(243\) | 243.000i | 0.0641500i | ||||||||
\(244\) | −3727.16 | −0.977897 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 170.556 | 0.0442044 | ||||||||
\(247\) | − 5220.78i | − 1.34490i | ||||||||
\(248\) | 5827.00i | 1.49200i | ||||||||
\(249\) | 1657.79 | 0.421920 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7888.22 | 1.98367 | 0.991833 | − | 0.127543i | \(-0.0407092\pi\) | ||||
0.991833 | + | 0.127543i | \(0.0407092\pi\) | |||||||
\(252\) | − 900.494i | − 0.225102i | ||||||||
\(253\) | 135.198i | 0.0335961i | ||||||||
\(254\) | −1944.98 | −0.480469 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −4345.49 | −1.06091 | ||||||||
\(257\) | 4755.32i | 1.15420i | 0.816674 | + | 0.577099i | \(0.195815\pi\) | ||||
−0.816674 | + | 0.577099i | \(0.804185\pi\) | |||||||
\(258\) | − 1538.80i | − 0.371324i | ||||||||
\(259\) | 6970.17 | 1.67222 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −280.644 | −0.0665572 | ||||||||
\(262\) | 1912.67i | 0.451013i | ||||||||
\(263\) | − 103.437i | − 0.0242517i | −0.999926 | − | 0.0121258i | \(-0.996140\pi\) | ||||
0.999926 | − | 0.0121258i | \(-0.00385987\pi\) | |||||||
\(264\) | −777.936 | −0.181358 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 3418.26 | 0.787921 | ||||||||
\(267\) | 4485.78i | 1.02818i | ||||||||
\(268\) | 160.606i | 0.0366067i | ||||||||
\(269\) | 2179.50 | 0.494002 | 0.247001 | − | 0.969015i | \(-0.420555\pi\) | ||||
0.247001 | + | 0.969015i | \(0.420555\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3688.54 | −0.826800 | −0.413400 | − | 0.910550i | \(-0.635659\pi\) | ||||
−0.413400 | + | 0.910550i | \(0.635659\pi\) | |||||||
\(272\) | − 34.6126i | − 0.00771579i | ||||||||
\(273\) | − 4588.16i | − 1.01717i | ||||||||
\(274\) | 5080.80 | 1.12023 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −160.972 | −0.0351064 | ||||||||
\(277\) | 3087.18i | 0.669641i | 0.942282 | + | 0.334821i | \(0.108676\pi\) | ||||
−0.942282 | + | 0.334821i | \(0.891324\pi\) | |||||||
\(278\) | − 4875.87i | − 1.05193i | ||||||||
\(279\) | −2224.63 | −0.477366 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3338.91 | 0.708836 | 0.354418 | − | 0.935087i | \(-0.384679\pi\) | ||||
0.354418 | + | 0.935087i | \(0.384679\pi\) | |||||||
\(282\) | 1289.46i | 0.272292i | ||||||||
\(283\) | 1483.75i | 0.311661i | 0.987784 | + | 0.155830i | \(0.0498054\pi\) | ||||
−0.987784 | + | 0.155830i | \(0.950195\pi\) | |||||||
\(284\) | 104.144 | 0.0217599 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1399.38 | −0.289325 | ||||||||
\(287\) | − 683.474i | − 0.140572i | ||||||||
\(288\) | − 1525.47i | − 0.312116i | ||||||||
\(289\) | 4901.06 | 0.997569 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3598.35 | 0.724877 | ||||||||
\(292\) | 3087.69i | 0.618812i | ||||||||
\(293\) | − 1590.55i | − 0.317137i | −0.987348 | − | 0.158569i | \(-0.949312\pi\) | ||||
0.987348 | − | 0.158569i | \(-0.0506879\pi\) | |||||||
\(294\) | 1042.38 | 0.206778 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 7169.45 | 1.40782 | ||||||||
\(297\) | − 297.000i | − 0.0580259i | ||||||||
\(298\) | 5041.76i | 0.980071i | ||||||||
\(299\) | −820.177 | −0.158636 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −6166.47 | −1.18083 | ||||||||
\(302\) | − 5474.10i | − 1.04304i | ||||||||
\(303\) | − 3028.98i | − 0.574291i | ||||||||
\(304\) | 783.577 | 0.147833 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 59.2943 | 0.0110772 | ||||||||
\(307\) | − 10175.3i | − 1.89164i | −0.324697 | − | 0.945818i | \(-0.605262\pi\) | ||||
0.324697 | − | 0.945818i | \(-0.394738\pi\) | |||||||
\(308\) | 1100.60i | 0.203613i | ||||||||
\(309\) | −3470.09 | −0.638857 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −6258.24 | −1.14107 | −0.570535 | − | 0.821274i | \(-0.693264\pi\) | ||||
−0.570535 | + | 0.821274i | \(0.693264\pi\) | |||||||
\(312\) | − 4719.34i | − 0.856346i | ||||||||
\(313\) | 9592.24i | 1.73222i | 0.499852 | + | 0.866111i | \(0.333388\pi\) | ||||
−0.499852 | + | 0.866111i | \(0.666612\pi\) | |||||||
\(314\) | 1998.88 | 0.359245 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1799.21 | 0.320295 | ||||||||
\(317\) | 10632.3i | 1.88381i | 0.335874 | + | 0.941907i | \(0.390969\pi\) | ||||
−0.335874 | + | 0.941907i | \(0.609031\pi\) | |||||||
\(318\) | 96.2943i | 0.0169809i | ||||||||
\(319\) | 343.009 | 0.0602033 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 1475.57 | 0.256568 | ||||||||
\(322\) | − 537.003i | − 0.0929380i | ||||||||
\(323\) | − 270.373i | − 0.0465758i | ||||||||
\(324\) | 353.619 | 0.0606343 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 3724.90 | 0.632832 | ||||||||
\(327\) | − 4022.30i | − 0.680226i | ||||||||
\(328\) | − 703.015i | − 0.118346i | ||||||||
\(329\) | 5167.28 | 0.865901 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8222.61 | 1.36542 | 0.682712 | − | 0.730687i | \(-0.260800\pi\) | ||||
0.682712 | + | 0.730687i | \(0.260800\pi\) | |||||||
\(332\) | − 2412.45i | − 0.398796i | ||||||||
\(333\) | 2737.15i | 0.450435i | ||||||||
\(334\) | 3976.34 | 0.651424 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 688.627 | 0.111809 | ||||||||
\(337\) | 2947.77i | 0.476484i | 0.971206 | + | 0.238242i | \(0.0765711\pi\) | ||||
−0.971206 | + | 0.238242i | \(0.923429\pi\) | |||||||
\(338\) | − 4300.96i | − 0.692134i | ||||||||
\(339\) | −5547.62 | −0.888806 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2718.99 | 0.431794 | ||||||||
\(342\) | 1342.33i | 0.212237i | ||||||||
\(343\) | 3683.92i | 0.579922i | ||||||||
\(344\) | −6342.77 | −0.994126 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 7624.20 | 1.18462 | ||||||||
\(347\) | − 3322.43i | − 0.513999i | −0.966412 | − | 0.256999i | \(-0.917266\pi\) | ||||
0.966412 | − | 0.256999i | \(-0.0827339\pi\) | |||||||
\(348\) | 408.400i | 0.0629096i | ||||||||
\(349\) | 9199.67 | 1.41102 | 0.705511 | − | 0.708699i | \(-0.250717\pi\) | ||||
0.705511 | + | 0.708699i | \(0.250717\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 1801.75 | 0.273989 | ||||||||
\(352\) | 1864.47i | 0.282319i | ||||||||
\(353\) | − 10105.2i | − 1.52363i | −0.647792 | − | 0.761817i | \(-0.724307\pi\) | ||||
0.647792 | − | 0.761817i | \(-0.275693\pi\) | |||||||
\(354\) | 160.538 | 0.0241031 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 6527.81 | 0.971835 | ||||||||
\(357\) | − 237.611i | − 0.0352261i | ||||||||
\(358\) | − 3901.62i | − 0.575997i | ||||||||
\(359\) | 5236.42 | 0.769826 | 0.384913 | − | 0.922953i | \(-0.374231\pi\) | ||||
0.384913 | + | 0.922953i | \(0.374231\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −738.148 | −0.107617 | ||||||||
\(362\) | 122.576i | 0.0177968i | ||||||||
\(363\) | 363.000i | 0.0524864i | ||||||||
\(364\) | −6676.79 | −0.961426 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 4882.70 | 0.697330 | ||||||||
\(367\) | 9337.95i | 1.32817i | 0.747659 | + | 0.664083i | \(0.231178\pi\) | ||||
−0.747659 | + | 0.664083i | \(0.768822\pi\) | |||||||
\(368\) | − 123.099i | − 0.0174374i | ||||||||
\(369\) | 268.397 | 0.0378650 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 385.882 | 0.0540000 | ||||||||
\(372\) | 3237.33i | 0.451204i | ||||||||
\(373\) | 14256.1i | 1.97896i | 0.144659 | + | 0.989482i | \(0.453791\pi\) | ||||
−0.144659 | + | 0.989482i | \(0.546209\pi\) | |||||||
\(374\) | −72.4708 | −0.0100197 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 5315.02 | 0.728992 | ||||||||
\(377\) | 2080.86i | 0.284270i | ||||||||
\(378\) | 1179.68i | 0.160519i | ||||||||
\(379\) | −1911.19 | −0.259027 | −0.129514 | − | 0.991578i | \(-0.541342\pi\) | ||||
−0.129514 | + | 0.991578i | \(0.541342\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −3060.73 | −0.411564 | ||||||||
\(382\) | 9182.32i | 1.22987i | ||||||||
\(383\) | 1743.91i | 0.232662i | 0.993210 | + | 0.116331i | \(0.0371134\pi\) | ||||
−0.993210 | + | 0.116331i | \(0.962887\pi\) | |||||||
\(384\) | −1761.66 | −0.234112 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 563.917 | 0.0743592 | ||||||||
\(387\) | − 2421.54i | − 0.318072i | ||||||||
\(388\) | − 5236.40i | − 0.685150i | ||||||||
\(389\) | 2734.88 | 0.356462 | 0.178231 | − | 0.983989i | \(-0.442963\pi\) | ||||
0.178231 | + | 0.983989i | \(0.442963\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −42.4752 | −0.00549377 | ||||||||
\(392\) | − 4296.57i | − 0.553596i | ||||||||
\(393\) | 3009.89i | 0.386332i | ||||||||
\(394\) | −4094.87 | −0.523596 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −432.201 | −0.0548458 | ||||||||
\(397\) | 14879.5i | 1.88106i | 0.339709 | + | 0.940530i | \(0.389671\pi\) | ||||
−0.339709 | + | 0.940530i | \(0.610329\pi\) | |||||||
\(398\) | 1670.50i | 0.210388i | ||||||||
\(399\) | 5379.16 | 0.674924 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −11638.2 | −1.44934 | −0.724668 | − | 0.689098i | \(-0.758007\pi\) | ||||
−0.724668 | + | 0.689098i | \(0.758007\pi\) | |||||||
\(402\) | − 210.400i | − 0.0261039i | ||||||||
\(403\) | 16494.7i | 2.03886i | ||||||||
\(404\) | −4407.84 | −0.542817 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1362.43 | −0.166542 | ||||||||
\(407\) | − 3345.41i | − 0.407434i | ||||||||
\(408\) | − 244.405i | − 0.0296564i | ||||||||
\(409\) | −936.594 | −0.113231 | −0.0566157 | − | 0.998396i | \(-0.518031\pi\) | ||||
−0.0566157 | + | 0.998396i | \(0.518031\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 7995.42 | 0.959574 | ||||||||
\(412\) | 5049.76i | 0.603845i | ||||||||
\(413\) | − 643.326i | − 0.0766489i | ||||||||
\(414\) | 210.878 | 0.0250341 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −11310.8 | −1.33307 | ||||||||
\(417\) | − 7672.93i | − 0.901067i | ||||||||
\(418\) | − 1640.63i | − 0.191976i | ||||||||
\(419\) | −128.037 | −0.0149285 | −0.00746425 | − | 0.999972i | \(-0.502376\pi\) | ||||
−0.00746425 | + | 0.999972i | \(0.502376\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −6628.97 | −0.767402 | −0.383701 | − | 0.923457i | \(-0.625351\pi\) | ||||
−0.383701 | + | 0.923457i | \(0.625351\pi\) | |||||||
\(422\) | 2695.61i | 0.310949i | ||||||||
\(423\) | 2029.16i | 0.233242i | ||||||||
\(424\) | 396.915 | 0.0454620 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | −136.432 | −0.0155168 | ||||||||
\(427\) | − 19566.5i | − 2.21754i | ||||||||
\(428\) | − 2147.29i | − 0.242507i | ||||||||
\(429\) | −2202.13 | −0.247832 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 14677.8 | 1.64038 | 0.820192 | − | 0.572089i | \(-0.193867\pi\) | ||||
0.820192 | + | 0.572089i | \(0.193867\pi\) | |||||||
\(432\) | 270.420i | 0.0301171i | ||||||||
\(433\) | − 1150.36i | − 0.127674i | −0.997960 | − | 0.0638369i | \(-0.979666\pi\) | ||||
0.997960 | − | 0.0638369i | \(-0.0203337\pi\) | |||||||
\(434\) | −10799.8 | −1.19448 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5853.35 | −0.642946 | ||||||||
\(437\) | − 961.576i | − 0.105259i | ||||||||
\(438\) | − 4044.97i | − 0.441270i | ||||||||
\(439\) | 9308.30 | 1.01198 | 0.505992 | − | 0.862538i | \(-0.331127\pi\) | ||||
0.505992 | + | 0.862538i | \(0.331127\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 1640.34 | 0.177124 | ||||||||
\(442\) | − 439.643i | − 0.0473115i | ||||||||
\(443\) | − 5689.21i | − 0.610164i | −0.952326 | − | 0.305082i | \(-0.901316\pi\) | ||||
0.952326 | − | 0.305082i | \(-0.0986839\pi\) | |||||||
\(444\) | 3983.17 | 0.425749 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −6416.02 | −0.681183 | ||||||||
\(447\) | 7933.98i | 0.839518i | ||||||||
\(448\) | − 9241.96i | − 0.974646i | ||||||||
\(449\) | 6644.91 | 0.698425 | 0.349212 | − | 0.937044i | \(-0.386449\pi\) | ||||
0.349212 | + | 0.937044i | \(0.386449\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −328.041 | −0.0342502 | ||||||||
\(452\) | 8073.02i | 0.840095i | ||||||||
\(453\) | − 8614.33i | − 0.893458i | ||||||||
\(454\) | −10912.8 | −1.12811 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 5532.95 | 0.568211 | ||||||||
\(457\) | 8355.11i | 0.855220i | 0.903963 | + | 0.427610i | \(0.140644\pi\) | ||||
−0.903963 | + | 0.427610i | \(0.859356\pi\) | |||||||
\(458\) | − 4931.33i | − 0.503114i | ||||||||
\(459\) | 93.3087 | 0.00948862 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −15580.5 | −1.57409 | −0.787044 | − | 0.616897i | \(-0.788389\pi\) | ||||
−0.787044 | + | 0.616897i | \(0.788389\pi\) | |||||||
\(462\) | − 1441.83i | − 0.145195i | ||||||||
\(463\) | 7139.16i | 0.716598i | 0.933607 | + | 0.358299i | \(0.116643\pi\) | ||||
−0.933607 | + | 0.358299i | \(0.883357\pi\) | |||||||
\(464\) | −312.312 | −0.0312473 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −10621.7 | −1.05588 | ||||||||
\(467\) | 12415.1i | 1.23019i | 0.788451 | + | 0.615097i | \(0.210883\pi\) | ||||
−0.788451 | + | 0.615097i | \(0.789117\pi\) | |||||||
\(468\) | − 2621.94i | − 0.258973i | ||||||||
\(469\) | −843.139 | −0.0830118 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 3145.54 | 0.307726 | ||||||||
\(472\) | − 661.719i | − 0.0645299i | ||||||||
\(473\) | 2959.66i | 0.287707i | ||||||||
\(474\) | −2357.02 | −0.228400 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −345.777 | −0.0332955 | ||||||||
\(477\) | 151.534i | 0.0145456i | ||||||||
\(478\) | 3475.21i | 0.332536i | ||||||||
\(479\) | 14151.0 | 1.34985 | 0.674925 | − | 0.737887i | \(-0.264176\pi\) | ||||
0.674925 | + | 0.737887i | \(0.264176\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 20294.9 | 1.92384 | ||||||||
\(482\) | − 4244.88i | − 0.401139i | ||||||||
\(483\) | − 845.057i | − 0.0796096i | ||||||||
\(484\) | 528.246 | 0.0496099 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −463.253 | −0.0432378 | ||||||||
\(487\) | 76.6358i | 0.00713080i | 0.999994 | + | 0.00356540i | \(0.00113490\pi\) | ||||
−0.999994 | + | 0.00356540i | \(0.998865\pi\) | |||||||
\(488\) | − 20126.0i | − 1.86693i | ||||||||
\(489\) | 5861.71 | 0.542077 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1707.54 | −0.156945 | −0.0784725 | − | 0.996916i | \(-0.525004\pi\) | ||||
−0.0784725 | + | 0.996916i | \(0.525004\pi\) | |||||||
\(492\) | − 390.577i | − 0.0357898i | ||||||||
\(493\) | 107.763i | 0.00984467i | ||||||||
\(494\) | 9952.86 | 0.906479 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −2475.66 | −0.224114 | ||||||||
\(497\) | 546.728i | 0.0493443i | ||||||||
\(498\) | 3160.39i | 0.284379i | ||||||||
\(499\) | 13168.5 | 1.18137 | 0.590686 | − | 0.806902i | \(-0.298857\pi\) | ||||
0.590686 | + | 0.806902i | \(0.298857\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 6257.38 | 0.558002 | ||||||||
\(502\) | 15038.0i | 1.33701i | ||||||||
\(503\) | − 1525.32i | − 0.135210i | −0.997712 | − | 0.0676052i | \(-0.978464\pi\) | ||||
0.997712 | − | 0.0676052i | \(-0.0215358\pi\) | |||||||
\(504\) | 4862.50 | 0.429748 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −257.740 | −0.0226442 | ||||||||
\(507\) | − 6768.22i | − 0.592874i | ||||||||
\(508\) | 4454.05i | 0.389009i | ||||||||
\(509\) | −9006.01 | −0.784253 | −0.392126 | − | 0.919911i | \(-0.628260\pi\) | ||||
−0.392126 | + | 0.919911i | \(0.628260\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −16209.5 | −1.40326 | ||||||||
\(512\) | − 3586.45i | − 0.309571i | ||||||||
\(513\) | 2112.37i | 0.181800i | ||||||||
\(514\) | −9065.51 | −0.777942 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −3523.88 | −0.300640 | ||||||||
\(517\) | − 2480.09i | − 0.210975i | ||||||||
\(518\) | 13287.9i | 1.12710i | ||||||||
\(519\) | 11997.8 | 1.01473 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 21707.8 | 1.82541 | 0.912703 | − | 0.408623i | \(-0.133991\pi\) | ||||
0.912703 | + | 0.408623i | \(0.133991\pi\) | |||||||
\(522\) | − 535.018i | − 0.0448603i | ||||||||
\(523\) | − 14015.0i | − 1.17177i | −0.810396 | − | 0.585883i | \(-0.800748\pi\) | ||||
0.810396 | − | 0.585883i | \(-0.199252\pi\) | |||||||
\(524\) | 4380.06 | 0.365160 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 197.191 | 0.0163459 | ||||||||
\(527\) | 854.227i | 0.0706086i | ||||||||
\(528\) | − 330.514i | − 0.0272420i | ||||||||
\(529\) | 12015.9 | 0.987584 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 252.631 | 0.0206464 | ||||||||
\(532\) | − 7827.88i | − 0.637935i | ||||||||
\(533\) | − 1990.05i | − 0.161724i | ||||||||
\(534\) | −8551.65 | −0.693008 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −867.244 | −0.0698867 | ||||||||
\(537\) | − 6139.79i | − 0.493392i | ||||||||
\(538\) | 4154.98i | 0.332963i | ||||||||
\(539\) | −2004.86 | −0.160214 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 14444.9 | 1.14793 | 0.573967 | − | 0.818878i | \(-0.305404\pi\) | ||||
0.573967 | + | 0.818878i | \(0.305404\pi\) | |||||||
\(542\) | − 7031.80i | − 0.557273i | ||||||||
\(543\) | 192.892i | 0.0152445i | ||||||||
\(544\) | −585.760 | −0.0461659 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 8746.83 | 0.685585 | ||||||||
\(547\) | − 20286.4i | − 1.58571i | −0.609412 | − | 0.792854i | \(-0.708594\pi\) | ||||
0.609412 | − | 0.792854i | \(-0.291406\pi\) | |||||||
\(548\) | − 11635.1i | − 0.906985i | ||||||||
\(549\) | 7683.68 | 0.597325 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2439.60 | −0.188622 | ||||||||
\(552\) | − 869.218i | − 0.0670224i | ||||||||
\(553\) | 9445.34i | 0.726323i | ||||||||
\(554\) | −5885.38 | −0.451346 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −11165.8 | −0.851684 | ||||||||
\(557\) | 24482.4i | 1.86239i | 0.364520 | + | 0.931196i | \(0.381233\pi\) | ||||
−0.364520 | + | 0.931196i | \(0.618767\pi\) | |||||||
\(558\) | − 4241.02i | − 0.321750i | ||||||||
\(559\) | −17954.7 | −1.35851 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −114.044 | −0.00858278 | ||||||||
\(562\) | 6365.27i | 0.477763i | ||||||||
\(563\) | − 20383.5i | − 1.52587i | −0.646478 | − | 0.762933i | \(-0.723759\pi\) | ||||
0.646478 | − | 0.762933i | \(-0.276241\pi\) | |||||||
\(564\) | 2952.89 | 0.220459 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −2828.62 | −0.210063 | ||||||||
\(567\) | 1856.40i | 0.137498i | ||||||||
\(568\) | 562.359i | 0.0415424i | ||||||||
\(569\) | −3297.74 | −0.242967 | −0.121484 | − | 0.992593i | \(-0.538765\pi\) | ||||
−0.121484 | + | 0.992593i | \(0.538765\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7213.03 | −0.528644 | −0.264322 | − | 0.964434i | \(-0.585148\pi\) | ||||
−0.264322 | + | 0.964434i | \(0.585148\pi\) | |||||||
\(572\) | 3204.60i | 0.234250i | ||||||||
\(573\) | 14449.8i | 1.05349i | ||||||||
\(574\) | 1302.97 | 0.0947472 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 3629.27 | 0.262534 | ||||||||
\(577\) | 18080.4i | 1.30450i | 0.758003 | + | 0.652251i | \(0.226175\pi\) | ||||
−0.758003 | + | 0.652251i | \(0.773825\pi\) | |||||||
\(578\) | 9343.34i | 0.672373i | ||||||||
\(579\) | 887.411 | 0.0636952 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 12664.7 | 0.904337 | ||||||||
\(582\) | 6859.87i | 0.488575i | ||||||||
\(583\) | − 185.208i | − 0.0131570i | ||||||||
\(584\) | −16672.9 | −1.18139 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 3032.22 | 0.213754 | ||||||||
\(587\) | − 13457.5i | − 0.946250i | −0.880995 | − | 0.473125i | \(-0.843126\pi\) | ||||
0.880995 | − | 0.473125i | \(-0.156874\pi\) | |||||||
\(588\) | − 2387.06i | − 0.167416i | ||||||||
\(589\) | −19338.4 | −1.35285 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −6443.91 | −0.448506 | ||||||||
\(592\) | 3046.01i | 0.211470i | ||||||||
\(593\) | − 10262.3i | − 0.710665i | −0.934740 | − | 0.355332i | \(-0.884368\pi\) | ||||
0.934740 | − | 0.355332i | \(-0.115632\pi\) | |||||||
\(594\) | 566.198 | 0.0391101 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 11545.7 | 0.793508 | ||||||||
\(597\) | 2628.78i | 0.180216i | ||||||||
\(598\) | − 1563.58i | − 0.106922i | ||||||||
\(599\) | −23153.3 | −1.57933 | −0.789665 | − | 0.613538i | \(-0.789746\pi\) | ||||
−0.789665 | + | 0.613538i | \(0.789746\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14414.8 | 0.978357 | 0.489178 | − | 0.872184i | \(-0.337297\pi\) | ||||
0.489178 | + | 0.872184i | \(0.337297\pi\) | |||||||
\(602\) | − 11755.7i | − 0.795891i | ||||||||
\(603\) | − 331.096i | − 0.0223603i | ||||||||
\(604\) | −12535.8 | −0.844492 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 5774.42 | 0.387079 | ||||||||
\(607\) | − 10808.8i | − 0.722757i | −0.932419 | − | 0.361379i | \(-0.882306\pi\) | ||||
0.932419 | − | 0.361379i | \(-0.117694\pi\) | |||||||
\(608\) | − 13260.7i | − 0.884530i | ||||||||
\(609\) | −2143.99 | −0.142658 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 15045.4 | 0.996191 | ||||||||
\(612\) | − 135.785i | − 0.00896860i | ||||||||
\(613\) | 12072.8i | 0.795455i | 0.917504 | + | 0.397727i | \(0.130201\pi\) | ||||
−0.917504 | + | 0.397727i | \(0.869799\pi\) | |||||||
\(614\) | 19398.0 | 1.27498 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −5943.06 | −0.388722 | ||||||||
\(617\) | − 11593.5i | − 0.756462i | −0.925711 | − | 0.378231i | \(-0.876532\pi\) | ||||
0.925711 | − | 0.378231i | \(-0.123468\pi\) | |||||||
\(618\) | − 6615.36i | − 0.430597i | ||||||||
\(619\) | −4037.96 | −0.262196 | −0.131098 | − | 0.991369i | \(-0.541850\pi\) | ||||
−0.131098 | + | 0.991369i | \(0.541850\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 331.850 | 0.0214439 | ||||||||
\(622\) | − 11930.7i | − 0.769094i | ||||||||
\(623\) | 34269.2i | 2.20380i | ||||||||
\(624\) | 2005.06 | 0.128632 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −18286.6 | −1.16754 | ||||||||
\(627\) | − 2581.78i | − 0.164444i | ||||||||
\(628\) | − 4577.46i | − 0.290861i | ||||||||
\(629\) | 1051.03 | 0.0666252 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2896.22 | 0.182721 | 0.0913604 | − | 0.995818i | \(-0.470878\pi\) | ||||
0.0913604 | + | 0.995818i | \(0.470878\pi\) | |||||||
\(632\) | 9715.39i | 0.611483i | ||||||||
\(633\) | 4241.96i | 0.266355i | ||||||||
\(634\) | −20269.3 | −1.26971 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 220.516 | 0.0137484 | ||||||||
\(637\) | − 12162.5i | − 0.756506i | ||||||||
\(638\) | 653.910i | 0.0405777i | ||||||||
\(639\) | −214.697 | −0.0132915 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 13371.2 | 0.823916 | 0.411958 | − | 0.911203i | \(-0.364845\pi\) | ||||
0.411958 | + | 0.911203i | \(0.364845\pi\) | |||||||
\(642\) | 2813.02i | 0.172930i | ||||||||
\(643\) | 14063.6i | 0.862544i | 0.902222 | + | 0.431272i | \(0.141935\pi\) | ||||
−0.902222 | + | 0.431272i | \(0.858065\pi\) | |||||||
\(644\) | −1229.75 | −0.0752466 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 515.438 | 0.0313926 | ||||||||
\(647\) | − 20899.7i | − 1.26994i | −0.772536 | − | 0.634971i | \(-0.781012\pi\) | ||||
0.772536 | − | 0.634971i | \(-0.218988\pi\) | |||||||
\(648\) | 1909.48i | 0.115758i | ||||||||
\(649\) | −308.771 | −0.0186754 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −16995.1 | −1.02318 | ||||||||
\(652\) | − 8530.09i | − 0.512368i | ||||||||
\(653\) | − 1607.80i | − 0.0963523i | −0.998839 | − | 0.0481761i | \(-0.984659\pi\) | ||||
0.998839 | − | 0.0481761i | \(-0.0153409\pi\) | |||||||
\(654\) | 7668.08 | 0.458480 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 298.683 | 0.0177768 | ||||||||
\(657\) | − 6365.39i | − 0.377987i | ||||||||
\(658\) | 9850.86i | 0.583627i | ||||||||
\(659\) | −14733.1 | −0.870896 | −0.435448 | − | 0.900214i | \(-0.643410\pi\) | ||||
−0.435448 | + | 0.900214i | \(0.643410\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −16442.2 | −0.967518 | −0.483759 | − | 0.875201i | \(-0.660729\pi\) | ||||
−0.483759 | + | 0.875201i | \(0.660729\pi\) | |||||||
\(662\) | 15675.5i | 0.920312i | ||||||||
\(663\) | − 691.846i | − 0.0405265i | ||||||||
\(664\) | 13026.8 | 0.761351 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5218.08 | −0.303598 | ||||||||
\(667\) | 383.258i | 0.0222486i | ||||||||
\(668\) | − 9105.88i | − 0.527421i | ||||||||
\(669\) | −10096.6 | −0.583493 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9391.16 | −0.540301 | ||||||||
\(672\) | − 11653.9i | − 0.668985i | ||||||||
\(673\) | − 25246.6i | − 1.44604i | −0.690826 | − | 0.723021i | \(-0.742753\pi\) | ||||
0.690826 | − | 0.723021i | \(-0.257247\pi\) | |||||||
\(674\) | −5619.60 | −0.321156 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9849.26 | −0.560381 | ||||||||
\(677\) | − 24582.6i | − 1.39555i | −0.716318 | − | 0.697774i | \(-0.754174\pi\) | ||||
0.716318 | − | 0.697774i | \(-0.245826\pi\) | |||||||
\(678\) | − 10575.9i | − 0.599065i | ||||||||
\(679\) | 27489.7 | 1.55369 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −17172.9 | −0.966327 | ||||||||
\(682\) | 5183.46i | 0.291034i | ||||||||
\(683\) | 11459.5i | 0.642000i | 0.947079 | + | 0.321000i | \(0.104019\pi\) | ||||
−0.947079 | + | 0.321000i | \(0.895981\pi\) | |||||||
\(684\) | 3073.97 | 0.171836 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −7023.00 | −0.390874 | ||||||||
\(687\) | − 7760.21i | − 0.430961i | ||||||||
\(688\) | − 2694.79i | − 0.149328i | ||||||||
\(689\) | 1123.56 | 0.0621253 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15683.8 | −0.863445 | −0.431723 | − | 0.902006i | \(-0.642094\pi\) | ||||
−0.431723 | + | 0.902006i | \(0.642094\pi\) | |||||||
\(692\) | − 17459.5i | − 0.959121i | ||||||||
\(693\) | − 2268.94i | − 0.124372i | ||||||||
\(694\) | 6333.86 | 0.346441 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −2205.28 | −0.120102 | ||||||||
\(697\) | − 103.061i | − 0.00560072i | ||||||||
\(698\) | 17538.2i | 0.951045i | ||||||||
\(699\) | −16714.9 | −0.904457 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 6185.65 | 0.333279 | 0.166640 | − | 0.986018i | \(-0.446708\pi\) | ||||
0.166640 | + | 0.986018i | \(0.446708\pi\) | |||||||
\(702\) | 3434.83i | 0.184672i | ||||||||
\(703\) | 23793.7i | 1.27652i | ||||||||
\(704\) | −4435.77 | −0.237471 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 19264.4 | 1.02695 | ||||||||
\(707\) | − 23139.9i | − 1.23093i | ||||||||
\(708\) | − 367.634i | − 0.0195149i | ||||||||
\(709\) | 28031.2 | 1.48481 | 0.742407 | − | 0.669950i | \(-0.233684\pi\) | ||||
0.742407 | + | 0.669950i | \(0.233684\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3709.14 | −0.195645 | ||||||||
\(712\) | 35249.0i | 1.85535i | ||||||||
\(713\) | 3038.03i | 0.159573i | ||||||||
\(714\) | 452.980 | 0.0237428 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8934.77 | −0.466352 | ||||||||
\(717\) | 5468.77i | 0.284847i | ||||||||
\(718\) | 9982.67i | 0.518872i | ||||||||
\(719\) | −23313.0 | −1.20922 | −0.604610 | − | 0.796522i | \(-0.706671\pi\) | ||||
−0.604610 | + | 0.796522i | \(0.706671\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −26509.9 | −1.36932 | ||||||||
\(722\) | − 1407.20i | − 0.0725354i | ||||||||
\(723\) | − 6679.98i | − 0.343611i | ||||||||
\(724\) | 280.701 | 0.0144091 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −692.020 | −0.0353764 | ||||||||
\(727\) | 69.6810i | 0.00355478i | 0.999998 | + | 0.00177739i | \(0.000565761\pi\) | ||||
−0.999998 | + | 0.00177739i | \(0.999434\pi\) | |||||||
\(728\) | − 36053.5i | − 1.83548i | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −929.838 | −0.0470469 | ||||||||
\(732\) | − 11181.5i | − 0.564589i | ||||||||
\(733\) | 15152.9i | 0.763552i | 0.924255 | + | 0.381776i | \(0.124687\pi\) | ||||
−0.924255 | + | 0.381776i | \(0.875313\pi\) | |||||||
\(734\) | −17801.8 | −0.895199 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2083.24 | −0.104333 | ||||||||
\(737\) | 404.673i | 0.0202257i | ||||||||
\(738\) | 511.669i | 0.0255214i | ||||||||
\(739\) | 31557.9 | 1.57087 | 0.785437 | − | 0.618941i | \(-0.212438\pi\) | ||||
0.785437 | + | 0.618941i | \(0.212438\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 15662.4 | 0.776479 | ||||||||
\(742\) | 735.642i | 0.0363966i | ||||||||
\(743\) | 6925.00i | 0.341929i | 0.985277 | + | 0.170965i | \(0.0546884\pi\) | ||||
−0.985277 | + | 0.170965i | \(0.945312\pi\) | |||||||
\(744\) | −17481.0 | −0.861404 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −27177.7 | −1.33384 | ||||||||
\(747\) | 4973.36i | 0.243595i | ||||||||
\(748\) | 165.959i | 0.00811240i | ||||||||
\(749\) | 11272.7 | 0.549925 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −22202.1 | −1.07878 | −0.539392 | − | 0.842055i | \(-0.681346\pi\) | ||||
−0.539392 | + | 0.842055i | \(0.681346\pi\) | |||||||
\(752\) | 2258.14i | 0.109502i | ||||||||
\(753\) | 23664.7i | 1.14527i | ||||||||
\(754\) | −3966.94 | −0.191601 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2701.48 | 0.129963 | ||||||||
\(757\) | − 18928.6i | − 0.908813i | −0.890795 | − | 0.454406i | \(-0.849851\pi\) | ||||
0.890795 | − | 0.454406i | \(-0.150149\pi\) | |||||||
\(758\) | − 3643.48i | − 0.174587i | ||||||||
\(759\) | −405.594 | −0.0193967 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −22883.3 | −1.09004 | −0.545019 | − | 0.838423i | \(-0.683478\pi\) | ||||
−0.545019 | + | 0.838423i | \(0.683478\pi\) | |||||||
\(762\) | − 5834.95i | − 0.277399i | ||||||||
\(763\) | − 30728.4i | − 1.45799i | ||||||||
\(764\) | 21027.7 | 0.995752 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −3324.57 | −0.156817 | ||||||||
\(767\) | − 1873.16i | − 0.0881822i | ||||||||
\(768\) | − 13036.5i | − 0.612516i | ||||||||
\(769\) | −8903.82 | −0.417529 | −0.208765 | − | 0.977966i | \(-0.566944\pi\) | ||||
−0.208765 | + | 0.977966i | \(0.566944\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −14266.0 | −0.666376 | ||||||||
\(772\) | − 1291.38i | − 0.0602044i | ||||||||
\(773\) | 24691.9i | 1.14891i | 0.818537 | + | 0.574454i | \(0.194786\pi\) | ||||
−0.818537 | + | 0.574454i | \(0.805214\pi\) | |||||||
\(774\) | 4616.40 | 0.214384 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 28275.6 | 1.30804 | ||||||||
\(777\) | 20910.5i | 0.965457i | ||||||||
\(778\) | 5213.75i | 0.240259i | ||||||||
\(779\) | 2333.14 | 0.107309 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 262.408 | 0.0120226 | ||||||||
\(782\) | − 80.9744i | − 0.00370286i | ||||||||
\(783\) | − 841.932i | − 0.0384268i | ||||||||
\(784\) | 1825.44 | 0.0831559 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −5738.02 | −0.260392 | ||||||||
\(787\) | 7418.83i | 0.336026i | 0.985785 | + | 0.168013i | \(0.0537351\pi\) | ||||
−0.985785 | + | 0.168013i | \(0.946265\pi\) | |||||||
\(788\) | 9377.33i | 0.423926i | ||||||||
\(789\) | 310.311 | 0.0140017 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −42381.1 | −1.90506 | ||||||||
\(792\) | − 2333.81i | − 0.104707i | ||||||||
\(793\) | − 56971.4i | − 2.55121i | ||||||||
\(794\) | −28366.2 | −1.26786 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3825.46 | 0.170339 | ||||||||
\(797\) | 27971.2i | 1.24315i | 0.783354 | + | 0.621576i | \(0.213507\pi\) | ||||
−0.783354 | + | 0.621576i | \(0.786493\pi\) | |||||||
\(798\) | 10254.8i | 0.454907i | ||||||||
\(799\) | 779.171 | 0.0344995 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −13457.3 | −0.593622 | ||||||||
\(802\) | − 22187.0i | − 0.976869i | ||||||||
\(803\) | 7779.92i | 0.341902i | ||||||||
\(804\) | −481.819 | −0.0211349 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −31445.4 | −1.37421 | ||||||||
\(807\) | 6538.51i | 0.285212i | ||||||||
\(808\) | − 23801.5i | − 1.03630i | ||||||||
\(809\) | 10670.0 | 0.463704 | 0.231852 | − | 0.972751i | \(-0.425521\pi\) | ||||
0.231852 | + | 0.972751i | \(0.425521\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 40618.3 | 1.75869 | 0.879346 | − | 0.476182i | \(-0.157980\pi\) | ||||
0.879346 | + | 0.476182i | \(0.157980\pi\) | |||||||
\(812\) | 3119.98i | 0.134840i | ||||||||
\(813\) | − 11065.6i | − 0.477353i | ||||||||
\(814\) | 6377.66 | 0.274615 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 103.838 | 0.00445471 | ||||||||
\(817\) | − 21050.1i | − 0.901409i | ||||||||
\(818\) | − 1785.52i | − 0.0763192i | ||||||||
\(819\) | 13764.5 | 0.587265 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 16710.5 | 0.710355 | 0.355178 | − | 0.934799i | \(-0.384420\pi\) | ||||
0.355178 | + | 0.934799i | \(0.384420\pi\) | |||||||
\(822\) | 15242.4i | 0.646764i | ||||||||
\(823\) | − 16920.5i | − 0.716661i | −0.933595 | − | 0.358331i | \(-0.883346\pi\) | ||||
0.933595 | − | 0.358331i | \(-0.116654\pi\) | |||||||
\(824\) | −27267.8 | −1.15281 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1226.43 | 0.0516623 | ||||||||
\(827\) | 9478.39i | 0.398544i | 0.979944 | + | 0.199272i | \(0.0638577\pi\) | ||||
−0.979944 | + | 0.199272i | \(0.936142\pi\) | |||||||
\(828\) | − 482.915i | − 0.0202687i | ||||||||
\(829\) | 31908.1 | 1.33681 | 0.668405 | − | 0.743798i | \(-0.266977\pi\) | ||||
0.668405 | + | 0.743798i | \(0.266977\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −9261.54 | −0.386618 | ||||||||
\(832\) | − 26909.6i | − 1.12130i | ||||||||
\(833\) | − 629.869i | − 0.0261989i | ||||||||
\(834\) | 14627.6 | 0.607329 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3757.07 | −0.155432 | ||||||||
\(837\) | − 6673.89i | − 0.275607i | ||||||||
\(838\) | − 244.090i | − 0.0100620i | ||||||||
\(839\) | −25195.7 | −1.03677 | −0.518386 | − | 0.855147i | \(-0.673467\pi\) | ||||
−0.518386 | + | 0.855147i | \(0.673467\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −23416.6 | −0.960131 | ||||||||
\(842\) | − 12637.4i | − 0.517238i | ||||||||
\(843\) | 10016.7i | 0.409246i | ||||||||
\(844\) | 6173.00 | 0.251758 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −3868.38 | −0.157208 | ||||||||
\(847\) | 2773.15i | 0.112499i | ||||||||
\(848\) | 168.633i | 0.00682887i | ||||||||
\(849\) | −4451.26 | −0.179938 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3737.95 | 0.150570 | ||||||||
\(852\) | 312.432i | 0.0125631i | ||||||||
\(853\) | 8239.19i | 0.330720i | 0.986233 | + | 0.165360i | \(0.0528786\pi\) | ||||
−0.986233 | + | 0.165360i | \(0.947121\pi\) | |||||||
\(854\) | 37301.5 | 1.49465 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 11594.9 | 0.462976 | ||||||||
\(857\) | − 12912.8i | − 0.514694i | −0.966319 | − | 0.257347i | \(-0.917152\pi\) | ||||
0.966319 | − | 0.257347i | \(-0.0828484\pi\) | |||||||
\(858\) | − 4198.13i | − 0.167042i | ||||||||
\(859\) | −18534.6 | −0.736196 | −0.368098 | − | 0.929787i | \(-0.619991\pi\) | ||||
−0.368098 | + | 0.929787i | \(0.619991\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2050.42 | 0.0811594 | ||||||||
\(862\) | 27981.7i | 1.10564i | ||||||||
\(863\) | − 18743.4i | − 0.739318i | −0.929168 | − | 0.369659i | \(-0.879475\pi\) | ||||
0.929168 | − | 0.369659i | \(-0.120525\pi\) | |||||||
\(864\) | 4576.42 | 0.180200 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 2193.04 | 0.0860536 | ||||||||
\(867\) | 14703.2i | 0.575947i | ||||||||
\(868\) | 24731.7i | 0.967105i | ||||||||
\(869\) | 4533.39 | 0.176967 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2454.94 | −0.0955024 | ||||||||
\(872\) | − 31607.0i | − 1.22746i | ||||||||
\(873\) | 10795.1i | 0.418508i | ||||||||
\(874\) | 1833.14 | 0.0709461 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −9263.06 | −0.357272 | ||||||||
\(877\) | − 25629.7i | − 0.986833i | −0.869793 | − | 0.493417i | \(-0.835748\pi\) | ||||
0.869793 | − | 0.493417i | \(-0.164252\pi\) | |||||||
\(878\) | 17745.3i | 0.682088i | ||||||||
\(879\) | 4771.66 | 0.183099 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 14336.5 | 0.548250 | 0.274125 | − | 0.961694i | \(-0.411612\pi\) | ||||
0.274125 | + | 0.961694i | \(0.411612\pi\) | |||||||
\(882\) | 3127.13i | 0.119383i | ||||||||
\(883\) | 1012.36i | 0.0385827i | 0.999814 | + | 0.0192914i | \(0.00614102\pi\) | ||||
−0.999814 | + | 0.0192914i | \(0.993859\pi\) | |||||||
\(884\) | −1006.79 | −0.0383054 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 10845.9 | 0.411258 | ||||||||
\(887\) | 2586.40i | 0.0979061i | 0.998801 | + | 0.0489530i | \(0.0155885\pi\) | ||||
−0.998801 | + | 0.0489530i | \(0.984412\pi\) | |||||||
\(888\) | 21508.4i | 0.812808i | ||||||||
\(889\) | −23382.5 | −0.882142 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 891.000 | 0.0335013 | ||||||||
\(892\) | 14692.8i | 0.551515i | ||||||||
\(893\) | 17639.3i | 0.661003i | ||||||||
\(894\) | −15125.3 | −0.565844 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −13458.2 | −0.501794 | ||||||||
\(897\) | − 2460.53i | − 0.0915883i | ||||||||
\(898\) | 12667.8i | 0.470746i | ||||||||
\(899\) | 7707.77 | 0.285949 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 58.1869 | 0.00215148 | ||||||||
\(902\) | − 625.374i | − 0.0230850i | ||||||||
\(903\) | − 18499.4i | − 0.681751i | ||||||||
\(904\) | −43592.8 | −1.60385 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 16422.3 | 0.602201 | ||||||||
\(907\) | − 43346.1i | − 1.58686i | −0.608660 | − | 0.793431i | \(-0.708293\pi\) | ||||
0.608660 | − | 0.793431i | \(-0.291707\pi\) | |||||||
\(908\) | 24990.5i | 0.913368i | ||||||||
\(909\) | 9086.93 | 0.331567 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −5218.71 | −0.189796 | −0.0948978 | − | 0.995487i | \(-0.530252\pi\) | ||||
−0.0948978 | + | 0.995487i | \(0.530252\pi\) | |||||||
\(912\) | 2350.73i | 0.0853514i | ||||||||
\(913\) | − 6078.55i | − 0.220340i | ||||||||
\(914\) | −15928.1 | −0.576428 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −11292.8 | −0.407343 | ||||||||
\(917\) | 22994.1i | 0.828060i | ||||||||
\(918\) | 177.883i | 0.00639544i | ||||||||
\(919\) | 29209.5 | 1.04846 | 0.524230 | − | 0.851577i | \(-0.324353\pi\) | ||||
0.524230 | + | 0.851577i | \(0.324353\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 30525.8 | 1.09214 | ||||||||
\(922\) | − 29702.5i | − 1.06095i | ||||||||
\(923\) | 1591.89i | 0.0567690i | ||||||||
\(924\) | −3301.81 | −0.117556 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −13610.0 | −0.482995 | ||||||||
\(927\) | − 10410.3i | − 0.368844i | ||||||||
\(928\) | 5285.37i | 0.186962i | ||||||||
\(929\) | 39401.0 | 1.39150 | 0.695751 | − | 0.718283i | \(-0.255072\pi\) | ||||
0.695751 | + | 0.718283i | \(0.255072\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14259.3 | 0.501965 | ||||||||
\(932\) | 24323.9i | 0.854888i | ||||||||
\(933\) | − 18774.7i | − 0.658797i | ||||||||
\(934\) | −23668.0 | −0.829165 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 14158.0 | 0.494411 | ||||||||
\(937\) | − 6099.66i | − 0.212665i | −0.994331 | − | 0.106332i | \(-0.966089\pi\) | ||||
0.994331 | − | 0.106332i | \(-0.0339108\pi\) | |||||||
\(938\) | − 1607.35i | − 0.0559509i | ||||||||
\(939\) | −28776.7 | −1.00010 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 11534.4 | 0.399587 | 0.199793 | − | 0.979838i | \(-0.435973\pi\) | ||||
0.199793 | + | 0.979838i | \(0.435973\pi\) | |||||||
\(942\) | 5996.63i | 0.207410i | ||||||||
\(943\) | − 366.532i | − 0.0126574i | ||||||||
\(944\) | 281.138 | 0.00969307 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5642.27 | −0.193918 | ||||||||
\(947\) | 16680.4i | 0.572376i | 0.958174 | + | 0.286188i | \(0.0923881\pi\) | ||||
−0.958174 | + | 0.286188i | \(0.907612\pi\) | |||||||
\(948\) | 5397.62i | 0.184923i | ||||||||
\(949\) | −47196.8 | −1.61441 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −31896.9 | −1.08762 | ||||||||
\(952\) | − 1867.13i | − 0.0635653i | ||||||||
\(953\) | − 17114.4i | − 0.581733i | −0.956764 | − | 0.290866i | \(-0.906057\pi\) | ||||
0.956764 | − | 0.290866i | \(-0.0939435\pi\) | |||||||
\(954\) | −288.883 | −0.00980391 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 7958.29 | 0.269236 | ||||||||
\(957\) | 1029.03i | 0.0347584i | ||||||||
\(958\) | 26977.4i | 0.909814i | ||||||||
\(959\) | 61081.2 | 2.05674 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 31307.5 | 1.05090 | ||||||||
\(962\) | 38690.0i | 1.29669i | ||||||||
\(963\) | 4426.71i | 0.148130i | ||||||||
\(964\) | −9720.86 | −0.324780 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 1611.01 | 0.0536578 | ||||||||
\(967\) | 35200.4i | 1.17060i | 0.810817 | + | 0.585299i | \(0.199023\pi\) | ||||
−0.810817 | + | 0.585299i | \(0.800977\pi\) | |||||||
\(968\) | 2852.43i | 0.0947114i | ||||||||
\(969\) | 811.120 | 0.0268906 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −43502.6 | −1.43776 | −0.718881 | − | 0.695134i | \(-0.755345\pi\) | ||||
−0.718881 | + | 0.695134i | \(0.755345\pi\) | |||||||
\(972\) | 1060.86i | 0.0350072i | ||||||||
\(973\) | − 58617.5i | − 1.93134i | ||||||||
\(974\) | −146.098 | −0.00480624 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 8550.71 | 0.280432 | ||||||||
\(977\) | 5365.50i | 0.175699i | 0.996134 | + | 0.0878494i | \(0.0279994\pi\) | ||||
−0.996134 | + | 0.0878494i | \(0.972001\pi\) | |||||||
\(978\) | 11174.7i | 0.365366i | ||||||||
\(979\) | 16447.9 | 0.536952 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 12066.9 | 0.392728 | ||||||||
\(982\) | − 3255.23i | − 0.105783i | ||||||||
\(983\) | 42459.0i | 1.37765i | 0.724926 | + | 0.688826i | \(0.241874\pi\) | ||||
−0.724926 | + | 0.688826i | \(0.758126\pi\) | |||||||
\(984\) | 2109.05 | 0.0683271 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −205.439 | −0.00663542 | ||||||||
\(987\) | 15501.8i | 0.499928i | ||||||||
\(988\) | − 22792.2i | − 0.733924i | ||||||||
\(989\) | −3306.94 | −0.106324 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −6881.29 | −0.220576 | −0.110288 | − | 0.993900i | \(-0.535177\pi\) | ||||
−0.110288 | + | 0.993900i | \(0.535177\pi\) | |||||||
\(992\) | 41896.4i | 1.34094i | ||||||||
\(993\) | 24667.8i | 0.788328i | ||||||||
\(994\) | −1042.28 | −0.0332586 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 7237.35 | 0.230245 | ||||||||
\(997\) | 3166.87i | 0.100597i | 0.998734 | + | 0.0502987i | \(0.0160173\pi\) | ||||
−0.998734 | + | 0.0502987i | \(0.983983\pi\) | |||||||
\(998\) | 25104.4i | 0.796258i | ||||||||
\(999\) | −8211.45 | −0.260059 |
(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 | 825.4.c.k.199.4 | 6 | ||
5.2 | odd | 4 | 165.4.a.e.1.2 | ✓ | 3 | ||
5.3 | odd | 4 | 825.4.a.r.1.2 | 3 | |||
5.4 | even | 2 | inner | 825.4.c.k.199.3 | 6 | ||
15.2 | even | 4 | 495.4.a.k.1.2 | 3 | |||
15.8 | even | 4 | 2475.4.a.t.1.2 | 3 | |||
55.32 | even | 4 | 1815.4.a.r.1.2 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
165.4.a.e.1.2 | ✓ | 3 | 5.2 | odd | 4 | ||
495.4.a.k.1.2 | 3 | 15.2 | even | 4 | |||
825.4.a.r.1.2 | 3 | 5.3 | odd | 4 | |||
825.4.c.k.199.3 | 6 | 5.4 | even | 2 | inner | ||
825.4.c.k.199.4 | 6 | 1.1 | even | 1 | trivial | ||
1815.4.a.r.1.2 | 3 | 55.32 | even | 4 | |||
2475.4.a.t.1.2 | 3 | 15.8 | even | 4 |