Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [324,4,Mod(109,324)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(324, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("324.109");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 324 = 2^{2} \cdot 3^{4} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 324.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: | \(19.1166188419\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 8.0.49787136.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} + 3x^{6} + 5x^{4} + 12x^{2} + 16 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{10} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 109.2 | ||
Root | \(-0.228425 + 1.39564i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 324.109 |
Dual form | 324.4.e.i.217.2 |
$q$-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 \(\left(\mathbb{Z}/324\mathbb{Z}\right)^\times\).
\(n\) | \(163\) | \(245\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −5.33918 | + | 9.24773i | −0.477551 | + | 0.827142i | −0.999669 | − | 0.0257312i | \(-0.991809\pi\) |
0.522118 | + | 0.852873i | \(0.325142\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −11.7477 | − | 20.3477i | −0.634318 | − | 1.09867i | −0.986659 | − | 0.162799i | \(-0.947948\pi\) |
0.352342 | − | 0.935871i | \(-0.385386\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.45505 | + | 4.25227i | 0.0672932 | + | 0.116555i | 0.897709 | − | 0.440589i | \(-0.145230\pi\) |
−0.830416 | + | 0.557144i | \(0.811897\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.752273 | + | 1.30297i | −0.0160495 | + | 0.0277985i | −0.873939 | − | 0.486036i | \(-0.838442\pi\) |
0.857889 | + | 0.513835i | \(0.171776\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 99.2990 | 1.41668 | 0.708340 | − | 0.705872i | \(-0.249445\pi\) | ||||
0.708340 | + | 0.705872i | \(0.249445\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 28.5045 | 0.344178 | 0.172089 | − | 0.985081i | \(-0.444948\pi\) | ||||
0.172089 | + | 0.985081i | \(0.444948\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 76.3454 | − | 132.234i | 0.692135 | − | 1.19881i | −0.279001 | − | 0.960291i | \(-0.590003\pi\) |
0.971137 | − | 0.238523i | \(-0.0766632\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 5.48636 | + | 9.50266i | 0.0438909 | + | 0.0760213i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 120.227 | + | 208.239i | 0.769846 | + | 1.33341i | 0.937646 | + | 0.347591i | \(0.113000\pi\) |
−0.167801 | + | 0.985821i | \(0.553666\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −128.486 | + | 222.545i | −0.744414 | + | 1.28936i | 0.206054 | + | 0.978541i | \(0.433938\pi\) |
−0.950468 | + | 0.310822i | \(0.899396\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 250.893 | 1.21168 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 359.468 | 1.59719 | 0.798597 | − | 0.601866i | \(-0.205576\pi\) | ||||
0.798597 | + | 0.601866i | \(0.205576\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −54.2499 | + | 93.9636i | −0.206644 | + | 0.357918i | −0.950655 | − | 0.310249i | \(-0.899588\pi\) |
0.744011 | + | 0.668167i | \(0.232921\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −205.730 | − | 356.334i | −0.729615 | − | 1.26373i | −0.957046 | − | 0.289937i | \(-0.906366\pi\) |
0.227430 | − | 0.973794i | \(-0.426968\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 155.885 | + | 270.000i | 0.483789 | + | 0.837948i | 0.999827 | − | 0.0186183i | \(-0.00592674\pi\) |
−0.516037 | + | 0.856566i | \(0.672593\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −104.518 | + | 181.031i | −0.304718 | + | 0.527787i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 702.578 | 1.82088 | 0.910438 | − | 0.413645i | \(-0.135745\pi\) | ||||
0.910438 | + | 0.413645i | \(0.135745\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −52.4318 | −0.128544 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 239.595 | − | 414.991i | 0.528689 | − | 0.915715i | −0.470752 | − | 0.882266i | \(-0.656017\pi\) |
0.999440 | − | 0.0334498i | \(-0.0106494\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −249.230 | − | 431.678i | −0.523124 | − | 0.906078i | −0.999638 | − | 0.0269106i | \(-0.991433\pi\) |
0.476514 | − | 0.879167i | \(-0.341900\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −8.03304 | − | 13.9136i | −0.0153289 | − | 0.0265504i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 166.216 | − | 287.894i | 0.303082 | − | 0.524954i | −0.673750 | − | 0.738959i | \(-0.735318\pi\) |
0.976832 | + | 0.214005i | \(0.0686510\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 884.729 | 1.47885 | 0.739423 | − | 0.673242i | \(-0.235099\pi\) | ||||
0.739423 | + | 0.673242i | \(0.235099\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 305.000 | 0.489008 | 0.244504 | − | 0.969648i | \(-0.421375\pi\) | ||||
0.244504 | + | 0.969648i | \(0.421375\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 57.6825 | − | 99.9091i | 0.0853706 | − | 0.147866i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 351.693 | + | 609.150i | 0.500868 | + | 0.867529i | 0.999999 | + | 0.00100260i | \(0.000319137\pi\) |
−0.499131 | + | 0.866526i | \(0.666348\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 210.373 | + | 364.377i | 0.278210 | + | 0.481875i | 0.970940 | − | 0.239323i | \(-0.0769254\pi\) |
−0.692730 | + | 0.721197i | \(0.743592\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −530.175 | + | 918.290i | −0.676536 | + | 1.17179i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1610.00 | −1.91752 | −0.958761 | − | 0.284212i | \(-0.908268\pi\) | ||||
−0.958761 | + | 0.284212i | \(0.908268\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 35.3500 | 0.0407218 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −152.191 | + | 263.602i | −0.164363 | + | 0.284684i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −198.009 | − | 342.962i | −0.207266 | − | 0.358995i | 0.743587 | − | 0.668640i | \(-0.233123\pi\) |
−0.950852 | + | 0.309645i | \(0.899790\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 136.483 | + | 236.395i | 0.134461 | + | 0.232893i | 0.925391 | − | 0.379013i | \(-0.123736\pi\) |
−0.790930 | + | 0.611906i | \(0.790403\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 198.541 | − | 343.883i | 0.189930 | − | 0.328969i | −0.755297 | − | 0.655383i | \(-0.772507\pi\) |
0.945227 | + | 0.326414i | \(0.105840\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −360.870 | −0.326043 | −0.163022 | − | 0.986622i | \(-0.552124\pi\) | ||||
−0.163022 | + | 0.986622i | \(0.552124\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 120.568 | 0.105948 | 0.0529740 | − | 0.998596i | \(-0.483130\pi\) | ||||
0.0529740 | + | 0.998596i | \(0.483130\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −612.311 | + | 1060.55i | −0.509747 | + | 0.882908i | 0.490189 | + | 0.871616i | \(0.336928\pi\) |
−0.999936 | + | 0.0112917i | \(0.996406\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 815.243 | + | 1412.04i | 0.661059 | + | 1.14499i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1166.54 | − | 2020.50i | −0.898625 | − | 1.55646i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 653.445 | − | 1131.80i | 0.490943 | − | 0.850339i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −1451.97 | −1.03894 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1991.46 | −1.39144 | −0.695722 | − | 0.718311i | \(-0.744915\pi\) | ||||
−0.695722 | + | 0.718311i | \(0.744915\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 788.743 | − | 1366.14i | 0.526052 | − | 0.911149i | −0.473487 | − | 0.880801i | \(-0.657005\pi\) |
0.999539 | − | 0.0303481i | \(-0.00966160\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −334.864 | − | 580.001i | −0.218318 | − | 0.378139i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −418.004 | − | 724.005i | −0.260675 | − | 0.451503i | 0.705746 | − | 0.708465i | \(-0.250612\pi\) |
−0.966422 | + | 0.256962i | \(0.917279\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 1364.30 | − | 2363.04i | 0.832509 | − | 1.44195i | −0.0635329 | − | 0.997980i | \(-0.520237\pi\) |
0.896042 | − | 0.443969i | \(-0.146430\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −7.38747 | −0.00432008 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −2567.65 | −1.47056 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1388.04 | + | 2404.16i | −0.763173 | + | 1.32185i | 0.178035 | + | 0.984024i | \(0.443026\pi\) |
−0.941207 | + | 0.337829i | \(0.890307\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 381.514 | + | 660.801i | 0.205610 | + | 0.356127i | 0.950327 | − | 0.311253i | \(-0.100749\pi\) |
−0.744717 | + | 0.667381i | \(0.767415\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1372.02 | − | 2376.41i | −0.710991 | − | 1.23147i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −352.743 | + | 610.969i | −0.179312 | + | 0.310577i | −0.941645 | − | 0.336607i | \(-0.890720\pi\) |
0.762333 | + | 0.647185i | \(0.224054\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3587.54 | −1.75613 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1587.60 | 0.762886 | 0.381443 | − | 0.924392i | \(-0.375427\pi\) | ||||
0.381443 | + | 0.924392i | \(0.375427\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 330.432 | − | 572.325i | 0.153111 | − | 0.265197i | −0.779258 | − | 0.626703i | \(-0.784404\pi\) |
0.932370 | + | 0.361506i | \(0.117737\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1097.37 | + | 1900.70i | 0.499485 | + | 0.865133i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 1018.69 | + | 1764.42i | 0.447684 | + | 0.775411i | 0.998235 | − | 0.0593907i | \(-0.0189158\pi\) |
−0.550551 | + | 0.834801i | \(0.685582\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 128.905 | − | 223.269i | 0.0556815 | − | 0.0964433i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2579.01 | −1.07690 | −0.538448 | − | 0.842659i | \(-0.680989\pi\) | ||||
−0.538448 | + | 0.842659i | \(0.680989\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1851.65 | 0.760400 | 0.380200 | − | 0.924904i | \(-0.375855\pi\) | ||||
0.380200 | + | 0.924904i | \(0.375855\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1919.26 | + | 3324.26i | −0.762741 | + | 1.32111i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 243.784 | + | 422.246i | 0.0953329 | + | 0.165121i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −28.4831 | − | 49.3341i | −0.0107904 | − | 0.0186895i | 0.860580 | − | 0.509316i | \(-0.170101\pi\) |
−0.871370 | + | 0.490626i | \(0.836768\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −907.014 | + | 1570.99i | −0.338281 | + | 0.585920i | −0.984110 | − | 0.177562i | \(-0.943179\pi\) |
0.645828 | + | 0.763483i | \(0.276512\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −873.334 | −0.315850 | −0.157925 | − | 0.987451i | \(-0.550480\pi\) | ||||
−0.157925 | + | 0.987451i | \(0.550480\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5063.60 | −1.80376 | −0.901882 | − | 0.431982i | \(-0.857814\pi\) | ||||
−0.901882 | + | 0.431982i | \(0.857814\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2824.78 | − | 4892.66i | 0.976653 | − | 1.69161i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −579.300 | − | 1003.38i | −0.197366 | − | 0.341848i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 69.9801 | + | 121.209i | 0.0231609 | + | 0.0401158i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −215.389 | + | 373.064i | −0.0702747 | + | 0.121719i | −0.899022 | − | 0.437904i | \(-0.855721\pi\) |
0.828747 | + | 0.559624i | \(0.189054\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 4393.71 | 1.39371 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 6037.69 | 1.88878 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −74.6999 | + | 129.384i | −0.0227369 | + | 0.0393815i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1631.84 | + | 2826.43i | 0.490027 | + | 0.848751i | 0.999934 | − | 0.0114779i | \(-0.00365361\pi\) |
−0.509907 | + | 0.860229i | \(0.670320\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 374.339 | + | 648.375i | 0.109453 | + | 0.189578i | 0.915549 | − | 0.402207i | \(-0.131757\pi\) |
−0.806096 | + | 0.591785i | \(0.798423\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1493.50 | − | 2586.81i | 0.430974 | − | 0.746469i | −0.565983 | − | 0.824417i | \(-0.691503\pi\) |
0.996957 | + | 0.0779474i | \(0.0248366\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3785.23 | 1.06429 | 0.532144 | − | 0.846654i | \(-0.321387\pi\) | ||||
0.532144 | + | 0.846654i | \(0.321387\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3329.18 | −0.924136 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 304.188 | − | 526.868i | 0.0823274 | − | 0.142595i | −0.821922 | − | 0.569600i | \(-0.807098\pi\) |
0.904249 | + | 0.427005i | \(0.140431\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2671.70 | − | 4627.53i | −0.714106 | − | 1.23687i | −0.963303 | − | 0.268416i | \(-0.913500\pi\) |
0.249197 | − | 0.968453i | \(-0.419833\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1116.08 | − | 1933.11i | −0.291036 | − | 0.504090i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −21.4432 | + | 37.1407i | −0.00552388 | + | 0.00956764i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6475.89 | 1.62850 | 0.814252 | − | 0.580512i | \(-0.197147\pi\) | ||||
0.814252 | + | 0.580512i | \(0.197147\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 749.727 | 0.186304 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.64532 | + | 4.58182i | −0.000642064 | + | 0.00111209i | −0.866346 | − | 0.499444i | \(-0.833538\pi\) |
0.865704 | + | 0.500556i | \(0.166871\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4222.93 | − | 7314.34i | −1.01313 | − | 1.75479i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3523.47 | + | 6102.83i | 0.826108 | + | 1.43086i | 0.901070 | + | 0.433675i | \(0.142783\pi\) |
−0.0749616 | + | 0.997186i | \(0.523883\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −3751.19 | + | 6497.25i | −0.869561 | + | 1.50612i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −787.057 | −0.178393 | −0.0891965 | − | 0.996014i | \(-0.528430\pi\) | ||||
−0.0891965 | + | 0.996014i | \(0.528430\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 5076.65 | 1.13795 | 0.568975 | − | 0.822355i | \(-0.307340\pi\) | ||||
0.568975 | + | 0.822355i | \(0.307340\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −26.9386 | + | 46.6590i | −0.00590712 | + | 0.0102314i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −408.891 | − | 708.220i | −0.0886927 | − | 0.153620i | 0.818266 | − | 0.574840i | \(-0.194936\pi\) |
−0.906959 | + | 0.421219i | \(0.861602\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2618.75 | + | 4535.80i | 0.555948 | + | 0.962929i | 0.997829 | + | 0.0658560i | \(0.0209778\pi\) |
−0.441882 | + | 0.897073i | \(0.645689\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1049.03 | − | 1816.97i | 0.220347 | − | 0.381652i | −0.734566 | − | 0.678537i | \(-0.762614\pi\) |
0.954913 | + | 0.296885i | \(0.0959477\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2549.25 | 0.524312 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 4947.29 | 1.00698 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −1245.03 | + | 2156.45i | −0.248243 | + | 0.429970i | −0.963039 | − | 0.269364i | \(-0.913187\pi\) |
0.714795 | + | 0.699334i | \(0.246520\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2558.48 | + | 4431.42i | 0.504951 | + | 0.874601i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 114.865 | + | 198.952i | 0.0222168 | + | 0.0384806i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4833.71 | + | 8372.23i | −0.925616 | + | 1.60321i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 5322.72 | 0.999273 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2068.21 | 0.384492 | 0.192246 | − | 0.981347i | \(-0.438423\pi\) | ||||
0.192246 | + | 0.981347i | \(0.438423\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 2455.78 | − | 4253.54i | 0.447764 | − | 0.775550i | −0.550476 | − | 0.834851i | \(-0.685554\pi\) |
0.998240 | + | 0.0593006i | \(0.0188871\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2648.17 | − | 4586.76i | −0.478221 | − | 0.828304i | 0.521467 | − | 0.853272i | \(-0.325385\pi\) |
−0.999688 | + | 0.0249677i | \(0.992052\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 715.401 | + | 1239.11i | 0.126754 | + | 0.219544i | 0.922417 | − | 0.386195i | \(-0.126211\pi\) |
−0.795663 | + | 0.605739i | \(0.792878\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −590.325 | + | 1022.47i | −0.103611 | + | 0.179459i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 2830.47 | 0.487590 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −16.5090 | −0.00281770 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3662.58 | − | 6343.77i | 0.613752 | − | 1.06305i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2667.26 | + | 4619.82i | 0.442917 | + | 0.767156i | 0.997905 | − | 0.0647034i | \(-0.0206101\pi\) |
−0.554987 | + | 0.831859i | \(0.687277\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1774.91 | + | 3074.24i | 0.289474 | + | 0.501384i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 4335.79 | − | 7509.81i | 0.700847 | − | 1.21390i | −0.267322 | − | 0.963607i | \(-0.586139\pi\) |
0.968169 | − | 0.250296i | \(-0.0805280\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1261.76 | −0.200376 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −3147.54 | −0.495484 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 2685.86 | − | 4652.05i | 0.415518 | − | 0.719698i | −0.579965 | − | 0.814642i | \(-0.696934\pi\) |
0.995483 | + | 0.0949434i | \(0.0302670\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2520.76 | + | 4366.09i | 0.386629 | + | 0.669660i | 0.991994 | − | 0.126288i | \(-0.0403062\pi\) |
−0.605365 | + | 0.795948i | \(0.706973\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 2425.89 | + | 4201.76i | 0.365771 | + | 0.633533i | 0.988900 | − | 0.148586i | \(-0.0474721\pi\) |
−0.623129 | + | 0.782119i | \(0.714139\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4723.72 | + | 8181.73i | −0.706223 | + | 1.22321i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3143.59 | 0.462151 | 0.231075 | − | 0.972936i | \(-0.425776\pi\) | ||||
0.231075 | + | 0.972936i | \(0.425776\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6046.49 | −0.881541 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1628.45 | + | 2820.56i | −0.233526 | + | 0.404479i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4990.91 | − | 8644.52i | −0.709873 | − | 1.22954i | −0.964904 | − | 0.262604i | \(-0.915419\pi\) |
0.255030 | − | 0.966933i | \(-0.417915\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8253.69 | − | 14295.8i | −1.15501 | − | 2.00054i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3032.42 | − | 5252.30i | 0.420945 | − | 0.729099i | −0.575087 | − | 0.818092i | \(-0.695032\pi\) |
0.996032 | + | 0.0889935i | \(0.0283650\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −361.773 | −0.0494224 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 11238.7 | 1.52321 | 0.761603 | − | 0.648044i | \(-0.224413\pi\) | ||||
0.761603 | + | 0.648044i | \(0.224413\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −7344.43 | + | 12720.9i | −0.979851 | + | 1.69715i | −0.316955 | + | 0.948441i | \(0.602660\pi\) |
−0.662896 | + | 0.748711i | \(0.730673\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 615.955 | + | 1066.86i | 0.0815375 | + | 0.141227i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −677.833 | − | 1174.04i | −0.0883483 | − | 0.153024i | 0.818465 | − | 0.574557i | \(-0.194826\pi\) |
−0.906813 | + | 0.421533i | \(0.861492\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 7581.02 | − | 13130.7i | 0.980534 | − | 1.69833i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −7511.01 | −0.956759 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −9070.50 | −1.14669 | −0.573345 | − | 0.819314i | \(-0.694354\pi\) | ||||
−0.573345 | + | 0.819314i | \(0.694354\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1641.92 | + | 2843.89i | −0.204473 | + | 0.354157i | −0.949965 | − | 0.312358i | \(-0.898881\pi\) |
0.745492 | + | 0.666515i | \(0.232215\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −193.314 | − | 334.829i | −0.0238949 | − | 0.0413871i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 882.513 | + | 1528.56i | 0.107480 | + | 0.186162i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3109.65 | + | 5386.07i | −0.375947 | + | 0.651159i | −0.990468 | − | 0.137741i | \(-0.956016\pi\) |
0.614521 | + | 0.788900i | \(0.289349\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −11258.8 | −1.34143 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −4492.88 | −0.531438 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2984.55 | + | 5169.40i | −0.347983 | + | 0.602724i | −0.985891 | − | 0.167388i | \(-0.946467\pi\) |
0.637908 | + | 0.770113i | \(0.279800\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3269.54 | − | 5663.01i | −0.378498 | − | 0.655578i | 0.612346 | − | 0.790590i | \(-0.290226\pi\) |
−0.990844 | + | 0.135012i | \(0.956893\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 544.790 | + | 943.604i | 0.0621793 | + | 0.107698i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5855.76 | + | 10142.5i | −0.663654 | + | 1.14948i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −11929.1 | −1.33319 | −0.666596 | − | 0.745419i | \(-0.732250\pi\) | ||||
−0.666596 | + | 0.745419i | \(0.732250\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4047.92 | −0.449262 | −0.224631 | − | 0.974444i | \(-0.572118\pi\) | ||||
−0.224631 | + | 0.974444i | \(0.572118\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 2176.19 | − | 3769.27i | 0.238218 | − | 0.412606i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6062.11 | + | 10499.9i | 0.659063 | + | 1.14153i | 0.980859 | + | 0.194722i | \(0.0623803\pi\) |
−0.321796 | + | 0.946809i | \(0.604286\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −6218.80 | − | 10771.3i | −0.666962 | − | 1.15521i | −0.978749 | − | 0.205060i | \(-0.934261\pi\) |
0.311787 | − | 0.950152i | \(-0.399072\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8596.07 | − | 14888.8i | 0.915714 | − | 1.58606i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 2925.50 | 0.307489 | 0.153745 | − | 0.988111i | \(-0.450867\pi\) | ||||
0.153745 | + | 0.988111i | \(0.450867\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −532.745 | −0.0556231 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −188.740 | + | 326.907i | −0.0194467 | + | 0.0336827i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 8661.76 | + | 15002.6i | 0.886608 | + | 1.53565i | 0.843859 | + | 0.536565i | \(0.180278\pi\) |
0.0427492 | + | 0.999086i | \(0.486388\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6694.22 | − | 11594.7i | −0.676314 | − | 1.17141i | −0.976083 | − | 0.217398i | \(-0.930243\pi\) |
0.299769 | − | 0.954012i | \(-0.403090\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5741.58 | − | 9944.71i | 0.576315 | − | 0.998207i | −0.419582 | − | 0.907717i | \(-0.637823\pi\) |
0.995897 | − | 0.0904898i | \(-0.0288433\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18016.7 | −1.78526 | −0.892629 | − | 0.450793i | \(-0.851141\pi\) | ||||
−0.892629 | + | 0.450793i | \(0.851141\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7810.64 | −0.769001 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1010.15 | − | 1749.64i | 0.0981964 | − | 0.170081i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 156.386 | + | 270.869i | 0.0151063 | + | 0.0261649i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8526.11 | + | 14767.7i | 0.813294 | + | 1.40867i | 0.910546 | + | 0.413407i | \(0.135661\pi\) |
−0.0972521 | + | 0.995260i | \(0.531005\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −270.418 | + | 468.378i | −0.0256341 | + | 0.0443996i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4228.82 | 0.395919 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3327.54 | 0.309620 | 0.154810 | − | 0.987944i | \(-0.450523\pi\) | ||||
0.154810 | + | 0.987944i | \(0.450523\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2986.10 | − | 5172.07i | 0.274462 | − | 0.475381i | −0.695538 | − | 0.718490i | \(-0.744834\pi\) |
0.969999 | + | 0.243108i | \(0.0781671\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11938.4 | + | 20677.9i | 1.09062 | + | 1.88902i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −10393.6 | − | 18002.2i | −0.938058 | − | 1.62476i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −3467.45 | + | 6005.80i | −0.311071 | + | 0.538791i | −0.978595 | − | 0.205798i | \(-0.934021\pi\) |
0.667523 | + | 0.744589i | \(0.267354\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −5751.15 | −0.509803 | −0.254902 | − | 0.966967i | \(-0.582043\pi\) | ||||
−0.254902 | + | 0.966967i | \(0.582043\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −2914.83 | −0.256848 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6006.24 | − | 10403.1i | 0.523029 | − | 0.905913i | −0.476612 | − | 0.879114i | \(-0.658135\pi\) |
0.999641 | − | 0.0267988i | \(-0.00853134\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3583.06 | − | 6206.04i | −0.310186 | − | 0.537258i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2120.09 | + | 3672.10i | 0.181403 | + | 0.314199i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −765.409 | + | 1325.73i | −0.0651115 | + | 0.112776i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13667.9 | −1.14933 | −0.574666 | − | 0.818388i | \(-0.694868\pi\) | ||||
−0.574666 | + | 0.818388i | \(0.694868\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −22339.9 | −1.86779 | −0.933895 | − | 0.357548i | \(-0.883613\pi\) | ||||
−0.933895 | + | 0.357548i | \(0.883613\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −12758.6 | + | 22098.5i | −1.05460 | + | 1.82661i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −5573.74 | − | 9653.99i | −0.458103 | − | 0.793457i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −81.6215 | − | 141.373i | −0.00663306 | − | 0.0114888i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1926.75 | − | 3337.23i | 0.155702 | − | 0.269684i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −1026.39 | −0.0820218 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22676.0 | 1.80207 | 0.901034 | − | 0.433749i | \(-0.142809\pi\) | ||||
0.901034 | + | 0.433749i | \(0.142809\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −643.735 | + | 1114.98i | −0.0505956 | + | 0.0876341i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5016.26 | − | 8688.42i | −0.392102 | − | 0.679141i | 0.600624 | − | 0.799531i | \(-0.294919\pi\) |
−0.992727 | + | 0.120390i | \(0.961585\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3427.01 | + | 5935.75i | 0.264964 | + | 0.458932i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8263.19 | − | 14312.3i | 0.635419 | − | 1.10058i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 12557.1 | 0.955224 | 0.477612 | − | 0.878571i | \(-0.341502\pi\) | ||||
0.477612 | + | 0.878571i | \(0.341502\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 619.059 | 0.0468397 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10053.8 | + | 17413.8i | −0.752609 | + | 1.30356i | 0.193945 | + | 0.981012i | \(0.437872\pi\) |
−0.946554 | + | 0.322545i | \(0.895462\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6538.48 | − | 11325.0i | −0.486860 | − | 0.843266i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −2695.40 | − | 4668.58i | −0.198589 | − | 0.343966i | 0.749482 | − | 0.662025i | \(-0.230303\pi\) |
−0.948071 | + | 0.318058i | \(0.896969\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −7115.10 | + | 12323.7i | −0.521467 | + | 0.903207i | 0.478221 | + | 0.878239i | \(0.341282\pi\) |
−0.999688 | + | 0.0249680i | \(0.992052\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1675.43 | 0.121514 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4781.42 | −0.344979 | −0.172490 | − | 0.985011i | \(-0.555181\pi\) | ||||
−0.172490 | + | 0.985011i | \(0.555181\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4942.82 | − | 8561.21i | 0.352948 | − | 0.611323i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 1724.86 | + | 2987.55i | 0.122533 | + | 0.212233i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −6368.41 | − | 11030.4i | −0.447790 | − | 0.775594i | 0.550452 | − | 0.834867i | \(-0.314455\pi\) |
−0.998242 | + | 0.0592724i | \(0.981122\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3662.45 | + | 6343.54i | −0.256211 | + | 0.443771i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 11262.9 | 0.779954 | 0.389977 | − | 0.920825i | \(-0.372483\pi\) | ||||
0.389977 | + | 0.920825i | \(0.372483\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 24913.4 | 1.71655 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1841.96 | + | 3190.37i | −0.125643 | + | 0.217621i | −0.921984 | − | 0.387227i | \(-0.873433\pi\) |
0.796341 | + | 0.604848i | \(0.206766\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4712.16 | + | 8161.71i | 0.319822 | + | 0.553948i | 0.980451 | − | 0.196765i | \(-0.0630435\pi\) |
−0.660629 | + | 0.750713i | \(0.729710\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6977.72 | + | 12085.8i | 0.468900 | + | 0.812159i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1355.64 | + | 2348.03i | −0.0906486 | + | 0.157008i | −0.907784 | − | 0.419438i | \(-0.862227\pi\) |
0.817136 | + | 0.576445i | \(0.195561\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −469.071 | −0.0310582 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −15014.7 | −0.989298 | −0.494649 | − | 0.869093i | \(-0.664703\pi\) | ||||
−0.494649 | + | 0.869093i | \(0.664703\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 12955.3 | − | 22439.3i | 0.845319 | − | 1.46414i | −0.0400251 | − | 0.999199i | \(-0.512744\pi\) |
0.885344 | − | 0.464937i | \(-0.153923\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −14573.2 | − | 25241.5i | −0.946278 | − | 1.63900i | −0.753173 | − | 0.657823i | \(-0.771478\pi\) |
−0.193105 | − | 0.981178i | \(-0.561856\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 18913.8 | + | 32759.7i | 1.21632 | + | 2.10673i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7066.50 | − | 12239.5i | 0.452256 | − | 0.783331i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 35694.8 | 2.26271 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −10221.9 | −0.644893 | −0.322446 | − | 0.946588i | \(-0.604505\pi\) | ||||
−0.322446 | + | 0.946588i | \(0.604505\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 10632.8 | − | 18416.5i | 0.664485 | − | 1.15092i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −157.252 | − | 272.369i | −0.00978111 | − | 0.0169414i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −5870.53 | − | 10168.1i | −0.361735 | − | 0.626543i | 0.626512 | − | 0.779412i | \(-0.284482\pi\) |
−0.988246 | + | 0.152869i | \(0.951149\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −7861.89 | + | 13617.2i | −0.482181 | + | 0.835162i | −0.999791 | − | 0.0204546i | \(-0.993489\pi\) |
0.517610 | + | 0.855617i | \(0.326822\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 6458.34 | 0.392432 | 0.196216 | − | 0.980561i | \(-0.437135\pi\) | ||||
0.196216 | + | 0.980561i | \(0.437135\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2352.87 | 0.142309 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1829.48 | − | 3168.76i | 0.109637 | − | 0.189898i | −0.805986 | − | 0.591935i | \(-0.798364\pi\) |
0.915623 | + | 0.402037i | \(0.131698\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 8422.48 | + | 14588.2i | 0.502433 | + | 0.870239i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5239.89 | − | 9075.76i | −0.309738 | − | 0.536482i | 0.668567 | − | 0.743652i | \(-0.266908\pi\) |
−0.978305 | + | 0.207170i | \(0.933575\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −9909.38 | + | 17163.5i | −0.583102 | + | 1.00996i | 0.412008 | + | 0.911180i | \(0.364828\pi\) |
−0.995109 | + | 0.0987812i | \(0.968506\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7151.59 | 0.417032 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 36715.0 | 2.13135 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1223.74 | − | 2119.58i | 0.0704054 | − | 0.121946i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 13934.0 | + | 24134.4i | 0.798094 | + | 1.38234i | 0.920856 | + | 0.389903i | \(0.127491\pi\) |
−0.122762 | + | 0.992436i | \(0.539175\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 7200.21 | + | 12471.1i | 0.408754 | + | 0.707983i | 0.994750 | − | 0.102331i | \(-0.0326300\pi\) |
−0.585996 | + | 0.810314i | \(0.699297\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4652.31 | + | 8058.04i | −0.262945 | + | 0.455433i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 8387.44 | 0.469892 | 0.234946 | − | 0.972008i | \(-0.424509\pi\) | ||||
0.234946 | + | 0.972008i | \(0.424509\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8927.20 | 0.497942 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −528.530 | + | 915.441i | −0.0292241 | + | 0.0506176i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −10587.8 | − | 18338.7i | −0.582895 | − | 1.00960i | −0.995134 | − | 0.0985283i | \(-0.968587\pi\) |
0.412239 | − | 0.911076i | \(-0.364747\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 14568.5 | + | 25233.4i | 0.795131 | + | 1.37721i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5386.96 | + | 9330.49i | −0.292749 | + | 0.507055i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 7467.68 | 0.402354 | 0.201177 | − | 0.979555i | \(-0.435523\pi\) | ||||
0.201177 | + | 0.979555i | \(0.435523\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 10246.5 | 0.549720 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 3206.73 | − | 5554.22i | 0.170582 | − | 0.295457i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −9532.58 | − | 16510.9i | −0.504942 | − | 0.874585i | −0.999984 | − | 0.00571568i | \(-0.998181\pi\) |
0.495042 | − | 0.868869i | \(-0.335153\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 19618.7 | + | 33980.6i | 1.03047 | + | 1.78483i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 39.4430 | − | 68.3173i | 0.00206306 | − | 0.00357332i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 6863.35 | 0.355994 | 0.177997 | − | 0.984031i | \(-0.443038\pi\) | ||||
0.177997 | + | 0.984031i | \(0.443038\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −9329.62 | −0.481904 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1319.21 | + | 2284.95i | −0.0675784 | + | 0.117049i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7391.78 | − | 12802.9i | −0.377092 | − | 0.653143i | 0.613546 | − | 0.789659i | \(-0.289743\pi\) |
−0.990638 | + | 0.136517i | \(0.956409\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −20428.7 | − | 35383.6i | −1.03363 | − | 1.79030i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2000.99 | + | 3465.82i | −0.100830 | + | 0.174642i | −0.912027 | − | 0.410131i | \(-0.865483\pi\) |
0.811197 | + | 0.584773i | \(0.198816\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1632.27 | 0.0815815 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 16889.8 | 0.840733 | 0.420367 | − | 0.907354i | \(-0.361901\pi\) | ||||
0.420367 | + | 0.907354i | \(0.361901\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15258.1 | + | 26427.8i | −0.753386 | + | 1.30490i | 0.192787 | + | 0.981241i | \(0.438247\pi\) |
−0.946173 | + | 0.323662i | \(0.895086\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −14822.0 | − | 25672.4i | −0.728907 | − | 1.26250i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4239.40 | + | 7342.86i | 0.206815 | + | 0.358214i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −6931.10 | + | 12005.0i | −0.336777 | + | 0.583314i | −0.983824 | − | 0.179135i | \(-0.942670\pi\) |
0.647048 | + | 0.762449i | \(0.276003\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8147.88 | −0.392757 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15205.3 | −0.730049 | −0.365024 | − | 0.930998i | \(-0.618939\pi\) | ||||
−0.365024 | + | 0.930998i | \(0.618939\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2420.42 | − | 4192.30i | 0.115296 | − | 0.199699i | −0.802602 | − | 0.596515i | \(-0.796552\pi\) |
0.917898 | + | 0.396816i | \(0.129885\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1416.40 | − | 2453.28i | −0.0672047 | − | 0.116402i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 360.482 | + | 624.373i | 0.0169703 | + | 0.0293935i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 8528.08 | − | 14771.1i | 0.399909 | − | 0.692663i | −0.593805 | − | 0.804609i | \(-0.702375\pi\) |
0.993714 | + | 0.111946i | \(0.0357083\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 10350.7 | 0.481618 | 0.240809 | − | 0.970573i | \(-0.422587\pi\) | ||||
0.240809 | + | 0.970573i | \(0.422587\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2819.69 | −0.130692 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1546.37 | + | 2678.39i | −0.0711225 | + | 0.123188i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2172.05 | + | 3762.11i | 0.0995163 | + | 0.172367i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −3766.72 | − | 6524.15i | −0.171261 | − | 0.296633i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −3200.44 | + | 5543.32i | −0.144960 | + | 0.251078i | −0.929358 | − | 0.369180i | \(-0.879639\pi\) |
0.784398 | + | 0.620258i | \(0.212972\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 28773.1 | 1.29337 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 749.955 | 0.0335834 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 15790.6 | − | 27350.1i | 0.701795 | − | 1.21554i | −0.266041 | − | 0.963962i | \(-0.585716\pi\) |
0.967836 | − | 0.251582i | \(-0.0809509\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 15479.2 | + | 26810.7i | 0.685374 | + | 1.18710i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 748.791 | + | 1296.94i | 0.0329069 | + | 0.0569964i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 19154.5 | − | 33176.6i | 0.838643 | − | 1.45257i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3349.34 | −0.145558 | −0.0727791 | − | 0.997348i | \(-0.523187\pi\) | ||||
−0.0727791 | + | 0.997348i | \(0.523187\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 5186.82 | 0.224579 | 0.112290 | − | 0.993676i | \(-0.464182\pi\) | ||||
0.112290 | + | 0.993676i | \(0.464182\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −8476.48 | + | 14681.7i | −0.364317 | + | 0.631015i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5864.23 | − | 10157.1i | −0.251118 | − | 0.434949i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −13332.5 | − | 23092.6i | −0.566758 | − | 0.981654i | −0.996884 | − | 0.0788846i | \(-0.974864\pi\) |
0.430126 | − | 0.902769i | \(-0.358469\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13152.1 | − | 22780.2i | 0.557053 | − | 0.964844i | −0.440688 | − | 0.897660i | \(-0.645265\pi\) |
0.997741 | − | 0.0671832i | \(-0.0214012\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −10768.0 | −0.452769 | −0.226385 | − | 0.974038i | \(-0.572691\pi\) | ||||
−0.226385 | + | 0.974038i | \(0.572691\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −11960.9 | −0.501110 | −0.250555 | − | 0.968102i | \(-0.580613\pi\) | ||||
−0.250555 | + | 0.968102i | \(0.580613\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −10378.6 | + | 17976.2i | −0.431687 | + | 0.747704i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3528.47 | + | 6111.49i | 0.146237 | + | 0.253290i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −7177.07 | − | 12431.1i | −0.295328 | − | 0.511523i | 0.679733 | − | 0.733459i | \(-0.262096\pi\) |
−0.975061 | + | 0.221937i | \(0.928762\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −16714.4 | + | 28950.2i | −0.685325 | + | 1.18702i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −23436.2 | −0.954117 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −30706.0 | −1.24566 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 27443.7 | − | 47533.9i | 1.10547 | − | 1.91474i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 6065.55 | + | 10505.8i | 0.243470 | + | 0.421703i | 0.961700 | − | 0.274103i | \(-0.0883808\pi\) |
−0.718230 | + | 0.695806i | \(0.755047\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −9376.46 | − | 16240.5i | −0.373739 | − | 0.647334i | 0.616399 | − | 0.787434i | \(-0.288591\pi\) |
−0.990137 | + | 0.140100i | \(0.955258\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5646.25 | − | 9779.58i | 0.224269 | − | 0.388446i | −0.731831 | − | 0.681487i | \(-0.761334\pi\) |
0.956100 | + | 0.293041i | \(0.0946671\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5959.72 | 0.235077 | 0.117538 | − | 0.993068i | \(-0.462500\pi\) | ||||
0.117538 | + | 0.993068i | \(0.462500\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −21755.8 | −0.855166 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −1726.85 | + | 2990.99i | −0.0674101 | + | 0.116758i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 250.079 | + | 433.150i | 0.00972861 | + | 0.0168504i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 17057.3 | + | 29544.1i | 0.659019 | + | 1.14145i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −8912.47 | + | 15436.9i | −0.343162 | + | 0.594374i | −0.985018 | − | 0.172451i | \(-0.944831\pi\) |
0.641856 | + | 0.766825i | \(0.278165\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −44756.5 | −1.71156 | −0.855781 | − | 0.517339i | \(-0.826923\pi\) | ||||
−0.855781 | + | 0.517339i | \(0.826923\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7241.57 | −0.275989 | −0.137995 | − | 0.990433i | \(-0.544066\pi\) | ||||
−0.137995 | + | 0.990433i | \(0.544066\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16668.9 | + | 28871.4i | −0.630990 | + | 1.09291i | 0.356360 | + | 0.934349i | \(0.384018\pi\) |
−0.987350 | + | 0.158557i | \(0.949316\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 23395.1 | + | 40521.5i | 0.882618 | + | 1.52874i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 4443.42 | + | 7696.23i | 0.166510 | + | 0.288404i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13769.8 | − | 23850.0i | 0.514273 | − | 0.890746i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −61789.9 | −2.29234 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 69765.2 | 2.57960 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −9886.31 | + | 17123.6i | −0.363129 | + | 0.628959i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 9254.13 | + | 16028.6i | 0.338785 | + | 0.586794i | 0.984205 | − | 0.177035i | \(-0.0566506\pi\) |
−0.645419 | + | 0.763829i | \(0.723317\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7352.80 | − | 12735.4i | −0.267409 | − | 0.463165i | 0.700783 | − | 0.713374i | \(-0.252834\pi\) |
−0.968192 | + | 0.250209i | \(0.919501\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1032.95 | + | 1789.13i | −0.0374434 | + | 0.0648538i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −37063.8 | −1.33474 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −44333.5 | −1.59132 | −0.795662 | − | 0.605741i | \(-0.792877\pi\) | ||||
−0.795662 | + | 0.605741i | \(0.792877\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −665.558 | + | 1152.78i | −0.0237347 | + | 0.0411096i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1972.17 | + | 3415.90i | 0.0701023 | + | 0.121421i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −15114.0 | − | 26178.3i | −0.533773 | − | 0.924522i | −0.999222 | − | 0.0394470i | \(-0.987440\pi\) |
0.465449 | − | 0.885075i | \(-0.345893\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2979.24 | + | 5160.20i | −0.104877 | + | 0.181653i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −5206.43 | −0.182105 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 22568.0 | 0.786834 | 0.393417 | − | 0.919360i | \(-0.371293\pi\) | ||||
0.393417 | + | 0.919360i | \(0.371293\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −17542.5 | + | 30384.6i | −0.607727 | + | 1.05261i | 0.383888 | + | 0.923380i | \(0.374585\pi\) |
−0.991614 | + | 0.129233i | \(0.958748\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8283.46 | + | 14347.4i | 0.286052 | + | 0.495456i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −17124.1 | − | 29659.7i | −0.587600 | − | 1.01775i | −0.994546 | − | 0.104301i | \(-0.966740\pi\) |
0.406946 | − | 0.913452i | \(-0.366594\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −229.443 | + | 397.407i | −0.00784831 | + | 0.0135937i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 38627.8 | 1.31299 | 0.656494 | − | 0.754331i | \(-0.272039\pi\) | ||||
0.656494 | + | 0.754331i | \(0.272039\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 608.304 | 0.0206118 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −9821.20 | + | 17010.8i | −0.330702 | + | 0.572792i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −18122.0 | − | 31388.2i | −0.608304 | − | 1.05361i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −9685.41 | − | 16775.6i | −0.323093 | − | 0.559613i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7814.39 | − | 13534.9i | 0.259869 | − | 0.450107i | −0.706337 | − | 0.707875i | \(-0.749654\pi\) |
0.966207 | + | 0.257768i | \(0.0829871\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −26637.8 | −0.880379 | −0.440190 | − | 0.897905i | \(-0.645089\pi\) | ||||
−0.440190 | + | 0.897905i | \(0.645089\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −64109.9 | −2.11230 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −888.789 | + | 1539.43i | −0.0291043 | + | 0.0504101i | −0.880211 | − | 0.474583i | \(-0.842599\pi\) |
0.851106 | + | 0.524993i | \(0.175932\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3952.63 | − | 6846.15i | −0.129036 | − | 0.223498i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 23817.2 | + | 41252.6i | 0.772788 | + | 1.33851i | 0.936029 | + | 0.351922i | \(0.114472\pi\) |
−0.163241 | + | 0.986586i | \(0.552195\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 4662.89 | − | 8076.36i | 0.150834 | − | 0.261253i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −62826.0 | −2.01997 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −33719.5 | −1.08086 | −0.540432 | − | 0.841388i | \(-0.681739\pi\) | ||||
−0.540432 | + | 0.841388i | \(0.681739\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 27035.5 | − | 46826.8i | 0.861389 | − | 1.49197i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 200.389 | + | 347.083i | 0.00636547 | + | 0.0110253i | 0.869191 | − | 0.494477i | \(-0.164640\pi\) |
−0.862825 | + | 0.505503i | \(0.831307\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 324.4.e.i.109.2 | 8 | ||
3.2 | odd | 2 | inner | 324.4.e.i.109.3 | 8 | ||
9.2 | odd | 6 | inner | 324.4.e.i.217.3 | 8 | ||
9.4 | even | 3 | 324.4.a.e.1.3 | yes | 4 | ||
9.5 | odd | 6 | 324.4.a.e.1.2 | ✓ | 4 | ||
9.7 | even | 3 | inner | 324.4.e.i.217.2 | 8 | ||
36.23 | even | 6 | 1296.4.a.z.1.2 | 4 | |||
36.31 | odd | 6 | 1296.4.a.z.1.3 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
324.4.a.e.1.2 | ✓ | 4 | 9.5 | odd | 6 | ||
324.4.a.e.1.3 | yes | 4 | 9.4 | even | 3 | ||
324.4.e.i.109.2 | 8 | 1.1 | even | 1 | trivial | ||
324.4.e.i.109.3 | 8 | 3.2 | odd | 2 | inner | ||
324.4.e.i.217.2 | 8 | 9.7 | even | 3 | inner | ||
324.4.e.i.217.3 | 8 | 9.2 | odd | 6 | inner | ||
1296.4.a.z.1.2 | 4 | 36.23 | even | 6 | |||
1296.4.a.z.1.3 | 4 | 36.31 | odd | 6 |