Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [360,4,Mod(289,360)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(360, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("360.289");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 360 = 2^{3} \cdot 3^{2} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 360.f (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(21.2406876021\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(i, \sqrt{6})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 9 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{7} \) |
Twist minimal: | no (minimal twist has level 40) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 289.2 | ||
Root | \(1.22474 - 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 360.289 |
Dual form | 360.4.f.e.289.1 |
$q$-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 \(\left(\mathbb{Z}/360\mathbb{Z}\right)^\times\).
\(n\) | \(181\) | \(217\) | \(271\) | \(281\) |
\(\chi(n)\) | \(1\) | \(-1\) | \(1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −8.79796 | + | 6.89898i | −0.786913 | + | 0.617063i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 16.6969i | − | 0.901550i | −0.892638 | − | 0.450775i | \(-0.851148\pi\) | ||
0.892638 | − | 0.450775i | \(-0.148852\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 19.1918 | 0.526051 | 0.263025 | − | 0.964789i | \(-0.415280\pi\) | ||||
0.263025 | + | 0.964789i | \(0.415280\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 61.7980i | 1.31844i | 0.751952 | + | 0.659218i | \(0.229113\pi\) | ||||
−0.751952 | + | 0.659218i | \(0.770887\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 30.3837i | − | 0.433478i | −0.976230 | − | 0.216739i | \(-0.930458\pi\) | ||
0.976230 | − | 0.216739i | \(-0.0695420\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −59.1918 | −0.714713 | −0.357356 | − | 0.933968i | \(-0.616322\pi\) | ||||
−0.357356 | + | 0.933968i | \(0.616322\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 205.687i | − | 1.86472i | −0.361526 | − | 0.932362i | \(-0.617744\pi\) | ||
0.361526 | − | 0.932362i | \(-0.382256\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 29.8082 | − | 121.394i | 0.238465 | − | 0.971151i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.38367 | 0.0536831 | 0.0268415 | − | 0.999640i | \(-0.491455\pi\) | ||||
0.0268415 | + | 0.999640i | \(0.491455\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 331.151 | 1.91860 | 0.959298 | − | 0.282396i | \(-0.0911291\pi\) | ||||
0.959298 | + | 0.282396i | \(0.0911291\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 115.192 | + | 146.899i | 0.556314 | + | 0.709442i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | − | 266.565i | − | 1.18441i | −0.805788 | − | 0.592204i | \(-0.798258\pi\) | ||
0.805788 | − | 0.592204i | \(-0.201742\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 320.788 | 1.22192 | 0.610959 | − | 0.791662i | \(-0.290784\pi\) | ||||
0.610959 | + | 0.791662i | \(0.290784\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 83.1214i | 0.294788i | 0.989078 | + | 0.147394i | \(0.0470886\pi\) | ||||
−0.989078 | + | 0.147394i | \(0.952911\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 276.434i | − | 0.857915i | −0.903325 | − | 0.428957i | \(-0.858881\pi\) | ||
0.903325 | − | 0.428957i | \(-0.141119\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 64.2122 | 0.187208 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 390.888i | − | 1.01307i | −0.862220 | − | 0.506534i | \(-0.830927\pi\) | ||
0.862220 | − | 0.506534i | \(-0.169073\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −168.849 | + | 132.404i | −0.413956 | + | 0.324607i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 779.110 | 1.71918 | 0.859589 | − | 0.510986i | \(-0.170720\pi\) | ||||
0.859589 | + | 0.510986i | \(0.170720\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −483.171 | −1.01416 | −0.507080 | − | 0.861899i | \(-0.669275\pi\) | ||||
−0.507080 | + | 0.861899i | \(0.669275\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −426.343 | − | 543.696i | −0.813559 | − | 1.03750i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 123.707i | − | 0.225571i | −0.993619 | − | 0.112785i | \(-0.964023\pi\) | ||
0.993619 | − | 0.112785i | \(-0.0359772\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −187.233 | −0.312964 | −0.156482 | − | 0.987681i | \(-0.550015\pi\) | ||||
−0.156482 | + | 0.987681i | \(0.550015\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − | 778.706i | − | 1.24850i | −0.781224 | − | 0.624251i | \(-0.785404\pi\) | ||
0.781224 | − | 0.624251i | \(-0.214596\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 320.445i | − | 0.474261i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 446.384 | 0.635723 | 0.317861 | − | 0.948137i | \(-0.397035\pi\) | ||||
0.317861 | + | 0.948137i | \(0.397035\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1054.05i | 1.39394i | 0.717100 | + | 0.696970i | \(0.245469\pi\) | ||||
−0.717100 | + | 0.696970i | \(0.754531\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 209.616 | + | 267.314i | 0.267483 | + | 0.341109i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −94.8490 | −0.112966 | −0.0564830 | − | 0.998404i | \(-0.517989\pi\) | ||||
−0.0564830 | + | 0.998404i | \(0.517989\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1031.84 | 1.18864 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 520.767 | − | 408.363i | 0.562417 | − | 0.441023i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 252.041i | − | 0.263823i | −0.991261 | − | 0.131912i | \(-0.957888\pi\) | ||
0.991261 | − | 0.131912i | \(-0.0421115\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −37.9184 | −0.0373566 | −0.0186783 | − | 0.999826i | \(-0.505946\pi\) | ||||
−0.0186783 | + | 0.999826i | \(0.505946\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 94.4133i | 0.0903186i | 0.998980 | + | 0.0451593i | \(0.0143795\pi\) | ||||
−0.998980 | + | 0.0451593i | \(0.985620\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 901.464i | − | 0.814466i | −0.913324 | − | 0.407233i | \(-0.866494\pi\) | ||
0.913324 | − | 0.407233i | \(-0.133506\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1415.69 | −1.24403 | −0.622013 | − | 0.783007i | \(-0.713685\pi\) | ||||
−0.622013 | + | 0.783007i | \(0.713685\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 293.576i | 0.244401i | 0.992505 | + | 0.122200i | \(0.0389950\pi\) | ||||
−0.992505 | + | 0.122200i | \(0.961005\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1419.03 | + | 1809.62i | 1.15065 | + | 1.46738i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −507.314 | −0.390802 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −962.673 | −0.723271 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 575.243 | + | 1273.66i | 0.411610 | + | 0.911360i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 774.717i | − | 0.541300i | −0.962678 | − | 0.270650i | \(-0.912761\pi\) | ||
0.962678 | − | 0.270650i | \(-0.0872385\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −334.343 | −0.222990 | −0.111495 | − | 0.993765i | \(-0.535564\pi\) | ||||
−0.111495 | + | 0.993765i | \(0.535564\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 988.322i | 0.644349i | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 323.514i | 0.201750i | 0.994899 | + | 0.100875i | \(0.0321641\pi\) | ||||
−0.994899 | + | 0.100875i | \(0.967836\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 396.482 | 0.241936 | 0.120968 | − | 0.992656i | \(-0.461400\pi\) | ||||
0.120968 | + | 0.992656i | \(0.461400\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1186.02i | 0.693564i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −73.7592 | + | 57.8388i | −0.0422439 | + | 0.0331259i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1682.89 | −0.925284 | −0.462642 | − | 0.886545i | \(-0.653099\pi\) | ||||
−0.462642 | + | 0.886545i | \(0.653099\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −2924.52 | −1.57612 | −0.788060 | − | 0.615598i | \(-0.788915\pi\) | ||||
−0.788060 | + | 0.615598i | \(0.788915\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −2913.45 | + | 2284.60i | −1.50977 | + | 1.18390i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 2768.42i | − | 1.40729i | −0.710553 | − | 0.703644i | \(-0.751555\pi\) | ||
0.710553 | − | 0.703644i | \(-0.248445\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −3434.34 | −1.68114 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2816.33i | 1.35333i | 0.736292 | + | 0.676663i | \(0.236575\pi\) | ||||
−0.736292 | + | 0.676663i | \(0.763425\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1836.41i | 0.850933i | 0.904974 | + | 0.425466i | \(0.139890\pi\) | ||||
−0.904974 | + | 0.425466i | \(0.860110\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1621.99 | −0.738274 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 1224.22i | − | 0.538011i | −0.963139 | − | 0.269006i | \(-0.913305\pi\) | ||
0.963139 | − | 0.269006i | \(-0.0866950\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2026.91 | − | 497.705i | −0.875541 | − | 0.214988i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 2729.58 | 1.13977 | 0.569883 | − | 0.821726i | \(-0.306989\pi\) | ||||
0.569883 | + | 0.821726i | \(0.306989\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2642.36 | 1.08511 | 0.542555 | − | 0.840020i | \(-0.317457\pi\) | ||||
0.542555 | + | 0.840020i | \(0.317457\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1839.03 | + | 2345.23i | 0.730854 | + | 0.932026i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 583.118i | − | 0.228031i | ||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 2339.23 | 0.886183 | 0.443091 | − | 0.896476i | \(-0.353882\pi\) | ||||
0.443091 | + | 0.896476i | \(0.353882\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 4601.61i | 1.71622i | 0.513464 | + | 0.858111i | \(0.328362\pi\) | ||||
−0.513464 | + | 0.858111i | \(0.671638\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 823.941i | − | 0.297987i | −0.988838 | − | 0.148993i | \(-0.952397\pi\) | ||
0.988838 | − | 0.148993i | \(-0.0476033\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3329.70 | 1.18611 | 0.593055 | − | 0.805162i | \(-0.297922\pi\) | ||||
0.593055 | + | 0.805162i | \(0.297922\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 139.982i | − | 0.0483980i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2822.28 | + | 2213.11i | −0.961543 | + | 0.754001i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1136.00 | −0.375975 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1018.78 | 0.332398 | 0.166199 | − | 0.986092i | \(-0.446851\pi\) | ||||
0.166199 | + | 0.986092i | \(0.446851\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −573.453 | − | 731.299i | −0.181903 | − | 0.231973i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 5529.21i | − | 1.72971i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1877.65 | 0.571513 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 99.1581i | − | 0.0297763i | −0.999889 | − | 0.0148882i | \(-0.995261\pi\) | ||
0.999889 | − | 0.0148882i | \(-0.00473922\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 1197.59i | − | 0.350163i | −0.984554 | − | 0.175081i | \(-0.943981\pi\) | ||
0.984554 | − | 0.175081i | \(-0.0560188\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 453.592 | 0.130892 | 0.0654458 | − | 0.997856i | \(-0.479153\pi\) | ||||
0.0654458 | + | 0.997856i | \(0.479153\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3788.49i | 1.06520i | 0.846367 | + | 0.532601i | \(0.178785\pi\) | ||||
−0.846367 | + | 0.532601i | \(0.821215\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1907.11 | + | 2432.05i | 0.529388 | + | 0.675105i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −6000.47 | −1.62401 | −0.812005 | − | 0.583651i | \(-0.801624\pi\) | ||||
−0.812005 | + | 0.583651i | \(0.801624\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1842.53 | 0.492480 | 0.246240 | − | 0.969209i | \(-0.420805\pi\) | ||||
0.246240 | + | 0.969209i | \(0.420805\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −564.937 | + | 442.999i | −0.147316 | + | 0.115519i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 3657.93i | − | 0.942303i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1149.46 | −0.289057 | −0.144529 | − | 0.989501i | \(-0.546167\pi\) | ||||
−0.144529 | + | 0.989501i | \(0.546167\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 3947.51i | − | 0.980939i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 5407.67i | − | 1.31253i | −0.754528 | − | 0.656267i | \(-0.772134\pi\) | ||
0.754528 | − | 0.656267i | \(-0.227866\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4450.82 | −1.06780 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | − | 2067.34i | − | 0.484705i | −0.970188 | − | 0.242352i | \(-0.922081\pi\) | ||
0.970188 | − | 0.242352i | \(-0.0779190\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2696.73 | + | 3439.01i | 0.625127 | + | 0.797196i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −592.388 | −0.134270 | −0.0671348 | − | 0.997744i | \(-0.521386\pi\) | ||||
−0.0671348 | + | 0.997744i | \(0.521386\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2583.27 | −0.579049 | −0.289524 | − | 0.957171i | \(-0.593497\pi\) | ||||
−0.289524 | + | 0.957171i | \(0.593497\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 572.073 | − | 2329.77i | 0.125445 | − | 0.510875i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4488.09i | 0.973513i | 0.873538 | + | 0.486756i | \(0.161820\pi\) | ||||
−0.873538 | + | 0.486756i | \(0.838180\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 6280.54 | 1.33333 | 0.666665 | − | 0.745357i | \(-0.267721\pi\) | ||||
0.666665 | + | 0.745357i | \(0.267721\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 5233.40i | − | 1.09927i | −0.835405 | − | 0.549635i | \(-0.814767\pi\) | ||
0.835405 | − | 0.549635i | \(-0.185233\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 5356.17i | − | 1.10162i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 3989.83 | 0.812097 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2438.21i | 0.486149i | 0.970008 | + | 0.243074i | \(0.0781559\pi\) | ||||
−0.970008 | + | 0.243074i | \(0.921844\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −6854.58 | + | 5375.07i | −1.35284 | + | 1.06084i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12711.0 | 2.45852 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1387.87 | 0.265766 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4250.92 | − | 3333.39i | 0.798056 | − | 0.625801i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 7910.44i | − | 1.47060i | −0.677744 | − | 0.735298i | \(-0.737042\pi\) | ||
0.677744 | − | 0.735298i | \(-0.262958\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −5419.71 | −0.988178 | −0.494089 | − | 0.869411i | \(-0.664498\pi\) | ||||
−0.494089 | + | 0.869411i | \(0.664498\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 5570.86i | 1.00602i | 0.864281 | + | 0.503009i | \(0.167774\pi\) | ||||
−0.864281 | + | 0.503009i | \(0.832226\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 3724.09i | − | 0.659829i | −0.944011 | − | 0.329915i | \(-0.892980\pi\) | ||
0.944011 | − | 0.329915i | \(-0.107020\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 160.898 | 0.0282400 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1798.47i | 0.309812i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 7501.89 | + | 1842.08i | 1.28040 | + | 0.314401i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4615.60 | −0.773453 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3223.96 | 0.535362 | 0.267681 | − | 0.963508i | \(-0.413743\pi\) | ||||
0.267681 | + | 0.963508i | \(0.413743\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 853.453 | + | 1088.37i | 0.139191 | + | 0.177505i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 9524.43i | − | 1.53955i | −0.638314 | − | 0.769776i | \(-0.720368\pi\) | ||
0.638314 | − | 0.769776i | \(-0.279632\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6355.40 | 1.00928 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | − | 6799.20i | − | 1.07033i | ||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 6042.30i | − | 0.934777i | −0.884052 | − | 0.467388i | \(-0.845195\pi\) | ||
0.884052 | − | 0.467388i | \(-0.154805\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1626.20 | 0.249422 | 0.124711 | − | 0.992193i | \(-0.460200\pi\) | ||||
0.124711 | + | 0.992193i | \(0.460200\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 886.955i | − | 0.133733i | −0.997762 | − | 0.0668667i | \(-0.978700\pi\) | ||
0.997762 | − | 0.0668667i | \(-0.0213002\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1647.27 | − | 1291.71i | 0.246275 | − | 0.193119i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1722.27 | 0.253198 | 0.126599 | − | 0.991954i | \(-0.459594\pi\) | ||||
0.126599 | + | 0.991954i | \(0.459594\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3355.33 | −0.489186 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5372.28 | + | 6851.02i | 0.770405 | + | 0.982463i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 9271.77i | − | 1.31875i | −0.751813 | − | 0.659377i | \(-0.770820\pi\) | ||
0.751813 | − | 0.659377i | \(-0.229180\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −6526.63 | −0.913331 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 5697.15i | 0.790850i | 0.918498 | + | 0.395425i | \(0.129403\pi\) | ||||
−0.918498 | + | 0.395425i | \(0.870597\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 518.094i | 0.0707777i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8526.24 | 1.15558 | 0.577789 | − | 0.816186i | \(-0.303916\pi\) | ||||
0.577789 | + | 0.816186i | \(0.303916\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 4069.23i | − | 0.542893i | −0.962453 | − | 0.271447i | \(-0.912498\pi\) | ||
0.962453 | − | 0.271447i | \(-0.0875020\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2210.74 | + | 2819.26i | 0.292649 | + | 0.373202i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2394.17 | −0.312054 | −0.156027 | − | 0.987753i | \(-0.549869\pi\) | ||||
−0.156027 | + | 0.987753i | \(0.549869\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −6249.52 | −0.808316 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −3927.27 | + | 3079.59i | −0.500259 | + | 0.392281i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 3497.79i | − | 0.442190i | −0.975252 | − | 0.221095i | \(-0.929037\pi\) | ||
0.975252 | − | 0.221095i | \(-0.0709630\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8608.89 | 1.07209 | 0.536044 | − | 0.844190i | \(-0.319918\pi\) | ||||
0.536044 | + | 0.844190i | \(0.319918\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 20464.5i | 2.52955i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 5115.88i | − | 0.623058i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1385.67 | −0.167523 | −0.0837615 | − | 0.996486i | \(-0.526693\pi\) | ||||
−0.0837615 | + | 0.996486i | \(0.526693\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 13008.8i | − | 1.54992i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −7271.87 | − | 9273.49i | −0.860149 | − | 1.09691i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3738.23 | 0.435858 | 0.217929 | − | 0.975965i | \(-0.430070\pi\) | ||||
0.217929 | + | 0.975965i | \(0.430070\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8993.95 | −1.04118 | −0.520592 | − | 0.853806i | \(-0.674289\pi\) | ||||
−0.520592 | + | 0.853806i | \(0.674289\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −3688.39 | − | 905.681i | −0.420972 | − | 0.103369i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 8067.48i | 0.914316i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −462.547 | −0.0516940 | −0.0258470 | − | 0.999666i | \(-0.508228\pi\) | ||||
−0.0258470 | + | 0.999666i | \(0.508228\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 5231.82i | − | 0.580659i | −0.956927 | − | 0.290329i | \(-0.906235\pi\) | ||
0.956927 | − | 0.290329i | \(-0.0937649\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 12175.0i | 1.33274i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −8995.77 | −0.978006 | −0.489003 | − | 0.872282i | \(-0.662639\pi\) | ||||
−0.489003 | + | 0.872282i | \(0.662639\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5549.52i | 0.595182i | 0.954694 | + | 0.297591i | \(0.0961831\pi\) | ||||
−0.954694 | + | 0.297591i | \(0.903817\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 834.477 | − | 654.361i | 0.0888944 | − | 0.0697072i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −5951.29 | −0.625521 | −0.312760 | − | 0.949832i | \(-0.601254\pi\) | ||||
−0.312760 | + | 0.949832i | \(0.601254\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6156.51 | 0.642791 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −9078.06 | + | 7118.62i | −0.935354 | + | 0.733464i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 13912.7i | 1.42409i | 0.702132 | + | 0.712047i | \(0.252232\pi\) | ||||
−0.702132 | + | 0.712047i | \(0.747768\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −17467.6 | −1.76475 | −0.882374 | − | 0.470549i | \(-0.844056\pi\) | ||||
−0.882374 | + | 0.470549i | \(0.844056\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1575.36i | 0.158127i | 0.996870 | + | 0.0790637i | \(0.0251931\pi\) | ||||
−0.996870 | + | 0.0790637i | \(0.974807\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 15618.3i | 1.54760i | 0.633430 | + | 0.773800i | \(0.281646\pi\) | ||||
−0.633430 | + | 0.773800i | \(0.718354\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −2065.53 | −0.203363 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1595.25i | 0.155074i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1764.40 | + | 7185.53i | −0.170434 | + | 0.694094i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 9527.90 | 0.908854 | 0.454427 | − | 0.890784i | \(-0.349844\pi\) | ||||
0.454427 | + | 0.890784i | \(0.349844\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 16473.2 | 1.56157 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1738.82 | + | 2217.44i | 0.162796 | + | 0.207606i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 15729.6i | − | 1.46361i | −0.681514 | − | 0.731805i | \(-0.738678\pi\) | ||
0.681514 | − | 0.731805i | \(-0.261322\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2566.49 | −0.235894 | −0.117947 | − | 0.993020i | \(-0.537631\pi\) | ||||
−0.117947 | + | 0.993020i | \(0.537631\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 254.727i | − | 0.0232704i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 3126.21i | 0.282152i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 13560.4 | 1.21652 | 0.608261 | − | 0.793737i | \(-0.291867\pi\) | ||||
0.608261 | + | 0.793737i | \(0.291867\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5222.51i | 0.462943i | 0.972842 | + | 0.231471i | \(0.0743540\pi\) | ||||
−0.972842 | + | 0.231471i | \(0.925646\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 333.604 | − | 261.598i | 0.0293964 | − | 0.0230514i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11875.9 | −1.03416 | −0.517082 | − | 0.855936i | \(-0.672982\pi\) | ||||
−0.517082 | + | 0.855936i | \(0.672982\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −13002.0 | −1.12559 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −651.355 | − | 830.644i | −0.0557323 | − | 0.0710729i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 5305.27i | − | 0.451307i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −2456.04 | −0.206528 | −0.103264 | − | 0.994654i | \(-0.532929\pi\) | ||||
−0.103264 | + | 0.994654i | \(0.532929\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 634.460i | 0.0530459i | 0.999648 | + | 0.0265229i | \(0.00844351\pi\) | ||||
−0.999648 | + | 0.0265229i | \(0.991556\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 10061.6i | − | 0.831669i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −30140.0 | −2.47720 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 19824.0i | 1.61102i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6219.18 | + | 7931.05i | 0.502577 | + | 0.640914i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1232.35 | 0.0984807 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 18078.4 | 1.43669 | 0.718347 | − | 0.695685i | \(-0.244899\pi\) | ||||
0.718347 | + | 0.695685i | \(0.244899\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 12455.2 | − | 9766.84i | 0.978941 | − | 0.767643i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 24815.3i | 1.93972i | 0.243661 | + | 0.969860i | \(0.421651\pi\) | ||||
−0.243661 | + | 0.969860i | \(0.578349\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −496.245 | −0.0383680 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 7453.24i | − | 0.573136i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 10073.7i | − | 0.766310i | −0.923684 | − | 0.383155i | \(-0.874838\pi\) | ||
0.923684 | − | 0.383155i | \(-0.125162\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5136.73 | −0.388660 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 7505.06i | − | 0.561813i | −0.959735 | − | 0.280906i | \(-0.909365\pi\) | ||
0.959735 | − | 0.280906i | \(-0.0906350\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2025.37 | − | 2582.87i | −0.150811 | − | 0.192322i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −15251.4 | −1.12368 | −0.561838 | − | 0.827247i | \(-0.689906\pi\) | ||||
−0.561838 | + | 0.827247i | \(0.689906\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2683.78 | −0.196695 | −0.0983474 | − | 0.995152i | \(-0.531356\pi\) | ||||
−0.0983474 | + | 0.995152i | \(0.531356\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −24969.1 | − | 6131.14i | −1.81093 | − | 0.444672i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7369.88i | 0.531737i | 0.964009 | + | 0.265868i | \(0.0856586\pi\) | ||||
−0.964009 | + | 0.265868i | \(0.914341\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17599.4 | 1.25671 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 7501.85i | − | 0.532925i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 20865.4i | 1.46713i | 0.679618 | + | 0.733567i | \(0.262146\pi\) | ||||
−0.679618 | + | 0.733567i | \(0.737854\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −19601.4 | −1.37124 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25894.0i | 1.79316i | 0.442886 | + | 0.896578i | \(0.353954\pi\) | ||||
−0.442886 | + | 0.896578i | \(0.646046\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4463.33 | − | 3499.95i | 0.307527 | − | 0.241150i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 5632.42 | 0.384198 | 0.192099 | − | 0.981376i | \(-0.438471\pi\) | ||||
0.192099 | + | 0.981376i | \(0.438471\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13079.7 | −0.887742 | −0.443871 | − | 0.896091i | \(-0.646395\pi\) | ||||
−0.443871 | + | 0.896091i | \(0.646395\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8469.56 | − | 6641.46i | 0.569151 | − | 0.446304i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 18890.2i | 1.26314i | 0.775317 | + | 0.631572i | \(0.217590\pi\) | ||||
−0.775317 | + | 0.631572i | \(0.782410\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 17083.0 | 1.13111 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 13631.5i | − | 0.898155i | −0.893493 | − | 0.449078i | \(-0.851753\pi\) | ||
0.893493 | − | 0.449078i | \(-0.148247\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 14982.2i | 0.977568i | 0.872405 | + | 0.488784i | \(0.162559\pi\) | ||||
−0.872405 | + | 0.488784i | \(0.837441\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 25049.9 | 1.62656 | 0.813279 | − | 0.581873i | \(-0.197680\pi\) | ||||
0.813279 | + | 0.581873i | \(0.197680\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1583.69i | 0.101844i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −13847.9 | − | 7237.06i | −0.886269 | − | 0.463172i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −8099.23 | −0.513414 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18711.0 | 1.18046 | 0.590232 | − | 0.807233i | \(-0.299036\pi\) | ||||
0.590232 | + | 0.807233i | \(0.299036\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 5344.76 | + | 6815.93i | 0.334016 | + | 0.425956i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3968.19i | 0.246821i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −25792.2 | −1.58929 | −0.794643 | − | 0.607077i | \(-0.792342\pi\) | ||||
−0.794643 | + | 0.607077i | \(0.792342\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 20256.7i | − | 1.24237i | −0.783663 | − | 0.621186i | \(-0.786651\pi\) | ||
0.783663 | − | 0.621186i | \(-0.213349\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | − | 6655.43i | − | 0.404408i | −0.979343 | − | 0.202204i | \(-0.935190\pi\) | ||
0.979343 | − | 0.202204i | \(-0.0648104\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 14952.6 | 0.904375 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 8490.91i | − | 0.508844i | −0.967093 | − | 0.254422i | \(-0.918115\pi\) | ||
0.967093 | − | 0.254422i | \(-0.0818852\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2941.53 | − | 2306.62i | 0.175474 | − | 0.137599i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 15543.8 | 0.918816 | 0.459408 | − | 0.888225i | \(-0.348062\pi\) | ||||
0.459408 | + | 0.888225i | \(0.348062\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −13519.8 | −0.795553 | −0.397777 | − | 0.917482i | \(-0.630218\pi\) | ||||
−0.397777 | + | 0.917482i | \(0.630218\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −6818.42 | − | 8695.22i | −0.397604 | − | 0.507047i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1724.41i | − | 0.100104i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −9272.95 | −0.533499 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11565.3i | 0.662421i | 0.943557 | + | 0.331211i | \(0.107457\pi\) | ||||
−0.943557 | + | 0.331211i | \(0.892543\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 28227.5i | − | 1.60247i | −0.598350 | − | 0.801235i | \(-0.704177\pi\) | ||
0.598350 | − | 0.801235i | \(-0.295823\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −4208.31 | −0.237850 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 6425.99i | 0.360005i | 0.983666 | + | 0.180003i | \(0.0576106\pi\) | ||||
−0.983666 | + | 0.180003i | \(0.942389\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −2231.92 | − | 2846.27i | −0.124492 | − | 0.158759i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 24156.1 | 1.33566 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −19066.9 | −1.04969 | −0.524846 | − | 0.851197i | \(-0.675877\pi\) | ||||
−0.524846 | + | 0.851197i | \(0.675877\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −3488.23 | + | 2735.32i | −0.190383 | + | 0.149290i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 9746.71i | − | 0.529674i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4796.00 | −0.258406 | −0.129203 | − | 0.991618i | \(-0.541242\pi\) | ||||
−0.129203 | + | 0.991618i | \(0.541242\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 15778.5i | 0.846511i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 633.121i | 0.0336789i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 9805.33 | 0.519389 | 0.259695 | − | 0.965691i | \(-0.416378\pi\) | ||||
0.259695 | + | 0.965691i | \(0.416378\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 68113.4i | − | 3.57765i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −8182.30 | − | 10434.5i | −0.427973 | − | 0.545775i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 27539.7 | 1.42845 | 0.714227 | − | 0.699915i | \(-0.246779\pi\) | ||||
0.714227 | + | 0.699915i | \(0.246779\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1576.41 | 0.0814267 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 249.902 | − | 1017.73i | 0.0128015 | − | 0.0521344i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16543.8i | 0.843985i | 0.906599 | + | 0.421993i | \(0.138669\pi\) | ||||
−0.906599 | + | 0.421993i | \(0.861331\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 2525.53 | 0.127784 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 16718.6i | − | 0.842450i | −0.906956 | − | 0.421225i | \(-0.861600\pi\) | ||
0.906956 | − | 0.421225i | \(-0.138400\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 2374.17i | − | 0.118662i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 24022.6 | 1.19579 | 0.597893 | − | 0.801576i | \(-0.296005\pi\) | ||||
0.597893 | + | 0.801576i | \(0.296005\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 26201.8i | − | 1.29374i | −0.762600 | − | 0.646871i | \(-0.776077\pi\) | ||
0.762600 | − | 0.646871i | \(-0.223923\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 14806.0 | − | 11610.2i | 0.728119 | − | 0.570959i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −15051.7 | −0.734282 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 24451.7 | 1.18809 | 0.594045 | − | 0.804432i | \(-0.297530\pi\) | ||||
0.594045 | + | 0.804432i | \(0.297530\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 25729.8 | − | 20176.2i | 1.24027 | − | 0.972567i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 21403.8i | 1.02765i | 0.857894 | + | 0.513827i | \(0.171773\pi\) | ||||
−0.857894 | + | 0.513827i | \(0.828227\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 28935.9 | 1.37835 | 0.689176 | − | 0.724594i | \(-0.257973\pi\) | ||||
0.689176 | + | 0.724594i | \(0.257973\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 23637.8i | 1.12155i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 48147.4i | 2.26663i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 11479.3 | 0.538301 | 0.269151 | − | 0.963098i | \(-0.413257\pi\) | ||||
0.269151 | + | 0.963098i | \(0.413257\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2512.27i | 0.116895i | 0.998290 | + | 0.0584477i | \(0.0186151\pi\) | ||||
−0.998290 | + | 0.0584477i | \(0.981385\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 9871.00 | − | 40199.7i | 0.457519 | − | 1.86325i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −18988.0 | −0.873320 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3593.34 | −0.164635 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 19099.3 | + | 24356.5i | 0.868386 | + | 1.10741i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2650.18i | 0.120036i | 0.998197 | + | 0.0600182i | \(0.0191159\pi\) | ||||
−0.998197 | + | 0.0600182i | \(0.980884\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 4901.81 | 0.220339 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | − | 29859.0i | − | 1.33711i | ||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24516.7i | 1.08962i | 0.838560 | + | 0.544810i | \(0.183398\pi\) | ||||
−0.838560 | + | 0.544810i | \(0.816602\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8399.07 | −0.371887 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | − | 14944.8i | − | 0.656775i | ||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 30215.2 | − | 23693.4i | 1.32291 | − | 1.03737i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −29725.5 | −1.29183 | −0.645917 | − | 0.763408i | \(-0.723525\pi\) | ||||
−0.645917 | + | 0.763408i | \(0.723525\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2050.38 | −0.0887773 | −0.0443887 | − | 0.999014i | \(-0.514134\pi\) | ||||
−0.0443887 | + | 0.999014i | \(0.514134\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19429.8 | − | 24778.0i | −0.835089 | − | 1.06495i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 4920.11i | − | 0.210689i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 33863.4 | 1.43952 | 0.719758 | − | 0.694225i | \(-0.244253\pi\) | ||||
0.719758 | + | 0.694225i | \(0.244253\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 1216.52i | − | 0.0515251i | −0.999668 | − | 0.0257625i | \(-0.991799\pi\) | ||
0.999668 | − | 0.0257625i | \(-0.00820138\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 25654.4i | − | 1.07871i | −0.842079 | − | 0.539355i | \(-0.818668\pi\) | ||
0.842079 | − | 0.539355i | \(-0.181332\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −24544.6 | −1.02831 | −0.514154 | − | 0.857698i | \(-0.671894\pi\) | ||||
−0.514154 | + | 0.857698i | \(0.671894\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | − | 1951.00i | − | 0.0811504i | ||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −12669.4 | − | 16156.7i | −0.525080 | − | 0.669610i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 16548.6 | 0.680954 | 0.340477 | − | 0.940253i | \(-0.389411\pi\) | ||||
0.340477 | + | 0.940253i | \(0.389411\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24318.7 | −0.997118 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 14270.2 | − | 11190.1i | 0.580958 | − | 0.455562i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 16073.7i | 0.652065i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −54828.9 | −2.20859 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 24363.5i | 0.977950i | 0.872298 | + | 0.488975i | \(0.162629\pi\) | ||||
−0.872298 | + | 0.488975i | \(0.837371\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 575.718i | 0.0229477i | 0.999934 | + | 0.0114738i | \(0.00365232\pi\) | ||||
−0.999934 | + | 0.0114738i | \(0.996348\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −1531.31 | −0.0608236 | −0.0304118 | − | 0.999537i | \(-0.509682\pi\) | ||||
−0.0304118 | + | 0.999537i | \(0.509682\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 7706.51i | 0.303978i | 0.988382 | + | 0.151989i | \(0.0485678\pi\) | ||||
−0.988382 | + | 0.151989i | \(0.951432\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8445.89 | + | 10770.7i | 0.331987 | + | 0.423368i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 8566.92 | 0.334422 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 7644.85 | 0.297400 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 21266.3 | − | 9604.79i | 0.821637 | − | 0.371087i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 43618.9i | 1.67948i | 0.542988 | + | 0.839741i | \(0.317293\pi\) | ||||
−0.542988 | + | 0.839741i | \(0.682707\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 13416.4 | 0.513066 | 0.256533 | − | 0.966536i | \(-0.417420\pi\) | ||||
0.256533 | + | 0.966536i | \(0.417420\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 29538.2i | − | 1.12575i | −0.826542 | − | 0.562875i | \(-0.809695\pi\) | ||
0.826542 | − | 0.562875i | \(-0.190305\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1950.88i | 0.0738490i | 0.999318 | + | 0.0369245i | \(0.0117561\pi\) | ||||
−0.999318 | + | 0.0369245i | \(0.988244\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12935.4 | −0.488009 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 16362.6i | 0.613162i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −24014.7 | + | 18831.3i | −0.896897 | + | 0.703308i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 2776.26 | 0.102996 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −11876.6 | −0.439142 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −23247.4 | + | 18229.6i | −0.853888 | + | 0.669582i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 3507.55i | 0.128408i | 0.997937 | + | 0.0642042i | \(0.0204509\pi\) | ||||
−0.997937 | + | 0.0642042i | \(0.979549\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 33841.4 | 1.23075 | 0.615377 | − | 0.788233i | \(-0.289004\pi\) | ||||
0.615377 | + | 0.788233i | \(0.289004\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 20229.2i | 0.733283i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 5582.50i | 0.201036i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25440.7 | −0.913178 | −0.456589 | − | 0.889678i | \(-0.650929\pi\) | ||||
−0.456589 | + | 0.889678i | \(0.650929\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 11570.6i | − | 0.412623i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −32359.4 | − | 7945.82i | −1.15024 | − | 0.282440i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −26416.7 | −0.932941 | −0.466471 | − | 0.884537i | \(-0.654475\pi\) | ||||
−0.466471 | + | 0.884537i | \(0.654475\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −3800.84 | −0.133800 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 4022.92 | + | 5130.25i | 0.140710 | + | 0.179441i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 1936.70i | − | 0.0675231i | −0.999430 | − | 0.0337616i | \(-0.989251\pi\) | ||
0.999430 | − | 0.0337616i | \(-0.0107487\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −23459.1 | −0.812694 | −0.406347 | − | 0.913719i | \(-0.633198\pi\) | ||||
−0.406347 | + | 0.913719i | \(0.633198\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 65981.8i | − | 2.27854i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 23606.8i | − | 0.810049i | −0.914306 | − | 0.405025i | \(-0.867263\pi\) | ||
0.914306 | − | 0.405025i | \(-0.132737\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 48122.4 | 1.64607 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 30164.2i | 1.02530i | 0.858596 | + | 0.512652i | \(0.171337\pi\) | ||||
−0.858596 | + | 0.512652i | \(0.828663\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −20580.5 | + | 16138.3i | −0.697349 | + | 0.546831i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 5401.70 | 0.181887 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 79870.0 | 2.68101 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −31746.4 | − | 40484.8i | −1.05902 | − | 1.35052i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 9034.04i | 0.300429i | 0.988653 | + | 0.150215i | \(0.0479965\pi\) | ||||
−0.988653 | + | 0.150215i | \(0.952004\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −36159.0 | −1.19506 | −0.597528 | − | 0.801848i | \(-0.703850\pi\) | ||||
−0.597528 | + | 0.801848i | \(0.703850\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | − | 6620.03i | − | 0.218118i | ||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 38584.0i | 1.26347i | 0.775184 | + | 0.631736i | \(0.217657\pi\) | ||||
−0.775184 | + | 0.631736i | \(0.782343\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1820.33 | −0.0594258 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 53046.3i | 1.72117i | 0.509303 | + | 0.860587i | \(0.329903\pi\) | ||||
−0.509303 | + | 0.860587i | \(0.670097\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 5684.35 | + | 7249.00i | 0.183877 | + | 0.234490i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 17097.0 | 0.549699 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −16425.7 | −0.526517 | −0.263259 | − | 0.964725i | \(-0.584797\pi\) | ||||
−0.263259 | + | 0.964725i | \(0.584797\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −29294.5 | + | 22971.5i | −0.933366 | + | 0.731906i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 20024.6i | 0.636092i | 0.948075 | + | 0.318046i | \(0.103027\pi\) | ||||
−0.948075 | + | 0.318046i | \(0.896973\pi\) | |||||||
\(998\) | 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 | 360.4.f.e.289.2 | 4 | ||
3.2 | odd | 2 | 40.4.c.a.9.2 | ✓ | 4 | ||
4.3 | odd | 2 | 720.4.f.m.289.2 | 4 | |||
5.2 | odd | 4 | 1800.4.a.bp.1.2 | 2 | |||
5.3 | odd | 4 | 1800.4.a.bk.1.1 | 2 | |||
5.4 | even | 2 | inner | 360.4.f.e.289.1 | 4 | ||
12.11 | even | 2 | 80.4.c.c.49.3 | 4 | |||
15.2 | even | 4 | 200.4.a.l.1.1 | 2 | |||
15.8 | even | 4 | 200.4.a.k.1.2 | 2 | |||
15.14 | odd | 2 | 40.4.c.a.9.3 | yes | 4 | ||
20.19 | odd | 2 | 720.4.f.m.289.1 | 4 | |||
24.5 | odd | 2 | 320.4.c.g.129.3 | 4 | |||
24.11 | even | 2 | 320.4.c.h.129.2 | 4 | |||
60.23 | odd | 4 | 400.4.a.x.1.1 | 2 | |||
60.47 | odd | 4 | 400.4.a.v.1.2 | 2 | |||
60.59 | even | 2 | 80.4.c.c.49.2 | 4 | |||
120.29 | odd | 2 | 320.4.c.g.129.2 | 4 | |||
120.53 | even | 4 | 1600.4.a.cl.1.1 | 2 | |||
120.59 | even | 2 | 320.4.c.h.129.3 | 4 | |||
120.77 | even | 4 | 1600.4.a.ce.1.2 | 2 | |||
120.83 | odd | 4 | 1600.4.a.cf.1.2 | 2 | |||
120.107 | odd | 4 | 1600.4.a.cm.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.4.c.a.9.2 | ✓ | 4 | 3.2 | odd | 2 | ||
40.4.c.a.9.3 | yes | 4 | 15.14 | odd | 2 | ||
80.4.c.c.49.2 | 4 | 60.59 | even | 2 | |||
80.4.c.c.49.3 | 4 | 12.11 | even | 2 | |||
200.4.a.k.1.2 | 2 | 15.8 | even | 4 | |||
200.4.a.l.1.1 | 2 | 15.2 | even | 4 | |||
320.4.c.g.129.2 | 4 | 120.29 | odd | 2 | |||
320.4.c.g.129.3 | 4 | 24.5 | odd | 2 | |||
320.4.c.h.129.2 | 4 | 24.11 | even | 2 | |||
320.4.c.h.129.3 | 4 | 120.59 | even | 2 | |||
360.4.f.e.289.1 | 4 | 5.4 | even | 2 | inner | ||
360.4.f.e.289.2 | 4 | 1.1 | even | 1 | trivial | ||
400.4.a.v.1.2 | 2 | 60.47 | odd | 4 | |||
400.4.a.x.1.1 | 2 | 60.23 | odd | 4 | |||
720.4.f.m.289.1 | 4 | 20.19 | odd | 2 | |||
720.4.f.m.289.2 | 4 | 4.3 | odd | 2 | |||
1600.4.a.ce.1.2 | 2 | 120.77 | even | 4 | |||
1600.4.a.cf.1.2 | 2 | 120.83 | odd | 4 | |||
1600.4.a.cl.1.1 | 2 | 120.53 | even | 4 | |||
1600.4.a.cm.1.1 | 2 | 120.107 | odd | 4 | |||
1800.4.a.bk.1.1 | 2 | 5.3 | odd | 4 | |||
1800.4.a.bp.1.2 | 2 | 5.2 | odd | 4 |