Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,4,Mod(107,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.107");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.f (of order \(4\), degree \(2\), 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: | \(13.2754297513\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(i)\) |
Coefficient field: | 16.0.11007531417600000000.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 7x^{12} + 48x^{8} - 7x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{16}\cdot 3^{12} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 107.4 | ||
Root | \(-0.418778 + 1.56290i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 225.107 |
Dual form | 225.4.f.d.143.4 |
$q$-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 \(\left(\mathbb{Z}/225\mathbb{Z}\right)^\times\).
\(n\) | \(101\) | \(127\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{1}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.07047 | + | 1.07047i | −0.378467 | + | 0.378467i | −0.870549 | − | 0.492082i | \(-0.836236\pi\) |
0.492082 | + | 0.870549i | \(0.336236\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 5.70820i | 0.713525i | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.85846 | + | 7.85846i | 0.424317 | + | 0.424317i | 0.886687 | − | 0.462370i | \(-0.153001\pi\) |
−0.462370 | + | 0.886687i | \(0.653001\pi\) | |||||||
\(8\) | −14.6742 | − | 14.6742i | −0.648513 | − | 0.648513i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 33.7047i | 0.923850i | 0.886919 | + | 0.461925i | \(0.152841\pi\) | ||||
−0.886919 | + | 0.461925i | \(0.847159\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −25.7196 | + | 25.7196i | −0.548719 | + | 0.548719i | −0.926070 | − | 0.377351i | \(-0.876835\pi\) |
0.377351 | + | 0.926070i | \(0.376835\pi\) | |||||||
\(14\) | −16.8244 | −0.321180 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −14.2492 | −0.222644 | ||||||||
\(17\) | 66.3461 | − | 66.3461i | 0.946547 | − | 0.946547i | −0.0520952 | − | 0.998642i | \(-0.516590\pi\) |
0.998642 | + | 0.0520952i | \(0.0165899\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 128.915i | 1.55658i | 0.627903 | + | 0.778292i | \(0.283914\pi\) | ||||
−0.627903 | + | 0.778292i | \(0.716086\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −36.0797 | − | 36.0797i | −0.349647 | − | 0.349647i | ||||
\(23\) | −110.948 | − | 110.948i | −1.00584 | − | 1.00584i | −0.999983 | − | 0.00585236i | \(-0.998137\pi\) |
−0.00585236 | − | 0.999983i | \(-0.501863\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | − | 55.0640i | − | 0.415344i | ||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −44.8577 | + | 44.8577i | −0.302761 | + | 0.302761i | ||||
\(29\) | −268.817 | −1.72131 | −0.860655 | − | 0.509189i | \(-0.829946\pi\) | ||||
−0.860655 | + | 0.509189i | \(0.829946\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −2.91486 | −0.0168879 | −0.00844393 | − | 0.999964i | \(-0.502688\pi\) | ||||
−0.00844393 | + | 0.999964i | \(0.502688\pi\) | |||||||
\(32\) | 132.647 | − | 132.647i | 0.732776 | − | 0.732776i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 142.043i | 0.716474i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −115.736 | − | 115.736i | −0.514242 | − | 0.514242i | 0.401581 | − | 0.915823i | \(-0.368461\pi\) |
−0.915823 | + | 0.401581i | \(0.868461\pi\) | |||||||
\(38\) | −137.999 | − | 137.999i | −0.589116 | − | 0.589116i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 251.610i | 0.958410i | 0.877703 | + | 0.479205i | \(0.159075\pi\) | ||||
−0.877703 | + | 0.479205i | \(0.840925\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −340.781 | + | 340.781i | −1.20857 | + | 1.20857i | −0.237081 | + | 0.971490i | \(0.576191\pi\) |
−0.971490 | + | 0.237081i | \(0.923809\pi\) | |||||||
\(44\) | −192.393 | −0.659190 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 237.532 | 0.761351 | ||||||||
\(47\) | −126.292 | + | 126.292i | −0.391949 | + | 0.391949i | −0.875382 | − | 0.483432i | \(-0.839390\pi\) |
0.483432 | + | 0.875382i | \(0.339390\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 219.489i | − | 0.639910i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −146.813 | − | 146.813i | −0.391525 | − | 0.391525i | ||||
\(53\) | −254.947 | − | 254.947i | −0.660747 | − | 0.660747i | 0.294809 | − | 0.955556i | \(-0.404744\pi\) |
−0.955556 | + | 0.294809i | \(0.904744\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | − | 230.633i | − | 0.550350i | ||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 287.759 | − | 287.759i | 0.651459 | − | 0.651459i | ||||
\(59\) | −131.161 | −0.289418 | −0.144709 | − | 0.989474i | \(-0.546225\pi\) | ||||
−0.144709 | + | 0.989474i | \(0.546225\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 225.170 | 0.472625 | 0.236312 | − | 0.971677i | \(-0.424061\pi\) | ||||
0.236312 | + | 0.971677i | \(0.424061\pi\) | |||||||
\(62\) | 3.12025 | − | 3.12025i | 0.00639149 | − | 0.00639149i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 169.994i | 0.332019i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 236.271 | + | 236.271i | 0.430823 | + | 0.430823i | 0.888908 | − | 0.458085i | \(-0.151465\pi\) |
−0.458085 | + | 0.888908i | \(0.651465\pi\) | |||||||
\(68\) | 378.717 | + | 378.717i | 0.675385 | + | 0.675385i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 29.8233i | 0.0498503i | 0.999689 | + | 0.0249252i | \(0.00793475\pi\) | ||||
−0.999689 | + | 0.0249252i | \(0.992065\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −41.4328 | + | 41.4328i | −0.0664293 | + | 0.0664293i | −0.739541 | − | 0.673112i | \(-0.764957\pi\) |
0.673112 | + | 0.739541i | \(0.264957\pi\) | |||||||
\(74\) | 247.784 | 0.389247 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −735.872 | −1.11066 | ||||||||
\(77\) | −264.867 | + | 264.867i | −0.392005 | + | 0.392005i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 450.170i | − | 0.641115i | −0.947229 | − | 0.320558i | \(-0.896130\pi\) | ||
0.947229 | − | 0.320558i | \(-0.103870\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −269.340 | − | 269.340i | −0.362727 | − | 0.362727i | ||||
\(83\) | 729.807 | + | 729.807i | 0.965142 | + | 0.965142i | 0.999413 | − | 0.0342709i | \(-0.0109109\pi\) |
−0.0342709 | + | 0.999413i | \(0.510911\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | − | 729.588i | − | 0.914808i | ||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 494.588 | − | 494.588i | 0.599128 | − | 0.599128i | ||||
\(89\) | 1478.30 | 1.76067 | 0.880337 | − | 0.474349i | \(-0.157317\pi\) | ||||
0.880337 | + | 0.474349i | \(0.157317\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −404.234 | −0.465662 | ||||||||
\(92\) | 633.313 | − | 633.313i | 0.717689 | − | 0.717689i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | − | 270.383i | − | 0.296680i | ||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1291.69 | + | 1291.69i | 1.35207 | + | 1.35207i | 0.883339 | + | 0.468734i | \(0.155290\pi\) |
0.468734 | + | 0.883339i | \(0.344710\pi\) | |||||||
\(98\) | 234.956 | + | 234.956i | 0.242185 | + | 0.242185i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1342.18i | 1.32229i | 0.750256 | + | 0.661147i | \(0.229930\pi\) | ||||
−0.750256 | + | 0.661147i | \(0.770070\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 888.748 | − | 888.748i | 0.850203 | − | 0.850203i | −0.139955 | − | 0.990158i | \(-0.544696\pi\) |
0.990158 | + | 0.139955i | \(0.0446958\pi\) | |||||||
\(104\) | 754.829 | 0.711702 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 545.823 | 0.500142 | ||||||||
\(107\) | −1367.01 | + | 1367.01i | −1.23509 | + | 1.23509i | −0.273101 | + | 0.961985i | \(0.588049\pi\) |
−0.961985 | + | 0.273101i | \(0.911951\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 155.177i | − | 0.136360i | −0.997673 | − | 0.0681799i | \(-0.978281\pi\) | ||
0.997673 | − | 0.0681799i | \(-0.0217192\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −111.977 | − | 111.977i | −0.0944717 | − | 0.0944717i | ||||
\(113\) | 241.613 | + | 241.613i | 0.201142 | + | 0.201142i | 0.800489 | − | 0.599347i | \(-0.204573\pi\) |
−0.599347 | + | 0.800489i | \(0.704573\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 1534.46i | − | 1.22820i | ||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 140.403 | − | 140.403i | 0.109535 | − | 0.109535i | ||||
\(119\) | 1042.76 | 0.803272 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 194.994 | 0.146502 | ||||||||
\(122\) | −241.037 | + | 241.037i | −0.178873 | + | 0.178873i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − | 16.6386i | − | 0.0120499i | ||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 597.467 | + | 597.467i | 0.417454 | + | 0.417454i | 0.884325 | − | 0.466871i | \(-0.154619\pi\) |
−0.466871 | + | 0.884325i | \(0.654619\pi\) | |||||||
\(128\) | 879.201 | + | 879.201i | 0.607118 | + | 0.607118i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1289.40i | 0.859966i | 0.902837 | + | 0.429983i | \(0.141480\pi\) | ||||
−0.902837 | + | 0.429983i | \(0.858520\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1013.07 | + | 1013.07i | −0.660485 | + | 0.660485i | ||||
\(134\) | −505.841 | −0.326105 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1947.15 | −1.22770 | ||||||||
\(137\) | −672.223 | + | 672.223i | −0.419211 | + | 0.419211i | −0.884932 | − | 0.465721i | \(-0.845795\pi\) |
0.465721 | + | 0.884932i | \(0.345795\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 1028.98i | − | 0.627891i | −0.949441 | − | 0.313945i | \(-0.898349\pi\) | ||
0.949441 | − | 0.313945i | \(-0.101651\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −31.9248 | − | 31.9248i | −0.0188667 | − | 0.0188667i | ||||
\(143\) | −866.873 | − | 866.873i | −0.506934 | − | 0.506934i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 88.7048i | − | 0.0502826i | ||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 660.647 | − | 660.647i | 0.366925 | − | 0.366925i | ||||
\(149\) | −1475.95 | −0.811509 | −0.405754 | − | 0.913982i | \(-0.632991\pi\) | ||||
−0.405754 | + | 0.913982i | \(0.632991\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3253.22 | 1.75327 | 0.876633 | − | 0.481160i | \(-0.159784\pi\) | ||||
0.876633 | + | 0.481160i | \(0.159784\pi\) | |||||||
\(152\) | 1891.72 | − | 1891.72i | 1.00946 | − | 1.00946i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | − | 567.062i | − | 0.296722i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2284.72 | − | 2284.72i | −1.16141 | − | 1.16141i | −0.984168 | − | 0.177237i | \(-0.943284\pi\) |
−0.177237 | − | 0.984168i | \(-0.556716\pi\) | |||||||
\(158\) | 481.892 | + | 481.892i | 0.242641 | + | 0.242641i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | − | 1743.76i | − | 0.853586i | ||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −65.0158 | + | 65.0158i | −0.0312419 | + | 0.0312419i | −0.722555 | − | 0.691313i | \(-0.757032\pi\) |
0.691313 | + | 0.722555i | \(0.257032\pi\) | |||||||
\(164\) | −1436.24 | −0.683850 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1562.47 | −0.730549 | ||||||||
\(167\) | 111.465 | − | 111.465i | 0.0516493 | − | 0.0516493i | −0.680810 | − | 0.732460i | \(-0.738372\pi\) |
0.732460 | + | 0.680810i | \(0.238372\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 874.000i | 0.397815i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1945.24 | − | 1945.24i | −0.862346 | − | 0.862346i | ||||
\(173\) | −2261.53 | − | 2261.53i | −0.993878 | − | 0.993878i | 0.00610303 | − | 0.999981i | \(-0.498057\pi\) |
−0.999981 | + | 0.00610303i | \(0.998057\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 480.266i | − | 0.205690i | ||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1582.47 | + | 1582.47i | −0.666357 | + | 0.666357i | ||||
\(179\) | −771.589 | −0.322186 | −0.161093 | − | 0.986939i | \(-0.551502\pi\) | ||||
−0.161093 | + | 0.986939i | \(0.551502\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 1010.32 | 0.414897 | 0.207449 | − | 0.978246i | \(-0.433484\pi\) | ||||
0.207449 | + | 0.978246i | \(0.433484\pi\) | |||||||
\(182\) | 432.719 | − | 432.719i | 0.176238 | − | 0.176238i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3256.13i | 1.30459i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2236.18 | + | 2236.18i | 0.874467 | + | 0.874467i | ||||
\(188\) | −720.902 | − | 720.902i | −0.279666 | − | 0.279666i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1285.52i | 0.487000i | 0.969901 | + | 0.243500i | \(0.0782956\pi\) | ||||
−0.969901 | + | 0.243500i | \(0.921704\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1987.54 | + | 1987.54i | −0.741275 | + | 0.741275i | −0.972823 | − | 0.231548i | \(-0.925621\pi\) |
0.231548 | + | 0.972823i | \(0.425621\pi\) | |||||||
\(194\) | −2765.42 | −1.02343 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1252.89 | 0.456592 | ||||||||
\(197\) | 91.4449 | − | 91.4449i | 0.0330720 | − | 0.0330720i | −0.690377 | − | 0.723449i | \(-0.742556\pi\) |
0.723449 | + | 0.690377i | \(0.242556\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1163.72i | 0.414543i | 0.978283 | + | 0.207272i | \(0.0664584\pi\) | ||||
−0.978283 | + | 0.207272i | \(0.933542\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1436.76 | − | 1436.76i | −0.500445 | − | 0.500445i | ||||
\(203\) | −2112.49 | − | 2112.49i | −0.730381 | − | 0.730381i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1902.75i | 0.643548i | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 366.485 | − | 366.485i | 0.122169 | − | 0.122169i | ||||
\(209\) | −4345.04 | −1.43805 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2121.60 | −0.692212 | −0.346106 | − | 0.938195i | \(-0.612496\pi\) | ||||
−0.346106 | + | 0.938195i | \(0.612496\pi\) | |||||||
\(212\) | 1455.29 | − | 1455.29i | 0.471460 | − | 0.471460i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | − | 2926.69i | − | 0.934879i | ||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −22.9063 | − | 22.9063i | −0.00716580 | − | 0.00716580i | ||||
\(218\) | 166.111 | + | 166.111i | 0.0516077 | + | 0.0516077i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3412.80i | 1.03878i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1439.60 | + | 1439.60i | −0.432298 | + | 0.432298i | −0.889410 | − | 0.457111i | \(-0.848884\pi\) |
0.457111 | + | 0.889410i | \(0.348884\pi\) | |||||||
\(224\) | 2084.80 | 0.621859 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −517.277 | −0.152251 | ||||||||
\(227\) | 501.434 | − | 501.434i | 0.146614 | − | 0.146614i | −0.629990 | − | 0.776604i | \(-0.716941\pi\) |
0.776604 | + | 0.629990i | \(0.216941\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6371.08i | 1.83848i | 0.393692 | + | 0.919242i | \(0.371198\pi\) | ||||
−0.393692 | + | 0.919242i | \(0.628802\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3944.66 | + | 3944.66i | 1.11629 | + | 1.11629i | ||||
\(233\) | −3586.88 | − | 3586.88i | −1.00852 | − | 1.00852i | −0.999963 | − | 0.00855336i | \(-0.997277\pi\) |
−0.00855336 | − | 0.999963i | \(-0.502723\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | − | 748.692i | − | 0.206507i | ||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1116.24 | + | 1116.24i | −0.304012 | + | 0.304012i | ||||
\(239\) | 5726.18 | 1.54977 | 0.774886 | − | 0.632100i | \(-0.217807\pi\) | ||||
0.774886 | + | 0.632100i | \(0.217807\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4533.68 | 1.21178 | 0.605892 | − | 0.795547i | \(-0.292816\pi\) | ||||
0.605892 | + | 0.795547i | \(0.292816\pi\) | |||||||
\(242\) | −208.734 | + | 208.734i | −0.0554461 | + | 0.0554461i | ||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1285.32i | 0.337230i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3315.64 | − | 3315.64i | −0.854127 | − | 0.854127i | ||||
\(248\) | 42.7731 | + | 42.7731i | 0.0109520 | + | 0.0109520i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 2022.81i | − | 0.508679i | −0.967115 | − | 0.254340i | \(-0.918142\pi\) | ||
0.967115 | − | 0.254340i | \(-0.0818581\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3739.46 | − | 3739.46i | 0.929241 | − | 0.929241i | ||||
\(254\) | −1279.14 | −0.315985 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −3242.26 | −0.791567 | ||||||||
\(257\) | 2225.48 | − | 2225.48i | 0.540161 | − | 0.540161i | −0.383415 | − | 0.923576i | \(-0.625252\pi\) |
0.923576 | + | 0.383415i | \(0.125252\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 1819.02i | − | 0.436404i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1380.26 | − | 1380.26i | −0.325469 | − | 0.325469i | ||||
\(263\) | 5187.30 | + | 5187.30i | 1.21621 | + | 1.21621i | 0.968950 | + | 0.247257i | \(0.0795291\pi\) |
0.247257 | + | 0.968950i | \(0.420471\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | − | 2168.92i | − | 0.499944i | ||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1348.69 | + | 1348.69i | −0.307403 | + | 0.307403i | ||||
\(269\) | −1505.47 | −0.341228 | −0.170614 | − | 0.985338i | \(-0.554575\pi\) | ||||
−0.170614 | + | 0.985338i | \(0.554575\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3810.34 | −0.854102 | −0.427051 | − | 0.904227i | \(-0.640448\pi\) | ||||
−0.427051 | + | 0.904227i | \(0.640448\pi\) | |||||||
\(272\) | −945.381 | + | 945.381i | −0.210743 | + | 0.210743i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | − | 1439.18i | − | 0.317315i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4620.91 | + | 4620.91i | 1.00232 | + | 1.00232i | 0.999997 | + | 0.00232589i | \(0.000740355\pi\) |
0.00232589 | + | 0.999997i | \(0.499260\pi\) | |||||||
\(278\) | 1101.49 | + | 1101.49i | 0.237636 | + | 0.237636i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1168.20i | − | 0.248004i | −0.992282 | − | 0.124002i | \(-0.960427\pi\) | ||
0.992282 | − | 0.124002i | \(-0.0395730\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4505.94 | − | 4505.94i | 0.946468 | − | 0.946468i | −0.0521705 | − | 0.998638i | \(-0.516614\pi\) |
0.998638 | + | 0.0521705i | \(0.0166139\pi\) | |||||||
\(284\) | −170.237 | −0.0355695 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1855.92 | 0.383715 | ||||||||
\(287\) | −1977.26 | + | 1977.26i | −0.406670 | + | 0.406670i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | − | 3890.62i | − | 0.791902i | ||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −236.507 | − | 236.507i | −0.0473990 | − | 0.0473990i | ||||
\(293\) | 3623.76 | + | 3623.76i | 0.722533 | + | 0.722533i | 0.969120 | − | 0.246588i | \(-0.0793094\pi\) |
−0.246588 | + | 0.969120i | \(0.579309\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3396.67i | 0.666985i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1579.96 | − | 1579.96i | 0.307129 | − | 0.307129i | ||||
\(299\) | 5707.07 | 1.10384 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −5356.02 | −1.02563 | ||||||||
\(302\) | −3482.46 | + | 3482.46i | −0.663553 | + | 0.663553i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | − | 1836.94i | − | 0.346564i | ||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1210.91 | − | 1210.91i | −0.225114 | − | 0.225114i | 0.585534 | − | 0.810648i | \(-0.300885\pi\) |
−0.810648 | + | 0.585534i | \(0.800885\pi\) | |||||||
\(308\) | −1511.92 | − | 1511.92i | −0.279706 | − | 0.279706i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 6608.74i | − | 1.20498i | −0.798128 | − | 0.602488i | \(-0.794176\pi\) | ||
0.798128 | − | 0.602488i | \(-0.205824\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4399.41 | + | 4399.41i | −0.794471 | + | 0.794471i | −0.982218 | − | 0.187746i | \(-0.939882\pi\) |
0.187746 | + | 0.982218i | \(0.439882\pi\) | |||||||
\(314\) | 4891.43 | 0.879107 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2569.66 | 0.457452 | ||||||||
\(317\) | −484.443 | + | 484.443i | −0.0858329 | + | 0.0858329i | −0.748720 | − | 0.662887i | \(-0.769331\pi\) |
0.662887 | + | 0.748720i | \(0.269331\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 9060.38i | − | 1.59023i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 1866.63 | + | 1866.63i | 0.323054 | + | 0.323054i | ||||
\(323\) | 8553.00 | + | 8553.00i | 1.47338 | + | 1.47338i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | − | 139.194i | − | 0.0236480i | ||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 3692.16 | − | 3692.16i | 0.621541 | − | 0.621541i | ||||
\(329\) | −1984.93 | −0.332622 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9323.92 | 1.54830 | 0.774152 | − | 0.632999i | \(-0.218176\pi\) | ||||
0.774152 | + | 0.632999i | \(0.218176\pi\) | |||||||
\(332\) | −4165.89 | + | 4165.89i | −0.688653 | + | 0.688653i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 238.639i | 0.0390951i | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4993.89 | − | 4993.89i | −0.807224 | − | 0.807224i | 0.176989 | − | 0.984213i | \(-0.443364\pi\) |
−0.984213 | + | 0.176989i | \(0.943364\pi\) | |||||||
\(338\) | −935.588 | − | 935.588i | −0.150560 | − | 0.150560i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 98.2443i | − | 0.0156018i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 4420.30 | − | 4420.30i | 0.695842 | − | 0.695842i | ||||
\(344\) | 10001.3 | 1.56755 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 4841.78 | 0.752300 | ||||||||
\(347\) | −4772.75 | + | 4772.75i | −0.738370 | + | 0.738370i | −0.972263 | − | 0.233892i | \(-0.924854\pi\) |
0.233892 | + | 0.972263i | \(0.424854\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − | 2130.21i | − | 0.326726i | −0.986566 | − | 0.163363i | \(-0.947766\pi\) | ||
0.986566 | − | 0.163363i | \(-0.0522342\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 4470.82 | + | 4470.82i | 0.676975 | + | 0.676975i | ||||
\(353\) | −3735.22 | − | 3735.22i | −0.563189 | − | 0.563189i | 0.367023 | − | 0.930212i | \(-0.380377\pi\) |
−0.930212 | + | 0.367023i | \(0.880377\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 8438.46i | 1.25629i | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 825.960 | − | 825.960i | 0.121937 | − | 0.121937i | ||||
\(359\) | −818.350 | −0.120309 | −0.0601544 | − | 0.998189i | \(-0.519159\pi\) | ||||
−0.0601544 | + | 0.998189i | \(0.519159\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −9760.04 | −1.42295 | ||||||||
\(362\) | −1081.51 | + | 1081.51i | −0.157025 | + | 0.157025i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | − | 2307.45i | − | 0.332261i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 6106.19 | + | 6106.19i | 0.868502 | + | 0.868502i | 0.992307 | − | 0.123805i | \(-0.0395096\pi\) |
−0.123805 | + | 0.992307i | \(0.539510\pi\) | |||||||
\(368\) | 1580.92 | + | 1580.92i | 0.223943 | + | 0.223943i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 4006.98i | − | 0.560733i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 741.335 | − | 741.335i | 0.102908 | − | 0.102908i | −0.653778 | − | 0.756686i | \(-0.726817\pi\) |
0.756686 | + | 0.653778i | \(0.226817\pi\) | |||||||
\(374\) | −4787.50 | −0.661914 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 3706.47 | 0.508368 | ||||||||
\(377\) | 6913.87 | − | 6913.87i | 0.944515 | − | 0.944515i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 56.6115i | − | 0.00767266i | −0.999993 | − | 0.00383633i | \(-0.998779\pi\) | ||
0.999993 | − | 0.00383633i | \(-0.00122115\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1376.11 | − | 1376.11i | −0.184313 | − | 0.184313i | ||||
\(383\) | 4830.26 | + | 4830.26i | 0.644425 | + | 0.644425i | 0.951640 | − | 0.307215i | \(-0.0993971\pi\) |
−0.307215 | + | 0.951640i | \(0.599397\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − | 4255.18i | − | 0.561096i | ||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7373.22 | + | 7373.22i | −0.964739 | + | 0.964739i | ||||
\(389\) | −1186.46 | −0.154643 | −0.0773213 | − | 0.997006i | \(-0.524637\pi\) | ||||
−0.0773213 | + | 0.997006i | \(0.524637\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −14721.9 | −1.90414 | ||||||||
\(392\) | −3220.82 | + | 3220.82i | −0.414990 | + | 0.414990i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 195.777i | 0.0250333i | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8913.20 | − | 8913.20i | −1.12680 | − | 1.12680i | −0.990694 | − | 0.136108i | \(-0.956540\pi\) |
−0.136108 | − | 0.990694i | \(-0.543460\pi\) | |||||||
\(398\) | −1245.73 | − | 1245.73i | −0.156891 | − | 0.156891i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 5637.87i | − | 0.702099i | −0.936357 | − | 0.351050i | \(-0.885825\pi\) | ||
0.936357 | − | 0.351050i | \(-0.114175\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 74.9690 | − | 74.9690i | 0.00926668 | − | 0.00926668i | ||||
\(404\) | −7661.43 | −0.943491 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4522.69 | 0.552850 | ||||||||
\(407\) | 3900.86 | − | 3900.86i | 0.475083 | − | 0.475083i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 12265.1i | 1.48282i | 0.671055 | + | 0.741408i | \(0.265841\pi\) | ||||
−0.671055 | + | 0.741408i | \(0.734159\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 5073.15 | + | 5073.15i | 0.606642 | + | 0.606642i | ||||
\(413\) | −1030.72 | − | 1030.72i | −0.122805 | − | 0.122805i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 6823.25i | 0.804176i | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 4651.21 | − | 4651.21i | 0.544254 | − | 0.544254i | ||||
\(419\) | 9519.10 | 1.10988 | 0.554938 | − | 0.831891i | \(-0.312742\pi\) | ||||
0.554938 | + | 0.831891i | \(0.312742\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4787.83 | 0.554263 | 0.277131 | − | 0.960832i | \(-0.410616\pi\) | ||||
0.277131 | + | 0.960832i | \(0.410616\pi\) | |||||||
\(422\) | 2271.10 | − | 2271.10i | 0.261979 | − | 0.261979i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 7482.26i | 0.857006i | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1769.49 | + | 1769.49i | 0.200543 | + | 0.200543i | ||||
\(428\) | −7803.20 | − | 7803.20i | −0.881266 | − | 0.881266i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8308.56i | 0.928560i | 0.885689 | + | 0.464280i | \(0.153687\pi\) | ||||
−0.885689 | + | 0.464280i | \(0.846313\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4885.19 | + | 4885.19i | −0.542188 | + | 0.542188i | −0.924170 | − | 0.381982i | \(-0.875242\pi\) |
0.381982 | + | 0.924170i | \(0.375242\pi\) | |||||||
\(434\) | 49.0408 | 0.00542404 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 885.779 | 0.0972962 | ||||||||
\(437\) | 14302.8 | − | 14302.8i | 1.56567 | − | 1.56567i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4105.93i | 0.446391i | 0.974774 | + | 0.223195i | \(0.0716488\pi\) | ||||
−0.974774 | + | 0.223195i | \(0.928351\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −3653.28 | − | 3653.28i | −0.393143 | − | 0.393143i | ||||
\(443\) | −1722.96 | − | 1722.96i | −0.184786 | − | 0.184786i | 0.608652 | − | 0.793438i | \(-0.291711\pi\) |
−0.793438 | + | 0.608652i | \(0.791711\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | − | 3082.08i | − | 0.327221i | ||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1335.89 | + | 1335.89i | −0.140881 | + | 0.140881i | ||||
\(449\) | −15259.1 | −1.60383 | −0.801917 | − | 0.597436i | \(-0.796186\pi\) | ||||
−0.801917 | + | 0.597436i | \(0.796186\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −8480.42 | −0.885427 | ||||||||
\(452\) | −1379.18 | + | 1379.18i | −0.143520 | + | 0.143520i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1073.54i | 0.110977i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5301.02 | − | 5301.02i | −0.542607 | − | 0.542607i | 0.381685 | − | 0.924292i | \(-0.375344\pi\) |
−0.924292 | + | 0.381685i | \(0.875344\pi\) | |||||||
\(458\) | −6820.03 | − | 6820.03i | −0.695806 | − | 0.695806i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 4117.47i | − | 0.415986i | −0.978130 | − | 0.207993i | \(-0.933307\pi\) | ||
0.978130 | − | 0.207993i | \(-0.0666932\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3550.72 | − | 3550.72i | 0.356406 | − | 0.356406i | −0.506081 | − | 0.862486i | \(-0.668906\pi\) |
0.862486 | + | 0.506081i | \(0.168906\pi\) | |||||||
\(464\) | 3830.43 | 0.383240 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 7679.27 | 0.763381 | ||||||||
\(467\) | 2539.40 | − | 2539.40i | 0.251626 | − | 0.251626i | −0.570011 | − | 0.821637i | \(-0.693061\pi\) |
0.821637 | + | 0.570011i | \(0.193061\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3713.46i | 0.365611i | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1924.67 | + | 1924.67i | 0.187691 | + | 0.187691i | ||||
\(473\) | −11485.9 | − | 11485.9i | −1.11654 | − | 1.11654i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 5952.27i | 0.573155i | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −6129.68 | + | 6129.68i | −0.586538 | + | 0.586538i | ||||
\(479\) | −15920.6 | −1.51865 | −0.759324 | − | 0.650712i | \(-0.774470\pi\) | ||||
−0.759324 | + | 0.650712i | \(0.774470\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5953.40 | 0.564349 | ||||||||
\(482\) | −4853.15 | + | 4853.15i | −0.458620 | + | 0.458620i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1113.06i | 0.104533i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 2724.10 | + | 2724.10i | 0.253472 | + | 0.253472i | 0.822393 | − | 0.568920i | \(-0.192639\pi\) |
−0.568920 | + | 0.822393i | \(0.692639\pi\) | |||||||
\(488\) | −3304.19 | − | 3304.19i | −0.306503 | − | 0.306503i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 4422.67i | 0.406502i | 0.979127 | + | 0.203251i | \(0.0651507\pi\) | ||||
−0.979127 | + | 0.203251i | \(0.934849\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −17834.9 | + | 17834.9i | −1.62930 | + | 1.62930i | ||||
\(494\) | 7098.57 | 0.646518 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 41.5344 | 0.00375998 | ||||||||
\(497\) | −234.365 | + | 234.365i | −0.0211523 | + | 0.0211523i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 653.980i | − | 0.0586697i | −0.999570 | − | 0.0293348i | \(-0.990661\pi\) | ||
0.999570 | − | 0.0293348i | \(-0.00933891\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2165.35 | + | 2165.35i | 0.192518 | + | 0.192518i | ||||
\(503\) | 7109.17 | + | 7109.17i | 0.630183 | + | 0.630183i | 0.948114 | − | 0.317931i | \(-0.102988\pi\) |
−0.317931 | + | 0.948114i | \(0.602988\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 8005.93i | 0.703374i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −3410.46 | + | 3410.46i | −0.297864 | + | 0.297864i | ||||
\(509\) | −15370.7 | −1.33849 | −0.669246 | − | 0.743041i | \(-0.733383\pi\) | ||||
−0.669246 | + | 0.743041i | \(0.733383\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −651.196 | −0.0563742 | ||||||||
\(512\) | −3562.88 | + | 3562.88i | −0.307536 | + | 0.307536i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 4764.59i | 0.408866i | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4256.64 | − | 4256.64i | −0.362102 | − | 0.362102i | ||||
\(518\) | 1947.20 | + | 1947.20i | 0.165164 | + | 0.165164i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 8014.41i | 0.673930i | 0.941517 | + | 0.336965i | \(0.109400\pi\) | ||||
−0.941517 | + | 0.336965i | \(0.890600\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 8470.99 | − | 8470.99i | 0.708242 | − | 0.708242i | −0.257924 | − | 0.966165i | \(-0.583038\pi\) |
0.966165 | + | 0.257924i | \(0.0830383\pi\) | |||||||
\(524\) | −7360.17 | −0.613608 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −11105.7 | −0.920588 | ||||||||
\(527\) | −193.389 | + | 193.389i | −0.0159851 | + | 0.0159851i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 12451.8i | 1.02341i | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −5782.82 | − | 5782.82i | −0.471273 | − | 0.471273i | ||||
\(533\) | −6471.31 | − | 6471.31i | −0.525898 | − | 0.525898i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | − | 6934.18i | − | 0.558789i | ||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1611.56 | − | 1611.56i | 0.129144 | − | 0.129144i | ||||
\(539\) | 7397.81 | 0.591181 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 16590.7 | 1.31846 | 0.659231 | − | 0.751941i | \(-0.270882\pi\) | ||||
0.659231 | + | 0.751941i | \(0.270882\pi\) | |||||||
\(542\) | 4078.84 | − | 4078.84i | 0.323249 | − | 0.323249i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | − | 17601.2i | − | 1.38721i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7105.34 | − | 7105.34i | −0.555397 | − | 0.555397i | 0.372596 | − | 0.927994i | \(-0.378468\pi\) |
−0.927994 | + | 0.372596i | \(0.878468\pi\) | |||||||
\(548\) | −3837.19 | − | 3837.19i | −0.299118 | − | 0.299118i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 34654.5i | − | 2.67936i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3537.65 | − | 3537.65i | 0.272036 | − | 0.272036i | ||||
\(554\) | −9893.05 | −0.758692 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 5873.62 | 0.448016 | ||||||||
\(557\) | −1686.40 | + | 1686.40i | −0.128286 | + | 0.128286i | −0.768334 | − | 0.640049i | \(-0.778914\pi\) |
0.640049 | + | 0.768334i | \(0.278914\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 17529.5i | − | 1.32633i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 1250.52 | + | 1250.52i | 0.0938614 | + | 0.0938614i | ||||
\(563\) | 4011.17 | + | 4011.17i | 0.300268 | + | 0.300268i | 0.841119 | − | 0.540851i | \(-0.181898\pi\) |
−0.540851 | + | 0.841119i | \(0.681898\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 9646.91i | 0.716414i | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 437.632 | − | 437.632i | 0.0323286 | − | 0.0323286i | ||||
\(569\) | 11917.1 | 0.878012 | 0.439006 | − | 0.898484i | \(-0.355331\pi\) | ||||
0.439006 | + | 0.898484i | \(0.355331\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 5233.00 | 0.383528 | 0.191764 | − | 0.981441i | \(-0.438579\pi\) | ||||
0.191764 | + | 0.981441i | \(0.438579\pi\) | |||||||
\(572\) | 4948.29 | − | 4948.29i | 0.361710 | − | 0.361710i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | − | 4233.19i | − | 0.307822i | ||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −471.420 | − | 471.420i | −0.0340130 | − | 0.0340130i | 0.689896 | − | 0.723909i | \(-0.257656\pi\) |
−0.723909 | + | 0.689896i | \(0.757656\pi\) | |||||||
\(578\) | 4164.77 | + | 4164.77i | 0.299709 | + | 0.299709i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 11470.3i | 0.819052i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8592.90 | − | 8592.90i | 0.610431 | − | 0.610431i | ||||
\(584\) | 1215.98 | 0.0861605 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −7758.22 | −0.546910 | ||||||||
\(587\) | −11088.0 | + | 11088.0i | −0.779645 | + | 0.779645i | −0.979770 | − | 0.200125i | \(-0.935865\pi\) |
0.200125 | + | 0.979770i | \(0.435865\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | − | 375.768i | − | 0.0262874i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1649.16 | + | 1649.16i | 0.114493 | + | 0.114493i | ||||
\(593\) | 4249.89 | + | 4249.89i | 0.294303 | + | 0.294303i | 0.838778 | − | 0.544474i | \(-0.183271\pi\) |
−0.544474 | + | 0.838778i | \(0.683271\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 8425.04i | − | 0.579032i | ||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6109.23 | + | 6109.23i | −0.417768 | + | 0.417768i | ||||
\(599\) | 25049.7 | 1.70868 | 0.854341 | − | 0.519712i | \(-0.173961\pi\) | ||||
0.854341 | + | 0.519712i | \(0.173961\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −23667.8 | −1.60637 | −0.803186 | − | 0.595728i | \(-0.796864\pi\) | ||||
−0.803186 | + | 0.595728i | \(0.796864\pi\) | |||||||
\(602\) | 5733.44 | − | 5733.44i | 0.388169 | − | 0.388169i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 18570.0i | 1.25100i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −1377.34 | − | 1377.34i | −0.0920997 | − | 0.0920997i | 0.659556 | − | 0.751656i | \(-0.270744\pi\) |
−0.751656 | + | 0.659556i | \(0.770744\pi\) | |||||||
\(608\) | 17100.1 | + | 17100.1i | 1.14063 | + | 1.14063i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 6496.38i | − | 0.430140i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 6308.16 | − | 6308.16i | 0.415635 | − | 0.415635i | −0.468061 | − | 0.883696i | \(-0.655047\pi\) |
0.883696 | + | 0.468061i | \(0.155047\pi\) | |||||||
\(614\) | 2592.47 | 0.170397 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 7773.41 | 0.508441 | ||||||||
\(617\) | 699.955 | − | 699.955i | 0.0456712 | − | 0.0456712i | −0.683902 | − | 0.729574i | \(-0.739719\pi\) |
0.729574 | + | 0.683902i | \(0.239719\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 19461.7i | − | 1.26370i | −0.775089 | − | 0.631852i | \(-0.782295\pi\) | ||
0.775089 | − | 0.631852i | \(-0.217705\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 7074.43 | + | 7074.43i | 0.456043 | + | 0.456043i | ||||
\(623\) | 11617.2 | + | 11617.2i | 0.747084 | + | 0.747084i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | − | 9418.84i | − | 0.601362i | ||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 13041.7 | − | 13041.7i | 0.828692 | − | 0.828692i | ||||
\(629\) | −15357.3 | −0.973509 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7257.30 | 0.457858 | 0.228929 | − | 0.973443i | \(-0.426478\pi\) | ||||
0.228929 | + | 0.973443i | \(0.426478\pi\) | |||||||
\(632\) | −6605.88 | + | 6605.88i | −0.415772 | + | 0.415772i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | − | 1037.16i | − | 0.0649699i | ||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 5645.18 | + | 5645.18i | 0.351131 | + | 0.351131i | ||||
\(638\) | 9698.83 | + | 9698.83i | 0.601850 | + | 0.601850i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 21156.1i | 1.30361i | 0.758385 | + | 0.651807i | \(0.225989\pi\) | ||||
−0.758385 | + | 0.651807i | \(0.774011\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8931.56 | + | 8931.56i | −0.547786 | + | 0.547786i | −0.925800 | − | 0.378014i | \(-0.876607\pi\) |
0.378014 | + | 0.925800i | \(0.376607\pi\) | |||||||
\(644\) | 9953.73 | 0.609055 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −18311.4 | −1.11525 | ||||||||
\(647\) | −16740.1 | + | 16740.1i | −1.01719 | + | 1.01719i | −0.0173412 | + | 0.999850i | \(0.505520\pi\) |
−0.999850 | + | 0.0173412i | \(0.994480\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 4420.73i | − | 0.267379i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −371.123 | − | 371.123i | −0.0222919 | − | 0.0222919i | ||||
\(653\) | −12157.8 | − | 12157.8i | −0.728592 | − | 0.728592i | 0.241747 | − | 0.970339i | \(-0.422280\pi\) |
−0.970339 | + | 0.241747i | \(0.922280\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 3585.24i | − | 0.213384i | ||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2124.80 | − | 2124.80i | 0.125886 | − | 0.125886i | ||||
\(659\) | 28300.0 | 1.67285 | 0.836427 | − | 0.548079i | \(-0.184641\pi\) | ||||
0.836427 | + | 0.548079i | \(0.184641\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4326.04 | 0.254559 | 0.127280 | − | 0.991867i | \(-0.459375\pi\) | ||||
0.127280 | + | 0.991867i | \(0.459375\pi\) | |||||||
\(662\) | −9980.94 | + | 9980.94i | −0.585982 | + | 0.585982i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | − | 21418.6i | − | 1.25181i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 29824.6 | + | 29824.6i | 1.73135 | + | 1.73135i | ||||
\(668\) | 636.266 | + | 636.266i | 0.0368531 | + | 0.0368531i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 7589.30i | 0.436634i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 11089.2 | − | 11089.2i | 0.635153 | − | 0.635153i | −0.314203 | − | 0.949356i | \(-0.601737\pi\) |
0.949356 | + | 0.314203i | \(0.101737\pi\) | |||||||
\(674\) | 10691.6 | 0.611015 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −4988.97 | −0.283851 | ||||||||
\(677\) | 3104.83 | − | 3104.83i | 0.176260 | − | 0.176260i | −0.613463 | − | 0.789723i | \(-0.710224\pi\) |
0.789723 | + | 0.613463i | \(0.210224\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20301.4i | 1.14742i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 105.167 | + | 105.167i | 0.00590478 | + | 0.00590478i | ||||
\(683\) | 2278.90 | + | 2278.90i | 0.127672 | + | 0.127672i | 0.768055 | − | 0.640384i | \(-0.221225\pi\) |
−0.640384 | + | 0.768055i | \(0.721225\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 9463.56i | 0.526706i | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4855.86 | − | 4855.86i | 0.269081 | − | 0.269081i | ||||
\(689\) | 13114.3 | 0.725129 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 6466.55 | 0.356004 | 0.178002 | − | 0.984030i | \(-0.443037\pi\) | ||||
0.178002 | + | 0.984030i | \(0.443037\pi\) | |||||||
\(692\) | 12909.3 | − | 12909.3i | 0.709158 | − | 0.709158i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | − | 10218.1i | − | 0.558897i | ||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 16693.3 | + | 16693.3i | 0.907180 | + | 0.907180i | ||||
\(698\) | 2280.32 | + | 2280.32i | 0.123655 | + | 0.123655i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 31472.6i | − | 1.69573i | −0.530214 | − | 0.847864i | \(-0.677888\pi\) | ||
0.530214 | − | 0.847864i | \(-0.322112\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 14920.2 | − | 14920.2i | 0.800461 | − | 0.800461i | ||||
\(704\) | −5729.59 | −0.306736 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7996.86 | 0.426297 | ||||||||
\(707\) | −10547.5 | + | 10547.5i | −0.561072 | + | 0.561072i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 21493.4i | 1.13851i | 0.822162 | + | 0.569254i | \(0.192768\pi\) | ||||
−0.822162 | + | 0.569254i | \(0.807232\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −21692.9 | − | 21692.9i | −1.14182 | − | 1.14182i | ||||
\(713\) | 323.397 | + | 323.397i | 0.0169864 | + | 0.0169864i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | − | 4404.39i | − | 0.229888i | ||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 876.016 | − | 876.016i | 0.0455329 | − | 0.0455329i | ||||
\(719\) | 34918.3 | 1.81117 | 0.905587 | − | 0.424160i | \(-0.139431\pi\) | ||||
0.905587 | + | 0.424160i | \(0.139431\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13968.4 | 0.721511 | ||||||||
\(722\) | 10447.8 | − | 10447.8i | 0.538541 | − | 0.538541i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 5767.11i | 0.296040i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14767.9 | − | 14767.9i | −0.753388 | − | 0.753388i | 0.221722 | − | 0.975110i | \(-0.428832\pi\) |
−0.975110 | + | 0.221722i | \(0.928832\pi\) | |||||||
\(728\) | 5931.79 | + | 5931.79i | 0.301988 | + | 0.301988i | ||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 45218.9i | 2.28794i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −15017.4 | + | 15017.4i | −0.756726 | + | 0.756726i | −0.975725 | − | 0.218999i | \(-0.929721\pi\) |
0.218999 | + | 0.975725i | \(0.429721\pi\) | |||||||
\(734\) | −13072.9 | −0.657399 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −29433.7 | −1.47410 | ||||||||
\(737\) | −7963.46 | + | 7963.46i | −0.398016 | + | 0.398016i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 30967.6i | − | 1.54149i | −0.637143 | − | 0.770746i | \(-0.719884\pi\) | ||
0.637143 | − | 0.770746i | \(-0.280116\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 4289.33 | + | 4289.33i | 0.212219 | + | 0.212219i | ||||
\(743\) | 9588.32 | + | 9588.32i | 0.473434 | + | 0.473434i | 0.903024 | − | 0.429590i | \(-0.141342\pi\) |
−0.429590 | + | 0.903024i | \(0.641342\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 1587.15i | 0.0778949i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −12764.5 | + | 12764.5i | −0.623955 | + | 0.623955i | ||||
\(749\) | −21485.3 | −1.04814 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8514.08 | 0.413693 | 0.206846 | − | 0.978373i | \(-0.433680\pi\) | ||||
0.206846 | + | 0.978373i | \(0.433680\pi\) | |||||||
\(752\) | 1799.57 | − | 1799.57i | 0.0872652 | − | 0.0872652i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 14802.1i | 0.714936i | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7031.43 | + | 7031.43i | 0.337598 | + | 0.337598i | 0.855463 | − | 0.517865i | \(-0.173273\pi\) |
−0.517865 | + | 0.855463i | \(0.673273\pi\) | |||||||
\(758\) | 60.6007 | + | 60.6007i | 0.00290385 | + | 0.00290385i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 15458.2i | − | 0.736346i | −0.929757 | − | 0.368173i | \(-0.879983\pi\) | ||
0.929757 | − | 0.368173i | \(-0.120017\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1219.45 | − | 1219.45i | 0.0578598 | − | 0.0578598i | ||||
\(764\) | −7338.01 | −0.347487 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10341.3 | −0.487787 | ||||||||
\(767\) | 3373.40 | − | 3373.40i | 0.158809 | − | 0.158809i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 10361.1i | − | 0.485865i | −0.970043 | − | 0.242933i | \(-0.921891\pi\) | ||
0.970043 | − | 0.242933i | \(-0.0781094\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −11345.3 | − | 11345.3i | −0.528919 | − | 0.528919i | ||||
\(773\) | −18766.0 | − | 18766.0i | −0.873179 | − | 0.873179i | 0.119638 | − | 0.992818i | \(-0.461827\pi\) |
−0.992818 | + | 0.119638i | \(0.961827\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 37908.9i | − | 1.75367i | ||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1270.07 | − | 1270.07i | 0.0585271 | − | 0.0585271i | ||||
\(779\) | −32436.2 | −1.49185 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1005.18 | −0.0460542 | ||||||||
\(782\) | 15759.3 | − | 15759.3i | 0.720654 | − | 0.720654i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3127.55i | 0.142472i | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7235.25 | + | 7235.25i | 0.327711 | + | 0.327711i | 0.851716 | − | 0.524004i | \(-0.175562\pi\) |
−0.524004 | + | 0.851716i | \(0.675562\pi\) | |||||||
\(788\) | 521.986 | + | 521.986i | 0.0235977 | + | 0.0235977i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 3797.41i | 0.170696i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −5791.30 | + | 5791.30i | −0.259338 | + | 0.259338i | ||||
\(794\) | 19082.6 | 0.852915 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6642.77 | −0.295787 | ||||||||
\(797\) | 1551.35 | − | 1551.35i | 0.0689483 | − | 0.0689483i | −0.671792 | − | 0.740740i | \(-0.734475\pi\) |
0.740740 | + | 0.671792i | \(0.234475\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 16758.0i | 0.741997i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 6035.15 | + | 6035.15i | 0.265721 | + | 0.265721i | ||||
\(803\) | −1396.48 | − | 1396.48i | −0.0613707 | − | 0.0613707i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 160.504i | 0.00701427i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 19695.4 | − | 19695.4i | 0.857525 | − | 0.857525i | ||||
\(809\) | −35332.5 | −1.53551 | −0.767753 | − | 0.640746i | \(-0.778625\pi\) | ||||
−0.767753 | + | 0.640746i | \(0.778625\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −3294.91 | −0.142663 | −0.0713316 | − | 0.997453i | \(-0.522725\pi\) | ||||
−0.0713316 | + | 0.997453i | \(0.522725\pi\) | |||||||
\(812\) | 12058.5 | − | 12058.5i | 0.521146 | − | 0.521146i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 8351.48i | 0.359606i | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −43931.7 | − | 43931.7i | −1.88124 | − | 1.88124i | ||||
\(818\) | −13129.4 | − | 13129.4i | −0.561197 | − | 0.561197i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 23285.6i | 0.989856i | 0.868934 | + | 0.494928i | \(0.164806\pi\) | ||||
−0.868934 | + | 0.494928i | \(0.835194\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −21867.6 | + | 21867.6i | −0.926193 | + | 0.926193i | −0.997457 | − | 0.0712645i | \(-0.977297\pi\) |
0.0712645 | + | 0.997457i | \(0.477297\pi\) | |||||||
\(824\) | −26083.3 | −1.10274 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 2206.70 | 0.0929553 | ||||||||
\(827\) | −9797.82 | + | 9797.82i | −0.411975 | + | 0.411975i | −0.882426 | − | 0.470451i | \(-0.844091\pi\) |
0.470451 | + | 0.882426i | \(0.344091\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 553.239i | 0.0231783i | 0.999933 | + | 0.0115891i | \(0.00368902\pi\) | ||||
−0.999933 | + | 0.0115891i | \(0.996311\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4372.18 | − | 4372.18i | −0.182185 | − | 0.182185i | ||||
\(833\) | −14562.3 | − | 14562.3i | −0.605705 | − | 0.605705i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | − | 24802.3i | − | 1.02609i | ||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −10189.9 | + | 10189.9i | −0.420052 | + | 0.420052i | ||||
\(839\) | −11448.4 | −0.471086 | −0.235543 | − | 0.971864i | \(-0.575687\pi\) | ||||
−0.235543 | + | 0.971864i | \(0.575687\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 47873.4 | 1.96291 | ||||||||
\(842\) | −5125.21 | + | 5125.21i | −0.209770 | + | 0.209770i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | − | 12110.5i | − | 0.493911i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1532.35 | + | 1532.35i | 0.0621632 | + | 0.0621632i | ||||
\(848\) | 3632.79 | + | 3632.79i | 0.147112 | + | 0.147112i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 25681.4i | 1.03449i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −21294.0 | + | 21294.0i | −0.854737 | + | 0.854737i | −0.990712 | − | 0.135975i | \(-0.956583\pi\) |
0.135975 | + | 0.990712i | \(0.456583\pi\) | |||||||
\(854\) | −3788.36 | −0.151798 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 40119.6 | 1.60194 | ||||||||
\(857\) | −7601.22 | + | 7601.22i | −0.302979 | + | 0.302979i | −0.842178 | − | 0.539199i | \(-0.818727\pi\) |
0.539199 | + | 0.842178i | \(0.318727\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 8245.11i | 0.327497i | 0.986502 | + | 0.163748i | \(0.0523585\pi\) | ||||
−0.986502 | + | 0.163748i | \(0.947642\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −8894.03 | − | 8894.03i | −0.351429 | − | 0.351429i | ||||
\(863\) | −28577.1 | − | 28577.1i | −1.12720 | − | 1.12720i | −0.990630 | − | 0.136571i | \(-0.956392\pi\) |
−0.136571 | − | 0.990630i | \(-0.543608\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | − | 10458.9i | − | 0.410400i | ||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 130.754 | − | 130.754i | 0.00511298 | − | 0.00511298i | ||||
\(869\) | 15172.9 | 0.592294 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −12153.6 | −0.472802 | ||||||||
\(872\) | −2277.09 | + | 2277.09i | −0.0884310 | + | 0.0884310i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 30621.4i | 1.18511i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7711.86 | + | 7711.86i | 0.296934 | + | 0.296934i | 0.839812 | − | 0.542878i | \(-0.182665\pi\) |
−0.542878 | + | 0.839812i | \(0.682665\pi\) | |||||||
\(878\) | −4395.26 | − | 4395.26i | −0.168944 | − | 0.168944i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 34974.5i | 1.33748i | 0.743496 | + | 0.668741i | \(0.233166\pi\) | ||||
−0.743496 | + | 0.668741i | \(0.766834\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7417.63 | + | 7417.63i | −0.282699 | + | 0.282699i | −0.834184 | − | 0.551486i | \(-0.814061\pi\) |
0.551486 | + | 0.834184i | \(0.314061\pi\) | |||||||
\(884\) | −19480.9 | −0.741193 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3688.73 | 0.139871 | ||||||||
\(887\) | 27827.0 | − | 27827.0i | 1.05337 | − | 1.05337i | 0.0548766 | − | 0.998493i | \(-0.482523\pi\) |
0.998493 | − | 0.0548766i | \(-0.0174765\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 9390.34i | 0.354265i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8217.51 | − | 8217.51i | −0.308456 | − | 0.308456i | ||||
\(893\) | −16280.9 | − | 16280.9i | −0.610102 | − | 0.610102i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 13818.3i | 0.515221i | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 16334.3 | − | 16334.3i | 0.606998 | − | 0.606998i | ||||
\(899\) | 783.561 | 0.0290692 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −33829.4 | −1.25086 | ||||||||
\(902\) | 9078.01 | − | 9078.01i | 0.335105 | − | 0.335105i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | − | 7090.94i | − | 0.260886i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 5203.68 | + | 5203.68i | 0.190502 | + | 0.190502i | 0.795913 | − | 0.605411i | \(-0.206991\pi\) |
−0.605411 | + | 0.795913i | \(0.706991\pi\) | |||||||
\(908\) | 2862.29 | + | 2862.29i | 0.104613 | + | 0.104613i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 32968.5i | − | 1.19900i | −0.800373 | − | 0.599502i | \(-0.795365\pi\) | ||
0.800373 | − | 0.599502i | \(-0.204635\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −24597.9 | + | 24597.9i | −0.891646 | + | 0.891646i | ||||
\(914\) | 11349.1 | 0.410718 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −36367.4 | −1.31181 | ||||||||
\(917\) | −10132.7 | + | 10132.7i | −0.364898 | + | 0.364898i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 27700.9i | − | 0.994306i | −0.867663 | − | 0.497153i | \(-0.834379\pi\) | ||
0.867663 | − | 0.497153i | \(-0.165621\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 4407.61 | + | 4407.61i | 0.157437 | + | 0.157437i | ||||
\(923\) | −767.044 | − | 767.044i | −0.0273538 | − | 0.0273538i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 7601.85i | 0.269776i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −35657.6 | + | 35657.6i | −1.26134 | + | 1.26134i | ||||
\(929\) | −43665.6 | −1.54211 | −0.771057 | − | 0.636767i | \(-0.780272\pi\) | ||||
−0.771057 | + | 0.636767i | \(0.780272\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 28295.4 | 0.996074 | ||||||||
\(932\) | 20474.7 | − | 20474.7i | 0.719602 | − | 0.719602i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5436.67i | 0.190464i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 26320.8 | + | 26320.8i | 0.917676 | + | 0.917676i | 0.996860 | − | 0.0791842i | \(-0.0252315\pi\) |
−0.0791842 | + | 0.996860i | \(0.525232\pi\) | |||||||
\(938\) | −3975.13 | − | 3975.13i | −0.138372 | − | 0.138372i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 24448.5i | 0.846969i | 0.905903 | + | 0.423484i | \(0.139193\pi\) | ||||
−0.905903 | + | 0.423484i | \(0.860807\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 27915.5 | − | 27915.5i | 0.964003 | − | 0.964003i | ||||
\(944\) | 1868.94 | 0.0644372 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 24590.5 | 0.845145 | ||||||||
\(947\) | −18184.0 | + | 18184.0i | −0.623971 | + | 0.623971i | −0.946544 | − | 0.322573i | \(-0.895452\pi\) |
0.322573 | + | 0.946544i | \(0.395452\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | − | 2131.27i | − | 0.0729020i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −15301.6 | − | 15301.6i | −0.520932 | − | 0.520932i | ||||
\(953\) | 3808.31 | + | 3808.31i | 0.129447 | + | 0.129447i | 0.768862 | − | 0.639415i | \(-0.220823\pi\) |
−0.639415 | + | 0.768862i | \(0.720823\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 32686.2i | 1.10580i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 17042.5 | − | 17042.5i | 0.574758 | − | 0.574758i | ||||
\(959\) | −10565.3 | −0.355757 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −29782.5 | −0.999715 | ||||||||
\(962\) | −6372.92 | + | 6372.92i | −0.213587 | + | 0.213587i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 25879.2i | 0.864639i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4380.51 | + | 4380.51i | 0.145675 | + | 0.145675i | 0.776183 | − | 0.630508i | \(-0.217153\pi\) |
−0.630508 | + | 0.776183i | \(0.717153\pi\) | |||||||
\(968\) | −2861.37 | − | 2861.37i | −0.0950082 | − | 0.0950082i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 32754.2i | − | 1.08252i | −0.840854 | − | 0.541262i | \(-0.817947\pi\) | ||
0.840854 | − | 0.541262i | \(-0.182053\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 8086.19 | − | 8086.19i | 0.266425 | − | 0.266425i | ||||
\(974\) | −5832.12 | −0.191862 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3208.50 | −0.105227 | ||||||||
\(977\) | 705.759 | − | 705.759i | 0.0231108 | − | 0.0231108i | −0.695457 | − | 0.718568i | \(-0.744798\pi\) |
0.718568 | + | 0.695457i | \(0.244798\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 49825.8i | 1.62660i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4734.32 | − | 4734.32i | −0.153847 | − | 0.153847i | ||||
\(983\) | 20743.7 | + | 20743.7i | 0.673064 | + | 0.673064i | 0.958421 | − | 0.285357i | \(-0.0921122\pi\) |
−0.285357 | + | 0.958421i | \(0.592112\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 38183.4i | − | 1.23327i | ||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 18926.4 | − | 18926.4i | 0.609441 | − | 0.609441i | ||||
\(989\) | 75617.7 | 2.43125 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5799.55 | −0.185902 | −0.0929509 | − | 0.995671i | \(-0.529630\pi\) | ||||
−0.0929509 | + | 0.995671i | \(0.529630\pi\) | |||||||
\(992\) | −386.646 | + | 386.646i | −0.0123750 | + | 0.0123750i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | − | 501.760i | − | 0.0160109i | ||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −10653.7 | − | 10653.7i | −0.338420 | − | 0.338420i | 0.517352 | − | 0.855773i | \(-0.326918\pi\) |
−0.855773 | + | 0.517352i | \(0.826918\pi\) | |||||||
\(998\) | 700.064 | + | 700.064i | 0.0222045 | + | 0.0222045i | ||||
\(999\) | 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 | 225.4.f.d.107.4 | yes | 16 | |
3.2 | odd | 2 | inner | 225.4.f.d.107.6 | yes | 16 | |
5.2 | odd | 4 | inner | 225.4.f.d.143.3 | yes | 16 | |
5.3 | odd | 4 | inner | 225.4.f.d.143.6 | yes | 16 | |
5.4 | even | 2 | inner | 225.4.f.d.107.5 | yes | 16 | |
15.2 | even | 4 | inner | 225.4.f.d.143.5 | yes | 16 | |
15.8 | even | 4 | inner | 225.4.f.d.143.4 | yes | 16 | |
15.14 | odd | 2 | inner | 225.4.f.d.107.3 | ✓ | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
225.4.f.d.107.3 | ✓ | 16 | 15.14 | odd | 2 | inner | |
225.4.f.d.107.4 | yes | 16 | 1.1 | even | 1 | trivial | |
225.4.f.d.107.5 | yes | 16 | 5.4 | even | 2 | inner | |
225.4.f.d.107.6 | yes | 16 | 3.2 | odd | 2 | inner | |
225.4.f.d.143.3 | yes | 16 | 5.2 | odd | 4 | inner | |
225.4.f.d.143.4 | yes | 16 | 15.8 | even | 4 | inner | |
225.4.f.d.143.5 | yes | 16 | 15.2 | even | 4 | inner | |
225.4.f.d.143.6 | yes | 16 | 5.3 | odd | 4 | inner |