Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1323,2,Mod(1322,1323)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1323, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1323.1322");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1323 = 3^{3} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1323.c (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: | \(10.5642081874\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 12x^{14} + 106x^{12} - 384x^{10} + 1005x^{8} - 1200x^{6} + 1030x^{4} - 252x^{2} + 49 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{8} \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1322.8 | ||
Root | \(0.441700 - 0.255016i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1323.1322 |
Dual form | 1323.2.c.e.1322.10 |
$q$-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 \(\left(\mathbb{Z}/1323\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(1081\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | − 0.510032i | − 0.360647i | −0.983607 | − | 0.180323i | \(-0.942286\pi\) | ||||
0.983607 | − | 0.180323i | \(-0.0577144\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.73987 | 0.869934 | ||||||||
\(5\) | 4.01755 | 1.79670 | 0.898351 | − | 0.439278i | \(-0.144766\pi\) | ||||
0.898351 | + | 0.439278i | \(0.144766\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | − 1.90745i | − 0.674386i | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | − 2.04908i | − 0.647975i | ||||||||
\(11\) | 4.55982i | 1.37484i | 0.726261 | + | 0.687419i | \(0.241257\pi\) | ||||
−0.726261 | + | 0.687419i | \(0.758743\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 1.36710i | 0.379165i | 0.981865 | + | 0.189582i | \(0.0607134\pi\) | ||||
−0.981865 | + | 0.189582i | \(0.939287\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.50688 | 0.626719 | ||||||||
\(17\) | −2.15716 | −0.523189 | −0.261594 | − | 0.965178i | \(-0.584248\pi\) | ||||
−0.261594 | + | 0.965178i | \(0.584248\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.66105i | 0.610488i | 0.952274 | + | 0.305244i | \(0.0987380\pi\) | ||||
−0.952274 | + | 0.305244i | \(0.901262\pi\) | |||||||
\(20\) | 6.99000 | 1.56301 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 2.32565 | 0.495831 | ||||||||
\(23\) | − 1.27649i | − 0.266167i | −0.991105 | − | 0.133084i | \(-0.957512\pi\) | ||||
0.991105 | − | 0.133084i | \(-0.0424879\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 11.1407 | 2.22814 | ||||||||
\(26\) | 0.697263 | 0.136744 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8.75700i | 1.62613i | 0.582170 | + | 0.813067i | \(0.302204\pi\) | ||||
−0.582170 | + | 0.813067i | \(0.697796\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 8.72803i | − 1.56760i | −0.621013 | − | 0.783801i | \(-0.713278\pi\) | ||||
0.621013 | − | 0.783801i | \(-0.286722\pi\) | |||||||
\(32\) | − 5.09349i | − 0.900410i | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.10022i | 0.188686i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 7.85727 | 1.29173 | 0.645863 | − | 0.763453i | \(-0.276498\pi\) | ||||
0.645863 | + | 0.763453i | \(0.276498\pi\) | |||||||
\(38\) | 1.35722 | 0.220170 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − 7.66327i | − 1.21167i | ||||||||
\(41\) | −8.92372 | −1.39365 | −0.696826 | − | 0.717241i | \(-0.745405\pi\) | ||||
−0.696826 | + | 0.717241i | \(0.745405\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −7.31781 | −1.11596 | −0.557978 | − | 0.829856i | \(-0.688423\pi\) | ||||
−0.557978 | + | 0.829856i | \(0.688423\pi\) | |||||||
\(44\) | 7.93349i | 1.19602i | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −0.651052 | −0.0959923 | ||||||||
\(47\) | −8.97751 | −1.30950 | −0.654752 | − | 0.755843i | \(-0.727227\pi\) | ||||
−0.654752 | + | 0.755843i | \(0.727227\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | − 5.68210i | − 0.803571i | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 2.37857i | 0.329848i | ||||||||
\(53\) | − 7.89115i | − 1.08393i | −0.840400 | − | 0.541967i | \(-0.817680\pi\) | ||||
0.840400 | − | 0.541967i | \(-0.182320\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 18.3193i | 2.47018i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 4.46635 | 0.586460 | ||||||||
\(59\) | −7.72819 | −1.00613 | −0.503063 | − | 0.864250i | \(-0.667793\pi\) | ||||
−0.503063 | + | 0.864250i | \(0.667793\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 6.02394i | − 0.771286i | −0.922648 | − | 0.385643i | \(-0.873980\pi\) | ||||
0.922648 | − | 0.385643i | \(-0.126020\pi\) | |||||||
\(62\) | −4.45157 | −0.565350 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 2.41591 | 0.301989 | ||||||||
\(65\) | 5.49238i | 0.681246i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 8.15818 | 0.996681 | 0.498340 | − | 0.866981i | \(-0.333943\pi\) | ||||
0.498340 | + | 0.866981i | \(0.333943\pi\) | |||||||
\(68\) | −3.75318 | −0.455140 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − 0.301598i | − 0.0357931i | −0.999840 | − | 0.0178965i | \(-0.994303\pi\) | ||||
0.999840 | − | 0.0178965i | \(-0.00569695\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 11.6457i | − 1.36303i | −0.731805 | − | 0.681514i | \(-0.761322\pi\) | ||||
0.731805 | − | 0.681514i | \(-0.238678\pi\) | |||||||
\(74\) | − 4.00745i | − 0.465857i | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.62988i | 0.531084i | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −4.86511 | −0.547368 | −0.273684 | − | 0.961820i | \(-0.588242\pi\) | ||||
−0.273684 | + | 0.961820i | \(0.588242\pi\) | |||||||
\(80\) | 10.0715 | 1.12603 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 4.55138i | 0.502616i | ||||||||
\(83\) | −4.38346 | −0.481148 | −0.240574 | − | 0.970631i | \(-0.577336\pi\) | ||||
−0.240574 | + | 0.970631i | \(0.577336\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −8.66650 | −0.940014 | ||||||||
\(86\) | 3.73231i | 0.402466i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 8.69764 | 0.927172 | ||||||||
\(89\) | 1.90928 | 0.202383 | 0.101191 | − | 0.994867i | \(-0.467735\pi\) | ||||
0.101191 | + | 0.994867i | \(0.467735\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | − 2.22093i | − 0.231548i | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.57881i | 0.472269i | ||||||||
\(95\) | 10.6909i | 1.09686i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 0.231417i | − 0.0234968i | −0.999931 | − | 0.0117484i | \(-0.996260\pi\) | ||||
0.999931 | − | 0.0117484i | \(-0.00373972\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 19.3833 | 1.93833 | ||||||||
\(101\) | 7.04379 | 0.700883 | 0.350442 | − | 0.936585i | \(-0.386031\pi\) | ||||
0.350442 | + | 0.936585i | \(0.386031\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − 6.67360i | − 0.657569i | −0.944405 | − | 0.328785i | \(-0.893361\pi\) | ||||
0.944405 | − | 0.328785i | \(-0.106639\pi\) | |||||||
\(104\) | 2.60767 | 0.255703 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −4.02474 | −0.390917 | ||||||||
\(107\) | − 16.4154i | − 1.58693i | −0.608614 | − | 0.793466i | \(-0.708274\pi\) | ||||
0.608614 | − | 0.793466i | \(-0.291726\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −6.07891 | −0.582254 | −0.291127 | − | 0.956684i | \(-0.594030\pi\) | ||||
−0.291127 | + | 0.956684i | \(0.594030\pi\) | |||||||
\(110\) | 9.34343 | 0.890861 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 12.0500i | 1.13357i | 0.823866 | + | 0.566784i | \(0.191813\pi\) | ||||
−0.823866 | + | 0.566784i | \(0.808187\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − 5.12837i | − 0.478223i | ||||||||
\(116\) | 15.2360i | 1.41463i | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.94162i | 0.362856i | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −9.79200 | −0.890182 | ||||||||
\(122\) | −3.07240 | −0.278162 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | − 15.1856i | − 1.36371i | ||||||||
\(125\) | 24.6705 | 2.20660 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.30791 | 0.293529 | 0.146765 | − | 0.989171i | \(-0.453114\pi\) | ||||
0.146765 | + | 0.989171i | \(0.453114\pi\) | |||||||
\(128\) | − 11.4192i | − 1.00932i | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.80129 | 0.245689 | ||||||||
\(131\) | −3.28845 | −0.287313 | −0.143657 | − | 0.989628i | \(-0.545886\pi\) | ||||
−0.143657 | + | 0.989628i | \(0.545886\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | − 4.16093i | − 0.359450i | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 4.11468i | 0.352831i | ||||||||
\(137\) | − 2.01367i | − 0.172039i | −0.996293 | − | 0.0860196i | \(-0.972585\pi\) | ||||
0.996293 | − | 0.0860196i | \(-0.0274148\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 10.1678i | − 0.862421i | −0.902251 | − | 0.431211i | \(-0.858087\pi\) | ||||
0.902251 | − | 0.431211i | \(-0.141913\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −0.153824 | −0.0129087 | ||||||||
\(143\) | −6.23373 | −0.521290 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 35.1817i | 2.92168i | ||||||||
\(146\) | −5.93968 | −0.491572 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 13.6706 | 1.12372 | ||||||||
\(149\) | − 15.9456i | − 1.30631i | −0.757223 | − | 0.653156i | \(-0.773445\pi\) | ||||
0.757223 | − | 0.653156i | \(-0.226555\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.63356 | 0.377074 | 0.188537 | − | 0.982066i | \(-0.439625\pi\) | ||||
0.188537 | + | 0.982066i | \(0.439625\pi\) | |||||||
\(152\) | 5.07583 | 0.411704 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | − 35.0653i | − 2.81651i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 7.39104i | − 0.589869i | −0.955517 | − | 0.294934i | \(-0.904702\pi\) | ||||
0.955517 | − | 0.294934i | \(-0.0952978\pi\) | |||||||
\(158\) | 2.48136i | 0.197406i | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | − 20.4633i | − 1.61777i | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.00026 | −0.0783462 | −0.0391731 | − | 0.999232i | \(-0.512472\pi\) | ||||
−0.0391731 | + | 0.999232i | \(0.512472\pi\) | |||||||
\(164\) | −15.5261 | −1.21238 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.23571i | 0.173524i | ||||||||
\(167\) | 9.28225 | 0.718282 | 0.359141 | − | 0.933283i | \(-0.383070\pi\) | ||||
0.359141 | + | 0.933283i | \(0.383070\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.1310 | 0.856234 | ||||||||
\(170\) | 4.42019i | 0.339013i | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −12.7320 | −0.970808 | ||||||||
\(173\) | 17.8848 | 1.35975 | 0.679876 | − | 0.733327i | \(-0.262034\pi\) | ||||
0.679876 | + | 0.733327i | \(0.262034\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 11.4309i | 0.861638i | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | − 0.973791i | − 0.0729887i | ||||||||
\(179\) | − 2.84001i | − 0.212272i | −0.994352 | − | 0.106136i | \(-0.966152\pi\) | ||||
0.994352 | − | 0.106136i | \(-0.0338479\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 7.95711i | 0.591447i | 0.955274 | + | 0.295724i | \(0.0955608\pi\) | ||||
−0.955274 | + | 0.295724i | \(0.904439\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.43485 | −0.179499 | ||||||||
\(185\) | 31.5669 | 2.32085 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 9.83628i | − 0.719300i | ||||||||
\(188\) | −15.6197 | −1.13918 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 5.45270 | 0.395581 | ||||||||
\(191\) | 13.9123i | 1.00666i | 0.864095 | + | 0.503328i | \(0.167891\pi\) | ||||
−0.864095 | + | 0.503328i | \(0.832109\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.05188 | 0.579587 | 0.289793 | − | 0.957089i | \(-0.406413\pi\) | ||||
0.289793 | + | 0.957089i | \(0.406413\pi\) | |||||||
\(194\) | −0.118030 | −0.00847404 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 7.00094i | 0.498796i | 0.968401 | + | 0.249398i | \(0.0802328\pi\) | ||||
−0.968401 | + | 0.249398i | \(0.919767\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 14.7197i | 1.04345i | 0.853114 | + | 0.521724i | \(0.174711\pi\) | ||||
−0.853114 | + | 0.521724i | \(0.825289\pi\) | |||||||
\(200\) | − 21.2503i | − 1.50262i | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | − 3.59256i | − 0.252771i | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −35.8515 | −2.50398 | ||||||||
\(206\) | −3.40374 | −0.237150 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 3.42714i | 0.237630i | ||||||||
\(209\) | −12.1339 | −0.839322 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −22.3102 | −1.53590 | −0.767950 | − | 0.640510i | \(-0.778723\pi\) | ||||
−0.767950 | + | 0.640510i | \(0.778723\pi\) | |||||||
\(212\) | − 13.7296i | − 0.942950i | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −8.37235 | −0.572322 | ||||||||
\(215\) | −29.3997 | −2.00504 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3.10044i | 0.209988i | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 31.8732i | 2.14889i | ||||||||
\(221\) | − 2.94905i | − 0.198375i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 6.40672i | − 0.429026i | −0.976721 | − | 0.214513i | \(-0.931184\pi\) | ||||
0.976721 | − | 0.214513i | \(-0.0688164\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 6.14588 | 0.408818 | ||||||||
\(227\) | −3.09048 | −0.205123 | −0.102561 | − | 0.994727i | \(-0.532704\pi\) | ||||
−0.102561 | + | 0.994727i | \(0.532704\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 13.5657i | 0.896447i | 0.893922 | + | 0.448223i | \(0.147943\pi\) | ||||
−0.893922 | + | 0.448223i | \(0.852057\pi\) | |||||||
\(230\) | −2.61563 | −0.172470 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 16.7035 | 1.09664 | ||||||||
\(233\) | 24.3065i | 1.59237i | 0.605052 | + | 0.796186i | \(0.293152\pi\) | ||||
−0.605052 | + | 0.796186i | \(0.706848\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −36.0676 | −2.35279 | ||||||||
\(236\) | −13.4460 | −0.875262 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.58210i | 0.231707i | 0.993266 | + | 0.115853i | \(0.0369603\pi\) | ||||
−0.993266 | + | 0.115853i | \(0.963040\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 7.01695i | − 0.452002i | −0.974127 | − | 0.226001i | \(-0.927435\pi\) | ||||
0.974127 | − | 0.226001i | \(-0.0725652\pi\) | |||||||
\(242\) | 4.99423i | 0.321041i | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | − 10.4809i | − 0.670968i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −3.63792 | −0.231475 | ||||||||
\(248\) | −16.6483 | −1.05717 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − 12.5827i | − 0.795803i | ||||||||
\(251\) | −5.29654 | −0.334314 | −0.167157 | − | 0.985930i | \(-0.553459\pi\) | ||||
−0.167157 | + | 0.985930i | \(0.553459\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.82058 | 0.365937 | ||||||||
\(254\) | − 1.68714i | − 0.105860i | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.992308 | −0.0620192 | ||||||||
\(257\) | −14.8634 | −0.927154 | −0.463577 | − | 0.886057i | \(-0.653434\pi\) | ||||
−0.463577 | + | 0.886057i | \(0.653434\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 9.55602i | 0.592639i | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.67721i | 0.103619i | ||||||||
\(263\) | 15.2311i | 0.939190i | 0.882882 | + | 0.469595i | \(0.155600\pi\) | ||||
−0.882882 | + | 0.469595i | \(0.844400\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 31.7031i | − 1.94751i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 14.1942 | 0.867047 | ||||||||
\(269\) | 13.3418 | 0.813461 | 0.406731 | − | 0.913548i | \(-0.366669\pi\) | ||||
0.406731 | + | 0.913548i | \(0.366669\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 24.2808i | 1.47496i | 0.675371 | + | 0.737478i | \(0.263983\pi\) | ||||
−0.675371 | + | 0.737478i | \(0.736017\pi\) | |||||||
\(272\) | −5.40774 | −0.327892 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.02703 | −0.0620454 | ||||||||
\(275\) | 50.7996i | 3.06333i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −16.3970 | −0.985199 | −0.492599 | − | 0.870256i | \(-0.663953\pi\) | ||||
−0.492599 | + | 0.870256i | \(0.663953\pi\) | |||||||
\(278\) | −5.18590 | −0.311029 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 14.6475i | 0.873799i | 0.899510 | + | 0.436900i | \(0.143923\pi\) | ||||
−0.899510 | + | 0.436900i | \(0.856077\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 8.38829i | 0.498632i | 0.968422 | + | 0.249316i | \(0.0802058\pi\) | ||||
−0.968422 | + | 0.249316i | \(0.919794\pi\) | |||||||
\(284\) | − 0.524741i | − 0.0311376i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.17940i | 0.188002i | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −12.3467 | −0.726274 | ||||||||
\(290\) | 17.9438 | 1.05369 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | − 20.2620i | − 1.18574i | ||||||||
\(293\) | 1.73053 | 0.101099 | 0.0505493 | − | 0.998722i | \(-0.483903\pi\) | ||||
0.0505493 | + | 0.998722i | \(0.483903\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −31.0484 | −1.80771 | ||||||||
\(296\) | − 14.9873i | − 0.871122i | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −8.13274 | −0.471117 | ||||||||
\(299\) | 1.74509 | 0.100921 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | − 2.36326i | − 0.135990i | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.67093i | 0.382604i | ||||||||
\(305\) | − 24.2015i | − 1.38577i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 14.0499i | 0.801873i | 0.916106 | + | 0.400936i | \(0.131315\pi\) | ||||
−0.916106 | + | 0.400936i | \(0.868685\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −17.8844 | −1.01577 | ||||||||
\(311\) | −16.2569 | −0.921844 | −0.460922 | − | 0.887441i | \(-0.652481\pi\) | ||||
−0.460922 | + | 0.887441i | \(0.652481\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 6.86733i | − 0.388165i | −0.980985 | − | 0.194082i | \(-0.937827\pi\) | ||||
0.980985 | − | 0.194082i | \(-0.0621729\pi\) | |||||||
\(314\) | −3.76966 | −0.212734 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.46465 | −0.476174 | ||||||||
\(317\) | − 16.2748i | − 0.914084i | −0.889445 | − | 0.457042i | \(-0.848909\pi\) | ||||
0.889445 | − | 0.457042i | \(-0.151091\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −39.9304 | −2.23567 | ||||||||
\(320\) | 9.70605 | 0.542585 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − 5.74032i | − 0.319400i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 15.2304i | 0.844831i | ||||||||
\(326\) | 0.510163i | 0.0282553i | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 17.0216i | 0.939858i | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −33.9193 | −1.86437 | −0.932187 | − | 0.361977i | \(-0.882102\pi\) | ||||
−0.932187 | + | 0.361977i | \(0.882102\pi\) | |||||||
\(332\) | −7.62665 | −0.418567 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | − 4.73424i | − 0.259046i | ||||||||
\(335\) | 32.7759 | 1.79074 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −0.427345 | −0.0232790 | −0.0116395 | − | 0.999932i | \(-0.503705\pi\) | ||||
−0.0116395 | + | 0.999932i | \(0.503705\pi\) | |||||||
\(338\) | − 5.67718i | − 0.308798i | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −15.0786 | −0.817750 | ||||||||
\(341\) | 39.7983 | 2.15520 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 13.9584i | 0.752584i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | − 9.12179i | − 0.490390i | ||||||||
\(347\) | − 9.03989i | − 0.485287i | −0.970116 | − | 0.242643i | \(-0.921986\pi\) | ||||
0.970116 | − | 0.242643i | \(-0.0780145\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 22.9568i | − 1.22885i | −0.788976 | − | 0.614424i | \(-0.789388\pi\) | ||||
0.788976 | − | 0.614424i | \(-0.210612\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 23.2254 | 1.23792 | ||||||||
\(353\) | −11.9601 | −0.636571 | −0.318286 | − | 0.947995i | \(-0.603107\pi\) | ||||
−0.318286 | + | 0.947995i | \(0.603107\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 1.21168i | − 0.0643095i | ||||||||
\(356\) | 3.32189 | 0.176060 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −1.44849 | −0.0765552 | ||||||||
\(359\) | − 18.7765i | − 0.990987i | −0.868612 | − | 0.495494i | \(-0.834987\pi\) | ||||
0.868612 | − | 0.495494i | \(-0.165013\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 11.9188 | 0.627305 | ||||||||
\(362\) | 4.05838 | 0.213304 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − 46.7872i | − 2.44896i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 27.1985i | 1.41975i | 0.704327 | + | 0.709876i | \(0.251249\pi\) | ||||
−0.704327 | + | 0.709876i | \(0.748751\pi\) | |||||||
\(368\) | − 3.20001i | − 0.166812i | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | − 16.1001i | − 0.837006i | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 0.697276 | 0.0361036 | 0.0180518 | − | 0.999837i | \(-0.494254\pi\) | ||||
0.0180518 | + | 0.999837i | \(0.494254\pi\) | |||||||
\(374\) | −5.01681 | −0.259413 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 17.1242i | 0.883111i | ||||||||
\(377\) | −11.9717 | −0.616573 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −0.998557 | −0.0512924 | −0.0256462 | − | 0.999671i | \(-0.508164\pi\) | ||||
−0.0256462 | + | 0.999671i | \(0.508164\pi\) | |||||||
\(380\) | 18.6008i | 0.954200i | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7.09570 | 0.363047 | ||||||||
\(383\) | 35.0709 | 1.79204 | 0.896019 | − | 0.444016i | \(-0.146446\pi\) | ||||
0.896019 | + | 0.444016i | \(0.146446\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | − 4.10671i | − 0.209026i | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | − 0.402634i | − 0.0204407i | ||||||||
\(389\) | 27.7273i | 1.40583i | 0.711275 | + | 0.702914i | \(0.248118\pi\) | ||||
−0.711275 | + | 0.702914i | \(0.751882\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.75360i | 0.139256i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.57070 | 0.179889 | ||||||||
\(395\) | −19.5458 | −0.983457 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − 1.10713i | − 0.0555653i | −0.999614 | − | 0.0277826i | \(-0.991155\pi\) | ||||
0.999614 | − | 0.0277826i | \(-0.00884463\pi\) | |||||||
\(398\) | 7.50749 | 0.376316 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 27.9283 | 1.39642 | ||||||||
\(401\) | − 32.4305i | − 1.61950i | −0.586775 | − | 0.809750i | \(-0.699603\pi\) | ||||
0.586775 | − | 0.809750i | \(-0.300397\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 11.9321 | 0.594379 | ||||||||
\(404\) | 12.2553 | 0.609722 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 35.8278i | 1.77592i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 0.201959i | 0.00998622i | 0.999988 | + | 0.00499311i | \(0.00158936\pi\) | ||||
−0.999988 | + | 0.00499311i | \(0.998411\pi\) | |||||||
\(410\) | 18.2854i | 0.903051i | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | − 11.6112i | − 0.572042i | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −17.6108 | −0.864479 | ||||||||
\(416\) | 6.96329 | 0.341404 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 6.18869i | 0.302699i | ||||||||
\(419\) | 2.89945 | 0.141647 | 0.0708236 | − | 0.997489i | \(-0.477437\pi\) | ||||
0.0708236 | + | 0.997489i | \(0.477437\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.9825 | 1.07136 | 0.535681 | − | 0.844420i | \(-0.320055\pi\) | ||||
0.535681 | + | 0.844420i | \(0.320055\pi\) | |||||||
\(422\) | 11.3789i | 0.553917i | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −15.0520 | −0.730989 | ||||||||
\(425\) | −24.0323 | −1.16574 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | − 28.5606i | − 1.38053i | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 14.9948i | 0.723111i | ||||||||
\(431\) | 22.1190i | 1.06543i | 0.846293 | + | 0.532717i | \(0.178829\pi\) | ||||
−0.846293 | + | 0.532717i | \(0.821171\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 17.7613i | 0.853552i | 0.904357 | + | 0.426776i | \(0.140351\pi\) | ||||
−0.904357 | + | 0.426776i | \(0.859649\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.5765 | −0.506523 | ||||||||
\(437\) | 3.39682 | 0.162492 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 8.96748i | 0.427994i | 0.976834 | + | 0.213997i | \(0.0686483\pi\) | ||||
−0.976834 | + | 0.213997i | \(0.931352\pi\) | |||||||
\(440\) | 34.9432 | 1.66585 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.50411 | −0.0715432 | ||||||||
\(443\) | − 16.5048i | − 0.784165i | −0.919930 | − | 0.392083i | \(-0.871755\pi\) | ||||
0.919930 | − | 0.392083i | \(-0.128245\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.67061 | 0.363622 | ||||||||
\(446\) | −3.26763 | −0.154727 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.93393i | 0.421618i | 0.977527 | + | 0.210809i | \(0.0676098\pi\) | ||||
−0.977527 | + | 0.210809i | \(0.932390\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 40.6906i | − 1.91605i | ||||||||
\(452\) | 20.9654i | 0.986129i | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.57624i | 0.0739768i | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 26.7557 | 1.25158 | 0.625789 | − | 0.779992i | \(-0.284777\pi\) | ||||
0.625789 | + | 0.779992i | \(0.284777\pi\) | |||||||
\(458\) | 6.91893 | 0.323301 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | − 8.92269i | − 0.416023i | ||||||||
\(461\) | 11.6692 | 0.543489 | 0.271745 | − | 0.962369i | \(-0.412399\pi\) | ||||
0.271745 | + | 0.962369i | \(0.412399\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −17.8823 | −0.831059 | −0.415530 | − | 0.909580i | \(-0.636404\pi\) | ||||
−0.415530 | + | 0.909580i | \(0.636404\pi\) | |||||||
\(464\) | 21.9527i | 1.01913i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 12.3971 | 0.574284 | ||||||||
\(467\) | 12.7961 | 0.592131 | 0.296066 | − | 0.955168i | \(-0.404325\pi\) | ||||
0.296066 | + | 0.955168i | \(0.404325\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 18.3956i | 0.848526i | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 14.7411i | 0.678516i | ||||||||
\(473\) | − 33.3679i | − 1.53426i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 29.6460i | 1.36025i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.82698 | 0.0835643 | ||||||||
\(479\) | 2.03391 | 0.0929315 | 0.0464658 | − | 0.998920i | \(-0.485204\pi\) | ||||
0.0464658 | + | 0.998920i | \(0.485204\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 10.7417i | 0.489777i | ||||||||
\(482\) | −3.57887 | −0.163013 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −17.0368 | −0.774399 | ||||||||
\(485\) | − 0.929727i | − 0.0422167i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14.0614 | 0.637184 | 0.318592 | − | 0.947892i | \(-0.396790\pi\) | ||||
0.318592 | + | 0.947892i | \(0.396790\pi\) | |||||||
\(488\) | −11.4904 | −0.520144 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 32.1988i | 1.45311i | 0.687107 | + | 0.726557i | \(0.258880\pi\) | ||||
−0.687107 | + | 0.726557i | \(0.741120\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − 18.8903i | − 0.850775i | ||||||||
\(494\) | 1.85545i | 0.0834808i | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − 21.8801i | − 0.982445i | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 17.0426 | 0.762931 | 0.381466 | − | 0.924383i | \(-0.375419\pi\) | ||||
0.381466 | + | 0.924383i | \(0.375419\pi\) | |||||||
\(500\) | 42.9235 | 1.91960 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.70140i | 0.120569i | ||||||||
\(503\) | −43.7250 | −1.94960 | −0.974801 | − | 0.223077i | \(-0.928390\pi\) | ||||
−0.974801 | + | 0.223077i | \(0.928390\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 28.2988 | 1.25928 | ||||||||
\(506\) | − 2.96868i | − 0.131974i | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 5.75532 | 0.255351 | ||||||||
\(509\) | −13.8222 | −0.612657 | −0.306329 | − | 0.951926i | \(-0.599101\pi\) | ||||
−0.306329 | + | 0.951926i | \(0.599101\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | − 22.3322i | − 0.986954i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 7.58081i | 0.334375i | ||||||||
\(515\) | − 26.8115i | − 1.18146i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 40.9359i | − 1.80036i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 10.4764 | 0.459422 | ||||||||
\(521\) | −4.28818 | −0.187868 | −0.0939342 | − | 0.995578i | \(-0.529944\pi\) | ||||
−0.0939342 | + | 0.995578i | \(0.529944\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − 31.9987i | − 1.39921i | −0.714532 | − | 0.699603i | \(-0.753360\pi\) | ||||
0.714532 | − | 0.699603i | \(-0.246640\pi\) | |||||||
\(524\) | −5.72147 | −0.249943 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 7.76834 | 0.338716 | ||||||||
\(527\) | 18.8278i | 0.820151i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 21.3706 | 0.929155 | ||||||||
\(530\) | −16.1696 | −0.702361 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 12.1996i | − 0.528423i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − 65.9495i | − 2.85124i | ||||||||
\(536\) | − 15.5613i | − 0.672147i | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | − 6.80472i | − 0.293372i | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −32.6342 | −1.40305 | −0.701527 | − | 0.712643i | \(-0.747498\pi\) | ||||
−0.701527 | + | 0.712643i | \(0.747498\pi\) | |||||||
\(542\) | 12.3840 | 0.531938 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 10.9875i | 0.471084i | ||||||||
\(545\) | −24.4223 | −1.04614 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.09795 | 0.0897019 | 0.0448510 | − | 0.998994i | \(-0.485719\pi\) | ||||
0.0448510 | + | 0.998994i | \(0.485719\pi\) | |||||||
\(548\) | − 3.50351i | − 0.149663i | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 25.9094 | 1.10478 | ||||||||
\(551\) | −23.3029 | −0.992735 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 8.36298i | 0.355309i | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | − 17.6906i | − 0.750250i | ||||||||
\(557\) | 30.3756i | 1.28706i | 0.765422 | + | 0.643528i | \(0.222530\pi\) | ||||
−0.765422 | + | 0.643528i | \(0.777470\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 10.0042i | − 0.423131i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 7.47071 | 0.315133 | ||||||||
\(563\) | −7.47998 | −0.315244 | −0.157622 | − | 0.987500i | \(-0.550383\pi\) | ||||
−0.157622 | + | 0.987500i | \(0.550383\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 48.4114i | 2.03668i | ||||||||
\(566\) | 4.27829 | 0.179830 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −0.575283 | −0.0241383 | ||||||||
\(569\) | 18.0817i | 0.758024i | 0.925392 | + | 0.379012i | \(0.123736\pi\) | ||||
−0.925392 | + | 0.379012i | \(0.876264\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.137188 | 0.00574112 | 0.00287056 | − | 0.999996i | \(-0.499086\pi\) | ||||
0.00287056 | + | 0.999996i | \(0.499086\pi\) | |||||||
\(572\) | −10.8459 | −0.453488 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − 14.2210i | − 0.593057i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 27.6089i | 1.14937i | 0.818373 | + | 0.574687i | \(0.194876\pi\) | ||||
−0.818373 | + | 0.574687i | \(0.805124\pi\) | |||||||
\(578\) | 6.29718i | 0.261928i | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 61.2115i | 2.54167i | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 35.9823 | 1.49023 | ||||||||
\(584\) | −22.2136 | −0.919207 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | − 0.882624i | − 0.0364609i | ||||||||
\(587\) | −46.4304 | −1.91639 | −0.958193 | − | 0.286123i | \(-0.907633\pi\) | ||||
−0.958193 | + | 0.286123i | \(0.907633\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23.2258 | 0.957001 | ||||||||
\(590\) | 15.8357i | 0.651944i | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 19.6972 | 0.809550 | ||||||||
\(593\) | −38.7090 | −1.58959 | −0.794794 | − | 0.606880i | \(-0.792421\pi\) | ||||
−0.794794 | + | 0.606880i | \(0.792421\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − 27.7432i | − 1.13641i | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | − 0.890051i | − 0.0363969i | ||||||||
\(599\) | − 24.1896i | − 0.988360i | −0.869360 | − | 0.494180i | \(-0.835468\pi\) | ||||
0.869360 | − | 0.494180i | \(-0.164532\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 43.4070i | 1.77061i | 0.465014 | + | 0.885304i | \(0.346049\pi\) | ||||
−0.465014 | + | 0.885304i | \(0.653951\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.06178 | 0.328029 | ||||||||
\(605\) | −39.3398 | −1.59939 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 41.4806i | − 1.68364i | −0.539756 | − | 0.841822i | \(-0.681483\pi\) | ||||
0.539756 | − | 0.841822i | \(-0.318517\pi\) | |||||||
\(608\) | 13.5540 | 0.549689 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −12.3435 | −0.499774 | ||||||||
\(611\) | − 12.2731i | − 0.496518i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 34.5432 | 1.39519 | 0.697594 | − | 0.716494i | \(-0.254254\pi\) | ||||
0.697594 | + | 0.716494i | \(0.254254\pi\) | |||||||
\(614\) | 7.16591 | 0.289193 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.87374i | 0.236468i | 0.992986 | + | 0.118234i | \(0.0377232\pi\) | ||||
−0.992986 | + | 0.118234i | \(0.962277\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 41.8903i | 1.68371i | 0.539702 | + | 0.841856i | \(0.318537\pi\) | ||||
−0.539702 | + | 0.841856i | \(0.681463\pi\) | |||||||
\(620\) | − 61.0090i | − 2.45018i | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 8.29153i | 0.332460i | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 43.4116 | 1.73646 | ||||||||
\(626\) | −3.50256 | −0.139990 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | − 12.8594i | − 0.513147i | ||||||||
\(629\) | −16.9494 | −0.675817 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −43.9572 | −1.74991 | −0.874954 | − | 0.484206i | \(-0.839109\pi\) | ||||
−0.874954 | + | 0.484206i | \(0.839109\pi\) | |||||||
\(632\) | 9.27996i | 0.369137i | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −8.30066 | −0.329661 | ||||||||
\(635\) | 13.2897 | 0.527385 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 20.3658i | 0.806288i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − 45.8770i | − 1.81345i | ||||||||
\(641\) | − 41.1337i | − 1.62468i | −0.583182 | − | 0.812341i | \(-0.698193\pi\) | ||||
0.583182 | − | 0.812341i | \(-0.301807\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 32.6357i | 1.28703i | 0.765435 | + | 0.643513i | \(0.222524\pi\) | ||||
−0.765435 | + | 0.643513i | \(0.777476\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.92775 | −0.115191 | ||||||||
\(647\) | 43.2586 | 1.70067 | 0.850335 | − | 0.526242i | \(-0.176399\pi\) | ||||
0.850335 | + | 0.526242i | \(0.176399\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 35.2392i | − 1.38326i | ||||||||
\(650\) | 7.76799 | 0.304686 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.74031 | −0.0681560 | ||||||||
\(653\) | − 38.0805i | − 1.49020i | −0.666951 | − | 0.745102i | \(-0.732401\pi\) | ||||
0.666951 | − | 0.745102i | \(-0.267599\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −13.2115 | −0.516216 | ||||||||
\(656\) | −22.3707 | −0.873428 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − 35.2754i | − 1.37413i | −0.726594 | − | 0.687067i | \(-0.758898\pi\) | ||||
0.726594 | − | 0.687067i | \(-0.241102\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − 19.2800i | − 0.749905i | −0.927044 | − | 0.374952i | \(-0.877659\pi\) | ||||
0.927044 | − | 0.374952i | \(-0.122341\pi\) | |||||||
\(662\) | 17.2999i | 0.672380i | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 8.36124i | 0.324479i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 11.1783 | 0.432824 | ||||||||
\(668\) | 16.1499 | 0.624858 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | − 16.7167i | − 0.645824i | ||||||||
\(671\) | 27.4681 | 1.06039 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.95341 | −0.152393 | −0.0761964 | − | 0.997093i | \(-0.524278\pi\) | ||||
−0.0761964 | + | 0.997093i | \(0.524278\pi\) | |||||||
\(674\) | 0.217959i | 0.00839548i | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 19.3665 | 0.744867 | ||||||||
\(677\) | 22.2397 | 0.854740 | 0.427370 | − | 0.904077i | \(-0.359440\pi\) | ||||
0.427370 | + | 0.904077i | \(0.359440\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 16.5309i | 0.633932i | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | − 20.2984i | − 0.777266i | ||||||||
\(683\) | 16.7827i | 0.642174i | 0.947050 | + | 0.321087i | \(0.104048\pi\) | ||||
−0.947050 | + | 0.321087i | \(0.895952\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − 8.09001i | − 0.309103i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −18.3448 | −0.699391 | ||||||||
\(689\) | 10.7880 | 0.410989 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 3.01862i | 0.114834i | 0.998350 | + | 0.0574169i | \(0.0182864\pi\) | ||||
−0.998350 | + | 0.0574169i | \(0.981714\pi\) | |||||||
\(692\) | 31.1171 | 1.18289 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −4.61063 | −0.175017 | ||||||||
\(695\) | − 40.8496i | − 1.54951i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 19.2499 | 0.729143 | ||||||||
\(698\) | −11.7087 | −0.443180 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 22.7605i | 0.859653i | 0.902911 | + | 0.429827i | \(0.141425\pi\) | ||||
−0.902911 | + | 0.429827i | \(0.858575\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20.9086i | 0.788583i | ||||||||
\(704\) | 11.0161i | 0.415186i | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.10002i | 0.229577i | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 16.9079 | 0.634988 | 0.317494 | − | 0.948260i | \(-0.397159\pi\) | ||||
0.317494 | + | 0.948260i | \(0.397159\pi\) | |||||||
\(710\) | −0.617997 | −0.0231930 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | − 3.64185i | − 0.136484i | ||||||||
\(713\) | −11.1413 | −0.417244 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −25.0443 | −0.936603 | ||||||||
\(716\) | − 4.94123i | − 0.184663i | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.57662 | −0.357396 | ||||||||
\(719\) | 18.4522 | 0.688149 | 0.344075 | − | 0.938942i | \(-0.388193\pi\) | ||||
0.344075 | + | 0.938942i | \(0.388193\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | − 6.07896i | − 0.226235i | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 13.8443i | 0.514520i | ||||||||
\(725\) | 97.5591i | 3.62325i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 46.9647i | 1.74182i | 0.491438 | + | 0.870912i | \(0.336471\pi\) | ||||
−0.491438 | + | 0.870912i | \(0.663529\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −23.8630 | −0.883208 | ||||||||
\(731\) | 15.7857 | 0.583855 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 49.7678i | 1.83822i | 0.394006 | + | 0.919108i | \(0.371089\pi\) | ||||
−0.394006 | + | 0.919108i | \(0.628911\pi\) | |||||||
\(734\) | 13.8721 | 0.512029 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.50180 | −0.239660 | ||||||||
\(737\) | 37.1999i | 1.37028i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 32.4025 | 1.19195 | 0.595973 | − | 0.803004i | \(-0.296766\pi\) | ||||
0.595973 | + | 0.803004i | \(0.296766\pi\) | |||||||
\(740\) | 54.9223 | 2.01898 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.49994i | 0.0917138i | 0.998948 | + | 0.0458569i | \(0.0146018\pi\) | ||||
−0.998948 | + | 0.0458569i | \(0.985398\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − 64.0621i | − 2.34705i | ||||||||
\(746\) | − 0.355633i | − 0.0130206i | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | − 17.1138i | − 0.625744i | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 17.5546 | 0.640578 | 0.320289 | − | 0.947320i | \(-0.396220\pi\) | ||||
0.320289 | + | 0.947320i | \(0.396220\pi\) | |||||||
\(752\) | −22.5055 | −0.820691 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.10593i | 0.222365i | ||||||||
\(755\) | 18.6156 | 0.677489 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 20.3609 | 0.740030 | 0.370015 | − | 0.929026i | \(-0.379353\pi\) | ||||
0.370015 | + | 0.929026i | \(0.379353\pi\) | |||||||
\(758\) | 0.509296i | 0.0184985i | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 20.3924 | 0.739710 | ||||||||
\(761\) | −41.9777 | −1.52169 | −0.760846 | − | 0.648932i | \(-0.775216\pi\) | ||||
−0.760846 | + | 0.648932i | \(0.775216\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 24.2055i | 0.875725i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | − 17.8873i | − 0.646293i | ||||||||
\(767\) | − 10.5652i | − 0.381487i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 12.0753i | 0.435447i | 0.976010 | + | 0.217724i | \(0.0698632\pi\) | ||||
−0.976010 | + | 0.217724i | \(0.930137\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 14.0092 | 0.504202 | ||||||||
\(773\) | −5.30144 | −0.190679 | −0.0953397 | − | 0.995445i | \(-0.530394\pi\) | ||||
−0.0953397 | + | 0.995445i | \(0.530394\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 97.2364i | − 3.49283i | ||||||||
\(776\) | −0.441416 | −0.0158459 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 14.1418 | 0.507007 | ||||||||
\(779\) | − 23.7465i | − 0.850807i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.37523 | 0.0492097 | ||||||||
\(782\) | 1.40442 | 0.0502221 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − 29.6938i | − 1.05982i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 28.2573i | 1.00726i | 0.863918 | + | 0.503632i | \(0.168003\pi\) | ||||
−0.863918 | + | 0.503632i | \(0.831997\pi\) | |||||||
\(788\) | 12.1807i | 0.433920i | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 9.96898i | 0.354680i | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.23531 | 0.292444 | ||||||||
\(794\) | −0.564672 | −0.0200394 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 25.6103i | 0.907731i | ||||||||
\(797\) | 32.1596 | 1.13915 | 0.569576 | − | 0.821939i | \(-0.307107\pi\) | ||||
0.569576 | + | 0.821939i | \(0.307107\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 19.3659 | 0.685118 | ||||||||
\(800\) | − 56.7450i | − 2.00624i | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −16.5406 | −0.584067 | ||||||||
\(803\) | 53.1024 | 1.87394 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | − 6.08573i | − 0.214361i | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | − 13.4357i | − 0.472666i | ||||||||
\(809\) | 29.9525i | 1.05307i | 0.850152 | + | 0.526537i | \(0.176510\pi\) | ||||
−0.850152 | + | 0.526537i | \(0.823490\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 14.6461i | 0.514293i | 0.966372 | + | 0.257146i | \(0.0827823\pi\) | ||||
−0.966372 | + | 0.257146i | \(0.917218\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 18.2733 | 0.640478 | ||||||||
\(815\) | −4.01858 | −0.140765 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 19.4731i | − 0.681277i | ||||||||
\(818\) | 0.103005 | 0.00360150 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −62.3768 | −2.17829 | ||||||||
\(821\) | 19.7174i | 0.688142i | 0.938944 | + | 0.344071i | \(0.111806\pi\) | ||||
−0.938944 | + | 0.344071i | \(0.888194\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −11.5526 | −0.402699 | −0.201349 | − | 0.979519i | \(-0.564533\pi\) | ||||
−0.201349 | + | 0.979519i | \(0.564533\pi\) | |||||||
\(824\) | −12.7296 | −0.443455 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 4.65207i | − 0.161768i | −0.996724 | − | 0.0808841i | \(-0.974226\pi\) | ||||
0.996724 | − | 0.0808841i | \(-0.0257744\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 9.41157i | − 0.326877i | −0.986553 | − | 0.163439i | \(-0.947741\pi\) | ||||
0.986553 | − | 0.163439i | \(-0.0522586\pi\) | |||||||
\(830\) | 8.98205i | 0.311772i | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 3.30279i | 0.114504i | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 37.2919 | 1.29054 | ||||||||
\(836\) | −21.1115 | −0.730155 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | − 1.47881i | − 0.0510846i | ||||||||
\(839\) | 3.85859 | 0.133213 | 0.0666067 | − | 0.997779i | \(-0.478783\pi\) | ||||
0.0666067 | + | 0.997779i | \(0.478783\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −47.6851 | −1.64431 | ||||||||
\(842\) | − 11.2118i | − 0.386383i | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −38.8168 | −1.33613 | ||||||||
\(845\) | 44.7195 | 1.53840 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | − 19.7821i | − 0.679322i | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 12.2572i | 0.420419i | ||||||||
\(851\) | − 10.0297i | − 0.343815i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 31.6208i | − 1.08268i | −0.840805 | − | 0.541338i | \(-0.817918\pi\) | ||||
0.840805 | − | 0.541338i | \(-0.182082\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −31.3115 | −1.07020 | ||||||||
\(857\) | −34.3673 | −1.17396 | −0.586982 | − | 0.809600i | \(-0.699684\pi\) | ||||
−0.586982 | + | 0.809600i | \(0.699684\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.52561i | 0.120292i | 0.998190 | + | 0.0601462i | \(0.0191567\pi\) | ||||
−0.998190 | + | 0.0601462i | \(0.980843\pi\) | |||||||
\(860\) | −51.1515 | −1.74425 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 11.2814 | 0.384246 | ||||||||
\(863\) | 35.7972i | 1.21855i | 0.792959 | + | 0.609275i | \(0.208539\pi\) | ||||
−0.792959 | + | 0.609275i | \(0.791461\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 71.8528 | 2.44307 | ||||||||
\(866\) | 9.05881 | 0.307831 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − 22.1840i | − 0.752542i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 11.1530i | 0.377906i | ||||||||
\(872\) | 11.5952i | 0.392664i | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | − 1.73248i | − 0.0586021i | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 40.2024 | 1.35754 | 0.678769 | − | 0.734352i | \(-0.262514\pi\) | ||||
0.678769 | + | 0.734352i | \(0.262514\pi\) | |||||||
\(878\) | 4.57370 | 0.154355 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 45.9242i | 1.54811i | ||||||||
\(881\) | 9.64863 | 0.325071 | 0.162535 | − | 0.986703i | \(-0.448033\pi\) | ||||
0.162535 | + | 0.986703i | \(0.448033\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 17.1497 | 0.577134 | 0.288567 | − | 0.957460i | \(-0.406821\pi\) | ||||
0.288567 | + | 0.957460i | \(0.406821\pi\) | |||||||
\(884\) | − 5.13096i | − 0.172573i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −8.41795 | −0.282807 | ||||||||
\(887\) | 32.1275 | 1.07874 | 0.539368 | − | 0.842070i | \(-0.318663\pi\) | ||||
0.539368 | + | 0.842070i | \(0.318663\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | − 3.91225i | − 0.131139i | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − 11.1468i | − 0.373224i | ||||||||
\(893\) | − 23.8896i | − 0.799436i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 11.4099i | − 0.381390i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 4.55658 | 0.152055 | ||||||||
\(899\) | 76.4314 | 2.54913 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 17.0225i | 0.567102i | ||||||||
\(902\) | −20.7535 | −0.691016 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 22.9848 | 0.764462 | ||||||||
\(905\) | 31.9681i | 1.06265i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −27.6267 | −0.917330 | −0.458665 | − | 0.888609i | \(-0.651672\pi\) | ||||
−0.458665 | + | 0.888609i | \(0.651672\pi\) | |||||||
\(908\) | −5.37703 | −0.178443 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 26.1620i | 0.866785i | 0.901205 | + | 0.433392i | \(0.142684\pi\) | ||||
−0.901205 | + | 0.433392i | \(0.857316\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 19.9878i | − 0.661501i | ||||||||
\(914\) | − 13.6462i | − 0.451378i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 23.6025i | 0.779849i | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −16.0437 | −0.529232 | −0.264616 | − | 0.964354i | \(-0.585245\pi\) | ||||
−0.264616 | + | 0.964354i | \(0.585245\pi\) | |||||||
\(920\) | −9.78212 | −0.322507 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | − 5.95167i | − 0.196008i | ||||||||
\(923\) | 0.412314 | 0.0135715 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 87.5354 | 2.87815 | ||||||||
\(926\) | 9.12052i | 0.299719i | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 44.6037 | 1.46419 | ||||||||
\(929\) | −34.0763 | −1.11801 | −0.559003 | − | 0.829166i | \(-0.688816\pi\) | ||||
−0.559003 | + | 0.829166i | \(0.688816\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 42.2901i | 1.38526i | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | − 6.52640i | − 0.213550i | ||||||||
\(935\) | − 39.5177i | − 1.29237i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 39.6263i | − 1.29454i | −0.762263 | − | 0.647268i | \(-0.775912\pi\) | ||||
0.762263 | − | 0.647268i | \(-0.224088\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −62.7528 | −2.04677 | ||||||||
\(941\) | −27.4892 | −0.896124 | −0.448062 | − | 0.894003i | \(-0.647886\pi\) | ||||
−0.448062 | + | 0.894003i | \(0.647886\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11.3911i | 0.370944i | ||||||||
\(944\) | −19.3736 | −0.630558 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −17.0187 | −0.553326 | ||||||||
\(947\) | 12.9435i | 0.420606i | 0.977636 | + | 0.210303i | \(0.0674451\pi\) | ||||
−0.977636 | + | 0.210303i | \(0.932555\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 15.9208 | 0.516812 | ||||||||
\(950\) | 15.1204 | 0.490570 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − 30.0287i | − 0.972726i | −0.873757 | − | 0.486363i | \(-0.838323\pi\) | ||||
0.873757 | − | 0.486363i | \(-0.161677\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 55.8932i | 1.80866i | ||||||||
\(956\) | 6.23238i | 0.201570i | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | − 1.03736i | − 0.0335155i | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −45.1786 | −1.45737 | ||||||||
\(962\) | 5.47858 | 0.176637 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | − 12.2086i | − 0.393212i | ||||||||
\(965\) | 32.3488 | 1.04134 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 33.1357 | 1.06557 | 0.532787 | − | 0.846250i | \(-0.321145\pi\) | ||||
0.532787 | + | 0.846250i | \(0.321145\pi\) | |||||||
\(968\) | 18.6778i | 0.600326i | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −0.474190 | −0.0152253 | ||||||||
\(971\) | −34.4484 | −1.10550 | −0.552752 | − | 0.833346i | \(-0.686422\pi\) | ||||
−0.552752 | + | 0.833346i | \(0.686422\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | − 7.17177i | − 0.229798i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | − 15.1013i | − 0.483380i | ||||||||
\(977\) | − 52.6834i | − 1.68549i | −0.538311 | − | 0.842746i | \(-0.680938\pi\) | ||||
0.538311 | − | 0.842746i | \(-0.319062\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.70596i | 0.278244i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 16.4224 | 0.524060 | ||||||||
\(983\) | 35.5076 | 1.13252 | 0.566259 | − | 0.824228i | \(-0.308390\pi\) | ||||
0.566259 | + | 0.824228i | \(0.308390\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 28.1266i | 0.896188i | ||||||||
\(986\) | −9.63464 | −0.306829 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −6.32950 | −0.201368 | ||||||||
\(989\) | 9.34114i | 0.297031i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −8.36244 | −0.265642 | −0.132821 | − | 0.991140i | \(-0.542404\pi\) | ||||
−0.132821 | + | 0.991140i | \(0.542404\pi\) | |||||||
\(992\) | −44.4561 | −1.41148 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 59.1369i | 1.87477i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 39.8996i | 1.26363i | 0.775118 | + | 0.631816i | \(0.217690\pi\) | ||||
−0.775118 | + | 0.631816i | \(0.782310\pi\) | |||||||
\(998\) | − 8.69226i | − 0.275149i | ||||||||
\(999\) | 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 | 1323.2.c.e.1322.8 | yes | 16 | |
3.2 | odd | 2 | inner | 1323.2.c.e.1322.9 | yes | 16 | |
7.6 | odd | 2 | inner | 1323.2.c.e.1322.7 | ✓ | 16 | |
21.20 | even | 2 | inner | 1323.2.c.e.1322.10 | yes | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1323.2.c.e.1322.7 | ✓ | 16 | 7.6 | odd | 2 | inner | |
1323.2.c.e.1322.8 | yes | 16 | 1.1 | even | 1 | trivial | |
1323.2.c.e.1322.9 | yes | 16 | 3.2 | odd | 2 | inner | |
1323.2.c.e.1322.10 | yes | 16 | 21.20 | even | 2 | inner |