Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [5520,2,Mod(1471,5520)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(5520, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("5520.1471");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 5520 = 2^{4} \cdot 3 \cdot 5 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 5520.be (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: | \(44.0774219157\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 1471.30 | ||
Character | \(\chi\) | \(=\) | 5520.1471 |
Dual form | 5520.2.be.c.1471.29 |
$q$-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 \(\left(\mathbb{Z}/5520\mathbb{Z}\right)^\times\).
\(n\) | \(1201\) | \(1381\) | \(1841\) | \(4417\) | \(4831\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) | \(1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.00000i | 0.577350i | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 1.00000i | 0.447214i | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.44765 | 0.547160 | 0.273580 | − | 0.961849i | \(-0.411792\pi\) | ||||
0.273580 | + | 0.961849i | \(0.411792\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −1.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −0.540073 | −0.162838 | −0.0814191 | − | 0.996680i | \(-0.525945\pi\) | ||||
−0.0814191 | + | 0.996680i | \(0.525945\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 4.25689 | 1.18065 | 0.590324 | − | 0.807166i | \(-0.299000\pi\) | ||||
0.590324 | + | 0.807166i | \(0.299000\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −1.00000 | −0.258199 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − | 7.14147i | − | 1.73206i | −0.499992 | − | 0.866030i | \(-0.666664\pi\) | ||
0.499992 | − | 0.866030i | \(-0.333336\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.941351 | −0.215961 | −0.107980 | − | 0.994153i | \(-0.534438\pi\) | ||||
−0.107980 | + | 0.994153i | \(0.534438\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1.44765i | 0.315903i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 2.91287 | + | 3.80988i | 0.607376 | + | 0.794415i | ||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.00000 | −0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − | 1.00000i | − | 0.192450i | ||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.26464 | 0.234838 | 0.117419 | − | 0.993082i | \(-0.462538\pi\) | ||||
0.117419 | + | 0.993082i | \(0.462538\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 3.15253i | − | 0.566212i | −0.959089 | − | 0.283106i | \(-0.908635\pi\) | ||
0.959089 | − | 0.283106i | \(-0.0913648\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 0.540073i | − | 0.0940147i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.44765i | 0.244697i | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 1.30413i | 0.214397i | 0.994238 | + | 0.107199i | \(0.0341881\pi\) | ||||
−0.994238 | + | 0.107199i | \(0.965812\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 4.25689i | 0.681648i | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.97953 | 0.933845 | 0.466923 | − | 0.884298i | \(-0.345363\pi\) | ||||
0.466923 | + | 0.884298i | \(0.345363\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.03228 | 0.309919 | 0.154960 | − | 0.987921i | \(-0.450475\pi\) | ||||
0.154960 | + | 0.987921i | \(0.450475\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | − | 1.00000i | − | 0.149071i | ||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − | 6.61495i | − | 0.964889i | −0.875927 | − | 0.482444i | \(-0.839749\pi\) | ||
0.875927 | − | 0.482444i | \(-0.160251\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −4.90431 | −0.700616 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 7.14147 | 1.00001 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 7.54328i | − | 1.03615i | −0.855335 | − | 0.518075i | \(-0.826649\pi\) | ||
0.855335 | − | 0.518075i | \(-0.173351\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − | 0.540073i | − | 0.0728234i | ||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | − | 0.941351i | − | 0.124685i | ||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 11.1974i | − | 1.45777i | −0.684635 | − | 0.728886i | \(-0.740038\pi\) | ||
0.684635 | − | 0.728886i | \(-0.259962\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00097i | 0.256197i | 0.991761 | + | 0.128099i | \(0.0408874\pi\) | ||||
−0.991761 | + | 0.128099i | \(0.959113\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −1.44765 | −0.182387 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.25689i | 0.528002i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 7.68722 | 0.939143 | 0.469572 | − | 0.882894i | \(-0.344408\pi\) | ||||
0.469572 | + | 0.882894i | \(0.344408\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −3.80988 | + | 2.91287i | −0.458656 | + | 0.350668i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 8.07158i | 0.957920i | 0.877837 | + | 0.478960i | \(0.158986\pi\) | ||||
−0.877837 | + | 0.478960i | \(0.841014\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1.91203 | 0.223787 | 0.111893 | − | 0.993720i | \(-0.464309\pi\) | ||||
0.111893 | + | 0.993720i | \(0.464309\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 1.00000i | − | 0.115470i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −0.781836 | −0.0890985 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.99026 | −0.448939 | −0.224470 | − | 0.974481i | \(-0.572065\pi\) | ||||
−0.224470 | + | 0.974481i | \(0.572065\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1.20991 | 0.132805 | 0.0664024 | − | 0.997793i | \(-0.478848\pi\) | ||||
0.0664024 | + | 0.997793i | \(0.478848\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 7.14147 | 0.774601 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.26464i | 0.135584i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 17.8161i | − | 1.88851i | −0.329222 | − | 0.944253i | \(-0.606786\pi\) | ||
0.329222 | − | 0.944253i | \(-0.393214\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 6.16248 | 0.646004 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 3.15253 | 0.326903 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | − | 0.941351i | − | 0.0965806i | ||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 11.5224i | − | 1.16992i | −0.811062 | − | 0.584960i | \(-0.801110\pi\) | ||
0.811062 | − | 0.584960i | \(-0.198890\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.540073 | 0.0542794 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 13.5957 | 1.35282 | 0.676412 | − | 0.736524i | \(-0.263534\pi\) | ||||
0.676412 | + | 0.736524i | \(0.263534\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 3.76574 | 0.371049 | 0.185524 | − | 0.982640i | \(-0.440602\pi\) | ||||
0.185524 | + | 0.982640i | \(0.440602\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.44765 | −0.141276 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 2.93296 | 0.283540 | 0.141770 | − | 0.989900i | \(-0.454721\pi\) | ||||
0.141770 | + | 0.989900i | \(0.454721\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 14.4914i | 1.38803i | 0.719962 | + | 0.694013i | \(0.244159\pi\) | ||||
−0.719962 | + | 0.694013i | \(0.755841\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.30413 | −0.123782 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 21.0266i | − | 1.97801i | −0.147875 | − | 0.989006i | \(-0.547243\pi\) | ||
0.147875 | − | 0.989006i | \(-0.452757\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −3.80988 | + | 2.91287i | −0.355273 | + | 0.271627i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −4.25689 | −0.393550 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | − | 10.3383i | − | 0.947714i | ||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.7083 | −0.973484 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.97953i | 0.539156i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 1.00000i | − | 0.0894427i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 1.36794i | − | 0.121385i | −0.998157 | − | 0.0606924i | \(-0.980669\pi\) | ||
0.998157 | − | 0.0606924i | \(-0.0193309\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.03228i | 0.178932i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | − | 11.8087i | − | 1.03173i | −0.856671 | − | 0.515863i | \(-0.827471\pi\) | ||
0.856671 | − | 0.515863i | \(-0.172529\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.36275 | −0.118165 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.00000 | 0.0860663 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 12.1571i | 1.03865i | 0.854576 | + | 0.519326i | \(0.173817\pi\) | ||||
−0.854576 | + | 0.519326i | \(0.826183\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 14.5794i | 1.23661i | 0.785939 | + | 0.618304i | \(0.212180\pi\) | ||||
−0.785939 | + | 0.618304i | \(0.787820\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.61495 | 0.557079 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −2.29903 | −0.192255 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.26464i | 0.105023i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 4.90431i | − | 0.404501i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 4.61311i | 0.377921i | 0.981985 | + | 0.188960i | \(0.0605118\pi\) | ||||
−0.981985 | + | 0.188960i | \(0.939488\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 22.2226i | 1.80845i | 0.427055 | + | 0.904226i | \(0.359551\pi\) | ||||
−0.427055 | + | 0.904226i | \(0.640449\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 7.14147i | 0.577354i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 3.15253 | 0.253218 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 23.2200i | − | 1.85316i | −0.376099 | − | 0.926579i | \(-0.622735\pi\) | ||
0.376099 | − | 0.926579i | \(-0.377265\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 7.54328 | 0.598221 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.21681 | + | 5.51537i | 0.332332 | + | 0.434672i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 19.5709i | 1.53291i | 0.642299 | + | 0.766454i | \(0.277981\pi\) | ||||
−0.642299 | + | 0.766454i | \(0.722019\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.540073 | 0.0420446 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 16.9663i | 1.31289i | 0.754374 | + | 0.656445i | \(0.227941\pi\) | ||||
−0.754374 | + | 0.656445i | \(0.772059\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 5.12112 | 0.393932 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0.941351 | 0.0719869 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 23.6431 | 1.79755 | 0.898774 | − | 0.438412i | \(-0.144459\pi\) | ||||
0.898774 | + | 0.438412i | \(0.144459\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.44765 | −0.109432 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 11.1974 | 0.841645 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 13.7587i | 1.02837i | 0.857678 | + | 0.514187i | \(0.171906\pi\) | ||||
−0.857678 | + | 0.514187i | \(0.828094\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 23.9965i | − | 1.78364i | −0.452387 | − | 0.891822i | \(-0.649428\pi\) | ||
0.452387 | − | 0.891822i | \(-0.350572\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −2.00097 | −0.147916 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.30413 | −0.0958814 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.85691i | 0.282046i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | − | 1.44765i | − | 0.105301i | ||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.662043 | 0.0479037 | 0.0239519 | − | 0.999713i | \(-0.492375\pi\) | ||||
0.0239519 | + | 0.999713i | \(0.492375\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 8.81504 | 0.634521 | 0.317260 | − | 0.948338i | \(-0.397237\pi\) | ||||
0.317260 | + | 0.948338i | \(0.397237\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.25689 | −0.304842 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −25.8264 | −1.84005 | −0.920027 | − | 0.391855i | \(-0.871833\pi\) | ||||
−0.920027 | + | 0.391855i | \(0.871833\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 19.6257 | 1.39123 | 0.695615 | − | 0.718415i | \(-0.255132\pi\) | ||||
0.695615 | + | 0.718415i | \(0.255132\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 7.68722i | 0.542215i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.83076 | 0.128494 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 5.97953i | 0.417628i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −2.91287 | − | 3.80988i | −0.202459 | − | 0.264805i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 0.508398 | 0.0351666 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 16.4801i | 1.13454i | 0.823532 | + | 0.567270i | \(0.192000\pi\) | ||||
−0.823532 | + | 0.567270i | \(0.808000\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.07158 | −0.553055 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 2.03228i | 0.138600i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 4.56376i | − | 0.309808i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 1.91203i | 0.129203i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 30.4005i | − | 2.04496i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − | 0.687718i | − | 0.0460530i | −0.999735 | − | 0.0230265i | \(-0.992670\pi\) | ||
0.999735 | − | 0.0230265i | \(-0.00733021\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.00000 | 0.0666667 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 17.6458 | 1.17119 | 0.585597 | − | 0.810603i | \(-0.300860\pi\) | ||||
0.585597 | + | 0.810603i | \(0.300860\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − | 6.99625i | − | 0.462325i | −0.972915 | − | 0.231163i | \(-0.925747\pi\) | ||
0.972915 | − | 0.231163i | \(-0.0742530\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 0.781836i | − | 0.0514410i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 3.36671 | 0.220560 | 0.110280 | − | 0.993901i | \(-0.464825\pi\) | ||||
0.110280 | + | 0.993901i | \(0.464825\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.61495 | 0.431511 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − | 3.99026i | − | 0.259195i | ||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 15.0526i | 0.973674i | 0.873493 | + | 0.486837i | \(0.161849\pi\) | ||||
−0.873493 | + | 0.486837i | \(0.838151\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6.51887i | 0.419917i | 0.977710 | + | 0.209959i | \(0.0673329\pi\) | ||||
−0.977710 | + | 0.209959i | \(0.932667\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.00000i | 0.0641500i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 4.90431i | − | 0.313325i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.00723 | −0.254974 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 1.20991i | 0.0766749i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 11.0617 | 0.698208 | 0.349104 | − | 0.937084i | \(-0.386486\pi\) | ||||
0.349104 | + | 0.937084i | \(0.386486\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.57316 | − | 2.05761i | −0.0989039 | − | 0.129361i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 7.14147i | 0.447216i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −4.60346 | −0.287156 | −0.143578 | − | 0.989639i | \(-0.545861\pi\) | ||||
−0.143578 | + | 0.989639i | \(0.545861\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.88792i | 0.117310i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −1.26464 | −0.0782793 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.952711 | 0.0587467 | 0.0293733 | − | 0.999569i | \(-0.490649\pi\) | ||||
0.0293733 | + | 0.999569i | \(0.490649\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 7.54328 | 0.463380 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 17.8161 | 1.09033 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 26.8660 | 1.63805 | 0.819025 | − | 0.573757i | \(-0.194515\pi\) | ||||
0.819025 | + | 0.573757i | \(0.194515\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 25.2660i | − | 1.53480i | −0.641167 | − | 0.767401i | \(-0.721550\pi\) | ||
0.641167 | − | 0.767401i | \(-0.278450\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 6.16248i | 0.372970i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0.540073 | 0.0325676 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −18.2298 | −1.09532 | −0.547660 | − | 0.836701i | \(-0.684481\pi\) | ||||
−0.547660 | + | 0.836701i | \(0.684481\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.15253i | 0.188737i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.9007i | 0.650282i | 0.945665 | + | 0.325141i | \(0.105412\pi\) | ||||
−0.945665 | + | 0.325141i | \(0.894588\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −13.1522 | −0.781817 | −0.390909 | − | 0.920430i | \(-0.627839\pi\) | ||||
−0.390909 | + | 0.920430i | \(0.627839\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0.941351 | 0.0557608 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.65626 | 0.510963 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −34.0006 | −2.00003 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.5224 | 0.675454 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 12.4528i | 0.727499i | 0.931497 | + | 0.363750i | \(0.118504\pi\) | ||||
−0.931497 | + | 0.363750i | \(0.881496\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 11.1974 | 0.651935 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0.540073i | 0.0313382i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 12.3998 | + | 16.2182i | 0.717097 | + | 0.937925i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.94202 | 0.169575 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 13.5957i | 0.781053i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −2.00097 | −0.114575 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.9864i | 1.25483i | 0.778684 | + | 0.627416i | \(0.215887\pi\) | ||||
−0.778684 | + | 0.627416i | \(0.784113\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.76574i | 0.214225i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 22.6678i | − | 1.28537i | −0.766128 | − | 0.642687i | \(-0.777819\pi\) | ||
0.766128 | − | 0.642687i | \(-0.222181\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 17.0883i | 0.965886i | 0.875652 | + | 0.482943i | \(0.160432\pi\) | ||||
−0.875652 | + | 0.482943i | \(0.839568\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | − | 1.44765i | − | 0.0815658i | ||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 29.7843 | 1.67285 | 0.836425 | − | 0.548081i | \(-0.184641\pi\) | ||||
0.836425 | + | 0.548081i | \(0.184641\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −0.682998 | −0.0382406 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 2.93296i | 0.163702i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 6.72263i | 0.374057i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −4.25689 | −0.236130 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −14.4914 | −0.801378 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 9.57612i | − | 0.527949i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 17.3613i | − | 0.954264i | −0.878832 | − | 0.477132i | \(-0.841676\pi\) | ||
0.878832 | − | 0.477132i | \(-0.158324\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 1.30413i | − | 0.0714658i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 7.68722i | 0.419998i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 9.95332i | 0.542192i | 0.962552 | + | 0.271096i | \(0.0873861\pi\) | ||||
−0.962552 | + | 0.271096i | \(0.912614\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 21.0266 | 1.14201 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.70260i | 0.0922009i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −17.2333 | −0.930509 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −2.91287 | − | 3.80988i | −0.156824 | − | 0.205117i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 10.6141i | − | 0.569793i | −0.958558 | − | 0.284896i | \(-0.908041\pi\) | ||
0.958558 | − | 0.284896i | \(-0.0919592\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 11.4277 | 0.611713 | 0.305856 | − | 0.952078i | \(-0.401057\pi\) | ||||
0.305856 | + | 0.952078i | \(0.401057\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 4.25689i | − | 0.227216i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −2.08495 | −0.110971 | −0.0554854 | − | 0.998459i | \(-0.517671\pi\) | ||||
−0.0554854 | + | 0.998459i | \(0.517671\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.07158 | −0.428395 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 10.3383 | 0.547163 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −21.6384 | −1.14203 | −0.571015 | − | 0.820939i | \(-0.693450\pi\) | ||||
−0.571015 | + | 0.820939i | \(0.693450\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.1139 | −0.953361 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 10.7083i | − | 0.562041i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.91203i | 0.100080i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 25.5833 | 1.33544 | 0.667720 | − | 0.744413i | \(-0.267270\pi\) | ||||
0.667720 | + | 0.744413i | \(0.267270\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −5.97953 | −0.311282 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | − | 10.9200i | − | 0.566939i | ||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.23189i | 0.374453i | 0.982317 | + | 0.187227i | \(0.0599499\pi\) | ||||
−0.982317 | + | 0.187227i | \(0.940050\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 1.00000 | 0.0516398 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.38344 | 0.277261 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 29.1313 | 1.49638 | 0.748188 | − | 0.663487i | \(-0.230924\pi\) | ||||
0.748188 | + | 0.663487i | \(0.230924\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.36794 | 0.0700815 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −23.5528 | −1.20349 | −0.601746 | − | 0.798688i | \(-0.705528\pi\) | ||||
−0.601746 | + | 0.798688i | \(0.705528\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | − | 0.781836i | − | 0.0398461i | ||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.03228 | −0.103306 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 31.4964i | − | 1.59693i | −0.602039 | − | 0.798466i | \(-0.705645\pi\) | ||
0.602039 | − | 0.798466i | \(-0.294355\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 27.2081 | − | 20.8022i | 1.37597 | − | 1.05201i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 11.8087 | 0.595668 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 3.99026i | − | 0.200772i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.30405 | 0.115637 | 0.0578184 | − | 0.998327i | \(-0.481586\pi\) | ||||
0.0578184 | + | 0.998327i | \(0.481586\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 1.36275i | − | 0.0682226i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6.47560i | 0.323376i | 0.986842 | + | 0.161688i | \(0.0516939\pi\) | ||||
−0.986842 | + | 0.161688i | \(0.948306\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | − | 13.4200i | − | 0.668498i | ||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.00000i | 0.0496904i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | − | 0.704325i | − | 0.0349121i | ||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 19.1498 | 0.946897 | 0.473449 | − | 0.880821i | \(-0.343009\pi\) | ||||
0.473449 | + | 0.880821i | \(0.343009\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12.1571 | −0.599666 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 16.2098i | − | 0.797634i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.20991i | 0.0593921i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −14.5794 | −0.713956 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.39634 | −0.361335 | −0.180668 | − | 0.983544i | \(-0.557826\pi\) | ||||
−0.180668 | + | 0.983544i | \(0.557826\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 3.32719i | − | 0.162157i | −0.996708 | − | 0.0810787i | \(-0.974163\pi\) | ||
0.996708 | − | 0.0810787i | \(-0.0258365\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.61495i | 0.321630i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 7.14147i | 0.346412i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 2.89670i | 0.140181i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 2.29903i | − | 0.110998i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 37.5082 | 1.80670 | 0.903352 | − | 0.428899i | \(-0.141098\pi\) | ||||
0.903352 | + | 0.428899i | \(0.141098\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 25.6190i | 1.23117i | 0.788070 | + | 0.615586i | \(0.211081\pi\) | ||||
−0.788070 | + | 0.615586i | \(0.788919\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.26464 | −0.0606349 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −2.74203 | − | 3.58643i | −0.131169 | − | 0.171562i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 10.5861i | 0.505246i | 0.967565 | + | 0.252623i | \(0.0812932\pi\) | ||||
−0.967565 | + | 0.252623i | \(0.918707\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 4.90431 | 0.233539 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 34.7424i | 1.65066i | 0.564649 | + | 0.825331i | \(0.309011\pi\) | ||||
−0.564649 | + | 0.825331i | \(0.690989\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 17.8161 | 0.844565 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −4.61311 | −0.218193 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −6.14217 | −0.289867 | −0.144933 | − | 0.989441i | \(-0.546297\pi\) | ||||
−0.144933 | + | 0.989441i | \(0.546297\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.22938 | −0.152066 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −22.2226 | −1.04411 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.16248i | 0.288902i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 9.20228i | 0.430464i | 0.976563 | + | 0.215232i | \(0.0690508\pi\) | ||||
−0.976563 | + | 0.215232i | \(0.930949\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −7.14147 | −0.333335 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.39680 | 0.391078 | 0.195539 | − | 0.980696i | \(-0.437354\pi\) | ||||
0.195539 | + | 0.980696i | \(0.437354\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 34.0880i | 1.58421i | 0.610387 | + | 0.792103i | \(0.291014\pi\) | ||||
−0.610387 | + | 0.792103i | \(0.708986\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 3.15253i | 0.146195i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −30.5287 | −1.41270 | −0.706351 | − | 0.707862i | \(-0.749660\pi\) | ||||
−0.706351 | + | 0.707862i | \(0.749660\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 11.1284 | 0.513862 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 23.2200 | 1.06992 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.09758 | −0.0504667 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0.941351 | 0.0431921 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.54328i | 0.345383i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.47938 | 0.387433 | 0.193716 | − | 0.981058i | \(-0.437946\pi\) | ||||
0.193716 | + | 0.981058i | \(0.437946\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 5.55153i | 0.253128i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5.51537 | + | 4.21681i | −0.250958 | + | 0.191872i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 11.5224 | 0.523204 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 15.8113i | − | 0.716480i | −0.933630 | − | 0.358240i | \(-0.883377\pi\) | ||
0.933630 | − | 0.358240i | \(-0.116623\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −19.5709 | −0.885025 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 0.139651i | − | 0.00630236i | −0.999995 | − | 0.00315118i | \(-0.998997\pi\) | ||
0.999995 | − | 0.00315118i | \(-0.00100305\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 9.03139i | − | 0.406753i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0.540073i | 0.0242745i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 11.6848i | 0.524135i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 21.9494i | − | 0.982588i | −0.870994 | − | 0.491294i | \(-0.836524\pi\) | ||
0.870994 | − | 0.491294i | \(-0.163476\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −16.9663 | −0.757998 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −40.7383 | −1.81643 | −0.908216 | − | 0.418501i | \(-0.862555\pi\) | ||||
−0.908216 | + | 0.418501i | \(0.862555\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.5957i | 0.605001i | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 5.12112i | 0.227437i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −11.4424 | −0.507177 | −0.253589 | − | 0.967312i | \(-0.581611\pi\) | ||||
−0.253589 | + | 0.967312i | \(0.581611\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.76795 | 0.122447 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0.941351i | 0.0415617i | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 3.76574i | 0.165938i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.57255i | 0.157121i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 23.6431i | 1.03781i | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 8.24736i | − | 0.361323i | −0.983545 | − | 0.180662i | \(-0.942176\pi\) | ||
0.983545 | − | 0.180662i | \(-0.0578239\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 27.7257 | 1.21236 | 0.606179 | − | 0.795328i | \(-0.292701\pi\) | ||||
0.606179 | + | 0.795328i | \(0.292701\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 1.44765i | − | 0.0631806i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −22.5137 | −0.980713 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.03037 | + | 22.1954i | −0.262190 | + | 0.965016i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 11.1974i | 0.485924i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 25.4542 | 1.10254 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.93296i | 0.126803i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −13.7587 | −0.593732 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 2.64869 | 0.114087 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.989076 | 0.0425237 | 0.0212619 | − | 0.999774i | \(-0.493232\pi\) | ||||
0.0212619 | + | 0.999774i | \(0.493232\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 23.9965 | 1.02979 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −14.4914 | −0.620744 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 22.6052i | 0.966530i | 0.875474 | + | 0.483265i | \(0.160549\pi\) | ||||
−0.875474 | + | 0.483265i | \(0.839451\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 2.00097i | − | 0.0853992i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.19047 | −0.0507158 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.77649 | −0.245641 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | − | 1.30413i | − | 0.0553572i | ||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 21.4269i | − | 0.907885i | −0.891031 | − | 0.453943i | \(-0.850017\pi\) | ||
0.891031 | − | 0.453943i | \(-0.149983\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.65118 | 0.365906 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.85691 | −0.162839 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 10.5157 | 0.443184 | 0.221592 | − | 0.975139i | \(-0.428875\pi\) | ||||
0.221592 | + | 0.975139i | \(0.428875\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 21.0266 | 0.884594 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.44765 | 0.0607955 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 12.1516i | − | 0.509420i | −0.967017 | − | 0.254710i | \(-0.918020\pi\) | ||
0.967017 | − | 0.254710i | \(-0.0819801\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 32.1688 | 1.34622 | 0.673112 | − | 0.739540i | \(-0.264957\pi\) | ||||
0.673112 | + | 0.739540i | \(0.264957\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.662043i | 0.0276572i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.91287 | − | 3.80988i | −0.121475 | − | 0.158883i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.14210 | 0.0891767 | 0.0445884 | − | 0.999005i | \(-0.485802\pi\) | ||||
0.0445884 | + | 0.999005i | \(0.485802\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 8.81504i | 0.366341i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 1.75152 | 0.0726654 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.07392i | 0.168725i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 4.25689i | − | 0.176001i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 5.47981i | − | 0.226176i | −0.993585 | − | 0.113088i | \(-0.963926\pi\) | ||
0.993585 | − | 0.113088i | \(-0.0360742\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.96764i | 0.122280i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 25.8264i | − | 1.06236i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9.42307 | 0.386959 | 0.193480 | − | 0.981104i | \(-0.438023\pi\) | ||||
0.193480 | + | 0.981104i | \(0.438023\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 10.3383 | 0.423831 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 19.6257i | 0.803227i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 5.88186i | − | 0.240326i | −0.992754 | − | 0.120163i | \(-0.961658\pi\) | ||
0.992754 | − | 0.120163i | \(-0.0383418\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −12.9854 | −0.529686 | −0.264843 | − | 0.964292i | \(-0.585320\pi\) | ||||
−0.264843 | + | 0.964292i | \(0.585320\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −7.68722 | −0.313048 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 10.7083i | − | 0.435355i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 16.2816i | 0.660851i | 0.943832 | + | 0.330426i | \(0.107192\pi\) | ||||
−0.943832 | + | 0.330426i | \(0.892808\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1.83076i | 0.0741860i | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 28.1591i | − | 1.13920i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 13.0103i | 0.525483i | 0.964866 | + | 0.262741i | \(0.0846266\pi\) | ||||
−0.964866 | + | 0.262741i | \(0.915373\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5.97953 | −0.241118 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 25.4926i | − | 1.02629i | −0.858301 | − | 0.513146i | \(-0.828480\pi\) | ||
0.858301 | − | 0.513146i | \(-0.171520\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −8.65453 | −0.347855 | −0.173927 | − | 0.984758i | \(-0.555646\pi\) | ||||
−0.173927 | + | 0.984758i | \(0.555646\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.80988 | − | 2.91287i | 0.152885 | − | 0.116889i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 25.7915i | − | 1.03331i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0.508398i | 0.0203035i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 9.31339 | 0.371349 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 12.9000 | 0.513542 | 0.256771 | − | 0.966472i | \(-0.417341\pi\) | ||||
0.256771 | + | 0.966472i | \(0.417341\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −16.4801 | −0.655027 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1.36794 | 0.0542849 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −20.8771 | −0.827182 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 8.07158i | − | 0.319307i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 4.96834i | − | 0.196238i | −0.995175 | − | 0.0981188i | \(-0.968717\pi\) | ||
0.995175 | − | 0.0981188i | \(-0.0312825\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −31.8422 | −1.25573 | −0.627866 | − | 0.778321i | \(-0.716071\pi\) | ||||
−0.627866 | + | 0.778321i | \(0.716071\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.03228 | −0.0800208 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 21.2108i | 0.833883i | 0.908933 | + | 0.416942i | \(0.136898\pi\) | ||||
−0.908933 | + | 0.416942i | \(0.863102\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 6.04739i | 0.237381i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 4.56376 | 0.178868 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 27.7171 | 1.08466 | 0.542328 | − | 0.840167i | \(-0.317543\pi\) | ||||
0.542328 | + | 0.840167i | \(0.317543\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 11.8087 | 0.461402 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −1.91203 | −0.0745955 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −5.96186 | −0.232241 | −0.116121 | − | 0.993235i | \(-0.537046\pi\) | ||||
−0.116121 | + | 0.993235i | \(0.537046\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 23.4766i | 0.913133i | 0.889689 | + | 0.456567i | \(0.150921\pi\) | ||||
−0.889689 | + | 0.456567i | \(0.849079\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 30.4005 | 1.18066 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | − | 1.36275i | − | 0.0528450i | ||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.68374 | + | 4.81813i | 0.142635 | + | 0.186559i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0.687718 | 0.0265887 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 1.08067i | − | 0.0417187i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −12.4021 | −0.478068 | −0.239034 | − | 0.971011i | \(-0.576831\pi\) | ||||
−0.239034 | + | 0.971011i | \(0.576831\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 1.00000i | 0.0384900i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 39.6505i | − | 1.52389i | −0.647639 | − | 0.761947i | \(-0.724244\pi\) | ||
0.647639 | − | 0.761947i | \(-0.275756\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | − | 16.6804i | − | 0.640134i | ||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 17.6458i | 0.676189i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 38.5043i | 1.47333i | 0.676260 | + | 0.736663i | \(0.263599\pi\) | ||||
−0.676260 | + | 0.736663i | \(0.736401\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −12.1571 | −0.464499 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 6.99625 | 0.266924 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 32.1109i | − | 1.22333i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 14.9388i | − | 0.568300i | −0.958780 | − | 0.284150i | \(-0.908289\pi\) | ||
0.958780 | − | 0.284150i | \(-0.0917114\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0.781836 | 0.0296995 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −14.5794 | −0.553028 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 42.7026i | − | 1.61748i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 3.36671i | 0.127341i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 32.4050i | − | 1.22392i | −0.790888 | − | 0.611961i | \(-0.790381\pi\) | ||
0.790888 | − | 0.611961i | \(-0.209619\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 1.22764i | − | 0.0463014i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 6.61495i | 0.249133i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 19.6818 | 0.740211 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.25259i | 0.122154i | 0.998133 | + | 0.0610768i | \(0.0194535\pi\) | ||||
−0.998133 | + | 0.0610768i | \(0.980547\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.99026 | 0.149646 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 12.0108 | − | 9.18293i | 0.449807 | − | 0.343903i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 2.29903i | − | 0.0859789i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −15.0526 | −0.562151 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 36.9865i | − | 1.37936i | −0.724112 | − | 0.689682i | \(-0.757750\pi\) | ||
0.724112 | − | 0.689682i | \(-0.242250\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.45146 | 0.203023 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6.51887 | −0.242439 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.26464 | −0.0469676 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 15.0714 | 0.558966 | 0.279483 | − | 0.960151i | \(-0.409837\pi\) | ||||
0.279483 | + | 0.960151i | \(0.409837\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.00000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | − | 14.5134i | − | 0.536799i | ||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | − | 30.7487i | − | 1.13573i | −0.823122 | − | 0.567864i | \(-0.807770\pi\) | ||
0.823122 | − | 0.567864i | \(-0.192230\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.90431 | 0.180898 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −4.15166 | −0.152928 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 47.1416i | − | 1.73413i | −0.498195 | − | 0.867065i | \(-0.666004\pi\) | ||
0.498195 | − | 0.867065i | \(-0.333996\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 4.00723i | − | 0.147209i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.60643 | 0.168993 | 0.0844967 | − | 0.996424i | \(-0.473072\pi\) | ||||
0.0844967 | + | 0.996424i | \(0.473072\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.61311 | −0.169011 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.20991 | −0.0442683 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4.24589 | 0.155142 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −44.2542 | −1.61486 | −0.807430 | − | 0.589964i | \(-0.799142\pi\) | ||||
−0.807430 | + | 0.589964i | \(0.799142\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.0617i | 0.403110i | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −22.2226 | −0.808764 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 3.88762i | 0.141298i | 0.997501 | + | 0.0706489i | \(0.0225070\pi\) | ||||
−0.997501 | + | 0.0706489i | \(0.977493\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 2.05761 | − | 1.57316i | 0.0746866 | − | 0.0571022i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −12.0227 | −0.435821 | −0.217911 | − | 0.975969i | \(-0.569924\pi\) | ||||
−0.217911 | + | 0.975969i | \(0.569924\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 20.9785i | 0.759473i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −7.14147 | −0.258200 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 47.6659i | − | 1.72112i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 30.0089i | 1.08215i | 0.840975 | + | 0.541074i | \(0.181982\pi\) | ||||
−0.840975 | + | 0.541074i | \(0.818018\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − | 4.60346i | − | 0.165789i | ||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 13.0739i | 0.470236i | 0.971967 | + | 0.235118i | \(0.0755476\pi\) | ||||
−0.971967 | + | 0.235118i | \(0.924452\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.15253i | 0.113242i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.88792 | −0.0677288 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −5.62883 | −0.201674 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 4.35924i | − | 0.155986i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 1.26464i | − | 0.0451946i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 23.2200 | 0.828758 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.22428 | 0.221872 | 0.110936 | − | 0.993828i | \(-0.464615\pi\) | ||||
0.110936 | + | 0.993828i | \(0.464615\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0.952711i | 0.0339174i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 30.4391i | − | 1.08229i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.51789i | 0.302479i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 7.54328i | 0.267533i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 14.1298i | − | 0.500502i | −0.968181 | − | 0.250251i | \(-0.919487\pi\) | ||
0.968181 | − | 0.250251i | \(-0.0805132\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −47.2404 | −1.67125 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 17.8161i | 0.629502i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.03264 | −0.0364410 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.51537 | + | 4.21681i | −0.194391 | + | 0.148623i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 26.8660i | 0.945729i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −35.4454 | −1.24620 | −0.623098 | − | 0.782144i | \(-0.714126\pi\) | ||||
−0.623098 | + | 0.782144i | \(0.714126\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.09154i | 0.108559i | 0.998526 | + | 0.0542794i | \(0.0172862\pi\) | ||||
−0.998526 | + | 0.0542794i | \(0.982714\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 25.2660 | 0.886118 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −19.5709 | −0.685537 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.91309 | −0.0669304 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −6.16248 | −0.215335 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 37.5294 | 1.30978 | 0.654892 | − | 0.755722i | \(-0.272714\pi\) | ||||
0.654892 | + | 0.755722i | \(0.272714\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.7913i | 1.00360i | 0.864983 | + | 0.501800i | \(0.167329\pi\) | ||||
−0.864983 | + | 0.501800i | \(0.832671\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0.540073i | 0.0188029i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −38.9124 | −1.35312 | −0.676558 | − | 0.736390i | \(-0.736529\pi\) | ||||
−0.676558 | + | 0.736390i | \(0.736529\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13.6829 | 0.475228 | 0.237614 | − | 0.971360i | \(-0.423635\pi\) | ||||
0.237614 | + | 0.971360i | \(0.423635\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 18.2298i | − | 0.632384i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 35.0240i | 1.21351i | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −16.9663 | −0.587142 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −3.15253 | −0.108968 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −46.2129 | −1.59545 | −0.797724 | − | 0.603023i | \(-0.793963\pi\) | ||||
−0.797724 | + | 0.603023i | \(0.793963\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.4007 | −0.944851 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −10.9007 | −0.375441 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.12112i | 0.176172i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −15.5019 | −0.532651 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 13.1522i | − | 0.451382i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.96857 | + | 3.79876i | −0.170320 | + | 0.130220i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.57168 | −0.259249 | −0.129625 | − | 0.991563i | \(-0.541377\pi\) | ||||
−0.129625 | + | 0.991563i | \(0.541377\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.941351i | 0.0321935i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 4.89067 | 0.167062 | 0.0835310 | − | 0.996505i | \(-0.473380\pi\) | ||||
0.0835310 | + | 0.996505i | \(0.473380\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 23.5029i | − | 0.801908i | −0.916098 | − | 0.400954i | \(-0.868679\pi\) | ||
0.916098 | − | 0.400954i | \(-0.131321\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 8.65626i | 0.295004i | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 4.60282i | − | 0.156682i | −0.996927 | − | 0.0783409i | \(-0.975038\pi\) | ||
0.996927 | − | 0.0783409i | \(-0.0249623\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 23.6431i | 0.803888i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 34.0006i | − | 1.15472i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.15503 | 0.0731044 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 32.7237 | 1.10880 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11.5224i | 0.389973i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | − | 1.44765i | − | 0.0489395i | ||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11.0430 | −0.372895 | −0.186448 | − | 0.982465i | \(-0.559697\pi\) | ||||
−0.186448 | + | 0.982465i | \(0.559697\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −12.4528 | −0.420022 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 26.0903i | − | 0.879003i | −0.898242 | − | 0.439502i | \(-0.855155\pi\) | ||
0.898242 | − | 0.439502i | \(-0.144845\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 38.2157i | 1.28606i | 0.765841 | + | 0.643030i | \(0.222323\pi\) | ||||
−0.765841 | + | 0.643030i | \(0.777677\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 11.1974i | 0.376395i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 49.6348i | − | 1.66657i | −0.552842 | − | 0.833286i | \(-0.686457\pi\) | ||
0.552842 | − | 0.833286i | \(-0.313543\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 1.98029i | − | 0.0664169i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.540073 | −0.0180931 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 6.22698i | 0.208378i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −13.7587 | −0.459903 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −16.2182 | + | 12.3998i | −0.541511 | + | 0.414016i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | − | 3.98682i | − | 0.132968i | ||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −53.8701 | −1.79467 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 2.94202i | 0.0979044i | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 23.9965 | 0.797669 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.35647 | −0.0782454 | −0.0391227 | − | 0.999234i | \(-0.512456\pi\) | ||||
−0.0391227 | + | 0.999234i | \(0.512456\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −13.5957 | −0.450941 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 30.4576 | 1.00910 | 0.504552 | − | 0.863381i | \(-0.331658\pi\) | ||||
0.504552 | + | 0.863381i | \(0.331658\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −0.653439 | −0.0216257 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 2.00097i | − | 0.0661499i | ||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 17.0948i | − | 0.564520i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −25.2389 | −0.832554 | −0.416277 | − | 0.909238i | \(-0.636665\pi\) | ||||
−0.416277 | + | 0.909238i | \(0.636665\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −21.9864 | −0.724477 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 34.3598i | 1.13097i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 1.30413i | − | 0.0428795i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.76574 | −0.123683 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −28.0820 | −0.921341 | −0.460671 | − | 0.887571i | \(-0.652391\pi\) | ||||
−0.460671 | + | 0.887571i | \(0.652391\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.61668 | 0.151306 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 22.6678 | 0.742112 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −3.85691 | −0.126135 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 56.1650i | 1.83483i | 0.397932 | + | 0.917415i | \(0.369728\pi\) | ||||
−0.397932 | + | 0.917415i | \(0.630272\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −17.0883 | −0.557655 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 13.7747i | − | 0.449044i | −0.974469 | − | 0.224522i | \(-0.927918\pi\) | ||
0.974469 | − | 0.224522i | \(-0.0720820\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 17.4176 | + | 22.7813i | 0.567195 | + | 0.741860i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 1.44765 | 0.0470920 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 20.6023i | − | 0.669486i | −0.942309 | − | 0.334743i | \(-0.891350\pi\) | ||
0.942309 | − | 0.334743i | \(-0.108650\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 8.13932 | 0.264213 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 29.7843i | 0.965821i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 34.7439i | 1.12546i | 0.826639 | + | 0.562732i | \(0.190250\pi\) | ||||
−0.826639 | + | 0.562732i | \(0.809750\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0.662043i | 0.0214232i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − | 0.682998i | − | 0.0220782i | ||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 17.5992i | 0.568308i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 21.0615 | 0.679404 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −2.93296 | −0.0945132 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 8.81504i | 0.283766i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 51.1563i | − | 1.64508i | −0.568709 | − | 0.822539i | \(-0.692557\pi\) | ||
0.568709 | − | 0.822539i | \(-0.307443\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −6.72263 | −0.215962 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −33.1319 | −1.06325 | −0.531627 | − | 0.846979i | \(-0.678419\pi\) | ||||
−0.531627 | + | 0.846979i | \(0.678419\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 21.1058i | 0.676622i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 4.25689i | − | 0.136330i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 23.6188i | 0.755634i | 0.925880 | + | 0.377817i | \(0.123325\pi\) | ||||
−0.925880 | + | 0.377817i | \(0.876675\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 9.62201i | 0.307521i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 14.4914i | − | 0.462676i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −42.2937 | −1.34896 | −0.674480 | − | 0.738293i | \(-0.735632\pi\) | ||||
−0.674480 | + | 0.738293i | \(0.735632\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 25.8264i | − | 0.822897i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.57612 | 0.304811 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.91976 | + | 7.74273i | 0.188237 | + | 0.246205i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.4372i | 0.585678i | 0.956162 | + | 0.292839i | \(0.0946000\pi\) | ||||
−0.956162 | + | 0.292839i | \(0.905400\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 17.3613 | 0.550945 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 19.6257i | 0.622177i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −0.813525 | −0.0257646 | −0.0128823 | − | 0.999917i | \(-0.504101\pi\) | ||||
−0.0128823 | + | 0.999917i | \(0.504101\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.30413 | 0.0412608 |
(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 | 5520.2.be.c.1471.30 | yes | 32 | |
4.3 | odd | 2 | 5520.2.be.d.1471.29 | yes | 32 | ||
23.22 | odd | 2 | 5520.2.be.d.1471.30 | yes | 32 | ||
92.91 | even | 2 | inner | 5520.2.be.c.1471.29 | ✓ | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
5520.2.be.c.1471.29 | ✓ | 32 | 92.91 | even | 2 | inner | |
5520.2.be.c.1471.30 | yes | 32 | 1.1 | even | 1 | trivial | |
5520.2.be.d.1471.29 | yes | 32 | 4.3 | odd | 2 | ||
5520.2.be.d.1471.30 | yes | 32 | 23.22 | odd | 2 |