Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [320,3,Mod(17,320)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(320, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([0, 3, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("320.17");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 320 = 2^{6} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 320.t (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.71936845953\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(22\) over \(\Q(i)\) |
Twist minimal: | no (minimal twist has level 80) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 17.17 | ||
Character | \(\chi\) | \(=\) | 320.17 |
Dual form | 320.3.t.a.113.17 |
$q$-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 \(\left(\mathbb{Z}/320\mathbb{Z}\right)^\times\).
\(n\) | \(191\) | \(257\) | \(261\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{4}\right)\) | \(e\left(\frac{3}{4}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 2.50699 | 0.835664 | 0.417832 | − | 0.908524i | \(-0.362790\pi\) | ||||
0.417832 | + | 0.908524i | \(0.362790\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.36488 | − | 2.43881i | −0.872977 | − | 0.487762i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −7.18571 | + | 7.18571i | −1.02653 | + | 1.02653i | −0.0268912 | + | 0.999638i | \(0.508561\pi\) |
−0.999638 | + | 0.0268912i | \(0.991439\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −2.71500 | −0.301666 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 8.38398 | − | 8.38398i | 0.762180 | − | 0.762180i | −0.214536 | − | 0.976716i | \(-0.568824\pi\) |
0.976716 | + | 0.214536i | \(0.0688239\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −12.9652 | −0.997321 | −0.498660 | − | 0.866797i | \(-0.666175\pi\) | ||||
−0.498660 | + | 0.866797i | \(0.666175\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −10.9427 | − | 6.11407i | −0.729515 | − | 0.407605i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −22.8157 | − | 22.8157i | −1.34210 | − | 1.34210i | −0.893967 | − | 0.448132i | \(-0.852089\pi\) |
−0.448132 | − | 0.893967i | \(-0.647911\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −3.16584 | + | 3.16584i | −0.166623 | + | 0.166623i | −0.785493 | − | 0.618870i | \(-0.787591\pi\) |
0.618870 | + | 0.785493i | \(0.287591\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −18.0145 | + | 18.0145i | −0.857833 | + | 0.857833i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −3.81600 | − | 3.81600i | −0.165913 | − | 0.165913i | 0.619267 | − | 0.785180i | \(-0.287430\pi\) |
−0.785180 | + | 0.619267i | \(0.787430\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 13.1044 | + | 21.2902i | 0.524177 | + | 0.851610i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −29.3694 | −1.08776 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −18.3544 | + | 18.3544i | −0.632911 | + | 0.632911i | −0.948797 | − | 0.315886i | \(-0.897698\pi\) |
0.315886 | + | 0.948797i | \(0.397698\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 8.78531 | 0.283397 | 0.141698 | − | 0.989910i | \(-0.454744\pi\) | ||||
0.141698 | + | 0.989910i | \(0.454744\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 21.0186 | − | 21.0186i | 0.636926 | − | 0.636926i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 48.8893 | − | 13.8402i | 1.39684 | − | 0.395434i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 32.4039 | 0.875781 | 0.437891 | − | 0.899028i | \(-0.355726\pi\) | ||||
0.437891 | + | 0.899028i | \(0.355726\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −32.5036 | −0.833425 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 0.937574i | 0.0228677i | 0.999935 | + | 0.0114338i | \(0.00363958\pi\) | ||||
−0.999935 | + | 0.0114338i | \(0.996360\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 57.8364i | 1.34503i | 0.740083 | + | 0.672516i | \(0.234786\pi\) | ||||
−0.740083 | + | 0.672516i | \(0.765214\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 11.8506 | + | 6.62136i | 0.263348 | + | 0.147141i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −27.9276 | − | 27.9276i | −0.594205 | − | 0.594205i | 0.344560 | − | 0.938764i | \(-0.388028\pi\) |
−0.938764 | + | 0.344560i | \(0.888028\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 54.2688i | − | 1.10753i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −57.1987 | − | 57.1987i | −1.12154 | − | 1.12154i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 20.6425i | − | 0.389482i | −0.980855 | − | 0.194741i | \(-0.937613\pi\) | ||
0.980855 | − | 0.194741i | \(-0.0623866\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −57.0420 | + | 16.1482i | −1.03713 | + | 0.293603i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.93674 | + | 7.93674i | −0.139241 | + | 0.139241i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 40.1490 | + | 40.1490i | 0.680492 | + | 0.680492i | 0.960111 | − | 0.279619i | \(-0.0902081\pi\) |
−0.279619 | + | 0.960111i | \(0.590208\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −25.3893 | − | 25.3893i | −0.416217 | − | 0.416217i | 0.467680 | − | 0.883898i | \(-0.345090\pi\) |
−0.883898 | + | 0.467680i | \(0.845090\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 19.5092 | − | 19.5092i | 0.309669 | − | 0.309669i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 56.5915 | + | 31.6196i | 0.870638 | + | 0.486455i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 29.3419i | 0.437938i | 0.975732 | + | 0.218969i | \(0.0702694\pi\) | ||||
−0.975732 | + | 0.218969i | \(0.929731\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −9.56668 | − | 9.56668i | −0.138648 | − | 0.138648i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 34.7686i | − | 0.489698i | −0.969561 | − | 0.244849i | \(-0.921262\pi\) | ||
0.969561 | − | 0.244849i | \(-0.0787385\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −76.2777 | − | 76.2777i | −1.04490 | − | 1.04490i | −0.998943 | − | 0.0459567i | \(-0.985366\pi\) |
−0.0459567 | − | 0.998943i | \(-0.514634\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 32.8527 | + | 53.3744i | 0.438035 | + | 0.711659i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 120.490i | 1.56480i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 17.2292i | 0.218092i | 0.994037 | + | 0.109046i | \(0.0347795\pi\) | ||||
−0.994037 | + | 0.109046i | \(0.965220\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −49.1938 | −0.607331 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 73.3919 | 0.884239 | 0.442120 | − | 0.896956i | \(-0.354227\pi\) | ||||
0.442120 | + | 0.896956i | \(0.354227\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 43.9447 | + | 155.231i | 0.516997 | + | 1.82625i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −46.0144 | + | 46.0144i | −0.528901 | + | 0.528901i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 96.9216 | 1.08901 | 0.544503 | − | 0.838759i | \(-0.316718\pi\) | ||||
0.544503 | + | 0.838759i | \(0.316718\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 93.1639 | − | 93.1639i | 1.02378 | − | 1.02378i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 22.0247 | 0.236825 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 21.5394 | − | 6.09765i | 0.226731 | − | 0.0641858i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −53.4378 | − | 53.4378i | −0.550905 | − | 0.550905i | 0.375797 | − | 0.926702i | \(-0.377369\pi\) |
−0.926702 | + | 0.375797i | \(0.877369\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −22.7625 | + | 22.7625i | −0.229924 | + | 0.229924i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 67.9450 | − | 67.9450i | 0.672723 | − | 0.672723i | −0.285620 | − | 0.958343i | \(-0.592200\pi\) |
0.958343 | + | 0.285620i | \(0.0921995\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −132.887 | − | 132.887i | −1.29017 | − | 1.29017i | −0.934681 | − | 0.355486i | \(-0.884315\pi\) |
−0.355486 | − | 0.934681i | \(-0.615685\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 122.565 | − | 34.6973i | 1.16729 | − | 0.330450i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 44.9125 | 0.419743 | 0.209872 | − | 0.977729i | \(-0.432695\pi\) | ||||
0.209872 | + | 0.977729i | \(0.432695\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −31.7568 | + | 31.7568i | −0.291346 | + | 0.291346i | −0.837612 | − | 0.546266i | \(-0.816049\pi\) |
0.546266 | + | 0.837612i | \(0.316049\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 81.2363 | 0.731859 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 5.56976 | − | 5.56976i | 0.0492899 | − | 0.0492899i | −0.682032 | − | 0.731322i | \(-0.738904\pi\) |
0.731322 | + | 0.682032i | \(0.238904\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 7.34990 | + | 25.9629i | 0.0639122 | + | 0.225764i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 35.2004 | 0.300858 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 327.894 | 2.75541 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 19.5823i | − | 0.161837i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 2.35049i | 0.0191097i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −5.27642 | − | 124.889i | −0.0422114 | − | 0.999109i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 106.254 | + | 106.254i | 0.836645 | + | 0.836645i | 0.988416 | − | 0.151771i | \(-0.0484977\pi\) |
−0.151771 | + | 0.988416i | \(0.548498\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 144.995i | 1.12399i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 59.7795 | + | 59.7795i | 0.456332 | + | 0.456332i | 0.897449 | − | 0.441117i | \(-0.145418\pi\) |
−0.441117 | + | 0.897449i | \(0.645418\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | − | 45.4976i | − | 0.342088i | ||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 128.194 | + | 71.6263i | 0.949585 | + | 0.530566i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −126.441 | + | 126.441i | −0.922925 | + | 0.922925i | −0.997235 | − | 0.0743099i | \(-0.976325\pi\) |
0.0743099 | + | 0.997235i | \(0.476325\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −41.3857 | − | 41.3857i | −0.297739 | − | 0.297739i | 0.542389 | − | 0.840128i | \(-0.317520\pi\) |
−0.840128 | + | 0.542389i | \(0.817520\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −70.0143 | − | 70.0143i | −0.496555 | − | 0.496555i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −108.700 | + | 108.700i | −0.760138 | + | 0.760138i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 124.878 | − | 35.3520i | 0.861227 | − | 0.243807i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 136.051i | − | 0.925519i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −30.0503 | − | 30.0503i | −0.201680 | − | 0.201680i | 0.599040 | − | 0.800719i | \(-0.295549\pi\) |
−0.800719 | + | 0.599040i | \(0.795549\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 26.0891i | − | 0.172776i | −0.996262 | − | 0.0863878i | \(-0.972468\pi\) | ||
0.996262 | − | 0.0863878i | \(-0.0275324\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 61.9445 | + | 61.9445i | 0.404866 | + | 0.404866i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −38.3468 | − | 21.4257i | −0.247399 | − | 0.138230i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 2.64846i | − | 0.0168691i | −0.999964 | − | 0.00843457i | \(-0.997315\pi\) | ||
0.999964 | − | 0.00843457i | \(-0.00268484\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − | 51.7507i | − | 0.325476i | ||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 54.8413 | 0.340629 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −143.714 | −0.881682 | −0.440841 | − | 0.897585i | \(-0.645320\pi\) | ||||
−0.440841 | + | 0.897585i | \(0.645320\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −143.004 | + | 40.4833i | −0.866690 | + | 0.245353i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −192.906 | + | 192.906i | −1.15513 | + | 1.15513i | −0.169619 | + | 0.985510i | \(0.554254\pi\) |
−0.985510 | + | 0.169619i | \(0.945746\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −0.904324 | −0.00535103 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 8.59526 | − | 8.59526i | 0.0502647 | − | 0.0502647i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.04705 | −0.0118326 | −0.00591632 | − | 0.999982i | \(-0.501883\pi\) | ||||
−0.00591632 | + | 0.999982i | \(0.501883\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −247.150 | − | 58.8209i | −1.41229 | − | 0.336119i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 100.653 | + | 100.653i | 0.568663 | + | 0.568663i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −101.208 | + | 101.208i | −0.565405 | + | 0.565405i | −0.930838 | − | 0.365432i | \(-0.880921\pi\) |
0.365432 | + | 0.930838i | \(0.380921\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 154.013 | − | 154.013i | 0.850901 | − | 0.850901i | −0.139343 | − | 0.990244i | \(-0.544499\pi\) |
0.990244 | + | 0.139343i | \(0.0444991\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −63.6506 | − | 63.6506i | −0.347818 | − | 0.347818i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −141.439 | − | 79.0270i | −0.764537 | − | 0.427173i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −382.573 | −2.04584 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 211.040 | − | 211.040i | 1.11661 | − | 1.11661i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −45.3049 | −0.237198 | −0.118599 | − | 0.992942i | \(-0.537840\pi\) | ||||
−0.118599 | + | 0.992942i | \(0.537840\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −176.113 | + | 176.113i | −0.912503 | + | 0.912503i | −0.996469 | − | 0.0839658i | \(-0.973241\pi\) |
0.0839658 | + | 0.996469i | \(0.473241\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 141.874 | + | 79.2700i | 0.727560 | + | 0.406513i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −308.173 | −1.56433 | −0.782164 | − | 0.623072i | \(-0.785884\pi\) | ||||
−0.782164 | + | 0.623072i | \(0.785884\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 190.912 | 0.959358 | 0.479679 | − | 0.877444i | \(-0.340753\pi\) | ||||
0.479679 | + | 0.877444i | \(0.340753\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 73.5598i | 0.365969i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 263.779i | − | 1.29940i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 2.28656 | − | 4.09240i | 0.0111540 | − | 0.0199629i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 10.3604 | + | 10.3604i | 0.0500504 | + | 0.0500504i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 53.0847i | 0.253994i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −230.999 | − | 230.999i | −1.09478 | − | 1.09478i | −0.995011 | − | 0.0997692i | \(-0.968190\pi\) |
−0.0997692 | − | 0.995011i | \(-0.531810\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | − | 87.1645i | − | 0.409223i | ||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 141.052 | − | 252.449i | 0.656055 | − | 1.17418i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −63.1286 | + | 63.1286i | −0.290915 | + | 0.290915i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −191.228 | − | 191.228i | −0.873185 | − | 0.873185i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 295.809 | + | 295.809i | 1.33850 | + | 1.33850i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 60.6724 | − | 60.6724i | 0.272073 | − | 0.272073i | −0.557861 | − | 0.829934i | \(-0.688378\pi\) |
0.829934 | + | 0.557861i | \(0.188378\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −35.5785 | − | 57.8030i | −0.158127 | − | 0.256902i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 202.529i | 0.892199i | 0.894983 | + | 0.446099i | \(0.147187\pi\) | ||||
−0.894983 | + | 0.446099i | \(0.852813\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −137.361 | − | 137.361i | −0.599829 | − | 0.599829i | 0.340438 | − | 0.940267i | \(-0.389425\pi\) |
−0.940267 | + | 0.340438i | \(0.889425\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 302.067i | 1.30765i | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −197.272 | − | 197.272i | −0.846660 | − | 0.846660i | 0.143055 | − | 0.989715i | \(-0.454308\pi\) |
−0.989715 | + | 0.143055i | \(0.954308\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 53.7907 | + | 190.011i | 0.228896 | + | 0.808557i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 43.1935i | 0.182251i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 411.923i | − | 1.72353i | −0.507310 | − | 0.861763i | \(-0.669360\pi\) | ||
0.507310 | − | 0.861763i | \(-0.330640\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −293.936 | −1.21965 | −0.609826 | − | 0.792535i | \(-0.708761\pi\) | ||||
−0.609826 | + | 0.792535i | \(0.708761\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 140.996 | 0.580231 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −132.351 | + | 236.877i | −0.540209 | + | 0.966844i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 41.0457 | − | 41.0457i | 0.166177 | − | 0.166177i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 183.993 | 0.738926 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −198.365 | + | 198.365i | −0.790298 | + | 0.790298i | −0.981542 | − | 0.191244i | \(-0.938748\pi\) |
0.191244 | + | 0.981542i | \(0.438748\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −63.9866 | −0.252911 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 110.169 | + | 389.163i | 0.432035 | + | 1.52613i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −239.646 | − | 239.646i | −0.932473 | − | 0.932473i | 0.0653871 | − | 0.997860i | \(-0.479172\pi\) |
−0.997860 | + | 0.0653871i | \(0.979172\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −232.845 | + | 232.845i | −0.899015 | + | 0.899015i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 49.8322 | − | 49.8322i | 0.190928 | − | 0.190928i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 142.437 | + | 142.437i | 0.541585 | + | 0.541585i | 0.923993 | − | 0.382408i | \(-0.124905\pi\) |
−0.382408 | + | 0.923993i | \(0.624905\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −50.3432 | + | 90.1023i | −0.189974 | + | 0.340009i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 242.981 | 0.910043 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 269.805 | − | 269.805i | 1.00299 | − | 1.00299i | 0.00299625 | − | 0.999996i | \(-0.499046\pi\) |
0.999996 | − | 0.00299625i | \(-0.000953737\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −71.4599 | −0.263690 | −0.131845 | − | 0.991270i | \(-0.542090\pi\) | ||||
−0.131845 | + | 0.991270i | \(0.542090\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 233.561 | − | 233.561i | 0.855535 | − | 0.855535i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 288.364 | + | 68.6298i | 1.04860 | + | 0.249563i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 256.078 | 0.924470 | 0.462235 | − | 0.886758i | \(-0.347048\pi\) | ||||
0.462235 | + | 0.886758i | \(0.347048\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −23.8521 | −0.0854914 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 315.882i | − | 1.12413i | −0.827092 | − | 0.562067i | \(-0.810006\pi\) | ||
0.827092 | − | 0.562067i | \(-0.189994\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 8.65428i | − | 0.0305805i | −0.999883 | − | 0.0152903i | \(-0.995133\pi\) | ||
0.999883 | − | 0.0152903i | \(-0.00486723\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 53.9991 | − | 15.2867i | 0.189471 | − | 0.0536377i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −6.73713 | − | 6.73713i | −0.0234743 | − | 0.0234743i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 752.111i | 2.60246i | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −133.968 | − | 133.968i | −0.460372 | − | 0.460372i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 533.382i | 1.82042i | 0.414151 | + | 0.910208i | \(0.364079\pi\) | ||||
−0.414151 | + | 0.910208i | \(0.635921\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −77.3300 | − | 273.162i | −0.262136 | − | 0.925972i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −246.232 | + | 246.232i | −0.829066 | + | 0.829066i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 49.4751 | + | 49.4751i | 0.165469 | + | 0.165469i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −415.595 | − | 415.595i | −1.38072 | − | 1.38072i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 170.338 | − | 170.338i | 0.562170 | − | 0.562170i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 48.9016 | + | 172.741i | 0.160333 | + | 0.566363i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 322.054i | − | 1.04903i | −0.851400 | − | 0.524517i | \(-0.824246\pi\) | ||
0.851400 | − | 0.524517i | \(-0.175754\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −333.147 | − | 333.147i | −1.07815 | − | 1.07815i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | − | 10.0499i | − | 0.0323149i | −0.999869 | − | 0.0161575i | \(-0.994857\pi\) | ||
0.999869 | − | 0.0161575i | \(-0.00514331\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 13.4351 | + | 13.4351i | 0.0429237 | + | 0.0429237i | 0.728243 | − | 0.685319i | \(-0.240337\pi\) |
−0.685319 | + | 0.728243i | \(0.740337\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −132.734 | + | 37.5761i | −0.421379 | + | 0.119289i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 182.394i | − | 0.575377i | −0.957724 | − | 0.287688i | \(-0.907113\pi\) | ||
0.957724 | − | 0.287688i | \(-0.0928867\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 307.766i | 0.964785i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 112.595 | 0.350764 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 144.462 | 0.447250 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −169.901 | − | 276.032i | −0.522772 | − | 0.849328i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −79.6139 | + | 79.6139i | −0.243468 | + | 0.243468i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 401.359 | 1.21994 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 213.565 | − | 213.565i | 0.645211 | − | 0.645211i | −0.306621 | − | 0.951832i | \(-0.599198\pi\) |
0.951832 | + | 0.306621i | \(0.0991983\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −87.9766 | −0.264194 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 71.5592 | − | 128.074i | 0.213610 | − | 0.382310i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −99.5263 | − | 99.5263i | −0.295330 | − | 0.295330i | 0.543851 | − | 0.839182i | \(-0.316966\pi\) |
−0.839182 | + | 0.543851i | \(0.816966\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.9633 | − | 13.9633i | 0.0411898 | − | 0.0411898i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 73.6559 | − | 73.6559i | 0.216000 | − | 0.216000i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 37.8598 | + | 37.8598i | 0.110378 | + | 0.110378i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 18.4261 | + | 65.0888i | 0.0534091 | + | 0.188663i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 481.819 | 1.38853 | 0.694264 | − | 0.719721i | \(-0.255730\pi\) | ||||
0.694264 | + | 0.719721i | \(0.255730\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −398.473 | + | 398.473i | −1.14176 | + | 1.14176i | −0.153628 | + | 0.988129i | \(0.549096\pi\) |
−0.988129 | + | 0.153628i | \(0.950904\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 380.779 | 1.08484 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 356.849 | − | 356.849i | 1.01090 | − | 1.01090i | 0.0109648 | − | 0.999940i | \(-0.496510\pi\) |
0.999940 | − | 0.0109648i | \(-0.00349027\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −84.7940 | + | 151.761i | −0.238856 | + | 0.427495i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 822.027 | 2.30260 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −417.857 | −1.16395 | −0.581974 | − | 0.813207i | \(-0.697719\pi\) | ||||
−0.581974 | + | 0.813207i | \(0.697719\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 340.955i | 0.944473i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 49.0927i | − | 0.135242i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 146.917 | + | 518.970i | 0.402511 | + | 1.42184i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 109.049 | + | 109.049i | 0.297136 | + | 0.297136i | 0.839891 | − | 0.542755i | \(-0.182619\pi\) |
−0.542755 | + | 0.839891i | \(0.682619\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 2.54551i | − | 0.00689841i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 148.331 | + | 148.331i | 0.399815 | + | 0.399815i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 308.832i | 0.827968i | 0.910284 | + | 0.413984i | \(0.135863\pi\) | ||||
−0.910284 | + | 0.413984i | \(0.864137\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −13.2279 | − | 313.095i | −0.0352745 | − | 0.834919i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 237.968 | − | 237.968i | 0.631216 | − | 0.631216i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −28.3677 | − | 28.3677i | −0.0748489 | − | 0.0748489i | 0.668691 | − | 0.743540i | \(-0.266855\pi\) |
−0.743540 | + | 0.668691i | \(0.766855\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 266.377 | + | 266.377i | 0.699153 | + | 0.699153i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −422.953 | + | 422.953i | −1.10432 | + | 1.10432i | −0.110433 | + | 0.993884i | \(0.535224\pi\) |
−0.993884 | + | 0.110433i | \(0.964776\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 293.851 | − | 525.923i | 0.763250 | − | 1.36603i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − | 157.026i | − | 0.405751i | ||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 178.975 | + | 178.975i | 0.460089 | + | 0.460089i | 0.898685 | − | 0.438595i | \(-0.144524\pi\) |
−0.438595 | + | 0.898685i | \(0.644524\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 174.129i | 0.445344i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 149.867 | + | 149.867i | 0.381340 | + | 0.381340i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 42.0188 | − | 75.2036i | 0.106377 | − | 0.190389i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 20.4646i | 0.0515480i | 0.999668 | + | 0.0257740i | \(0.00820503\pi\) | ||||
−0.999668 | + | 0.0257740i | \(0.991795\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | − | 114.062i | − | 0.285870i | ||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 97.7306 | 0.243717 | 0.121859 | − | 0.992547i | \(-0.461115\pi\) | ||||
0.121859 | + | 0.992547i | \(0.461115\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −113.903 | −0.282638 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 214.725 | + | 119.974i | 0.530186 | + | 0.296233i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 271.674 | − | 271.674i | 0.667503 | − | 0.667503i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −346.930 | −0.848239 | −0.424120 | − | 0.905606i | \(-0.639416\pi\) | ||||
−0.424120 | + | 0.905606i | \(0.639416\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −316.986 | + | 316.986i | −0.771255 | + | 0.771255i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −576.998 | −1.39709 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −320.347 | − | 178.989i | −0.771920 | − | 0.431298i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −103.753 | − | 103.753i | −0.248809 | − | 0.248809i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −94.6547 | + | 94.6547i | −0.225906 | + | 0.225906i | −0.810980 | − | 0.585074i | \(-0.801065\pi\) |
0.585074 | + | 0.810980i | \(0.301065\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 303.154 | − | 303.154i | 0.720080 | − | 0.720080i | −0.248541 | − | 0.968621i | \(-0.579951\pi\) |
0.968621 | + | 0.248541i | \(0.0799512\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 75.8234 | + | 75.8234i | 0.179252 | + | 0.179252i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 186.765 | − | 784.738i | 0.439447 | − | 1.84644i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 364.880 | 0.854519 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −272.509 | + | 272.509i | −0.635220 | + | 0.635220i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −505.491 | −1.17283 | −0.586416 | − | 0.810010i | \(-0.699462\pi\) | ||||
−0.586416 | + | 0.810010i | \(0.699462\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.23935 | − | 8.23935i | 0.0190285 | − | 0.0190285i | −0.697529 | − | 0.716557i | \(-0.745717\pi\) |
0.716557 | + | 0.697529i | \(0.245717\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 313.068 | − | 88.6271i | 0.719696 | − | 0.203740i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 24.1617 | 0.0552900 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 195.298 | 0.444870 | 0.222435 | − | 0.974948i | \(-0.428600\pi\) | ||||
0.222435 | + | 0.974948i | \(0.428600\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 147.340i | 0.334103i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 401.681i | 0.906729i | 0.891325 | + | 0.453365i | \(0.149776\pi\) | ||||
−0.891325 | + | 0.453365i | \(0.850224\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −423.051 | − | 236.373i | −0.950677 | − | 0.531176i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −75.3357 | − | 75.3357i | −0.168536 | − | 0.168536i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 189.448i | − | 0.421934i | −0.977493 | − | 0.210967i | \(-0.932339\pi\) | ||
0.977493 | − | 0.210967i | \(-0.0676613\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.86061 | + | 7.86061i | 0.0174293 | + | 0.0174293i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − | 65.4052i | − | 0.144382i | ||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −633.859 | + | 179.441i | −1.39310 | + | 0.394375i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 488.804 | − | 488.804i | 1.06959 | − | 1.06959i | 0.0722037 | − | 0.997390i | \(-0.476997\pi\) |
0.997390 | − | 0.0722037i | \(-0.0230032\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 670.083 | + | 670.083i | 1.45988 | + | 1.45988i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 392.290 | + | 392.290i | 0.850954 | + | 0.850954i | 0.990251 | − | 0.139297i | \(-0.0444842\pi\) |
−0.139297 | + | 0.990251i | \(0.544484\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 70.7053 | − | 70.7053i | 0.152711 | − | 0.152711i | −0.626616 | − | 0.779328i | \(-0.715561\pi\) |
0.779328 | + | 0.626616i | \(0.215561\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −96.1352 | − | 53.7140i | −0.206742 | − | 0.115514i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 918.293i | − | 1.96637i | −0.182623 | − | 0.983183i | \(-0.558459\pi\) | ||
0.182623 | − | 0.983183i | \(-0.441541\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −210.842 | − | 210.842i | −0.449557 | − | 0.449557i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 6.63965i | − | 0.0140969i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 484.899 | + | 484.899i | 1.02516 | + | 1.02516i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −108.888 | − | 25.9150i | −0.229238 | − | 0.0545579i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 56.0445i | 0.117494i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 49.5880i | 0.103524i | 0.998659 | + | 0.0517620i | \(0.0164837\pi\) | ||||
−0.998659 | + | 0.0517620i | \(0.983516\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −420.122 | −0.873435 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 137.487 | 0.284652 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 102.925 | + | 363.575i | 0.212217 | + | 0.749638i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −644.145 | + | 644.145i | −1.32268 | + | 1.32268i | −0.411081 | + | 0.911599i | \(0.634849\pi\) |
−0.911599 | + | 0.411081i | \(0.865151\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −360.290 | −0.736790 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 541.213 | − | 541.213i | 1.10227 | − | 1.10227i | 0.108130 | − | 0.994137i | \(-0.465514\pi\) |
0.994137 | − | 0.108130i | \(-0.0344861\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 837.538 | 1.69886 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 154.869 | − | 43.8423i | 0.312867 | − | 0.0885702i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 249.837 | + | 249.837i | 0.502690 | + | 0.502690i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 142.483 | − | 142.483i | 0.285537 | − | 0.285537i | −0.549775 | − | 0.835313i | \(-0.685287\pi\) |
0.835313 | + | 0.549775i | \(0.185287\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −483.615 | + | 483.615i | −0.965299 | + | 0.965299i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −307.222 | − | 307.222i | −0.610780 | − | 0.610780i | 0.332370 | − | 0.943149i | \(-0.392152\pi\) |
−0.943149 | + | 0.332370i | \(0.892152\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −462.277 | + | 130.867i | −0.915400 | + | 0.259143i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.26713 | −0.00447166 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 268.080 | − | 268.080i | 0.526681 | − | 0.526681i | −0.392900 | − | 0.919581i | \(-0.628528\pi\) |
0.919581 | + | 0.392900i | \(0.128528\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 1096.22 | 2.14524 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 92.9789 | − | 92.9789i | 0.181245 | − | 0.181245i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 255.951 | + | 904.124i | 0.496992 | + | 1.75558i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −468.289 | −0.905782 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −5.13193 | −0.00988811 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 364.737i | 0.700071i | 0.936736 | + | 0.350036i | \(0.113831\pi\) | ||||
−0.936736 | + | 0.350036i | \(0.886169\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 434.085i | 0.829991i | 0.909823 | + | 0.414996i | \(0.136217\pi\) | ||||
−0.909823 | + | 0.414996i | \(0.863783\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −619.603 | − | 147.463i | −1.18020 | − | 0.280883i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −200.443 | − | 200.443i | −0.380347 | − | 0.380347i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 499.876i | − | 0.944946i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −109.005 | − | 109.005i | −0.205282 | − | 0.205282i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 12.1558i | − | 0.0228064i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −196.038 | − | 109.533i | −0.366426 | − | 0.204735i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −253.726 | + | 253.726i | −0.472489 | + | 0.472489i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −454.988 | − | 454.988i | −0.844134 | − | 0.844134i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −299.573 | − | 299.573i | −0.553739 | − | 0.553739i | 0.373779 | − | 0.927518i | \(-0.378062\pi\) |
−0.927518 | + | 0.373779i | \(0.878062\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 386.109 | − | 386.109i | 0.711067 | − | 0.711067i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 216.063 | − | 61.1659i | 0.396446 | − | 0.112231i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.98799i | 0.0182596i | 0.999958 | + | 0.00912979i | \(0.00290614\pi\) | ||||
−0.999958 | + | 0.00912979i | \(0.997094\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 68.9318 | + | 68.9318i | 0.125559 | + | 0.125559i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − | 116.214i | − | 0.210916i | ||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −123.804 | − | 123.804i | −0.223877 | − | 0.223877i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −354.587 | − | 198.120i | −0.638896 | − | 0.356973i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 360.011i | − | 0.646339i | −0.946341 | − | 0.323170i | \(-0.895252\pi\) | ||
0.946341 | − | 0.323170i | \(-0.104748\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 749.859i | − | 1.34143i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −959.106 | −1.70964 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 524.373 | 0.931392 | 0.465696 | − | 0.884945i | \(-0.345804\pi\) | ||||
0.465696 | + | 0.884945i | \(0.345804\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −37.8949 | + | 10.7278i | −0.0670707 | + | 0.0189872i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 353.492 | − | 353.492i | 0.623443 | − | 0.623443i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −606.955 | −1.06670 | −0.533352 | − | 0.845893i | \(-0.679068\pi\) | ||||
−0.533352 | + | 0.845893i | \(0.679068\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −763.721 | + | 763.721i | −1.33752 | + | 1.33752i | −0.439056 | + | 0.898460i | \(0.644687\pi\) |
−0.898460 | + | 0.439056i | \(0.855313\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −113.579 | −0.198218 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 31.2371 | − | 131.250i | 0.0543254 | − | 0.228261i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −95.1565 | − | 95.1565i | −0.164916 | − | 0.164916i | 0.619824 | − | 0.784740i | \(-0.287204\pi\) |
−0.784740 | + | 0.619824i | \(0.787204\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −441.514 | + | 441.514i | −0.762545 | + | 0.762545i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −527.372 | + | 527.372i | −0.907698 | + | 0.907698i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −173.067 | − | 173.067i | −0.296855 | − | 0.296855i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −153.646 | − | 85.8471i | −0.262642 | − | 0.146747i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −445.447 | −0.758853 | −0.379427 | − | 0.925222i | \(-0.623879\pi\) | ||||
−0.379427 | + | 0.925222i | \(0.623879\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −27.8129 | + | 27.8129i | −0.0472205 | + | 0.0472205i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −772.586 | −1.30725 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −359.016 | + | 359.016i | −0.605424 | + | 0.605424i | −0.941747 | − | 0.336323i | \(-0.890817\pi\) |
0.336323 | + | 0.941747i | \(0.390817\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1431.22 | − | 799.670i | −2.40541 | − | 1.34398i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 478.615 | 0.801700 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −66.3175 | −0.110714 | −0.0553568 | − | 0.998467i | \(-0.517630\pi\) | ||||
−0.0553568 | + | 0.998467i | \(0.517630\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 512.825i | 0.853287i | 0.904420 | + | 0.426643i | \(0.140304\pi\) | ||||
−0.904420 | + | 0.426643i | \(0.859696\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 79.6631i | − | 0.132111i | ||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −47.7576 | + | 85.4746i | −0.0789381 | + | 0.141280i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 700.017 | + | 700.017i | 1.15324 | + | 1.15324i | 0.985899 | + | 0.167341i | \(0.0535182\pi\) |
0.167341 | + | 0.985899i | \(0.446482\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | − | 661.292i | − | 1.08586i | ||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 362.086 | + | 362.086i | 0.592613 | + | 0.592613i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 402.030i | − | 0.655840i | −0.944705 | − | 0.327920i | \(-0.893652\pi\) | ||
0.944705 | − | 0.327920i | \(-0.106348\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 5.73240 | − | 10.2596i | 0.00932097 | − | 0.0166823i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 451.281 | − | 451.281i | 0.731412 | − | 0.731412i | −0.239488 | − | 0.970899i | \(-0.576979\pi\) |
0.970899 | + | 0.239488i | \(0.0769794\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −141.521 | − | 141.521i | −0.228629 | − | 0.228629i | 0.583491 | − | 0.812120i | \(-0.301686\pi\) |
−0.812120 | + | 0.583491i | \(0.801686\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 112.074 | + | 112.074i | 0.180473 | + | 0.180473i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −696.450 | + | 696.450i | −1.11790 | + | 1.11790i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −281.549 | + | 557.992i | −0.450478 | + | 0.892788i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 133.083i | 0.212254i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −739.318 | − | 739.318i | −1.17539 | − | 1.17539i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 430.554i | 0.682335i | 0.940002 | + | 0.341168i | \(0.110822\pi\) | ||||
−0.940002 | + | 0.341168i | \(0.889178\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −579.111 | − | 579.111i | −0.914868 | − | 0.914868i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −204.653 | − | 722.919i | −0.322288 | − | 1.13845i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 703.604i | 1.10456i | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 94.3966i | 0.147726i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 244.316 | 0.381147 | 0.190574 | − | 0.981673i | \(-0.438965\pi\) | ||||
0.190574 | + | 0.981673i | \(0.438965\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 521.720 | 0.811384 | 0.405692 | − | 0.914010i | \(-0.367031\pi\) | ||||
0.405692 | + | 0.914010i | \(0.367031\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 353.616 | − | 632.887i | 0.548242 | − | 0.981221i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.36567 | − | 7.36567i | 0.0113843 | − | 0.0113843i | −0.701392 | − | 0.712776i | \(-0.747438\pi\) |
0.712776 | + | 0.701392i | \(0.247438\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 673.218 | 1.03732 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −158.263 | + | 158.263i | −0.243107 | + | 0.243107i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 171.839 | 0.263154 | 0.131577 | − | 0.991306i | \(-0.457996\pi\) | ||||
0.131577 | + | 0.991306i | \(0.457996\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −115.140 | − | 406.721i | −0.175786 | − | 0.620949i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 207.094 | + | 207.094i | 0.315211 | + | 0.315211i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 66.3827 | − | 66.3827i | 0.100732 | − | 0.100732i | −0.654945 | − | 0.755677i | \(-0.727308\pi\) |
0.755677 | + | 0.654945i | \(0.227308\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −38.9121 | + | 38.9121i | −0.0588685 | + | 0.0588685i | −0.735928 | − | 0.677060i | \(-0.763254\pi\) |
0.677060 | + | 0.735928i | \(0.263254\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 741.591 | + | 741.591i | 1.11854 | + | 1.11854i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −110.960 | + | 198.592i | −0.166857 | + | 0.298634i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 140.081 | 0.210017 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 152.105 | − | 152.105i | 0.227362 | − | 0.227362i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −425.726 | −0.634465 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 58.7394 | − | 58.7394i | 0.0872799 | − | 0.0872799i | −0.662119 | − | 0.749399i | \(-0.730343\pi\) |
0.749399 | + | 0.662119i | \(0.230343\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −384.869 | − | 625.281i | −0.570176 | − | 0.926343i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −408.523 | −0.603431 | −0.301716 | − | 0.953398i | \(-0.597559\pi\) | ||||
−0.301716 | + | 0.953398i | \(0.597559\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 767.977 | 1.13104 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 507.738i | 0.745578i | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 611.720i | 0.895636i | 0.894125 | + | 0.447818i | \(0.147799\pi\) | ||||
−0.894125 | + | 0.447818i | \(0.852201\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 860.264 | − | 243.534i | 1.25586 | − | 0.355524i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −344.363 | − | 344.363i | −0.501256 | − | 0.501256i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 267.634i | 0.388438i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 528.007 | + | 528.007i | 0.764120 | + | 0.764120i | 0.977064 | − | 0.212944i | \(-0.0683053\pi\) |
−0.212944 | + | 0.977064i | \(0.568305\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | − | 327.129i | − | 0.472048i | ||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 79.7119 | + | 281.575i | 0.114693 | + | 0.405144i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 21.3914 | − | 21.3914i | 0.0306907 | − | 0.0306907i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −494.559 | − | 494.559i | −0.707523 | − | 0.707523i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 163.932 | + | 163.932i | 0.233855 | + | 0.233855i | 0.814300 | − | 0.580445i | \(-0.197121\pi\) |
−0.580445 | + | 0.814300i | \(0.697121\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −102.586 | + | 102.586i | −0.145926 | + | 0.145926i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 134.853 | + | 476.356i | 0.191280 | + | 0.675682i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 976.466i | 1.38114i | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 820.614 | + | 820.614i | 1.15742 | + | 1.15742i | 0.985027 | + | 0.172397i | \(0.0551513\pi\) |
0.172397 | + | 0.985027i | \(0.444849\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 46.7773i | − | 0.0657909i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −33.5248 | − | 33.5248i | −0.0470193 | − | 0.0470193i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 739.560 | − | 209.364i | 1.03435 | − | 0.292817i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 1032.69i | − | 1.44029i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 578.830i | 0.805048i | 0.915409 | + | 0.402524i | \(0.131867\pi\) | ||||
−0.915409 | + | 0.402524i | \(0.868133\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1909.78 | 2.64879 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −736.896 | −1.01922 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −631.294 | − | 150.246i | −0.870751 | − | 0.207236i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 771.845 | − | 771.845i | 1.06168 | − | 1.06168i | 0.0637163 | − | 0.997968i | \(-0.479705\pi\) |
0.997968 | − | 0.0637163i | \(-0.0202953\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 796.220 | 1.09221 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1319.58 | − | 1319.58i | 1.80517 | − | 1.80517i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 455.036 | 0.620785 | 0.310393 | − | 0.950608i | \(-0.399539\pi\) | ||||
0.310393 | + | 0.950608i | \(0.399539\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −331.803 | + | 593.848i | −0.451433 | + | 0.807957i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 246.002 | + | 246.002i | 0.333788 | + | 0.333788i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 723.106 | − | 723.106i | 0.978493 | − | 0.978493i | −0.0212803 | − | 0.999774i | \(-0.506774\pi\) |
0.999774 | + | 0.0212803i | \(0.00677425\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 102.901 | − | 102.901i | 0.138868 | − | 0.138868i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 134.068 | + | 134.068i | 0.180442 | + | 0.180442i | 0.791548 | − | 0.611107i | \(-0.209275\pi\) |
−0.611107 | + | 0.791548i | \(0.709275\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 57.8790 | + | 204.453i | 0.0776900 | + | 0.274433i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −199.259 | −0.266745 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −322.728 | + | 322.728i | −0.430879 | + | 0.430879i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 216.822 | 0.288711 | 0.144356 | − | 0.989526i | \(-0.453889\pi\) | ||||
0.144356 | + | 0.989526i | \(0.453889\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −497.299 | + | 497.299i | −0.660423 | + | 0.660423i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −63.6264 | + | 113.876i | −0.0842733 | + | 0.150829i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 747.764 | 0.987800 | 0.493900 | − | 0.869519i | \(-0.335571\pi\) | ||||
0.493900 | + | 0.869519i | \(0.335571\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −160.414 | −0.211349 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 1410.33i | − | 1.85326i | −0.375978 | − | 0.926629i | \(-0.622693\pi\) | ||
0.375978 | − | 0.926629i | \(-0.377307\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | − | 456.390i | − | 0.598152i | ||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −119.310 | − | 421.452i | −0.155961 | − | 0.550917i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −520.539 | − | 520.539i | −0.678669 | − | 0.678669i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 925.036i | 1.20291i | 0.798907 | + | 0.601454i | \(0.205412\pi\) | ||||
−0.798907 | + | 0.601454i | \(0.794588\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −600.789 | − | 600.789i | −0.779234 | − | 0.779234i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 146.591i | − | 0.189639i | −0.995494 | − | 0.0948196i | \(-0.969773\pi\) | ||
0.995494 | − | 0.0948196i | \(-0.0302274\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 115.126 | + | 187.041i | 0.148550 | + | 0.241344i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −583.740 | + | 583.740i | −0.751274 | + | 0.751274i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −2.96821 | − | 2.96821i | −0.00381029 | − | 0.00381029i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −291.499 | − | 291.499i | −0.373238 | − | 0.373238i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 539.058 | − | 539.058i | 0.688453 | − | 0.688453i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.45908 | + | 11.5602i | −0.00822813 | + | 0.0147264i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 389.164i | 0.494491i | 0.968953 | + | 0.247245i | \(0.0795254\pi\) | ||||
−0.968953 | + | 0.247245i | \(0.920475\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 357.088 | + | 357.088i | 0.452583 | + | 0.452583i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 80.0453i | 0.101195i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 329.176 | + | 329.176i | 0.415102 | + | 0.415102i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −126.210 | + | 225.886i | −0.158755 | + | 0.284133i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 225.230i | 0.282597i | 0.989967 | + | 0.141298i | \(0.0451277\pi\) | ||||
−0.989967 | + | 0.141298i | \(0.954872\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1274.38i | 1.59496i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −263.142 | −0.328517 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1279.02 | −1.59280 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −239.376 | − | 133.748i | −0.297362 | − | 0.166146i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 676.398 | − | 676.398i | 0.838164 | − | 0.838164i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −389.024 | −0.480870 | −0.240435 | − | 0.970665i | \(-0.577290\pi\) | ||||
−0.240435 | + | 0.970665i | \(0.577290\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −235.660 | + | 235.660i | −0.290580 | + | 0.290580i | −0.837309 | − | 0.546730i | \(-0.815873\pi\) |
0.546730 | + | 0.837309i | \(0.315873\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −179.149 | −0.220356 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 627.296 | + | 350.492i | 0.769688 | + | 0.430051i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −183.101 | − | 183.101i | −0.224114 | − | 0.224114i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −252.940 | + | 252.940i | −0.308840 | + | 0.308840i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 423.452 | − | 423.452i | 0.515775 | − | 0.515775i | −0.400515 | − | 0.916290i | \(-0.631169\pi\) |
0.916290 | + | 0.400515i | \(0.131169\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 543.405 | + | 543.405i | 0.660274 | + | 0.660274i | 0.955445 | − | 0.295171i | \(-0.0953765\pi\) |
−0.295171 | + | 0.955445i | \(0.595377\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 722.926 | + | 172.054i | 0.876274 | + | 0.208551i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −912.383 | −1.10324 | −0.551622 | − | 0.834094i | \(-0.685991\pi\) | ||||
−0.551622 | + | 0.834094i | \(0.685991\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 401.447 | − | 401.447i | 0.484254 | − | 0.484254i | −0.422233 | − | 0.906487i | \(-0.638754\pi\) |
0.906487 | + | 0.422233i | \(0.138754\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 641.985 | 0.772546 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1238.18 | + | 1238.18i | −1.48641 | + | 1.48641i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1312.48 | − | 371.552i | 1.57183 | − | 0.444973i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −258.019 | −0.308267 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −355.908 | −0.424205 | −0.212102 | − | 0.977247i | \(-0.568031\pi\) | ||||
−0.212102 | + | 0.977247i | \(0.568031\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 167.230i | 0.198847i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − | 791.912i | − | 0.939398i | ||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 3.94727 | + | 2.20547i | 0.00467133 | + | 0.00261003i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 140.713 | + | 140.713i | 0.166131 | + | 0.166131i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | − | 21.6962i | − | 0.0255550i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −123.653 | − | 123.653i | −0.145304 | − | 0.145304i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 184.144i | − | 0.215878i | −0.994158 | − | 0.107939i | \(-0.965575\pi\) | ||
0.994158 | − | 0.107939i | \(-0.0344252\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −58.4795 | + | 16.5551i | −0.0683971 | + | 0.0193627i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 503.631 | − | 503.631i | 0.587667 | − | 0.587667i | −0.349332 | − | 0.936999i | \(-0.613591\pi\) |
0.936999 | + | 0.349332i | \(0.113591\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −136.193 | − | 136.193i | −0.158548 | − | 0.158548i | 0.623375 | − | 0.781923i | \(-0.285761\pi\) |
−0.781923 | + | 0.623375i | \(0.785761\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −16.8899 | − | 16.8899i | −0.0196166 | − | 0.0196166i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 778.037 | − | 778.037i | 0.901550 | − | 0.901550i | −0.0940206 | − | 0.995570i | \(-0.529972\pi\) |
0.995570 | + | 0.0940206i | \(0.0299720\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.93512 | + | 4.99236i | 0.0103296 | + | 0.00577151i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 1885.54i | 2.17478i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 144.450 | + | 144.450i | 0.166225 | + | 0.166225i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 380.422i | − | 0.436765i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 145.084 | + | 145.084i | 0.166190 | + | 0.166190i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 935.328 | + | 859.498i | 1.06895 | + | 0.982283i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 450.954i | − | 0.514201i | −0.966385 | − | 0.257101i | \(-0.917233\pi\) | ||
0.966385 | − | 0.257101i | \(-0.0827672\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1337.18i | 1.52126i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 929.171 | 1.05468 | 0.527339 | − | 0.849655i | \(-0.323190\pi\) | ||||
0.527339 | + | 0.849655i | \(0.323190\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 244.738 | 0.277166 | 0.138583 | − | 0.990351i | \(-0.455745\pi\) | ||||
0.138583 | + | 0.990351i | \(0.455745\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −193.866 | − | 684.814i | −0.219057 | − | 0.773801i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 987.070 | − | 987.070i | 1.11282 | − | 1.11282i | 0.120050 | − | 0.992768i | \(-0.461694\pi\) |
0.992768 | − | 0.120050i | \(-0.0383056\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1527.02 | −1.71768 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −412.440 | + | 412.440i | −0.462896 | + | 0.462896i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 176.829 | 0.198017 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 688.585 | − | 194.933i | 0.769369 | − | 0.217803i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 124.034 | + | 124.034i | 0.138276 | + | 0.138276i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −161.249 | + | 161.249i | −0.179365 | + | 0.179365i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −470.974 | + | 470.974i | −0.522723 | + | 0.522723i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −1041.89 | − | 1041.89i | −1.15381 | − | 1.15381i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1047.86 | + | 296.641i | −1.15785 | + | 0.327780i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −160.752 | −0.177235 | −0.0886177 | − | 0.996066i | \(-0.528245\pi\) | ||||
−0.0886177 | + | 0.996066i | \(0.528245\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −184.471 | + | 184.471i | −0.202938 | + | 0.202938i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −36.8062 | −0.0404020 | −0.0202010 | − | 0.999796i | \(-0.506431\pi\) | ||||
−0.0202010 | + | 0.999796i | \(0.506431\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 615.316 | − | 615.316i | 0.673950 | − | 0.673950i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 122.596 | + | 433.059i | 0.133985 | + | 0.473289i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −859.116 | −0.936877 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −502.632 | −0.546934 | −0.273467 | − | 0.961881i | \(-0.588170\pi\) | ||||
−0.273467 | + | 0.961881i | \(0.588170\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | − | 807.386i | − | 0.876640i | ||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 450.781i | 0.488386i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 424.634 | + | 689.887i | 0.459064 | + | 0.745824i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 360.789 | + | 360.789i | 0.389200 | + | 0.389200i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 1098.03i | − | 1.18195i | −0.806690 | − | 0.590975i | \(-0.798743\pi\) | ||
0.806690 | − | 0.590975i | \(-0.201257\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 171.806 | + | 171.806i | 0.184540 | + | 0.184540i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − | 25.1951i | − | 0.0270044i | ||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1669.89 | + | 933.022i | 1.78597 | + | 0.997884i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −68.4855 | + | 68.4855i | −0.0730902 | + | 0.0730902i | −0.742707 | − | 0.669617i | \(-0.766458\pi\) |
0.669617 | + | 0.742707i | \(0.266458\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 33.6817 | + | 33.6817i | 0.0358698 | + | 0.0358698i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −517.439 | − | 517.439i | −0.549882 | − | 0.549882i | 0.376525 | − | 0.926407i | \(-0.377119\pi\) |
−0.926407 | + | 0.376525i | \(0.877119\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.57779 | − | 3.57779i | 0.00379405 | − | 0.00379405i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1435.85 | + | 406.478i | −1.51942 | + | 0.430136i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 1065.70i | − | 1.12534i | −0.826680 | − | 0.562672i | \(-0.809773\pi\) | ||
0.826680 | − | 0.562672i | \(-0.190227\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 988.954 | + | 988.954i | 1.04210 | + | 1.04210i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 457.261i | − | 0.480821i | ||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −620.695 | − | 620.695i | −0.651306 | − | 0.651306i | 0.302001 | − | 0.953307i | \(-0.402345\pi\) |
−0.953307 | + | 0.302001i | \(0.902345\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 197.751 | + | 110.490i | 0.207069 | + | 0.115696i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 771.567i | 0.806236i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | − | 1817.13i | − | 1.89482i | ||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −883.818 | −0.919686 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −121.937 | −0.126622 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1198.22 | − | 339.207i | 1.24168 | − | 0.351510i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1139.87 | + | 1139.87i | −1.17877 | + | 1.17877i | −0.198709 | + | 0.980059i | \(0.563675\pi\) |
−0.980059 | + | 0.198709i | \(0.936325\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 362.164 | 0.373751 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −470.641 | + | 470.641i | −0.484697 | + | 0.484697i | −0.906628 | − | 0.421931i | \(-0.861352\pi\) |
0.421931 | + | 0.906628i | \(0.361352\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 594.771 | 0.611275 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −425.940 | − | 692.009i | −0.436862 | − | 0.709752i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.84469 | − | 2.84469i | −0.00291165 | − | 0.00291165i | 0.705649 | − | 0.708561i | \(-0.250655\pi\) |
−0.708561 | + | 0.705649i | \(0.750655\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 812.589 | − | 812.589i | 0.830019 | − | 0.830019i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 86.2195 | − | 86.2195i | 0.0878894 | − | 0.0878894i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −177.652 | − | 177.652i | −0.180724 | − | 0.180724i | 0.610947 | − | 0.791671i | \(-0.290789\pi\) |
−0.791671 | + | 0.610947i | \(0.790789\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1345.14 | + | 751.575i | 1.36562 | + | 0.763020i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1006.20 | 1.01946 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 220.704 | − | 220.704i | 0.223158 | − | 0.223158i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1697.53 | −1.71295 | −0.856474 | − | 0.516190i | \(-0.827350\pi\) | ||||
−0.856474 | + | 0.516190i | \(0.827350\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 535.405 | − | 535.405i | 0.539179 | − | 0.539179i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −833.309 | − | 465.598i | −0.837497 | − | 0.467938i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1315.01 | −1.31897 | −0.659483 | − | 0.751720i | \(-0.729225\pi\) | ||||
−0.659483 | + | 0.751720i | \(0.729225\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −951.683 | −0.952636 |
(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 | 320.3.t.a.17.17 | 44 | ||
4.3 | odd | 2 | 80.3.t.a.77.11 | yes | 44 | ||
5.3 | odd | 4 | 320.3.i.a.273.17 | 44 | |||
8.3 | odd | 2 | 640.3.t.b.417.17 | 44 | |||
8.5 | even | 2 | 640.3.t.a.417.6 | 44 | |||
16.3 | odd | 4 | 640.3.i.b.97.6 | 44 | |||
16.5 | even | 4 | 320.3.i.a.177.6 | 44 | |||
16.11 | odd | 4 | 80.3.i.a.37.22 | yes | 44 | ||
16.13 | even | 4 | 640.3.i.a.97.17 | 44 | |||
20.3 | even | 4 | 80.3.i.a.13.22 | ✓ | 44 | ||
20.7 | even | 4 | 400.3.i.b.93.1 | 44 | |||
20.19 | odd | 2 | 400.3.t.b.157.12 | 44 | |||
40.3 | even | 4 | 640.3.i.b.33.17 | 44 | |||
40.13 | odd | 4 | 640.3.i.a.33.6 | 44 | |||
80.3 | even | 4 | 640.3.t.b.353.17 | 44 | |||
80.13 | odd | 4 | 640.3.t.a.353.6 | 44 | |||
80.27 | even | 4 | 400.3.t.b.293.12 | 44 | |||
80.43 | even | 4 | 80.3.t.a.53.11 | yes | 44 | ||
80.53 | odd | 4 | inner | 320.3.t.a.113.17 | 44 | ||
80.59 | odd | 4 | 400.3.i.b.357.1 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
80.3.i.a.13.22 | ✓ | 44 | 20.3 | even | 4 | ||
80.3.i.a.37.22 | yes | 44 | 16.11 | odd | 4 | ||
80.3.t.a.53.11 | yes | 44 | 80.43 | even | 4 | ||
80.3.t.a.77.11 | yes | 44 | 4.3 | odd | 2 | ||
320.3.i.a.177.6 | 44 | 16.5 | even | 4 | |||
320.3.i.a.273.17 | 44 | 5.3 | odd | 4 | |||
320.3.t.a.17.17 | 44 | 1.1 | even | 1 | trivial | ||
320.3.t.a.113.17 | 44 | 80.53 | odd | 4 | inner | ||
400.3.i.b.93.1 | 44 | 20.7 | even | 4 | |||
400.3.i.b.357.1 | 44 | 80.59 | odd | 4 | |||
400.3.t.b.157.12 | 44 | 20.19 | odd | 2 | |||
400.3.t.b.293.12 | 44 | 80.27 | even | 4 | |||
640.3.i.a.33.6 | 44 | 40.13 | odd | 4 | |||
640.3.i.a.97.17 | 44 | 16.13 | even | 4 | |||
640.3.i.b.33.17 | 44 | 40.3 | even | 4 | |||
640.3.i.b.97.6 | 44 | 16.3 | odd | 4 | |||
640.3.t.a.353.6 | 44 | 80.13 | odd | 4 | |||
640.3.t.a.417.6 | 44 | 8.5 | even | 2 | |||
640.3.t.b.353.17 | 44 | 80.3 | even | 4 | |||
640.3.t.b.417.17 | 44 | 8.3 | odd | 2 |