Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,8,Mod(1,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.a (trivial) |
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: | yes |
Analytic conductor: | \(70.2866307339\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 45) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 225.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 5.00000 | 0.441942 | 0.220971 | − | 0.975280i | \(-0.429077\pi\) | ||||
0.220971 | + | 0.975280i | \(0.429077\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −103.000 | −0.804688 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −930.000 | −1.02480 | −0.512401 | − | 0.858746i | \(-0.671244\pi\) | ||||
−0.512401 | + | 0.858746i | \(0.671244\pi\) | |||||||
\(8\) | −1155.00 | −0.797567 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −8450.00 | −1.91418 | −0.957089 | − | 0.289794i | \(-0.906413\pi\) | ||||
−0.957089 | + | 0.289794i | \(0.906413\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −6220.00 | −0.785215 | −0.392608 | − | 0.919706i | \(-0.628427\pi\) | ||||
−0.392608 | + | 0.919706i | \(0.628427\pi\) | |||||||
\(14\) | −4650.00 | −0.452903 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 7409.00 | 0.452209 | ||||||||
\(17\) | 9590.00 | 0.473421 | 0.236710 | − | 0.971580i | \(-0.423931\pi\) | ||||
0.236710 | + | 0.971580i | \(0.423931\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −45884.0 | −1.53470 | −0.767350 | − | 0.641228i | \(-0.778425\pi\) | ||||
−0.767350 | + | 0.641228i | \(0.778425\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −42250.0 | −0.845955 | ||||||||
\(23\) | 102120. | 1.75010 | 0.875051 | − | 0.484031i | \(-0.160828\pi\) | ||||
0.875051 | + | 0.484031i | \(0.160828\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −31100.0 | −0.347019 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 95790.0 | 0.824645 | ||||||||
\(29\) | −87550.0 | −0.666597 | −0.333298 | − | 0.942821i | \(-0.608162\pi\) | ||||
−0.333298 | + | 0.942821i | \(0.608162\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −76212.0 | −0.459470 | −0.229735 | − | 0.973253i | \(-0.573786\pi\) | ||||
−0.229735 | + | 0.973253i | \(0.573786\pi\) | |||||||
\(32\) | 184885. | 0.997417 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 47950.0 | 0.209224 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −264440. | −0.858264 | −0.429132 | − | 0.903242i | \(-0.641181\pi\) | ||||
−0.429132 | + | 0.903242i | \(0.641181\pi\) | |||||||
\(38\) | −229420. | −0.678248 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −103600. | −0.234756 | −0.117378 | − | 0.993087i | \(-0.537449\pi\) | ||||
−0.117378 | + | 0.993087i | \(0.537449\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 324680. | 0.622753 | 0.311377 | − | 0.950287i | \(-0.399210\pi\) | ||||
0.311377 | + | 0.950287i | \(0.399210\pi\) | |||||||
\(44\) | 870350. | 1.54032 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 510600. | 0.773443 | ||||||||
\(47\) | −855880. | −1.20246 | −0.601230 | − | 0.799076i | \(-0.705322\pi\) | ||||
−0.601230 | + | 0.799076i | \(0.705322\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 41357.0 | 0.0502184 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 640660. | 0.631853 | ||||||||
\(53\) | 958190. | 0.884069 | 0.442034 | − | 0.896998i | \(-0.354257\pi\) | ||||
0.442034 | + | 0.896998i | \(0.354257\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.07415e6 | 0.817348 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −437750. | −0.294597 | ||||||||
\(59\) | 1.23955e6 | 0.785746 | 0.392873 | − | 0.919593i | \(-0.371481\pi\) | ||||
0.392873 | + | 0.919593i | \(0.371481\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 628522. | 0.354541 | 0.177270 | − | 0.984162i | \(-0.443273\pi\) | ||||
0.177270 | + | 0.984162i | \(0.443273\pi\) | |||||||
\(62\) | −381060. | −0.203059 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −23927.0 | −0.0114093 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −310380. | −0.126076 | −0.0630379 | − | 0.998011i | \(-0.520079\pi\) | ||||
−0.0630379 | + | 0.998011i | \(0.520079\pi\) | |||||||
\(68\) | −987770. | −0.380956 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.93430e6 | −1.30456 | −0.652279 | − | 0.757979i | \(-0.726187\pi\) | ||||
−0.652279 | + | 0.757979i | \(0.726187\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.55609e6 | 1.37076 | 0.685381 | − | 0.728184i | \(-0.259636\pi\) | ||||
0.685381 | + | 0.728184i | \(0.259636\pi\) | |||||||
\(74\) | −1.32220e6 | −0.379303 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 4.72605e6 | 1.23495 | ||||||||
\(77\) | 7.85850e6 | 1.96165 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.37164e6 | 1.22578 | 0.612890 | − | 0.790168i | \(-0.290007\pi\) | ||||
0.612890 | + | 0.790168i | \(0.290007\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −518000. | −0.103748 | ||||||||
\(83\) | 6.71106e6 | 1.28830 | 0.644151 | − | 0.764898i | \(-0.277211\pi\) | ||||
0.644151 | + | 0.764898i | \(0.277211\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1.62340e6 | 0.275221 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 9.75975e6 | 1.52668 | ||||||||
\(89\) | −3.34650e6 | −0.503183 | −0.251591 | − | 0.967834i | \(-0.580954\pi\) | ||||
−0.251591 | + | 0.967834i | \(0.580954\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 5.78460e6 | 0.804690 | ||||||||
\(92\) | −1.05184e7 | −1.40829 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −4.27940e6 | −0.531417 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.58297e7 | −1.76105 | −0.880527 | − | 0.473997i | \(-0.842811\pi\) | ||||
−0.880527 | + | 0.473997i | \(0.842811\pi\) | |||||||
\(98\) | 206785. | 0.0221936 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.51995e6 | −0.146793 | −0.0733964 | − | 0.997303i | \(-0.523384\pi\) | ||||
−0.0733964 | + | 0.997303i | \(0.523384\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.98367e7 | 1.78870 | 0.894352 | − | 0.447364i | \(-0.147637\pi\) | ||||
0.894352 | + | 0.447364i | \(0.147637\pi\) | |||||||
\(104\) | 7.18410e6 | 0.626261 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.79095e6 | 0.390707 | ||||||||
\(107\) | 413460. | 0.0326280 | 0.0163140 | − | 0.999867i | \(-0.494807\pi\) | ||||
0.0163140 | + | 0.999867i | \(0.494807\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.24127e7 | −0.918067 | −0.459034 | − | 0.888419i | \(-0.651804\pi\) | ||||
−0.459034 | + | 0.888419i | \(0.651804\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −6.89037e6 | −0.463425 | ||||||||
\(113\) | −2.42499e7 | −1.58101 | −0.790507 | − | 0.612453i | \(-0.790183\pi\) | ||||
−0.790507 | + | 0.612453i | \(0.790183\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 9.01765e6 | 0.536402 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 6.19775e6 | 0.347254 | ||||||||
\(119\) | −8.91870e6 | −0.485162 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.19153e7 | 2.66408 | ||||||||
\(122\) | 3.14261e6 | 0.156686 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 7.84984e6 | 0.369730 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −259570. | −0.0112445 | −0.00562227 | − | 0.999984i | \(-0.501790\pi\) | ||||
−0.00562227 | + | 0.999984i | \(0.501790\pi\) | |||||||
\(128\) | −2.37849e7 | −1.00246 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.41784e7 | 0.551035 | 0.275518 | − | 0.961296i | \(-0.411151\pi\) | ||||
0.275518 | + | 0.961296i | \(0.411151\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 4.26721e7 | 1.57276 | ||||||||
\(134\) | −1.55190e6 | −0.0557182 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.10764e7 | −0.377585 | ||||||||
\(137\) | −2.49710e7 | −0.829685 | −0.414842 | − | 0.909893i | \(-0.636163\pi\) | ||||
−0.414842 | + | 0.909893i | \(0.636163\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 3.31920e7 | 1.04829 | 0.524145 | − | 0.851629i | \(-0.324385\pi\) | ||||
0.524145 | + | 0.851629i | \(0.324385\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.96715e7 | −0.576538 | ||||||||
\(143\) | 5.25590e7 | 1.50304 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 2.27804e7 | 0.605797 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.72373e7 | 0.690635 | ||||||||
\(149\) | −3.85424e7 | −0.954525 | −0.477263 | − | 0.878761i | \(-0.658371\pi\) | ||||
−0.477263 | + | 0.878761i | \(0.658371\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2.34988e7 | 0.555427 | 0.277714 | − | 0.960664i | \(-0.410423\pi\) | ||||
0.277714 | + | 0.960664i | \(0.410423\pi\) | |||||||
\(152\) | 5.29960e7 | 1.22403 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.92925e7 | 0.866936 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 5.97169e7 | 1.23154 | 0.615770 | − | 0.787926i | \(-0.288845\pi\) | ||||
0.615770 | + | 0.787926i | \(0.288845\pi\) | |||||||
\(158\) | 2.68582e7 | 0.541723 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −9.49716e7 | −1.79351 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.81491e7 | 0.509106 | 0.254553 | − | 0.967059i | \(-0.418072\pi\) | ||||
0.254553 | + | 0.967059i | \(0.418072\pi\) | |||||||
\(164\) | 1.06708e7 | 0.188905 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.35553e7 | 0.569355 | ||||||||
\(167\) | −2.22233e7 | −0.369233 | −0.184617 | − | 0.982811i | \(-0.559104\pi\) | ||||
−0.184617 | + | 0.982811i | \(0.559104\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −2.40601e7 | −0.383437 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −3.34420e7 | −0.501122 | ||||||||
\(173\) | −1.00047e8 | −1.46908 | −0.734539 | − | 0.678567i | \(-0.762601\pi\) | ||||
−0.734539 | + | 0.678567i | \(0.762601\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −6.26060e7 | −0.865609 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.67325e7 | −0.222377 | ||||||||
\(179\) | 4.19711e7 | 0.546972 | 0.273486 | − | 0.961876i | \(-0.411823\pi\) | ||||
0.273486 | + | 0.961876i | \(0.411823\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.22283e7 | −0.153281 | −0.0766407 | − | 0.997059i | \(-0.524419\pi\) | ||||
−0.0766407 | + | 0.997059i | \(0.524419\pi\) | |||||||
\(182\) | 2.89230e7 | 0.355626 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.17949e8 | −1.39582 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −8.10355e7 | −0.906212 | ||||||||
\(188\) | 8.81556e7 | 0.967604 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.56531e8 | 1.62549 | 0.812746 | − | 0.582618i | \(-0.197972\pi\) | ||||
0.812746 | + | 0.582618i | \(0.197972\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.08056e8 | −1.08193 | −0.540965 | − | 0.841045i | \(-0.681941\pi\) | ||||
−0.540965 | + | 0.841045i | \(0.681941\pi\) | |||||||
\(194\) | −7.91486e7 | −0.778283 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.25977e6 | −0.0404101 | ||||||||
\(197\) | −1.95971e7 | −0.182625 | −0.0913125 | − | 0.995822i | \(-0.529106\pi\) | ||||
−0.0913125 | + | 0.995822i | \(0.529106\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.22581e7 | 0.110265 | 0.0551323 | − | 0.998479i | \(-0.482442\pi\) | ||||
0.0551323 | + | 0.998479i | \(0.482442\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −7.59975e6 | −0.0648738 | ||||||||
\(203\) | 8.14215e7 | 0.683129 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 9.91834e7 | 0.790503 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −4.60840e7 | −0.355082 | ||||||||
\(209\) | 3.87720e8 | 2.93769 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.89778e8 | −1.39077 | −0.695387 | − | 0.718636i | \(-0.744767\pi\) | ||||
−0.695387 | + | 0.718636i | \(0.744767\pi\) | |||||||
\(212\) | −9.86936e7 | −0.711399 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.06730e6 | 0.0144197 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 7.08772e7 | 0.470866 | ||||||||
\(218\) | −6.20636e7 | −0.405732 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −5.96498e7 | −0.371737 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.09802e7 | −0.0663044 | −0.0331522 | − | 0.999450i | \(-0.510555\pi\) | ||||
−0.0331522 | + | 0.999450i | \(0.510555\pi\) | |||||||
\(224\) | −1.71943e8 | −1.02215 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.21250e8 | −0.698716 | ||||||||
\(227\) | −5.04802e7 | −0.286438 | −0.143219 | − | 0.989691i | \(-0.545745\pi\) | ||||
−0.143219 | + | 0.989691i | \(0.545745\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 6.18516e7 | 0.340351 | 0.170175 | − | 0.985414i | \(-0.445567\pi\) | ||||
0.170175 | + | 0.985414i | \(0.445567\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.01120e8 | 0.531655 | ||||||||
\(233\) | −1.37871e8 | −0.714050 | −0.357025 | − | 0.934095i | \(-0.616209\pi\) | ||||
−0.357025 | + | 0.934095i | \(0.616209\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −1.27674e8 | −0.632280 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −4.45935e7 | −0.214414 | ||||||||
\(239\) | −6.27719e7 | −0.297422 | −0.148711 | − | 0.988881i | \(-0.547512\pi\) | ||||
−0.148711 | + | 0.988881i | \(0.547512\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.37149e8 | −0.631153 | −0.315576 | − | 0.948900i | \(-0.602198\pi\) | ||||
−0.315576 | + | 0.948900i | \(0.602198\pi\) | |||||||
\(242\) | 2.59577e8 | 1.17737 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −6.47378e7 | −0.285294 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.85398e8 | 1.20507 | ||||||||
\(248\) | 8.80249e7 | 0.366458 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −4.05726e8 | −1.61948 | −0.809739 | − | 0.586790i | \(-0.800391\pi\) | ||||
−0.809739 | + | 0.586790i | \(0.800391\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.62914e8 | −3.35001 | ||||||||
\(254\) | −1.29785e6 | −0.00496943 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −1.15862e8 | −0.431619 | ||||||||
\(257\) | −9.00525e7 | −0.330925 | −0.165463 | − | 0.986216i | \(-0.552912\pi\) | ||||
−0.165463 | + | 0.986216i | \(0.552912\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.45929e8 | 0.879551 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 7.08922e7 | 0.243525 | ||||||||
\(263\) | 2.06256e8 | 0.699135 | 0.349568 | − | 0.936911i | \(-0.386328\pi\) | ||||
0.349568 | + | 0.936911i | \(0.386328\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 2.13361e8 | 0.695070 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.19691e7 | 0.101452 | ||||||||
\(269\) | −4.91222e8 | −1.53867 | −0.769334 | − | 0.638847i | \(-0.779412\pi\) | ||||
−0.769334 | + | 0.638847i | \(0.779412\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −3.69529e8 | −1.12786 | −0.563931 | − | 0.825822i | \(-0.690712\pi\) | ||||
−0.563931 | + | 0.825822i | \(0.690712\pi\) | |||||||
\(272\) | 7.10523e7 | 0.214085 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.24855e8 | −0.366672 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.31059e8 | 0.653196 | 0.326598 | − | 0.945163i | \(-0.394098\pi\) | ||||
0.326598 | + | 0.945163i | \(0.394098\pi\) | |||||||
\(278\) | 1.65960e8 | 0.463283 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.73019e8 | 1.54063 | 0.770313 | − | 0.637666i | \(-0.220100\pi\) | ||||
0.770313 | + | 0.637666i | \(0.220100\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −3.64618e8 | −0.956281 | −0.478140 | − | 0.878283i | \(-0.658689\pi\) | ||||
−0.478140 | + | 0.878283i | \(0.658689\pi\) | |||||||
\(284\) | 4.05233e8 | 1.04976 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.62795e8 | 0.664257 | ||||||||
\(287\) | 9.63480e7 | 0.240578 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3.18371e8 | −0.775873 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.69277e8 | −1.10304 | ||||||||
\(293\) | −2.12858e8 | −0.494372 | −0.247186 | − | 0.968968i | \(-0.579506\pi\) | ||||
−0.247186 | + | 0.968968i | \(0.579506\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 3.05428e8 | 0.684523 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1.92712e8 | −0.421845 | ||||||||
\(299\) | −6.35186e8 | −1.37421 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.01952e8 | −0.638198 | ||||||||
\(302\) | 1.17494e8 | 0.245467 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.39955e8 | −0.694006 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.55586e8 | 1.29314 | 0.646570 | − | 0.762855i | \(-0.276203\pi\) | ||||
0.646570 | + | 0.762855i | \(0.276203\pi\) | |||||||
\(308\) | −8.09426e8 | −1.57852 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −9.17157e8 | −1.72895 | −0.864474 | − | 0.502677i | \(-0.832349\pi\) | ||||
−0.864474 | + | 0.502677i | \(0.832349\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.52969e8 | 1.20361 | 0.601807 | − | 0.798641i | \(-0.294447\pi\) | ||||
0.601807 | + | 0.798641i | \(0.294447\pi\) | |||||||
\(314\) | 2.98584e8 | 0.544269 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −5.53279e8 | −0.986370 | ||||||||
\(317\) | −7.34479e8 | −1.29501 | −0.647503 | − | 0.762063i | \(-0.724187\pi\) | ||||
−0.647503 | + | 0.762063i | \(0.724187\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 7.39797e8 | 1.27598 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −4.74858e8 | −0.792626 | ||||||||
\(323\) | −4.40028e8 | −0.726559 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.40746e8 | 0.224995 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.19658e8 | 0.187233 | ||||||||
\(329\) | 7.95968e8 | 1.23228 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 8.79164e8 | 1.33251 | 0.666257 | − | 0.745722i | \(-0.267895\pi\) | ||||
0.666257 | + | 0.745722i | \(0.267895\pi\) | |||||||
\(332\) | −6.91239e8 | −1.03668 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −1.11116e8 | −0.163179 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.65182e8 | −0.519762 | −0.259881 | − | 0.965641i | \(-0.583683\pi\) | ||||
−0.259881 | + | 0.965641i | \(0.583683\pi\) | |||||||
\(338\) | −1.20301e8 | −0.169457 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 6.43991e8 | 0.879508 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.27433e8 | 0.973338 | ||||||||
\(344\) | −3.75005e8 | −0.496687 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −5.00237e8 | −0.649247 | ||||||||
\(347\) | 1.03136e9 | 1.32513 | 0.662563 | − | 0.749006i | \(-0.269469\pi\) | ||||
0.662563 | + | 0.749006i | \(0.269469\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.24452e8 | −0.156716 | −0.0783579 | − | 0.996925i | \(-0.524968\pi\) | ||||
−0.0783579 | + | 0.996925i | \(0.524968\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.56228e9 | −1.90923 | ||||||||
\(353\) | 1.32311e9 | 1.60097 | 0.800487 | − | 0.599350i | \(-0.204574\pi\) | ||||
0.800487 | + | 0.599350i | \(0.204574\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 3.44690e8 | 0.404905 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.09856e8 | 0.241730 | ||||||||
\(359\) | −1.18844e8 | −0.135564 | −0.0677822 | − | 0.997700i | \(-0.521592\pi\) | ||||
−0.0677822 | + | 0.997700i | \(0.521592\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 1.21147e9 | 1.35531 | ||||||||
\(362\) | −6.11413e7 | −0.0677415 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.95814e8 | −0.647524 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.10304e9 | 1.16482 | 0.582412 | − | 0.812893i | \(-0.302109\pi\) | ||||
0.582412 | + | 0.812893i | \(0.302109\pi\) | |||||||
\(368\) | 7.56607e8 | 0.791413 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −8.91117e8 | −0.905995 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −4.53965e8 | −0.452941 | −0.226470 | − | 0.974018i | \(-0.572719\pi\) | ||||
−0.226470 | + | 0.974018i | \(0.572719\pi\) | |||||||
\(374\) | −4.05178e8 | −0.400493 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 9.88541e8 | 0.959042 | ||||||||
\(377\) | 5.44561e8 | 0.523422 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.28520e8 | 0.498683 | 0.249341 | − | 0.968416i | \(-0.419786\pi\) | ||||
0.249341 | + | 0.968416i | \(0.419786\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 7.82658e8 | 0.718373 | ||||||||
\(383\) | 3.03673e8 | 0.276192 | 0.138096 | − | 0.990419i | \(-0.455902\pi\) | ||||
0.138096 | + | 0.990419i | \(0.455902\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −5.40281e8 | −0.478150 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 1.63046e9 | 1.41710 | ||||||||
\(389\) | 2.38311e8 | 0.205267 | 0.102634 | − | 0.994719i | \(-0.467273\pi\) | ||||
0.102634 | + | 0.994719i | \(0.467273\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.79331e8 | 0.828535 | ||||||||
\(392\) | −4.77673e7 | −0.0400525 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −9.79856e7 | −0.0807096 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 7.12127e8 | 0.571203 | 0.285601 | − | 0.958348i | \(-0.407807\pi\) | ||||
0.285601 | + | 0.958348i | \(0.407807\pi\) | |||||||
\(398\) | 6.12903e7 | 0.0487305 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.42308e8 | −0.110211 | −0.0551053 | − | 0.998481i | \(-0.517549\pi\) | ||||
−0.0551053 | + | 0.998481i | \(0.517549\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.74039e8 | 0.360783 | ||||||||
\(404\) | 1.56555e8 | 0.118122 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.07108e8 | 0.301903 | ||||||||
\(407\) | 2.23452e9 | 1.64287 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.81943e9 | 1.31493 | 0.657466 | − | 0.753484i | \(-0.271628\pi\) | ||||
0.657466 | + | 0.753484i | \(0.271628\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.04318e9 | −1.43935 | ||||||||
\(413\) | −1.15278e9 | −0.805233 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.14998e9 | −0.783187 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.93860e9 | 1.29829 | ||||||||
\(419\) | 2.51122e8 | 0.166777 | 0.0833883 | − | 0.996517i | \(-0.473426\pi\) | ||||
0.0833883 | + | 0.996517i | \(0.473426\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.49600e7 | 0.0424286 | 0.0212143 | − | 0.999775i | \(-0.493247\pi\) | ||||
0.0212143 | + | 0.999775i | \(0.493247\pi\) | |||||||
\(422\) | −9.48888e8 | −0.614641 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.10671e9 | −0.705104 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −5.84525e8 | −0.363334 | ||||||||
\(428\) | −4.25864e7 | −0.0262553 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.64855e8 | 0.460160 | 0.230080 | − | 0.973172i | \(-0.426101\pi\) | ||||
0.230080 | + | 0.973172i | \(0.426101\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.64928e9 | 0.976308 | 0.488154 | − | 0.872758i | \(-0.337670\pi\) | ||||
0.488154 | + | 0.872758i | \(0.337670\pi\) | |||||||
\(434\) | 3.54386e8 | 0.208095 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.27851e9 | 0.738757 | ||||||||
\(437\) | −4.68567e9 | −2.68588 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.27102e9 | 1.28113 | 0.640567 | − | 0.767902i | \(-0.278699\pi\) | ||||
0.640567 | + | 0.767902i | \(0.278699\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.98249e8 | −0.164286 | ||||||||
\(443\) | 1.47221e9 | 0.804559 | 0.402279 | − | 0.915517i | \(-0.368218\pi\) | ||||
0.402279 | + | 0.915517i | \(0.368218\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −5.49008e7 | −0.0293027 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 2.22521e7 | 0.0116923 | ||||||||
\(449\) | 3.41486e9 | 1.78037 | 0.890185 | − | 0.455600i | \(-0.150575\pi\) | ||||
0.890185 | + | 0.455600i | \(0.150575\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 8.75420e8 | 0.449364 | ||||||||
\(452\) | 2.49774e9 | 1.27222 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.52401e8 | −0.126589 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.10215e9 | 0.540174 | 0.270087 | − | 0.962836i | \(-0.412948\pi\) | ||||
0.270087 | + | 0.962836i | \(0.412948\pi\) | |||||||
\(458\) | 3.09258e8 | 0.150415 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 3.76947e9 | 1.79195 | 0.895976 | − | 0.444102i | \(-0.146477\pi\) | ||||
0.895976 | + | 0.444102i | \(0.146477\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.10706e9 | 0.518366 | 0.259183 | − | 0.965828i | \(-0.416547\pi\) | ||||
0.259183 | + | 0.965828i | \(0.416547\pi\) | |||||||
\(464\) | −6.48658e8 | −0.301441 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −6.89357e8 | −0.315568 | ||||||||
\(467\) | −1.50674e9 | −0.684586 | −0.342293 | − | 0.939593i | \(-0.611204\pi\) | ||||
−0.342293 | + | 0.939593i | \(0.611204\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.88653e8 | 0.129203 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.43168e9 | −0.626685 | ||||||||
\(473\) | −2.74355e9 | −1.19206 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 9.18626e8 | 0.390404 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.13860e8 | −0.131443 | ||||||||
\(479\) | −3.55245e9 | −1.47691 | −0.738454 | − | 0.674304i | \(-0.764444\pi\) | ||||
−0.738454 | + | 0.674304i | \(0.764444\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 1.64482e9 | 0.673922 | ||||||||
\(482\) | −6.85747e8 | −0.278933 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −5.34728e9 | −2.14375 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.62227e9 | −1.02879 | −0.514395 | − | 0.857553i | \(-0.671983\pi\) | ||||
−0.514395 | + | 0.857553i | \(0.671983\pi\) | |||||||
\(488\) | −7.25943e8 | −0.282770 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −1.76846e9 | −0.674232 | −0.337116 | − | 0.941463i | \(-0.609451\pi\) | ||||
−0.337116 | + | 0.941463i | \(0.609451\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −8.39604e8 | −0.315581 | ||||||||
\(494\) | 1.42699e9 | 0.532571 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −5.64655e8 | −0.207777 | ||||||||
\(497\) | 3.65890e9 | 1.33691 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.46316e9 | −0.887442 | −0.443721 | − | 0.896165i | \(-0.646342\pi\) | ||||
−0.443721 | + | 0.896165i | \(0.646342\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.02863e9 | −0.715715 | ||||||||
\(503\) | −1.50060e9 | −0.525748 | −0.262874 | − | 0.964830i | \(-0.584670\pi\) | ||||
−0.262874 | + | 0.964830i | \(0.584670\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −4.31457e9 | −1.48051 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.67357e7 | 0.00904834 | ||||||||
\(509\) | −4.31485e9 | −1.45029 | −0.725143 | − | 0.688598i | \(-0.758226\pi\) | ||||
−0.725143 | + | 0.688598i | \(0.758226\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.23716e9 | −1.40476 | ||||||||
\(512\) | 2.46516e9 | 0.811709 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.50262e8 | −0.146250 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 7.23219e9 | 2.30172 | ||||||||
\(518\) | 1.22965e9 | 0.388710 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 9.53559e8 | 0.295404 | 0.147702 | − | 0.989032i | \(-0.452812\pi\) | ||||
0.147702 | + | 0.989032i | \(0.452812\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −4.25294e9 | −1.29997 | −0.649986 | − | 0.759946i | \(-0.725225\pi\) | ||||
−0.649986 | + | 0.759946i | \(0.725225\pi\) | |||||||
\(524\) | −1.46038e9 | −0.443411 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.03128e9 | 0.308977 | ||||||||
\(527\) | −7.30873e8 | −0.217523 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.02367e9 | 2.06286 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4.39523e9 | −1.26558 | ||||||||
\(533\) | 6.44392e8 | 0.184334 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.58489e8 | 0.100554 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.45611e9 | −0.680002 | ||||||||
\(539\) | −3.49467e8 | −0.0961269 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.25815e9 | −0.613144 | −0.306572 | − | 0.951848i | \(-0.599182\pi\) | ||||
−0.306572 | + | 0.951848i | \(0.599182\pi\) | |||||||
\(542\) | −1.84765e9 | −0.498450 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.77305e9 | 0.472198 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 6.43075e9 | 1.67999 | 0.839994 | − | 0.542595i | \(-0.182558\pi\) | ||||
0.839994 | + | 0.542595i | \(0.182558\pi\) | |||||||
\(548\) | 2.57201e9 | 0.667637 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.01714e9 | 1.02303 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −4.99563e9 | −1.25618 | ||||||||
\(554\) | 1.15529e9 | 0.288675 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −3.41878e9 | −0.843546 | ||||||||
\(557\) | 7.37598e8 | 0.180853 | 0.0904266 | − | 0.995903i | \(-0.471177\pi\) | ||||
0.0904266 | + | 0.995903i | \(0.471177\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −2.01951e9 | −0.488995 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 2.86510e9 | 0.680867 | ||||||||
\(563\) | 3.56268e9 | 0.841390 | 0.420695 | − | 0.907202i | \(-0.361786\pi\) | ||||
0.420695 | + | 0.907202i | \(0.361786\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −1.82309e9 | −0.422620 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 4.54412e9 | 1.04047 | ||||||||
\(569\) | 2.20501e9 | 0.501785 | 0.250892 | − | 0.968015i | \(-0.419276\pi\) | ||||
0.250892 | + | 0.968015i | \(0.419276\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.41646e8 | −0.121756 | −0.0608778 | − | 0.998145i | \(-0.519390\pi\) | ||||
−0.0608778 | + | 0.998145i | \(0.519390\pi\) | |||||||
\(572\) | −5.41358e9 | −1.20948 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 4.81740e8 | 0.106321 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 1.71040e9 | 0.370665 | 0.185333 | − | 0.982676i | \(-0.440664\pi\) | ||||
0.185333 | + | 0.982676i | \(0.440664\pi\) | |||||||
\(578\) | −1.59185e9 | −0.342891 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −6.24129e9 | −1.32025 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.09671e9 | −1.69227 | ||||||||
\(584\) | −5.26228e9 | −1.09327 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.06429e9 | −0.218483 | ||||||||
\(587\) | 1.60774e9 | 0.328083 | 0.164041 | − | 0.986453i | \(-0.447547\pi\) | ||||
0.164041 | + | 0.986453i | \(0.447547\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 3.49691e9 | 0.705149 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −1.95924e9 | −0.388115 | ||||||||
\(593\) | −6.40212e9 | −1.26076 | −0.630380 | − | 0.776286i | \(-0.717101\pi\) | ||||
−0.630380 | + | 0.776286i | \(0.717101\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 3.96987e9 | 0.768094 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.17593e9 | −0.607319 | ||||||||
\(599\) | 7.65106e9 | 1.45455 | 0.727274 | − | 0.686347i | \(-0.240787\pi\) | ||||
0.727274 | + | 0.686347i | \(0.240787\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −6.49677e9 | −1.22078 | −0.610389 | − | 0.792102i | \(-0.708987\pi\) | ||||
−0.610389 | + | 0.792102i | \(0.708987\pi\) | |||||||
\(602\) | −1.50976e9 | −0.282047 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −2.42038e9 | −0.446945 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 8.27081e9 | 1.50102 | 0.750512 | − | 0.660857i | \(-0.229807\pi\) | ||||
0.750512 | + | 0.660857i | \(0.229807\pi\) | |||||||
\(608\) | −8.48326e9 | −1.53074 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 5.32357e9 | 0.944189 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.95155e9 | −0.342190 | −0.171095 | − | 0.985255i | \(-0.554731\pi\) | ||||
−0.171095 | + | 0.985255i | \(0.554731\pi\) | |||||||
\(614\) | 3.27793e9 | 0.571492 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −9.07657e9 | −1.56455 | ||||||||
\(617\) | 1.00173e10 | 1.71693 | 0.858464 | − | 0.512874i | \(-0.171419\pi\) | ||||
0.858464 | + | 0.512874i | \(0.171419\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.54387e9 | −0.261634 | −0.130817 | − | 0.991407i | \(-0.541760\pi\) | ||||
−0.130817 | + | 0.991407i | \(0.541760\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4.58578e9 | −0.764095 | ||||||||
\(623\) | 3.11224e9 | 0.515663 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 3.26485e9 | 0.531928 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −6.15084e9 | −0.991005 | ||||||||
\(629\) | −2.53598e9 | −0.406320 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.16453e9 | 1.13523 | 0.567616 | − | 0.823293i | \(-0.307866\pi\) | ||||
0.567616 | + | 0.823293i | \(0.307866\pi\) | |||||||
\(632\) | −6.20425e9 | −0.977641 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3.67239e9 | −0.572317 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.57241e8 | −0.0394322 | ||||||||
\(638\) | 3.69899e9 | 0.563911 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −3.32101e9 | −0.498043 | −0.249021 | − | 0.968498i | \(-0.580109\pi\) | ||||
−0.249021 | + | 0.968498i | \(0.580109\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −6.42196e9 | −0.952641 | −0.476320 | − | 0.879272i | \(-0.658030\pi\) | ||||
−0.476320 | + | 0.879272i | \(0.658030\pi\) | |||||||
\(644\) | 9.78207e9 | 1.44321 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −2.20014e9 | −0.321097 | ||||||||
\(647\) | −4.97907e9 | −0.722743 | −0.361371 | − | 0.932422i | \(-0.617691\pi\) | ||||
−0.361371 | + | 0.932422i | \(0.617691\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.04742e10 | −1.50406 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −2.89936e9 | −0.409671 | ||||||||
\(653\) | 1.08435e10 | 1.52396 | 0.761978 | − | 0.647603i | \(-0.224229\pi\) | ||||
0.761978 | + | 0.647603i | \(0.224229\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −7.67572e8 | −0.106159 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.97984e9 | 0.544597 | ||||||||
\(659\) | −3.26221e9 | −0.444030 | −0.222015 | − | 0.975043i | \(-0.571263\pi\) | ||||
−0.222015 | + | 0.975043i | \(0.571263\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.36712e8 | 0.126154 | 0.0630770 | − | 0.998009i | \(-0.479909\pi\) | ||||
0.0630770 | + | 0.998009i | \(0.479909\pi\) | |||||||
\(662\) | 4.39582e9 | 0.588894 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −7.75127e9 | −1.02751 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −8.94061e9 | −1.16661 | ||||||||
\(668\) | 2.28900e9 | 0.297117 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.31101e9 | −0.678654 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 3.64203e9 | 0.460565 | 0.230282 | − | 0.973124i | \(-0.426035\pi\) | ||||
0.230282 | + | 0.973124i | \(0.426035\pi\) | |||||||
\(674\) | −1.82591e9 | −0.229705 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.47819e9 | 0.308547 | ||||||||
\(677\) | −7.13369e9 | −0.883597 | −0.441798 | − | 0.897114i | \(-0.645659\pi\) | ||||
−0.441798 | + | 0.897114i | \(0.645659\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1.47216e10 | 1.80473 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 3.21996e9 | 0.388691 | ||||||||
\(683\) | 7.57192e9 | 0.909355 | 0.454678 | − | 0.890656i | \(-0.349754\pi\) | ||||
0.454678 | + | 0.890656i | \(0.349754\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 3.63716e9 | 0.430159 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 2.40555e9 | 0.281615 | ||||||||
\(689\) | −5.95994e9 | −0.694184 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.66534e8 | −0.111441 | −0.0557204 | − | 0.998446i | \(-0.517746\pi\) | ||||
−0.0557204 | + | 0.998446i | \(0.517746\pi\) | |||||||
\(692\) | 1.03049e10 | 1.18215 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 5.15680e9 | 0.585629 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −9.93524e8 | −0.111138 | ||||||||
\(698\) | −6.22260e8 | −0.0692593 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −1.35138e10 | −1.48172 | −0.740859 | − | 0.671660i | \(-0.765582\pi\) | ||||
−0.740859 | + | 0.671660i | \(0.765582\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.21336e10 | 1.31718 | ||||||||
\(704\) | 2.02183e8 | 0.0218394 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.61555e9 | 0.707537 | ||||||||
\(707\) | 1.41355e9 | 0.150433 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 5.99067e9 | 0.631268 | 0.315634 | − | 0.948881i | \(-0.397783\pi\) | ||||
0.315634 | + | 0.948881i | \(0.397783\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.86521e9 | 0.401322 | ||||||||
\(713\) | −7.78277e9 | −0.804120 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −4.32303e9 | −0.440142 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −5.94219e8 | −0.0599116 | ||||||||
\(719\) | −1.52251e9 | −0.152760 | −0.0763800 | − | 0.997079i | \(-0.524336\pi\) | ||||
−0.0763800 | + | 0.997079i | \(0.524336\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.84481e10 | −1.83307 | ||||||||
\(722\) | 6.05735e9 | 0.598966 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.25951e9 | 0.123344 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 5.91664e9 | 0.571091 | 0.285545 | − | 0.958365i | \(-0.407825\pi\) | ||||
0.285545 | + | 0.958365i | \(0.407825\pi\) | |||||||
\(728\) | −6.68121e9 | −0.641794 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 3.11368e9 | 0.294824 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.26254e9 | 0.212194 | 0.106097 | − | 0.994356i | \(-0.466165\pi\) | ||||
0.106097 | + | 0.994356i | \(0.466165\pi\) | |||||||
\(734\) | 5.51521e9 | 0.514785 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 1.88805e10 | 1.74558 | ||||||||
\(737\) | 2.62271e9 | 0.241332 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.50501e9 | −0.866358 | −0.433179 | − | 0.901308i | \(-0.642608\pi\) | ||||
−0.433179 | + | 0.901308i | \(0.642608\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.45558e9 | −0.400397 | ||||||||
\(743\) | −7.55711e9 | −0.675919 | −0.337960 | − | 0.941161i | \(-0.609737\pi\) | ||||
−0.337960 | + | 0.941161i | \(0.609737\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −2.26982e9 | −0.200173 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 8.34666e9 | 0.729217 | ||||||||
\(749\) | −3.84518e8 | −0.0334372 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 7.06008e9 | 0.608233 | 0.304117 | − | 0.952635i | \(-0.401639\pi\) | ||||
0.304117 | + | 0.952635i | \(0.401639\pi\) | |||||||
\(752\) | −6.34121e9 | −0.543763 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.72281e9 | 0.231322 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.38354e10 | −1.15919 | −0.579595 | − | 0.814905i | \(-0.696789\pi\) | ||||
−0.579595 | + | 0.814905i | \(0.696789\pi\) | |||||||
\(758\) | 2.64260e9 | 0.220389 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 9.16838e9 | 0.754131 | 0.377065 | − | 0.926187i | \(-0.376933\pi\) | ||||
0.377065 | + | 0.926187i | \(0.376933\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.15438e10 | 0.940837 | ||||||||
\(764\) | −1.61227e10 | −1.30801 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.51837e9 | 0.122061 | ||||||||
\(767\) | −7.71000e9 | −0.616979 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.09798e10 | 0.870664 | 0.435332 | − | 0.900270i | \(-0.356631\pi\) | ||||
0.435332 | + | 0.900270i | \(0.356631\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.11298e10 | 0.870615 | ||||||||
\(773\) | 1.33749e10 | 1.04151 | 0.520753 | − | 0.853707i | \(-0.325651\pi\) | ||||
0.520753 | + | 0.853707i | \(0.325651\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 1.82833e10 | 1.40456 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.19155e9 | 0.0907162 | ||||||||
\(779\) | 4.75358e9 | 0.360280 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 3.32448e10 | 2.49716 | ||||||||
\(782\) | 4.89665e9 | 0.366164 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 3.06414e8 | 0.0227092 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 6.82502e9 | 0.499105 | 0.249553 | − | 0.968361i | \(-0.419716\pi\) | ||||
0.249553 | + | 0.968361i | \(0.419716\pi\) | |||||||
\(788\) | 2.01850e9 | 0.146956 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.25524e10 | 1.62023 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.90941e9 | −0.278391 | ||||||||
\(794\) | 3.56063e9 | 0.252438 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.26258e9 | −0.0887285 | ||||||||
\(797\) | −1.56291e10 | −1.09353 | −0.546765 | − | 0.837286i | \(-0.684141\pi\) | ||||
−0.546765 | + | 0.837286i | \(0.684141\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.20789e9 | −0.569269 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −7.11538e8 | −0.0487066 | ||||||||
\(803\) | −3.84990e10 | −2.62388 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.37019e9 | 0.159445 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.75554e9 | 0.117077 | ||||||||
\(809\) | 1.52410e10 | 1.01203 | 0.506016 | − | 0.862524i | \(-0.331118\pi\) | ||||
0.506016 | + | 0.862524i | \(0.331118\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.52930e10 | 1.00675 | 0.503373 | − | 0.864069i | \(-0.332092\pi\) | ||||
0.503373 | + | 0.864069i | \(0.332092\pi\) | |||||||
\(812\) | −8.38641e9 | −0.549706 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.11726e10 | 0.726053 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.48976e10 | −0.955740 | ||||||||
\(818\) | 9.09714e9 | 0.581123 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.84785e9 | −0.242671 | −0.121335 | − | 0.992612i | \(-0.538718\pi\) | ||||
−0.121335 | + | 0.992612i | \(0.538718\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.44305e10 | 1.52768 | 0.763840 | − | 0.645405i | \(-0.223312\pi\) | ||||
0.763840 | + | 0.645405i | \(0.223312\pi\) | |||||||
\(824\) | −2.29114e10 | −1.42661 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.76391e9 | −0.355866 | ||||||||
\(827\) | −2.44311e9 | −0.150201 | −0.0751007 | − | 0.997176i | \(-0.523928\pi\) | ||||
−0.0751007 | + | 0.997176i | \(0.523928\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.35220e10 | −1.43395 | −0.716974 | − | 0.697100i | \(-0.754474\pi\) | ||||
−0.716974 | + | 0.697100i | \(0.754474\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.48826e8 | 0.00895874 | ||||||||
\(833\) | 3.96614e8 | 0.0237744 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | −3.99351e10 | −2.36392 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.25561e9 | 0.0737055 | ||||||||
\(839\) | 2.27195e10 | 1.32810 | 0.664050 | − | 0.747688i | \(-0.268836\pi\) | ||||
0.664050 | + | 0.747688i | \(0.268836\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −9.58487e9 | −0.555649 | ||||||||
\(842\) | 3.24800e8 | 0.0187510 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 1.95471e10 | 1.11914 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −4.82813e10 | −2.73015 | ||||||||
\(848\) | 7.09923e9 | 0.399784 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −2.70046e10 | −1.50205 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 3.13423e10 | 1.72906 | 0.864528 | − | 0.502584i | \(-0.167617\pi\) | ||||
0.864528 | + | 0.502584i | \(0.167617\pi\) | |||||||
\(854\) | −2.92263e9 | −0.160572 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.77546e8 | −0.0260230 | ||||||||
\(857\) | 2.95845e10 | 1.60558 | 0.802790 | − | 0.596262i | \(-0.203348\pi\) | ||||
0.802790 | + | 0.596262i | \(0.203348\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 7.18615e9 | 0.386830 | 0.193415 | − | 0.981117i | \(-0.438044\pi\) | ||||
0.193415 | + | 0.981117i | \(0.438044\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 3.82427e9 | 0.203364 | ||||||||
\(863\) | −2.82174e10 | −1.49444 | −0.747221 | − | 0.664575i | \(-0.768613\pi\) | ||||
−0.747221 | + | 0.664575i | \(0.768613\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 8.24640e9 | 0.431471 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.30035e9 | −0.378900 | ||||||||
\(869\) | −4.53904e10 | −2.34636 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 1.93056e9 | 0.0989967 | ||||||||
\(872\) | 1.43367e10 | 0.732220 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.34284e10 | −1.18700 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.44481e10 | 1.72451 | 0.862256 | − | 0.506472i | \(-0.169051\pi\) | ||||
0.862256 | + | 0.506472i | \(0.169051\pi\) | |||||||
\(878\) | 1.13551e10 | 0.566187 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.96916e10 | 0.970211 | 0.485105 | − | 0.874456i | \(-0.338781\pi\) | ||||
0.485105 | + | 0.874456i | \(0.338781\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.79896e10 | 1.36815 | 0.684075 | − | 0.729412i | \(-0.260206\pi\) | ||||
0.684075 | + | 0.729412i | \(0.260206\pi\) | |||||||
\(884\) | 6.14393e9 | 0.299132 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 7.36107e9 | 0.355568 | ||||||||
\(887\) | −1.03338e10 | −0.497198 | −0.248599 | − | 0.968606i | \(-0.579970\pi\) | ||||
−0.248599 | + | 0.968606i | \(0.579970\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.41400e8 | 0.0115234 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.13096e9 | 0.0533543 | ||||||||
\(893\) | 3.92712e10 | 1.84541 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.21200e10 | 1.02732 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.70743e10 | 0.786820 | ||||||||
\(899\) | 6.67236e9 | 0.306281 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 9.18904e9 | 0.418537 | ||||||||
\(902\) | 4.37710e9 | 0.198593 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.80086e10 | 1.26096 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.24060e10 | −0.997099 | −0.498550 | − | 0.866861i | \(-0.666134\pi\) | ||||
−0.498550 | + | 0.866861i | \(0.666134\pi\) | |||||||
\(908\) | 5.19946e9 | 0.230493 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.53010e10 | −1.10872 | −0.554361 | − | 0.832276i | \(-0.687037\pi\) | ||||
−0.554361 | + | 0.832276i | \(0.687037\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.67085e10 | −2.46604 | ||||||||
\(914\) | 5.51075e9 | 0.238725 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.37072e9 | −0.273876 | ||||||||
\(917\) | −1.31860e10 | −0.564702 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.88277e10 | −0.800191 | −0.400095 | − | 0.916474i | \(-0.631023\pi\) | ||||
−0.400095 | + | 0.916474i | \(0.631023\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.88473e10 | 0.791939 | ||||||||
\(923\) | 2.44713e10 | 1.02436 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 5.53528e9 | 0.229087 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.61867e10 | −0.664875 | ||||||||
\(929\) | 9.06966e9 | 0.371138 | 0.185569 | − | 0.982631i | \(-0.440587\pi\) | ||||
0.185569 | + | 0.982631i | \(0.440587\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.89762e9 | −0.0770702 | ||||||||
\(932\) | 1.42008e10 | 0.574587 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −7.53368e9 | −0.302547 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.38178e10 | −0.945828 | −0.472914 | − | 0.881109i | \(-0.656798\pi\) | ||||
−0.472914 | + | 0.881109i | \(0.656798\pi\) | |||||||
\(938\) | 1.44327e9 | 0.0571001 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 6.64810e9 | 0.260096 | 0.130048 | − | 0.991508i | \(-0.458487\pi\) | ||||
0.130048 | + | 0.991508i | \(0.458487\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.05796e10 | −0.410847 | ||||||||
\(944\) | 9.18383e9 | 0.355322 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.37177e10 | −0.526821 | ||||||||
\(947\) | −1.09645e10 | −0.419532 | −0.209766 | − | 0.977752i | \(-0.567270\pi\) | ||||
−0.209766 | + | 0.977752i | \(0.567270\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.83389e10 | −1.07634 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.03011e10 | 0.386949 | ||||||||
\(953\) | 1.79028e10 | 0.670032 | 0.335016 | − | 0.942212i | \(-0.391258\pi\) | ||||
0.335016 | + | 0.942212i | \(0.391258\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 6.46551e9 | 0.239332 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −1.77622e10 | −0.652707 | ||||||||
\(959\) | 2.32230e10 | 0.850262 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.17043e10 | −0.788887 | ||||||||
\(962\) | 8.22408e9 | 0.297834 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.41264e10 | 0.507881 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.39231e10 | 1.20643 | 0.603216 | − | 0.797578i | \(-0.293886\pi\) | ||||
0.603216 | + | 0.797578i | \(0.293886\pi\) | |||||||
\(968\) | −5.99622e10 | −2.12478 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −1.00724e7 | −0.000353072 0 | −0.000176536 | − | 1.00000i | \(-0.500056\pi\) | ||||
−0.000176536 | 1.00000i | \(0.500056\pi\) | ||||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −3.08686e10 | −1.07429 | ||||||||
\(974\) | −1.31114e10 | −0.454665 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 4.65672e9 | 0.160327 | ||||||||
\(977\) | 7.44894e9 | 0.255543 | 0.127771 | − | 0.991804i | \(-0.459218\pi\) | ||||
0.127771 | + | 0.991804i | \(0.459218\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 2.82779e10 | 0.963181 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −8.84229e9 | −0.297971 | ||||||||
\(983\) | −1.43718e10 | −0.482584 | −0.241292 | − | 0.970453i | \(-0.577571\pi\) | ||||
−0.241292 | + | 0.970453i | \(0.577571\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −4.19802e9 | −0.139468 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −2.93960e10 | −0.969705 | ||||||||
\(989\) | 3.31563e10 | 1.08988 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.76560e10 | −1.22907 | −0.614535 | − | 0.788890i | \(-0.710656\pi\) | ||||
−0.614535 | + | 0.788890i | \(0.710656\pi\) | |||||||
\(992\) | −1.40905e10 | −0.458283 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.82945e10 | 0.590838 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 2.47986e10 | 0.792490 | 0.396245 | − | 0.918145i | \(-0.370313\pi\) | ||||
0.396245 | + | 0.918145i | \(0.370313\pi\) | |||||||
\(998\) | −1.23158e10 | −0.392198 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 225.8.a.h.1.1 | 1 | ||
3.2 | odd | 2 | 225.8.a.e.1.1 | 1 | |||
5.2 | odd | 4 | 225.8.b.g.199.2 | 2 | |||
5.3 | odd | 4 | 225.8.b.g.199.1 | 2 | |||
5.4 | even | 2 | 45.8.a.b.1.1 | ✓ | 1 | ||
15.2 | even | 4 | 225.8.b.h.199.1 | 2 | |||
15.8 | even | 4 | 225.8.b.h.199.2 | 2 | |||
15.14 | odd | 2 | 45.8.a.c.1.1 | yes | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
45.8.a.b.1.1 | ✓ | 1 | 5.4 | even | 2 | ||
45.8.a.c.1.1 | yes | 1 | 15.14 | odd | 2 | ||
225.8.a.e.1.1 | 1 | 3.2 | odd | 2 | |||
225.8.a.h.1.1 | 1 | 1.1 | even | 1 | trivial | ||
225.8.b.g.199.1 | 2 | 5.3 | odd | 4 | |||
225.8.b.g.199.2 | 2 | 5.2 | odd | 4 | |||
225.8.b.h.199.1 | 2 | 15.2 | even | 4 | |||
225.8.b.h.199.2 | 2 | 15.8 | even | 4 |