Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [54,8,Mod(1,54)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(54, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("54.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 54 = 2 \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 54.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: | \(16.8687913761\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 54.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 64.0000 | 0.500000 | ||||||||
\(5\) | −120.000 | −0.429325 | −0.214663 | − | 0.976688i | \(-0.568865\pi\) | ||||
−0.214663 | + | 0.976688i | \(0.568865\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 377.000 | 0.415430 | 0.207715 | − | 0.978189i | \(-0.433397\pi\) | ||||
0.207715 | + | 0.978189i | \(0.433397\pi\) | |||||||
\(8\) | −512.000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 960.000 | 0.303579 | ||||||||
\(11\) | −600.000 | −0.135918 | −0.0679590 | − | 0.997688i | \(-0.521649\pi\) | ||||
−0.0679590 | + | 0.997688i | \(0.521649\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 5369.00 | 0.677785 | 0.338892 | − | 0.940825i | \(-0.389948\pi\) | ||||
0.338892 | + | 0.940825i | \(0.389948\pi\) | |||||||
\(14\) | −3016.00 | −0.293754 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | −12168.0 | −0.600687 | −0.300343 | − | 0.953831i | \(-0.597101\pi\) | ||||
−0.300343 | + | 0.953831i | \(0.597101\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 16211.0 | 0.542216 | 0.271108 | − | 0.962549i | \(-0.412610\pi\) | ||||
0.271108 | + | 0.962549i | \(0.412610\pi\) | |||||||
\(20\) | −7680.00 | −0.214663 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 4800.00 | 0.0961085 | ||||||||
\(23\) | −106392. | −1.82331 | −0.911657 | − | 0.410952i | \(-0.865197\pi\) | ||||
−0.911657 | + | 0.410952i | \(0.865197\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −63725.0 | −0.815680 | ||||||||
\(26\) | −42952.0 | −0.479266 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 24128.0 | 0.207715 | ||||||||
\(29\) | −177216. | −1.34930 | −0.674652 | − | 0.738136i | \(-0.735706\pi\) | ||||
−0.674652 | + | 0.738136i | \(0.735706\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −268060. | −1.61609 | −0.808046 | − | 0.589119i | \(-0.799475\pi\) | ||||
−0.808046 | + | 0.589119i | \(0.799475\pi\) | |||||||
\(32\) | −32768.0 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 97344.0 | 0.424750 | ||||||||
\(35\) | −45240.0 | −0.178355 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 114959. | 0.373110 | 0.186555 | − | 0.982445i | \(-0.440268\pi\) | ||||
0.186555 | + | 0.982445i | \(0.440268\pi\) | |||||||
\(38\) | −129688. | −0.383404 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 61440.0 | 0.151789 | ||||||||
\(41\) | 112128. | 0.254080 | 0.127040 | − | 0.991898i | \(-0.459452\pi\) | ||||
0.127040 | + | 0.991898i | \(0.459452\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −115048. | −0.220668 | −0.110334 | − | 0.993895i | \(-0.535192\pi\) | ||||
−0.110334 | + | 0.993895i | \(0.535192\pi\) | |||||||
\(44\) | −38400.0 | −0.0679590 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 851136. | 1.28928 | ||||||||
\(47\) | −561336. | −0.788643 | −0.394321 | − | 0.918973i | \(-0.629020\pi\) | ||||
−0.394321 | + | 0.918973i | \(0.629020\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −681414. | −0.827418 | ||||||||
\(50\) | 509800. | 0.576773 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 343616. | 0.338892 | ||||||||
\(53\) | 1.78776e6 | 1.64947 | 0.824734 | − | 0.565521i | \(-0.191325\pi\) | ||||
0.824734 | + | 0.565521i | \(0.191325\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 72000.0 | 0.0583530 | ||||||||
\(56\) | −193024. | −0.146877 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.41773e6 | 0.954102 | ||||||||
\(59\) | 1.78634e6 | 1.13236 | 0.566178 | − | 0.824283i | \(-0.308421\pi\) | ||||
0.566178 | + | 0.824283i | \(0.308421\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.30684e6 | −0.737169 | −0.368584 | − | 0.929594i | \(-0.620157\pi\) | ||||
−0.368584 | + | 0.929594i | \(0.620157\pi\) | |||||||
\(62\) | 2.14448e6 | 1.14275 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | −644280. | −0.290990 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.01382e6 | −0.818009 | −0.409005 | − | 0.912532i | \(-0.634124\pi\) | ||||
−0.409005 | + | 0.912532i | \(0.634124\pi\) | |||||||
\(68\) | −778752. | −0.300343 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 361920. | 0.126116 | ||||||||
\(71\) | 4.06094e6 | 1.34655 | 0.673275 | − | 0.739392i | \(-0.264887\pi\) | ||||
0.673275 | + | 0.739392i | \(0.264887\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.85064e6 | −1.15852 | −0.579259 | − | 0.815144i | \(-0.696658\pi\) | ||||
−0.579259 | + | 0.815144i | \(0.696658\pi\) | |||||||
\(74\) | −919672. | −0.263829 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.03750e6 | 0.271108 | ||||||||
\(77\) | −226200. | −0.0564644 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.03723e6 | 0.236690 | 0.118345 | − | 0.992973i | \(-0.462241\pi\) | ||||
0.118345 | + | 0.992973i | \(0.462241\pi\) | |||||||
\(80\) | −491520. | −0.107331 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −897024. | −0.179662 | ||||||||
\(83\) | −9.20357e6 | −1.76678 | −0.883391 | − | 0.468637i | \(-0.844745\pi\) | ||||
−0.883391 | + | 0.468637i | \(0.844745\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.46016e6 | 0.257890 | ||||||||
\(86\) | 920384. | 0.156036 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 307200. | 0.0480543 | ||||||||
\(89\) | 1.28930e6 | 0.193861 | 0.0969305 | − | 0.995291i | \(-0.469098\pi\) | ||||
0.0969305 | + | 0.995291i | \(0.469098\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.02411e6 | 0.281572 | ||||||||
\(92\) | −6.80909e6 | −0.911657 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.49069e6 | 0.557655 | ||||||||
\(95\) | −1.94532e6 | −0.232787 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 8.55588e6 | 0.951840 | 0.475920 | − | 0.879489i | \(-0.342115\pi\) | ||||
0.475920 | + | 0.879489i | \(0.342115\pi\) | |||||||
\(98\) | 5.45131e6 | 0.585073 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −4.07840e6 | −0.407840 | ||||||||
\(101\) | −1.99006e7 | −1.92195 | −0.960974 | − | 0.276639i | \(-0.910779\pi\) | ||||
−0.960974 | + | 0.276639i | \(0.910779\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.99984e6 | 0.631187 | 0.315594 | − | 0.948894i | \(-0.397796\pi\) | ||||
0.315594 | + | 0.948894i | \(0.397796\pi\) | |||||||
\(104\) | −2.74893e6 | −0.239633 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1.43021e7 | −1.16635 | ||||||||
\(107\) | 4.48063e6 | 0.353587 | 0.176793 | − | 0.984248i | \(-0.443428\pi\) | ||||
0.176793 | + | 0.984248i | \(0.443428\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.47074e6 | −0.108779 | −0.0543893 | − | 0.998520i | \(-0.517321\pi\) | ||||
−0.0543893 | + | 0.998520i | \(0.517321\pi\) | |||||||
\(110\) | −576000. | −0.0412618 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.54419e6 | 0.103858 | ||||||||
\(113\) | −3.47786e6 | −0.226745 | −0.113373 | − | 0.993553i | \(-0.536165\pi\) | ||||
−0.113373 | + | 0.993553i | \(0.536165\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.27670e7 | 0.782795 | ||||||||
\(116\) | −1.13418e7 | −0.674652 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.42908e7 | −0.800697 | ||||||||
\(119\) | −4.58734e6 | −0.249543 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.91272e7 | −0.981526 | ||||||||
\(122\) | 1.04547e7 | 0.521257 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.71558e7 | −0.808046 | ||||||||
\(125\) | 1.70220e7 | 0.779517 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.10378e7 | 0.911353 | 0.455677 | − | 0.890145i | \(-0.349397\pi\) | ||||
0.455677 | + | 0.890145i | \(0.349397\pi\) | |||||||
\(128\) | −2.09715e6 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 5.15424e6 | 0.205761 | ||||||||
\(131\) | 2.06906e7 | 0.804125 | 0.402062 | − | 0.915612i | \(-0.368294\pi\) | ||||
0.402062 | + | 0.915612i | \(0.368294\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6.11155e6 | 0.225253 | ||||||||
\(134\) | 1.61105e7 | 0.578420 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.23002e6 | 0.212375 | ||||||||
\(137\) | 5.31521e7 | 1.76603 | 0.883016 | − | 0.469343i | \(-0.155509\pi\) | ||||
0.883016 | + | 0.469343i | \(0.155509\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.95009e7 | −0.615890 | −0.307945 | − | 0.951404i | \(-0.599641\pi\) | ||||
−0.307945 | + | 0.951404i | \(0.599641\pi\) | |||||||
\(140\) | −2.89536e6 | −0.0891773 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −3.24876e7 | −0.952155 | ||||||||
\(143\) | −3.22140e6 | −0.0921231 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.12659e7 | 0.579290 | ||||||||
\(146\) | 3.08051e7 | 0.819196 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 7.35738e6 | 0.186555 | ||||||||
\(149\) | −8.51563e6 | −0.210894 | −0.105447 | − | 0.994425i | \(-0.533627\pi\) | ||||
−0.105447 | + | 0.994425i | \(0.533627\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 6.37020e7 | 1.50568 | 0.752841 | − | 0.658202i | \(-0.228683\pi\) | ||||
0.752841 | + | 0.658202i | \(0.228683\pi\) | |||||||
\(152\) | −8.30003e6 | −0.191702 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1.80960e6 | 0.0399264 | ||||||||
\(155\) | 3.21672e7 | 0.693829 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.36342e7 | −1.31233 | −0.656163 | − | 0.754619i | \(-0.727822\pi\) | ||||
−0.656163 | + | 0.754619i | \(0.727822\pi\) | |||||||
\(158\) | −8.29785e6 | −0.167365 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.93216e6 | 0.0758947 | ||||||||
\(161\) | −4.01098e7 | −0.757460 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.87301e7 | 1.24305 | 0.621527 | − | 0.783392i | \(-0.286512\pi\) | ||||
0.621527 | + | 0.783392i | \(0.286512\pi\) | |||||||
\(164\) | 7.17619e6 | 0.127040 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 7.36285e7 | 1.24930 | ||||||||
\(167\) | −1.29434e7 | −0.215051 | −0.107525 | − | 0.994202i | \(-0.534293\pi\) | ||||
−0.107525 | + | 0.994202i | \(0.534293\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −3.39224e7 | −0.540608 | ||||||||
\(170\) | −1.16813e7 | −0.182356 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −7.36307e6 | −0.110334 | ||||||||
\(173\) | 4.22124e7 | 0.619838 | 0.309919 | − | 0.950763i | \(-0.399698\pi\) | ||||
0.309919 | + | 0.950763i | \(0.399698\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −2.40243e7 | −0.338858 | ||||||||
\(176\) | −2.45760e6 | −0.0339795 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.03144e7 | −0.137080 | ||||||||
\(179\) | −1.13640e8 | −1.48096 | −0.740482 | − | 0.672076i | \(-0.765403\pi\) | ||||
−0.740482 | + | 0.672076i | \(0.765403\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.27922e8 | −1.60350 | −0.801752 | − | 0.597658i | \(-0.796098\pi\) | ||||
−0.801752 | + | 0.597658i | \(0.796098\pi\) | |||||||
\(182\) | −1.61929e7 | −0.199102 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 5.44727e7 | 0.644639 | ||||||||
\(185\) | −1.37951e7 | −0.160185 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7.30080e6 | 0.0816441 | ||||||||
\(188\) | −3.59255e7 | −0.394321 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 1.55626e7 | 0.164605 | ||||||||
\(191\) | 2.10840e7 | 0.218946 | 0.109473 | − | 0.993990i | \(-0.465084\pi\) | ||||
0.109473 | + | 0.993990i | \(0.465084\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.39821e8 | −1.39998 | −0.699990 | − | 0.714152i | \(-0.746812\pi\) | ||||
−0.699990 | + | 0.714152i | \(0.746812\pi\) | |||||||
\(194\) | −6.84471e7 | −0.673052 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −4.36105e7 | −0.413709 | ||||||||
\(197\) | −1.45966e8 | −1.36025 | −0.680127 | − | 0.733094i | \(-0.738076\pi\) | ||||
−0.680127 | + | 0.733094i | \(0.738076\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −5.11146e7 | −0.459790 | −0.229895 | − | 0.973215i | \(-0.573838\pi\) | ||||
−0.229895 | + | 0.973215i | \(0.573838\pi\) | |||||||
\(200\) | 3.26272e7 | 0.288386 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.59205e8 | 1.35902 | ||||||||
\(203\) | −6.68104e7 | −0.560542 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.34554e7 | −0.109083 | ||||||||
\(206\) | −5.59988e7 | −0.446317 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.19914e7 | 0.169446 | ||||||||
\(209\) | −9.72660e6 | −0.0736969 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 9.80537e7 | 0.718581 | 0.359290 | − | 0.933226i | \(-0.383019\pi\) | ||||
0.359290 | + | 0.933226i | \(0.383019\pi\) | |||||||
\(212\) | 1.14417e8 | 0.824734 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3.58451e7 | −0.250024 | ||||||||
\(215\) | 1.38058e7 | 0.0947383 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.01059e8 | −0.671374 | ||||||||
\(218\) | 1.17659e7 | 0.0769181 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 4.60800e6 | 0.0291765 | ||||||||
\(221\) | −6.53300e7 | −0.407136 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.16758e8 | 1.30891 | 0.654453 | − | 0.756103i | \(-0.272899\pi\) | ||||
0.654453 | + | 0.756103i | \(0.272899\pi\) | |||||||
\(224\) | −1.23535e7 | −0.0734384 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 2.78229e7 | 0.160333 | ||||||||
\(227\) | 1.39865e8 | 0.793629 | 0.396814 | − | 0.917899i | \(-0.370116\pi\) | ||||
0.396814 | + | 0.917899i | \(0.370116\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −9.49569e7 | −0.522519 | −0.261260 | − | 0.965269i | \(-0.584138\pi\) | ||||
−0.261260 | + | 0.965269i | \(0.584138\pi\) | |||||||
\(230\) | −1.02136e8 | −0.553519 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 9.07346e7 | 0.477051 | ||||||||
\(233\) | 2.10948e8 | 1.09252 | 0.546261 | − | 0.837615i | \(-0.316051\pi\) | ||||
0.546261 | + | 0.837615i | \(0.316051\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 6.73603e7 | 0.338584 | ||||||||
\(236\) | 1.14326e8 | 0.566178 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 3.66987e7 | 0.176454 | ||||||||
\(239\) | 1.29152e8 | 0.611939 | 0.305969 | − | 0.952041i | \(-0.401019\pi\) | ||||
0.305969 | + | 0.952041i | \(0.401019\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.01868e7 | −0.184937 | −0.0924685 | − | 0.995716i | \(-0.529476\pi\) | ||||
−0.0924685 | + | 0.995716i | \(0.529476\pi\) | |||||||
\(242\) | 1.53017e8 | 0.694044 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −8.36376e7 | −0.368584 | ||||||||
\(245\) | 8.17697e7 | 0.355231 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.70369e7 | 0.367506 | ||||||||
\(248\) | 1.37247e8 | 0.571375 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.36176e8 | −0.551202 | ||||||||
\(251\) | 2.68201e8 | 1.07054 | 0.535270 | − | 0.844681i | \(-0.320210\pi\) | ||||
0.535270 | + | 0.844681i | \(0.320210\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 6.38352e7 | 0.247821 | ||||||||
\(254\) | −1.68302e8 | −0.644424 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | 1.71864e8 | 0.631566 | 0.315783 | − | 0.948831i | \(-0.397733\pi\) | ||||
0.315783 | + | 0.948831i | \(0.397733\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 4.33395e7 | 0.155001 | ||||||||
\(260\) | −4.12339e7 | −0.145495 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −1.65525e8 | −0.568602 | ||||||||
\(263\) | −2.02033e8 | −0.684822 | −0.342411 | − | 0.939550i | \(-0.611243\pi\) | ||||
−0.342411 | + | 0.939550i | \(0.611243\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.14531e8 | −0.708158 | ||||||||
\(266\) | −4.88924e7 | −0.159278 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.28884e8 | −0.409005 | ||||||||
\(269\) | 9.73917e7 | 0.305063 | 0.152531 | − | 0.988299i | \(-0.451257\pi\) | ||||
0.152531 | + | 0.988299i | \(0.451257\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 4.51945e8 | 1.37941 | 0.689705 | − | 0.724091i | \(-0.257740\pi\) | ||||
0.689705 | + | 0.724091i | \(0.257740\pi\) | |||||||
\(272\) | −4.98401e7 | −0.150172 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.25217e8 | −1.24877 | ||||||||
\(275\) | 3.82350e7 | 0.110866 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.09703e8 | −0.592823 | −0.296411 | − | 0.955060i | \(-0.595790\pi\) | ||||
−0.296411 | + | 0.955060i | \(0.595790\pi\) | |||||||
\(278\) | 1.56007e8 | 0.435500 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 2.31629e7 | 0.0630579 | ||||||||
\(281\) | −5.32204e8 | −1.43089 | −0.715444 | − | 0.698670i | \(-0.753776\pi\) | ||||
−0.715444 | + | 0.698670i | \(0.753776\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.74761e8 | 1.24515 | 0.622576 | − | 0.782559i | \(-0.286086\pi\) | ||||
0.622576 | + | 0.782559i | \(0.286086\pi\) | |||||||
\(284\) | 2.59900e8 | 0.673275 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 2.57712e7 | 0.0651409 | ||||||||
\(287\) | 4.22723e7 | 0.105553 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.62278e8 | −0.639176 | ||||||||
\(290\) | −1.70127e8 | −0.409620 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.46441e8 | −0.579259 | ||||||||
\(293\) | 2.32118e8 | 0.539104 | 0.269552 | − | 0.962986i | \(-0.413124\pi\) | ||||
0.269552 | + | 0.962986i | \(0.413124\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.14361e8 | −0.486149 | ||||||||
\(296\) | −5.88590e7 | −0.131914 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 6.81251e7 | 0.149125 | ||||||||
\(299\) | −5.71219e8 | −1.23581 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4.33731e7 | −0.0916722 | ||||||||
\(302\) | −5.09616e8 | −1.06468 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 6.64003e7 | 0.135554 | ||||||||
\(305\) | 1.56820e8 | 0.316485 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 7.53314e8 | 1.48591 | 0.742953 | − | 0.669343i | \(-0.233424\pi\) | ||||
0.742953 | + | 0.669343i | \(0.233424\pi\) | |||||||
\(308\) | −1.44768e7 | −0.0282322 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −2.57338e8 | −0.490611 | ||||||||
\(311\) | −4.79778e8 | −0.904439 | −0.452219 | − | 0.891907i | \(-0.649368\pi\) | ||||
−0.452219 | + | 0.891907i | \(0.649368\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6.55525e8 | 1.20833 | 0.604163 | − | 0.796861i | \(-0.293508\pi\) | ||||
0.604163 | + | 0.796861i | \(0.293508\pi\) | |||||||
\(314\) | 5.09074e8 | 0.927955 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 6.63828e7 | 0.118345 | ||||||||
\(317\) | −6.93361e8 | −1.22251 | −0.611255 | − | 0.791434i | \(-0.709335\pi\) | ||||
−0.611255 | + | 0.791434i | \(0.709335\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 1.06330e8 | 0.183395 | ||||||||
\(320\) | −3.14573e7 | −0.0536656 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.20878e8 | 0.535605 | ||||||||
\(323\) | −1.97255e8 | −0.325702 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.42140e8 | −0.552855 | ||||||||
\(326\) | −5.49841e8 | −0.878972 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −5.74095e7 | −0.0898309 | ||||||||
\(329\) | −2.11624e8 | −0.327626 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.84653e8 | −0.279872 | −0.139936 | − | 0.990161i | \(-0.544690\pi\) | ||||
−0.139936 | + | 0.990161i | \(0.544690\pi\) | |||||||
\(332\) | −5.89028e8 | −0.883391 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.03547e8 | 0.152064 | ||||||||
\(335\) | 2.41658e8 | 0.351192 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.43883e8 | 1.20110 | 0.600548 | − | 0.799589i | \(-0.294949\pi\) | ||||
0.600548 | + | 0.799589i | \(0.294949\pi\) | |||||||
\(338\) | 2.71379e8 | 0.382268 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 9.34502e7 | 0.128945 | ||||||||
\(341\) | 1.60836e8 | 0.219656 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5.67369e8 | −0.759165 | ||||||||
\(344\) | 5.89046e7 | 0.0780179 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −3.37699e8 | −0.438292 | ||||||||
\(347\) | −1.22250e8 | −0.157071 | −0.0785353 | − | 0.996911i | \(-0.525024\pi\) | ||||
−0.0785353 | + | 0.996911i | \(0.525024\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.05296e9 | −1.32594 | −0.662969 | − | 0.748646i | \(-0.730704\pi\) | ||||
−0.662969 | + | 0.748646i | \(0.730704\pi\) | |||||||
\(350\) | 1.92195e8 | 0.239609 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.96608e7 | 0.0240271 | ||||||||
\(353\) | 6.24584e8 | 0.755752 | 0.377876 | − | 0.925856i | \(-0.376654\pi\) | ||||
0.377876 | + | 0.925856i | \(0.376654\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.87313e8 | −0.578108 | ||||||||
\(356\) | 8.25155e7 | 0.0969305 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.09118e8 | 1.04720 | ||||||||
\(359\) | 7.95194e8 | 0.907074 | 0.453537 | − | 0.891237i | \(-0.350162\pi\) | ||||
0.453537 | + | 0.891237i | \(0.350162\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.31075e8 | −0.706002 | ||||||||
\(362\) | 1.02337e9 | 1.13385 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.29543e8 | 0.140786 | ||||||||
\(365\) | 4.62077e8 | 0.497381 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.09445e9 | −1.15575 | −0.577876 | − | 0.816125i | \(-0.696118\pi\) | ||||
−0.577876 | + | 0.816125i | \(0.696118\pi\) | |||||||
\(368\) | −4.35782e8 | −0.455829 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.10361e8 | 0.113268 | ||||||||
\(371\) | 6.73986e8 | 0.685239 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 8.82044e8 | 0.880054 | 0.440027 | − | 0.897985i | \(-0.354969\pi\) | ||||
0.440027 | + | 0.897985i | \(0.354969\pi\) | |||||||
\(374\) | −5.84064e7 | −0.0577311 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.87404e8 | 0.278827 | ||||||||
\(377\) | −9.51473e8 | −0.914538 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −1.04251e9 | −0.983651 | −0.491826 | − | 0.870694i | \(-0.663670\pi\) | ||||
−0.491826 | + | 0.870694i | \(0.663670\pi\) | |||||||
\(380\) | −1.24500e8 | −0.116393 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.68672e8 | −0.154818 | ||||||||
\(383\) | 8.36847e8 | 0.761115 | 0.380558 | − | 0.924757i | \(-0.375732\pi\) | ||||
0.380558 | + | 0.924757i | \(0.375732\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.71440e7 | 0.0242416 | ||||||||
\(386\) | 1.11857e9 | 0.989936 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 5.47577e8 | 0.475920 | ||||||||
\(389\) | 1.47060e9 | 1.26669 | 0.633345 | − | 0.773870i | \(-0.281681\pi\) | ||||
0.633345 | + | 0.773870i | \(0.281681\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.29458e9 | 1.09524 | ||||||||
\(392\) | 3.48884e8 | 0.292536 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.16773e9 | 0.961845 | ||||||||
\(395\) | −1.24468e8 | −0.101617 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.26746e9 | −1.01664 | −0.508322 | − | 0.861167i | \(-0.669734\pi\) | ||||
−0.508322 | + | 0.861167i | \(0.669734\pi\) | |||||||
\(398\) | 4.08917e8 | 0.325121 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.61018e8 | −0.203920 | ||||||||
\(401\) | −5.27858e8 | −0.408801 | −0.204401 | − | 0.978887i | \(-0.565524\pi\) | ||||
−0.204401 | + | 0.978887i | \(0.565524\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.43921e9 | −1.09536 | ||||||||
\(404\) | −1.27364e9 | −0.960974 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.34483e8 | 0.396363 | ||||||||
\(407\) | −6.89754e7 | −0.0507124 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.22791e8 | −0.161015 | −0.0805073 | − | 0.996754i | \(-0.525654\pi\) | ||||
−0.0805073 | + | 0.996754i | \(0.525654\pi\) | |||||||
\(410\) | 1.07643e8 | 0.0771333 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 4.47990e8 | 0.315594 | ||||||||
\(413\) | 6.73452e8 | 0.470415 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.10443e9 | 0.758524 | ||||||||
\(416\) | −1.75931e8 | −0.119817 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.78128e7 | 0.0521116 | ||||||||
\(419\) | 4.40581e8 | 0.292602 | 0.146301 | − | 0.989240i | \(-0.453263\pi\) | ||||
0.146301 | + | 0.989240i | \(0.453263\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.18934e9 | 1.42997 | 0.714984 | − | 0.699140i | \(-0.246434\pi\) | ||||
0.714984 | + | 0.699140i | \(0.246434\pi\) | |||||||
\(422\) | −7.84430e8 | −0.508113 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9.15333e8 | −0.583175 | ||||||||
\(425\) | 7.75406e8 | 0.489968 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.92678e8 | −0.306242 | ||||||||
\(428\) | 2.86760e8 | 0.176793 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −1.10446e8 | −0.0669901 | ||||||||
\(431\) | −3.03634e9 | −1.82675 | −0.913377 | − | 0.407114i | \(-0.866535\pi\) | ||||
−0.913377 | + | 0.407114i | \(0.866535\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.21735e9 | 1.31258 | 0.656290 | − | 0.754509i | \(-0.272125\pi\) | ||||
0.656290 | + | 0.754509i | \(0.272125\pi\) | |||||||
\(434\) | 8.08469e8 | 0.474733 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −9.41275e7 | −0.0543893 | ||||||||
\(437\) | −1.72472e9 | −0.988630 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.50094e9 | −1.41084 | −0.705419 | − | 0.708791i | \(-0.749241\pi\) | ||||
−0.705419 | + | 0.708791i | \(0.749241\pi\) | |||||||
\(440\) | −3.68640e7 | −0.0206309 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 5.22640e8 | 0.287889 | ||||||||
\(443\) | 2.40387e9 | 1.31370 | 0.656852 | − | 0.754019i | \(-0.271887\pi\) | ||||
0.656852 | + | 0.754019i | \(0.271887\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1.54716e8 | −0.0832294 | ||||||||
\(446\) | −1.73407e9 | −0.925536 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 9.88283e7 | 0.0519288 | ||||||||
\(449\) | −2.14935e9 | −1.12059 | −0.560294 | − | 0.828294i | \(-0.689312\pi\) | ||||
−0.560294 | + | 0.828294i | \(0.689312\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.72768e7 | −0.0345340 | ||||||||
\(452\) | −2.22583e8 | −0.113373 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −1.11892e9 | −0.561180 | ||||||||
\(455\) | −2.42894e8 | −0.120886 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.30159e9 | 1.12803 | 0.564015 | − | 0.825765i | \(-0.309256\pi\) | ||||
0.564015 | + | 0.825765i | \(0.309256\pi\) | |||||||
\(458\) | 7.59655e8 | 0.369477 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 8.17091e8 | 0.391397 | ||||||||
\(461\) | −1.37928e9 | −0.655689 | −0.327844 | − | 0.944732i | \(-0.606322\pi\) | ||||
−0.327844 | + | 0.944732i | \(0.606322\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −1.72054e9 | −0.805620 | −0.402810 | − | 0.915284i | \(-0.631967\pi\) | ||||
−0.402810 | + | 0.915284i | \(0.631967\pi\) | |||||||
\(464\) | −7.25877e8 | −0.337326 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.68759e9 | −0.772530 | ||||||||
\(467\) | −1.58750e9 | −0.721280 | −0.360640 | − | 0.932705i | \(-0.617442\pi\) | ||||
−0.360640 | + | 0.932705i | \(0.617442\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −7.59209e8 | −0.339826 | ||||||||
\(470\) | −5.38883e8 | −0.239415 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −9.14608e8 | −0.400348 | ||||||||
\(473\) | 6.90288e7 | 0.0299928 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.03305e9 | −0.442275 | ||||||||
\(476\) | −2.93590e8 | −0.124772 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.03321e9 | −0.432706 | ||||||||
\(479\) | −1.75670e9 | −0.730336 | −0.365168 | − | 0.930942i | \(-0.618988\pi\) | ||||
−0.365168 | + | 0.930942i | \(0.618988\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 6.17215e8 | 0.252888 | ||||||||
\(482\) | 3.21494e8 | 0.130770 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.22414e9 | −0.490763 | ||||||||
\(485\) | −1.02671e9 | −0.408649 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.52004e9 | 0.596353 | 0.298177 | − | 0.954511i | \(-0.403622\pi\) | ||||
0.298177 | + | 0.954511i | \(0.403622\pi\) | |||||||
\(488\) | 6.69101e8 | 0.260629 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.54157e8 | −0.251186 | ||||||||
\(491\) | −3.64824e9 | −1.39091 | −0.695453 | − | 0.718572i | \(-0.744796\pi\) | ||||
−0.695453 | + | 0.718572i | \(0.744796\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.15636e9 | 0.810509 | ||||||||
\(494\) | −6.96295e8 | −0.259866 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.09797e9 | −0.404023 | ||||||||
\(497\) | 1.53098e9 | 0.559398 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 4.83503e8 | 0.174200 | 0.0870998 | − | 0.996200i | \(-0.472240\pi\) | ||||
0.0870998 | + | 0.996200i | \(0.472240\pi\) | |||||||
\(500\) | 1.08941e9 | 0.389758 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −2.14561e9 | −0.756986 | ||||||||
\(503\) | 4.20389e9 | 1.47287 | 0.736434 | − | 0.676510i | \(-0.236508\pi\) | ||||
0.736434 | + | 0.676510i | \(0.236508\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.38807e9 | 0.825140 | ||||||||
\(506\) | −5.10682e8 | −0.175236 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.34642e9 | 0.455677 | ||||||||
\(509\) | 2.67771e9 | 0.900018 | 0.450009 | − | 0.893024i | \(-0.351421\pi\) | ||||
0.450009 | + | 0.893024i | \(0.351421\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.45169e9 | −0.481284 | ||||||||
\(512\) | −1.34218e8 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.37491e9 | −0.446585 | ||||||||
\(515\) | −8.39981e8 | −0.270984 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 3.36802e8 | 0.107191 | ||||||||
\(518\) | −3.46716e8 | −0.109602 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3.29871e8 | 0.102880 | ||||||||
\(521\) | 4.83951e9 | 1.49923 | 0.749616 | − | 0.661873i | \(-0.230238\pi\) | ||||
0.749616 | + | 0.661873i | \(0.230238\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.47019e8 | 0.197770 | 0.0988851 | − | 0.995099i | \(-0.468472\pi\) | ||||
0.0988851 | + | 0.995099i | \(0.468472\pi\) | |||||||
\(524\) | 1.32420e9 | 0.402062 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.61626e9 | 0.484242 | ||||||||
\(527\) | 3.26175e9 | 0.970765 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.91443e9 | 2.32448 | ||||||||
\(530\) | 1.71625e9 | 0.500743 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.91139e8 | 0.112626 | ||||||||
\(533\) | 6.02015e8 | 0.172212 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.37676e8 | −0.151804 | ||||||||
\(536\) | 1.03107e9 | 0.289210 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −7.79134e8 | −0.215712 | ||||||||
\(539\) | 4.08848e8 | 0.112461 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.47237e8 | −0.0942835 | −0.0471418 | − | 0.998888i | \(-0.515011\pi\) | ||||
−0.0471418 | + | 0.998888i | \(0.515011\pi\) | |||||||
\(542\) | −3.61556e9 | −0.975390 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 3.98721e8 | 0.106187 | ||||||||
\(545\) | 1.76489e8 | 0.0467014 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.88628e9 | −0.754021 | −0.377010 | − | 0.926209i | \(-0.623048\pi\) | ||||
−0.377010 | + | 0.926209i | \(0.623048\pi\) | |||||||
\(548\) | 3.40173e9 | 0.883016 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −3.05880e8 | −0.0783938 | ||||||||
\(551\) | −2.87285e9 | −0.731614 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 3.91036e8 | 0.0983284 | ||||||||
\(554\) | 1.67762e9 | 0.419189 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.24806e9 | −0.307945 | ||||||||
\(557\) | 8.74890e8 | 0.214516 | 0.107258 | − | 0.994231i | \(-0.465793\pi\) | ||||
0.107258 | + | 0.994231i | \(0.465793\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.17693e8 | −0.149565 | ||||||||
\(560\) | −1.85303e8 | −0.0445887 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 4.25763e9 | 1.01179 | ||||||||
\(563\) | 8.07444e9 | 1.90692 | 0.953462 | − | 0.301515i | \(-0.0974922\pi\) | ||||
0.953462 | + | 0.301515i | \(0.0974922\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.17344e8 | 0.0973474 | ||||||||
\(566\) | −3.79809e9 | −0.880456 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.07920e9 | −0.476078 | ||||||||
\(569\) | −5.50834e9 | −1.25351 | −0.626755 | − | 0.779216i | \(-0.715617\pi\) | ||||
−0.626755 | + | 0.779216i | \(0.715617\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.81462e9 | −0.632693 | −0.316347 | − | 0.948644i | \(-0.602456\pi\) | ||||
−0.316347 | + | 0.948644i | \(0.602456\pi\) | |||||||
\(572\) | −2.06170e8 | −0.0460615 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −3.38178e8 | −0.0746369 | ||||||||
\(575\) | 6.77983e9 | 1.48724 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −4.74376e9 | −1.02803 | −0.514017 | − | 0.857780i | \(-0.671843\pi\) | ||||
−0.514017 | + | 0.857780i | \(0.671843\pi\) | |||||||
\(578\) | 2.09823e9 | 0.451965 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.36102e9 | 0.289645 | ||||||||
\(581\) | −3.46975e9 | −0.733975 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.07266e9 | −0.224192 | ||||||||
\(584\) | 1.97153e9 | 0.409598 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.85695e9 | −0.381204 | ||||||||
\(587\) | −4.92039e9 | −1.00408 | −0.502038 | − | 0.864846i | \(-0.667416\pi\) | ||||
−0.502038 | + | 0.864846i | \(0.667416\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.34552e9 | −0.876271 | ||||||||
\(590\) | 1.71489e9 | 0.343759 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4.70872e8 | 0.0932775 | ||||||||
\(593\) | 1.96899e9 | 0.387750 | 0.193875 | − | 0.981026i | \(-0.437894\pi\) | ||||
0.193875 | + | 0.981026i | \(0.437894\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.50480e8 | 0.107135 | ||||||||
\(596\) | −5.45000e8 | −0.105447 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.56975e9 | 0.873853 | ||||||||
\(599\) | −8.28842e9 | −1.57572 | −0.787858 | − | 0.615857i | \(-0.788810\pi\) | ||||
−0.787858 | + | 0.615857i | \(0.788810\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 7.19345e9 | 1.35169 | 0.675844 | − | 0.737045i | \(-0.263779\pi\) | ||||
0.675844 | + | 0.737045i | \(0.263779\pi\) | |||||||
\(602\) | 3.46985e8 | 0.0648220 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 4.07693e9 | 0.752841 | ||||||||
\(605\) | 2.29526e9 | 0.421394 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.35656e9 | −0.972132 | −0.486066 | − | 0.873922i | \(-0.661569\pi\) | ||||
−0.486066 | + | 0.873922i | \(0.661569\pi\) | |||||||
\(608\) | −5.31202e8 | −0.0958511 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.25456e9 | −0.223789 | ||||||||
\(611\) | −3.01381e9 | −0.534530 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.01444e10 | −1.77874 | −0.889371 | − | 0.457187i | \(-0.848857\pi\) | ||||
−0.889371 | + | 0.457187i | \(0.848857\pi\) | |||||||
\(614\) | −6.02651e9 | −1.05069 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.15814e8 | 0.0199632 | ||||||||
\(617\) | 2.40428e9 | 0.412085 | 0.206043 | − | 0.978543i | \(-0.433941\pi\) | ||||
0.206043 | + | 0.978543i | \(0.433941\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −2.75619e9 | −0.467081 | −0.233541 | − | 0.972347i | \(-0.575031\pi\) | ||||
−0.233541 | + | 0.972347i | \(0.575031\pi\) | |||||||
\(620\) | 2.05870e9 | 0.346914 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 3.83823e9 | 0.639535 | ||||||||
\(623\) | 4.86068e8 | 0.0805357 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.93588e9 | 0.481014 | ||||||||
\(626\) | −5.24420e9 | −0.854415 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.07259e9 | −0.656163 | ||||||||
\(629\) | −1.39882e9 | −0.224122 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 3.92975e9 | 0.622676 | 0.311338 | − | 0.950299i | \(-0.399223\pi\) | ||||
0.311338 | + | 0.950299i | \(0.399223\pi\) | |||||||
\(632\) | −5.31062e8 | −0.0836827 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5.54689e9 | 0.864445 | ||||||||
\(635\) | −2.52453e9 | −0.391267 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.65851e9 | −0.560811 | ||||||||
\(638\) | −8.50637e8 | −0.129680 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 2.51658e8 | 0.0379473 | ||||||||
\(641\) | −1.21986e10 | −1.82939 | −0.914696 | − | 0.404143i | \(-0.867570\pi\) | ||||
−0.914696 | + | 0.404143i | \(0.867570\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 4.64582e8 | 0.0689166 | 0.0344583 | − | 0.999406i | \(-0.489029\pi\) | ||||
0.0344583 | + | 0.999406i | \(0.489029\pi\) | |||||||
\(644\) | −2.56703e9 | −0.378730 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.57804e9 | 0.230306 | ||||||||
\(647\) | −6.98889e9 | −1.01448 | −0.507239 | − | 0.861805i | \(-0.669334\pi\) | ||||
−0.507239 | + | 0.861805i | \(0.669334\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.07181e9 | −0.153908 | ||||||||
\(650\) | 2.73712e9 | 0.390928 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 4.39872e9 | 0.621527 | ||||||||
\(653\) | −3.44988e9 | −0.484850 | −0.242425 | − | 0.970170i | \(-0.577943\pi\) | ||||
−0.242425 | + | 0.970170i | \(0.577943\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.48287e9 | −0.345231 | ||||||||
\(656\) | 4.59276e8 | 0.0635200 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 1.69299e9 | 0.231667 | ||||||||
\(659\) | 9.87453e9 | 1.34406 | 0.672029 | − | 0.740525i | \(-0.265423\pi\) | ||||
0.672029 | + | 0.740525i | \(0.265423\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.22825e10 | −1.65417 | −0.827087 | − | 0.562075i | \(-0.810003\pi\) | ||||
−0.827087 | + | 0.562075i | \(0.810003\pi\) | |||||||
\(662\) | 1.47723e9 | 0.197899 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.71223e9 | 0.624652 | ||||||||
\(665\) | −7.33386e8 | −0.0967067 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.88544e10 | 2.46021 | ||||||||
\(668\) | −8.28379e8 | −0.107525 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.93326e9 | −0.248330 | ||||||||
\(671\) | 7.84102e8 | 0.100194 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.21233e9 | 1.16498 | 0.582488 | − | 0.812840i | \(-0.302079\pi\) | ||||
0.582488 | + | 0.812840i | \(0.302079\pi\) | |||||||
\(674\) | −6.75106e9 | −0.849303 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −2.17103e9 | −0.270304 | ||||||||
\(677\) | −3.74226e9 | −0.463525 | −0.231763 | − | 0.972772i | \(-0.574449\pi\) | ||||
−0.231763 | + | 0.972772i | \(0.574449\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3.22557e9 | 0.395423 | ||||||||
\(680\) | −7.47602e8 | −0.0911778 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.28669e9 | −0.155320 | ||||||||
\(683\) | 4.17620e9 | 0.501544 | 0.250772 | − | 0.968046i | \(-0.419316\pi\) | ||||
0.250772 | + | 0.968046i | \(0.419316\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −6.37825e9 | −0.758202 | ||||||||
\(686\) | 4.53895e9 | 0.536811 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −4.71237e8 | −0.0551670 | ||||||||
\(689\) | 9.59848e9 | 1.11798 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.94731e9 | −0.801020 | −0.400510 | − | 0.916292i | \(-0.631167\pi\) | ||||
−0.400510 | + | 0.916292i | \(0.631167\pi\) | |||||||
\(692\) | 2.70159e9 | 0.309919 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 9.77998e8 | 0.111066 | ||||||||
\(695\) | 2.34011e9 | 0.264417 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.36437e9 | −0.152622 | ||||||||
\(698\) | 8.42369e9 | 0.937580 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −1.53756e9 | −0.169429 | ||||||||
\(701\) | −9.64715e9 | −1.05776 | −0.528879 | − | 0.848697i | \(-0.677387\pi\) | ||||
−0.528879 | + | 0.848697i | \(0.677387\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.86360e9 | 0.202306 | ||||||||
\(704\) | −1.57286e8 | −0.0169897 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −4.99667e9 | −0.534398 | ||||||||
\(707\) | −7.50253e9 | −0.798435 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 7.72407e9 | 0.813925 | 0.406962 | − | 0.913445i | \(-0.366588\pi\) | ||||
0.406962 | + | 0.913445i | \(0.366588\pi\) | |||||||
\(710\) | 3.89851e9 | 0.408784 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −6.60124e8 | −0.0685402 | ||||||||
\(713\) | 2.85194e10 | 2.94664 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.86568e8 | 0.0395508 | ||||||||
\(716\) | −7.27294e9 | −0.740482 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6.36156e9 | −0.641398 | ||||||||
\(719\) | −1.11572e9 | −0.111945 | −0.0559725 | − | 0.998432i | \(-0.517826\pi\) | ||||
−0.0559725 | + | 0.998432i | \(0.517826\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.63894e9 | 0.262214 | ||||||||
\(722\) | 5.04860e9 | 0.499219 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −8.18700e9 | −0.801752 | ||||||||
\(725\) | 1.12931e10 | 1.10060 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.85026e9 | −0.757728 | −0.378864 | − | 0.925452i | \(-0.623685\pi\) | ||||
−0.378864 | + | 0.925452i | \(0.623685\pi\) | |||||||
\(728\) | −1.03635e9 | −0.0995508 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −3.69661e9 | −0.351701 | ||||||||
\(731\) | 1.39990e9 | 0.132552 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.43652e10 | −1.34725 | −0.673625 | − | 0.739073i | \(-0.735264\pi\) | ||||
−0.673625 | + | 0.739073i | \(0.735264\pi\) | |||||||
\(734\) | 8.75560e9 | 0.817240 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.48625e9 | 0.322319 | ||||||||
\(737\) | 1.20829e9 | 0.111182 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.13869e9 | 0.468379 | 0.234189 | − | 0.972191i | \(-0.424756\pi\) | ||||
0.234189 | + | 0.972191i | \(0.424756\pi\) | |||||||
\(740\) | −8.82885e8 | −0.0800927 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.39188e9 | −0.484537 | ||||||||
\(743\) | 1.12182e10 | 1.00338 | 0.501688 | − | 0.865049i | \(-0.332713\pi\) | ||||
0.501688 | + | 0.865049i | \(0.332713\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.02188e9 | 0.0905422 | ||||||||
\(746\) | −7.05635e9 | −0.622292 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.67251e8 | 0.0408221 | ||||||||
\(749\) | 1.68920e9 | 0.146891 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 2.16341e10 | 1.86380 | 0.931899 | − | 0.362717i | \(-0.118151\pi\) | ||||
0.931899 | + | 0.362717i | \(0.118151\pi\) | |||||||
\(752\) | −2.29923e9 | −0.197161 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 7.61178e9 | 0.646676 | ||||||||
\(755\) | −7.64424e9 | −0.646427 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.67963e10 | −1.40727 | −0.703635 | − | 0.710561i | \(-0.748441\pi\) | ||||
−0.703635 | + | 0.710561i | \(0.748441\pi\) | |||||||
\(758\) | 8.34005e9 | 0.695547 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 9.96004e8 | 0.0823026 | ||||||||
\(761\) | −2.41213e10 | −1.98406 | −0.992030 | − | 0.126002i | \(-0.959785\pi\) | ||||
−0.992030 | + | 0.126002i | \(0.959785\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.54470e8 | −0.0451900 | ||||||||
\(764\) | 1.34938e9 | 0.109473 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −6.69478e9 | −0.538190 | ||||||||
\(767\) | 9.59088e9 | 0.767494 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.66703e10 | 1.32191 | 0.660954 | − | 0.750426i | \(-0.270152\pi\) | ||||
0.660954 | + | 0.750426i | \(0.270152\pi\) | |||||||
\(770\) | −2.17152e8 | −0.0171414 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −8.94855e9 | −0.699990 | ||||||||
\(773\) | 1.34400e10 | 1.04658 | 0.523288 | − | 0.852156i | \(-0.324705\pi\) | ||||
0.523288 | + | 0.852156i | \(0.324705\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 1.70821e10 | 1.31821 | ||||||||
\(776\) | −4.38061e9 | −0.336526 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.17648e10 | −0.895685 | ||||||||
\(779\) | 1.81771e9 | 0.137766 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2.43657e9 | −0.183020 | ||||||||
\(782\) | −1.03566e10 | −0.774452 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.79107e9 | −0.206854 | ||||||||
\(785\) | 7.63611e9 | 0.563415 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.88162e10 | 1.37601 | 0.688004 | − | 0.725707i | \(-0.258487\pi\) | ||||
0.688004 | + | 0.725707i | \(0.258487\pi\) | |||||||
\(788\) | −9.34183e9 | −0.680127 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 9.95742e8 | 0.0718542 | ||||||||
\(791\) | −1.31115e9 | −0.0941968 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.01641e9 | −0.499642 | ||||||||
\(794\) | 1.01397e10 | 0.718876 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −3.27134e9 | −0.229895 | ||||||||
\(797\) | −5.78944e9 | −0.405072 | −0.202536 | − | 0.979275i | \(-0.564918\pi\) | ||||
−0.202536 | + | 0.979275i | \(0.564918\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 6.83034e9 | 0.473727 | ||||||||
\(800\) | 2.08814e9 | 0.144193 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4.22287e9 | 0.289066 | ||||||||
\(803\) | 2.31038e9 | 0.157463 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.81317e9 | 0.325197 | ||||||||
\(806\) | 1.15137e10 | 0.774538 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.01891e10 | 0.679511 | ||||||||
\(809\) | −2.81286e10 | −1.86779 | −0.933897 | − | 0.357543i | \(-0.883615\pi\) | ||||
−0.933897 | + | 0.357543i | \(0.883615\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.63925e9 | 0.437065 | 0.218532 | − | 0.975830i | \(-0.429873\pi\) | ||||
0.218532 | + | 0.975830i | \(0.429873\pi\) | |||||||
\(812\) | −4.27587e9 | −0.280271 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 5.51803e8 | 0.0358591 | ||||||||
\(815\) | −8.24761e9 | −0.533674 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.86504e9 | −0.119650 | ||||||||
\(818\) | 1.78233e9 | 0.113855 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −8.61143e8 | −0.0545415 | ||||||||
\(821\) | −5.35199e9 | −0.337532 | −0.168766 | − | 0.985656i | \(-0.553978\pi\) | ||||
−0.168766 | + | 0.985656i | \(0.553978\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.10559e9 | 0.0691343 | 0.0345672 | − | 0.999402i | \(-0.488995\pi\) | ||||
0.0345672 | + | 0.999402i | \(0.488995\pi\) | |||||||
\(824\) | −3.58392e9 | −0.223158 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −5.38761e9 | −0.332634 | ||||||||
\(827\) | −9.56978e9 | −0.588346 | −0.294173 | − | 0.955752i | \(-0.595044\pi\) | ||||
−0.294173 | + | 0.955752i | \(0.595044\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −2.36632e10 | −1.44256 | −0.721278 | − | 0.692646i | \(-0.756445\pi\) | ||||
−0.721278 | + | 0.692646i | \(0.756445\pi\) | |||||||
\(830\) | −8.83543e9 | −0.536357 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.40745e9 | 0.0847231 | ||||||||
\(833\) | 8.29145e9 | 0.497019 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.55321e9 | 0.0923267 | ||||||||
\(836\) | −6.22502e8 | −0.0368484 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −3.52465e9 | −0.206901 | ||||||||
\(839\) | −2.07240e10 | −1.21145 | −0.605726 | − | 0.795673i | \(-0.707117\pi\) | ||||
−0.605726 | + | 0.795673i | \(0.707117\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.41556e10 | 0.820622 | ||||||||
\(842\) | −1.75147e10 | −1.01114 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6.27544e9 | 0.359290 | ||||||||
\(845\) | 4.07068e9 | 0.232097 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −7.21094e9 | −0.407756 | ||||||||
\(848\) | 7.32266e9 | 0.412367 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −6.20325e9 | −0.346460 | ||||||||
\(851\) | −1.22307e10 | −0.680297 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.96254e10 | −1.08267 | −0.541336 | − | 0.840806i | \(-0.682081\pi\) | ||||
−0.541336 | + | 0.840806i | \(0.682081\pi\) | |||||||
\(854\) | 3.94142e9 | 0.216546 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −2.29408e9 | −0.125012 | ||||||||
\(857\) | −2.34086e10 | −1.27040 | −0.635202 | − | 0.772346i | \(-0.719083\pi\) | ||||
−0.635202 | + | 0.772346i | \(0.719083\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 6.37986e9 | 0.343428 | 0.171714 | − | 0.985147i | \(-0.445070\pi\) | ||||
0.171714 | + | 0.985147i | \(0.445070\pi\) | |||||||
\(860\) | 8.83569e8 | 0.0473692 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.42907e10 | 1.29171 | ||||||||
\(863\) | −1.63727e9 | −0.0867127 | −0.0433564 | − | 0.999060i | \(-0.513805\pi\) | ||||
−0.0433564 | + | 0.999060i | \(0.513805\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.06548e9 | −0.266112 | ||||||||
\(866\) | −1.77388e10 | −0.928134 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.46775e9 | −0.335687 | ||||||||
\(869\) | −6.22339e8 | −0.0321705 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.08122e10 | −0.554434 | ||||||||
\(872\) | 7.53020e8 | 0.0384591 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 1.37978e10 | 0.699067 | ||||||||
\(875\) | 6.41729e9 | 0.323835 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −3.31776e10 | −1.66091 | −0.830455 | − | 0.557085i | \(-0.811920\pi\) | ||||
−0.830455 | + | 0.557085i | \(0.811920\pi\) | |||||||
\(878\) | 2.00075e10 | 0.997613 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.94912e8 | 0.0145882 | ||||||||
\(881\) | 5.88175e9 | 0.289795 | 0.144897 | − | 0.989447i | \(-0.453715\pi\) | ||||
0.144897 | + | 0.989447i | \(0.453715\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 5.84882e9 | 0.285894 | 0.142947 | − | 0.989730i | \(-0.454342\pi\) | ||||
0.142947 | + | 0.989730i | \(0.454342\pi\) | |||||||
\(884\) | −4.18112e9 | −0.203568 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.92310e10 | −0.928930 | ||||||||
\(887\) | 7.81095e9 | 0.375813 | 0.187906 | − | 0.982187i | \(-0.439830\pi\) | ||||
0.187906 | + | 0.982187i | \(0.439830\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 7.93124e9 | 0.378604 | ||||||||
\(890\) | 1.23773e9 | 0.0588520 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 1.38725e10 | 0.654453 | ||||||||
\(893\) | −9.09982e9 | −0.427615 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.36368e10 | 0.635815 | ||||||||
\(896\) | −7.90626e8 | −0.0367192 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.71948e10 | 0.792375 | ||||||||
\(899\) | 4.75045e10 | 2.18060 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.17535e10 | −0.990813 | ||||||||
\(902\) | 5.38214e8 | 0.0244193 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.78067e9 | 0.0801665 | ||||||||
\(905\) | 1.53506e10 | 0.688424 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.12701e10 | −1.83658 | −0.918289 | − | 0.395910i | \(-0.870429\pi\) | ||||
−0.918289 | + | 0.395910i | \(0.870429\pi\) | |||||||
\(908\) | 8.95134e9 | 0.396814 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 1.94315e9 | 0.0854793 | ||||||||
\(911\) | −6.66422e9 | −0.292035 | −0.146017 | − | 0.989282i | \(-0.546646\pi\) | ||||
−0.146017 | + | 0.989282i | \(0.546646\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.52214e9 | 0.240137 | ||||||||
\(914\) | −1.84127e10 | −0.797637 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −6.07724e9 | −0.261260 | ||||||||
\(917\) | 7.80035e9 | 0.334058 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 5.45018e9 | 0.231636 | 0.115818 | − | 0.993270i | \(-0.463051\pi\) | ||||
0.115818 | + | 0.993270i | \(0.463051\pi\) | |||||||
\(920\) | −6.53672e9 | −0.276760 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.10342e10 | 0.463642 | ||||||||
\(923\) | 2.18032e10 | 0.912671 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.32576e9 | −0.304338 | ||||||||
\(926\) | 1.37643e10 | 0.569660 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 5.80701e9 | 0.238526 | ||||||||
\(929\) | −7.78356e9 | −0.318510 | −0.159255 | − | 0.987237i | \(-0.550909\pi\) | ||||
−0.159255 | + | 0.987237i | \(0.550909\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.10464e10 | −0.448639 | ||||||||
\(932\) | 1.35007e10 | 0.546261 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.27000e10 | 0.510022 | ||||||||
\(935\) | −8.76096e8 | −0.0350519 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.59669e10 | 1.82539 | 0.912697 | − | 0.408638i | \(-0.133996\pi\) | ||||
0.912697 | + | 0.408638i | \(0.133996\pi\) | |||||||
\(938\) | 6.07367e9 | 0.240293 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 4.31106e9 | 0.169292 | ||||||||
\(941\) | 1.63152e10 | 0.638305 | 0.319152 | − | 0.947703i | \(-0.396602\pi\) | ||||
0.319152 | + | 0.947703i | \(0.396602\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.19295e10 | −0.463268 | ||||||||
\(944\) | 7.31687e9 | 0.283089 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −5.52230e8 | −0.0212081 | ||||||||
\(947\) | −3.13934e10 | −1.20119 | −0.600597 | − | 0.799552i | \(-0.705071\pi\) | ||||
−0.600597 | + | 0.799552i | \(0.705071\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.06741e10 | −0.785226 | ||||||||
\(950\) | 8.26437e9 | 0.312735 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.34872e9 | 0.0882269 | ||||||||
\(953\) | 4.82350e10 | 1.80525 | 0.902625 | − | 0.430428i | \(-0.141637\pi\) | ||||
0.902625 | + | 0.430428i | \(0.141637\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.53008e9 | −0.0939989 | ||||||||
\(956\) | 8.26572e9 | 0.305969 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 1.40536e10 | 0.516425 | ||||||||
\(959\) | 2.00383e10 | 0.733663 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.43435e10 | 1.61175 | ||||||||
\(962\) | −4.93772e9 | −0.178819 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.57195e9 | −0.0924685 | ||||||||
\(965\) | 1.67785e10 | 0.601047 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.22238e9 | 0.114600 | 0.0572999 | − | 0.998357i | \(-0.481751\pi\) | ||||
0.0572999 | + | 0.998357i | \(0.481751\pi\) | |||||||
\(968\) | 9.79311e9 | 0.347022 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 8.21365e9 | 0.288958 | ||||||||
\(971\) | −2.25397e10 | −0.790096 | −0.395048 | − | 0.918660i | \(-0.629272\pi\) | ||||
−0.395048 | + | 0.918660i | \(0.629272\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −7.35184e9 | −0.255859 | ||||||||
\(974\) | −1.21603e10 | −0.421685 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −5.35280e9 | −0.184292 | ||||||||
\(977\) | −4.31576e10 | −1.48056 | −0.740280 | − | 0.672298i | \(-0.765307\pi\) | ||||
−0.740280 | + | 0.672298i | \(0.765307\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.73582e8 | −0.0263492 | ||||||||
\(980\) | 5.23326e9 | 0.177616 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 2.91859e10 | 0.983519 | ||||||||
\(983\) | 2.28659e10 | 0.767806 | 0.383903 | − | 0.923373i | \(-0.374580\pi\) | ||||
0.383903 | + | 0.923373i | \(0.374580\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 1.75159e10 | 0.583991 | ||||||||
\(986\) | −1.72509e10 | −0.573117 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.57036e9 | 0.183753 | ||||||||
\(989\) | 1.22402e10 | 0.402347 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.13727e10 | 0.371198 | 0.185599 | − | 0.982626i | \(-0.440577\pi\) | ||||
0.185599 | + | 0.982626i | \(0.440577\pi\) | |||||||
\(992\) | 8.78379e9 | 0.285687 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −1.22478e10 | −0.395554 | ||||||||
\(995\) | 6.13376e9 | 0.197399 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.31535e10 | −1.37906 | −0.689530 | − | 0.724257i | \(-0.742183\pi\) | ||||
−0.689530 | + | 0.724257i | \(0.742183\pi\) | |||||||
\(998\) | −3.86802e9 | −0.123178 | ||||||||
\(999\) | 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 | 54.8.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 54.8.a.f.1.1 | yes | 1 | ||
4.3 | odd | 2 | 432.8.a.b.1.1 | 1 | |||
9.2 | odd | 6 | 162.8.c.b.109.1 | 2 | |||
9.4 | even | 3 | 162.8.c.k.55.1 | 2 | |||
9.5 | odd | 6 | 162.8.c.b.55.1 | 2 | |||
9.7 | even | 3 | 162.8.c.k.109.1 | 2 | |||
12.11 | even | 2 | 432.8.a.g.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
54.8.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
54.8.a.f.1.1 | yes | 1 | 3.2 | odd | 2 | ||
162.8.c.b.55.1 | 2 | 9.5 | odd | 6 | |||
162.8.c.b.109.1 | 2 | 9.2 | odd | 6 | |||
162.8.c.k.55.1 | 2 | 9.4 | even | 3 | |||
162.8.c.k.109.1 | 2 | 9.7 | even | 3 | |||
432.8.a.b.1.1 | 1 | 4.3 | odd | 2 | |||
432.8.a.g.1.1 | 1 | 12.11 | even | 2 |