Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [531,8,Mod(1,531)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(531, 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("531.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 531 = 3^{2} \cdot 59 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 531.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: | \(165.876448532\) |
Analytic rank: | \(0\) |
Dimension: | \(17\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{17} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{17} - 2 x^{16} - 1639 x^{15} + 1625 x^{14} + 1070274 x^{13} - 274939 x^{12} - 357079564 x^{11} - 89298188 x^{10} + 64650816672 x^{9} + \cdots - 58\!\cdots\!76 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | multiple of \( 2^{10}\cdot 3^{5} \) |
Twist minimal: | no (minimal twist has level 177) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(18.2619\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 531.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −16.2619 | −1.43737 | −0.718683 | − | 0.695338i | \(-0.755255\pi\) | ||||
−0.718683 | + | 0.695338i | \(0.755255\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 136.450 | 1.06602 | ||||||||
\(5\) | 30.6671 | 0.109718 | 0.0548590 | − | 0.998494i | \(-0.482529\pi\) | ||||
0.0548590 | + | 0.998494i | \(0.482529\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1356.62 | −1.49491 | −0.747455 | − | 0.664313i | \(-0.768724\pi\) | ||||
−0.747455 | + | 0.664313i | \(0.768724\pi\) | |||||||
\(8\) | −137.421 | −0.0948936 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −498.706 | −0.157705 | ||||||||
\(11\) | −1825.79 | −0.413595 | −0.206798 | − | 0.978384i | \(-0.566304\pi\) | ||||
−0.206798 | + | 0.978384i | \(0.566304\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1173.55 | −0.148150 | −0.0740750 | − | 0.997253i | \(-0.523600\pi\) | ||||
−0.0740750 | + | 0.997253i | \(0.523600\pi\) | |||||||
\(14\) | 22061.2 | 2.14873 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −15230.9 | −0.929622 | ||||||||
\(17\) | −13185.9 | −0.650937 | −0.325468 | − | 0.945553i | \(-0.605522\pi\) | ||||
−0.325468 | + | 0.945553i | \(0.605522\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −18595.5 | −0.621971 | −0.310985 | − | 0.950415i | \(-0.600659\pi\) | ||||
−0.310985 | + | 0.950415i | \(0.600659\pi\) | |||||||
\(20\) | 4184.54 | 0.116961 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 29690.8 | 0.594488 | ||||||||
\(23\) | 14566.3 | 0.249633 | 0.124817 | − | 0.992180i | \(-0.460166\pi\) | ||||
0.124817 | + | 0.992180i | \(0.460166\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −77184.5 | −0.987962 | ||||||||
\(26\) | 19084.3 | 0.212946 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −185111. | −1.59360 | ||||||||
\(29\) | 183281. | 1.39549 | 0.697743 | − | 0.716348i | \(-0.254188\pi\) | ||||
0.697743 | + | 0.716348i | \(0.254188\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −265230. | −1.59903 | −0.799515 | − | 0.600646i | \(-0.794910\pi\) | ||||
−0.799515 | + | 0.600646i | \(0.794910\pi\) | |||||||
\(32\) | 265274. | 1.43110 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 214428. | 0.935634 | ||||||||
\(35\) | −41603.6 | −0.164018 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −260898. | −0.846769 | −0.423385 | − | 0.905950i | \(-0.639158\pi\) | ||||
−0.423385 | + | 0.905950i | \(0.639158\pi\) | |||||||
\(38\) | 302399. | 0.893999 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −4214.29 | −0.0104115 | ||||||||
\(41\) | −719268. | −1.62985 | −0.814924 | − | 0.579568i | \(-0.803221\pi\) | ||||
−0.814924 | + | 0.579568i | \(0.803221\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −707870. | −1.35773 | −0.678866 | − | 0.734262i | \(-0.737528\pi\) | ||||
−0.678866 | + | 0.734262i | \(0.737528\pi\) | |||||||
\(44\) | −249129. | −0.440900 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −236876. | −0.358814 | ||||||||
\(47\) | −1.30218e6 | −1.82948 | −0.914742 | − | 0.404038i | \(-0.867606\pi\) | ||||
−0.914742 | + | 0.404038i | \(0.867606\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.01687e6 | 1.23475 | ||||||||
\(50\) | 1.25517e6 | 1.42006 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −160132. | −0.157931 | ||||||||
\(53\) | 1.80784e6 | 1.66799 | 0.833996 | − | 0.551770i | \(-0.186047\pi\) | ||||
0.833996 | + | 0.551770i | \(0.186047\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −55991.6 | −0.0453788 | ||||||||
\(56\) | 186427. | 0.141857 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.98051e6 | −2.00582 | ||||||||
\(59\) | 205379. | 0.130189 | ||||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 1.38182e6 | 0.779468 | 0.389734 | − | 0.920928i | \(-0.372567\pi\) | ||||
0.389734 | + | 0.920928i | \(0.372567\pi\) | |||||||
\(62\) | 4.31315e6 | 2.29839 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −2.36431e6 | −1.12739 | ||||||||
\(65\) | −35989.5 | −0.0162547 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.41963e6 | 0.982849 | 0.491424 | − | 0.870920i | \(-0.336476\pi\) | ||||
0.491424 | + | 0.870920i | \(0.336476\pi\) | |||||||
\(68\) | −1.79922e6 | −0.693911 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 676555. | 0.235754 | ||||||||
\(71\) | −2.72507e6 | −0.903595 | −0.451797 | − | 0.892121i | \(-0.649217\pi\) | ||||
−0.451797 | + | 0.892121i | \(0.649217\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.97598e6 | 1.19623 | 0.598115 | − | 0.801411i | \(-0.295917\pi\) | ||||
0.598115 | + | 0.801411i | \(0.295917\pi\) | |||||||
\(74\) | 4.24271e6 | 1.21712 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.53736e6 | −0.663033 | ||||||||
\(77\) | 2.47690e6 | 0.618287 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.91787e6 | −1.57862 | −0.789310 | − | 0.613995i | \(-0.789562\pi\) | ||||
−0.789310 | + | 0.613995i | \(0.789562\pi\) | |||||||
\(80\) | −467089. | −0.101996 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.16967e7 | 2.34269 | ||||||||
\(83\) | −8.32910e6 | −1.59891 | −0.799456 | − | 0.600725i | \(-0.794879\pi\) | ||||
−0.799456 | + | 0.600725i | \(0.794879\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −404374. | −0.0714195 | ||||||||
\(86\) | 1.15113e7 | 1.95156 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 250901. | 0.0392476 | ||||||||
\(89\) | 6.71890e6 | 1.01026 | 0.505130 | − | 0.863043i | \(-0.331444\pi\) | ||||
0.505130 | + | 0.863043i | \(0.331444\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 1.59207e6 | 0.221471 | ||||||||
\(92\) | 1.98758e6 | 0.266114 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 2.11760e7 | 2.62964 | ||||||||
\(95\) | −570270. | −0.0682414 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.77557e6 | −0.531281 | −0.265640 | − | 0.964072i | \(-0.585583\pi\) | ||||
−0.265640 | + | 0.964072i | \(0.585583\pi\) | |||||||
\(98\) | −1.65363e7 | −1.77479 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −1.05319e7 | −1.05319 | ||||||||
\(101\) | −1.79352e7 | −1.73213 | −0.866066 | − | 0.499930i | \(-0.833359\pi\) | ||||
−0.866066 | + | 0.499930i | \(0.833359\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.83344e7 | −1.65324 | −0.826619 | − | 0.562762i | \(-0.809739\pi\) | ||||
−0.826619 | + | 0.562762i | \(0.809739\pi\) | |||||||
\(104\) | 161271. | 0.0140585 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2.93990e7 | −2.39752 | ||||||||
\(107\) | −1.58268e7 | −1.24896 | −0.624480 | − | 0.781041i | \(-0.714689\pi\) | ||||
−0.624480 | + | 0.781041i | \(0.714689\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.43687e6 | 0.328159 | 0.164079 | − | 0.986447i | \(-0.447535\pi\) | ||||
0.164079 | + | 0.986447i | \(0.447535\pi\) | |||||||
\(110\) | 910531. | 0.0652260 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 2.06626e7 | 1.38970 | ||||||||
\(113\) | −2.03544e7 | −1.32704 | −0.663520 | − | 0.748159i | \(-0.730938\pi\) | ||||
−0.663520 | + | 0.748159i | \(0.730938\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 446707. | 0.0273892 | ||||||||
\(116\) | 2.50088e7 | 1.48761 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −3.33986e6 | −0.187129 | ||||||||
\(119\) | 1.78883e7 | 0.973091 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.61537e7 | −0.828939 | ||||||||
\(122\) | −2.24711e7 | −1.12038 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −3.61907e7 | −1.70460 | ||||||||
\(125\) | −4.76289e6 | −0.218115 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.80807e6 | −0.424884 | −0.212442 | − | 0.977174i | \(-0.568142\pi\) | ||||
−0.212442 | + | 0.977174i | \(0.568142\pi\) | |||||||
\(128\) | 4.49319e6 | 0.189374 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 585259. | 0.0233640 | ||||||||
\(131\) | 2.55344e7 | 0.992377 | 0.496189 | − | 0.868215i | \(-0.334732\pi\) | ||||
0.496189 | + | 0.868215i | \(0.334732\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 2.52270e7 | 0.929790 | ||||||||
\(134\) | −3.93478e7 | −1.41271 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.81202e6 | 0.0617698 | ||||||||
\(137\) | 5.60036e6 | 0.186078 | 0.0930388 | − | 0.995662i | \(-0.470342\pi\) | ||||
0.0930388 | + | 0.995662i | \(0.470342\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −994215. | −0.0313999 | −0.0157000 | − | 0.999877i | \(-0.504998\pi\) | ||||
−0.0157000 | + | 0.999877i | \(0.504998\pi\) | |||||||
\(140\) | −5.67683e6 | −0.174847 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 4.43149e7 | 1.29880 | ||||||||
\(143\) | 2.14266e6 | 0.0612741 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.62071e6 | 0.153110 | ||||||||
\(146\) | −6.46572e7 | −1.71942 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.55997e7 | −0.902672 | ||||||||
\(149\) | −2.61359e7 | −0.647269 | −0.323635 | − | 0.946182i | \(-0.604905\pi\) | ||||
−0.323635 | + | 0.946182i | \(0.604905\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.02885e7 | −1.66136 | −0.830682 | − | 0.556747i | \(-0.812049\pi\) | ||||
−0.830682 | + | 0.556747i | \(0.812049\pi\) | |||||||
\(152\) | 2.55540e6 | 0.0590211 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.02791e7 | −0.888705 | ||||||||
\(155\) | −8.13383e6 | −0.175442 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.28654e7 | −0.471553 | −0.235776 | − | 0.971807i | \(-0.575763\pi\) | ||||
−0.235776 | + | 0.971807i | \(0.575763\pi\) | |||||||
\(158\) | 1.12498e8 | 2.26905 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 8.13519e6 | 0.157017 | ||||||||
\(161\) | −1.97609e7 | −0.373179 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −6.26397e7 | −1.13290 | −0.566452 | − | 0.824095i | \(-0.691684\pi\) | ||||
−0.566452 | + | 0.824095i | \(0.691684\pi\) | |||||||
\(164\) | −9.81444e7 | −1.73745 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.35447e8 | 2.29822 | ||||||||
\(167\) | 2.02935e7 | 0.337171 | 0.168586 | − | 0.985687i | \(-0.446080\pi\) | ||||
0.168586 | + | 0.985687i | \(0.446080\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.13713e7 | −0.978052 | ||||||||
\(170\) | 6.57590e6 | 0.102656 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −9.65892e7 | −1.44737 | ||||||||
\(173\) | 4.43065e7 | 0.650588 | 0.325294 | − | 0.945613i | \(-0.394537\pi\) | ||||
0.325294 | + | 0.945613i | \(0.394537\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.04710e8 | 1.47691 | ||||||||
\(176\) | 2.78084e7 | 0.384487 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.09262e8 | −1.45211 | ||||||||
\(179\) | −1.30339e8 | −1.69858 | −0.849292 | − | 0.527923i | \(-0.822971\pi\) | ||||
−0.849292 | + | 0.527923i | \(0.822971\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.67394e7 | −1.08728 | −0.543640 | − | 0.839319i | \(-0.682954\pi\) | ||||
−0.543640 | + | 0.839319i | \(0.682954\pi\) | |||||||
\(182\) | −2.58901e7 | −0.318334 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2.00171e6 | −0.0236886 | ||||||||
\(185\) | −8.00099e6 | −0.0929058 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.40746e7 | 0.269224 | ||||||||
\(188\) | −1.77683e8 | −1.95027 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.27369e6 | 0.0980878 | ||||||||
\(191\) | 1.00406e8 | 1.04266 | 0.521330 | − | 0.853355i | \(-0.325436\pi\) | ||||
0.521330 | + | 0.853355i | \(0.325436\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.63066e8 | 1.63272 | 0.816361 | − | 0.577542i | \(-0.195988\pi\) | ||||
0.816361 | + | 0.577542i | \(0.195988\pi\) | |||||||
\(194\) | 7.76600e7 | 0.763645 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.38753e8 | 1.31627 | ||||||||
\(197\) | −1.22832e8 | −1.14467 | −0.572335 | − | 0.820020i | \(-0.693962\pi\) | ||||
−0.572335 | + | 0.820020i | \(0.693962\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.85902e8 | 1.67224 | 0.836119 | − | 0.548549i | \(-0.184820\pi\) | ||||
0.836119 | + | 0.548549i | \(0.184820\pi\) | |||||||
\(200\) | 1.06067e7 | 0.0937513 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 2.91661e8 | 2.48971 | ||||||||
\(203\) | −2.48643e8 | −2.08612 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −2.20579e7 | −0.178824 | ||||||||
\(206\) | 2.98152e8 | 2.37631 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.78743e7 | 0.137724 | ||||||||
\(209\) | 3.39514e7 | 0.257244 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 4.25639e6 | 0.0311927 | 0.0155963 | − | 0.999878i | \(-0.495035\pi\) | ||||
0.0155963 | + | 0.999878i | \(0.495035\pi\) | |||||||
\(212\) | 2.46680e8 | 1.77811 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.57374e8 | 1.79521 | ||||||||
\(215\) | −2.17083e7 | −0.148968 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.59816e8 | 2.39040 | ||||||||
\(218\) | −7.21521e7 | −0.471684 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −7.64008e6 | −0.0483747 | ||||||||
\(221\) | 1.54744e7 | 0.0964362 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.01090e8 | −0.610437 | −0.305219 | − | 0.952282i | \(-0.598730\pi\) | ||||
−0.305219 | + | 0.952282i | \(0.598730\pi\) | |||||||
\(224\) | −3.59876e8 | −2.13937 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.31002e8 | 1.90744 | ||||||||
\(227\) | 1.56725e8 | 0.889299 | 0.444650 | − | 0.895705i | \(-0.353328\pi\) | ||||
0.444650 | + | 0.895705i | \(0.353328\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.30104e8 | 1.26619 | 0.633097 | − | 0.774072i | \(-0.281783\pi\) | ||||
0.633097 | + | 0.774072i | \(0.281783\pi\) | |||||||
\(230\) | −7.26431e6 | −0.0393683 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.51866e7 | −0.132423 | ||||||||
\(233\) | −9.45434e7 | −0.489649 | −0.244825 | − | 0.969567i | \(-0.578730\pi\) | ||||
−0.244825 | + | 0.969567i | \(0.578730\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.99341e7 | −0.200727 | ||||||||
\(236\) | 2.80241e7 | 0.138784 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2.90898e8 | −1.39869 | ||||||||
\(239\) | 2.18199e8 | 1.03385 | 0.516927 | − | 0.856029i | \(-0.327076\pi\) | ||||
0.516927 | + | 0.856029i | \(0.327076\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −7.52814e7 | −0.346440 | −0.173220 | − | 0.984883i | \(-0.555417\pi\) | ||||
−0.173220 | + | 0.984883i | \(0.555417\pi\) | |||||||
\(242\) | 2.62690e8 | 1.19149 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.88550e8 | 0.830927 | ||||||||
\(245\) | 3.11845e7 | 0.135475 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.18228e7 | 0.0921450 | ||||||||
\(248\) | 3.64481e7 | 0.151738 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 7.74539e7 | 0.313511 | ||||||||
\(251\) | 2.48536e8 | 0.992046 | 0.496023 | − | 0.868309i | \(-0.334793\pi\) | ||||
0.496023 | + | 0.868309i | \(0.334793\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.65950e7 | −0.103247 | ||||||||
\(254\) | 1.59498e8 | 0.610714 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 2.29564e8 | 0.855193 | ||||||||
\(257\) | −9.48986e7 | −0.348734 | −0.174367 | − | 0.984681i | \(-0.555788\pi\) | ||||
−0.174367 | + | 0.984681i | \(0.555788\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 3.53939e8 | 1.26584 | ||||||||
\(260\) | −4.91079e6 | −0.0173278 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.15239e8 | −1.42641 | ||||||||
\(263\) | −7.74187e7 | −0.262422 | −0.131211 | − | 0.991354i | \(-0.541887\pi\) | ||||
−0.131211 | + | 0.991354i | \(0.541887\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5.54412e7 | 0.183009 | ||||||||
\(266\) | −4.10240e8 | −1.33645 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.30159e8 | 1.04774 | ||||||||
\(269\) | 1.48368e8 | 0.464738 | 0.232369 | − | 0.972628i | \(-0.425352\pi\) | ||||
0.232369 | + | 0.972628i | \(0.425352\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.14037e8 | 0.653275 | 0.326637 | − | 0.945150i | \(-0.394084\pi\) | ||||
0.326637 | + | 0.945150i | \(0.394084\pi\) | |||||||
\(272\) | 2.00834e8 | 0.605125 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.10727e7 | −0.267462 | ||||||||
\(275\) | 1.40922e8 | 0.408616 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.49384e8 | −1.27039 | −0.635196 | − | 0.772351i | \(-0.719081\pi\) | ||||
−0.635196 | + | 0.772351i | \(0.719081\pi\) | |||||||
\(278\) | 1.61679e7 | 0.0451331 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.71719e6 | 0.0155643 | ||||||||
\(281\) | −5.47292e7 | −0.147145 | −0.0735727 | − | 0.997290i | \(-0.523440\pi\) | ||||
−0.0735727 | + | 0.997290i | \(0.523440\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −6.96310e8 | −1.82621 | −0.913104 | − | 0.407727i | \(-0.866322\pi\) | ||||
−0.913104 | + | 0.407727i | \(0.866322\pi\) | |||||||
\(284\) | −3.71837e8 | −0.963249 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −3.48438e7 | −0.0880733 | ||||||||
\(287\) | 9.75773e8 | 2.43648 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.36471e8 | −0.576281 | ||||||||
\(290\) | −9.14036e7 | −0.220075 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 5.42525e8 | 1.27520 | ||||||||
\(293\) | 1.58823e8 | 0.368874 | 0.184437 | − | 0.982844i | \(-0.440954\pi\) | ||||
0.184437 | + | 0.982844i | \(0.440954\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 6.29838e6 | 0.0142841 | ||||||||
\(296\) | 3.58528e7 | 0.0803530 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 4.25020e8 | 0.930363 | ||||||||
\(299\) | −1.70944e7 | −0.0369831 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 9.60310e8 | 2.02969 | ||||||||
\(302\) | 1.14303e9 | 2.38799 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 2.83227e8 | 0.578198 | ||||||||
\(305\) | 4.23765e7 | 0.0855216 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.01551e8 | 0.397558 | 0.198779 | − | 0.980044i | \(-0.436302\pi\) | ||||
0.198779 | + | 0.980044i | \(0.436302\pi\) | |||||||
\(308\) | 3.37974e8 | 0.659106 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 1.32272e8 | 0.252175 | ||||||||
\(311\) | −3.80395e8 | −0.717090 | −0.358545 | − | 0.933513i | \(-0.616727\pi\) | ||||
−0.358545 | + | 0.933513i | \(0.616727\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.43971e8 | 0.265382 | 0.132691 | − | 0.991157i | \(-0.457638\pi\) | ||||
0.132691 | + | 0.991157i | \(0.457638\pi\) | |||||||
\(314\) | 3.71836e8 | 0.677794 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.43947e8 | −1.68284 | ||||||||
\(317\) | 3.85345e8 | 0.679426 | 0.339713 | − | 0.940529i | \(-0.389670\pi\) | ||||
0.339713 | + | 0.940529i | \(0.389670\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.34633e8 | −0.577166 | ||||||||
\(320\) | −7.25066e7 | −0.123695 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.21351e8 | 0.536394 | ||||||||
\(323\) | 2.45198e8 | 0.404864 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 9.05803e7 | 0.146367 | ||||||||
\(326\) | 1.01864e9 | 1.62840 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 9.88423e7 | 0.154662 | ||||||||
\(329\) | 1.76656e9 | 2.73491 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −5.09634e8 | −0.772432 | −0.386216 | − | 0.922408i | \(-0.626218\pi\) | ||||
−0.386216 | + | 0.922408i | \(0.626218\pi\) | |||||||
\(332\) | −1.13651e9 | −1.70447 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −3.30012e8 | −0.484638 | ||||||||
\(335\) | 7.42030e7 | 0.107836 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3.29994e8 | 0.469679 | 0.234840 | − | 0.972034i | \(-0.424543\pi\) | ||||
0.234840 | + | 0.972034i | \(0.424543\pi\) | |||||||
\(338\) | 9.98016e8 | 1.40582 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −5.51770e7 | −0.0761345 | ||||||||
\(341\) | 4.84253e8 | 0.661351 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.62274e8 | −0.350935 | ||||||||
\(344\) | 9.72760e7 | 0.128840 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.20510e8 | −0.935133 | ||||||||
\(347\) | 1.54205e9 | 1.98128 | 0.990642 | − | 0.136488i | \(-0.0435816\pi\) | ||||
0.990642 | + | 0.136488i | \(0.0435816\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.37260e8 | −0.424694 | −0.212347 | − | 0.977194i | \(-0.568111\pi\) | ||||
−0.212347 | + | 0.977194i | \(0.568111\pi\) | |||||||
\(350\) | −1.70279e9 | −2.12286 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −4.84334e8 | −0.591896 | ||||||||
\(353\) | 8.38966e8 | 1.01516 | 0.507578 | − | 0.861606i | \(-0.330541\pi\) | ||||
0.507578 | + | 0.861606i | \(0.330541\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8.35701e7 | −0.0991406 | ||||||||
\(356\) | 9.16797e8 | 1.07696 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 2.11956e9 | 2.44149 | ||||||||
\(359\) | 5.75290e8 | 0.656231 | 0.328115 | − | 0.944638i | \(-0.393587\pi\) | ||||
0.328115 | + | 0.944638i | \(0.393587\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −5.48079e8 | −0.613152 | ||||||||
\(362\) | 1.41055e9 | 1.56282 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 2.17238e8 | 0.236092 | ||||||||
\(365\) | 1.21932e8 | 0.131248 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.63254e8 | −0.172398 | −0.0861990 | − | 0.996278i | \(-0.527472\pi\) | ||||
−0.0861990 | + | 0.996278i | \(0.527472\pi\) | |||||||
\(368\) | −2.21859e8 | −0.232065 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.30112e8 | 0.133540 | ||||||||
\(371\) | −2.45255e9 | −2.49350 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −5.02935e8 | −0.501801 | −0.250900 | − | 0.968013i | \(-0.580727\pi\) | ||||
−0.250900 | + | 0.968013i | \(0.580727\pi\) | |||||||
\(374\) | −3.91500e8 | −0.386974 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 1.78947e8 | 0.173606 | ||||||||
\(377\) | −2.15091e8 | −0.206741 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.84658e9 | 1.74234 | 0.871168 | − | 0.490986i | \(-0.163363\pi\) | ||||
0.871168 | + | 0.490986i | \(0.163363\pi\) | |||||||
\(380\) | −7.78136e7 | −0.0727466 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.63279e9 | −1.49868 | ||||||||
\(383\) | −78579.0 | −7.14679e−5 0 | −3.57339e−5 | − | 1.00000i | \(-0.500011\pi\) | ||||
−3.57339e−5 | 1.00000i | \(0.500011\pi\) | ||||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 7.59593e7 | 0.0678372 | ||||||||
\(386\) | −2.65176e9 | −2.34682 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −6.51629e8 | −0.566355 | ||||||||
\(389\) | −1.01883e9 | −0.877561 | −0.438780 | − | 0.898594i | \(-0.644589\pi\) | ||||
−0.438780 | + | 0.898594i | \(0.644589\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.92070e8 | −0.162495 | ||||||||
\(392\) | −1.39739e8 | −0.117170 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.99749e9 | 1.64531 | ||||||||
\(395\) | −2.12151e8 | −0.173203 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.45551e8 | 0.277170 | 0.138585 | − | 0.990351i | \(-0.455745\pi\) | ||||
0.138585 | + | 0.990351i | \(0.455745\pi\) | |||||||
\(398\) | −3.02312e9 | −2.40362 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.17559e9 | 0.918431 | ||||||||
\(401\) | 2.15091e9 | 1.66578 | 0.832890 | − | 0.553439i | \(-0.186685\pi\) | ||||
0.832890 | + | 0.553439i | \(0.186685\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.11262e8 | 0.236896 | ||||||||
\(404\) | −2.44726e9 | −1.84649 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 4.04342e9 | 2.99852 | ||||||||
\(407\) | 4.76344e8 | 0.350220 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.23244e8 | −0.161342 | −0.0806710 | − | 0.996741i | \(-0.525706\pi\) | ||||
−0.0806710 | + | 0.996741i | \(0.525706\pi\) | |||||||
\(410\) | 3.58704e8 | 0.257035 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −2.50173e9 | −1.76238 | ||||||||
\(413\) | −2.78621e8 | −0.194621 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.55429e8 | −0.175429 | ||||||||
\(416\) | −3.11314e8 | −0.212017 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5.52115e8 | −0.369754 | ||||||||
\(419\) | 1.16588e9 | 0.774291 | 0.387146 | − | 0.922019i | \(-0.373461\pi\) | ||||
0.387146 | + | 0.922019i | \(0.373461\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −9.44097e8 | −0.616637 | −0.308318 | − | 0.951283i | \(-0.599766\pi\) | ||||
−0.308318 | + | 0.951283i | \(0.599766\pi\) | |||||||
\(422\) | −6.92171e7 | −0.0448353 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −2.48434e8 | −0.158282 | ||||||||
\(425\) | 1.01775e9 | 0.643101 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.87461e9 | −1.16523 | ||||||||
\(428\) | −2.15957e9 | −1.33142 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.53019e8 | 0.214121 | ||||||||
\(431\) | 1.01990e9 | 0.613600 | 0.306800 | − | 0.951774i | \(-0.400742\pi\) | ||||
0.306800 | + | 0.951774i | \(0.400742\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −4.96072e8 | −0.293655 | −0.146827 | − | 0.989162i | \(-0.546906\pi\) | ||||
−0.146827 | + | 0.989162i | \(0.546906\pi\) | |||||||
\(434\) | −5.85130e9 | −3.43588 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.05413e8 | 0.349824 | ||||||||
\(437\) | −2.70868e8 | −0.155265 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.84581e9 | 1.04126 | 0.520632 | − | 0.853781i | \(-0.325697\pi\) | ||||
0.520632 | + | 0.853781i | \(0.325697\pi\) | |||||||
\(440\) | 7.69440e6 | 0.00430616 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.51643e8 | −0.138614 | ||||||||
\(443\) | −2.12406e8 | −0.116079 | −0.0580394 | − | 0.998314i | \(-0.518485\pi\) | ||||
−0.0580394 | + | 0.998314i | \(0.518485\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.06049e8 | 0.110844 | ||||||||
\(446\) | 1.64392e9 | 0.877421 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 3.20747e9 | 1.68535 | ||||||||
\(449\) | 3.53221e9 | 1.84155 | 0.920777 | − | 0.390090i | \(-0.127556\pi\) | ||||
0.920777 | + | 0.390090i | \(0.127556\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.31323e9 | 0.674098 | ||||||||
\(452\) | −2.77737e9 | −1.41465 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −2.54865e9 | −1.27825 | ||||||||
\(455\) | 4.88241e7 | 0.0242993 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.05595e9 | 1.00764 | 0.503821 | − | 0.863808i | \(-0.331927\pi\) | ||||
0.503821 | + | 0.863808i | \(0.331927\pi\) | |||||||
\(458\) | −3.74194e9 | −1.81998 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.09533e7 | 0.0291975 | ||||||||
\(461\) | 1.34533e9 | 0.639551 | 0.319776 | − | 0.947493i | \(-0.396392\pi\) | ||||
0.319776 | + | 0.947493i | \(0.396392\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.16277e9 | 0.544452 | 0.272226 | − | 0.962233i | \(-0.412240\pi\) | ||||
0.272226 | + | 0.962233i | \(0.412240\pi\) | |||||||
\(464\) | −2.79155e9 | −1.29727 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.53746e9 | 0.703805 | ||||||||
\(467\) | −3.37053e9 | −1.53140 | −0.765700 | − | 0.643198i | \(-0.777607\pi\) | ||||
−0.765700 | + | 0.643198i | \(0.777607\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3.28251e9 | −1.46927 | ||||||||
\(470\) | 6.49406e8 | 0.288519 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.82233e7 | −0.0123541 | ||||||||
\(473\) | 1.29242e9 | 0.561552 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.43528e9 | 0.614484 | ||||||||
\(476\) | 2.44086e9 | 1.03733 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −3.54833e9 | −1.48603 | ||||||||
\(479\) | 1.66586e9 | 0.692571 | 0.346286 | − | 0.938129i | \(-0.387443\pi\) | ||||
0.346286 | + | 0.938129i | \(0.387443\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3.06178e8 | 0.125449 | ||||||||
\(482\) | 1.22422e9 | 0.497961 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.20418e9 | −0.883665 | ||||||||
\(485\) | −1.46453e8 | −0.0582910 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.02449e9 | −0.401934 | −0.200967 | − | 0.979598i | \(-0.564408\pi\) | ||||
−0.200967 | + | 0.979598i | \(0.564408\pi\) | |||||||
\(488\) | −1.89891e8 | −0.0739665 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −5.07121e8 | −0.194727 | ||||||||
\(491\) | −2.27469e9 | −0.867235 | −0.433618 | − | 0.901097i | \(-0.642763\pi\) | ||||
−0.433618 | + | 0.901097i | \(0.642763\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.41673e9 | −0.908373 | ||||||||
\(494\) | −3.54881e8 | −0.132446 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.03970e9 | 1.48649 | ||||||||
\(497\) | 3.69688e9 | 1.35079 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.02609e9 | 0.729971 | 0.364986 | − | 0.931013i | \(-0.381074\pi\) | ||||
0.364986 | + | 0.931013i | \(0.381074\pi\) | |||||||
\(500\) | −6.49899e8 | −0.232515 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −4.04168e9 | −1.42593 | ||||||||
\(503\) | −1.54149e9 | −0.540073 | −0.270037 | − | 0.962850i | \(-0.587036\pi\) | ||||
−0.270037 | + | 0.962850i | \(0.587036\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −5.50020e8 | −0.190046 | ||||||||
\(506\) | 4.32486e8 | 0.148404 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.33832e9 | −0.452935 | ||||||||
\(509\) | −3.87817e9 | −1.30351 | −0.651755 | − | 0.758430i | \(-0.725967\pi\) | ||||
−0.651755 | + | 0.758430i | \(0.725967\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −5.39389e9 | −1.78825 | ||||||||
\(512\) | −4.30828e9 | −1.41860 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 1.54323e9 | 0.501258 | ||||||||
\(515\) | −5.62262e8 | −0.181390 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.37750e9 | 0.756666 | ||||||||
\(518\) | −5.75574e9 | −1.81948 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 4.94570e6 | 0.00154247 | ||||||||
\(521\) | 4.39564e8 | 0.136173 | 0.0680864 | − | 0.997679i | \(-0.478311\pi\) | ||||
0.0680864 | + | 0.997679i | \(0.478311\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −6.36830e9 | −1.94656 | −0.973280 | − | 0.229623i | \(-0.926251\pi\) | ||||
−0.973280 | + | 0.229623i | \(0.926251\pi\) | |||||||
\(524\) | 3.48419e9 | 1.05789 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.25898e9 | 0.377197 | ||||||||
\(527\) | 3.49730e9 | 1.04087 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −3.19265e9 | −0.937683 | ||||||||
\(530\) | −9.01581e8 | −0.263051 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 3.44224e9 | 0.991174 | ||||||||
\(533\) | 8.44100e8 | 0.241462 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −4.85361e8 | −0.137033 | ||||||||
\(536\) | −3.32507e8 | −0.0932661 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −2.41276e9 | −0.667999 | ||||||||
\(539\) | −1.85659e9 | −0.510688 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −1.34859e9 | −0.366175 | −0.183088 | − | 0.983097i | \(-0.558609\pi\) | ||||
−0.183088 | + | 0.983097i | \(0.558609\pi\) | |||||||
\(542\) | −3.48065e9 | −0.938995 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −3.49788e9 | −0.931556 | ||||||||
\(545\) | 1.36066e8 | 0.0360049 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.38331e9 | −0.622622 | −0.311311 | − | 0.950308i | \(-0.600768\pi\) | ||||
−0.311311 | + | 0.950308i | \(0.600768\pi\) | |||||||
\(548\) | 7.64172e8 | 0.198362 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.29167e9 | −0.587331 | ||||||||
\(551\) | −3.40821e9 | −0.867951 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 9.38492e9 | 2.35989 | ||||||||
\(554\) | 7.30785e9 | 1.82602 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −1.35661e8 | −0.0334729 | ||||||||
\(557\) | 2.39992e8 | 0.0588442 | 0.0294221 | − | 0.999567i | \(-0.490633\pi\) | ||||
0.0294221 | + | 0.999567i | \(0.490633\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 8.30724e8 | 0.201148 | ||||||||
\(560\) | 6.33661e8 | 0.152475 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 8.90002e8 | 0.211502 | ||||||||
\(563\) | 1.44852e9 | 0.342093 | 0.171047 | − | 0.985263i | \(-0.445285\pi\) | ||||
0.171047 | + | 0.985263i | \(0.445285\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −6.24211e8 | −0.145600 | ||||||||
\(566\) | 1.13234e10 | 2.62493 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 3.74481e8 | 0.0857454 | ||||||||
\(569\) | −7.46267e9 | −1.69825 | −0.849124 | − | 0.528193i | \(-0.822870\pi\) | ||||
−0.849124 | + | 0.528193i | \(0.822870\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.56608e9 | 0.352036 | 0.176018 | − | 0.984387i | \(-0.443678\pi\) | ||||
0.176018 | + | 0.984387i | \(0.443678\pi\) | |||||||
\(572\) | 2.92367e8 | 0.0653194 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.58679e10 | −3.50211 | ||||||||
\(575\) | −1.12429e9 | −0.246628 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.11728e7 | −0.0132569 | −0.00662847 | − | 0.999978i | \(-0.502110\pi\) | ||||
−0.00662847 | + | 0.999978i | \(0.502110\pi\) | |||||||
\(578\) | 3.84547e9 | 0.828327 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 7.66948e8 | 0.163218 | ||||||||
\(581\) | 1.12994e10 | 2.39023 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.30073e9 | −0.689874 | ||||||||
\(584\) | −5.46382e8 | −0.113515 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −2.58277e9 | −0.530206 | ||||||||
\(587\) | −2.95616e9 | −0.603245 | −0.301623 | − | 0.953427i | \(-0.597528\pi\) | ||||
−0.301623 | + | 0.953427i | \(0.597528\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.93208e9 | 0.994550 | ||||||||
\(590\) | −1.02424e8 | −0.0205314 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 3.97372e9 | 0.787175 | ||||||||
\(593\) | −1.97406e8 | −0.0388748 | −0.0194374 | − | 0.999811i | \(-0.506188\pi\) | ||||
−0.0194374 | + | 0.999811i | \(0.506188\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 5.48581e8 | 0.106766 | ||||||||
\(596\) | −3.56625e9 | −0.690002 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 2.77987e8 | 0.0531583 | ||||||||
\(599\) | −8.20815e8 | −0.156046 | −0.0780228 | − | 0.996952i | \(-0.524861\pi\) | ||||
−0.0780228 | + | 0.996952i | \(0.524861\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.75118e9 | 1.83230 | 0.916150 | − | 0.400837i | \(-0.131280\pi\) | ||||
0.916150 | + | 0.400837i | \(0.131280\pi\) | |||||||
\(602\) | −1.56165e10 | −2.91740 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −9.59089e9 | −1.77105 | ||||||||
\(605\) | −4.95386e8 | −0.0909495 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −5.21137e9 | −0.945784 | −0.472892 | − | 0.881120i | \(-0.656790\pi\) | ||||
−0.472892 | + | 0.881120i | \(0.656790\pi\) | |||||||
\(608\) | −4.93290e9 | −0.890103 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −6.89124e8 | −0.122926 | ||||||||
\(611\) | 1.52818e9 | 0.271038 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.02466e9 | −0.179666 | −0.0898330 | − | 0.995957i | \(-0.528633\pi\) | ||||
−0.0898330 | + | 0.995957i | \(0.528633\pi\) | |||||||
\(614\) | −3.27761e9 | −0.571437 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.40377e8 | −0.0586715 | ||||||||
\(617\) | 1.71355e9 | 0.293696 | 0.146848 | − | 0.989159i | \(-0.453087\pi\) | ||||
0.146848 | + | 0.989159i | \(0.453087\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.38211e9 | 0.573153 | 0.286577 | − | 0.958057i | \(-0.407483\pi\) | ||||
0.286577 | + | 0.958057i | \(0.407483\pi\) | |||||||
\(620\) | −1.10987e9 | −0.187025 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 6.18596e9 | 1.03072 | ||||||||
\(623\) | −9.11499e9 | −1.51025 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 5.88398e9 | 0.964031 | ||||||||
\(626\) | −2.34125e9 | −0.381451 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −3.12000e9 | −0.502684 | ||||||||
\(629\) | 3.44018e9 | 0.551193 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.96207e8 | 0.0469345 | 0.0234673 | − | 0.999725i | \(-0.492529\pi\) | ||||
0.0234673 | + | 0.999725i | \(0.492529\pi\) | |||||||
\(632\) | 9.50658e8 | 0.149801 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −6.26645e9 | −0.976583 | ||||||||
\(635\) | −3.00785e8 | −0.0466174 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.19336e9 | −0.182929 | ||||||||
\(638\) | 5.44177e9 | 0.829599 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.37793e8 | 0.0207777 | ||||||||
\(641\) | −5.82615e9 | −0.873732 | −0.436866 | − | 0.899526i | \(-0.643912\pi\) | ||||
−0.436866 | + | 0.899526i | \(0.643912\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.33573e9 | −0.791508 | −0.395754 | − | 0.918357i | \(-0.629517\pi\) | ||||
−0.395754 | + | 0.918357i | \(0.629517\pi\) | |||||||
\(644\) | −2.69639e9 | −0.397816 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −3.98740e9 | −0.581937 | ||||||||
\(647\) | −1.10418e10 | −1.60279 | −0.801393 | − | 0.598138i | \(-0.795907\pi\) | ||||
−0.801393 | + | 0.598138i | \(0.795907\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.74978e8 | −0.0538455 | ||||||||
\(650\) | −1.47301e9 | −0.210382 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.54722e9 | −1.20770 | ||||||||
\(653\) | 7.56490e9 | 1.06318 | 0.531590 | − | 0.847002i | \(-0.321595\pi\) | ||||
0.531590 | + | 0.847002i | \(0.321595\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 7.83068e8 | 0.108882 | ||||||||
\(656\) | 1.09551e10 | 1.51514 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −2.87277e10 | −3.93107 | ||||||||
\(659\) | 5.59162e9 | 0.761095 | 0.380547 | − | 0.924761i | \(-0.375736\pi\) | ||||
0.380547 | + | 0.924761i | \(0.375736\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.88074e9 | −0.253293 | −0.126647 | − | 0.991948i | \(-0.540421\pi\) | ||||
−0.126647 | + | 0.991948i | \(0.540421\pi\) | |||||||
\(662\) | 8.28763e9 | 1.11027 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1.14459e9 | 0.151727 | ||||||||
\(665\) | 7.73639e8 | 0.102015 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.66973e9 | 0.348359 | ||||||||
\(668\) | 2.76906e9 | 0.359431 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.20668e9 | −0.155000 | ||||||||
\(671\) | −2.52291e9 | −0.322384 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.51715e9 | 1.07706 | 0.538532 | − | 0.842605i | \(-0.318979\pi\) | ||||
0.538532 | + | 0.842605i | \(0.318979\pi\) | |||||||
\(674\) | −5.36634e9 | −0.675101 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −8.37414e9 | −1.04262 | ||||||||
\(677\) | 1.19888e10 | 1.48497 | 0.742484 | − | 0.669864i | \(-0.233648\pi\) | ||||
0.742484 | + | 0.669864i | \(0.233648\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 6.47863e9 | 0.794216 | ||||||||
\(680\) | 5.55693e7 | 0.00677725 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −7.87489e9 | −0.950603 | ||||||||
\(683\) | 7.29599e9 | 0.876217 | 0.438109 | − | 0.898922i | \(-0.355649\pi\) | ||||
0.438109 | + | 0.898922i | \(0.355649\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 1.71747e8 | 0.0204161 | ||||||||
\(686\) | 4.26509e9 | 0.504422 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.07815e10 | 1.26218 | ||||||||
\(689\) | −2.12160e9 | −0.247113 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.48922e9 | 0.287006 | 0.143503 | − | 0.989650i | \(-0.454163\pi\) | ||||
0.143503 | + | 0.989650i | \(0.454163\pi\) | |||||||
\(692\) | 6.04564e9 | 0.693540 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.50768e10 | −2.84783 | ||||||||
\(695\) | −3.04897e7 | −0.00344513 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 9.48420e9 | 1.06093 | ||||||||
\(698\) | 5.48450e9 | 0.610440 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.42877e10 | 1.57442 | ||||||||
\(701\) | −1.04516e10 | −1.14596 | −0.572980 | − | 0.819570i | \(-0.694213\pi\) | ||||
−0.572980 | + | 0.819570i | \(0.694213\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.85153e9 | 0.526666 | ||||||||
\(704\) | 4.31673e9 | 0.466284 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −1.36432e10 | −1.45915 | ||||||||
\(707\) | 2.43312e10 | 2.58938 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 4.68714e9 | 0.493908 | 0.246954 | − | 0.969027i | \(-0.420570\pi\) | ||||
0.246954 | + | 0.969027i | \(0.420570\pi\) | |||||||
\(710\) | 1.35901e9 | 0.142501 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.23316e8 | −0.0958673 | ||||||||
\(713\) | −3.86342e9 | −0.399171 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 6.57092e7 | 0.00672287 | ||||||||
\(716\) | −1.77847e10 | −1.81072 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −9.35533e9 | −0.943243 | ||||||||
\(719\) | 1.88048e10 | 1.88676 | 0.943381 | − | 0.331710i | \(-0.107626\pi\) | ||||
0.943381 | + | 0.331710i | \(0.107626\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 2.48727e10 | 2.47144 | ||||||||
\(722\) | 8.91283e9 | 0.881324 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.18356e10 | −1.15906 | ||||||||
\(725\) | −1.41465e10 | −1.37869 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.41494e10 | −1.36574 | −0.682869 | − | 0.730541i | \(-0.739268\pi\) | ||||
−0.682869 | + | 0.730541i | \(0.739268\pi\) | |||||||
\(728\) | −2.18783e8 | −0.0210162 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.98285e9 | −0.188651 | ||||||||
\(731\) | 9.33391e9 | 0.883798 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.16913e10 | −1.09647 | −0.548237 | − | 0.836323i | \(-0.684701\pi\) | ||||
−0.548237 | + | 0.836323i | \(0.684701\pi\) | |||||||
\(734\) | 2.65482e9 | 0.247799 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 3.86407e9 | 0.357250 | ||||||||
\(737\) | −4.41772e9 | −0.406502 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.53323e9 | 0.777782 | 0.388891 | − | 0.921284i | \(-0.372858\pi\) | ||||
0.388891 | + | 0.921284i | \(0.372858\pi\) | |||||||
\(740\) | −1.09174e9 | −0.0990393 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 3.98832e10 | 3.58407 | ||||||||
\(743\) | 2.88722e9 | 0.258237 | 0.129119 | − | 0.991629i | \(-0.458785\pi\) | ||||
0.129119 | + | 0.991629i | \(0.458785\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −8.01512e8 | −0.0710171 | ||||||||
\(746\) | 8.17870e9 | 0.721271 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.28500e9 | 0.286998 | ||||||||
\(749\) | 2.14709e10 | 1.86708 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.71155e10 | 1.47452 | 0.737258 | − | 0.675611i | \(-0.236120\pi\) | ||||
0.737258 | + | 0.675611i | \(0.236120\pi\) | |||||||
\(752\) | 1.98334e10 | 1.70073 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.49779e9 | 0.297162 | ||||||||
\(755\) | −2.15554e9 | −0.182281 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.12521e10 | 0.942751 | 0.471375 | − | 0.881933i | \(-0.343758\pi\) | ||||
0.471375 | + | 0.881933i | \(0.343758\pi\) | |||||||
\(758\) | −3.00290e10 | −2.50437 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 7.83669e7 | 0.00647567 | ||||||||
\(761\) | −9.66355e9 | −0.794859 | −0.397430 | − | 0.917633i | \(-0.630098\pi\) | ||||
−0.397430 | + | 0.917633i | \(0.630098\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −6.01915e9 | −0.490568 | ||||||||
\(764\) | 1.37004e10 | 1.11150 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 1.27785e6 | 0.000102725 0 | ||||||||
\(767\) | −2.41023e8 | −0.0192875 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 6.93012e8 | 0.0549539 | 0.0274769 | − | 0.999622i | \(-0.491253\pi\) | ||||
0.0274769 | + | 0.999622i | \(0.491253\pi\) | |||||||
\(770\) | −1.23524e9 | −0.0975069 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.22504e10 | 1.74051 | ||||||||
\(773\) | 6.71030e8 | 0.0522533 | 0.0261266 | − | 0.999659i | \(-0.491683\pi\) | ||||
0.0261266 | + | 0.999659i | \(0.491683\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2.04716e10 | 1.57978 | ||||||||
\(776\) | 6.56262e8 | 0.0504152 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.65681e10 | 1.26138 | ||||||||
\(779\) | 1.33751e10 | 1.01372 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.97540e9 | 0.373723 | ||||||||
\(782\) | 3.12343e9 | 0.233565 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.54879e10 | −1.14785 | ||||||||
\(785\) | −7.01216e8 | −0.0517378 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.62943e10 | −1.19158 | −0.595790 | − | 0.803141i | \(-0.703161\pi\) | ||||
−0.595790 | + | 0.803141i | \(0.703161\pi\) | |||||||
\(788\) | −1.67605e10 | −1.22024 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.44999e9 | 0.248956 | ||||||||
\(791\) | 2.76132e10 | 1.98380 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.62165e9 | −0.115478 | ||||||||
\(794\) | −5.61933e9 | −0.398394 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 2.53664e10 | 1.78264 | ||||||||
\(797\) | −6.31608e9 | −0.441920 | −0.220960 | − | 0.975283i | \(-0.570919\pi\) | ||||
−0.220960 | + | 0.975283i | \(0.570919\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.71704e10 | 1.19088 | ||||||||
\(800\) | −2.04751e10 | −1.41387 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −3.49780e10 | −2.39433 | ||||||||
\(803\) | −7.25929e9 | −0.494755 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −6.06011e8 | −0.0409444 | ||||||||
\(806\) | −5.06172e9 | −0.340506 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.46466e9 | 0.164368 | ||||||||
\(809\) | 5.93171e9 | 0.393876 | 0.196938 | − | 0.980416i | \(-0.436900\pi\) | ||||
0.196938 | + | 0.980416i | \(0.436900\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 3.74376e9 | 0.246454 | 0.123227 | − | 0.992379i | \(-0.460676\pi\) | ||||
0.123227 | + | 0.992379i | \(0.460676\pi\) | |||||||
\(812\) | −3.39274e10 | −2.22385 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −7.74628e9 | −0.503394 | ||||||||
\(815\) | −1.92098e9 | −0.124300 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.31632e10 | 0.844470 | ||||||||
\(818\) | 3.63037e9 | 0.231907 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −3.00981e9 | −0.190629 | ||||||||
\(821\) | −2.22338e10 | −1.40221 | −0.701103 | − | 0.713060i | \(-0.747309\pi\) | ||||
−0.701103 | + | 0.713060i | \(0.747309\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −2.57937e10 | −1.61292 | −0.806462 | − | 0.591286i | \(-0.798620\pi\) | ||||
−0.806462 | + | 0.591286i | \(0.798620\pi\) | |||||||
\(824\) | 2.51952e9 | 0.156882 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 4.53092e9 | 0.279741 | ||||||||
\(827\) | −2.36853e10 | −1.45616 | −0.728082 | − | 0.685490i | \(-0.759588\pi\) | ||||
−0.728082 | + | 0.685490i | \(0.759588\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.07672e10 | −1.87563 | −0.937815 | − | 0.347137i | \(-0.887154\pi\) | ||||
−0.937815 | + | 0.347137i | \(0.887154\pi\) | |||||||
\(830\) | 4.15377e9 | 0.252156 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 2.77465e9 | 0.167023 | ||||||||
\(833\) | −1.34084e10 | −0.803746 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 6.22344e8 | 0.0369937 | ||||||||
\(836\) | 4.63268e9 | 0.274227 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.89594e10 | −1.11294 | ||||||||
\(839\) | 9.92051e9 | 0.579919 | 0.289959 | − | 0.957039i | \(-0.406358\pi\) | ||||
0.289959 | + | 0.957039i | \(0.406358\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 1.63422e10 | 0.947379 | ||||||||
\(842\) | 1.53528e10 | 0.886332 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 5.80786e8 | 0.0332520 | ||||||||
\(845\) | −1.88208e9 | −0.107310 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.19144e10 | 1.23919 | ||||||||
\(848\) | −2.75351e10 | −1.55060 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.65505e10 | −0.924371 | ||||||||
\(851\) | −3.80032e9 | −0.211382 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.89035e10 | 1.04285 | 0.521424 | − | 0.853298i | \(-0.325401\pi\) | ||||
0.521424 | + | 0.853298i | \(0.325401\pi\) | |||||||
\(854\) | 3.04847e10 | 1.67487 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.17492e9 | 0.118518 | ||||||||
\(857\) | −1.56380e10 | −0.848688 | −0.424344 | − | 0.905501i | \(-0.639495\pi\) | ||||
−0.424344 | + | 0.905501i | \(0.639495\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.59002e10 | 1.93251 | 0.966254 | − | 0.257592i | \(-0.0829291\pi\) | ||||
0.966254 | + | 0.257592i | \(0.0829291\pi\) | |||||||
\(860\) | −2.96211e9 | −0.158802 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −1.65855e10 | −0.881968 | ||||||||
\(863\) | 3.31160e10 | 1.75388 | 0.876941 | − | 0.480599i | \(-0.159581\pi\) | ||||
0.876941 | + | 0.480599i | \(0.159581\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1.35875e9 | 0.0713812 | ||||||||
\(866\) | 8.06708e9 | 0.422089 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 4.90970e10 | 2.54822 | ||||||||
\(869\) | 1.26306e10 | 0.652910 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.83956e9 | −0.145609 | ||||||||
\(872\) | −6.09718e8 | −0.0311402 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 4.40483e9 | 0.223172 | ||||||||
\(875\) | 6.46143e9 | 0.326062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.12644e10 | 1.56513 | 0.782567 | − | 0.622566i | \(-0.213910\pi\) | ||||
0.782567 | + | 0.622566i | \(0.213910\pi\) | |||||||
\(878\) | −3.00164e10 | −1.49668 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 8.52804e8 | 0.0421852 | ||||||||
\(881\) | 1.15281e9 | 0.0567991 | 0.0283996 | − | 0.999597i | \(-0.490959\pi\) | ||||
0.0283996 | + | 0.999597i | \(0.490959\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.36328e9 | −0.359922 | −0.179961 | − | 0.983674i | \(-0.557597\pi\) | ||||
−0.179961 | + | 0.983674i | \(0.557597\pi\) | |||||||
\(884\) | 2.11149e9 | 0.102803 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.45413e9 | 0.166848 | ||||||||
\(887\) | −2.01350e10 | −0.968765 | −0.484383 | − | 0.874856i | \(-0.660956\pi\) | ||||
−0.484383 | + | 0.874856i | \(0.660956\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.33058e10 | 0.635163 | ||||||||
\(890\) | −3.35076e9 | −0.159323 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −1.37938e10 | −0.650738 | ||||||||
\(893\) | 2.42147e10 | 1.13789 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.99710e9 | −0.186365 | ||||||||
\(896\) | −6.09554e9 | −0.283096 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −5.74406e10 | −2.64698 | ||||||||
\(899\) | −4.86117e10 | −2.23142 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.38380e10 | −1.08576 | ||||||||
\(902\) | −2.13557e10 | −0.968925 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 2.79712e9 | 0.125928 | ||||||||
\(905\) | −2.66005e9 | −0.119294 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −4.37196e10 | −1.94559 | −0.972793 | − | 0.231677i | \(-0.925579\pi\) | ||||
−0.972793 | + | 0.231677i | \(0.925579\pi\) | |||||||
\(908\) | 2.13852e10 | 0.948010 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −7.93974e8 | −0.0349270 | ||||||||
\(911\) | −2.71783e10 | −1.19099 | −0.595494 | − | 0.803360i | \(-0.703044\pi\) | ||||
−0.595494 | + | 0.803360i | \(0.703044\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.52071e10 | 0.661302 | ||||||||
\(914\) | −3.34337e10 | −1.44835 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 3.13978e10 | 1.34979 | ||||||||
\(917\) | −3.46405e10 | −1.48351 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1.97736e10 | −0.840393 | −0.420196 | − | 0.907433i | \(-0.638039\pi\) | ||||
−0.420196 | + | 0.907433i | \(0.638039\pi\) | |||||||
\(920\) | −6.13867e7 | −0.00259906 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −2.18777e10 | −0.919269 | ||||||||
\(923\) | 3.19802e9 | 0.133868 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.01373e10 | 0.836576 | ||||||||
\(926\) | −1.89088e10 | −0.782576 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.86198e10 | 1.99708 | ||||||||
\(929\) | 3.68821e10 | 1.50925 | 0.754625 | − | 0.656156i | \(-0.227819\pi\) | ||||
0.754625 | + | 0.656156i | \(0.227819\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.89092e10 | −0.767981 | ||||||||
\(932\) | −1.29005e10 | −0.521976 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 5.48113e10 | 2.20118 | ||||||||
\(935\) | 7.38300e8 | 0.0295388 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.54302e10 | −1.00986 | −0.504930 | − | 0.863160i | \(-0.668482\pi\) | ||||
−0.504930 | + | 0.863160i | \(0.668482\pi\) | |||||||
\(938\) | 5.33800e10 | 2.11188 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −5.44903e9 | −0.213979 | ||||||||
\(941\) | 1.08449e10 | 0.424288 | 0.212144 | − | 0.977238i | \(-0.431955\pi\) | ||||
0.212144 | + | 0.977238i | \(0.431955\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.04771e10 | −0.406864 | ||||||||
\(944\) | −3.12811e9 | −0.121027 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −2.10172e10 | −0.807155 | ||||||||
\(947\) | 2.44245e9 | 0.0934547 | 0.0467273 | − | 0.998908i | \(-0.485121\pi\) | ||||
0.0467273 | + | 0.998908i | \(0.485121\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.66603e9 | −0.177221 | ||||||||
\(950\) | −2.33405e10 | −0.883237 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −2.45822e9 | −0.0923402 | ||||||||
\(953\) | 3.90381e10 | 1.46104 | 0.730522 | − | 0.682890i | \(-0.239277\pi\) | ||||
0.730522 | + | 0.682890i | \(0.239277\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.07916e9 | 0.114398 | ||||||||
\(956\) | 2.97733e10 | 1.10211 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.70901e10 | −0.995478 | ||||||||
\(959\) | −7.59756e9 | −0.278169 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.28343e10 | 1.55690 | ||||||||
\(962\) | −4.97905e9 | −0.180316 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.02722e10 | −0.369312 | ||||||||
\(965\) | 5.00076e9 | 0.179139 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.52051e10 | −0.896388 | −0.448194 | − | 0.893936i | \(-0.647933\pi\) | ||||
−0.448194 | + | 0.893936i | \(0.647933\pi\) | |||||||
\(968\) | 2.21985e9 | 0.0786610 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.38161e9 | 0.0837855 | ||||||||
\(971\) | 6.22835e9 | 0.218326 | 0.109163 | − | 0.994024i | \(-0.465183\pi\) | ||||
0.109163 | + | 0.994024i | \(0.465183\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.34877e9 | 0.0469400 | ||||||||
\(974\) | 1.66601e10 | 0.577726 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −2.10465e10 | −0.724611 | ||||||||
\(977\) | −1.86878e10 | −0.641103 | −0.320551 | − | 0.947231i | \(-0.603868\pi\) | ||||
−0.320551 | + | 0.947231i | \(0.603868\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.22673e10 | −0.417839 | ||||||||
\(980\) | 4.25514e9 | 0.144419 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 3.69908e10 | 1.24653 | ||||||||
\(983\) | −4.26187e10 | −1.43108 | −0.715538 | − | 0.698574i | \(-0.753818\pi\) | ||||
−0.715538 | + | 0.698574i | \(0.753818\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −3.76691e9 | −0.125591 | ||||||||
\(986\) | 3.93007e10 | 1.30566 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.97773e9 | 0.0982283 | ||||||||
\(989\) | −1.03111e10 | −0.338935 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.72023e9 | −0.121426 | −0.0607130 | − | 0.998155i | \(-0.519337\pi\) | ||||
−0.0607130 | + | 0.998155i | \(0.519337\pi\) | |||||||
\(992\) | −7.03586e10 | −2.28837 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −6.01185e10 | −1.94158 | ||||||||
\(995\) | 5.70107e9 | 0.183474 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.00026e10 | 0.958794 | 0.479397 | − | 0.877598i | \(-0.340855\pi\) | ||||
0.479397 | + | 0.877598i | \(0.340855\pi\) | |||||||
\(998\) | −3.29481e10 | −1.04924 | ||||||||
\(999\) | 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 | 531.8.a.d.1.2 | 17 | ||
3.2 | odd | 2 | 177.8.a.b.1.16 | ✓ | 17 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
177.8.a.b.1.16 | ✓ | 17 | 3.2 | odd | 2 | ||
531.8.a.d.1.2 | 17 | 1.1 | even | 1 | trivial |