Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [225,10,Mod(1,225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("225.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 225 = 3^{2} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 225.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(115.883063137\) |
Analytic rank: | \(0\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 3) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 225.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 18.0000 | 0.795495 | 0.397748 | − | 0.917495i | \(-0.369792\pi\) | ||||
0.397748 | + | 0.917495i | \(0.369792\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −188.000 | −0.367188 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −9128.00 | −1.43693 | −0.718463 | − | 0.695565i | \(-0.755154\pi\) | ||||
−0.718463 | + | 0.695565i | \(0.755154\pi\) | |||||||
\(8\) | −12600.0 | −1.08759 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −21132.0 | −0.435185 | −0.217592 | − | 0.976040i | \(-0.569820\pi\) | ||||
−0.217592 | + | 0.976040i | \(0.569820\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −31214.0 | −0.303113 | −0.151556 | − | 0.988449i | \(-0.548429\pi\) | ||||
−0.151556 | + | 0.988449i | \(0.548429\pi\) | |||||||
\(14\) | −164304. | −1.14307 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −130544. | −0.497986 | ||||||||
\(17\) | −279342. | −0.811178 | −0.405589 | − | 0.914056i | \(-0.632934\pi\) | ||||
−0.405589 | + | 0.914056i | \(0.632934\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 144020. | 0.253531 | 0.126766 | − | 0.991933i | \(-0.459540\pi\) | ||||
0.126766 | + | 0.991933i | \(0.459540\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −380376. | −0.346187 | ||||||||
\(23\) | −1.76350e6 | −1.31401 | −0.657006 | − | 0.753885i | \(-0.728177\pi\) | ||||
−0.657006 | + | 0.753885i | \(0.728177\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −561852. | −0.241125 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.71606e6 | 0.527621 | ||||||||
\(29\) | −4.69251e6 | −1.23201 | −0.616005 | − | 0.787742i | \(-0.711250\pi\) | ||||
−0.616005 | + | 0.787742i | \(0.711250\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −369088. | −0.0717798 | −0.0358899 | − | 0.999356i | \(-0.511427\pi\) | ||||
−0.0358899 | + | 0.999356i | \(0.511427\pi\) | |||||||
\(32\) | 4.10141e6 | 0.691446 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −5.02816e6 | −0.645288 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −9.34708e6 | −0.819914 | −0.409957 | − | 0.912105i | \(-0.634456\pi\) | ||||
−0.409957 | + | 0.912105i | \(0.634456\pi\) | |||||||
\(38\) | 2.59236e6 | 0.201683 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 7.22684e6 | 0.399412 | 0.199706 | − | 0.979856i | \(-0.436001\pi\) | ||||
0.199706 | + | 0.979856i | \(0.436001\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.31475e7 | 1.03251 | 0.516257 | − | 0.856434i | \(-0.327325\pi\) | ||||
0.516257 | + | 0.856434i | \(0.327325\pi\) | |||||||
\(44\) | 3.97282e6 | 0.159794 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −3.17429e7 | −1.04529 | ||||||||
\(47\) | 2.29719e7 | 0.686683 | 0.343342 | − | 0.939211i | \(-0.388441\pi\) | ||||
0.343342 | + | 0.939211i | \(0.388441\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 4.29668e7 | 1.06476 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 5.86823e6 | 0.111299 | ||||||||
\(53\) | 7.84772e7 | 1.36616 | 0.683081 | − | 0.730343i | \(-0.260640\pi\) | ||||
0.683081 | + | 0.730343i | \(0.260640\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 1.15013e8 | 1.56279 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −8.44652e7 | −0.980058 | ||||||||
\(59\) | 2.03107e7 | 0.218218 | 0.109109 | − | 0.994030i | \(-0.465200\pi\) | ||||
0.109109 | + | 0.994030i | \(0.465200\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.79340e8 | −1.65841 | −0.829207 | − | 0.558942i | \(-0.811207\pi\) | ||||
−0.829207 | + | 0.558942i | \(0.811207\pi\) | |||||||
\(62\) | −6.64358e6 | −0.0571005 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.40664e8 | 1.04803 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −2.74528e8 | −1.66437 | −0.832186 | − | 0.554496i | \(-0.812911\pi\) | ||||
−0.832186 | + | 0.554496i | \(0.812911\pi\) | |||||||
\(68\) | 5.25163e7 | 0.297854 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.63426e7 | 0.169728 | 0.0848641 | − | 0.996393i | \(-0.472954\pi\) | ||||
0.0848641 | + | 0.996393i | \(0.472954\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.47090e8 | 1.01836 | 0.509180 | − | 0.860660i | \(-0.329949\pi\) | ||||
0.509180 | + | 0.860660i | \(0.329949\pi\) | |||||||
\(74\) | −1.68247e8 | −0.652237 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −2.70758e7 | −0.0930935 | ||||||||
\(77\) | 1.92893e8 | 0.625328 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.91875e8 | 0.554238 | 0.277119 | − | 0.960836i | \(-0.410620\pi\) | ||||
0.277119 | + | 0.960836i | \(0.410620\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 1.30083e8 | 0.317730 | ||||||||
\(83\) | −2.76159e8 | −0.638717 | −0.319358 | − | 0.947634i | \(-0.603467\pi\) | ||||
−0.319358 | + | 0.947634i | \(0.603467\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.16655e8 | 0.821359 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 2.66263e8 | 0.473303 | ||||||||
\(89\) | 6.78997e8 | 1.14713 | 0.573566 | − | 0.819160i | \(-0.305560\pi\) | ||||
0.573566 | + | 0.819160i | \(0.305560\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 2.84921e8 | 0.435551 | ||||||||
\(92\) | 3.31537e8 | 0.482489 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 4.13494e8 | 0.546253 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 5.67658e8 | 0.651049 | 0.325524 | − | 0.945534i | \(-0.394459\pi\) | ||||
0.325524 | + | 0.945534i | \(0.394459\pi\) | |||||||
\(98\) | 7.73402e8 | 0.847009 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1.62282e9 | −1.55176 | −0.775881 | − | 0.630879i | \(-0.782694\pi\) | ||||
−0.775881 | + | 0.630879i | \(0.782694\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.75103e9 | 1.53294 | 0.766470 | − | 0.642280i | \(-0.222011\pi\) | ||||
0.766470 | + | 0.642280i | \(0.222011\pi\) | |||||||
\(104\) | 3.93296e8 | 0.329663 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 1.41259e9 | 1.08677 | ||||||||
\(107\) | −1.54296e9 | −1.13796 | −0.568980 | − | 0.822352i | \(-0.692662\pi\) | ||||
−0.568980 | + | 0.822352i | \(0.692662\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 4.57665e8 | 0.310548 | 0.155274 | − | 0.987871i | \(-0.450374\pi\) | ||||
0.155274 | + | 0.987871i | \(0.450374\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.19161e9 | 0.715569 | ||||||||
\(113\) | 3.26794e9 | 1.88548 | 0.942739 | − | 0.333531i | \(-0.108240\pi\) | ||||
0.942739 | + | 0.333531i | \(0.108240\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 8.82192e8 | 0.452379 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3.65592e8 | 0.173591 | ||||||||
\(119\) | 2.54983e9 | 1.16560 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.91139e9 | −0.810614 | ||||||||
\(122\) | −3.22812e9 | −1.31926 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 6.93885e7 | 0.0263566 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.28879e8 | −0.316842 | −0.158421 | − | 0.987372i | \(-0.550640\pi\) | ||||
−0.158421 | + | 0.987372i | \(0.550640\pi\) | |||||||
\(128\) | 4.32029e8 | 0.142255 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 9.88659e8 | 0.293309 | 0.146655 | − | 0.989188i | \(-0.453149\pi\) | ||||
0.146655 | + | 0.989188i | \(0.453149\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.31461e9 | −0.364306 | ||||||||
\(134\) | −4.94151e9 | −1.32400 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3.51971e9 | 0.882230 | ||||||||
\(137\) | −5.73253e7 | −0.0139028 | −0.00695142 | − | 0.999976i | \(-0.502213\pi\) | ||||
−0.00695142 | + | 0.999976i | \(0.502213\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.65052e9 | −1.05666 | −0.528330 | − | 0.849039i | \(-0.677182\pi\) | ||||
−0.528330 | + | 0.849039i | \(0.677182\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 6.54168e8 | 0.135018 | ||||||||
\(143\) | 6.59614e8 | 0.131910 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 4.44761e9 | 0.810101 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.75725e9 | 0.301062 | ||||||||
\(149\) | 1.40236e9 | 0.233089 | 0.116545 | − | 0.993185i | \(-0.462818\pi\) | ||||
0.116545 | + | 0.993185i | \(0.462818\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.01548e10 | 1.58955 | 0.794773 | − | 0.606907i | \(-0.207590\pi\) | ||||
0.794773 | + | 0.606907i | \(0.207590\pi\) | |||||||
\(152\) | −1.81465e9 | −0.275738 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 3.47207e9 | 0.497445 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −9.36605e9 | −1.23029 | −0.615146 | − | 0.788413i | \(-0.710903\pi\) | ||||
−0.615146 | + | 0.788413i | \(0.710903\pi\) | |||||||
\(158\) | 3.45375e9 | 0.440893 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.60972e10 | 1.88814 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 7.34780e8 | 0.0815292 | 0.0407646 | − | 0.999169i | \(-0.487021\pi\) | ||||
0.0407646 | + | 0.999169i | \(0.487021\pi\) | |||||||
\(164\) | −1.35865e9 | −0.146659 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.97087e9 | −0.508096 | ||||||||
\(167\) | 1.55584e9 | 0.154789 | 0.0773947 | − | 0.997001i | \(-0.475340\pi\) | ||||
0.0773947 | + | 0.997001i | \(0.475340\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.63019e9 | −0.908123 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −4.35173e9 | −0.379126 | ||||||||
\(173\) | 1.90448e10 | 1.61648 | 0.808238 | − | 0.588856i | \(-0.200421\pi\) | ||||
0.808238 | + | 0.588856i | \(0.200421\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 2.75866e9 | 0.216716 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.22220e10 | 0.912537 | ||||||||
\(179\) | −4.32852e9 | −0.315138 | −0.157569 | − | 0.987508i | \(-0.550366\pi\) | ||||
−0.157569 | + | 0.987508i | \(0.550366\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.56757e8 | −0.0662595 | −0.0331298 | − | 0.999451i | \(-0.510547\pi\) | ||||
−0.0331298 | + | 0.999451i | \(0.510547\pi\) | |||||||
\(182\) | 5.12859e9 | 0.346479 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 2.22200e10 | 1.42911 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 5.90306e9 | 0.353012 | ||||||||
\(188\) | −4.31871e9 | −0.252141 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 1.76438e10 | 0.959274 | 0.479637 | − | 0.877467i | \(-0.340768\pi\) | ||||
0.479637 | + | 0.877467i | \(0.340768\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.30993e10 | −0.679581 | −0.339790 | − | 0.940501i | \(-0.610356\pi\) | ||||
−0.339790 | + | 0.940501i | \(0.610356\pi\) | |||||||
\(194\) | 1.02178e10 | 0.517906 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.07775e9 | −0.390965 | ||||||||
\(197\) | 4.74589e9 | 0.224502 | 0.112251 | − | 0.993680i | \(-0.464194\pi\) | ||||
0.112251 | + | 0.993680i | \(0.464194\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.92102e10 | −0.868348 | −0.434174 | − | 0.900829i | \(-0.642960\pi\) | ||||
−0.434174 | + | 0.900829i | \(0.642960\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −2.92108e10 | −1.23442 | ||||||||
\(203\) | 4.28332e10 | 1.77031 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.15185e10 | 1.21945 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 4.07480e9 | 0.150946 | ||||||||
\(209\) | −3.04343e9 | −0.110333 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.81273e10 | −0.629597 | −0.314798 | − | 0.949159i | \(-0.601937\pi\) | ||||
−0.314798 | + | 0.949159i | \(0.601937\pi\) | |||||||
\(212\) | −1.47537e10 | −0.501637 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −2.77732e10 | −0.905241 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3.36904e9 | 0.103142 | ||||||||
\(218\) | 8.23797e9 | 0.247039 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 8.71938e9 | 0.245878 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3.91081e9 | −0.105900 | −0.0529499 | − | 0.998597i | \(-0.516862\pi\) | ||||
−0.0529499 | + | 0.998597i | \(0.516862\pi\) | |||||||
\(224\) | −3.74377e10 | −0.993556 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 5.88230e10 | 1.49989 | ||||||||
\(227\) | −3.58126e10 | −0.895199 | −0.447599 | − | 0.894234i | \(-0.647721\pi\) | ||||
−0.447599 | + | 0.894234i | \(0.647721\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.30445e9 | 0.127462 | 0.0637310 | − | 0.997967i | \(-0.479700\pi\) | ||||
0.0637310 | + | 0.997967i | \(0.479700\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 5.91256e10 | 1.33992 | ||||||||
\(233\) | −2.54172e10 | −0.564970 | −0.282485 | − | 0.959272i | \(-0.591159\pi\) | ||||
−0.282485 | + | 0.959272i | \(0.591159\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.81840e9 | −0.0801268 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 4.58970e10 | 0.927231 | ||||||||
\(239\) | 6.33494e10 | 1.25589 | 0.627946 | − | 0.778257i | \(-0.283896\pi\) | ||||
0.627946 | + | 0.778257i | \(0.283896\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.01929e11 | 1.94635 | 0.973173 | − | 0.230073i | \(-0.0738965\pi\) | ||||
0.973173 | + | 0.230073i | \(0.0738965\pi\) | |||||||
\(242\) | −3.44050e10 | −0.644840 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 3.37159e10 | 0.608949 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −4.49544e9 | −0.0768486 | ||||||||
\(248\) | 4.65051e9 | 0.0780671 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.64745e10 | −1.53420 | −0.767098 | − | 0.641530i | \(-0.778300\pi\) | ||||
−0.767098 | + | 0.641530i | \(0.778300\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.72662e10 | 0.571838 | ||||||||
\(254\) | −1.67198e10 | −0.252046 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −6.42434e10 | −0.934864 | ||||||||
\(257\) | −7.99591e9 | −0.114332 | −0.0571661 | − | 0.998365i | \(-0.518206\pi\) | ||||
−0.0571661 | + | 0.998365i | \(0.518206\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 8.53201e10 | 1.17816 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.77959e10 | 0.233326 | ||||||||
\(263\) | 1.06269e11 | 1.36964 | 0.684821 | − | 0.728712i | \(-0.259881\pi\) | ||||
0.684821 | + | 0.728712i | \(0.259881\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −2.36631e10 | −0.289803 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 5.16113e10 | 0.611137 | ||||||||
\(269\) | 1.00886e11 | 1.17475 | 0.587377 | − | 0.809313i | \(-0.300160\pi\) | ||||
0.587377 | + | 0.809313i | \(0.300160\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −2.86345e10 | −0.322498 | −0.161249 | − | 0.986914i | \(-0.551552\pi\) | ||||
−0.161249 | + | 0.986914i | \(0.551552\pi\) | |||||||
\(272\) | 3.64664e10 | 0.403955 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.03186e9 | −0.0110596 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4.12251e10 | −0.420729 | −0.210365 | − | 0.977623i | \(-0.567465\pi\) | ||||
−0.210365 | + | 0.977623i | \(0.567465\pi\) | |||||||
\(278\) | −8.37094e10 | −0.840568 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1.21800e11 | −1.16538 | −0.582692 | − | 0.812693i | \(-0.698001\pi\) | ||||
−0.582692 | + | 0.812693i | \(0.698001\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.32820e10 | −0.215765 | −0.107883 | − | 0.994164i | \(-0.534407\pi\) | ||||
−0.107883 | + | 0.994164i | \(0.534407\pi\) | |||||||
\(284\) | −6.83242e9 | −0.0623221 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 1.18731e10 | 0.104934 | ||||||||
\(287\) | −6.59666e10 | −0.573925 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −4.05559e10 | −0.341990 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −4.64528e10 | −0.373929 | ||||||||
\(293\) | −9.12801e10 | −0.723555 | −0.361778 | − | 0.932264i | \(-0.617830\pi\) | ||||
−0.361778 | + | 0.932264i | \(0.617830\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 1.17773e11 | 0.891731 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.52425e10 | 0.185421 | ||||||||
\(299\) | 5.50458e10 | 0.398294 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.11290e11 | −1.48365 | ||||||||
\(302\) | 1.82786e11 | 1.26448 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.88009e10 | −0.126255 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4.39070e10 | 0.282105 | 0.141053 | − | 0.990002i | \(-0.454951\pi\) | ||||
0.141053 | + | 0.990002i | \(0.454951\pi\) | |||||||
\(308\) | −3.62639e10 | −0.229613 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 7.64835e10 | 0.463603 | 0.231801 | − | 0.972763i | \(-0.425538\pi\) | ||||
0.231801 | + | 0.972763i | \(0.425538\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −2.68488e11 | −1.58116 | −0.790580 | − | 0.612359i | \(-0.790221\pi\) | ||||
−0.790580 | + | 0.612359i | \(0.790221\pi\) | |||||||
\(314\) | −1.68589e11 | −0.978691 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3.60725e10 | −0.203509 | ||||||||
\(317\) | 1.52056e11 | 0.845738 | 0.422869 | − | 0.906191i | \(-0.361023\pi\) | ||||
0.422869 | + | 0.906191i | \(0.361023\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 9.91621e10 | 0.536152 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 2.89749e11 | 1.50200 | ||||||||
\(323\) | −4.02308e10 | −0.205659 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 1.32260e10 | 0.0648561 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −9.10582e10 | −0.434397 | ||||||||
\(329\) | −2.09687e11 | −0.986713 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.63057e11 | −1.20455 | −0.602274 | − | 0.798289i | \(-0.705739\pi\) | ||||
−0.602274 | + | 0.798289i | \(0.705739\pi\) | |||||||
\(332\) | 5.19179e10 | 0.234529 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 2.80051e10 | 0.123134 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −2.97183e11 | −1.25513 | −0.627566 | − | 0.778564i | \(-0.715949\pi\) | ||||
−0.627566 | + | 0.778564i | \(0.715949\pi\) | |||||||
\(338\) | −1.73343e11 | −0.722407 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 7.79957e9 | 0.0312375 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −2.38530e10 | −0.0930507 | ||||||||
\(344\) | −2.91658e11 | −1.12295 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.42807e11 | 1.28590 | ||||||||
\(347\) | 1.40219e11 | 0.519186 | 0.259593 | − | 0.965718i | \(-0.416412\pi\) | ||||
0.259593 | + | 0.965718i | \(0.416412\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.14891e11 | −1.13618 | −0.568088 | − | 0.822968i | \(-0.692317\pi\) | ||||
−0.568088 | + | 0.822968i | \(0.692317\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −8.66710e10 | −0.300907 | ||||||||
\(353\) | −5.31195e11 | −1.82082 | −0.910411 | − | 0.413704i | \(-0.864235\pi\) | ||||
−0.910411 | + | 0.413704i | \(0.864235\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −1.27652e11 | −0.421212 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −7.79133e10 | −0.250691 | ||||||||
\(359\) | 4.97684e11 | 1.58135 | 0.790676 | − | 0.612235i | \(-0.209729\pi\) | ||||
0.790676 | + | 0.612235i | \(0.209729\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.01946e11 | −0.935722 | ||||||||
\(362\) | −1.72216e10 | −0.0527091 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −5.35652e10 | −0.159929 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.77743e11 | −0.799183 | −0.399591 | − | 0.916693i | \(-0.630848\pi\) | ||||
−0.399591 | + | 0.916693i | \(0.630848\pi\) | |||||||
\(368\) | 2.30214e11 | 0.654359 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.16340e11 | −1.96307 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.55319e11 | −0.682957 | −0.341478 | − | 0.939890i | \(-0.610928\pi\) | ||||
−0.341478 | + | 0.939890i | \(0.610928\pi\) | |||||||
\(374\) | 1.06255e11 | 0.280819 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −2.89446e11 | −0.746830 | ||||||||
\(377\) | 1.46472e11 | 0.373438 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8.12103e10 | 0.202178 | 0.101089 | − | 0.994877i | \(-0.467767\pi\) | ||||
0.101089 | + | 0.994877i | \(0.467767\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 3.17589e11 | 0.763097 | ||||||||
\(383\) | −4.13123e11 | −0.981036 | −0.490518 | − | 0.871431i | \(-0.663192\pi\) | ||||
−0.490518 | + | 0.871431i | \(0.663192\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −2.35788e11 | −0.540603 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −1.06720e11 | −0.239057 | ||||||||
\(389\) | −2.53052e11 | −0.560321 | −0.280160 | − | 0.959953i | \(-0.590388\pi\) | ||||
−0.280160 | + | 0.959953i | \(0.590388\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 4.92618e11 | 1.06590 | ||||||||
\(392\) | −5.41381e11 | −1.15802 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 8.54259e10 | 0.178590 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 6.53562e10 | 0.132047 | 0.0660236 | − | 0.997818i | \(-0.478969\pi\) | ||||
0.0660236 | + | 0.997818i | \(0.478969\pi\) | |||||||
\(398\) | −3.45784e11 | −0.690766 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.40886e11 | 0.465225 | 0.232612 | − | 0.972570i | \(-0.425273\pi\) | ||||
0.232612 | + | 0.972570i | \(0.425273\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.15207e10 | 0.0217574 | ||||||||
\(404\) | 3.05091e11 | 0.569788 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.70998e11 | 1.40827 | ||||||||
\(407\) | 1.97522e11 | 0.356814 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −3.78340e11 | −0.668540 | −0.334270 | − | 0.942477i | \(-0.608490\pi\) | ||||
−0.334270 | + | 0.942477i | \(0.608490\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −3.29193e11 | −0.562876 | ||||||||
\(413\) | −1.85396e11 | −0.313563 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −1.28021e11 | −0.209586 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −5.47818e10 | −0.0877693 | ||||||||
\(419\) | −9.68766e11 | −1.53552 | −0.767760 | − | 0.640737i | \(-0.778629\pi\) | ||||
−0.767760 | + | 0.640737i | \(0.778629\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.43789e11 | −0.223077 | −0.111539 | − | 0.993760i | \(-0.535578\pi\) | ||||
−0.111539 | + | 0.993760i | \(0.535578\pi\) | |||||||
\(422\) | −3.26292e11 | −0.500841 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −9.88812e11 | −1.48582 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.63701e12 | 2.38302 | ||||||||
\(428\) | 2.90076e11 | 0.417845 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −2.06890e11 | −0.288796 | −0.144398 | − | 0.989520i | \(-0.546125\pi\) | ||||
−0.144398 | + | 0.989520i | \(0.546125\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 4.81883e10 | 0.0658789 | 0.0329394 | − | 0.999457i | \(-0.489513\pi\) | ||||
0.0329394 | + | 0.999457i | \(0.489513\pi\) | |||||||
\(434\) | 6.06426e10 | 0.0820492 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −8.60411e10 | −0.114029 | ||||||||
\(437\) | −2.53979e11 | −0.333143 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 4.37941e11 | 0.562763 | 0.281381 | − | 0.959596i | \(-0.409207\pi\) | ||||
0.281381 | + | 0.959596i | \(0.409207\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 1.56949e11 | 0.195595 | ||||||||
\(443\) | 7.58665e11 | 0.935908 | 0.467954 | − | 0.883753i | \(-0.344991\pi\) | ||||
0.467954 | + | 0.883753i | \(0.344991\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −7.03946e10 | −0.0842427 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.28398e12 | −1.50594 | ||||||||
\(449\) | 1.37280e11 | 0.159403 | 0.0797017 | − | 0.996819i | \(-0.474603\pi\) | ||||
0.0797017 | + | 0.996819i | \(0.474603\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.52718e11 | −0.173818 | ||||||||
\(452\) | −6.14373e11 | −0.692324 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.44627e11 | −0.712126 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.31091e11 | −0.140589 | −0.0702944 | − | 0.997526i | \(-0.522394\pi\) | ||||
−0.0702944 | + | 0.997526i | \(0.522394\pi\) | |||||||
\(458\) | 9.54800e10 | 0.101395 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8.03508e11 | 0.828583 | 0.414291 | − | 0.910144i | \(-0.364029\pi\) | ||||
0.414291 | + | 0.910144i | \(0.364029\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.78582e12 | 1.80602 | 0.903009 | − | 0.429621i | \(-0.141353\pi\) | ||||
0.903009 | + | 0.429621i | \(0.141353\pi\) | |||||||
\(464\) | 6.12579e11 | 0.613524 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −4.57509e11 | −0.449431 | ||||||||
\(467\) | 6.44366e11 | 0.626912 | 0.313456 | − | 0.949603i | \(-0.398513\pi\) | ||||
0.313456 | + | 0.949603i | \(0.398513\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.50590e12 | 2.39158 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −2.55914e11 | −0.237332 | ||||||||
\(473\) | −4.89152e11 | −0.449334 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −4.79369e11 | −0.427995 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.14029e12 | 0.999056 | ||||||||
\(479\) | 1.87701e12 | 1.62913 | 0.814565 | − | 0.580073i | \(-0.196976\pi\) | ||||
0.814565 | + | 0.580073i | \(0.196976\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.91760e11 | 0.248526 | ||||||||
\(482\) | 1.83472e12 | 1.54831 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 3.59341e11 | 0.297647 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.49355e12 | −1.20321 | −0.601603 | − | 0.798795i | \(-0.705471\pi\) | ||||
−0.601603 | + | 0.798795i | \(0.705471\pi\) | |||||||
\(488\) | 2.25968e12 | 1.80368 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.47313e11 | 0.580278 | 0.290139 | − | 0.956985i | \(-0.406298\pi\) | ||||
0.290139 | + | 0.956985i | \(0.406298\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.31082e12 | 0.999379 | ||||||||
\(494\) | −8.09179e10 | −0.0611327 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4.81822e10 | 0.0357453 | ||||||||
\(497\) | −3.31736e11 | −0.243887 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 1.01300e12 | 0.731402 | 0.365701 | − | 0.930732i | \(-0.380829\pi\) | ||||
0.365701 | + | 0.930732i | \(0.380829\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.73654e12 | −1.22044 | ||||||||
\(503\) | 2.03399e11 | 0.141675 | 0.0708373 | − | 0.997488i | \(-0.477433\pi\) | ||||
0.0708373 | + | 0.997488i | \(0.477433\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 6.70792e11 | 0.454894 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1.74629e11 | 0.116340 | ||||||||
\(509\) | −5.93699e11 | −0.392045 | −0.196023 | − | 0.980599i | \(-0.562803\pi\) | ||||
−0.196023 | + | 0.980599i | \(0.562803\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.25543e12 | −1.46331 | ||||||||
\(512\) | −1.37758e12 | −0.885935 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.43926e11 | −0.0909508 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.85442e11 | −0.298834 | ||||||||
\(518\) | 1.53576e12 | 0.937217 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 1.74950e12 | 1.04027 | 0.520133 | − | 0.854085i | \(-0.325882\pi\) | ||||
0.520133 | + | 0.854085i | \(0.325882\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −3.20555e11 | −0.187346 | −0.0936731 | − | 0.995603i | \(-0.529861\pi\) | ||||
−0.0936731 | + | 0.995603i | \(0.529861\pi\) | |||||||
\(524\) | −1.85868e11 | −0.107699 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.91285e12 | 1.08954 | ||||||||
\(527\) | 1.03102e11 | 0.0582262 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.30877e12 | 0.726627 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 2.47148e11 | 0.133769 | ||||||||
\(533\) | −2.25579e11 | −0.121067 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 3.45906e12 | 1.81016 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.81595e12 | 0.934512 | ||||||||
\(539\) | −9.07974e11 | −0.463366 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 3.50229e11 | 0.175778 | 0.0878889 | − | 0.996130i | \(-0.471988\pi\) | ||||
0.0878889 | + | 0.996130i | \(0.471988\pi\) | |||||||
\(542\) | −5.15421e11 | −0.256546 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −1.14570e12 | −0.560885 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2.46037e12 | 1.17505 | 0.587527 | − | 0.809205i | \(-0.300102\pi\) | ||||
0.587527 | + | 0.809205i | \(0.300102\pi\) | |||||||
\(548\) | 1.07772e10 | 0.00510495 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −6.75815e11 | −0.312353 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.75143e12 | −0.796399 | ||||||||
\(554\) | −7.42051e11 | −0.334688 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 8.74299e11 | 0.387992 | ||||||||
\(557\) | 1.04356e12 | 0.459376 | 0.229688 | − | 0.973264i | \(-0.426229\pi\) | ||||
0.229688 | + | 0.973264i | \(0.426229\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −7.22525e11 | −0.312968 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −2.19240e12 | −0.927057 | ||||||||
\(563\) | 3.81849e12 | 1.60179 | 0.800893 | − | 0.598808i | \(-0.204359\pi\) | ||||
0.800893 | + | 0.598808i | \(0.204359\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −4.19076e11 | −0.171640 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4.57917e11 | −0.184595 | ||||||||
\(569\) | −4.84062e11 | −0.193596 | −0.0967979 | − | 0.995304i | \(-0.530860\pi\) | ||||
−0.0967979 | + | 0.995304i | \(0.530860\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 1.77044e10 | 0.00696978 | 0.00348489 | − | 0.999994i | \(-0.498891\pi\) | ||||
0.00348489 | + | 0.999994i | \(0.498891\pi\) | |||||||
\(572\) | −1.24007e11 | −0.0484357 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.18740e12 | −0.456555 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.46985e11 | 0.280557 | 0.140278 | − | 0.990112i | \(-0.455200\pi\) | ||||
0.140278 | + | 0.990112i | \(0.455200\pi\) | |||||||
\(578\) | −7.30007e11 | −0.272052 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2.52078e12 | 0.917789 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.65838e12 | −0.594532 | ||||||||
\(584\) | −3.11333e12 | −1.10756 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −1.64304e12 | −0.575585 | ||||||||
\(587\) | −4.33948e12 | −1.50857 | −0.754286 | − | 0.656546i | \(-0.772017\pi\) | ||||
−0.754286 | + | 0.656546i | \(0.772017\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −5.31561e10 | −0.0181984 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 1.22020e12 | 0.408305 | ||||||||
\(593\) | 1.90120e12 | 0.631366 | 0.315683 | − | 0.948865i | \(-0.397766\pi\) | ||||
0.315683 | + | 0.948865i | \(0.397766\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −2.63644e11 | −0.0855874 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9.90824e11 | 0.316841 | ||||||||
\(599\) | 5.49649e12 | 1.74447 | 0.872237 | − | 0.489083i | \(-0.162668\pi\) | ||||
0.872237 | + | 0.489083i | \(0.162668\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 4.77698e12 | 1.49355 | 0.746773 | − | 0.665079i | \(-0.231602\pi\) | ||||
0.746773 | + | 0.665079i | \(0.231602\pi\) | |||||||
\(602\) | −3.80322e12 | −1.18023 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.90909e12 | −0.583661 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −8.25000e11 | −0.246663 | −0.123332 | − | 0.992366i | \(-0.539358\pi\) | ||||
−0.123332 | + | 0.992366i | \(0.539358\pi\) | |||||||
\(608\) | 5.90685e11 | 0.175303 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.17045e11 | −0.208142 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.46985e12 | 0.420438 | 0.210219 | − | 0.977654i | \(-0.432582\pi\) | ||||
0.210219 | + | 0.977654i | \(0.432582\pi\) | |||||||
\(614\) | 7.90326e11 | 0.224413 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −2.43045e12 | −0.680101 | ||||||||
\(617\) | 5.17373e12 | 1.43721 | 0.718606 | − | 0.695418i | \(-0.244781\pi\) | ||||
0.718606 | + | 0.695418i | \(0.244781\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −4.80274e12 | −1.31487 | −0.657433 | − | 0.753513i | \(-0.728358\pi\) | ||||
−0.657433 | + | 0.753513i | \(0.728358\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.37670e12 | 0.368794 | ||||||||
\(623\) | −6.19789e12 | −1.64834 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −4.83279e12 | −1.25780 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.76082e12 | 0.451748 | ||||||||
\(629\) | 2.61103e12 | 0.665096 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 5.93992e12 | 1.49159 | 0.745794 | − | 0.666177i | \(-0.232071\pi\) | ||||
0.745794 | + | 0.666177i | \(0.232071\pi\) | |||||||
\(632\) | −2.41762e12 | −0.602784 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 2.73700e12 | 0.672780 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.34116e12 | −0.322741 | ||||||||
\(638\) | 1.78492e12 | 0.426506 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −6.47738e12 | −1.51544 | −0.757720 | − | 0.652580i | \(-0.773687\pi\) | ||||
−0.757720 | + | 0.652580i | \(0.773687\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.74519e12 | 0.402619 | 0.201309 | − | 0.979528i | \(-0.435480\pi\) | ||||
0.201309 | + | 0.979528i | \(0.435480\pi\) | |||||||
\(644\) | −3.02627e12 | −0.693301 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −7.24155e11 | −0.163601 | ||||||||
\(647\) | 4.97244e12 | 1.11558 | 0.557790 | − | 0.829982i | \(-0.311650\pi\) | ||||
0.557790 | + | 0.829982i | \(0.311650\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.29205e11 | −0.0949650 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1.38139e11 | −0.0299365 | ||||||||
\(653\) | −1.45057e12 | −0.312198 | −0.156099 | − | 0.987741i | \(-0.549892\pi\) | ||||
−0.156099 | + | 0.987741i | \(0.549892\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −9.43420e11 | −0.198901 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.77437e12 | −0.784925 | ||||||||
\(659\) | 3.05175e12 | 0.630325 | 0.315162 | − | 0.949038i | \(-0.397941\pi\) | ||||
0.315162 | + | 0.949038i | \(0.397941\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.88315e12 | −0.383688 | −0.191844 | − | 0.981425i | \(-0.561447\pi\) | ||||
−0.191844 | + | 0.981425i | \(0.561447\pi\) | |||||||
\(662\) | −4.73503e12 | −0.958213 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.47961e12 | 0.694662 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8.27522e12 | 1.61888 | ||||||||
\(668\) | −2.92498e11 | −0.0568367 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.78981e12 | 0.721716 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.84359e12 | −1.47383 | −0.736914 | − | 0.675986i | \(-0.763718\pi\) | ||||
−0.736914 | + | 0.675986i | \(0.763718\pi\) | |||||||
\(674\) | −5.34929e12 | −0.998451 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.81047e12 | 0.333451 | ||||||||
\(677\) | 2.32420e12 | 0.425230 | 0.212615 | − | 0.977136i | \(-0.431802\pi\) | ||||
0.212615 | + | 0.977136i | \(0.431802\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −5.18158e12 | −0.935509 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.40392e11 | 0.0248493 | ||||||||
\(683\) | −6.89265e12 | −1.21197 | −0.605986 | − | 0.795475i | \(-0.707221\pi\) | ||||
−0.605986 | + | 0.795475i | \(0.707221\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −4.29354e11 | −0.0740214 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −3.02176e12 | −0.514177 | ||||||||
\(689\) | −2.44959e12 | −0.414101 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.11430e13 | 1.85931 | 0.929654 | − | 0.368434i | \(-0.120106\pi\) | ||||
0.929654 | + | 0.368434i | \(0.120106\pi\) | |||||||
\(692\) | −3.58043e12 | −0.593550 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 2.52393e12 | 0.413010 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.01876e12 | −0.323994 | ||||||||
\(698\) | −5.66803e12 | −0.903822 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.78015e12 | 0.904082 | 0.452041 | − | 0.891997i | \(-0.350696\pi\) | ||||
0.452041 | + | 0.891997i | \(0.350696\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.34617e12 | −0.207874 | ||||||||
\(704\) | −2.97251e12 | −0.456085 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −9.56151e12 | −1.44846 | ||||||||
\(707\) | 1.48131e13 | 2.22977 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −3.39902e12 | −0.505180 | −0.252590 | − | 0.967573i | \(-0.581282\pi\) | ||||
−0.252590 | + | 0.967573i | \(0.581282\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8.55537e12 | −1.24761 | ||||||||
\(713\) | 6.50885e11 | 0.0943195 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 8.13761e11 | 0.115715 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 8.95831e12 | 1.25796 | ||||||||
\(719\) | −2.71272e11 | −0.0378551 | −0.0189276 | − | 0.999821i | \(-0.506025\pi\) | ||||
−0.0189276 | + | 0.999821i | \(0.506025\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.59834e13 | −2.20272 | ||||||||
\(722\) | −5.43503e12 | −0.744362 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 1.79870e11 | 0.0243297 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 2.13863e12 | 0.283943 | 0.141972 | − | 0.989871i | \(-0.454656\pi\) | ||||
0.141972 | + | 0.989871i | \(0.454656\pi\) | |||||||
\(728\) | −3.59001e12 | −0.473701 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.46606e12 | −0.837552 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.60033e12 | −0.588601 | −0.294301 | − | 0.955713i | \(-0.595087\pi\) | ||||
−0.294301 | + | 0.955713i | \(0.595087\pi\) | |||||||
\(734\) | −4.99938e12 | −0.635746 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −7.23282e12 | −0.908568 | ||||||||
\(737\) | 5.80133e12 | 0.724309 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.60245e12 | 1.06102 | 0.530508 | − | 0.847680i | \(-0.322001\pi\) | ||||
0.530508 | + | 0.847680i | \(0.322001\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −1.28941e13 | −1.56161 | ||||||||
\(743\) | 1.31407e12 | 0.158187 | 0.0790934 | − | 0.996867i | \(-0.474797\pi\) | ||||
0.0790934 | + | 0.996867i | \(0.474797\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −4.59574e12 | −0.543289 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −1.10977e12 | −0.129622 | ||||||||
\(749\) | 1.40841e13 | 1.63516 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.95810e12 | −0.912913 | −0.456457 | − | 0.889746i | \(-0.650882\pi\) | ||||
−0.456457 | + | 0.889746i | \(0.650882\pi\) | |||||||
\(752\) | −2.99884e12 | −0.341958 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 2.63650e12 | 0.297068 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 6.95936e12 | 0.770261 | 0.385131 | − | 0.922862i | \(-0.374156\pi\) | ||||
0.385131 | + | 0.922862i | \(0.374156\pi\) | |||||||
\(758\) | 1.46179e12 | 0.160832 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.38632e13 | 1.49841 | 0.749207 | − | 0.662336i | \(-0.230435\pi\) | ||||
0.749207 | + | 0.662336i | \(0.230435\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −4.17757e12 | −0.446234 | ||||||||
\(764\) | −3.31704e12 | −0.352233 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −7.43621e12 | −0.780409 | ||||||||
\(767\) | −6.33977e11 | −0.0661446 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.35604e13 | 1.39832 | 0.699158 | − | 0.714967i | \(-0.253558\pi\) | ||||
0.699158 | + | 0.714967i | \(0.253558\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 2.46267e12 | 0.249534 | ||||||||
\(773\) | 4.96740e12 | 0.500405 | 0.250203 | − | 0.968194i | \(-0.419503\pi\) | ||||
0.250203 | + | 0.968194i | \(0.419503\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | −7.15248e12 | −0.708075 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.55494e12 | −0.445732 | ||||||||
\(779\) | 1.04081e12 | 0.101263 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.67993e11 | −0.0738631 | ||||||||
\(782\) | 8.86713e12 | 0.847916 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −5.60905e12 | −0.530234 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.25809e12 | 0.488587 | 0.244293 | − | 0.969701i | \(-0.421444\pi\) | ||||
0.244293 | + | 0.969701i | \(0.421444\pi\) | |||||||
\(788\) | −8.92227e11 | −0.0824342 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.98298e13 | −2.70929 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5.59792e12 | 0.502686 | ||||||||
\(794\) | 1.17641e12 | 0.105043 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.61152e12 | 0.318846 | ||||||||
\(797\) | 1.61816e13 | 1.42056 | 0.710281 | − | 0.703918i | \(-0.248568\pi\) | ||||
0.710281 | + | 0.703918i | \(0.248568\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.41701e12 | −0.557022 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 4.33596e12 | 0.370084 | ||||||||
\(803\) | −5.22150e12 | −0.443175 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.07373e11 | 0.0173079 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.04476e13 | 1.68768 | ||||||||
\(809\) | 1.39276e13 | 1.14317 | 0.571583 | − | 0.820544i | \(-0.306329\pi\) | ||||
0.571583 | + | 0.820544i | \(0.306329\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.38190e13 | 1.12171 | 0.560857 | − | 0.827913i | \(-0.310472\pi\) | ||||
0.560857 | + | 0.827913i | \(0.310472\pi\) | |||||||
\(812\) | −8.05265e12 | −0.650035 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 3.55540e12 | 0.283844 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 3.33370e12 | 0.261774 | ||||||||
\(818\) | −6.81012e12 | −0.531820 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −3.48578e12 | −0.267766 | −0.133883 | − | 0.990997i | \(-0.542745\pi\) | ||||
−0.133883 | + | 0.990997i | \(0.542745\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 1.21472e13 | 0.922948 | 0.461474 | − | 0.887154i | \(-0.347321\pi\) | ||||
0.461474 | + | 0.887154i | \(0.347321\pi\) | |||||||
\(824\) | −2.20629e13 | −1.66721 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −3.33712e12 | −0.249438 | ||||||||
\(827\) | −1.70702e13 | −1.26901 | −0.634504 | − | 0.772919i | \(-0.718796\pi\) | ||||
−0.634504 | + | 0.772919i | \(0.718796\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.58071e12 | 0.410387 | 0.205194 | − | 0.978721i | \(-0.434218\pi\) | ||||
0.205194 | + | 0.978721i | \(0.434218\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −4.39068e12 | −0.317671 | ||||||||
\(833\) | −1.20024e13 | −0.863707 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 5.72165e11 | 0.0405129 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −1.74378e13 | −1.22150 | ||||||||
\(839\) | −1.28642e13 | −0.896304 | −0.448152 | − | 0.893957i | \(-0.647918\pi\) | ||||
−0.448152 | + | 0.893957i | \(0.647918\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 7.51250e12 | 0.517849 | ||||||||
\(842\) | −2.58819e12 | −0.177457 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 3.40793e12 | 0.231180 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.74471e13 | 1.16479 | ||||||||
\(848\) | −1.02447e13 | −0.680329 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.64835e13 | 1.07738 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.03465e13 | −0.669147 | −0.334574 | − | 0.942370i | \(-0.608592\pi\) | ||||
−0.334574 | + | 0.942370i | \(0.608592\pi\) | |||||||
\(854\) | 2.94663e13 | 1.89568 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.94413e13 | 1.23763 | ||||||||
\(857\) | 5.63216e12 | 0.356666 | 0.178333 | − | 0.983970i | \(-0.442930\pi\) | ||||
0.178333 | + | 0.983970i | \(0.442930\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.28289e13 | −1.43059 | −0.715295 | − | 0.698822i | \(-0.753708\pi\) | ||||
−0.715295 | + | 0.698822i | \(0.753708\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.72401e12 | −0.229736 | ||||||||
\(863\) | 4.62918e12 | 0.284090 | 0.142045 | − | 0.989860i | \(-0.454632\pi\) | ||||
0.142045 | + | 0.989860i | \(0.454632\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 8.67389e11 | 0.0524063 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −6.33379e11 | −0.0378726 | ||||||||
\(869\) | −4.05470e12 | −0.241196 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 8.56913e12 | 0.504493 | ||||||||
\(872\) | −5.76658e12 | −0.337749 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.57162e12 | −0.265014 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.33611e12 | −0.304598 | −0.152299 | − | 0.988334i | \(-0.548668\pi\) | ||||
−0.152299 | + | 0.988334i | \(0.548668\pi\) | |||||||
\(878\) | 7.88294e12 | 0.447675 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −7.87890e12 | −0.440630 | −0.220315 | − | 0.975429i | \(-0.570709\pi\) | ||||
−0.220315 | + | 0.975429i | \(0.570709\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.38973e13 | −0.769320 | −0.384660 | − | 0.923058i | \(-0.625681\pi\) | ||||
−0.384660 | + | 0.923058i | \(0.625681\pi\) | |||||||
\(884\) | −1.63924e12 | −0.0902835 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.36560e13 | 0.744510 | ||||||||
\(887\) | −5.86607e12 | −0.318193 | −0.159097 | − | 0.987263i | \(-0.550858\pi\) | ||||
−0.159097 | + | 0.987263i | \(0.550858\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 8.47881e12 | 0.455278 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.35232e11 | 0.0388851 | ||||||||
\(893\) | 3.30841e12 | 0.174096 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −3.94356e12 | −0.204410 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 2.47103e12 | 0.126805 | ||||||||
\(899\) | 1.73195e12 | 0.0884334 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.19220e13 | −1.10820 | ||||||||
\(902\) | −2.74892e12 | −0.138271 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −4.11761e13 | −2.05063 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −8.52250e12 | −0.418152 | −0.209076 | − | 0.977899i | \(-0.567046\pi\) | ||||
−0.209076 | + | 0.977899i | \(0.567046\pi\) | |||||||
\(908\) | 6.73277e12 | 0.328706 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.63369e13 | −0.785843 | −0.392921 | − | 0.919572i | \(-0.628536\pi\) | ||||
−0.392921 | + | 0.919572i | \(0.628536\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.83580e12 | 0.277960 | ||||||||
\(914\) | −2.35964e12 | −0.111838 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −9.97236e11 | −0.0468024 | ||||||||
\(917\) | −9.02448e12 | −0.421464 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.24712e13 | 1.50169 | 0.750843 | − | 0.660481i | \(-0.229648\pi\) | ||||
0.750843 | + | 0.660481i | \(0.229648\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.44631e13 | 0.659134 | ||||||||
\(923\) | −1.13440e12 | −0.0514468 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 3.21447e13 | 1.43668 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.92459e13 | −0.851868 | ||||||||
\(929\) | 1.24571e13 | 0.548716 | 0.274358 | − | 0.961628i | \(-0.411535\pi\) | ||||
0.274358 | + | 0.961628i | \(0.411535\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.18808e12 | 0.269949 | ||||||||
\(932\) | 4.77843e12 | 0.207450 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.15986e13 | 0.498706 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −9.29012e12 | −0.393725 | −0.196863 | − | 0.980431i | \(-0.563075\pi\) | ||||
−0.196863 | + | 0.980431i | \(0.563075\pi\) | |||||||
\(938\) | 4.51061e13 | 1.90249 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.24831e13 | 1.35053 | 0.675265 | − | 0.737575i | \(-0.264029\pi\) | ||||
0.675265 | + | 0.737575i | \(0.264029\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.27445e13 | −0.524832 | ||||||||
\(944\) | −2.65143e12 | −0.108669 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −8.80474e12 | −0.357443 | ||||||||
\(947\) | −4.16258e13 | −1.68185 | −0.840926 | − | 0.541151i | \(-0.817989\pi\) | ||||
−0.840926 | + | 0.541151i | \(0.817989\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −7.71265e12 | −0.308678 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.21279e13 | −1.26770 | ||||||||
\(953\) | 1.86479e13 | 0.732339 | 0.366169 | − | 0.930548i | \(-0.380669\pi\) | ||||
0.366169 | + | 0.930548i | \(0.380669\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.19097e13 | −0.461148 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 3.37861e13 | 1.29596 | ||||||||
\(959\) | 5.23265e11 | 0.0199774 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.63034e13 | −0.994848 | ||||||||
\(962\) | 5.25167e12 | 0.197702 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −1.91626e13 | −0.714674 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.32990e13 | 0.856875 | 0.428437 | − | 0.903572i | \(-0.359064\pi\) | ||||
0.428437 | + | 0.903572i | \(0.359064\pi\) | |||||||
\(968\) | 2.40835e13 | 0.881617 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 3.63628e13 | 1.31272 | 0.656358 | − | 0.754450i | \(-0.272096\pi\) | ||||
0.656358 | + | 0.754450i | \(0.272096\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.24500e13 | 1.51834 | ||||||||
\(974\) | −2.68839e13 | −0.957145 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 2.34118e13 | 0.825866 | ||||||||
\(977\) | 5.18141e13 | 1.81938 | 0.909688 | − | 0.415291i | \(-0.136320\pi\) | ||||
0.909688 | + | 0.415291i | \(0.136320\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −1.43486e13 | −0.499214 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 1.34516e13 | 0.461608 | ||||||||
\(983\) | −2.54862e13 | −0.870592 | −0.435296 | − | 0.900287i | \(-0.643356\pi\) | ||||
−0.435296 | + | 0.900287i | \(0.643356\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 2.35947e13 | 0.795001 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.45143e11 | 0.0282178 | ||||||||
\(989\) | −4.08205e13 | −1.35673 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.92830e13 | 1.29382 | 0.646910 | − | 0.762567i | \(-0.276061\pi\) | ||||
0.646910 | + | 0.762567i | \(0.276061\pi\) | |||||||
\(992\) | −1.51378e12 | −0.0496318 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5.97124e12 | −0.194011 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.98389e13 | −1.59750 | −0.798748 | − | 0.601665i | \(-0.794504\pi\) | ||||
−0.798748 | + | 0.601665i | \(0.794504\pi\) | |||||||
\(998\) | 1.82340e13 | 0.581827 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 225.10.a.e.1.1 | 1 | ||
3.2 | odd | 2 | 75.10.a.b.1.1 | 1 | |||
5.2 | odd | 4 | 225.10.b.c.199.2 | 2 | |||
5.3 | odd | 4 | 225.10.b.c.199.1 | 2 | |||
5.4 | even | 2 | 9.10.a.a.1.1 | 1 | |||
15.2 | even | 4 | 75.10.b.c.49.1 | 2 | |||
15.8 | even | 4 | 75.10.b.c.49.2 | 2 | |||
15.14 | odd | 2 | 3.10.a.b.1.1 | ✓ | 1 | ||
20.19 | odd | 2 | 144.10.a.m.1.1 | 1 | |||
45.4 | even | 6 | 81.10.c.d.55.1 | 2 | |||
45.14 | odd | 6 | 81.10.c.b.55.1 | 2 | |||
45.29 | odd | 6 | 81.10.c.b.28.1 | 2 | |||
45.34 | even | 6 | 81.10.c.d.28.1 | 2 | |||
60.59 | even | 2 | 48.10.a.a.1.1 | 1 | |||
105.104 | even | 2 | 147.10.a.c.1.1 | 1 | |||
120.29 | odd | 2 | 192.10.a.g.1.1 | 1 | |||
120.59 | even | 2 | 192.10.a.n.1.1 | 1 | |||
165.164 | even | 2 | 363.10.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
3.10.a.b.1.1 | ✓ | 1 | 15.14 | odd | 2 | ||
9.10.a.a.1.1 | 1 | 5.4 | even | 2 | |||
48.10.a.a.1.1 | 1 | 60.59 | even | 2 | |||
75.10.a.b.1.1 | 1 | 3.2 | odd | 2 | |||
75.10.b.c.49.1 | 2 | 15.2 | even | 4 | |||
75.10.b.c.49.2 | 2 | 15.8 | even | 4 | |||
81.10.c.b.28.1 | 2 | 45.29 | odd | 6 | |||
81.10.c.b.55.1 | 2 | 45.14 | odd | 6 | |||
81.10.c.d.28.1 | 2 | 45.34 | even | 6 | |||
81.10.c.d.55.1 | 2 | 45.4 | even | 6 | |||
144.10.a.m.1.1 | 1 | 20.19 | odd | 2 | |||
147.10.a.c.1.1 | 1 | 105.104 | even | 2 | |||
192.10.a.g.1.1 | 1 | 120.29 | odd | 2 | |||
192.10.a.n.1.1 | 1 | 120.59 | even | 2 | |||
225.10.a.e.1.1 | 1 | 1.1 | even | 1 | trivial | ||
225.10.b.c.199.1 | 2 | 5.3 | odd | 4 | |||
225.10.b.c.199.2 | 2 | 5.2 | odd | 4 | |||
363.10.a.a.1.1 | 1 | 165.164 | even | 2 |