Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [80,10,Mod(1,80)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(80, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("80.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 80 = 2^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 80.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: | \(41.2028668931\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\sqrt{46}) \) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 46 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{3}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 40) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-6.78233\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 80.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −216.776 | −1.54513 | −0.772566 | − | 0.634935i | \(-0.781027\pi\) | ||||
−0.772566 | + | 0.634935i | \(0.781027\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −625.000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1662.09 | −0.261645 | −0.130823 | − | 0.991406i | \(-0.541762\pi\) | ||||
−0.130823 | + | 0.991406i | \(0.541762\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 27308.8 | 1.38743 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −34372.0 | −0.707844 | −0.353922 | − | 0.935275i | \(-0.615152\pi\) | ||||
−0.353922 | + | 0.935275i | \(0.615152\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 162675. | 1.57971 | 0.789853 | − | 0.613296i | \(-0.210157\pi\) | ||||
0.789853 | + | 0.613296i | \(0.210157\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 135485. | 0.691004 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 91796.1 | 0.266566 | 0.133283 | − | 0.991078i | \(-0.457448\pi\) | ||||
0.133283 | + | 0.991078i | \(0.457448\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 536227. | 0.943969 | 0.471985 | − | 0.881607i | \(-0.343538\pi\) | ||||
0.471985 | + | 0.881607i | \(0.343538\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 360300. | 0.404276 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −234899. | −0.175027 | −0.0875136 | − | 0.996163i | \(-0.527892\pi\) | ||||
−0.0875136 | + | 0.996163i | \(0.527892\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 390625. | 0.200000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.65309e6 | −0.598631 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.25706e6 | 1.90533 | 0.952665 | − | 0.304023i | \(-0.0983301\pi\) | ||||
0.952665 | + | 0.304023i | \(0.0983301\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −8.23051e6 | −1.60066 | −0.800330 | − | 0.599559i | \(-0.795343\pi\) | ||||
−0.800330 | + | 0.599559i | \(0.795343\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 7.45102e6 | 1.09371 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1.03880e6 | 0.117011 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.56850e7 | −1.37587 | −0.687936 | − | 0.725771i | \(-0.741483\pi\) | ||||
−0.687936 | + | 0.725771i | \(0.741483\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −3.52641e7 | −2.44085 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −1.67318e7 | −0.924730 | −0.462365 | − | 0.886690i | \(-0.652999\pi\) | ||||
−0.462365 | + | 0.886690i | \(0.652999\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.36208e6 | −0.417604 | −0.208802 | − | 0.977958i | \(-0.566956\pi\) | ||||
−0.208802 | + | 0.977958i | \(0.566956\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −1.70680e7 | −0.620478 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.69410e7 | 0.805328 | 0.402664 | − | 0.915348i | \(-0.368084\pi\) | ||||
0.402664 | + | 0.915348i | \(0.368084\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −3.75911e7 | −0.931542 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −1.98992e7 | −0.411879 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.41105e7 | 0.593809 | 0.296905 | − | 0.954907i | \(-0.404046\pi\) | ||||
0.296905 | + | 0.954907i | \(0.404046\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.14825e7 | 0.316557 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.16241e8 | −1.45856 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −1.12155e8 | −1.20499 | −0.602496 | − | 0.798122i | \(-0.705827\pi\) | ||||
−0.602496 | + | 0.798122i | \(0.705827\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.49531e6 | 0.0508168 | 0.0254084 | − | 0.999677i | \(-0.491911\pi\) | ||||
0.0254084 | + | 0.999677i | \(0.491911\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −4.53896e7 | −0.363014 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.01672e8 | −0.706466 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 2.40686e8 | 1.45920 | 0.729598 | − | 0.683876i | \(-0.239707\pi\) | ||||
0.729598 | + | 0.683876i | \(0.239707\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 5.09204e7 | 0.270440 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.58502e8 | 1.20726 | 0.603631 | − | 0.797264i | \(-0.293720\pi\) | ||||
0.603631 | + | 0.797264i | \(0.293720\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.53583e8 | −1.45726 | −0.728632 | − | 0.684905i | \(-0.759844\pi\) | ||||
−0.728632 | + | 0.684905i | \(0.759844\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.46781e7 | −0.309026 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 5.71292e7 | 0.185204 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −3.66190e8 | −1.05775 | −0.528876 | − | 0.848699i | \(-0.677386\pi\) | ||||
−0.528876 | + | 0.848699i | \(0.677386\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −1.79169e8 | −0.462467 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 9.74953e6 | 0.0225493 | 0.0112746 | − | 0.999936i | \(-0.496411\pi\) | ||||
0.0112746 | + | 0.999936i | \(0.496411\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.73726e7 | −0.119212 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.57316e9 | −2.94398 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1.14201e9 | −1.92937 | −0.964687 | − | 0.263397i | \(-0.915157\pi\) | ||||
−0.964687 | + | 0.263397i | \(0.915157\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −2.70380e8 | −0.413322 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.78418e9 | 2.47323 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −3.35142e8 | −0.422156 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1.25555e9 | 1.44000 | 0.719999 | − | 0.693975i | \(-0.244142\pi\) | ||||
0.719999 | + | 0.693975i | \(0.244142\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −9.38657e8 | −0.982084 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.63563e8 | 0.252022 | 0.126011 | − | 0.992029i | \(-0.459783\pi\) | ||||
0.126011 | + | 0.992029i | \(0.459783\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 2.09532e9 | 1.83435 | 0.917176 | − | 0.398482i | \(-0.130463\pi\) | ||||
0.917176 | + | 0.398482i | \(0.130463\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −2.25188e8 | −0.180798 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 3.30509e8 | 0.243757 | 0.121878 | − | 0.992545i | \(-0.461108\pi\) | ||||
0.121878 | + | 0.992545i | \(0.461108\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −1.65293e9 | −1.12160 | −0.560798 | − | 0.827953i | \(-0.689505\pi\) | ||||
−0.560798 | + | 0.827953i | \(0.689505\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 3.40014e9 | 2.12590 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.15695e9 | 0.667513 | 0.333757 | − | 0.942659i | \(-0.391684\pi\) | ||||
0.333757 | + | 0.942659i | \(0.391684\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.46812e8 | 0.0782745 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 4.44246e9 | 2.19173 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1.52573e8 | −0.0697456 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.17652e9 | −0.498957 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 3.62705e9 | 1.42883 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −2.44141e8 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.56129e9 | −0.532559 | −0.266280 | − | 0.963896i | \(-0.585794\pi\) | ||||
−0.266280 | + | 0.963896i | \(0.585794\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 2.02947e9 | 0.645253 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.75445e9 | 1.41052 | 0.705261 | − | 0.708948i | \(-0.250830\pi\) | ||||
0.705261 | + | 0.708948i | \(0.250830\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.91256e8 | −0.246985 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 1.03318e9 | 0.267716 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1.57706e9 | 0.382478 | 0.191239 | − | 0.981543i | \(-0.438749\pi\) | ||||
0.191239 | + | 0.981543i | \(0.438749\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −3.40723e9 | −0.774167 | −0.387084 | − | 0.922045i | \(-0.626518\pi\) | ||||
−0.387084 | + | 0.922045i | \(0.626518\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −5.84015e9 | −1.24434 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.59147e9 | −1.11818 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −4.53567e9 | −0.852089 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 8.14884e9 | 1.43935 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.20713e8 | −0.0699274 | −0.0349637 | − | 0.999389i | \(-0.511132\pi\) | ||||
−0.0349637 | + | 0.999389i | \(0.511132\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.74377e9 | 0.272957 | 0.136478 | − | 0.990643i | \(-0.456422\pi\) | ||||
0.136478 | + | 0.990643i | \(0.456422\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.50684e9 | 0.369841 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.14407e9 | 0.715837 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.13142e9 | −0.805402 | −0.402701 | − | 0.915332i | \(-0.631929\pi\) | ||||
−0.402701 | + | 0.915332i | \(0.631929\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −7.39434e9 | −0.917513 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 3.90422e8 | 0.0457950 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.07953e10 | −1.19782 | −0.598910 | − | 0.800816i | \(-0.704399\pi\) | ||||
−0.598910 | + | 0.800816i | \(0.704399\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −4.65689e9 | −0.489123 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −1.55417e10 | −1.54623 | −0.773115 | − | 0.634266i | \(-0.781302\pi\) | ||||
−0.773115 | + | 0.634266i | \(0.781302\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.58587e10 | 1.49547 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.46437e10 | 1.30969 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3.21498e9 | 0.272880 | 0.136440 | − | 0.990648i | \(-0.456434\pi\) | ||||
0.136440 | + | 0.990648i | \(0.456434\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −6.49253e8 | −0.0523290 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.43125e10 | 1.86187 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.10234e10 | −1.53061 | −0.765305 | − | 0.643667i | \(-0.777412\pi\) | ||||
−0.765305 | + | 0.643667i | \(0.777412\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.54514e10 | −1.07008 | −0.535038 | − | 0.844828i | \(-0.679703\pi\) | ||||
−0.535038 | + | 0.844828i | \(0.679703\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.19125e9 | −0.0785187 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 9.80315e9 | 0.615309 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −3.15521e9 | −0.188687 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.74758e9 | 0.156629 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −2.53988e10 | −1.38090 | −0.690451 | − | 0.723380i | \(-0.742588\pi\) | ||||
−0.690451 | + | 0.723380i | \(0.742588\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1.70167e10 | −0.882809 | −0.441404 | − | 0.897308i | \(-0.645520\pi\) | ||||
−0.441404 | + | 0.897308i | \(0.645520\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2.20400e10 | 1.09158 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 4.38218e9 | 0.207297 | 0.103648 | − | 0.994614i | \(-0.466948\pi\) | ||||
0.103648 | + | 0.994614i | \(0.466948\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 1.37237e10 | 0.620343 | 0.310171 | − | 0.950681i | \(-0.399614\pi\) | ||||
0.310171 | + | 0.950681i | \(0.399614\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −5.21749e10 | −2.25465 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −1.20619e10 | −0.498520 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.04574e10 | 0.413552 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −6.41480e9 | −0.242838 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.84312e10 | −0.668183 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.21366e10 | 0.421526 | 0.210763 | − | 0.977537i | \(-0.432405\pi\) | ||||
0.210763 | + | 0.977537i | \(0.432405\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −5.60370e10 | −1.86538 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 5.85130e9 | 0.186758 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.36798e10 | 0.418805 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 7.66483e10 | 2.25166 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.49330e10 | 0.421095 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −6.20297e10 | −1.67968 | −0.839842 | − | 0.542830i | \(-0.817353\pi\) | ||||
−0.839842 | + | 0.542830i | \(0.817353\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.06675e10 | 0.277486 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −3.51959e10 | −0.879783 | −0.439891 | − | 0.898051i | \(-0.644983\pi\) | ||||
−0.439891 | + | 0.898051i | \(0.644983\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3.83973e10 | −0.922659 | −0.461329 | − | 0.887229i | \(-0.652627\pi\) | ||||
−0.461329 | + | 0.887229i | \(0.652627\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −1.23842e10 | −0.286164 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −2.59156e10 | −0.576049 | −0.288024 | − | 0.957623i | \(-0.592998\pi\) | ||||
−0.288024 | + | 0.957623i | \(0.592998\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.68381e10 | −0.360153 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 7.93811e10 | 1.63437 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −5.76903e10 | −1.14370 | −0.571850 | − | 0.820358i | \(-0.693774\pi\) | ||||
−0.571850 | + | 0.820358i | \(0.693774\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −4.59383e10 | −0.877200 | −0.438600 | − | 0.898682i | \(-0.644525\pi\) | ||||
−0.438600 | + | 0.898682i | \(0.644525\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 7.13773e10 | 1.31320 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.34944e10 | 0.416598 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 8.72309e10 | 1.49119 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −2.11346e9 | −0.0348416 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6.33143e10 | 1.00686 | 0.503431 | − | 0.864035i | \(-0.332071\pi\) | ||||
0.503431 | + | 0.864035i | \(0.332071\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 8.07393e9 | 0.123892 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 1.24370e10 | 0.184198 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 4.21910e10 | 0.603283 | 0.301642 | − | 0.953421i | \(-0.402465\pi\) | ||||
0.301642 | + | 0.953421i | \(0.402465\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.60699e10 | 0.359990 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.98182e11 | 2.64351 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.01270e10 | −0.646057 | −0.323028 | − | 0.946389i | \(-0.604701\pi\) | ||||
−0.323028 | + | 0.946389i | \(0.604701\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.13191e10 | −0.265560 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.47561e11 | 2.98114 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 7.21552e10 | 0.840199 | 0.420099 | − | 0.907478i | \(-0.361995\pi\) | ||||
0.420099 | + | 0.907478i | \(0.361995\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.23276e10 | −0.589344 | −0.294672 | − | 0.955598i | \(-0.595210\pi\) | ||||
−0.294672 | + | 0.955598i | \(0.595210\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 5.86119e10 | 0.638637 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −1.34266e10 | −0.141569 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −5.78954e10 | −0.590860 | −0.295430 | − | 0.955364i | \(-0.595463\pi\) | ||||
−0.295430 | + | 0.955364i | \(0.595463\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −2.24765e11 | −2.22081 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 7.31211e10 | 0.699623 | 0.349812 | − | 0.936820i | \(-0.386246\pi\) | ||||
0.349812 | + | 0.936820i | \(0.386246\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 5.12368e10 | 0.474835 | 0.237418 | − | 0.971408i | \(-0.423699\pi\) | ||||
0.237418 | + | 0.971408i | \(0.423699\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 7.26507e10 | 0.652286 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 2.78097e10 | 0.241951 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.10161e11 | −0.928943 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −2.72173e11 | −2.22499 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 1.95934e11 | 1.55312 | 0.776561 | − | 0.630043i | \(-0.216963\pi\) | ||||
0.776561 | + | 0.630043i | \(0.216963\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.00968e10 | 0.538889 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 5.68200e10 | 0.423737 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −3.82122e10 | −0.276491 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.55606e10 | 0.109264 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.71341e10 | −0.389407 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.43457e9 | −0.0227260 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.29564e11 | 1.47496 | 0.737481 | − | 0.675368i | \(-0.236015\pi\) | ||||
0.737481 | + | 0.675368i | \(0.236015\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −4.54215e11 | −2.83431 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.99151e10 | −0.302559 | −0.151280 | − | 0.988491i | \(-0.548339\pi\) | ||||
−0.151280 | + | 0.988491i | \(0.548339\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.19272e11 | −0.702408 | −0.351204 | − | 0.936299i | \(-0.614228\pi\) | ||||
−0.351204 | + | 0.936299i | \(0.614228\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 2.83685e10 | 0.162345 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −2.85879e11 | −1.59007 | −0.795034 | − | 0.606565i | \(-0.792547\pi\) | ||||
−0.795034 | + | 0.606565i | \(0.792547\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.49440e11 | −1.34868 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.16464e10 | −0.376636 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 4.92236e10 | 0.251630 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 6.35450e10 | 0.315941 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 3.58316e11 | 1.73301 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −4.47782e10 | −0.210710 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2.12047e11 | 0.970973 | 0.485486 | − | 0.874244i | \(-0.338643\pi\) | ||||
0.485486 | + | 0.874244i | \(0.338643\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −4.28340e11 | −1.90893 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −1.50429e11 | −0.652573 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.00430e11 | 0.846502 | 0.423251 | − | 0.906012i | \(-0.360889\pi\) | ||||
0.423251 | + | 0.906012i | \(0.360889\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.50798e11 | −1.03140 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 2.82899e11 | 1.13302 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.29551e11 | 0.505378 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −3.18252e10 | −0.120944 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 9.86210e10 | 0.365163 | 0.182582 | − | 0.983191i | \(-0.441555\pi\) | ||||
0.182582 | + | 0.983191i | \(0.441555\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −4.79143e11 | −1.72882 | −0.864411 | − | 0.502785i | \(-0.832309\pi\) | ||||
−0.864411 | + | 0.502785i | \(0.832309\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.68917e11 | −0.945662 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.56755e11 | 1.56566 | 0.782830 | − | 0.622235i | \(-0.213775\pi\) | ||||
0.782830 | + | 0.622235i | \(0.213775\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.61564e11 | −0.539904 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 3.30742e10 | 0.107766 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.54059e11 | 0.489509 | 0.244755 | − | 0.969585i | \(-0.421293\pi\) | ||||
0.244755 | + | 0.969585i | \(0.421293\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.51479e10 | −0.108922 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 2.55040e11 | 0.770954 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.20989e11 | 0.651708 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −3.42604e11 | −0.985815 | −0.492908 | − | 0.870082i | \(-0.664066\pi\) | ||||
−0.492908 | + | 0.870082i | \(0.664066\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −4.56925e11 | −1.28300 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −5.66947e10 | −0.155367 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.68130e11 | −0.449734 | −0.224867 | − | 0.974389i | \(-0.572195\pi\) | ||||
−0.224867 | + | 0.974389i | \(0.572195\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 5.29238e10 | 0.138201 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1.18054e12 | 3.00986 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.00434e11 | 0.250038 | 0.125019 | − | 0.992154i | \(-0.460101\pi\) | ||||
0.125019 | + | 0.992154i | \(0.460101\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 3.38451e11 | 0.822874 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −5.07533e11 | −1.20523 | −0.602615 | − | 0.798032i | \(-0.705874\pi\) | ||||
−0.602615 | + | 0.798032i | \(0.705874\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −3.57058e10 | −0.0828257 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −2.55667e11 | −0.579396 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.26566e11 | −0.280249 | −0.140125 | − | 0.990134i | \(-0.544750\pi\) | ||||
−0.140125 | + | 0.990134i | \(0.544750\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.15628e10 | −0.0466562 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.03065e12 | −2.17944 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 2.28868e11 | 0.473041 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.70667e11 | −0.950948 | −0.475474 | − | 0.879730i | \(-0.657723\pi\) | ||||
−0.475474 | + | 0.879730i | \(0.657723\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.93203e11 | 0.381624 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −9.20810e11 | −1.77836 | −0.889182 | − | 0.457554i | \(-0.848726\pi\) | ||||
−0.889182 | + | 0.457554i | \(0.848726\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.33890e12 | −2.52857 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1.11981e11 | 0.206821 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.39126e11 | 0.973902 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.23952e11 | 1.45595 | 0.727976 | − | 0.685603i | \(-0.240461\pi\) | ||||
0.727976 | + | 0.685603i | \(0.240461\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −3.41870e11 | −0.590979 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.86411e11 | 0.315280 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −6.09345e9 | −0.0100843 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 7.38605e11 | 1.19619 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −7.01758e11 | −1.11231 | −0.556153 | − | 0.831080i | \(-0.687723\pi\) | ||||
−0.556153 | + | 0.831080i | \(0.687723\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.22669e11 | 0.190311 | 0.0951555 | − | 0.995462i | \(-0.469665\pi\) | ||||
0.0951555 | + | 0.995462i | \(0.469665\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 7.35725e11 | 1.11734 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.58579e10 | 0.0533131 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −9.13368e9 | −0.0132960 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.21210e12 | 1.72774 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 4.82937e11 | 0.674129 | 0.337064 | − | 0.941482i | \(-0.390566\pi\) | ||||
0.337064 | + | 0.941482i | \(0.390566\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 7.71175e11 | 1.05428 | 0.527142 | − | 0.849777i | \(-0.323264\pi\) | ||||
0.527142 | + | 0.849777i | \(0.323264\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.83223e11 | 1.31659 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.25959e11 | −0.165220 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 6.62301e11 | 0.851070 | 0.425535 | − | 0.904942i | \(-0.360086\pi\) | ||||
0.425535 | + | 0.904942i | \(0.360086\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.02657e12 | −1.29245 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.76774e11 | 0.464798 | 0.232399 | − | 0.972621i | \(-0.425343\pi\) | ||||
0.232399 | + | 0.972621i | \(0.425343\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 7.13759e11 | 0.862843 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 9.12004e10 | 0.108047 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 5.77774e11 | 0.670888 | 0.335444 | − | 0.942060i | \(-0.391114\pi\) | ||||
0.335444 | + | 0.942060i | \(0.391114\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 5.75105e11 | 0.654564 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.78008e11 | −0.421754 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.68988e11 | 0.184843 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.28175e11 | −0.888176 | −0.444088 | − | 0.895983i | \(-0.646472\pi\) | ||||
−0.444088 | + | 0.895983i | \(0.646472\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −1.51747e11 | −0.159575 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.77554e11 | 0.286216 | 0.143108 | − | 0.989707i | \(-0.454290\pi\) | ||||
0.143108 | + | 0.989707i | \(0.454290\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.01088e11 | 0.102232 | 0.0511159 | − | 0.998693i | \(-0.483722\pi\) | ||||
0.0511159 | + | 0.998693i | \(0.483722\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.11511e12 | −1.10606 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.30742e12 | 1.27201 | 0.636004 | − | 0.771686i | \(-0.280586\pi\) | ||||
0.636004 | + | 0.771686i | \(0.280586\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −4.00041e11 | −0.381792 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1.32914e12 | 1.24445 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 3.21793e11 | 0.295598 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.09464e11 | 0.188794 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 9.31518e11 | 0.823869 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.38500e12 | 1.20210 | 0.601049 | − | 0.799212i | \(-0.294750\pi\) | ||||
0.601049 | + | 0.799212i | \(0.294750\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.55157e12 | −2.17347 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −8.46341e10 | −0.0707593 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −7.84720e11 | −0.643987 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −9.54305e11 | −0.768789 | −0.384394 | − | 0.923169i | \(-0.625590\pi\) | ||||
−0.384394 | + | 0.923169i | \(0.625590\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 2.34017e12 | 1.85079 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 7.41251e11 | 0.575571 | 0.287785 | − | 0.957695i | \(-0.407081\pi\) | ||||
0.287785 | + | 0.957695i | \(0.407081\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.66171e11 | 0.507895 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 5.86661e11 | 0.439201 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −4.29653e11 | −0.315874 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.51393e12 | −1.09308 | −0.546542 | − | 0.837432i | \(-0.684056\pi\) | ||||
−0.546542 | + | 0.837432i | \(0.684056\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 3.36906e12 | 2.38913 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.58191e12 | −1.10186 | −0.550929 | − | 0.834552i | \(-0.685726\pi\) | ||||
−0.550929 | + | 0.834552i | \(0.685726\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.64727e11 | −0.112708 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −3.43779e12 | −2.31070 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −2.29553e11 | −0.151584 | −0.0757918 | − | 0.997124i | \(-0.524148\pi\) | ||||
−0.0757918 | + | 0.997124i | \(0.524148\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 5.87686e11 | 0.381286 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −8.86432e11 | −0.565089 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.30957e12 | −0.820347 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.26014e11 | −0.570046 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −6.96931e11 | −0.421635 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −1.73274e12 | −1.03030 | −0.515149 | − | 0.857101i | \(-0.672263\pi\) | ||||
−0.515149 | + | 0.857101i | \(0.672263\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.45691e12 | −1.43592 | −0.717961 | − | 0.696083i | \(-0.754925\pi\) | ||||
−0.717961 | + | 0.696083i | \(0.754925\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 1.40742e11 | 0.0808552 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.55529e11 | −0.426681 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.74598e12 | −0.969366 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −3.06281e12 | −1.67184 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.72185e12 | −1.46080 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.06568e11 | −0.109011 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.55737e12 | 2.36499 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.29208e12 | 0.659386 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.10080e12 | −1.05438 | −0.527190 | − | 0.849748i | \(-0.676754\pi\) | ||||
−0.527190 | + | 0.849748i | \(0.676754\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 3.34949e12 | 1.65341 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 1.03308e12 | 0.501593 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −3.58621e12 | −1.71275 | −0.856373 | − | 0.516357i | \(-0.827288\pi\) | ||||
−0.856373 | + | 0.516357i | \(0.827288\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1.50070e11 | 0.0705048 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 3.89144e12 | 1.79857 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 6.08639e11 | 0.276756 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.12509e12 | −0.950733 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −3.15166e12 | −1.38737 | −0.693683 | − | 0.720280i | \(-0.744013\pi\) | ||||
−0.693683 | + | 0.720280i | \(0.744013\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.52298e12 | −0.659691 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 6.83975e11 | 0.291546 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 3.70986e12 | 1.55621 | 0.778107 | − | 0.628131i | \(-0.216180\pi\) | ||||
0.778107 | + | 0.628131i | \(0.216180\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −7.23091e11 | −0.298521 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 2.97795e11 | 0.121002 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.52350e12 | −0.609308 | −0.304654 | − | 0.952463i | \(-0.598541\pi\) | ||||
−0.304654 | + | 0.952463i | \(0.598541\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.81914e12 | −1.10982 | −0.554911 | − | 0.831909i | \(-0.687248\pi\) | ||||
−0.554911 | + | 0.831909i | \(0.687248\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 5.50584e12 | 2.13367 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −9.17573e10 | −0.0350054 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −2.80815e11 | −0.105470 | −0.0527350 | − | 0.998609i | \(-0.516794\pi\) | ||||
−0.0527350 | + | 0.998609i | \(0.516794\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 3.68880e12 | 1.36406 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.62046e10 | −0.00589990 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.17245e12 | −0.420324 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −2.77654e12 | −0.980173 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.71929e12 | −0.597691 | −0.298845 | − | 0.954302i | \(-0.596601\pi\) | ||||
−0.298845 | + | 0.954302i | \(0.596601\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −4.41343e12 | −1.51097 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.49952e11 | −0.320301 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.82940e12 | 1.60379 | 0.801895 | − | 0.597465i | \(-0.203825\pi\) | ||||
0.801895 | + | 0.597465i | \(0.203825\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.53582e10 | 0.0311912 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −2.97496e12 | −0.958511 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1.72589e12 | −0.547763 | −0.273881 | − | 0.961763i | \(-0.588308\pi\) | ||||
−0.273881 | + | 0.961763i | \(0.588308\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5.06692e12 | 1.58420 | 0.792098 | − | 0.610394i | \(-0.208989\pi\) | ||||
0.792098 | + | 0.610394i | \(0.208989\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 6.57284e12 | 2.02453 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.35322e11 | 0.223140 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.57706e12 | 0.471520 | 0.235760 | − | 0.971811i | \(-0.424242\pi\) | ||||
0.235760 | + | 0.971811i | \(0.424242\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 2.61472e12 | 0.770279 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.38263e12 | 1.27218 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.35557e12 | −0.387747 | −0.193874 | − | 0.981026i | \(-0.562105\pi\) | ||||
−0.193874 | + | 0.981026i | \(0.562105\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −2.26691e12 | −0.638992 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −4.35935e12 | −1.21098 | −0.605492 | − | 0.795852i | \(-0.707023\pi\) | ||||
−0.605492 | + | 0.795852i | \(0.707023\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.67780e12 | −0.459338 | −0.229669 | − | 0.973269i | \(-0.573764\pi\) | ||||
−0.229669 | + | 0.973269i | \(0.573764\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.88309e11 | 0.104777 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.89813e12 | 0.504811 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.52588e11 | 0.0400000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 3.99544e12 | 1.03243 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.43983e12 | −0.366760 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.12439e12 | −1.03568 | −0.517842 | − | 0.855476i | \(-0.673264\pi\) | ||||
−0.517842 | + | 0.855476i | \(0.673264\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.63091e12 | −0.651313 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 9.75808e11 | 0.238168 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −6.11514e12 | −1.47156 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 7.05938e12 | 1.67499 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 2.54925e12 | 0.596420 | 0.298210 | − | 0.954500i | \(-0.403610\pi\) | ||||
0.298210 | + | 0.954500i | \(0.403610\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1.49409e11 | 0.0344688 | 0.0172344 | − | 0.999851i | \(-0.494514\pi\) | ||||
0.0172344 | + | 0.999851i | \(0.494514\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.26842e12 | −0.288566 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.88552e11 | 0.176913 | 0.0884567 | − | 0.996080i | \(-0.471806\pi\) | ||||
0.0884567 | + | 0.996080i | \(0.471806\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 3.85498e12 | 0.852946 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.96546e12 | −0.647109 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.87557e12 | 0.403668 | 0.201834 | − | 0.979420i | \(-0.435310\pi\) | ||||
0.201834 | + | 0.979420i | \(0.435310\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.97153e12 | −0.630805 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −9.65592e12 | −2.02185 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 2.02453e11 | 0.0418158 | 0.0209079 | − | 0.999781i | \(-0.493344\pi\) | ||||
0.0209079 | + | 0.999781i | \(0.493344\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 2.41063e12 | 0.491160 | 0.245580 | − | 0.969376i | \(-0.421022\pi\) | ||||
0.245580 | + | 0.969376i | \(0.421022\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −3.23711e12 | −0.650648 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 5.57035e11 | 0.110455 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.70468e12 | −0.333484 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.34465e13 | 2.59533 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.88885e11 | −0.0359704 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −5.63582e11 | −0.105898 | −0.0529491 | − | 0.998597i | \(-0.516862\pi\) | ||||
−0.0529491 | + | 0.998597i | \(0.516862\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −6.45738e11 | −0.119726 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 8.43518e11 | 0.154328 | 0.0771641 | − | 0.997018i | \(-0.475413\pi\) | ||||
0.0771641 | + | 0.997018i | \(0.475413\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −2.08684e12 | −0.376768 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.62962e12 | 1.35938 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.43927e12 | −0.956418 | −0.478209 | − | 0.878246i | \(-0.658714\pi\) | ||||
−0.478209 | + | 0.878246i | \(0.658714\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.85665e11 | −0.171050 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.32361e12 | 1.42563 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 5.54894e12 | 0.938044 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.41900e12 | 0.236773 | 0.118386 | − | 0.992968i | \(-0.462228\pi\) | ||||
0.118386 | + | 0.992968i | \(0.462228\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 1.56013e12 | 0.256957 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 2.12952e12 | 0.346218 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.53591e12 | −0.246501 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.61787e12 | 0.890071 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 9.10116e12 | 1.42353 | 0.711763 | − | 0.702419i | \(-0.247897\pi\) | ||||
0.711763 | + | 0.702419i | \(0.247897\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.41075e12 | −1.29878 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 3.65009e12 | 0.556484 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.38064e11 | −0.0659402 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 3.00283e12 | 0.446296 | 0.223148 | − | 0.974785i | \(-0.428367\pi\) | ||||
0.223148 | + | 0.974785i | \(0.428367\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.00002e13 | −1.46756 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.93334e12 | 0.280159 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.49467e12 | 0.500068 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 1.25059e13 | 1.76717 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 8.40313e12 | 1.17263 | 0.586315 | − | 0.810083i | \(-0.300578\pi\) | ||||
0.586315 | + | 0.810083i | \(0.300578\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.48260e12 | −0.479949 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 9.95833e12 | 1.35539 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.83479e12 | 0.381066 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −6.70907e12 | −0.890753 | −0.445377 | − | 0.895343i | \(-0.646930\pi\) | ||||
−0.445377 | + | 0.895343i | \(0.646930\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.19463e13 | −1.56660 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −8.59403e11 | −0.111319 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.50813e12 | 0.192962 | 0.0964810 | − | 0.995335i | \(-0.469241\pi\) | ||||
0.0964810 | + | 0.995335i | \(0.469241\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −5.09302e12 | −0.643699 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −8.27285e12 | −1.03288 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.48289e13 | 1.82898 | 0.914492 | − | 0.404603i | \(-0.132590\pi\) | ||||
0.914492 | + | 0.404603i | \(0.132590\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.89096e13 | −2.30409 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1.91312e12 | 0.230299 | 0.115150 | − | 0.993348i | \(-0.463265\pi\) | ||||
0.115150 | + | 0.993348i | \(0.463265\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.62945e11 | 0.0312725 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.66248e11 | 0.0312855 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −5.49335e11 | −0.0637777 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.50309e12 | 0.746002 | 0.373001 | − | 0.927831i | \(-0.378329\pi\) | ||||
0.373001 | + | 0.927831i | \(0.378329\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.37250e13 | −1.55573 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −1.08986e12 | −0.122070 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.11069e11 | −0.0122931 | −0.00614653 | − | 0.999981i | \(-0.501957\pi\) | ||||
−0.00614653 | + | 0.999981i | \(0.501957\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −1.75023e12 | −0.191429 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.21294e13 | 1.31102 | 0.655510 | − | 0.755186i | \(-0.272454\pi\) | ||||
0.655510 | + | 0.755186i | \(0.272454\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 2.74732e12 | 0.293460 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −1.56678e12 | −0.165398 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −1.82448e13 | −1.90353 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.19313e13 | −1.23033 | −0.615164 | − | 0.788399i | \(-0.710910\pi\) | ||||
−0.615164 | + | 0.788399i | \(0.710910\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −9.14600e12 | −0.932152 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.71471e13 | −1.72736 | −0.863681 | − | 0.504038i | \(-0.831847\pi\) | ||||
−0.863681 | + | 0.504038i | \(0.831847\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −3.21504e12 | −0.320132 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −5.65133e12 | −0.556232 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −8.97204e12 | −0.872917 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −8.88523e12 | −0.854553 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.19966e13 | −1.14059 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.83214e12 | 0.360187 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.12129e11 | 0.0197112 | 0.00985561 | − | 0.999951i | \(-0.496863\pi\) | ||||
0.00985561 | + | 0.999951i | \(0.496863\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1.08663e13 | 0.998242 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.92294e12 | −0.174652 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 8.93950e11 | 0.0802757 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.62146e12 | 0.410325 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 9.75044e12 | 0.855976 | 0.427988 | − | 0.903784i | \(-0.359223\pi\) | ||||
0.427988 | + | 0.903784i | \(0.359223\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.47308e12 | 0.214673 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −3.11870e13 | −2.67687 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1.21533e13 | 1.03152 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −2.44014e11 | −0.0204801 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1.56415e13 | −1.29822 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1.00162e13 | 0.822120 | 0.411060 | − | 0.911608i | \(-0.365159\pi\) | ||||
0.411060 | + | 0.911608i | \(0.365159\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.09433e11 | −0.00888287 | −0.00444143 | − | 0.999990i | \(-0.501414\pi\) | ||||
−0.00444143 | + | 0.999990i | \(0.501414\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.13434e13 | 0.910614 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 6.74708e12 | 0.535681 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5.02020e12 | −0.394205 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −7.38376e12 | −0.573456 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.10914e13 | −1.62017 | −0.810086 | − | 0.586312i | \(-0.800579\pi\) | ||||
−0.810086 | + | 0.586312i | \(0.800579\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −6.07029e12 | −0.461222 | −0.230611 | − | 0.973046i | \(-0.574073\pi\) | ||||
−0.230611 | + | 0.973046i | \(0.574073\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 2.91055e12 | 0.218742 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.09879e13 | 0.816846 | 0.408423 | − | 0.912793i | \(-0.366079\pi\) | ||||
0.408423 | + | 0.912793i | \(0.366079\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.34601e13 | −0.989811 | −0.494906 | − | 0.868947i | \(-0.664797\pi\) | ||||
−0.494906 | + | 0.868947i | \(0.664797\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 1.25503e13 | 0.912957 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.45072e12 | −0.248317 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 9.71355e12 | 0.691495 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 1.36058e13 | 0.958206 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 4.34425e12 | 0.302681 | 0.151341 | − | 0.988482i | \(-0.451641\pi\) | ||||
0.151341 | + | 0.988482i | \(0.451641\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3.81578e13 | 2.63028 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.58509e13 | −1.08101 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −9.91170e12 | −0.668795 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.95547e12 | 0.130550 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.11069e13 | −0.733683 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 3.68440e12 | 0.240815 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −1.33638e13 | −0.864290 | −0.432145 | − | 0.901804i | \(-0.642243\pi\) | ||||
−0.432145 | + | 0.901804i | \(0.642243\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −9.15233e12 | −0.585712 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.60497e13 | 1.64964 | 0.824819 | − | 0.565397i | \(-0.191277\pi\) | ||||
0.824819 | + | 0.565397i | \(0.191277\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −2.01187e12 | −0.126076 | −0.0630379 | − | 0.998011i | \(-0.520079\pi\) | ||||
−0.0630379 | + | 0.998011i | \(0.520079\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −6.02847e12 | −0.373846 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.36870e13 | −1.45366 | −0.726828 | − | 0.686819i | \(-0.759006\pi\) | ||||
−0.726828 | + | 0.686819i | \(0.759006\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.00936e12 | −0.122036 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.38803e13 | 1.43534 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.25867e13 | 0.748723 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.91536e13 | 2.30510 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 3.42876e13 | 1.99790 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 4.05783e11 | 0.0234022 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.83122e13 | 1.04531 | 0.522653 | − | 0.852545i | \(-0.324942\pi\) | ||||
0.522653 | + | 0.852545i | \(0.324942\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.24738e13 | −2.39978 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 3.34824e13 | 1.87251 | 0.936256 | − | 0.351320i | \(-0.114267\pi\) | ||||
0.936256 | + | 0.351320i | \(0.114267\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.73556e13 | 0.960763 | 0.480382 | − | 0.877060i | \(-0.340498\pi\) | ||||
0.480382 | + | 0.877060i | \(0.340498\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.51953e13 | −0.832654 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.34047e13 | 0.727109 | 0.363555 | − | 0.931573i | \(-0.381563\pi\) | ||||
0.363555 | + | 0.931573i | \(0.381563\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 2.59501e12 | 0.139341 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 6.15839e12 | 0.327354 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.44465e13 | 0.760204 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.31396e13 | 0.684510 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 8.28348e12 | 0.427216 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.97294e13 | −3.04979 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 3.13122e12 | 0.158289 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −3.37316e12 | −0.168827 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 9.65713e12 | 0.478552 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −9.01114e12 | −0.442127 | −0.221064 | − | 0.975259i | \(-0.570953\pi\) | ||||
−0.221064 | + | 0.975259i | \(0.570953\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 7.19758e12 | 0.349663 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.64836e12 | −0.367905 | −0.183952 | − | 0.982935i | \(-0.558889\pi\) | ||||
−0.183952 | + | 0.982935i | \(0.558889\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.35110e11 | −0.0159613 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.44531e11 | 0.0351146 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7.90232e12 | −0.369056 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.19451e13 | −1.47735 | −0.738676 | − | 0.674060i | \(-0.764549\pi\) | ||||
−0.738676 | + | 0.674060i | \(0.764549\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.97639e13 | −2.27901 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.20519e13 | 1.90712 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −6.12697e12 | −0.275174 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 5.72207e13 | 2.54504 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −1.36029e13 | −0.599186 | −0.299593 | − | 0.954067i | \(-0.596851\pi\) | ||||
−0.299593 | + | 0.954067i | \(0.596851\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.01574e13 | −0.879347 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 1.08204e13 | 0.467494 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.97201e12 | 0.0843833 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.10891e13 | −0.469966 | −0.234983 | − | 0.971999i | \(-0.575503\pi\) | ||||
−0.234983 | + | 0.971999i | \(0.575503\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.58553e13 | 1.08531 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −2.46259e13 | −1.02385 | −0.511927 | − | 0.859029i | \(-0.671068\pi\) | ||||
−0.511927 | + | 0.859029i | \(0.671068\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 3.93028e12 | 0.161853 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1.71724e12 | −0.0700466 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −4.82162e13 | −1.94813 | −0.974065 | − | 0.226267i | \(-0.927348\pi\) | ||||
−0.974065 | + | 0.226267i | \(0.927348\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.75192e13 | −2.30205 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.19717e13 | 2.45686 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.00142e12 | −0.117872 | −0.0589358 | − | 0.998262i | \(-0.518771\pi\) | ||||
−0.0589358 | + | 0.998262i | \(0.518771\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.58742e13 | 0.617558 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 5.40725e13 | 2.08388 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.62122e12 | −0.100074 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 4.13017e13 | 1.56211 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9.02581e12 | 0.338195 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.06354e13 | 0.394804 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 1.36956e13 | 0.503690 | 0.251845 | − | 0.967768i | \(-0.418963\pi\) | ||||
0.251845 | + | 0.967768i | \(0.418963\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.06705e13 | −0.388801 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.83646e12 | −0.102398 | −0.0511988 | − | 0.998688i | \(-0.516304\pi\) | ||||
−0.0511988 | + | 0.998688i | \(0.516304\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.66311e12 | 0.202557 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −1.37750e13 | −0.488171 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −9.66226e12 | −0.339276 | −0.169638 | − | 0.985506i | \(-0.554260\pi\) | ||||
−0.169638 | + | 0.985506i | \(0.554260\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 3.92533e13 | 1.36570 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −4.51396e13 | −1.55614 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1.05400e13 | 0.360039 | 0.180019 | − | 0.983663i | \(-0.442384\pi\) | ||||
0.180019 | + | 0.983663i | \(0.442384\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −2.73886e12 | −0.0927059 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 9.70684e12 | 0.325575 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.19914e12 | 0.0730920 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.01597e13 | −0.993335 | −0.496668 | − | 0.867941i | \(-0.665443\pi\) | ||||
−0.496668 | + | 0.867941i | \(0.665443\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −4.59668e13 | −1.50028 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −8.57730e12 | −0.277426 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.98318e13 | 0.635675 | 0.317837 | − | 0.948145i | \(-0.397043\pi\) | ||||
0.317837 | + | 0.948145i | \(0.397043\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 2.59288e13 | 0.823640 |
(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 | 80.10.a.g.1.1 | 2 | ||
4.3 | odd | 2 | 40.10.a.c.1.2 | ✓ | 2 | ||
5.2 | odd | 4 | 400.10.c.m.49.4 | 4 | |||
5.3 | odd | 4 | 400.10.c.m.49.1 | 4 | |||
5.4 | even | 2 | 400.10.a.r.1.2 | 2 | |||
8.3 | odd | 2 | 320.10.a.n.1.1 | 2 | |||
8.5 | even | 2 | 320.10.a.q.1.2 | 2 | |||
12.11 | even | 2 | 360.10.a.g.1.2 | 2 | |||
20.3 | even | 4 | 200.10.c.d.49.4 | 4 | |||
20.7 | even | 4 | 200.10.c.d.49.1 | 4 | |||
20.19 | odd | 2 | 200.10.a.c.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
40.10.a.c.1.2 | ✓ | 2 | 4.3 | odd | 2 | ||
80.10.a.g.1.1 | 2 | 1.1 | even | 1 | trivial | ||
200.10.a.c.1.1 | 2 | 20.19 | odd | 2 | |||
200.10.c.d.49.1 | 4 | 20.7 | even | 4 | |||
200.10.c.d.49.4 | 4 | 20.3 | even | 4 | |||
320.10.a.n.1.1 | 2 | 8.3 | odd | 2 | |||
320.10.a.q.1.2 | 2 | 8.5 | even | 2 | |||
360.10.a.g.1.2 | 2 | 12.11 | even | 2 | |||
400.10.a.r.1.2 | 2 | 5.4 | even | 2 | |||
400.10.c.m.49.1 | 4 | 5.3 | odd | 4 | |||
400.10.c.m.49.4 | 4 | 5.2 | odd | 4 |