Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [27,10,Mod(10,27)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(27, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("27.10");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 27 = 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 27.c (of order \(3\), degree \(2\), not minimal) |
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: | no |
Analytic conductor: | \(13.9059675764\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 8 x^{15} + 1984 x^{14} - 13748 x^{13} + 1552498 x^{12} - 9136628 x^{11} + 609566956 x^{10} + \cdots + 13\!\cdots\!25 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{14}\cdot 3^{40}\cdot 17^{2} \) |
Twist minimal: | no (minimal twist has level 9) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 10.6 | ||
Root | \(0.500000 + 13.2694i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 27.10 |
Dual form | 27.10.c.a.19.6 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/27\mathbb{Z}\right)^\times\).
\(n\) | \(2\) |
\(\chi(n)\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 10.7416 | + | 18.6050i | 0.474717 | + | 0.822233i | 0.999581 | − | 0.0289528i | \(-0.00921724\pi\) |
−0.524864 | + | 0.851186i | \(0.675884\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 25.2357 | − | 43.7094i | 0.0492884 | − | 0.0853700i | ||||
\(5\) | −22.4201 | + | 38.8327i | −0.0160425 | + | 0.0277864i | −0.873935 | − | 0.486042i | \(-0.838440\pi\) |
0.857893 | + | 0.513829i | \(0.171773\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −4672.78 | − | 8093.49i | −0.735587 | − | 1.27407i | −0.954465 | − | 0.298321i | \(-0.903573\pi\) |
0.218879 | − | 0.975752i | \(-0.429760\pi\) | |||||||
\(8\) | 12083.7 | 1.04303 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −963.310 | −0.0304625 | ||||||||
\(11\) | −27578.5 | − | 47767.3i | −0.567941 | − | 0.983702i | −0.996769 | − | 0.0803165i | \(-0.974407\pi\) |
0.428829 | − | 0.903386i | \(-0.358926\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 39984.4 | − | 69255.0i | 0.388280 | − | 0.672521i | −0.603938 | − | 0.797031i | \(-0.706403\pi\) |
0.992218 | + | 0.124510i | \(0.0397359\pi\) | |||||||
\(14\) | 100386. | − | 173874.i | 0.698390 | − | 1.20965i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 116878. | + | 202438.i | 0.445853 | + | 0.772240i | ||||
\(17\) | −8591.55 | −0.0249489 | −0.0124745 | − | 0.999922i | \(-0.503971\pi\) | ||||
−0.0124745 | + | 0.999922i | \(0.503971\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 643299. | 1.13246 | 0.566229 | − | 0.824248i | \(-0.308402\pi\) | ||||
0.566229 | + | 0.824248i | \(0.308402\pi\) | |||||||
\(20\) | 1131.57 | + | 1959.94i | 0.00158142 | + | 0.00273909i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 592474. | − | 1.02620e6i | 0.539222 | − | 0.933960i | ||||
\(23\) | 266733. | − | 461996.i | 0.198748 | − | 0.344241i | −0.749375 | − | 0.662146i | \(-0.769646\pi\) |
0.948123 | + | 0.317905i | \(0.102979\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 975557. | + | 1.68971e6i | 0.499485 | + | 0.865134i | ||||
\(26\) | 1.71799e6 | 0.737292 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −471682. | −0.145024 | ||||||||
\(29\) | −2.64026e6 | − | 4.57306e6i | −0.693195 | − | 1.20065i | −0.970785 | − | 0.239950i | \(-0.922869\pi\) |
0.277590 | − | 0.960700i | \(-0.410464\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.67161e6 | − | 2.89532e6i | 0.325094 | − | 0.563079i | −0.656438 | − | 0.754380i | \(-0.727938\pi\) |
0.981531 | + | 0.191302i | \(0.0612708\pi\) | |||||||
\(32\) | 582517. | − | 1.00895e6i | 0.0982050 | − | 0.170096i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −92287.1 | − | 159846.i | −0.0118437 | − | 0.0205138i | ||||
\(35\) | 419056. | 0.0472026 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.03491e7 | −1.78500 | −0.892500 | − | 0.451048i | \(-0.851050\pi\) | ||||
−0.892500 | + | 0.451048i | \(0.851050\pi\) | |||||||
\(38\) | 6.91007e6 | + | 1.19686e7i | 0.537596 | + | 0.931144i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −270917. | + | 469242.i | −0.0167327 | + | 0.0289819i | ||||
\(41\) | −1.59074e7 | + | 2.75524e7i | −0.879168 | + | 1.52276i | −0.0269120 | + | 0.999638i | \(0.508567\pi\) |
−0.852256 | + | 0.523125i | \(0.824766\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.27763e6 | + | 3.94496e6i | 0.101595 | + | 0.175968i | 0.912342 | − | 0.409429i | \(-0.134272\pi\) |
−0.810747 | + | 0.585397i | \(0.800939\pi\) | |||||||
\(44\) | −2.78384e6 | −0.111972 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.14606e7 | 0.377395 | ||||||||
\(47\) | −9.00010e6 | − | 1.55886e7i | −0.269034 | − | 0.465980i | 0.699579 | − | 0.714555i | \(-0.253371\pi\) |
−0.968613 | + | 0.248575i | \(0.920038\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −2.34929e7 | + | 4.06909e7i | −0.582175 | + | 1.00836i | ||||
\(50\) | −2.09581e7 | + | 3.63005e7i | −0.474228 | + | 0.821387i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.01806e6 | − | 3.49539e6i | −0.0382754 | − | 0.0662950i | ||||
\(53\) | 6.95534e7 | 1.21081 | 0.605406 | − | 0.795917i | \(-0.293011\pi\) | ||||
0.605406 | + | 0.795917i | \(0.293011\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 2.47324e6 | 0.0364447 | ||||||||
\(56\) | −5.64644e7 | − | 9.77992e7i | −0.767235 | − | 1.32889i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 5.67213e7 | − | 9.82441e7i | 0.658143 | − | 1.13994i | ||||
\(59\) | 3.24115e7 | − | 5.61383e7i | 0.348229 | − | 0.603150i | −0.637706 | − | 0.770280i | \(-0.720117\pi\) |
0.985935 | + | 0.167130i | \(0.0534499\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.37764e7 | − | 7.58229e7i | −0.404814 | − | 0.701159i | 0.589486 | − | 0.807779i | \(-0.299330\pi\) |
−0.994300 | + | 0.106620i | \(0.965997\pi\) | |||||||
\(62\) | 7.18233e7 | 0.617309 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.44711e8 | 1.07818 | ||||||||
\(65\) | 1.79290e6 | + | 3.10540e6i | 0.0124580 | + | 0.0215778i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.37026e7 | + | 1.44977e8i | −0.507461 | + | 0.878948i | 0.492502 | + | 0.870311i | \(0.336082\pi\) |
−0.999963 | + | 0.00863632i | \(0.997251\pi\) | |||||||
\(68\) | −216813. | + | 375532.i | −0.00122969 | + | 0.00212989i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 4.50133e6 | + | 7.79654e6i | 0.0224078 | + | 0.0388115i | ||||
\(71\) | 1.55996e8 | 0.728537 | 0.364268 | − | 0.931294i | \(-0.381319\pi\) | ||||
0.364268 | + | 0.931294i | \(0.381319\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 3.05377e8 | 1.25859 | 0.629294 | − | 0.777168i | \(-0.283344\pi\) | ||||
0.629294 | + | 0.777168i | \(0.283344\pi\) | |||||||
\(74\) | −2.18582e8 | − | 3.78596e8i | −0.847369 | − | 1.46769i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.62341e7 | − | 2.81182e7i | 0.0558170 | − | 0.0966778i | ||||
\(77\) | −2.57736e8 | + | 4.46412e8i | −0.835539 | + | 1.44720i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.79955e8 | + | 3.11692e8i | 0.519808 | + | 0.900333i | 0.999735 | + | 0.0230250i | \(0.00732973\pi\) |
−0.479927 | + | 0.877308i | \(0.659337\pi\) | |||||||
\(80\) | −1.04816e7 | −0.0286104 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −6.83484e8 | −1.66942 | ||||||||
\(83\) | 2.31984e8 | + | 4.01807e8i | 0.536545 | + | 0.929323i | 0.999087 | + | 0.0427255i | \(0.0136041\pi\) |
−0.462542 | + | 0.886597i | \(0.653063\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 192623. | − | 333633.i | 0.000400242 | − | 0.000693240i | ||||
\(86\) | −4.89307e7 | + | 8.47505e7i | −0.0964581 | + | 0.167070i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −3.33250e8 | − | 5.77206e8i | −0.592377 | − | 1.02603i | ||||
\(89\) | 2.70335e8 | 0.456717 | 0.228358 | − | 0.973577i | \(-0.426664\pi\) | ||||
0.228358 | + | 0.973577i | \(0.426664\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −7.47352e8 | −1.14246 | ||||||||
\(92\) | −1.34624e7 | − | 2.33175e7i | −0.0195919 | − | 0.0339342i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 1.93351e8 | − | 3.34894e8i | 0.255430 | − | 0.442417i | ||||
\(95\) | −1.44228e7 | + | 2.49810e7i | −0.0181674 | + | 0.0314669i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 7.54926e7 | + | 1.30757e8i | 0.0865828 | + | 0.149966i | 0.906065 | − | 0.423139i | \(-0.139072\pi\) |
−0.819482 | + | 0.573105i | \(0.805739\pi\) | |||||||
\(98\) | −1.00941e9 | −1.10547 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 9.84753e7 | 0.0984753 | ||||||||
\(101\) | 1.56102e8 | + | 2.70377e8i | 0.149267 | + | 0.258538i | 0.930957 | − | 0.365130i | \(-0.118975\pi\) |
−0.781690 | + | 0.623667i | \(0.785642\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −4.29318e8 | + | 7.43601e8i | −0.375848 | + | 0.650987i | −0.990454 | − | 0.137847i | \(-0.955982\pi\) |
0.614606 | + | 0.788834i | \(0.289315\pi\) | |||||||
\(104\) | 4.83159e8 | − | 8.36856e8i | 0.404986 | − | 0.701457i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 7.47115e8 | + | 1.29404e9i | 0.574793 | + | 0.995570i | ||||
\(107\) | 2.37971e8 | 0.175508 | 0.0877542 | − | 0.996142i | \(-0.472031\pi\) | ||||
0.0877542 | + | 0.996142i | \(0.472031\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.89834e8 | 0.535940 | 0.267970 | − | 0.963427i | \(-0.413647\pi\) | ||||
0.267970 | + | 0.963427i | \(0.413647\pi\) | |||||||
\(110\) | 2.65666e7 | + | 4.60147e7i | 0.0173009 | + | 0.0299661i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.09229e9 | − | 1.89190e9i | 0.655927 | − | 1.13610i | ||||
\(113\) | −2.63143e7 | + | 4.55777e7i | −0.0151823 | + | 0.0262966i | −0.873517 | − | 0.486794i | \(-0.838166\pi\) |
0.858334 | + | 0.513091i | \(0.171500\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.19604e7 | + | 2.07159e7i | 0.00637681 | + | 0.0110450i | ||||
\(116\) | −2.66515e8 | −0.136666 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.39260e9 | 0.661240 | ||||||||
\(119\) | 4.01464e7 | + | 6.95356e7i | 0.0183521 | + | 0.0317867i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.42170e8 | + | 5.92656e8i | −0.145114 | + | 0.251344i | ||||
\(122\) | 9.40458e8 | − | 1.62892e9i | 0.384344 | − | 0.665703i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −8.43686e7 | − | 1.46131e8i | −0.0320467 | − | 0.0555065i | ||||
\(125\) | −1.75067e8 | −0.0641369 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.15652e9 | 0.394489 | 0.197244 | − | 0.980354i | \(-0.436801\pi\) | ||||
0.197244 | + | 0.980354i | \(0.436801\pi\) | |||||||
\(128\) | 1.25618e9 | + | 2.17578e9i | 0.413627 | + | 0.716423i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −3.85174e7 | + | 6.67140e7i | −0.0118280 | + | 0.0204867i | ||||
\(131\) | 2.97421e9 | − | 5.15149e9i | 0.882371 | − | 1.52831i | 0.0336741 | − | 0.999433i | \(-0.489279\pi\) |
0.848697 | − | 0.528879i | \(-0.177388\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.00599e9 | − | 5.20653e9i | −0.833020 | − | 1.44283i | ||||
\(134\) | −3.59640e9 | −0.963600 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −1.03818e8 | −0.0260223 | ||||||||
\(137\) | −7.47351e8 | − | 1.29445e9i | −0.181252 | − | 0.313937i | 0.761055 | − | 0.648687i | \(-0.224682\pi\) |
−0.942307 | + | 0.334750i | \(0.891348\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.56437e9 | + | 4.44162e9i | −0.582658 | + | 1.00919i | 0.412505 | + | 0.910955i | \(0.364654\pi\) |
−0.995163 | + | 0.0982382i | \(0.968679\pi\) | |||||||
\(140\) | 1.05751e7 | − | 1.83167e7i | 0.00232654 | − | 0.00402968i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.67565e9 | + | 2.90231e9i | 0.345849 | + | 0.599027i | ||||
\(143\) | −4.41083e9 | −0.882081 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2.36779e8 | 0.0444823 | ||||||||
\(146\) | 3.28024e9 | + | 5.68154e9i | 0.597472 | + | 1.03485i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −5.13523e8 | + | 8.89449e8i | −0.0879797 | + | 0.152385i | ||||
\(149\) | −5.20851e9 | + | 9.02140e9i | −0.865715 | + | 1.49946i | 0.000619610 | 1.00000i | \(0.499803\pi\) | |
−0.866335 | + | 0.499463i | \(0.833531\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.59960e8 | − | 7.96674e8i | −0.0719985 | − | 0.124705i | 0.827779 | − | 0.561055i | \(-0.189604\pi\) |
−0.899777 | + | 0.436350i | \(0.856271\pi\) | |||||||
\(152\) | 7.77343e9 | 1.18118 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −1.10740e10 | −1.58658 | ||||||||
\(155\) | 7.49554e7 | + | 1.29827e8i | 0.0104306 | + | 0.0180664i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.67288e9 | − | 4.62957e9i | 0.351100 | − | 0.608123i | −0.635342 | − | 0.772231i | \(-0.719141\pi\) |
0.986443 | + | 0.164107i | \(0.0524743\pi\) | |||||||
\(158\) | −3.86602e9 | + | 6.69614e9i | −0.493523 | + | 0.854806i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2.61201e7 | + | 4.52414e7i | 0.00315091 | + | 0.00545753i | ||||
\(161\) | −4.98554e9 | −0.584785 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.82475e9 | 0.757256 | 0.378628 | − | 0.925549i | \(-0.376396\pi\) | ||||
0.378628 | + | 0.925549i | \(0.376396\pi\) | |||||||
\(164\) | 8.02867e8 | + | 1.39061e9i | 0.0866655 | + | 0.150109i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −4.98376e9 | + | 8.63212e9i | −0.509413 | + | 0.882330i | ||||
\(167\) | 2.90778e9 | − | 5.03642e9i | 0.289293 | − | 0.501069i | −0.684348 | − | 0.729155i | \(-0.739913\pi\) |
0.973641 | + | 0.228086i | \(0.0732466\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 2.10475e9 | + | 3.64553e9i | 0.198477 | + | 0.343772i | ||||
\(170\) | 8.27633e6 | 0.000760007 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.29909e8 | 0.0200299 | ||||||||
\(173\) | −6.15871e9 | − | 1.06672e10i | −0.522736 | − | 0.905405i | −0.999650 | − | 0.0264553i | \(-0.991578\pi\) |
0.476914 | − | 0.878950i | \(-0.341755\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 9.11712e9 | − | 1.57913e10i | 0.734829 | − | 1.27276i | ||||
\(176\) | 6.44662e9 | − | 1.11659e10i | 0.506436 | − | 0.877173i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 2.90383e9 | + | 5.02958e9i | 0.216811 | + | 0.375528i | ||||
\(179\) | 1.65764e10 | 1.20684 | 0.603422 | − | 0.797422i | \(-0.293804\pi\) | ||||
0.603422 | + | 0.797422i | \(0.293804\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −1.06374e9 | −0.0736685 | −0.0368343 | − | 0.999321i | \(-0.511727\pi\) | ||||
−0.0368343 | + | 0.999321i | \(0.511727\pi\) | |||||||
\(182\) | −8.02777e9 | − | 1.39045e10i | −0.542342 | − | 0.939365i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 3.22312e9 | − | 5.58262e9i | 0.207299 | − | 0.359052i | ||||
\(185\) | 4.56229e8 | − | 7.90211e8i | 0.0286358 | − | 0.0495987i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 2.36942e8 | + | 4.10395e8i | 0.0141695 | + | 0.0245423i | ||||
\(188\) | −9.08493e8 | −0.0530410 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −6.19696e8 | −0.0344975 | ||||||||
\(191\) | −6.49586e9 | − | 1.12512e10i | −0.353172 | − | 0.611712i | 0.633631 | − | 0.773635i | \(-0.281564\pi\) |
−0.986803 | + | 0.161923i | \(0.948230\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 5.59579e9 | − | 9.69218e9i | 0.290304 | − | 0.502821i | −0.683577 | − | 0.729878i | \(-0.739577\pi\) |
0.973882 | + | 0.227057i | \(0.0729102\pi\) | |||||||
\(194\) | −1.62182e9 | + | 2.80908e9i | −0.0822045 | + | 0.142382i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1.18572e9 | + | 2.05372e9i | 0.0573890 | + | 0.0994006i | ||||
\(197\) | 3.23317e10 | 1.52943 | 0.764716 | − | 0.644368i | \(-0.222879\pi\) | ||||
0.764716 | + | 0.644368i | \(0.222879\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 7.46055e9 | 0.337234 | 0.168617 | − | 0.985682i | \(-0.446070\pi\) | ||||
0.168617 | + | 0.985682i | \(0.446070\pi\) | |||||||
\(200\) | 1.17883e10 | + | 2.04180e10i | 0.520976 | + | 0.902356i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3.35358e9 | + | 5.80857e9i | −0.141719 | + | 0.245464i | ||||
\(203\) | −2.46747e10 | + | 4.27378e10i | −1.01981 | + | 1.76636i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −7.13289e8 | − | 1.23545e9i | −0.0282081 | − | 0.0488578i | ||||
\(206\) | −1.84463e10 | −0.713684 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.86931e10 | 0.692464 | ||||||||
\(209\) | −1.77412e10 | − | 3.07287e10i | −0.643169 | − | 1.11400i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.84818e10 | + | 3.20113e10i | −0.641907 | + | 1.11182i | 0.343100 | + | 0.939299i | \(0.388523\pi\) |
−0.985007 | + | 0.172516i | \(0.944810\pi\) | |||||||
\(212\) | 1.75522e9 | − | 3.04014e9i | 0.0596790 | − | 0.103367i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 2.55620e9 | + | 4.42746e9i | 0.0833167 | + | 0.144309i | ||||
\(215\) | −2.04258e8 | −0.00651937 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3.12443e10 | −0.956538 | ||||||||
\(218\) | 8.48408e9 | + | 1.46949e10i | 0.254420 | + | 0.440668i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6.24139e7 | − | 1.08104e8i | 0.00179630 | − | 0.00311129i | ||||
\(221\) | −3.43528e8 | + | 5.95008e8i | −0.00968717 | + | 0.0167787i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −8.77631e9 | − | 1.52010e10i | −0.237651 | − | 0.411624i | 0.722389 | − | 0.691487i | \(-0.243044\pi\) |
−0.960040 | + | 0.279863i | \(0.909711\pi\) | |||||||
\(224\) | −1.08879e10 | −0.288953 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −1.13063e9 | −0.0288292 | ||||||||
\(227\) | 1.76110e10 | + | 3.05031e10i | 0.440217 | + | 0.762479i | 0.997705 | − | 0.0677064i | \(-0.0215681\pi\) |
−0.557488 | + | 0.830185i | \(0.688235\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.79995e10 | + | 3.11760e10i | −0.432514 | + | 0.749136i | −0.997089 | − | 0.0762454i | \(-0.975707\pi\) |
0.564575 | + | 0.825382i | \(0.309040\pi\) | |||||||
\(230\) | −2.56947e8 | + | 4.45045e8i | −0.00605436 | + | 0.0104865i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3.19041e10 | − | 5.52595e10i | −0.723020 | − | 1.25231i | ||||
\(233\) | −1.22534e10 | −0.272367 | −0.136184 | − | 0.990684i | \(-0.543484\pi\) | ||||
−0.136184 | + | 0.990684i | \(0.543484\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.07131e8 | 0.0172639 | ||||||||
\(236\) | −1.63585e9 | − | 2.83337e9i | −0.0343273 | − | 0.0594565i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −8.62474e8 | + | 1.49385e9i | −0.0174241 | + | 0.0301794i | ||||
\(239\) | 6.28307e9 | − | 1.08826e10i | 0.124561 | − | 0.215745i | −0.797000 | − | 0.603979i | \(-0.793581\pi\) |
0.921561 | + | 0.388233i | \(0.126915\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −5.74525e9 | − | 9.95107e9i | −0.109707 | − | 0.190017i | 0.805945 | − | 0.591991i | \(-0.201658\pi\) |
−0.915651 | + | 0.401973i | \(0.868324\pi\) | |||||||
\(242\) | −1.47018e10 | −0.275551 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −4.41890e9 | −0.0798105 | ||||||||
\(245\) | −1.05342e9 | − | 1.82458e9i | −0.0186791 | − | 0.0323531i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.57219e10 | − | 4.45517e10i | 0.439711 | − | 0.761601i | ||||
\(248\) | 2.01993e10 | − | 3.49862e10i | 0.339081 | − | 0.587305i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.88050e9 | − | 3.25712e9i | −0.0304469 | − | 0.0527355i | ||||
\(251\) | 4.00421e10 | 0.636774 | 0.318387 | − | 0.947961i | \(-0.396859\pi\) | ||||
0.318387 | + | 0.947961i | \(0.396859\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.94244e10 | −0.451508 | ||||||||
\(254\) | 1.24228e10 | + | 2.15170e10i | 0.187270 | + | 0.324362i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00592e10 | − | 1.74231e10i | 0.146381 | − | 0.253539i | ||||
\(257\) | −2.20727e10 | + | 3.82311e10i | −0.315615 | + | 0.546661i | −0.979568 | − | 0.201113i | \(-0.935544\pi\) |
0.663953 | + | 0.747774i | \(0.268877\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.50869e10 | + | 1.64695e11i | 1.31302 | + | 2.27422i | ||||
\(260\) | 1.80980e8 | 0.00245613 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.27791e11 | 1.67551 | ||||||||
\(263\) | −1.36277e10 | − | 2.36038e10i | −0.175639 | − | 0.304215i | 0.764743 | − | 0.644335i | \(-0.222866\pi\) |
−0.940382 | + | 0.340120i | \(0.889532\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.55939e9 | + | 2.70094e9i | −0.0194244 | + | 0.0336441i | ||||
\(266\) | 6.45784e10 | − | 1.11853e11i | 0.790897 | − | 1.36987i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 4.22458e9 | + | 7.31719e9i | 0.0500238 | + | 0.0866438i | ||||
\(269\) | −1.37243e11 | −1.59810 | −0.799051 | − | 0.601263i | \(-0.794664\pi\) | ||||
−0.799051 | + | 0.601263i | \(0.794664\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 9.04089e9 | 0.101824 | 0.0509119 | − | 0.998703i | \(-0.483787\pi\) | ||||
0.0509119 | + | 0.998703i | \(0.483787\pi\) | |||||||
\(272\) | −1.00416e9 | − | 1.73926e9i | −0.0111235 | − | 0.0192665i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 1.60555e10 | − | 2.78090e10i | 0.172086 | − | 0.298062i | ||||
\(275\) | 5.38088e10 | − | 9.31995e10i | 0.567356 | − | 0.982690i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.06072e10 | − | 3.56927e10i | −0.210310 | − | 0.364267i | 0.741502 | − | 0.670951i | \(-0.234114\pi\) |
−0.951811 | + | 0.306684i | \(0.900781\pi\) | |||||||
\(278\) | −1.10182e11 | −1.10639 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 5.06374e9 | 0.0492335 | ||||||||
\(281\) | 7.23643e10 | + | 1.25339e11i | 0.692383 | + | 1.19924i | 0.971055 | + | 0.238856i | \(0.0767723\pi\) |
−0.278673 | + | 0.960386i | \(0.589894\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.80193e10 | − | 3.12103e10i | 0.166993 | − | 0.289240i | −0.770368 | − | 0.637599i | \(-0.779928\pi\) |
0.937361 | + | 0.348359i | \(0.113261\pi\) | |||||||
\(284\) | 3.93667e9 | − | 6.81851e9i | 0.0359084 | − | 0.0621952i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −4.73794e10 | − | 8.20636e10i | −0.418738 | − | 0.725276i | ||||
\(287\) | 2.97327e11 | 2.58682 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.18514e11 | −0.999378 | ||||||||
\(290\) | 2.54339e9 | + | 4.40528e9i | 0.0211165 | + | 0.0365748i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 7.70639e9 | − | 1.33479e10i | 0.0620337 | − | 0.107446i | ||||
\(293\) | −1.96451e10 | + | 3.40262e10i | −0.155722 | + | 0.269718i | −0.933322 | − | 0.359042i | \(-0.883104\pi\) |
0.777600 | + | 0.628759i | \(0.216437\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.45333e9 | + | 2.51725e9i | 0.0111729 | + | 0.0193520i | ||||
\(296\) | −2.45893e11 | −1.86180 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −2.23791e11 | −1.64388 | ||||||||
\(299\) | −2.13303e10 | − | 3.69452e10i | −0.154340 | − | 0.267324i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.12857e10 | − | 3.68679e10i | 0.149464 | − | 0.258880i | ||||
\(302\) | 9.88142e9 | − | 1.71151e10i | 0.0683578 | − | 0.118399i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 7.51873e10 | + | 1.30228e11i | 0.504909 | + | 0.874529i | ||||
\(305\) | 3.92588e9 | 0.0259769 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 6.02560e10 | 0.387148 | 0.193574 | − | 0.981086i | \(-0.437992\pi\) | ||||
0.193574 | + | 0.981086i | \(0.437992\pi\) | |||||||
\(308\) | 1.30083e10 | + | 2.25310e10i | 0.0823648 | + | 0.142660i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −1.61028e9 | + | 2.78909e9i | −0.00990318 | + | 0.0171528i | ||||
\(311\) | −1.40942e11 | + | 2.44119e11i | −0.854319 | + | 1.47972i | 0.0229572 | + | 0.999736i | \(0.492692\pi\) |
−0.877276 | + | 0.479987i | \(0.840641\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −7.42999e10 | − | 1.28691e11i | −0.437561 | − | 0.757878i | 0.559940 | − | 0.828533i | \(-0.310824\pi\) |
−0.997501 | + | 0.0706552i | \(0.977491\pi\) | |||||||
\(314\) | 1.14844e11 | 0.666692 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.81652e10 | 0.102482 | ||||||||
\(317\) | −7.01595e10 | − | 1.21520e11i | −0.390229 | − | 0.675897i | 0.602250 | − | 0.798307i | \(-0.294271\pi\) |
−0.992480 | + | 0.122411i | \(0.960938\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.45629e11 | + | 2.52236e11i | −0.787388 | + | 1.36380i | ||||
\(320\) | −3.24444e9 | + | 5.61953e9i | −0.0172968 | + | 0.0299589i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.35528e10 | − | 9.27561e10i | −0.277607 | − | 0.480829i | ||||
\(323\) | −5.52694e9 | −0.0282536 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.56028e11 | 0.775761 | ||||||||
\(326\) | 7.33088e10 | + | 1.26975e11i | 0.359482 | + | 0.622641i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.92220e11 | + | 3.32935e11i | −0.916994 | + | 1.58828i | ||||
\(329\) | −8.41109e10 | + | 1.45684e11i | −0.395795 | + | 0.685538i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.96051e10 | + | 1.03239e11i | 0.272934 | + | 0.472735i | 0.969612 | − | 0.244649i | \(-0.0786727\pi\) |
−0.696678 | + | 0.717384i | \(0.745339\pi\) | |||||||
\(332\) | 2.34170e10 | 0.105782 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.24937e11 | 0.549328 | ||||||||
\(335\) | −3.75323e9 | − | 6.50079e9i | −0.0162819 | − | 0.0282010i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.75620e11 | − | 3.04183e11i | 0.741720 | − | 1.28470i | −0.209991 | − | 0.977703i | \(-0.567343\pi\) |
0.951711 | − | 0.306994i | \(-0.0993232\pi\) | |||||||
\(338\) | −4.52167e10 | + | 7.83177e10i | −0.188440 | + | 0.326388i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −9.72194e6 | − | 1.68389e7i | −3.94546e−5 | − | 6.83374e-5i | ||||
\(341\) | −1.84402e11 | −0.738536 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 6.19811e10 | 0.241789 | ||||||||
\(344\) | 2.75221e10 | + | 4.76697e10i | 0.105967 | + | 0.183540i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 1.32309e11 | − | 2.29166e11i | 0.496303 | − | 0.859622i | ||||
\(347\) | 1.78653e11 | − | 3.09436e11i | 0.661496 | − | 1.14574i | −0.318727 | − | 0.947847i | \(-0.603255\pi\) |
0.980223 | − | 0.197898i | \(-0.0634114\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2.15106e11 | − | 3.72574e11i | −0.776136 | − | 1.34431i | −0.934154 | − | 0.356871i | \(-0.883843\pi\) |
0.158017 | − | 0.987436i | \(-0.449490\pi\) | |||||||
\(350\) | 3.91730e11 | 1.39534 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −6.42597e10 | −0.223099 | ||||||||
\(353\) | −2.59498e11 | − | 4.49464e11i | −0.889505 | − | 1.54067i | −0.840462 | − | 0.541871i | \(-0.817716\pi\) |
−0.0490434 | − | 0.998797i | \(-0.515617\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3.49744e9 | + | 6.05775e9i | −0.0116875 | + | 0.0202434i | ||||
\(356\) | 6.82207e9 | − | 1.18162e10i | 0.0225108 | − | 0.0389899i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.78057e11 | + | 3.08404e11i | 0.572908 | + | 0.992307i | ||||
\(359\) | 4.22565e11 | 1.34267 | 0.671334 | − | 0.741155i | \(-0.265721\pi\) | ||||
0.671334 | + | 0.741155i | \(0.265721\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 9.11460e10 | 0.282459 | ||||||||
\(362\) | −1.14263e10 | − | 1.97909e10i | −0.0349717 | − | 0.0605727i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.88599e10 | + | 3.26663e10i | −0.0563098 | + | 0.0975314i | ||||
\(365\) | −6.84657e9 | + | 1.18586e10i | −0.0201909 | + | 0.0349716i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9.37397e10 | + | 1.62362e11i | 0.269728 | + | 0.467183i | 0.968792 | − | 0.247877i | \(-0.0797329\pi\) |
−0.699064 | + | 0.715060i | \(0.746400\pi\) | |||||||
\(368\) | 1.24701e11 | 0.354449 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.96025e10 | 0.0543756 | ||||||||
\(371\) | −3.25007e11 | − | 5.62929e11i | −0.890657 | − | 1.54266i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.77249e10 | + | 3.07005e10i | −0.0474127 | + | 0.0821212i | −0.888758 | − | 0.458377i | \(-0.848431\pi\) |
0.841345 | + | 0.540498i | \(0.181764\pi\) | |||||||
\(374\) | −5.09027e9 | + | 8.81661e9i | −0.0134530 | + | 0.0233013i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −1.08754e11 | − | 1.88368e11i | −0.280609 | − | 0.486029i | ||||
\(377\) | −4.22277e11 | −1.07662 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 2.58921e11 | 0.644602 | 0.322301 | − | 0.946637i | \(-0.395544\pi\) | ||||
0.322301 | + | 0.946637i | \(0.395544\pi\) | |||||||
\(380\) | 7.27938e8 | + | 1.26082e9i | 0.00179089 | + | 0.00310191i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1.39552e11 | − | 2.41711e11i | 0.335313 | − | 0.580779i | ||||
\(383\) | 5.85055e10 | − | 1.01334e11i | 0.138932 | − | 0.240637i | −0.788161 | − | 0.615470i | \(-0.788966\pi\) |
0.927093 | + | 0.374832i | \(0.122300\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1.15569e10 | − | 2.00172e10i | −0.0268083 | − | 0.0464333i | ||||
\(386\) | 2.40431e11 | 0.551249 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7.62042e9 | 0.0170701 | ||||||||
\(389\) | 2.08184e11 | + | 3.60585e11i | 0.460971 | + | 0.798425i | 0.999010 | − | 0.0444950i | \(-0.0141679\pi\) |
−0.538039 | + | 0.842920i | \(0.680835\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.29165e9 | + | 3.96926e9i | −0.00495854 | + | 0.00858844i | ||||
\(392\) | −2.83881e11 | + | 4.91696e11i | −0.607224 | + | 1.05174i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.47294e11 | + | 6.01531e11i | 0.726047 | + | 1.25755i | ||||
\(395\) | −1.61384e10 | −0.0333560 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −4.63043e11 | −0.935544 | −0.467772 | − | 0.883849i | \(-0.654943\pi\) | ||||
−0.467772 | + | 0.883849i | \(0.654943\pi\) | |||||||
\(398\) | 8.01383e10 | + | 1.38804e11i | 0.160091 | + | 0.277285i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −2.28042e11 | + | 3.94980e11i | −0.445394 | + | 0.771445i | ||||
\(401\) | −3.17986e11 | + | 5.50767e11i | −0.614127 | + | 1.06370i | 0.376411 | + | 0.926453i | \(0.377158\pi\) |
−0.990537 | + | 0.137245i | \(0.956175\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.33677e11 | − | 2.31535e11i | −0.252455 | − | 0.437265i | ||||
\(404\) | 1.57574e10 | 0.0294285 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −1.06018e12 | −1.93648 | ||||||||
\(407\) | 5.61198e11 | + | 9.72023e11i | 1.01377 | + | 1.75591i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 6.14694e10 | − | 1.06468e11i | 0.108619 | − | 0.188133i | −0.806592 | − | 0.591108i | \(-0.798691\pi\) |
0.915211 | + | 0.402975i | \(0.132024\pi\) | |||||||
\(410\) | 1.53238e10 | − | 2.65415e10i | 0.0267817 | − | 0.0463872i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 2.16683e10 | + | 3.75305e10i | 0.0370498 | + | 0.0641722i | ||||
\(413\) | −6.05806e11 | −1.02461 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.08043e10 | −0.0344300 | ||||||||
\(416\) | −4.65832e10 | − | 8.06844e10i | −0.0762622 | − | 0.132090i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 3.81138e11 | − | 6.60151e11i | 0.610646 | − | 1.05767i | ||||
\(419\) | 4.29042e11 | − | 7.43123e11i | 0.680044 | − | 1.17787i | −0.294923 | − | 0.955521i | \(-0.595294\pi\) |
0.974967 | − | 0.222350i | \(-0.0713726\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.32546e11 | − | 2.29576e11i | −0.205635 | − | 0.356170i | 0.744700 | − | 0.667400i | \(-0.232593\pi\) |
−0.950335 | + | 0.311229i | \(0.899259\pi\) | |||||||
\(422\) | −7.94095e11 | −1.21890 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 8.40462e11 | 1.26291 | ||||||||
\(425\) | −8.38155e9 | − | 1.45173e10i | −0.0124616 | − | 0.0215841i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −4.09115e11 | + | 7.08607e11i | −0.595552 | + | 1.03153i | ||||
\(428\) | 6.00537e9 | − | 1.04016e10i | 0.00865053 | − | 0.0149831i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.19406e9 | − | 3.80022e9i | −0.00309485 | − | 0.00536045i | ||||
\(431\) | 2.69116e11 | 0.375658 | 0.187829 | − | 0.982202i | \(-0.439855\pi\) | ||||
0.187829 | + | 0.982202i | \(0.439855\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.07088e12 | −1.46401 | −0.732006 | − | 0.681298i | \(-0.761416\pi\) | ||||
−0.732006 | + | 0.681298i | \(0.761416\pi\) | |||||||
\(434\) | −3.35614e11 | − | 5.81301e11i | −0.454085 | − | 0.786497i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1.99320e10 | − | 3.45232e10i | 0.0264156 | − | 0.0457532i | ||||
\(437\) | 1.71589e11 | − | 2.97201e11i | 0.225073 | − | 0.389838i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.56418e11 | + | 4.44129e11i | 0.329502 | + | 0.570714i | 0.982413 | − | 0.186721i | \(-0.0597859\pi\) |
−0.652911 | + | 0.757434i | \(0.726453\pi\) | |||||||
\(440\) | 2.98859e10 | 0.0380128 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −1.47602e10 | −0.0183946 | ||||||||
\(443\) | 1.15112e11 | + | 1.99381e11i | 0.142006 | + | 0.245961i | 0.928252 | − | 0.371953i | \(-0.121312\pi\) |
−0.786246 | + | 0.617913i | \(0.787978\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.06092e9 | + | 1.04978e10i | −0.00732687 | + | 0.0126905i | ||||
\(446\) | 1.88543e11 | − | 3.26567e11i | 0.225634 | − | 0.390809i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −6.76204e11 | − | 1.17122e12i | −0.793098 | − | 1.37369i | ||||
\(449\) | 1.09130e12 | 1.26717 | 0.633586 | − | 0.773672i | \(-0.281582\pi\) | ||||
0.633586 | + | 0.773672i | \(0.281582\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1.75481e12 | 1.99726 | ||||||||
\(452\) | 1.32812e9 | + | 2.30037e9i | 0.00149663 | + | 0.00259223i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −3.78340e11 | + | 6.55305e11i | −0.417957 | + | 0.723922i | ||||
\(455\) | 1.67557e10 | − | 2.90217e10i | 0.0183278 | − | 0.0317447i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 4.57932e10 | + | 7.93162e10i | 0.0491109 | + | 0.0850626i | 0.889536 | − | 0.456865i | \(-0.151028\pi\) |
−0.840425 | + | 0.541928i | \(0.817695\pi\) | |||||||
\(458\) | −7.73373e11 | −0.821286 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 1.20731e9 | 0.00125721 | ||||||||
\(461\) | 2.32909e11 | + | 4.03410e11i | 0.240177 | + | 0.415999i | 0.960765 | − | 0.277365i | \(-0.0894611\pi\) |
−0.720587 | + | 0.693364i | \(0.756128\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.34865e11 | − | 9.26413e11i | 0.540916 | − | 0.936893i | −0.457936 | − | 0.888985i | \(-0.651411\pi\) |
0.998852 | − | 0.0479083i | \(-0.0152555\pi\) | |||||||
\(464\) | 6.17175e11 | − | 1.06898e12i | 0.618126 | − | 1.07063i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.31621e11 | − | 2.27975e11i | −0.129297 | − | 0.223950i | ||||
\(467\) | −1.30619e12 | −1.27081 | −0.635406 | − | 0.772178i | \(-0.719167\pi\) | ||||
−0.635406 | + | 0.772178i | \(0.719167\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.56449e12 | 1.49313 | ||||||||
\(470\) | 8.66988e9 | + | 1.50167e10i | 0.00819545 | + | 0.0141949i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.91650e11 | − | 6.78358e11i | 0.363211 | − | 0.629100i | ||||
\(473\) | 1.25627e11 | − | 2.17592e11i | 0.115400 | − | 0.199879i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 6.27575e11 | + | 1.08699e12i | 0.565646 | + | 0.979727i | ||||
\(476\) | 4.05248e9 | 0.00361818 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 2.69961e11 | 0.236524 | ||||||||
\(479\) | 1.06821e12 | + | 1.85019e12i | 0.927139 | + | 1.60585i | 0.788084 | + | 0.615568i | \(0.211073\pi\) |
0.139055 | + | 0.990285i | \(0.455593\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −8.13647e11 | + | 1.40928e12i | −0.693080 | + | 1.20045i | ||||
\(482\) | 1.23427e11 | − | 2.13781e11i | 0.104159 | − | 0.180409i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.72698e10 | + | 2.99121e10i | 0.0143048 | + | 0.0247767i | ||||
\(485\) | −6.77019e9 | −0.00555601 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.44314e12 | −1.16259 | −0.581297 | − | 0.813692i | \(-0.697454\pi\) | ||||
−0.581297 | + | 0.813692i | \(0.697454\pi\) | |||||||
\(488\) | −5.28980e11 | − | 9.16221e11i | −0.422231 | − | 0.731326i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.26309e10 | − | 3.91979e10i | 0.0177345 | − | 0.0307171i | ||||
\(491\) | −3.86766e11 | + | 6.69898e11i | −0.300318 | + | 0.520166i | −0.976208 | − | 0.216837i | \(-0.930426\pi\) |
0.675890 | + | 0.737002i | \(0.263759\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.26839e10 | + | 3.92897e10i | 0.0172945 | + | 0.0299549i | ||||
\(494\) | 1.10518e12 | 0.834952 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 7.81498e11 | 0.579776 | ||||||||
\(497\) | −7.28936e11 | − | 1.26255e12i | −0.535902 | − | 0.928210i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.59942e11 | − | 4.50233e11i | 0.187683 | − | 0.325076i | −0.756794 | − | 0.653653i | \(-0.773236\pi\) |
0.944477 | + | 0.328577i | \(0.106569\pi\) | |||||||
\(500\) | −4.41792e9 | + | 7.65206e9i | −0.00316120 | + | 0.00547537i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 4.30117e11 | + | 7.44984e11i | 0.302287 | + | 0.523577i | ||||
\(503\) | −1.32324e12 | −0.921683 | −0.460842 | − | 0.887482i | \(-0.652452\pi\) | ||||
−0.460842 | + | 0.887482i | \(0.652452\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.39993e10 | −0.00957844 | ||||||||
\(506\) | −3.16065e11 | − | 5.47441e11i | −0.214338 | − | 0.371245i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 2.91854e10 | − | 5.05506e10i | 0.0194437 | − | 0.0336775i | ||||
\(509\) | 8.27751e11 | − | 1.43371e12i | 0.546600 | − | 0.946739i | −0.451904 | − | 0.892066i | \(-0.649255\pi\) |
0.998504 | − | 0.0546727i | \(-0.0174115\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −1.42696e12 | − | 2.47156e12i | −0.925800 | − | 1.60353i | ||||
\(512\) | 1.71854e12 | 1.10521 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −9.48387e11 | −0.599310 | ||||||||
\(515\) | −1.92507e10 | − | 3.33432e10i | −0.0120591 | − | 0.0208869i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −4.96418e11 | + | 8.59821e11i | −0.305591 | + | 0.529298i | ||||
\(518\) | −2.04277e12 | + | 3.53819e12i | −1.24663 | + | 2.15922i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 2.16649e10 | + | 3.75247e10i | 0.0129940 | + | 0.0225062i | ||||
\(521\) | −3.36913e11 | −0.200331 | −0.100165 | − | 0.994971i | \(-0.531937\pi\) | ||||
−0.100165 | + | 0.994971i | \(0.531937\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.63804e12 | −1.54179 | −0.770893 | − | 0.636964i | \(-0.780190\pi\) | ||||
−0.770893 | + | 0.636964i | \(0.780190\pi\) | |||||||
\(524\) | −1.50112e11 | − | 2.60002e11i | −0.0869813 | − | 0.150656i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 2.92766e11 | − | 5.07086e11i | 0.166757 | − | 0.288832i | ||||
\(527\) | −1.43618e10 | + | 2.48753e10i | −0.00811073 | + | 0.0140482i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.58283e11 | + | 1.31338e12i | 0.420999 | + | 0.729191i | ||||
\(530\) | −6.70014e10 | −0.0368844 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −3.03433e11 | −0.164233 | ||||||||
\(533\) | 1.27209e12 | + | 2.20333e12i | 0.682727 | + | 1.18252i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.33533e9 | + | 9.24107e9i | −0.00281559 | + | 0.00487675i | ||||
\(536\) | −1.01144e12 | + | 1.75186e12i | −0.529294 | + | 0.916764i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −1.47421e12 | − | 2.55341e12i | −0.758646 | − | 1.31401i | ||||
\(539\) | 2.59159e12 | 1.32256 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2.84689e12 | −1.42884 | −0.714419 | − | 0.699718i | \(-0.753309\pi\) | ||||
−0.714419 | + | 0.699718i | \(0.753309\pi\) | |||||||
\(542\) | 9.71137e10 | + | 1.68206e11i | 0.0483375 | + | 0.0837229i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −5.00473e9 | + | 8.66844e9i | −0.00245011 | + | 0.00424371i | ||||
\(545\) | −1.77081e10 | + | 3.06714e10i | −0.00859781 | + | 0.0148918i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.98785e12 | + | 3.44306e12i | 0.949381 | + | 1.64438i | 0.746732 | + | 0.665125i | \(0.231622\pi\) |
0.202649 | + | 0.979251i | \(0.435045\pi\) | |||||||
\(548\) | −7.54396e10 | −0.0357344 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 2.31197e12 | 1.07733 | ||||||||
\(551\) | −1.69848e12 | − | 2.94185e12i | −0.785014 | − | 1.35968i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.68178e12 | − | 2.91293e12i | 0.764727 | − | 1.32455i | ||||
\(554\) | 4.42709e11 | − | 7.66794e11i | 0.199675 | − | 0.345848i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.29427e11 | + | 2.24174e11i | 0.0574366 | + | 0.0994831i | ||||
\(557\) | −3.04474e12 | −1.34030 | −0.670151 | − | 0.742225i | \(-0.733771\pi\) | ||||
−0.670151 | + | 0.742225i | \(0.733771\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.64278e11 | 0.157790 | ||||||||
\(560\) | 4.89782e10 | + | 8.48328e10i | 0.0210454 | + | 0.0364517i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.55462e12 | + | 2.69268e12i | −0.657371 | + | 1.13860i | ||||
\(563\) | −1.20598e12 | + | 2.08882e12i | −0.505886 | + | 0.876220i | 0.494091 | + | 0.869410i | \(0.335501\pi\) |
−0.999977 | + | 0.00680972i | \(0.997832\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −1.17994e9 | − | 2.04371e9i | −0.000487125 | − | 0.000843725i | ||||
\(566\) | 7.74224e11 | 0.317097 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.88501e12 | 0.759882 | ||||||||
\(569\) | 7.15985e11 | + | 1.24012e12i | 0.286351 | + | 0.495974i | 0.972936 | − | 0.231075i | \(-0.0742243\pi\) |
−0.686585 | + | 0.727050i | \(0.740891\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −1.08784e10 | + | 1.88419e10i | −0.00428254 | + | 0.00741758i | −0.868159 | − | 0.496287i | \(-0.834697\pi\) |
0.863876 | + | 0.503704i | \(0.168030\pi\) | |||||||
\(572\) | −1.11310e11 | + | 1.92795e11i | −0.0434763 | + | 0.0753032i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 3.19377e12 | + | 5.53177e12i | 1.22800 | + | 2.12697i | ||||
\(575\) | 1.04085e12 | 0.397086 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.44386e12 | 0.917879 | 0.458940 | − | 0.888467i | \(-0.348229\pi\) | ||||
0.458940 | + | 0.888467i | \(0.348229\pi\) | |||||||
\(578\) | −1.27303e12 | − | 2.20496e12i | −0.474421 | − | 0.821721i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 5.97527e9 | − | 1.03495e10i | 0.00219246 | − | 0.00379745i | ||||
\(581\) | 2.16802e12 | − | 3.75511e12i | 0.789350 | − | 1.36719i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.91818e12 | − | 3.32238e12i | −0.687670 | − | 1.19108i | ||||
\(584\) | 3.69008e12 | 1.31274 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.44078e11 | −0.295694 | ||||||||
\(587\) | −2.07376e12 | − | 3.59186e12i | −0.720919 | − | 1.24867i | −0.960632 | − | 0.277825i | \(-0.910386\pi\) |
0.239712 | − | 0.970844i | \(-0.422947\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.07535e12 | − | 1.86256e12i | 0.368155 | − | 0.637662i | ||||
\(590\) | −3.12223e10 | + | 5.40786e10i | −0.0106079 | + | 0.0183735i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.37836e12 | − | 4.11944e12i | −0.795847 | − | 1.37845i | ||||
\(593\) | 1.12036e12 | 0.372059 | 0.186029 | − | 0.982544i | \(-0.440438\pi\) | ||||
0.186029 | + | 0.982544i | \(0.440438\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.60034e9 | −0.00117765 | ||||||||
\(596\) | 2.62880e11 | + | 4.55322e11i | 0.0853394 | + | 0.147812i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 4.58244e11 | − | 7.93703e11i | 0.146535 | − | 0.253806i | ||||
\(599\) | 4.84352e10 | − | 8.38922e10i | 0.0153724 | − | 0.0266257i | −0.858237 | − | 0.513254i | \(-0.828440\pi\) |
0.873609 | + | 0.486628i | \(0.161773\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.21998e11 | − | 7.30923e11i | −0.131940 | − | 0.228526i | 0.792484 | − | 0.609892i | \(-0.208787\pi\) |
−0.924424 | + | 0.381366i | \(0.875454\pi\) | |||||||
\(602\) | 9.14569e11 | 0.283813 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.64295e10 | −0.0141948 | ||||||||
\(605\) | −1.53430e10 | − | 2.65748e10i | −0.00465597 | − | 0.00806437i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.56121e12 | − | 2.70409e12i | 0.466779 | − | 0.808485i | −0.532501 | − | 0.846429i | \(-0.678748\pi\) |
0.999280 | + | 0.0379447i | \(0.0120811\pi\) | |||||||
\(608\) | 3.74733e11 | − | 6.49056e11i | 0.111213 | − | 0.192627i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 4.21702e10 | + | 7.30410e10i | 0.0123317 | + | 0.0213591i | ||||
\(611\) | −1.43945e12 | −0.417842 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 5.54993e12 | 1.58751 | 0.793753 | − | 0.608240i | \(-0.208124\pi\) | ||||
0.793753 | + | 0.608240i | \(0.208124\pi\) | |||||||
\(614\) | 6.47246e11 | + | 1.12106e12i | 0.183786 | + | 0.318326i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.11440e12 | + | 5.39431e12i | −0.871489 | + | 1.50946i | ||||
\(617\) | −1.37092e12 | + | 2.37450e12i | −0.380828 | + | 0.659613i | −0.991181 | − | 0.132517i | \(-0.957694\pi\) |
0.610353 | + | 0.792129i | \(0.291028\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −1.41847e12 | − | 2.45686e12i | −0.388339 | − | 0.672624i | 0.603887 | − | 0.797070i | \(-0.293618\pi\) |
−0.992226 | + | 0.124446i | \(0.960285\pi\) | |||||||
\(620\) | 7.56619e9 | 0.00205643 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −6.05579e12 | −1.62224 | ||||||||
\(623\) | −1.26321e12 | − | 2.18795e12i | −0.335955 | − | 0.581891i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −1.90146e12 | + | 3.29343e12i | −0.498456 | + | 0.863352i | ||||
\(626\) | 1.59620e12 | − | 2.76470e12i | 0.415435 | − | 0.719555i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −1.34904e11 | − | 2.33660e11i | −0.0346103 | − | 0.0599468i | ||||
\(629\) | 1.74831e11 | 0.0445338 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 4.50954e12 | 1.13240 | 0.566200 | − | 0.824268i | \(-0.308413\pi\) | ||||
0.566200 | + | 0.824268i | \(0.308413\pi\) | |||||||
\(632\) | 2.17452e12 | + | 3.76639e12i | 0.542172 | + | 0.939070i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.50725e12 | − | 2.61064e12i | 0.370496 | − | 0.641719i | ||||
\(635\) | −2.59291e10 | + | 4.49106e10i | −0.00632858 | + | 0.0109614i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.87870e12 | + | 3.25400e12i | 0.452095 | + | 0.783051i | ||||
\(638\) | −6.25715e12 | −1.49514 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.12655e11 | −0.0265424 | ||||||||
\(641\) | 2.81867e12 | + | 4.88208e12i | 0.659453 | + | 1.14221i | 0.980758 | + | 0.195230i | \(0.0625452\pi\) |
−0.321305 | + | 0.946976i | \(0.604121\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −2.24664e12 | + | 3.89130e12i | −0.518304 | + | 0.897730i | 0.481469 | + | 0.876463i | \(0.340103\pi\) |
−0.999774 | + | 0.0212667i | \(0.993230\pi\) | |||||||
\(644\) | −1.25813e11 | + | 2.17915e11i | −0.0288231 | + | 0.0499231i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.93682e10 | − | 1.02829e11i | −0.0134124 | − | 0.0232310i | ||||
\(647\) | −2.52863e12 | −0.567304 | −0.283652 | − | 0.958927i | \(-0.591546\pi\) | ||||
−0.283652 | + | 0.958927i | \(0.591546\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.57543e12 | −0.791093 | ||||||||
\(650\) | 1.67599e12 | + | 2.90291e12i | 0.368267 | + | 0.637857i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.72227e11 | − | 2.98306e11i | 0.0373239 | − | 0.0646469i | ||||
\(653\) | 4.79425e11 | − | 8.30389e11i | 0.103184 | − | 0.178720i | −0.809811 | − | 0.586691i | \(-0.800430\pi\) |
0.912995 | + | 0.407971i | \(0.133764\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1.33364e11 | + | 2.30993e11i | 0.0283109 | + | 0.0490358i | ||||
\(656\) | −7.43688e12 | −1.56792 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −3.61395e12 | −0.751562 | ||||||||
\(659\) | 6.89533e11 | + | 1.19431e12i | 0.142420 | + | 0.246679i | 0.928407 | − | 0.371564i | \(-0.121178\pi\) |
−0.785987 | + | 0.618242i | \(0.787845\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 5.80937e11 | − | 1.00621e12i | 0.118365 | − | 0.205014i | −0.800755 | − | 0.598992i | \(-0.795568\pi\) |
0.919120 | + | 0.393978i | \(0.128901\pi\) | |||||||
\(662\) | −1.28051e12 | + | 2.21791e12i | −0.259132 | + | 0.448830i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 2.80322e12 | + | 4.85532e12i | 0.559630 | + | 0.969307i | ||||
\(665\) | 2.69578e11 | 0.0534549 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −2.81698e12 | −0.551084 | ||||||||
\(668\) | −1.46759e11 | − | 2.54195e11i | −0.0285175 | − | 0.0493938i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 8.06315e10 | − | 1.39658e11i | 0.0154585 | − | 0.0267750i | ||||
\(671\) | −2.41457e12 | + | 4.18216e12i | −0.459821 | + | 0.796433i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −1.13997e12 | − | 1.97449e12i | −0.214203 | − | 0.371010i | 0.738823 | − | 0.673900i | \(-0.235382\pi\) |
−0.953026 | + | 0.302889i | \(0.902049\pi\) | |||||||
\(674\) | 7.54578e12 | 1.40843 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 2.12459e11 | 0.0391304 | ||||||||
\(677\) | 1.06948e12 | + | 1.85240e12i | 0.195670 | + | 0.338911i | 0.947120 | − | 0.320879i | \(-0.103978\pi\) |
−0.751450 | + | 0.659790i | \(0.770645\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.05520e11 | − | 1.22200e12i | 0.127378 | − | 0.220626i | ||||
\(680\) | 2.32760e9 | − | 4.03152e9i | 0.000417463 | − | 0.000723067i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −1.98078e12 | − | 3.43081e12i | −0.350595 | − | 0.607249i | ||||
\(683\) | −4.62393e11 | −0.0813051 | −0.0406526 | − | 0.999173i | \(-0.512944\pi\) | ||||
−0.0406526 | + | 0.999173i | \(0.512944\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 6.70226e10 | 0.0116309 | ||||||||
\(686\) | 6.65777e11 | + | 1.15316e12i | 0.114781 | + | 0.198807i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −5.32407e11 | + | 9.22156e11i | −0.0905932 | + | 0.156912i | ||||
\(689\) | 2.78105e12 | − | 4.81692e12i | 0.470134 | − | 0.814297i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4.60548e12 | − | 7.97693e12i | −0.768465 | − | 1.33102i | −0.938395 | − | 0.345564i | \(-0.887688\pi\) |
0.169930 | − | 0.985456i | \(-0.445646\pi\) | |||||||
\(692\) | −6.21676e11 | −0.103059 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 7.67607e12 | 1.25609 | ||||||||
\(695\) | −1.14987e11 | − | 1.99163e11i | −0.0186946 | − | 0.0323800i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 1.36669e11 | − | 2.36718e11i | 0.0219343 | − | 0.0379913i | ||||
\(698\) | 4.62117e12 | − | 8.00410e12i | 0.736890 | − | 1.27633i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −4.60153e11 | − | 7.97008e11i | −0.0724371 | − | 0.125465i | ||||
\(701\) | −1.30164e12 | −0.203592 | −0.101796 | − | 0.994805i | \(-0.532459\pi\) | ||||
−0.101796 | + | 0.994805i | \(0.532459\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.30906e13 | −2.02143 | ||||||||
\(704\) | −3.99092e12 | − | 6.91248e12i | −0.612345 | − | 1.06061i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 5.57486e12 | − | 9.65594e12i | 0.844525 | − | 1.46276i | ||||
\(707\) | 1.45886e12 | − | 2.52682e12i | 0.219597 | − | 0.380354i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.16559e12 | + | 1.06791e13i | 0.916361 | + | 1.58718i | 0.804896 | + | 0.593416i | \(0.202221\pi\) |
0.111465 | + | 0.993768i | \(0.464446\pi\) | |||||||
\(710\) | −1.50273e11 | −0.0221931 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.26664e12 | 0.476367 | ||||||||
\(713\) | −8.91751e11 | − | 1.54456e12i | −0.129223 | − | 0.223821i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 9.88911e10 | − | 1.71284e11i | 0.0141508 | − | 0.0245099i | ||||
\(716\) | 4.18316e11 | − | 7.24544e11i | 0.0594833 | − | 0.103028i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4.53903e12 | + | 7.86184e12i | 0.637387 | + | 1.10399i | ||||
\(719\) | 1.63948e12 | 0.228784 | 0.114392 | − | 0.993436i | \(-0.463508\pi\) | ||||
0.114392 | + | 0.993436i | \(0.463508\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 8.02443e12 | 1.10587 | ||||||||
\(722\) | 9.79055e11 | + | 1.69577e12i | 0.134088 | + | 0.232247i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −2.68442e10 | + | 4.64955e10i | −0.00363100 | + | 0.00628908i | ||||
\(725\) | 5.15145e12 | − | 8.92257e12i | 0.692482 | − | 1.19941i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.01670e12 | + | 5.22507e12i | 0.400522 | + | 0.693725i | 0.993789 | − | 0.111281i | \(-0.0354953\pi\) |
−0.593267 | + | 0.805006i | \(0.702162\pi\) | |||||||
\(728\) | −9.03078e12 | −1.19161 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −2.94173e11 | −0.0383398 | ||||||||
\(731\) | −1.95683e10 | − | 3.38934e10i | −0.00253470 | − | 0.00439022i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −4.71833e11 | + | 8.17239e11i | −0.0603699 | + | 0.104564i | −0.894631 | − | 0.446806i | \(-0.852561\pi\) |
0.834261 | + | 0.551370i | \(0.185895\pi\) | |||||||
\(734\) | −2.01383e12 | + | 3.48806e12i | −0.256089 | + | 0.443559i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.10754e11 | − | 5.38241e11i | −0.0390361 | − | 0.0676124i | ||||
\(737\) | 9.23356e12 | 1.15283 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.35026e12 | 0.289879 | 0.144939 | − | 0.989441i | \(-0.453701\pi\) | ||||
0.144939 | + | 0.989441i | \(0.453701\pi\) | |||||||
\(740\) | −2.30264e10 | − | 3.98830e10i | −0.00282283 | − | 0.00488928i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.98220e12 | − | 1.20935e13i | 0.845619 | − | 1.46466i | ||||
\(743\) | −5.30074e12 | + | 9.18116e12i | −0.638098 | + | 1.10522i | 0.347752 | + | 0.937587i | \(0.386945\pi\) |
−0.985850 | + | 0.167631i | \(0.946388\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −2.33550e11 | − | 4.04521e11i | −0.0277765 | − | 0.0481102i | ||||
\(746\) | −7.61577e11 | −0.0900304 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 2.39175e10 | 0.00279357 | ||||||||
\(749\) | −1.11199e12 | − | 1.92602e12i | −0.129102 | − | 0.223611i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7.14006e12 | + | 1.23669e13i | −0.819072 | + | 1.41867i | 0.0872949 | + | 0.996183i | \(0.472178\pi\) |
−0.906367 | + | 0.422492i | \(0.861156\pi\) | |||||||
\(752\) | 2.10382e12 | − | 3.64392e12i | 0.239899 | − | 0.415517i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −4.53593e12 | − | 7.85646e12i | −0.511088 | − | 0.885230i | ||||
\(755\) | 4.12493e10 | 0.00462014 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.98242e12 | 0.330094 | 0.165047 | − | 0.986286i | \(-0.447222\pi\) | ||||
0.165047 | + | 0.986286i | \(0.447222\pi\) | |||||||
\(758\) | 2.78123e12 | + | 4.81724e12i | 0.306003 | + | 0.530013i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.74281e11 | + | 3.01863e11i | −0.0189491 | + | 0.0328208i | ||||
\(761\) | −5.75362e12 | + | 9.96555e12i | −0.621885 | + | 1.07714i | 0.367250 | + | 0.930122i | \(0.380299\pi\) |
−0.989134 | + | 0.147014i | \(0.953034\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −3.69072e12 | − | 6.39251e12i | −0.394230 | − | 0.682827i | ||||
\(764\) | −6.55709e11 | −0.0696291 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.51377e12 | 0.263813 | ||||||||
\(767\) | −2.59190e12 | − | 4.48931e12i | −0.270421 | − | 0.468382i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7.67871e12 | + | 1.32999e13i | −0.791807 | + | 1.37145i | 0.133040 | + | 0.991111i | \(0.457526\pi\) |
−0.924847 | + | 0.380340i | \(0.875807\pi\) | |||||||
\(770\) | 2.48280e11 | − | 4.30033e11i | 0.0254526 | − | 0.0440853i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2.82427e11 | − | 4.89177e11i | −0.0286172 | − | 0.0495665i | ||||
\(773\) | 1.55153e13 | 1.56298 | 0.781491 | − | 0.623917i | \(-0.214460\pi\) | ||||
0.781491 | + | 0.623917i | \(0.214460\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 6.52302e12 | 0.649518 | ||||||||
\(776\) | 9.12229e11 | + | 1.58003e12i | 0.0903080 | + | 0.156418i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −4.47246e12 | + | 7.74652e12i | −0.437661 | + | 0.758051i | ||||
\(779\) | −1.02332e13 | + | 1.77244e13i | −0.995620 | + | 1.72446i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −4.30214e12 | − | 7.45152e12i | −0.413766 | − | 0.716664i | ||||
\(782\) | −9.84642e10 | −0.00941560 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −1.09832e13 | −1.03826 | ||||||||
\(785\) | 1.19852e11 | + | 2.07590e11i | 0.0112650 | + | 0.0195116i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 7.46149e12 | − | 1.29237e13i | 0.693329 | − | 1.20088i | −0.277412 | − | 0.960751i | \(-0.589477\pi\) |
0.970741 | − | 0.240130i | \(-0.0771901\pi\) | |||||||
\(788\) | 8.15911e11 | − | 1.41320e12i | 0.0753832 | − | 0.130568i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.73353e11 | − | 3.00256e11i | −0.0158347 | − | 0.0274264i | ||||
\(791\) | 4.91843e11 | 0.0446717 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7.00149e12 | −0.628725 | ||||||||
\(794\) | −4.97383e12 | − | 8.61493e12i | −0.444118 | − | 0.769236i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 1.88272e11 | − | 3.26096e11i | 0.0166217 | − | 0.0287897i | ||||
\(797\) | −4.03047e11 | + | 6.98098e11i | −0.0353829 | + | 0.0612849i | −0.883175 | − | 0.469044i | \(-0.844598\pi\) |
0.847792 | + | 0.530329i | \(0.177932\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 7.73248e10 | + | 1.33931e11i | 0.00671210 | + | 0.0116257i | ||||
\(800\) | 2.27312e12 | 0.196208 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −1.36627e13 | −1.16614 | ||||||||
\(803\) | −8.42183e12 | − | 1.45870e13i | −0.714803 | − | 1.23808i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.11776e11 | − | 1.93602e11i | 0.00938140 | − | 0.0162491i | ||||
\(806\) | 2.87181e12 | − | 4.97412e12i | 0.239689 | − | 0.415154i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.88629e12 | + | 3.26715e12i | 0.155689 | + | 0.269661i | ||||
\(809\) | −1.37229e13 | −1.12636 | −0.563179 | − | 0.826335i | \(-0.690422\pi\) | ||||
−0.563179 | + | 0.826335i | \(0.690422\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.34290e12 | 0.514866 | 0.257433 | − | 0.966296i | \(-0.417123\pi\) | ||||
0.257433 | + | 0.966296i | \(0.417123\pi\) | |||||||
\(812\) | 1.24536e12 | + | 2.15703e12i | 0.100530 | + | 0.174122i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −1.20563e13 | + | 2.08822e13i | −0.962511 | + | 1.66712i | ||||
\(815\) | −1.53011e11 | + | 2.65023e11i | −0.0121483 | + | 0.0210414i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.46519e12 | + | 2.53779e12i | 0.115052 | + | 0.199277i | ||||
\(818\) | 2.64112e12 | 0.206252 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.20013e10 | −0.00556132 | ||||||||
\(821\) | 6.19717e12 | + | 1.07338e13i | 0.476046 | + | 0.824536i | 0.999623 | − | 0.0274419i | \(-0.00873614\pi\) |
−0.523577 | + | 0.851978i | \(0.675403\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.70558e12 | − | 9.88236e12i | 0.433511 | − | 0.750864i | −0.563661 | − | 0.826006i | \(-0.690608\pi\) |
0.997173 | + | 0.0751421i | \(0.0239410\pi\) | |||||||
\(824\) | −5.18775e12 | + | 8.98545e12i | −0.392019 | + | 0.678996i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −6.50733e12 | − | 1.12710e13i | −0.486399 | − | 0.842468i | ||||
\(827\) | 1.74662e13 | 1.29844 | 0.649222 | − | 0.760599i | \(-0.275095\pi\) | ||||
0.649222 | + | 0.760599i | \(0.275095\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −4.32053e12 | −0.317718 | −0.158859 | − | 0.987301i | \(-0.550781\pi\) | ||||
−0.158859 | + | 0.987301i | \(0.550781\pi\) | |||||||
\(830\) | −2.23472e11 | − | 3.87065e11i | −0.0163445 | − | 0.0283095i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.78620e12 | − | 1.00220e13i | 0.418638 | − | 0.725102i | ||||
\(833\) | 2.01840e11 | − | 3.49598e11i | 0.0145246 | − | 0.0251574i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.30385e11 | + | 2.25834e11i | 0.00928194 | + | 0.0160768i | ||||
\(836\) | −1.79084e12 | −0.126803 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 1.84344e13 | 1.29131 | ||||||||
\(839\) | 1.97625e12 | + | 3.42296e12i | 0.137693 | + | 0.238491i | 0.926623 | − | 0.375992i | \(-0.122698\pi\) |
−0.788930 | + | 0.614483i | \(0.789365\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −6.68837e12 | + | 1.15846e13i | −0.461040 | + | 0.798545i | ||||
\(842\) | 2.84751e12 | − | 4.93204e12i | 0.195237 | − | 0.338160i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 9.32798e11 | + | 1.61565e12i | 0.0632771 | + | 0.109599i | ||||
\(845\) | −1.88754e11 | −0.0127362 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 6.39554e12 | 0.426975 | ||||||||
\(848\) | 8.12924e12 | + | 1.40802e13i | 0.539844 | + | 0.935037i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.80063e11 | − | 3.11878e11i | 0.0118315 | − | 0.0204927i | ||||
\(851\) | −5.42779e12 | + | 9.40121e12i | −0.354765 | + | 0.614470i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 7.49575e12 | + | 1.29830e13i | 0.484780 | + | 0.839663i | 0.999847 | − | 0.0174864i | \(-0.00556639\pi\) |
−0.515067 | + | 0.857150i | \(0.672233\pi\) | |||||||
\(854\) | −1.75782e13 | −1.13087 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 2.87557e12 | 0.183060 | ||||||||
\(857\) | −7.05290e12 | − | 1.22160e13i | −0.446636 | − | 0.773597i | 0.551528 | − | 0.834156i | \(-0.314045\pi\) |
−0.998165 | + | 0.0605596i | \(0.980711\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.12478e13 | − | 1.94818e13i | 0.704853 | − | 1.22084i | −0.261891 | − | 0.965097i | \(-0.584346\pi\) |
0.966744 | − | 0.255744i | \(-0.0823205\pi\) | |||||||
\(860\) | −5.15458e9 | + | 8.92800e9i | −0.000321329 | + | 0.000556559i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.89074e12 | + | 5.00691e12i | 0.178331 | + | 0.308878i | ||||
\(863\) | 1.15572e13 | 0.709259 | 0.354629 | − | 0.935007i | \(-0.384607\pi\) | ||||
0.354629 | + | 0.935007i | \(0.384607\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 5.52315e11 | 0.0335439 | ||||||||
\(866\) | −1.15030e13 | − | 1.99237e13i | −0.694991 | − | 1.20376i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −7.88471e11 | + | 1.36567e12i | −0.0471462 | + | 0.0816596i | ||||
\(869\) | 9.92578e12 | − | 1.71920e13i | 0.590440 | − | 1.02267i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.69359e12 | + | 1.15936e13i | 0.394074 | + | 0.682556i | ||||
\(872\) | 9.54411e12 | 0.558999 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 7.37258e12 | 0.427384 | ||||||||
\(875\) | 8.18047e11 | + | 1.41690e12i | 0.0471783 | + | 0.0817151i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 9.73218e12 | − | 1.68566e13i | 0.555536 | − | 0.962216i | −0.442326 | − | 0.896854i | \(-0.645847\pi\) |
0.997862 | − | 0.0653615i | \(-0.0208201\pi\) | |||||||
\(878\) | −5.50868e12 | + | 9.54131e12i | −0.312840 | + | 0.541855i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.89067e11 | + | 5.00679e11i | 0.0162490 | + | 0.0281441i | ||||
\(881\) | 8.46829e12 | 0.473592 | 0.236796 | − | 0.971559i | \(-0.423903\pi\) | ||||
0.236796 | + | 0.971559i | \(0.423903\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −1.77577e13 | −0.983025 | −0.491513 | − | 0.870870i | \(-0.663556\pi\) | ||||
−0.491513 | + | 0.870870i | \(0.663556\pi\) | |||||||
\(884\) | 1.73383e10 | + | 3.00308e10i | 0.000954930 | + | 0.00165399i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −2.47298e12 | + | 4.28334e12i | −0.134825 | + | 0.233523i | ||||
\(887\) | 1.23119e13 | − | 2.13248e13i | 0.667833 | − | 1.15672i | −0.310676 | − | 0.950516i | \(-0.600555\pi\) |
0.978509 | − | 0.206205i | \(-0.0661112\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.40414e12 | − | 9.36024e12i | −0.290181 | − | 0.502608i | ||||
\(890\) | −2.60416e11 | −0.0139127 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −8.85903e11 | −0.0468538 | ||||||||
\(893\) | −5.78975e12 | − | 1.00281e13i | −0.304669 | − | 0.527703i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.71643e11 | + | 6.43705e11i | −0.0193608 | + | 0.0335338i | ||||
\(896\) | 1.17397e13 | − | 2.03338e13i | 0.608517 | − | 1.05398i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.17223e13 | + | 2.03037e13i | 0.601548 | + | 1.04191i | ||||
\(899\) | −1.76540e13 | −0.901414 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.97571e11 | −0.0302084 | ||||||||
\(902\) | 1.88494e13 | + | 3.26482e13i | 0.948133 | + | 1.64221i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.17974e11 | + | 5.50747e11i | −0.0158356 | + | 0.0274280i | ||||
\(905\) | 2.38491e10 | − | 4.13079e10i | 0.00118183 | − | 0.00204698i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.13193e12 | + | 1.96056e12i | 0.0555376 | + | 0.0961939i | 0.892458 | − | 0.451131i | \(-0.148979\pi\) |
−0.836920 | + | 0.547325i | \(0.815646\pi\) | |||||||
\(908\) | 1.77770e12 | 0.0867904 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 7.19932e11 | 0.0348021 | ||||||||
\(911\) | −1.22110e13 | − | 2.11500e13i | −0.587377 | − | 1.01737i | −0.994574 | − | 0.104027i | \(-0.966827\pi\) |
0.407197 | − | 0.913340i | \(-0.366506\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.27955e13 | − | 2.21625e13i | 0.609451 | − | 1.05560i | ||||
\(914\) | −9.83785e11 | + | 1.70397e12i | −0.0466275 | + | 0.0807613i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.08457e11 | + | 1.57349e12i | 0.0426358 | + | 0.0738474i | ||||
\(917\) | −5.55914e13 | −2.59624 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.43274e12 | −0.436233 | −0.218116 | − | 0.975923i | \(-0.569991\pi\) | ||||
−0.218116 | + | 0.975923i | \(0.569991\pi\) | |||||||
\(920\) | 1.44525e11 | + | 2.50325e11i | 0.00665118 | + | 0.0115202i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −5.00363e12 | + | 8.66655e12i | −0.228032 | + | 0.394964i | ||||
\(923\) | 6.23741e12 | − | 1.08035e13i | 0.282877 | − | 0.489957i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.98517e13 | − | 3.43842e13i | −0.891581 | − | 1.54426i | ||||
\(926\) | 2.29812e13 | 1.02713 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −6.15199e12 | −0.272301 | ||||||||
\(929\) | 1.38200e13 | + | 2.39370e13i | 0.608749 | + | 1.05438i | 0.991447 | + | 0.130511i | \(0.0416618\pi\) |
−0.382698 | + | 0.923874i | \(0.625005\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.51129e13 | + | 2.61764e13i | −0.659289 | + | 1.14192i | ||||
\(932\) | −3.09223e11 | + | 5.35589e11i | −0.0134246 | + | 0.0232520i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −1.40306e13 | − | 2.43017e13i | −0.603276 | − | 1.04490i | ||||
\(935\) | −2.12490e10 | −0.000909256 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −2.24945e13 | −0.953341 | −0.476671 | − | 0.879082i | \(-0.658157\pi\) | ||||
−0.476671 | + | 0.879082i | \(0.658157\pi\) | |||||||
\(938\) | 1.68052e13 | + | 2.91074e13i | 0.708811 | + | 1.22770i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.03685e10 | − | 3.52792e10i | 0.000850909 | − | 0.00147382i | ||||
\(941\) | −1.64166e12 | + | 2.84344e12i | −0.0682542 | + | 0.118220i | −0.898133 | − | 0.439724i | \(-0.855076\pi\) |
0.829879 | + | 0.557944i | \(0.188410\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 8.48607e12 | + | 1.46983e13i | 0.349465 | + | 0.605291i | ||||
\(944\) | 1.51527e13 | 0.621035 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 5.39774e12 | 0.219130 | ||||||||
\(947\) | 2.32562e13 | + | 4.02809e13i | 0.939645 | + | 1.62751i | 0.766134 | + | 0.642681i | \(0.222178\pi\) |
0.173511 | + | 0.984832i | \(0.444489\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.22103e13 | − | 2.11489e13i | 0.488685 | − | 0.846427i | ||||
\(950\) | −1.34823e13 | + | 2.33521e13i | −0.537043 | + | 0.930185i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 4.85117e11 | + | 8.40247e11i | 0.0191417 | + | 0.0331544i | ||||
\(953\) | −3.34707e13 | −1.31446 | −0.657229 | − | 0.753691i | \(-0.728271\pi\) | ||||
−0.657229 | + | 0.753691i | \(0.728271\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5.82550e11 | 0.0226630 | ||||||||
\(956\) | −3.17115e11 | − | 5.49258e11i | −0.0122788 | − | 0.0212675i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.29485e13 | + | 3.97480e13i | −0.880257 | + | 1.52465i | ||||
\(959\) | −6.98441e12 | + | 1.20974e13i | −0.266653 | + | 0.461856i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.63122e12 | + | 1.32177e13i | 0.288628 | + | 0.499919i | ||||
\(962\) | −3.49595e13 | −1.31607 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −5.79941e11 | −0.0216290 | ||||||||
\(965\) | 2.50916e11 | + | 4.34599e11i | 0.00931440 | + | 0.0161330i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −2.49162e13 | + | 4.31562e13i | −0.916354 | + | 1.58717i | −0.111447 | + | 0.993770i | \(0.535548\pi\) |
−0.804907 | + | 0.593401i | \(0.797785\pi\) | |||||||
\(968\) | −4.13468e12 | + | 7.16148e12i | −0.151357 | + | 0.262158i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −7.27227e10 | − | 1.25959e11i | −0.00263753 | − | 0.00456834i | ||||
\(971\) | 2.07241e13 | 0.748149 | 0.374075 | − | 0.927399i | \(-0.377960\pi\) | ||||
0.374075 | + | 0.927399i | \(0.377960\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 4.79309e13 | 1.71438 | ||||||||
\(974\) | −1.55016e13 | − | 2.68496e13i | −0.551902 | − | 0.955923i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.02330e13 | − | 1.77240e13i | 0.360975 | − | 0.625227i | ||||
\(977\) | −3.97242e11 | + | 6.88044e11i | −0.0139486 | + | 0.0241596i | −0.872915 | − | 0.487872i | \(-0.837773\pi\) |
0.858967 | + | 0.512031i | \(0.171107\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −7.45542e12 | − | 1.29132e13i | −0.259388 | − | 0.449273i | ||||
\(980\) | −1.06335e11 | −0.00368265 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.66179e13 | −0.570263 | ||||||||
\(983\) | −2.66645e13 | − | 4.61842e13i | −0.910840 | − | 1.57762i | −0.812880 | − | 0.582431i | \(-0.802101\pi\) |
−0.0979604 | − | 0.995190i | \(-0.531232\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7.24878e11 | + | 1.25553e12i | −0.0245359 | + | 0.0424974i | ||||
\(986\) | −4.87324e11 | + | 8.44070e11i | −0.0164199 | + | 0.0284402i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −1.29822e12 | − | 2.24858e12i | −0.0433453 | − | 0.0750762i | ||||
\(989\) | 2.43007e12 | 0.0807674 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 3.10566e13 | 1.02288 | 0.511438 | − | 0.859320i | \(-0.329113\pi\) | ||||
0.511438 | + | 0.859320i | \(0.329113\pi\) | |||||||
\(992\) | −1.94749e12 | − | 3.37315e12i | −0.0638517 | − | 0.110594i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.56599e13 | − | 2.71237e13i | 0.508803 | − | 0.881273i | ||||
\(995\) | −1.67266e11 | + | 2.89713e11i | −0.00541008 | + | 0.00937053i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.24632e13 | + | 2.15868e13i | 0.399484 | + | 0.691927i | 0.993662 | − | 0.112406i | \(-0.0358558\pi\) |
−0.594178 | + | 0.804334i | \(0.702523\pi\) | |||||||
\(998\) | 1.11688e13 | 0.356384 | ||||||||
\(999\) | 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 | 27.10.c.a.10.6 | 16 | ||
3.2 | odd | 2 | 9.10.c.a.4.3 | ✓ | 16 | ||
9.2 | odd | 6 | 9.10.c.a.7.3 | yes | 16 | ||
9.4 | even | 3 | 81.10.a.d.1.3 | 8 | |||
9.5 | odd | 6 | 81.10.a.c.1.6 | 8 | |||
9.7 | even | 3 | inner | 27.10.c.a.19.6 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
9.10.c.a.4.3 | ✓ | 16 | 3.2 | odd | 2 | ||
9.10.c.a.7.3 | yes | 16 | 9.2 | odd | 6 | ||
27.10.c.a.10.6 | 16 | 1.1 | even | 1 | trivial | ||
27.10.c.a.19.6 | 16 | 9.7 | even | 3 | inner | ||
81.10.a.c.1.6 | 8 | 9.5 | odd | 6 | |||
81.10.a.d.1.3 | 8 | 9.4 | even | 3 |