Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [98,10,Mod(1,98)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(98, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0]))
N = Newforms(chi, 10, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("98.1");
S:= CuspForms(chi, 10);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 98 = 2 \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 10 \) |
Character orbit: | \([\chi]\) | \(=\) | 98.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: | \(50.4735119441\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{3} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4037x + 70980 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{3}\cdot 7 \) |
Twist minimal: | no (minimal twist has level 14) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(52.2593\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 98.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −16.0000 | −0.707107 | ||||||||
\(3\) | −76.8690 | −0.547905 | −0.273953 | − | 0.961743i | \(-0.588331\pi\) | ||||
−0.273953 | + | 0.961743i | \(0.588331\pi\) | |||||||
\(4\) | 256.000 | 0.500000 | ||||||||
\(5\) | −1092.26 | −0.781557 | −0.390779 | − | 0.920485i | \(-0.627794\pi\) | ||||
−0.390779 | + | 0.920485i | \(0.627794\pi\) | |||||||
\(6\) | 1229.90 | 0.387427 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −4096.00 | −0.353553 | ||||||||
\(9\) | −13774.2 | −0.699800 | ||||||||
\(10\) | 17476.2 | 0.552644 | ||||||||
\(11\) | 54060.9 | 1.11331 | 0.556655 | − | 0.830744i | \(-0.312085\pi\) | ||||
0.556655 | + | 0.830744i | \(0.312085\pi\) | |||||||
\(12\) | −19678.5 | −0.273953 | ||||||||
\(13\) | 37802.6 | 0.367093 | 0.183547 | − | 0.983011i | \(-0.441242\pi\) | ||||
0.183547 | + | 0.983011i | \(0.441242\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 83960.9 | 0.428219 | ||||||||
\(16\) | 65536.0 | 0.250000 | ||||||||
\(17\) | −353470. | −1.02644 | −0.513218 | − | 0.858258i | \(-0.671547\pi\) | ||||
−0.513218 | + | 0.858258i | \(0.671547\pi\) | |||||||
\(18\) | 220387. | 0.494833 | ||||||||
\(19\) | 50210.7 | 0.0883903 | 0.0441952 | − | 0.999023i | \(-0.485928\pi\) | ||||
0.0441952 | + | 0.999023i | \(0.485928\pi\) | |||||||
\(20\) | −279618. | −0.390779 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −864974. | −0.787228 | ||||||||
\(23\) | 2.45852e6 | 1.83189 | 0.915944 | − | 0.401305i | \(-0.131443\pi\) | ||||
0.915944 | + | 0.401305i | \(0.131443\pi\) | |||||||
\(24\) | 314855. | 0.193714 | ||||||||
\(25\) | −760094. | −0.389168 | ||||||||
\(26\) | −604841. | −0.259574 | ||||||||
\(27\) | 2.57182e6 | 0.931329 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 1.40865e6 | 0.369840 | 0.184920 | − | 0.982754i | \(-0.440797\pi\) | ||||
0.184920 | + | 0.982754i | \(0.440797\pi\) | |||||||
\(30\) | −1.34337e6 | −0.302797 | ||||||||
\(31\) | 5.78323e6 | 1.12472 | 0.562358 | − | 0.826894i | \(-0.309894\pi\) | ||||
0.562358 | + | 0.826894i | \(0.309894\pi\) | |||||||
\(32\) | −1.04858e6 | −0.176777 | ||||||||
\(33\) | −4.15560e6 | −0.609988 | ||||||||
\(34\) | 5.65552e6 | 0.725800 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −3.52619e6 | −0.349900 | ||||||||
\(37\) | 5.45877e6 | 0.478836 | 0.239418 | − | 0.970917i | \(-0.423043\pi\) | ||||
0.239418 | + | 0.970917i | \(0.423043\pi\) | |||||||
\(38\) | −803370. | −0.0625014 | ||||||||
\(39\) | −2.90584e6 | −0.201132 | ||||||||
\(40\) | 4.47390e6 | 0.276322 | ||||||||
\(41\) | −1.73066e7 | −0.956501 | −0.478251 | − | 0.878223i | \(-0.658729\pi\) | ||||
−0.478251 | + | 0.878223i | \(0.658729\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.43644e6 | 0.0640735 | 0.0320367 | − | 0.999487i | \(-0.489801\pi\) | ||||
0.0320367 | + | 0.999487i | \(0.489801\pi\) | |||||||
\(44\) | 1.38396e7 | 0.556655 | ||||||||
\(45\) | 1.50450e7 | 0.546934 | ||||||||
\(46\) | −3.93364e7 | −1.29534 | ||||||||
\(47\) | 3.04387e7 | 0.909883 | 0.454942 | − | 0.890521i | \(-0.349660\pi\) | ||||
0.454942 | + | 0.890521i | \(0.349660\pi\) | |||||||
\(48\) | −5.03768e6 | −0.136976 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 1.21615e7 | 0.275183 | ||||||||
\(51\) | 2.71709e7 | 0.562390 | ||||||||
\(52\) | 9.67746e6 | 0.183547 | ||||||||
\(53\) | −4.30796e6 | −0.0749947 | −0.0374973 | − | 0.999297i | \(-0.511939\pi\) | ||||
−0.0374973 | + | 0.999297i | \(0.511939\pi\) | |||||||
\(54\) | −4.11491e7 | −0.658549 | ||||||||
\(55\) | −5.90485e7 | −0.870115 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3.85964e6 | −0.0484295 | ||||||||
\(58\) | −2.25385e7 | −0.261516 | ||||||||
\(59\) | −6.61456e7 | −0.710668 | −0.355334 | − | 0.934739i | \(-0.615633\pi\) | ||||
−0.355334 | + | 0.934739i | \(0.615633\pi\) | |||||||
\(60\) | 2.14940e7 | 0.214110 | ||||||||
\(61\) | −2.00925e8 | −1.85802 | −0.929008 | − | 0.370061i | \(-0.879337\pi\) | ||||
−0.929008 | + | 0.370061i | \(0.879337\pi\) | |||||||
\(62\) | −9.25317e7 | −0.795295 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.67772e7 | 0.125000 | ||||||||
\(65\) | −4.12902e7 | −0.286904 | ||||||||
\(66\) | 6.64896e7 | 0.431327 | ||||||||
\(67\) | −2.72602e8 | −1.65269 | −0.826347 | − | 0.563161i | \(-0.809585\pi\) | ||||
−0.826347 | + | 0.563161i | \(0.809585\pi\) | |||||||
\(68\) | −9.04883e7 | −0.513218 | ||||||||
\(69\) | −1.88984e8 | −1.00370 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.43433e8 | 0.669866 | 0.334933 | − | 0.942242i | \(-0.391286\pi\) | ||||
0.334933 | + | 0.942242i | \(0.391286\pi\) | |||||||
\(72\) | 5.64190e7 | 0.247417 | ||||||||
\(73\) | −3.68032e8 | −1.51681 | −0.758407 | − | 0.651781i | \(-0.774022\pi\) | ||||
−0.758407 | + | 0.651781i | \(0.774022\pi\) | |||||||
\(74\) | −8.73403e7 | −0.338588 | ||||||||
\(75\) | 5.84276e7 | 0.213227 | ||||||||
\(76\) | 1.28539e7 | 0.0441952 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 4.64935e7 | 0.142222 | ||||||||
\(79\) | 4.63995e8 | 1.34027 | 0.670134 | − | 0.742240i | \(-0.266236\pi\) | ||||
0.670134 | + | 0.742240i | \(0.266236\pi\) | |||||||
\(80\) | −7.15823e7 | −0.195389 | ||||||||
\(81\) | 7.34239e7 | 0.189520 | ||||||||
\(82\) | 2.76906e8 | 0.676349 | ||||||||
\(83\) | −7.47626e8 | −1.72915 | −0.864576 | − | 0.502503i | \(-0.832413\pi\) | ||||
−0.864576 | + | 0.502503i | \(0.832413\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 3.86081e8 | 0.802219 | ||||||||
\(86\) | −2.29830e7 | −0.0453068 | ||||||||
\(87\) | −1.08282e8 | −0.202637 | ||||||||
\(88\) | −2.21433e8 | −0.393614 | ||||||||
\(89\) | −1.12789e9 | −1.90551 | −0.952753 | − | 0.303746i | \(-0.901763\pi\) | ||||
−0.952753 | + | 0.303746i | \(0.901763\pi\) | |||||||
\(90\) | −2.40719e8 | −0.386741 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 6.29382e8 | 0.915944 | ||||||||
\(93\) | −4.44551e8 | −0.616238 | ||||||||
\(94\) | −4.87019e8 | −0.643385 | ||||||||
\(95\) | −5.48431e7 | −0.0690821 | ||||||||
\(96\) | 8.06029e7 | 0.0968569 | ||||||||
\(97\) | −1.27313e8 | −0.146016 | −0.0730079 | − | 0.997331i | \(-0.523260\pi\) | ||||
−0.0730079 | + | 0.997331i | \(0.523260\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −7.44643e8 | −0.779094 | ||||||||
\(100\) | −1.94584e8 | −0.194584 | ||||||||
\(101\) | 1.50545e9 | 1.43953 | 0.719764 | − | 0.694219i | \(-0.244250\pi\) | ||||
0.719764 | + | 0.694219i | \(0.244250\pi\) | |||||||
\(102\) | −4.34734e8 | −0.397670 | ||||||||
\(103\) | −5.94955e8 | −0.520855 | −0.260428 | − | 0.965493i | \(-0.583864\pi\) | ||||
−0.260428 | + | 0.965493i | \(0.583864\pi\) | |||||||
\(104\) | −1.54839e8 | −0.129787 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 6.89274e7 | 0.0530292 | ||||||||
\(107\) | 1.35491e9 | 0.999274 | 0.499637 | − | 0.866235i | \(-0.333467\pi\) | ||||
0.499637 | + | 0.866235i | \(0.333467\pi\) | |||||||
\(108\) | 6.58385e8 | 0.465665 | ||||||||
\(109\) | −1.93784e9 | −1.31492 | −0.657459 | − | 0.753490i | \(-0.728369\pi\) | ||||
−0.657459 | + | 0.753490i | \(0.728369\pi\) | |||||||
\(110\) | 9.44776e8 | 0.615264 | ||||||||
\(111\) | −4.19610e8 | −0.262357 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −1.98306e9 | −1.14415 | −0.572074 | − | 0.820202i | \(-0.693861\pi\) | ||||
−0.572074 | + | 0.820202i | \(0.693861\pi\) | |||||||
\(114\) | 6.17543e7 | 0.0342448 | ||||||||
\(115\) | −2.68535e9 | −1.43173 | ||||||||
\(116\) | 3.60616e8 | 0.184920 | ||||||||
\(117\) | −5.20699e8 | −0.256892 | ||||||||
\(118\) | 1.05833e9 | 0.502518 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −3.43904e8 | −0.151398 | ||||||||
\(121\) | 5.64628e8 | 0.239457 | ||||||||
\(122\) | 3.21480e9 | 1.31382 | ||||||||
\(123\) | 1.33034e9 | 0.524072 | ||||||||
\(124\) | 1.48051e9 | 0.562358 | ||||||||
\(125\) | 2.96354e9 | 1.08571 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.90286e7 | 0.0133127 | 0.00665635 | − | 0.999978i | \(-0.497881\pi\) | ||||
0.00665635 | + | 0.999978i | \(0.497881\pi\) | |||||||
\(128\) | −2.68435e8 | −0.0883883 | ||||||||
\(129\) | −1.10417e8 | −0.0351062 | ||||||||
\(130\) | 6.60643e8 | 0.202872 | ||||||||
\(131\) | 1.59378e9 | 0.472832 | 0.236416 | − | 0.971652i | \(-0.424027\pi\) | ||||
0.236416 | + | 0.971652i | \(0.424027\pi\) | |||||||
\(132\) | −1.06383e9 | −0.304994 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 4.36163e9 | 1.16863 | ||||||||
\(135\) | −2.80909e9 | −0.727887 | ||||||||
\(136\) | 1.44781e9 | 0.362900 | ||||||||
\(137\) | 5.63635e9 | 1.36696 | 0.683479 | − | 0.729970i | \(-0.260466\pi\) | ||||
0.683479 | + | 0.729970i | \(0.260466\pi\) | |||||||
\(138\) | 3.02375e9 | 0.709724 | ||||||||
\(139\) | 2.40520e9 | 0.546493 | 0.273246 | − | 0.961944i | \(-0.411903\pi\) | ||||
0.273246 | + | 0.961944i | \(0.411903\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −2.33979e9 | −0.498530 | ||||||||
\(142\) | −2.29494e9 | −0.473667 | ||||||||
\(143\) | 2.04364e9 | 0.408688 | ||||||||
\(144\) | −9.02704e8 | −0.174950 | ||||||||
\(145\) | −1.53862e9 | −0.289051 | ||||||||
\(146\) | 5.88851e9 | 1.07255 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 1.39744e9 | 0.239418 | ||||||||
\(149\) | 4.82927e9 | 0.802682 | 0.401341 | − | 0.915929i | \(-0.368544\pi\) | ||||
0.401341 | + | 0.915929i | \(0.368544\pi\) | |||||||
\(150\) | −9.34842e8 | −0.150774 | ||||||||
\(151\) | 1.06662e10 | 1.66960 | 0.834802 | − | 0.550550i | \(-0.185582\pi\) | ||||
0.834802 | + | 0.550550i | \(0.185582\pi\) | |||||||
\(152\) | −2.05663e8 | −0.0312507 | ||||||||
\(153\) | 4.86875e9 | 0.718300 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −6.31679e9 | −0.879030 | ||||||||
\(156\) | −7.43896e8 | −0.100566 | ||||||||
\(157\) | −9.90602e9 | −1.30122 | −0.650610 | − | 0.759412i | \(-0.725487\pi\) | ||||
−0.650610 | + | 0.759412i | \(0.725487\pi\) | |||||||
\(158\) | −7.42393e9 | −0.947713 | ||||||||
\(159\) | 3.31149e8 | 0.0410900 | ||||||||
\(160\) | 1.14532e9 | 0.138161 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | −1.17478e9 | −0.134011 | ||||||||
\(163\) | −1.24288e10 | −1.37907 | −0.689533 | − | 0.724255i | \(-0.742184\pi\) | ||||
−0.689533 | + | 0.724255i | \(0.742184\pi\) | |||||||
\(164\) | −4.43050e9 | −0.478251 | ||||||||
\(165\) | 4.53900e9 | 0.476740 | ||||||||
\(166\) | 1.19620e10 | 1.22269 | ||||||||
\(167\) | −5.48234e9 | −0.545434 | −0.272717 | − | 0.962094i | \(-0.587922\pi\) | ||||
−0.272717 | + | 0.962094i | \(0.587922\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.17547e9 | −0.865243 | ||||||||
\(170\) | −6.17729e9 | −0.567255 | ||||||||
\(171\) | −6.91610e8 | −0.0618555 | ||||||||
\(172\) | 3.67728e8 | 0.0320367 | ||||||||
\(173\) | −4.59767e9 | −0.390238 | −0.195119 | − | 0.980780i | \(-0.562509\pi\) | ||||
−0.195119 | + | 0.980780i | \(0.562509\pi\) | |||||||
\(174\) | 1.73251e9 | 0.143286 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.54293e9 | 0.278327 | ||||||||
\(177\) | 5.08454e9 | 0.389379 | ||||||||
\(178\) | 1.80462e10 | 1.34740 | ||||||||
\(179\) | 2.56403e9 | 0.186674 | 0.0933370 | − | 0.995635i | \(-0.470247\pi\) | ||||
0.0933370 | + | 0.995635i | \(0.470247\pi\) | |||||||
\(180\) | 3.85151e9 | 0.273467 | ||||||||
\(181\) | −3.58323e9 | −0.248154 | −0.124077 | − | 0.992273i | \(-0.539597\pi\) | ||||
−0.124077 | + | 0.992273i | \(0.539597\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.54449e10 | 1.01802 | ||||||||
\(184\) | −1.00701e10 | −0.647671 | ||||||||
\(185\) | −5.96239e9 | −0.374238 | ||||||||
\(186\) | 7.11282e9 | 0.435746 | ||||||||
\(187\) | −1.91089e10 | −1.14274 | ||||||||
\(188\) | 7.79231e9 | 0.454942 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.77489e8 | 0.0488484 | ||||||||
\(191\) | −6.97388e8 | −0.0379162 | −0.0189581 | − | 0.999820i | \(-0.506035\pi\) | ||||
−0.0189581 | + | 0.999820i | \(0.506035\pi\) | |||||||
\(192\) | −1.28965e9 | −0.0684881 | ||||||||
\(193\) | −5.70859e8 | −0.0296156 | −0.0148078 | − | 0.999890i | \(-0.504714\pi\) | ||||
−0.0148078 | + | 0.999890i | \(0.504714\pi\) | |||||||
\(194\) | 2.03701e9 | 0.103249 | ||||||||
\(195\) | 3.17394e9 | 0.157196 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −4.88945e9 | −0.231293 | −0.115646 | − | 0.993290i | \(-0.536894\pi\) | ||||
−0.115646 | + | 0.993290i | \(0.536894\pi\) | |||||||
\(198\) | 1.19143e10 | 0.550902 | ||||||||
\(199\) | 1.01824e10 | 0.460269 | 0.230134 | − | 0.973159i | \(-0.426083\pi\) | ||||
0.230134 | + | 0.973159i | \(0.426083\pi\) | |||||||
\(200\) | 3.11335e9 | 0.137592 | ||||||||
\(201\) | 2.09546e10 | 0.905519 | ||||||||
\(202\) | −2.40872e10 | −1.01790 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 6.95574e9 | 0.281195 | ||||||||
\(205\) | 1.89033e10 | 0.747561 | ||||||||
\(206\) | 9.51929e9 | 0.368300 | ||||||||
\(207\) | −3.38641e10 | −1.28196 | ||||||||
\(208\) | 2.47743e9 | 0.0917733 | ||||||||
\(209\) | 2.71443e9 | 0.0984058 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −2.89906e10 | −1.00690 | −0.503450 | − | 0.864025i | \(-0.667936\pi\) | ||||
−0.503450 | + | 0.864025i | \(0.667936\pi\) | |||||||
\(212\) | −1.10284e9 | −0.0374973 | ||||||||
\(213\) | −1.10256e10 | −0.367023 | ||||||||
\(214\) | −2.16786e10 | −0.706594 | ||||||||
\(215\) | −1.56896e9 | −0.0500771 | ||||||||
\(216\) | −1.05342e10 | −0.329275 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 3.10054e10 | 0.929788 | ||||||||
\(219\) | 2.82902e10 | 0.831070 | ||||||||
\(220\) | −1.51164e10 | −0.435057 | ||||||||
\(221\) | −1.33621e10 | −0.376798 | ||||||||
\(222\) | 6.71376e9 | 0.185514 | ||||||||
\(223\) | −9.01973e9 | −0.244243 | −0.122121 | − | 0.992515i | \(-0.538970\pi\) | ||||
−0.122121 | + | 0.992515i | \(0.538970\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.04697e10 | 0.272340 | ||||||||
\(226\) | 3.17289e10 | 0.809035 | ||||||||
\(227\) | 1.32631e10 | 0.331533 | 0.165767 | − | 0.986165i | \(-0.446990\pi\) | ||||
0.165767 | + | 0.986165i | \(0.446990\pi\) | |||||||
\(228\) | −9.88068e8 | −0.0242148 | ||||||||
\(229\) | −7.67667e10 | −1.84465 | −0.922323 | − | 0.386420i | \(-0.873712\pi\) | ||||
−0.922323 | + | 0.386420i | \(0.873712\pi\) | |||||||
\(230\) | 4.29655e10 | 1.01238 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −5.76985e9 | −0.130758 | ||||||||
\(233\) | −2.29389e9 | −0.0509883 | −0.0254942 | − | 0.999675i | \(-0.508116\pi\) | ||||
−0.0254942 | + | 0.999675i | \(0.508116\pi\) | |||||||
\(234\) | 8.33118e9 | 0.181650 | ||||||||
\(235\) | −3.32470e10 | −0.711126 | ||||||||
\(236\) | −1.69333e10 | −0.355334 | ||||||||
\(237\) | −3.56669e10 | −0.734340 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4.06748e10 | −0.806372 | −0.403186 | − | 0.915118i | \(-0.632097\pi\) | ||||
−0.403186 | + | 0.915118i | \(0.632097\pi\) | |||||||
\(240\) | 5.50246e9 | 0.107055 | ||||||||
\(241\) | 9.43703e9 | 0.180202 | 0.0901008 | − | 0.995933i | \(-0.471281\pi\) | ||||
0.0901008 | + | 0.995933i | \(0.471281\pi\) | |||||||
\(242\) | −9.03405e9 | −0.169322 | ||||||||
\(243\) | −5.62651e10 | −1.03517 | ||||||||
\(244\) | −5.14367e10 | −0.929008 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −2.12855e10 | −0.370575 | ||||||||
\(247\) | 1.89809e9 | 0.0324475 | ||||||||
\(248\) | −2.36881e10 | −0.397647 | ||||||||
\(249\) | 5.74692e10 | 0.947411 | ||||||||
\(250\) | −4.74166e10 | −0.767716 | ||||||||
\(251\) | −7.60552e10 | −1.20948 | −0.604738 | − | 0.796425i | \(-0.706722\pi\) | ||||
−0.604738 | + | 0.796425i | \(0.706722\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.32910e11 | 2.03946 | ||||||||
\(254\) | −6.24457e8 | −0.00941350 | ||||||||
\(255\) | −2.96776e10 | −0.439540 | ||||||||
\(256\) | 4.29497e9 | 0.0625000 | ||||||||
\(257\) | 9.02211e10 | 1.29006 | 0.645028 | − | 0.764159i | \(-0.276846\pi\) | ||||
0.645028 | + | 0.764159i | \(0.276846\pi\) | |||||||
\(258\) | 1.76668e9 | 0.0248238 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −1.05703e10 | −0.143452 | ||||||||
\(261\) | −1.94030e10 | −0.258814 | ||||||||
\(262\) | −2.55005e10 | −0.334343 | ||||||||
\(263\) | −9.35682e10 | −1.20594 | −0.602972 | − | 0.797762i | \(-0.706017\pi\) | ||||
−0.602972 | + | 0.797762i | \(0.706017\pi\) | |||||||
\(264\) | 1.70213e10 | 0.215663 | ||||||||
\(265\) | 4.70541e9 | 0.0586126 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 8.66995e10 | 1.04404 | ||||||||
\(268\) | −6.97861e10 | −0.826347 | ||||||||
\(269\) | 1.48563e10 | 0.172992 | 0.0864960 | − | 0.996252i | \(-0.472433\pi\) | ||||
0.0864960 | + | 0.996252i | \(0.472433\pi\) | |||||||
\(270\) | 4.49455e10 | 0.514694 | ||||||||
\(271\) | 1.17185e11 | 1.31980 | 0.659902 | − | 0.751352i | \(-0.270598\pi\) | ||||
0.659902 | + | 0.751352i | \(0.270598\pi\) | |||||||
\(272\) | −2.31650e10 | −0.256609 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.01815e10 | −0.966585 | ||||||||
\(275\) | −4.10913e10 | −0.433264 | ||||||||
\(276\) | −4.83799e10 | −0.501851 | ||||||||
\(277\) | −2.87224e10 | −0.293131 | −0.146565 | − | 0.989201i | \(-0.546822\pi\) | ||||
−0.146565 | + | 0.989201i | \(0.546822\pi\) | |||||||
\(278\) | −3.84832e10 | −0.386429 | ||||||||
\(279\) | −7.96592e10 | −0.787076 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −7.39690e10 | −0.707736 | −0.353868 | − | 0.935295i | \(-0.615134\pi\) | ||||
−0.353868 | + | 0.935295i | \(0.615134\pi\) | |||||||
\(282\) | 3.74367e10 | 0.352514 | ||||||||
\(283\) | −7.27488e10 | −0.674197 | −0.337098 | − | 0.941469i | \(-0.609446\pi\) | ||||
−0.337098 | + | 0.941469i | \(0.609446\pi\) | |||||||
\(284\) | 3.67190e10 | 0.334933 | ||||||||
\(285\) | 4.21573e9 | 0.0378504 | ||||||||
\(286\) | −3.26982e10 | −0.288986 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 1.44433e10 | 0.123708 | ||||||||
\(289\) | 6.35304e9 | 0.0535724 | ||||||||
\(290\) | 2.46179e10 | 0.204390 | ||||||||
\(291\) | 9.78642e9 | 0.0800028 | ||||||||
\(292\) | −9.42161e10 | −0.758407 | ||||||||
\(293\) | 2.43926e11 | 1.93354 | 0.966771 | − | 0.255644i | \(-0.0822876\pi\) | ||||
0.966771 | + | 0.255644i | \(0.0822876\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 7.22481e10 | 0.555428 | ||||||||
\(296\) | −2.23591e10 | −0.169294 | ||||||||
\(297\) | 1.39035e11 | 1.03686 | ||||||||
\(298\) | −7.72683e10 | −0.567582 | ||||||||
\(299\) | 9.29385e10 | 0.672474 | ||||||||
\(300\) | 1.49575e10 | 0.106614 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −1.70659e11 | −1.18059 | ||||||||
\(303\) | −1.15722e11 | −0.788725 | ||||||||
\(304\) | 3.29061e9 | 0.0220976 | ||||||||
\(305\) | 2.19462e11 | 1.45215 | ||||||||
\(306\) | −7.79000e10 | −0.507915 | ||||||||
\(307\) | 1.41661e11 | 0.910182 | 0.455091 | − | 0.890445i | \(-0.349607\pi\) | ||||
0.455091 | + | 0.890445i | \(0.349607\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.57336e10 | 0.285379 | ||||||||
\(310\) | 1.01069e11 | 0.621568 | ||||||||
\(311\) | 1.29174e11 | 0.782986 | 0.391493 | − | 0.920181i | \(-0.371959\pi\) | ||||
0.391493 | + | 0.920181i | \(0.371959\pi\) | |||||||
\(312\) | 1.19023e10 | 0.0711110 | ||||||||
\(313\) | 4.44649e10 | 0.261859 | 0.130930 | − | 0.991392i | \(-0.458204\pi\) | ||||
0.130930 | + | 0.991392i | \(0.458204\pi\) | |||||||
\(314\) | 1.58496e11 | 0.920101 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.18783e11 | 0.670134 | ||||||||
\(317\) | −2.48426e11 | −1.38175 | −0.690877 | − | 0.722973i | \(-0.742775\pi\) | ||||
−0.690877 | + | 0.722973i | \(0.742775\pi\) | |||||||
\(318\) | −5.29838e9 | −0.0290550 | ||||||||
\(319\) | 7.61531e10 | 0.411746 | ||||||||
\(320\) | −1.83251e10 | −0.0976947 | ||||||||
\(321\) | −1.04151e11 | −0.547508 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −1.77480e10 | −0.0907271 | ||||||||
\(324\) | 1.87965e10 | 0.0947600 | ||||||||
\(325\) | −2.87335e10 | −0.142861 | ||||||||
\(326\) | 1.98861e11 | 0.975146 | ||||||||
\(327\) | 1.48960e11 | 0.720451 | ||||||||
\(328\) | 7.08880e10 | 0.338174 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −7.26239e10 | −0.337106 | ||||||||
\(331\) | 3.62219e11 | 1.65861 | 0.829307 | − | 0.558793i | \(-0.188735\pi\) | ||||
0.829307 | + | 0.558793i | \(0.188735\pi\) | |||||||
\(332\) | −1.91392e11 | −0.864576 | ||||||||
\(333\) | −7.51900e10 | −0.335089 | ||||||||
\(334\) | 8.77175e10 | 0.385680 | ||||||||
\(335\) | 2.97752e11 | 1.29167 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.33951e11 | −1.83276 | −0.916380 | − | 0.400309i | \(-0.868903\pi\) | ||||
−0.916380 | + | 0.400309i | \(0.868903\pi\) | |||||||
\(338\) | 1.46807e11 | 0.611819 | ||||||||
\(339\) | 1.52435e11 | 0.626884 | ||||||||
\(340\) | 9.88367e10 | 0.401110 | ||||||||
\(341\) | 3.12646e11 | 1.25216 | ||||||||
\(342\) | 1.10658e10 | 0.0437385 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −5.88364e9 | −0.0226534 | ||||||||
\(345\) | 2.06420e11 | 0.784450 | ||||||||
\(346\) | 7.35626e10 | 0.275940 | ||||||||
\(347\) | 1.92978e11 | 0.714537 | 0.357268 | − | 0.934002i | \(-0.383708\pi\) | ||||
0.357268 | + | 0.934002i | \(0.383708\pi\) | |||||||
\(348\) | −2.77201e10 | −0.101319 | ||||||||
\(349\) | 2.85795e11 | 1.03119 | 0.515596 | − | 0.856832i | \(-0.327570\pi\) | ||||
0.515596 | + | 0.856832i | \(0.327570\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 9.72213e10 | 0.341884 | ||||||||
\(352\) | −5.66869e10 | −0.196807 | ||||||||
\(353\) | 4.16138e10 | 0.142643 | 0.0713217 | − | 0.997453i | \(-0.477278\pi\) | ||||
0.0713217 | + | 0.997453i | \(0.477278\pi\) | |||||||
\(354\) | −8.13526e10 | −0.275332 | ||||||||
\(355\) | −1.56667e11 | −0.523539 | ||||||||
\(356\) | −2.88739e11 | −0.952753 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −4.10244e10 | −0.131998 | ||||||||
\(359\) | −4.10775e11 | −1.30521 | −0.652604 | − | 0.757699i | \(-0.726323\pi\) | ||||
−0.652604 | + | 0.757699i | \(0.726323\pi\) | |||||||
\(360\) | −6.16242e10 | −0.193370 | ||||||||
\(361\) | −3.20167e11 | −0.992187 | ||||||||
\(362\) | 5.73316e10 | 0.175471 | ||||||||
\(363\) | −4.34024e10 | −0.131200 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.01986e11 | 1.18548 | ||||||||
\(366\) | −2.47118e11 | −0.719846 | ||||||||
\(367\) | 1.83042e11 | 0.526688 | 0.263344 | − | 0.964702i | \(-0.415175\pi\) | ||||
0.263344 | + | 0.964702i | \(0.415175\pi\) | |||||||
\(368\) | 1.61122e11 | 0.457972 | ||||||||
\(369\) | 2.38385e11 | 0.669360 | ||||||||
\(370\) | 9.53983e10 | 0.264626 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −1.13805e11 | −0.308119 | ||||||||
\(373\) | −2.85765e11 | −0.764396 | −0.382198 | − | 0.924080i | \(-0.624833\pi\) | ||||
−0.382198 | + | 0.924080i | \(0.624833\pi\) | |||||||
\(374\) | 3.05742e11 | 0.808040 | ||||||||
\(375\) | −2.27804e11 | −0.594869 | ||||||||
\(376\) | −1.24677e11 | −0.321692 | ||||||||
\(377\) | 5.32508e10 | 0.135766 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.76362e10 | 0.118593 | 0.0592967 | − | 0.998240i | \(-0.481114\pi\) | ||||
0.0592967 | + | 0.998240i | \(0.481114\pi\) | |||||||
\(380\) | −1.40398e10 | −0.0345410 | ||||||||
\(381\) | −3.00009e9 | −0.00729409 | ||||||||
\(382\) | 1.11582e10 | 0.0268108 | ||||||||
\(383\) | −4.08991e11 | −0.971223 | −0.485611 | − | 0.874175i | \(-0.661403\pi\) | ||||
−0.485611 | + | 0.874175i | \(0.661403\pi\) | |||||||
\(384\) | 2.06344e10 | 0.0484284 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 9.13374e9 | 0.0209414 | ||||||||
\(387\) | −1.97857e10 | −0.0448386 | ||||||||
\(388\) | −3.25921e10 | −0.0730079 | ||||||||
\(389\) | −1.12325e11 | −0.248716 | −0.124358 | − | 0.992237i | \(-0.539687\pi\) | ||||
−0.124358 | + | 0.992237i | \(0.539687\pi\) | |||||||
\(390\) | −5.07830e10 | −0.111155 | ||||||||
\(391\) | −8.69014e11 | −1.88032 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.22512e11 | −0.259067 | ||||||||
\(394\) | 7.82311e10 | 0.163549 | ||||||||
\(395\) | −5.06804e11 | −1.04750 | ||||||||
\(396\) | −1.90629e11 | −0.389547 | ||||||||
\(397\) | −3.85685e11 | −0.779248 | −0.389624 | − | 0.920974i | \(-0.627395\pi\) | ||||
−0.389624 | + | 0.920974i | \(0.627395\pi\) | |||||||
\(398\) | −1.62918e11 | −0.325459 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.98135e10 | −0.0972920 | ||||||||
\(401\) | 1.80685e11 | 0.348958 | 0.174479 | − | 0.984661i | \(-0.444176\pi\) | ||||
0.174479 | + | 0.984661i | \(0.444176\pi\) | |||||||
\(402\) | −3.35274e11 | −0.640299 | ||||||||
\(403\) | 2.18621e11 | 0.412876 | ||||||||
\(404\) | 3.85395e11 | 0.719764 | ||||||||
\(405\) | −8.01980e10 | −0.148121 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.95106e11 | 0.533093 | ||||||||
\(408\) | −1.11292e11 | −0.198835 | ||||||||
\(409\) | −2.48017e11 | −0.438255 | −0.219127 | − | 0.975696i | \(-0.570321\pi\) | ||||
−0.219127 | + | 0.975696i | \(0.570321\pi\) | |||||||
\(410\) | −3.02454e11 | −0.528605 | ||||||||
\(411\) | −4.33260e11 | −0.748963 | ||||||||
\(412\) | −1.52309e11 | −0.260428 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 5.41826e11 | 0.906480 | ||||||||
\(415\) | 8.16602e11 | 1.35143 | ||||||||
\(416\) | −3.96389e10 | −0.0648935 | ||||||||
\(417\) | −1.84885e11 | −0.299426 | ||||||||
\(418\) | −4.34309e10 | −0.0695834 | ||||||||
\(419\) | −2.26007e11 | −0.358227 | −0.179113 | − | 0.983828i | \(-0.557323\pi\) | ||||
−0.179113 | + | 0.983828i | \(0.557323\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.76981e11 | −0.584858 | −0.292429 | − | 0.956287i | \(-0.594464\pi\) | ||||
−0.292429 | + | 0.956287i | \(0.594464\pi\) | |||||||
\(422\) | 4.63849e11 | 0.711985 | ||||||||
\(423\) | −4.19268e11 | −0.636736 | ||||||||
\(424\) | 1.76454e10 | 0.0265146 | ||||||||
\(425\) | 2.68670e11 | 0.399456 | ||||||||
\(426\) | 1.76409e11 | 0.259525 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 3.46858e11 | 0.499637 | ||||||||
\(429\) | −1.57092e11 | −0.223922 | ||||||||
\(430\) | 2.51034e10 | 0.0354099 | ||||||||
\(431\) | −1.43102e11 | −0.199756 | −0.0998779 | − | 0.995000i | \(-0.531845\pi\) | ||||
−0.0998779 | + | 0.995000i | \(0.531845\pi\) | |||||||
\(432\) | 1.68547e11 | 0.232832 | ||||||||
\(433\) | −1.36985e12 | −1.87275 | −0.936373 | − | 0.351007i | \(-0.885839\pi\) | ||||
−0.936373 | + | 0.351007i | \(0.885839\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 1.18272e11 | 0.158373 | ||||||||
\(436\) | −4.96087e11 | −0.657459 | ||||||||
\(437\) | 1.23444e11 | 0.161921 | ||||||||
\(438\) | −4.52643e11 | −0.587655 | ||||||||
\(439\) | −1.05555e12 | −1.35641 | −0.678203 | − | 0.734875i | \(-0.737241\pi\) | ||||
−0.678203 | + | 0.734875i | \(0.737241\pi\) | |||||||
\(440\) | 2.41863e11 | 0.307632 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 2.13793e11 | 0.266436 | ||||||||
\(443\) | 7.36777e11 | 0.908906 | 0.454453 | − | 0.890771i | \(-0.349835\pi\) | ||||
0.454453 | + | 0.890771i | \(0.349835\pi\) | |||||||
\(444\) | −1.07420e11 | −0.131178 | ||||||||
\(445\) | 1.23194e12 | 1.48926 | ||||||||
\(446\) | 1.44316e11 | 0.172706 | ||||||||
\(447\) | −3.71221e11 | −0.439793 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.37800e11 | −0.160007 | −0.0800036 | − | 0.996795i | \(-0.525493\pi\) | ||||
−0.0800036 | + | 0.996795i | \(0.525493\pi\) | |||||||
\(450\) | −1.67515e11 | −0.192573 | ||||||||
\(451\) | −9.35612e11 | −1.06488 | ||||||||
\(452\) | −5.07662e11 | −0.572074 | ||||||||
\(453\) | −8.19900e11 | −0.914785 | ||||||||
\(454\) | −2.12209e11 | −0.234429 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.58091e10 | 0.0171224 | ||||||||
\(457\) | −8.17482e11 | −0.876708 | −0.438354 | − | 0.898802i | \(-0.644438\pi\) | ||||
−0.438354 | + | 0.898802i | \(0.644438\pi\) | |||||||
\(458\) | 1.22827e12 | 1.30436 | ||||||||
\(459\) | −9.09060e11 | −0.955950 | ||||||||
\(460\) | −6.87449e11 | −0.715863 | ||||||||
\(461\) | 1.54090e12 | 1.58899 | 0.794495 | − | 0.607270i | \(-0.207735\pi\) | ||||
0.794495 | + | 0.607270i | \(0.207735\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.47957e11 | −0.756419 | −0.378209 | − | 0.925720i | \(-0.623460\pi\) | ||||
−0.378209 | + | 0.925720i | \(0.623460\pi\) | |||||||
\(464\) | 9.23176e10 | 0.0924599 | ||||||||
\(465\) | 4.85565e11 | 0.481625 | ||||||||
\(466\) | 3.67022e10 | 0.0360542 | ||||||||
\(467\) | 2.41074e11 | 0.234544 | 0.117272 | − | 0.993100i | \(-0.462585\pi\) | ||||
0.117272 | + | 0.993100i | \(0.462585\pi\) | |||||||
\(468\) | −1.33299e11 | −0.128446 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 5.31951e11 | 0.502842 | ||||||||
\(471\) | 7.61465e11 | 0.712945 | ||||||||
\(472\) | 2.70932e11 | 0.251259 | ||||||||
\(473\) | 7.76550e10 | 0.0713336 | ||||||||
\(474\) | 5.70670e11 | 0.519257 | ||||||||
\(475\) | −3.81648e10 | −0.0343987 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 5.93386e10 | 0.0524813 | ||||||||
\(478\) | 6.50797e11 | 0.570191 | ||||||||
\(479\) | 4.18088e11 | 0.362876 | 0.181438 | − | 0.983402i | \(-0.441925\pi\) | ||||
0.181438 | + | 0.983402i | \(0.441925\pi\) | |||||||
\(480\) | −8.80393e10 | −0.0756992 | ||||||||
\(481\) | 2.06355e11 | 0.175777 | ||||||||
\(482\) | −1.50992e11 | −0.127422 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1.44545e11 | 0.119729 | ||||||||
\(485\) | 1.39059e11 | 0.114120 | ||||||||
\(486\) | 9.00242e11 | 0.731974 | ||||||||
\(487\) | −1.71573e12 | −1.38219 | −0.691095 | − | 0.722764i | \(-0.742871\pi\) | ||||
−0.691095 | + | 0.722764i | \(0.742871\pi\) | |||||||
\(488\) | 8.22988e11 | 0.656908 | ||||||||
\(489\) | 9.55388e11 | 0.755597 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 3.34731e11 | 0.259914 | 0.129957 | − | 0.991520i | \(-0.458516\pi\) | ||||
0.129957 | + | 0.991520i | \(0.458516\pi\) | |||||||
\(492\) | 3.40568e11 | 0.262036 | ||||||||
\(493\) | −4.97917e11 | −0.379617 | ||||||||
\(494\) | −3.03695e10 | −0.0229438 | ||||||||
\(495\) | 8.13343e11 | 0.608906 | ||||||||
\(496\) | 3.79010e11 | 0.281179 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −9.19508e11 | −0.669921 | ||||||||
\(499\) | 7.10044e11 | 0.512664 | 0.256332 | − | 0.966589i | \(-0.417486\pi\) | ||||
0.256332 | + | 0.966589i | \(0.417486\pi\) | |||||||
\(500\) | 7.58666e11 | 0.542857 | ||||||||
\(501\) | 4.21422e11 | 0.298846 | ||||||||
\(502\) | 1.21688e12 | 0.855228 | ||||||||
\(503\) | −2.16835e12 | −1.51033 | −0.755167 | − | 0.655532i | \(-0.772444\pi\) | ||||
−0.755167 | + | 0.655532i | \(0.772444\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.64434e12 | −1.12507 | ||||||||
\(506\) | −2.12656e12 | −1.44212 | ||||||||
\(507\) | 7.05308e11 | 0.474071 | ||||||||
\(508\) | 9.99132e9 | 0.00665635 | ||||||||
\(509\) | 7.69897e11 | 0.508396 | 0.254198 | − | 0.967152i | \(-0.418188\pi\) | ||||
0.254198 | + | 0.967152i | \(0.418188\pi\) | |||||||
\(510\) | 4.74842e11 | 0.310802 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −6.87195e10 | −0.0441942 | ||||||||
\(513\) | 1.29133e11 | 0.0823205 | ||||||||
\(514\) | −1.44354e12 | −0.912208 | ||||||||
\(515\) | 6.49846e11 | 0.407078 | ||||||||
\(516\) | −2.82668e10 | −0.0175531 | ||||||||
\(517\) | 1.64554e12 | 1.01298 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.53418e11 | 0.213814 | ||||||||
\(520\) | 1.69125e11 | 0.101436 | ||||||||
\(521\) | 2.32093e11 | 0.138004 | 0.0690021 | − | 0.997617i | \(-0.478018\pi\) | ||||
0.0690021 | + | 0.997617i | \(0.478018\pi\) | |||||||
\(522\) | 3.10449e11 | 0.183009 | ||||||||
\(523\) | −2.08260e12 | −1.21716 | −0.608580 | − | 0.793493i | \(-0.708260\pi\) | ||||
−0.608580 | + | 0.793493i | \(0.708260\pi\) | |||||||
\(524\) | 4.08007e11 | 0.236416 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.49709e12 | 0.852731 | ||||||||
\(527\) | −2.04420e12 | −1.15445 | ||||||||
\(528\) | −2.72341e11 | −0.152497 | ||||||||
\(529\) | 4.24319e12 | 2.35582 | ||||||||
\(530\) | −7.52866e10 | −0.0414454 | ||||||||
\(531\) | 9.11100e11 | 0.497325 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −6.54236e11 | −0.351125 | ||||||||
\(534\) | −1.38719e12 | −0.738245 | ||||||||
\(535\) | −1.47992e12 | −0.780990 | ||||||||
\(536\) | 1.11658e12 | 0.584316 | ||||||||
\(537\) | −1.97094e11 | −0.102280 | ||||||||
\(538\) | −2.37701e11 | −0.122324 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | −7.19128e11 | −0.363944 | ||||||||
\(541\) | −8.39742e11 | −0.421462 | −0.210731 | − | 0.977544i | \(-0.567584\pi\) | ||||
−0.210731 | + | 0.977544i | \(0.567584\pi\) | |||||||
\(542\) | −1.87496e12 | −0.933242 | ||||||||
\(543\) | 2.75439e11 | 0.135965 | ||||||||
\(544\) | 3.70640e11 | 0.181450 | ||||||||
\(545\) | 2.11662e12 | 1.02768 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.58235e11 | −0.362127 | −0.181064 | − | 0.983471i | \(-0.557954\pi\) | ||||
−0.181064 | + | 0.983471i | \(0.557954\pi\) | |||||||
\(548\) | 1.44290e12 | 0.683479 | ||||||||
\(549\) | 2.76757e12 | 1.30024 | ||||||||
\(550\) | 6.57461e11 | 0.306364 | ||||||||
\(551\) | 7.07295e10 | 0.0326903 | ||||||||
\(552\) | 7.74079e11 | 0.354862 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 4.59558e11 | 0.207275 | ||||||||
\(555\) | 4.58323e11 | 0.205047 | ||||||||
\(556\) | 6.15731e11 | 0.273246 | ||||||||
\(557\) | 1.59724e12 | 0.703110 | 0.351555 | − | 0.936167i | \(-0.385653\pi\) | ||||
0.351555 | + | 0.936167i | \(0.385653\pi\) | |||||||
\(558\) | 1.27455e12 | 0.556547 | ||||||||
\(559\) | 5.43010e10 | 0.0235209 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.46888e12 | 0.626114 | ||||||||
\(562\) | 1.18350e12 | 0.500445 | ||||||||
\(563\) | 2.60961e11 | 0.109468 | 0.0547340 | − | 0.998501i | \(-0.482569\pi\) | ||||
0.0547340 | + | 0.998501i | \(0.482569\pi\) | |||||||
\(564\) | −5.98987e11 | −0.249265 | ||||||||
\(565\) | 2.16601e12 | 0.894217 | ||||||||
\(566\) | 1.16398e12 | 0.476729 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.87504e11 | −0.236833 | ||||||||
\(569\) | −1.53339e12 | −0.613264 | −0.306632 | − | 0.951828i | \(-0.599202\pi\) | ||||
−0.306632 | + | 0.951828i | \(0.599202\pi\) | |||||||
\(570\) | −6.74517e10 | −0.0267643 | ||||||||
\(571\) | −2.76112e12 | −1.08698 | −0.543492 | − | 0.839415i | \(-0.682898\pi\) | ||||
−0.543492 | + | 0.839415i | \(0.682898\pi\) | |||||||
\(572\) | 5.23172e11 | 0.204344 | ||||||||
\(573\) | 5.36075e10 | 0.0207745 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.86871e12 | −0.712913 | ||||||||
\(576\) | −2.31092e11 | −0.0874750 | ||||||||
\(577\) | −4.00470e12 | −1.50411 | −0.752054 | − | 0.659101i | \(-0.770937\pi\) | ||||
−0.752054 | + | 0.659101i | \(0.770937\pi\) | |||||||
\(578\) | −1.01649e11 | −0.0378814 | ||||||||
\(579\) | 4.38813e10 | 0.0162265 | ||||||||
\(580\) | −3.93886e11 | −0.144525 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | −1.56583e11 | −0.0565705 | ||||||||
\(583\) | −2.32892e11 | −0.0834923 | ||||||||
\(584\) | 1.50746e12 | 0.536275 | ||||||||
\(585\) | 5.68738e11 | 0.200776 | ||||||||
\(586\) | −3.90281e12 | −1.36722 | ||||||||
\(587\) | −1.31451e12 | −0.456976 | −0.228488 | − | 0.973547i | \(-0.573378\pi\) | ||||
−0.228488 | + | 0.973547i | \(0.573378\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 2.90380e11 | 0.0994140 | ||||||||
\(590\) | −1.15597e12 | −0.392747 | ||||||||
\(591\) | 3.75847e11 | 0.126726 | ||||||||
\(592\) | 3.57746e11 | 0.119709 | ||||||||
\(593\) | 4.18573e12 | 1.39003 | 0.695016 | − | 0.718994i | \(-0.255397\pi\) | ||||
0.695016 | + | 0.718994i | \(0.255397\pi\) | |||||||
\(594\) | −2.22455e12 | −0.733169 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 1.23629e12 | 0.401341 | ||||||||
\(597\) | −7.82710e11 | −0.252183 | ||||||||
\(598\) | −1.48702e12 | −0.475511 | ||||||||
\(599\) | −1.94567e12 | −0.617517 | −0.308758 | − | 0.951140i | \(-0.599913\pi\) | ||||
−0.308758 | + | 0.951140i | \(0.599913\pi\) | |||||||
\(600\) | −2.39320e11 | −0.0753872 | ||||||||
\(601\) | 4.58168e12 | 1.43248 | 0.716242 | − | 0.697852i | \(-0.245861\pi\) | ||||
0.716242 | + | 0.697852i | \(0.245861\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 3.75486e12 | 1.15656 | ||||||||
\(604\) | 2.73055e12 | 0.834802 | ||||||||
\(605\) | −6.16720e11 | −0.187150 | ||||||||
\(606\) | 1.85156e12 | 0.557713 | ||||||||
\(607\) | −3.73888e12 | −1.11787 | −0.558936 | − | 0.829211i | \(-0.688790\pi\) | ||||
−0.558936 | + | 0.829211i | \(0.688790\pi\) | |||||||
\(608\) | −5.26497e10 | −0.0156253 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.51139e12 | −1.02682 | ||||||||
\(611\) | 1.15066e12 | 0.334012 | ||||||||
\(612\) | 1.24640e12 | 0.359150 | ||||||||
\(613\) | 1.12397e12 | 0.321501 | 0.160751 | − | 0.986995i | \(-0.448608\pi\) | ||||
0.160751 | + | 0.986995i | \(0.448608\pi\) | |||||||
\(614\) | −2.26658e12 | −0.643596 | ||||||||
\(615\) | −1.45308e12 | −0.409592 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 8.34463e11 | 0.231805 | 0.115903 | − | 0.993261i | \(-0.463024\pi\) | ||||
0.115903 | + | 0.993261i | \(0.463024\pi\) | |||||||
\(618\) | −7.31738e11 | −0.201794 | ||||||||
\(619\) | 2.47746e12 | 0.678264 | 0.339132 | − | 0.940739i | \(-0.389867\pi\) | ||||
0.339132 | + | 0.940739i | \(0.389867\pi\) | |||||||
\(620\) | −1.61710e12 | −0.439515 | ||||||||
\(621\) | 6.32287e12 | 1.70609 | ||||||||
\(622\) | −2.06679e12 | −0.553655 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −1.90437e11 | −0.0502830 | ||||||||
\(625\) | −1.75240e12 | −0.459380 | ||||||||
\(626\) | −7.11439e11 | −0.185163 | ||||||||
\(627\) | −2.08655e11 | −0.0539170 | ||||||||
\(628\) | −2.53594e12 | −0.650610 | ||||||||
\(629\) | −1.92951e12 | −0.491495 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.00841e12 | 0.253223 | 0.126612 | − | 0.991952i | \(-0.459590\pi\) | ||||
0.126612 | + | 0.991952i | \(0.459590\pi\) | |||||||
\(632\) | −1.90053e12 | −0.473857 | ||||||||
\(633\) | 2.22848e12 | 0.551685 | ||||||||
\(634\) | 3.97482e12 | 0.977047 | ||||||||
\(635\) | −4.26293e10 | −0.0104046 | ||||||||
\(636\) | 8.47740e10 | 0.0205450 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.21845e12 | −0.291148 | ||||||||
\(639\) | −1.97568e12 | −0.468772 | ||||||||
\(640\) | 2.93201e11 | 0.0690806 | ||||||||
\(641\) | −6.98225e12 | −1.63356 | −0.816778 | − | 0.576952i | \(-0.804242\pi\) | ||||
−0.816778 | + | 0.576952i | \(0.804242\pi\) | |||||||
\(642\) | 1.66641e12 | 0.387146 | ||||||||
\(643\) | −5.09779e12 | −1.17607 | −0.588034 | − | 0.808836i | \(-0.700098\pi\) | ||||
−0.588034 | + | 0.808836i | \(0.700098\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.20604e11 | 0.0274375 | ||||||||
\(646\) | 2.83967e11 | 0.0641537 | ||||||||
\(647\) | 2.20736e12 | 0.495226 | 0.247613 | − | 0.968859i | \(-0.420354\pi\) | ||||
0.247613 | + | 0.968859i | \(0.420354\pi\) | |||||||
\(648\) | −3.00744e11 | −0.0670054 | ||||||||
\(649\) | −3.57589e12 | −0.791193 | ||||||||
\(650\) | 4.59736e11 | 0.101018 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.18177e12 | −0.689533 | ||||||||
\(653\) | 8.20909e12 | 1.76679 | 0.883397 | − | 0.468626i | \(-0.155251\pi\) | ||||
0.883397 | + | 0.468626i | \(0.155251\pi\) | |||||||
\(654\) | −2.38336e12 | −0.509435 | ||||||||
\(655\) | −1.74082e12 | −0.369546 | ||||||||
\(656\) | −1.13421e12 | −0.239125 | ||||||||
\(657\) | 5.06933e12 | 1.06147 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.75171e12 | 1.18799 | 0.593994 | − | 0.804469i | \(-0.297550\pi\) | ||||
0.593994 | + | 0.804469i | \(0.297550\pi\) | |||||||
\(660\) | 1.16198e12 | 0.238370 | ||||||||
\(661\) | 3.40404e12 | 0.693566 | 0.346783 | − | 0.937945i | \(-0.387274\pi\) | ||||
0.346783 | + | 0.937945i | \(0.387274\pi\) | |||||||
\(662\) | −5.79551e12 | −1.17282 | ||||||||
\(663\) | 1.02713e12 | 0.206449 | ||||||||
\(664\) | 3.06228e12 | 0.611347 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 1.20304e12 | 0.236944 | ||||||||
\(667\) | 3.46321e12 | 0.677505 | ||||||||
\(668\) | −1.40348e12 | −0.272717 | ||||||||
\(669\) | 6.93337e11 | 0.133822 | ||||||||
\(670\) | −4.76403e12 | −0.913352 | ||||||||
\(671\) | −1.08622e13 | −2.06855 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.13050e12 | −1.33984 | −0.669918 | − | 0.742435i | \(-0.733671\pi\) | ||||
−0.669918 | + | 0.742435i | \(0.733671\pi\) | |||||||
\(674\) | 6.94321e12 | 1.29596 | ||||||||
\(675\) | −1.95482e12 | −0.362444 | ||||||||
\(676\) | −2.34892e12 | −0.432621 | ||||||||
\(677\) | −1.30195e12 | −0.238202 | −0.119101 | − | 0.992882i | \(-0.538001\pi\) | ||||
−0.119101 | + | 0.992882i | \(0.538001\pi\) | |||||||
\(678\) | −2.43897e12 | −0.443274 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −1.58139e12 | −0.283627 | ||||||||
\(681\) | −1.01952e12 | −0.181649 | ||||||||
\(682\) | −5.00234e12 | −0.885409 | ||||||||
\(683\) | −4.62558e12 | −0.813341 | −0.406671 | − | 0.913575i | \(-0.633310\pi\) | ||||
−0.406671 | + | 0.913575i | \(0.633310\pi\) | |||||||
\(684\) | −1.77052e11 | −0.0309278 | ||||||||
\(685\) | −6.15635e12 | −1.06836 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 5.90097e12 | 1.01069 | ||||||||
\(688\) | 9.41383e10 | 0.0160184 | ||||||||
\(689\) | −1.62852e11 | −0.0275300 | ||||||||
\(690\) | −3.30272e12 | −0.554690 | ||||||||
\(691\) | −2.92633e12 | −0.488284 | −0.244142 | − | 0.969740i | \(-0.578506\pi\) | ||||
−0.244142 | + | 0.969740i | \(0.578506\pi\) | |||||||
\(692\) | −1.17700e12 | −0.195119 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.08764e12 | −0.505254 | ||||||||
\(695\) | −2.62710e12 | −0.427116 | ||||||||
\(696\) | 4.43522e11 | 0.0716430 | ||||||||
\(697\) | 6.11738e12 | 0.981788 | ||||||||
\(698\) | −4.57272e12 | −0.729163 | ||||||||
\(699\) | 1.76329e11 | 0.0279368 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 5.32710e12 | 0.833220 | 0.416610 | − | 0.909085i | \(-0.363218\pi\) | ||||
0.416610 | + | 0.909085i | \(0.363218\pi\) | |||||||
\(702\) | −1.55554e12 | −0.241749 | ||||||||
\(703\) | 2.74088e11 | 0.0423245 | ||||||||
\(704\) | 9.06991e11 | 0.139164 | ||||||||
\(705\) | 2.55566e12 | 0.389630 | ||||||||
\(706\) | −6.65821e11 | −0.100864 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 1.30164e12 | 0.194689 | ||||||||
\(709\) | 3.14221e12 | 0.467012 | 0.233506 | − | 0.972355i | \(-0.424980\pi\) | ||||
0.233506 | + | 0.972355i | \(0.424980\pi\) | |||||||
\(710\) | 2.50667e12 | 0.370198 | ||||||||
\(711\) | −6.39115e12 | −0.937920 | ||||||||
\(712\) | 4.61982e12 | 0.673698 | ||||||||
\(713\) | 1.42182e13 | 2.06036 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.23218e12 | −0.319413 | ||||||||
\(716\) | 6.56391e11 | 0.0933370 | ||||||||
\(717\) | 3.12663e12 | 0.441815 | ||||||||
\(718\) | 6.57241e12 | 0.922921 | ||||||||
\(719\) | 1.59235e12 | 0.222207 | 0.111104 | − | 0.993809i | \(-0.464561\pi\) | ||||
0.111104 | + | 0.993809i | \(0.464561\pi\) | |||||||
\(720\) | 9.85987e11 | 0.136733 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 5.12267e12 | 0.701582 | ||||||||
\(723\) | −7.25415e11 | −0.0987334 | ||||||||
\(724\) | −9.17306e11 | −0.124077 | ||||||||
\(725\) | −1.07071e12 | −0.143930 | ||||||||
\(726\) | 6.94438e11 | 0.0927724 | ||||||||
\(727\) | 6.30493e11 | 0.0837096 | 0.0418548 | − | 0.999124i | \(-0.486673\pi\) | ||||
0.0418548 | + | 0.999124i | \(0.486673\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 2.87984e12 | 0.377654 | ||||||||
\(730\) | −6.43178e12 | −0.838259 | ||||||||
\(731\) | −5.07737e11 | −0.0657674 | ||||||||
\(732\) | 3.95389e12 | 0.509008 | ||||||||
\(733\) | −1.19410e13 | −1.52782 | −0.763910 | − | 0.645323i | \(-0.776723\pi\) | ||||
−0.763910 | + | 0.645323i | \(0.776723\pi\) | |||||||
\(734\) | −2.92867e12 | −0.372424 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −2.57795e12 | −0.323835 | ||||||||
\(737\) | −1.47371e13 | −1.83996 | ||||||||
\(738\) | −3.81415e12 | −0.473309 | ||||||||
\(739\) | −5.36462e11 | −0.0661667 | −0.0330833 | − | 0.999453i | \(-0.510533\pi\) | ||||
−0.0330833 | + | 0.999453i | \(0.510533\pi\) | |||||||
\(740\) | −1.52637e12 | −0.187119 | ||||||||
\(741\) | −1.45904e11 | −0.0177781 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 7.16300e12 | 0.862274 | 0.431137 | − | 0.902286i | \(-0.358112\pi\) | ||||
0.431137 | + | 0.902286i | \(0.358112\pi\) | |||||||
\(744\) | 1.82088e12 | 0.217873 | ||||||||
\(745\) | −5.27482e12 | −0.627342 | ||||||||
\(746\) | 4.57223e12 | 0.540510 | ||||||||
\(747\) | 1.02979e13 | 1.21006 | ||||||||
\(748\) | −4.89187e12 | −0.571371 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 3.64487e12 | 0.420636 | ||||||||
\(751\) | 1.28950e13 | 1.47925 | 0.739623 | − | 0.673022i | \(-0.235004\pi\) | ||||
0.739623 | + | 0.673022i | \(0.235004\pi\) | |||||||
\(752\) | 1.99483e12 | 0.227471 | ||||||||
\(753\) | 5.84628e12 | 0.662678 | ||||||||
\(754\) | −8.52012e11 | −0.0960008 | ||||||||
\(755\) | −1.16503e13 | −1.30489 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.53380e13 | −1.69761 | −0.848804 | − | 0.528708i | \(-0.822677\pi\) | ||||
−0.848804 | + | 0.528708i | \(0.822677\pi\) | |||||||
\(758\) | −7.62179e11 | −0.0838582 | ||||||||
\(759\) | −1.02166e13 | −1.11743 | ||||||||
\(760\) | 2.24637e11 | 0.0244242 | ||||||||
\(761\) | 8.55348e12 | 0.924511 | 0.462256 | − | 0.886747i | \(-0.347040\pi\) | ||||
0.462256 | + | 0.886747i | \(0.347040\pi\) | |||||||
\(762\) | 4.80014e10 | 0.00515770 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −1.78531e11 | −0.0189581 | ||||||||
\(765\) | −5.31794e12 | −0.561393 | ||||||||
\(766\) | 6.54385e12 | 0.686758 | ||||||||
\(767\) | −2.50047e12 | −0.260881 | ||||||||
\(768\) | −3.30150e11 | −0.0342441 | ||||||||
\(769\) | 5.63703e12 | 0.581275 | 0.290638 | − | 0.956833i | \(-0.406133\pi\) | ||||
0.290638 | + | 0.956833i | \(0.406133\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.93520e12 | −0.706829 | ||||||||
\(772\) | −1.46140e11 | −0.0148078 | ||||||||
\(773\) | −2.48942e12 | −0.250779 | −0.125390 | − | 0.992108i | \(-0.540018\pi\) | ||||
−0.125390 | + | 0.992108i | \(0.540018\pi\) | |||||||
\(774\) | 3.16571e11 | 0.0317057 | ||||||||
\(775\) | −4.39580e12 | −0.437704 | ||||||||
\(776\) | 5.21474e11 | 0.0516244 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 1.79720e12 | 0.175869 | ||||||||
\(779\) | −8.68978e11 | −0.0845454 | ||||||||
\(780\) | 8.12528e11 | 0.0785982 | ||||||||
\(781\) | 7.75414e12 | 0.745768 | ||||||||
\(782\) | 1.39042e13 | 1.32959 | ||||||||
\(783\) | 3.62280e12 | 0.344443 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 1.08199e13 | 1.01698 | ||||||||
\(786\) | 1.96019e12 | 0.183188 | ||||||||
\(787\) | −1.37507e13 | −1.27773 | −0.638866 | − | 0.769318i | \(-0.720596\pi\) | ||||
−0.638866 | + | 0.769318i | \(0.720596\pi\) | |||||||
\(788\) | −1.25170e12 | −0.115646 | ||||||||
\(789\) | 7.19249e12 | 0.660743 | ||||||||
\(790\) | 8.10886e12 | 0.740692 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 3.05006e12 | 0.275451 | ||||||||
\(793\) | −7.59547e12 | −0.682065 | ||||||||
\(794\) | 6.17096e12 | 0.551011 | ||||||||
\(795\) | −3.61700e11 | −0.0321142 | ||||||||
\(796\) | 2.60669e12 | 0.230134 | ||||||||
\(797\) | 1.44214e12 | 0.126603 | 0.0633016 | − | 0.997994i | \(-0.479837\pi\) | ||||
0.0633016 | + | 0.997994i | \(0.479837\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.07592e13 | −0.933938 | ||||||||
\(800\) | 7.97016e11 | 0.0687959 | ||||||||
\(801\) | 1.55357e13 | 1.33347 | ||||||||
\(802\) | −2.89096e12 | −0.246751 | ||||||||
\(803\) | −1.98961e13 | −1.68868 | ||||||||
\(804\) | 5.36439e12 | 0.452760 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −3.49794e12 | −0.291947 | ||||||||
\(807\) | −1.14199e12 | −0.0947832 | ||||||||
\(808\) | −6.16632e12 | −0.508950 | ||||||||
\(809\) | 2.70988e11 | 0.0222424 | 0.0111212 | − | 0.999938i | \(-0.496460\pi\) | ||||
0.0111212 | + | 0.999938i | \(0.496460\pi\) | |||||||
\(810\) | 1.28317e12 | 0.104737 | ||||||||
\(811\) | 1.23287e13 | 1.00075 | 0.500373 | − | 0.865810i | \(-0.333196\pi\) | ||||
0.500373 | + | 0.865810i | \(0.333196\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −9.00787e12 | −0.723127 | ||||||||
\(814\) | −4.72169e12 | −0.376953 | ||||||||
\(815\) | 1.35755e13 | 1.07782 | ||||||||
\(816\) | 1.78067e12 | 0.140597 | ||||||||
\(817\) | 7.21244e10 | 0.00566348 | ||||||||
\(818\) | 3.96827e12 | 0.309893 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 4.83926e12 | 0.373780 | ||||||||
\(821\) | −8.75616e12 | −0.672620 | −0.336310 | − | 0.941751i | \(-0.609179\pi\) | ||||
−0.336310 | + | 0.941751i | \(0.609179\pi\) | |||||||
\(822\) | 6.93216e12 | 0.529597 | ||||||||
\(823\) | 1.32813e13 | 1.00911 | 0.504557 | − | 0.863379i | \(-0.331656\pi\) | ||||
0.504557 | + | 0.863379i | \(0.331656\pi\) | |||||||
\(824\) | 2.43694e12 | 0.184150 | ||||||||
\(825\) | 3.15865e12 | 0.237388 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −1.28106e13 | −0.952345 | −0.476173 | − | 0.879352i | \(-0.657976\pi\) | ||||
−0.476173 | + | 0.879352i | \(0.657976\pi\) | |||||||
\(828\) | −8.66921e12 | −0.640978 | ||||||||
\(829\) | 1.42592e13 | 1.04858 | 0.524289 | − | 0.851540i | \(-0.324331\pi\) | ||||
0.524289 | + | 0.851540i | \(0.324331\pi\) | |||||||
\(830\) | −1.30656e13 | −0.955606 | ||||||||
\(831\) | 2.20786e12 | 0.160608 | ||||||||
\(832\) | 6.34222e11 | 0.0458866 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 2.95816e12 | 0.211726 | ||||||||
\(835\) | 5.98814e12 | 0.426288 | ||||||||
\(836\) | 6.94894e11 | 0.0492029 | ||||||||
\(837\) | 1.48734e13 | 1.04748 | ||||||||
\(838\) | 3.61611e12 | 0.253305 | ||||||||
\(839\) | 5.62810e12 | 0.392133 | 0.196066 | − | 0.980591i | \(-0.437183\pi\) | ||||
0.196066 | + | 0.980591i | \(0.437183\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.25228e13 | −0.863219 | ||||||||
\(842\) | 6.03170e12 | 0.413557 | ||||||||
\(843\) | 5.68592e12 | 0.387772 | ||||||||
\(844\) | −7.42159e12 | −0.503450 | ||||||||
\(845\) | 1.00220e13 | 0.676237 | ||||||||
\(846\) | 6.70828e12 | 0.450241 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −2.82327e11 | −0.0187487 | ||||||||
\(849\) | 5.59212e12 | 0.369396 | ||||||||
\(850\) | −4.29872e12 | −0.282458 | ||||||||
\(851\) | 1.34205e13 | 0.877174 | ||||||||
\(852\) | −2.82255e12 | −0.183512 | ||||||||
\(853\) | 1.54422e13 | 0.998709 | 0.499354 | − | 0.866398i | \(-0.333571\pi\) | ||||
0.499354 | + | 0.866398i | \(0.333571\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 7.55417e11 | 0.0483437 | ||||||||
\(856\) | −5.54973e12 | −0.353297 | ||||||||
\(857\) | −1.60833e13 | −1.01850 | −0.509251 | − | 0.860618i | \(-0.670077\pi\) | ||||
−0.509251 | + | 0.860618i | \(0.670077\pi\) | |||||||
\(858\) | 2.51348e12 | 0.158337 | ||||||||
\(859\) | −3.02922e12 | −0.189828 | −0.0949141 | − | 0.995485i | \(-0.530258\pi\) | ||||
−0.0949141 | + | 0.995485i | \(0.530258\pi\) | |||||||
\(860\) | −4.01654e11 | −0.0250386 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 2.28964e12 | 0.141249 | ||||||||
\(863\) | 1.35636e13 | 0.832391 | 0.416195 | − | 0.909275i | \(-0.363363\pi\) | ||||
0.416195 | + | 0.909275i | \(0.363363\pi\) | |||||||
\(864\) | −2.69675e12 | −0.164637 | ||||||||
\(865\) | 5.02184e12 | 0.304994 | ||||||||
\(866\) | 2.19177e13 | 1.32423 | ||||||||
\(867\) | −4.88351e11 | −0.0293526 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 2.50840e13 | 1.49213 | ||||||||
\(870\) | −1.89235e12 | −0.111986 | ||||||||
\(871\) | −1.03051e13 | −0.606692 | ||||||||
\(872\) | 7.93740e12 | 0.464894 | ||||||||
\(873\) | 1.75363e12 | 0.102182 | ||||||||
\(874\) | −1.97511e12 | −0.114496 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 7.24229e12 | 0.415535 | ||||||||
\(877\) | 2.08383e13 | 1.18950 | 0.594751 | − | 0.803910i | \(-0.297251\pi\) | ||||
0.594751 | + | 0.803910i | \(0.297251\pi\) | |||||||
\(878\) | 1.68888e13 | 0.959124 | ||||||||
\(879\) | −1.87503e13 | −1.05940 | ||||||||
\(880\) | −3.86980e12 | −0.217529 | ||||||||
\(881\) | −1.45413e13 | −0.813225 | −0.406612 | − | 0.913601i | \(-0.633290\pi\) | ||||
−0.406612 | + | 0.913601i | \(0.633290\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.56890e12 | 0.363638 | 0.181819 | − | 0.983332i | \(-0.441802\pi\) | ||||
0.181819 | + | 0.983332i | \(0.441802\pi\) | |||||||
\(884\) | −3.42069e12 | −0.188399 | ||||||||
\(885\) | −5.55364e12 | −0.304322 | ||||||||
\(886\) | −1.17884e13 | −0.642694 | ||||||||
\(887\) | 1.22620e12 | 0.0665130 | 0.0332565 | − | 0.999447i | \(-0.489412\pi\) | ||||
0.0332565 | + | 0.999447i | \(0.489412\pi\) | |||||||
\(888\) | 1.71872e12 | 0.0927571 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −1.97111e13 | −1.05307 | ||||||||
\(891\) | 3.96936e12 | 0.210994 | ||||||||
\(892\) | −2.30905e12 | −0.122121 | ||||||||
\(893\) | 1.52835e12 | 0.0804249 | ||||||||
\(894\) | 5.93954e12 | 0.310981 | ||||||||
\(895\) | −2.80058e12 | −0.145896 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −7.14409e12 | −0.368452 | ||||||||
\(898\) | 2.20479e12 | 0.113142 | ||||||||
\(899\) | 8.14658e12 | 0.415965 | ||||||||
\(900\) | 2.68023e12 | 0.136170 | ||||||||
\(901\) | 1.52273e12 | 0.0769773 | ||||||||
\(902\) | 1.49698e13 | 0.752985 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 8.12260e12 | 0.404517 | ||||||||
\(905\) | 3.91381e12 | 0.193946 | ||||||||
\(906\) | 1.31184e13 | 0.646851 | ||||||||
\(907\) | −1.39154e13 | −0.682752 | −0.341376 | − | 0.939927i | \(-0.610893\pi\) | ||||
−0.341376 | + | 0.939927i | \(0.610893\pi\) | |||||||
\(908\) | 3.39534e12 | 0.165767 | ||||||||
\(909\) | −2.07363e13 | −1.00738 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 5.99228e11 | 0.0288243 | 0.0144122 | − | 0.999896i | \(-0.495412\pi\) | ||||
0.0144122 | + | 0.999896i | \(0.495412\pi\) | |||||||
\(912\) | −2.52945e11 | −0.0121074 | ||||||||
\(913\) | −4.04173e13 | −1.92508 | ||||||||
\(914\) | 1.30797e13 | 0.619926 | ||||||||
\(915\) | −1.68698e13 | −0.795638 | ||||||||
\(916\) | −1.96523e13 | −0.922323 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 1.45450e13 | 0.675959 | ||||||||
\(919\) | −5.20770e12 | −0.240839 | −0.120419 | − | 0.992723i | \(-0.538424\pi\) | ||||
−0.120419 | + | 0.992723i | \(0.538424\pi\) | |||||||
\(920\) | 1.09992e13 | 0.506192 | ||||||||
\(921\) | −1.08893e13 | −0.498693 | ||||||||
\(922\) | −2.46545e13 | −1.12359 | ||||||||
\(923\) | 5.42215e12 | 0.245903 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.14918e12 | −0.186348 | ||||||||
\(926\) | 1.19673e13 | 0.534869 | ||||||||
\(927\) | 8.19501e12 | 0.364494 | ||||||||
\(928\) | −1.47708e12 | −0.0653790 | ||||||||
\(929\) | −2.02860e13 | −0.893565 | −0.446783 | − | 0.894643i | \(-0.647430\pi\) | ||||
−0.446783 | + | 0.894643i | \(0.647430\pi\) | |||||||
\(930\) | −7.76904e12 | −0.340560 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −5.87236e11 | −0.0254942 | ||||||||
\(933\) | −9.92949e12 | −0.429002 | ||||||||
\(934\) | −3.85718e12 | −0.165848 | ||||||||
\(935\) | 2.08719e13 | 0.893118 | ||||||||
\(936\) | 2.13278e12 | 0.0908249 | ||||||||
\(937\) | −3.47244e13 | −1.47166 | −0.735828 | − | 0.677169i | \(-0.763207\pi\) | ||||
−0.735828 | + | 0.677169i | \(0.763207\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −3.41797e12 | −0.143474 | ||||||||
\(940\) | −8.51122e12 | −0.355563 | ||||||||
\(941\) | −4.65584e12 | −0.193573 | −0.0967866 | − | 0.995305i | \(-0.530856\pi\) | ||||
−0.0967866 | + | 0.995305i | \(0.530856\pi\) | |||||||
\(942\) | −1.21834e13 | −0.504128 | ||||||||
\(943\) | −4.25488e13 | −1.75220 | ||||||||
\(944\) | −4.33492e12 | −0.177667 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −1.24248e12 | −0.0504405 | ||||||||
\(947\) | −3.96340e13 | −1.60137 | −0.800687 | − | 0.599083i | \(-0.795532\pi\) | ||||
−0.800687 | + | 0.599083i | \(0.795532\pi\) | |||||||
\(948\) | −9.13071e12 | −0.367170 | ||||||||
\(949\) | −1.39125e13 | −0.556812 | ||||||||
\(950\) | 6.10637e11 | 0.0243236 | ||||||||
\(951\) | 1.90963e13 | 0.757070 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.33592e13 | −1.31008 | −0.655040 | − | 0.755594i | \(-0.727348\pi\) | ||||
−0.655040 | + | 0.755594i | \(0.727348\pi\) | |||||||
\(954\) | −9.49417e11 | −0.0371099 | ||||||||
\(955\) | 7.61729e11 | 0.0296337 | ||||||||
\(956\) | −1.04128e13 | −0.403186 | ||||||||
\(957\) | −5.85381e12 | −0.225598 | ||||||||
\(958\) | −6.68941e12 | −0.256592 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 1.40863e12 | 0.0535274 | ||||||||
\(961\) | 7.00615e12 | 0.264987 | ||||||||
\(962\) | −3.30169e12 | −0.124293 | ||||||||
\(963\) | −1.86628e13 | −0.699292 | ||||||||
\(964\) | 2.41588e12 | 0.0901008 | ||||||||
\(965\) | 6.23526e11 | 0.0231463 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.72454e13 | 1.36979 | 0.684893 | − | 0.728643i | \(-0.259849\pi\) | ||||
0.684893 | + | 0.728643i | \(0.259849\pi\) | |||||||
\(968\) | −2.31272e12 | −0.0846610 | ||||||||
\(969\) | 1.36427e12 | 0.0497098 | ||||||||
\(970\) | −2.22494e12 | −0.0806948 | ||||||||
\(971\) | 2.47356e13 | 0.892969 | 0.446485 | − | 0.894791i | \(-0.352676\pi\) | ||||
0.446485 | + | 0.894791i | \(0.352676\pi\) | |||||||
\(972\) | −1.44039e13 | −0.517584 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 2.74516e13 | 0.977356 | ||||||||
\(975\) | 2.20871e12 | 0.0782742 | ||||||||
\(976\) | −1.31678e13 | −0.464504 | ||||||||
\(977\) | −3.93652e13 | −1.38225 | −0.691125 | − | 0.722736i | \(-0.742884\pi\) | ||||
−0.691125 | + | 0.722736i | \(0.742884\pi\) | |||||||
\(978\) | −1.52862e13 | −0.534288 | ||||||||
\(979\) | −6.09745e13 | −2.12142 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.66921e13 | 0.920180 | ||||||||
\(982\) | −5.35570e12 | −0.183787 | ||||||||
\(983\) | −3.70349e13 | −1.26509 | −0.632544 | − | 0.774524i | \(-0.717989\pi\) | ||||
−0.632544 | + | 0.774524i | \(0.717989\pi\) | |||||||
\(984\) | −5.44909e12 | −0.185287 | ||||||||
\(985\) | 5.34054e12 | 0.180768 | ||||||||
\(986\) | 7.96667e12 | 0.268430 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 4.85911e11 | 0.0162237 | ||||||||
\(989\) | 3.53151e12 | 0.117376 | ||||||||
\(990\) | −1.30135e13 | −0.430562 | ||||||||
\(991\) | 2.82296e13 | 0.929766 | 0.464883 | − | 0.885372i | \(-0.346096\pi\) | ||||
0.464883 | + | 0.885372i | \(0.346096\pi\) | |||||||
\(992\) | −6.06416e12 | −0.198824 | ||||||||
\(993\) | −2.78434e13 | −0.908763 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.11218e13 | −0.359726 | ||||||||
\(996\) | 1.47121e13 | 0.473705 | ||||||||
\(997\) | 3.44510e13 | 1.10426 | 0.552132 | − | 0.833757i | \(-0.313814\pi\) | ||||
0.552132 | + | 0.833757i | \(0.313814\pi\) | |||||||
\(998\) | −1.13607e13 | −0.362508 | ||||||||
\(999\) | 1.40390e13 | 0.445954 |
(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 | 98.10.a.g.1.2 | 3 | ||
7.2 | even | 3 | 14.10.c.b.11.2 | yes | 6 | ||
7.3 | odd | 6 | 98.10.c.l.79.2 | 6 | |||
7.4 | even | 3 | 14.10.c.b.9.2 | ✓ | 6 | ||
7.5 | odd | 6 | 98.10.c.l.67.2 | 6 | |||
7.6 | odd | 2 | 98.10.a.h.1.2 | 3 | |||
21.2 | odd | 6 | 126.10.g.e.109.1 | 6 | |||
21.11 | odd | 6 | 126.10.g.e.37.1 | 6 | |||
28.11 | odd | 6 | 112.10.i.a.65.2 | 6 | |||
28.23 | odd | 6 | 112.10.i.a.81.2 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
14.10.c.b.9.2 | ✓ | 6 | 7.4 | even | 3 | ||
14.10.c.b.11.2 | yes | 6 | 7.2 | even | 3 | ||
98.10.a.g.1.2 | 3 | 1.1 | even | 1 | trivial | ||
98.10.a.h.1.2 | 3 | 7.6 | odd | 2 | |||
98.10.c.l.67.2 | 6 | 7.5 | odd | 6 | |||
98.10.c.l.79.2 | 6 | 7.3 | odd | 6 | |||
112.10.i.a.65.2 | 6 | 28.11 | odd | 6 | |||
112.10.i.a.81.2 | 6 | 28.23 | odd | 6 | |||
126.10.g.e.37.1 | 6 | 21.11 | odd | 6 | |||
126.10.g.e.109.1 | 6 | 21.2 | odd | 6 |