Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [414,8,Mod(1,414)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(414, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 8, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("414.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 414 = 2 \cdot 3^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 414.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: | \(129.327400550\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 8367x^{2} - 89140x + 11077220 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{5}\cdot 3 \) |
Twist minimal: | no (minimal twist has level 138) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-56.1267\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 414.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −8.00000 | −0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 64.0000 | 0.500000 | ||||||||
\(5\) | −366.876 | −1.31257 | −0.656287 | − | 0.754511i | \(-0.727874\pi\) | ||||
−0.656287 | + | 0.754511i | \(0.727874\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −561.721 | −0.618981 | −0.309491 | − | 0.950903i | \(-0.600159\pi\) | ||||
−0.309491 | + | 0.950903i | \(0.600159\pi\) | |||||||
\(8\) | −512.000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 2935.00 | 0.928130 | ||||||||
\(11\) | 1096.20 | 0.248322 | 0.124161 | − | 0.992262i | \(-0.460376\pi\) | ||||
0.124161 | + | 0.992262i | \(0.460376\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 6925.11 | 0.874229 | 0.437115 | − | 0.899406i | \(-0.356000\pi\) | ||||
0.437115 | + | 0.899406i | \(0.356000\pi\) | |||||||
\(14\) | 4493.77 | 0.437686 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 4096.00 | 0.250000 | ||||||||
\(17\) | −13654.6 | −0.674075 | −0.337038 | − | 0.941491i | \(-0.609425\pi\) | ||||
−0.337038 | + | 0.941491i | \(0.609425\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 29540.8 | 0.988064 | 0.494032 | − | 0.869444i | \(-0.335523\pi\) | ||||
0.494032 | + | 0.869444i | \(0.335523\pi\) | |||||||
\(20\) | −23480.0 | −0.656287 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −8769.58 | −0.175590 | ||||||||
\(23\) | 12167.0 | 0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 56472.7 | 0.722851 | ||||||||
\(26\) | −55400.9 | −0.618173 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −35950.1 | −0.309491 | ||||||||
\(29\) | −150266. | −1.14411 | −0.572054 | − | 0.820216i | \(-0.693853\pi\) | ||||
−0.572054 | + | 0.820216i | \(0.693853\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −204841. | −1.23496 | −0.617479 | − | 0.786588i | \(-0.711846\pi\) | ||||
−0.617479 | + | 0.786588i | \(0.711846\pi\) | |||||||
\(32\) | −32768.0 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 109237. | 0.476643 | ||||||||
\(35\) | 206082. | 0.812459 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −492163. | −1.59736 | −0.798681 | − | 0.601755i | \(-0.794468\pi\) | ||||
−0.798681 | + | 0.601755i | \(0.794468\pi\) | |||||||
\(38\) | −236327. | −0.698667 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 187840. | 0.464065 | ||||||||
\(41\) | −416521. | −0.943829 | −0.471915 | − | 0.881644i | \(-0.656437\pi\) | ||||
−0.471915 | + | 0.881644i | \(0.656437\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 371500. | 0.712557 | 0.356279 | − | 0.934380i | \(-0.384045\pi\) | ||||
0.356279 | + | 0.934380i | \(0.384045\pi\) | |||||||
\(44\) | 70156.6 | 0.124161 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −97336.0 | −0.147442 | ||||||||
\(47\) | −930660. | −1.30752 | −0.653760 | − | 0.756702i | \(-0.726809\pi\) | ||||
−0.653760 | + | 0.756702i | \(0.726809\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −508013. | −0.616862 | ||||||||
\(50\) | −451782. | −0.511133 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 443207. | 0.437115 | ||||||||
\(53\) | −1.01318e6 | −0.934804 | −0.467402 | − | 0.884045i | \(-0.654810\pi\) | ||||
−0.467402 | + | 0.884045i | \(0.654810\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −402168. | −0.325940 | ||||||||
\(56\) | 287601. | 0.218843 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.20213e6 | 0.809007 | ||||||||
\(59\) | 2.28957e6 | 1.45135 | 0.725676 | − | 0.688036i | \(-0.241527\pi\) | ||||
0.725676 | + | 0.688036i | \(0.241527\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.95586e6 | 1.66736 | 0.833681 | − | 0.552246i | \(-0.186229\pi\) | ||||
0.833681 | + | 0.552246i | \(0.186229\pi\) | |||||||
\(62\) | 1.63873e6 | 0.873246 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 262144. | 0.125000 | ||||||||
\(65\) | −2.54066e6 | −1.14749 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.46138e6 | −0.593609 | −0.296804 | − | 0.954938i | \(-0.595921\pi\) | ||||
−0.296804 | + | 0.954938i | \(0.595921\pi\) | |||||||
\(68\) | −873896. | −0.337038 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1.64865e6 | −0.574495 | ||||||||
\(71\) | 1.82588e6 | 0.605437 | 0.302718 | − | 0.953080i | \(-0.402106\pi\) | ||||
0.302718 | + | 0.953080i | \(0.402106\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −40352.1 | −0.0121405 | −0.00607024 | − | 0.999982i | \(-0.501932\pi\) | ||||
−0.00607024 | + | 0.999982i | \(0.501932\pi\) | |||||||
\(74\) | 3.93731e6 | 1.12951 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 1.89061e6 | 0.494032 | ||||||||
\(77\) | −615757. | −0.153706 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −2.36229e6 | −0.539061 | −0.269531 | − | 0.962992i | \(-0.586869\pi\) | ||||
−0.269531 | + | 0.962992i | \(0.586869\pi\) | |||||||
\(80\) | −1.50272e6 | −0.328144 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3.33217e6 | 0.667388 | ||||||||
\(83\) | −1.27885e6 | −0.245497 | −0.122749 | − | 0.992438i | \(-0.539171\pi\) | ||||
−0.122749 | + | 0.992438i | \(0.539171\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 5.00955e6 | 0.884774 | ||||||||
\(86\) | −2.97200e6 | −0.503854 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −561253. | −0.0877949 | ||||||||
\(89\) | −3.88462e6 | −0.584095 | −0.292047 | − | 0.956404i | \(-0.594336\pi\) | ||||
−0.292047 | + | 0.956404i | \(0.594336\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −3.88998e6 | −0.541131 | ||||||||
\(92\) | 778688. | 0.104257 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.44528e6 | 0.924556 | ||||||||
\(95\) | −1.08378e7 | −1.29691 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −8.46502e6 | −0.941731 | −0.470865 | − | 0.882205i | \(-0.656058\pi\) | ||||
−0.470865 | + | 0.882205i | \(0.656058\pi\) | |||||||
\(98\) | 4.06410e6 | 0.436188 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 3.61425e6 | 0.361425 | ||||||||
\(101\) | −5.79563e6 | −0.559727 | −0.279863 | − | 0.960040i | \(-0.590289\pi\) | ||||
−0.279863 | + | 0.960040i | \(0.590289\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1.34033e6 | 0.120860 | 0.0604298 | − | 0.998172i | \(-0.480753\pi\) | ||||
0.0604298 | + | 0.998172i | \(0.480753\pi\) | |||||||
\(104\) | −3.54566e6 | −0.309087 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 8.10543e6 | 0.661006 | ||||||||
\(107\) | 1.37815e7 | 1.08756 | 0.543779 | − | 0.839229i | \(-0.316993\pi\) | ||||
0.543779 | + | 0.839229i | \(0.316993\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 9.40692e6 | 0.695752 | 0.347876 | − | 0.937541i | \(-0.386903\pi\) | ||||
0.347876 | + | 0.937541i | \(0.386903\pi\) | |||||||
\(110\) | 3.21734e6 | 0.230475 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −2.30081e6 | −0.154745 | ||||||||
\(113\) | 776740. | 0.0506409 | 0.0253204 | − | 0.999679i | \(-0.491939\pi\) | ||||
0.0253204 | + | 0.999679i | \(0.491939\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −4.46378e6 | −0.273691 | ||||||||
\(116\) | −9.61701e6 | −0.572054 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.83166e7 | −1.02626 | ||||||||
\(119\) | 7.67008e6 | 0.417240 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.82855e7 | −0.938336 | ||||||||
\(122\) | −2.36469e7 | −1.17900 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −1.31099e7 | −0.617479 | ||||||||
\(125\) | 7.94369e6 | 0.363779 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.02779e7 | −0.878434 | −0.439217 | − | 0.898381i | \(-0.644744\pi\) | ||||
−0.439217 | + | 0.898381i | \(0.644744\pi\) | |||||||
\(128\) | −2.09715e6 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 2.03252e7 | 0.811398 | ||||||||
\(131\) | 5.73353e6 | 0.222829 | 0.111415 | − | 0.993774i | \(-0.464462\pi\) | ||||
0.111415 | + | 0.993774i | \(0.464462\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.65937e7 | −0.611593 | ||||||||
\(134\) | 1.16910e7 | 0.419745 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.99116e6 | 0.238322 | ||||||||
\(137\) | 2.96971e7 | 0.986716 | 0.493358 | − | 0.869826i | \(-0.335769\pi\) | ||||
0.493358 | + | 0.869826i | \(0.335769\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 2.70200e7 | 0.853362 | 0.426681 | − | 0.904402i | \(-0.359683\pi\) | ||||
0.426681 | + | 0.904402i | \(0.359683\pi\) | |||||||
\(140\) | 1.31892e7 | 0.406229 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1.46071e7 | −0.428108 | ||||||||
\(143\) | 7.59129e6 | 0.217090 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 5.51289e7 | 1.50173 | ||||||||
\(146\) | 322816. | 0.00858461 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −3.14984e7 | −0.798681 | ||||||||
\(149\) | 1.22268e7 | 0.302803 | 0.151401 | − | 0.988472i | \(-0.451621\pi\) | ||||
0.151401 | + | 0.988472i | \(0.451621\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −7.91442e7 | −1.87068 | −0.935341 | − | 0.353747i | \(-0.884907\pi\) | ||||
−0.935341 | + | 0.353747i | \(0.884907\pi\) | |||||||
\(152\) | −1.51249e7 | −0.349333 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 4.92606e6 | 0.108687 | ||||||||
\(155\) | 7.51513e7 | 1.62097 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −6.65855e7 | −1.37319 | −0.686595 | − | 0.727040i | \(-0.740895\pi\) | ||||
−0.686595 | + | 0.727040i | \(0.740895\pi\) | |||||||
\(158\) | 1.88983e7 | 0.381174 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.20218e7 | 0.232033 | ||||||||
\(161\) | −6.83446e6 | −0.129066 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 5.57898e7 | 1.00902 | 0.504508 | − | 0.863407i | \(-0.331674\pi\) | ||||
0.504508 | + | 0.863407i | \(0.331674\pi\) | |||||||
\(164\) | −2.66573e7 | −0.471915 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 1.02308e7 | 0.173593 | ||||||||
\(167\) | 2.85952e7 | 0.475100 | 0.237550 | − | 0.971375i | \(-0.423656\pi\) | ||||
0.237550 | + | 0.971375i | \(0.423656\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.47913e7 | −0.235724 | ||||||||
\(170\) | −4.00764e7 | −0.625629 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 2.37760e7 | 0.356279 | ||||||||
\(173\) | 5.94429e7 | 0.872847 | 0.436424 | − | 0.899741i | \(-0.356245\pi\) | ||||
0.436424 | + | 0.899741i | \(0.356245\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3.17219e7 | −0.447431 | ||||||||
\(176\) | 4.49002e6 | 0.0620804 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 3.10769e7 | 0.413017 | ||||||||
\(179\) | 1.09127e8 | 1.42216 | 0.711079 | − | 0.703112i | \(-0.248207\pi\) | ||||
0.711079 | + | 0.703112i | \(0.248207\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −9.89431e7 | −1.24025 | −0.620127 | − | 0.784501i | \(-0.712919\pi\) | ||||
−0.620127 | + | 0.784501i | \(0.712919\pi\) | |||||||
\(182\) | 3.11199e7 | 0.382638 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −6.22950e6 | −0.0737210 | ||||||||
\(185\) | 1.80563e8 | 2.09666 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −1.49682e7 | −0.167387 | ||||||||
\(188\) | −5.95622e7 | −0.653760 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 8.67025e7 | 0.917052 | ||||||||
\(191\) | 6.19114e7 | 0.642916 | 0.321458 | − | 0.946924i | \(-0.395827\pi\) | ||||
0.321458 | + | 0.946924i | \(0.395827\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.03484e8 | 1.03615 | 0.518076 | − | 0.855334i | \(-0.326648\pi\) | ||||
0.518076 | + | 0.855334i | \(0.326648\pi\) | |||||||
\(194\) | 6.77201e7 | 0.665904 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.25128e7 | −0.308431 | ||||||||
\(197\) | 1.11986e8 | 1.04360 | 0.521798 | − | 0.853069i | \(-0.325261\pi\) | ||||
0.521798 | + | 0.853069i | \(0.325261\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.09861e7 | −0.0988228 | −0.0494114 | − | 0.998779i | \(-0.515735\pi\) | ||||
−0.0494114 | + | 0.998779i | \(0.515735\pi\) | |||||||
\(200\) | −2.89140e7 | −0.255566 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 4.63651e7 | 0.395787 | ||||||||
\(203\) | 8.44074e7 | 0.708182 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.52811e8 | 1.23885 | ||||||||
\(206\) | −1.07226e7 | −0.0854606 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 2.83653e7 | 0.218557 | ||||||||
\(209\) | 3.23826e7 | 0.245357 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.14052e7 | 0.523289 | 0.261644 | − | 0.965164i | \(-0.415735\pi\) | ||||
0.261644 | + | 0.965164i | \(0.415735\pi\) | |||||||
\(212\) | −6.48434e7 | −0.467402 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −1.10252e8 | −0.769019 | ||||||||
\(215\) | −1.36294e8 | −0.935284 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.15064e8 | 0.764415 | ||||||||
\(218\) | −7.52553e7 | −0.491971 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.57388e7 | −0.162970 | ||||||||
\(221\) | −9.45598e7 | −0.589296 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.21124e8 | 0.731415 | 0.365707 | − | 0.930730i | \(-0.380827\pi\) | ||||
0.365707 | + | 0.930730i | \(0.380827\pi\) | |||||||
\(224\) | 1.84065e7 | 0.109421 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −6.21392e6 | −0.0358085 | ||||||||
\(227\) | −3.23693e7 | −0.183672 | −0.0918360 | − | 0.995774i | \(-0.529274\pi\) | ||||
−0.0918360 | + | 0.995774i | \(0.529274\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2.14673e8 | 1.18128 | 0.590642 | − | 0.806934i | \(-0.298875\pi\) | ||||
0.590642 | + | 0.806934i | \(0.298875\pi\) | |||||||
\(230\) | 3.57102e7 | 0.193528 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 7.69361e7 | 0.404503 | ||||||||
\(233\) | 2.34580e8 | 1.21491 | 0.607457 | − | 0.794353i | \(-0.292190\pi\) | ||||
0.607457 | + | 0.794353i | \(0.292190\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 3.41436e8 | 1.71622 | ||||||||
\(236\) | 1.46533e8 | 0.725676 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −6.13607e7 | −0.295033 | ||||||||
\(239\) | 1.73526e8 | 0.822189 | 0.411095 | − | 0.911593i | \(-0.365147\pi\) | ||||
0.411095 | + | 0.911593i | \(0.365147\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.89649e8 | 0.872752 | 0.436376 | − | 0.899764i | \(-0.356262\pi\) | ||||
0.436376 | + | 0.899764i | \(0.356262\pi\) | |||||||
\(242\) | 1.46284e8 | 0.663504 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 1.89175e8 | 0.833681 | ||||||||
\(245\) | 1.86377e8 | 0.809678 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.04574e8 | 0.863794 | ||||||||
\(248\) | 1.04879e8 | 0.436623 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −6.35495e7 | −0.257230 | ||||||||
\(251\) | −2.71105e8 | −1.08213 | −0.541064 | − | 0.840981i | \(-0.681978\pi\) | ||||
−0.541064 | + | 0.840981i | \(0.681978\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.33374e7 | 0.0517786 | ||||||||
\(254\) | 1.62223e8 | 0.621147 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.67772e7 | 0.0625000 | ||||||||
\(257\) | −4.36260e8 | −1.60317 | −0.801584 | − | 0.597882i | \(-0.796009\pi\) | ||||
−0.801584 | + | 0.597882i | \(0.796009\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.76458e8 | 0.988737 | ||||||||
\(260\) | −1.62602e8 | −0.573745 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −4.58682e7 | −0.157564 | ||||||||
\(263\) | −1.27332e8 | −0.431609 | −0.215805 | − | 0.976437i | \(-0.569237\pi\) | ||||
−0.215805 | + | 0.976437i | \(0.569237\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.71711e8 | 1.22700 | ||||||||
\(266\) | 1.32750e8 | 0.432461 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −9.35281e7 | −0.296804 | ||||||||
\(269\) | −2.50990e8 | −0.786182 | −0.393091 | − | 0.919500i | \(-0.628594\pi\) | ||||
−0.393091 | + | 0.919500i | \(0.628594\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.19209e8 | 0.363844 | 0.181922 | − | 0.983313i | \(-0.441768\pi\) | ||||
0.181922 | + | 0.983313i | \(0.441768\pi\) | |||||||
\(272\) | −5.59293e7 | −0.168519 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2.37577e8 | −0.697714 | ||||||||
\(275\) | 6.19052e7 | 0.179499 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.70183e8 | −0.763799 | −0.381899 | − | 0.924204i | \(-0.624730\pi\) | ||||
−0.381899 | + | 0.924204i | \(0.624730\pi\) | |||||||
\(278\) | −2.16160e8 | −0.603418 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1.05514e8 | −0.287248 | ||||||||
\(281\) | 6.33010e8 | 1.70192 | 0.850958 | − | 0.525233i | \(-0.176022\pi\) | ||||
0.850958 | + | 0.525233i | \(0.176022\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.68305e8 | 1.75276 | 0.876379 | − | 0.481622i | \(-0.159952\pi\) | ||||
0.876379 | + | 0.481622i | \(0.159952\pi\) | |||||||
\(284\) | 1.16857e8 | 0.302718 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −6.07303e7 | −0.153506 | ||||||||
\(287\) | 2.33969e8 | 0.584213 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.23890e8 | −0.545623 | ||||||||
\(290\) | −4.41031e8 | −1.06188 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.58253e6 | −0.00607024 | ||||||||
\(293\) | −5.36402e8 | −1.24582 | −0.622908 | − | 0.782295i | \(-0.714049\pi\) | ||||
−0.622908 | + | 0.782295i | \(0.714049\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8.39989e8 | −1.90501 | ||||||||
\(296\) | 2.51988e8 | 0.564753 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −9.78141e7 | −0.214114 | ||||||||
\(299\) | 8.42579e7 | 0.182289 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −2.08680e8 | −0.441059 | ||||||||
\(302\) | 6.33154e8 | 1.32277 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.20999e8 | 0.247016 | ||||||||
\(305\) | −1.08443e9 | −2.18854 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.07221e8 | −0.211493 | −0.105746 | − | 0.994393i | \(-0.533723\pi\) | ||||
−0.105746 | + | 0.994393i | \(0.533723\pi\) | |||||||
\(308\) | −3.94084e7 | −0.0768532 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −6.01211e8 | −1.14620 | ||||||||
\(311\) | 9.74611e8 | 1.83726 | 0.918629 | − | 0.395122i | \(-0.129298\pi\) | ||||
0.918629 | + | 0.395122i | \(0.129298\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6.47093e8 | −1.19278 | −0.596392 | − | 0.802693i | \(-0.703400\pi\) | ||||
−0.596392 | + | 0.802693i | \(0.703400\pi\) | |||||||
\(314\) | 5.32684e8 | 0.970992 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.51186e8 | −0.269531 | ||||||||
\(317\) | −5.22962e8 | −0.922068 | −0.461034 | − | 0.887382i | \(-0.652521\pi\) | ||||
−0.461034 | + | 0.887382i | \(0.652521\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.64721e8 | −0.284107 | ||||||||
\(320\) | −9.61742e7 | −0.164072 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 5.46757e7 | 0.0912638 | ||||||||
\(323\) | −4.03369e8 | −0.666029 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 3.91080e8 | 0.631937 | ||||||||
\(326\) | −4.46319e8 | −0.713483 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.13259e8 | 0.333694 | ||||||||
\(329\) | 5.22771e8 | 0.809330 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.00533e8 | −0.152373 | −0.0761867 | − | 0.997094i | \(-0.524275\pi\) | ||||
−0.0761867 | + | 0.997094i | \(0.524275\pi\) | |||||||
\(332\) | −8.18465e7 | −0.122749 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −2.28761e8 | −0.335946 | ||||||||
\(335\) | 5.36144e8 | 0.779156 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −4.77653e8 | −0.679842 | −0.339921 | − | 0.940454i | \(-0.610400\pi\) | ||||
−0.339921 | + | 0.940454i | \(0.610400\pi\) | |||||||
\(338\) | 1.18330e8 | 0.166682 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 3.20611e8 | 0.442387 | ||||||||
\(341\) | −2.24547e8 | −0.306666 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 7.47963e8 | 1.00081 | ||||||||
\(344\) | −1.90208e8 | −0.251927 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −4.75543e8 | −0.617196 | ||||||||
\(347\) | 9.37582e8 | 1.20464 | 0.602318 | − | 0.798256i | \(-0.294244\pi\) | ||||
0.602318 | + | 0.798256i | \(0.294244\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.69080e8 | 1.22031 | 0.610155 | − | 0.792282i | \(-0.291107\pi\) | ||||
0.610155 | + | 0.792282i | \(0.291107\pi\) | |||||||
\(350\) | 2.53775e8 | 0.316382 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −3.59202e7 | −0.0438975 | ||||||||
\(353\) | 4.61929e8 | 0.558938 | 0.279469 | − | 0.960155i | \(-0.409842\pi\) | ||||
0.279469 | + | 0.960155i | \(0.409842\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.69872e8 | −0.794680 | ||||||||
\(356\) | −2.48616e8 | −0.292047 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −8.73019e8 | −1.00562 | ||||||||
\(359\) | 7.75397e8 | 0.884491 | 0.442245 | − | 0.896894i | \(-0.354182\pi\) | ||||
0.442245 | + | 0.896894i | \(0.354182\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.12115e7 | −0.0237299 | ||||||||
\(362\) | 7.91545e8 | 0.876992 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −2.48959e8 | −0.270566 | ||||||||
\(365\) | 1.48042e7 | 0.0159353 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −2.89183e8 | −0.305381 | −0.152690 | − | 0.988274i | \(-0.548794\pi\) | ||||
−0.152690 | + | 0.988274i | \(0.548794\pi\) | |||||||
\(368\) | 4.98360e7 | 0.0521286 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −1.44450e9 | −1.48256 | ||||||||
\(371\) | 5.69124e8 | 0.578626 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 6.15666e8 | 0.614277 | 0.307138 | − | 0.951665i | \(-0.400629\pi\) | ||||
0.307138 | + | 0.951665i | \(0.400629\pi\) | |||||||
\(374\) | 1.19745e8 | 0.118361 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.76498e8 | 0.462278 | ||||||||
\(377\) | −1.04061e9 | −1.00021 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 9.95325e8 | 0.939134 | 0.469567 | − | 0.882897i | \(-0.344410\pi\) | ||||
0.469567 | + | 0.882897i | \(0.344410\pi\) | |||||||
\(380\) | −6.93620e8 | −0.648453 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −4.95292e8 | −0.454610 | ||||||||
\(383\) | 2.09760e8 | 0.190777 | 0.0953887 | − | 0.995440i | \(-0.469591\pi\) | ||||
0.0953887 | + | 0.995440i | \(0.469591\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.25906e8 | 0.201751 | ||||||||
\(386\) | −8.27874e8 | −0.732671 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.41761e8 | −0.470865 | ||||||||
\(389\) | −2.53008e8 | −0.217927 | −0.108963 | − | 0.994046i | \(-0.534753\pi\) | ||||
−0.108963 | + | 0.994046i | \(0.534753\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.66136e8 | −0.140554 | ||||||||
\(392\) | 2.60102e8 | 0.218094 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −8.95889e8 | −0.737934 | ||||||||
\(395\) | 8.66666e8 | 0.707558 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 1.23414e9 | 0.989914 | 0.494957 | − | 0.868917i | \(-0.335184\pi\) | ||||
0.494957 | + | 0.868917i | \(0.335184\pi\) | |||||||
\(398\) | 8.78887e7 | 0.0698783 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.31312e8 | 0.180713 | ||||||||
\(401\) | −1.41825e9 | −1.09837 | −0.549185 | − | 0.835701i | \(-0.685062\pi\) | ||||
−0.549185 | + | 0.835701i | \(0.685062\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.41855e9 | −1.07964 | ||||||||
\(404\) | −3.70921e8 | −0.279863 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −6.75260e8 | −0.500760 | ||||||||
\(407\) | −5.39508e8 | −0.396659 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 8.33868e8 | 0.602651 | 0.301325 | − | 0.953521i | \(-0.402571\pi\) | ||||
0.301325 | + | 0.953521i | \(0.402571\pi\) | |||||||
\(410\) | −1.22249e9 | −0.875996 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 8.57810e7 | 0.0604298 | ||||||||
\(413\) | −1.28610e9 | −0.898360 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.69180e8 | 0.322234 | ||||||||
\(416\) | −2.26922e8 | −0.154543 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2.59061e8 | −0.173494 | ||||||||
\(419\) | 5.56088e8 | 0.369313 | 0.184656 | − | 0.982803i | \(-0.440883\pi\) | ||||
0.184656 | + | 0.982803i | \(0.440883\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.76819e9 | 1.15489 | 0.577447 | − | 0.816428i | \(-0.304049\pi\) | ||||
0.577447 | + | 0.816428i | \(0.304049\pi\) | |||||||
\(422\) | −5.71242e8 | −0.370021 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 5.18747e8 | 0.330503 | ||||||||
\(425\) | −7.71113e8 | −0.487256 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1.66037e9 | −1.03207 | ||||||||
\(428\) | 8.82014e8 | 0.543779 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.09036e9 | 0.661346 | ||||||||
\(431\) | −1.86575e9 | −1.12249 | −0.561244 | − | 0.827650i | \(-0.689677\pi\) | ||||
−0.561244 | + | 0.827650i | \(0.689677\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −8.86037e8 | −0.524498 | −0.262249 | − | 0.965000i | \(-0.584464\pi\) | ||||
−0.262249 | + | 0.965000i | \(0.584464\pi\) | |||||||
\(434\) | −9.20510e8 | −0.540523 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 6.02043e8 | 0.347876 | ||||||||
\(437\) | 3.59423e8 | 0.206026 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1.11162e9 | −0.627094 | −0.313547 | − | 0.949573i | \(-0.601517\pi\) | ||||
−0.313547 | + | 0.949573i | \(0.601517\pi\) | |||||||
\(440\) | 2.05910e8 | 0.115237 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.56478e8 | 0.416695 | ||||||||
\(443\) | −3.79851e8 | −0.207587 | −0.103794 | − | 0.994599i | \(-0.533098\pi\) | ||||
−0.103794 | + | 0.994599i | \(0.533098\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.42517e9 | 0.766668 | ||||||||
\(446\) | −9.68993e8 | −0.517188 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1.47252e8 | −0.0773726 | ||||||||
\(449\) | −1.04853e9 | −0.546664 | −0.273332 | − | 0.961920i | \(-0.588126\pi\) | ||||
−0.273332 | + | 0.961920i | \(0.588126\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −4.56589e8 | −0.234373 | ||||||||
\(452\) | 4.97114e7 | 0.0253204 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 2.58955e8 | 0.129876 | ||||||||
\(455\) | 1.42714e9 | 0.710275 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.49813e9 | −0.734250 | −0.367125 | − | 0.930172i | \(-0.619658\pi\) | ||||
−0.367125 | + | 0.930172i | \(0.619658\pi\) | |||||||
\(458\) | −1.71739e9 | −0.835293 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −2.85682e8 | −0.136845 | ||||||||
\(461\) | −1.49236e9 | −0.709447 | −0.354723 | − | 0.934971i | \(-0.615425\pi\) | ||||
−0.354723 | + | 0.934971i | \(0.615425\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.06867e9 | −1.43687 | −0.718433 | − | 0.695596i | \(-0.755140\pi\) | ||||
−0.718433 | + | 0.695596i | \(0.755140\pi\) | |||||||
\(464\) | −6.15489e8 | −0.286027 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −1.87664e9 | −0.859074 | ||||||||
\(467\) | −1.68526e9 | −0.765698 | −0.382849 | − | 0.923811i | \(-0.625057\pi\) | ||||
−0.382849 | + | 0.923811i | \(0.625057\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 8.20886e8 | 0.367433 | ||||||||
\(470\) | −2.73149e9 | −1.21355 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.17226e9 | −0.513131 | ||||||||
\(473\) | 4.07238e8 | 0.176943 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.66825e9 | 0.714223 | ||||||||
\(476\) | 4.90885e8 | 0.208620 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −1.38821e9 | −0.581376 | ||||||||
\(479\) | 2.69509e9 | 1.12047 | 0.560233 | − | 0.828335i | \(-0.310712\pi\) | ||||
0.560233 | + | 0.828335i | \(0.310712\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.40829e9 | −1.39646 | ||||||||
\(482\) | −1.51719e9 | −0.617129 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −1.17027e9 | −0.469168 | ||||||||
\(485\) | 3.10561e9 | 1.23609 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.88969e9 | −1.13371 | −0.566853 | − | 0.823819i | \(-0.691839\pi\) | ||||
−0.566853 | + | 0.823819i | \(0.691839\pi\) | |||||||
\(488\) | −1.51340e9 | −0.589502 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −1.49102e9 | −0.572528 | ||||||||
\(491\) | 2.94886e9 | 1.12427 | 0.562133 | − | 0.827047i | \(-0.309981\pi\) | ||||
0.562133 | + | 0.827047i | \(0.309981\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.05182e9 | 0.771215 | ||||||||
\(494\) | −1.63659e9 | −0.610795 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −8.39030e8 | −0.308739 | ||||||||
\(497\) | −1.02564e9 | −0.374754 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.10068e9 | 1.11713 | 0.558567 | − | 0.829459i | \(-0.311351\pi\) | ||||
0.558567 | + | 0.829459i | \(0.311351\pi\) | |||||||
\(500\) | 5.08396e8 | 0.181889 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 2.16884e9 | 0.765181 | ||||||||
\(503\) | 6.25596e8 | 0.219183 | 0.109591 | − | 0.993977i | \(-0.465046\pi\) | ||||
0.109591 | + | 0.993977i | \(0.465046\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.12628e9 | 0.734683 | ||||||||
\(506\) | −1.06699e8 | −0.0366130 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.29778e9 | −0.439217 | ||||||||
\(509\) | −4.35887e9 | −1.46508 | −0.732541 | − | 0.680723i | \(-0.761666\pi\) | ||||
−0.732541 | + | 0.680723i | \(0.761666\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.26666e7 | 0.00751472 | ||||||||
\(512\) | −1.34218e8 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 3.49008e9 | 1.13361 | ||||||||
\(515\) | −4.91734e8 | −0.158637 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.02019e9 | −0.324685 | ||||||||
\(518\) | −2.21167e9 | −0.699142 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.30082e9 | 0.405699 | ||||||||
\(521\) | −1.86006e9 | −0.576229 | −0.288115 | − | 0.957596i | \(-0.593028\pi\) | ||||
−0.288115 | + | 0.957596i | \(0.593028\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 1.89981e9 | 0.580703 | 0.290352 | − | 0.956920i | \(-0.406228\pi\) | ||||
0.290352 | + | 0.956920i | \(0.406228\pi\) | |||||||
\(524\) | 3.66946e8 | 0.111415 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.01865e9 | 0.305194 | ||||||||
\(527\) | 2.79703e9 | 0.832454 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.48036e8 | 0.0434783 | ||||||||
\(530\) | −2.97368e9 | −0.867620 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.06200e9 | −0.305796 | ||||||||
\(533\) | −2.88446e9 | −0.825123 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −5.05608e9 | −1.42750 | ||||||||
\(536\) | 7.48225e8 | 0.209872 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 2.00792e9 | 0.555914 | ||||||||
\(539\) | −5.56882e8 | −0.153180 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 6.17189e9 | 1.67582 | 0.837910 | − | 0.545808i | \(-0.183777\pi\) | ||||
0.837910 | + | 0.545808i | \(0.183777\pi\) | |||||||
\(542\) | −9.53670e8 | −0.257277 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 4.47435e8 | 0.119161 | ||||||||
\(545\) | −3.45117e9 | −0.913226 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.97696e9 | 1.30020 | 0.650098 | − | 0.759851i | \(-0.274728\pi\) | ||||
0.650098 | + | 0.759851i | \(0.274728\pi\) | |||||||
\(548\) | 1.90061e9 | 0.493358 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −4.95242e8 | −0.126925 | ||||||||
\(551\) | −4.43898e9 | −1.13045 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1.32695e9 | 0.333669 | ||||||||
\(554\) | 2.16146e9 | 0.540087 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.72928e9 | 0.426681 | ||||||||
\(557\) | 2.16771e9 | 0.531506 | 0.265753 | − | 0.964041i | \(-0.414379\pi\) | ||||
0.265753 | + | 0.964041i | \(0.414379\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 2.57268e9 | 0.622938 | ||||||||
\(560\) | 8.44111e8 | 0.203115 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −5.06408e9 | −1.20344 | ||||||||
\(563\) | −4.33727e9 | −1.02432 | −0.512162 | − | 0.858889i | \(-0.671155\pi\) | ||||
−0.512162 | + | 0.858889i | \(0.671155\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −2.84967e8 | −0.0664699 | ||||||||
\(566\) | −5.34644e9 | −1.23939 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.34852e8 | −0.214054 | ||||||||
\(569\) | 1.76759e9 | 0.402243 | 0.201122 | − | 0.979566i | \(-0.435541\pi\) | ||||
0.201122 | + | 0.979566i | \(0.435541\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.35096e9 | 0.978046 | 0.489023 | − | 0.872271i | \(-0.337353\pi\) | ||||
0.489023 | + | 0.872271i | \(0.337353\pi\) | |||||||
\(572\) | 4.85843e8 | 0.108545 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.87175e9 | −0.413101 | ||||||||
\(575\) | 6.87104e8 | 0.150725 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 7.46172e9 | 1.61705 | 0.808525 | − | 0.588462i | \(-0.200266\pi\) | ||||
0.808525 | + | 0.588462i | \(0.200266\pi\) | |||||||
\(578\) | 1.79112e9 | 0.385813 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 3.52825e9 | 0.750864 | ||||||||
\(581\) | 7.18358e8 | 0.151958 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −1.11064e9 | −0.232132 | ||||||||
\(584\) | 2.06603e7 | 0.00429231 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.29122e9 | 0.880925 | ||||||||
\(587\) | 3.27341e9 | 0.667985 | 0.333992 | − | 0.942576i | \(-0.391604\pi\) | ||||
0.333992 | + | 0.942576i | \(0.391604\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −6.05118e9 | −1.22022 | ||||||||
\(590\) | 6.71991e9 | 1.34704 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −2.01590e9 | −0.399340 | ||||||||
\(593\) | 5.07631e9 | 0.999670 | 0.499835 | − | 0.866121i | \(-0.333394\pi\) | ||||
0.499835 | + | 0.866121i | \(0.333394\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.81397e9 | −0.547658 | ||||||||
\(596\) | 7.82513e8 | 0.151401 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −6.74063e8 | −0.128898 | ||||||||
\(599\) | 9.57665e9 | 1.82062 | 0.910311 | − | 0.413926i | \(-0.135843\pi\) | ||||
0.910311 | + | 0.413926i | \(0.135843\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.02812e9 | −0.193189 | −0.0965945 | − | 0.995324i | \(-0.530795\pi\) | ||||
−0.0965945 | + | 0.995324i | \(0.530795\pi\) | |||||||
\(602\) | 1.66944e9 | 0.311876 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −5.06523e9 | −0.935341 | ||||||||
\(605\) | 6.70851e9 | 1.23164 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 2.45045e9 | 0.444719 | 0.222359 | − | 0.974965i | \(-0.428624\pi\) | ||||
0.222359 | + | 0.974965i | \(0.428624\pi\) | |||||||
\(608\) | −9.67994e8 | −0.174667 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 8.67548e9 | 1.54753 | ||||||||
\(611\) | −6.44492e9 | −1.14307 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.90460e8 | 0.156136 | 0.0780679 | − | 0.996948i | \(-0.475125\pi\) | ||||
0.0780679 | + | 0.996948i | \(0.475125\pi\) | |||||||
\(614\) | 8.57767e8 | 0.149548 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 3.15268e8 | 0.0543434 | ||||||||
\(617\) | −3.73214e9 | −0.639675 | −0.319838 | − | 0.947472i | \(-0.603628\pi\) | ||||
−0.319838 | + | 0.947472i | \(0.603628\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9.73916e9 | −1.65046 | −0.825228 | − | 0.564799i | \(-0.808954\pi\) | ||||
−0.825228 | + | 0.564799i | \(0.808954\pi\) | |||||||
\(620\) | 4.80968e9 | 0.810486 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −7.79689e9 | −1.29914 | ||||||||
\(623\) | 2.18207e9 | 0.361544 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −7.32628e9 | −1.20034 | ||||||||
\(626\) | 5.17675e9 | 0.843426 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −4.26147e9 | −0.686595 | ||||||||
\(629\) | 6.72030e9 | 1.07674 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.10602e8 | −0.128441 | −0.0642207 | − | 0.997936i | \(-0.520456\pi\) | ||||
−0.0642207 | + | 0.997936i | \(0.520456\pi\) | |||||||
\(632\) | 1.20949e9 | 0.190587 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.18370e9 | 0.652001 | ||||||||
\(635\) | 7.43946e9 | 1.15301 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −3.51805e9 | −0.539279 | ||||||||
\(638\) | 1.31777e9 | 0.200894 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 7.69394e8 | 0.116016 | ||||||||
\(641\) | 1.53566e9 | 0.230299 | 0.115150 | − | 0.993348i | \(-0.463265\pi\) | ||||
0.115150 | + | 0.993348i | \(0.463265\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 9.03556e9 | 1.34035 | 0.670173 | − | 0.742205i | \(-0.266220\pi\) | ||||
0.670173 | + | 0.742205i | \(0.266220\pi\) | |||||||
\(644\) | −4.37405e8 | −0.0645332 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.22695e9 | 0.470954 | ||||||||
\(647\) | 6.44225e8 | 0.0935132 | 0.0467566 | − | 0.998906i | \(-0.485111\pi\) | ||||
0.0467566 | + | 0.998906i | \(0.485111\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.50983e9 | 0.360402 | ||||||||
\(650\) | −3.12864e9 | −0.446847 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.57055e9 | 0.504508 | ||||||||
\(653\) | 3.14760e9 | 0.442368 | 0.221184 | − | 0.975232i | \(-0.429008\pi\) | ||||
0.221184 | + | 0.975232i | \(0.429008\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −2.10349e9 | −0.292480 | ||||||||
\(656\) | −1.70607e9 | −0.235957 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −4.18217e9 | −0.572283 | ||||||||
\(659\) | −1.35636e10 | −1.84619 | −0.923093 | − | 0.384577i | \(-0.874347\pi\) | ||||
−0.923093 | + | 0.384577i | \(0.874347\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.38238e10 | 1.86176 | 0.930880 | − | 0.365325i | \(-0.119042\pi\) | ||||
0.930880 | + | 0.365325i | \(0.119042\pi\) | |||||||
\(662\) | 8.04261e8 | 0.107744 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 6.54772e8 | 0.0867964 | ||||||||
\(665\) | 6.08782e9 | 0.802761 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.82828e9 | −0.238563 | ||||||||
\(668\) | 1.83009e9 | 0.237550 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −4.28915e9 | −0.550946 | ||||||||
\(671\) | 3.24021e9 | 0.414042 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −3.45394e9 | −0.436780 | −0.218390 | − | 0.975862i | \(-0.570080\pi\) | ||||
−0.218390 | + | 0.975862i | \(0.570080\pi\) | |||||||
\(674\) | 3.82123e9 | 0.480721 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.46644e8 | −0.117862 | ||||||||
\(677\) | −6.53708e9 | −0.809699 | −0.404849 | − | 0.914383i | \(-0.632676\pi\) | ||||
−0.404849 | + | 0.914383i | \(0.632676\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4.75498e9 | 0.582914 | ||||||||
\(680\) | −2.56489e9 | −0.312815 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.79637e9 | 0.216846 | ||||||||
\(683\) | 1.53942e10 | 1.84877 | 0.924386 | − | 0.381457i | \(-0.124578\pi\) | ||||
0.924386 | + | 0.381457i | \(0.124578\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.08951e10 | −1.29514 | ||||||||
\(686\) | −5.98370e9 | −0.707678 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.52167e9 | 0.178139 | ||||||||
\(689\) | −7.01638e9 | −0.817233 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.43606e9 | −0.742074 | −0.371037 | − | 0.928618i | \(-0.620998\pi\) | ||||
−0.371037 | + | 0.928618i | \(0.620998\pi\) | |||||||
\(692\) | 3.80434e9 | 0.436424 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −7.50066e9 | −0.851807 | ||||||||
\(695\) | −9.91297e9 | −1.12010 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.68744e9 | 0.636212 | ||||||||
\(698\) | −7.75264e9 | −0.862890 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −2.03020e9 | −0.223716 | ||||||||
\(701\) | −3.29232e9 | −0.360985 | −0.180492 | − | 0.983576i | \(-0.557769\pi\) | ||||
−0.180492 | + | 0.983576i | \(0.557769\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.45389e10 | −1.57829 | ||||||||
\(704\) | 2.87362e8 | 0.0310402 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.69543e9 | −0.395229 | ||||||||
\(707\) | 3.25553e9 | 0.346460 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.33790e10 | −1.40981 | −0.704907 | − | 0.709300i | \(-0.749011\pi\) | ||||
−0.704907 | + | 0.709300i | \(0.749011\pi\) | |||||||
\(710\) | 5.35898e9 | 0.561924 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 1.98892e9 | 0.206509 | ||||||||
\(713\) | −2.49231e9 | −0.257506 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.78506e9 | −0.284947 | ||||||||
\(716\) | 6.98415e9 | 0.711079 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −6.20317e9 | −0.625430 | ||||||||
\(719\) | −9.99931e9 | −1.00327 | −0.501636 | − | 0.865079i | \(-0.667268\pi\) | ||||
−0.501636 | + | 0.865079i | \(0.667268\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −7.52890e8 | −0.0748098 | ||||||||
\(722\) | 1.69692e8 | 0.0167796 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −6.33236e9 | −0.620127 | ||||||||
\(725\) | −8.48592e9 | −0.827020 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.87514e9 | 0.374039 | 0.187019 | − | 0.982356i | \(-0.440117\pi\) | ||||
0.187019 | + | 0.982356i | \(0.440117\pi\) | |||||||
\(728\) | 1.99167e9 | 0.191319 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.18433e8 | −0.0112679 | ||||||||
\(731\) | −5.07270e9 | −0.480317 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.03185e10 | 1.90559 | 0.952793 | − | 0.303620i | \(-0.0981954\pi\) | ||||
0.952793 | + | 0.303620i | \(0.0981954\pi\) | |||||||
\(734\) | 2.31346e9 | 0.215937 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.98688e8 | −0.0368605 | ||||||||
\(737\) | −1.60196e9 | −0.147406 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.01270e9 | 0.548042 | 0.274021 | − | 0.961724i | \(-0.411646\pi\) | ||||
0.274021 | + | 0.961724i | \(0.411646\pi\) | |||||||
\(740\) | 1.15560e10 | 1.04833 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −4.55299e9 | −0.409150 | ||||||||
\(743\) | −7.10581e9 | −0.635554 | −0.317777 | − | 0.948165i | \(-0.602936\pi\) | ||||
−0.317777 | + | 0.948165i | \(0.602936\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −4.48570e9 | −0.397451 | ||||||||
\(746\) | −4.92533e9 | −0.434359 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −9.57962e8 | −0.0836937 | ||||||||
\(749\) | −7.74134e9 | −0.673178 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.66674e9 | −0.229743 | −0.114871 | − | 0.993380i | \(-0.536646\pi\) | ||||
−0.114871 | + | 0.993380i | \(0.536646\pi\) | |||||||
\(752\) | −3.81198e9 | −0.326880 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 8.32486e9 | 0.707257 | ||||||||
\(755\) | 2.90361e10 | 2.45541 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.21053e10 | 1.01424 | 0.507119 | − | 0.861876i | \(-0.330711\pi\) | ||||
0.507119 | + | 0.861876i | \(0.330711\pi\) | |||||||
\(758\) | −7.96260e9 | −0.664068 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 5.54896e9 | 0.458526 | ||||||||
\(761\) | 2.97000e9 | 0.244293 | 0.122146 | − | 0.992512i | \(-0.461022\pi\) | ||||
0.122146 | + | 0.992512i | \(0.461022\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.28406e9 | −0.430657 | ||||||||
\(764\) | 3.96233e9 | 0.321458 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.67808e9 | −0.134900 | ||||||||
\(767\) | 1.58556e10 | 1.26881 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.95706e10 | 1.55190 | 0.775948 | − | 0.630797i | \(-0.217272\pi\) | ||||
0.775948 | + | 0.630797i | \(0.217272\pi\) | |||||||
\(770\) | −1.80725e9 | −0.142659 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.62299e9 | 0.518076 | ||||||||
\(773\) | 1.54223e9 | 0.120094 | 0.0600468 | − | 0.998196i | \(-0.480875\pi\) | ||||
0.0600468 | + | 0.998196i | \(0.480875\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −1.15680e10 | −0.892690 | ||||||||
\(776\) | 4.33409e9 | 0.332952 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.02406e9 | 0.154098 | ||||||||
\(779\) | −1.23044e10 | −0.932564 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 2.00153e9 | 0.150343 | ||||||||
\(782\) | 1.32909e9 | 0.0993870 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.08082e9 | −0.154216 | ||||||||
\(785\) | 2.44286e10 | 1.80241 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.76348e10 | −1.28961 | −0.644805 | − | 0.764347i | \(-0.723061\pi\) | ||||
−0.644805 | + | 0.764347i | \(0.723061\pi\) | |||||||
\(788\) | 7.16712e9 | 0.521798 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −6.93333e9 | −0.500319 | ||||||||
\(791\) | −4.36311e8 | −0.0313458 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.04697e10 | 1.45766 | ||||||||
\(794\) | −9.87312e9 | −0.699975 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.03110e8 | −0.0494114 | ||||||||
\(797\) | −2.10641e10 | −1.47380 | −0.736901 | − | 0.676000i | \(-0.763712\pi\) | ||||
−0.736901 | + | 0.676000i | \(0.763712\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 1.27078e10 | 0.881367 | ||||||||
\(800\) | −1.85050e9 | −0.127783 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 1.13460e10 | 0.776664 | ||||||||
\(803\) | −4.42338e7 | −0.00301474 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.50740e9 | 0.169409 | ||||||||
\(806\) | 1.13484e10 | 0.763417 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.96736e9 | 0.197893 | ||||||||
\(809\) | 2.12308e10 | 1.40977 | 0.704884 | − | 0.709323i | \(-0.250999\pi\) | ||||
0.704884 | + | 0.709323i | \(0.250999\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 9.31477e9 | 0.613196 | 0.306598 | − | 0.951839i | \(-0.400809\pi\) | ||||
0.306598 | + | 0.951839i | \(0.400809\pi\) | |||||||
\(812\) | 5.40208e9 | 0.354091 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.31606e9 | 0.280480 | ||||||||
\(815\) | −2.04679e10 | −1.32441 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.09744e10 | 0.704052 | ||||||||
\(818\) | −6.67094e9 | −0.426138 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 9.77993e9 | 0.619423 | ||||||||
\(821\) | 1.51846e10 | 0.957642 | 0.478821 | − | 0.877913i | \(-0.341064\pi\) | ||||
0.478821 | + | 0.877913i | \(0.341064\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −9.38917e9 | −0.587121 | −0.293561 | − | 0.955940i | \(-0.594840\pi\) | ||||
−0.293561 | + | 0.955940i | \(0.594840\pi\) | |||||||
\(824\) | −6.86248e8 | −0.0427303 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.02888e10 | 0.635236 | ||||||||
\(827\) | −1.40878e10 | −0.866114 | −0.433057 | − | 0.901366i | \(-0.642565\pi\) | ||||
−0.433057 | + | 0.901366i | \(0.642565\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 1.99910e10 | 1.21869 | 0.609345 | − | 0.792905i | \(-0.291432\pi\) | ||||
0.609345 | + | 0.792905i | \(0.291432\pi\) | |||||||
\(830\) | −3.75344e9 | −0.227854 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 1.81538e9 | 0.109279 | ||||||||
\(833\) | 6.93672e9 | 0.415812 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −1.04909e10 | −0.623604 | ||||||||
\(836\) | 2.07248e9 | 0.122679 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −4.44870e9 | −0.261143 | ||||||||
\(839\) | −2.49729e10 | −1.45983 | −0.729915 | − | 0.683538i | \(-0.760440\pi\) | ||||
−0.729915 | + | 0.683538i | \(0.760440\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.32994e9 | 0.308984 | ||||||||
\(842\) | −1.41455e10 | −0.816633 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.56993e9 | 0.261644 | ||||||||
\(845\) | 5.42657e9 | 0.309405 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.02714e10 | 0.580813 | ||||||||
\(848\) | −4.14998e9 | −0.233701 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.16891e9 | 0.344542 | ||||||||
\(851\) | −5.98815e9 | −0.333073 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 2.15537e10 | 1.18905 | 0.594526 | − | 0.804077i | \(-0.297340\pi\) | ||||
0.594526 | + | 0.804077i | \(0.297340\pi\) | |||||||
\(854\) | 1.32830e10 | 0.729781 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −7.05611e9 | −0.384510 | ||||||||
\(857\) | 1.83252e9 | 0.0994524 | 0.0497262 | − | 0.998763i | \(-0.484165\pi\) | ||||
0.0497262 | + | 0.998763i | \(0.484165\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.88323e10 | 1.55204 | 0.776020 | − | 0.630708i | \(-0.217235\pi\) | ||||
0.776020 | + | 0.630708i | \(0.217235\pi\) | |||||||
\(860\) | −8.72284e9 | −0.467642 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.49260e10 | 0.793719 | ||||||||
\(863\) | 2.80605e10 | 1.48613 | 0.743067 | − | 0.669217i | \(-0.233370\pi\) | ||||
0.743067 | + | 0.669217i | \(0.233370\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −2.18081e10 | −1.14568 | ||||||||
\(866\) | 7.08829e9 | 0.370876 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7.36408e9 | 0.382208 | ||||||||
\(869\) | −2.58953e9 | −0.133860 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1.01202e10 | −0.518950 | ||||||||
\(872\) | −4.81634e9 | −0.245986 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −2.87539e9 | −0.145682 | ||||||||
\(875\) | −4.46214e9 | −0.225172 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −1.07928e10 | −0.540299 | −0.270149 | − | 0.962818i | \(-0.587073\pi\) | ||||
−0.270149 | + | 0.962818i | \(0.587073\pi\) | |||||||
\(878\) | 8.89300e9 | 0.443422 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −1.64728e9 | −0.0814851 | ||||||||
\(881\) | 2.86597e10 | 1.41207 | 0.706034 | − | 0.708178i | \(-0.250483\pi\) | ||||
0.706034 | + | 0.708178i | \(0.250483\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.47774e10 | −1.69994 | −0.849972 | − | 0.526828i | \(-0.823381\pi\) | ||||
−0.849972 | + | 0.526828i | \(0.823381\pi\) | |||||||
\(884\) | −6.05183e9 | −0.294648 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 3.03881e9 | 0.146786 | ||||||||
\(887\) | −6.42202e9 | −0.308986 | −0.154493 | − | 0.987994i | \(-0.549374\pi\) | ||||
−0.154493 | + | 0.987994i | \(0.549374\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.13905e10 | 0.543734 | ||||||||
\(890\) | −1.14014e10 | −0.542116 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 7.75195e9 | 0.365707 | ||||||||
\(893\) | −2.74925e10 | −1.29191 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −4.00362e10 | −1.86669 | ||||||||
\(896\) | 1.17801e9 | 0.0547107 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 8.38827e9 | 0.386550 | ||||||||
\(899\) | 3.07807e10 | 1.41292 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.38346e10 | 0.630128 | ||||||||
\(902\) | 3.65271e9 | 0.165727 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −3.97691e8 | −0.0179043 | ||||||||
\(905\) | 3.62998e10 | 1.62793 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −3.96724e10 | −1.76548 | −0.882740 | − | 0.469861i | \(-0.844304\pi\) | ||||
−0.882740 | + | 0.469861i | \(0.844304\pi\) | |||||||
\(908\) | −2.07164e9 | −0.0918360 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.14171e10 | −0.502240 | ||||||||
\(911\) | −3.39607e10 | −1.48820 | −0.744102 | − | 0.668066i | \(-0.767122\pi\) | ||||
−0.744102 | + | 0.668066i | \(0.767122\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.40187e9 | −0.0609623 | ||||||||
\(914\) | 1.19851e10 | 0.519193 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.37391e10 | 0.590642 | ||||||||
\(917\) | −3.22064e9 | −0.137927 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 1.98186e10 | 0.842304 | 0.421152 | − | 0.906990i | \(-0.361626\pi\) | ||||
0.421152 | + | 0.906990i | \(0.361626\pi\) | |||||||
\(920\) | 2.28545e9 | 0.0967642 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 1.19389e10 | 0.501655 | ||||||||
\(923\) | 1.26444e10 | 0.529290 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −2.77938e10 | −1.15465 | ||||||||
\(926\) | 2.45493e10 | 1.01602 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 4.92391e9 | 0.202252 | ||||||||
\(929\) | 2.08980e10 | 0.855164 | 0.427582 | − | 0.903976i | \(-0.359365\pi\) | ||||
0.427582 | + | 0.903976i | \(0.359365\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.50071e10 | −0.609499 | ||||||||
\(932\) | 1.50131e10 | 0.607457 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 1.34821e10 | 0.541430 | ||||||||
\(935\) | 5.49145e9 | 0.219708 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.61325e9 | −0.183197 | −0.0915986 | − | 0.995796i | \(-0.529198\pi\) | ||||
−0.0915986 | + | 0.995796i | \(0.529198\pi\) | |||||||
\(938\) | −6.56709e9 | −0.259814 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.18519e10 | 0.858109 | ||||||||
\(941\) | −2.61949e10 | −1.02483 | −0.512417 | − | 0.858737i | \(-0.671250\pi\) | ||||
−0.512417 | + | 0.858737i | \(0.671250\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −5.06781e9 | −0.196802 | ||||||||
\(944\) | 9.37810e9 | 0.362838 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.25790e9 | −0.125118 | ||||||||
\(947\) | 1.01216e10 | 0.387278 | 0.193639 | − | 0.981073i | \(-0.437971\pi\) | ||||
0.193639 | + | 0.981073i | \(0.437971\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.79443e8 | −0.0106136 | ||||||||
\(950\) | −1.33460e10 | −0.505032 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.92708e9 | −0.147517 | ||||||||
\(953\) | 5.16517e9 | 0.193312 | 0.0966562 | − | 0.995318i | \(-0.469185\pi\) | ||||
0.0966562 | + | 0.995318i | \(0.469185\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −2.27138e10 | −0.843875 | ||||||||
\(956\) | 1.11057e10 | 0.411095 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −2.15607e10 | −0.792289 | ||||||||
\(959\) | −1.66815e10 | −0.610759 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 1.44474e10 | 0.525119 | ||||||||
\(962\) | 2.72663e10 | 0.987446 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 1.21375e10 | 0.436376 | ||||||||
\(965\) | −3.79659e10 | −1.36003 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 2.33871e10 | 0.831734 | 0.415867 | − | 0.909425i | \(-0.363478\pi\) | ||||
0.415867 | + | 0.909425i | \(0.363478\pi\) | |||||||
\(968\) | 9.36219e9 | 0.331752 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −2.48449e10 | −0.874049 | ||||||||
\(971\) | 4.05447e9 | 0.142124 | 0.0710619 | − | 0.997472i | \(-0.477361\pi\) | ||||
0.0710619 | + | 0.997472i | \(0.477361\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1.51777e10 | −0.528215 | ||||||||
\(974\) | 2.31176e10 | 0.801651 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 1.21072e10 | 0.416841 | ||||||||
\(977\) | −5.68903e10 | −1.95167 | −0.975837 | − | 0.218499i | \(-0.929884\pi\) | ||||
−0.975837 | + | 0.218499i | \(0.929884\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −4.25831e9 | −0.145043 | ||||||||
\(980\) | 1.19282e10 | 0.404839 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −2.35909e10 | −0.794977 | ||||||||
\(983\) | −3.74559e10 | −1.25772 | −0.628859 | − | 0.777519i | \(-0.716478\pi\) | ||||
−0.628859 | + | 0.777519i | \(0.716478\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.10850e10 | −1.36980 | ||||||||
\(986\) | −1.64146e10 | −0.545331 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.30927e10 | 0.431897 | ||||||||
\(989\) | 4.52004e9 | 0.148578 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.00112e8 | 0.00326759 | 0.00163379 | − | 0.999999i | \(-0.499480\pi\) | ||||
0.00163379 | + | 0.999999i | \(0.499480\pi\) | |||||||
\(992\) | 6.71224e9 | 0.218312 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 8.20509e9 | 0.264991 | ||||||||
\(995\) | 4.03053e9 | 0.129712 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −3.72236e10 | −1.18956 | −0.594779 | − | 0.803889i | \(-0.702760\pi\) | ||||
−0.594779 | + | 0.803889i | \(0.702760\pi\) | |||||||
\(998\) | −2.48055e10 | −0.789934 | ||||||||
\(999\) | 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 | 414.8.a.i.1.1 | 4 | ||
3.2 | odd | 2 | 138.8.a.h.1.4 | ✓ | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
138.8.a.h.1.4 | ✓ | 4 | 3.2 | odd | 2 | ||
414.8.a.i.1.1 | 4 | 1.1 | even | 1 | trivial |