Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [207,8,Mod(1,207)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(207, 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("207.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 207 = 3^{2} \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 207.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: | \(64.6637002752\) |
Analytic rank: | \(1\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 757x^{6} - 1170x^{5} + 170343x^{4} + 424132x^{3} - 9973075x^{2} - 5161010x + 130545120 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{6}\cdot 3^{2} \) |
Twist minimal: | no (minimal twist has level 69) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.6 | ||
Root | \(5.38924\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 207.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.38924 | 0.211181 | 0.105590 | − | 0.994410i | \(-0.466327\pi\) | ||||
0.105590 | + | 0.994410i | \(0.466327\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −122.292 | −0.955403 | ||||||||
\(5\) | 147.281 | 0.526927 | 0.263464 | − | 0.964669i | \(-0.415135\pi\) | ||||
0.263464 | + | 0.964669i | \(0.415135\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1223.93 | −1.34869 | −0.674347 | − | 0.738415i | \(-0.735575\pi\) | ||||
−0.674347 | + | 0.738415i | \(0.735575\pi\) | |||||||
\(8\) | −598.006 | −0.412944 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 351.889 | 0.111277 | ||||||||
\(11\) | 1637.33 | 0.370904 | 0.185452 | − | 0.982653i | \(-0.440625\pi\) | ||||
0.185452 | + | 0.982653i | \(0.440625\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 12894.7 | 1.62784 | 0.813919 | − | 0.580978i | \(-0.197330\pi\) | ||||
0.813919 | + | 0.580978i | \(0.197330\pi\) | |||||||
\(14\) | −2924.26 | −0.284818 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 14224.5 | 0.868197 | ||||||||
\(17\) | 12052.3 | 0.594977 | 0.297489 | − | 0.954725i | \(-0.403851\pi\) | ||||
0.297489 | + | 0.954725i | \(0.403851\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 27609.1 | 0.923454 | 0.461727 | − | 0.887022i | \(-0.347230\pi\) | ||||
0.461727 | + | 0.887022i | \(0.347230\pi\) | |||||||
\(20\) | −18011.2 | −0.503428 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 3911.97 | 0.0783279 | ||||||||
\(23\) | −12167.0 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −56433.4 | −0.722348 | ||||||||
\(26\) | 30808.6 | 0.343768 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 149676. | 1.28855 | ||||||||
\(29\) | −240721. | −1.83283 | −0.916413 | − | 0.400235i | \(-0.868929\pi\) | ||||
−0.916413 | + | 0.400235i | \(0.868929\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −128196. | −0.772874 | −0.386437 | − | 0.922316i | \(-0.626294\pi\) | ||||
−0.386437 | + | 0.922316i | \(0.626294\pi\) | |||||||
\(32\) | 110531. | 0.596290 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 28795.9 | 0.125648 | ||||||||
\(35\) | −180261. | −0.710664 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 179159. | 0.581476 | 0.290738 | − | 0.956803i | \(-0.406099\pi\) | ||||
0.290738 | + | 0.956803i | \(0.406099\pi\) | |||||||
\(38\) | 65964.8 | 0.195016 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −88074.8 | −0.217591 | ||||||||
\(41\) | −473457. | −1.07285 | −0.536423 | − | 0.843949i | \(-0.680225\pi\) | ||||
−0.536423 | + | 0.843949i | \(0.680225\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 936296. | 1.79586 | 0.897932 | − | 0.440135i | \(-0.145069\pi\) | ||||
0.897932 | + | 0.440135i | \(0.145069\pi\) | |||||||
\(44\) | −200232. | −0.354363 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −29069.9 | −0.0440343 | ||||||||
\(47\) | −796871. | −1.11956 | −0.559778 | − | 0.828643i | \(-0.689113\pi\) | ||||
−0.559778 | + | 0.828643i | \(0.689113\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 674461. | 0.818975 | ||||||||
\(50\) | −134833. | −0.152546 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.57692e6 | −1.55524 | ||||||||
\(53\) | 2.04568e6 | 1.88743 | 0.943717 | − | 0.330755i | \(-0.107303\pi\) | ||||
0.943717 | + | 0.330755i | \(0.107303\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 241147. | 0.195440 | ||||||||
\(56\) | 731918. | 0.556935 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −575140. | −0.387058 | ||||||||
\(59\) | −1.90819e6 | −1.20959 | −0.604796 | − | 0.796380i | \(-0.706746\pi\) | ||||
−0.604796 | + | 0.796380i | \(0.706746\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.32363e6 | −1.87481 | −0.937407 | − | 0.348236i | \(-0.886781\pi\) | ||||
−0.937407 | + | 0.348236i | \(0.886781\pi\) | |||||||
\(62\) | −306291. | −0.163216 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −1.55666e6 | −0.742272 | ||||||||
\(65\) | 1.89915e6 | 0.857752 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −285366. | −0.115915 | −0.0579576 | − | 0.998319i | \(-0.518459\pi\) | ||||
−0.0579576 | + | 0.998319i | \(0.518459\pi\) | |||||||
\(68\) | −1.47390e6 | −0.568443 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −430687. | −0.150079 | ||||||||
\(71\) | −3.91888e6 | −1.29944 | −0.649722 | − | 0.760172i | \(-0.725115\pi\) | ||||
−0.649722 | + | 0.760172i | \(0.725115\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −3.52247e6 | −1.05978 | −0.529891 | − | 0.848065i | \(-0.677767\pi\) | ||||
−0.529891 | + | 0.848065i | \(0.677767\pi\) | |||||||
\(74\) | 428053. | 0.122797 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −3.37636e6 | −0.882270 | ||||||||
\(77\) | −2.00398e6 | −0.500236 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 1.10676e6 | 0.252556 | 0.126278 | − | 0.991995i | \(-0.459697\pi\) | ||||
0.126278 | + | 0.991995i | \(0.459697\pi\) | |||||||
\(80\) | 2.09500e6 | 0.457477 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.13120e6 | −0.226565 | ||||||||
\(83\) | 3.81576e6 | 0.732501 | 0.366250 | − | 0.930516i | \(-0.380641\pi\) | ||||
0.366250 | + | 0.930516i | \(0.380641\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.77508e6 | 0.313510 | ||||||||
\(86\) | 2.23703e6 | 0.379252 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −979134. | −0.153163 | ||||||||
\(89\) | −5.29119e6 | −0.795588 | −0.397794 | − | 0.917475i | \(-0.630224\pi\) | ||||
−0.397794 | + | 0.917475i | \(0.630224\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.57823e7 | −2.19546 | ||||||||
\(92\) | 1.48792e6 | 0.199215 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.90392e6 | −0.236429 | ||||||||
\(95\) | 4.06629e6 | 0.486593 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 6.41098e6 | 0.713220 | 0.356610 | − | 0.934253i | \(-0.383932\pi\) | ||||
0.356610 | + | 0.934253i | \(0.383932\pi\) | |||||||
\(98\) | 1.61145e6 | 0.172952 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 6.90133e6 | 0.690133 | ||||||||
\(101\) | −7.39048e6 | −0.713752 | −0.356876 | − | 0.934152i | \(-0.616158\pi\) | ||||
−0.356876 | + | 0.934152i | \(0.616158\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 6.97336e6 | 0.628799 | 0.314400 | − | 0.949291i | \(-0.398197\pi\) | ||||
0.314400 | + | 0.949291i | \(0.398197\pi\) | |||||||
\(104\) | −7.71114e6 | −0.672205 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 4.88761e6 | 0.398590 | ||||||||
\(107\) | 1.70173e7 | 1.34291 | 0.671456 | − | 0.741045i | \(-0.265669\pi\) | ||||
0.671456 | + | 0.741045i | \(0.265669\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −4.11126e6 | −0.304076 | −0.152038 | − | 0.988375i | \(-0.548584\pi\) | ||||
−0.152038 | + | 0.988375i | \(0.548584\pi\) | |||||||
\(110\) | 576158. | 0.0412731 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −1.74098e7 | −1.17093 | ||||||||
\(113\) | −2.09127e7 | −1.36344 | −0.681721 | − | 0.731613i | \(-0.738768\pi\) | ||||
−0.681721 | + | 0.731613i | \(0.738768\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −1.79196e6 | −0.109872 | ||||||||
\(116\) | 2.94381e7 | 1.75109 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −4.55912e6 | −0.255443 | ||||||||
\(119\) | −1.47512e7 | −0.802442 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.68063e7 | −0.862430 | ||||||||
\(122\) | −7.94095e6 | −0.395925 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1.56773e7 | 0.738406 | ||||||||
\(125\) | −1.98178e7 | −0.907552 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2.31258e7 | 1.00181 | 0.500903 | − | 0.865503i | \(-0.333001\pi\) | ||||
0.500903 | + | 0.865503i | \(0.333001\pi\) | |||||||
\(128\) | −1.78671e7 | −0.753044 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 4.53752e6 | 0.181141 | ||||||||
\(131\) | −4.03840e7 | −1.56950 | −0.784748 | − | 0.619815i | \(-0.787208\pi\) | ||||
−0.784748 | + | 0.619815i | \(0.787208\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −3.37917e7 | −1.24546 | ||||||||
\(134\) | −681808. | −0.0244791 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −7.20738e6 | −0.245692 | ||||||||
\(137\) | −4.05545e7 | −1.34746 | −0.673732 | − | 0.738976i | \(-0.735310\pi\) | ||||
−0.673732 | + | 0.738976i | \(0.735310\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −2.68652e7 | −0.848474 | −0.424237 | − | 0.905551i | \(-0.639458\pi\) | ||||
−0.424237 | + | 0.905551i | \(0.639458\pi\) | |||||||
\(140\) | 2.20444e7 | 0.678970 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −9.36314e6 | −0.274418 | ||||||||
\(143\) | 2.11130e7 | 0.603772 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −3.54536e7 | −0.965766 | ||||||||
\(146\) | −8.41602e6 | −0.223806 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2.19096e7 | −0.555544 | ||||||||
\(149\) | 1.26633e7 | 0.313614 | 0.156807 | − | 0.987629i | \(-0.449880\pi\) | ||||
0.156807 | + | 0.987629i | \(0.449880\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 840099. | 0.0198569 | 0.00992844 | − | 0.999951i | \(-0.496840\pi\) | ||||
0.00992844 | + | 0.999951i | \(0.496840\pi\) | |||||||
\(152\) | −1.65104e7 | −0.381335 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −4.78798e6 | −0.105640 | ||||||||
\(155\) | −1.88808e7 | −0.407248 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −960571. | −0.0198098 | −0.00990491 | − | 0.999951i | \(-0.503153\pi\) | ||||
−0.00990491 | + | 0.999951i | \(0.503153\pi\) | |||||||
\(158\) | 2.64431e6 | 0.0533350 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.62790e7 | 0.314202 | ||||||||
\(161\) | 1.48916e7 | 0.281222 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 3.15848e7 | 0.571245 | 0.285622 | − | 0.958342i | \(-0.407800\pi\) | ||||
0.285622 | + | 0.958342i | \(0.407800\pi\) | |||||||
\(164\) | 5.78998e7 | 1.02500 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 9.11677e6 | 0.154690 | ||||||||
\(167\) | 7.78579e7 | 1.29358 | 0.646792 | − | 0.762666i | \(-0.276110\pi\) | ||||
0.646792 | + | 0.762666i | \(0.276110\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.03526e8 | 1.64986 | ||||||||
\(170\) | 4.24108e6 | 0.0662072 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1.14501e8 | −1.71577 | ||||||||
\(173\) | −5.01041e7 | −0.735719 | −0.367860 | − | 0.929881i | \(-0.619909\pi\) | ||||
−0.367860 | + | 0.929881i | \(0.619909\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 6.90705e7 | 0.974226 | ||||||||
\(176\) | 2.32903e7 | 0.322018 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −1.26419e7 | −0.168013 | ||||||||
\(179\) | 3.80878e7 | 0.496365 | 0.248182 | − | 0.968713i | \(-0.420167\pi\) | ||||
0.248182 | + | 0.968713i | \(0.420167\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3.63781e7 | 0.456000 | 0.228000 | − | 0.973661i | \(-0.426781\pi\) | ||||
0.228000 | + | 0.973661i | \(0.426781\pi\) | |||||||
\(182\) | −3.77076e7 | −0.463638 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 7.27594e6 | 0.0861047 | ||||||||
\(185\) | 2.63866e7 | 0.306396 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.97337e7 | 0.220679 | ||||||||
\(188\) | 9.74506e7 | 1.06963 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 9.71534e6 | 0.102759 | ||||||||
\(191\) | −9.38592e7 | −0.974676 | −0.487338 | − | 0.873214i | \(-0.662032\pi\) | ||||
−0.487338 | + | 0.873214i | \(0.662032\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −9.36357e7 | −0.937543 | −0.468771 | − | 0.883320i | \(-0.655303\pi\) | ||||
−0.468771 | + | 0.883320i | \(0.655303\pi\) | |||||||
\(194\) | 1.53174e7 | 0.150618 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −8.24809e7 | −0.782451 | ||||||||
\(197\) | −6.82715e7 | −0.636220 | −0.318110 | − | 0.948054i | \(-0.603048\pi\) | ||||
−0.318110 | + | 0.948054i | \(0.603048\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 6.37165e7 | 0.573147 | 0.286573 | − | 0.958058i | \(-0.407484\pi\) | ||||
0.286573 | + | 0.958058i | \(0.407484\pi\) | |||||||
\(200\) | 3.37475e7 | 0.298289 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.76576e7 | −0.150731 | ||||||||
\(203\) | 2.94626e8 | 2.47192 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −6.97311e7 | −0.565312 | ||||||||
\(206\) | 1.66610e7 | 0.132790 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 1.83422e8 | 1.41328 | ||||||||
\(209\) | 4.52053e7 | 0.342513 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.67268e7 | −0.269150 | −0.134575 | − | 0.990903i | \(-0.542967\pi\) | ||||
−0.134575 | + | 0.990903i | \(0.542967\pi\) | |||||||
\(212\) | −2.50169e8 | −1.80326 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 4.06584e7 | 0.283597 | ||||||||
\(215\) | 1.37898e8 | 0.946289 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.56903e8 | 1.04237 | ||||||||
\(218\) | −9.82278e6 | −0.0642150 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −2.94902e7 | −0.186723 | ||||||||
\(221\) | 1.55412e8 | 0.968526 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.94555e8 | 1.17483 | 0.587415 | − | 0.809286i | \(-0.300146\pi\) | ||||
0.587415 | + | 0.809286i | \(0.300146\pi\) | |||||||
\(224\) | −1.35282e8 | −0.804213 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.99655e7 | −0.287933 | ||||||||
\(227\) | −2.74851e8 | −1.55958 | −0.779789 | − | 0.626043i | \(-0.784674\pi\) | ||||
−0.779789 | + | 0.626043i | \(0.784674\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.43628e8 | −0.790344 | −0.395172 | − | 0.918607i | \(-0.629315\pi\) | ||||
−0.395172 | + | 0.918607i | \(0.629315\pi\) | |||||||
\(230\) | −4.28143e6 | −0.0232029 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.43953e8 | 0.756854 | ||||||||
\(233\) | −3.20512e8 | −1.65996 | −0.829982 | − | 0.557790i | \(-0.811649\pi\) | ||||
−0.829982 | + | 0.557790i | \(0.811649\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.17364e8 | −0.589924 | ||||||||
\(236\) | 2.33355e8 | 1.15565 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −3.52442e7 | −0.169460 | ||||||||
\(239\) | 4.41622e7 | 0.209247 | 0.104623 | − | 0.994512i | \(-0.466636\pi\) | ||||
0.104623 | + | 0.994512i | \(0.466636\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 7.53980e7 | 0.346977 | 0.173488 | − | 0.984836i | \(-0.444496\pi\) | ||||
0.173488 | + | 0.984836i | \(0.444496\pi\) | |||||||
\(242\) | −4.01543e7 | −0.182129 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 4.06452e8 | 1.79120 | ||||||||
\(245\) | 9.93351e7 | 0.431540 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 3.56013e8 | 1.50323 | ||||||||
\(248\) | 7.66620e7 | 0.319153 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −4.73496e7 | −0.191658 | ||||||||
\(251\) | −7.67520e7 | −0.306360 | −0.153180 | − | 0.988198i | \(-0.548951\pi\) | ||||
−0.153180 | + | 0.988198i | \(0.548951\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.99214e7 | −0.0773389 | ||||||||
\(254\) | 5.52530e7 | 0.211562 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.56563e8 | 0.583243 | ||||||||
\(257\) | −8.08367e6 | −0.0297059 | −0.0148529 | − | 0.999890i | \(-0.504728\pi\) | ||||
−0.0148529 | + | 0.999890i | \(0.504728\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −2.19278e8 | −0.784234 | ||||||||
\(260\) | −2.32250e8 | −0.819499 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −9.64871e7 | −0.331448 | ||||||||
\(263\) | −2.78979e8 | −0.945640 | −0.472820 | − | 0.881159i | \(-0.656764\pi\) | ||||
−0.472820 | + | 0.881159i | \(0.656764\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 3.01289e8 | 0.994540 | ||||||||
\(266\) | −8.07364e7 | −0.263017 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 3.48978e7 | 0.110746 | ||||||||
\(269\) | 3.28037e8 | 1.02752 | 0.513760 | − | 0.857934i | \(-0.328252\pi\) | ||||
0.513760 | + | 0.857934i | \(0.328252\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.91549e8 | −0.584639 | −0.292319 | − | 0.956321i | \(-0.594427\pi\) | ||||
−0.292319 | + | 0.956321i | \(0.594427\pi\) | |||||||
\(272\) | 1.71439e8 | 0.516557 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −9.68944e7 | −0.284558 | ||||||||
\(275\) | −9.24001e7 | −0.267922 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1.80215e8 | 0.509463 | 0.254731 | − | 0.967012i | \(-0.418013\pi\) | ||||
0.254731 | + | 0.967012i | \(0.418013\pi\) | |||||||
\(278\) | −6.41874e7 | −0.179181 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.07797e8 | 0.293464 | ||||||||
\(281\) | 1.57503e8 | 0.423465 | 0.211733 | − | 0.977328i | \(-0.432089\pi\) | ||||
0.211733 | + | 0.977328i | \(0.432089\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.94865e8 | 1.82242 | 0.911208 | − | 0.411946i | \(-0.135151\pi\) | ||||
0.911208 | + | 0.411946i | \(0.135151\pi\) | |||||||
\(284\) | 4.79246e8 | 1.24149 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 5.04439e7 | 0.127505 | ||||||||
\(287\) | 5.79479e8 | 1.44694 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.65080e8 | −0.646002 | ||||||||
\(290\) | −8.47070e7 | −0.203951 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 4.30768e8 | 1.01252 | ||||||||
\(293\) | 3.61524e8 | 0.839653 | 0.419827 | − | 0.907604i | \(-0.362091\pi\) | ||||
0.419827 | + | 0.907604i | \(0.362091\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.81039e8 | −0.637367 | ||||||||
\(296\) | −1.07138e8 | −0.240117 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 3.02557e7 | 0.0662293 | ||||||||
\(299\) | −1.56890e8 | −0.339428 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −1.14596e9 | −2.42207 | ||||||||
\(302\) | 2.00720e6 | 0.00419339 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 3.92727e8 | 0.801740 | ||||||||
\(305\) | −4.89506e8 | −0.987891 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −3.33653e8 | −0.658129 | −0.329065 | − | 0.944307i | \(-0.606733\pi\) | ||||
−0.329065 | + | 0.944307i | \(0.606733\pi\) | |||||||
\(308\) | 2.45069e8 | 0.477927 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4.51107e7 | −0.0860031 | ||||||||
\(311\) | −2.96226e8 | −0.558421 | −0.279211 | − | 0.960230i | \(-0.590073\pi\) | ||||
−0.279211 | + | 0.960230i | \(0.590073\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.47401e8 | −0.640363 | −0.320181 | − | 0.947356i | \(-0.603744\pi\) | ||||
−0.320181 | + | 0.947356i | \(0.603744\pi\) | |||||||
\(314\) | −2.29503e6 | −0.00418346 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.35347e8 | −0.241293 | ||||||||
\(317\) | 2.12080e8 | 0.373931 | 0.186966 | − | 0.982366i | \(-0.440135\pi\) | ||||
0.186966 | + | 0.982366i | \(0.440135\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −3.94140e8 | −0.679803 | ||||||||
\(320\) | −2.29265e8 | −0.391123 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 3.55795e7 | 0.0593887 | ||||||||
\(323\) | 3.32755e8 | 0.549434 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −7.27695e8 | −1.17586 | ||||||||
\(326\) | 7.54638e7 | 0.120636 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 2.83130e8 | 0.443025 | ||||||||
\(329\) | 9.75314e8 | 1.50994 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.92104e8 | 0.594296 | 0.297148 | − | 0.954831i | \(-0.403964\pi\) | ||||
0.297148 | + | 0.954831i | \(0.403964\pi\) | |||||||
\(332\) | −4.66636e8 | −0.699833 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 1.86021e8 | 0.273180 | ||||||||
\(335\) | −4.20289e7 | −0.0610789 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9.07353e8 | −1.29143 | −0.645716 | − | 0.763578i | \(-0.723441\pi\) | ||||
−0.645716 | + | 0.763578i | \(0.723441\pi\) | |||||||
\(338\) | 2.47348e8 | 0.348418 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −2.17077e8 | −0.299528 | ||||||||
\(341\) | −2.09899e8 | −0.286662 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 1.82465e8 | 0.244147 | ||||||||
\(344\) | −5.59911e8 | −0.741591 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −1.19711e8 | −0.155370 | ||||||||
\(347\) | 3.73740e8 | 0.480194 | 0.240097 | − | 0.970749i | \(-0.422821\pi\) | ||||
0.240097 | + | 0.970749i | \(0.422821\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.88713e8 | −0.237636 | −0.118818 | − | 0.992916i | \(-0.537910\pi\) | ||||
−0.118818 | + | 0.992916i | \(0.537910\pi\) | |||||||
\(350\) | 1.65026e8 | 0.205738 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.80975e8 | 0.221167 | ||||||||
\(353\) | −1.22544e9 | −1.48279 | −0.741395 | − | 0.671069i | \(-0.765836\pi\) | ||||
−0.741395 | + | 0.671069i | \(0.765836\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −5.77175e8 | −0.684712 | ||||||||
\(356\) | 6.47067e8 | 0.760107 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 9.10010e7 | 0.104823 | ||||||||
\(359\) | 4.27509e8 | 0.487657 | 0.243829 | − | 0.969818i | \(-0.421597\pi\) | ||||
0.243829 | + | 0.969818i | \(0.421597\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.31607e8 | −0.147232 | ||||||||
\(362\) | 8.69159e7 | 0.0962984 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 1.93004e9 | 2.09754 | ||||||||
\(365\) | −5.18791e8 | −0.558428 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.58489e9 | −1.67366 | −0.836831 | − | 0.547462i | \(-0.815594\pi\) | ||||
−0.836831 | + | 0.547462i | \(0.815594\pi\) | |||||||
\(368\) | −1.73070e8 | −0.181032 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 6.30439e7 | 0.0647049 | ||||||||
\(371\) | −2.50377e9 | −2.54557 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.23598e9 | −1.23320 | −0.616598 | − | 0.787278i | \(-0.711490\pi\) | ||||
−0.616598 | + | 0.787278i | \(0.711490\pi\) | |||||||
\(374\) | 4.71484e7 | 0.0466033 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 4.76534e8 | 0.462313 | ||||||||
\(377\) | −3.10404e9 | −2.98354 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 6.22899e8 | 0.587733 | 0.293867 | − | 0.955846i | \(-0.405058\pi\) | ||||
0.293867 | + | 0.955846i | \(0.405058\pi\) | |||||||
\(380\) | −4.97273e8 | −0.464892 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −2.24252e8 | −0.205833 | ||||||||
\(383\) | 1.18281e9 | 1.07577 | 0.537884 | − | 0.843019i | \(-0.319224\pi\) | ||||
0.537884 | + | 0.843019i | \(0.319224\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.95147e8 | −0.263588 | ||||||||
\(386\) | −2.23718e8 | −0.197991 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −7.84009e8 | −0.681412 | ||||||||
\(389\) | −7.89553e8 | −0.680077 | −0.340038 | − | 0.940412i | \(-0.610440\pi\) | ||||
−0.340038 | + | 0.940412i | \(0.610440\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.46641e8 | −0.124061 | ||||||||
\(392\) | −4.03332e8 | −0.338191 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −1.63117e8 | −0.134358 | ||||||||
\(395\) | 1.63004e8 | 0.133079 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.58576e9 | −1.27195 | −0.635977 | − | 0.771708i | \(-0.719403\pi\) | ||||
−0.635977 | + | 0.771708i | \(0.719403\pi\) | |||||||
\(398\) | 1.52234e8 | 0.121038 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −8.02739e8 | −0.627140 | ||||||||
\(401\) | 9.63924e8 | 0.746513 | 0.373256 | − | 0.927728i | \(-0.378241\pi\) | ||||
0.373256 | + | 0.927728i | \(0.378241\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.65306e9 | −1.25811 | ||||||||
\(404\) | 9.03793e8 | 0.681921 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 7.03931e8 | 0.522022 | ||||||||
\(407\) | 2.93342e8 | 0.215672 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.37917e9 | 0.996752 | 0.498376 | − | 0.866961i | \(-0.333930\pi\) | ||||
0.498376 | + | 0.866961i | \(0.333930\pi\) | |||||||
\(410\) | −1.66604e8 | −0.119383 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −8.52783e8 | −0.600756 | ||||||||
\(413\) | 2.33549e9 | 1.63137 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 5.61988e8 | 0.385975 | ||||||||
\(416\) | 1.42526e9 | 0.970664 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.08006e8 | 0.0723322 | ||||||||
\(419\) | −2.43158e9 | −1.61487 | −0.807437 | − | 0.589953i | \(-0.799146\pi\) | ||||
−0.807437 | + | 0.589953i | \(0.799146\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.63767e7 | 0.0172279 | 0.00861396 | − | 0.999963i | \(-0.497258\pi\) | ||||
0.00861396 | + | 0.999963i | \(0.497258\pi\) | |||||||
\(422\) | −8.77491e7 | −0.0568393 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −1.22333e9 | −0.779404 | ||||||||
\(425\) | −6.80155e8 | −0.429780 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.06789e9 | 2.52855 | ||||||||
\(428\) | −2.08107e9 | −1.28302 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3.29472e8 | 0.199838 | ||||||||
\(431\) | 2.18762e9 | 1.31614 | 0.658070 | − | 0.752957i | \(-0.271373\pi\) | ||||
0.658070 | + | 0.752957i | \(0.271373\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.05899e6 | −0.000626880 0 | −0.000313440 | − | 1.00000i | \(-0.500100\pi\) | ||||
−0.000313440 | 1.00000i | \(0.500100\pi\) | ||||||||
\(434\) | 3.74879e8 | 0.220129 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 5.02772e8 | 0.290515 | ||||||||
\(437\) | −3.35920e8 | −0.192553 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.62942e9 | 1.48332 | 0.741660 | − | 0.670776i | \(-0.234039\pi\) | ||||
0.741660 | + | 0.670776i | \(0.234039\pi\) | |||||||
\(440\) | −1.44207e8 | −0.0807055 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3.71316e8 | 0.204534 | ||||||||
\(443\) | −6.92479e8 | −0.378437 | −0.189219 | − | 0.981935i | \(-0.560595\pi\) | ||||
−0.189219 | + | 0.981935i | \(0.560595\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −7.79289e8 | −0.419217 | ||||||||
\(446\) | 4.64838e8 | 0.248102 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.90524e9 | 1.00110 | ||||||||
\(449\) | 1.34070e9 | 0.698990 | 0.349495 | − | 0.936938i | \(-0.386353\pi\) | ||||
0.349495 | + | 0.936938i | \(0.386353\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −7.75206e8 | −0.397923 | ||||||||
\(452\) | 2.55745e9 | 1.30264 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −6.56685e8 | −0.329353 | ||||||||
\(455\) | −2.32442e9 | −1.15685 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.96222e8 | 0.0961701 | 0.0480851 | − | 0.998843i | \(-0.484688\pi\) | ||||
0.0480851 | + | 0.998843i | \(0.484688\pi\) | |||||||
\(458\) | −3.43162e8 | −0.166905 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 2.19142e8 | 0.104972 | ||||||||
\(461\) | 2.83515e9 | 1.34779 | 0.673895 | − | 0.738827i | \(-0.264620\pi\) | ||||
0.673895 | + | 0.738827i | \(0.264620\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −2.19801e9 | −1.02919 | −0.514595 | − | 0.857433i | \(-0.672058\pi\) | ||||
−0.514595 | + | 0.857433i | \(0.672058\pi\) | |||||||
\(464\) | −3.42415e9 | −1.59125 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −7.65780e8 | −0.350553 | ||||||||
\(467\) | −1.42423e9 | −0.647100 | −0.323550 | − | 0.946211i | \(-0.604876\pi\) | ||||
−0.323550 | + | 0.946211i | \(0.604876\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 3.49268e8 | 0.156334 | ||||||||
\(470\) | −2.80410e8 | −0.124581 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 1.14111e9 | 0.499494 | ||||||||
\(473\) | 1.53302e9 | 0.666093 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.55808e9 | −0.667055 | ||||||||
\(476\) | 1.80395e9 | 0.766655 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.05514e8 | 0.0441889 | ||||||||
\(479\) | −3.08517e9 | −1.28264 | −0.641320 | − | 0.767274i | \(-0.721613\pi\) | ||||
−0.641320 | + | 0.767274i | \(0.721613\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.31021e9 | 0.946549 | ||||||||
\(482\) | 1.80144e8 | 0.0732749 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.05527e9 | 0.823968 | ||||||||
\(485\) | 9.44214e8 | 0.375815 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −2.32140e9 | −0.910748 | −0.455374 | − | 0.890300i | \(-0.650494\pi\) | ||||
−0.455374 | + | 0.890300i | \(0.650494\pi\) | |||||||
\(488\) | 1.98755e9 | 0.774193 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 2.37335e8 | 0.0911331 | ||||||||
\(491\) | 3.13714e8 | 0.119605 | 0.0598024 | − | 0.998210i | \(-0.480953\pi\) | ||||
0.0598024 | + | 0.998210i | \(0.480953\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −2.90125e9 | −1.09049 | ||||||||
\(494\) | 8.50600e8 | 0.317454 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.82353e9 | −0.671007 | ||||||||
\(497\) | 4.79643e9 | 1.75255 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 5.75078e8 | 0.207193 | 0.103596 | − | 0.994619i | \(-0.466965\pi\) | ||||
0.103596 | + | 0.994619i | \(0.466965\pi\) | |||||||
\(500\) | 2.42356e9 | 0.867077 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −1.83379e8 | −0.0646973 | ||||||||
\(503\) | 1.87631e9 | 0.657379 | 0.328690 | − | 0.944438i | \(-0.393393\pi\) | ||||
0.328690 | + | 0.944438i | \(0.393393\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.08847e9 | −0.376096 | ||||||||
\(506\) | −4.75970e7 | −0.0163325 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.82809e9 | −0.957128 | ||||||||
\(509\) | −4.24575e9 | −1.42706 | −0.713529 | − | 0.700625i | \(-0.752904\pi\) | ||||
−0.713529 | + | 0.700625i | \(0.752904\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 4.31125e9 | 1.42932 | ||||||||
\(512\) | 2.66106e9 | 0.876214 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −1.93138e7 | −0.00627331 | ||||||||
\(515\) | 1.02704e9 | 0.331331 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −1.30474e9 | −0.415248 | ||||||||
\(518\) | −5.23907e8 | −0.165615 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.13570e9 | −0.354203 | ||||||||
\(521\) | −2.59048e9 | −0.802506 | −0.401253 | − | 0.915967i | \(-0.631425\pi\) | ||||
−0.401253 | + | 0.915967i | \(0.631425\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 6.54783e8 | 0.200144 | 0.100072 | − | 0.994980i | \(-0.468093\pi\) | ||||
0.100072 | + | 0.994980i | \(0.468093\pi\) | |||||||
\(524\) | 4.93863e9 | 1.49950 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −6.66547e8 | −0.199701 | ||||||||
\(527\) | −1.54506e9 | −0.459842 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.48036e8 | 0.0434783 | ||||||||
\(530\) | 7.19851e8 | 0.210028 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4.13243e9 | 1.18991 | ||||||||
\(533\) | −6.10511e9 | −1.74642 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 2.50632e9 | 0.707617 | ||||||||
\(536\) | 1.70651e8 | 0.0478665 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 7.83759e8 | 0.216992 | ||||||||
\(539\) | 1.10432e9 | 0.303761 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −4.31638e9 | −1.17200 | −0.586002 | − | 0.810310i | \(-0.699299\pi\) | ||||
−0.586002 | + | 0.810310i | \(0.699299\pi\) | |||||||
\(542\) | −4.57657e8 | −0.123465 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.33215e9 | 0.354779 | ||||||||
\(545\) | −6.05509e8 | −0.160226 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −5.33812e9 | −1.39455 | −0.697273 | − | 0.716806i | \(-0.745603\pi\) | ||||
−0.697273 | + | 0.716806i | \(0.745603\pi\) | |||||||
\(548\) | 4.95947e9 | 1.28737 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −2.20766e8 | −0.0565800 | ||||||||
\(551\) | −6.64610e9 | −1.69253 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −1.35459e9 | −0.340621 | ||||||||
\(554\) | 4.30577e8 | 0.107589 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 3.28539e9 | 0.810634 | ||||||||
\(557\) | 5.69967e9 | 1.39751 | 0.698757 | − | 0.715359i | \(-0.253737\pi\) | ||||
0.698757 | + | 0.715359i | \(0.253737\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1.20733e10 | 2.92337 | ||||||||
\(560\) | −2.56413e9 | −0.616996 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 3.76313e8 | 0.0894278 | ||||||||
\(563\) | −4.19873e9 | −0.991605 | −0.495802 | − | 0.868435i | \(-0.665126\pi\) | ||||
−0.495802 | + | 0.868435i | \(0.665126\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −3.08004e9 | −0.718434 | ||||||||
\(566\) | 1.66020e9 | 0.384860 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 2.34351e9 | 0.536597 | ||||||||
\(569\) | 1.69971e9 | 0.386795 | 0.193398 | − | 0.981120i | \(-0.438049\pi\) | ||||
0.193398 | + | 0.981120i | \(0.438049\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 6.47824e9 | 1.45623 | 0.728116 | − | 0.685454i | \(-0.240396\pi\) | ||||
0.728116 | + | 0.685454i | \(0.240396\pi\) | |||||||
\(572\) | −2.58194e9 | −0.576845 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 1.38451e9 | 0.305566 | ||||||||
\(575\) | 6.86625e8 | 0.150620 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.45826e9 | 0.749450 | 0.374725 | − | 0.927136i | \(-0.377737\pi\) | ||||
0.374725 | + | 0.927136i | \(0.377737\pi\) | |||||||
\(578\) | −6.33339e8 | −0.136423 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 4.33567e9 | 0.922695 | ||||||||
\(581\) | −4.67023e9 | −0.987920 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3.34945e9 | 0.700057 | ||||||||
\(584\) | 2.10646e9 | 0.437631 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 8.63766e8 | 0.177319 | ||||||||
\(587\) | −1.31138e9 | −0.267606 | −0.133803 | − | 0.991008i | \(-0.542719\pi\) | ||||
−0.133803 | + | 0.991008i | \(0.542719\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −3.53938e9 | −0.713714 | ||||||||
\(590\) | −6.71470e8 | −0.134600 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.54845e9 | 0.504836 | ||||||||
\(593\) | 9.08126e9 | 1.78836 | 0.894179 | − | 0.447709i | \(-0.147760\pi\) | ||||
0.894179 | + | 0.447709i | \(0.147760\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −2.17257e9 | −0.422828 | ||||||||
\(596\) | −1.54862e9 | −0.299628 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −3.74849e8 | −0.0716806 | ||||||||
\(599\) | 6.26416e8 | 0.119088 | 0.0595441 | − | 0.998226i | \(-0.481035\pi\) | ||||
0.0595441 | + | 0.998226i | \(0.481035\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.92718e9 | 1.86537 | 0.932686 | − | 0.360690i | \(-0.117459\pi\) | ||||
0.932686 | + | 0.360690i | \(0.117459\pi\) | |||||||
\(602\) | −2.73797e9 | −0.511495 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −1.02737e8 | −0.0189713 | ||||||||
\(605\) | −2.47525e9 | −0.454438 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.65614e9 | 0.300563 | 0.150282 | − | 0.988643i | \(-0.451982\pi\) | ||||
0.150282 | + | 0.988643i | \(0.451982\pi\) | |||||||
\(608\) | 3.05166e9 | 0.550647 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −1.16955e9 | −0.208624 | ||||||||
\(611\) | −1.02755e10 | −1.82245 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 4.45864e8 | 0.0781791 | 0.0390895 | − | 0.999236i | \(-0.487554\pi\) | ||||
0.0390895 | + | 0.999236i | \(0.487554\pi\) | |||||||
\(614\) | −7.97178e8 | −0.138984 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.19839e9 | 0.206569 | ||||||||
\(617\) | 6.91965e9 | 1.18600 | 0.593002 | − | 0.805201i | \(-0.297943\pi\) | ||||
0.593002 | + | 0.805201i | \(0.297943\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.02751e9 | −1.02146 | −0.510729 | − | 0.859742i | \(-0.670624\pi\) | ||||
−0.510729 | + | 0.859742i | \(0.670624\pi\) | |||||||
\(620\) | 2.30896e9 | 0.389086 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −7.07755e8 | −0.117928 | ||||||||
\(623\) | 6.47604e9 | 1.07300 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.49008e9 | 0.244134 | ||||||||
\(626\) | −8.30025e8 | −0.135232 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 1.17470e8 | 0.0189264 | ||||||||
\(629\) | 2.15928e9 | 0.345965 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −8.87449e9 | −1.40618 | −0.703089 | − | 0.711102i | \(-0.748197\pi\) | ||||
−0.703089 | + | 0.711102i | \(0.748197\pi\) | |||||||
\(632\) | −6.61848e8 | −0.104291 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 5.06709e8 | 0.0789671 | ||||||||
\(635\) | 3.40598e9 | 0.527879 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 8.69701e9 | 1.33316 | ||||||||
\(638\) | −9.41694e8 | −0.143561 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −2.63148e9 | −0.396799 | ||||||||
\(641\) | −6.81517e9 | −1.02205 | −0.511027 | − | 0.859565i | \(-0.670735\pi\) | ||||
−0.511027 | + | 0.859565i | \(0.670735\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −8.35764e9 | −1.23978 | −0.619891 | − | 0.784688i | \(-0.712823\pi\) | ||||
−0.619891 | + | 0.784688i | \(0.712823\pi\) | |||||||
\(644\) | −1.82111e9 | −0.268680 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 7.95031e8 | 0.116030 | ||||||||
\(647\) | −3.48454e9 | −0.505802 | −0.252901 | − | 0.967492i | \(-0.581385\pi\) | ||||
−0.252901 | + | 0.967492i | \(0.581385\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −3.12433e9 | −0.448643 | ||||||||
\(650\) | −1.73864e9 | −0.248320 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −3.86256e9 | −0.545769 | ||||||||
\(653\) | 1.41407e10 | 1.98736 | 0.993678 | − | 0.112267i | \(-0.0358110\pi\) | ||||
0.993678 | + | 0.112267i | \(0.0358110\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.94779e9 | −0.827010 | ||||||||
\(656\) | −6.73471e9 | −0.931441 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 2.33026e9 | 0.318870 | ||||||||
\(659\) | −4.91129e9 | −0.668492 | −0.334246 | − | 0.942486i | \(-0.608482\pi\) | ||||
−0.334246 | + | 0.942486i | \(0.608482\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 6.95658e8 | 0.0936894 | 0.0468447 | − | 0.998902i | \(-0.485083\pi\) | ||||
0.0468447 | + | 0.998902i | \(0.485083\pi\) | |||||||
\(662\) | 9.36830e8 | 0.125504 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −2.28185e9 | −0.302482 | ||||||||
\(665\) | −4.97686e9 | −0.656265 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.92885e9 | 0.382171 | ||||||||
\(668\) | −9.52136e9 | −1.23589 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.00417e8 | −0.0128987 | ||||||||
\(671\) | −5.44188e9 | −0.695376 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2.86105e9 | −0.361804 | −0.180902 | − | 0.983501i | \(-0.557902\pi\) | ||||
−0.180902 | + | 0.983501i | \(0.557902\pi\) | |||||||
\(674\) | −2.16788e9 | −0.272726 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.26604e10 | −1.57628 | ||||||||
\(677\) | 5.03345e9 | 0.623455 | 0.311728 | − | 0.950171i | \(-0.399092\pi\) | ||||
0.311728 | + | 0.950171i | \(0.399092\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −7.84659e9 | −0.961916 | ||||||||
\(680\) | −1.06151e9 | −0.129462 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −5.01499e8 | −0.0605376 | ||||||||
\(683\) | −7.71371e9 | −0.926383 | −0.463192 | − | 0.886258i | \(-0.653296\pi\) | ||||
−0.463192 | + | 0.886258i | \(0.653296\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −5.97289e9 | −0.710015 | ||||||||
\(686\) | 4.35953e8 | 0.0515591 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.33184e10 | 1.55916 | ||||||||
\(689\) | 2.63785e10 | 3.07244 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −1.62102e10 | −1.86903 | −0.934515 | − | 0.355923i | \(-0.884167\pi\) | ||||
−0.934515 | + | 0.355923i | \(0.884167\pi\) | |||||||
\(692\) | 6.12731e9 | 0.702908 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 8.92954e8 | 0.101408 | ||||||||
\(695\) | −3.95672e9 | −0.447084 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −5.70627e9 | −0.638319 | ||||||||
\(698\) | −4.50879e8 | −0.0501841 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −8.44674e9 | −0.930778 | ||||||||
\(701\) | −1.56994e10 | −1.72135 | −0.860674 | − | 0.509156i | \(-0.829958\pi\) | ||||
−0.860674 | + | 0.509156i | \(0.829958\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 4.94642e9 | 0.536967 | ||||||||
\(704\) | −2.54876e9 | −0.275312 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −2.92786e9 | −0.313137 | ||||||||
\(707\) | 9.04543e9 | 0.962634 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 8.60054e6 | 0.000906283 0 | 0.000453141 | − | 1.00000i | \(-0.499856\pi\) | ||||
0.000453141 | 1.00000i | \(0.499856\pi\) | ||||||||
\(710\) | −1.37901e9 | −0.144598 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 3.16416e9 | 0.328533 | ||||||||
\(713\) | 1.55976e9 | 0.161155 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 3.10953e9 | 0.318144 | ||||||||
\(716\) | −4.65782e9 | −0.474228 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 1.02142e9 | 0.102984 | ||||||||
\(719\) | 1.69098e10 | 1.69663 | 0.848314 | − | 0.529493i | \(-0.177618\pi\) | ||||
0.848314 | + | 0.529493i | \(0.177618\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −8.53491e9 | −0.848058 | ||||||||
\(722\) | −3.14441e8 | −0.0310927 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −4.44873e9 | −0.435663 | ||||||||
\(725\) | 1.35847e10 | 1.32394 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.35812e10 | 1.31089 | 0.655447 | − | 0.755242i | \(-0.272480\pi\) | ||||
0.655447 | + | 0.755242i | \(0.272480\pi\) | |||||||
\(728\) | 9.43790e9 | 0.906599 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −1.23952e9 | −0.117929 | ||||||||
\(731\) | 1.12846e10 | 1.06850 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −7.43282e9 | −0.697092 | −0.348546 | − | 0.937292i | \(-0.613324\pi\) | ||||
−0.348546 | + | 0.937292i | \(0.613324\pi\) | |||||||
\(734\) | −3.78668e9 | −0.353445 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.34483e9 | −0.124335 | ||||||||
\(737\) | −4.67238e8 | −0.0429934 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 5.64451e9 | 0.514483 | 0.257242 | − | 0.966347i | \(-0.417186\pi\) | ||||
0.257242 | + | 0.966347i | \(0.417186\pi\) | |||||||
\(740\) | −3.22686e9 | −0.292731 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.98210e9 | −0.537576 | ||||||||
\(743\) | 9.78408e9 | 0.875103 | 0.437552 | − | 0.899193i | \(-0.355846\pi\) | ||||
0.437552 | + | 0.899193i | \(0.355846\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.86506e9 | 0.165252 | ||||||||
\(746\) | −2.95306e9 | −0.260428 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −2.41326e9 | −0.210838 | ||||||||
\(749\) | −2.08280e10 | −1.81118 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.20646e10 | −1.03937 | −0.519687 | − | 0.854356i | \(-0.673952\pi\) | ||||
−0.519687 | + | 0.854356i | \(0.673952\pi\) | |||||||
\(752\) | −1.13351e10 | −0.971994 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −7.41629e9 | −0.630067 | ||||||||
\(755\) | 1.23730e8 | 0.0104631 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.24335e10 | 1.04174 | 0.520869 | − | 0.853637i | \(-0.325608\pi\) | ||||
0.520869 | + | 0.853637i | \(0.325608\pi\) | |||||||
\(758\) | 1.48825e9 | 0.124118 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −2.43167e9 | −0.200936 | ||||||||
\(761\) | −1.74989e10 | −1.43935 | −0.719673 | − | 0.694313i | \(-0.755708\pi\) | ||||
−0.719673 | + | 0.694313i | \(0.755708\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 5.03189e9 | 0.410105 | ||||||||
\(764\) | 1.14782e10 | 0.931208 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.82601e9 | 0.227182 | ||||||||
\(767\) | −2.46056e10 | −1.96902 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −8.61237e9 | −0.682937 | −0.341469 | − | 0.939893i | \(-0.610924\pi\) | ||||
−0.341469 | + | 0.939893i | \(0.610924\pi\) | |||||||
\(770\) | −7.05177e8 | −0.0556648 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.14509e10 | 0.895731 | ||||||||
\(773\) | 3.27403e9 | 0.254950 | 0.127475 | − | 0.991842i | \(-0.459313\pi\) | ||||
0.127475 | + | 0.991842i | \(0.459313\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 7.23454e9 | 0.558284 | ||||||||
\(776\) | −3.83381e9 | −0.294520 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −1.88643e9 | −0.143619 | ||||||||
\(779\) | −1.30717e10 | −0.990724 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −6.41649e9 | −0.481969 | ||||||||
\(782\) | −3.50360e8 | −0.0261994 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 9.59390e9 | 0.711032 | ||||||||
\(785\) | −1.41473e8 | −0.0104383 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.90391e10 | 1.39231 | 0.696154 | − | 0.717893i | \(-0.254893\pi\) | ||||
0.696154 | + | 0.717893i | \(0.254893\pi\) | |||||||
\(788\) | 8.34902e9 | 0.607846 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.89456e8 | 0.0281037 | ||||||||
\(791\) | 2.55957e10 | 1.83887 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −4.28574e10 | −3.05189 | ||||||||
\(794\) | −3.78876e9 | −0.268612 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −7.79198e9 | −0.547586 | ||||||||
\(797\) | 1.09654e10 | 0.767222 | 0.383611 | − | 0.923495i | \(-0.374680\pi\) | ||||
0.383611 | + | 0.923495i | \(0.374680\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −9.60416e9 | −0.666110 | ||||||||
\(800\) | −6.23762e9 | −0.430729 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2.30304e9 | 0.157649 | ||||||||
\(803\) | −5.76744e9 | −0.393078 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 2.19324e9 | 0.148184 | ||||||||
\(806\) | −3.94955e9 | −0.265690 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 4.41955e9 | 0.294740 | ||||||||
\(809\) | −2.54612e10 | −1.69067 | −0.845336 | − | 0.534235i | \(-0.820600\pi\) | ||||
−0.845336 | + | 0.534235i | \(0.820600\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.38636e10 | 0.912645 | 0.456323 | − | 0.889814i | \(-0.349166\pi\) | ||||
0.456323 | + | 0.889814i | \(0.349166\pi\) | |||||||
\(812\) | −3.60302e10 | −2.36168 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 7.00864e8 | 0.0455458 | ||||||||
\(815\) | 4.65184e9 | 0.301004 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 2.58503e10 | 1.65840 | ||||||||
\(818\) | 3.29517e9 | 0.210495 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 8.52752e9 | 0.540100 | ||||||||
\(821\) | −1.57708e10 | −0.994607 | −0.497304 | − | 0.867577i | \(-0.665677\pi\) | ||||
−0.497304 | + | 0.867577i | \(0.665677\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.42493e7 | −0.00339231 | −0.00169615 | − | 0.999999i | \(-0.500540\pi\) | ||||
−0.00169615 | + | 0.999999i | \(0.500540\pi\) | |||||||
\(824\) | −4.17011e9 | −0.259659 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.58004e9 | 0.344514 | ||||||||
\(827\) | 2.41236e10 | 1.48311 | 0.741554 | − | 0.670893i | \(-0.234089\pi\) | ||||
0.741554 | + | 0.670893i | \(0.234089\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.13296e7 | 0.00190991 | 0.000954956 | − | 1.00000i | \(-0.499696\pi\) | ||||
0.000954956 | 1.00000i | \(0.499696\pi\) | ||||||||
\(830\) | 1.34272e9 | 0.0815105 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.00727e10 | −1.20830 | ||||||||
\(833\) | 8.12884e9 | 0.487272 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.14670e10 | 0.681625 | ||||||||
\(836\) | −5.52822e9 | −0.327238 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5.80962e9 | −0.341031 | ||||||||
\(839\) | 2.29764e8 | 0.0134312 | 0.00671559 | − | 0.999977i | \(-0.497862\pi\) | ||||
0.00671559 | + | 0.999977i | \(0.497862\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.06968e10 | 2.35925 | ||||||||
\(842\) | 6.30202e7 | 0.00363821 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 4.49137e9 | 0.257147 | ||||||||
\(845\) | 1.52474e10 | 0.869354 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.05698e10 | 1.16315 | ||||||||
\(848\) | 2.90988e10 | 1.63866 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.62505e9 | −0.0907614 | ||||||||
\(851\) | −2.17982e9 | −0.121246 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −3.52100e10 | −1.94243 | −0.971213 | − | 0.238213i | \(-0.923439\pi\) | ||||
−0.971213 | + | 0.238213i | \(0.923439\pi\) | |||||||
\(854\) | 9.71916e9 | 0.533982 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.01765e10 | −0.554547 | ||||||||
\(857\) | −2.17887e10 | −1.18249 | −0.591246 | − | 0.806491i | \(-0.701364\pi\) | ||||
−0.591246 | + | 0.806491i | \(0.701364\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.04776e10 | 1.10231 | 0.551155 | − | 0.834403i | \(-0.314187\pi\) | ||||
0.551155 | + | 0.834403i | \(0.314187\pi\) | |||||||
\(860\) | −1.68638e10 | −0.904087 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 5.22676e9 | 0.277944 | ||||||||
\(863\) | −2.39053e9 | −0.126606 | −0.0633032 | − | 0.997994i | \(-0.520164\pi\) | ||||
−0.0633032 | + | 0.997994i | \(0.520164\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.37937e9 | −0.387670 | ||||||||
\(866\) | −2.53018e6 | −0.000132385 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −1.91879e10 | −0.995883 | ||||||||
\(869\) | 1.81213e9 | 0.0936741 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.67972e9 | −0.188691 | ||||||||
\(872\) | 2.45856e9 | 0.125566 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −8.02594e8 | −0.0406636 | ||||||||
\(875\) | 2.42557e10 | 1.22401 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −5.33337e9 | −0.266995 | −0.133497 | − | 0.991049i | \(-0.542621\pi\) | ||||
−0.133497 | + | 0.991049i | \(0.542621\pi\) | |||||||
\(878\) | 6.28232e9 | 0.313249 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 3.43020e9 | 0.169680 | ||||||||
\(881\) | 7.74528e9 | 0.381612 | 0.190806 | − | 0.981628i | \(-0.438890\pi\) | ||||
0.190806 | + | 0.981628i | \(0.438890\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −7.35743e9 | −0.359636 | −0.179818 | − | 0.983700i | \(-0.557551\pi\) | ||||
−0.179818 | + | 0.983700i | \(0.557551\pi\) | |||||||
\(884\) | −1.90056e10 | −0.925332 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −1.65450e9 | −0.0799187 | ||||||||
\(887\) | −2.53512e10 | −1.21974 | −0.609869 | − | 0.792502i | \(-0.708778\pi\) | ||||
−0.609869 | + | 0.792502i | \(0.708778\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −2.83043e10 | −1.35113 | ||||||||
\(890\) | −1.86191e9 | −0.0885306 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −2.37924e10 | −1.12244 | ||||||||
\(893\) | −2.20009e10 | −1.03386 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.60960e9 | 0.261548 | ||||||||
\(896\) | 2.18681e10 | 1.01563 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 3.20326e9 | 0.147613 | ||||||||
\(899\) | 3.08595e10 | 1.41654 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.46552e10 | 1.12298 | ||||||||
\(902\) | −1.85215e9 | −0.0840337 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 1.25060e10 | 0.563025 | ||||||||
\(905\) | 5.35778e9 | 0.240279 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.17598e10 | 0.523329 | 0.261665 | − | 0.965159i | \(-0.415729\pi\) | ||||
0.261665 | + | 0.965159i | \(0.415729\pi\) | |||||||
\(908\) | 3.36120e10 | 1.49002 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −5.55360e9 | −0.244304 | ||||||||
\(911\) | −1.28379e10 | −0.562572 | −0.281286 | − | 0.959624i | \(-0.590761\pi\) | ||||
−0.281286 | + | 0.959624i | \(0.590761\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.24766e9 | 0.271688 | ||||||||
\(914\) | 4.68820e8 | 0.0203093 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 1.75645e10 | 0.755096 | ||||||||
\(917\) | 4.94272e10 | 2.11677 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 2.54812e10 | 1.08297 | 0.541485 | − | 0.840711i | \(-0.317862\pi\) | ||||
0.541485 | + | 0.840711i | \(0.317862\pi\) | |||||||
\(920\) | 1.07161e9 | 0.0453709 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.77384e9 | 0.284627 | ||||||||
\(923\) | −5.05329e10 | −2.11528 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1.01105e10 | −0.420028 | ||||||||
\(926\) | −5.25156e9 | −0.217345 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.66071e10 | −1.09290 | ||||||||
\(929\) | 4.93247e9 | 0.201841 | 0.100921 | − | 0.994894i | \(-0.467821\pi\) | ||||
0.100921 | + | 0.994894i | \(0.467821\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.86213e10 | 0.756286 | ||||||||
\(932\) | 3.91959e10 | 1.58593 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −3.40283e9 | −0.136655 | ||||||||
\(935\) | 2.90639e9 | 0.116282 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.62092e9 | 0.342346 | 0.171173 | − | 0.985241i | \(-0.445244\pi\) | ||||
0.171173 | + | 0.985241i | \(0.445244\pi\) | |||||||
\(938\) | 8.34485e8 | 0.0330148 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 1.43526e10 | 0.563615 | ||||||||
\(941\) | 2.08832e10 | 0.817022 | 0.408511 | − | 0.912753i | \(-0.366048\pi\) | ||||
0.408511 | + | 0.912753i | \(0.366048\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 5.76055e9 | 0.223704 | ||||||||
\(944\) | −2.71431e10 | −1.05016 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 3.66276e9 | 0.140666 | ||||||||
\(947\) | −4.19780e10 | −1.60619 | −0.803095 | − | 0.595851i | \(-0.796815\pi\) | ||||
−0.803095 | + | 0.595851i | \(0.796815\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −4.54213e10 | −1.72515 | ||||||||
\(950\) | −3.72262e9 | −0.140869 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 8.82132e9 | 0.331363 | ||||||||
\(953\) | 3.26688e10 | 1.22267 | 0.611333 | − | 0.791373i | \(-0.290634\pi\) | ||||
0.611333 | + | 0.791373i | \(0.290634\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.38236e10 | −0.513583 | ||||||||
\(956\) | −5.40067e9 | −0.199915 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7.37121e9 | −0.270869 | ||||||||
\(959\) | 4.96358e10 | 1.81732 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.10784e10 | −0.402666 | ||||||||
\(962\) | 5.51964e9 | 0.199893 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −9.22054e9 | −0.331502 | ||||||||
\(965\) | −1.37907e10 | −0.494017 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.39963e10 | 1.92031 | 0.960155 | − | 0.279467i | \(-0.0901576\pi\) | ||||
0.960155 | + | 0.279467i | \(0.0901576\pi\) | |||||||
\(968\) | 1.00503e10 | 0.356135 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.25595e9 | 0.0793650 | ||||||||
\(971\) | −1.25581e10 | −0.440207 | −0.220104 | − | 0.975476i | \(-0.570640\pi\) | ||||
−0.220104 | + | 0.975476i | \(0.570640\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.28811e10 | 1.14433 | ||||||||
\(974\) | −5.54638e9 | −0.192333 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −4.72771e10 | −1.62771 | ||||||||
\(977\) | 1.93161e10 | 0.662657 | 0.331329 | − | 0.943515i | \(-0.392503\pi\) | ||||
0.331329 | + | 0.943515i | \(0.392503\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −8.66342e9 | −0.295087 | ||||||||
\(980\) | −1.21478e10 | −0.412295 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 7.49538e8 | 0.0252583 | ||||||||
\(983\) | 3.38434e10 | 1.13642 | 0.568208 | − | 0.822885i | \(-0.307637\pi\) | ||||
0.568208 | + | 0.822885i | \(0.307637\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.00551e10 | −0.335242 | ||||||||
\(986\) | −6.93179e9 | −0.230290 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −4.35374e10 | −1.43619 | ||||||||
\(989\) | −1.13919e10 | −0.374463 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.92468e10 | 0.954599 | 0.477300 | − | 0.878741i | \(-0.341616\pi\) | ||||
0.477300 | + | 0.878741i | \(0.341616\pi\) | |||||||
\(992\) | −1.41696e10 | −0.460857 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 1.14598e10 | 0.370105 | ||||||||
\(995\) | 9.38420e9 | 0.302007 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −2.05938e9 | −0.0658117 | −0.0329059 | − | 0.999458i | \(-0.510476\pi\) | ||||
−0.0329059 | + | 0.999458i | \(0.510476\pi\) | |||||||
\(998\) | 1.37400e9 | 0.0437552 | ||||||||
\(999\) | 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 | 207.8.a.e.1.6 | 8 | ||
3.2 | odd | 2 | 69.8.a.d.1.3 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
69.8.a.d.1.3 | ✓ | 8 | 3.2 | odd | 2 | ||
207.8.a.e.1.6 | 8 | 1.1 | even | 1 | trivial |