Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [276,8,Mod(1,276)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(276, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("276.1");
S:= CuspForms(chi, 8);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 276 = 2^{2} \cdot 3 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 8 \) |
Character orbit: | \([\chi]\) | \(=\) | 276.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: | \(86.2182670336\) |
Analytic rank: | \(1\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - x^{4} - 82397x^{3} + 7346801x^{2} + 425424304x - 21076942492 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{4}\cdot 3 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-62.3694\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 276.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −27.0000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −386.322 | −1.38215 | −0.691074 | − | 0.722784i | \(-0.742862\pi\) | ||||
−0.691074 | + | 0.722784i | \(0.742862\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −1140.12 | −1.25634 | −0.628172 | − | 0.778074i | \(-0.716197\pi\) | ||||
−0.628172 | + | 0.778074i | \(0.716197\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 729.000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 932.227 | 0.211177 | 0.105589 | − | 0.994410i | \(-0.466327\pi\) | ||||
0.105589 | + | 0.994410i | \(0.466327\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −3778.85 | −0.477043 | −0.238522 | − | 0.971137i | \(-0.576663\pi\) | ||||
−0.238522 | + | 0.971137i | \(0.576663\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 10430.7 | 0.797983 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 35079.1 | 1.73172 | 0.865860 | − | 0.500287i | \(-0.166772\pi\) | ||||
0.865860 | + | 0.500287i | \(0.166772\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 38980.1 | 1.30378 | 0.651892 | − | 0.758312i | \(-0.273976\pi\) | ||||
0.651892 | + | 0.758312i | \(0.273976\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 30783.3 | 0.725351 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −12167.0 | −0.208514 | ||||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 71119.6 | 0.910331 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −19683.0 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −97548.6 | −0.742725 | −0.371363 | − | 0.928488i | \(-0.621109\pi\) | ||||
−0.371363 | + | 0.928488i | \(0.621109\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 115987. | 0.699267 | 0.349633 | − | 0.936887i | \(-0.386306\pi\) | ||||
0.349633 | + | 0.936887i | \(0.386306\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −25170.1 | −0.121923 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 440455. | 1.73645 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 398847. | 1.29450 | 0.647248 | − | 0.762280i | \(-0.275920\pi\) | ||||
0.647248 | + | 0.762280i | \(0.275920\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 102029. | 0.275421 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −347416. | −0.787238 | −0.393619 | − | 0.919274i | \(-0.628777\pi\) | ||||
−0.393619 | + | 0.919274i | \(0.628777\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −16634.5 | −0.0319059 | −0.0159530 | − | 0.999873i | \(-0.505078\pi\) | ||||
−0.0159530 | + | 0.999873i | \(0.505078\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −281629. | −0.460716 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −666822. | −0.936844 | −0.468422 | − | 0.883505i | \(-0.655177\pi\) | ||||
−0.468422 | + | 0.883505i | \(0.655177\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 476339. | 0.578402 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −947136. | −0.999809 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 656028. | 0.605281 | 0.302640 | − | 0.953105i | \(-0.402132\pi\) | ||||
0.302640 | + | 0.953105i | \(0.402132\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −360140. | −0.291878 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −1.05246e6 | −0.752740 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 566943. | 0.359383 | 0.179692 | − | 0.983723i | \(-0.442490\pi\) | ||||
0.179692 | + | 0.983723i | \(0.442490\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −2.74032e6 | −1.54578 | −0.772888 | − | 0.634543i | \(-0.781188\pi\) | ||||
−0.772888 | + | 0.634543i | \(0.781188\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −831150. | −0.418782 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 1.45985e6 | 0.659344 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.67050e6 | −0.678555 | −0.339278 | − | 0.940686i | \(-0.610183\pi\) | ||||
−0.339278 | + | 0.940686i | \(0.610183\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 328509. | 0.120386 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 1.60434e6 | 0.531977 | 0.265988 | − | 0.963976i | \(-0.414302\pi\) | ||||
0.265988 | + | 0.963976i | \(0.414302\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4.30426e6 | 1.29500 | 0.647499 | − | 0.762067i | \(-0.275815\pi\) | ||||
0.647499 | + | 0.762067i | \(0.275815\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −1.92023e6 | −0.525580 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −1.06285e6 | −0.265311 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 5.13482e6 | 1.17174 | 0.585868 | − | 0.810406i | \(-0.300754\pi\) | ||||
0.585868 | + | 0.810406i | \(0.300754\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 531441. | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.63957e6 | 0.506711 | 0.253355 | − | 0.967373i | \(-0.418466\pi\) | ||||
0.253355 | + | 0.967373i | \(0.418466\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.35518e7 | −2.39349 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.63381e6 | 0.428813 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −6.63888e6 | −0.998228 | −0.499114 | − | 0.866536i | \(-0.666341\pi\) | ||||
−0.499114 | + | 0.866536i | \(0.666341\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.30835e6 | 0.599331 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −3.13165e6 | −0.403722 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −1.50589e7 | −1.80202 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −7.96456e6 | −0.886055 | −0.443027 | − | 0.896508i | \(-0.646096\pi\) | ||||
−0.443027 | + | 0.896508i | \(0.646096\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 679593. | 0.0703924 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.88096e7 | 1.81659 | 0.908293 | − | 0.418335i | \(-0.137386\pi\) | ||||
0.908293 | + | 0.418335i | \(0.137386\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.59860e7 | −1.44149 | −0.720744 | − | 0.693202i | \(-0.756199\pi\) | ||||
−0.720744 | + | 0.693202i | \(0.756199\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −1.18923e7 | −1.00254 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 5.54484e6 | 0.437568 | 0.218784 | − | 0.975773i | \(-0.429791\pi\) | ||||
0.218784 | + | 0.975773i | \(0.429791\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −810325. | −0.0599331 | −0.0299666 | − | 0.999551i | \(-0.509540\pi\) | ||||
−0.0299666 | + | 0.999551i | \(0.509540\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −1.07689e7 | −0.747377 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.38865e7 | 0.905355 | 0.452677 | − | 0.891674i | \(-0.350469\pi\) | ||||
0.452677 | + | 0.891674i | \(0.350469\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 4.70038e6 | 0.288198 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −2.75478e6 | −0.159014 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −3.99945e7 | −2.17564 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.86181e7 | −0.955404 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 9.38022e6 | 0.454512 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.70634e6 | 0.123936 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −9.91017e6 | −0.429307 | −0.214654 | − | 0.976690i | \(-0.568862\pi\) | ||||
−0.214654 | + | 0.976690i | \(0.568862\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 449133. | 0.0184209 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 1.82273e7 | 0.708390 | 0.354195 | − | 0.935172i | \(-0.384755\pi\) | ||||
0.354195 | + | 0.935172i | \(0.384755\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −4.44421e7 | −1.63800 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 7.60397e6 | 0.265994 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −2.24792e6 | −0.0746895 | −0.0373448 | − | 0.999302i | \(-0.511890\pi\) | ||||
−0.0373448 | + | 0.999302i | \(0.511890\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −4.77969e7 | −1.50955 | −0.754775 | − | 0.655983i | \(-0.772254\pi\) | ||||
−0.754775 | + | 0.655983i | \(0.772254\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.80042e7 | 0.540887 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −3.52274e6 | −0.100741 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.76852e7 | 1.02656 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1.28611e7 | −0.333940 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −6.35196e7 | −1.57310 | −0.786549 | − | 0.617528i | \(-0.788134\pi\) | ||||
−0.786549 | + | 0.617528i | \(0.788134\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −4.67865e7 | −1.10586 | −0.552932 | − | 0.833227i | \(-0.686491\pi\) | ||||
−0.552932 | + | 0.833227i | \(0.686491\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 2.55727e7 | 0.577240 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.48083e7 | −0.966490 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.66238e7 | 0.549062 | 0.274531 | − | 0.961578i | \(-0.411477\pi\) | ||||
0.274531 | + | 0.961578i | \(0.411477\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.77128e7 | −0.349459 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1.38719e7 | 0.261966 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2.77746e7 | −0.502332 | −0.251166 | − | 0.967944i | \(-0.580814\pi\) | ||||
−0.251166 | + | 0.967944i | \(0.580814\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 9.72377e6 | 0.168516 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.36477e7 | 0.226752 | 0.113376 | − | 0.993552i | \(-0.463834\pi\) | ||||
0.113376 | + | 0.993552i | \(0.463834\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −4.84688e7 | −0.772430 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 2.84165e7 | 0.434595 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −8.79997e7 | −1.29217 | −0.646086 | − | 0.763265i | \(-0.723595\pi\) | ||||
−0.646086 | + | 0.763265i | \(0.723595\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −8.10851e7 | −1.14369 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −1.53075e7 | −0.207490 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 9.19112e7 | 1.19780 | 0.598898 | − | 0.800826i | \(-0.295606\pi\) | ||||
0.598898 | + | 0.800826i | \(0.295606\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.55401e7 | 0.821547 | 0.410773 | − | 0.911737i | \(-0.365259\pi\) | ||||
0.410773 | + | 0.911737i | \(0.365259\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 7.39886e7 | 0.892454 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −1.54083e8 | −1.78918 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.27017e7 | 0.365700 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 2.24411e7 | 0.241784 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1.05724e8 | −1.09789 | −0.548944 | − | 0.835859i | \(-0.684970\pi\) | ||||
−0.548944 | + | 0.835859i | \(0.684970\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 1.25689e8 | 1.25848 | 0.629242 | − | 0.777209i | \(-0.283365\pi\) | ||||
0.629242 | + | 0.777209i | \(0.283365\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −3.94160e7 | −0.380672 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −1.01808e8 | −0.948748 | −0.474374 | − | 0.880323i | \(-0.657326\pi\) | ||||
−0.474374 | + | 0.880323i | \(0.657326\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 3.72028e7 | 0.334649 | 0.167325 | − | 0.985902i | \(-0.446487\pi\) | ||||
0.167325 | + | 0.985902i | \(0.446487\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 4.51035e7 | 0.391764 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.11217e8 | 0.933119 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1.34214e8 | 1.08808 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −8.86974e6 | −0.0695048 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.63383e7 | 0.275329 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.02297e8 | −0.749679 | −0.374840 | − | 0.927090i | \(-0.622302\pi\) | ||||
−0.374840 | + | 0.927090i | \(0.622302\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −4.33172e7 | −0.307137 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 6.42629e6 | 0.0440987 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.32239e8 | −0.878520 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.16215e8 | −0.747667 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.32559e8 | −0.826105 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.19172e8 | 0.719625 | 0.359813 | − | 0.933025i | \(-0.382841\pi\) | ||||
0.359813 | + | 0.933025i | \(0.382841\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 5.18462e7 | 0.303444 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 2.56106e8 | 1.45321 | 0.726606 | − | 0.687055i | \(-0.241097\pi\) | ||||
0.726606 | + | 0.687055i | \(0.241097\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −8.41116e7 | −0.462841 | −0.231421 | − | 0.972854i | \(-0.574337\pi\) | ||||
−0.231421 | + | 0.972854i | \(0.574337\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2.86970e7 | 0.153178 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.90836e7 | −0.0988357 | −0.0494179 | − | 0.998778i | \(-0.515737\pi\) | ||||
−0.0494179 | + | 0.998778i | \(0.515737\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2.57608e8 | 1.29486 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −1.38640e8 | −0.676503 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.27027e8 | 0.601872 | 0.300936 | − | 0.953644i | \(-0.402701\pi\) | ||||
0.300936 | + | 0.953644i | \(0.402701\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.56957e7 | −0.440385 | −0.220193 | − | 0.975456i | \(-0.570669\pi\) | ||||
−0.220193 | + | 0.975456i | \(0.570669\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.43489e7 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.84020e8 | −0.799436 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.47300e8 | −0.621961 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −7.12685e7 | −0.292550 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 3.88164e8 | 1.54938 | 0.774688 | − | 0.632344i | \(-0.217907\pi\) | ||||
0.774688 | + | 0.632344i | \(0.217907\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.13424e7 | −0.0440335 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 3.65900e8 | 1.38188 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −2.51104e8 | −0.922758 | −0.461379 | − | 0.887203i | \(-0.652645\pi\) | ||||
−0.461379 | + | 0.887203i | \(0.652645\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −4.54735e8 | −1.62633 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −7.11129e7 | −0.247575 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 3.45366e8 | 1.17067 | 0.585335 | − | 0.810792i | \(-0.300963\pi\) | ||||
0.585335 | + | 0.810792i | \(0.300963\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −2.53438e8 | −0.836587 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1.79250e8 | 0.576327 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −3.92699e8 | −1.23006 | −0.615030 | − | 0.788504i | \(-0.710856\pi\) | ||||
−0.615030 | + | 0.788504i | \(0.710856\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −5.33998e8 | −1.62985 | −0.814924 | − | 0.579568i | \(-0.803221\pi\) | ||||
−0.814924 | + | 0.579568i | \(0.803221\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.16326e8 | −0.346024 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.62996e7 | 0.192241 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −3.67834e8 | −1.03986 | −0.519928 | − | 0.854210i | \(-0.674041\pi\) | ||||
−0.519928 | + | 0.854210i | \(0.674041\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 8.45545e7 | 0.233089 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.15344e7 | 0.0847836 | 0.0423918 | − | 0.999101i | \(-0.486502\pi\) | ||||
0.0423918 | + | 0.999101i | \(0.486502\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 4.88658e8 | 1.28160 | 0.640800 | − | 0.767708i | \(-0.278603\pi\) | ||||
0.640800 | + | 0.767708i | \(0.278603\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 4.06590e8 | 1.04040 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 3.96097e8 | 0.989042 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.20206e8 | 1.99885 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 2.15043e8 | 0.511564 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.64216e7 | 0.0845906 | 0.0422953 | − | 0.999105i | \(-0.486533\pi\) | ||||
0.0422953 | + | 0.999105i | \(0.486533\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −2.19023e8 | −0.496720 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1.83490e7 | −0.0406411 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 4.59772e7 | 0.0994704 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.89654e7 | 0.0400848 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −5.07860e8 | −1.04881 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1.05864e9 | 2.13649 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.10846e8 | −0.218643 | −0.109321 | − | 0.994006i | \(-0.534868\pi\) | ||||
−0.109321 | + | 0.994006i | \(0.534868\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 4.31623e8 | 0.832243 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.68967e8 | 0.884057 | 0.442029 | − | 0.897001i | \(-0.354259\pi\) | ||||
0.442029 | + | 0.897001i | \(0.354259\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −4.55497e8 | −0.839615 | −0.419807 | − | 0.907613i | \(-0.637902\pi\) | ||||
−0.419807 | + | 0.907613i | \(0.637902\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 3.21091e8 | 0.578818 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 7.61877e8 | 1.34331 | 0.671657 | − | 0.740863i | \(-0.265583\pi\) | ||||
0.671657 | + | 0.740863i | \(0.265583\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −9.09374e7 | −0.156847 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1.49711e8 | −0.252630 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.36739e9 | 2.25779 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −2.68750e8 | −0.434267 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.18788e7 | 0.0346024 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 7.60259e8 | 1.17700 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6.46629e8 | 0.980070 | 0.490035 | − | 0.871703i | \(-0.336984\pi\) | ||||
0.490035 | + | 0.871703i | \(0.336984\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.90760e8 | 0.431499 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 6.45351e8 | 0.937863 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1.75588e8 | −0.249914 | −0.124957 | − | 0.992162i | \(-0.539879\pi\) | ||||
−0.124957 | + | 0.992162i | \(0.539879\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.74936e8 | −0.522707 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.08126e8 | 0.147669 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 3.95856e8 | 0.529673 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.26910e8 | −0.166391 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 8.63741e8 | 1.10976 | 0.554882 | − | 0.831929i | \(-0.312764\pi\) | ||||
0.554882 | + | 0.831929i | \(0.312764\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1.87858e8 | 0.236560 | 0.118280 | − | 0.992980i | \(-0.462262\pi\) | ||||
0.118280 | + | 0.992980i | \(0.462262\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 7.43791e7 | 0.0918070 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 6.16831e8 | 0.746371 | 0.373186 | − | 0.927757i | \(-0.378265\pi\) | ||||
0.373186 | + | 0.927757i | \(0.378265\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −6.19792e8 | −0.735270 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 1.07985e9 | 1.25610 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.20164e8 | 0.365209 | 0.182605 | − | 0.983186i | \(-0.441547\pi\) | ||||
0.182605 | + | 0.983186i | \(0.441547\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 6.25577e8 | 0.699851 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5.02689e8 | 0.551603 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.66283e9 | −1.78988 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.50839e9 | −1.59288 | −0.796438 | − | 0.604720i | \(-0.793285\pi\) | ||||
−0.796438 | + | 0.604720i | \(0.793285\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.53266e8 | −0.262413 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −7.47953e8 | −0.760441 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.75709e9 | −1.75313 | −0.876565 | − | 0.481283i | \(-0.840171\pi\) | ||||
−0.876565 | + | 0.481283i | \(0.840171\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −7.30712e7 | −0.0715544 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 3.68621e8 | 0.354312 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.17325e8 | −0.393765 | −0.196883 | − | 0.980427i | \(-0.563082\pi\) | ||||
−0.196883 | + | 0.980427i | \(0.563082\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.67575e8 | 0.247861 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −6.24218e8 | −0.567728 | −0.283864 | − | 0.958864i | \(-0.591616\pi\) | ||||
−0.283864 | + | 0.958864i | \(0.591616\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 4.10604e8 | 0.366699 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.21266e7 | −0.0106353 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −8.26279e8 | −0.711710 | −0.355855 | − | 0.934541i | \(-0.615810\pi\) | ||||
−0.355855 | + | 0.934541i | \(0.615810\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.26808e8 | −0.361088 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −4.92137e8 | −0.408989 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1.98369e9 | −1.61951 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −1.53014e7 | −0.0122733 | −0.00613667 | − | 0.999981i | \(-0.501953\pi\) | ||||
−0.00613667 | + | 0.999981i | \(0.501953\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 1.19994e9 | 0.945701 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −1.07538e9 | −0.832832 | −0.416416 | − | 0.909174i | \(-0.636714\pi\) | ||||
−0.416416 | + | 0.909174i | \(0.636714\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −4.38297e8 | −0.333581 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.05307e8 | −0.153572 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.71816e8 | 0.273368 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.95803e8 | 0.575141 | 0.287570 | − | 0.957760i | \(-0.407152\pi\) | ||||
0.287570 | + | 0.957760i | \(0.407152\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 6.06940e7 | 0.0431220 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −6.46385e8 | −0.451509 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.01972e9 | −0.700349 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 1.29052e9 | 0.871540 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.72767e9 | −1.14739 | −0.573695 | − | 0.819069i | \(-0.694490\pi\) | ||||
−0.573695 | + | 0.819069i | \(0.694490\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −2.70780e9 | −1.76860 | −0.884299 | − | 0.466921i | \(-0.845363\pi\) | ||||
−0.884299 | + | 0.466921i | \(0.845363\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.86113e8 | −0.312281 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 2.49481e9 | 1.57644 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3.12430e9 | 1.94203 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 9.51140e7 | 0.0581626 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.01796e9 | −0.612436 | −0.306218 | − | 0.951961i | \(-0.599064\pi\) | ||||
−0.306218 | + | 0.951961i | \(0.599064\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −1.04837e9 | −0.620594 | −0.310297 | − | 0.950640i | \(-0.600428\pi\) | ||||
−0.310297 | + | 0.950640i | \(0.600428\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.01750e9 | −0.592682 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −4.74271e8 | −0.271858 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2.02197e9 | −1.14064 | −0.570320 | − | 0.821423i | \(-0.693181\pi\) | ||||
−0.570320 | + | 0.821423i | \(0.693181\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.47251e8 | 0.192801 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 2.75110e9 | 1.50347 | 0.751733 | − | 0.659468i | \(-0.229218\pi\) | ||||
0.751733 | + | 0.659468i | \(0.229218\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 2.56474e9 | 1.37970 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 1.71503e9 | 0.908229 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.41557e9 | −0.738024 | −0.369012 | − | 0.929425i | \(-0.620304\pi\) | ||||
−0.369012 | + | 0.929425i | \(0.620304\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −3.23870e8 | −0.166247 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 1.26324e9 | 0.638471 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −1.66441e9 | −0.828363 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.84914e8 | 0.188650 | 0.0943249 | − | 0.995541i | \(-0.469931\pi\) | ||||
0.0943249 | + | 0.995541i | \(0.469931\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −6.90462e8 | −0.333270 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −4.09299e9 | −1.94575 | −0.972876 | − | 0.231329i | \(-0.925693\pi\) | ||||
−0.972876 | + | 0.231329i | \(0.925693\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.11228e9 | −1.45729 | −0.728643 | − | 0.684894i | \(-0.759849\pi\) | ||||
−0.728643 | + | 0.684894i | \(0.759849\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 1.20982e9 | 0.558003 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.61214e8 | −0.391293 | −0.195646 | − | 0.980674i | \(-0.562681\pi\) | ||||
−0.195646 | + | 0.980674i | \(0.562681\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1.90458e9 | 0.852499 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −7.18843e8 | −0.317001 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.55072e7 | −0.00673780 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.77225e9 | 1.18687 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.78244e8 | 0.201760 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.49752e9 | 1.45407 | 0.727035 | − | 0.686600i | \(-0.240898\pi\) | ||||
0.727035 | + | 0.686600i | \(0.240898\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −1.50718e9 | −0.617530 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −3.74541e8 | −0.151246 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 3.07688e9 | 1.22466 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −1.45097e9 | −0.569255 | −0.284628 | − | 0.958638i | \(-0.591870\pi\) | ||||
−0.284628 | + | 0.958638i | \(0.591870\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 7.49913e8 | 0.290021 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.03432e9 | 0.394339 | 0.197170 | − | 0.980369i | \(-0.436825\pi\) | ||||
0.197170 | + | 0.980369i | \(0.436825\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.42192e9 | −1.28619 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −2.62542e8 | −0.0972927 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −1.82915e9 | −0.668346 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −1.12992e9 | −0.407094 | −0.203547 | − | 0.979065i | \(-0.565247\pi\) | ||||
−0.203547 | + | 0.979065i | \(0.565247\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.68487e8 | −0.130915 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.72161e8 | 0.200461 | 0.100231 | − | 0.994964i | \(-0.468042\pi\) | ||||
0.100231 | + | 0.994964i | \(0.468042\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −7.26658e9 | −2.51079 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 1.30866e9 | 0.445963 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.96761e9 | 0.661344 | 0.330672 | − | 0.943746i | \(-0.392725\pi\) | ||||
0.330672 | + | 0.943746i | \(0.392725\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −4.90739e9 | −1.62696 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −7.67246e8 | −0.250913 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 6.17576e9 | 1.99235 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −6.21629e8 | −0.197840 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 2.37599e9 | 0.746035 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −5.90281e9 | −1.82863 | −0.914316 | − | 0.405001i | \(-0.867271\pi\) | ||||
−0.914316 | + | 0.405001i | \(0.867271\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2.27685e9 | −0.695951 | −0.347975 | − | 0.937504i | \(-0.613131\pi\) | ||||
−0.347975 | + | 0.937504i | \(0.613131\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 2.18930e9 | 0.660309 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4.06872e9 | 1.21093 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.48036e8 | 0.0434783 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.13302e8 | 0.119794 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.31283e9 | 0.375546 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2.14209e9 | −0.604783 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −2.48160e9 | −0.691547 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 4.44056e8 | 0.122145 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −5.81625e9 | −1.57926 | −0.789629 | − | 0.613585i | \(-0.789727\pi\) | ||||
−0.789629 | + | 0.613585i | \(0.789727\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.76958e9 | −0.474320 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.13046e8 | 0.0828364 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 4.01140e9 | 1.04795 | 0.523975 | − | 0.851734i | \(-0.324449\pi\) | ||||
0.523975 | + | 0.851734i | \(0.324449\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1.99769e9 | −0.515258 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3.80246e9 | −0.968353 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5.85432e9 | −1.47211 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 4.16025e9 | 1.03299 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.04583e9 | −1.23720 | −0.618600 | − | 0.785706i | \(-0.712300\pi\) | ||||
−0.618600 | + | 0.785706i | \(0.712300\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.28594e7 | 0.0152205 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −8.82946e8 | −0.211137 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 5.42106e9 | 1.28028 | 0.640140 | − | 0.768258i | \(-0.278876\pi\) | ||||
0.640140 | + | 0.768258i | \(0.278876\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −5.36466e9 | −1.25133 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −6.05908e8 | −0.139594 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −8.77026e9 | −1.99581 | −0.997905 | − | 0.0646923i | \(-0.979393\pi\) | ||||
−0.997905 | + | 0.0646923i | \(0.979393\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.61343e8 | 0.0812257 | 0.0406128 | − | 0.999175i | \(-0.487069\pi\) | ||||
0.0406128 | + | 0.999175i | \(0.487069\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 2.85456e9 | 0.633866 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −8.65312e8 | −0.189817 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −3.75627e9 | −0.814032 | −0.407016 | − | 0.913421i | \(-0.633431\pi\) | ||||
−0.407016 | + | 0.913421i | \(0.633431\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −3.39361e9 | −0.726586 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −3.00944e9 | −0.636604 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.11567e8 | 0.127821 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 1.06423e9 | 0.219781 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 7.98967e9 | 1.63041 | 0.815203 | − | 0.579175i | \(-0.196625\pi\) | ||||
0.815203 | + | 0.579175i | \(0.196625\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4.52118e9 | 0.911693 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 2.74882e9 | 0.547760 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 7.75480e9 | 1.52714 | 0.763570 | − | 0.645725i | \(-0.223445\pi\) | ||||
0.763570 | + | 0.645725i | \(0.223445\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.54508e10 | 3.00705 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.00448e9 | −0.193210 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −7.99111e9 | −1.51919 | −0.759597 | − | 0.650394i | \(-0.774604\pi\) | ||||
−0.759597 | + | 0.650394i | \(0.774604\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.00290e10 | −1.88451 | −0.942253 | − | 0.334903i | \(-0.891296\pi\) | ||||
−0.942253 | + | 0.334903i | \(0.891296\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.21780e9 | −0.226185 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 7.19259e9 | 1.32051 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 9.54835e9 | 1.73288 | 0.866439 | − | 0.499283i | \(-0.166403\pi\) | ||||
0.866439 | + | 0.499283i | \(0.166403\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −3.00287e9 | −0.538736 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 2.51982e9 | 0.446915 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.94379e9 | −0.516173 | −0.258087 | − | 0.966122i | \(-0.583092\pi\) | ||||
−0.258087 | + | 0.966122i | \(0.583092\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −3.62379e9 | −0.628202 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −9.00119e9 | −1.54277 | −0.771386 | − | 0.636368i | \(-0.780436\pi\) | ||||
−0.771386 | + | 0.636368i | \(0.780436\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −6.10081e9 | −1.03388 | −0.516940 | − | 0.856022i | \(-0.672929\pi\) | ||||
−0.516940 | + | 0.856022i | \(0.672929\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.39483e8 | 0.0401286 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 7.56914e9 | 1.25412 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −6.60174e9 | −1.08163 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.81134e8 | −0.158961 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.39912e10 | 2.24170 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.72064e9 | 1.22335 | 0.611675 | − | 0.791109i | \(-0.290496\pi\) | ||||
0.611675 | + | 0.791109i | \(0.290496\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 2.76203e9 | 0.432827 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 3.82852e9 | 0.593366 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.80001e9 | −0.275923 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 1.16957e9 | 0.177326 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.52841e9 | 0.829081 | 0.414541 | − | 0.910031i | \(-0.363942\pi\) | ||||
0.414541 | + | 0.910031i | \(0.363942\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 2.42023e9 | 0.359019 | 0.179510 | − | 0.983756i | \(-0.442549\pi\) | ||||
0.179510 | + | 0.983756i | \(0.442549\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.73510e8 | −0.0254604 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.28197e9 | −0.186086 | −0.0930430 | − | 0.995662i | \(-0.529659\pi\) | ||||
−0.0930430 | + | 0.995662i | \(0.529659\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.28520e8 | 0.0758935 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.57046e9 | 0.507214 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.11169e9 | −0.296780 | −0.148390 | − | 0.988929i | \(-0.547409\pi\) | ||||
−0.148390 | + | 0.988929i | \(0.547409\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −7.04160e9 | −0.979100 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 3.13781e9 | 0.431666 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −8.13028e9 | −1.10664 | −0.553320 | − | 0.832969i | \(-0.686639\pi\) | ||||
−0.553320 | + | 0.832969i | \(0.686639\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.19282e10 | 1.60645 | 0.803227 | − | 0.595674i | \(-0.203115\pi\) | ||||
0.803227 | + | 0.595674i | \(0.203115\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.57908e9 | 0.476952 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.71690e10 | 2.26396 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 1.18687e9 | 0.154869 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.21764e9 | −0.415476 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −2.55460e9 | −0.326433 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −8.55668e9 | −1.08206 | −0.541032 | − | 0.841002i | \(-0.681966\pi\) | ||||
−0.541032 | + | 0.841002i | \(0.681966\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −1.39985e9 | −0.175193 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.71171e9 | −0.335879 | −0.167939 | − | 0.985797i | \(-0.553711\pi\) | ||||
−0.167939 | + | 0.985797i | \(0.553711\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 9.08058e9 | 1.11319 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.91485e9 | −0.839012 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −5.01237e9 | −0.601964 | −0.300982 | − | 0.953630i | \(-0.597314\pi\) | ||||
−0.300982 | + | 0.953630i | \(0.597314\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 8.68423e8 | 0.103232 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.27101e9 | 0.267221 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −2.47903e9 | −0.288745 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −6.92473e9 | −0.798417 | −0.399208 | − | 0.916860i | \(-0.630715\pi\) | ||||
−0.399208 | + | 0.916860i | \(0.630715\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −7.74820e8 | −0.0884371 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 1.84650e10 | 2.08642 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1.21870e10 | −1.36327 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 5.15256e8 | 0.0570628 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −9.23924e9 | −1.01303 | −0.506516 | − | 0.862231i | \(-0.669067\pi\) | ||||
−0.506516 | + | 0.862231i | \(0.669067\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.55471e10 | 1.68774 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −6.95541e9 | −0.747585 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −2.14453e10 | −2.28226 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.83216e10 | 1.93064 | 0.965321 | − | 0.261067i | \(-0.0840744\pi\) | ||||
0.965321 | + | 0.261067i | \(0.0840744\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 3.74328e9 | 0.390579 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −1.41121e9 | −0.145807 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.36091e9 | 0.139238 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −3.42974e9 | −0.347491 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.29207e9 | −0.229973 | −0.114987 | − | 0.993367i | \(-0.536682\pi\) | ||||
−0.114987 | + | 0.993367i | \(0.536682\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.82261e10 | 1.81100 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.58378e9 | 0.254257 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −6.93762e9 | −0.676126 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.08806e9 | −0.684159 | −0.342080 | − | 0.939671i | \(-0.611131\pi\) | ||||
−0.342080 | + | 0.939671i | \(0.611131\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 3.87420e8 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −5.83525e8 | −0.0552521 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.69156e9 | −0.252429 | −0.126215 | − | 0.992003i | \(-0.540283\pi\) | ||||
−0.126215 | + | 0.992003i | \(0.540283\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 4.96854e9 | 0.461555 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −1.55729e9 | −0.143295 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 6.42829e9 | 0.585922 | 0.292961 | − | 0.956124i | \(-0.405359\pi\) | ||||
0.292961 | + | 0.956124i | \(0.405359\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 3.97710e9 | 0.359089 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.65165e9 | −0.326609 | −0.163304 | − | 0.986576i | \(-0.552215\pi\) | ||||
−0.163304 | + | 0.986576i | \(0.552215\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 2.45390e10 | 2.17425 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.92425e9 | 0.168904 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | −6.32180e9 | −0.549736 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 6.45024e9 | 0.555694 | 0.277847 | − | 0.960625i | \(-0.410379\pi\) | ||||
0.277847 | + | 0.960625i | \(0.410379\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −1.04804e10 | −0.894533 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 1.80747e10 | 1.52847 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.27767e10 | 1.90834 | 0.954169 | − | 0.299268i | \(-0.0967424\pi\) | ||||
0.954169 | + | 0.299268i | \(0.0967424\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3.06245e8 | 0.0254227 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −2.99181e9 | −0.246086 | −0.123043 | − | 0.992401i | \(-0.539265\pi\) | ||||
−0.123043 | + | 0.992401i | \(0.539265\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 9.23871e8 | 0.0752966 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −9.87929e9 | −0.797830 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.14239e9 | −0.171441 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.30214e9 | −0.103256 | −0.0516279 | − | 0.998666i | \(-0.516441\pi\) | ||||
−0.0516279 | + | 0.998666i | \(0.516441\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 6.77981e9 | 0.532755 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 3.60764e9 | 0.280928 | 0.140464 | − | 0.990086i | \(-0.455141\pi\) | ||||
0.140464 | + | 0.990086i | \(0.455141\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 8.24894e9 | 0.636564 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1.22778e10 | 0.938964 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.35423e10 | −1.02639 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 1.49561e9 | 0.112341 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 1.92005e9 | 0.142938 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.02854e10 | −0.758885 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.15458e9 | −0.157562 | −0.0787809 | − | 0.996892i | \(-0.525103\pi\) | ||||
−0.0787809 | + | 0.996892i | \(0.525103\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −9.32488e9 | −0.675886 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −1.58323e10 | −1.13744 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.03552e10 | 0.737402 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 6.84282e9 | 0.483004 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 6.12829e9 | 0.428780 | 0.214390 | − | 0.976748i | \(-0.431224\pi\) | ||||
0.214390 | + | 0.976748i | \(0.431224\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.33915e10 | −1.62235 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −4.83974e9 | −0.332743 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4.01255e9 | 0.273474 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.35901e9 | −0.362076 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.06029e10 | 0.710176 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.11433e10 | −0.739938 | −0.369969 | − | 0.929044i | \(-0.620632\pi\) | ||||
−0.369969 | + | 0.929044i | \(0.620632\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 7.98553e9 | 0.525691 | 0.262846 | − | 0.964838i | \(-0.415339\pi\) | ||||
0.262846 | + | 0.964838i | \(0.415339\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.44179e10 | 0.940993 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.07299e10 | 0.694296 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −6.48416e8 | −0.0415984 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3.14079e9 | 0.199777 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.84292e10 | 1.16227 | 0.581134 | − | 0.813808i | \(-0.302609\pi\) | ||||
0.581134 | + | 0.813808i | \(0.302609\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.28514e9 | −0.330489 | −0.165244 | − | 0.986253i | \(-0.552841\pi\) | ||||
−0.165244 | + | 0.986253i | \(0.552841\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.79009e9 | −0.110990 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 2.20880e10 | 1.35796 | 0.678979 | − | 0.734157i | \(-0.262423\pi\) | ||||
0.678979 | + | 0.734157i | \(0.262423\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 9.35771e9 | 0.570465 | 0.285232 | − | 0.958458i | \(-0.407929\pi\) | ||||
0.285232 | + | 0.958458i | \(0.407929\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 9.93152e9 | 0.600361 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 1.67095e10 | 1.00163 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −5.27239e9 | −0.313405 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −2.28297e9 | −0.134574 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −1.92901e9 | −0.112763 | −0.0563815 | − | 0.998409i | \(-0.517956\pi\) | ||||
−0.0563815 | + | 0.998409i | \(0.517956\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −7.73415e9 | −0.448359 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8.51428e8 | −0.0489498 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 1.87246e10 | 1.06761 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 2.12270e10 | 1.20032 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −1.31938e10 | −0.739932 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −4.85277e9 | −0.269921 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.25735e10 | −1.24531 | −0.622655 | − | 0.782497i | \(-0.713946\pi\) | ||||
−0.622655 | + | 0.782497i | \(0.713946\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −1.09779e10 | −0.600674 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.00830e10 | 0.547213 | 0.273607 | − | 0.961842i | \(-0.411783\pi\) | ||||
0.273607 | + | 0.961842i | \(0.411783\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 2.42564e10 | 1.30572 | 0.652862 | − | 0.757477i | \(-0.273568\pi\) | ||||
0.652862 | + | 0.757477i | \(0.273568\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.06946e10 | −0.571024 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −1.27819e10 | −0.676951 | −0.338475 | − | 0.940975i | \(-0.609911\pi\) | ||||
−0.338475 | + | 0.940975i | \(0.609911\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 3.39962e10 | 1.78597 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2.21456e10 | −1.15404 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 4.78681e9 | 0.247444 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.31257e9 | 0.323700 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −5.80616e9 | −0.295352 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −3.08556e9 | −0.155706 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −2.06695e10 | −1.03474 | −0.517371 | − | 0.855761i | \(-0.673089\pi\) | ||||
−0.517371 | + | 0.855761i | \(0.673089\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −9.83383e8 | −0.0488384 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.61893e10 | −1.29035 | −0.645175 | − | 0.764035i | \(-0.723216\pi\) | ||||
−0.645175 | + | 0.764035i | \(0.723216\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −3.17941e10 | −1.55412 | −0.777060 | − | 0.629427i | \(-0.783290\pi\) | ||||
−0.777060 | + | 0.629427i | \(0.783290\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 5.91361e9 | 0.286782 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −5.22762e9 | −0.251519 | −0.125760 | − | 0.992061i | \(-0.540137\pi\) | ||||
−0.125760 | + | 0.992061i | \(0.540137\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.12988e10 | 0.539358 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 4.95423e8 | 0.0234641 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.59928e10 | −1.22144 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −3.55073e10 | −1.65553 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1.24139e9 | −0.0574292 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −1.13144e10 | −0.519363 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 2.30129e10 | 1.04818 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −5.12067e8 | −0.0231430 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.53196e10 | −1.13550 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2.74180e10 | −1.22014 | −0.610070 | − | 0.792347i | \(-0.708859\pi\) | ||||
−0.610070 | + | 0.792347i | \(0.708859\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.37122e10 | 0.605528 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.41618e10 | 1.05880 | 0.529402 | − | 0.848371i | \(-0.322417\pi\) | ||||
0.529402 | + | 0.848371i | \(0.322417\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.46068e9 | 0.107006 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −2.85834e10 | −1.23350 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.07814e10 | −0.889982 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −4.27301e10 | −1.81606 | −0.908029 | − | 0.418908i | \(-0.862413\pi\) | ||||
−0.908029 | + | 0.418908i | \(0.862413\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.99283e9 | 0.126233 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −6.06256e9 | −0.253776 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.83659e10 | 1.17842 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −1.16538e10 | −0.480496 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4.37039e9 | 0.178840 | 0.0894201 | − | 0.995994i | \(-0.471499\pi\) | ||||
0.0894201 | + | 0.995994i | \(0.471499\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 1.85677e10 | 0.754111 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.26621e10 | −0.510411 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.26334e10 | −0.505451 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −3.32817e10 | −1.32165 | −0.660826 | − | 0.750539i | \(-0.729794\pi\) | ||||
−0.660826 | + | 0.750539i | \(0.729794\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.22984e10 | 0.484752 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 2.85629e10 | 1.11748 | 0.558739 | − | 0.829344i | \(-0.311285\pi\) | ||||
0.558739 | + | 0.829344i | \(0.311285\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 4.22701e9 | 0.164150 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.66947e9 | −0.334181 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6.07030e9 | 0.232266 | 0.116133 | − | 0.993234i | \(-0.462950\pi\) | ||||
0.116133 | + | 0.993234i | \(0.462950\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.62652e10 | −0.617770 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −2.05707e10 | −0.775562 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −2.67399e10 | −1.00077 | −0.500386 | − | 0.865802i | \(-0.666809\pi\) | ||||
−0.500386 | + | 0.865802i | \(0.666809\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.08436e10 | 1.51744 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 2.45531e9 | 0.0905554 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.56291e9 | 0.0938358 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.40597e10 | −0.511026 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 4.04219e9 | 0.145856 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −4.85565e10 | −1.73941 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 4.14235e10 | 1.47317 | 0.736587 | − | 0.676343i | \(-0.236436\pi\) | ||||
0.736587 | + | 0.676343i | \(0.236436\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −3.69195e10 | −1.30353 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2.88858e10 | −1.01255 | −0.506276 | − | 0.862372i | \(-0.668978\pi\) | ||||
−0.506276 | + | 0.862372i | \(0.668978\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5.44943e10 | 1.89652 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.25625e9 | 0.250724 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −7.53761e9 | −0.258585 | −0.129292 | − | 0.991607i | \(-0.541271\pi\) | ||||
−0.129292 | + | 0.991607i | \(0.541271\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −6.18894e9 | −0.210803 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.90727e8 | −0.0199777 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.47825e10 | −0.496375 | −0.248188 | − | 0.968712i | \(-0.579835\pi\) | ||||
−0.248188 | + | 0.968712i | \(0.579835\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 3.93307e10 | 1.31131 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −2.05270e10 | −0.679540 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 2.02392e8 | 0.00665284 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 2.90508e10 | 0.948201 | 0.474101 | − | 0.880471i | \(-0.342773\pi\) | ||||
0.474101 | + | 0.880471i | \(0.342773\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −1.74590e10 | −0.565844 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −1.43723e10 | −0.462534 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.38617e8 | 0.00442979 | 0.00221490 | − | 0.999998i | \(-0.499295\pi\) | ||||
0.00221490 | + | 0.999998i | \(0.499295\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −7.85051e9 | −0.249126 |
(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 | 276.8.a.a.1.1 | ✓ | 5 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
276.8.a.a.1.1 | ✓ | 5 | 1.1 | even | 1 | trivial |