Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [684,7,Mod(37,684)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(684, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 1]))
N = Newforms(chi, 7, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("684.37");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 684 = 2^{2} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 684.h (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(157.356993196\) |
Analytic rank: | \(0\) |
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: | \( x^{8} + 5090x^{6} + 8905881x^{4} + 5831691048x^{2} + 827887219200 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{29}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3^{3}\cdot 5 \) |
Twist minimal: | no (minimal twist has level 76) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 37.6 | ||
Root | \(-13.8790i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 684.37 |
Dual form | 684.7.h.c.37.5 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/684\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(343\) | \(533\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(1\) |
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 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 18.1155 | 0.144924 | 0.0724619 | − | 0.997371i | \(-0.476914\pi\) | ||||
0.0724619 | + | 0.997371i | \(0.476914\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 85.5200 | 0.249330 | 0.124665 | − | 0.992199i | \(-0.460214\pi\) | ||||
0.124665 | + | 0.992199i | \(0.460214\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 316.255 | 0.237607 | 0.118803 | − | 0.992918i | \(-0.462094\pi\) | ||||
0.118803 | + | 0.992918i | \(0.462094\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2456.75i | 1.11823i | 0.829091 | + | 0.559114i | \(0.188859\pi\) | ||||
−0.829091 | + | 0.559114i | \(0.811141\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 3224.36 | 0.656291 | 0.328146 | − | 0.944627i | \(-0.393576\pi\) | ||||
0.328146 | + | 0.944627i | \(0.393576\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2503.10 | + | 6385.95i | 0.364936 | + | 0.931033i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 7826.52 | 0.643258 | 0.321629 | − | 0.946866i | \(-0.395770\pi\) | ||||
0.321629 | + | 0.946866i | \(0.395770\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −15296.8 | −0.978997 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 18986.6i | − | 0.778489i | −0.921135 | − | 0.389244i | \(-0.872736\pi\) | ||
0.921135 | − | 0.389244i | \(-0.127264\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 32356.9i | 1.08613i | 0.839691 | + | 0.543065i | \(0.182736\pi\) | ||||
−0.839691 | + | 0.543065i | \(0.817264\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 1549.24 | 0.0361338 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 15447.1i | 0.304960i | 0.988307 | + | 0.152480i | \(0.0487259\pi\) | ||||
−0.988307 | + | 0.152480i | \(0.951274\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 94131.1i | − | 1.36578i | −0.730520 | − | 0.682892i | \(-0.760722\pi\) | ||
0.730520 | − | 0.682892i | \(-0.239278\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 39236.1 | 0.493493 | 0.246746 | − | 0.969080i | \(-0.420639\pi\) | ||||
0.246746 | + | 0.969080i | \(0.420639\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −92363.2 | −0.889622 | −0.444811 | − | 0.895625i | \(-0.646729\pi\) | ||||
−0.444811 | + | 0.895625i | \(0.646729\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −110335. | −0.937835 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 130058.i | 0.873597i | 0.899559 | + | 0.436798i | \(0.143888\pi\) | ||||
−0.899559 | + | 0.436798i | \(0.856112\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5729.10 | 0.0344349 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 180241.i | 0.877602i | 0.898584 | + | 0.438801i | \(0.144597\pi\) | ||||
−0.898584 | + | 0.438801i | \(0.855403\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 124818. | 0.549907 | 0.274953 | − | 0.961458i | \(-0.411338\pi\) | ||||
0.274953 | + | 0.961458i | \(0.411338\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 44505.1i | 0.162058i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 154005.i | − | 0.512048i | −0.966670 | − | 0.256024i | \(-0.917587\pi\) | ||
0.966670 | − | 0.256024i | \(-0.0824126\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 177431.i | 0.495740i | 0.968793 | + | 0.247870i | \(0.0797305\pi\) | ||||
−0.968793 | + | 0.247870i | \(0.920269\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 314866. | 0.809389 | 0.404694 | − | 0.914452i | \(-0.367378\pi\) | ||||
0.404694 | + | 0.914452i | \(0.367378\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 27046.1 | 0.0592424 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 462999.i | − | 0.939071i | −0.882914 | − | 0.469535i | \(-0.844421\pi\) | ||
0.882914 | − | 0.469535i | \(-0.155579\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −601062. | −1.05120 | −0.525600 | − | 0.850732i | \(-0.676159\pi\) | ||||
−0.525600 | + | 0.850732i | \(0.676159\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 58410.8 | 0.0951122 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 275459.i | − | 0.390739i | −0.980730 | − | 0.195369i | \(-0.937409\pi\) | ||
0.980730 | − | 0.195369i | \(-0.0625906\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 210101.i | 0.278807i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 45344.8 | + | 115685.i | 0.0528879 | + | 0.134929i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 852579.i | 0.934156i | 0.884216 | + | 0.467078i | \(0.154693\pi\) | ||||
−0.884216 | + | 0.467078i | \(0.845307\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 702454. | 0.681795 | 0.340898 | − | 0.940100i | \(-0.389269\pi\) | ||||
0.340898 | + | 0.940100i | \(0.389269\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 955700.i | − | 0.874600i | −0.899316 | − | 0.437300i | \(-0.855935\pi\) | ||
0.899316 | − | 0.437300i | \(-0.144065\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 406564.i | 0.331877i | 0.986136 | + | 0.165938i | \(0.0530653\pi\) | ||||
−0.986136 | + | 0.165938i | \(0.946935\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.98600e6i | 1.53356i | 0.641912 | + | 0.766779i | \(0.278142\pi\) | ||||
−0.641912 | + | 0.766779i | \(0.721858\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1.34434e6i | − | 0.931692i | −0.884866 | − | 0.465846i | \(-0.845750\pi\) | ||
0.884866 | − | 0.465846i | \(-0.154250\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 141781. | 0.0932234 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 275747. | 0.163633 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.67154e6 | −0.943543 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −560164. | −0.286804 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1.59869e6i | 0.780464i | 0.920717 | + | 0.390232i | \(0.127605\pi\) | ||||
−0.920717 | + | 0.390232i | \(0.872395\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −3.03821e6 | −1.35146 | −0.675732 | − | 0.737148i | \(-0.736172\pi\) | ||||
−0.675732 | + | 0.737148i | \(0.736172\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 214065. | + | 546127.i | 0.0909893 | + | 0.232134i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 312378. | 0.121484 | 0.0607420 | − | 0.998153i | \(-0.480653\pi\) | ||||
0.0607420 | + | 0.998153i | \(0.480653\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 383927. | 0.142956 | 0.0714782 | − | 0.997442i | \(-0.477228\pi\) | ||||
0.0714782 | + | 0.997442i | \(0.477228\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 776957.i | 0.265698i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 343951.i | − | 0.112822i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 874420. | 0.264339 | 0.132169 | − | 0.991227i | \(-0.457806\pi\) | ||||
0.132169 | + | 0.991227i | \(0.457806\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2.08195e6i | − | 0.604698i | −0.953197 | − | 0.302349i | \(-0.902229\pi\) | ||
0.953197 | − | 0.302349i | \(-0.0977709\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 586161.i | 0.157406i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −359939. | −0.0930100 | −0.0465050 | − | 0.998918i | \(-0.514808\pi\) | ||||
−0.0465050 | + | 0.998918i | \(0.514808\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 669324. | 0.160383 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 2.96880e6 | 0.685517 | 0.342759 | − | 0.939424i | \(-0.388639\pi\) | ||||
0.342759 | + | 0.939424i | \(0.388639\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 8.76081e6i | 1.88103i | 0.339758 | + | 0.940513i | \(0.389655\pi\) | ||||
−0.339758 | + | 0.940513i | \(0.610345\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.20879e6 | −0.250433 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 4.80027e6i | 0.927101i | 0.886070 | + | 0.463551i | \(0.153425\pi\) | ||||
−0.886070 | + | 0.463551i | \(0.846575\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.30819e6 | −0.244093 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 8.65531e6i | 1.50912i | 0.656231 | + | 0.754560i | \(0.272150\pi\) | ||||
−0.656231 | + | 0.754560i | \(0.727850\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 4.56974e6i | − | 0.770647i | −0.922782 | − | 0.385324i | \(-0.874090\pi\) | ||
0.922782 | − | 0.385324i | \(-0.125910\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 279832.i | 0.0441960i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.01972e6 | 0.155939 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −3.05071e6 | −0.437826 | −0.218913 | − | 0.975744i | \(-0.570251\pi\) | ||||
−0.218913 | + | 0.975744i | \(0.570251\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.92508e6i | 0.963281i | 0.876369 | + | 0.481641i | \(0.159959\pi\) | ||||
−0.876369 | + | 0.481641i | \(0.840041\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −5.70028e6 | −0.745585 | −0.372793 | − | 0.927915i | \(-0.621600\pi\) | ||||
−0.372793 | + | 0.927915i | \(0.621600\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.19083e6 | −0.404897 | −0.202449 | − | 0.979293i | \(-0.564890\pi\) | ||||
−0.202449 | + | 0.979293i | \(0.564890\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | − | 1.62373e6i | − | 0.194100i | ||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 1.70523e6i | − | 0.197935i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 791615. | + | 2.01959e6i | 0.0867112 | + | 0.221220i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 3.07525e6i | 0.327365i | 0.986513 | + | 0.163683i | \(0.0523373\pi\) | ||||
−0.986513 | + | 0.163683i | \(0.947663\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 710781. | 0.0715188 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.76716e6i | 0.270804i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 7.92143e6i | 0.733883i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1.25510e7i | 1.13179i | 0.824478 | + | 0.565893i | \(0.191469\pi\) | ||||
−0.824478 | + | 0.565893i | \(0.808531\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 4.77970e6i | − | 0.408623i | −0.978906 | − | 0.204312i | \(-0.934504\pi\) | ||
0.978906 | − | 0.204312i | \(-0.0654956\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.74322e7 | −1.45159 | −0.725796 | − | 0.687910i | \(-0.758529\pi\) | ||||
−0.725796 | + | 0.687910i | \(0.758529\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.39490e7 | −1.10274 | −0.551371 | − | 0.834260i | \(-0.685895\pi\) | ||||
−0.551371 | + | 0.834260i | \(0.685895\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.67320e6 | −0.128927 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.10947e7 | 0.812684 | 0.406342 | − | 0.913721i | \(-0.366804\pi\) | ||||
0.406342 | + | 0.913721i | \(0.366804\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.24275e7i | 0.887834i | 0.896068 | + | 0.443917i | \(0.146411\pi\) | ||||
−0.896068 | + | 0.443917i | \(0.853589\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.99878e6 | −0.135915 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.56887e7 | + | 6.14947e6i | −1.04111 | + | 0.408082i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.16292e7 | 0.735408 | 0.367704 | − | 0.929943i | \(-0.380144\pi\) | ||||
0.367704 | + | 0.929943i | \(0.380144\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.47517e6 | 0.152842 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 1.30041e7i | 0.766091i | 0.923729 | + | 0.383046i | \(0.125125\pi\) | ||||
−0.923729 | + | 0.383046i | \(0.874875\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.32104e6i | 0.0760355i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −9.63641e6 | −0.529722 | −0.264861 | − | 0.964287i | \(-0.585326\pi\) | ||||
−0.264861 | + | 0.964287i | \(0.585326\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.35607e6i | 0.126605i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.24713e7i | 0.640700i | 0.947299 | + | 0.320350i | \(0.103800\pi\) | ||||
−0.947299 | + | 0.320350i | \(0.896200\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.03869e7 | 0.521889 | 0.260945 | − | 0.965354i | \(-0.415966\pi\) | ||||
0.260945 | + | 0.965354i | \(0.415966\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −4.83769e6 | −0.232616 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 2.60469e7 | 1.22551 | 0.612755 | − | 0.790273i | \(-0.290061\pi\) | ||||
0.612755 | + | 0.790273i | \(0.290061\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 1.69484e7i | 0.763855i | 0.924192 | + | 0.381927i | \(0.124740\pi\) | ||||
−0.924192 | + | 0.381927i | \(0.875260\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.25463e6 | 0.275958 | 0.137979 | − | 0.990435i | \(-0.455939\pi\) | ||||
0.137979 | + | 0.990435i | \(0.455939\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 8.05010e6i | − | 0.340530i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.37411e7 | −0.569282 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 3.85805e7i | 1.53379i | 0.641775 | + | 0.766893i | \(0.278198\pi\) | ||||
−0.641775 | + | 0.766893i | \(0.721802\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.26515e6i | 0.127185i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 1.92278e7i | 0.719309i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.35547e6 | 0.123042 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.26114e6 | 0.0796946 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1.08507e7i | 0.375011i | 0.982264 | + | 0.187505i | \(0.0600402\pi\) | ||||
−0.982264 | + | 0.187505i | \(0.939960\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −4.76110e7 | −1.58280 | −0.791400 | − | 0.611298i | \(-0.790648\pi\) | ||||
−0.791400 | + | 0.611298i | \(0.790648\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.98712e7 | −0.648023 | −0.324011 | − | 0.946053i | \(-0.605032\pi\) | ||||
−0.324011 | + | 0.946053i | \(0.605032\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 5.27458e7i | 1.65581i | 0.560869 | + | 0.827904i | \(0.310467\pi\) | ||||
−0.560869 | + | 0.827904i | \(0.689533\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 6.00459e6i | − | 0.184974i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8.07088e6 | + | 2.05906e7i | 0.239504 | + | 0.611029i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 3.75804e7i | − | 1.09474i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −7.89890e6 | −0.221809 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3.89340e7i | 1.07361i | 0.843708 | + | 0.536803i | \(0.180368\pi\) | ||||
−0.843708 | + | 0.536803i | \(0.819632\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 2.78988e6i | − | 0.0742080i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 1.68475e7i | − | 0.440197i | −0.975478 | − | 0.220098i | \(-0.929362\pi\) | ||
0.975478 | − | 0.220098i | \(-0.0706378\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 1.02330e7i | 0.258072i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.94972e7 | −0.483159 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −3.85116e7 | −0.921729 | −0.460864 | − | 0.887471i | \(-0.652461\pi\) | ||||
−0.460864 | + | 0.887471i | \(0.652461\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.79730e7 | 0.658056 | 0.329028 | − | 0.944320i | \(-0.393279\pi\) | ||||
0.329028 | + | 0.944320i | \(0.393279\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −4.77207e7 | −1.08488 | −0.542441 | − | 0.840094i | \(-0.682500\pi\) | ||||
−0.542441 | + | 0.840094i | \(0.682500\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.21424e6i | 0.0718445i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −3.95639e7 | −0.855098 | −0.427549 | − | 0.903992i | \(-0.640623\pi\) | ||||
−0.427549 | + | 0.903992i | \(0.640623\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.45149e7 | + | 3.19693e7i | −0.733643 | + | 0.679535i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 5.70395e6 | 0.117300 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 2.36899e7 | 0.479254 | 0.239627 | − | 0.970865i | \(-0.422975\pi\) | ||||
0.239627 | + | 0.970865i | \(0.422975\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.11226e7i | 0.217813i | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 3.34668e7i | 0.644893i | 0.946588 | + | 0.322446i | \(0.104505\pi\) | ||||
−0.946588 | + | 0.322446i | \(0.895495\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 4.66452e7 | 0.870528 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.72230e7i | 0.316368i | 0.987410 | + | 0.158184i | \(0.0505638\pi\) | ||||
−0.987410 | + | 0.158184i | \(0.949436\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − | 3.87861e7i | − | 0.690367i | −0.938535 | − | 0.345184i | \(-0.887817\pi\) | ||
0.938535 | − | 0.345184i | \(-0.112183\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 489953. | 0.00858563 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.82796e7 | 1.15996 | 0.579979 | − | 0.814631i | \(-0.303061\pi\) | ||||
0.579979 | + | 0.814631i | \(0.303061\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.52355e7 | 0.422165 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 8.38744e6i | − | 0.136094i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.29750e7 | 0.846641 | 0.423320 | − | 0.905980i | \(-0.360864\pi\) | ||||
0.423320 | + | 0.905980i | \(0.360864\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 8.04949e7i | − | 1.24835i | −0.781286 | − | 0.624173i | \(-0.785436\pi\) | ||
0.781286 | − | 0.624173i | \(-0.214564\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.94927e7 | −1.21454 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 4.88523e6i | 0.0724605i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7.86984e7i | 1.15026i | 0.818062 | + | 0.575130i | \(0.195049\pi\) | ||||
−0.818062 | + | 0.575130i | \(0.804951\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 1.54142e7i | 0.218812i | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.08885e7 | −0.152344 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1.33352e8 | 1.81283 | 0.906415 | − | 0.422389i | \(-0.138808\pi\) | ||||
0.906415 | + | 0.422389i | \(0.138808\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 8.03244e7i | − | 1.07647i | −0.842795 | − | 0.538234i | \(-0.819092\pi\) | ||
0.842795 | − | 0.538234i | \(-0.180908\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.93225e7 | −0.642507 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.06745e7 | 0.137108 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.75808e7i | 1.09390i | 0.837166 | + | 0.546950i | \(0.184211\pi\) | ||||
−0.837166 | + | 0.546950i | \(0.815789\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.28661e8i | 1.58483i | 0.609983 | + | 0.792414i | \(0.291176\pi\) | ||||
−0.609983 | + | 0.792414i | \(0.708824\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 1.95905e7 | + | 4.99798e7i | 0.234748 | + | 0.598894i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.59660e7i | 0.306911i | 0.988156 | + | 0.153455i | \(0.0490401\pi\) | ||||
−0.988156 | + | 0.153455i | \(0.950960\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 3.50548e6 | 0.0403215 | 0.0201607 | − | 0.999797i | \(-0.493582\pi\) | ||||
0.0201607 | + | 0.999797i | \(0.493582\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 4.99007e6i | − | 0.0566274i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 8.29521e7i | − | 0.916407i | −0.888847 | − | 0.458203i | \(-0.848493\pi\) | ||
0.888847 | − | 0.458203i | \(-0.151507\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 2.97694e7i | − | 0.324519i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 3.80608e6i | 0.0404058i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −1.51174e8 | −1.58390 | −0.791951 | − | 0.610584i | \(-0.790935\pi\) | ||||
−0.791951 | + | 0.610584i | \(0.790935\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −1.72984e8 | −1.76565 | −0.882824 | − | 0.469705i | \(-0.844360\pi\) | ||||
−0.882824 | + | 0.469705i | \(0.844360\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.27212e8 | 1.28169 | 0.640847 | − | 0.767668i | \(-0.278583\pi\) | ||||
0.640847 | + | 0.767668i | \(0.278583\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −1.69010e8 | −1.65944 | −0.829722 | − | 0.558177i | \(-0.811501\pi\) | ||||
−0.829722 | + | 0.558177i | \(0.811501\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 1.31705e7i | − | 0.127669i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.24086e7 | 0.117257 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.82894e7 | − | 9.76848e7i | −0.357271 | − | 0.911478i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 8.22265e7 | 0.748179 | 0.374089 | − | 0.927393i | \(-0.377955\pi\) | ||||
0.374089 | + | 0.927393i | \(0.377955\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.79497e7 | −0.341015 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1.54449e7i | 0.135381i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 2.07542e8i | − | 1.79688i | −0.439100 | − | 0.898438i | \(-0.644703\pi\) | ||
0.439100 | − | 0.898438i | \(-0.355297\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 2.56953e6 | 0.0217074 | 0.0108537 | − | 0.999941i | \(-0.496545\pi\) | ||||
0.0108537 | + | 0.999941i | \(0.496545\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 6.12195e7i | − | 0.510915i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.51739e7i | 0.123602i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 2.18130e8 | 1.75555 | 0.877774 | − | 0.479074i | \(-0.159028\pi\) | ||||
0.877774 | + | 0.479074i | \(0.159028\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 1.23404e8 | 0.969672 | 0.484836 | − | 0.874605i | \(-0.338879\pi\) | ||||
0.484836 | + | 0.874605i | \(0.338879\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.27253e7 | 0.0988084 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1.41684e7i | 0.107441i | 0.998556 | + | 0.0537203i | \(0.0171079\pi\) | ||||
−0.998556 | + | 0.0537203i | \(0.982892\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.69273e7 | 0.201804 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − | 1.73130e7i | − | 0.126750i | ||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.92103e7 | −0.211380 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 5.98342e7i | − | 0.423094i | −0.977368 | − | 0.211547i | \(-0.932150\pi\) | ||
0.977368 | − | 0.211547i | \(-0.0678501\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 5.41820e7i | − | 0.378747i | −0.981905 | − | 0.189374i | \(-0.939354\pi\) | ||
0.981905 | − | 0.189374i | \(-0.0606458\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.04330e8i | 0.712818i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.67814e7 | −0.586219 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.31256e8 | 1.52726 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.36509e6i | 0.0480969i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −3.48940e7 | −0.222836 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −6.50918e7 | −0.411088 | −0.205544 | − | 0.978648i | \(-0.565896\pi\) | ||||
−0.205544 | + | 0.978648i | \(0.565896\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3.59774e7i | 0.222249i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − | 3.47709e7i | − | 0.212449i | −0.994342 | − | 0.106224i | \(-0.966124\pi\) | ||
0.994342 | − | 0.106224i | \(-0.0338762\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.21247e8 | − | 4.75252e7i | 0.724799 | − | 0.284099i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 3.95956e7i | − | 0.234138i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −4.97836e7 | −0.288085 | −0.144043 | − | 0.989571i | \(-0.546010\pi\) | ||||
−0.144043 | + | 0.989571i | \(0.546010\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.63932e7i | 0.551837i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 2.74472e8i | − | 1.53806i | −0.639215 | − | 0.769028i | \(-0.720740\pi\) | ||
0.639215 | − | 0.769028i | \(-0.279260\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 2.43533e7i | − | 0.135024i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 2.65773e8i | − | 1.44270i | −0.692573 | − | 0.721348i | \(-0.743523\pi\) | ||
0.692573 | − | 0.721348i | \(-0.256477\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.28689e8 | −1.22839 | −0.614197 | − | 0.789153i | \(-0.710520\pi\) | ||||
−0.614197 | + | 0.789153i | \(0.710520\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.19721e8 | −0.629748 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 3.19929e8 | 1.66543 | 0.832715 | − | 0.553701i | \(-0.186785\pi\) | ||||
0.832715 | + | 0.553701i | \(0.186785\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −5.14029e7 | −0.262095 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.11316e7i | 0.207572i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.80875e7 | −0.138867 | −0.0694334 | − | 0.997587i | \(-0.522119\pi\) | ||||
−0.0694334 | + | 0.997587i | \(0.522119\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.06630e8 | + | 8.09924e7i | −1.01122 | + | 0.396368i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 3.59440e8 | 1.72370 | 0.861850 | − | 0.507163i | \(-0.169306\pi\) | ||||
0.861850 | + | 0.507163i | \(0.169306\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.99529e6 | 0.0237143 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 3.80247e8i | − | 1.76923i | −0.466318 | − | 0.884617i | \(-0.654420\pi\) | ||
0.466318 | − | 0.884617i | \(-0.345580\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.65922e8i | 0.764329i | 0.924094 | + | 0.382165i | \(0.124821\pi\) | ||||
−0.924094 | + | 0.382165i | \(0.875179\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.02808e7 | −0.136742 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 1.16620e8i | − | 0.521441i | −0.965414 | − | 0.260721i | \(-0.916040\pi\) | ||
0.965414 | − | 0.260721i | \(-0.0839601\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − | 2.26913e8i | − | 0.994800i | ||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 2.26238e8 | 0.982166 | 0.491083 | − | 0.871113i | \(-0.336601\pi\) | ||||
0.491083 | + | 0.871113i | \(0.336601\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 2.64442e8 | 1.12584 | 0.562918 | − | 0.826513i | \(-0.309679\pi\) | ||||
0.562918 | + | 0.826513i | \(0.309679\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.93952e8 | 1.66101 | 0.830504 | − | 0.557013i | \(-0.188053\pi\) | ||||
0.830504 | + | 0.557013i | \(0.188053\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 2.35572e7i | − | 0.0974227i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.28865e8 | 0.937432 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.98071e7i | 0.200143i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −4.29945e8 | −1.71129 | −0.855647 | − | 0.517559i | \(-0.826841\pi\) | ||||
−0.855647 | + | 0.517559i | \(0.826841\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 2.89610e7i | 0.113108i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 2.71066e8i | − | 1.04871i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 3.42337e8i | − | 1.29981i | −0.760015 | − | 0.649906i | \(-0.774808\pi\) | ||
0.760015 | − | 0.649906i | \(-0.225192\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.03299e8 | −1.14087 | −0.570437 | − | 0.821342i | \(-0.693226\pi\) | ||||
−0.570437 | + | 0.821342i | \(0.693226\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 3.03991e8 | 1.12240 | 0.561199 | − | 0.827681i | \(-0.310340\pi\) | ||||
0.561199 | + | 0.827681i | \(0.310340\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.70020e7i | 0.208524i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −2.88590e8 | −1.03643 | −0.518217 | − | 0.855249i | \(-0.673404\pi\) | ||||
−0.518217 | + | 0.855249i | \(0.673404\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.50387e7 | −0.195859 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 5.42749e8i | − | 1.89646i | −0.317591 | − | 0.948228i | \(-0.602874\pi\) | ||
0.317591 | − | 0.948228i | \(-0.397126\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 2.52061e8i | − | 0.872774i | −0.899759 | − | 0.436387i | \(-0.856258\pi\) | ||
0.899759 | − | 0.436387i | \(-0.143742\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 3.87789e6 | + | 9.89335e6i | 0.0131865 | + | 0.0336417i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1.48599e8i | − | 0.500769i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 3.94744e7 | 0.130662 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | − | 1.26000e8i | − | 0.413356i | −0.978409 | − | 0.206678i | \(-0.933735\pi\) | ||
0.978409 | − | 0.206678i | \(-0.0662652\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.11022e8i | 1.64692i | 0.567371 | + | 0.823462i | \(0.307961\pi\) | ||||
−0.567371 | + | 0.823462i | \(0.692039\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.29126e7i | 0.232913i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 5.66185e7i | − | 0.177704i | −0.996045 | − | 0.0888518i | \(-0.971680\pi\) | ||
0.996045 | − | 0.0888518i | \(-0.0283197\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.65888e6 | 0.0176059 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −3.19521e8 | −0.976880 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.08142e8 | 1.23702 | 0.618511 | − | 0.785776i | \(-0.287736\pi\) | ||||
0.618511 | + | 0.785776i | \(0.287736\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 6.95501e6 | 0.0207178 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 3.03513e8i | − | 0.896352i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −4.90639e8 | −1.42432 | −0.712161 | − | 0.702016i | \(-0.752283\pi\) | ||||
−0.712161 | + | 0.702016i | \(0.752283\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.86447e7 | + | 3.86657e7i | −0.283928 | + | 0.111291i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 6.00739e7 | 0.169992 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.65761e6 | 0.0186801 | 0.00934006 | − | 0.999956i | \(-0.497027\pi\) | ||||
0.00934006 | + | 0.999956i | \(0.497027\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 2.53242e8i | 0.698662i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.40749e7i | 0.0385060i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 2.02239e8 | 0.544098 | 0.272049 | − | 0.962283i | \(-0.412299\pi\) | ||||
0.272049 | + | 0.962283i | \(0.412299\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 8.17314e7i | − | 0.218064i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 2.90434e8i | 0.762138i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 6.15946e8 | 1.60302 | 0.801511 | − | 0.597980i | \(-0.204030\pi\) | ||||
0.801511 | + | 0.597980i | \(0.204030\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.26511e8 | 0.323875 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 2.80626e8 | 0.712551 | 0.356275 | − | 0.934381i | \(-0.384046\pi\) | ||||
0.356275 | + | 0.934381i | \(0.384046\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | − | 4.87048e7i | − | 0.121666i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1.30355e8 | −0.322993 | −0.161496 | − | 0.986873i | \(-0.551632\pi\) | ||||
−0.161496 | + | 0.986873i | \(0.551632\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | − | 4.17618e8i | − | 1.01815i | −0.860721 | − | 0.509076i | \(-0.829987\pi\) | ||
0.860721 | − | 0.509076i | \(-0.170013\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.58405e7 | 0.0383090 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.47693e7i | 0.0827467i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.16726e8i | 0.275579i | 0.990462 | + | 0.137790i | \(0.0439998\pi\) | ||||
−0.990462 | + | 0.137790i | \(0.956000\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 3.77155e7i | − | 0.0876352i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 5.08428e7 | 0.117204 | 0.0586019 | − | 0.998281i | \(-0.481336\pi\) | ||||
0.0586019 | + | 0.998281i | \(0.481336\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 3.41887e8 | 0.775763 | 0.387881 | − | 0.921709i | \(-0.373207\pi\) | ||||
0.387881 | + | 0.921709i | \(0.373207\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.69843e8i | 0.382361i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −4.42806e8 | −0.981359 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −4.63630e8 | −1.01951 | −0.509757 | − | 0.860319i | \(-0.670265\pi\) | ||||
−0.509757 | + | 0.860319i | \(0.670265\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 2.27556e8i | − | 0.492663i | −0.969186 | − | 0.246332i | \(-0.920775\pi\) | ||
0.969186 | − | 0.246332i | \(-0.0792253\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 4.94958e8i | − | 1.06332i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 6.01117e8 | − | 2.35619e8i | 1.27159 | − | 0.498423i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.61132e7i | 0.117791i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −6.52046e6 | −0.0134794 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 5.56749e8i | − | 1.14218i | −0.820887 | − | 0.571091i | \(-0.806520\pi\) | ||
0.820887 | − | 0.571091i | \(-0.193480\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | − | 1.14968e8i | − | 0.232298i | ||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.06647e8i | 0.614921i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 5.93972e7i | − | 0.117325i | −0.998278 | − | 0.0586626i | \(-0.981316\pi\) | ||
0.998278 | − | 0.0586626i | \(-0.0186836\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.97812e8 | −0.583851 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 9.95778e7 | 0.192316 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.21251e7 | 0.0232434 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3.52427e7 | −0.0665615 | −0.0332808 | − | 0.999446i | \(-0.510596\pi\) | ||||
−0.0332808 | + | 0.999446i | \(0.510596\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.92642e8i | 0.923568i | 0.886992 | + | 0.461784i | \(0.152791\pi\) | ||||
−0.886992 | + | 0.461784i | \(0.847209\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.37813e7 | 0.0993478 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.82118e7 | + | 2.50560e8i | 0.180093 | + | 0.459458i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.95856e8 | 0.353921 | 0.176961 | − | 0.984218i | \(-0.443373\pi\) | ||||
0.176961 | + | 0.984218i | \(0.443373\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.67464e6 | 0.0173554 | 0.00867771 | − | 0.999962i | \(-0.497238\pi\) | ||||
0.00867771 | + | 0.999962i | \(0.497238\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.64699e7i | 0.0291188i | 0.999894 | + | 0.0145594i | \(0.00463456\pi\) | ||||
−0.999894 | + | 0.0145594i | \(0.995365\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.92536e8i | 1.04004i | 0.854153 | + | 0.520022i | \(0.174076\pi\) | ||||
−0.854153 | + | 0.520022i | \(0.825924\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −3.55761e8 | −0.615493 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.58706e8i | 0.272605i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − | 6.70735e8i | − | 1.13570i | −0.823131 | − | 0.567852i | \(-0.807775\pi\) | ||
0.823131 | − | 0.567852i | \(-0.192225\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.34334e8 | 0.393955 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.18979e7 | −0.0362938 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.42950e8 | −0.235253 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.20897e8i | 0.196168i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −7.92744e8 | −1.27728 | −0.638640 | − | 0.769506i | \(-0.720503\pi\) | ||||
−0.638640 | + | 0.769506i | \(0.720503\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 1.10391e9i | 1.75385i | 0.480630 | + | 0.876923i | \(0.340408\pi\) | ||||
−0.480630 | + | 0.876923i | \(0.659592\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.48554e8 | 0.234372 | 0.117186 | − | 0.993110i | \(-0.462613\pi\) | ||||
0.117186 | + | 0.993110i | \(0.462613\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 8.48412e8i | − | 1.32000i | −0.751265 | − | 0.660001i | \(-0.770556\pi\) | ||
0.751265 | − | 0.660001i | \(-0.229444\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.69591e7i | 0.134359i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | − | 1.46425e8i | − | 0.223130i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.78352e8 | 0.572587 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −4.79052e7 | −0.0715086 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.48915e8i | 0.369022i | 0.982830 | + | 0.184511i | \(0.0590701\pi\) | ||||
−0.982830 | + | 0.184511i | \(0.940930\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −1.43974e8 | −0.210551 | −0.105275 | − | 0.994443i | \(-0.533572\pi\) | ||||
−0.105275 | + | 0.994443i | \(0.533572\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.57167e8 | 0.228286 | 0.114143 | − | 0.993464i | \(-0.463588\pi\) | ||||
0.114143 | + | 0.993464i | \(0.463588\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.52557e8i | 0.791784i | 0.918297 | + | 0.395892i | \(0.129564\pi\) | ||||
−0.918297 | + | 0.395892i | \(0.870436\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.36720e8i | 0.194593i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −2.31194e8 | − | 5.89827e8i | −0.324655 | − | 0.828267i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.56795e8i | 0.218707i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 6.14346e8 | 0.845540 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.19355e8i | 0.573334i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 8.27830e7i | − | 0.111685i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 1.14270e9i | − | 1.53147i | −0.643155 | − | 0.765736i | \(-0.722375\pi\) | ||
0.643155 | − | 0.765736i | \(-0.277625\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1.15658e9i | 1.52975i | 0.644180 | + | 0.764874i | \(0.277199\pi\) | ||||
−0.644180 | + | 0.764874i | \(0.722801\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.90089e8 | −0.249772 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −2.59828e8 | −0.336960 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −8.12112e8 | −1.04633 | −0.523166 | − | 0.852231i | \(-0.675249\pi\) | ||||
−0.523166 | + | 0.852231i | \(0.675249\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −4.35902e8 | −0.554350 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 2.36292e8i | − | 0.298555i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −6.43310e8 | −0.802367 | −0.401183 | − | 0.915998i | \(-0.631401\pi\) | ||||
−0.401183 | + | 0.915998i | \(0.631401\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.76180e8 | − | 7.04596e8i | −0.342250 | − | 0.873155i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 1.84727e7 | 0.0225993 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 8.50189e7 | 0.103347 | 0.0516734 | − | 0.998664i | \(-0.483545\pi\) | ||||
0.0516734 | + | 0.998664i | \(0.483545\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 5.09558e8i | 0.611540i | 0.952105 | + | 0.305770i | \(0.0989139\pi\) | ||||
−0.952105 | + | 0.305770i | \(0.901086\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 7.36720e8i | − | 0.878551i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 3.61074e8 | 0.425154 | 0.212577 | − | 0.977144i | \(-0.431814\pi\) | ||||
0.212577 | + | 0.977144i | \(0.431814\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.73546e8i | 0.905081i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 9.37652e8i | 1.08334i | 0.840593 | + | 0.541668i | \(0.182207\pi\) | ||||
−0.840593 | + | 0.541668i | \(0.817793\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.52651e7 | −0.0634514 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 2.67146e7 | 0.0302896 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.59465e8 | −0.179679 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 1.25451e8i | 0.139602i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 7.22341e8 | 0.798845 | 0.399423 | − | 0.916767i | \(-0.369211\pi\) | ||||
0.399423 | + | 0.916767i | \(0.369211\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 7.06080e8i | 0.771252i | 0.922655 | + | 0.385626i | \(0.126015\pi\) | ||||
−0.922655 | + | 0.385626i | \(0.873985\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.28334e7 | 0.0356433 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.22331e9i | 1.31176i | 0.754866 | + | 0.655879i | \(0.227702\pi\) | ||||
−0.754866 | + | 0.655879i | \(0.772298\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 8.71151e7i | − | 0.0928422i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 4.63662e8i | 0.488136i | 0.969758 | + | 0.244068i | \(0.0784820\pi\) | ||||
−0.969758 | + | 0.244068i | \(0.921518\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.03263e8 | −0.108053 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 3.07082e8 | 0.317443 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 4.33129e8i | − | 0.445038i | −0.974928 | − | 0.222519i | \(-0.928572\pi\) | ||
0.974928 | − | 0.222519i | \(-0.0714279\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.78034e7 | −0.0586792 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 3.18610e8 | 0.321495 | 0.160747 | − | 0.986996i | \(-0.448610\pi\) | ||||
0.160747 | + | 0.986996i | \(0.448610\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 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 | 684.7.h.c.37.6 | 8 | ||
3.2 | odd | 2 | 76.7.c.b.37.5 | yes | 8 | ||
12.11 | even | 2 | 304.7.e.c.113.4 | 8 | |||
19.18 | odd | 2 | inner | 684.7.h.c.37.5 | 8 | ||
57.56 | even | 2 | 76.7.c.b.37.4 | ✓ | 8 | ||
228.227 | odd | 2 | 304.7.e.c.113.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
76.7.c.b.37.4 | ✓ | 8 | 57.56 | even | 2 | ||
76.7.c.b.37.5 | yes | 8 | 3.2 | odd | 2 | ||
304.7.e.c.113.4 | 8 | 12.11 | even | 2 | |||
304.7.e.c.113.5 | 8 | 228.227 | odd | 2 | |||
684.7.h.c.37.5 | 8 | 19.18 | odd | 2 | inner | ||
684.7.h.c.37.6 | 8 | 1.1 | even | 1 | trivial |