Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [76,7,Mod(37,76)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(76, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("76.37");
S:= CuspForms(chi, 7);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 76 = 2^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 7 \) |
Character orbit: | \([\chi]\) | \(=\) | 76.c (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: | \(17.4841103551\) |
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: | \(\Z[a_1, \ldots, a_{19}]\) |
Coefficient ring index: | \( 2^{8}\cdot 3\cdot 5 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 37.5 | ||
Root | \(13.8790i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 76.37 |
Dual form | 76.7.c.b.37.4 |
$q$-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 \(\left(\mathbb{Z}/76\mathbb{Z}\right)^\times\).
\(n\) | \(21\) | \(39\) |
\(\chi(n)\) | \(-1\) | \(1\) |
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 | ||||||||
\(3\) | 13.8790i | 0.514036i | 0.966407 | + | 0.257018i | \(0.0827400\pi\) | ||||
−0.966407 | + | 0.257018i | \(0.917260\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −18.1155 | −0.144924 | −0.0724619 | − | 0.997371i | \(-0.523086\pi\) | ||||
−0.0724619 | + | 0.997371i | \(0.523086\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 85.5200 | 0.249330 | 0.124665 | − | 0.992199i | \(-0.460214\pi\) | ||||
0.124665 | + | 0.992199i | \(0.460214\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 536.374 | 0.735767 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −316.255 | −0.237607 | −0.118803 | − | 0.992918i | \(-0.537906\pi\) | ||||
−0.118803 | + | 0.992918i | \(0.537906\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2456.75i | 1.11823i | 0.829091 | + | 0.559114i | \(0.188859\pi\) | ||||
−0.829091 | + | 0.559114i | \(0.811141\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 251.424i | − | 0.0744960i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −3224.36 | −0.656291 | −0.328146 | − | 0.944627i | \(-0.606424\pi\) | ||||
−0.328146 | + | 0.944627i | \(0.606424\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2503.10 | + | 6385.95i | 0.364936 | + | 0.931033i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 1186.93i | 0.128164i | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −7826.52 | −0.643258 | −0.321629 | − | 0.946866i | \(-0.604230\pi\) | ||||
−0.321629 | + | 0.946866i | \(0.604230\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −15296.8 | −0.978997 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 17562.1i | 0.892247i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 18986.6i | 0.778489i | 0.921135 | + | 0.389244i | \(0.127264\pi\) | ||||
−0.921135 | + | 0.389244i | \(0.872736\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 32356.9i | 1.08613i | 0.839691 | + | 0.543065i | \(0.182736\pi\) | ||||
−0.839691 | + | 0.543065i | \(0.817264\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 4389.29i | − | 0.122138i | ||||||
\(34\) | 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 | ||||||||
\(39\) | −34097.1 | −0.574809 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 94131.1i | 1.36578i | 0.730520 | + | 0.682892i | \(0.239278\pi\) | ||||
−0.730520 | + | 0.682892i | \(0.760722\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 39236.1 | 0.493493 | 0.246746 | − | 0.969080i | \(-0.420639\pi\) | ||||
0.246746 | + | 0.969080i | \(0.420639\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −9716.67 | −0.106630 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 92363.2 | 0.889622 | 0.444811 | − | 0.895625i | \(-0.353271\pi\) | ||||
0.444811 | + | 0.895625i | \(0.353271\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −110335. | −0.937835 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 44750.8i | − | 0.337357i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | − | 130058.i | − | 0.873597i | −0.899559 | − | 0.436798i | \(-0.856112\pi\) | ||
0.899559 | − | 0.436798i | \(-0.143888\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5729.10 | 0.0344349 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −88630.4 | + | 34740.4i | −0.478584 | + | 0.187590i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − | 180241.i | − | 0.877602i | −0.898584 | − | 0.438801i | \(-0.855403\pi\) | ||
0.898584 | − | 0.438801i | \(-0.144597\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 124818. | 0.549907 | 0.274953 | − | 0.961458i | \(-0.411338\pi\) | ||||
0.274953 | + | 0.961458i | \(0.411338\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 45870.7 | 0.183448 | ||||||||
\(64\) | 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 | ||||||||
\(69\) | − | 108624.i | − | 0.330658i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 177431.i | − | 0.495740i | −0.968793 | − | 0.247870i | \(-0.920269\pi\) | ||
0.968793 | − | 0.247870i | \(-0.0797305\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 314866. | 0.809389 | 0.404694 | − | 0.914452i | \(-0.367378\pi\) | ||||
0.404694 | + | 0.914452i | \(0.367378\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 212304.i | − | 0.503240i | ||||||
\(76\) | 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 | ||||||||
\(81\) | 147273. | 0.277120 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 601062. | 1.05120 | 0.525600 | − | 0.850732i | \(-0.323841\pi\) | ||||
0.525600 | + | 0.850732i | \(0.323841\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 58410.8 | 0.0951122 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −263514. | −0.400171 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 275459.i | 0.390739i | 0.980730 | + | 0.195369i | \(0.0625906\pi\) | ||||
−0.980730 | + | 0.195369i | \(0.937409\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 210101.i | 0.278807i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −449080. | −0.558310 | ||||||||
\(94\) | 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 | ||||||||
\(99\) | −169631. | −0.174823 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −702454. | −0.681795 | −0.340898 | − | 0.940100i | \(-0.610731\pi\) | ||||
−0.340898 | + | 0.940100i | \(0.610731\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 955700.i | − | 0.874600i | −0.899316 | − | 0.437300i | \(-0.855935\pi\) | ||
0.899316 | − | 0.437300i | \(-0.144065\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 21501.8i | − | 0.0185741i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − | 406564.i | − | 0.331877i | −0.986136 | − | 0.165938i | \(-0.946935\pi\) | ||
0.986136 | − | 0.165938i | \(-0.0530653\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1.98600e6i | 1.53356i | 0.641912 | + | 0.766779i | \(0.278142\pi\) | ||||
−0.641912 | + | 0.766779i | \(0.721858\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −214390. | −0.156760 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.34434e6i | 0.931692i | 0.884866 | + | 0.465846i | \(0.154250\pi\) | ||||
−0.884866 | + | 0.465846i | \(0.845750\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 141781. | 0.0932234 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 1.31774e6i | 0.822755i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −275747. | −0.163633 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1.67154e6 | −0.943543 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1.30644e6 | −0.702062 | ||||||||
\(124\) | 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 | ||||||||
\(129\) | 544557.i | 0.253673i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 3.03821e6 | 1.35146 | 0.675732 | − | 0.737148i | \(-0.263828\pi\) | ||||
0.675732 | + | 0.737148i | \(0.263828\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 214065. | + | 546127.i | 0.0909893 | + | 0.232134i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 318146.i | − | 0.129308i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −312378. | −0.121484 | −0.0607420 | − | 0.998153i | \(-0.519347\pi\) | ||||
−0.0607420 | + | 0.998153i | \(0.519347\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 383927. | 0.142956 | 0.0714782 | − | 0.997442i | \(-0.477228\pi\) | ||||
0.0714782 | + | 0.997442i | \(0.477228\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 1.28191e6i | 0.457297i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 776957.i | − | 0.265698i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | − | 343951.i | − | 0.112822i | ||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | − | 1.53134e6i | − | 0.482081i | ||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −874420. | −0.264339 | −0.132169 | − | 0.991227i | \(-0.542194\pi\) | ||||
−0.132169 | + | 0.991227i | \(0.542194\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2.08195e6i | − | 0.604698i | −0.953197 | − | 0.302349i | \(-0.902229\pi\) | ||
0.953197 | − | 0.302349i | \(-0.0977709\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −1.72946e6 | −0.482878 | ||||||||
\(154\) | 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 | ||||||||
\(159\) | 1.80508e6 | 0.449060 | ||||||||
\(160\) | 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 | ||||||||
\(165\) | 79514.0i | 0.0177008i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | − | 8.76081e6i | − | 1.88103i | −0.339758 | − | 0.940513i | \(-0.610345\pi\) | ||
0.339758 | − | 0.940513i | \(-0.389655\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1.20879e6 | −0.250433 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 1.34260e6 | + | 3.42526e6i | 0.268508 | + | 0.685023i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − | 4.80027e6i | − | 0.927101i | −0.886070 | − | 0.463551i | \(-0.846575\pi\) | ||
0.886070 | − | 0.463551i | \(-0.153425\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −1.30819e6 | −0.244093 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2.50156e6 | 0.451119 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 8.65531e6i | − | 1.50912i | −0.656231 | − | 0.754560i | \(-0.727850\pi\) | ||
0.656231 | − | 0.754560i | \(-0.272150\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 4.56974e6i | − | 0.770647i | −0.922782 | − | 0.385324i | \(-0.874090\pi\) | ||
0.922782 | − | 0.385324i | \(-0.125910\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1.73235e6i | 0.282672i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 279832.i | − | 0.0441960i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.01972e6 | 0.155939 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 1.50191e6i | 0.222463i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3.05071e6 | 0.437826 | 0.218913 | − | 0.975744i | \(-0.429749\pi\) | ||||
0.218913 | + | 0.975744i | \(0.429749\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.92508e6i | 0.963281i | 0.876369 | + | 0.481641i | \(0.159959\pi\) | ||||
−0.876369 | + | 0.481641i | \(0.840041\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 617685. | 0.0833035 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.70028e6 | 0.745585 | 0.372793 | − | 0.927915i | \(-0.378400\pi\) | ||||
0.372793 | + | 0.927915i | \(0.378400\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −3.19083e6 | −0.404897 | −0.202449 | − | 0.979293i | \(-0.564890\pi\) | ||||
−0.202449 | + | 0.979293i | \(0.564890\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 2.13743e6 | 0.263211 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1.62373e6i | 0.194100i | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − | 1.70523e6i | − | 0.197935i | ||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −4.19795e6 | −0.473288 | ||||||||
\(208\) | 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 | ||||||||
\(213\) | 2.46255e6 | 0.254828 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −710781. | −0.0715188 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 2.76716e6i | 0.270804i | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 4.37001e6i | 0.416055i | ||||||||
\(220\) | 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 | ||||||||
\(225\) | −8.20482e6 | −0.720314 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 4.77970e6i | 0.408623i | 0.978906 | + | 0.204312i | \(0.0654956\pi\) | ||||
−0.978906 | + | 0.204312i | \(0.934504\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.74322e7 | −1.45159 | −0.725796 | − | 0.687910i | \(-0.758529\pi\) | ||||
−0.725796 | + | 0.687910i | \(0.758529\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 375372.i | − | 0.0304527i | ||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.39490e7 | 1.10274 | 0.551371 | − | 0.834260i | \(-0.314105\pi\) | ||||
0.551371 | + | 0.834260i | \(0.314105\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.67320e6 | −0.128927 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 6.42594e6 | 0.482716 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.10947e7 | −0.812684 | −0.406342 | − | 0.913721i | \(-0.633196\pi\) | ||||
−0.406342 | + | 0.913721i | \(0.633196\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.24275e7i | 0.887834i | 0.896068 | + | 0.443917i | \(0.146411\pi\) | ||||
−0.896068 | + | 0.443917i | \(0.853589\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.48468e7i | 1.03470i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1.99878e6 | 0.135915 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.56887e7 | + | 6.14947e6i | −1.04111 | + | 0.408082i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 8.34213e6i | 0.540354i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.16292e7 | −0.735408 | −0.367704 | − | 0.929943i | \(-0.619856\pi\) | ||||
−0.367704 | + | 0.929943i | \(0.619856\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 2.47517e6 | 0.152842 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 810682.i | 0.0488911i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 1.30041e7i | − | 0.766091i | −0.923729 | − | 0.383046i | \(-0.874875\pi\) | ||
0.923729 | − | 0.383046i | \(-0.125125\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1.32104e6i | 0.0760355i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.01839e7i | 0.572786i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 9.63641e6 | 0.529722 | 0.264861 | − | 0.964287i | \(-0.414674\pi\) | ||||
0.264861 | + | 0.964287i | \(0.414674\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 2.35607e6i | 0.126605i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −3.82308e6 | −0.200854 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 1.24713e7i | − | 0.640700i | −0.947299 | − | 0.320350i | \(-0.896200\pi\) | ||
0.947299 | − | 0.320350i | \(-0.103800\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.03869e7 | 0.521889 | 0.260945 | − | 0.965354i | \(-0.415966\pi\) | ||||
0.260945 | + | 0.965354i | \(0.415966\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −2.91599e6 | −0.143317 | ||||||||
\(274\) | 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 | ||||||||
\(279\) | 1.73554e7i | 0.799139i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 1.69484e7i | − | 0.763855i | −0.924192 | − | 0.381927i | \(-0.875260\pi\) | ||
0.924192 | − | 0.381927i | \(-0.124740\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6.25463e6 | 0.275958 | 0.137979 | − | 0.990435i | \(-0.455939\pi\) | ||||
0.137979 | + | 0.990435i | \(0.455939\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.60558e6 | − | 629339.i | 0.0693582 | − | 0.0271863i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 8.05010e6i | 0.340530i | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.37411e7 | −0.569282 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.18329e7 | −0.480190 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 3.85805e7i | − | 1.53379i | −0.641775 | − | 0.766893i | \(-0.721802\pi\) | ||
0.641775 | − | 0.766893i | \(-0.278198\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 3.26515e6i | 0.127185i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 5.55409e6i | − | 0.212004i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 1.92278e7i | − | 0.719309i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.35547e6 | 0.123042 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 9.74934e6i | − | 0.350467i | ||||||
\(304\) | 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 | ||||||||
\(309\) | 1.32641e7 | 0.449576 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 4.76110e7 | 1.58280 | 0.791400 | − | 0.611298i | \(-0.209352\pi\) | ||||
0.791400 | + | 0.611298i | \(0.209352\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.98712e7 | −0.648023 | −0.324011 | − | 0.946053i | \(-0.605032\pi\) | ||||
−0.324011 | + | 0.946053i | \(0.605032\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −830970. | −0.0265860 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 5.27458e7i | − | 1.65581i | −0.560869 | − | 0.827904i | \(-0.689533\pi\) | ||
0.560869 | − | 0.827904i | \(-0.310467\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 6.00459e6i | − | 0.184974i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 5.64268e6 | 0.170597 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −8.07088e6 | − | 2.05906e7i | −0.239504 | − | 0.611029i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 3.75804e7i | − | 1.09474i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −2.75636e7 | −0.788303 | ||||||||
\(328\) | 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 | ||||||||
\(333\) | 8.28544e6i | 0.224379i | ||||||||
\(334\) | 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 | ||||||||
\(339\) | −1.86580e7 | −0.478923 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 1.02330e7i | − | 0.258072i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −1.94972e7 | −0.483159 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1.96778e6i | 0.0479202i | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.85116e7 | 0.921729 | 0.460864 | − | 0.887471i | \(-0.347539\pi\) | ||||
0.460864 | + | 0.887471i | \(0.347539\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.79730e7 | 0.658056 | 0.329028 | − | 0.944320i | \(-0.393279\pi\) | ||||
0.329028 | + | 0.944320i | \(0.393279\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.31456e7 | −0.997735 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 4.77207e7 | 1.08488 | 0.542441 | − | 0.840094i | \(-0.317500\pi\) | ||||
0.542441 | + | 0.840094i | \(0.317500\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.21424e6i | 0.0718445i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | − | 3.82709e6i | − | 0.0841131i | ||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 3.95639e7 | 0.855098 | 0.427549 | − | 0.903992i | \(-0.359377\pi\) | ||||
0.427549 | + | 0.903992i | \(0.359377\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −3.45149e7 | + | 3.19693e7i | −0.733643 | + | 0.679535i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 2.31993e7i | − | 0.485015i | ||||||
\(364\) | 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 | ||||||||
\(369\) | 5.04895e7i | 1.00490i | ||||||||
\(370\) | 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 | ||||||||
\(375\) | 7.77449e6i | 0.147427i | ||||||||
\(376\) | 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 | ||||||||
\(381\) | −2.21882e7 | −0.401187 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.87861e7i | 0.690367i | 0.938535 | + | 0.345184i | \(0.112183\pi\) | ||||
−0.938535 | + | 0.345184i | \(0.887817\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 489953. | 0.00858563 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2.10452e7 | 0.363096 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −6.82796e7 | −1.15996 | −0.579979 | − | 0.814631i | \(-0.696939\pi\) | ||||
−0.579979 | + | 0.814631i | \(0.696939\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.52355e7 | 0.422165 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 4.21673e7i | 0.694701i | ||||||||
\(394\) | 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 | ||||||||
\(399\) | −7.57968e6 | + | 2.97100e6i | −0.119325 | + | 0.0467718i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 8.04949e7i | 1.24835i | 0.781286 | + | 0.624173i | \(0.214564\pi\) | ||||
−0.781286 | + | 0.624173i | \(0.785436\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −7.94927e7 | −1.21454 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −2.66792e6 | −0.0401613 | ||||||||
\(406\) | 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 | ||||||||
\(411\) | − | 4.33549e6i | − | 0.0624472i | ||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 1.54142e7i | − | 0.218812i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.08885e7 | −0.152344 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.32850e6i | 0.0734847i | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −1.33352e8 | −1.81283 | −0.906415 | − | 0.422389i | \(-0.861192\pi\) | ||||
−0.906415 | + | 0.422389i | \(0.861192\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 8.03244e7i | − | 1.07647i | −0.842795 | − | 0.538234i | \(-0.819092\pi\) | ||
0.842795 | − | 0.538234i | \(-0.180908\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 4.95412e7 | 0.654554 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 4.93225e7 | 0.642507 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1.06745e7 | 0.137108 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 1.07834e7 | 0.136579 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 8.75808e7i | − | 1.09390i | −0.837166 | − | 0.546950i | \(-0.815789\pi\) | ||
0.837166 | − | 0.546950i | \(-0.184211\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.28661e8i | 1.58483i | 0.609983 | + | 0.792414i | \(0.291176\pi\) | ||||
−0.609983 | + | 0.792414i | \(0.708824\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.77368e6 | 0.0579943 | ||||||||
\(436\) | 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 | ||||||||
\(441\) | −5.91810e7 | −0.690028 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.50548e6 | −0.0403215 | −0.0201607 | − | 0.999797i | \(-0.506418\pi\) | ||||
−0.0201607 | + | 0.999797i | \(0.506418\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − | 4.99007e6i | − | 0.0566274i | ||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 1.21360e7i | − | 0.135880i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 8.29521e7i | 0.916407i | 0.888847 | + | 0.458203i | \(0.151507\pi\) | ||||
−0.888847 | + | 0.458203i | \(0.848493\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 2.97694e7i | − | 0.324519i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 2.88953e7 | 0.310837 | ||||||||
\(454\) | 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 | ||||||||
\(459\) | − | 5.66265e7i | − | 0.585574i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 1.72984e8 | 1.76565 | 0.882824 | − | 0.469705i | \(-0.155640\pi\) | ||||
0.882824 | + | 0.469705i | \(0.155640\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 1.27212e8 | 1.28169 | 0.640847 | − | 0.767668i | \(-0.278583\pi\) | ||||
0.640847 | + | 0.767668i | \(0.278583\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.13531e6 | 0.0809124 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 1.69010e8 | 1.65944 | 0.829722 | − | 0.558177i | \(-0.188499\pi\) | ||||
0.829722 | + | 0.558177i | \(0.188499\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | − | 1.31705e7i | − | 0.127669i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 4.99558e6i | − | 0.0478105i | ||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1.24086e7 | −0.117257 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −3.82894e7 | − | 9.76848e7i | −0.357271 | − | 0.911478i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 6.97600e7i | − | 0.642764i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −8.22265e7 | −0.748179 | −0.374089 | − | 0.927393i | \(-0.622045\pi\) | ||||
−0.374089 | + | 0.927393i | \(0.622045\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.79497e7 | −0.341015 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | − | 9.28953e6i | − | 0.0824428i | ||||||
\(484\) | 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 | ||||||||
\(489\) | 4.12039e7i | 0.352380i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −2.56953e6 | −0.0217074 | −0.0108537 | − | 0.999941i | \(-0.503455\pi\) | ||||
−0.0108537 | + | 0.999941i | \(0.503455\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | − | 6.12195e7i | − | 0.510915i | ||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 3.07294e6 | 0.0253360 | ||||||||
\(496\) | 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 | ||||||||
\(501\) | 1.21591e8 | 0.966915 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −1.23404e8 | −0.969672 | −0.484836 | − | 0.874605i | \(-0.661121\pi\) | ||||
−0.484836 | + | 0.874605i | \(0.661121\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.27253e7 | 0.0988084 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | − | 1.67768e7i | − | 0.128732i | ||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | − | 1.41684e7i | − | 0.107441i | −0.998556 | − | 0.0537203i | \(-0.982892\pi\) | ||
0.998556 | − | 0.0537203i | \(-0.0171079\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 2.69273e7 | 0.201804 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.12151e8 | + | 4.39596e7i | −0.830711 | + | 0.325613i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.73130e7i | 0.126750i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −2.92103e7 | −0.211380 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 6.66228e7 | 0.476563 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.98342e7i | 0.423094i | 0.977368 | + | 0.211547i | \(0.0678501\pi\) | ||||
−0.977368 | + | 0.211547i | \(0.932150\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 5.41820e7i | − | 0.378747i | −0.981905 | − | 0.189374i | \(-0.939354\pi\) | ||
0.981905 | − | 0.189374i | \(-0.0606458\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | − | 1.81563e7i | − | 0.125472i | ||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 1.04330e8i | − | 0.712818i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −8.67814e7 | −0.586219 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 9.66766e7i | − | 0.645711i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −2.31256e8 | −1.52726 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 7.36509e6i | 0.0480969i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 1.20127e8 | 0.775742 | ||||||||
\(538\) | 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 | ||||||||
\(543\) | 6.34233e7 | 0.396140 | ||||||||
\(544\) | 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 | ||||||||
\(549\) | 6.69494e7 | 0.404603 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −1.21247e8 | + | 4.75252e7i | −0.724799 | + | 0.284099i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 3.95956e7i | − | 0.234138i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 3.88378e6 | 0.0227183 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 4.97836e7 | 0.288085 | 0.144043 | − | 0.989571i | \(-0.453990\pi\) | ||||
0.144043 | + | 0.989571i | \(0.453990\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.63932e7i | 0.551837i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1.41526e7i | 0.0801584i | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.74472e8i | 1.53806i | 0.639215 | + | 0.769028i | \(0.279260\pi\) | ||||
−0.639215 | + | 0.769028i | \(0.720740\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − | 2.43533e7i | − | 0.135024i | ||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 1.25948e7 | 0.0690943 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 2.65773e8i | 1.44270i | 0.692573 | + | 0.721348i | \(0.256477\pi\) | ||||
−0.692573 | + | 0.721348i | \(0.743523\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.28689e8 | −1.22839 | −0.614197 | − | 0.789153i | \(-0.710520\pi\) | ||||
−0.614197 | + | 0.789153i | \(0.710520\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.23408e7i | 0.225058i | ||||||||
\(574\) | 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 | ||||||||
\(579\) | −9.61130e7 | −0.495161 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.14029e7 | 0.262095 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4.11316e7i | 0.207572i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | − | 2.38714e7i | − | 0.119237i | ||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 2.80875e7 | 0.138867 | 0.0694334 | − | 0.997587i | \(-0.477881\pi\) | ||||
0.0694334 | + | 0.997587i | \(0.477881\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −2.06630e8 | + | 8.09924e7i | −1.01122 | + | 0.396368i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 7.91140e7i | 0.383258i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.59440e8 | −1.72370 | −0.861850 | − | 0.507163i | \(-0.830694\pi\) | ||||
−0.861850 | + | 0.507163i | \(0.830694\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 4.99529e6 | 0.0237143 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | − | 4.42855e7i | − | 0.208132i | ||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 3.80247e8i | 1.76923i | 0.466318 | + | 0.884617i | \(0.345580\pi\) | ||||
−0.466318 | + | 0.884617i | \(0.654420\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.65922e8i | 0.764329i | 0.924094 | + | 0.382165i | \(0.124821\pi\) | ||||
−0.924094 | + | 0.382165i | \(0.875179\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | − | 8.26044e7i | − | 0.376748i | ||||||
\(604\) | 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 | ||||||||
\(609\) | −2.25357e7 | −0.0997745 | ||||||||
\(610\) | 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 | ||||||||
\(615\) | 2.36668e7 | 0.101745 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −2.64442e8 | −1.12584 | −0.562918 | − | 0.826513i | \(-0.690321\pi\) | ||||
−0.562918 | + | 0.826513i | \(0.690321\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.93952e8 | 1.66101 | 0.830504 | − | 0.557013i | \(-0.188053\pi\) | ||||
0.830504 | + | 0.557013i | \(0.188053\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 1.37450e8i | − | 0.573945i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.35572e7i | 0.0974227i | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.28865e8 | 0.937432 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.80298e7 | − | 1.09868e7i | 0.113715 | − | 0.0445727i | ||||
\(628\) | 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 | ||||||||
\(633\) | −4.26813e7 | −0.168278 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 2.89610e7i | − | 0.113108i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | − | 2.71066e8i | − | 1.04871i | ||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 9.51692e7i | − | 0.364749i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 3.42337e8i | 1.29981i | 0.760015 | + | 0.649906i | \(0.225192\pi\) | ||||
−0.760015 | + | 0.649906i | \(0.774808\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −3.03299e8 | −1.14087 | −0.570437 | − | 0.821342i | \(-0.693226\pi\) | ||||
−0.570437 | + | 0.821342i | \(0.693226\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | − | 9.86491e6i | − | 0.0367632i | ||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −3.03991e8 | −1.12240 | −0.561199 | − | 0.827681i | \(-0.689660\pi\) | ||||
−0.561199 | + | 0.827681i | \(0.689660\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 5.70020e7i | 0.208524i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −3.84054e7 | −0.139203 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 2.88590e8 | 1.03643 | 0.518217 | − | 0.855249i | \(-0.326596\pi\) | ||||
0.518217 | + | 0.855249i | \(0.326596\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −5.50387e7 | −0.195859 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.68886e8 | 0.595521 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.42749e8i | 1.89646i | 0.317591 | + | 0.948228i | \(0.397126\pi\) | ||||
−0.317591 | + | 0.948228i | \(0.602874\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 2.52061e8i | − | 0.872774i | −0.899759 | − | 0.436387i | \(-0.856258\pi\) | ||
0.899759 | − | 0.436387i | \(-0.143742\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 1.09941e8 | 0.377242 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.87789e6 | − | 9.89335e6i | −0.0131865 | − | 0.0336417i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | − | 1.48599e8i | − | 0.500769i | ||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.74195e8 | −0.581779 | ||||||||
\(670\) | 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 | ||||||||
\(675\) | − | 2.68644e8i | − | 0.873507i | ||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 5.11022e8i | − | 1.64692i | −0.567371 | − | 0.823462i | \(-0.692039\pi\) | ||
0.567371 | − | 0.823462i | \(-0.307961\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.29126e7i | 0.232913i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.63373e7 | −0.210047 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 5.66185e7i | 0.177704i | 0.996045 | + | 0.0888518i | \(0.0283197\pi\) | ||||
−0.996045 | + | 0.0888518i | \(0.971680\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 5.65888e6 | 0.0176059 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 2.41940e8i | − | 0.746171i | ||||||
\(688\) | 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 | ||||||||
\(693\) | −1.45068e7 | −0.0435886 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −6.95501e6 | −0.0207178 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | − | 3.03513e8i | − | 0.896352i | ||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.93597e8i | 0.566849i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 4.90639e8 | 1.42432 | 0.712161 | − | 0.702016i | \(-0.247717\pi\) | ||||
0.712161 | + | 0.702016i | \(0.247717\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −9.86447e7 | + | 3.86657e7i | −0.283928 | + | 0.111291i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 2.32223e7i | − | 0.0662733i | ||||||
\(706\) | 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 | ||||||||
\(711\) | − | 2.48340e8i | − | 0.690937i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 2.53242e8i | − | 0.698662i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.40749e7i | 0.0385060i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − | 1.53983e8i | − | 0.417749i | ||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.02239e8 | −0.544098 | −0.272049 | − | 0.962283i | \(-0.587701\pi\) | ||||
−0.272049 | + | 0.962283i | \(0.587701\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 8.17314e7i | − | 0.218064i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −1.72480e8 | −0.456378 | ||||||||
\(724\) | 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 | ||||||||
\(729\) | −9.86957e7 | −0.254751 | ||||||||
\(730\) | 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 | ||||||||
\(735\) | 2.77410e7i | 0.0698650i | ||||||||
\(736\) | 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 | ||||||||
\(741\) | −8.53483e7 | − | 2.17743e8i | −0.209769 | − | 0.535166i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 4.17618e8i | 1.01815i | 0.860721 | + | 0.509076i | \(0.170013\pi\) | ||||
−0.860721 | + | 0.509076i | \(0.829987\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.58405e7 | 0.0383090 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 3.22394e8 | 0.773438 | ||||||||
\(748\) | 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 | ||||||||
\(753\) | − | 1.61401e8i | − | 0.378026i | ||||||
\(754\) | 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 | ||||||||
\(759\) | 3.43529e7i | 0.0785665i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −3.41887e8 | −0.775763 | −0.387881 | − | 0.921709i | \(-0.626793\pi\) | ||||
−0.387881 | + | 0.921709i | \(0.626793\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.69843e8i | 0.382361i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 3.13300e7 | 0.0699805 | ||||||||
\(766\) | 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 | ||||||||
\(771\) | 1.80483e8 | 0.393799 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.27556e8i | 0.492663i | 0.969186 | + | 0.246332i | \(0.0792253\pi\) | ||||
−0.969186 | + | 0.246332i | \(0.920775\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 4.94958e8i | − | 1.06332i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.83347e7 | −0.0390850 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −6.01117e8 | + | 2.35619e8i | −1.27159 | + | 0.498423i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 5.61132e7i | 0.117791i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −3.33444e8 | −0.694604 | ||||||||
\(784\) | 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 | ||||||||
\(789\) | 1.33743e8i | 0.272296i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1.14968e8i | 0.232298i | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.06647e8i | 0.614921i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.26998e7 | −0.0650795 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 5.93972e7i | 0.117325i | 0.998278 | + | 0.0586626i | \(0.0186836\pi\) | ||||
−0.998278 | + | 0.0586626i | \(0.981316\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −2.97812e8 | −0.583851 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.47749e8i | 0.287493i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −9.95778e7 | −0.192316 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 1.21251e7 | 0.0232434 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 1.73089e8 | 0.329343 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 3.52427e7 | 0.0665615 | 0.0332808 | − | 0.999446i | \(-0.489404\pi\) | ||||
0.0332808 | + | 0.999446i | \(0.489404\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 4.92642e8i | 0.923568i | 0.886992 | + | 0.461784i | \(0.152791\pi\) | ||||
−0.886992 | + | 0.461784i | \(0.847209\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1.44160e8i | 0.268270i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −5.37813e7 | −0.0993478 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 9.82118e7 | + | 2.50560e8i | 0.180093 | + | 0.459458i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 1.12693e8i | 0.205137i | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.95856e8 | −0.353921 | −0.176961 | − | 0.984218i | \(-0.556627\pi\) | ||||
−0.176961 | + | 0.984218i | \(0.556627\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 9.67464e6 | 0.0173554 | 0.00867771 | − | 0.999962i | \(-0.497238\pi\) | ||||
0.00867771 | + | 0.999962i | \(0.497238\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 6.71422e7i | 0.119573i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − | 1.64699e7i | − | 0.0291188i | −0.999894 | − | 0.0145594i | \(-0.995365\pi\) | ||
0.999894 | − | 0.0145594i | \(-0.00463456\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 5.92536e8i | 1.04004i | 0.854153 | + | 0.520022i | \(0.174076\pi\) | ||||
−0.854153 | + | 0.520022i | \(0.825924\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.61504e8i | 0.629957i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.55761e8 | 0.615493 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 1.58706e8i | 0.272605i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −5.68255e8 | −0.969096 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 6.70735e8i | 1.13570i | 0.823131 | + | 0.567852i | \(0.192225\pi\) | ||||
−0.823131 | + | 0.567852i | \(0.807775\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.34334e8 | 0.393955 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.35227e8 | 0.392649 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 2.18979e7 | 0.0362938 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −1.42950e8 | −0.235253 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 8.68078e7i | 0.141852i | ||||||||
\(850\) | 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 | ||||||||
\(855\) | −2.43218e7 | − | 6.20502e7i | −0.0389132 | − | 0.0992762i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 1.10391e9i | − | 1.75385i | −0.480630 | − | 0.876923i | \(-0.659592\pi\) | ||
0.480630 | − | 0.876923i | \(-0.340408\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.48554e8 | 0.234372 | 0.117186 | − | 0.993110i | \(-0.462613\pi\) | ||||
0.117186 | + | 0.993110i | \(0.462613\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.11727e8 | −0.175045 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 8.48412e8i | 1.32000i | 0.751265 | + | 0.660001i | \(0.229444\pi\) | ||||
−0.751265 | + | 0.660001i | \(0.770556\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.69591e7i | 0.134359i | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − | 1.90712e8i | − | 0.292631i | ||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.46425e8i | 0.223130i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.78352e8 | 0.572587 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.57301e8i | 0.687321i | ||||||||
\(874\) | 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 | ||||||||
\(879\) | 5.35457e8 | 0.788421 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.43974e8 | 0.210551 | 0.105275 | − | 0.994443i | \(-0.466428\pi\) | ||||
0.105275 | + | 0.994443i | \(0.466428\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.57167e8 | 0.228286 | 0.114143 | − | 0.993464i | \(-0.463588\pi\) | ||||
0.114143 | + | 0.993464i | \(0.463588\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −4.53169e7 | −0.0653779 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − | 5.52557e8i | − | 0.791784i | −0.918297 | − | 0.395892i | \(-0.870436\pi\) | ||
0.918297 | − | 0.395892i | \(-0.129564\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 1.36720e8i | 0.194593i | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −4.65758e7 | −0.0658456 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 2.31194e8 | + | 5.89827e8i | 0.324655 | + | 0.828267i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.56795e8i | 0.218707i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 2.66862e8 | 0.369751 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −6.14346e8 | −0.845540 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 4.19355e8i | 0.573334i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 4.65705e7i | 0.0632481i | ||||||||
\(904\) | 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 | ||||||||
\(909\) | −3.76778e8 | −0.501643 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1.15658e9i | − | 1.52975i | −0.644180 | − | 0.764874i | \(-0.722801\pi\) | ||
0.644180 | − | 0.764874i | \(-0.277199\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −1.90089e8 | −0.249772 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − | 3.13824e7i | − | 0.0409659i | ||||||
\(916\) | 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 | ||||||||
\(921\) | −1.50597e8 | −0.192769 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 4.35902e8 | 0.554350 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 2.36292e8i | − | 0.298555i | ||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − | 5.12613e8i | − | 0.643502i | ||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 6.43310e8 | 0.802367 | 0.401183 | − | 0.915998i | \(-0.368599\pi\) | ||||
0.401183 | + | 0.915998i | \(0.368599\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.76180e8 | − | 7.04596e8i | −0.342250 | − | 0.873155i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 6.60792e8i | 0.813616i | ||||||||
\(934\) | 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 | ||||||||
\(939\) | − | 2.75791e8i | − | 0.333107i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 5.09558e8i | − | 0.611540i | −0.952105 | − | 0.305770i | \(-0.901086\pi\) | ||
0.952105 | − | 0.305770i | \(-0.0989139\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 7.36720e8i | − | 0.878551i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 2.72078e7i | − | 0.0322402i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −3.61074e8 | −0.425154 | −0.212577 | − | 0.977144i | \(-0.568186\pi\) | ||||
−0.212577 | + | 0.977144i | \(0.568186\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 7.73546e8i | 0.905081i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 7.32057e8 | 0.851145 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 9.37652e8i | − | 1.08334i | −0.840593 | − | 0.541668i | \(-0.817793\pi\) | ||
0.840593 | − | 0.541668i | \(-0.182207\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −5.52651e7 | −0.0634514 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 8.33375e7 | 0.0950834 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.67146e7 | −0.0302896 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.59465e8 | −0.179679 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | − | 2.18070e8i | − | 0.244184i | ||||||
\(964\) | 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 | ||||||||
\(969\) | 2.85776e8 | − | 1.12016e8i | 0.314091 | − | 0.123114i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 7.06080e8i | − | 0.771252i | −0.922655 | − | 0.385626i | \(-0.873985\pi\) | ||
0.922655 | − | 0.385626i | \(-0.126015\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 3.28334e7 | 0.0356433 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 5.21578e8 | 0.562737 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 1.22331e9i | − | 1.31176i | −0.754866 | − | 0.655879i | \(-0.772298\pi\) | ||
0.754866 | − | 0.655879i | \(-0.227702\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 8.71151e7i | − | 0.0928422i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 1.06524e9i | 1.12834i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − | 4.63662e8i | − | 0.488136i | −0.969758 | − | 0.244068i | \(-0.921518\pi\) | ||
0.969758 | − | 0.244068i | \(-0.0784820\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −1.03263e8 | −0.108053 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1.09629e8i | 0.114018i | ||||||||
\(988\) | 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 | ||||||||
\(993\) | −5.40363e8 | −0.551872 | ||||||||
\(994\) | 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 | ||||||||
\(999\) | −2.71284e8 | −0.272099 |
(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 | 76.7.c.b.37.5 | yes | 8 | |
3.2 | odd | 2 | 684.7.h.c.37.6 | 8 | |||
4.3 | odd | 2 | 304.7.e.c.113.4 | 8 | |||
19.18 | odd | 2 | inner | 76.7.c.b.37.4 | ✓ | 8 | |
57.56 | even | 2 | 684.7.h.c.37.5 | 8 | |||
76.75 | even | 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 | 19.18 | odd | 2 | inner | |
76.7.c.b.37.5 | yes | 8 | 1.1 | even | 1 | trivial | |
304.7.e.c.113.4 | 8 | 4.3 | odd | 2 | |||
304.7.e.c.113.5 | 8 | 76.75 | even | 2 | |||
684.7.h.c.37.5 | 8 | 57.56 | even | 2 | |||
684.7.h.c.37.6 | 8 | 3.2 | odd | 2 |