Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [784,6,Mod(1,784)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(784, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 6, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("784.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 784 = 2^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 784.a (trivial) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | yes |
Analytic conductor: | \(125.740914733\) |
Analytic rank: | \(0\) |
Dimension: | \(5\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{5} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{5} - 200x^{3} - 99x^{2} + 5803x - 3615 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 2^{9}\cdot 7 \) |
Twist minimal: | no (minimal twist has level 56) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-12.3209\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 784.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −23.6419 | −1.51663 | −0.758314 | − | 0.651890i | \(-0.773977\pi\) | ||||
−0.758314 | + | 0.651890i | \(0.773977\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −20.0456 | −0.358587 | −0.179293 | − | 0.983796i | \(-0.557381\pi\) | ||||
−0.179293 | + | 0.983796i | \(0.557381\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 315.939 | 1.30016 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −58.7531 | −0.146403 | −0.0732014 | − | 0.997317i | \(-0.523322\pi\) | ||||
−0.0732014 | + | 0.997317i | \(0.523322\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 691.185 | 1.13432 | 0.567160 | − | 0.823607i | \(-0.308042\pi\) | ||||
0.567160 | + | 0.823607i | \(0.308042\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 473.916 | 0.543842 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 526.776 | 0.442083 | 0.221041 | − | 0.975264i | \(-0.429054\pi\) | ||||
0.221041 | + | 0.975264i | \(0.429054\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 127.568 | 0.0810692 | 0.0405346 | − | 0.999178i | \(-0.487094\pi\) | ||||
0.0405346 | + | 0.999178i | \(0.487094\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2268.61 | −0.894210 | −0.447105 | − | 0.894482i | \(-0.647545\pi\) | ||||
−0.447105 | + | 0.894482i | \(0.647545\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2723.17 | −0.871416 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1724.41 | −0.455230 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 8636.30 | 1.90692 | 0.953461 | − | 0.301518i | \(-0.0974933\pi\) | ||||
0.953461 | + | 0.301518i | \(0.0974933\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 10290.8 | 1.92330 | 0.961648 | − | 0.274288i | \(-0.0884422\pi\) | ||||
0.961648 | + | 0.274288i | \(0.0884422\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 1389.03 | 0.222039 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −4723.11 | −0.567183 | −0.283592 | − | 0.958945i | \(-0.591526\pi\) | ||||
−0.283592 | + | 0.958945i | \(0.591526\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −16340.9 | −1.72034 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6676.64 | 0.620295 | 0.310147 | − | 0.950688i | \(-0.399622\pi\) | ||||
0.310147 | + | 0.950688i | \(0.399622\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −22926.7 | −1.89091 | −0.945455 | − | 0.325754i | \(-0.894382\pi\) | ||||
−0.945455 | + | 0.325754i | \(0.894382\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6333.18 | −0.466220 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −24112.0 | −1.59217 | −0.796085 | − | 0.605185i | \(-0.793099\pi\) | ||||
−0.796085 | + | 0.605185i | \(0.793099\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −12454.0 | −0.670475 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −8242.96 | −0.403082 | −0.201541 | − | 0.979480i | \(-0.564595\pi\) | ||||
−0.201541 | + | 0.979480i | \(0.564595\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 1177.74 | 0.0524981 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −3015.94 | −0.122952 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −36134.3 | −1.35142 | −0.675709 | − | 0.737169i | \(-0.736162\pi\) | ||||
−0.675709 | + | 0.737169i | \(0.736162\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 15654.8 | 0.538672 | 0.269336 | − | 0.963046i | \(-0.413196\pi\) | ||||
0.269336 | + | 0.963046i | \(0.413196\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −13855.2 | −0.406752 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −29371.7 | −0.799361 | −0.399680 | − | 0.916655i | \(-0.630879\pi\) | ||||
−0.399680 | + | 0.916655i | \(0.630879\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 53634.1 | 1.35618 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 9025.02 | 0.212472 | 0.106236 | − | 0.994341i | \(-0.466120\pi\) | ||||
0.106236 | + | 0.994341i | \(0.466120\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 4435.42 | 0.0974154 | 0.0487077 | − | 0.998813i | \(-0.484490\pi\) | ||||
0.0487077 | + | 0.998813i | \(0.484490\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 64381.0 | 1.32161 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8201.62 | −0.147854 | −0.0739268 | − | 0.997264i | \(-0.523553\pi\) | ||||
−0.0739268 | + | 0.997264i | \(0.523553\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −36004.8 | −0.609745 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 54575.9 | 0.869572 | 0.434786 | − | 0.900534i | \(-0.356824\pi\) | ||||
0.434786 | + | 0.900534i | \(0.356824\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −10559.5 | −0.158525 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −204178. | −2.89209 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −86933.9 | −1.16336 | −0.581680 | − | 0.813418i | \(-0.697604\pi\) | ||||
−0.581680 | + | 0.813418i | \(0.697604\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −243294. | −2.91692 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −2557.17 | −0.0290703 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 157783. | 1.70268 | 0.851338 | − | 0.524617i | \(-0.175792\pi\) | ||||
0.851338 | + | 0.524617i | \(0.175792\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −18562.4 | −0.190347 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 77781.9 | 0.758709 | 0.379354 | − | 0.925251i | \(-0.376146\pi\) | ||||
0.379354 | + | 0.925251i | \(0.376146\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −107006. | −0.993840 | −0.496920 | − | 0.867796i | \(-0.665536\pi\) | ||||
−0.496920 | + | 0.867796i | \(0.665536\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 160396. | 1.35436 | 0.677182 | − | 0.735816i | \(-0.263201\pi\) | ||||
0.677182 | + | 0.735816i | \(0.263201\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 80176.6 | 0.646371 | 0.323185 | − | 0.946336i | \(-0.395246\pi\) | ||||
0.323185 | + | 0.946336i | \(0.395246\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 111663. | 0.860206 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −99679.0 | −0.734358 | −0.367179 | − | 0.930150i | \(-0.619676\pi\) | ||||
−0.367179 | + | 0.930150i | \(0.619676\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 45475.6 | 0.320652 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 218372. | 1.47480 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −157599. | −0.978566 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −157848. | −0.940756 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 117230. | 0.671065 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 120594. | 0.663463 | 0.331732 | − | 0.943374i | \(-0.392367\pi\) | ||||
0.331732 | + | 0.943374i | \(0.392367\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 542031. | 2.86781 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 50227.8 | 0.255721 | 0.127860 | − | 0.991792i | \(-0.459189\pi\) | ||||
0.127860 | + | 0.991792i | \(0.459189\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 34566.8 | 0.163239 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −208225. | −0.947834 | −0.473917 | − | 0.880569i | \(-0.657160\pi\) | ||||
−0.473917 | + | 0.880569i | \(0.657160\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −215032. | −0.943988 | −0.471994 | − | 0.881602i | \(-0.656466\pi\) | ||||
−0.471994 | + | 0.881602i | \(0.656466\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 570054. | 2.41473 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −40609.3 | −0.166068 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −173120. | −0.683796 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 383526. | 1.41524 | 0.707618 | − | 0.706595i | \(-0.249770\pi\) | ||||
0.707618 | + | 0.706595i | \(0.249770\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −410918. | −1.46660 | −0.733302 | − | 0.679903i | \(-0.762022\pi\) | ||||
−0.733302 | + | 0.679903i | \(0.762022\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 166429. | 0.574778 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −206286. | −0.689668 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −329710. | −1.06754 | −0.533769 | − | 0.845630i | \(-0.679225\pi\) | ||||
−0.533769 | + | 0.845630i | \(0.679225\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 194879. | 0.611326 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 381832. | 1.12565 | 0.562824 | − | 0.826577i | \(-0.309715\pi\) | ||||
0.562824 | + | 0.826577i | \(0.309715\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −27844.0 | −0.0796200 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −195870. | −0.543471 | −0.271735 | − | 0.962372i | \(-0.587598\pi\) | ||||
−0.271735 | + | 0.962372i | \(0.587598\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 106443. | 0.286683 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 40303.5 | 0.105403 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 531987. | 1.35141 | 0.675703 | − | 0.737174i | \(-0.263840\pi\) | ||||
0.675703 | + | 0.737174i | \(0.263840\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 854283. | 2.04960 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 374611. | 0.873873 | 0.436937 | − | 0.899492i | \(-0.356063\pi\) | ||||
0.436937 | + | 0.899492i | \(0.356063\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 148562. | 0.337063 | 0.168532 | − | 0.985696i | \(-0.446097\pi\) | ||||
0.168532 | + | 0.985696i | \(0.446097\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −370110. | −0.816965 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 94677.5 | 0.203384 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −30949.7 | −0.0647222 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 616890. | 1.22356 | 0.611779 | − | 0.791029i | \(-0.290454\pi\) | ||||
0.611779 | + | 0.791029i | \(0.290454\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 69951.0 | 0.135176 | 0.0675882 | − | 0.997713i | \(-0.478470\pi\) | ||||
0.0675882 | + | 0.997713i | \(0.478470\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 327563. | 0.616892 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 440150. | 0.808045 | 0.404022 | − | 0.914749i | \(-0.367612\pi\) | ||||
0.404022 | + | 0.914749i | \(0.367612\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 350409. | 0.627253 | 0.313627 | − | 0.949546i | \(-0.398456\pi\) | ||||
0.313627 | + | 0.949546i | \(0.398456\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 694403. | 1.21233 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −133837. | −0.222429 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −716740. | −1.16262 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −7494.99 | −0.0118688 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 637860. | 0.986323 | 0.493161 | − | 0.869938i | \(-0.335841\pi\) | ||||
0.493161 | + | 0.869938i | \(0.335841\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −213369. | −0.322241 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 459580. | 0.678055 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −104862. | −0.147743 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 364100. | 0.501464 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 56418.4 | 0.0759729 | 0.0379864 | − | 0.999278i | \(-0.487906\pi\) | ||||
0.0379864 | + | 0.999278i | \(0.487906\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −860356. | −1.13298 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 293499. | 0.378043 | 0.189022 | − | 0.981973i | \(-0.439468\pi\) | ||||
0.189022 | + | 0.981973i | \(0.439468\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 620574. | 0.781996 | 0.390998 | − | 0.920391i | \(-0.372130\pi\) | ||||
0.390998 | + | 0.920391i | \(0.372130\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −724323. | −0.874062 | −0.437031 | − | 0.899446i | \(-0.643970\pi\) | ||||
−0.437031 | + | 0.899446i | \(0.643970\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 483340. | 0.570931 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 193902. | 0.224239 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 272208. | 0.308252 | 0.154126 | − | 0.988051i | \(-0.450744\pi\) | ||||
0.154126 | + | 0.988051i | \(0.450744\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 850014. | 0.942722 | 0.471361 | − | 0.881940i | \(-0.343763\pi\) | ||||
0.471361 | + | 0.881940i | \(0.343763\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.27025e6 | 1.37999 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 88172.7 | 0.0919585 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −1.29028e6 | −1.31882 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 1.62295e6 | 1.62601 | 0.813003 | − | 0.582260i | \(-0.197831\pi\) | ||||
0.813003 | + | 0.582260i | \(0.197831\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 133288. | 0.130915 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 249648. | 0.240423 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −1.29876e6 | −1.22658 | −0.613292 | − | 0.789857i | \(-0.710155\pi\) | ||||
−0.613292 | + | 0.789857i | \(0.710155\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 2.72854e6 | 2.47930 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1.58814e6 | 1.41579 | 0.707895 | − | 0.706318i | \(-0.249645\pi\) | ||||
0.707895 | + | 0.706318i | \(0.249645\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 165235. | 0.144540 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.05528e6 | 1.76438 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −850606. | −0.716717 | −0.358358 | − | 0.933584i | \(-0.616663\pi\) | ||||
−0.358358 | + | 0.933584i | \(0.616663\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 1.75962e6 | 1.45544 | 0.727722 | − | 0.685872i | \(-0.240579\pi\) | ||||
0.727722 | + | 0.685872i | \(0.240579\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 159995. | 0.127578 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.74579e6 | −1.36707 | −0.683537 | − | 0.729916i | \(-0.739559\pi\) | ||||
−0.683537 | + | 0.729916i | \(0.739559\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 3.25127e6 | 2.50059 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.07171e6 | −1.56518 | −0.782588 | − | 0.622541i | \(-0.786101\pi\) | ||||
−0.782588 | + | 0.622541i | \(0.786101\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 314936. | 0.233752 | 0.116876 | − | 0.993146i | \(-0.462712\pi\) | ||||
0.116876 | + | 0.993146i | \(0.462712\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 60456.3 | 0.0440889 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.14236e6 | −0.804563 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.73030e6 | −2.58233 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 2.07017e6 | 1.40876 | 0.704381 | − | 0.709822i | \(-0.251225\pi\) | ||||
0.704381 | + | 0.709822i | \(0.251225\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 724334. | 0.484600 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 101314. | 0.0666470 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.56803e6 | −1.01432 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −1.83891e6 | −1.15068 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −313811. | −0.193161 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −1.16092e6 | −0.703000 | −0.351500 | − | 0.936188i | \(-0.614328\pi\) | ||||
−0.351500 | + | 0.936188i | \(0.614328\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.52983e6 | 1.50728 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 663375. | 0.388918 | 0.194459 | − | 0.980911i | \(-0.437705\pi\) | ||||
0.194459 | + | 0.980911i | \(0.437705\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 620692. | 0.358109 | 0.179054 | − | 0.983839i | \(-0.442696\pi\) | ||||
0.179054 | + | 0.983839i | \(0.442696\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.82339e6 | 1.01914 | 0.509568 | − | 0.860431i | \(-0.329805\pi\) | ||||
0.509568 | + | 0.860431i | \(0.329805\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −507410. | −0.279179 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.79207e6 | −2.05407 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 67199.5 | 0.0358393 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.88222e6 | −0.988465 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −1.89553e6 | −0.980304 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.34113e6 | −0.672822 | −0.336411 | − | 0.941715i | \(-0.609213\pi\) | ||||
−0.336411 | + | 0.941715i | \(0.609213\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −1.49221e6 | −0.737429 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 588774. | 0.286640 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 320075. | 0.153524 | 0.0767621 | − | 0.997049i | \(-0.475542\pi\) | ||||
0.0767621 | + | 0.997049i | \(0.475542\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 2.35660e6 | 1.11375 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −604618. | −0.281576 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −1.07513e6 | −0.486309 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −697566. | −0.311001 | −0.155500 | − | 0.987836i | \(-0.549699\pi\) | ||||
−0.155500 | + | 0.987836i | \(0.549699\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.08445e6 | 0.916068 | 0.458034 | − | 0.888935i | \(-0.348554\pi\) | ||||
0.458034 | + | 0.888935i | \(0.348554\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −1.19189e6 | −0.516377 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.13719e6 | −1.34000 | −0.669998 | − | 0.742363i | \(-0.733705\pi\) | ||||
−0.669998 | + | 0.742363i | \(0.733705\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −180912. | −0.0761897 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 1.80529e6 | 0.739284 | 0.369642 | − | 0.929174i | \(-0.379480\pi\) | ||||
0.369642 | + | 0.929174i | \(0.379480\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −2.45983e6 | −0.993428 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 3.72594e6 | 1.48412 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −88910.6 | −0.0349318 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.58136e6 | 0.612864 | 0.306432 | − | 0.951893i | \(-0.400865\pi\) | ||||
0.306432 | + | 0.951893i | \(0.400865\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 2.10941e6 | 0.806482 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1.70096e6 | 0.633028 | 0.316514 | − | 0.948588i | \(-0.397487\pi\) | ||||
0.316514 | + | 0.948588i | \(0.397487\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −2.77154e6 | −1.01776 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.96928e6 | 2.16306 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −4.93679e6 | −1.76541 | −0.882707 | − | 0.469923i | \(-0.844282\pi\) | ||||
−0.882707 | + | 0.469923i | \(0.844282\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −2.85107e6 | −1.00623 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 448450. | 0.156213 | 0.0781065 | − | 0.996945i | \(-0.475113\pi\) | ||||
0.0781065 | + | 0.996945i | \(0.475113\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.24344e6 | −2.45848 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 245076. | 0.0821157 | 0.0410579 | − | 0.999157i | \(-0.486927\pi\) | ||||
0.0410579 | + | 0.999157i | \(0.486927\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.19505e6 | −0.395315 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −1.18748e6 | −0.387833 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 164406. | 0.0530183 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.06740e6 | −0.976774 | −0.488387 | − | 0.872627i | \(-0.662414\pi\) | ||||
−0.488387 | + | 0.872627i | \(0.662414\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −4.51686e6 | −1.40274 | −0.701368 | − | 0.712800i | \(-0.747427\pi\) | ||||
−0.701368 | + | 0.712800i | \(0.747427\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 7.11286e6 | 2.18163 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 721738. | 0.218646 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 277497. | 0.0830372 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.08298e6 | 1.50249 | 0.751243 | − | 0.660026i | \(-0.229455\pi\) | ||||
0.751243 | + | 0.660026i | \(0.229455\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 4.92284e6 | 1.43751 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.09401e6 | −0.311817 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 5.08377e6 | 1.43168 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 2.14263e6 | 0.596227 | 0.298114 | − | 0.954530i | \(-0.403643\pi\) | ||||
0.298114 | + | 0.954530i | \(0.403643\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.63121e6 | 0.998497 | 0.499248 | − | 0.866459i | \(-0.333609\pi\) | ||||
0.499248 | + | 0.866459i | \(0.333609\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −7.61793e6 | −2.07007 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −1.43450e6 | −0.385238 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 960080. | 0.251863 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.95928e6 | −0.508046 | −0.254023 | − | 0.967198i | \(-0.581754\pi\) | ||||
−0.254023 | + | 0.967198i | \(0.581754\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2.49301e6 | −0.639005 | −0.319502 | − | 0.947585i | \(-0.603516\pi\) | ||||
−0.319502 | + | 0.947585i | \(0.603516\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.09288e6 | 1.03706 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −289400. | −0.0724929 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4.02098e6 | −0.995796 | −0.497898 | − | 0.867236i | \(-0.665895\pi\) | ||||
−0.497898 | + | 0.867236i | \(0.665895\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 4.46554e6 | 1.08110 | 0.540548 | − | 0.841313i | \(-0.318217\pi\) | ||||
0.540548 | + | 0.841313i | \(0.318217\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.74264e6 | 0.417165 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −9.06727e6 | −2.14639 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −3.68564e6 | −0.862774 | −0.431387 | − | 0.902167i | \(-0.641976\pi\) | ||||
−0.431387 | + | 0.902167i | \(0.641976\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −392273. | −0.0908129 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 9.71488e6 | 2.22429 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.13435e6 | −0.478051 | −0.239025 | − | 0.971013i | \(-0.576828\pi\) | ||||
−0.239025 | + | 0.971013i | \(0.576828\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −908378. | −0.201250 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −3.11136e6 | −0.681865 | −0.340932 | − | 0.940088i | \(-0.610743\pi\) | ||||
−0.340932 | + | 0.940088i | \(0.610743\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.03151e6 | 0.874009 | 0.437004 | − | 0.899459i | \(-0.356039\pi\) | ||||
0.437004 | + | 0.899459i | \(0.356039\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 4.87698e6 | 1.04597 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −465000. | −0.0986644 | −0.0493322 | − | 0.998782i | \(-0.515709\pi\) | ||||
−0.0493322 | + | 0.998782i | \(0.515709\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.79498e6 | 1.61906 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.34702e6 | 0.276834 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −347389. | −0.0706450 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −2.60427e6 | −0.524071 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −3.88192e6 | −0.773050 | −0.386525 | − | 0.922279i | \(-0.626325\pi\) | ||||
−0.386525 | + | 0.922279i | \(0.626325\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −3.26454e6 | −0.643368 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −3.16286e6 | −0.610557 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.77230e6 | 0.720750 | 0.360375 | − | 0.932808i | \(-0.382649\pi\) | ||||
0.360375 | + | 0.932808i | \(0.382649\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −9.02722e6 | −1.70719 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −3.97153e6 | −0.743455 | −0.371727 | − | 0.928342i | \(-0.621234\pi\) | ||||
−0.371727 | + | 0.928342i | \(0.621234\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 4.54940e6 | 0.843017 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 372094. | 0.0682559 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 9.30366e6 | 1.67264 | 0.836320 | − | 0.548241i | \(-0.184702\pi\) | ||||
0.836320 | + | 0.548241i | \(0.184702\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.63073e6 | 0.824243 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −2.66706e6 | −0.470016 | −0.235008 | − | 0.971993i | \(-0.575512\pi\) | ||||
−0.235008 | + | 0.971993i | \(0.575512\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.55918e6 | −0.272063 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.51652e6 | −0.434792 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −5.93994e6 | −1.01622 | −0.508110 | − | 0.861292i | \(-0.669656\pi\) | ||||
−0.508110 | + | 0.861292i | \(0.669656\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −219979. | −0.0369052 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 2.14501e6 | 0.356378 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.41666e6 | 0.233098 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1.25772e7 | −2.04958 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 6.49423e6 | 1.04817 | 0.524087 | − | 0.851665i | \(-0.324407\pi\) | ||||
0.524087 | + | 0.851665i | \(0.324407\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.26803e6 | −0.842158 | −0.421079 | − | 0.907024i | \(-0.638349\pi\) | ||||
−0.421079 | + | 0.907024i | \(0.638349\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 5.42096e6 | 0.850256 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −1.28977e6 | −0.200389 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −1.14162e7 | −1.75706 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 4.61479e6 | 0.703613 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −3.21524e6 | −0.485657 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −8.85652e6 | −1.32534 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.94194e6 | −0.579052 | −0.289526 | − | 0.957170i | \(-0.593498\pi\) | ||||
−0.289526 | + | 0.957170i | \(0.593498\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −3.51229e6 | −0.511200 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −1.60719e6 | −0.231780 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.04260e7 | 1.48987 | 0.744934 | − | 0.667138i | \(-0.232481\pi\) | ||||
0.744934 | + | 0.667138i | \(0.232481\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.94597e6 | 0.700359 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 1.10171e6 | 0.154593 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.23835e6 | −0.308458 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 9.10886e6 | 1.24402 | 0.622008 | − | 0.783011i | \(-0.286317\pi\) | ||||
0.622008 | + | 0.783011i | \(0.286317\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.58466e7 | −2.14490 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 731710. | 0.0981594 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 9.52612e6 | 1.26662 | 0.633308 | − | 0.773900i | \(-0.281697\pi\) | ||||
0.633308 | + | 0.773900i | \(0.281697\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.99813e6 | 0.263331 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.26911e7 | 1.64331 | 0.821656 | − | 0.569983i | \(-0.193050\pi\) | ||||
0.821656 | + | 0.569983i | \(0.193050\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 4.00866e6 | 0.514528 | 0.257264 | − | 0.966341i | \(-0.417179\pi\) | ||||
0.257264 | + | 0.966341i | \(0.417179\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −1.45845e7 | −1.85568 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 6.17781e6 | 0.779228 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1.44306e6 | −0.180445 | −0.0902224 | − | 0.995922i | \(-0.528758\pi\) | ||||
−0.0902224 | + | 0.995922i | \(0.528758\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −1.65377e6 | −0.205012 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 484300. | 0.0590124 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −4.37740e6 | −0.528843 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −3.38345e6 | −0.405289 | −0.202645 | − | 0.979252i | \(-0.564954\pi\) | ||||
−0.202645 | + | 0.979252i | \(0.564954\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.31278e6 | 0.155920 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −1.04060e7 | −1.22550 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.94666e6 | 0.577664 | 0.288832 | − | 0.957380i | \(-0.406733\pi\) | ||||
0.288832 | + | 0.957380i | \(0.406733\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −8.28434e6 | −0.951310 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.29641e7 | 1.47631 | 0.738153 | − | 0.674633i | \(-0.235698\pi\) | ||||
0.738153 | + | 0.674633i | \(0.235698\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.52347e7 | 1.72047 | 0.860235 | − | 0.509897i | \(-0.170317\pi\) | ||||
0.860235 | + | 0.509897i | \(0.170317\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −9.27967e6 | −1.03930 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 3.15917e6 | 0.350901 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −6.50606e6 | −0.716714 | −0.358357 | − | 0.933585i | \(-0.616663\pi\) | ||||
−0.358357 | + | 0.933585i | \(0.616663\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.66659e7 | −1.80603 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 7.28274e6 | 0.782787 | 0.391394 | − | 0.920223i | \(-0.371993\pi\) | ||||
0.391394 | + | 0.920223i | \(0.371993\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.16416e6 | 0.337343 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1.34924e7 | 1.42684 | 0.713422 | − | 0.700734i | \(-0.247144\pi\) | ||||
0.713422 | + | 0.700734i | \(0.247144\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 7.05648e6 | 0.740221 | 0.370111 | − | 0.928988i | \(-0.379320\pi\) | ||||
0.370111 | + | 0.928988i | \(0.379320\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.91201e6 | 0.407071 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 6.15997e6 | 0.630781 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 177196. | 0.0180005 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −2.48802e6 | −0.250742 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1.46502e7 | −1.46477 | −0.732384 | − | 0.680891i | \(-0.761593\pi\) | ||||
−0.732384 | + | 0.680891i | \(0.761593\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −1.50802e7 | −1.49588 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −2.41738e6 | −0.237909 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 2.85135e6 | 0.276248 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.99039e7 | 1.91335 | 0.956673 | − | 0.291166i | \(-0.0940432\pi\) | ||||
0.956673 | + | 0.291166i | \(0.0940432\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.52786e6 | 0.527266 | 0.263633 | − | 0.964623i | \(-0.415079\pi\) | ||||
0.263633 | + | 0.964623i | \(0.415079\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −1.08653e7 | −1.02836 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.81508e6 | 0.170465 | 0.0852323 | − | 0.996361i | \(-0.472837\pi\) | ||||
0.0852323 | + | 0.996361i | \(0.472837\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.12300e6 | 0.197851 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −1.59251e7 | −1.46151 | −0.730753 | − | 0.682642i | \(-0.760831\pi\) | ||||
−0.730753 | + | 0.682642i | \(0.760831\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −1.00685e6 | −0.0916980 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1.40132e6 | 0.126656 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −38652.4 | −0.00346707 | −0.00173353 | − | 0.999998i | \(-0.500552\pi\) | ||||
−0.00173353 | + | 0.999998i | \(0.500552\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.52544e7 | −1.35797 | −0.678986 | − | 0.734151i | \(-0.737580\pi\) | ||||
−0.678986 | + | 0.734151i | \(0.737580\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −8.60800e6 | −0.760534 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −1.95924e7 | −1.70519 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −1.33384e6 | −0.115223 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −919771. | −0.0788631 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 2.71207e6 | 0.230815 | 0.115407 | − | 0.993318i | \(-0.463183\pi\) | ||||
0.115407 | + | 0.993318i | \(0.463183\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.69587e6 | 0.396695 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1.27201e7 | −1.06664 | −0.533319 | − | 0.845914i | \(-0.679056\pi\) | ||||
−0.533319 | + | 0.845914i | \(0.679056\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.93886e6 | −0.573351 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 4.90908e6 | 0.402669 | 0.201335 | − | 0.979523i | \(-0.435472\pi\) | ||||
0.201335 | + | 0.979523i | \(0.435472\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.17401e6 | 0.339881 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −1.46715e7 | −1.18600 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −5.69741e6 | −0.457224 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.59865e6 | −0.605399 | −0.302699 | − | 0.953086i | \(-0.597888\pi\) | ||||
−0.302699 | + | 0.953086i | \(0.597888\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 4.31045e6 | 0.338502 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 3.51709e6 | 0.274222 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.71244e7 | 1.32563 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −3.72699e6 | −0.286460 | −0.143230 | − | 0.989689i | \(-0.545749\pi\) | ||||
−0.143230 | + | 0.989689i | \(0.545749\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −602515. | −0.0459811 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −1.14271e7 | −0.865889 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 94232.7 | 0.00704022 | 0.00352011 | − | 0.999994i | \(-0.498880\pi\) | ||||
0.00352011 | + | 0.999994i | \(0.498880\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −2.59121e6 | −0.192233 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −2.33458e7 | −1.71983 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 814037. | 0.0595497 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.43550e6 | −0.467503 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 1.52391e7 | 1.09935 | 0.549675 | − | 0.835379i | \(-0.314752\pi\) | ||||
0.549675 | + | 0.835379i | \(0.314752\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.00959e7 | −1.42976 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −2.35181e7 | −1.66172 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.09483e6 | 0.217171 | 0.108585 | − | 0.994087i | \(-0.465368\pi\) | ||||
0.108585 | + | 0.994087i | \(0.465368\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −2.12820e7 | −1.48318 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.20772e7 | −0.835939 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 6.11165e6 | 0.420144 | 0.210072 | − | 0.977686i | \(-0.432630\pi\) | ||||
0.210072 | + | 0.977686i | \(0.432630\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.72568e6 | 0.117029 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 3.67820e6 | 0.247756 | 0.123878 | − | 0.992297i | \(-0.460467\pi\) | ||||
0.123878 | + | 0.992297i | \(0.460467\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −2.08457e6 | −0.139467 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 2.68224e7 | 1.78249 | 0.891243 | − | 0.453526i | \(-0.149834\pi\) | ||||
0.891243 | + | 0.453526i | \(0.149834\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −7.68801e6 | −0.507485 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 1.72426e7 | 1.13058 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −1.57747e7 | −1.02061 | −0.510306 | − | 0.859993i | \(-0.670468\pi\) | ||||
−0.510306 | + | 0.859993i | \(0.670468\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −3.83697e7 | −2.46604 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 8.23710e6 | 0.525905 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −2.33178e7 | −1.47893 | −0.739466 | − | 0.673194i | \(-0.764922\pi\) | ||||
−0.739466 | + | 0.673194i | \(0.764922\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −3.15117e6 | −0.198549 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 5.84571e6 | 0.365911 | 0.182956 | − | 0.983121i | \(-0.441434\pi\) | ||||
0.182956 | + | 0.983121i | \(0.441434\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −3.33617e6 | −0.206108 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −2.49755e7 | −1.53294 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 1.79261e7 | 1.09313 | 0.546563 | − | 0.837418i | \(-0.315936\pi\) | ||||
0.546563 | + | 0.837418i | \(0.315936\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.07052e7 | 1.86027 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 2.15535e7 | 1.29739 | 0.648694 | − | 0.761049i | \(-0.275315\pi\) | ||||
0.648694 | + | 0.761049i | \(0.275315\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −2.80237e7 | −1.67599 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 851722. | 0.0502868 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −530248. | −0.0311065 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.48925e7 | −0.868088 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 6.60924e6 | 0.382805 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.56889e6 | 0.147846 | 0.0739228 | − | 0.997264i | \(-0.476448\pi\) | ||||
0.0739228 | + | 0.997264i | \(0.476448\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −3.75466e7 | −2.14723 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.08204e7 | 0.611027 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −3.90647e6 | −0.219213 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.63767e7 | −1.47087 | −0.735437 | − | 0.677593i | \(-0.763023\pi\) | ||||
−0.735437 | + | 0.677593i | \(0.763023\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.27016e7 | −0.703871 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −2.74658e7 | −1.51255 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −260595. | −0.0142619 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.01099e7 | 1.08699 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.28856e7 | 1.22939 | 0.614696 | − | 0.788764i | \(-0.289279\pi\) | ||||
0.614696 | + | 0.788764i | \(0.289279\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 1.52953e6 | 0.0816592 | 0.0408296 | − | 0.999166i | \(-0.487000\pi\) | ||||
0.0408296 | + | 0.999166i | \(0.487000\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −4.16007e7 | −2.20737 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −7.65404e6 | −0.403642 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.92470e6 | −0.153295 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 1.58749e7 | 0.821963 | 0.410982 | − | 0.911644i | \(-0.365186\pi\) | ||||
0.410982 | + | 0.911644i | \(0.365186\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 3.10952e7 | 1.60027 | 0.800136 | − | 0.599819i | \(-0.204761\pi\) | ||||
0.800136 | + | 0.599819i | \(0.204761\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.78258e6 | −0.193488 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 4.81422e6 | 0.244772 | 0.122386 | − | 0.992483i | \(-0.460945\pi\) | ||||
0.122386 | + | 0.992483i | \(0.460945\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.54355e7 | 1.28545 | 0.642724 | − | 0.766098i | \(-0.277804\pi\) | ||||
0.642724 | + | 0.766098i | \(0.277804\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 4.12737e7 | 2.07334 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 3.92633e6 | 0.194881 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1.77456e7 | −0.875542 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.74688e7 | 1.34721 | 0.673605 | − | 0.739091i | \(-0.264745\pi\) | ||||
0.673605 | + | 0.739091i | \(0.264745\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.40745e7 | 2.63635 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 4.89791e7 | 2.37379 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.13372e6 | −0.102801 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −7.44568e6 | −0.354515 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1.07149e7 | 0.507181 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.98613e6 | 0.281691 | 0.140846 | − | 0.990032i | \(-0.455018\pi\) | ||||
0.140846 | + | 0.990032i | \(0.455018\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −807909. | −0.0377961 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −1.30595e7 | −0.607397 | −0.303699 | − | 0.952768i | \(-0.598222\pi\) | ||||
−0.303699 | + | 0.952768i | \(0.598222\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.51349e6 | −0.347423 | −0.173712 | − | 0.984797i | \(-0.555576\pi\) | ||||
−0.173712 | + | 0.984797i | \(0.555576\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 834999. | 0.0381644 | 0.0190822 | − | 0.999818i | \(-0.493926\pi\) | ||||
0.0190822 | + | 0.999818i | \(0.493926\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1.06640e7 | −0.484596 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.70076e7 | 1.22022 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 481871. | 0.0216462 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2.03013e7 | −0.906731 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 4.98499e7 | 2.21375 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.35679e7 | 0.595679 | 0.297840 | − | 0.954616i | \(-0.403734\pi\) | ||||
0.297840 | + | 0.954616i | \(0.403734\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −4.89428e7 | −2.13657 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 1.02028e7 | 0.442873 | 0.221436 | − | 0.975175i | \(-0.428926\pi\) | ||||
0.221436 | + | 0.975175i | \(0.428926\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.57631e7 | 1.11198 | 0.555989 | − | 0.831190i | \(-0.312340\pi\) | ||||
0.555989 | + | 0.831190i | \(0.312340\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −1.71246e7 | −0.734958 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1.71056e7 | −0.730012 | −0.365006 | − | 0.931005i | \(-0.618933\pi\) | ||||
−0.365006 | + | 0.931005i | \(0.618933\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.11540e6 | 0.0892683 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −3.07591e6 | −0.129076 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −7.50931e6 | −0.313359 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.70711e7 | 1.53835 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 8.88746e7 | 3.66757 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −4.34220e6 | −0.178196 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −2.97802e6 | −0.120866 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.41290e6 | 0.0973915 | 0.0486958 | − | 0.998814i | \(-0.484494\pi\) | ||||
0.0486958 | + | 0.998814i | \(0.484494\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.45743e7 | 0.986442 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −2.36633e7 | −0.944668 | −0.472334 | − | 0.881420i | \(-0.656588\pi\) | ||||
−0.472334 | + | 0.881420i | \(0.656588\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −3.20650e6 | −0.127308 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 7.41908e6 | 0.292953 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.62159e6 | −0.141452 | −0.0707262 | − | 0.997496i | \(-0.522532\pi\) | ||||
−0.0707262 | + | 0.997496i | \(0.522532\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 2.74463e7 | 1.06619 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.23796e6 | 0.241012 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 1.28618e7 | 0.494252 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.38074e7 | −1.29215 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 3.21340e7 | 1.22159 | 0.610796 | − | 0.791788i | \(-0.290850\pi\) | ||||
0.610796 | + | 0.791788i | \(0.290850\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −1.56834e7 | −0.589844 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 620406. | 0.0232085 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −1.50936e7 | −0.561621 | −0.280811 | − | 0.959763i | \(-0.590603\pi\) | ||||
−0.280811 | + | 0.959763i | \(0.590603\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −1.46743e7 | −0.543118 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 3.88634e7 | 1.43076 | 0.715379 | − | 0.698736i | \(-0.246254\pi\) | ||||
0.715379 | + | 0.698736i | \(0.246254\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.51467e7 | −0.554674 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.94261e7 | −0.703898 | −0.351949 | − | 0.936019i | \(-0.614481\pi\) | ||||
−0.351949 | + | 0.936019i | \(0.614481\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 3.06569e6 | 0.110500 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −4.31084e7 | −1.54565 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.32921e7 | −1.18743 | −0.593717 | − | 0.804674i | \(-0.702340\pi\) | ||||
−0.593717 | + | 0.804674i | \(0.702340\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −1.23659e7 | −0.438752 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 1.19961e7 | 0.423410 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.72719e7 | 2.69906 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 5.06755e7 | 1.76089 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −1.40221e6 | −0.0484724 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.99707e7 | −0.686796 | −0.343398 | − | 0.939190i | \(-0.611578\pi\) | ||||
−0.343398 | + | 0.939190i | \(0.611578\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −1.58872e6 | −0.0543549 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.92737e7 | 1.67713 | 0.838567 | − | 0.544799i | \(-0.183394\pi\) | ||||
0.838567 | + | 0.544799i | \(0.183394\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 4.44991e7 | 1.49913 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 4.75393e7 | 1.59337 | 0.796684 | − | 0.604396i | \(-0.206586\pi\) | ||||
0.796684 | + | 0.604396i | \(0.206586\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.10764e6 | 0.170319 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 2.53309e7 | 0.840385 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −1.82946e7 | −0.603863 | −0.301932 | − | 0.953330i | \(-0.597631\pi\) | ||||
−0.301932 | + | 0.953330i | \(0.597631\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.82308e6 | −0.289754 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 5.20117e7 | 1.69087 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −5.61760e6 | −0.181705 | −0.0908524 | − | 0.995864i | \(-0.528959\pi\) | ||||
−0.0908524 | + | 0.995864i | \(0.528959\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 3.17068e7 | 1.02042 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −7.02416e6 | −0.224925 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 1.97151e7 | 0.628146 | 0.314073 | − | 0.949399i | \(-0.398306\pi\) | ||||
0.314073 | + | 0.949399i | \(0.398306\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.14457e6 | 0.258199 |
(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 | 784.6.a.bl.1.1 | 5 | ||
4.3 | odd | 2 | 392.6.a.j.1.5 | 5 | |||
7.3 | odd | 6 | 112.6.i.f.65.1 | 10 | |||
7.5 | odd | 6 | 112.6.i.f.81.1 | 10 | |||
7.6 | odd | 2 | 784.6.a.bk.1.5 | 5 | |||
28.3 | even | 6 | 56.6.i.b.9.5 | ✓ | 10 | ||
28.11 | odd | 6 | 392.6.i.o.177.1 | 10 | |||
28.19 | even | 6 | 56.6.i.b.25.5 | yes | 10 | ||
28.23 | odd | 6 | 392.6.i.o.361.1 | 10 | |||
28.27 | even | 2 | 392.6.a.k.1.1 | 5 | |||
84.47 | odd | 6 | 504.6.s.b.361.3 | 10 | |||
84.59 | odd | 6 | 504.6.s.b.289.3 | 10 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.6.i.b.9.5 | ✓ | 10 | 28.3 | even | 6 | ||
56.6.i.b.25.5 | yes | 10 | 28.19 | even | 6 | ||
112.6.i.f.65.1 | 10 | 7.3 | odd | 6 | |||
112.6.i.f.81.1 | 10 | 7.5 | odd | 6 | |||
392.6.a.j.1.5 | 5 | 4.3 | odd | 2 | |||
392.6.a.k.1.1 | 5 | 28.27 | even | 2 | |||
392.6.i.o.177.1 | 10 | 28.11 | odd | 6 | |||
392.6.i.o.361.1 | 10 | 28.23 | odd | 6 | |||
504.6.s.b.289.3 | 10 | 84.59 | odd | 6 | |||
504.6.s.b.361.3 | 10 | 84.47 | odd | 6 | |||
784.6.a.bk.1.5 | 5 | 7.6 | odd | 2 | |||
784.6.a.bl.1.1 | 5 | 1.1 | even | 1 | trivial |