Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [200,6,Mod(1,200)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(200, 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("200.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 200 = 2^{3} \cdot 5^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 200.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: | \(32.0767639626\) |
Analytic rank: | \(0\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.47217.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 38x - 24 \) |
Coefficient ring: | \(\Z[a_1, a_2, a_3]\) |
Coefficient ring index: | \( 2^{4}\cdot 5 \) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(-0.649919\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 200.1 |
$q$-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 | ||||||||
\(3\) | 22.6278 | 1.45158 | 0.725789 | − | 0.687918i | \(-0.241475\pi\) | ||||
0.725789 | + | 0.687918i | \(0.241475\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −107.252 | −0.827298 | −0.413649 | − | 0.910436i | \(-0.635746\pi\) | ||||
−0.413649 | + | 0.910436i | \(0.635746\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 269.020 | 1.10708 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −290.903 | −0.724881 | −0.362440 | − | 0.932007i | \(-0.618056\pi\) | ||||
−0.362440 | + | 0.932007i | \(0.618056\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 519.583 | 0.852701 | 0.426350 | − | 0.904558i | \(-0.359799\pi\) | ||||
0.426350 | + | 0.904558i | \(0.359799\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2031.17 | 1.70460 | 0.852301 | − | 0.523051i | \(-0.175206\pi\) | ||||
0.852301 | + | 0.523051i | \(0.175206\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1709.34 | 1.08629 | 0.543144 | − | 0.839640i | \(-0.317234\pi\) | ||||
0.543144 | + | 0.839640i | \(0.317234\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2426.89 | −1.20089 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 4355.36 | 1.71674 | 0.858370 | − | 0.513030i | \(-0.171477\pi\) | ||||
0.858370 | + | 0.513030i | \(0.171477\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 588.766 | 0.155430 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4791.56 | 1.05799 | 0.528996 | − | 0.848624i | \(-0.322569\pi\) | ||||
0.528996 | + | 0.848624i | \(0.322569\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7597.89 | 1.42000 | 0.710000 | − | 0.704201i | \(-0.248695\pi\) | ||||
0.710000 | + | 0.704201i | \(0.248695\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −6582.51 | −1.05222 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 5260.87 | 0.631761 | 0.315881 | − | 0.948799i | \(-0.397700\pi\) | ||||
0.315881 | + | 0.948799i | \(0.397700\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 11757.0 | 1.23776 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −10109.1 | −0.939185 | −0.469593 | − | 0.882883i | \(-0.655599\pi\) | ||||
−0.469593 | + | 0.882883i | \(0.655599\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −23414.4 | −1.93113 | −0.965566 | − | 0.260158i | \(-0.916225\pi\) | ||||
−0.965566 | + | 0.260158i | \(0.916225\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3319.92 | −0.219222 | −0.109611 | − | 0.993975i | \(-0.534960\pi\) | ||||
−0.109611 | + | 0.993975i | \(0.534960\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −5303.91 | −0.315578 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 45960.9 | 2.47436 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −28948.8 | −1.41560 | −0.707800 | − | 0.706413i | \(-0.750312\pi\) | ||||
−0.707800 | + | 0.706413i | \(0.750312\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 38678.7 | 1.57683 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 14553.4 | 0.544295 | 0.272147 | − | 0.962256i | \(-0.412266\pi\) | ||||
0.272147 | + | 0.962256i | \(0.412266\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 24379.4 | 0.838876 | 0.419438 | − | 0.907784i | \(-0.362227\pi\) | ||||
0.419438 | + | 0.907784i | \(0.362227\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −28853.0 | −0.915882 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −5931.14 | −0.161418 | −0.0807089 | − | 0.996738i | \(-0.525718\pi\) | ||||
−0.0807089 | + | 0.996738i | \(0.525718\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 98552.5 | 2.49198 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −14407.4 | −0.339188 | −0.169594 | − | 0.985514i | \(-0.554246\pi\) | ||||
−0.169594 | + | 0.985514i | \(0.554246\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 28153.4 | 0.618334 | 0.309167 | − | 0.951008i | \(-0.399950\pi\) | ||||
0.309167 | + | 0.951008i | \(0.399950\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 31200.1 | 0.599693 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 21655.0 | 0.390383 | 0.195191 | − | 0.980765i | \(-0.437467\pi\) | ||||
0.195191 | + | 0.980765i | \(0.437467\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −52049.2 | −0.881458 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −37344.7 | −0.595022 | −0.297511 | − | 0.954718i | \(-0.596157\pi\) | ||||
−0.297511 | + | 0.954718i | \(0.596157\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 108423. | 1.53576 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 90586.5 | 1.21224 | 0.606120 | − | 0.795374i | \(-0.292725\pi\) | ||||
0.606120 | + | 0.795374i | \(0.292725\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −55726.6 | −0.705438 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 171924. | 2.06124 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −73882.4 | −0.797281 | −0.398641 | − | 0.917107i | \(-0.630518\pi\) | ||||
−0.398641 | + | 0.917107i | \(0.630518\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −78258.6 | −0.802498 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 62790.5 | 0.612478 | 0.306239 | − | 0.951955i | \(-0.400929\pi\) | ||||
0.306239 | + | 0.951955i | \(0.400929\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −135312. | −1.25673 | −0.628365 | − | 0.777919i | \(-0.716276\pi\) | ||||
−0.628365 | + | 0.777919i | \(0.716276\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −27359.0 | −0.231015 | −0.115507 | − | 0.993307i | \(-0.536849\pi\) | ||||
−0.115507 | + | 0.993307i | \(0.536849\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 119952. | 0.967036 | 0.483518 | − | 0.875334i | \(-0.339359\pi\) | ||||
0.483518 | + | 0.875334i | \(0.339359\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 119042. | 0.917050 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 230568. | 1.69864 | 0.849322 | − | 0.527875i | \(-0.177011\pi\) | ||||
0.849322 | + | 0.527875i | \(0.177011\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 139778. | 0.944005 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −217848. | −1.41021 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −76426.4 | −0.474548 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −228746. | −1.36330 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −321572. | −1.76917 | −0.884584 | − | 0.466381i | \(-0.845558\pi\) | ||||
−0.884584 | + | 0.466381i | \(0.845558\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −529818. | −2.80319 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −103701. | −0.527966 | −0.263983 | − | 0.964527i | \(-0.585036\pi\) | ||||
−0.263983 | + | 0.964527i | \(0.585036\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −183331. | −0.898684 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −400259. | −1.82197 | −0.910983 | − | 0.412444i | \(-0.864675\pi\) | ||||
−0.910983 | + | 0.412444i | \(0.864675\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −180530. | −0.792523 | −0.396262 | − | 0.918138i | \(-0.629693\pi\) | ||||
−0.396262 | + | 0.918138i | \(0.629693\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −75122.7 | −0.318217 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −151148. | −0.618106 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −120016. | −0.458085 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 308066. | 1.13678 | 0.568392 | − | 0.822758i | \(-0.307566\pi\) | ||||
0.568392 | + | 0.822758i | \(0.307566\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 293359. | 1.04703 | 0.523513 | − | 0.852018i | \(-0.324621\pi\) | ||||
0.523513 | + | 0.852018i | \(0.324621\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 546423. | 1.88713 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 276321. | 0.894673 | 0.447336 | − | 0.894366i | \(-0.352373\pi\) | ||||
0.447336 | + | 0.894366i | \(0.352373\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −655049. | −2.05485 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −467123. | −1.42026 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 557207. | 1.64266 | 0.821330 | − | 0.570454i | \(-0.193233\pi\) | ||||
0.821330 | + | 0.570454i | \(0.193233\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −217034. | −0.602193 | −0.301097 | − | 0.953594i | \(-0.597353\pi\) | ||||
−0.301097 | + | 0.953594i | \(0.597353\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −101326. | −0.272902 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 459846. | 1.20260 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −152453. | −0.387276 | −0.193638 | − | 0.981073i | \(-0.562029\pi\) | ||||
−0.193638 | + | 0.981073i | \(0.562029\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 329312. | 0.790086 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 183447. | 0.427935 | 0.213968 | − | 0.976841i | \(-0.431361\pi\) | ||||
0.213968 | + | 0.976841i | \(0.431361\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −808678. | −1.83476 | −0.917380 | − | 0.398013i | \(-0.869700\pi\) | ||||
−0.917380 | + | 0.398013i | \(0.869700\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 551653. | 1.21769 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −590872. | −1.23563 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −63146.6 | −0.128587 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −429516. | −0.851913 | −0.425957 | − | 0.904744i | \(-0.640062\pi\) | ||||
−0.425957 | + | 0.904744i | \(0.640062\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 610774. | 1.18029 | 0.590143 | − | 0.807299i | \(-0.299071\pi\) | ||||
0.590143 | + | 0.807299i | \(0.299071\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 260379. | 0.478014 | 0.239007 | − | 0.971018i | \(-0.423178\pi\) | ||||
0.239007 | + | 0.971018i | \(0.423178\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 763493. | 1.36670 | 0.683349 | − | 0.730092i | \(-0.260523\pi\) | ||||
0.683349 | + | 0.730092i | \(0.260523\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −134209. | −0.234310 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −513907. | −0.875275 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 1.17168e6 | 1.90056 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −497253. | −0.787429 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −189676. | −0.293297 | −0.146648 | − | 0.989189i | \(-0.546849\pi\) | ||||
−0.146648 | + | 0.989189i | \(0.546849\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −326009. | −0.492357 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −814892. | −1.17476 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 637050. | 0.897560 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 1.05536e6 | 1.45352 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 50555.3 | 0.0680776 | 0.0340388 | − | 0.999421i | \(-0.489163\pi\) | ||||
0.0340388 | + | 0.999421i | \(0.489163\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −641272. | −0.825996 | −0.412998 | − | 0.910732i | \(-0.635518\pi\) | ||||
−0.412998 | + | 0.910732i | \(0.635518\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.20712e6 | 1.52111 | 0.760554 | − | 0.649275i | \(-0.224927\pi\) | ||||
0.760554 | + | 0.649275i | \(0.224927\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 705990. | 0.870500 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.06486e6 | −1.28500 | −0.642501 | − | 0.766285i | \(-0.722103\pi\) | ||||
−0.642501 | + | 0.766285i | \(0.722103\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 490006. | 0.566671 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −358903. | −0.406426 | −0.203213 | − | 0.979135i | \(-0.565138\pi\) | ||||
−0.203213 | + | 0.979135i | \(0.565138\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.58522e6 | 1.75811 | 0.879056 | − | 0.476719i | \(-0.158174\pi\) | ||||
0.879056 | + | 0.476719i | \(0.158174\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −1.32083e6 | −1.43493 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 888145. | 0.926278 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −845029. | −0.863721 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.09079e6 | −1.09284 | −0.546418 | − | 0.837513i | \(-0.684009\pi\) | ||||
−0.546418 | + | 0.837513i | \(0.684009\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −1.26699e6 | −1.24443 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 140503. | 0.132694 | 0.0663472 | − | 0.997797i | \(-0.478866\pi\) | ||||
0.0663472 | + | 0.997797i | \(0.478866\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −564241. | −0.522655 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.28902e6 | 1.17128 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −1688.29 | −0.00150508 | −0.000752538 | − | 1.00000i | \(-0.500240\pi\) | ||||
−0.000752538 | 1.00000i | \(0.500240\pi\) | ||||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 2.04978e6 | 1.75966 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.03111e6 | 0.868810 | 0.434405 | − | 0.900718i | \(-0.356959\pi\) | ||||
0.434405 | + | 0.900718i | \(0.356959\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 152323. | 0.125992 | 0.0629959 | − | 0.998014i | \(-0.479934\pi\) | ||||
0.0629959 | + | 0.998014i | \(0.479934\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1.26097e6 | −1.02400 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1.45824e6 | −1.14190 | −0.570952 | − | 0.820983i | \(-0.693426\pi\) | ||||
−0.570952 | + | 0.820983i | \(0.693426\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2.04398e6 | 1.57205 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −509886. | −0.385218 | −0.192609 | − | 0.981276i | \(-0.561695\pi\) | ||||
−0.192609 | + | 0.981276i | \(0.561695\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 139645. | 0.103648 | 0.0518239 | − | 0.998656i | \(-0.483497\pi\) | ||||
0.0518239 | + | 0.998656i | \(0.483497\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 1.08422e6 | 0.776987 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 2.70578e6 | 1.90567 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1.67180e6 | −1.15732 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 316162. | 0.215150 | 0.107575 | − | 0.994197i | \(-0.465691\pi\) | ||||
0.107575 | + | 0.994197i | \(0.465691\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −171274. | −0.112668 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 2.26297e6 | 1.46387 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.51125e6 | 1.59762 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 1.42081e6 | 0.889059 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.12429e6 | −1.28637 | −0.643186 | − | 0.765710i | \(-0.722388\pi\) | ||||
−0.643186 | + | 0.765710i | \(0.722388\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −3.06181e6 | −1.82424 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −1.00247e6 | −0.587720 | −0.293860 | − | 0.955848i | \(-0.594940\pi\) | ||||
−0.293860 | + | 0.955848i | \(0.594940\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −268434. | −0.154874 | −0.0774368 | − | 0.996997i | \(-0.524674\pi\) | ||||
−0.0774368 | + | 0.996997i | \(0.524674\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 1.47341e6 | 0.823521 | 0.411761 | − | 0.911292i | \(-0.364914\pi\) | ||||
0.411761 | + | 0.911292i | \(0.364914\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.39388e6 | −0.766918 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −619074. | −0.335336 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 3.47196e6 | 1.85169 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 2.71426e6 | 1.40373 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 356070. | 0.181362 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −1.40915e6 | −0.706948 | −0.353474 | − | 0.935444i | \(-0.615000\pi\) | ||||
−0.353474 | + | 0.935444i | \(0.615000\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 1.41528e6 | 0.699408 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 2.00961e6 | 0.963909 | 0.481955 | − | 0.876196i | \(-0.339927\pi\) | ||||
0.481955 | + | 0.876196i | \(0.339927\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 5.21725e6 | 2.46571 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.21025e6 | −1.02933 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 2.37145e6 | 1.08838 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.51970e6 | −0.677538 | −0.338769 | − | 0.940870i | \(-0.610011\pi\) | ||||
−0.338769 | + | 0.940870i | \(0.610011\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −3.65792e6 | −1.60757 | −0.803786 | − | 0.594919i | \(-0.797184\pi\) | ||||
−0.803786 | + | 0.594919i | \(0.797184\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 305913. | 0.132535 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −3.13110e6 | −1.33739 | −0.668697 | − | 0.743535i | \(-0.733148\pi\) | ||||
−0.668697 | + | 0.743535i | \(0.733148\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −4.92942e6 | −2.04704 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4.69349e6 | −1.92203 | −0.961013 | − | 0.276503i | \(-0.910825\pi\) | ||||
−0.961013 | + | 0.276503i | \(0.910825\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 445748. | 0.180020 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −1.72936e6 | −0.688843 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 66533.6 | 0.0257855 | 0.0128928 | − | 0.999917i | \(-0.495896\pi\) | ||||
0.0128928 | + | 0.999917i | \(0.495896\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −2.71954e6 | −1.03975 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 3.10483e6 | 1.17112 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 436576. | 0.162475 | 0.0812376 | − | 0.996695i | \(-0.474113\pi\) | ||||
0.0812376 | + | 0.996695i | \(0.474113\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 2.48962e6 | 0.902150 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −640711. | −0.229120 | −0.114560 | − | 0.993416i | \(-0.536546\pi\) | ||||
−0.114560 | + | 0.993416i | \(0.536546\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −7.27648e6 | −2.56808 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 476798. | 0.166088 | 0.0830438 | − | 0.996546i | \(-0.473536\pi\) | ||||
0.0830438 | + | 0.996546i | \(0.473536\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −6.29893e6 | −2.13791 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −2.43449e6 | −0.815707 | −0.407854 | − | 0.913047i | \(-0.633723\pi\) | ||||
−0.407854 | + | 0.913047i | \(0.633723\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 8.84647e6 | 2.92636 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2.34654e6 | −0.766384 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −3.69898e6 | −1.17789 | −0.588946 | − | 0.808172i | \(-0.700457\pi\) | ||||
−0.588946 | + | 0.808172i | \(0.700457\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −4.14839e6 | −1.30451 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 3.17381e6 | 0.985643 | 0.492822 | − | 0.870130i | \(-0.335966\pi\) | ||||
0.492822 | + | 0.870130i | \(0.335966\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 3.94773e6 | 1.21084 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −1.53040e6 | −0.457952 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.92926e6 | 0.570272 | 0.285136 | − | 0.958487i | \(-0.407961\pi\) | ||||
0.285136 | + | 0.958487i | \(0.407961\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −9.05701e6 | −2.64472 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −1.56089e6 | −0.450294 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −4.08500e6 | −1.15041 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −5.28590e6 | −1.47090 | −0.735451 | − | 0.677578i | \(-0.763030\pi\) | ||||
−0.735451 | + | 0.677578i | \(0.763030\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 4.63926e6 | 1.27568 | 0.637842 | − | 0.770167i | \(-0.279827\pi\) | ||||
0.637842 | + | 0.770167i | \(0.279827\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −893124. | −0.242695 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −2.61475e6 | −0.694001 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3.42016e6 | −0.897229 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −5.05569e6 | −1.31095 | −0.655477 | − | 0.755215i | \(-0.727532\pi\) | ||||
−0.655477 | + | 0.755215i | \(0.727532\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 3.02308e6 | 0.774873 | 0.387437 | − | 0.921896i | \(-0.373361\pi\) | ||||
0.387437 | + | 0.921896i | \(0.373361\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 7.44480e6 | 1.86487 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 493181. | 0.122136 | 0.0610682 | − | 0.998134i | \(-0.480549\pi\) | ||||
0.0610682 | + | 0.998134i | \(0.480549\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −1.42686e6 | −0.349368 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −5.86117e6 | −1.41898 | −0.709488 | − | 0.704717i | \(-0.751074\pi\) | ||||
−0.709488 | + | 0.704717i | \(0.751074\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 6.97086e6 | 1.65013 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 983425. | 0.230211 | 0.115105 | − | 0.993353i | \(-0.463279\pi\) | ||||
0.115105 | + | 0.993353i | \(0.463279\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.94076e6 | 0.680798 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 6.63808e6 | 1.51984 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 3.78555e6 | 0.847887 | 0.423944 | − | 0.905689i | \(-0.360645\pi\) | ||||
0.423944 | + | 0.905689i | \(0.360645\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 1.19588e6 | 0.264946 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −5.84423e6 | −1.28078 | −0.640391 | − | 0.768049i | \(-0.721228\pi\) | ||||
−0.640391 | + | 0.768049i | \(0.721228\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 4.65701e6 | 1.00961 | 0.504807 | − | 0.863232i | \(-0.331564\pi\) | ||||
0.504807 | + | 0.863232i | \(0.331564\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −2.35873e6 | −0.500479 | −0.250239 | − | 0.968184i | \(-0.580509\pi\) | ||||
−0.250239 | + | 0.968184i | \(0.580509\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 636130. | 0.133541 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 6.25254e6 | 1.29869 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 6.81132e6 | 1.39984 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −7.78779e6 | −1.56718 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 1.87288e6 | 0.372968 | 0.186484 | − | 0.982458i | \(-0.440291\pi\) | ||||
0.186484 | + | 0.982458i | \(0.440291\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 2.73346e6 | 0.538703 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.05700e7 | −2.06161 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.94339e6 | 0.371311 | 0.185655 | − | 0.982615i | \(-0.440559\pi\) | ||||
0.185655 | + | 0.982615i | \(0.440559\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 1.26084e7 | 2.38445 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −8.02560e6 | −1.50236 | −0.751179 | − | 0.660098i | \(-0.770515\pi\) | ||||
−0.751179 | + | 0.660098i | \(0.770515\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 9.73246e6 | 1.80346 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 1.54523e6 | 0.280609 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.53659e6 | 0.635818 | 0.317909 | − | 0.948121i | \(-0.397019\pi\) | ||||
0.317909 | + | 0.948121i | \(0.397019\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −4.91101e6 | −0.874130 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 2.81866e6 | 0.496733 | 0.248367 | − | 0.968666i | \(-0.420106\pi\) | ||||
0.248367 | + | 0.968666i | \(0.420106\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.29280e6 | −0.396138 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 538808. | 0.0921806 | 0.0460903 | − | 0.998937i | \(-0.485324\pi\) | ||||
0.0460903 | + | 0.998937i | \(0.485324\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −3.01952e6 | −0.511547 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 1.00640e6 | 0.168841 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 965776. | 0.158910 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −3.44968e6 | −0.562160 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.25606e6 | 0.848332 | 0.424166 | − | 0.905584i | \(-0.360567\pi\) | ||||
0.424166 | + | 0.905584i | \(0.360567\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −5.36466e6 | −0.857606 | −0.428803 | − | 0.903398i | \(-0.641065\pi\) | ||||
−0.428803 | + | 0.903398i | \(0.641065\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 1.54326e7 | 2.42054 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1.25328e7 | 1.94720 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.91514e6 | 0.602576 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −5.25250e6 | −0.800844 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.15101e6 | 0.621181 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.54292e6 | 0.228756 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.05037e7 | 1.54294 | 0.771471 | − | 0.636264i | \(-0.219521\pi\) | ||||
0.771471 | + | 0.636264i | \(0.219521\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −1.82986e7 | −2.66330 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −7.64670e6 | −1.09271 | −0.546356 | − | 0.837553i | \(-0.683985\pi\) | ||||
−0.546356 | + | 0.837553i | \(0.683985\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 6.55853e6 | 0.928700 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 8.19042e6 | 1.14928 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −2.32255e6 | −0.322963 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.93235e6 | 0.946766 | 0.473383 | − | 0.880857i | \(-0.343033\pi\) | ||||
0.473383 | + | 0.880857i | \(0.343033\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.21657e7 | −1.64668 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −1.33702e7 | −1.79362 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −7.26755e6 | −0.966311 | −0.483156 | − | 0.875535i | \(-0.660509\pi\) | ||||
−0.483156 | + | 0.875535i | \(0.660509\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 5.58241e6 | 0.729229 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −1.33658e7 | −1.73067 | −0.865336 | − | 0.501193i | \(-0.832895\pi\) | ||||
−0.865336 | + | 0.501193i | \(0.832895\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 9.84651e6 | 1.26384 | 0.631920 | − | 0.775034i | \(-0.282267\pi\) | ||||
0.631920 | + | 0.775034i | \(0.282267\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −9.71901e6 | −1.23662 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.93536e6 | −1.24235 | −0.621175 | − | 0.783672i | \(-0.713344\pi\) | ||||
−0.621175 | + | 0.783672i | \(0.713344\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 1.38205e7 | 1.71328 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 4.00531e6 | 0.492261 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 8.42129e6 | 1.02614 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −8.55552e6 | −1.02483 | −0.512414 | − | 0.858738i | \(-0.671249\pi\) | ||||
−0.512414 | + | 0.858738i | \(0.671249\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 1.29874e7 | 1.54253 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 5.89182e6 | 0.693874 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −3.07038e6 | −0.358555 | −0.179277 | − | 0.983799i | \(-0.557376\pi\) | ||||
−0.179277 | + | 0.983799i | \(0.557376\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.72762e7 | 1.98387 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 174294. | 0.0198480 | 0.00992398 | − | 0.999951i | \(-0.496841\pi\) | ||||
0.00992398 | + | 0.999951i | \(0.496841\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 3.73604e6 | 0.421915 | 0.210958 | − | 0.977495i | \(-0.432342\pi\) | ||||
0.210958 | + | 0.977495i | \(0.432342\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1.59559e6 | −0.178702 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.02370e6 | −0.333094 | −0.166547 | − | 0.986033i | \(-0.553262\pi\) | ||||
−0.166547 | + | 0.986033i | \(0.553262\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1.16286e7 | −1.27053 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.72498e6 | −0.186930 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 3.07263e6 | 0.330263 | 0.165131 | − | 0.986272i | \(-0.447195\pi\) | ||||
0.165131 | + | 0.986272i | \(0.447195\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 6.60221e6 | 0.698195 | 0.349097 | − | 0.937086i | \(-0.386488\pi\) | ||||
0.349097 | + | 0.937086i | \(0.386488\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 2.68055e6 | 0.281189 | 0.140594 | − | 0.990067i | \(-0.455099\pi\) | ||||
0.140594 | + | 0.990067i | \(0.455099\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2.56429e6 | 0.266832 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | −9.71562e6 | −1.00288 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −1.12518e7 | −1.14301 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1.06857e7 | 1.07690 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 1.72975e7 | 1.72946 | 0.864728 | − | 0.502240i | \(-0.167491\pi\) | ||||
0.864728 | + | 0.502240i | \(0.167491\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4.29197e6 | −0.425743 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2.75582e6 | −0.269093 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −3.87588e6 | −0.375507 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.50990e7 | −1.45145 | −0.725725 | − | 0.687984i | \(-0.758496\pi\) | ||||
−0.725725 | + | 0.687984i | \(0.758496\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 8.40104e6 | 0.801319 | 0.400660 | − | 0.916227i | \(-0.368781\pi\) | ||||
0.400660 | + | 0.916227i | \(0.368781\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −1.69105e7 | −1.58816 | −0.794080 | − | 0.607813i | \(-0.792047\pi\) | ||||
−0.794080 | + | 0.607813i | \(0.792047\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −4.23362e6 | −0.394549 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −1.84393e7 | −1.70526 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −3.38875e6 | −0.310997 | −0.155499 | − | 0.987836i | \(-0.549698\pi\) | ||||
−0.155499 | + | 0.987836i | \(0.549698\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 7.57381e6 | 0.684543 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.21397e7 | 1.08891 | 0.544457 | − | 0.838789i | \(-0.316736\pi\) | ||||
0.544457 | + | 0.838789i | \(0.316736\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.67377e7 | −1.49002 | −0.745009 | − | 0.667055i | \(-0.767555\pi\) | ||||
−0.745009 | + | 0.667055i | \(0.767555\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.38805e7 | 2.10989 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.08690e7 | 1.81630 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.14396e6 | 0.0988199 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −7.09204e6 | −0.608085 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.36101e6 | 0.626469 | 0.313235 | − | 0.949676i | \(-0.398587\pi\) | ||||
0.313235 | + | 0.949676i | \(0.398587\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −5.68650e6 | −0.476841 | −0.238420 | − | 0.971162i | \(-0.576630\pi\) | ||||
−0.238420 | + | 0.971162i | \(0.576630\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 7.92407e6 | 0.659589 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1.45106e7 | −1.19900 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −229728. | −0.0188435 | −0.00942175 | − | 0.999956i | \(-0.502999\pi\) | ||||
−0.00942175 | + | 0.999956i | \(0.502999\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 2.73144e7 | 2.20801 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −1.50413e7 | −1.20708 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1.32222e7 | 1.05344 | 0.526720 | − | 0.850039i | \(-0.323422\pi\) | ||||
0.526720 | + | 0.850039i | \(0.323422\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 8.39343e6 | 0.663906 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.05332e7 | −1.60094 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.40955e7 | −1.86528 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.59857e6 | 0.660893 | 0.330447 | − | 0.943825i | \(-0.392801\pi\) | ||||
0.330447 | + | 0.943825i | \(0.392801\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 8.99261e6 | 0.686274 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −6.73443e6 | −0.506702 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.00967e7 | −0.754336 | −0.377168 | − | 0.926145i | \(-0.623102\pi\) | ||||
−0.377168 | + | 0.926145i | \(0.623102\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 5.82562e6 | 0.432184 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3.30916e7 | 2.43777 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −8.12120e6 | −0.589959 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 3.34106e6 | 0.241025 | 0.120513 | − | 0.992712i | \(-0.461546\pi\) | ||||
0.120513 | + | 0.992712i | \(0.461546\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 1.45125e7 | 1.03969 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 3.58701e7 | 2.55203 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −1.35160e7 | −0.948447 | −0.474224 | − | 0.880404i | \(-0.657271\pi\) | ||||
−0.474224 | + | 0.880404i | \(0.657271\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −1.72396e7 | −1.20146 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −4.75585e7 | −3.29181 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −2.86786e7 | −1.97150 | −0.985752 | − | 0.168202i | \(-0.946204\pi\) | ||||
−0.985752 | + | 0.168202i | \(0.946204\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.72539e6 | 0.117009 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 1.81256e7 | 1.22090 | 0.610452 | − | 0.792053i | \(-0.290988\pi\) | ||||
0.610452 | + | 0.792053i | \(0.290988\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 2.00968e7 | 1.34456 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −7.08132e6 | −0.470590 | −0.235295 | − | 0.971924i | \(-0.575606\pi\) | ||||
−0.235295 | + | 0.971924i | \(0.575606\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.00464e7 | −0.658735 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 2.93431e6 | 0.191118 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −4.00260e6 | −0.258966 | −0.129483 | − | 0.991582i | \(-0.541332\pi\) | ||||
−0.129483 | + | 0.991582i | \(0.541332\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −2.46821e7 | −1.58634 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −1.71922e7 | −1.09041 | −0.545207 | − | 0.838302i | \(-0.683549\pi\) | ||||
−0.545207 | + | 0.838302i | \(0.683549\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.86692e7 | −1.80639 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 1.98543e6 | 0.124277 | 0.0621387 | − | 0.998068i | \(-0.480208\pi\) | ||||
0.0621387 | + | 0.998068i | \(0.480208\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.28652e7 | −0.800027 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 7.56169e6 | 0.464120 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.30522e7 | −0.795915 | −0.397958 | − | 0.917404i | \(-0.630281\pi\) | ||||
−0.397958 | + | 0.917404i | \(0.630281\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 3.17928e6 | 0.192616 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −1.33637e7 | −0.804408 | −0.402204 | − | 0.915550i | \(-0.631756\pi\) | ||||
−0.402204 | + | 0.915550i | \(0.631756\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −1.27676e7 | −0.758674 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −1.72798e7 | −1.02023 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.19116e6 | 0.245871 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 2.82111e6 | 0.164443 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −2.84001e7 | −1.63449 | −0.817246 | − | 0.576289i | \(-0.804500\pi\) | ||||
−0.817246 | + | 0.576289i | \(0.804500\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −38202.4 | −0.00218473 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −2.47290e7 | −1.40529 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 1.26671e7 | 0.715310 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.56843e7 | 1.43226 | 0.716130 | − | 0.697967i | \(-0.245912\pi\) | ||||
0.716130 | + | 0.697967i | \(0.245912\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −6.74332e6 | −0.373686 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 2.43695e7 | 1.34204 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −8.18990e6 | −0.448219 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.33318e7 | 1.26114 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −1.39936e7 | −0.751721 | −0.375861 | − | 0.926676i | \(-0.622653\pi\) | ||||
−0.375861 | + | 0.926676i | \(0.622653\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 6.58958e6 | 0.351808 | 0.175904 | − | 0.984407i | \(-0.443715\pi\) | ||||
0.175904 | + | 0.984407i | \(0.443715\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 3.44674e6 | 0.182887 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.00232e7 | −2.09776 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.49915e7 | −0.780973 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 8.99703e6 | 0.465845 | 0.232922 | − | 0.972495i | \(-0.425171\pi\) | ||||
0.232922 | + | 0.972495i | \(0.425171\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 5.23574e6 | 0.269450 | 0.134725 | − | 0.990883i | \(-0.456985\pi\) | ||||
0.134725 | + | 0.990883i | \(0.456985\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −315583. | −0.0160454 | −0.00802268 | − | 0.999968i | \(-0.502554\pi\) | ||||
−0.00802268 | + | 0.999968i | \(0.502554\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −8.50851e6 | −0.429999 | −0.214999 | − | 0.976614i | \(-0.568975\pi\) | ||||
−0.214999 | + | 0.976614i | \(0.568975\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −3.29968e7 | −1.65756 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −1.07731e7 | −0.537934 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 4.47338e6 | 0.220710 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 2.91278e7 | 1.42858 | 0.714288 | − | 0.699852i | \(-0.246751\pi\) | ||||
0.714288 | + | 0.699852i | \(0.246751\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 2.44793e6 | 0.119346 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −1.15376e7 | −0.559174 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 8.19692e6 | 0.392593 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 3.15987e6 | 0.150453 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.29130e7 | 1.08457 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.70286e6 | 0.268361 | 0.134181 | − | 0.990957i | \(-0.457160\pi\) | ||||
0.134181 | + | 0.990957i | \(0.457160\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −2.92322e7 | −1.35959 | −0.679797 | − | 0.733400i | \(-0.737932\pi\) | ||||
−0.679797 | + | 0.733400i | \(0.737932\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.74800e7 | 0.808274 | 0.404137 | − | 0.914698i | \(-0.367572\pi\) | ||||
0.404137 | + | 0.914698i | \(0.367572\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2.45336e7 | 1.12786 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 5.53579e6 | 0.253018 | 0.126509 | − | 0.991965i | \(-0.459623\pi\) | ||||
0.126509 | + | 0.991965i | \(0.459623\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 6.12260e7 | 2.76623 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −6.29951e6 | −0.282981 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −3.08172e6 | −0.137641 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −1.98758e7 | −0.882651 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 4.87087e6 | 0.213849 | 0.106925 | − | 0.994267i | \(-0.465900\pi\) | ||||
0.106925 | + | 0.994267i | \(0.465900\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 7.15407e6 | 0.312306 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 2.25286e7 | 0.977900 | 0.488950 | − | 0.872312i | \(-0.337380\pi\) | ||||
0.488950 | + | 0.872312i | \(0.337380\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2.27462e7 | 0.981762 | 0.490881 | − | 0.871227i | \(-0.336675\pi\) | ||||
0.490881 | + | 0.871227i | \(0.336675\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.52256e7 | −1.07655 | −0.538274 | − | 0.842770i | \(-0.680923\pi\) | ||||
−0.538274 | + | 0.842770i | \(0.680923\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.44894e7 | 1.46363 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 1.51413e7 | 0.638952 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −5.67488e6 | −0.238138 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.12062e7 | 2.12491 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3.64058e7 | 1.50235 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.87998e7 | −2.41304 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.68242e7 | 2.31907 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.51254e7 | 1.01413 | 0.507066 | − | 0.861907i | \(-0.330730\pi\) | ||||
0.507066 | + | 0.861907i | \(0.330730\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1.68919e7 | 0.678060 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.81254e6 | 0.112280 | 0.0561400 | − | 0.998423i | \(-0.482121\pi\) | ||||
0.0561400 | + | 0.998423i | \(0.482121\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1.08637e7 | 0.431320 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 1.11222e7 | 0.436785 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 3.18718e7 | 1.24485 | 0.622426 | − | 0.782679i | \(-0.286147\pi\) | ||||
0.622426 | + | 0.782679i | \(0.286147\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −4.80680e7 | −1.86727 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −7.48585e6 | −0.289226 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −3.64015e7 | −1.39130 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −3.38523e6 | −0.128691 | −0.0643455 | − | 0.997928i | \(-0.520496\pi\) | ||||
−0.0643455 | + | 0.997928i | \(0.520496\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −9.06619e6 | −0.342808 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.26838e7 | −0.853122 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 4.33776e7 | 1.61405 | 0.807025 | − | 0.590517i | \(-0.201076\pi\) | ||||
0.807025 | + | 0.590517i | \(0.201076\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −6.07409e6 | −0.224811 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −3.32026e7 | −1.22236 | −0.611178 | − | 0.791493i | \(-0.709304\pi\) | ||||
−0.611178 | + | 0.791493i | \(0.709304\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −4.40286e7 | −1.61234 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.31754e7 | −0.477407 | −0.238704 | − | 0.971092i | \(-0.576722\pi\) | ||||
−0.238704 | + | 0.971092i | \(0.576722\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 1.46280e7 | 0.527254 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 3.33400e7 | 1.19540 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −1.24126e7 | −0.442721 | −0.221360 | − | 0.975192i | \(-0.571050\pi\) | ||||
−0.221360 | + | 0.975192i | \(0.571050\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −3.15405e7 | −1.11324 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 4.29288e7 | 1.50731 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.90987e7 | 1.01640 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −7.36009e6 | −0.255751 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3.35785e7 | 1.15477 | 0.577385 | − | 0.816472i | \(-0.304073\pi\) | ||||
0.577385 | + | 0.816472i | \(0.304073\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 7.85629e7 | 2.68787 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.27945e6 | 0.179697 | 0.0898485 | − | 0.995955i | \(-0.471362\pi\) | ||||
0.0898485 | + | 0.995955i | \(0.471362\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 1.93623e7 | 0.655653 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 1.27469e7 | 0.427237 | 0.213619 | − | 0.976917i | \(-0.431475\pi\) | ||||
0.213619 | + | 0.976917i | \(0.431475\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2.63519e7 | −0.878729 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 3.22695e7 | 1.07058 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −2.38142e7 | −0.786052 | −0.393026 | − | 0.919527i | \(-0.628572\pi\) | ||||
−0.393026 | + | 0.919527i | \(0.628572\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 8.05710e6 | 0.263261 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −1.01978e8 | −3.31525 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1.23214e7 | 0.398545 | 0.199273 | − | 0.979944i | \(-0.436142\pi\) | ||||
0.199273 | + | 0.979944i | \(0.436142\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.18861e7 | −1.02619 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 7.52318e6 | 0.239697 | 0.119849 | − | 0.992792i | \(-0.461759\pi\) | ||||
0.119849 | + | 0.992792i | \(0.461759\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 3.09742e6 | 0.0981943 |
(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 | 200.6.a.i.1.3 | yes | 3 | |
4.3 | odd | 2 | 400.6.a.x.1.1 | 3 | |||
5.2 | odd | 4 | 200.6.c.g.49.1 | 6 | |||
5.3 | odd | 4 | 200.6.c.g.49.6 | 6 | |||
5.4 | even | 2 | 200.6.a.h.1.1 | ✓ | 3 | ||
20.3 | even | 4 | 400.6.c.p.49.1 | 6 | |||
20.7 | even | 4 | 400.6.c.p.49.6 | 6 | |||
20.19 | odd | 2 | 400.6.a.y.1.3 | 3 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
200.6.a.h.1.1 | ✓ | 3 | 5.4 | even | 2 | ||
200.6.a.i.1.3 | yes | 3 | 1.1 | even | 1 | trivial | |
200.6.c.g.49.1 | 6 | 5.2 | odd | 4 | |||
200.6.c.g.49.6 | 6 | 5.3 | odd | 4 | |||
400.6.a.x.1.1 | 3 | 4.3 | odd | 2 | |||
400.6.a.y.1.3 | 3 | 20.19 | odd | 2 | |||
400.6.c.p.49.1 | 6 | 20.3 | even | 4 | |||
400.6.c.p.49.6 | 6 | 20.7 | even | 4 |