Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [135,6,Mod(1,135)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(135, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("135.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 135 = 3^{3} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 135.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: | \(21.6518156748\) |
Analytic rank: | \(1\) |
Dimension: | \(1\) |
Coefficient field: | \(\mathbb{Q}\) |
Coefficient ring: | \(\mathbb{Z}\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Character | \(\chi\) | \(=\) | 135.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −10.0000 | −1.76777 | −0.883883 | − | 0.467707i | \(-0.845080\pi\) | ||||
−0.883883 | + | 0.467707i | \(0.845080\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 68.0000 | 2.12500 | ||||||||
\(5\) | 25.0000 | 0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 6.00000 | 0.0462814 | 0.0231407 | − | 0.999732i | \(-0.492633\pi\) | ||||
0.0231407 | + | 0.999732i | \(0.492633\pi\) | |||||||
\(8\) | −360.000 | −1.98874 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −250.000 | −0.790569 | ||||||||
\(11\) | −685.000 | −1.70690 | −0.853452 | − | 0.521172i | \(-0.825495\pi\) | ||||
−0.853452 | + | 0.521172i | \(0.825495\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 685.000 | 1.12417 | 0.562085 | − | 0.827079i | \(-0.309999\pi\) | ||||
0.562085 | + | 0.827079i | \(0.309999\pi\) | |||||||
\(14\) | −60.0000 | −0.0818147 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1424.00 | 1.39062 | ||||||||
\(17\) | −1045.00 | −0.876989 | −0.438494 | − | 0.898734i | \(-0.644488\pi\) | ||||
−0.438494 | + | 0.898734i | \(0.644488\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1108.00 | 0.704135 | 0.352067 | − | 0.935975i | \(-0.385479\pi\) | ||||
0.352067 | + | 0.935975i | \(0.385479\pi\) | |||||||
\(20\) | 1700.00 | 0.950329 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 6850.00 | 3.01741 | ||||||||
\(23\) | 3855.00 | 1.51951 | 0.759757 | − | 0.650207i | \(-0.225318\pi\) | ||||
0.759757 | + | 0.650207i | \(0.225318\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 625.000 | 0.200000 | ||||||||
\(26\) | −6850.00 | −1.98727 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 408.000 | 0.0983479 | ||||||||
\(29\) | 1315.00 | 0.290356 | 0.145178 | − | 0.989406i | \(-0.453625\pi\) | ||||
0.145178 | + | 0.989406i | \(0.453625\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −9909.00 | −1.85193 | −0.925967 | − | 0.377604i | \(-0.876748\pi\) | ||||
−0.925967 | + | 0.377604i | \(0.876748\pi\) | |||||||
\(32\) | −2720.00 | −0.469563 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 10450.0 | 1.55031 | ||||||||
\(35\) | 150.000 | 0.0206977 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6826.00 | −0.819713 | −0.409857 | − | 0.912150i | \(-0.634421\pi\) | ||||
−0.409857 | + | 0.912150i | \(0.634421\pi\) | |||||||
\(38\) | −11080.0 | −1.24475 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −9000.00 | −0.889391 | ||||||||
\(41\) | −4520.00 | −0.419932 | −0.209966 | − | 0.977709i | \(-0.567335\pi\) | ||||
−0.209966 | + | 0.977709i | \(0.567335\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 9097.00 | 0.750286 | 0.375143 | − | 0.926967i | \(-0.377594\pi\) | ||||
0.375143 | + | 0.926967i | \(0.377594\pi\) | |||||||
\(44\) | −46580.0 | −3.62717 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −38550.0 | −2.68615 | ||||||||
\(47\) | −2095.00 | −0.138337 | −0.0691687 | − | 0.997605i | \(-0.522035\pi\) | ||||
−0.0691687 | + | 0.997605i | \(0.522035\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −16771.0 | −0.997858 | ||||||||
\(50\) | −6250.00 | −0.353553 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 46580.0 | 2.38886 | ||||||||
\(53\) | −10060.0 | −0.491936 | −0.245968 | − | 0.969278i | \(-0.579106\pi\) | ||||
−0.245968 | + | 0.969278i | \(0.579106\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −17125.0 | −0.763350 | ||||||||
\(56\) | −2160.00 | −0.0920415 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −13150.0 | −0.513282 | ||||||||
\(59\) | −24820.0 | −0.928265 | −0.464132 | − | 0.885766i | \(-0.653634\pi\) | ||||
−0.464132 | + | 0.885766i | \(0.653634\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −46286.0 | −1.59267 | −0.796334 | − | 0.604858i | \(-0.793230\pi\) | ||||
−0.796334 | + | 0.604858i | \(0.793230\pi\) | |||||||
\(62\) | 99090.0 | 3.27379 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −18368.0 | −0.560547 | ||||||||
\(65\) | 17125.0 | 0.502744 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 13860.0 | 0.377204 | 0.188602 | − | 0.982054i | \(-0.439604\pi\) | ||||
0.188602 | + | 0.982054i | \(0.439604\pi\) | |||||||
\(68\) | −71060.0 | −1.86360 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −1500.00 | −0.0365886 | ||||||||
\(71\) | 75580.0 | 1.77935 | 0.889674 | − | 0.456596i | \(-0.150931\pi\) | ||||
0.889674 | + | 0.456596i | \(0.150931\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −32738.0 | −0.719027 | −0.359513 | − | 0.933140i | \(-0.617057\pi\) | ||||
−0.359513 | + | 0.933140i | \(0.617057\pi\) | |||||||
\(74\) | 68260.0 | 1.44906 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 75344.0 | 1.49629 | ||||||||
\(77\) | −4110.00 | −0.0789978 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 74877.0 | 1.34984 | 0.674918 | − | 0.737893i | \(-0.264179\pi\) | ||||
0.674918 | + | 0.737893i | \(0.264179\pi\) | |||||||
\(80\) | 35600.0 | 0.621906 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 45200.0 | 0.742342 | ||||||||
\(83\) | −93930.0 | −1.49661 | −0.748306 | − | 0.663354i | \(-0.769132\pi\) | ||||
−0.748306 | + | 0.663354i | \(0.769132\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −26125.0 | −0.392201 | ||||||||
\(86\) | −90970.0 | −1.32633 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 246600. | 3.39458 | ||||||||
\(89\) | −123540. | −1.65323 | −0.826614 | − | 0.562770i | \(-0.809736\pi\) | ||||
−0.826614 | + | 0.562770i | \(0.809736\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4110.00 | 0.0520281 | ||||||||
\(92\) | 262140. | 3.22897 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 20950.0 | 0.244548 | ||||||||
\(95\) | 27700.0 | 0.314899 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −85966.0 | −0.927678 | −0.463839 | − | 0.885919i | \(-0.653528\pi\) | ||||
−0.463839 | + | 0.885919i | \(0.653528\pi\) | |||||||
\(98\) | 167710. | 1.76398 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 42500.0 | 0.425000 | ||||||||
\(101\) | −62415.0 | −0.608815 | −0.304408 | − | 0.952542i | \(-0.598458\pi\) | ||||
−0.304408 | + | 0.952542i | \(0.598458\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −169522. | −1.57446 | −0.787232 | − | 0.616656i | \(-0.788487\pi\) | ||||
−0.787232 | + | 0.616656i | \(0.788487\pi\) | |||||||
\(104\) | −246600. | −2.23568 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 100600. | 0.869628 | ||||||||
\(107\) | −2850.00 | −0.0240650 | −0.0120325 | − | 0.999928i | \(-0.503830\pi\) | ||||
−0.0120325 | + | 0.999928i | \(0.503830\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −210628. | −1.69805 | −0.849024 | − | 0.528355i | \(-0.822809\pi\) | ||||
−0.849024 | + | 0.528355i | \(0.822809\pi\) | |||||||
\(110\) | 171250. | 1.34943 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 8544.00 | 0.0643600 | ||||||||
\(113\) | 81335.0 | 0.599213 | 0.299607 | − | 0.954063i | \(-0.403145\pi\) | ||||
0.299607 | + | 0.954063i | \(0.403145\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 96375.0 | 0.679547 | ||||||||
\(116\) | 89420.0 | 0.617006 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 248200. | 1.64096 | ||||||||
\(119\) | −6270.00 | −0.0405882 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 308174. | 1.91352 | ||||||||
\(122\) | 462860. | 2.81546 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −673812. | −3.93536 | ||||||||
\(125\) | 15625.0 | 0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −237410. | −1.30614 | −0.653070 | − | 0.757298i | \(-0.726519\pi\) | ||||
−0.653070 | + | 0.757298i | \(0.726519\pi\) | |||||||
\(128\) | 270720. | 1.46048 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −171250. | −0.888735 | ||||||||
\(131\) | −158115. | −0.804998 | −0.402499 | − | 0.915420i | \(-0.631858\pi\) | ||||
−0.402499 | + | 0.915420i | \(0.631858\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 6648.00 | 0.0325883 | ||||||||
\(134\) | −138600. | −0.666809 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 376200. | 1.74410 | ||||||||
\(137\) | 195270. | 0.888862 | 0.444431 | − | 0.895813i | \(-0.353406\pi\) | ||||
0.444431 | + | 0.895813i | \(0.353406\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 13238.0 | 0.0581146 | 0.0290573 | − | 0.999578i | \(-0.490749\pi\) | ||||
0.0290573 | + | 0.999578i | \(0.490749\pi\) | |||||||
\(140\) | 10200.0 | 0.0439825 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −755800. | −3.14547 | ||||||||
\(143\) | −469225. | −1.91885 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 32875.0 | 0.129851 | ||||||||
\(146\) | 327380. | 1.27107 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −464168. | −1.74189 | ||||||||
\(149\) | −242405. | −0.894491 | −0.447245 | − | 0.894411i | \(-0.647595\pi\) | ||||
−0.447245 | + | 0.894411i | \(0.647595\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −446459. | −1.59345 | −0.796726 | − | 0.604340i | \(-0.793437\pi\) | ||||
−0.796726 | + | 0.604340i | \(0.793437\pi\) | |||||||
\(152\) | −398880. | −1.40034 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 41100.0 | 0.139650 | ||||||||
\(155\) | −247725. | −0.828210 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 332411. | 1.07628 | 0.538141 | − | 0.842855i | \(-0.319127\pi\) | ||||
0.538141 | + | 0.842855i | \(0.319127\pi\) | |||||||
\(158\) | −748770. | −2.38619 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −68000.0 | −0.209995 | ||||||||
\(161\) | 23130.0 | 0.0703252 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 442925. | 1.30575 | 0.652877 | − | 0.757464i | \(-0.273562\pi\) | ||||
0.652877 | + | 0.757464i | \(0.273562\pi\) | |||||||
\(164\) | −307360. | −0.892355 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 939300. | 2.64566 | ||||||||
\(167\) | 7140.00 | 0.0198110 | 0.00990551 | − | 0.999951i | \(-0.496847\pi\) | ||||
0.00990551 | + | 0.999951i | \(0.496847\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 97932.0 | 0.263759 | ||||||||
\(170\) | 261250. | 0.693320 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 618596. | 1.59436 | ||||||||
\(173\) | −292650. | −0.743418 | −0.371709 | − | 0.928349i | \(-0.621228\pi\) | ||||
−0.371709 | + | 0.928349i | \(0.621228\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 3750.00 | 0.00925627 | ||||||||
\(176\) | −975440. | −2.37366 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1.23540e6 | 2.92252 | ||||||||
\(179\) | 609980. | 1.42293 | 0.711464 | − | 0.702722i | \(-0.248032\pi\) | ||||
0.711464 | + | 0.702722i | \(0.248032\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −79852.0 | −0.181171 | −0.0905856 | − | 0.995889i | \(-0.528874\pi\) | ||||
−0.0905856 | + | 0.995889i | \(0.528874\pi\) | |||||||
\(182\) | −41100.0 | −0.0919736 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −1.38780e6 | −3.02192 | ||||||||
\(185\) | −170650. | −0.366587 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 715825. | 1.49693 | ||||||||
\(188\) | −142460. | −0.293967 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −277000. | −0.556667 | ||||||||
\(191\) | 150910. | 0.299319 | 0.149660 | − | 0.988738i | \(-0.452182\pi\) | ||||
0.149660 | + | 0.988738i | \(0.452182\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 170702. | 0.329872 | 0.164936 | − | 0.986304i | \(-0.447258\pi\) | ||||
0.164936 | + | 0.986304i | \(0.447258\pi\) | |||||||
\(194\) | 859660. | 1.63992 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −1.14043e6 | −2.12045 | ||||||||
\(197\) | −333360. | −0.611995 | −0.305998 | − | 0.952032i | \(-0.598990\pi\) | ||||
−0.305998 | + | 0.952032i | \(0.598990\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 57511.0 | 0.102948 | 0.0514740 | − | 0.998674i | \(-0.483608\pi\) | ||||
0.0514740 | + | 0.998674i | \(0.483608\pi\) | |||||||
\(200\) | −225000. | −0.397748 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 624150. | 1.07624 | ||||||||
\(203\) | 7890.00 | 0.0134381 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −113000. | −0.187799 | ||||||||
\(206\) | 1.69522e6 | 2.78329 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 975440. | 1.56330 | ||||||||
\(209\) | −758980. | −1.20189 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 428102. | 0.661974 | 0.330987 | − | 0.943635i | \(-0.392618\pi\) | ||||
0.330987 | + | 0.943635i | \(0.392618\pi\) | |||||||
\(212\) | −684080. | −1.04536 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 28500.0 | 0.0425413 | ||||||||
\(215\) | 227425. | 0.335538 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −59454.0 | −0.0857100 | ||||||||
\(218\) | 2.10628e6 | 3.00175 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.16450e6 | −1.62212 | ||||||||
\(221\) | −715825. | −0.985885 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 699368. | 0.941767 | 0.470884 | − | 0.882195i | \(-0.343935\pi\) | ||||
0.470884 | + | 0.882195i | \(0.343935\pi\) | |||||||
\(224\) | −16320.0 | −0.0217320 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −813350. | −1.05927 | ||||||||
\(227\) | −471200. | −0.606933 | −0.303466 | − | 0.952842i | \(-0.598144\pi\) | ||||
−0.303466 | + | 0.952842i | \(0.598144\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.44071e6 | 1.81546 | 0.907731 | − | 0.419552i | \(-0.137813\pi\) | ||||
0.907731 | + | 0.419552i | \(0.137813\pi\) | |||||||
\(230\) | −963750. | −1.20128 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −473400. | −0.577442 | ||||||||
\(233\) | 294090. | 0.354887 | 0.177444 | − | 0.984131i | \(-0.443217\pi\) | ||||
0.177444 | + | 0.984131i | \(0.443217\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −52375.0 | −0.0618663 | ||||||||
\(236\) | −1.68776e6 | −1.97256 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 62700.0 | 0.0717505 | ||||||||
\(239\) | 833330. | 0.943675 | 0.471837 | − | 0.881686i | \(-0.343591\pi\) | ||||
0.471837 | + | 0.881686i | \(0.343591\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 436477. | 0.484082 | 0.242041 | − | 0.970266i | \(-0.422183\pi\) | ||||
0.242041 | + | 0.970266i | \(0.422183\pi\) | |||||||
\(242\) | −3.08174e6 | −3.38265 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −3.14745e6 | −3.38442 | ||||||||
\(245\) | −419275. | −0.446256 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 758980. | 0.791567 | ||||||||
\(248\) | 3.56724e6 | 3.68301 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −156250. | −0.158114 | ||||||||
\(251\) | 676695. | 0.677967 | 0.338984 | − | 0.940792i | \(-0.389917\pi\) | ||||
0.338984 | + | 0.940792i | \(0.389917\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.64068e6 | −2.59366 | ||||||||
\(254\) | 2.37410e6 | 2.30895 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2.11942e6 | −2.02124 | ||||||||
\(257\) | 669735. | 0.632514 | 0.316257 | − | 0.948674i | \(-0.397574\pi\) | ||||
0.316257 | + | 0.948674i | \(0.397574\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −40956.0 | −0.0379374 | ||||||||
\(260\) | 1.16450e6 | 1.06833 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 1.58115e6 | 1.42305 | ||||||||
\(263\) | −1.92650e6 | −1.71743 | −0.858716 | − | 0.512451i | \(-0.828737\pi\) | ||||
−0.858716 | + | 0.512451i | \(0.828737\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −251500. | −0.220000 | ||||||||
\(266\) | −66480.0 | −0.0576085 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 942480. | 0.801558 | ||||||||
\(269\) | −1.06518e6 | −0.897512 | −0.448756 | − | 0.893654i | \(-0.648133\pi\) | ||||
−0.448756 | + | 0.893654i | \(0.648133\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −1.39806e6 | −1.15638 | −0.578191 | − | 0.815901i | \(-0.696241\pi\) | ||||
−0.578191 | + | 0.815901i | \(0.696241\pi\) | |||||||
\(272\) | −1.48808e6 | −1.21956 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −1.95270e6 | −1.57130 | ||||||||
\(275\) | −428125. | −0.341381 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −91866.0 | −0.0719375 | −0.0359688 | − | 0.999353i | \(-0.511452\pi\) | ||||
−0.0359688 | + | 0.999353i | \(0.511452\pi\) | |||||||
\(278\) | −132380. | −0.102733 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −54000.0 | −0.0411622 | ||||||||
\(281\) | 1.81323e6 | 1.36989 | 0.684947 | − | 0.728593i | \(-0.259825\pi\) | ||||
0.684947 | + | 0.728593i | \(0.259825\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 1.24205e6 | 0.921876 | 0.460938 | − | 0.887432i | \(-0.347513\pi\) | ||||
0.460938 | + | 0.887432i | \(0.347513\pi\) | |||||||
\(284\) | 5.13944e6 | 3.78112 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 4.69225e6 | 3.39208 | ||||||||
\(287\) | −27120.0 | −0.0194350 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −327832. | −0.230891 | ||||||||
\(290\) | −328750. | −0.229547 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −2.22618e6 | −1.52793 | ||||||||
\(293\) | −453690. | −0.308738 | −0.154369 | − | 0.988013i | \(-0.549334\pi\) | ||||
−0.154369 | + | 0.988013i | \(0.549334\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −620500. | −0.415133 | ||||||||
\(296\) | 2.45736e6 | 1.63019 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 2.42405e6 | 1.58125 | ||||||||
\(299\) | 2.64068e6 | 1.70819 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 54582.0 | 0.0347243 | ||||||||
\(302\) | 4.46459e6 | 2.81685 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.57779e6 | 0.979187 | ||||||||
\(305\) | −1.15715e6 | −0.712262 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.37090e6 | −1.43571 | −0.717856 | − | 0.696192i | \(-0.754876\pi\) | ||||
−0.717856 | + | 0.696192i | \(0.754876\pi\) | |||||||
\(308\) | −279480. | −0.167870 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.47725e6 | 1.46408 | ||||||||
\(311\) | 981600. | 0.575484 | 0.287742 | − | 0.957708i | \(-0.407095\pi\) | ||||
0.287742 | + | 0.957708i | \(0.407095\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 1.16432e6 | 0.671756 | 0.335878 | − | 0.941906i | \(-0.390967\pi\) | ||||
0.335878 | + | 0.941906i | \(0.390967\pi\) | |||||||
\(314\) | −3.32411e6 | −1.90262 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 5.09164e6 | 2.86840 | ||||||||
\(317\) | −855800. | −0.478326 | −0.239163 | − | 0.970979i | \(-0.576873\pi\) | ||||
−0.239163 | + | 0.970979i | \(0.576873\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −900775. | −0.495609 | ||||||||
\(320\) | −459200. | −0.250684 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −231300. | −0.124319 | ||||||||
\(323\) | −1.15786e6 | −0.617518 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 428125. | 0.224834 | ||||||||
\(326\) | −4.42925e6 | −2.30827 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1.62720e6 | 0.835134 | ||||||||
\(329\) | −12570.0 | −0.00640244 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 65994.0 | 0.0331081 | 0.0165541 | − | 0.999863i | \(-0.494730\pi\) | ||||
0.0165541 | + | 0.999863i | \(0.494730\pi\) | |||||||
\(332\) | −6.38724e6 | −3.18030 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −71400.0 | −0.0350213 | ||||||||
\(335\) | 346500. | 0.168691 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −820040. | −0.393333 | −0.196666 | − | 0.980470i | \(-0.563012\pi\) | ||||
−0.196666 | + | 0.980470i | \(0.563012\pi\) | |||||||
\(338\) | −979320. | −0.466265 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −1.77650e6 | −0.833428 | ||||||||
\(341\) | 6.78766e6 | 3.16107 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −201468. | −0.0924636 | ||||||||
\(344\) | −3.27492e6 | −1.49212 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 2.92650e6 | 1.31419 | ||||||||
\(347\) | 851960. | 0.379835 | 0.189918 | − | 0.981800i | \(-0.439178\pi\) | ||||
0.189918 | + | 0.981800i | \(0.439178\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.11612e6 | −0.490510 | −0.245255 | − | 0.969459i | \(-0.578872\pi\) | ||||
−0.245255 | + | 0.969459i | \(0.578872\pi\) | |||||||
\(350\) | −37500.0 | −0.0163629 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.86320e6 | 0.801499 | ||||||||
\(353\) | −4.18808e6 | −1.78887 | −0.894433 | − | 0.447202i | \(-0.852420\pi\) | ||||
−0.894433 | + | 0.447202i | \(0.852420\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1.88950e6 | 0.795749 | ||||||||
\(356\) | −8.40072e6 | −3.51311 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −6.09980e6 | −2.51541 | ||||||||
\(359\) | 1.37034e6 | 0.561167 | 0.280584 | − | 0.959830i | \(-0.409472\pi\) | ||||
0.280584 | + | 0.959830i | \(0.409472\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.24843e6 | −0.504194 | ||||||||
\(362\) | 798520. | 0.320269 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 279480. | 0.110560 | ||||||||
\(365\) | −818450. | −0.321558 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −1.42773e6 | −0.553326 | −0.276663 | − | 0.960967i | \(-0.589229\pi\) | ||||
−0.276663 | + | 0.960967i | \(0.589229\pi\) | |||||||
\(368\) | 5.48952e6 | 2.11307 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 1.70650e6 | 0.648040 | ||||||||
\(371\) | −60360.0 | −0.0227675 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 821623. | 0.305774 | 0.152887 | − | 0.988244i | \(-0.451143\pi\) | ||||
0.152887 | + | 0.988244i | \(0.451143\pi\) | |||||||
\(374\) | −7.15825e6 | −2.64623 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 754200. | 0.275117 | ||||||||
\(377\) | 900775. | 0.326410 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −609536. | −0.217972 | −0.108986 | − | 0.994043i | \(-0.534760\pi\) | ||||
−0.108986 | + | 0.994043i | \(0.534760\pi\) | |||||||
\(380\) | 1.88360e6 | 0.669160 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −1.50910e6 | −0.529127 | ||||||||
\(383\) | 1.08650e6 | 0.378469 | 0.189235 | − | 0.981932i | \(-0.439399\pi\) | ||||
0.189235 | + | 0.981932i | \(0.439399\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −102750. | −0.0353289 | ||||||||
\(386\) | −1.70702e6 | −0.583137 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −5.84569e6 | −1.97132 | ||||||||
\(389\) | −2.26594e6 | −0.759233 | −0.379617 | − | 0.925144i | \(-0.623944\pi\) | ||||
−0.379617 | + | 0.925144i | \(0.623944\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −4.02847e6 | −1.33260 | ||||||||
\(392\) | 6.03756e6 | 1.98448 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 3.33360e6 | 1.08186 | ||||||||
\(395\) | 1.87192e6 | 0.603665 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 3.85253e6 | 1.22679 | 0.613394 | − | 0.789777i | \(-0.289804\pi\) | ||||
0.613394 | + | 0.789777i | \(0.289804\pi\) | |||||||
\(398\) | −575110. | −0.181988 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 890000. | 0.278125 | ||||||||
\(401\) | 293700. | 0.0912101 | 0.0456051 | − | 0.998960i | \(-0.485478\pi\) | ||||
0.0456051 | + | 0.998960i | \(0.485478\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −6.78766e6 | −2.08189 | ||||||||
\(404\) | −4.24422e6 | −1.29373 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −78900.0 | −0.0237554 | ||||||||
\(407\) | 4.67581e6 | 1.39917 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1.54596e6 | −0.456973 | −0.228486 | − | 0.973547i | \(-0.573378\pi\) | ||||
−0.228486 | + | 0.973547i | \(0.573378\pi\) | |||||||
\(410\) | 1.13000e6 | 0.331985 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.15275e7 | −3.34574 | ||||||||
\(413\) | −148920. | −0.0429613 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −2.34825e6 | −0.669305 | ||||||||
\(416\) | −1.86320e6 | −0.527869 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 7.58980e6 | 2.12466 | ||||||||
\(419\) | −274355. | −0.0763445 | −0.0381723 | − | 0.999271i | \(-0.512154\pi\) | ||||
−0.0381723 | + | 0.999271i | \(0.512154\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 122836. | 0.0337769 | 0.0168885 | − | 0.999857i | \(-0.494624\pi\) | ||||
0.0168885 | + | 0.999857i | \(0.494624\pi\) | |||||||
\(422\) | −4.28102e6 | −1.17022 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.62160e6 | 0.978331 | ||||||||
\(425\) | −653125. | −0.175398 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −277716. | −0.0737108 | ||||||||
\(428\) | −193800. | −0.0511381 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −2.27425e6 | −0.593153 | ||||||||
\(431\) | 3.85980e6 | 1.00086 | 0.500428 | − | 0.865778i | \(-0.333176\pi\) | ||||
0.500428 | + | 0.865778i | \(0.333176\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.18754e6 | 0.560707 | 0.280353 | − | 0.959897i | \(-0.409548\pi\) | ||||
0.280353 | + | 0.959897i | \(0.409548\pi\) | |||||||
\(434\) | 594540. | 0.151515 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −1.43227e7 | −3.60835 | ||||||||
\(437\) | 4.27134e6 | 1.06994 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 1.26527e6 | 0.313345 | 0.156672 | − | 0.987651i | \(-0.449923\pi\) | ||||
0.156672 | + | 0.987651i | \(0.449923\pi\) | |||||||
\(440\) | 6.16500e6 | 1.51810 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 7.15825e6 | 1.74281 | ||||||||
\(443\) | −672180. | −0.162733 | −0.0813666 | − | 0.996684i | \(-0.525928\pi\) | ||||
−0.0813666 | + | 0.996684i | \(0.525928\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −3.08850e6 | −0.739346 | ||||||||
\(446\) | −6.99368e6 | −1.66483 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −110208. | −0.0259429 | ||||||||
\(449\) | −1.26013e6 | −0.294985 | −0.147492 | − | 0.989063i | \(-0.547120\pi\) | ||||
−0.147492 | + | 0.989063i | \(0.547120\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.09620e6 | 0.716783 | ||||||||
\(452\) | 5.53078e6 | 1.27333 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 4.71200e6 | 1.07292 | ||||||||
\(455\) | 102750. | 0.0232677 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 6.81838e6 | 1.52718 | 0.763591 | − | 0.645700i | \(-0.223435\pi\) | ||||
0.763591 | + | 0.645700i | \(0.223435\pi\) | |||||||
\(458\) | −1.44071e7 | −3.20931 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 6.55350e6 | 1.44404 | ||||||||
\(461\) | −6.55773e6 | −1.43715 | −0.718574 | − | 0.695451i | \(-0.755205\pi\) | ||||
−0.718574 | + | 0.695451i | \(0.755205\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 3.15148e6 | 0.683223 | 0.341611 | − | 0.939841i | \(-0.389027\pi\) | ||||
0.341611 | + | 0.939841i | \(0.389027\pi\) | |||||||
\(464\) | 1.87256e6 | 0.403776 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −2.94090e6 | −0.627358 | ||||||||
\(467\) | 7.80490e6 | 1.65606 | 0.828028 | − | 0.560686i | \(-0.189463\pi\) | ||||
0.828028 | + | 0.560686i | \(0.189463\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 83160.0 | 0.0174575 | ||||||||
\(470\) | 523750. | 0.109365 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 8.93520e6 | 1.84607 | ||||||||
\(473\) | −6.23145e6 | −1.28067 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 692500. | 0.140827 | ||||||||
\(476\) | −426360. | −0.0862500 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −8.33330e6 | −1.66820 | ||||||||
\(479\) | 729660. | 0.145305 | 0.0726527 | − | 0.997357i | \(-0.476854\pi\) | ||||
0.0726527 | + | 0.997357i | \(0.476854\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.67581e6 | −0.921498 | ||||||||
\(482\) | −4.36477e6 | −0.855744 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 2.09558e7 | 4.06623 | ||||||||
\(485\) | −2.14915e6 | −0.414870 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9.35510e6 | 1.78742 | 0.893709 | − | 0.448647i | \(-0.148094\pi\) | ||||
0.893709 | + | 0.448647i | \(0.148094\pi\) | |||||||
\(488\) | 1.66630e7 | 3.16740 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 4.19275e6 | 0.788876 | ||||||||
\(491\) | 9.39394e6 | 1.75851 | 0.879253 | − | 0.476354i | \(-0.158042\pi\) | ||||
0.879253 | + | 0.476354i | \(0.158042\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −1.37418e6 | −0.254639 | ||||||||
\(494\) | −7.58980e6 | −1.39931 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1.41104e7 | −2.57535 | ||||||||
\(497\) | 453480. | 0.0823507 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.54473e6 | 1.17663 | 0.588316 | − | 0.808631i | \(-0.299791\pi\) | ||||
0.588316 | + | 0.808631i | \(0.299791\pi\) | |||||||
\(500\) | 1.06250e6 | 0.190066 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −6.76695e6 | −1.19849 | ||||||||
\(503\) | −6.68478e6 | −1.17806 | −0.589030 | − | 0.808111i | \(-0.700490\pi\) | ||||
−0.589030 | + | 0.808111i | \(0.700490\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.56037e6 | −0.272270 | ||||||||
\(506\) | 2.64068e7 | 4.58499 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1.61439e7 | −2.77555 | ||||||||
\(509\) | 3.61198e6 | 0.617946 | 0.308973 | − | 0.951071i | \(-0.400015\pi\) | ||||
0.308973 | + | 0.951071i | \(0.400015\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −196428. | −0.0332775 | ||||||||
\(512\) | 1.25312e7 | 2.11260 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −6.69735e6 | −1.11814 | ||||||||
\(515\) | −4.23805e6 | −0.704122 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1.43508e6 | 0.236128 | ||||||||
\(518\) | 409560. | 0.0670646 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −6.16500e6 | −0.999827 | ||||||||
\(521\) | 572740. | 0.0924407 | 0.0462203 | − | 0.998931i | \(-0.485282\pi\) | ||||
0.0462203 | + | 0.998931i | \(0.485282\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.40826e6 | 0.864577 | 0.432288 | − | 0.901735i | \(-0.357706\pi\) | ||||
0.432288 | + | 0.901735i | \(0.357706\pi\) | |||||||
\(524\) | −1.07518e7 | −1.71062 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.92650e7 | 3.03602 | ||||||||
\(527\) | 1.03549e7 | 1.62413 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.42468e6 | 1.30892 | ||||||||
\(530\) | 2.51500e6 | 0.388909 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 452064. | 0.0692502 | ||||||||
\(533\) | −3.09620e6 | −0.472075 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −71250.0 | −0.0107622 | ||||||||
\(536\) | −4.98960e6 | −0.750160 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 1.06518e7 | 1.58659 | ||||||||
\(539\) | 1.14881e7 | 1.70325 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −7.26253e6 | −1.06683 | −0.533414 | − | 0.845854i | \(-0.679091\pi\) | ||||
−0.533414 | + | 0.845854i | \(0.679091\pi\) | |||||||
\(542\) | 1.39806e7 | 2.04421 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 2.84240e6 | 0.411802 | ||||||||
\(545\) | −5.26570e6 | −0.759390 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30901.0 | 0.00441575 | 0.00220787 | − | 0.999998i | \(-0.499297\pi\) | ||||
0.00220787 | + | 0.999998i | \(0.499297\pi\) | |||||||
\(548\) | 1.32784e7 | 1.88883 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 4.28125e6 | 0.603481 | ||||||||
\(551\) | 1.45702e6 | 0.204450 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 449262. | 0.0624722 | ||||||||
\(554\) | 918660. | 0.127169 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 900184. | 0.123494 | ||||||||
\(557\) | −6.29634e6 | −0.859904 | −0.429952 | − | 0.902852i | \(-0.641470\pi\) | ||||
−0.429952 | + | 0.902852i | \(0.641470\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 6.23144e6 | 0.843450 | ||||||||
\(560\) | 213600. | 0.0287827 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.81323e7 | −2.42165 | ||||||||
\(563\) | −1.23597e6 | −0.164338 | −0.0821688 | − | 0.996618i | \(-0.526185\pi\) | ||||
−0.0821688 | + | 0.996618i | \(0.526185\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2.03338e6 | 0.267976 | ||||||||
\(566\) | −1.24205e7 | −1.62966 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −2.72088e7 | −3.53866 | ||||||||
\(569\) | −6.30000e6 | −0.815755 | −0.407878 | − | 0.913037i | \(-0.633731\pi\) | ||||
−0.407878 | + | 0.913037i | \(0.633731\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.12369e6 | −0.272584 | −0.136292 | − | 0.990669i | \(-0.543519\pi\) | ||||
−0.136292 | + | 0.990669i | \(0.543519\pi\) | |||||||
\(572\) | −3.19073e7 | −4.07756 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 271200. | 0.0343566 | ||||||||
\(575\) | 2.40938e6 | 0.303903 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −7.58210e6 | −0.948090 | −0.474045 | − | 0.880501i | \(-0.657207\pi\) | ||||
−0.474045 | + | 0.880501i | \(0.657207\pi\) | |||||||
\(578\) | 3.27832e6 | 0.408161 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 2.23550e6 | 0.275934 | ||||||||
\(581\) | −563580. | −0.0692652 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.89110e6 | 0.839686 | ||||||||
\(584\) | 1.17857e7 | 1.42996 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 4.53690e6 | 0.545777 | ||||||||
\(587\) | −1.24694e7 | −1.49366 | −0.746828 | − | 0.665017i | \(-0.768424\pi\) | ||||
−0.746828 | + | 0.665017i | \(0.768424\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −1.09792e7 | −1.30401 | ||||||||
\(590\) | 6.20500e6 | 0.733858 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −9.72022e6 | −1.13991 | ||||||||
\(593\) | 2.94156e6 | 0.343511 | 0.171755 | − | 0.985140i | \(-0.445056\pi\) | ||||
0.171755 | + | 0.985140i | \(0.445056\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −156750. | −0.0181516 | ||||||||
\(596\) | −1.64835e7 | −1.90079 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −2.64067e7 | −3.01969 | ||||||||
\(599\) | −1.58779e7 | −1.80812 | −0.904058 | − | 0.427410i | \(-0.859426\pi\) | ||||
−0.904058 | + | 0.427410i | \(0.859426\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.59290e6 | −0.518681 | −0.259341 | − | 0.965786i | \(-0.583505\pi\) | ||||
−0.259341 | + | 0.965786i | \(0.583505\pi\) | |||||||
\(602\) | −545820. | −0.0613844 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −3.03592e7 | −3.38609 | ||||||||
\(605\) | 7.70435e6 | 0.855751 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 5.59659e6 | 0.616527 | 0.308263 | − | 0.951301i | \(-0.400252\pi\) | ||||
0.308263 | + | 0.951301i | \(0.400252\pi\) | |||||||
\(608\) | −3.01376e6 | −0.330636 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1.15715e7 | 1.25911 | ||||||||
\(611\) | −1.43508e6 | −0.155515 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.01497e7 | 1.09095 | 0.545473 | − | 0.838128i | \(-0.316350\pi\) | ||||
0.545473 | + | 0.838128i | \(0.316350\pi\) | |||||||
\(614\) | 2.37090e7 | 2.53800 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1.47960e6 | 0.157106 | ||||||||
\(617\) | −1.53162e7 | −1.61971 | −0.809854 | − | 0.586631i | \(-0.800454\pi\) | ||||
−0.809854 | + | 0.586631i | \(0.800454\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −5.20008e6 | −0.545486 | −0.272743 | − | 0.962087i | \(-0.587931\pi\) | ||||
−0.272743 | + | 0.962087i | \(0.587931\pi\) | |||||||
\(620\) | −1.68453e7 | −1.75995 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −9.81600e6 | −1.01732 | ||||||||
\(623\) | −741240. | −0.0765136 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 390625. | 0.0400000 | ||||||||
\(626\) | −1.16432e7 | −1.18751 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 2.26039e7 | 2.28710 | ||||||||
\(629\) | 7.13317e6 | 0.718879 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 7.34675e6 | 0.734551 | 0.367276 | − | 0.930112i | \(-0.380291\pi\) | ||||
0.367276 | + | 0.930112i | \(0.380291\pi\) | |||||||
\(632\) | −2.69557e7 | −2.68447 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 8.55800e6 | 0.845569 | ||||||||
\(635\) | −5.93525e6 | −0.584124 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.14881e7 | −1.12176 | ||||||||
\(638\) | 9.00775e6 | 0.876122 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 6.76800e6 | 0.653146 | ||||||||
\(641\) | 1.17297e6 | 0.112757 | 0.0563783 | − | 0.998409i | \(-0.482045\pi\) | ||||
0.0563783 | + | 0.998409i | \(0.482045\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.92135e7 | −1.83264 | −0.916322 | − | 0.400443i | \(-0.868856\pi\) | ||||
−0.916322 | + | 0.400443i | \(0.868856\pi\) | |||||||
\(644\) | 1.57284e6 | 0.149441 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 1.15786e7 | 1.09163 | ||||||||
\(647\) | 8.64470e6 | 0.811875 | 0.405938 | − | 0.913901i | \(-0.366945\pi\) | ||||
0.405938 | + | 0.913901i | \(0.366945\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 1.70017e7 | 1.58446 | ||||||||
\(650\) | −4.28125e6 | −0.397454 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.01189e7 | 2.77473 | ||||||||
\(653\) | −4.50206e6 | −0.413170 | −0.206585 | − | 0.978429i | \(-0.566235\pi\) | ||||
−0.206585 | + | 0.978429i | \(0.566235\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −3.95288e6 | −0.360006 | ||||||||
\(656\) | −6.43648e6 | −0.583968 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 125700. | 0.0113180 | ||||||||
\(659\) | 1.51573e7 | 1.35959 | 0.679795 | − | 0.733403i | \(-0.262069\pi\) | ||||
0.679795 | + | 0.733403i | \(0.262069\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 1.03752e7 | 0.923618 | 0.461809 | − | 0.886979i | \(-0.347201\pi\) | ||||
0.461809 | + | 0.886979i | \(0.347201\pi\) | |||||||
\(662\) | −659940. | −0.0585274 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.38148e7 | 2.97637 | ||||||||
\(665\) | 166200. | 0.0145739 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 5.06932e6 | 0.441200 | ||||||||
\(668\) | 485520. | 0.0420984 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −3.46500e6 | −0.298206 | ||||||||
\(671\) | 3.17059e7 | 2.71853 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.49638e7 | 1.27352 | 0.636758 | − | 0.771064i | \(-0.280275\pi\) | ||||
0.636758 | + | 0.771064i | \(0.280275\pi\) | |||||||
\(674\) | 8.20040e6 | 0.695321 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 6.65938e6 | 0.560489 | ||||||||
\(677\) | −8.83758e6 | −0.741074 | −0.370537 | − | 0.928818i | \(-0.620826\pi\) | ||||
−0.370537 | + | 0.928818i | \(0.620826\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −515796. | −0.0429342 | ||||||||
\(680\) | 9.40500e6 | 0.779985 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −6.78766e7 | −5.58804 | ||||||||
\(683\) | 1.09012e7 | 0.894172 | 0.447086 | − | 0.894491i | \(-0.352462\pi\) | ||||
0.447086 | + | 0.894491i | \(0.352462\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 4.88175e6 | 0.397511 | ||||||||
\(686\) | 2.01468e6 | 0.163454 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.29541e7 | 1.04337 | ||||||||
\(689\) | −6.89110e6 | −0.553020 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −9.02310e6 | −0.718887 | −0.359444 | − | 0.933167i | \(-0.617033\pi\) | ||||
−0.359444 | + | 0.933167i | \(0.617033\pi\) | |||||||
\(692\) | −1.99002e7 | −1.57976 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −8.51960e6 | −0.671461 | ||||||||
\(695\) | 330950. | 0.0259896 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.72340e6 | 0.368275 | ||||||||
\(698\) | 1.11612e7 | 0.867108 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 255000. | 0.0196696 | ||||||||
\(701\) | −2.15578e7 | −1.65695 | −0.828474 | − | 0.560028i | \(-0.810790\pi\) | ||||
−0.828474 | + | 0.560028i | \(0.810790\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −7.56321e6 | −0.577189 | ||||||||
\(704\) | 1.25821e7 | 0.956799 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 4.18808e7 | 3.16230 | ||||||||
\(707\) | −374490. | −0.0281768 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −1.69473e7 | −1.26615 | −0.633076 | − | 0.774090i | \(-0.718208\pi\) | ||||
−0.633076 | + | 0.774090i | \(0.718208\pi\) | |||||||
\(710\) | −1.88950e7 | −1.40670 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4.44744e7 | 3.28784 | ||||||||
\(713\) | −3.81992e7 | −2.81404 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.17306e7 | −0.858136 | ||||||||
\(716\) | 4.14786e7 | 3.02372 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −1.37034e7 | −0.992013 | ||||||||
\(719\) | −2.05676e7 | −1.48375 | −0.741874 | − | 0.670539i | \(-0.766063\pi\) | ||||
−0.741874 | + | 0.670539i | \(0.766063\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −1.01713e6 | −0.0728684 | ||||||||
\(722\) | 1.24844e7 | 0.891298 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −5.42994e6 | −0.384989 | ||||||||
\(725\) | 821875. | 0.0580712 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.66714e7 | 1.16986 | 0.584931 | − | 0.811083i | \(-0.301121\pi\) | ||||
0.584931 | + | 0.811083i | \(0.301121\pi\) | |||||||
\(728\) | −1.47960e6 | −0.103470 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 8.18450e6 | 0.568440 | ||||||||
\(731\) | −9.50636e6 | −0.657993 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.32270e7 | −0.909284 | −0.454642 | − | 0.890674i | \(-0.650233\pi\) | ||||
−0.454642 | + | 0.890674i | \(0.650233\pi\) | |||||||
\(734\) | 1.42773e7 | 0.978151 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.04856e7 | −0.713508 | ||||||||
\(737\) | −9.49410e6 | −0.643851 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −9.00924e6 | −0.606844 | −0.303422 | − | 0.952856i | \(-0.598129\pi\) | ||||
−0.303422 | + | 0.952856i | \(0.598129\pi\) | |||||||
\(740\) | −1.16042e7 | −0.778997 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 603600. | 0.0402476 | ||||||||
\(743\) | 2.44168e7 | 1.62262 | 0.811309 | − | 0.584618i | \(-0.198756\pi\) | ||||
0.811309 | + | 0.584618i | \(0.198756\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.06012e6 | −0.400028 | ||||||||
\(746\) | −8.21623e6 | −0.540537 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 4.86761e7 | 3.18099 | ||||||||
\(749\) | −17100.0 | −0.00111376 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −2.35907e7 | −1.52630 | −0.763151 | − | 0.646220i | \(-0.776349\pi\) | ||||
−0.763151 | + | 0.646220i | \(0.776349\pi\) | |||||||
\(752\) | −2.98328e6 | −0.192375 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −9.00775e6 | −0.577016 | ||||||||
\(755\) | −1.11615e7 | −0.712614 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 2.76229e7 | 1.75198 | 0.875991 | − | 0.482328i | \(-0.160209\pi\) | ||||
0.875991 | + | 0.482328i | \(0.160209\pi\) | |||||||
\(758\) | 6.09536e6 | 0.385324 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −9.97200e6 | −0.626251 | ||||||||
\(761\) | −1.20776e7 | −0.755992 | −0.377996 | − | 0.925807i | \(-0.623387\pi\) | ||||
−0.377996 | + | 0.925807i | \(0.623387\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −1.26377e6 | −0.0785880 | ||||||||
\(764\) | 1.02619e7 | 0.636053 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −1.08650e7 | −0.669046 | ||||||||
\(767\) | −1.70017e7 | −1.04353 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 3.49831e6 | 0.213325 | 0.106663 | − | 0.994295i | \(-0.465983\pi\) | ||||
0.106663 | + | 0.994295i | \(0.465983\pi\) | |||||||
\(770\) | 1.02750e6 | 0.0624532 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 1.16077e7 | 0.700978 | ||||||||
\(773\) | −2.99115e6 | −0.180048 | −0.0900242 | − | 0.995940i | \(-0.528694\pi\) | ||||
−0.0900242 | + | 0.995940i | \(0.528694\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −6.19312e6 | −0.370387 | ||||||||
\(776\) | 3.09478e7 | 1.84491 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 2.26594e7 | 1.34215 | ||||||||
\(779\) | −5.00816e6 | −0.295689 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −5.17723e7 | −3.03718 | ||||||||
\(782\) | 4.02848e7 | 2.35572 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −2.38819e7 | −1.38765 | ||||||||
\(785\) | 8.31028e6 | 0.481328 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −1.38920e7 | −0.799520 | −0.399760 | − | 0.916620i | \(-0.630906\pi\) | ||||
−0.399760 | + | 0.916620i | \(0.630906\pi\) | |||||||
\(788\) | −2.26685e7 | −1.30049 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −1.87192e7 | −1.06714 | ||||||||
\(791\) | 488010. | 0.0277324 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −3.17059e7 | −1.79043 | ||||||||
\(794\) | −3.85253e7 | −2.16868 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 3.91075e6 | 0.218765 | ||||||||
\(797\) | −8.13974e6 | −0.453905 | −0.226952 | − | 0.973906i | \(-0.572876\pi\) | ||||
−0.226952 | + | 0.973906i | \(0.572876\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.18928e6 | 0.121320 | ||||||||
\(800\) | −1.70000e6 | −0.0939126 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.93700e6 | −0.161238 | ||||||||
\(803\) | 2.24255e7 | 1.22731 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 578250. | 0.0314504 | ||||||||
\(806\) | 6.78766e7 | 3.68030 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2.24694e7 | 1.21077 | ||||||||
\(809\) | 2.68094e7 | 1.44017 | 0.720087 | − | 0.693883i | \(-0.244102\pi\) | ||||
0.720087 | + | 0.693883i | \(0.244102\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −1.97282e7 | −1.05326 | −0.526629 | − | 0.850095i | \(-0.676544\pi\) | ||||
−0.526629 | + | 0.850095i | \(0.676544\pi\) | |||||||
\(812\) | 536520. | 0.0285559 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.67581e7 | −2.47341 | ||||||||
\(815\) | 1.10731e7 | 0.583951 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1.00795e7 | 0.528303 | ||||||||
\(818\) | 1.54596e7 | 0.807821 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −7.68400e6 | −0.399073 | ||||||||
\(821\) | −2.16090e7 | −1.11886 | −0.559432 | − | 0.828876i | \(-0.688981\pi\) | ||||
−0.559432 | + | 0.828876i | \(0.688981\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6.99026e6 | 0.359744 | 0.179872 | − | 0.983690i | \(-0.442432\pi\) | ||||
0.179872 | + | 0.983690i | \(0.442432\pi\) | |||||||
\(824\) | 6.10279e7 | 3.13120 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1.48920e6 | 0.0759457 | ||||||||
\(827\) | 2.68441e7 | 1.36485 | 0.682425 | − | 0.730955i | \(-0.260925\pi\) | ||||
0.682425 | + | 0.730955i | \(0.260925\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 2.11268e7 | 1.06770 | 0.533848 | − | 0.845580i | \(-0.320745\pi\) | ||||
0.533848 | + | 0.845580i | \(0.320745\pi\) | |||||||
\(830\) | 2.34825e7 | 1.18318 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.25821e7 | −0.630150 | ||||||||
\(833\) | 1.75257e7 | 0.875110 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 178500. | 0.00885976 | ||||||||
\(836\) | −5.16106e7 | −2.55402 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 2.74355e6 | 0.134959 | ||||||||
\(839\) | 2.28583e7 | 1.12108 | 0.560542 | − | 0.828126i | \(-0.310593\pi\) | ||||
0.560542 | + | 0.828126i | \(0.310593\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.87819e7 | −0.915693 | ||||||||
\(842\) | −1.22836e6 | −0.0597098 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 2.91109e7 | 1.40670 | ||||||||
\(845\) | 2.44830e6 | 0.117957 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 1.84904e6 | 0.0885602 | ||||||||
\(848\) | −1.43254e7 | −0.684098 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 6.53125e6 | 0.310062 | ||||||||
\(851\) | −2.63142e7 | −1.24557 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 5.75945e6 | 0.271024 | 0.135512 | − | 0.990776i | \(-0.456732\pi\) | ||||
0.135512 | + | 0.990776i | \(0.456732\pi\) | |||||||
\(854\) | 2.77716e6 | 0.130304 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.02600e6 | 0.0478589 | ||||||||
\(857\) | 1.43880e7 | 0.669188 | 0.334594 | − | 0.942362i | \(-0.391401\pi\) | ||||
0.334594 | + | 0.942362i | \(0.391401\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.28619e7 | 1.51953 | 0.759766 | − | 0.650197i | \(-0.225314\pi\) | ||||
0.759766 | + | 0.650197i | \(0.225314\pi\) | |||||||
\(860\) | 1.54649e7 | 0.713019 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3.85980e7 | −1.76928 | ||||||||
\(863\) | 4.34132e6 | 0.198425 | 0.0992123 | − | 0.995066i | \(-0.468368\pi\) | ||||
0.0992123 | + | 0.995066i | \(0.468368\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.31625e6 | −0.332467 | ||||||||
\(866\) | −2.18754e7 | −0.991199 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −4.04287e6 | −0.182134 | ||||||||
\(869\) | −5.12907e7 | −2.30404 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 9.49410e6 | 0.424042 | ||||||||
\(872\) | 7.58261e7 | 3.37697 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −4.27134e7 | −1.89141 | ||||||||
\(875\) | 93750.0 | 0.00413953 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.70727e7 | 1.18859 | 0.594296 | − | 0.804246i | \(-0.297431\pi\) | ||||
0.594296 | + | 0.804246i | \(0.297431\pi\) | |||||||
\(878\) | −1.26527e7 | −0.553921 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2.43860e7 | −1.06153 | ||||||||
\(881\) | −4.98787e6 | −0.216509 | −0.108254 | − | 0.994123i | \(-0.534526\pi\) | ||||
−0.108254 | + | 0.994123i | \(0.534526\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.69054e7 | 0.729667 | 0.364833 | − | 0.931073i | \(-0.381126\pi\) | ||||
0.364833 | + | 0.931073i | \(0.381126\pi\) | |||||||
\(884\) | −4.86761e7 | −2.09501 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 6.72180e6 | 0.287674 | ||||||||
\(887\) | −3.06531e7 | −1.30817 | −0.654087 | − | 0.756419i | \(-0.726947\pi\) | ||||
−0.654087 | + | 0.756419i | \(0.726947\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −1.42446e6 | −0.0604499 | ||||||||
\(890\) | 3.08850e7 | 1.30699 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 4.75570e7 | 2.00126 | ||||||||
\(893\) | −2.32126e6 | −0.0974081 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.52495e7 | 0.636353 | ||||||||
\(896\) | 1.62432e6 | 0.0675930 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.26013e7 | 0.521464 | ||||||||
\(899\) | −1.30303e7 | −0.537720 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.05127e7 | 0.431422 | ||||||||
\(902\) | −3.09620e7 | −1.26711 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.92806e7 | −1.19168 | ||||||||
\(905\) | −1.99630e6 | −0.0810223 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.73344e7 | 0.699667 | 0.349833 | − | 0.936812i | \(-0.386238\pi\) | ||||
0.349833 | + | 0.936812i | \(0.386238\pi\) | |||||||
\(908\) | −3.20416e7 | −1.28973 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.02750e6 | −0.0411319 | ||||||||
\(911\) | 9.85196e6 | 0.393302 | 0.196651 | − | 0.980474i | \(-0.436993\pi\) | ||||
0.196651 | + | 0.980474i | \(0.436993\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 6.43420e7 | 2.55457 | ||||||||
\(914\) | −6.81838e7 | −2.69970 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 9.79681e7 | 3.85786 | ||||||||
\(917\) | −948690. | −0.0372564 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −3.67691e7 | −1.43613 | −0.718066 | − | 0.695975i | \(-0.754973\pi\) | ||||
−0.718066 | + | 0.695975i | \(0.754973\pi\) | |||||||
\(920\) | −3.46950e7 | −1.35144 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 6.55773e7 | 2.54054 | ||||||||
\(923\) | 5.17723e7 | 2.00029 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.26625e6 | −0.163943 | ||||||||
\(926\) | −3.15148e7 | −1.20778 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −3.57680e6 | −0.136340 | ||||||||
\(929\) | −1.27151e7 | −0.483371 | −0.241685 | − | 0.970355i | \(-0.577700\pi\) | ||||
−0.241685 | + | 0.970355i | \(0.577700\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1.85823e7 | −0.702626 | ||||||||
\(932\) | 1.99981e7 | 0.754136 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −7.80490e7 | −2.92752 | ||||||||
\(935\) | 1.78956e7 | 0.669450 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −5.26250e7 | −1.95814 | −0.979068 | − | 0.203533i | \(-0.934758\pi\) | ||||
−0.979068 | + | 0.203533i | \(0.934758\pi\) | |||||||
\(938\) | −831600. | −0.0308608 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −3.56150e6 | −0.131466 | ||||||||
\(941\) | −1.26678e6 | −0.0466368 | −0.0233184 | − | 0.999728i | \(-0.507423\pi\) | ||||
−0.0233184 | + | 0.999728i | \(0.507423\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1.74246e7 | −0.638092 | ||||||||
\(944\) | −3.53437e7 | −1.29087 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 6.23144e7 | 2.26392 | ||||||||
\(947\) | 2.45637e7 | 0.890058 | 0.445029 | − | 0.895516i | \(-0.353193\pi\) | ||||
0.445029 | + | 0.895516i | \(0.353193\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −2.24255e7 | −0.808309 | ||||||||
\(950\) | −6.92500e6 | −0.248949 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 2.25720e6 | 0.0807194 | ||||||||
\(953\) | −2.58428e7 | −0.921737 | −0.460868 | − | 0.887469i | \(-0.652462\pi\) | ||||
−0.460868 | + | 0.887469i | \(0.652462\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.77275e6 | 0.133860 | ||||||||
\(956\) | 5.66664e7 | 2.00531 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −7.29660e6 | −0.256866 | ||||||||
\(959\) | 1.17162e6 | 0.0411377 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 6.95591e7 | 2.42966 | ||||||||
\(962\) | 4.67581e7 | 1.62899 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 2.96804e7 | 1.02867 | ||||||||
\(965\) | 4.26755e6 | 0.147523 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.34437e7 | −0.462331 | −0.231165 | − | 0.972914i | \(-0.574254\pi\) | ||||
−0.231165 | + | 0.972914i | \(0.574254\pi\) | |||||||
\(968\) | −1.10943e8 | −3.80549 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.14915e7 | 0.733394 | ||||||||
\(971\) | −4.08522e7 | −1.39049 | −0.695244 | − | 0.718774i | \(-0.744704\pi\) | ||||
−0.695244 | + | 0.718774i | \(0.744704\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 79428.0 | 0.00268962 | ||||||||
\(974\) | −9.35510e7 | −3.15974 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −6.59113e7 | −2.21480 | ||||||||
\(977\) | 2.66025e7 | 0.891634 | 0.445817 | − | 0.895124i | \(-0.352913\pi\) | ||||
0.445817 | + | 0.895124i | \(0.352913\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 8.46249e7 | 2.82190 | ||||||||
\(980\) | −2.85107e7 | −0.948293 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −9.39394e7 | −3.10863 | ||||||||
\(983\) | 5.59346e6 | 0.184627 | 0.0923137 | − | 0.995730i | \(-0.470574\pi\) | ||||
0.0923137 | + | 0.995730i | \(0.470574\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.33400e6 | −0.273693 | ||||||||
\(986\) | 1.37417e7 | 0.450142 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 5.16106e7 | 1.68208 | ||||||||
\(989\) | 3.50689e7 | 1.14007 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1.67296e7 | −0.541130 | −0.270565 | − | 0.962702i | \(-0.587211\pi\) | ||||
−0.270565 | + | 0.962702i | \(0.587211\pi\) | |||||||
\(992\) | 2.69525e7 | 0.869600 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −4.53480e6 | −0.145577 | ||||||||
\(995\) | 1.43778e6 | 0.0460398 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.48356e7 | 1.42851 | 0.714257 | − | 0.699883i | \(-0.246765\pi\) | ||||
0.714257 | + | 0.699883i | \(0.246765\pi\) | |||||||
\(998\) | −6.54473e7 | −2.08001 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 135.6.a.a.1.1 | ✓ | 1 | |
3.2 | odd | 2 | 135.6.a.b.1.1 | yes | 1 | ||
5.4 | even | 2 | 675.6.a.e.1.1 | 1 | |||
15.14 | odd | 2 | 675.6.a.a.1.1 | 1 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.6.a.a.1.1 | ✓ | 1 | 1.1 | even | 1 | trivial | |
135.6.a.b.1.1 | yes | 1 | 3.2 | odd | 2 | ||
675.6.a.a.1.1 | 1 | 15.14 | odd | 2 | |||
675.6.a.e.1.1 | 1 | 5.4 | even | 2 |