Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,6,Mod(1,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, 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("441.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.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: | \(70.7292645375\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{4} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - x^{3} - 97x^{2} + 7x + 294 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 7 \) |
Twist minimal: | no (minimal twist has level 21) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(1.79080\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 441.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.790805 | 0.139796 | 0.0698979 | − | 0.997554i | \(-0.477733\pi\) | ||||
0.0698979 | + | 0.997554i | \(0.477733\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | −31.3746 | −0.980457 | ||||||||
\(5\) | 104.192 | 1.86384 | 0.931919 | − | 0.362667i | \(-0.118134\pi\) | ||||
0.931919 | + | 0.362667i | \(0.118134\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −50.1170 | −0.276860 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 82.3953 | 0.260557 | ||||||||
\(11\) | 497.660 | 1.24008 | 0.620041 | − | 0.784569i | \(-0.287116\pi\) | ||||
0.620041 | + | 0.784569i | \(0.287116\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −206.551 | −0.338977 | −0.169488 | − | 0.985532i | \(-0.554211\pi\) | ||||
−0.169488 | + | 0.985532i | \(0.554211\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 964.355 | 0.941753 | ||||||||
\(17\) | −63.1586 | −0.0530042 | −0.0265021 | − | 0.999649i | \(-0.508437\pi\) | ||||
−0.0265021 | + | 0.999649i | \(0.508437\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 1323.95 | 0.841374 | 0.420687 | − | 0.907206i | \(-0.361789\pi\) | ||||
0.420687 | + | 0.907206i | \(0.361789\pi\) | |||||||
\(20\) | −3268.98 | −1.82741 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 393.552 | 0.173358 | ||||||||
\(23\) | 194.437 | 0.0766408 | 0.0383204 | − | 0.999266i | \(-0.487799\pi\) | ||||
0.0383204 | + | 0.999266i | \(0.487799\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 7730.91 | 2.47389 | ||||||||
\(26\) | −163.342 | −0.0473875 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −4323.14 | −0.954562 | −0.477281 | − | 0.878751i | \(-0.658378\pi\) | ||||
−0.477281 | + | 0.878751i | \(0.658378\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −7525.31 | −1.40644 | −0.703219 | − | 0.710974i | \(-0.748255\pi\) | ||||
−0.703219 | + | 0.710974i | \(0.748255\pi\) | |||||||
\(32\) | 2366.36 | 0.408513 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −49.9461 | −0.00740977 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10355.6 | 1.24358 | 0.621789 | − | 0.783185i | \(-0.286406\pi\) | ||||
0.621789 | + | 0.783185i | \(0.286406\pi\) | |||||||
\(38\) | 1046.99 | 0.117621 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −5221.77 | −0.516022 | ||||||||
\(41\) | 4180.92 | 0.388429 | 0.194215 | − | 0.980959i | \(-0.437784\pi\) | ||||
0.194215 | + | 0.980959i | \(0.437784\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 5960.87 | 0.491630 | 0.245815 | − | 0.969317i | \(-0.420944\pi\) | ||||
0.245815 | + | 0.969317i | \(0.420944\pi\) | |||||||
\(44\) | −15613.9 | −1.21585 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 153.762 | 0.0107141 | ||||||||
\(47\) | 4389.74 | 0.289864 | 0.144932 | − | 0.989442i | \(-0.453704\pi\) | ||||
0.144932 | + | 0.989442i | \(0.453704\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 6113.64 | 0.345840 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 6480.47 | 0.332352 | ||||||||
\(53\) | −17784.8 | −0.869679 | −0.434839 | − | 0.900508i | \(-0.643195\pi\) | ||||
−0.434839 | + | 0.900508i | \(0.643195\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 51852.0 | 2.31131 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −3418.76 | −0.133444 | ||||||||
\(59\) | −3500.47 | −0.130917 | −0.0654585 | − | 0.997855i | \(-0.520851\pi\) | ||||
−0.0654585 | + | 0.997855i | \(0.520851\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −10632.5 | −0.365855 | −0.182928 | − | 0.983126i | \(-0.558557\pi\) | ||||
−0.182928 | + | 0.983126i | \(0.558557\pi\) | |||||||
\(62\) | −5951.06 | −0.196614 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −28988.0 | −0.884645 | ||||||||
\(65\) | −21520.9 | −0.631797 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −13274.7 | −0.361276 | −0.180638 | − | 0.983550i | \(-0.557816\pi\) | ||||
−0.180638 | + | 0.983550i | \(0.557816\pi\) | |||||||
\(68\) | 1981.58 | 0.0519683 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −38811.1 | −0.913713 | −0.456857 | − | 0.889540i | \(-0.651025\pi\) | ||||
−0.456857 | + | 0.889540i | \(0.651025\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 31375.6 | 0.689105 | 0.344552 | − | 0.938767i | \(-0.388031\pi\) | ||||
0.344552 | + | 0.938767i | \(0.388031\pi\) | |||||||
\(74\) | 8189.30 | 0.173847 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −41538.6 | −0.824931 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 39491.5 | 0.711927 | 0.355964 | − | 0.934500i | \(-0.384153\pi\) | ||||
0.355964 | + | 0.934500i | \(0.384153\pi\) | |||||||
\(80\) | 100478. | 1.75528 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 3306.29 | 0.0543008 | ||||||||
\(83\) | 102372. | 1.63112 | 0.815559 | − | 0.578675i | \(-0.196430\pi\) | ||||
0.815559 | + | 0.578675i | \(0.196430\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −6580.60 | −0.0987912 | ||||||||
\(86\) | 4713.88 | 0.0687279 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −24941.2 | −0.343329 | ||||||||
\(89\) | 112821. | 1.50978 | 0.754892 | − | 0.655849i | \(-0.227689\pi\) | ||||
0.754892 | + | 0.655849i | \(0.227689\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −6100.40 | −0.0751430 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 3471.43 | 0.0405218 | ||||||||
\(95\) | 137945. | 1.56818 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 30334.3 | 0.327345 | 0.163672 | − | 0.986515i | \(-0.447666\pi\) | ||||
0.163672 | + | 0.986515i | \(0.447666\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −242554. | −2.42554 | ||||||||
\(101\) | −106796. | −1.04172 | −0.520862 | − | 0.853641i | \(-0.674390\pi\) | ||||
−0.520862 | + | 0.853641i | \(0.674390\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 157536. | 1.46314 | 0.731570 | − | 0.681767i | \(-0.238788\pi\) | ||||
0.731570 | + | 0.681767i | \(0.238788\pi\) | |||||||
\(104\) | 10351.7 | 0.0938490 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −14064.3 | −0.121578 | ||||||||
\(107\) | 89324.3 | 0.754241 | 0.377121 | − | 0.926164i | \(-0.376914\pi\) | ||||
0.377121 | + | 0.926164i | \(0.376914\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 167605. | 1.35120 | 0.675600 | − | 0.737268i | \(-0.263885\pi\) | ||||
0.675600 | + | 0.737268i | \(0.263885\pi\) | |||||||
\(110\) | 41004.8 | 0.323112 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 115794. | 0.853079 | 0.426539 | − | 0.904469i | \(-0.359733\pi\) | ||||
0.426539 | + | 0.904469i | \(0.359733\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 20258.8 | 0.142846 | ||||||||
\(116\) | 135637. | 0.935907 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −2768.19 | −0.0183017 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 86614.1 | 0.537805 | ||||||||
\(122\) | −8408.20 | −0.0511451 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 236104. | 1.37895 | ||||||||
\(125\) | 479898. | 2.74709 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 201513. | 1.10865 | 0.554325 | − | 0.832300i | \(-0.312977\pi\) | ||||
0.554325 | + | 0.832300i | \(0.312977\pi\) | |||||||
\(128\) | −98647.4 | −0.532183 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −17018.9 | −0.0883227 | ||||||||
\(131\) | −38469.6 | −0.195857 | −0.0979285 | − | 0.995193i | \(-0.531222\pi\) | ||||
−0.0979285 | + | 0.995193i | \(0.531222\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −10497.7 | −0.0505049 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 3165.32 | 0.0146747 | ||||||||
\(137\) | 241722. | 1.10031 | 0.550155 | − | 0.835063i | \(-0.314569\pi\) | ||||
0.550155 | + | 0.835063i | \(0.314569\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −53112.2 | −0.233162 | −0.116581 | − | 0.993181i | \(-0.537193\pi\) | ||||
−0.116581 | + | 0.993181i | \(0.537193\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −30692.0 | −0.127733 | ||||||||
\(143\) | −102792. | −0.420359 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −450435. | −1.77915 | ||||||||
\(146\) | 24812.0 | 0.0963340 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −324905. | −1.21927 | ||||||||
\(149\) | −129062. | −0.476248 | −0.238124 | − | 0.971235i | \(-0.576532\pi\) | ||||
−0.238124 | + | 0.971235i | \(0.576532\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 153206. | 0.546808 | 0.273404 | − | 0.961899i | \(-0.411850\pi\) | ||||
0.273404 | + | 0.961899i | \(0.411850\pi\) | |||||||
\(152\) | −66352.6 | −0.232943 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −784075. | −2.62137 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −151188. | −0.489517 | −0.244758 | − | 0.969584i | \(-0.578709\pi\) | ||||
−0.244758 | + | 0.969584i | \(0.578709\pi\) | |||||||
\(158\) | 31230.0 | 0.0995245 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 246555. | 0.761402 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −32916.7 | −0.0970392 | −0.0485196 | − | 0.998822i | \(-0.515450\pi\) | ||||
−0.0485196 | + | 0.998822i | \(0.515450\pi\) | |||||||
\(164\) | −131175. | −0.380838 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 80956.1 | 0.228023 | ||||||||
\(167\) | −217586. | −0.603725 | −0.301862 | − | 0.953352i | \(-0.597608\pi\) | ||||
−0.301862 | + | 0.953352i | \(0.597608\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −328630. | −0.885095 | ||||||||
\(170\) | −5203.97 | −0.0138106 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −187020. | −0.482022 | ||||||||
\(173\) | 421242. | 1.07008 | 0.535041 | − | 0.844826i | \(-0.320296\pi\) | ||||
0.535041 | + | 0.844826i | \(0.320296\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 479921. | 1.16785 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 89219.4 | 0.211062 | ||||||||
\(179\) | −3494.06 | −0.00815075 | −0.00407538 | − | 0.999992i | \(-0.501297\pi\) | ||||
−0.00407538 | + | 0.999992i | \(0.501297\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 594611. | 1.34908 | 0.674538 | − | 0.738240i | \(-0.264343\pi\) | ||||
0.674538 | + | 0.738240i | \(0.264343\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −9744.61 | −0.0212188 | ||||||||
\(185\) | 1.07897e6 | 2.31783 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −31431.5 | −0.0657296 | ||||||||
\(188\) | −137726. | −0.284199 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 109088. | 0.219226 | ||||||||
\(191\) | −828644. | −1.64356 | −0.821778 | − | 0.569807i | \(-0.807018\pi\) | ||||
−0.821778 | + | 0.569807i | \(0.807018\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 219739. | 0.424633 | 0.212316 | − | 0.977201i | \(-0.431899\pi\) | ||||
0.212316 | + | 0.977201i | \(0.431899\pi\) | |||||||
\(194\) | 23988.5 | 0.0457614 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −475612. | −0.873146 | −0.436573 | − | 0.899669i | \(-0.643808\pi\) | ||||
−0.436573 | + | 0.899669i | \(0.643808\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 627555. | 1.12336 | 0.561681 | − | 0.827354i | \(-0.310155\pi\) | ||||
0.561681 | + | 0.827354i | \(0.310155\pi\) | |||||||
\(200\) | −387450. | −0.684921 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −84455.1 | −0.145629 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 435617. | 0.723969 | ||||||||
\(206\) | 124580. | 0.204541 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −199189. | −0.319232 | ||||||||
\(209\) | 658879. | 1.04337 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 570989. | 0.882920 | 0.441460 | − | 0.897281i | \(-0.354461\pi\) | ||||
0.441460 | + | 0.897281i | \(0.354461\pi\) | |||||||
\(212\) | 557991. | 0.852683 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 70638.1 | 0.105440 | ||||||||
\(215\) | 621073. | 0.916319 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 132543. | 0.188892 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −1.62684e6 | −2.26614 | ||||||||
\(221\) | 13045.5 | 0.0179672 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4233.11 | 0.00570029 | 0.00285015 | − | 0.999996i | \(-0.499093\pi\) | ||||
0.00285015 | + | 0.999996i | \(0.499093\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 91570.3 | 0.119257 | ||||||||
\(227\) | −1.12986e6 | −1.45533 | −0.727664 | − | 0.685934i | \(-0.759394\pi\) | ||||
−0.727664 | + | 0.685934i | \(0.759394\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 804643. | 1.01395 | 0.506973 | − | 0.861962i | \(-0.330764\pi\) | ||||
0.506973 | + | 0.861962i | \(0.330764\pi\) | |||||||
\(230\) | 16020.7 | 0.0199693 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 216663. | 0.264280 | ||||||||
\(233\) | −1.16927e6 | −1.41100 | −0.705498 | − | 0.708712i | \(-0.749277\pi\) | ||||
−0.705498 | + | 0.708712i | \(0.749277\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 457374. | 0.540259 | ||||||||
\(236\) | 109826. | 0.128358 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.70554e6 | 1.93138 | 0.965689 | − | 0.259700i | \(-0.0836238\pi\) | ||||
0.965689 | + | 0.259700i | \(0.0836238\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 951196. | 1.05494 | 0.527470 | − | 0.849574i | \(-0.323141\pi\) | ||||
0.527470 | + | 0.849574i | \(0.323141\pi\) | |||||||
\(242\) | 68494.9 | 0.0751830 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 333590. | 0.358705 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −273465. | −0.285206 | ||||||||
\(248\) | 377146. | 0.389386 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 379505. | 0.384032 | ||||||||
\(251\) | −1.14498e6 | −1.14713 | −0.573566 | − | 0.819159i | \(-0.694440\pi\) | ||||
−0.573566 | + | 0.819159i | \(0.694440\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 96763.6 | 0.0950409 | ||||||||
\(254\) | 159358. | 0.154985 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 849606. | 0.810248 | ||||||||
\(257\) | −1.18374e6 | −1.11795 | −0.558976 | − | 0.829184i | \(-0.688806\pi\) | ||||
−0.558976 | + | 0.829184i | \(0.688806\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 675211. | 0.619450 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −30421.9 | −0.0273800 | ||||||||
\(263\) | −448316. | −0.399664 | −0.199832 | − | 0.979830i | \(-0.564040\pi\) | ||||
−0.199832 | + | 0.979830i | \(0.564040\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.85303e6 | −1.62094 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 416490. | 0.354216 | ||||||||
\(269\) | −747474. | −0.629819 | −0.314909 | − | 0.949122i | \(-0.601974\pi\) | ||||
−0.314909 | + | 0.949122i | \(0.601974\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −232637. | −0.192423 | −0.0962114 | − | 0.995361i | \(-0.530672\pi\) | ||||
−0.0962114 | + | 0.995361i | \(0.530672\pi\) | |||||||
\(272\) | −60907.3 | −0.0499169 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 191155. | 0.153819 | ||||||||
\(275\) | 3.84736e6 | 3.06783 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2.42924e6 | −1.90227 | −0.951134 | − | 0.308778i | \(-0.900080\pi\) | ||||
−0.951134 | + | 0.308778i | \(0.900080\pi\) | |||||||
\(278\) | −42001.4 | −0.0325951 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.51704e6 | −1.90163 | −0.950813 | − | 0.309766i | \(-0.899749\pi\) | ||||
−0.950813 | + | 0.309766i | \(0.899749\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 260994. | 0.193716 | 0.0968579 | − | 0.995298i | \(-0.469121\pi\) | ||||
0.0968579 | + | 0.995298i | \(0.469121\pi\) | |||||||
\(284\) | 1.21768e6 | 0.895857 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −81288.6 | −0.0587645 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.41587e6 | −0.997191 | ||||||||
\(290\) | −356206. | −0.248718 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −984399. | −0.675638 | ||||||||
\(293\) | −65011.7 | −0.0442408 | −0.0221204 | − | 0.999755i | \(-0.507042\pi\) | ||||
−0.0221204 | + | 0.999755i | \(0.507042\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −364720. | −0.244008 | ||||||||
\(296\) | −518994. | −0.344297 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −102063. | −0.0665775 | ||||||||
\(299\) | −40161.3 | −0.0259794 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 121156. | 0.0764414 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 1.27676e6 | 0.792367 | ||||||||
\(305\) | −1.10781e6 | −0.681895 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −2.35599e6 | −1.42668 | −0.713342 | − | 0.700816i | \(-0.752819\pi\) | ||||
−0.713342 | + | 0.700816i | \(0.752819\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −620051. | −0.366457 | ||||||||
\(311\) | 2.11805e6 | 1.24176 | 0.620878 | − | 0.783907i | \(-0.286776\pi\) | ||||
0.620878 | + | 0.783907i | \(0.286776\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −187514. | −0.108186 | −0.0540931 | − | 0.998536i | \(-0.517227\pi\) | ||||
−0.0540931 | + | 0.998536i | \(0.517227\pi\) | |||||||
\(314\) | −119560. | −0.0684324 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −1.23903e6 | −0.698014 | ||||||||
\(317\) | 1.00541e6 | 0.561947 | 0.280974 | − | 0.959716i | \(-0.409343\pi\) | ||||
0.280974 | + | 0.959716i | \(0.409343\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −2.15145e6 | −1.18374 | ||||||||
\(320\) | −3.02031e6 | −1.64883 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −83619.1 | −0.0445964 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.59683e6 | −0.838591 | ||||||||
\(326\) | −26030.7 | −0.0135657 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −209535. | −0.107540 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 1.67984e6 | 0.842748 | 0.421374 | − | 0.906887i | \(-0.361548\pi\) | ||||
0.421374 | + | 0.906887i | \(0.361548\pi\) | |||||||
\(332\) | −3.21188e6 | −1.59924 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −172068. | −0.0843982 | ||||||||
\(335\) | −1.38312e6 | −0.673360 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −995036. | −0.477270 | −0.238635 | − | 0.971109i | \(-0.576700\pi\) | ||||
−0.238635 | + | 0.971109i | \(0.576700\pi\) | |||||||
\(338\) | −259882. | −0.123733 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 206464. | 0.0968605 | ||||||||
\(341\) | −3.74505e6 | −1.74410 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −298741. | −0.136113 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 333121. | 0.149593 | ||||||||
\(347\) | −4.05665e6 | −1.80861 | −0.904304 | − | 0.426890i | \(-0.859609\pi\) | ||||
−0.904304 | + | 0.426890i | \(0.859609\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 2.86202e6 | 1.25779 | 0.628897 | − | 0.777488i | \(-0.283507\pi\) | ||||
0.628897 | + | 0.777488i | \(0.283507\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 1.17764e6 | 0.506590 | ||||||||
\(353\) | −832685. | −0.355667 | −0.177834 | − | 0.984061i | \(-0.556909\pi\) | ||||
−0.177834 | + | 0.984061i | \(0.556909\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −4.04379e6 | −1.70301 | ||||||||
\(356\) | −3.53972e6 | −1.48028 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2763.12 | −0.00113944 | ||||||||
\(359\) | 2.69751e6 | 1.10465 | 0.552327 | − | 0.833627i | \(-0.313740\pi\) | ||||
0.552327 | + | 0.833627i | \(0.313740\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −723243. | −0.292090 | ||||||||
\(362\) | 470221. | 0.188595 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 3.26908e6 | 1.28438 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 1.45482e6 | 0.563826 | 0.281913 | − | 0.959440i | \(-0.409031\pi\) | ||||
0.281913 | + | 0.959440i | \(0.409031\pi\) | |||||||
\(368\) | 187507. | 0.0721767 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 853257. | 0.324023 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2.04689e6 | −0.761766 | −0.380883 | − | 0.924623i | \(-0.624380\pi\) | ||||
−0.380883 | + | 0.924623i | \(0.624380\pi\) | |||||||
\(374\) | −24856.2 | −0.00918872 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −220000. | −0.0802516 | ||||||||
\(377\) | 892950. | 0.323574 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −416898. | −0.149084 | −0.0745421 | − | 0.997218i | \(-0.523750\pi\) | ||||
−0.0745421 | + | 0.997218i | \(0.523750\pi\) | |||||||
\(380\) | −4.32798e6 | −1.53754 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −655296. | −0.229762 | ||||||||
\(383\) | 3.87626e6 | 1.35025 | 0.675127 | − | 0.737701i | \(-0.264089\pi\) | ||||
0.675127 | + | 0.737701i | \(0.264089\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 173771. | 0.0593619 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −951729. | −0.320947 | ||||||||
\(389\) | −2.83802e6 | −0.950915 | −0.475458 | − | 0.879739i | \(-0.657717\pi\) | ||||
−0.475458 | + | 0.879739i | \(0.657717\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12280.4 | −0.00406228 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −376116. | −0.122062 | ||||||||
\(395\) | 4.11468e6 | 1.32692 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.34266e6 | 1.38286 | 0.691432 | − | 0.722442i | \(-0.256980\pi\) | ||||
0.691432 | + | 0.722442i | \(0.256980\pi\) | |||||||
\(398\) | 496274. | 0.157041 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 7.45534e6 | 2.32979 | ||||||||
\(401\) | −3.40304e6 | −1.05683 | −0.528417 | − | 0.848985i | \(-0.677214\pi\) | ||||
−0.528417 | + | 0.848985i | \(0.677214\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 1.55436e6 | 0.476749 | ||||||||
\(404\) | 3.35070e6 | 1.02137 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 5.15359e6 | 1.54214 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −5.29431e6 | −1.56495 | −0.782477 | − | 0.622680i | \(-0.786044\pi\) | ||||
−0.782477 | + | 0.622680i | \(0.786044\pi\) | |||||||
\(410\) | 344488. | 0.101208 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4.94262e6 | −1.43455 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 1.06663e7 | 3.04014 | ||||||||
\(416\) | −488775. | −0.138476 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 521045. | 0.145859 | ||||||||
\(419\) | −2.87267e6 | −0.799376 | −0.399688 | − | 0.916651i | \(-0.630881\pi\) | ||||
−0.399688 | + | 0.916651i | \(0.630881\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 2.08688e6 | 0.573843 | 0.286921 | − | 0.957954i | \(-0.407368\pi\) | ||||
0.286921 | + | 0.957954i | \(0.407368\pi\) | |||||||
\(422\) | 451541. | 0.123429 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 891319. | 0.240779 | ||||||||
\(425\) | −488273. | −0.131127 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −2.80252e6 | −0.739501 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 491148. | 0.128098 | ||||||||
\(431\) | 2.42863e6 | 0.629751 | 0.314876 | − | 0.949133i | \(-0.398037\pi\) | ||||
0.314876 | + | 0.949133i | \(0.398037\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 956219. | 0.245097 | 0.122548 | − | 0.992463i | \(-0.460893\pi\) | ||||
0.122548 | + | 0.992463i | \(0.460893\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −5.25853e6 | −1.32479 | ||||||||
\(437\) | 257426. | 0.0644836 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 2.64205e6 | 0.654304 | 0.327152 | − | 0.944972i | \(-0.393911\pi\) | ||||
0.327152 | + | 0.944972i | \(0.393911\pi\) | |||||||
\(440\) | −2.59867e6 | −0.639910 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 10316.4 | 0.00251174 | ||||||||
\(443\) | 3.43966e6 | 0.832733 | 0.416366 | − | 0.909197i | \(-0.363303\pi\) | ||||
0.416366 | + | 0.909197i | \(0.363303\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.17550e7 | 2.81399 | ||||||||
\(446\) | 3347.56 | 0.000796878 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −4.39903e6 | −1.02977 | −0.514886 | − | 0.857259i | \(-0.672166\pi\) | ||||
−0.514886 | + | 0.857259i | \(0.672166\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.08067e6 | 0.481684 | ||||||||
\(452\) | −3.63299e6 | −0.836407 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −893501. | −0.203449 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −2.25110e6 | −0.504202 | −0.252101 | − | 0.967701i | \(-0.581122\pi\) | ||||
−0.252101 | + | 0.967701i | \(0.581122\pi\) | |||||||
\(458\) | 636316. | 0.141745 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −635611. | −0.140054 | ||||||||
\(461\) | −1.85307e6 | −0.406107 | −0.203053 | − | 0.979168i | \(-0.565087\pi\) | ||||
−0.203053 | + | 0.979168i | \(0.565087\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −3.01089e6 | −0.652744 | −0.326372 | − | 0.945241i | \(-0.605826\pi\) | ||||
−0.326372 | + | 0.945241i | \(0.605826\pi\) | |||||||
\(464\) | −4.16904e6 | −0.898962 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −924667. | −0.197252 | ||||||||
\(467\) | 1.06725e6 | 0.226452 | 0.113226 | − | 0.993569i | \(-0.463882\pi\) | ||||
0.113226 | + | 0.993569i | \(0.463882\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 361694. | 0.0755260 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 175433. | 0.0362456 | ||||||||
\(473\) | 2.96648e6 | 0.609662 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1.02354e7 | 2.08147 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 1.34875e6 | 0.269999 | ||||||||
\(479\) | 5.68788e6 | 1.13269 | 0.566346 | − | 0.824168i | \(-0.308357\pi\) | ||||
0.566346 | + | 0.824168i | \(0.308357\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.13897e6 | −0.421544 | ||||||||
\(482\) | 752211. | 0.147476 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −2.71749e6 | −0.527295 | ||||||||
\(485\) | 3.16059e6 | 0.610117 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −6.84477e6 | −1.30779 | −0.653893 | − | 0.756587i | \(-0.726865\pi\) | ||||
−0.653893 | + | 0.756587i | \(0.726865\pi\) | |||||||
\(488\) | 532867. | 0.101291 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −5.60132e6 | −1.04854 | −0.524272 | − | 0.851551i | \(-0.675662\pi\) | ||||
−0.524272 | + | 0.851551i | \(0.675662\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 273043. | 0.0505958 | ||||||||
\(494\) | −216257. | −0.0398706 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −7.25708e6 | −1.32452 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.33529e6 | −0.419845 | −0.209923 | − | 0.977718i | \(-0.567321\pi\) | ||||
−0.209923 | + | 0.977718i | \(0.567321\pi\) | |||||||
\(500\) | −1.50566e7 | −2.69341 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −905455. | −0.160364 | ||||||||
\(503\) | 1.08278e7 | 1.90819 | 0.954093 | − | 0.299510i | \(-0.0968233\pi\) | ||||
0.954093 | + | 0.299510i | \(0.0968233\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −1.11273e7 | −1.94161 | ||||||||
\(506\) | 76521.1 | 0.0132863 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −6.32240e6 | −1.08698 | ||||||||
\(509\) | −3.17847e6 | −0.543781 | −0.271890 | − | 0.962328i | \(-0.587649\pi\) | ||||
−0.271890 | + | 0.962328i | \(0.587649\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 3.82859e6 | 0.645452 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −936107. | −0.156285 | ||||||||
\(515\) | 1.64139e7 | 2.72705 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.18460e6 | 0.359455 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 1.07856e6 | 0.174919 | ||||||||
\(521\) | 6.35837e6 | 1.02625 | 0.513123 | − | 0.858315i | \(-0.328489\pi\) | ||||
0.513123 | + | 0.858315i | \(0.328489\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −7.22187e6 | −1.15450 | −0.577252 | − | 0.816566i | \(-0.695875\pi\) | ||||
−0.577252 | + | 0.816566i | \(0.695875\pi\) | |||||||
\(524\) | 1.20697e6 | 0.192029 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −354531. | −0.0558714 | ||||||||
\(527\) | 475288. | 0.0745471 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −6.39854e6 | −0.994126 | ||||||||
\(530\) | −1.46538e6 | −0.226601 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −863574. | −0.131668 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 9.30685e6 | 1.40578 | ||||||||
\(536\) | 665290. | 0.100023 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −591106. | −0.0880461 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −9.43165e6 | −1.38546 | −0.692731 | − | 0.721196i | \(-0.743593\pi\) | ||||
−0.692731 | + | 0.721196i | \(0.743593\pi\) | |||||||
\(542\) | −183971. | −0.0268999 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | −149456. | −0.0216529 | ||||||||
\(545\) | 1.74630e7 | 2.51842 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9.91568e6 | 1.41695 | 0.708474 | − | 0.705737i | \(-0.249384\pi\) | ||||
0.708474 | + | 0.705737i | \(0.249384\pi\) | |||||||
\(548\) | −7.58394e6 | −1.07881 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 3.04251e6 | 0.428870 | ||||||||
\(551\) | −5.72364e6 | −0.803144 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −1.92106e6 | −0.265929 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1.66638e6 | 0.228605 | ||||||||
\(557\) | −9.64613e6 | −1.31739 | −0.658696 | − | 0.752409i | \(-0.728892\pi\) | ||||
−0.658696 | + | 0.752409i | \(0.728892\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.23123e6 | −0.166651 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.99049e6 | −0.265839 | ||||||||
\(563\) | −3.09504e6 | −0.411524 | −0.205762 | − | 0.978602i | \(-0.565967\pi\) | ||||
−0.205762 | + | 0.978602i | \(0.565967\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.20648e7 | 1.59000 | ||||||||
\(566\) | 206396. | 0.0270807 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 1.94509e6 | 0.252970 | ||||||||
\(569\) | 1.23185e7 | 1.59507 | 0.797533 | − | 0.603275i | \(-0.206138\pi\) | ||||
0.797533 | + | 0.603275i | \(0.206138\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −3.23510e6 | −0.415238 | −0.207619 | − | 0.978210i | \(-0.566571\pi\) | ||||
−0.207619 | + | 0.978210i | \(0.566571\pi\) | |||||||
\(572\) | 3.22507e6 | 0.412144 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 1.50318e6 | 0.189601 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −9.05049e6 | −1.13170 | −0.565852 | − | 0.824507i | \(-0.691453\pi\) | ||||
−0.565852 | + | 0.824507i | \(0.691453\pi\) | |||||||
\(578\) | −1.11968e6 | −0.139403 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.41322e7 | 1.74438 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −8.85077e6 | −1.07847 | ||||||||
\(584\) | −1.57245e6 | −0.190785 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −51411.6 | −0.00618468 | ||||||||
\(587\) | 2.13170e6 | 0.255347 | 0.127673 | − | 0.991816i | \(-0.459249\pi\) | ||||
0.127673 | + | 0.991816i | \(0.459249\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −9.96318e6 | −1.18334 | ||||||||
\(590\) | −288422. | −0.0341113 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 9.98652e6 | 1.17114 | ||||||||
\(593\) | 7.26933e6 | 0.848903 | 0.424451 | − | 0.905451i | \(-0.360467\pi\) | ||||
0.424451 | + | 0.905451i | \(0.360467\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 4.04927e6 | 0.466941 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −31759.8 | −0.00363182 | ||||||||
\(599\) | 2.20565e6 | 0.251171 | 0.125585 | − | 0.992083i | \(-0.459919\pi\) | ||||
0.125585 | + | 0.992083i | \(0.459919\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −1.00121e7 | −1.13067 | −0.565336 | − | 0.824860i | \(-0.691254\pi\) | ||||
−0.565336 | + | 0.824860i | \(0.691254\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −4.80679e6 | −0.536121 | ||||||||
\(605\) | 9.02447e6 | 1.00238 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.32139e6 | 0.696371 | 0.348185 | − | 0.937426i | \(-0.386798\pi\) | ||||
0.348185 | + | 0.937426i | \(0.386798\pi\) | |||||||
\(608\) | 3.13295e6 | 0.343712 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −876065. | −0.0953261 | ||||||||
\(611\) | −906706. | −0.0982570 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 1.43078e7 | 1.53788 | 0.768941 | − | 0.639319i | \(-0.220784\pi\) | ||||
0.768941 | + | 0.639319i | \(0.220784\pi\) | |||||||
\(614\) | −1.86313e6 | −0.199445 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −1.73991e7 | −1.83999 | −0.919993 | − | 0.391936i | \(-0.871806\pi\) | ||||
−0.919993 | + | 0.391936i | \(0.871806\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 8.26736e6 | 0.867242 | 0.433621 | − | 0.901095i | \(-0.357236\pi\) | ||||
0.433621 | + | 0.901095i | \(0.357236\pi\) | |||||||
\(620\) | 2.46001e7 | 2.57014 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 1.67497e6 | 0.173592 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2.58422e7 | 2.64625 | ||||||||
\(626\) | −148287. | −0.0151240 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 4.74346e6 | 0.479950 | ||||||||
\(629\) | −654048. | −0.0659148 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2.83238e6 | 0.283190 | 0.141595 | − | 0.989925i | \(-0.454777\pi\) | ||||
0.141595 | + | 0.989925i | \(0.454777\pi\) | |||||||
\(632\) | −1.97919e6 | −0.197104 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 795084. | 0.0785579 | ||||||||
\(635\) | 2.09960e7 | 2.06634 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −1.70138e6 | −0.165481 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −1.02782e7 | −0.991902 | ||||||||
\(641\) | 3.57176e6 | 0.343350 | 0.171675 | − | 0.985154i | \(-0.445082\pi\) | ||||
0.171675 | + | 0.985154i | \(0.445082\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5.96911e6 | −0.569354 | −0.284677 | − | 0.958624i | \(-0.591886\pi\) | ||||
−0.284677 | + | 0.958624i | \(0.591886\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −66126.4 | −0.00623439 | ||||||||
\(647\) | 1.68276e6 | 0.158038 | 0.0790189 | − | 0.996873i | \(-0.474821\pi\) | ||||
0.0790189 | + | 0.996873i | \(0.474821\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −1.74204e6 | −0.162348 | ||||||||
\(650\) | −1.26278e6 | −0.117232 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 1.03275e6 | 0.0951427 | ||||||||
\(653\) | −1.70305e7 | −1.56295 | −0.781475 | − | 0.623937i | \(-0.785532\pi\) | ||||
−0.781475 | + | 0.623937i | \(0.785532\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.00821e6 | −0.365046 | ||||||||
\(656\) | 4.03189e6 | 0.365804 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 1.99303e7 | 1.78772 | 0.893862 | − | 0.448342i | \(-0.147985\pi\) | ||||
0.893862 | + | 0.448342i | \(0.147985\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.55735e6 | 0.850812 | 0.425406 | − | 0.905003i | \(-0.360131\pi\) | ||||
0.425406 | + | 0.905003i | \(0.360131\pi\) | |||||||
\(662\) | 1.32843e6 | 0.117813 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −5.13056e6 | −0.451591 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −840579. | −0.0731584 | ||||||||
\(668\) | 6.82666e6 | 0.591926 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.09378e6 | −0.0941330 | ||||||||
\(671\) | −5.29135e6 | −0.453691 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 1.80397e7 | 1.53530 | 0.767648 | − | 0.640872i | \(-0.221427\pi\) | ||||
0.767648 | + | 0.640872i | \(0.221427\pi\) | |||||||
\(674\) | −786879. | −0.0667204 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 1.03106e7 | 0.867798 | ||||||||
\(677\) | 1.44741e7 | 1.21372 | 0.606861 | − | 0.794808i | \(-0.292429\pi\) | ||||
0.606861 | + | 0.794808i | \(0.292429\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 329800. | 0.0273513 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −2.96160e6 | −0.243818 | ||||||||
\(683\) | −2.68785e6 | −0.220472 | −0.110236 | − | 0.993905i | \(-0.535161\pi\) | ||||
−0.110236 | + | 0.993905i | \(0.535161\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 2.51854e7 | 2.05080 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 5.74839e6 | 0.462994 | ||||||||
\(689\) | 3.67347e6 | 0.294801 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 4.67627e6 | 0.372567 | 0.186284 | − | 0.982496i | \(-0.440356\pi\) | ||||
0.186284 | + | 0.982496i | \(0.440356\pi\) | |||||||
\(692\) | −1.32163e7 | −1.04917 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −3.20802e6 | −0.252836 | ||||||||
\(695\) | −5.53385e6 | −0.434576 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −264061. | −0.0205884 | ||||||||
\(698\) | 2.26330e6 | 0.175834 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6.34801e6 | −0.487913 | −0.243957 | − | 0.969786i | \(-0.578445\pi\) | ||||
−0.243957 | + | 0.969786i | \(0.578445\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 1.37104e7 | 1.04631 | ||||||||
\(704\) | −1.44262e7 | −1.09703 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −658492. | −0.0497208 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −6.41052e6 | −0.478936 | −0.239468 | − | 0.970904i | \(-0.576973\pi\) | ||||
−0.239468 | + | 0.970904i | \(0.576973\pi\) | |||||||
\(710\) | −3.19785e6 | −0.238074 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −5.65425e6 | −0.417998 | ||||||||
\(713\) | −1.46320e6 | −0.107790 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.07101e7 | −0.783481 | ||||||||
\(716\) | 109625. | 0.00799146 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 2.13320e6 | 0.154426 | ||||||||
\(719\) | −7.34505e6 | −0.529874 | −0.264937 | − | 0.964266i | \(-0.585351\pi\) | ||||
−0.264937 | + | 0.964266i | \(0.585351\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −571944. | −0.0408329 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −1.86557e7 | −1.32271 | ||||||||
\(725\) | −3.34218e7 | −2.36148 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1.57839e7 | 1.10759 | 0.553793 | − | 0.832655i | \(-0.313180\pi\) | ||||
0.553793 | + | 0.832655i | \(0.313180\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 2.58520e6 | 0.179551 | ||||||||
\(731\) | −376480. | −0.0260584 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.35367e7 | 0.930579 | 0.465289 | − | 0.885159i | \(-0.345950\pi\) | ||||
0.465289 | + | 0.885159i | \(0.345950\pi\) | |||||||
\(734\) | 1.15048e6 | 0.0788205 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 460109. | 0.0313088 | ||||||||
\(737\) | −6.60631e6 | −0.448012 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −7.33702e6 | −0.494207 | −0.247103 | − | 0.968989i | \(-0.579479\pi\) | ||||
−0.247103 | + | 0.968989i | \(0.579479\pi\) | |||||||
\(740\) | −3.38524e7 | −2.27253 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.20844e7 | −0.803068 | −0.401534 | − | 0.915844i | \(-0.631523\pi\) | ||||
−0.401534 | + | 0.915844i | \(0.631523\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.34472e7 | −0.887649 | ||||||||
\(746\) | −1.61869e6 | −0.106492 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 986151. | 0.0644450 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8.78176e6 | 0.568175 | 0.284087 | − | 0.958798i | \(-0.408309\pi\) | ||||
0.284087 | + | 0.958798i | \(0.408309\pi\) | |||||||
\(752\) | 4.23327e6 | 0.272980 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 706149. | 0.0452343 | ||||||||
\(755\) | 1.59628e7 | 1.01916 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 465874. | 0.0295480 | 0.0147740 | − | 0.999891i | \(-0.495297\pi\) | ||||
0.0147740 | + | 0.999891i | \(0.495297\pi\) | |||||||
\(758\) | −329685. | −0.0208414 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −6.91339e6 | −0.434167 | ||||||||
\(761\) | −1.49978e7 | −0.938786 | −0.469393 | − | 0.882989i | \(-0.655527\pi\) | ||||
−0.469393 | + | 0.882989i | \(0.655527\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 2.59984e7 | 1.61144 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 3.06536e6 | 0.188760 | ||||||||
\(767\) | 723026. | 0.0443778 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.85606e7 | −1.13181 | −0.565907 | − | 0.824469i | \(-0.691474\pi\) | ||||
−0.565907 | + | 0.824469i | \(0.691474\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −6.89422e6 | −0.416334 | ||||||||
\(773\) | −1.22760e7 | −0.738941 | −0.369470 | − | 0.929243i | \(-0.620461\pi\) | ||||
−0.369470 | + | 0.929243i | \(0.620461\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −5.81775e7 | −3.47937 | ||||||||
\(776\) | −1.52027e6 | −0.0906286 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −2.24432e6 | −0.132934 | ||||||||
\(779\) | 5.53534e6 | 0.326814 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.93147e7 | −1.13308 | ||||||||
\(782\) | −9711.39 | −0.000567890 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −1.57525e7 | −0.912380 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 5.26991e6 | 0.303296 | 0.151648 | − | 0.988435i | \(-0.451542\pi\) | ||||
0.151648 | + | 0.988435i | \(0.451542\pi\) | |||||||
\(788\) | 1.49221e7 | 0.856082 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 3.25391e6 | 0.185497 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 2.19615e6 | 0.124016 | ||||||||
\(794\) | 3.43420e6 | 0.193319 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −1.96893e7 | −1.10141 | ||||||||
\(797\) | −1.11889e7 | −0.623940 | −0.311970 | − | 0.950092i | \(-0.600989\pi\) | ||||
−0.311970 | + | 0.950092i | \(0.600989\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −277250. | −0.0153640 | ||||||||
\(800\) | 1.82941e7 | 1.01062 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −2.69114e6 | −0.147741 | ||||||||
\(803\) | 1.56144e7 | 0.854547 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 1.22920e6 | 0.0666476 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5.35231e6 | 0.288412 | ||||||||
\(809\) | −7.05051e6 | −0.378747 | −0.189374 | − | 0.981905i | \(-0.560646\pi\) | ||||
−0.189374 | + | 0.981905i | \(0.560646\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.54873e7 | −1.36073 | −0.680364 | − | 0.732875i | \(-0.738178\pi\) | ||||
−0.680364 | + | 0.732875i | \(0.738178\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 4.07548e6 | 0.215585 | ||||||||
\(815\) | −3.42964e6 | −0.180865 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 7.89192e6 | 0.413645 | ||||||||
\(818\) | −4.18677e6 | −0.218774 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.36673e7 | −0.709820 | ||||||||
\(821\) | 2.34879e7 | 1.21615 | 0.608073 | − | 0.793881i | \(-0.291943\pi\) | ||||
0.608073 | + | 0.793881i | \(0.291943\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.20903e7 | −0.622213 | −0.311107 | − | 0.950375i | \(-0.600700\pi\) | ||||
−0.311107 | + | 0.950375i | \(0.600700\pi\) | |||||||
\(824\) | −7.89521e6 | −0.405084 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −3.33335e6 | −0.169480 | −0.0847398 | − | 0.996403i | \(-0.527006\pi\) | ||||
−0.0847398 | + | 0.996403i | \(0.527006\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −7.70534e6 | −0.389408 | −0.194704 | − | 0.980862i | \(-0.562375\pi\) | ||||
−0.194704 | + | 0.980862i | \(0.562375\pi\) | |||||||
\(830\) | 8.43496e6 | 0.424999 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 5.98752e6 | 0.299874 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −2.26706e7 | −1.12524 | ||||||||
\(836\) | −2.06721e7 | −1.02298 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −2.27172e6 | −0.111749 | ||||||||
\(839\) | −2.40843e7 | −1.18121 | −0.590607 | − | 0.806959i | \(-0.701112\pi\) | ||||
−0.590607 | + | 0.806959i | \(0.701112\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.82163e6 | −0.0888116 | ||||||||
\(842\) | 1.65032e6 | 0.0802208 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.79146e7 | −0.865665 | ||||||||
\(845\) | −3.42405e7 | −1.64967 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −1.71509e7 | −0.819023 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −386129. | −0.0183310 | ||||||||
\(851\) | 2.01352e6 | 0.0953088 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −2.82938e7 | −1.33143 | −0.665716 | − | 0.746206i | \(-0.731874\pi\) | ||||
−0.665716 | + | 0.746206i | \(0.731874\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −4.47666e6 | −0.208819 | ||||||||
\(857\) | −2.16176e7 | −1.00544 | −0.502719 | − | 0.864450i | \(-0.667667\pi\) | ||||
−0.502719 | + | 0.864450i | \(0.667667\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 3.25382e7 | 1.50456 | 0.752282 | − | 0.658841i | \(-0.228953\pi\) | ||||
0.752282 | + | 0.658841i | \(0.228953\pi\) | |||||||
\(860\) | −1.94859e7 | −0.898411 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.92058e6 | 0.0880366 | ||||||||
\(863\) | −8.06384e6 | −0.368566 | −0.184283 | − | 0.982873i | \(-0.558996\pi\) | ||||
−0.184283 | + | 0.982873i | \(0.558996\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 4.38900e7 | 1.99446 | ||||||||
\(866\) | 756183. | 0.0342635 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.96533e7 | 0.882849 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.74192e6 | 0.122464 | ||||||||
\(872\) | −8.39983e6 | −0.374093 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 203574. | 0.00901454 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.70312e7 | 0.747732 | 0.373866 | − | 0.927483i | \(-0.378032\pi\) | ||||
0.373866 | + | 0.927483i | \(0.378032\pi\) | |||||||
\(878\) | 2.08934e6 | 0.0914690 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5.00038e7 | 2.17669 | ||||||||
\(881\) | −1.24740e7 | −0.541459 | −0.270729 | − | 0.962655i | \(-0.587265\pi\) | ||||
−0.270729 | + | 0.962655i | \(0.587265\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 7.28955e6 | 0.314629 | 0.157315 | − | 0.987549i | \(-0.449716\pi\) | ||||
0.157315 | + | 0.987549i | \(0.449716\pi\) | |||||||
\(884\) | −409298. | −0.0176160 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 2.72010e6 | 0.116413 | ||||||||
\(887\) | −1.87675e7 | −0.800937 | −0.400469 | − | 0.916310i | \(-0.631153\pi\) | ||||
−0.400469 | + | 0.916310i | \(0.631153\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 9.29592e6 | 0.393385 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −132812. | −0.00558889 | ||||||||
\(893\) | 5.81181e6 | 0.243884 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −364052. | −0.0151917 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −3.47878e6 | −0.143958 | ||||||||
\(899\) | 3.25330e7 | 1.34253 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.12326e6 | 0.0460966 | ||||||||
\(902\) | 1.64541e6 | 0.0673375 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −5.80323e6 | −0.236183 | ||||||||
\(905\) | 6.19535e7 | 2.51446 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1.26367e6 | 0.0510052 | 0.0255026 | − | 0.999675i | \(-0.491881\pi\) | ||||
0.0255026 | + | 0.999675i | \(0.491881\pi\) | |||||||
\(908\) | 3.54490e7 | 1.42689 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.47718e7 | 0.988921 | 0.494461 | − | 0.869200i | \(-0.335366\pi\) | ||||
0.494461 | + | 0.869200i | \(0.335366\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 5.09463e7 | 2.02272 | ||||||||
\(914\) | −1.78018e6 | −0.0704854 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −2.52454e7 | −0.994130 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −9.36676e6 | −0.365848 | −0.182924 | − | 0.983127i | \(-0.558556\pi\) | ||||
−0.182924 | + | 0.983127i | \(0.558556\pi\) | |||||||
\(920\) | −1.01531e6 | −0.0395483 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1.46542e6 | −0.0567721 | ||||||||
\(923\) | 8.01648e6 | 0.309727 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8.00586e7 | 3.07648 | ||||||||
\(926\) | −2.38103e6 | −0.0912509 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −1.02301e7 | −0.389951 | ||||||||
\(929\) | 6.87350e6 | 0.261300 | 0.130650 | − | 0.991429i | \(-0.458294\pi\) | ||||
0.130650 | + | 0.991429i | \(0.458294\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 3.66855e7 | 1.38342 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 843990. | 0.0316570 | ||||||||
\(935\) | −3.27490e6 | −0.122509 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −4.26197e7 | −1.58585 | −0.792923 | − | 0.609322i | \(-0.791442\pi\) | ||||
−0.792923 | + | 0.609322i | \(0.791442\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −1.43499e7 | −0.529701 | ||||||||
\(941\) | −4.50226e6 | −0.165751 | −0.0828755 | − | 0.996560i | \(-0.526410\pi\) | ||||
−0.0828755 | + | 0.996560i | \(0.526410\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 812926. | 0.0297695 | ||||||||
\(944\) | −3.37569e6 | −0.123291 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.34591e6 | 0.0852282 | ||||||||
\(947\) | −3.37725e7 | −1.22374 | −0.611870 | − | 0.790959i | \(-0.709582\pi\) | ||||
−0.611870 | + | 0.790959i | \(0.709582\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −6.48068e6 | −0.233590 | ||||||||
\(950\) | 8.09419e6 | 0.290981 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −4.81813e7 | −1.71849 | −0.859244 | − | 0.511566i | \(-0.829066\pi\) | ||||
−0.859244 | + | 0.511566i | \(0.829066\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −8.63379e7 | −3.06332 | ||||||||
\(956\) | −5.35107e7 | −1.89363 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 4.49800e6 | 0.158346 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.80012e7 | 0.978066 | ||||||||
\(962\) | −1.69151e6 | −0.0589301 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −2.98434e7 | −1.03432 | ||||||||
\(965\) | 2.28950e7 | 0.791446 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −3.54640e7 | −1.21961 | −0.609805 | − | 0.792551i | \(-0.708752\pi\) | ||||
−0.609805 | + | 0.792551i | \(0.708752\pi\) | |||||||
\(968\) | −4.34084e6 | −0.148897 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 2.49941e6 | 0.0852919 | ||||||||
\(971\) | 7.84296e6 | 0.266951 | 0.133476 | − | 0.991052i | \(-0.457386\pi\) | ||||
0.133476 | + | 0.991052i | \(0.457386\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −5.41288e6 | −0.182823 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −1.02535e7 | −0.344545 | ||||||||
\(977\) | 2.47534e7 | 0.829658 | 0.414829 | − | 0.909899i | \(-0.363841\pi\) | ||||
0.414829 | + | 0.909899i | \(0.363841\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 5.61464e7 | 1.87226 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −4.42955e6 | −0.146582 | ||||||||
\(983\) | −4.53129e7 | −1.49568 | −0.747838 | − | 0.663881i | \(-0.768908\pi\) | ||||
−0.747838 | + | 0.663881i | \(0.768908\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −4.95548e7 | −1.62740 | ||||||||
\(986\) | 215924. | 0.00707308 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 8.57985e6 | 0.279632 | ||||||||
\(989\) | 1.15902e6 | 0.0376789 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −3.74143e7 | −1.21019 | −0.605095 | − | 0.796154i | \(-0.706865\pi\) | ||||
−0.605095 | + | 0.796154i | \(0.706865\pi\) | |||||||
\(992\) | −1.78076e7 | −0.574548 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 6.53861e7 | 2.09376 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 4.65278e7 | 1.48243 | 0.741216 | − | 0.671267i | \(-0.234249\pi\) | ||||
0.741216 | + | 0.671267i | \(0.234249\pi\) | |||||||
\(998\) | −1.84676e6 | −0.0586926 | ||||||||
\(999\) | 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 | 441.6.a.w.1.3 | 4 | ||
3.2 | odd | 2 | 147.6.a.m.1.2 | 4 | |||
7.2 | even | 3 | 63.6.e.e.46.2 | 8 | |||
7.4 | even | 3 | 63.6.e.e.37.2 | 8 | |||
7.6 | odd | 2 | 441.6.a.v.1.3 | 4 | |||
21.2 | odd | 6 | 21.6.e.c.4.3 | ✓ | 8 | ||
21.5 | even | 6 | 147.6.e.o.67.3 | 8 | |||
21.11 | odd | 6 | 21.6.e.c.16.3 | yes | 8 | ||
21.17 | even | 6 | 147.6.e.o.79.3 | 8 | |||
21.20 | even | 2 | 147.6.a.l.1.2 | 4 | |||
84.11 | even | 6 | 336.6.q.j.289.4 | 8 | |||
84.23 | even | 6 | 336.6.q.j.193.4 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
21.6.e.c.4.3 | ✓ | 8 | 21.2 | odd | 6 | ||
21.6.e.c.16.3 | yes | 8 | 21.11 | odd | 6 | ||
63.6.e.e.37.2 | 8 | 7.4 | even | 3 | |||
63.6.e.e.46.2 | 8 | 7.2 | even | 3 | |||
147.6.a.l.1.2 | 4 | 21.20 | even | 2 | |||
147.6.a.m.1.2 | 4 | 3.2 | odd | 2 | |||
147.6.e.o.67.3 | 8 | 21.5 | even | 6 | |||
147.6.e.o.79.3 | 8 | 21.17 | even | 6 | |||
336.6.q.j.193.4 | 8 | 84.23 | even | 6 | |||
336.6.q.j.289.4 | 8 | 84.11 | even | 6 | |||
441.6.a.v.1.3 | 4 | 7.6 | odd | 2 | |||
441.6.a.w.1.3 | 4 | 1.1 | even | 1 | trivial |