Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1028,6,Mod(1,1028)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1028, 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("1028.1");
S:= CuspForms(chi, 6);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1028 = 2^{2} \cdot 257 \) |
Weight: | \( k \) | \(=\) | \( 6 \) |
Character orbit: | \([\chi]\) | \(=\) | 1028.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: | \(164.874566768\) |
Analytic rank: | \(0\) |
Dimension: | \(57\) |
Twist minimal: | yes |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.11 | ||
Character | \(\chi\) | \(=\) | 1028.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −20.8847 | −1.33976 | −0.669878 | − | 0.742471i | \(-0.733654\pi\) | ||||
−0.669878 | + | 0.742471i | \(0.733654\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 110.347 | 1.97395 | 0.986974 | − | 0.160881i | \(-0.0514334\pi\) | ||||
0.986974 | + | 0.160881i | \(0.0514334\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 192.813 | 1.48728 | 0.743638 | − | 0.668583i | \(-0.233099\pi\) | ||||
0.743638 | + | 0.668583i | \(0.233099\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 193.172 | 0.794948 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 794.045 | 1.97862 | 0.989312 | − | 0.145815i | \(-0.0465803\pi\) | ||||
0.989312 | + | 0.145815i | \(0.0465803\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −404.777 | −0.664290 | −0.332145 | − | 0.943228i | \(-0.607772\pi\) | ||||
−0.332145 | + | 0.943228i | \(0.607772\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2304.57 | −2.64461 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 426.850 | 0.358222 | 0.179111 | − | 0.983829i | \(-0.442678\pi\) | ||||
0.179111 | + | 0.983829i | \(0.442678\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1457.62 | −0.926317 | −0.463158 | − | 0.886276i | \(-0.653284\pi\) | ||||
−0.463158 | + | 0.886276i | \(0.653284\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4026.85 | −1.99259 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 3779.96 | 1.48994 | 0.744969 | − | 0.667099i | \(-0.232464\pi\) | ||||
0.744969 | + | 0.667099i | \(0.232464\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9051.47 | 2.89647 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 1040.64 | 0.274720 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −1888.95 | −0.417086 | −0.208543 | − | 0.978013i | \(-0.566872\pi\) | ||||
−0.208543 | + | 0.978013i | \(0.566872\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 5239.34 | 0.979202 | 0.489601 | − | 0.871947i | \(-0.337143\pi\) | ||||
0.489601 | + | 0.871947i | \(0.337143\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −16583.4 | −2.65087 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 21276.4 | 2.93580 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 10898.0 | 1.30870 | 0.654351 | − | 0.756191i | \(-0.272942\pi\) | ||||
0.654351 | + | 0.756191i | \(0.272942\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 8453.67 | 0.889987 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 4855.04 | 0.451059 | 0.225529 | − | 0.974236i | \(-0.427589\pi\) | ||||
0.225529 | + | 0.974236i | \(0.427589\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 16020.3 | 1.32129 | 0.660647 | − | 0.750697i | \(-0.270282\pi\) | ||||
0.660647 | + | 0.750697i | \(0.270282\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 21316.0 | 1.56919 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −12201.2 | −0.805673 | −0.402837 | − | 0.915272i | \(-0.631976\pi\) | ||||
−0.402837 | + | 0.915272i | \(0.631976\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 20369.9 | 1.21199 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −8914.64 | −0.479931 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −6173.22 | −0.301871 | −0.150936 | − | 0.988544i | \(-0.548229\pi\) | ||||
−0.150936 | + | 0.988544i | \(0.548229\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 87620.5 | 3.90570 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 30442.0 | 1.24104 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −37464.9 | −1.40118 | −0.700591 | − | 0.713563i | \(-0.747080\pi\) | ||||
−0.700591 | + | 0.713563i | \(0.747080\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 21659.6 | 0.745290 | 0.372645 | − | 0.927974i | \(-0.378451\pi\) | ||||
0.372645 | + | 0.927974i | \(0.378451\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 37246.2 | 1.18231 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −44666.0 | −1.31127 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 12301.2 | 0.334780 | 0.167390 | − | 0.985891i | \(-0.446466\pi\) | ||||
0.167390 | + | 0.985891i | \(0.446466\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −78943.6 | −1.99615 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −15148.1 | −0.356626 | −0.178313 | − | 0.983974i | \(-0.557064\pi\) | ||||
−0.178313 | + | 0.983974i | \(0.557064\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −13003.2 | −0.285590 | −0.142795 | − | 0.989752i | \(-0.545609\pi\) | ||||
−0.142795 | + | 0.989752i | \(0.545609\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −189038. | −3.88056 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 153102. | 2.94276 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −38739.7 | −0.698375 | −0.349187 | − | 0.937053i | \(-0.613542\pi\) | ||||
−0.349187 | + | 0.937053i | \(0.613542\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −68674.3 | −1.16301 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −98224.4 | −1.56503 | −0.782517 | − | 0.622629i | \(-0.786065\pi\) | ||||
−0.782517 | + | 0.622629i | \(0.786065\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 47101.6 | 0.707112 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 39450.3 | 0.558794 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 82375.6 | 1.10236 | 0.551180 | − | 0.834386i | \(-0.314178\pi\) | ||||
0.551180 | + | 0.834386i | \(0.314178\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −78046.4 | −0.987983 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −109422. | −1.31189 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −160844. | −1.82850 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −159472. | −1.72090 | −0.860450 | − | 0.509535i | \(-0.829817\pi\) | ||||
−0.860450 | + | 0.509535i | \(0.829817\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 153387. | 1.57290 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 115137. | 1.12309 | 0.561543 | − | 0.827448i | \(-0.310208\pi\) | ||||
0.561543 | + | 0.827448i | \(0.310208\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −134219. | −1.24658 | −0.623289 | − | 0.781992i | \(-0.714204\pi\) | ||||
−0.623289 | + | 0.781992i | \(0.714204\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −444351. | −3.93326 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 156602. | 1.32233 | 0.661163 | − | 0.750243i | \(-0.270063\pi\) | ||||
0.661163 | + | 0.750243i | \(0.270063\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −27368.8 | −0.220642 | −0.110321 | − | 0.993896i | \(-0.535188\pi\) | ||||
−0.110321 | + | 0.993896i | \(0.535188\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −227601. | −1.75334 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 120043. | 0.884384 | 0.442192 | − | 0.896920i | \(-0.354201\pi\) | ||||
0.442192 | + | 0.896920i | \(0.354201\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 417108. | 2.94106 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −78191.8 | −0.528076 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 82302.2 | 0.532775 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 469456. | 2.91495 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −101396. | −0.604309 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 653968. | 3.74353 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −294183. | −1.61849 | −0.809243 | − | 0.587475i | \(-0.800122\pi\) | ||||
−0.809243 | + | 0.587475i | \(0.800122\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −334580. | −1.77021 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 184270. | 0.938160 | 0.469080 | − | 0.883156i | \(-0.344586\pi\) | ||||
0.469080 | + | 0.883156i | \(0.344586\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −281048. | −1.37769 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 114831. | 0.542283 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −133573. | −0.608021 | −0.304011 | − | 0.952669i | \(-0.598326\pi\) | ||||
−0.304011 | + | 0.952669i | \(0.598326\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −137075. | −0.601757 | −0.300879 | − | 0.953662i | \(-0.597280\pi\) | ||||
−0.300879 | + | 0.953662i | \(0.597280\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 254819. | 1.07941 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −321411. | −1.31438 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −208440. | −0.823306 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −425420. | −1.62377 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −12315.5 | −0.0454450 | −0.0227225 | − | 0.999742i | \(-0.507233\pi\) | ||||
−0.0227225 | + | 0.999742i | \(0.507233\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −278499. | −0.993987 | −0.496993 | − | 0.867754i | \(-0.665563\pi\) | ||||
−0.496993 | + | 0.867754i | \(0.665563\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 82455.5 | 0.284768 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 578145. | 1.93289 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −373812. | −1.21033 | −0.605165 | − | 0.796100i | \(-0.706893\pi\) | ||||
−0.605165 | + | 0.796100i | \(0.706893\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 128926. | 0.404434 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 728827. | 2.21595 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −283288. | −0.835138 | −0.417569 | − | 0.908645i | \(-0.637118\pi\) | ||||
−0.417569 | + | 0.908645i | \(0.637118\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −1.82993e6 | −5.23269 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −285390. | −0.791857 | −0.395929 | − | 0.918281i | \(-0.629577\pi\) | ||||
−0.395929 | + | 0.918281i | \(0.629577\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −207448. | −0.558718 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −281571. | −0.736373 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −667502. | −1.69565 | −0.847827 | − | 0.530272i | \(-0.822090\pi\) | ||||
−0.847827 | + | 0.530272i | \(0.822090\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.74524e6 | 4.30785 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 782445. | 1.87724 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 496895. | 1.15913 | 0.579564 | − | 0.814926i | \(-0.303223\pi\) | ||||
0.579564 | + | 0.814926i | \(0.303223\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −472766. | −1.07263 | −0.536315 | − | 0.844018i | \(-0.680184\pi\) | ||||
−0.536315 | + | 0.844018i | \(0.680184\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −452354. | −0.998507 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 1.20256e6 | 2.58331 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 338938. | 0.708787 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 200649. | 0.408585 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 334336. | 0.663131 | 0.331565 | − | 0.943432i | \(-0.392423\pi\) | ||||
0.331565 | + | 0.943432i | \(0.392423\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 396036. | 0.765318 | 0.382659 | − | 0.923890i | \(-0.375008\pi\) | ||||
0.382659 | + | 0.923890i | \(0.375008\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 932838. | 1.75679 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −726938. | −1.33454 | −0.667270 | − | 0.744816i | \(-0.732537\pi\) | ||||
−0.667270 | + | 0.744816i | \(0.732537\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −504159. | −0.902474 | −0.451237 | − | 0.892404i | \(-0.649017\pi\) | ||||
−0.451237 | + | 0.892404i | \(0.649017\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −256906. | −0.448523 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −364215. | −0.620322 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 535739. | 0.890367 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 730184. | 1.18442 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −1.15741e6 | −1.83283 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −271940. | −0.420502 | −0.210251 | − | 0.977647i | \(-0.567428\pi\) | ||||
−0.210251 | + | 0.977647i | \(0.567428\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 316364. | 0.477791 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 1.76779e6 | 2.60817 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 1.01021e6 | 1.45634 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 271568. | 0.382620 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −172779. | −0.237964 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −1.08792e6 | −1.46499 | −0.732496 | − | 0.680771i | \(-0.761645\pi\) | ||||
−0.732496 | + | 0.680771i | \(0.761645\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1.74849e6 | 2.30254 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −100002. | −0.128809 | −0.0644043 | − | 0.997924i | \(-0.520515\pi\) | ||||
−0.0644043 | + | 0.997924i | \(0.520515\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 1.11277e6 | 1.40223 | 0.701113 | − | 0.713050i | \(-0.252687\pi\) | ||||
0.701113 | + | 0.713050i | \(0.252687\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −3.19750e6 | −3.94258 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1.14661e6 | 1.38365 | 0.691827 | − | 0.722064i | \(-0.256806\pi\) | ||||
0.691827 | + | 0.722064i | \(0.256806\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −1.34637e6 | −1.59036 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 809069. | 0.935652 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −1.41917e6 | −1.60709 | −0.803545 | − | 0.595244i | \(-0.797055\pi\) | ||||
−0.803545 | + | 0.595244i | \(0.797055\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 259371. | 0.287659 | 0.143830 | − | 0.989602i | \(-0.454058\pi\) | ||||
0.143830 | + | 0.989602i | \(0.454058\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.18137e6 | 1.28342 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 2.24776e6 | 2.39240 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 590011. | 0.615343 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2.05139e6 | 2.09677 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −1.22005e6 | −1.22234 | −0.611170 | − | 0.791499i | \(-0.709301\pi\) | ||||
−0.611170 | + | 0.791499i | \(0.709301\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.00146e6 | 2.94803 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −983704. | −0.947358 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −66049.0 | −0.0623783 | ||||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.10127e6 | 1.94640 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −364893. | −0.331562 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 744297. | 0.663525 | 0.331762 | − | 0.943363i | \(-0.392357\pi\) | ||||
0.331762 | + | 0.943363i | \(0.392357\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −681197. | −0.595879 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1.72039e6 | −1.47689 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −1.09166e6 | −0.919825 | −0.459913 | − | 0.887964i | \(-0.652119\pi\) | ||||
−0.459913 | + | 0.887964i | \(0.652119\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −276500. | −0.228703 | −0.114351 | − | 0.993440i | \(-0.536479\pi\) | ||||
−0.114351 | + | 0.993440i | \(0.536479\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1.62998e6 | 1.32366 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 7.18727e6 | 5.73102 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 292738. | 0.229234 | 0.114617 | − | 0.993410i | \(-0.463436\pi\) | ||||
0.114617 | + | 0.993410i | \(0.463436\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 1.01209e6 | 0.778414 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 2.25276e6 | 1.70196 | 0.850980 | − | 0.525199i | \(-0.176009\pi\) | ||||
0.850980 | + | 0.525199i | \(0.176009\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −472045. | −0.350362 | −0.175181 | − | 0.984536i | \(-0.556051\pi\) | ||||
−0.175181 | + | 0.984536i | \(0.556051\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 3.35918e6 | 2.44975 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 936116. | 0.670849 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1.23766e6 | −0.871677 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 3.33054e6 | 2.30559 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 273462. | 0.186092 | 0.0930460 | − | 0.995662i | \(-0.470340\pi\) | ||||
0.0930460 | + | 0.995662i | \(0.470340\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −4.13414e6 | −2.76586 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 826313. | 0.543568 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1.53004e6 | −0.989751 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.08892e6 | 1.96513 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.40461e6 | −1.50466 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 2.39007e6 | 1.47116 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 526185. | 0.318634 | 0.159317 | − | 0.987227i | \(-0.449071\pi\) | ||||
0.159317 | + | 0.987227i | \(0.449071\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 2.80312e6 | 1.67011 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.18866e6 | 0.696877 | 0.348438 | − | 0.937332i | \(-0.386712\pi\) | ||||
0.348438 | + | 0.937332i | \(0.386712\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.12023e6 | −0.646315 | −0.323158 | − | 0.946345i | \(-0.604744\pi\) | ||||
−0.323158 | + | 0.946345i | \(0.604744\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 4.11000e6 | 2.33381 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 446448. | 0.249530 | 0.124765 | − | 0.992186i | \(-0.460182\pi\) | ||||
0.124765 | + | 0.992186i | \(0.460182\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1.49991e6 | −0.825257 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −3.27060e6 | −1.77159 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −622183. | −0.331827 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.66383e6 | −1.92410 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 571589. | 0.295607 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2.35256e6 | −1.19826 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 148961. | 0.0747314 | 0.0373657 | − | 0.999302i | \(-0.488103\pi\) | ||||
0.0373657 | + | 0.999302i | \(0.488103\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 2.10518e6 | 1.04035 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 1.35740e6 | 0.660837 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.86279e6 | 0.893489 | 0.446744 | − | 0.894662i | \(-0.352583\pi\) | ||||
0.446744 | + | 0.894662i | \(0.352583\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −2.50707e6 | −1.18486 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 4.16027e6 | 1.93747 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 686976. | 0.315287 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −8.71119e6 | −3.94030 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −1.36567e6 | −0.608866 | −0.304433 | − | 0.952534i | \(-0.598467\pi\) | ||||
−0.304433 | + | 0.952534i | \(0.598467\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −1.35367e6 | −0.594906 | −0.297453 | − | 0.954737i | \(-0.596137\pi\) | ||||
−0.297453 | + | 0.954737i | \(0.596137\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −421227. | −0.182494 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 3.73757e6 | 1.59644 | 0.798219 | − | 0.602367i | \(-0.205776\pi\) | ||||
0.798219 | + | 0.602367i | \(0.205776\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −1.67155e6 | −0.703960 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −1.71886e6 | −0.713789 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −308057. | −0.126152 | −0.0630760 | − | 0.998009i | \(-0.520091\pi\) | ||||
−0.0630760 | + | 0.998009i | \(0.520091\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −351452. | −0.141938 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −9.80447e6 | −3.90533 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1.43486e6 | −0.563739 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −4.15689e6 | −1.61103 | −0.805515 | − | 0.592575i | \(-0.798111\pi\) | ||||
−0.805515 | + | 0.592575i | \(0.798111\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 937859. | 0.358568 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1.19028e6 | −0.448966 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 164576. | 0.0612484 | 0.0306242 | − | 0.999531i | \(-0.490250\pi\) | ||||
0.0306242 | + | 0.999531i | \(0.490250\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −1.36580e7 | −5.01542 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 764605. | 0.277066 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.03093e6 | 0.368663 | 0.184332 | − | 0.982864i | \(-0.440988\pi\) | ||||
0.184332 | + | 0.982864i | \(0.440988\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 6.14394e6 | 2.16838 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 3.69550e6 | 1.28729 | 0.643645 | − | 0.765324i | \(-0.277421\pi\) | ||||
0.643645 | + | 0.765324i | \(0.277421\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 1.68944e7 | 5.80885 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 3.09468e6 | 1.05036 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −3.08466e6 | −1.03356 | −0.516778 | − | 0.856120i | \(-0.672869\pi\) | ||||
−0.516778 | + | 0.856120i | \(0.672869\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.61348e6 | 0.533729 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −3.84844e6 | −1.25691 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.27481e6 | −1.37856 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5.00594e6 | 1.59408 | 0.797039 | − | 0.603928i | \(-0.206399\pi\) | ||||
0.797039 | + | 0.603928i | \(0.206399\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 5.86961e6 | 1.84577 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1.38736e6 | 0.430853 | 0.215426 | − | 0.976520i | \(-0.430886\pi\) | ||||
0.215426 | + | 0.976520i | \(0.430886\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −2.12077e6 | −0.650474 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −7.57801e6 | −2.29571 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.65347e6 | 2.58943 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 5.77382e6 | 1.70669 | 0.853346 | − | 0.521346i | \(-0.174570\pi\) | ||||
0.853346 | + | 0.521346i | \(0.174570\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 2.78965e6 | 0.814600 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −7.22373e6 | −2.08395 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.08388e7 | −3.08930 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 2.86278e6 | 0.806209 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3.75522e6 | 1.04496 | 0.522480 | − | 0.852651i | \(-0.325007\pi\) | ||||
0.522480 | + | 0.852651i | \(0.325007\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −1.91071e6 | −0.525398 | −0.262699 | − | 0.964878i | \(-0.584613\pi\) | ||||
−0.262699 | + | 0.964878i | \(0.584613\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2.35694e6 | −0.640468 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 3.86362e6 | 1.03758 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.17625e6 | 1.10845 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 6.71259e6 | 1.76095 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −1.96783e6 | −0.510263 | −0.255131 | − | 0.966906i | \(-0.582119\pi\) | ||||
−0.255131 | + | 0.966906i | \(0.582119\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1.76747e6 | 0.453034 | 0.226517 | − | 0.974007i | \(-0.427266\pi\) | ||||
0.226517 | + | 0.974007i | \(0.427266\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 4.35322e6 | 1.10303 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.50974e6 | −1.38015 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.43488e6 | −1.84125 | −0.920625 | − | 0.390449i | \(-0.872320\pi\) | ||||
−0.920625 | + | 0.390449i | \(0.872320\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.93490e6 | 0.963468 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.32537e6 | 1.28926 | 0.644630 | − | 0.764495i | \(-0.277011\pi\) | ||||
0.644630 | + | 0.764495i | \(0.277011\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9.08990e6 | 2.17600 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 257206. | 0.0608852 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −1.98961e6 | −0.465749 | −0.232875 | − | 0.972507i | \(-0.574813\pi\) | ||||
−0.232875 | + | 0.972507i | \(0.574813\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 3.85512e6 | 0.892476 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 5.81637e6 | 1.33170 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −8.61219e6 | −1.95023 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 90415.6 | 0.0202513 | 0.0101257 | − | 0.999949i | \(-0.496777\pi\) | ||||
0.0101257 | + | 0.999949i | \(0.496777\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 444196. | 0.0984109 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −6.87067e6 | −1.50573 | −0.752865 | − | 0.658175i | \(-0.771329\pi\) | ||||
−0.752865 | + | 0.658175i | \(0.771329\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −808881. | −0.175361 | −0.0876804 | − | 0.996149i | \(-0.527945\pi\) | ||||
−0.0876804 | + | 0.996149i | \(0.527945\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −1.20744e7 | −2.58961 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −5.92999e6 | −1.25824 | −0.629118 | − | 0.777310i | \(-0.716584\pi\) | ||||
−0.629118 | + | 0.777310i | \(0.716584\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 2.37182e6 | 0.497910 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.80696e6 | 1.62155 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 1.27208e7 | 2.61434 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.31936e7 | −2.68305 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.19250e6 | −0.239972 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.96847e6 | −1.38771 | −0.693855 | − | 0.720115i | \(-0.744089\pi\) | ||||
−0.693855 | + | 0.720115i | \(0.744089\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.41125e6 | −0.869358 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −1.52214e7 | −2.96883 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −1.75973e7 | −3.39697 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 3.42851e6 | 0.655062 | 0.327531 | − | 0.944840i | \(-0.393783\pi\) | ||||
0.327531 | + | 0.944840i | \(0.393783\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 5.91639e6 | 1.11888 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 5.09346e6 | 0.953474 | 0.476737 | − | 0.879046i | \(-0.341819\pi\) | ||||
0.476737 | + | 0.879046i | \(0.341819\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −806298. | −0.149410 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.69258e7 | 3.10483 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −2.92075e6 | −0.530401 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.61877e6 | −0.470811 | −0.235405 | − | 0.971897i | \(-0.575642\pi\) | ||||
−0.235405 | + | 0.971897i | \(0.575642\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 5.96029e6 | 1.06090 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −7.94806e6 | −1.40069 | −0.700344 | − | 0.713806i | \(-0.746970\pi\) | ||||
−0.700344 | + | 0.713806i | \(0.746970\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.27051e7 | 2.21691 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 4.33250e6 | 0.748547 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 6.20695e6 | 1.06190 | 0.530950 | − | 0.847403i | \(-0.321835\pi\) | ||||
0.530950 | + | 0.847403i | \(0.321835\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −2.50718e6 | −0.424750 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −1.51685e6 | −0.254478 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −1.48106e7 | −2.46068 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.68832e6 | −1.59412 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.39406e7 | 2.27176 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −9.62731e6 | −1.55385 | −0.776927 | − | 0.629590i | \(-0.783223\pi\) | ||||
−0.776927 | + | 0.629590i | \(0.783223\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 5.34167e6 | 0.853932 | 0.426966 | − | 0.904268i | \(-0.359582\pi\) | ||||
0.426966 | + | 0.904268i | \(0.359582\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −3.64489e7 | −5.77147 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 2.23641e6 | 0.350772 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 7.85179e6 | 1.21991 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −7.23719e6 | −1.11387 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −1.96521e6 | −0.299634 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.72806e7 | 2.61020 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −1.03775e7 | −1.55295 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 1.61746e7 | 2.39807 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 72038.5 | 0.0105821 | 0.00529105 | − | 0.999986i | \(-0.498316\pi\) | ||||
0.00529105 | + | 0.999986i | \(0.498316\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 9.87359e6 | 1.43706 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3.02006e6 | −0.435536 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2.82127e6 | −0.403159 | −0.201579 | − | 0.979472i | \(-0.564607\pi\) | ||||
−0.201579 | + | 0.979472i | \(0.564607\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 4.18403e6 | 0.592467 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2.75337e6 | 0.386354 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7.46952e6 | −1.03868 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2.51151e7 | −3.46101 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 6.16618e6 | 0.842128 | 0.421064 | − | 0.907031i | \(-0.361657\pi\) | ||||
0.421064 | + | 0.907031i | \(0.361657\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −6.48466e6 | −0.877723 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −7.07863e6 | −0.949602 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −6.58342e6 | −0.875348 | −0.437674 | − | 0.899134i | \(-0.644198\pi\) | ||||
−0.437674 | + | 0.899134i | \(0.644198\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.32464e7 | 1.74573 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −1.32413e7 | −1.72971 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 1.35465e7 | 1.75407 | 0.877033 | − | 0.480430i | \(-0.159519\pi\) | ||||
0.877033 | + | 0.480430i | \(0.159519\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7.02418e6 | 0.901583 | 0.450791 | − | 0.892629i | \(-0.351142\pi\) | ||||
0.450791 | + | 0.892629i | \(0.351142\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −6.98251e6 | −0.888434 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 3.42142e7 | 4.31556 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −313473. | −0.0391977 | −0.0195988 | − | 0.999808i | \(-0.506239\pi\) | ||||
−0.0195988 | + | 0.999808i | \(0.506239\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −8.27112e6 | −1.02534 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −1.89389e7 | −2.32764 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.90181e6 | −0.597290 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −8.62823e6 | −1.04239 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −2.05217e6 | −0.245820 | −0.122910 | − | 0.992418i | \(-0.539223\pi\) | ||||
−0.122910 | + | 0.992418i | \(0.539223\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.63695e6 | −0.907051 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.51819e7 | 1.78796 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 2.52449e6 | 0.294806 | 0.147403 | − | 0.989076i | \(-0.452909\pi\) | ||||
0.147403 | + | 0.989076i | \(0.452909\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 9.08181e6 | 1.05167 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1.05292e7 | 1.20910 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.50781e7 | 1.71704 | 0.858520 | − | 0.512780i | \(-0.171384\pi\) | ||||
0.858520 | + | 0.512780i | \(0.171384\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −7.61765e6 | −0.860271 | −0.430135 | − | 0.902764i | \(-0.641534\pi\) | ||||
−0.430135 | + | 0.902764i | \(0.641534\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 2.37624e6 | 0.266132 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 5.18031e7 | 5.75396 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 1.39216e7 | 1.53362 | 0.766811 | − | 0.641873i | \(-0.221842\pi\) | ||||
0.766811 | + | 0.641873i | \(0.221842\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 7.60653e6 | 0.831081 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 4.93878e6 | 0.535201 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −1.18835e7 | −1.27730 | −0.638651 | − | 0.769496i | \(-0.720507\pi\) | ||||
−0.638651 | + | 0.769496i | \(0.720507\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.11888e7 | −1.19287 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 7.25035e6 | 0.766737 | 0.383368 | − | 0.923596i | \(-0.374764\pi\) | ||||
0.383368 | + | 0.923596i | \(0.374764\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.28254e6 | 0.344337 | 0.172169 | − | 0.985067i | \(-0.444923\pi\) | ||||
0.172169 | + | 0.985067i | \(0.444923\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.93358e6 | 0.409316 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 1.58831e7 | 1.63951 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.38776e7 | 4.49307 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 2.41723e7 | 2.45555 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 4.65179e6 | 0.468806 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2.91300e6 | −0.291251 | −0.145626 | − | 0.989340i | \(-0.546519\pi\) | ||||
−0.145626 | + | 0.989340i | \(0.546519\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 5.67940e6 | 0.563370 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.24623e7 | −3.19481 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −8.24528e6 | −0.805113 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −2.92619e6 | −0.283499 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −1.40125e7 | −1.34701 | −0.673503 | − | 0.739184i | \(-0.735211\pi\) | ||||
−0.673503 | + | 0.739184i | \(0.735211\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −1.03234e7 | −0.984677 | −0.492339 | − | 0.870404i | \(-0.663858\pi\) | ||||
−0.492339 | + | 0.870404i | \(0.663858\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −3.69199e7 | −3.49431 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1.54764e7 | 1.45348 | 0.726739 | − | 0.686913i | \(-0.241035\pi\) | ||||
0.726739 | + | 0.686913i | \(0.241035\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −2.97488e7 | −2.77241 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −2.10980e7 | −1.95115 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 1.12287e6 | 0.103049 | 0.0515246 | − | 0.998672i | \(-0.483592\pi\) | ||||
0.0515246 | + | 0.998672i | \(0.483592\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.03337e7 | 1.85188 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −2.51185e6 | −0.227029 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −1.29384e7 | −1.16056 | −0.580281 | − | 0.814416i | \(-0.697057\pi\) | ||||
−0.580281 | + | 0.814416i | \(0.697057\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 4.99794e6 | 0.444926 | 0.222463 | − | 0.974941i | \(-0.428590\pi\) | ||||
0.222463 | + | 0.974941i | \(0.428590\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 3.60845e6 | 0.318813 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −3.10128e7 | −2.71948 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −7.14017e6 | −0.621432 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.27210e7 | 1.96273 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1.71987e7 | 1.47465 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 8.08858e6 | 0.688391 | 0.344195 | − | 0.938898i | \(-0.388152\pi\) | ||||
0.344195 | + | 0.938898i | \(0.388152\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 9.41931e6 | 0.795718 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −4.39938e6 | −0.368909 | −0.184455 | − | 0.982841i | \(-0.559052\pi\) | ||||
−0.184455 | + | 0.982841i | \(0.559052\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −3.07483e7 | −2.55945 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 2.08852e6 | 0.172572 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 1.49006e7 | 1.22223 | 0.611115 | − | 0.791542i | \(-0.290721\pi\) | ||||
0.611115 | + | 0.791542i | \(0.290721\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1.47394e7 | −1.20020 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −2.32400e7 | −1.87864 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 2.49878e6 | 0.200530 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.55047e6 | 0.203200 | 0.101600 | − | 0.994825i | \(-0.467604\pi\) | ||||
0.101600 | + | 0.994825i | \(0.467604\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 2.95751e7 | 2.33934 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −1.51258e7 | −1.18784 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 2.07237e6 | 0.161579 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −2.39467e7 | −1.85376 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 1.23849e7 | 0.951910 | 0.475955 | − | 0.879470i | \(-0.342102\pi\) | ||||
0.475955 | + | 0.879470i | \(0.342102\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1.58851e7 | −1.21227 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 2.81186e7 | 2.13069 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 2.22000e7 | 1.67034 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.83655e6 | −0.436055 | −0.218027 | − | 0.975943i | \(-0.569962\pi\) | ||||
−0.218027 | + | 0.975943i | \(0.569962\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −7.48344e6 | −0.555172 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.98045e7 | 1.45895 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −3.54668e7 | −2.59452 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 2.96390e7 | 2.15311 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −1.07585e7 | −0.776125 | −0.388062 | − | 0.921633i | \(-0.626855\pi\) | ||||
−0.388062 | + | 0.921633i | \(0.626855\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −2.58791e7 | −1.85400 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −5.41689e6 | −0.385393 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −1.70978e7 | −1.20808 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −4.80788e6 | −0.337378 | −0.168689 | − | 0.985669i | \(-0.553953\pi\) | ||||
−0.168689 | + | 0.985669i | \(0.553953\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −7.98475e6 | −0.556471 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 6.83826e6 | 0.473317 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 1.64981e7 | 1.13416 | 0.567078 | − | 0.823664i | \(-0.308074\pi\) | ||||
0.567078 | + | 0.823664i | \(0.308074\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −4.69439e7 | −3.20524 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 9.76767e6 | 0.662403 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.77693e7 | 1.87048 | 0.935242 | − | 0.354008i | \(-0.115182\pi\) | ||||
0.935242 | + | 0.354008i | \(0.115182\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −1.23222e7 | −0.824410 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 197982. | 0.0131569 | 0.00657844 | − | 0.999978i | \(-0.497906\pi\) | ||||
0.00657844 | + | 0.999978i | \(0.497906\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.35898e6 | −0.0897060 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −1.89742e7 | −1.24412 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 3.01950e7 | 1.96666 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 1.83046e7 | 1.18430 | 0.592148 | − | 0.805829i | \(-0.298280\pi\) | ||||
0.592148 | + | 0.805829i | \(0.298280\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 2.54804e7 | 1.63764 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.07315e7 | −1.96208 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 1.65525e7 | 1.04984 | 0.524921 | − | 0.851151i | \(-0.324095\pi\) | ||||
0.524921 | + | 0.851151i | \(0.324095\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −6.26847e7 | −3.94964 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 2.36177e7 | 1.47835 | 0.739173 | − | 0.673516i | \(-0.235217\pi\) | ||||
0.739173 | + | 0.673516i | \(0.235217\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5.27706e6 | −0.328156 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.09872e6 | 0.562117 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1.51650e7 | 0.930792 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.31858e7 | −0.804061 | −0.402031 | − | 0.915626i | \(-0.631696\pi\) | ||||
−0.402031 | + | 0.915626i | \(0.631696\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 1.37942e6 | 0.0835717 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1.33093e7 | 0.801133 | 0.400567 | − | 0.916268i | \(-0.368813\pi\) | ||||
0.400567 | + | 0.916268i | \(0.368813\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4.74237e7 | 2.83623 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −4.38845e7 | −2.60770 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −7.07679e6 | −0.417823 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −1.20283e7 | −0.705628 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −1.96572e6 | −0.114582 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −4.12490e7 | −2.38913 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 2.07453e7 | 1.19394 | 0.596970 | − | 0.802264i | \(-0.296371\pi\) | ||||
0.596970 | + | 0.802264i | \(0.296371\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −1.55445e7 | −0.888961 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.31459e7 | 1.31532 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8.76731e6 | −0.495089 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 1.42266e7 | 0.798332 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −2.62040e7 | −1.46124 | −0.730621 | − | 0.682783i | \(-0.760769\pi\) | ||||
−0.730621 | + | 0.682783i | \(0.760769\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −5.20809e6 | −0.288610 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.59127e7 | 0.876319 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −1.03251e7 | −0.565074 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 8.04239e7 | 4.37417 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 2.27990e7 | 1.23234 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 2.23194e7 | 1.19898 | 0.599488 | − | 0.800383i | \(-0.295371\pi\) | ||||
0.599488 | + | 0.800383i | \(0.295371\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −2.22624e7 | −1.18856 | −0.594279 | − | 0.804259i | \(-0.702562\pi\) | ||||
−0.594279 | + | 0.804259i | \(0.702562\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 5.77463e6 | 0.306406 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −3.12599e7 | −1.64852 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −2.33515e7 | −1.22394 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1.50764e7 | −0.785395 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1.17866e7 | −0.610280 | −0.305140 | − | 0.952307i | \(-0.598703\pi\) | ||||
−0.305140 | + | 0.952307i | \(0.598703\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −1.67547e7 | −0.862257 | −0.431129 | − | 0.902291i | \(-0.641884\pi\) | ||||
−0.431129 | + | 0.902291i | \(0.641884\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −1.50104e8 | −7.67818 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 3.24872e6 | 0.165177 | 0.0825883 | − | 0.996584i | \(-0.473681\pi\) | ||||
0.0825883 | + | 0.996584i | \(0.473681\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −3.08883e7 | −1.56102 | −0.780509 | − | 0.625144i | \(-0.785040\pi\) | ||||
−0.780509 | + | 0.625144i | \(0.785040\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −6.11376e6 | −0.307118 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 8.69489e6 | 0.434162 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −3.14919e7 | −1.56308 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 5.45226e6 | 0.269006 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2.09150e7 | −1.02578 | −0.512888 | − | 0.858455i | \(-0.671425\pi\) | ||||
−0.512888 | + | 0.858455i | \(0.671425\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −1.69430e7 | −0.826039 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −4.70483e7 | −2.28021 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −2.28913e7 | −1.10288 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 9.05173e7 | 4.33534 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 9.85854e6 | 0.469400 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 4.11939e7 | 1.94988 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.67213e7 | 0.786860 | 0.393430 | − | 0.919355i | \(-0.371288\pi\) | ||||
0.393430 | + | 0.919355i | \(0.371288\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −3.10706e7 | −1.45356 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 2.68169e7 | 1.24726 | 0.623629 | − | 0.781721i | \(-0.285658\pi\) | ||||
0.623629 | + | 0.781721i | \(0.285658\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3.05573e7 | −1.41297 | −0.706483 | − | 0.707730i | \(-0.749719\pi\) | ||||
−0.706483 | + | 0.707730i | \(0.749719\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −1.95505e7 | −0.898774 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −2.26266e7 | −1.03417 | −0.517085 | − | 0.855934i | \(-0.672983\pi\) | ||||
−0.517085 | + | 0.855934i | \(0.672983\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −7.36569e7 | −3.34713 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 2.58481e7 | 1.16783 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −3.07611e7 | −1.38182 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −4.97923e6 | −0.222391 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.08056e7 | −1.36803 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 1.26094e8 | 5.56767 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −4.12251e6 | −0.180993 | −0.0904967 | − | 0.995897i | \(-0.528845\pi\) | ||||
−0.0904967 | + | 0.995897i | \(0.528845\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.71118e6 | −0.249318 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −2.64021e7 | −1.14604 | −0.573018 | − | 0.819543i | \(-0.694228\pi\) | ||||
−0.573018 | + | 0.819543i | \(0.694228\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 1.31956e7 | 0.569544 | 0.284772 | − | 0.958595i | \(-0.408082\pi\) | ||||
0.284772 | + | 0.958595i | \(0.408082\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.63405e7 | 3.70558 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 1.11848e7 | 0.477331 | 0.238666 | − | 0.971102i | \(-0.423290\pi\) | ||||
0.238666 | + | 0.971102i | \(0.423290\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −5.67224e7 | −2.40713 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.45305e7 | −2.30115 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1.77847e7 | 0.746308 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 5.48308e7 | 2.28806 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 3.19546e7 | 1.32603 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −9.89685e6 | −0.408411 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −2.63504e6 | −0.108137 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −6.45114e7 | −2.63279 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −5.21683e7 | −2.11731 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 2.48247e7 | 1.00200 | 0.500998 | − | 0.865449i | \(-0.332967\pi\) | ||||
0.500998 | + | 0.865449i | \(0.332967\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 2.22413e7 | 0.892794 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −1.93536e7 | −0.772619 | −0.386310 | − | 0.922369i | \(-0.626250\pi\) | ||||
−0.386310 | + | 0.922369i | \(0.626250\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −7.79945e7 | −3.09662 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4.99160e7 | −1.97100 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 3.55297e7 | 1.39530 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −2.99383e7 | −1.16933 | −0.584666 | − | 0.811274i | \(-0.698774\pi\) | ||||
−0.584666 | + | 0.811274i | \(0.698774\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1.09892e7 | −0.426892 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.13161e6 | 0.236903 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 9.86425e7 | 3.79062 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −2.59273e7 | −0.990964 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 2.51196e7 | 0.954935 | 0.477467 | − | 0.878649i | \(-0.341555\pi\) | ||||
0.477467 | + | 0.878649i | \(0.341555\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −2.96915e7 | −1.12269 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2.48248e7 | −0.933645 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 3.74008e7 | 1.39911 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 3.83706e7 | 1.42774 | 0.713872 | − | 0.700277i | \(-0.246940\pi\) | ||||
0.713872 | + | 0.700277i | \(0.246940\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.33956e7 | 0.865905 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.09088e7 | −1.50606 | −0.753031 | − | 0.657985i | \(-0.771409\pi\) | ||||
−0.753031 | + | 0.657985i | \(0.771409\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1.83519e7 | 0.672050 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 2.21410e7 | 0.806525 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1.78552e7 | −0.646979 | −0.323489 | − | 0.946232i | \(-0.604856\pi\) | ||||
−0.323489 | + | 0.946232i | \(0.604856\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 5.26339e6 | 0.189714 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −9.32394e6 | −0.334309 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.42787e7 | −1.22262 | −0.611311 | − | 0.791391i | \(-0.709357\pi\) | ||||
−0.611311 | + | 0.791391i | \(0.709357\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 3.68929e7 | 1.30899 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 3.13253e7 | 1.10564 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −2.57547e7 | −0.904295 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −1.17850e6 | −0.0411643 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 3.02512e7 | 1.05118 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 4.37014e7 | 1.51070 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −9.90057e6 | −0.340482 | −0.170241 | − | 0.985402i | \(-0.554455\pi\) | ||||
−0.170241 | + | 0.985402i | \(0.554455\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 1.29941e7 | 0.444568 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 5.37946e7 | 1.83101 | 0.915504 | − | 0.402309i | \(-0.131792\pi\) | ||||
0.915504 | + | 0.402309i | \(0.131792\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −2.64299e7 | −0.894979 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 7.65181e7 | 2.57782 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.49602e7 | −0.836589 | −0.418295 | − | 0.908311i | \(-0.637372\pi\) | ||||
−0.418295 | + | 0.908311i | \(0.637372\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 6.54099e7 | 2.18116 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −5.28689e6 | −0.175399 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −5.73829e6 | −0.189408 | −0.0947041 | − | 0.995505i | \(-0.530190\pi\) | ||||
−0.0947041 | + | 0.995505i | \(0.530190\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.02154e7 | −2.63431 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 4.91325e7 | 1.60537 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 6.05562e7 | 1.96865 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 4.27533e6 | 0.138288 | 0.0691442 | − | 0.997607i | \(-0.477973\pi\) | ||||
0.0691442 | + | 0.997607i | \(0.477973\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −3.11101e6 | −0.100122 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5.56324e7 | −1.78144 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −1.38984e7 | −0.442818 | −0.221409 | − | 0.975181i | \(-0.571066\pi\) | ||||
−0.221409 | + | 0.975181i | \(0.571066\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1.13408e7 | 0.359527 |
(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 | 1028.6.a.b.1.11 | ✓ | 57 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1028.6.a.b.1.11 | ✓ | 57 | 1.1 | even | 1 | trivial |