Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [693,4,Mod(1,693)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(693, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0, 0]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("693.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 693 = 3^{2} \cdot 7 \cdot 11 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 693.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: | \(40.8883236340\) |
Analytic rank: | \(0\) |
Dimension: | \(8\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{8} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{8} - 2x^{7} - 43x^{6} + 57x^{5} + 560x^{4} - 439x^{3} - 2246x^{2} + 384x + 1056 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2} \) |
Twist minimal: | yes |
Fricke sign: | \(+1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(5.45684\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 693.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −4.45684 | −1.57573 | −0.787865 | − | 0.615848i | \(-0.788814\pi\) | ||||
−0.787865 | + | 0.615848i | \(0.788814\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 11.8634 | 1.48293 | ||||||||
\(5\) | 12.1911 | 1.09041 | 0.545203 | − | 0.838304i | \(-0.316452\pi\) | ||||
0.545203 | + | 0.838304i | \(0.316452\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 7.00000 | 0.377964 | ||||||||
\(8\) | −17.2186 | −0.760961 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −54.3338 | −1.71819 | ||||||||
\(11\) | 11.0000 | 0.301511 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −15.6475 | −0.333833 | −0.166917 | − | 0.985971i | \(-0.553381\pi\) | ||||
−0.166917 | + | 0.985971i | \(0.553381\pi\) | |||||||
\(14\) | −31.1979 | −0.595570 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −18.1668 | −0.283857 | ||||||||
\(17\) | 43.3250 | 0.618109 | 0.309055 | − | 0.951044i | \(-0.399987\pi\) | ||||
0.309055 | + | 0.951044i | \(0.399987\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 51.7758 | 0.625167 | 0.312584 | − | 0.949890i | \(-0.398806\pi\) | ||||
0.312584 | + | 0.949890i | \(0.398806\pi\) | |||||||
\(20\) | 144.628 | 1.61699 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −49.0252 | −0.475101 | ||||||||
\(23\) | 121.245 | 1.09919 | 0.549595 | − | 0.835431i | \(-0.314782\pi\) | ||||
0.549595 | + | 0.835431i | \(0.314782\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 23.6233 | 0.188986 | ||||||||
\(26\) | 69.7383 | 0.526031 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 83.0439 | 0.560493 | ||||||||
\(29\) | 187.274 | 1.19917 | 0.599586 | − | 0.800310i | \(-0.295332\pi\) | ||||
0.599586 | + | 0.800310i | \(0.295332\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 91.9030 | 0.532460 | 0.266230 | − | 0.963910i | \(-0.414222\pi\) | ||||
0.266230 | + | 0.963910i | \(0.414222\pi\) | |||||||
\(32\) | 218.715 | 1.20824 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | −193.093 | −0.973974 | ||||||||
\(35\) | 85.3378 | 0.412135 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −226.675 | −1.00717 | −0.503583 | − | 0.863947i | \(-0.667985\pi\) | ||||
−0.503583 | + | 0.863947i | \(0.667985\pi\) | |||||||
\(38\) | −230.756 | −0.985095 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −209.914 | −0.829757 | ||||||||
\(41\) | −11.2971 | −0.0430318 | −0.0215159 | − | 0.999769i | \(-0.506849\pi\) | ||||
−0.0215159 | + | 0.999769i | \(0.506849\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −98.0582 | −0.347761 | −0.173881 | − | 0.984767i | \(-0.555631\pi\) | ||||
−0.173881 | + | 0.984767i | \(0.555631\pi\) | |||||||
\(44\) | 130.497 | 0.447119 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −540.371 | −1.73203 | ||||||||
\(47\) | 186.239 | 0.577994 | 0.288997 | − | 0.957330i | \(-0.406678\pi\) | ||||
0.288997 | + | 0.957330i | \(0.406678\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 49.0000 | 0.142857 | ||||||||
\(50\) | −105.285 | −0.297791 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −185.632 | −0.495050 | ||||||||
\(53\) | 487.456 | 1.26334 | 0.631671 | − | 0.775236i | \(-0.282369\pi\) | ||||
0.631671 | + | 0.775236i | \(0.282369\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 134.102 | 0.328770 | ||||||||
\(56\) | −120.530 | −0.287616 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −834.652 | −1.88957 | ||||||||
\(59\) | −697.760 | −1.53967 | −0.769835 | − | 0.638243i | \(-0.779662\pi\) | ||||
−0.769835 | + | 0.638243i | \(0.779662\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 486.332 | 1.02079 | 0.510397 | − | 0.859939i | \(-0.329498\pi\) | ||||
0.510397 | + | 0.859939i | \(0.329498\pi\) | |||||||
\(62\) | −409.597 | −0.839013 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −829.444 | −1.62001 | ||||||||
\(65\) | −190.760 | −0.364014 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −436.739 | −0.796361 | −0.398181 | − | 0.917307i | \(-0.630358\pi\) | ||||
−0.398181 | + | 0.917307i | \(0.630358\pi\) | |||||||
\(68\) | 513.982 | 0.916610 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −380.337 | −0.649413 | ||||||||
\(71\) | −715.665 | −1.19625 | −0.598125 | − | 0.801403i | \(-0.704087\pi\) | ||||
−0.598125 | + | 0.801403i | \(0.704087\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −860.777 | −1.38009 | −0.690043 | − | 0.723768i | \(-0.742408\pi\) | ||||
−0.690043 | + | 0.723768i | \(0.742408\pi\) | |||||||
\(74\) | 1010.25 | 1.58702 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 614.237 | 0.927076 | ||||||||
\(77\) | 77.0000 | 0.113961 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 157.939 | 0.224930 | 0.112465 | − | 0.993656i | \(-0.464125\pi\) | ||||
0.112465 | + | 0.993656i | \(0.464125\pi\) | |||||||
\(80\) | −221.474 | −0.309519 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 50.3492 | 0.0678066 | ||||||||
\(83\) | 397.064 | 0.525102 | 0.262551 | − | 0.964918i | \(-0.415436\pi\) | ||||
0.262551 | + | 0.964918i | \(0.415436\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 528.180 | 0.673990 | ||||||||
\(86\) | 437.030 | 0.547978 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −189.404 | −0.229438 | ||||||||
\(89\) | −237.813 | −0.283238 | −0.141619 | − | 0.989921i | \(-0.545231\pi\) | ||||
−0.141619 | + | 0.989921i | \(0.545231\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −109.532 | −0.126177 | ||||||||
\(92\) | 1438.38 | 1.63002 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −830.036 | −0.910763 | ||||||||
\(95\) | 631.204 | 0.681686 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 590.116 | 0.617703 | 0.308851 | − | 0.951110i | \(-0.400055\pi\) | ||||
0.308851 | + | 0.951110i | \(0.400055\pi\) | |||||||
\(98\) | −218.385 | −0.225104 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 280.252 | 0.280252 | ||||||||
\(101\) | 858.491 | 0.845773 | 0.422886 | − | 0.906183i | \(-0.361017\pi\) | ||||
0.422886 | + | 0.906183i | \(0.361017\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 18.6313 | 0.0178233 | 0.00891164 | − | 0.999960i | \(-0.497163\pi\) | ||||
0.00891164 | + | 0.999960i | \(0.497163\pi\) | |||||||
\(104\) | 269.427 | 0.254034 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −2172.51 | −1.99069 | ||||||||
\(107\) | −202.961 | −0.183373 | −0.0916866 | − | 0.995788i | \(-0.529226\pi\) | ||||
−0.0916866 | + | 0.995788i | \(0.529226\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1023.62 | 0.899495 | 0.449748 | − | 0.893156i | \(-0.351514\pi\) | ||||
0.449748 | + | 0.893156i | \(0.351514\pi\) | |||||||
\(110\) | −597.672 | −0.518053 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −127.168 | −0.107288 | ||||||||
\(113\) | 1011.17 | 0.841792 | 0.420896 | − | 0.907109i | \(-0.361716\pi\) | ||||
0.420896 | + | 0.907109i | \(0.361716\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1478.11 | 1.19856 | ||||||||
\(116\) | 2221.71 | 1.77828 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 3109.80 | 2.42611 | ||||||||
\(119\) | 303.275 | 0.233623 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 121.000 | 0.0909091 | ||||||||
\(122\) | −2167.50 | −1.60850 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1090.28 | 0.789599 | ||||||||
\(125\) | −1235.90 | −0.884335 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 2232.29 | 1.55971 | 0.779855 | − | 0.625960i | \(-0.215293\pi\) | ||||
0.779855 | + | 0.625960i | \(0.215293\pi\) | |||||||
\(128\) | 1946.98 | 1.34445 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 850.188 | 0.573588 | ||||||||
\(131\) | −553.340 | −0.369050 | −0.184525 | − | 0.982828i | \(-0.559075\pi\) | ||||
−0.184525 | + | 0.982828i | \(0.559075\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 362.430 | 0.236291 | ||||||||
\(134\) | 1946.48 | 1.25485 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −745.995 | −0.470357 | ||||||||
\(137\) | 778.408 | 0.485430 | 0.242715 | − | 0.970098i | \(-0.421962\pi\) | ||||
0.242715 | + | 0.970098i | \(0.421962\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 890.735 | 0.543533 | 0.271767 | − | 0.962363i | \(-0.412392\pi\) | ||||
0.271767 | + | 0.962363i | \(0.412392\pi\) | |||||||
\(140\) | 1012.40 | 0.611166 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 3189.60 | 1.88497 | ||||||||
\(143\) | −172.122 | −0.100654 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 2283.08 | 1.30759 | ||||||||
\(146\) | 3836.34 | 2.17464 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −2689.14 | −1.49355 | ||||||||
\(149\) | −1810.56 | −0.995481 | −0.497740 | − | 0.867326i | \(-0.665837\pi\) | ||||
−0.497740 | + | 0.867326i | \(0.665837\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3043.06 | 1.64001 | 0.820003 | − | 0.572359i | \(-0.193972\pi\) | ||||
0.820003 | + | 0.572359i | \(0.193972\pi\) | |||||||
\(152\) | −891.505 | −0.475728 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −343.177 | −0.179571 | ||||||||
\(155\) | 1120.40 | 0.580598 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1299.44 | −0.660551 | −0.330276 | − | 0.943885i | \(-0.607142\pi\) | ||||
−0.330276 | + | 0.943885i | \(0.607142\pi\) | |||||||
\(158\) | −703.908 | −0.354430 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 2666.38 | 1.31748 | ||||||||
\(161\) | 848.717 | 0.415455 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1550.80 | −0.745202 | −0.372601 | − | 0.927992i | \(-0.621534\pi\) | ||||
−0.372601 | + | 0.927992i | \(0.621534\pi\) | |||||||
\(164\) | −134.022 | −0.0638130 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −1769.65 | −0.827420 | ||||||||
\(167\) | 1346.23 | 0.623799 | 0.311900 | − | 0.950115i | \(-0.399035\pi\) | ||||
0.311900 | + | 0.950115i | \(0.399035\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1952.16 | −0.888555 | ||||||||
\(170\) | −2354.01 | −1.06203 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −1163.30 | −0.515704 | ||||||||
\(173\) | 3058.10 | 1.34395 | 0.671975 | − | 0.740574i | \(-0.265446\pi\) | ||||
0.671975 | + | 0.740574i | \(0.265446\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 165.363 | 0.0714301 | ||||||||
\(176\) | −199.835 | −0.0855860 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 1059.90 | 0.446307 | ||||||||
\(179\) | 1139.10 | 0.475645 | 0.237822 | − | 0.971309i | \(-0.423566\pi\) | ||||
0.237822 | + | 0.971309i | \(0.423566\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3156.25 | 1.29615 | 0.648073 | − | 0.761578i | \(-0.275575\pi\) | ||||
0.648073 | + | 0.761578i | \(0.275575\pi\) | |||||||
\(182\) | 488.168 | 0.198821 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −2087.67 | −0.836441 | ||||||||
\(185\) | −2763.42 | −1.09822 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 476.575 | 0.186367 | ||||||||
\(188\) | 2209.43 | 0.857122 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2813.18 | −1.07415 | ||||||||
\(191\) | −2195.74 | −0.831822 | −0.415911 | − | 0.909405i | \(-0.636537\pi\) | ||||
−0.415911 | + | 0.909405i | \(0.636537\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1224.61 | −0.456733 | −0.228366 | − | 0.973575i | \(-0.573338\pi\) | ||||
−0.228366 | + | 0.973575i | \(0.573338\pi\) | |||||||
\(194\) | −2630.05 | −0.973333 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 581.307 | 0.211847 | ||||||||
\(197\) | 4502.49 | 1.62837 | 0.814186 | − | 0.580605i | \(-0.197184\pi\) | ||||
0.814186 | + | 0.580605i | \(0.197184\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 5332.05 | 1.89939 | 0.949696 | − | 0.313174i | \(-0.101392\pi\) | ||||
0.949696 | + | 0.313174i | \(0.101392\pi\) | |||||||
\(200\) | −406.759 | −0.143811 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −3826.15 | −1.33271 | ||||||||
\(203\) | 1310.92 | 0.453245 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −137.724 | −0.0469222 | ||||||||
\(206\) | −83.0367 | −0.0280847 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 284.265 | 0.0947607 | ||||||||
\(209\) | 569.533 | 0.188495 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1925.26 | −0.628152 | −0.314076 | − | 0.949398i | \(-0.601695\pi\) | ||||
−0.314076 | + | 0.949398i | \(0.601695\pi\) | |||||||
\(212\) | 5782.88 | 1.87344 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 904.562 | 0.288947 | ||||||||
\(215\) | −1195.44 | −0.379201 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 643.321 | 0.201251 | ||||||||
\(218\) | −4562.11 | −1.41736 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 1590.91 | 0.487541 | ||||||||
\(221\) | −677.927 | −0.206345 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1794.01 | 0.538724 | 0.269362 | − | 0.963039i | \(-0.413187\pi\) | ||||
0.269362 | + | 0.963039i | \(0.413187\pi\) | |||||||
\(224\) | 1531.01 | 0.456673 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4506.60 | −1.32644 | ||||||||
\(227\) | 2809.22 | 0.821385 | 0.410692 | − | 0.911774i | \(-0.365287\pi\) | ||||
0.410692 | + | 0.911774i | \(0.365287\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −2445.83 | −0.705785 | −0.352893 | − | 0.935664i | \(-0.614802\pi\) | ||||
−0.352893 | + | 0.935664i | \(0.614802\pi\) | |||||||
\(230\) | −6587.72 | −1.88861 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −3224.60 | −0.912524 | ||||||||
\(233\) | −3143.08 | −0.883735 | −0.441868 | − | 0.897080i | \(-0.645684\pi\) | ||||
−0.441868 | + | 0.897080i | \(0.645684\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 2270.46 | 0.630248 | ||||||||
\(236\) | −8277.81 | −2.28322 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −1351.65 | −0.368127 | ||||||||
\(239\) | −1011.71 | −0.273817 | −0.136909 | − | 0.990584i | \(-0.543717\pi\) | ||||
−0.136909 | + | 0.990584i | \(0.543717\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −2449.72 | −0.654773 | −0.327387 | − | 0.944890i | \(-0.606168\pi\) | ||||
−0.327387 | + | 0.944890i | \(0.606168\pi\) | |||||||
\(242\) | −539.277 | −0.143248 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5769.56 | 1.51376 | ||||||||
\(245\) | 597.365 | 0.155772 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −810.160 | −0.208701 | ||||||||
\(248\) | −1582.44 | −0.405181 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 5508.19 | 1.39347 | ||||||||
\(251\) | 2605.03 | 0.655092 | 0.327546 | − | 0.944835i | \(-0.393778\pi\) | ||||
0.327546 | + | 0.944835i | \(0.393778\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1333.70 | 0.331418 | ||||||||
\(254\) | −9948.93 | −2.45768 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −2041.80 | −0.498487 | ||||||||
\(257\) | −2323.64 | −0.563987 | −0.281994 | − | 0.959416i | \(-0.590996\pi\) | ||||
−0.281994 | + | 0.959416i | \(0.590996\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1586.73 | −0.380673 | ||||||||
\(260\) | −2263.07 | −0.539805 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 2466.15 | 0.581523 | ||||||||
\(263\) | −2382.09 | −0.558502 | −0.279251 | − | 0.960218i | \(-0.590086\pi\) | ||||
−0.279251 | + | 0.960218i | \(0.590086\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 5942.63 | 1.37756 | ||||||||
\(266\) | −1615.29 | −0.372331 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −5181.22 | −1.18095 | ||||||||
\(269\) | −4768.03 | −1.08071 | −0.540357 | − | 0.841436i | \(-0.681711\pi\) | ||||
−0.540357 | + | 0.841436i | \(0.681711\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6275.87 | −1.40676 | −0.703380 | − | 0.710814i | \(-0.748327\pi\) | ||||
−0.703380 | + | 0.710814i | \(0.748327\pi\) | |||||||
\(272\) | −787.078 | −0.175454 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3469.24 | −0.764906 | ||||||||
\(275\) | 259.856 | 0.0569815 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 1833.05 | 0.397607 | 0.198803 | − | 0.980039i | \(-0.436295\pi\) | ||||
0.198803 | + | 0.980039i | \(0.436295\pi\) | |||||||
\(278\) | −3969.86 | −0.856462 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1469.40 | −0.313619 | ||||||||
\(281\) | 7948.23 | 1.68737 | 0.843686 | − | 0.536837i | \(-0.180381\pi\) | ||||
0.843686 | + | 0.536837i | \(0.180381\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3141.50 | 0.659869 | 0.329935 | − | 0.944004i | \(-0.392973\pi\) | ||||
0.329935 | + | 0.944004i | \(0.392973\pi\) | |||||||
\(284\) | −8490.22 | −1.77395 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 767.121 | 0.158604 | ||||||||
\(287\) | −79.0795 | −0.0162645 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3035.94 | −0.617941 | ||||||||
\(290\) | −10175.3 | −2.06040 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −10211.7 | −2.04657 | ||||||||
\(293\) | 3083.66 | 0.614845 | 0.307422 | − | 0.951573i | \(-0.400534\pi\) | ||||
0.307422 | + | 0.951573i | \(0.400534\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −8506.47 | −1.67887 | ||||||||
\(296\) | 3903.02 | 0.766414 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 8069.36 | 1.56861 | ||||||||
\(299\) | −1897.18 | −0.366946 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −686.408 | −0.131441 | ||||||||
\(302\) | −13562.4 | −2.58421 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −940.601 | −0.177458 | ||||||||
\(305\) | 5928.93 | 1.11308 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 8216.45 | 1.52748 | 0.763742 | − | 0.645521i | \(-0.223360\pi\) | ||||
0.763742 | + | 0.645521i | \(0.223360\pi\) | |||||||
\(308\) | 913.482 | 0.168995 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −4993.44 | −0.914866 | ||||||||
\(311\) | 3241.70 | 0.591062 | 0.295531 | − | 0.955333i | \(-0.404503\pi\) | ||||
0.295531 | + | 0.955333i | \(0.404503\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −10645.0 | −1.92233 | −0.961167 | − | 0.275969i | \(-0.911001\pi\) | ||||
−0.961167 | + | 0.275969i | \(0.911001\pi\) | |||||||
\(314\) | 5791.39 | 1.04085 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1873.69 | 0.333555 | ||||||||
\(317\) | 741.966 | 0.131460 | 0.0657302 | − | 0.997837i | \(-0.479062\pi\) | ||||
0.0657302 | + | 0.997837i | \(0.479062\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 2060.02 | 0.361564 | ||||||||
\(320\) | −10111.8 | −1.76647 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −3782.59 | −0.654645 | ||||||||
\(323\) | 2243.19 | 0.386422 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −369.645 | −0.0630898 | ||||||||
\(326\) | 6911.66 | 1.17424 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 194.519 | 0.0327455 | ||||||||
\(329\) | 1303.67 | 0.218461 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 3842.77 | 0.638120 | 0.319060 | − | 0.947735i | \(-0.396633\pi\) | ||||
0.319060 | + | 0.947735i | \(0.396633\pi\) | |||||||
\(332\) | 4710.54 | 0.778688 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5999.93 | −0.982939 | ||||||||
\(335\) | −5324.34 | −0.868358 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1251.97 | −0.202371 | −0.101186 | − | 0.994868i | \(-0.532264\pi\) | ||||
−0.101186 | + | 0.994868i | \(0.532264\pi\) | |||||||
\(338\) | 8700.44 | 1.40012 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6266.02 | 0.999478 | ||||||||
\(341\) | 1010.93 | 0.160543 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 343.000 | 0.0539949 | ||||||||
\(344\) | 1688.42 | 0.264633 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −13629.5 | −2.11770 | ||||||||
\(347\) | 12167.3 | 1.88234 | 0.941172 | − | 0.337927i | \(-0.109726\pi\) | ||||
0.941172 | + | 0.337927i | \(0.109726\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2862.41 | −0.439029 | −0.219514 | − | 0.975609i | \(-0.570447\pi\) | ||||
−0.219514 | + | 0.975609i | \(0.570447\pi\) | |||||||
\(350\) | −736.996 | −0.112555 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 2405.87 | 0.364299 | ||||||||
\(353\) | 8633.06 | 1.30167 | 0.650837 | − | 0.759217i | \(-0.274418\pi\) | ||||
0.650837 | + | 0.759217i | \(0.274418\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −8724.75 | −1.30440 | ||||||||
\(356\) | −2821.28 | −0.420021 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5076.79 | −0.749488 | ||||||||
\(359\) | −1013.23 | −0.148958 | −0.0744791 | − | 0.997223i | \(-0.523729\pi\) | ||||
−0.0744791 | + | 0.997223i | \(0.523729\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4178.27 | −0.609166 | ||||||||
\(362\) | −14066.9 | −2.04238 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1299.43 | −0.187111 | ||||||||
\(365\) | −10493.8 | −1.50486 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5282.35 | 0.751325 | 0.375662 | − | 0.926757i | \(-0.377415\pi\) | ||||
0.375662 | + | 0.926757i | \(0.377415\pi\) | |||||||
\(368\) | −2202.64 | −0.312013 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 12316.1 | 1.73050 | ||||||||
\(371\) | 3412.19 | 0.477499 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −8770.95 | −1.21754 | −0.608770 | − | 0.793347i | \(-0.708337\pi\) | ||||
−0.608770 | + | 0.793347i | \(0.708337\pi\) | |||||||
\(374\) | −2124.02 | −0.293664 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3206.77 | −0.439831 | ||||||||
\(377\) | −2930.37 | −0.400323 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 8431.99 | 1.14280 | 0.571401 | − | 0.820671i | \(-0.306400\pi\) | ||||
0.571401 | + | 0.820671i | \(0.306400\pi\) | |||||||
\(380\) | 7488.23 | 1.01089 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 9786.04 | 1.31073 | ||||||||
\(383\) | 11598.9 | 1.54745 | 0.773727 | − | 0.633519i | \(-0.218390\pi\) | ||||
0.773727 | + | 0.633519i | \(0.218390\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 938.716 | 0.124263 | ||||||||
\(386\) | 5457.89 | 0.719688 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 7000.79 | 0.916008 | ||||||||
\(389\) | 1396.44 | 0.182011 | 0.0910053 | − | 0.995850i | \(-0.470992\pi\) | ||||
0.0910053 | + | 0.995850i | \(0.470992\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5252.95 | 0.679420 | ||||||||
\(392\) | −843.711 | −0.108709 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −20066.9 | −2.56587 | ||||||||
\(395\) | 1925.45 | 0.245266 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 5773.49 | 0.729882 | 0.364941 | − | 0.931031i | \(-0.381089\pi\) | ||||
0.364941 | + | 0.931031i | \(0.381089\pi\) | |||||||
\(398\) | −23764.1 | −2.99293 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −429.160 | −0.0536450 | ||||||||
\(401\) | −505.794 | −0.0629880 | −0.0314940 | − | 0.999504i | \(-0.510027\pi\) | ||||
−0.0314940 | + | 0.999504i | \(0.510027\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1438.05 | −0.177753 | ||||||||
\(404\) | 10184.6 | 1.25422 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −5842.57 | −0.714191 | ||||||||
\(407\) | −2493.43 | −0.303672 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1865.46 | 0.225528 | 0.112764 | − | 0.993622i | \(-0.464030\pi\) | ||||
0.112764 | + | 0.993622i | \(0.464030\pi\) | |||||||
\(410\) | 613.813 | 0.0739367 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 221.031 | 0.0264306 | ||||||||
\(413\) | −4884.32 | −0.581941 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4840.66 | 0.572575 | ||||||||
\(416\) | −3422.34 | −0.403351 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −2538.32 | −0.297017 | ||||||||
\(419\) | −7706.74 | −0.898566 | −0.449283 | − | 0.893390i | \(-0.648320\pi\) | ||||
−0.449283 | + | 0.893390i | \(0.648320\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −4534.79 | −0.524969 | −0.262485 | − | 0.964936i | \(-0.584542\pi\) | ||||
−0.262485 | + | 0.964936i | \(0.584542\pi\) | |||||||
\(422\) | 8580.56 | 0.989798 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −8393.29 | −0.961355 | ||||||||
\(425\) | 1023.48 | 0.116814 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 3404.33 | 0.385824 | ||||||||
\(428\) | −2407.80 | −0.271929 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 5327.88 | 0.597519 | ||||||||
\(431\) | 700.548 | 0.0782928 | 0.0391464 | − | 0.999233i | \(-0.487536\pi\) | ||||
0.0391464 | + | 0.999233i | \(0.487536\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 13305.9 | 1.47676 | 0.738382 | − | 0.674382i | \(-0.235590\pi\) | ||||
0.738382 | + | 0.674382i | \(0.235590\pi\) | |||||||
\(434\) | −2867.18 | −0.317117 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 12143.6 | 1.33389 | ||||||||
\(437\) | 6277.57 | 0.687178 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 992.131 | 0.107863 | 0.0539315 | − | 0.998545i | \(-0.482825\pi\) | ||||
0.0539315 | + | 0.998545i | \(0.482825\pi\) | |||||||
\(440\) | −2309.05 | −0.250181 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 3021.41 | 0.325145 | ||||||||
\(443\) | 7180.05 | 0.770055 | 0.385027 | − | 0.922905i | \(-0.374192\pi\) | ||||
0.385027 | + | 0.922905i | \(0.374192\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −2899.21 | −0.308844 | ||||||||
\(446\) | −7995.59 | −0.848884 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −5806.11 | −0.612305 | ||||||||
\(449\) | −17736.0 | −1.86417 | −0.932087 | − | 0.362236i | \(-0.882014\pi\) | ||||
−0.932087 | + | 0.362236i | \(0.882014\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −124.268 | −0.0129746 | ||||||||
\(452\) | 11995.9 | 1.24832 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −12520.2 | −1.29428 | ||||||||
\(455\) | −1335.32 | −0.137584 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5926.25 | −0.606604 | −0.303302 | − | 0.952894i | \(-0.598089\pi\) | ||||
−0.303302 | + | 0.952894i | \(0.598089\pi\) | |||||||
\(458\) | 10900.7 | 1.11213 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 17535.5 | 1.77738 | ||||||||
\(461\) | −11831.2 | −1.19531 | −0.597653 | − | 0.801755i | \(-0.703900\pi\) | ||||
−0.597653 | + | 0.801755i | \(0.703900\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2756.08 | 0.276643 | 0.138322 | − | 0.990387i | \(-0.455829\pi\) | ||||
0.138322 | + | 0.990387i | \(0.455829\pi\) | |||||||
\(464\) | −3402.18 | −0.340393 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 14008.2 | 1.39253 | ||||||||
\(467\) | −7795.11 | −0.772408 | −0.386204 | − | 0.922413i | \(-0.626214\pi\) | ||||
−0.386204 | + | 0.922413i | \(0.626214\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −3057.18 | −0.300996 | ||||||||
\(470\) | −10119.1 | −0.993101 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 12014.4 | 1.17163 | ||||||||
\(473\) | −1078.64 | −0.104854 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 1223.11 | 0.118148 | ||||||||
\(476\) | 3597.88 | 0.346446 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 4509.04 | 0.431462 | ||||||||
\(479\) | 13277.4 | 1.26651 | 0.633257 | − | 0.773942i | \(-0.281718\pi\) | ||||
0.633257 | + | 0.773942i | \(0.281718\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 3546.89 | 0.336226 | ||||||||
\(482\) | 10918.0 | 1.03175 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 1435.47 | 0.134811 | ||||||||
\(485\) | 7194.17 | 0.673547 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 10601.3 | 0.986429 | 0.493214 | − | 0.869908i | \(-0.335822\pi\) | ||||
0.493214 | + | 0.869908i | \(0.335822\pi\) | |||||||
\(488\) | −8373.95 | −0.776785 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −2662.36 | −0.245455 | ||||||||
\(491\) | −6095.15 | −0.560225 | −0.280112 | − | 0.959967i | \(-0.590372\pi\) | ||||
−0.280112 | + | 0.959967i | \(0.590372\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 8113.67 | 0.741220 | ||||||||
\(494\) | 3610.75 | 0.328857 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −1669.58 | −0.151142 | ||||||||
\(497\) | −5009.65 | −0.452140 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −18897.8 | −1.69535 | −0.847676 | − | 0.530515i | \(-0.821999\pi\) | ||||
−0.847676 | + | 0.530515i | \(0.821999\pi\) | |||||||
\(500\) | −14661.9 | −1.31140 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −11610.2 | −1.03225 | ||||||||
\(503\) | 12952.6 | 1.14817 | 0.574085 | − | 0.818796i | \(-0.305358\pi\) | ||||
0.574085 | + | 0.818796i | \(0.305358\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 10466.0 | 0.922236 | ||||||||
\(506\) | −5944.08 | −0.522226 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 26482.5 | 2.31294 | ||||||||
\(509\) | 13187.2 | 1.14835 | 0.574176 | − | 0.818732i | \(-0.305323\pi\) | ||||
0.574176 | + | 0.818732i | \(0.305323\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −6025.44 | −0.521624 | ||||||||
\(512\) | −6475.82 | −0.558971 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 10356.1 | 0.888691 | ||||||||
\(515\) | 227.136 | 0.0194346 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2048.63 | 0.174272 | ||||||||
\(518\) | 7071.78 | 0.599838 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 3284.62 | 0.277000 | ||||||||
\(521\) | 2254.72 | 0.189599 | 0.0947995 | − | 0.995496i | \(-0.469779\pi\) | ||||
0.0947995 | + | 0.995496i | \(0.469779\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10786.8 | 0.901859 | 0.450929 | − | 0.892560i | \(-0.351093\pi\) | ||||
0.450929 | + | 0.892560i | \(0.351093\pi\) | |||||||
\(524\) | −6564.50 | −0.547274 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 10616.6 | 0.880049 | ||||||||
\(527\) | 3981.70 | 0.329119 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2533.42 | 0.208220 | ||||||||
\(530\) | −26485.3 | −2.17066 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 4299.66 | 0.350402 | ||||||||
\(533\) | 176.771 | 0.0143655 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2474.32 | −0.199951 | ||||||||
\(536\) | 7520.03 | 0.606000 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 21250.3 | 1.70291 | ||||||||
\(539\) | 539.000 | 0.0430730 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −19113.2 | −1.51893 | −0.759464 | − | 0.650549i | \(-0.774539\pi\) | ||||
−0.759464 | + | 0.650549i | \(0.774539\pi\) | |||||||
\(542\) | 27970.5 | 2.21668 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 9475.84 | 0.746826 | ||||||||
\(545\) | 12479.1 | 0.980816 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 2707.11 | 0.211604 | 0.105802 | − | 0.994387i | \(-0.466259\pi\) | ||||
0.105802 | + | 0.994387i | \(0.466259\pi\) | |||||||
\(548\) | 9234.57 | 0.719856 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1158.14 | −0.0897874 | ||||||||
\(551\) | 9696.28 | 0.749683 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 1105.57 | 0.0850157 | ||||||||
\(554\) | −8169.59 | −0.626521 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 10567.1 | 0.806019 | ||||||||
\(557\) | −1527.87 | −0.116226 | −0.0581131 | − | 0.998310i | \(-0.518508\pi\) | ||||
−0.0581131 | + | 0.998310i | \(0.518508\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 1534.36 | 0.116094 | ||||||||
\(560\) | −1550.32 | −0.116987 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −35424.0 | −2.65884 | ||||||||
\(563\) | 5678.01 | 0.425043 | 0.212522 | − | 0.977156i | \(-0.431832\pi\) | ||||
0.212522 | + | 0.977156i | \(0.431832\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 12327.2 | 0.917896 | ||||||||
\(566\) | −14001.2 | −1.03978 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 12322.7 | 0.910300 | ||||||||
\(569\) | 19704.3 | 1.45175 | 0.725877 | − | 0.687824i | \(-0.241434\pi\) | ||||
0.725877 | + | 0.687824i | \(0.241434\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19744.0 | −1.44704 | −0.723519 | − | 0.690304i | \(-0.757477\pi\) | ||||
−0.723519 | + | 0.690304i | \(0.757477\pi\) | |||||||
\(572\) | −2041.96 | −0.149263 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 352.444 | 0.0256285 | ||||||||
\(575\) | 2864.21 | 0.207732 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −16525.4 | −1.19231 | −0.596153 | − | 0.802871i | \(-0.703305\pi\) | ||||
−0.596153 | + | 0.802871i | \(0.703305\pi\) | |||||||
\(578\) | 13530.7 | 0.973708 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 27085.2 | 1.93905 | ||||||||
\(581\) | 2779.45 | 0.198470 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 5362.01 | 0.380912 | ||||||||
\(584\) | 14821.4 | 1.05019 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −13743.4 | −0.968830 | ||||||||
\(587\) | −15341.2 | −1.07870 | −0.539351 | − | 0.842081i | \(-0.681330\pi\) | ||||
−0.539351 | + | 0.842081i | \(0.681330\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 4758.35 | 0.332876 | ||||||||
\(590\) | 37911.9 | 2.64544 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 4117.97 | 0.285891 | ||||||||
\(593\) | −3742.99 | −0.259201 | −0.129600 | − | 0.991566i | \(-0.541369\pi\) | ||||
−0.129600 | + | 0.991566i | \(0.541369\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 3697.26 | 0.254744 | ||||||||
\(596\) | −21479.4 | −1.47622 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 8455.44 | 0.578208 | ||||||||
\(599\) | −11362.5 | −0.775057 | −0.387529 | − | 0.921858i | \(-0.626671\pi\) | ||||
−0.387529 | + | 0.921858i | \(0.626671\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 6080.27 | 0.412678 | 0.206339 | − | 0.978481i | \(-0.433845\pi\) | ||||
0.206339 | + | 0.978481i | \(0.433845\pi\) | |||||||
\(602\) | 3059.21 | 0.207116 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 36101.1 | 2.43201 | ||||||||
\(605\) | 1475.12 | 0.0991279 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −21318.7 | −1.42553 | −0.712766 | − | 0.701402i | \(-0.752558\pi\) | ||||
−0.712766 | + | 0.701402i | \(0.752558\pi\) | |||||||
\(608\) | 11324.1 | 0.755353 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −26424.3 | −1.75391 | ||||||||
\(611\) | −2914.17 | −0.192954 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −7505.66 | −0.494536 | −0.247268 | − | 0.968947i | \(-0.579533\pi\) | ||||
−0.247268 | + | 0.968947i | \(0.579533\pi\) | |||||||
\(614\) | −36619.4 | −2.40690 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1325.83 | −0.0867196 | ||||||||
\(617\) | 4837.21 | 0.315622 | 0.157811 | − | 0.987469i | \(-0.449556\pi\) | ||||
0.157811 | + | 0.987469i | \(0.449556\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −11483.4 | −0.745649 | −0.372824 | − | 0.927902i | \(-0.621611\pi\) | ||||
−0.372824 | + | 0.927902i | \(0.621611\pi\) | |||||||
\(620\) | 13291.8 | 0.860984 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −14447.8 | −0.931354 | ||||||||
\(623\) | −1664.69 | −0.107054 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −18019.8 | −1.15327 | ||||||||
\(626\) | 47443.0 | 3.02908 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −15415.8 | −0.979548 | ||||||||
\(629\) | −9820.70 | −0.622539 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 6720.61 | 0.423999 | 0.211999 | − | 0.977270i | \(-0.432003\pi\) | ||||
0.211999 | + | 0.977270i | \(0.432003\pi\) | |||||||
\(632\) | −2719.48 | −0.171163 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −3306.82 | −0.207146 | ||||||||
\(635\) | 27214.0 | 1.70072 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −766.727 | −0.0476904 | ||||||||
\(638\) | −9181.17 | −0.569728 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 23735.8 | 1.46600 | ||||||||
\(641\) | −24827.3 | −1.52983 | −0.764915 | − | 0.644131i | \(-0.777219\pi\) | ||||
−0.764915 | + | 0.644131i | \(0.777219\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 15682.9 | 0.961859 | 0.480929 | − | 0.876759i | \(-0.340299\pi\) | ||||
0.480929 | + | 0.876759i | \(0.340299\pi\) | |||||||
\(644\) | 10068.7 | 0.616089 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9997.52 | −0.608896 | ||||||||
\(647\) | 22025.9 | 1.33838 | 0.669188 | − | 0.743093i | \(-0.266642\pi\) | ||||
0.669188 | + | 0.743093i | \(0.266642\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −7675.36 | −0.464228 | ||||||||
\(650\) | 1647.45 | 0.0994126 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −18397.8 | −1.10508 | ||||||||
\(653\) | 14258.3 | 0.854469 | 0.427235 | − | 0.904141i | \(-0.359488\pi\) | ||||
0.427235 | + | 0.904141i | \(0.359488\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −6745.83 | −0.402414 | ||||||||
\(656\) | 205.232 | 0.0122149 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −5810.25 | −0.344236 | ||||||||
\(659\) | 11822.2 | 0.698829 | 0.349414 | − | 0.936968i | \(-0.386381\pi\) | ||||
0.349414 | + | 0.936968i | \(0.386381\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −27196.3 | −1.60033 | −0.800163 | − | 0.599783i | \(-0.795254\pi\) | ||||
−0.800163 | + | 0.599783i | \(0.795254\pi\) | |||||||
\(662\) | −17126.6 | −1.00550 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −6836.89 | −0.399582 | ||||||||
\(665\) | 4418.43 | 0.257653 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 22706.1 | 1.31812 | ||||||||
\(668\) | 15970.9 | 0.925048 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 23729.7 | 1.36830 | ||||||||
\(671\) | 5349.65 | 0.307781 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −2020.00 | −0.115699 | −0.0578495 | − | 0.998325i | \(-0.518424\pi\) | ||||
−0.0578495 | + | 0.998325i | \(0.518424\pi\) | |||||||
\(674\) | 5579.82 | 0.318882 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −23159.2 | −1.31766 | ||||||||
\(677\) | −16276.1 | −0.923989 | −0.461994 | − | 0.886883i | \(-0.652866\pi\) | ||||
−0.461994 | + | 0.886883i | \(0.652866\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 4130.81 | 0.233470 | ||||||||
\(680\) | −9094.52 | −0.512880 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −4505.56 | −0.252972 | ||||||||
\(683\) | 9926.97 | 0.556142 | 0.278071 | − | 0.960561i | \(-0.410305\pi\) | ||||
0.278071 | + | 0.960561i | \(0.410305\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 9489.66 | 0.529316 | ||||||||
\(686\) | −1528.70 | −0.0850814 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1781.41 | 0.0987144 | ||||||||
\(689\) | −7627.45 | −0.421746 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13631.7 | −0.750471 | −0.375236 | − | 0.926930i | \(-0.622438\pi\) | ||||
−0.375236 | + | 0.926930i | \(0.622438\pi\) | |||||||
\(692\) | 36279.5 | 1.99298 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −54227.6 | −2.96607 | ||||||||
\(695\) | 10859.0 | 0.592672 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −489.446 | −0.0265984 | ||||||||
\(698\) | 12757.3 | 0.691791 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1961.77 | 0.105925 | ||||||||
\(701\) | 27909.6 | 1.50375 | 0.751875 | − | 0.659305i | \(-0.229149\pi\) | ||||
0.751875 | + | 0.659305i | \(0.229149\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −11736.3 | −0.629647 | ||||||||
\(704\) | −9123.88 | −0.488451 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −38476.1 | −2.05109 | ||||||||
\(707\) | 6009.44 | 0.319672 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 12864.8 | 0.681452 | 0.340726 | − | 0.940163i | \(-0.389327\pi\) | ||||
0.340726 | + | 0.940163i | \(0.389327\pi\) | |||||||
\(710\) | 38884.8 | 2.05538 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 4094.81 | 0.215533 | ||||||||
\(713\) | 11142.8 | 0.585275 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2098.36 | −0.109754 | ||||||||
\(716\) | 13513.6 | 0.705346 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 4515.78 | 0.234718 | ||||||||
\(719\) | −27741.1 | −1.43890 | −0.719451 | − | 0.694544i | \(-0.755606\pi\) | ||||
−0.719451 | + | 0.694544i | \(0.755606\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 130.419 | 0.00673656 | ||||||||
\(722\) | 18621.9 | 0.959882 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 37443.9 | 1.92209 | ||||||||
\(725\) | 4424.04 | 0.226627 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −33694.0 | −1.71890 | −0.859450 | − | 0.511220i | \(-0.829194\pi\) | ||||
−0.859450 | + | 0.511220i | \(0.829194\pi\) | |||||||
\(728\) | 1885.99 | 0.0960158 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 46769.3 | 2.37125 | ||||||||
\(731\) | −4248.37 | −0.214955 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −38697.7 | −1.94998 | −0.974988 | − | 0.222256i | \(-0.928658\pi\) | ||||
−0.974988 | + | 0.222256i | \(0.928658\pi\) | |||||||
\(734\) | −23542.6 | −1.18389 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 26518.2 | 1.32809 | ||||||||
\(737\) | −4804.13 | −0.240112 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −22086.4 | −1.09941 | −0.549704 | − | 0.835359i | \(-0.685260\pi\) | ||||
−0.549704 | + | 0.835359i | \(0.685260\pi\) | |||||||
\(740\) | −32783.6 | −1.62858 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −15207.6 | −0.752409 | ||||||||
\(743\) | −181.397 | −0.00895666 | −0.00447833 | − | 0.999990i | \(-0.501426\pi\) | ||||
−0.00447833 | + | 0.999990i | \(0.501426\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −22072.7 | −1.08548 | ||||||||
\(746\) | 39090.7 | 1.91852 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 5653.81 | 0.276368 | ||||||||
\(749\) | −1420.72 | −0.0693086 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7735.78 | −0.375876 | −0.187938 | − | 0.982181i | \(-0.560180\pi\) | ||||
−0.187938 | + | 0.982181i | \(0.560180\pi\) | |||||||
\(752\) | −3383.37 | −0.164067 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 13060.2 | 0.630802 | ||||||||
\(755\) | 37098.3 | 1.78827 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −17569.4 | −0.843552 | −0.421776 | − | 0.906700i | \(-0.638593\pi\) | ||||
−0.421776 | + | 0.906700i | \(0.638593\pi\) | |||||||
\(758\) | −37580.0 | −1.80075 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −10868.4 | −0.518737 | ||||||||
\(761\) | −20086.4 | −0.956807 | −0.478404 | − | 0.878140i | \(-0.658784\pi\) | ||||
−0.478404 | + | 0.878140i | \(0.658784\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 7165.34 | 0.339977 | ||||||||
\(764\) | −26048.9 | −1.23353 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −51694.3 | −2.43837 | ||||||||
\(767\) | 10918.2 | 0.513993 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −7772.56 | −0.364481 | −0.182240 | − | 0.983254i | \(-0.558335\pi\) | ||||
−0.182240 | + | 0.983254i | \(0.558335\pi\) | |||||||
\(770\) | −4183.70 | −0.195806 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −14528.1 | −0.677301 | ||||||||
\(773\) | −1055.68 | −0.0491204 | −0.0245602 | − | 0.999698i | \(-0.507819\pi\) | ||||
−0.0245602 | + | 0.999698i | \(0.507819\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 2171.05 | 0.100628 | ||||||||
\(776\) | −10161.0 | −0.470048 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −6223.69 | −0.286800 | ||||||||
\(779\) | −584.914 | −0.0269021 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7872.31 | −0.360683 | ||||||||
\(782\) | −23411.6 | −1.07058 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −890.174 | −0.0405509 | ||||||||
\(785\) | −15841.6 | −0.720269 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −34605.2 | −1.56740 | −0.783700 | − | 0.621140i | \(-0.786670\pi\) | ||||
−0.783700 | + | 0.621140i | \(0.786670\pi\) | |||||||
\(788\) | 53414.9 | 2.41475 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8581.42 | −0.386472 | ||||||||
\(791\) | 7078.16 | 0.318168 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −7609.87 | −0.340775 | ||||||||
\(794\) | −25731.5 | −1.15010 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 63256.3 | 2.81666 | ||||||||
\(797\) | −34013.8 | −1.51171 | −0.755853 | − | 0.654741i | \(-0.772778\pi\) | ||||
−0.755853 | + | 0.654741i | \(0.772778\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 8068.80 | 0.357264 | ||||||||
\(800\) | 5166.77 | 0.228341 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 2254.24 | 0.0992520 | ||||||||
\(803\) | −9468.55 | −0.416112 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 10346.8 | 0.453015 | ||||||||
\(806\) | 6409.16 | 0.280090 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −14782.0 | −0.643600 | ||||||||
\(809\) | −19962.0 | −0.867525 | −0.433763 | − | 0.901027i | \(-0.642814\pi\) | ||||
−0.433763 | + | 0.901027i | \(0.642814\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −31886.3 | −1.38061 | −0.690307 | − | 0.723517i | \(-0.742525\pi\) | ||||
−0.690307 | + | 0.723517i | \(0.742525\pi\) | |||||||
\(812\) | 15552.0 | 0.672128 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 11112.8 | 0.478505 | ||||||||
\(815\) | −18906.0 | −0.812573 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −5077.04 | −0.217409 | ||||||||
\(818\) | −8314.04 | −0.355371 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1633.87 | −0.0695821 | ||||||||
\(821\) | −6951.19 | −0.295491 | −0.147745 | − | 0.989025i | \(-0.547202\pi\) | ||||
−0.147745 | + | 0.989025i | \(0.547202\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 36694.6 | 1.55418 | 0.777091 | − | 0.629388i | \(-0.216694\pi\) | ||||
0.777091 | + | 0.629388i | \(0.216694\pi\) | |||||||
\(824\) | −320.805 | −0.0135628 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 21768.6 | 0.916982 | ||||||||
\(827\) | −22074.4 | −0.928176 | −0.464088 | − | 0.885789i | \(-0.653618\pi\) | ||||
−0.464088 | + | 0.885789i | \(0.653618\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 23458.4 | 0.982802 | 0.491401 | − | 0.870933i | \(-0.336485\pi\) | ||||
0.491401 | + | 0.870933i | \(0.336485\pi\) | |||||||
\(830\) | −21574.0 | −0.902224 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 12978.7 | 0.540812 | ||||||||
\(833\) | 2122.93 | 0.0883013 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16412.1 | 0.680195 | ||||||||
\(836\) | 6756.61 | 0.279524 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 34347.7 | 1.41590 | ||||||||
\(839\) | −37736.8 | −1.55282 | −0.776412 | − | 0.630225i | \(-0.782963\pi\) | ||||
−0.776412 | + | 0.630225i | \(0.782963\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 10682.7 | 0.438015 | ||||||||
\(842\) | 20210.8 | 0.827210 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −22840.1 | −0.931503 | ||||||||
\(845\) | −23799.0 | −0.968887 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 847.000 | 0.0343604 | ||||||||
\(848\) | −8855.52 | −0.358608 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −4561.48 | −0.184068 | ||||||||
\(851\) | −27483.3 | −1.10707 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26345.9 | 1.05752 | 0.528762 | − | 0.848770i | \(-0.322656\pi\) | ||||
0.528762 | + | 0.848770i | \(0.322656\pi\) | |||||||
\(854\) | −15172.5 | −0.607955 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3494.69 | 0.139540 | ||||||||
\(857\) | −47972.7 | −1.91215 | −0.956077 | − | 0.293116i | \(-0.905308\pi\) | ||||
−0.956077 | + | 0.293116i | \(0.905308\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −30428.2 | −1.20861 | −0.604306 | − | 0.796752i | \(-0.706549\pi\) | ||||
−0.604306 | + | 0.796752i | \(0.706549\pi\) | |||||||
\(860\) | −14182.0 | −0.562327 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −3122.23 | −0.123368 | ||||||||
\(863\) | 8351.59 | 0.329422 | 0.164711 | − | 0.986342i | \(-0.447331\pi\) | ||||
0.164711 | + | 0.986342i | \(0.447331\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 37281.7 | 1.46545 | ||||||||
\(866\) | −59302.1 | −2.32698 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 7631.98 | 0.298440 | ||||||||
\(869\) | 1737.33 | 0.0678191 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6833.87 | 0.265852 | ||||||||
\(872\) | −17625.3 | −0.684481 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −27978.1 | −1.08281 | ||||||||
\(875\) | −8651.27 | −0.334247 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −24609.5 | −0.947552 | −0.473776 | − | 0.880645i | \(-0.657109\pi\) | ||||
−0.473776 | + | 0.880645i | \(0.657109\pi\) | |||||||
\(878\) | −4421.77 | −0.169963 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −2436.21 | −0.0933235 | ||||||||
\(881\) | 17386.9 | 0.664901 | 0.332451 | − | 0.943121i | \(-0.392125\pi\) | ||||
0.332451 | + | 0.943121i | \(0.392125\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 35566.6 | 1.35551 | 0.677753 | − | 0.735290i | \(-0.262954\pi\) | ||||
0.677753 | + | 0.735290i | \(0.262954\pi\) | |||||||
\(884\) | −8042.53 | −0.305995 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −32000.3 | −1.21340 | ||||||||
\(887\) | 21087.4 | 0.798248 | 0.399124 | − | 0.916897i | \(-0.369314\pi\) | ||||
0.399124 | + | 0.916897i | \(0.369314\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 15626.0 | 0.589515 | ||||||||
\(890\) | 12921.3 | 0.486655 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 21283.0 | 0.798888 | ||||||||
\(893\) | 9642.65 | 0.361343 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13886.9 | 0.518646 | ||||||||
\(896\) | 13628.8 | 0.508155 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 79046.5 | 2.93743 | ||||||||
\(899\) | 17211.1 | 0.638511 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21119.0 | 0.780884 | ||||||||
\(902\) | 553.841 | 0.0204444 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −17410.8 | −0.640571 | ||||||||
\(905\) | 38478.2 | 1.41333 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −46282.0 | −1.69434 | −0.847171 | − | 0.531321i | \(-0.821696\pi\) | ||||
−0.847171 | + | 0.531321i | \(0.821696\pi\) | |||||||
\(908\) | 33326.9 | 1.21805 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 5951.31 | 0.216796 | ||||||||
\(911\) | 14001.3 | 0.509203 | 0.254601 | − | 0.967046i | \(-0.418056\pi\) | ||||
0.254601 | + | 0.967046i | \(0.418056\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 4367.71 | 0.158324 | ||||||||
\(914\) | 26412.3 | 0.955845 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −29015.8 | −1.04663 | ||||||||
\(917\) | −3873.38 | −0.139488 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −7587.94 | −0.272364 | −0.136182 | − | 0.990684i | \(-0.543483\pi\) | ||||
−0.136182 | + | 0.990684i | \(0.543483\pi\) | |||||||
\(920\) | −25451.0 | −0.912061 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 52730.0 | 1.88348 | ||||||||
\(923\) | 11198.4 | 0.399348 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −5354.81 | −0.190341 | ||||||||
\(926\) | −12283.4 | −0.435915 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 40959.8 | 1.44889 | ||||||||
\(929\) | −33002.7 | −1.16554 | −0.582768 | − | 0.812638i | \(-0.698030\pi\) | ||||
−0.582768 | + | 0.812638i | \(0.698030\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2537.01 | 0.0893096 | ||||||||
\(932\) | −37287.7 | −1.31051 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 34741.5 | 1.21711 | ||||||||
\(935\) | 5809.98 | 0.203216 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −15187.7 | −0.529519 | −0.264760 | − | 0.964314i | \(-0.585293\pi\) | ||||
−0.264760 | + | 0.964314i | \(0.585293\pi\) | |||||||
\(938\) | 13625.3 | 0.474289 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 26935.4 | 0.934612 | ||||||||
\(941\) | −32513.8 | −1.12638 | −0.563188 | − | 0.826328i | \(-0.690425\pi\) | ||||
−0.563188 | + | 0.826328i | \(0.690425\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −1369.72 | −0.0473002 | ||||||||
\(944\) | 12676.1 | 0.437046 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 4807.33 | 0.165222 | ||||||||
\(947\) | 14865.8 | 0.510108 | 0.255054 | − | 0.966927i | \(-0.417907\pi\) | ||||
0.255054 | + | 0.966927i | \(0.417907\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13469.0 | 0.460719 | ||||||||
\(950\) | −5451.22 | −0.186169 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −5221.97 | −0.177778 | ||||||||
\(953\) | −19708.9 | −0.669920 | −0.334960 | − | 0.942232i | \(-0.608723\pi\) | ||||
−0.334960 | + | 0.942232i | \(0.608723\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −26768.5 | −0.907024 | ||||||||
\(956\) | −12002.4 | −0.406050 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −59175.2 | −1.99568 | ||||||||
\(959\) | 5448.85 | 0.183475 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21344.8 | −0.716486 | ||||||||
\(962\) | −15807.9 | −0.529801 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −29062.0 | −0.970981 | ||||||||
\(965\) | −14929.4 | −0.498024 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 3670.99 | 0.122080 | 0.0610398 | − | 0.998135i | \(-0.480558\pi\) | ||||
0.0610398 | + | 0.998135i | \(0.480558\pi\) | |||||||
\(968\) | −2083.45 | −0.0691783 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −32063.3 | −1.06133 | ||||||||
\(971\) | 12572.5 | 0.415521 | 0.207761 | − | 0.978180i | \(-0.433383\pi\) | ||||
0.207761 | + | 0.978180i | \(0.433383\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 6235.14 | 0.205436 | ||||||||
\(974\) | −47248.3 | −1.55435 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −8835.11 | −0.289759 | ||||||||
\(977\) | 14573.7 | 0.477232 | 0.238616 | − | 0.971114i | \(-0.423306\pi\) | ||||
0.238616 | + | 0.971114i | \(0.423306\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −2615.95 | −0.0853994 | ||||||||
\(980\) | 7086.78 | 0.230999 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 27165.1 | 0.882763 | ||||||||
\(983\) | −26717.6 | −0.866896 | −0.433448 | − | 0.901179i | \(-0.642703\pi\) | ||||
−0.433448 | + | 0.901179i | \(0.642703\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 54890.4 | 1.77559 | ||||||||
\(986\) | −36161.3 | −1.16796 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −9611.26 | −0.309489 | ||||||||
\(989\) | −11889.1 | −0.382256 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 22048.7 | 0.706761 | 0.353380 | − | 0.935480i | \(-0.385032\pi\) | ||||
0.353380 | + | 0.935480i | \(0.385032\pi\) | |||||||
\(992\) | 20100.6 | 0.643341 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 22327.2 | 0.712451 | ||||||||
\(995\) | 65003.6 | 2.07111 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 29571.1 | 0.939345 | 0.469673 | − | 0.882841i | \(-0.344372\pi\) | ||||
0.469673 | + | 0.882841i | \(0.344372\pi\) | |||||||
\(998\) | 84224.3 | 2.67142 | ||||||||
\(999\) | 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 | 693.4.a.u.1.1 | yes | 8 | |
3.2 | odd | 2 | 693.4.a.r.1.8 | ✓ | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
693.4.a.r.1.8 | ✓ | 8 | 3.2 | odd | 2 | ||
693.4.a.u.1.1 | yes | 8 | 1.1 | even | 1 | trivial |