Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2178,4,Mod(1,2178)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2178, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([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("2178.1");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2178 = 2 \cdot 3^{2} \cdot 11^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 2178.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: | \(128.506159993\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | 4.4.12421225.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 2x^{3} - 355x^{2} + 356x + 30964 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 11 \) |
Twist minimal: | no (minimal twist has level 66) |
Fricke sign: | \(-1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.3 | ||
Root | \(12.8052\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 2178.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 4.00000 | 0.500000 | ||||||||
\(5\) | 6.18714 | 0.553394 | 0.276697 | − | 0.960957i | \(-0.410760\pi\) | ||||
0.276697 | + | 0.960957i | \(0.410760\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −25.7192 | −1.38871 | −0.694353 | − | 0.719634i | \(-0.744309\pi\) | ||||
−0.694353 | + | 0.719634i | \(0.744309\pi\) | |||||||
\(8\) | 8.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 12.3743 | 0.391309 | ||||||||
\(11\) | 0 | 0 | ||||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −30.7630 | −0.656318 | −0.328159 | − | 0.944623i | \(-0.606428\pi\) | ||||
−0.328159 | + | 0.944623i | \(0.606428\pi\) | |||||||
\(14\) | −51.4384 | −0.981964 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 16.0000 | 0.250000 | ||||||||
\(17\) | 47.9850 | 0.684592 | 0.342296 | − | 0.939592i | \(-0.388795\pi\) | ||||
0.342296 | + | 0.939592i | \(0.388795\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 46.7480 | 0.564459 | 0.282230 | − | 0.959347i | \(-0.408926\pi\) | ||||
0.282230 | + | 0.959347i | \(0.408926\pi\) | |||||||
\(20\) | 24.7485 | 0.276697 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −2.04459 | −0.0185359 | −0.00926795 | − | 0.999957i | \(-0.502950\pi\) | ||||
−0.00926795 | + | 0.999957i | \(0.502950\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −86.7194 | −0.693755 | ||||||||
\(26\) | −61.5261 | −0.464087 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −102.877 | −0.694353 | ||||||||
\(29\) | 59.0080 | 0.377845 | 0.188923 | − | 0.981992i | \(-0.439500\pi\) | ||||
0.188923 | + | 0.981992i | \(0.439500\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 304.896 | 1.76648 | 0.883241 | − | 0.468920i | \(-0.155357\pi\) | ||||
0.883241 | + | 0.468920i | \(0.155357\pi\) | |||||||
\(32\) | 32.0000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 95.9699 | 0.484079 | ||||||||
\(35\) | −159.128 | −0.768502 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −303.823 | −1.34995 | −0.674976 | − | 0.737840i | \(-0.735846\pi\) | ||||
−0.674976 | + | 0.737840i | \(0.735846\pi\) | |||||||
\(38\) | 93.4960 | 0.399133 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 49.4971 | 0.195654 | ||||||||
\(41\) | 145.553 | 0.554428 | 0.277214 | − | 0.960808i | \(-0.410589\pi\) | ||||
0.277214 | + | 0.960808i | \(0.410589\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 284.084 | 1.00750 | 0.503748 | − | 0.863850i | \(-0.331954\pi\) | ||||
0.503748 | + | 0.863850i | \(0.331954\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −4.08917 | −0.0131069 | ||||||||
\(47\) | −577.251 | −1.79151 | −0.895753 | − | 0.444552i | \(-0.853363\pi\) | ||||
−0.895753 | + | 0.444552i | \(0.853363\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 318.477 | 0.928505 | ||||||||
\(50\) | −173.439 | −0.490559 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −123.052 | −0.328159 | ||||||||
\(53\) | −655.216 | −1.69813 | −0.849065 | − | 0.528289i | \(-0.822834\pi\) | ||||
−0.849065 | + | 0.528289i | \(0.822834\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −205.754 | −0.490982 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 118.016 | 0.267177 | ||||||||
\(59\) | 23.1802 | 0.0511492 | 0.0255746 | − | 0.999673i | \(-0.491858\pi\) | ||||
0.0255746 | + | 0.999673i | \(0.491858\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 631.874 | 1.32628 | 0.663140 | − | 0.748495i | \(-0.269223\pi\) | ||||
0.663140 | + | 0.748495i | \(0.269223\pi\) | |||||||
\(62\) | 609.792 | 1.24909 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 64.0000 | 0.125000 | ||||||||
\(65\) | −190.335 | −0.363202 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −655.918 | −1.19602 | −0.598009 | − | 0.801490i | \(-0.704041\pi\) | ||||
−0.598009 | + | 0.801490i | \(0.704041\pi\) | |||||||
\(68\) | 191.940 | 0.342296 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | −318.256 | −0.543413 | ||||||||
\(71\) | −528.602 | −0.883571 | −0.441786 | − | 0.897121i | \(-0.645655\pi\) | ||||
−0.441786 | + | 0.897121i | \(0.645655\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −447.652 | −0.717723 | −0.358861 | − | 0.933391i | \(-0.616835\pi\) | ||||
−0.358861 | + | 0.933391i | \(0.616835\pi\) | |||||||
\(74\) | −607.646 | −0.954560 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 186.992 | 0.282230 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −985.464 | −1.40346 | −0.701730 | − | 0.712443i | \(-0.747589\pi\) | ||||
−0.701730 | + | 0.712443i | \(0.747589\pi\) | |||||||
\(80\) | 98.9942 | 0.138349 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 291.106 | 0.392040 | ||||||||
\(83\) | 128.459 | 0.169882 | 0.0849411 | − | 0.996386i | \(-0.472930\pi\) | ||||
0.0849411 | + | 0.996386i | \(0.472930\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 296.889 | 0.378849 | ||||||||
\(86\) | 568.167 | 0.712408 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −1425.15 | −1.69736 | −0.848682 | − | 0.528904i | \(-0.822603\pi\) | ||||
−0.848682 | + | 0.528904i | \(0.822603\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 791.201 | 0.911432 | ||||||||
\(92\) | −8.17835 | −0.00926795 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1154.50 | −1.26679 | ||||||||
\(95\) | 289.236 | 0.312368 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −142.553 | −0.149217 | −0.0746084 | − | 0.997213i | \(-0.523771\pi\) | ||||
−0.0746084 | + | 0.997213i | \(0.523771\pi\) | |||||||
\(98\) | 636.954 | 0.656552 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −346.877 | −0.346877 | ||||||||
\(101\) | 293.830 | 0.289477 | 0.144738 | − | 0.989470i | \(-0.453766\pi\) | ||||
0.144738 | + | 0.989470i | \(0.453766\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1001.55 | −0.958112 | −0.479056 | − | 0.877784i | \(-0.659021\pi\) | ||||
−0.479056 | + | 0.877784i | \(0.659021\pi\) | |||||||
\(104\) | −246.104 | −0.232043 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −1310.43 | −1.20076 | ||||||||
\(107\) | −1604.00 | −1.44920 | −0.724602 | − | 0.689168i | \(-0.757976\pi\) | ||||
−0.724602 | + | 0.689168i | \(0.757976\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 323.134 | 0.283951 | 0.141975 | − | 0.989870i | \(-0.454655\pi\) | ||||
0.141975 | + | 0.989870i | \(0.454655\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | −411.507 | −0.347177 | ||||||||
\(113\) | 464.460 | 0.386661 | 0.193331 | − | 0.981134i | \(-0.438071\pi\) | ||||
0.193331 | + | 0.981134i | \(0.438071\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −12.6501 | −0.0102577 | ||||||||
\(116\) | 236.032 | 0.188923 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 46.3604 | 0.0361680 | ||||||||
\(119\) | −1234.13 | −0.950697 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 0 | 0 | ||||||||
\(122\) | 1263.75 | 0.937822 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 1219.58 | 0.883241 | ||||||||
\(125\) | −1309.94 | −0.937314 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 327.549 | 0.228861 | 0.114430 | − | 0.993431i | \(-0.463496\pi\) | ||||
0.114430 | + | 0.993431i | \(0.463496\pi\) | |||||||
\(128\) | 128.000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −380.670 | −0.256823 | ||||||||
\(131\) | −2871.12 | −1.91489 | −0.957447 | − | 0.288610i | \(-0.906807\pi\) | ||||
−0.957447 | + | 0.288610i | \(0.906807\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1202.32 | −0.783868 | ||||||||
\(134\) | −1311.84 | −0.845712 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 383.880 | 0.242040 | ||||||||
\(137\) | −1143.36 | −0.713018 | −0.356509 | − | 0.934292i | \(-0.616033\pi\) | ||||
−0.356509 | + | 0.934292i | \(0.616033\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 336.573 | 0.205379 | 0.102690 | − | 0.994713i | \(-0.467255\pi\) | ||||
0.102690 | + | 0.994713i | \(0.467255\pi\) | |||||||
\(140\) | −636.513 | −0.384251 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −1057.20 | −0.624779 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 365.091 | 0.209097 | ||||||||
\(146\) | −895.305 | −0.507507 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −1215.29 | −0.674976 | ||||||||
\(149\) | −858.353 | −0.471940 | −0.235970 | − | 0.971760i | \(-0.575827\pi\) | ||||
−0.235970 | + | 0.971760i | \(0.575827\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3086.90 | 1.66363 | 0.831814 | − | 0.555054i | \(-0.187302\pi\) | ||||
0.831814 | + | 0.555054i | \(0.187302\pi\) | |||||||
\(152\) | 373.984 | 0.199566 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 1886.43 | 0.977560 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 1737.12 | 0.883039 | 0.441519 | − | 0.897252i | \(-0.354440\pi\) | ||||
0.441519 | + | 0.897252i | \(0.354440\pi\) | |||||||
\(158\) | −1970.93 | −0.992396 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 197.988 | 0.0978272 | ||||||||
\(161\) | 52.5851 | 0.0257409 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −2382.91 | −1.14506 | −0.572528 | − | 0.819885i | \(-0.694037\pi\) | ||||
−0.572528 | + | 0.819885i | \(0.694037\pi\) | |||||||
\(164\) | 582.212 | 0.277214 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 256.918 | 0.120125 | ||||||||
\(167\) | −2961.84 | −1.37242 | −0.686209 | − | 0.727404i | \(-0.740726\pi\) | ||||
−0.686209 | + | 0.727404i | \(0.740726\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −1250.64 | −0.569247 | ||||||||
\(170\) | 593.779 | 0.267887 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1136.33 | 0.503748 | ||||||||
\(173\) | 314.894 | 0.138387 | 0.0691936 | − | 0.997603i | \(-0.477957\pi\) | ||||
0.0691936 | + | 0.997603i | \(0.477957\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 2230.35 | 0.963422 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −2850.30 | −1.20022 | ||||||||
\(179\) | 2412.21 | 1.00725 | 0.503624 | − | 0.863923i | \(-0.332000\pi\) | ||||
0.503624 | + | 0.863923i | \(0.332000\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3908.18 | 1.60493 | 0.802466 | − | 0.596698i | \(-0.203521\pi\) | ||||
0.802466 | + | 0.596698i | \(0.203521\pi\) | |||||||
\(182\) | 1582.40 | 0.644480 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −16.3567 | −0.00655343 | ||||||||
\(185\) | −1879.80 | −0.747056 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −2309.01 | −0.895753 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 578.472 | 0.220878 | ||||||||
\(191\) | 912.609 | 0.345728 | 0.172864 | − | 0.984946i | \(-0.444698\pi\) | ||||
0.172864 | + | 0.984946i | \(0.444698\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −533.160 | −0.198848 | −0.0994241 | − | 0.995045i | \(-0.531700\pi\) | ||||
−0.0994241 | + | 0.995045i | \(0.531700\pi\) | |||||||
\(194\) | −285.105 | −0.105512 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 1273.91 | 0.464252 | ||||||||
\(197\) | −2700.49 | −0.976659 | −0.488329 | − | 0.872659i | \(-0.662394\pi\) | ||||
−0.488329 | + | 0.872659i | \(0.662394\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4409.62 | 1.57080 | 0.785401 | − | 0.618987i | \(-0.212457\pi\) | ||||
0.785401 | + | 0.618987i | \(0.212457\pi\) | |||||||
\(200\) | −693.755 | −0.245279 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 587.659 | 0.204691 | ||||||||
\(203\) | −1517.64 | −0.524716 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 900.555 | 0.306817 | ||||||||
\(206\) | −2003.10 | −0.677488 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −492.208 | −0.164079 | ||||||||
\(209\) | 0 | 0 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −5804.51 | −1.89383 | −0.946917 | − | 0.321479i | \(-0.895820\pi\) | ||||
−0.946917 | + | 0.321479i | \(0.895820\pi\) | |||||||
\(212\) | −2620.86 | −0.849065 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | −3208.01 | −1.02474 | ||||||||
\(215\) | 1757.66 | 0.557543 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −7841.68 | −2.45312 | ||||||||
\(218\) | 646.268 | 0.200784 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1476.16 | −0.449310 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −3466.84 | −1.04106 | −0.520530 | − | 0.853843i | \(-0.674266\pi\) | ||||
−0.520530 | + | 0.853843i | \(0.674266\pi\) | |||||||
\(224\) | −823.014 | −0.245491 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 928.920 | 0.273411 | ||||||||
\(227\) | 4036.58 | 1.18025 | 0.590127 | − | 0.807311i | \(-0.299078\pi\) | ||||
0.590127 | + | 0.807311i | \(0.299078\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −3078.22 | −0.888272 | −0.444136 | − | 0.895959i | \(-0.646489\pi\) | ||||
−0.444136 | + | 0.895959i | \(0.646489\pi\) | |||||||
\(230\) | −25.3003 | −0.00725326 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 472.064 | 0.133589 | ||||||||
\(233\) | −1687.61 | −0.474501 | −0.237251 | − | 0.971449i | \(-0.576246\pi\) | ||||
−0.237251 | + | 0.971449i | \(0.576246\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3571.53 | −0.991409 | ||||||||
\(236\) | 92.7208 | 0.0255746 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −2468.27 | −0.672244 | ||||||||
\(239\) | −2421.76 | −0.655442 | −0.327721 | − | 0.944775i | \(-0.606281\pi\) | ||||
−0.327721 | + | 0.944775i | \(0.606281\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 6935.97 | 1.85388 | 0.926940 | − | 0.375209i | \(-0.122429\pi\) | ||||
0.926940 | + | 0.375209i | \(0.122429\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 2527.49 | 0.663140 | ||||||||
\(245\) | 1970.46 | 0.513829 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1438.11 | −0.370464 | ||||||||
\(248\) | 2439.17 | 0.624545 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −2619.87 | −0.662781 | ||||||||
\(251\) | 764.367 | 0.192217 | 0.0961085 | − | 0.995371i | \(-0.469360\pi\) | ||||
0.0961085 | + | 0.995371i | \(0.469360\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0 | 0 | ||||||||
\(254\) | 655.099 | 0.161829 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 256.000 | 0.0625000 | ||||||||
\(257\) | −1828.90 | −0.443906 | −0.221953 | − | 0.975057i | \(-0.571243\pi\) | ||||
−0.221953 | + | 0.975057i | \(0.571243\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 7814.09 | 1.87469 | ||||||||
\(260\) | −761.340 | −0.181601 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −5742.24 | −1.35403 | ||||||||
\(263\) | 7853.83 | 1.84140 | 0.920700 | − | 0.390271i | \(-0.127619\pi\) | ||||
0.920700 | + | 0.390271i | \(0.127619\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −4053.91 | −0.939735 | ||||||||
\(266\) | −2404.64 | −0.554278 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −2623.67 | −0.598009 | ||||||||
\(269\) | 7656.82 | 1.73548 | 0.867741 | − | 0.497017i | \(-0.165571\pi\) | ||||
0.867741 | + | 0.497017i | \(0.165571\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 7351.92 | 1.64796 | 0.823981 | − | 0.566618i | \(-0.191749\pi\) | ||||
0.823981 | + | 0.566618i | \(0.191749\pi\) | |||||||
\(272\) | 767.759 | 0.171148 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −2286.71 | −0.504180 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −4238.60 | −0.919396 | −0.459698 | − | 0.888075i | \(-0.652042\pi\) | ||||
−0.459698 | + | 0.888075i | \(0.652042\pi\) | |||||||
\(278\) | 673.146 | 0.145225 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −1273.03 | −0.271706 | ||||||||
\(281\) | −4243.25 | −0.900822 | −0.450411 | − | 0.892821i | \(-0.648723\pi\) | ||||
−0.450411 | + | 0.892821i | \(0.648723\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −4069.93 | −0.854883 | −0.427442 | − | 0.904043i | \(-0.640585\pi\) | ||||
−0.427442 | + | 0.904043i | \(0.640585\pi\) | |||||||
\(284\) | −2114.41 | −0.441786 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −3743.50 | −0.769937 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2610.44 | −0.531334 | ||||||||
\(290\) | 730.181 | 0.147854 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −1790.61 | −0.358861 | ||||||||
\(293\) | −7903.75 | −1.57591 | −0.787955 | − | 0.615733i | \(-0.788860\pi\) | ||||
−0.787955 | + | 0.615733i | \(0.788860\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 143.419 | 0.0283057 | ||||||||
\(296\) | −2430.59 | −0.477280 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −1716.71 | −0.333712 | ||||||||
\(299\) | 62.8977 | 0.0121654 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −7306.40 | −1.39912 | ||||||||
\(302\) | 6173.79 | 1.17636 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 747.968 | 0.141115 | ||||||||
\(305\) | 3909.49 | 0.733956 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 4887.27 | 0.908570 | 0.454285 | − | 0.890856i | \(-0.349895\pi\) | ||||
0.454285 | + | 0.890856i | \(0.349895\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 3772.86 | 0.691240 | ||||||||
\(311\) | 6555.16 | 1.19521 | 0.597603 | − | 0.801792i | \(-0.296120\pi\) | ||||
0.597603 | + | 0.801792i | \(0.296120\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −6473.07 | −1.16894 | −0.584472 | − | 0.811414i | \(-0.698698\pi\) | ||||
−0.584472 | + | 0.811414i | \(0.698698\pi\) | |||||||
\(314\) | 3474.23 | 0.624403 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −3941.86 | −0.701730 | ||||||||
\(317\) | −3732.52 | −0.661322 | −0.330661 | − | 0.943750i | \(-0.607272\pi\) | ||||
−0.330661 | + | 0.943750i | \(0.607272\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0 | 0 | ||||||||
\(320\) | 395.977 | 0.0691743 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 105.170 | 0.0182016 | ||||||||
\(323\) | 2243.20 | 0.386424 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2667.75 | 0.455324 | ||||||||
\(326\) | −4765.82 | −0.809676 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 1164.42 | 0.196020 | ||||||||
\(329\) | 14846.4 | 2.48788 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 6093.87 | 1.01193 | 0.505966 | − | 0.862554i | \(-0.331136\pi\) | ||||
0.505966 | + | 0.862554i | \(0.331136\pi\) | |||||||
\(332\) | 513.837 | 0.0849411 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −5923.67 | −0.970446 | ||||||||
\(335\) | −4058.26 | −0.661869 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 3220.27 | 0.520531 | 0.260266 | − | 0.965537i | \(-0.416190\pi\) | ||||
0.260266 | + | 0.965537i | \(0.416190\pi\) | |||||||
\(338\) | −2501.27 | −0.402518 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1187.56 | 0.189425 | ||||||||
\(341\) | 0 | 0 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 630.707 | 0.0992857 | ||||||||
\(344\) | 2272.67 | 0.356204 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 629.789 | 0.0978545 | ||||||||
\(347\) | −2922.59 | −0.452141 | −0.226071 | − | 0.974111i | \(-0.572588\pi\) | ||||
−0.226071 | + | 0.974111i | \(0.572588\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −2398.61 | −0.367893 | −0.183946 | − | 0.982936i | \(-0.558887\pi\) | ||||
−0.183946 | + | 0.982936i | \(0.558887\pi\) | |||||||
\(350\) | 4460.70 | 0.681242 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8037.61 | 1.21189 | 0.605947 | − | 0.795505i | \(-0.292794\pi\) | ||||
0.605947 | + | 0.795505i | \(0.292794\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −3270.53 | −0.488963 | ||||||||
\(356\) | −5700.59 | −0.848682 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 4824.43 | 0.712231 | ||||||||
\(359\) | 6245.09 | 0.918115 | 0.459058 | − | 0.888406i | \(-0.348187\pi\) | ||||
0.459058 | + | 0.888406i | \(0.348187\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −4673.63 | −0.681386 | ||||||||
\(362\) | 7816.36 | 1.13486 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 3164.80 | 0.455716 | ||||||||
\(365\) | −2769.69 | −0.397184 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 3605.89 | 0.512878 | 0.256439 | − | 0.966560i | \(-0.417451\pi\) | ||||
0.256439 | + | 0.966560i | \(0.417451\pi\) | |||||||
\(368\) | −32.7134 | −0.00463398 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −3759.59 | −0.528248 | ||||||||
\(371\) | 16851.6 | 2.35820 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 1535.30 | 0.213123 | 0.106561 | − | 0.994306i | \(-0.466016\pi\) | ||||
0.106561 | + | 0.994306i | \(0.466016\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4618.01 | −0.633393 | ||||||||
\(377\) | −1815.27 | −0.247987 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −12947.9 | −1.75485 | −0.877426 | − | 0.479713i | \(-0.840741\pi\) | ||||
−0.877426 | + | 0.479713i | \(0.840741\pi\) | |||||||
\(380\) | 1156.94 | 0.156184 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 1825.22 | 0.244467 | ||||||||
\(383\) | 3063.26 | 0.408683 | 0.204341 | − | 0.978900i | \(-0.434495\pi\) | ||||
0.204341 | + | 0.978900i | \(0.434495\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1066.32 | −0.140607 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −570.211 | −0.0746084 | ||||||||
\(389\) | −3662.10 | −0.477316 | −0.238658 | − | 0.971104i | \(-0.576707\pi\) | ||||
−0.238658 | + | 0.971104i | \(0.576707\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −98.1094 | −0.0126895 | ||||||||
\(392\) | 2547.82 | 0.328276 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | −5400.97 | −0.690602 | ||||||||
\(395\) | −6097.20 | −0.776667 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −5438.40 | −0.687520 | −0.343760 | − | 0.939057i | \(-0.611701\pi\) | ||||
−0.343760 | + | 0.939057i | \(0.611701\pi\) | |||||||
\(398\) | 8819.24 | 1.11072 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −1387.51 | −0.173439 | ||||||||
\(401\) | −3275.54 | −0.407912 | −0.203956 | − | 0.978980i | \(-0.565380\pi\) | ||||
−0.203956 | + | 0.978980i | \(0.565380\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9379.52 | −1.15937 | ||||||||
\(404\) | 1175.32 | 0.144738 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −3035.28 | −0.371030 | ||||||||
\(407\) | 0 | 0 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 28.2549 | 0.00341593 | 0.00170797 | − | 0.999999i | \(-0.499456\pi\) | ||||
0.00170797 | + | 0.999999i | \(0.499456\pi\) | |||||||
\(410\) | 1801.11 | 0.216952 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −4006.20 | −0.479056 | ||||||||
\(413\) | −596.176 | −0.0710312 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 794.795 | 0.0940119 | ||||||||
\(416\) | −984.417 | −0.116022 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −2788.66 | −0.325143 | −0.162572 | − | 0.986697i | \(-0.551979\pi\) | ||||
−0.162572 | + | 0.986697i | \(0.551979\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8006.82 | −0.926908 | −0.463454 | − | 0.886121i | \(-0.653390\pi\) | ||||
−0.463454 | + | 0.886121i | \(0.653390\pi\) | |||||||
\(422\) | −11609.0 | −1.33914 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5241.73 | −0.600380 | ||||||||
\(425\) | −4161.22 | −0.474939 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −16251.3 | −1.84181 | ||||||||
\(428\) | −6416.01 | −0.724602 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 3515.33 | 0.394242 | ||||||||
\(431\) | −11372.5 | −1.27099 | −0.635495 | − | 0.772105i | \(-0.719204\pi\) | ||||
−0.635495 | + | 0.772105i | \(0.719204\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −2336.59 | −0.259329 | −0.129664 | − | 0.991558i | \(-0.541390\pi\) | ||||
−0.129664 | + | 0.991558i | \(0.541390\pi\) | |||||||
\(434\) | −15683.4 | −1.73462 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 1292.54 | 0.141975 | ||||||||
\(437\) | −95.5803 | −0.0104628 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −1689.97 | −0.183731 | −0.0918655 | − | 0.995771i | \(-0.529283\pi\) | ||||
−0.0918655 | + | 0.995771i | \(0.529283\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2952.33 | −0.317710 | ||||||||
\(443\) | −6847.10 | −0.734347 | −0.367173 | − | 0.930153i | \(-0.619674\pi\) | ||||
−0.367173 | + | 0.930153i | \(0.619674\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −8817.58 | −0.939311 | ||||||||
\(446\) | −6933.67 | −0.736141 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −1646.03 | −0.173588 | ||||||||
\(449\) | −16416.6 | −1.72550 | −0.862749 | − | 0.505633i | \(-0.831259\pi\) | ||||
−0.862749 | + | 0.505633i | \(0.831259\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 0 | 0 | ||||||||
\(452\) | 1857.84 | 0.193331 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 8073.17 | 0.834565 | ||||||||
\(455\) | 4895.26 | 0.504381 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −14619.7 | −1.49646 | −0.748228 | − | 0.663442i | \(-0.769095\pi\) | ||||
−0.748228 | + | 0.663442i | \(0.769095\pi\) | |||||||
\(458\) | −6156.43 | −0.628103 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −50.6005 | −0.00512883 | ||||||||
\(461\) | −932.481 | −0.0942082 | −0.0471041 | − | 0.998890i | \(-0.514999\pi\) | ||||
−0.0471041 | + | 0.998890i | \(0.514999\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5806.81 | 0.582862 | 0.291431 | − | 0.956592i | \(-0.405869\pi\) | ||||
0.291431 | + | 0.956592i | \(0.405869\pi\) | |||||||
\(464\) | 944.128 | 0.0944613 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −3375.21 | −0.335523 | ||||||||
\(467\) | 2143.97 | 0.212444 | 0.106222 | − | 0.994342i | \(-0.466125\pi\) | ||||
0.106222 | + | 0.994342i | \(0.466125\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 16869.7 | 1.66092 | ||||||||
\(470\) | −7143.07 | −0.701032 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 185.442 | 0.0180840 | ||||||||
\(473\) | 0 | 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −4053.96 | −0.391596 | ||||||||
\(476\) | −4936.54 | −0.475348 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4843.52 | −0.463467 | ||||||||
\(479\) | 3401.22 | 0.324437 | 0.162219 | − | 0.986755i | \(-0.448135\pi\) | ||||
0.162219 | + | 0.986755i | \(0.448135\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 9346.52 | 0.885997 | ||||||||
\(482\) | 13871.9 | 1.31089 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −881.993 | −0.0825758 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 9632.81 | 0.896313 | 0.448156 | − | 0.893955i | \(-0.352081\pi\) | ||||
0.448156 | + | 0.893955i | \(0.352081\pi\) | |||||||
\(488\) | 5054.99 | 0.468911 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 3940.92 | 0.363332 | ||||||||
\(491\) | 5594.16 | 0.514177 | 0.257088 | − | 0.966388i | \(-0.417237\pi\) | ||||
0.257088 | + | 0.966388i | \(0.417237\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2831.50 | 0.258670 | ||||||||
\(494\) | −2876.22 | −0.261958 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 4878.33 | 0.441620 | ||||||||
\(497\) | 13595.2 | 1.22702 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2295.31 | −0.205917 | −0.102958 | − | 0.994686i | \(-0.532831\pi\) | ||||
−0.102958 | + | 0.994686i | \(0.532831\pi\) | |||||||
\(500\) | −5239.75 | −0.468657 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 1528.73 | 0.135918 | ||||||||
\(503\) | −6271.41 | −0.555921 | −0.277961 | − | 0.960592i | \(-0.589658\pi\) | ||||
−0.277961 | + | 0.960592i | \(0.589658\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1817.96 | 0.160195 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 1310.20 | 0.114430 | ||||||||
\(509\) | −8882.04 | −0.773457 | −0.386729 | − | 0.922194i | \(-0.626395\pi\) | ||||
−0.386729 | + | 0.922194i | \(0.626395\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 11513.3 | 0.996706 | ||||||||
\(512\) | 512.000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −3657.81 | −0.313889 | ||||||||
\(515\) | −6196.72 | −0.530214 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 0 | 0 | ||||||||
\(518\) | 15628.2 | 1.32560 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1522.68 | −0.128411 | ||||||||
\(521\) | −506.901 | −0.0426252 | −0.0213126 | − | 0.999773i | \(-0.506785\pi\) | ||||
−0.0213126 | + | 0.999773i | \(0.506785\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −8415.97 | −0.703642 | −0.351821 | − | 0.936067i | \(-0.614437\pi\) | ||||
−0.351821 | + | 0.936067i | \(0.614437\pi\) | |||||||
\(524\) | −11484.5 | −0.957447 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 15707.7 | 1.30207 | ||||||||
\(527\) | 14630.4 | 1.20932 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −12162.8 | −0.999656 | ||||||||
\(530\) | −8107.82 | −0.664493 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −4809.28 | −0.391934 | ||||||||
\(533\) | −4477.65 | −0.363881 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −9924.18 | −0.801981 | ||||||||
\(536\) | −5247.35 | −0.422856 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 15313.6 | 1.22717 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2292.00 | 0.182145 | 0.0910727 | − | 0.995844i | \(-0.470970\pi\) | ||||
0.0910727 | + | 0.995844i | \(0.470970\pi\) | |||||||
\(542\) | 14703.8 | 1.16528 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1535.52 | 0.121020 | ||||||||
\(545\) | 1999.28 | 0.157137 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 9334.79 | 0.729665 | 0.364833 | − | 0.931073i | \(-0.381126\pi\) | ||||
0.364833 | + | 0.931073i | \(0.381126\pi\) | |||||||
\(548\) | −4573.43 | −0.356509 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 2758.51 | 0.213278 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 25345.3 | 1.94899 | ||||||||
\(554\) | −8477.20 | −0.650111 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 1346.29 | 0.102690 | ||||||||
\(557\) | −3681.18 | −0.280030 | −0.140015 | − | 0.990149i | \(-0.544715\pi\) | ||||
−0.140015 | + | 0.990149i | \(0.544715\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −8739.27 | −0.661238 | ||||||||
\(560\) | −2546.05 | −0.192125 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −8486.50 | −0.636978 | ||||||||
\(563\) | 23961.3 | 1.79369 | 0.896846 | − | 0.442342i | \(-0.145852\pi\) | ||||
0.896846 | + | 0.442342i | \(0.145852\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2873.68 | 0.213976 | ||||||||
\(566\) | −8139.85 | −0.604494 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −4228.82 | −0.312390 | ||||||||
\(569\) | 3727.10 | 0.274601 | 0.137301 | − | 0.990529i | \(-0.456157\pi\) | ||||
0.137301 | + | 0.990529i | \(0.456157\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 23463.5 | 1.71965 | 0.859823 | − | 0.510593i | \(-0.170574\pi\) | ||||
0.859823 | + | 0.510593i | \(0.170574\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −7487.01 | −0.544428 | ||||||||
\(575\) | 177.305 | 0.0128594 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −1118.13 | −0.0806729 | −0.0403365 | − | 0.999186i | \(-0.512843\pi\) | ||||
−0.0403365 | + | 0.999186i | \(0.512843\pi\) | |||||||
\(578\) | −5220.89 | −0.375710 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1460.36 | 0.104549 | ||||||||
\(581\) | −3303.87 | −0.235917 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 0 | 0 | ||||||||
\(584\) | −3581.22 | −0.253753 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −15807.5 | −1.11434 | ||||||||
\(587\) | 20399.2 | 1.43436 | 0.717178 | − | 0.696890i | \(-0.245434\pi\) | ||||
0.717178 | + | 0.696890i | \(0.245434\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 14253.3 | 0.997106 | ||||||||
\(590\) | 286.838 | 0.0200151 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | −4861.17 | −0.337488 | ||||||||
\(593\) | −2722.97 | −0.188565 | −0.0942826 | − | 0.995545i | \(-0.530056\pi\) | ||||
−0.0942826 | + | 0.995545i | \(0.530056\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −7635.76 | −0.526110 | ||||||||
\(596\) | −3433.41 | −0.235970 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 125.795 | 0.00860227 | ||||||||
\(599\) | 444.486 | 0.0303192 | 0.0151596 | − | 0.999885i | \(-0.495174\pi\) | ||||
0.0151596 | + | 0.999885i | \(0.495174\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −3564.00 | −0.241895 | −0.120947 | − | 0.992659i | \(-0.538593\pi\) | ||||
−0.120947 | + | 0.992659i | \(0.538593\pi\) | |||||||
\(602\) | −14612.8 | −0.989325 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 12347.6 | 0.831814 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −9182.13 | −0.613989 | −0.306994 | − | 0.951711i | \(-0.599323\pi\) | ||||
−0.306994 | + | 0.951711i | \(0.599323\pi\) | |||||||
\(608\) | 1495.94 | 0.0997832 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 7818.97 | 0.518985 | ||||||||
\(611\) | 17758.0 | 1.17580 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 15822.6 | 1.04253 | 0.521263 | − | 0.853396i | \(-0.325461\pi\) | ||||
0.521263 | + | 0.853396i | \(0.325461\pi\) | |||||||
\(614\) | 9774.53 | 0.642456 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −15442.0 | −1.00757 | −0.503784 | − | 0.863830i | \(-0.668059\pi\) | ||||
−0.503784 | + | 0.863830i | \(0.668059\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4205.61 | 0.273082 | 0.136541 | − | 0.990634i | \(-0.456401\pi\) | ||||
0.136541 | + | 0.990634i | \(0.456401\pi\) | |||||||
\(620\) | 7545.73 | 0.488780 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 13110.3 | 0.845138 | ||||||||
\(623\) | 36653.7 | 2.35714 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 2735.17 | 0.175051 | ||||||||
\(626\) | −12946.1 | −0.826568 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6948.47 | 0.441519 | ||||||||
\(629\) | −14578.9 | −0.924166 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18506.4 | 1.16755 | 0.583777 | − | 0.811914i | \(-0.301574\pi\) | ||||
0.583777 | + | 0.811914i | \(0.301574\pi\) | |||||||
\(632\) | −7883.71 | −0.496198 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −7465.03 | −0.467625 | ||||||||
\(635\) | 2026.59 | 0.126650 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −9797.32 | −0.609394 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 791.953 | 0.0489136 | ||||||||
\(641\) | −20000.4 | −1.23240 | −0.616201 | − | 0.787589i | \(-0.711329\pi\) | ||||
−0.616201 | + | 0.787589i | \(0.711329\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 22453.5 | 1.37710 | 0.688552 | − | 0.725187i | \(-0.258247\pi\) | ||||
0.688552 | + | 0.725187i | \(0.258247\pi\) | |||||||
\(644\) | 210.341 | 0.0128705 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 4486.40 | 0.273243 | ||||||||
\(647\) | −12963.8 | −0.787727 | −0.393863 | − | 0.919169i | \(-0.628862\pi\) | ||||
−0.393863 | + | 0.919169i | \(0.628862\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 0 | 0 | ||||||||
\(650\) | 5335.50 | 0.321962 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −9531.65 | −0.572528 | ||||||||
\(653\) | 5075.91 | 0.304189 | 0.152095 | − | 0.988366i | \(-0.451398\pi\) | ||||
0.152095 | + | 0.988366i | \(0.451398\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −17764.0 | −1.05969 | ||||||||
\(656\) | 2328.85 | 0.138607 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 29692.9 | 1.75919 | ||||||||
\(659\) | 29578.3 | 1.74842 | 0.874210 | − | 0.485548i | \(-0.161380\pi\) | ||||
0.874210 | + | 0.485548i | \(0.161380\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 13835.2 | 0.814113 | 0.407056 | − | 0.913403i | \(-0.366555\pi\) | ||||
0.407056 | + | 0.913403i | \(0.366555\pi\) | |||||||
\(662\) | 12187.7 | 0.715543 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 1027.67 | 0.0600625 | ||||||||
\(665\) | −7438.92 | −0.433788 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −120.647 | −0.00700371 | ||||||||
\(668\) | −11847.3 | −0.686209 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −8116.51 | −0.468012 | ||||||||
\(671\) | 0 | 0 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 14592.6 | 0.835812 | 0.417906 | − | 0.908490i | \(-0.362764\pi\) | ||||
0.417906 | + | 0.908490i | \(0.362764\pi\) | |||||||
\(674\) | 6440.53 | 0.368071 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5002.54 | −0.284624 | ||||||||
\(677\) | −6957.20 | −0.394959 | −0.197479 | − | 0.980307i | \(-0.563276\pi\) | ||||
−0.197479 | + | 0.980307i | \(0.563276\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 3666.34 | 0.207218 | ||||||||
\(680\) | 2375.12 | 0.133943 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −4828.48 | −0.270508 | −0.135254 | − | 0.990811i | \(-0.543185\pi\) | ||||
−0.135254 | + | 0.990811i | \(0.543185\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −7074.10 | −0.394580 | ||||||||
\(686\) | 1261.41 | 0.0702056 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 4545.34 | 0.251874 | ||||||||
\(689\) | 20156.4 | 1.11451 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −13876.3 | −0.763934 | −0.381967 | − | 0.924176i | \(-0.624753\pi\) | ||||
−0.381967 | + | 0.924176i | \(0.624753\pi\) | |||||||
\(692\) | 1259.58 | 0.0691936 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −5845.19 | −0.319712 | ||||||||
\(695\) | 2082.42 | 0.113656 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 6984.35 | 0.379557 | ||||||||
\(698\) | −4797.22 | −0.260140 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 8921.41 | 0.481711 | ||||||||
\(701\) | 10253.4 | 0.552445 | 0.276222 | − | 0.961094i | \(-0.410917\pi\) | ||||
0.276222 | + | 0.961094i | \(0.410917\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14203.1 | −0.761993 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 16075.2 | 0.856939 | ||||||||
\(707\) | −7557.06 | −0.401998 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 28775.1 | 1.52422 | 0.762111 | − | 0.647447i | \(-0.224163\pi\) | ||||
0.762111 | + | 0.647447i | \(0.224163\pi\) | |||||||
\(710\) | −6541.07 | −0.345749 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −11401.2 | −0.600109 | ||||||||
\(713\) | −623.386 | −0.0327433 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 9648.85 | 0.503624 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 12490.2 | 0.649206 | ||||||||
\(719\) | −10314.7 | −0.535011 | −0.267506 | − | 0.963556i | \(-0.586199\pi\) | ||||
−0.267506 | + | 0.963556i | \(0.586199\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 25759.0 | 1.33054 | ||||||||
\(722\) | −9347.25 | −0.481813 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 15632.7 | 0.802466 | ||||||||
\(725\) | −5117.14 | −0.262132 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 16485.6 | 0.841013 | 0.420506 | − | 0.907290i | \(-0.361852\pi\) | ||||
0.420506 | + | 0.907290i | \(0.361852\pi\) | |||||||
\(728\) | 6329.60 | 0.322240 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −5539.37 | −0.280851 | ||||||||
\(731\) | 13631.7 | 0.689724 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −10119.9 | −0.509943 | −0.254971 | − | 0.966949i | \(-0.582066\pi\) | ||||
−0.254971 | + | 0.966949i | \(0.582066\pi\) | |||||||
\(734\) | 7211.79 | 0.362659 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −65.4268 | −0.00327672 | ||||||||
\(737\) | 0 | 0 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2713.38 | 0.135065 | 0.0675326 | − | 0.997717i | \(-0.478487\pi\) | ||||
0.0675326 | + | 0.997717i | \(0.478487\pi\) | |||||||
\(740\) | −7519.18 | −0.373528 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 33703.3 | 1.66750 | ||||||||
\(743\) | 13700.9 | 0.676497 | 0.338249 | − | 0.941057i | \(-0.390166\pi\) | ||||
0.338249 | + | 0.941057i | \(0.390166\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −5310.75 | −0.261169 | ||||||||
\(746\) | 3070.60 | 0.150700 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 41253.7 | 2.01252 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −7831.68 | −0.380535 | −0.190268 | − | 0.981732i | \(-0.560936\pi\) | ||||
−0.190268 | + | 0.981732i | \(0.560936\pi\) | |||||||
\(752\) | −9236.02 | −0.447877 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −3630.53 | −0.175353 | ||||||||
\(755\) | 19099.0 | 0.920643 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36879.2 | 1.77067 | 0.885335 | − | 0.464953i | \(-0.153929\pi\) | ||||
0.885335 | + | 0.464953i | \(0.153929\pi\) | |||||||
\(758\) | −25895.8 | −1.24087 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 2313.89 | 0.110439 | ||||||||
\(761\) | −30071.5 | −1.43245 | −0.716224 | − | 0.697871i | \(-0.754131\pi\) | ||||
−0.716224 | + | 0.697871i | \(0.754131\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −8310.75 | −0.394324 | ||||||||
\(764\) | 3650.44 | 0.172864 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 6126.53 | 0.288982 | ||||||||
\(767\) | −713.093 | −0.0335701 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −23609.8 | −1.10714 | −0.553571 | − | 0.832802i | \(-0.686735\pi\) | ||||
−0.553571 | + | 0.832802i | \(0.686735\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −2132.64 | −0.0994241 | ||||||||
\(773\) | −16132.1 | −0.750622 | −0.375311 | − | 0.926899i | \(-0.622464\pi\) | ||||
−0.375311 | + | 0.926899i | \(0.622464\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −26440.4 | −1.22550 | ||||||||
\(776\) | −1140.42 | −0.0527561 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −7324.20 | −0.337513 | ||||||||
\(779\) | 6804.30 | 0.312952 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 0 | 0 | ||||||||
\(782\) | −196.219 | −0.00897285 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 5095.63 | 0.232126 | ||||||||
\(785\) | 10747.8 | 0.488668 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −12473.2 | −0.564959 | −0.282480 | − | 0.959273i | \(-0.591157\pi\) | ||||
−0.282480 | + | 0.959273i | \(0.591157\pi\) | |||||||
\(788\) | −10801.9 | −0.488329 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −12194.4 | −0.549186 | ||||||||
\(791\) | −11945.5 | −0.536959 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −19438.3 | −0.870461 | ||||||||
\(794\) | −10876.8 | −0.486150 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 17638.5 | 0.785401 | ||||||||
\(797\) | 10468.1 | 0.465246 | 0.232623 | − | 0.972567i | \(-0.425269\pi\) | ||||
0.232623 | + | 0.972567i | \(0.425269\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −27699.4 | −1.22645 | ||||||||
\(800\) | −2775.02 | −0.122640 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6551.08 | −0.288437 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 325.351 | 0.0142449 | ||||||||
\(806\) | −18759.0 | −0.819800 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 2350.64 | 0.102345 | ||||||||
\(809\) | −17641.7 | −0.766686 | −0.383343 | − | 0.923606i | \(-0.625227\pi\) | ||||
−0.383343 | + | 0.923606i | \(0.625227\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 17854.5 | 0.773066 | 0.386533 | − | 0.922276i | \(-0.373672\pi\) | ||||
0.386533 | + | 0.922276i | \(0.373672\pi\) | |||||||
\(812\) | −6070.56 | −0.262358 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14743.4 | −0.633667 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 13280.3 | 0.568691 | ||||||||
\(818\) | 56.5099 | 0.00241543 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 3602.22 | 0.153409 | ||||||||
\(821\) | 14573.5 | 0.619511 | 0.309755 | − | 0.950816i | \(-0.399753\pi\) | ||||
0.309755 | + | 0.950816i | \(0.399753\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 18565.3 | 0.786326 | 0.393163 | − | 0.919469i | \(-0.371381\pi\) | ||||
0.393163 | + | 0.919469i | \(0.371381\pi\) | |||||||
\(824\) | −8012.39 | −0.338744 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1192.35 | −0.0502267 | ||||||||
\(827\) | 38779.4 | 1.63058 | 0.815291 | − | 0.579052i | \(-0.196577\pi\) | ||||
0.815291 | + | 0.579052i | \(0.196577\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 12060.0 | 0.505263 | 0.252631 | − | 0.967563i | \(-0.418704\pi\) | ||||
0.252631 | + | 0.967563i | \(0.418704\pi\) | |||||||
\(830\) | 1589.59 | 0.0664764 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1968.83 | −0.0820397 | ||||||||
\(833\) | 15282.1 | 0.635647 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −18325.3 | −0.759488 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −5577.32 | −0.229911 | ||||||||
\(839\) | 28708.8 | 1.18133 | 0.590666 | − | 0.806916i | \(-0.298865\pi\) | ||||
0.590666 | + | 0.806916i | \(0.298865\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −20907.1 | −0.857233 | ||||||||
\(842\) | −16013.6 | −0.655423 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −23218.0 | −0.946917 | ||||||||
\(845\) | −7737.85 | −0.315018 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −10483.5 | −0.424532 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −8322.45 | −0.335833 | ||||||||
\(851\) | 621.193 | 0.0250226 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8281.48 | −0.332418 | −0.166209 | − | 0.986091i | \(-0.553153\pi\) | ||||
−0.166209 | + | 0.986091i | \(0.553153\pi\) | |||||||
\(854\) | −32502.6 | −1.30236 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −12832.0 | −0.512371 | ||||||||
\(857\) | −21003.8 | −0.837195 | −0.418597 | − | 0.908172i | \(-0.637478\pi\) | ||||
−0.418597 | + | 0.908172i | \(0.637478\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 120.604 | 0.00479040 | 0.00239520 | − | 0.999997i | \(-0.499238\pi\) | ||||
0.00239520 | + | 0.999997i | \(0.499238\pi\) | |||||||
\(860\) | 7030.66 | 0.278771 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −22745.1 | −0.898725 | ||||||||
\(863\) | 24086.3 | 0.950065 | 0.475033 | − | 0.879968i | \(-0.342436\pi\) | ||||
0.475033 | + | 0.879968i | \(0.342436\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 1948.29 | 0.0765827 | ||||||||
\(866\) | −4673.18 | −0.183373 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −31366.7 | −1.22656 | ||||||||
\(869\) | 0 | 0 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 20178.0 | 0.784967 | ||||||||
\(872\) | 2585.07 | 0.100392 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −191.161 | −0.00739829 | ||||||||
\(875\) | 33690.5 | 1.30165 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3898.55 | 0.150108 | 0.0750539 | − | 0.997179i | \(-0.476087\pi\) | ||||
0.0750539 | + | 0.997179i | \(0.476087\pi\) | |||||||
\(878\) | −3379.94 | −0.129918 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −27751.9 | −1.06128 | −0.530639 | − | 0.847598i | \(-0.678048\pi\) | ||||
−0.530639 | + | 0.847598i | \(0.678048\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −9931.42 | −0.378504 | −0.189252 | − | 0.981929i | \(-0.560606\pi\) | ||||
−0.189252 | + | 0.981929i | \(0.560606\pi\) | |||||||
\(884\) | −5904.65 | −0.224655 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −13694.2 | −0.519261 | ||||||||
\(887\) | −16262.0 | −0.615586 | −0.307793 | − | 0.951453i | \(-0.599590\pi\) | ||||
−0.307793 | + | 0.951453i | \(0.599590\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −8424.31 | −0.317820 | ||||||||
\(890\) | −17635.2 | −0.664193 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −13867.3 | −0.520530 | ||||||||
\(893\) | −26985.3 | −1.01123 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 14924.7 | 0.557405 | ||||||||
\(896\) | −3292.06 | −0.122745 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | −32833.2 | −1.22011 | ||||||||
\(899\) | 17991.3 | 0.667457 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −31440.5 | −1.16253 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3715.68 | 0.136705 | ||||||||
\(905\) | 24180.4 | 0.888160 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 31520.9 | 1.15395 | 0.576976 | − | 0.816761i | \(-0.304233\pi\) | ||||
0.576976 | + | 0.816761i | \(0.304233\pi\) | |||||||
\(908\) | 16146.3 | 0.590127 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 9790.53 | 0.356652 | ||||||||
\(911\) | 48867.3 | 1.77722 | 0.888609 | − | 0.458665i | \(-0.151672\pi\) | ||||
0.888609 | + | 0.458665i | \(0.151672\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 0 | 0 | ||||||||
\(914\) | −29239.4 | −1.05815 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −12312.9 | −0.444136 | ||||||||
\(917\) | 73843.0 | 2.65922 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −18472.9 | −0.663073 | −0.331536 | − | 0.943442i | \(-0.607567\pi\) | ||||
−0.331536 | + | 0.943442i | \(0.607567\pi\) | |||||||
\(920\) | −101.201 | −0.00362663 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −1864.96 | −0.0666153 | ||||||||
\(923\) | 16261.4 | 0.579904 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 26347.4 | 0.936536 | ||||||||
\(926\) | 11613.6 | 0.412146 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1888.26 | 0.0667943 | ||||||||
\(929\) | 40016.6 | 1.41324 | 0.706622 | − | 0.707591i | \(-0.250218\pi\) | ||||
0.706622 | + | 0.707591i | \(0.250218\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 14888.2 | 0.524103 | ||||||||
\(932\) | −6750.42 | −0.237251 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4287.95 | 0.150220 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20667.1 | 0.720562 | 0.360281 | − | 0.932844i | \(-0.382681\pi\) | ||||
0.360281 | + | 0.932844i | \(0.382681\pi\) | |||||||
\(938\) | 33739.4 | 1.17445 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −14286.1 | −0.495705 | ||||||||
\(941\) | −47773.6 | −1.65502 | −0.827510 | − | 0.561451i | \(-0.810243\pi\) | ||||
−0.827510 | + | 0.561451i | \(0.810243\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −297.595 | −0.0102768 | ||||||||
\(944\) | 370.883 | 0.0127873 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −46098.8 | −1.58185 | −0.790924 | − | 0.611914i | \(-0.790400\pi\) | ||||
−0.790924 | + | 0.611914i | \(0.790400\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 13771.1 | 0.471054 | ||||||||
\(950\) | −8107.91 | −0.276900 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −9873.08 | −0.336122 | ||||||||
\(953\) | −57230.1 | −1.94529 | −0.972646 | − | 0.232290i | \(-0.925378\pi\) | ||||
−0.972646 | + | 0.232290i | \(0.925378\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 5646.44 | 0.191324 | ||||||||
\(956\) | −9687.03 | −0.327721 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 6802.43 | 0.229412 | ||||||||
\(959\) | 29406.2 | 0.990173 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 63170.5 | 2.12046 | ||||||||
\(962\) | 18693.0 | 0.626495 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 27743.9 | 0.926940 | ||||||||
\(965\) | −3298.73 | −0.110041 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 43977.3 | 1.46247 | 0.731237 | − | 0.682123i | \(-0.238943\pi\) | ||||
0.731237 | + | 0.682123i | \(0.238943\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1763.99 | −0.0583899 | ||||||||
\(971\) | −3968.54 | −0.131160 | −0.0655800 | − | 0.997847i | \(-0.520890\pi\) | ||||
−0.0655800 | + | 0.997847i | \(0.520890\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8656.38 | −0.285212 | ||||||||
\(974\) | 19265.6 | 0.633789 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 10110.0 | 0.331570 | ||||||||
\(977\) | −2691.26 | −0.0881278 | −0.0440639 | − | 0.999029i | \(-0.514031\pi\) | ||||
−0.0440639 | + | 0.999029i | \(0.514031\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 0 | 0 | ||||||||
\(980\) | 7881.85 | 0.256915 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 11188.3 | 0.363578 | ||||||||
\(983\) | −45874.5 | −1.48847 | −0.744237 | − | 0.667916i | \(-0.767187\pi\) | ||||
−0.744237 | + | 0.667916i | \(0.767187\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −16708.3 | −0.540477 | ||||||||
\(986\) | 5663.00 | 0.182907 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −5752.44 | −0.185232 | ||||||||
\(989\) | −580.834 | −0.0186749 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1102.69 | −0.0353462 | −0.0176731 | − | 0.999844i | \(-0.505626\pi\) | ||||
−0.0176731 | + | 0.999844i | \(0.505626\pi\) | |||||||
\(992\) | 9756.67 | 0.312273 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 27190.5 | 0.867635 | ||||||||
\(995\) | 27282.9 | 0.869273 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 46230.7 | 1.46855 | 0.734274 | − | 0.678853i | \(-0.237523\pi\) | ||||
0.734274 | + | 0.678853i | \(0.237523\pi\) | |||||||
\(998\) | −4590.63 | −0.145605 | ||||||||
\(999\) | 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 | 2178.4.a.bz.1.3 | 4 | ||
3.2 | odd | 2 | 726.4.a.w.1.2 | 4 | |||
11.7 | odd | 10 | 198.4.f.f.181.2 | 8 | |||
11.8 | odd | 10 | 198.4.f.f.163.2 | 8 | |||
11.10 | odd | 2 | 2178.4.a.bu.1.3 | 4 | |||
33.8 | even | 10 | 66.4.e.c.31.1 | ✓ | 8 | ||
33.29 | even | 10 | 66.4.e.c.49.1 | yes | 8 | ||
33.32 | even | 2 | 726.4.a.z.1.2 | 4 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
66.4.e.c.31.1 | ✓ | 8 | 33.8 | even | 10 | ||
66.4.e.c.49.1 | yes | 8 | 33.29 | even | 10 | ||
198.4.f.f.163.2 | 8 | 11.8 | odd | 10 | |||
198.4.f.f.181.2 | 8 | 11.7 | odd | 10 | |||
726.4.a.w.1.2 | 4 | 3.2 | odd | 2 | |||
726.4.a.z.1.2 | 4 | 33.32 | even | 2 | |||
2178.4.a.bu.1.3 | 4 | 11.10 | odd | 2 | |||
2178.4.a.bz.1.3 | 4 | 1.1 | even | 1 | trivial |