Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [289,4,Mod(288,289)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(289, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("289.288");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 289 = 17^{2} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 289.b (of order \(2\), degree \(1\), not minimal) |
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: | no |
Analytic conductor: | \(17.0515519917\) |
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: | \( x^{8} + 43x^{6} + 505x^{4} + 1528x^{2} + 1296 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 288.8 | ||
Root | \(3.68488i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 289.288 |
Dual form | 289.4.b.d.288.7 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/289\mathbb{Z}\right)^\times\).
\(n\) | \(3\) |
\(\chi(n)\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 3.68488 | 1.30280 | 0.651400 | − | 0.758734i | \(-0.274182\pi\) | ||||
0.651400 | + | 0.758734i | \(0.274182\pi\) | |||||||
\(3\) | 9.05894i | 1.74339i | 0.490046 | + | 0.871697i | \(0.336980\pi\) | ||||
−0.490046 | + | 0.871697i | \(0.663020\pi\) | |||||||
\(4\) | 5.57832 | 0.697290 | ||||||||
\(5\) | − 7.08909i | − 0.634067i | −0.948414 | − | 0.317034i | \(-0.897313\pi\) | ||||
0.948414 | − | 0.317034i | \(-0.102687\pi\) | |||||||
\(6\) | 33.3811i | 2.27129i | ||||||||
\(7\) | 28.1854i | 1.52187i | 0.648828 | + | 0.760935i | \(0.275259\pi\) | ||||
−0.648828 | + | 0.760935i | \(0.724741\pi\) | |||||||
\(8\) | −8.92359 | −0.394371 | ||||||||
\(9\) | −55.0643 | −2.03942 | ||||||||
\(10\) | − 26.1224i | − 0.826064i | ||||||||
\(11\) | − 15.3047i | − 0.419503i | −0.977755 | − | 0.209751i | \(-0.932735\pi\) | ||||
0.977755 | − | 0.209751i | \(-0.0672655\pi\) | |||||||
\(12\) | 50.5336i | 1.21565i | ||||||||
\(13\) | 2.51532 | 0.0536634 | 0.0268317 | − | 0.999640i | \(-0.491458\pi\) | ||||
0.0268317 | + | 0.999640i | \(0.491458\pi\) | |||||||
\(14\) | 103.860i | 1.98269i | ||||||||
\(15\) | 64.2196 | 1.10543 | ||||||||
\(16\) | −77.5089 | −1.21108 | ||||||||
\(17\) | 0 | 0 | ||||||||
\(18\) | −202.905 | −2.65696 | ||||||||
\(19\) | −14.3453 | −0.173212 | −0.0866062 | − | 0.996243i | \(-0.527602\pi\) | ||||
−0.0866062 | + | 0.996243i | \(0.527602\pi\) | |||||||
\(20\) | − 39.5452i | − 0.442129i | ||||||||
\(21\) | −255.330 | −2.65322 | ||||||||
\(22\) | − 56.3958i | − 0.546529i | ||||||||
\(23\) | 180.191i | 1.63359i | 0.576931 | + | 0.816793i | \(0.304250\pi\) | ||||
−0.576931 | + | 0.816793i | \(0.695750\pi\) | |||||||
\(24\) | − 80.8383i | − 0.687544i | ||||||||
\(25\) | 74.7448 | 0.597958 | ||||||||
\(26\) | 9.26864 | 0.0699127 | ||||||||
\(27\) | − 254.233i | − 1.81212i | ||||||||
\(28\) | 157.227i | 1.06118i | ||||||||
\(29\) | − 41.2425i | − 0.264088i | −0.991244 | − | 0.132044i | \(-0.957846\pi\) | ||||
0.991244 | − | 0.132044i | \(-0.0421540\pi\) | |||||||
\(30\) | 236.641 | 1.44015 | ||||||||
\(31\) | − 155.242i | − 0.899426i | −0.893173 | − | 0.449713i | \(-0.851526\pi\) | ||||
0.893173 | − | 0.449713i | \(-0.148474\pi\) | |||||||
\(32\) | −214.222 | −1.18342 | ||||||||
\(33\) | 138.644 | 0.731358 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 199.809 | 0.964968 | ||||||||
\(36\) | −307.167 | −1.42207 | ||||||||
\(37\) | 225.676i | 1.00273i | 0.865237 | + | 0.501363i | \(0.167168\pi\) | ||||
−0.865237 | + | 0.501363i | \(0.832832\pi\) | |||||||
\(38\) | −52.8606 | −0.225661 | ||||||||
\(39\) | 22.7861i | 0.0935564i | ||||||||
\(40\) | 63.2602i | 0.250058i | ||||||||
\(41\) | 234.306i | 0.892497i | 0.894909 | + | 0.446249i | \(0.147240\pi\) | ||||
−0.894909 | + | 0.446249i | \(0.852760\pi\) | |||||||
\(42\) | −940.860 | −3.45661 | ||||||||
\(43\) | 321.875 | 1.14152 | 0.570761 | − | 0.821117i | \(-0.306648\pi\) | ||||
0.570761 | + | 0.821117i | \(0.306648\pi\) | |||||||
\(44\) | − 85.3743i | − 0.292515i | ||||||||
\(45\) | 390.356i | 1.29313i | ||||||||
\(46\) | 663.983i | 2.12824i | ||||||||
\(47\) | −326.183 | −1.01231 | −0.506156 | − | 0.862442i | \(-0.668934\pi\) | ||||
−0.506156 | + | 0.862442i | \(0.668934\pi\) | |||||||
\(48\) | − 702.148i | − 2.11138i | ||||||||
\(49\) | −451.418 | −1.31609 | ||||||||
\(50\) | 275.425 | 0.779021 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 14.0313 | 0.0374189 | ||||||||
\(53\) | 57.1579 | 0.148137 | 0.0740683 | − | 0.997253i | \(-0.476402\pi\) | ||||
0.0740683 | + | 0.997253i | \(0.476402\pi\) | |||||||
\(54\) | − 936.818i | − 2.36083i | ||||||||
\(55\) | −108.496 | −0.265993 | ||||||||
\(56\) | − 251.515i | − 0.600181i | ||||||||
\(57\) | − 129.953i | − 0.301977i | ||||||||
\(58\) | − 151.974i | − 0.344054i | ||||||||
\(59\) | 241.623 | 0.533164 | 0.266582 | − | 0.963812i | \(-0.414106\pi\) | ||||
0.266582 | + | 0.963812i | \(0.414106\pi\) | |||||||
\(60\) | 358.238 | 0.770805 | ||||||||
\(61\) | 460.925i | 0.967465i | 0.875216 | + | 0.483732i | \(0.160719\pi\) | ||||
−0.875216 | + | 0.483732i | \(0.839281\pi\) | |||||||
\(62\) | − 572.046i | − 1.17177i | ||||||||
\(63\) | − 1552.01i | − 3.10373i | ||||||||
\(64\) | −169.311 | −0.330685 | ||||||||
\(65\) | − 17.8313i | − 0.0340262i | ||||||||
\(66\) | 510.886 | 0.952814 | ||||||||
\(67\) | 392.696 | 0.716052 | 0.358026 | − | 0.933712i | \(-0.383450\pi\) | ||||
0.358026 | + | 0.933712i | \(0.383450\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1632.34 | −2.84798 | ||||||||
\(70\) | 736.272 | 1.25716 | ||||||||
\(71\) | − 615.558i | − 1.02892i | −0.857515 | − | 0.514460i | \(-0.827993\pi\) | ||||
0.857515 | − | 0.514460i | \(-0.172007\pi\) | |||||||
\(72\) | 491.372 | 0.804288 | ||||||||
\(73\) | 697.452i | 1.11823i | 0.829091 | + | 0.559114i | \(0.188858\pi\) | ||||
−0.829091 | + | 0.559114i | \(0.811142\pi\) | |||||||
\(74\) | 831.587i | 1.30635i | ||||||||
\(75\) | 677.109i | 1.04248i | ||||||||
\(76\) | −80.0226 | −0.120779 | ||||||||
\(77\) | 431.369 | 0.638429 | ||||||||
\(78\) | 83.9641i | 0.121885i | ||||||||
\(79\) | 991.317i | 1.41180i | 0.708313 | + | 0.705898i | \(0.249456\pi\) | ||||
−0.708313 | + | 0.705898i | \(0.750544\pi\) | |||||||
\(80\) | 549.468i | 0.767904i | ||||||||
\(81\) | 816.345 | 1.11981 | ||||||||
\(82\) | 863.387i | 1.16275i | ||||||||
\(83\) | 98.9057 | 0.130799 | 0.0653995 | − | 0.997859i | \(-0.479168\pi\) | ||||
0.0653995 | + | 0.997859i | \(0.479168\pi\) | |||||||
\(84\) | −1424.31 | −1.85006 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 1186.07 | 1.48717 | ||||||||
\(87\) | 373.613 | 0.460409 | ||||||||
\(88\) | 136.573i | 0.165440i | ||||||||
\(89\) | 698.470 | 0.831884 | 0.415942 | − | 0.909391i | \(-0.363452\pi\) | ||||
0.415942 | + | 0.909391i | \(0.363452\pi\) | |||||||
\(90\) | 1438.41i | 1.68469i | ||||||||
\(91\) | 70.8954i | 0.0816687i | ||||||||
\(92\) | 1005.16i | 1.13908i | ||||||||
\(93\) | 1406.32 | 1.56805 | ||||||||
\(94\) | −1201.94 | −1.31884 | ||||||||
\(95\) | 101.695i | 0.109828i | ||||||||
\(96\) | − 1940.62i | − 2.06317i | ||||||||
\(97\) | 1428.66i | 1.49545i | 0.664009 | + | 0.747725i | \(0.268854\pi\) | ||||
−0.664009 | + | 0.747725i | \(0.731146\pi\) | |||||||
\(98\) | −1663.42 | −1.71460 | ||||||||
\(99\) | 842.741i | 0.855542i | ||||||||
\(100\) | 416.950 | 0.416950 | ||||||||
\(101\) | 408.671 | 0.402617 | 0.201308 | − | 0.979528i | \(-0.435481\pi\) | ||||
0.201308 | + | 0.979528i | \(0.435481\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1649.55 | 1.57801 | 0.789007 | − | 0.614384i | \(-0.210596\pi\) | ||||
0.789007 | + | 0.614384i | \(0.210596\pi\) | |||||||
\(104\) | −22.4457 | −0.0211633 | ||||||||
\(105\) | 1810.06i | 1.68232i | ||||||||
\(106\) | 210.620 | 0.192993 | ||||||||
\(107\) | − 2055.01i | − 1.85668i | −0.371731 | − | 0.928340i | \(-0.621236\pi\) | ||||
0.371731 | − | 0.928340i | \(-0.378764\pi\) | |||||||
\(108\) | − 1418.19i | − 1.26357i | ||||||||
\(109\) | − 445.064i | − 0.391095i | −0.980694 | − | 0.195548i | \(-0.937352\pi\) | ||||
0.980694 | − | 0.195548i | \(-0.0626485\pi\) | |||||||
\(110\) | −399.795 | −0.346536 | ||||||||
\(111\) | −2044.38 | −1.74814 | ||||||||
\(112\) | − 2184.62i | − 1.84310i | ||||||||
\(113\) | 1226.02i | 1.02066i | 0.859979 | + | 0.510330i | \(0.170477\pi\) | ||||
−0.859979 | + | 0.510330i | \(0.829523\pi\) | |||||||
\(114\) | − 478.861i | − 0.393416i | ||||||||
\(115\) | 1277.39 | 1.03580 | ||||||||
\(116\) | − 230.064i | − 0.184146i | ||||||||
\(117\) | −138.504 | −0.109442 | ||||||||
\(118\) | 890.352 | 0.694607 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −573.070 | −0.435949 | ||||||||
\(121\) | 1096.77 | 0.824017 | ||||||||
\(122\) | 1698.45i | 1.26041i | ||||||||
\(123\) | −2122.56 | −1.55597 | ||||||||
\(124\) | − 865.987i | − 0.627161i | ||||||||
\(125\) | − 1416.01i | − 1.01321i | ||||||||
\(126\) | − 5718.97i | − 4.04354i | ||||||||
\(127\) | 591.124 | 0.413022 | 0.206511 | − | 0.978444i | \(-0.433789\pi\) | ||||
0.206511 | + | 0.978444i | \(0.433789\pi\) | |||||||
\(128\) | 1089.89 | 0.752604 | ||||||||
\(129\) | 2915.84i | 1.99012i | ||||||||
\(130\) | − 65.7063i | − 0.0443294i | ||||||||
\(131\) | − 2025.27i | − 1.35075i | −0.737474 | − | 0.675375i | \(-0.763982\pi\) | ||||
0.737474 | − | 0.675375i | \(-0.236018\pi\) | |||||||
\(132\) | 773.401 | 0.509969 | ||||||||
\(133\) | − 404.328i | − 0.263607i | ||||||||
\(134\) | 1447.04 | 0.932873 | ||||||||
\(135\) | −1802.28 | −1.14901 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 623.919 | 0.389087 | 0.194544 | − | 0.980894i | \(-0.437677\pi\) | ||||
0.194544 | + | 0.980894i | \(0.437677\pi\) | |||||||
\(138\) | −6014.98 | −3.71036 | ||||||||
\(139\) | 1033.14i | 0.630429i | 0.949020 | + | 0.315214i | \(0.102076\pi\) | ||||
−0.949020 | + | 0.315214i | \(0.897924\pi\) | |||||||
\(140\) | 1114.60 | 0.672863 | ||||||||
\(141\) | − 2954.87i | − 1.76486i | ||||||||
\(142\) | − 2268.25i | − 1.34048i | ||||||||
\(143\) | − 38.4961i | − 0.0225119i | ||||||||
\(144\) | 4267.98 | 2.46989 | ||||||||
\(145\) | −292.372 | −0.167449 | ||||||||
\(146\) | 2570.02i | 1.45683i | ||||||||
\(147\) | − 4089.37i | − 2.29446i | ||||||||
\(148\) | 1258.89i | 0.699190i | ||||||||
\(149\) | −284.476 | −0.156411 | −0.0782054 | − | 0.996937i | \(-0.524919\pi\) | ||||
−0.0782054 | + | 0.996937i | \(0.524919\pi\) | |||||||
\(150\) | 2495.06i | 1.35814i | ||||||||
\(151\) | −3153.25 | −1.69939 | −0.849696 | − | 0.527273i | \(-0.823214\pi\) | ||||
−0.849696 | + | 0.527273i | \(0.823214\pi\) | |||||||
\(152\) | 128.012 | 0.0683099 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 1589.54 | 0.831745 | ||||||||
\(155\) | −1100.52 | −0.570297 | ||||||||
\(156\) | 127.108i | 0.0652359i | ||||||||
\(157\) | −482.335 | −0.245188 | −0.122594 | − | 0.992457i | \(-0.539121\pi\) | ||||
−0.122594 | + | 0.992457i | \(0.539121\pi\) | |||||||
\(158\) | 3652.88i | 1.83929i | ||||||||
\(159\) | 517.790i | 0.258261i | ||||||||
\(160\) | 1518.64i | 0.750369i | ||||||||
\(161\) | −5078.77 | −2.48611 | ||||||||
\(162\) | 3008.13 | 1.45890 | ||||||||
\(163\) | − 3717.39i | − 1.78631i | −0.449749 | − | 0.893155i | \(-0.648487\pi\) | ||||
0.449749 | − | 0.893155i | \(-0.351513\pi\) | |||||||
\(164\) | 1307.03i | 0.622329i | ||||||||
\(165\) | − 982.860i | − 0.463731i | ||||||||
\(166\) | 364.455 | 0.170405 | ||||||||
\(167\) | − 2128.93i | − 0.986475i | −0.869895 | − | 0.493237i | \(-0.835813\pi\) | ||||
0.869895 | − | 0.493237i | \(-0.164187\pi\) | |||||||
\(168\) | 2278.46 | 1.04635 | ||||||||
\(169\) | −2190.67 | −0.997120 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 789.914 | 0.353253 | ||||||||
\(172\) | 1795.52 | 0.795971 | ||||||||
\(173\) | 1197.86i | 0.526426i | 0.964738 | + | 0.263213i | \(0.0847822\pi\) | ||||
−0.964738 | + | 0.263213i | \(0.915218\pi\) | |||||||
\(174\) | 1376.72 | 0.599821 | ||||||||
\(175\) | 2106.71i | 0.910015i | ||||||||
\(176\) | 1186.25i | 0.508050i | ||||||||
\(177\) | 2188.85i | 0.929515i | ||||||||
\(178\) | 2573.78 | 1.08378 | ||||||||
\(179\) | −4095.63 | −1.71018 | −0.855089 | − | 0.518482i | \(-0.826497\pi\) | ||||
−0.855089 | + | 0.518482i | \(0.826497\pi\) | |||||||
\(180\) | 2177.53i | 0.901687i | ||||||||
\(181\) | 1297.08i | 0.532660i | 0.963882 | + | 0.266330i | \(0.0858110\pi\) | ||||
−0.963882 | + | 0.266330i | \(0.914189\pi\) | |||||||
\(182\) | 261.241i | 0.106398i | ||||||||
\(183\) | −4175.49 | −1.68667 | ||||||||
\(184\) | − 1607.95i | − 0.644239i | ||||||||
\(185\) | 1599.83 | 0.635795 | ||||||||
\(186\) | 5182.13 | 2.04286 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | −1819.55 | −0.705876 | ||||||||
\(189\) | 7165.67 | 2.75781 | ||||||||
\(190\) | 374.734i | 0.143084i | ||||||||
\(191\) | 4381.72 | 1.65995 | 0.829974 | − | 0.557803i | \(-0.188355\pi\) | ||||
0.829974 | + | 0.557803i | \(0.188355\pi\) | |||||||
\(192\) | − 1533.77i | − 0.576514i | ||||||||
\(193\) | − 1022.20i | − 0.381240i | −0.981664 | − | 0.190620i | \(-0.938950\pi\) | ||||
0.981664 | − | 0.190620i | \(-0.0610498\pi\) | |||||||
\(194\) | 5264.44i | 1.94827i | ||||||||
\(195\) | 161.533 | 0.0593211 | ||||||||
\(196\) | −2518.15 | −0.917695 | ||||||||
\(197\) | 2202.50i | 0.796555i | 0.917265 | + | 0.398278i | \(0.130392\pi\) | ||||
−0.917265 | + | 0.398278i | \(0.869608\pi\) | |||||||
\(198\) | 3105.40i | 1.11460i | ||||||||
\(199\) | − 76.0165i | − 0.0270787i | −0.999908 | − | 0.0135394i | \(-0.995690\pi\) | ||||
0.999908 | − | 0.0135394i | \(-0.00430985\pi\) | |||||||
\(200\) | −666.992 | −0.235817 | ||||||||
\(201\) | 3557.41i | 1.24836i | ||||||||
\(202\) | 1505.90 | 0.524529 | ||||||||
\(203\) | 1162.44 | 0.401907 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 1661.01 | 0.565904 | ||||||||
\(206\) | 6078.40 | 2.05584 | ||||||||
\(207\) | − 9922.12i | − 3.33157i | ||||||||
\(208\) | −194.960 | −0.0649905 | ||||||||
\(209\) | 219.550i | 0.0726631i | ||||||||
\(210\) | 6669.84i | 2.19173i | ||||||||
\(211\) | − 1972.63i | − 0.643609i | −0.946806 | − | 0.321804i | \(-0.895711\pi\) | ||||
0.946806 | − | 0.321804i | \(-0.104289\pi\) | |||||||
\(212\) | 318.845 | 0.103294 | ||||||||
\(213\) | 5576.30 | 1.79381 | ||||||||
\(214\) | − 7572.44i | − 2.41889i | ||||||||
\(215\) | − 2281.80i | − 0.723801i | ||||||||
\(216\) | 2268.67i | 0.714647i | ||||||||
\(217\) | 4375.55 | 1.36881 | ||||||||
\(218\) | − 1640.01i | − 0.509520i | ||||||||
\(219\) | −6318.17 | −1.94951 | ||||||||
\(220\) | −605.226 | −0.185474 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −7533.29 | −2.27748 | ||||||||
\(223\) | −1177.47 | −0.353584 | −0.176792 | − | 0.984248i | \(-0.556572\pi\) | ||||
−0.176792 | + | 0.984248i | \(0.556572\pi\) | |||||||
\(224\) | − 6037.94i | − 1.80101i | ||||||||
\(225\) | −4115.77 | −1.21949 | ||||||||
\(226\) | 4517.75i | 1.32972i | ||||||||
\(227\) | − 2845.44i | − 0.831976i | −0.909370 | − | 0.415988i | \(-0.863436\pi\) | ||||
0.909370 | − | 0.415988i | \(-0.136564\pi\) | |||||||
\(228\) | − 724.920i | − 0.210566i | ||||||||
\(229\) | −3605.93 | −1.04055 | −0.520277 | − | 0.853998i | \(-0.674171\pi\) | ||||
−0.520277 | + | 0.853998i | \(0.674171\pi\) | |||||||
\(230\) | 4707.03 | 1.34945 | ||||||||
\(231\) | 3907.74i | 1.11303i | ||||||||
\(232\) | 368.032i | 0.104149i | ||||||||
\(233\) | − 835.204i | − 0.234833i | −0.993083 | − | 0.117416i | \(-0.962539\pi\) | ||||
0.993083 | − | 0.117416i | \(-0.0374612\pi\) | |||||||
\(234\) | −510.372 | −0.142581 | ||||||||
\(235\) | 2312.34i | 0.641875i | ||||||||
\(236\) | 1347.85 | 0.371770 | ||||||||
\(237\) | −8980.28 | −2.46132 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −4057.52 | −1.09816 | −0.549078 | − | 0.835771i | \(-0.685021\pi\) | ||||
−0.549078 | + | 0.835771i | \(0.685021\pi\) | |||||||
\(240\) | −4977.59 | −1.33876 | ||||||||
\(241\) | − 2130.64i | − 0.569487i | −0.958604 | − | 0.284743i | \(-0.908092\pi\) | ||||
0.958604 | − | 0.284743i | \(-0.0919084\pi\) | |||||||
\(242\) | 4041.45 | 1.07353 | ||||||||
\(243\) | 530.923i | 0.140159i | ||||||||
\(244\) | 2571.19i | 0.674604i | ||||||||
\(245\) | 3200.14i | 0.834489i | ||||||||
\(246\) | −7821.37 | −2.02712 | ||||||||
\(247\) | −36.0830 | −0.00929516 | ||||||||
\(248\) | 1385.31i | 0.354708i | ||||||||
\(249\) | 895.981i | 0.228034i | ||||||||
\(250\) | − 5217.82i | − 1.32002i | ||||||||
\(251\) | 2164.17 | 0.544227 | 0.272113 | − | 0.962265i | \(-0.412277\pi\) | ||||
0.272113 | + | 0.962265i | \(0.412277\pi\) | |||||||
\(252\) | − 8657.62i | − 2.16420i | ||||||||
\(253\) | 2757.77 | 0.685294 | ||||||||
\(254\) | 2178.22 | 0.538085 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 5370.59 | 1.31118 | ||||||||
\(257\) | −6991.31 | −1.69691 | −0.848456 | − | 0.529267i | \(-0.822467\pi\) | ||||
−0.848456 | + | 0.529267i | \(0.822467\pi\) | |||||||
\(258\) | 10744.5i | 2.59273i | ||||||||
\(259\) | −6360.76 | −1.52602 | ||||||||
\(260\) | − 99.4688i | − 0.0237261i | ||||||||
\(261\) | 2270.99i | 0.538586i | ||||||||
\(262\) | − 7462.85i | − 1.75976i | ||||||||
\(263\) | 2985.57 | 0.699993 | 0.349996 | − | 0.936751i | \(-0.386183\pi\) | ||||
0.349996 | + | 0.936751i | \(0.386183\pi\) | |||||||
\(264\) | −1237.20 | −0.288426 | ||||||||
\(265\) | − 405.198i | − 0.0939287i | ||||||||
\(266\) | − 1489.90i | − 0.343427i | ||||||||
\(267\) | 6327.40i | 1.45030i | ||||||||
\(268\) | 2190.58 | 0.499296 | ||||||||
\(269\) | − 4063.25i | − 0.920969i | −0.887668 | − | 0.460484i | \(-0.847676\pi\) | ||||
0.887668 | − | 0.460484i | \(-0.152324\pi\) | |||||||
\(270\) | −6641.19 | −1.49693 | ||||||||
\(271\) | 6295.85 | 1.41124 | 0.705619 | − | 0.708591i | \(-0.250669\pi\) | ||||
0.705619 | + | 0.708591i | \(0.250669\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −642.237 | −0.142381 | ||||||||
\(274\) | 2299.06 | 0.506903 | ||||||||
\(275\) | − 1143.94i | − 0.250845i | ||||||||
\(276\) | −9105.72 | −1.98587 | ||||||||
\(277\) | − 4710.13i | − 1.02168i | −0.859677 | − | 0.510838i | \(-0.829335\pi\) | ||||
0.859677 | − | 0.510838i | \(-0.170665\pi\) | |||||||
\(278\) | 3806.99i | 0.821323i | ||||||||
\(279\) | 8548.28i | 1.83431i | ||||||||
\(280\) | −1783.01 | −0.380555 | ||||||||
\(281\) | 2458.26 | 0.521878 | 0.260939 | − | 0.965355i | \(-0.415968\pi\) | ||||
0.260939 | + | 0.965355i | \(0.415968\pi\) | |||||||
\(282\) | − 10888.3i | − 2.29926i | ||||||||
\(283\) | 9204.70i | 1.93344i | 0.255843 | + | 0.966718i | \(0.417647\pi\) | ||||
−0.255843 | + | 0.966718i | \(0.582353\pi\) | |||||||
\(284\) | − 3433.78i | − 0.717455i | ||||||||
\(285\) | −921.249 | −0.191474 | ||||||||
\(286\) | − 141.854i | − 0.0293286i | ||||||||
\(287\) | −6604.00 | −1.35826 | ||||||||
\(288\) | 11796.0 | 2.41349 | ||||||||
\(289\) | 0 | 0 | ||||||||
\(290\) | −1077.35 | −0.218153 | ||||||||
\(291\) | −12942.2 | −2.60716 | ||||||||
\(292\) | 3890.61i | 0.779729i | ||||||||
\(293\) | 423.010 | 0.0843431 | 0.0421716 | − | 0.999110i | \(-0.486572\pi\) | ||||
0.0421716 | + | 0.999110i | \(0.486572\pi\) | |||||||
\(294\) | − 15068.8i | − 2.98922i | ||||||||
\(295\) | − 1712.89i | − 0.338062i | ||||||||
\(296\) | − 2013.84i | − 0.395446i | ||||||||
\(297\) | −3890.95 | −0.760189 | ||||||||
\(298\) | −1048.26 | −0.203772 | ||||||||
\(299\) | 453.239i | 0.0876638i | ||||||||
\(300\) | 3777.13i | 0.726909i | ||||||||
\(301\) | 9072.17i | 1.73725i | ||||||||
\(302\) | −11619.4 | −2.21397 | ||||||||
\(303\) | 3702.12i | 0.701919i | ||||||||
\(304\) | 1111.89 | 0.209773 | ||||||||
\(305\) | 3267.54 | 0.613438 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 632.590 | 0.117602 | 0.0588010 | − | 0.998270i | \(-0.481272\pi\) | ||||
0.0588010 | + | 0.998270i | \(0.481272\pi\) | |||||||
\(308\) | 2406.31 | 0.445170 | ||||||||
\(309\) | 14943.2i | 2.75110i | ||||||||
\(310\) | −4055.29 | −0.742983 | ||||||||
\(311\) | 5293.07i | 0.965089i | 0.875872 | + | 0.482544i | \(0.160287\pi\) | ||||
−0.875872 | + | 0.482544i | \(0.839713\pi\) | |||||||
\(312\) | − 203.334i | − 0.0368959i | ||||||||
\(313\) | − 3817.93i | − 0.689464i | −0.938701 | − | 0.344732i | \(-0.887970\pi\) | ||||
0.938701 | − | 0.344732i | \(-0.112030\pi\) | |||||||
\(314\) | −1777.35 | −0.319431 | ||||||||
\(315\) | −11002.4 | −1.96798 | ||||||||
\(316\) | 5529.88i | 0.984431i | ||||||||
\(317\) | − 1389.54i | − 0.246197i | −0.992394 | − | 0.123098i | \(-0.960717\pi\) | ||||
0.992394 | − | 0.123098i | \(-0.0392830\pi\) | |||||||
\(318\) | 1907.99i | 0.336462i | ||||||||
\(319\) | −631.203 | −0.110786 | ||||||||
\(320\) | 1200.26i | 0.209677i | ||||||||
\(321\) | 18616.2 | 3.23692 | ||||||||
\(322\) | −18714.6 | −3.23890 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 4553.83 | 0.780836 | ||||||||
\(325\) | 188.007 | 0.0320885 | ||||||||
\(326\) | − 13698.1i | − 2.32721i | ||||||||
\(327\) | 4031.81 | 0.681833 | ||||||||
\(328\) | − 2090.85i | − 0.351975i | ||||||||
\(329\) | − 9193.61i | − 1.54061i | ||||||||
\(330\) | − 3621.72i | − 0.604149i | ||||||||
\(331\) | 5736.36 | 0.952565 | 0.476282 | − | 0.879292i | \(-0.341984\pi\) | ||||
0.476282 | + | 0.879292i | \(0.341984\pi\) | |||||||
\(332\) | 551.728 | 0.0912048 | ||||||||
\(333\) | − 12426.7i | − 2.04498i | ||||||||
\(334\) | − 7844.83i | − 1.28518i | ||||||||
\(335\) | − 2783.86i | − 0.454025i | ||||||||
\(336\) | 19790.3 | 3.21325 | ||||||||
\(337\) | 3997.46i | 0.646159i | 0.946372 | + | 0.323080i | \(0.104718\pi\) | ||||
−0.946372 | + | 0.323080i | \(0.895282\pi\) | |||||||
\(338\) | −8072.36 | −1.29905 | ||||||||
\(339\) | −11106.5 | −1.77941 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2375.92 | −0.377312 | ||||||||
\(342\) | 2910.74 | 0.460218 | ||||||||
\(343\) | − 3055.81i | − 0.481045i | ||||||||
\(344\) | −2872.28 | −0.450183 | ||||||||
\(345\) | 11571.8i | 1.80581i | ||||||||
\(346\) | 4413.97i | 0.685828i | ||||||||
\(347\) | − 2485.37i | − 0.384500i | −0.981346 | − | 0.192250i | \(-0.938422\pi\) | ||||
0.981346 | − | 0.192250i | \(-0.0615785\pi\) | |||||||
\(348\) | 2084.14 | 0.321038 | ||||||||
\(349\) | 9518.10 | 1.45986 | 0.729932 | − | 0.683520i | \(-0.239552\pi\) | ||||
0.729932 | + | 0.683520i | \(0.239552\pi\) | |||||||
\(350\) | 7762.98i | 1.18557i | ||||||||
\(351\) | − 639.478i | − 0.0972444i | ||||||||
\(352\) | 3278.60i | 0.496448i | ||||||||
\(353\) | 174.509 | 0.0263121 | 0.0131561 | − | 0.999913i | \(-0.495812\pi\) | ||||
0.0131561 | + | 0.999913i | \(0.495812\pi\) | |||||||
\(354\) | 8065.65i | 1.21097i | ||||||||
\(355\) | −4363.74 | −0.652404 | ||||||||
\(356\) | 3896.29 | 0.580065 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −15091.9 | −2.22802 | ||||||||
\(359\) | 8112.87 | 1.19270 | 0.596352 | − | 0.802723i | \(-0.296616\pi\) | ||||
0.596352 | + | 0.802723i | \(0.296616\pi\) | |||||||
\(360\) | − 3483.38i | − 0.509973i | ||||||||
\(361\) | −6653.21 | −0.969997 | ||||||||
\(362\) | 4779.59i | 0.693949i | ||||||||
\(363\) | 9935.55i | 1.43659i | ||||||||
\(364\) | 395.477i | 0.0569468i | ||||||||
\(365\) | 4944.30 | 0.709031 | ||||||||
\(366\) | −15386.2 | −2.19740 | ||||||||
\(367\) | 41.1424i | 0.00585181i | 0.999996 | + | 0.00292591i | \(0.000931346\pi\) | ||||
−0.999996 | + | 0.00292591i | \(0.999069\pi\) | |||||||
\(368\) | − 13966.4i | − 1.97840i | ||||||||
\(369\) | − 12901.9i | − 1.82018i | ||||||||
\(370\) | 5895.19 | 0.828315 | ||||||||
\(371\) | 1611.02i | 0.225445i | ||||||||
\(372\) | 7844.93 | 1.09339 | ||||||||
\(373\) | 1275.50 | 0.177059 | 0.0885296 | − | 0.996074i | \(-0.471783\pi\) | ||||
0.0885296 | + | 0.996074i | \(0.471783\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12827.5 | 1.76643 | ||||||||
\(376\) | 2910.73 | 0.399227 | ||||||||
\(377\) | − 103.738i | − 0.0141718i | ||||||||
\(378\) | 26404.6 | 3.59288 | ||||||||
\(379\) | − 4101.12i | − 0.555832i | −0.960605 | − | 0.277916i | \(-0.910356\pi\) | ||||
0.960605 | − | 0.277916i | \(-0.0896438\pi\) | |||||||
\(380\) | 567.287i | 0.0765822i | ||||||||
\(381\) | 5354.95i | 0.720059i | ||||||||
\(382\) | 16146.1 | 2.16258 | ||||||||
\(383\) | 10390.1 | 1.38619 | 0.693094 | − | 0.720848i | \(-0.256247\pi\) | ||||
0.693094 | + | 0.720848i | \(0.256247\pi\) | |||||||
\(384\) | 9873.22i | 1.31209i | ||||||||
\(385\) | − 3058.01i | − 0.404807i | ||||||||
\(386\) | − 3766.67i | − 0.496679i | ||||||||
\(387\) | −17723.8 | −2.32804 | ||||||||
\(388\) | 7969.53i | 1.04276i | ||||||||
\(389\) | −6213.37 | −0.809846 | −0.404923 | − | 0.914351i | \(-0.632702\pi\) | ||||
−0.404923 | + | 0.914351i | \(0.632702\pi\) | |||||||
\(390\) | 595.229 | 0.0772835 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 4028.27 | 0.519027 | ||||||||
\(393\) | 18346.8 | 2.35489 | ||||||||
\(394\) | 8115.93i | 1.03775i | ||||||||
\(395\) | 7027.54 | 0.895174 | ||||||||
\(396\) | 4701.08i | 0.596561i | ||||||||
\(397\) | 171.318i | 0.0216580i | 0.999941 | + | 0.0108290i | \(0.00344704\pi\) | ||||
−0.999941 | + | 0.0108290i | \(0.996553\pi\) | |||||||
\(398\) | − 280.111i | − 0.0352782i | ||||||||
\(399\) | 3662.78 | 0.459570 | ||||||||
\(400\) | −5793.39 | −0.724174 | ||||||||
\(401\) | 9328.60i | 1.16172i | 0.814005 | + | 0.580858i | \(0.197283\pi\) | ||||
−0.814005 | + | 0.580858i | \(0.802717\pi\) | |||||||
\(402\) | 13108.6i | 1.62636i | ||||||||
\(403\) | − 390.482i | − 0.0482663i | ||||||||
\(404\) | 2279.70 | 0.280741 | ||||||||
\(405\) | − 5787.14i | − 0.710038i | ||||||||
\(406\) | 4283.44 | 0.523605 | ||||||||
\(407\) | 3453.89 | 0.420646 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −6370.74 | −0.770202 | −0.385101 | − | 0.922874i | \(-0.625833\pi\) | ||||
−0.385101 | + | 0.922874i | \(0.625833\pi\) | |||||||
\(410\) | 6120.63 | 0.737260 | ||||||||
\(411\) | 5652.04i | 0.678332i | ||||||||
\(412\) | 9201.74 | 1.10033 | ||||||||
\(413\) | 6810.26i | 0.811406i | ||||||||
\(414\) | − 36561.8i | − 4.34037i | ||||||||
\(415\) | − 701.152i | − 0.0829354i | ||||||||
\(416\) | −538.837 | −0.0635064 | ||||||||
\(417\) | −9359.13 | −1.09909 | ||||||||
\(418\) | 809.014i | 0.0946655i | ||||||||
\(419\) | 8067.75i | 0.940657i | 0.882491 | + | 0.470329i | \(0.155865\pi\) | ||||
−0.882491 | + | 0.470329i | \(0.844135\pi\) | |||||||
\(420\) | 10097.1i | 1.17306i | ||||||||
\(421\) | −6254.81 | −0.724088 | −0.362044 | − | 0.932161i | \(-0.617921\pi\) | ||||
−0.362044 | + | 0.932161i | \(0.617921\pi\) | |||||||
\(422\) | − 7268.90i | − 0.838494i | ||||||||
\(423\) | 17961.1 | 2.06453 | ||||||||
\(424\) | −510.054 | −0.0584208 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 20548.0 | 2.33698 | ||||||||
\(427\) | −12991.4 | −1.47236 | ||||||||
\(428\) | − 11463.5i | − 1.29464i | ||||||||
\(429\) | 348.734 | 0.0392472 | ||||||||
\(430\) | − 8408.14i | − 0.942969i | ||||||||
\(431\) | 5910.99i | 0.660609i | 0.943874 | + | 0.330305i | \(0.107151\pi\) | ||||
−0.943874 | + | 0.330305i | \(0.892849\pi\) | |||||||
\(432\) | 19705.3i | 2.19461i | ||||||||
\(433\) | −11833.5 | −1.31335 | −0.656677 | − | 0.754172i | \(-0.728038\pi\) | ||||
−0.656677 | + | 0.754172i | \(0.728038\pi\) | |||||||
\(434\) | 16123.4 | 1.78329 | ||||||||
\(435\) | − 2648.58i | − 0.291930i | ||||||||
\(436\) | − 2482.71i | − 0.272707i | ||||||||
\(437\) | − 2584.90i | − 0.282957i | ||||||||
\(438\) | −23281.7 | −2.53982 | ||||||||
\(439\) | − 7520.94i | − 0.817665i | −0.912609 | − | 0.408833i | \(-0.865936\pi\) | ||||
0.912609 | − | 0.408833i | \(-0.134064\pi\) | |||||||
\(440\) | 968.176 | 0.104900 | ||||||||
\(441\) | 24857.0 | 2.68406 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 8478.34 | 0.909296 | 0.454648 | − | 0.890671i | \(-0.349765\pi\) | ||||
0.454648 | + | 0.890671i | \(0.349765\pi\) | |||||||
\(444\) | −11404.2 | −1.21896 | ||||||||
\(445\) | − 4951.52i | − 0.527471i | ||||||||
\(446\) | −4338.83 | −0.460649 | ||||||||
\(447\) | − 2577.05i | − 0.272685i | ||||||||
\(448\) | − 4772.09i | − 0.503259i | ||||||||
\(449\) | − 1078.67i | − 0.113375i | −0.998392 | − | 0.0566877i | \(-0.981946\pi\) | ||||
0.998392 | − | 0.0566877i | \(-0.0180539\pi\) | |||||||
\(450\) | −15166.1 | −1.58875 | ||||||||
\(451\) | 3585.97 | 0.374405 | ||||||||
\(452\) | 6839.15i | 0.711696i | ||||||||
\(453\) | − 28565.1i | − 2.96271i | ||||||||
\(454\) | − 10485.1i | − 1.08390i | ||||||||
\(455\) | 502.584 | 0.0517835 | ||||||||
\(456\) | 1159.65i | 0.119091i | ||||||||
\(457\) | −5664.74 | −0.579837 | −0.289918 | − | 0.957051i | \(-0.593628\pi\) | ||||
−0.289918 | + | 0.957051i | \(0.593628\pi\) | |||||||
\(458\) | −13287.4 | −1.35563 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 7125.70 | 0.722256 | ||||||||
\(461\) | −710.717 | −0.0718034 | −0.0359017 | − | 0.999355i | \(-0.511430\pi\) | ||||
−0.0359017 | + | 0.999355i | \(0.511430\pi\) | |||||||
\(462\) | 14399.5i | 1.45006i | ||||||||
\(463\) | 8328.23 | 0.835952 | 0.417976 | − | 0.908458i | \(-0.362740\pi\) | ||||
0.417976 | + | 0.908458i | \(0.362740\pi\) | |||||||
\(464\) | 3196.66i | 0.319831i | ||||||||
\(465\) | − 9969.56i | − 0.994252i | ||||||||
\(466\) | − 3077.62i | − 0.305940i | ||||||||
\(467\) | 14132.8 | 1.40040 | 0.700201 | − | 0.713946i | \(-0.253094\pi\) | ||||
0.700201 | + | 0.713946i | \(0.253094\pi\) | |||||||
\(468\) | −772.622 | −0.0763130 | ||||||||
\(469\) | 11068.3i | 1.08974i | ||||||||
\(470\) | 8520.69i | 0.836235i | ||||||||
\(471\) | − 4369.44i | − 0.427459i | ||||||||
\(472\) | −2156.15 | −0.210264 | ||||||||
\(473\) | − 4926.18i | − 0.478871i | ||||||||
\(474\) | −33091.2 | −3.20660 | ||||||||
\(475\) | −1072.24 | −0.103574 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −3147.36 | −0.302113 | ||||||||
\(478\) | −14951.5 | −1.43068 | ||||||||
\(479\) | − 6522.89i | − 0.622210i | −0.950376 | − | 0.311105i | \(-0.899301\pi\) | ||||
0.950376 | − | 0.311105i | \(-0.100699\pi\) | |||||||
\(480\) | −13757.3 | −1.30819 | ||||||||
\(481\) | 567.646i | 0.0538096i | ||||||||
\(482\) | − 7851.13i | − 0.741928i | ||||||||
\(483\) | − 46008.3i | − 4.33426i | ||||||||
\(484\) | 6118.12 | 0.574579 | ||||||||
\(485\) | 10127.9 | 0.948216 | ||||||||
\(486\) | 1956.39i | 0.182600i | ||||||||
\(487\) | − 2178.49i | − 0.202704i | −0.994851 | − | 0.101352i | \(-0.967683\pi\) | ||||
0.994851 | − | 0.101352i | \(-0.0323168\pi\) | |||||||
\(488\) | − 4113.11i | − 0.381540i | ||||||||
\(489\) | 33675.6 | 3.11424 | ||||||||
\(490\) | 11792.1i | 1.08717i | ||||||||
\(491\) | 12618.8 | 1.15983 | 0.579915 | − | 0.814677i | \(-0.303086\pi\) | ||||
0.579915 | + | 0.814677i | \(0.303086\pi\) | |||||||
\(492\) | −11840.3 | −1.08496 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | −132.961 | −0.0121097 | ||||||||
\(495\) | 5974.27 | 0.542472 | ||||||||
\(496\) | 12032.6i | 1.08927i | ||||||||
\(497\) | 17349.8 | 1.56588 | ||||||||
\(498\) | 3301.58i | 0.297083i | ||||||||
\(499\) | 13762.8i | 1.23469i | 0.786694 | + | 0.617343i | \(0.211791\pi\) | ||||
−0.786694 | + | 0.617343i | \(0.788209\pi\) | |||||||
\(500\) | − 7898.95i | − 0.706504i | ||||||||
\(501\) | 19285.8 | 1.71981 | ||||||||
\(502\) | 7974.69 | 0.709019 | ||||||||
\(503\) | 491.671i | 0.0435836i | 0.999763 | + | 0.0217918i | \(0.00693709\pi\) | ||||
−0.999763 | + | 0.0217918i | \(0.993063\pi\) | |||||||
\(504\) | 13849.5i | 1.22402i | ||||||||
\(505\) | − 2897.11i | − 0.255286i | ||||||||
\(506\) | 10162.0 | 0.892802 | ||||||||
\(507\) | − 19845.2i | − 1.73837i | ||||||||
\(508\) | 3297.48 | 0.287996 | ||||||||
\(509\) | 576.514 | 0.0502034 | 0.0251017 | − | 0.999685i | \(-0.492009\pi\) | ||||
0.0251017 | + | 0.999685i | \(0.492009\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −19658.0 | −1.70180 | ||||||||
\(512\) | 11070.9 | 0.955600 | ||||||||
\(513\) | 3647.05i | 0.313881i | ||||||||
\(514\) | −25762.1 | −2.21074 | ||||||||
\(515\) | − 11693.8i | − 1.00057i | ||||||||
\(516\) | 16265.5i | 1.38769i | ||||||||
\(517\) | 4992.12i | 0.424668i | ||||||||
\(518\) | −23438.6 | −1.98810 | ||||||||
\(519\) | −10851.4 | −0.917768 | ||||||||
\(520\) | 159.120i | 0.0134189i | ||||||||
\(521\) | 6102.95i | 0.513196i | 0.966518 | + | 0.256598i | \(0.0826016\pi\) | ||||
−0.966518 | + | 0.256598i | \(0.917398\pi\) | |||||||
\(522\) | 8368.33i | 0.701670i | ||||||||
\(523\) | 13593.3 | 1.13651 | 0.568255 | − | 0.822853i | \(-0.307619\pi\) | ||||
0.568255 | + | 0.822853i | \(0.307619\pi\) | |||||||
\(524\) | − 11297.6i | − 0.941864i | ||||||||
\(525\) | −19084.6 | −1.58651 | ||||||||
\(526\) | 11001.5 | 0.911951 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | −10746.1 | −0.885731 | ||||||||
\(529\) | −20301.9 | −1.66860 | ||||||||
\(530\) | − 1493.10i | − 0.122370i | ||||||||
\(531\) | −13304.8 | −1.08735 | ||||||||
\(532\) | − 2255.47i | − 0.183810i | ||||||||
\(533\) | 589.354i | 0.0478944i | ||||||||
\(534\) | 23315.7i | 1.88945i | ||||||||
\(535\) | −14568.1 | −1.17726 | ||||||||
\(536\) | −3504.26 | −0.282390 | ||||||||
\(537\) | − 37102.1i | − 2.98151i | ||||||||
\(538\) | − 14972.6i | − 1.19984i | ||||||||
\(539\) | 6908.80i | 0.552103i | ||||||||
\(540\) | −10053.7 | −0.801190 | ||||||||
\(541\) | 20360.3i | 1.61803i | 0.587786 | + | 0.809017i | \(0.300000\pi\) | ||||
−0.587786 | + | 0.809017i | \(0.700000\pi\) | |||||||
\(542\) | 23199.4 | 1.83856 | ||||||||
\(543\) | −11750.2 | −0.928635 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −3155.10 | −0.247981 | ||||||||
\(546\) | −2366.56 | −0.185494 | ||||||||
\(547\) | 253.860i | 0.0198433i | 0.999951 | + | 0.00992164i | \(0.00315821\pi\) | ||||
−0.999951 | + | 0.00992164i | \(0.996842\pi\) | |||||||
\(548\) | 3480.42 | 0.271307 | ||||||||
\(549\) | − 25380.5i | − 1.97307i | ||||||||
\(550\) | − 4215.29i | − 0.326801i | ||||||||
\(551\) | 591.636i | 0.0457433i | ||||||||
\(552\) | 14566.4 | 1.12316 | ||||||||
\(553\) | −27940.7 | −2.14857 | ||||||||
\(554\) | − 17356.2i | − 1.33104i | ||||||||
\(555\) | 14492.8i | 1.10844i | ||||||||
\(556\) | 5763.17i | 0.439592i | ||||||||
\(557\) | 1519.94 | 0.115623 | 0.0578116 | − | 0.998328i | \(-0.481588\pi\) | ||||
0.0578116 | + | 0.998328i | \(0.481588\pi\) | |||||||
\(558\) | 31499.4i | 2.38974i | ||||||||
\(559\) | 809.617 | 0.0612579 | ||||||||
\(560\) | −15487.0 | −1.16865 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 9058.40 | 0.679903 | ||||||||
\(563\) | 25112.9 | 1.87990 | 0.939948 | − | 0.341317i | \(-0.110873\pi\) | ||||
0.939948 | + | 0.341317i | \(0.110873\pi\) | |||||||
\(564\) | − 16483.2i | − 1.23062i | ||||||||
\(565\) | 8691.39 | 0.647168 | ||||||||
\(566\) | 33918.2i | 2.51888i | ||||||||
\(567\) | 23009.0i | 1.70421i | ||||||||
\(568\) | 5492.99i | 0.405776i | ||||||||
\(569\) | −3649.16 | −0.268859 | −0.134430 | − | 0.990923i | \(-0.542920\pi\) | ||||
−0.134430 | + | 0.990923i | \(0.542920\pi\) | |||||||
\(570\) | −3394.69 | −0.249452 | ||||||||
\(571\) | 4111.91i | 0.301362i | 0.988582 | + | 0.150681i | \(0.0481467\pi\) | ||||
−0.988582 | + | 0.150681i | \(0.951853\pi\) | |||||||
\(572\) | − 214.744i | − 0.0156974i | ||||||||
\(573\) | 39693.7i | 2.89394i | ||||||||
\(574\) | −24334.9 | −1.76955 | ||||||||
\(575\) | 13468.4i | 0.976817i | ||||||||
\(576\) | 9322.98 | 0.674405 | ||||||||
\(577\) | 25307.1 | 1.82591 | 0.912954 | − | 0.408062i | \(-0.133795\pi\) | ||||
0.912954 | + | 0.408062i | \(0.133795\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 9260.01 | 0.664651 | ||||||||
\(580\) | −1630.94 | −0.116761 | ||||||||
\(581\) | 2787.70i | 0.199059i | ||||||||
\(582\) | −47690.3 | −3.39661 | ||||||||
\(583\) | − 874.783i | − 0.0621438i | ||||||||
\(584\) | − 6223.78i | − 0.440996i | ||||||||
\(585\) | 981.870i | 0.0693938i | ||||||||
\(586\) | 1558.74 | 0.109882 | ||||||||
\(587\) | −6734.14 | −0.473506 | −0.236753 | − | 0.971570i | \(-0.576083\pi\) | ||||
−0.236753 | + | 0.971570i | \(0.576083\pi\) | |||||||
\(588\) | − 22811.8i | − 1.59990i | ||||||||
\(589\) | 2226.99i | 0.155792i | ||||||||
\(590\) | − 6311.79i | − 0.440427i | ||||||||
\(591\) | −19952.3 | −1.38871 | ||||||||
\(592\) | − 17491.9i | − 1.21438i | ||||||||
\(593\) | −885.596 | −0.0613273 | −0.0306636 | − | 0.999530i | \(-0.509762\pi\) | ||||
−0.0306636 | + | 0.999530i | \(0.509762\pi\) | |||||||
\(594\) | −14337.7 | −0.990374 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −1586.90 | −0.109064 | ||||||||
\(597\) | 688.629 | 0.0472089 | ||||||||
\(598\) | 1670.13i | 0.114208i | ||||||||
\(599\) | 7411.88 | 0.505578 | 0.252789 | − | 0.967521i | \(-0.418652\pi\) | ||||
0.252789 | + | 0.967521i | \(0.418652\pi\) | |||||||
\(600\) | − 6042.24i | − 0.411123i | ||||||||
\(601\) | 19232.0i | 1.30531i | 0.757657 | + | 0.652653i | \(0.226344\pi\) | ||||
−0.757657 | + | 0.652653i | \(0.773656\pi\) | |||||||
\(602\) | 33429.8i | 2.26329i | ||||||||
\(603\) | −21623.6 | −1.46033 | ||||||||
\(604\) | −17589.9 | −1.18497 | ||||||||
\(605\) | − 7775.08i | − 0.522483i | ||||||||
\(606\) | 13641.9i | 0.914461i | ||||||||
\(607\) | 3485.07i | 0.233039i | 0.993188 | + | 0.116519i | \(0.0371737\pi\) | ||||
−0.993188 | + | 0.116519i | \(0.962826\pi\) | |||||||
\(608\) | 3073.08 | 0.204983 | ||||||||
\(609\) | 10530.5i | 0.700682i | ||||||||
\(610\) | 12040.5 | 0.799188 | ||||||||
\(611\) | −820.455 | −0.0543241 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −27347.9 | −1.80191 | −0.900954 | − | 0.433915i | \(-0.857132\pi\) | ||||
−0.900954 | + | 0.433915i | \(0.857132\pi\) | |||||||
\(614\) | 2331.02 | 0.153212 | ||||||||
\(615\) | 15047.0i | 0.986592i | ||||||||
\(616\) | −3849.36 | −0.251778 | ||||||||
\(617\) | − 12625.9i | − 0.823822i | −0.911224 | − | 0.411911i | \(-0.864861\pi\) | ||||
0.911224 | − | 0.411911i | \(-0.135139\pi\) | |||||||
\(618\) | 55063.9i | 3.58413i | ||||||||
\(619\) | 16469.8i | 1.06943i | 0.845033 | + | 0.534714i | \(0.179581\pi\) | ||||
−0.845033 | + | 0.534714i | \(0.820419\pi\) | |||||||
\(620\) | −6139.06 | −0.397662 | ||||||||
\(621\) | 45810.6 | 2.96025 | ||||||||
\(622\) | 19504.3i | 1.25732i | ||||||||
\(623\) | 19686.7i | 1.26602i | ||||||||
\(624\) | − 1766.13i | − 0.113304i | ||||||||
\(625\) | −695.113 | −0.0444872 | ||||||||
\(626\) | − 14068.6i | − 0.898235i | ||||||||
\(627\) | −1988.89 | −0.126680 | ||||||||
\(628\) | −2690.62 | −0.170967 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | −40542.3 | −2.56388 | ||||||||
\(631\) | −6691.13 | −0.422139 | −0.211069 | − | 0.977471i | \(-0.567695\pi\) | ||||
−0.211069 | + | 0.977471i | \(0.567695\pi\) | |||||||
\(632\) | − 8846.11i | − 0.556771i | ||||||||
\(633\) | 17869.9 | 1.12206 | ||||||||
\(634\) | − 5120.28i | − 0.320745i | ||||||||
\(635\) | − 4190.53i | − 0.261884i | ||||||||
\(636\) | 2888.40i | 0.180082i | ||||||||
\(637\) | −1135.46 | −0.0706258 | ||||||||
\(638\) | −2325.91 | −0.144332 | ||||||||
\(639\) | 33895.3i | 2.09840i | ||||||||
\(640\) | − 7726.31i | − 0.477202i | ||||||||
\(641\) | − 14335.5i | − 0.883335i | −0.897179 | − | 0.441668i | \(-0.854387\pi\) | ||||
0.897179 | − | 0.441668i | \(-0.145613\pi\) | |||||||
\(642\) | 68598.3 | 4.21707 | ||||||||
\(643\) | − 30421.9i | − 1.86582i | −0.360109 | − | 0.932910i | \(-0.617260\pi\) | ||||
0.360109 | − | 0.932910i | \(-0.382740\pi\) | |||||||
\(644\) | −28331.0 | −1.73354 | ||||||||
\(645\) | 20670.7 | 1.26187 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −9221.00 | −0.560301 | −0.280151 | − | 0.959956i | \(-0.590384\pi\) | ||||
−0.280151 | + | 0.959956i | \(0.590384\pi\) | |||||||
\(648\) | −7284.73 | −0.441622 | ||||||||
\(649\) | − 3697.96i | − 0.223664i | ||||||||
\(650\) | 692.783 | 0.0418049 | ||||||||
\(651\) | 39637.8i | 2.38637i | ||||||||
\(652\) | − 20736.8i | − 1.24558i | ||||||||
\(653\) | − 24958.5i | − 1.49572i | −0.663859 | − | 0.747858i | \(-0.731082\pi\) | ||||
0.663859 | − | 0.747858i | \(-0.268918\pi\) | |||||||
\(654\) | 14856.7 | 0.888293 | ||||||||
\(655\) | −14357.3 | −0.856467 | ||||||||
\(656\) | − 18160.8i | − 1.08088i | ||||||||
\(657\) | − 38404.7i | − 2.28054i | ||||||||
\(658\) | − 33877.3i | − 2.00711i | ||||||||
\(659\) | −3367.32 | −0.199047 | −0.0995236 | − | 0.995035i | \(-0.531732\pi\) | ||||
−0.0995236 | + | 0.995035i | \(0.531732\pi\) | |||||||
\(660\) | − 5482.71i | − 0.323355i | ||||||||
\(661\) | 6389.67 | 0.375990 | 0.187995 | − | 0.982170i | \(-0.439801\pi\) | ||||
0.187995 | + | 0.982170i | \(0.439801\pi\) | |||||||
\(662\) | 21137.8 | 1.24100 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −882.595 | −0.0515833 | ||||||||
\(665\) | −2866.32 | −0.167144 | ||||||||
\(666\) | − 45790.8i | − 2.66420i | ||||||||
\(667\) | 7431.55 | 0.431410 | ||||||||
\(668\) | − 11875.8i | − 0.687859i | ||||||||
\(669\) | − 10666.6i | − 0.616436i | ||||||||
\(670\) | − 10258.2i | − 0.591504i | ||||||||
\(671\) | 7054.30 | 0.405854 | ||||||||
\(672\) | 54697.3 | 3.13987 | ||||||||
\(673\) | − 27441.4i | − 1.57175i | −0.618383 | − | 0.785877i | \(-0.712212\pi\) | ||||
0.618383 | − | 0.785877i | \(-0.287788\pi\) | |||||||
\(674\) | 14730.2i | 0.841817i | ||||||||
\(675\) | − 19002.6i | − 1.08357i | ||||||||
\(676\) | −12220.3 | −0.695282 | ||||||||
\(677\) | 16931.5i | 0.961194i | 0.876941 | + | 0.480597i | \(0.159580\pi\) | ||||
−0.876941 | + | 0.480597i | \(0.840420\pi\) | |||||||
\(678\) | −40926.0 | −2.31822 | ||||||||
\(679\) | −40267.4 | −2.27588 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 25776.7 | 1.45046 | ||||||||
\(682\) | −8754.98 | −0.491562 | ||||||||
\(683\) | − 69.2829i | − 0.00388146i | −0.999998 | − | 0.00194073i | \(-0.999382\pi\) | ||||
0.999998 | − | 0.00194073i | \(-0.000617754\pi\) | |||||||
\(684\) | 4406.39 | 0.246320 | ||||||||
\(685\) | − 4423.01i | − 0.246708i | ||||||||
\(686\) | − 11260.3i | − 0.626705i | ||||||||
\(687\) | − 32665.9i | − 1.81409i | ||||||||
\(688\) | −24948.1 | −1.38247 | ||||||||
\(689\) | 143.770 | 0.00794952 | ||||||||
\(690\) | 42640.7i | 2.35262i | ||||||||
\(691\) | − 1509.96i | − 0.0831282i | −0.999136 | − | 0.0415641i | \(-0.986766\pi\) | ||||
0.999136 | − | 0.0415641i | \(-0.0132341\pi\) | |||||||
\(692\) | 6682.05i | 0.367072i | ||||||||
\(693\) | −23753.0 | −1.30202 | ||||||||
\(694\) | − 9158.27i | − 0.500927i | ||||||||
\(695\) | 7324.01 | 0.399734 | ||||||||
\(696\) | −3333.98 | −0.181572 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 35073.0 | 1.90191 | ||||||||
\(699\) | 7566.06 | 0.409406 | ||||||||
\(700\) | 11751.9i | 0.634544i | ||||||||
\(701\) | −16452.5 | −0.886449 | −0.443224 | − | 0.896411i | \(-0.646165\pi\) | ||||
−0.443224 | + | 0.896411i | \(0.646165\pi\) | |||||||
\(702\) | − 2356.40i | − 0.126690i | ||||||||
\(703\) | − 3237.38i | − 0.173684i | ||||||||
\(704\) | 2591.24i | 0.138723i | ||||||||
\(705\) | −20947.4 | −1.11904 | ||||||||
\(706\) | 643.045 | 0.0342795 | ||||||||
\(707\) | 11518.6i | 0.612730i | ||||||||
\(708\) | 12210.1i | 0.648141i | ||||||||
\(709\) | 4602.45i | 0.243792i | 0.992543 | + | 0.121896i | \(0.0388975\pi\) | ||||
−0.992543 | + | 0.121896i | \(0.961103\pi\) | |||||||
\(710\) | −16079.9 | −0.849953 | ||||||||
\(711\) | − 54586.2i | − 2.87925i | ||||||||
\(712\) | −6232.87 | −0.328071 | ||||||||
\(713\) | 27973.2 | 1.46929 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −272.903 | −0.0142741 | ||||||||
\(716\) | −22846.7 | −1.19249 | ||||||||
\(717\) | − 36756.8i | − 1.91452i | ||||||||
\(718\) | 29894.9 | 1.55386 | ||||||||
\(719\) | 23515.7i | 1.21973i | 0.792505 | + | 0.609865i | \(0.208776\pi\) | ||||
−0.792505 | + | 0.609865i | \(0.791224\pi\) | |||||||
\(720\) | − 30256.1i | − 1.56608i | ||||||||
\(721\) | 46493.4i | 2.40153i | ||||||||
\(722\) | −24516.3 | −1.26371 | ||||||||
\(723\) | 19301.3 | 0.992839 | ||||||||
\(724\) | 7235.54i | 0.371418i | ||||||||
\(725\) | − 3082.66i | − 0.157914i | ||||||||
\(726\) | 36611.3i | 1.87159i | ||||||||
\(727\) | −8389.04 | −0.427968 | −0.213984 | − | 0.976837i | \(-0.568644\pi\) | ||||
−0.213984 | + | 0.976837i | \(0.568644\pi\) | |||||||
\(728\) | − 632.641i | − 0.0322078i | ||||||||
\(729\) | 17231.7 | 0.875462 | ||||||||
\(730\) | 18219.1 | 0.923727 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | −23292.2 | −1.17610 | ||||||||
\(733\) | 7677.37 | 0.386863 | 0.193431 | − | 0.981114i | \(-0.438038\pi\) | ||||
0.193431 | + | 0.981114i | \(0.438038\pi\) | |||||||
\(734\) | 151.605i | 0.00762374i | ||||||||
\(735\) | −28989.9 | −1.45484 | ||||||||
\(736\) | − 38601.0i | − 1.93322i | ||||||||
\(737\) | − 6010.08i | − 0.300386i | ||||||||
\(738\) | − 47541.9i | − 2.37133i | ||||||||
\(739\) | −26617.3 | −1.32494 | −0.662472 | − | 0.749087i | \(-0.730493\pi\) | ||||
−0.662472 | + | 0.749087i | \(0.730493\pi\) | |||||||
\(740\) | 8924.39 | 0.443334 | ||||||||
\(741\) | − 326.873i | − 0.0162051i | ||||||||
\(742\) | 5936.41i | 0.293710i | ||||||||
\(743\) | 20951.6i | 1.03451i | 0.855832 | + | 0.517253i | \(0.173046\pi\) | ||||
−0.855832 | + | 0.517253i | \(0.826954\pi\) | |||||||
\(744\) | −12549.5 | −0.618395 | ||||||||
\(745\) | 2016.68i | 0.0991750i | ||||||||
\(746\) | 4700.07 | 0.230673 | ||||||||
\(747\) | −5446.18 | −0.266754 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 57921.2 | 2.82563 | ||||||||
\(750\) | 47267.9 | 2.30131 | ||||||||
\(751\) | 8252.35i | 0.400975i | 0.979696 | + | 0.200488i | \(0.0642527\pi\) | ||||
−0.979696 | + | 0.200488i | \(0.935747\pi\) | |||||||
\(752\) | 25282.1 | 1.22599 | ||||||||
\(753\) | 19605.0i | 0.948801i | ||||||||
\(754\) | − 382.262i | − 0.0184631i | ||||||||
\(755\) | 22353.7i | 1.07753i | ||||||||
\(756\) | 39972.4 | 1.92299 | ||||||||
\(757\) | 21203.1 | 1.01802 | 0.509010 | − | 0.860760i | \(-0.330012\pi\) | ||||
0.509010 | + | 0.860760i | \(0.330012\pi\) | |||||||
\(758\) | − 15112.1i | − 0.724139i | ||||||||
\(759\) | 24982.4i | 1.19474i | ||||||||
\(760\) | − 907.485i | − 0.0433131i | ||||||||
\(761\) | 29378.2 | 1.39942 | 0.699711 | − | 0.714426i | \(-0.253312\pi\) | ||||
0.699711 | + | 0.714426i | \(0.253312\pi\) | |||||||
\(762\) | 19732.3i | 0.938094i | ||||||||
\(763\) | 12544.3 | 0.595196 | ||||||||
\(764\) | 24442.6 | 1.15746 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 38286.3 | 1.80593 | ||||||||
\(767\) | 607.760 | 0.0286114 | ||||||||
\(768\) | 48651.8i | 2.28590i | ||||||||
\(769\) | −16559.6 | −0.776532 | −0.388266 | − | 0.921547i | \(-0.626926\pi\) | ||||
−0.388266 | + | 0.921547i | \(0.626926\pi\) | |||||||
\(770\) | − 11268.4i | − 0.527383i | ||||||||
\(771\) | − 63333.9i | − 2.95838i | ||||||||
\(772\) | − 5702.13i | − 0.265835i | ||||||||
\(773\) | 39537.3 | 1.83966 | 0.919830 | − | 0.392317i | \(-0.128327\pi\) | ||||
0.919830 | + | 0.392317i | \(0.128327\pi\) | |||||||
\(774\) | −65310.1 | −3.03297 | ||||||||
\(775\) | − 11603.5i | − 0.537820i | ||||||||
\(776\) | − 12748.8i | − 0.589762i | ||||||||
\(777\) | − 57621.7i | − 2.66045i | ||||||||
\(778\) | −22895.5 | −1.05507 | ||||||||
\(779\) | − 3361.18i | − 0.154592i | ||||||||
\(780\) | 901.082 | 0.0413640 | ||||||||
\(781\) | −9420.91 | −0.431634 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −10485.2 | −0.478558 | ||||||||
\(784\) | 34988.9 | 1.59388 | ||||||||
\(785\) | 3419.32i | 0.155466i | ||||||||
\(786\) | 67605.5 | 3.06795 | ||||||||
\(787\) | 17801.2i | 0.806280i | 0.915138 | + | 0.403140i | \(0.132081\pi\) | ||||
−0.915138 | + | 0.403140i | \(0.867919\pi\) | |||||||
\(788\) | 12286.2i | 0.555430i | ||||||||
\(789\) | 27046.1i | 1.22036i | ||||||||
\(790\) | 25895.6 | 1.16623 | ||||||||
\(791\) | −34556.0 | −1.55331 | ||||||||
\(792\) | − 7520.28i | − 0.337401i | ||||||||
\(793\) | 1159.37i | 0.0519175i | ||||||||
\(794\) | 631.287i | 0.0282161i | ||||||||
\(795\) | 3670.66 | 0.163755 | ||||||||
\(796\) | − 424.044i | − 0.0188817i | ||||||||
\(797\) | −34006.4 | −1.51138 | −0.755688 | − | 0.654932i | \(-0.772697\pi\) | ||||
−0.755688 | + | 0.654932i | \(0.772697\pi\) | |||||||
\(798\) | 13496.9 | 0.598728 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | −16012.0 | −0.707636 | ||||||||
\(801\) | −38460.8 | −1.69656 | ||||||||
\(802\) | 34374.7i | 1.51348i | ||||||||
\(803\) | 10674.3 | 0.469099 | ||||||||
\(804\) | 19844.4i | 0.870469i | ||||||||
\(805\) | 36003.8i | 1.57636i | ||||||||
\(806\) | − 1438.88i | − 0.0628813i | ||||||||
\(807\) | 36808.7 | 1.60561 | ||||||||
\(808\) | −3646.81 | −0.158780 | ||||||||
\(809\) | 7943.98i | 0.345235i | 0.984989 | + | 0.172618i | \(0.0552225\pi\) | ||||
−0.984989 | + | 0.172618i | \(0.944777\pi\) | |||||||
\(810\) | − 21324.9i | − 0.925038i | ||||||||
\(811\) | 29182.7i | 1.26355i | 0.775150 | + | 0.631777i | \(0.217674\pi\) | ||||
−0.775150 | + | 0.631777i | \(0.782326\pi\) | |||||||
\(812\) | 6484.45 | 0.280246 | ||||||||
\(813\) | 57033.7i | 2.46034i | ||||||||
\(814\) | 12727.2 | 0.548018 | ||||||||
\(815\) | −26352.9 | −1.13264 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4617.38 | −0.197726 | ||||||||
\(818\) | −23475.4 | −1.00342 | ||||||||
\(819\) | − 3903.81i | − 0.166557i | ||||||||
\(820\) | 9265.66 | 0.394599 | ||||||||
\(821\) | − 29589.4i | − 1.25783i | −0.777475 | − | 0.628913i | \(-0.783500\pi\) | ||||
0.777475 | − | 0.628913i | \(-0.216500\pi\) | |||||||
\(822\) | 20827.1i | 0.883732i | ||||||||
\(823\) | − 11121.5i | − 0.471046i | −0.971869 | − | 0.235523i | \(-0.924320\pi\) | ||||
0.971869 | − | 0.235523i | \(-0.0756803\pi\) | |||||||
\(824\) | −14720.0 | −0.622323 | ||||||||
\(825\) | 10362.9 | 0.437322 | ||||||||
\(826\) | 25095.0i | 1.05710i | ||||||||
\(827\) | − 12401.7i | − 0.521461i | −0.965412 | − | 0.260730i | \(-0.916037\pi\) | ||||
0.965412 | − | 0.260730i | \(-0.0839634\pi\) | |||||||
\(828\) | − 55348.7i | − 2.32307i | ||||||||
\(829\) | −6224.06 | −0.260761 | −0.130380 | − | 0.991464i | \(-0.541620\pi\) | ||||
−0.130380 | + | 0.991464i | \(0.541620\pi\) | |||||||
\(830\) | − 2583.66i | − 0.108048i | ||||||||
\(831\) | 42668.8 | 1.78118 | ||||||||
\(832\) | −425.870 | −0.0177457 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −34487.3 | −1.43189 | ||||||||
\(835\) | −15092.1 | −0.625491 | ||||||||
\(836\) | 1224.72i | 0.0506672i | ||||||||
\(837\) | −39467.6 | −1.62987 | ||||||||
\(838\) | 29728.7i | 1.22549i | ||||||||
\(839\) | 36811.6i | 1.51475i | 0.652978 | + | 0.757377i | \(0.273519\pi\) | ||||
−0.652978 | + | 0.757377i | \(0.726481\pi\) | |||||||
\(840\) | − 16152.2i | − 0.663458i | ||||||||
\(841\) | 22688.1 | 0.930258 | ||||||||
\(842\) | −23048.2 | −0.943342 | ||||||||
\(843\) | 22269.3i | 0.909839i | ||||||||
\(844\) | − 11004.0i | − 0.448782i | ||||||||
\(845\) | 15529.9i | 0.632241i | ||||||||
\(846\) | 66184.3 | 2.68967 | ||||||||
\(847\) | 30912.8i | 1.25405i | ||||||||
\(848\) | −4430.25 | −0.179405 | ||||||||
\(849\) | −83384.8 | −3.37074 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −40664.8 | −1.63804 | ||||||||
\(852\) | 31106.4 | 1.25081 | ||||||||
\(853\) | − 3319.10i | − 0.133228i | −0.997779 | − | 0.0666141i | \(-0.978780\pi\) | ||||
0.997779 | − | 0.0666141i | \(-0.0212196\pi\) | |||||||
\(854\) | −47871.6 | −1.91819 | ||||||||
\(855\) | − 5599.77i | − 0.223986i | ||||||||
\(856\) | 18338.0i | 0.732221i | ||||||||
\(857\) | − 8084.66i | − 0.322248i | −0.986934 | − | 0.161124i | \(-0.948488\pi\) | ||||
0.986934 | − | 0.161124i | \(-0.0515119\pi\) | |||||||
\(858\) | 1285.04 | 0.0511313 | ||||||||
\(859\) | 23619.8 | 0.938181 | 0.469091 | − | 0.883150i | \(-0.344582\pi\) | ||||
0.469091 | + | 0.883150i | \(0.344582\pi\) | |||||||
\(860\) | − 12728.6i | − 0.504699i | ||||||||
\(861\) | − 59825.3i | − 2.36799i | ||||||||
\(862\) | 21781.3i | 0.860642i | ||||||||
\(863\) | −34938.3 | −1.37812 | −0.689058 | − | 0.724706i | \(-0.741975\pi\) | ||||
−0.689058 | + | 0.724706i | \(0.741975\pi\) | |||||||
\(864\) | 54462.4i | 2.14450i | ||||||||
\(865\) | 8491.75 | 0.333790 | ||||||||
\(866\) | −43605.0 | −1.71104 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 24408.2 | 0.954457 | ||||||||
\(869\) | 15171.8 | 0.592252 | ||||||||
\(870\) | − 9759.69i | − 0.380327i | ||||||||
\(871\) | 987.756 | 0.0384258 | ||||||||
\(872\) | 3971.57i | 0.154237i | ||||||||
\(873\) | − 78668.3i | − 3.04985i | ||||||||
\(874\) | − 9525.02i | − 0.368637i | ||||||||
\(875\) | 39910.8 | 1.54198 | ||||||||
\(876\) | −35244.8 | −1.35937 | ||||||||
\(877\) | 20700.0i | 0.797022i | 0.917164 | + | 0.398511i | \(0.130473\pi\) | ||||
−0.917164 | + | 0.398511i | \(0.869527\pi\) | |||||||
\(878\) | − 27713.8i | − 1.06525i | ||||||||
\(879\) | 3832.02i | 0.147043i | ||||||||
\(880\) | 8409.42 | 0.322138 | ||||||||
\(881\) | 5183.11i | 0.198211i | 0.995077 | + | 0.0991053i | \(0.0315981\pi\) | ||||
−0.995077 | + | 0.0991053i | \(0.968402\pi\) | |||||||
\(882\) | 91595.2 | 3.49679 | ||||||||
\(883\) | 7357.34 | 0.280401 | 0.140201 | − | 0.990123i | \(-0.455225\pi\) | ||||
0.140201 | + | 0.990123i | \(0.455225\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 15517.0 | 0.589375 | ||||||||
\(886\) | 31241.6 | 1.18463 | ||||||||
\(887\) | 35702.2i | 1.35148i | 0.737140 | + | 0.675740i | \(0.236176\pi\) | ||||
−0.737140 | + | 0.675740i | \(0.763824\pi\) | |||||||
\(888\) | 18243.2 | 0.689417 | ||||||||
\(889\) | 16661.1i | 0.628565i | ||||||||
\(890\) | − 18245.7i | − 0.687189i | ||||||||
\(891\) | − 12493.9i | − 0.469765i | ||||||||
\(892\) | −6568.30 | −0.246550 | ||||||||
\(893\) | 4679.19 | 0.175345 | ||||||||
\(894\) | − 9496.12i | − 0.355255i | ||||||||
\(895\) | 29034.3i | 1.08437i | ||||||||
\(896\) | 30718.9i | 1.14537i | ||||||||
\(897\) | −4105.86 | −0.152832 | ||||||||
\(898\) | − 3974.77i | − 0.147706i | ||||||||
\(899\) | −6402.56 | −0.237528 | ||||||||
\(900\) | −22959.1 | −0.850337 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 13213.9 | 0.487775 | ||||||||
\(903\) | −82184.2 | −3.02870 | ||||||||
\(904\) | − 10940.5i | − 0.402519i | ||||||||
\(905\) | 9195.14 | 0.337742 | ||||||||
\(906\) | − 105259.i | − 3.85982i | ||||||||
\(907\) | − 5660.56i | − 0.207228i | −0.994618 | − | 0.103614i | \(-0.966959\pi\) | ||||
0.994618 | − | 0.103614i | \(-0.0330407\pi\) | |||||||
\(908\) | − 15872.8i | − 0.580128i | ||||||||
\(909\) | −22503.2 | −0.821105 | ||||||||
\(910\) | 1851.96 | 0.0674636 | ||||||||
\(911\) | − 11754.9i | − 0.427506i | −0.976888 | − | 0.213753i | \(-0.931431\pi\) | ||||
0.976888 | − | 0.213753i | \(-0.0685687\pi\) | |||||||
\(912\) | 10072.5i | 0.365718i | ||||||||
\(913\) | − 1513.72i | − 0.0548705i | ||||||||
\(914\) | −20873.9 | −0.755412 | ||||||||
\(915\) | 29600.4i | 1.06946i | ||||||||
\(916\) | −20115.0 | −0.725567 | ||||||||
\(917\) | 57083.0 | 2.05567 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 4513.88 | 0.162023 | 0.0810116 | − | 0.996713i | \(-0.474185\pi\) | ||||
0.0810116 | + | 0.996713i | \(0.474185\pi\) | |||||||
\(920\) | −11398.9 | −0.408491 | ||||||||
\(921\) | 5730.59i | 0.205027i | ||||||||
\(922\) | −2618.90 | −0.0935455 | ||||||||
\(923\) | − 1548.32i | − 0.0552153i | ||||||||
\(924\) | 21798.6i | 0.776106i | ||||||||
\(925\) | 16868.1i | 0.599588i | ||||||||
\(926\) | 30688.5 | 1.08908 | ||||||||
\(927\) | −90831.6 | −3.21823 | ||||||||
\(928\) | 8835.06i | 0.312527i | ||||||||
\(929\) | − 15124.4i | − 0.534138i | −0.963677 | − | 0.267069i | \(-0.913945\pi\) | ||||
0.963677 | − | 0.267069i | \(-0.0860552\pi\) | |||||||
\(930\) | − 36736.6i | − 1.29531i | ||||||||
\(931\) | 6475.72 | 0.227963 | ||||||||
\(932\) | − 4659.03i | − 0.163746i | ||||||||
\(933\) | −47949.6 | −1.68253 | ||||||||
\(934\) | 52077.6 | 1.82444 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 1235.96 | 0.0431608 | ||||||||
\(937\) | 19918.8 | 0.694470 | 0.347235 | − | 0.937778i | \(-0.387121\pi\) | ||||
0.347235 | + | 0.937778i | \(0.387121\pi\) | |||||||
\(938\) | 40785.4i | 1.41971i | ||||||||
\(939\) | 34586.4 | 1.20201 | ||||||||
\(940\) | 12899.0i | 0.447573i | ||||||||
\(941\) | 2072.11i | 0.0717843i | 0.999356 | + | 0.0358921i | \(0.0114273\pi\) | ||||
−0.999356 | + | 0.0358921i | \(0.988573\pi\) | |||||||
\(942\) | − 16100.9i | − 0.556894i | ||||||||
\(943\) | −42219.8 | −1.45797 | ||||||||
\(944\) | −18728.0 | −0.645703 | ||||||||
\(945\) | − 50798.1i | − 1.74864i | ||||||||
\(946\) | − 18152.4i | − 0.623874i | ||||||||
\(947\) | 5522.83i | 0.189512i | 0.995501 | + | 0.0947560i | \(0.0302071\pi\) | ||||
−0.995501 | + | 0.0947560i | \(0.969793\pi\) | |||||||
\(948\) | −50094.9 | −1.71625 | ||||||||
\(949\) | 1754.31i | 0.0600079i | ||||||||
\(950\) | −3951.06 | −0.134936 | ||||||||
\(951\) | 12587.8 | 0.429217 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −39192.3 | −1.33218 | −0.666089 | − | 0.745873i | \(-0.732033\pi\) | ||||
−0.666089 | + | 0.745873i | \(0.732033\pi\) | |||||||
\(954\) | −11597.6 | −0.393593 | ||||||||
\(955\) | − 31062.4i | − 1.05252i | ||||||||
\(956\) | −22634.1 | −0.765733 | ||||||||
\(957\) | − 5718.03i | − 0.193143i | ||||||||
\(958\) | − 24036.1i | − 0.810616i | ||||||||
\(959\) | 17585.4i | 0.592140i | ||||||||
\(960\) | −10873.1 | −0.365549 | ||||||||
\(961\) | 5691.04 | 0.191032 | ||||||||
\(962\) | 2091.71i | 0.0701033i | ||||||||
\(963\) | 113158.i | 3.78655i | ||||||||
\(964\) | − 11885.4i | − 0.397097i | ||||||||
\(965\) | −7246.44 | −0.241732 | ||||||||
\(966\) | − 169535.i | − 5.64668i | ||||||||
\(967\) | −53414.4 | −1.77631 | −0.888155 | − | 0.459543i | \(-0.848013\pi\) | ||||
−0.888155 | + | 0.459543i | \(0.848013\pi\) | |||||||
\(968\) | −9787.11 | −0.324968 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 37320.1 | 1.23534 | ||||||||
\(971\) | 39644.8 | 1.31026 | 0.655130 | − | 0.755516i | \(-0.272614\pi\) | ||||
0.655130 | + | 0.755516i | \(0.272614\pi\) | |||||||
\(972\) | 2961.66i | 0.0977317i | ||||||||
\(973\) | −29119.4 | −0.959431 | ||||||||
\(974\) | − 8027.47i | − 0.264083i | ||||||||
\(975\) | 1703.14i | 0.0559428i | ||||||||
\(976\) | − 35725.8i | − 1.17167i | ||||||||
\(977\) | −40232.8 | −1.31746 | −0.658732 | − | 0.752378i | \(-0.728907\pi\) | ||||
−0.658732 | + | 0.752378i | \(0.728907\pi\) | |||||||
\(978\) | 124090. | 4.05723 | ||||||||
\(979\) | − 10689.9i | − 0.348978i | ||||||||
\(980\) | 17851.4i | 0.581880i | ||||||||
\(981\) | 24507.2i | 0.797608i | ||||||||
\(982\) | 46498.6 | 1.51103 | ||||||||
\(983\) | 40449.2i | 1.31244i | 0.754569 | + | 0.656220i | \(0.227846\pi\) | ||||
−0.754569 | + | 0.656220i | \(0.772154\pi\) | |||||||
\(984\) | 18940.9 | 0.613631 | ||||||||
\(985\) | 15613.7 | 0.505070 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 83284.3 | 2.68589 | ||||||||
\(988\) | −201.282 | −0.00648142 | ||||||||
\(989\) | 57999.0i | 1.86477i | ||||||||
\(990\) | 22014.5 | 0.706733 | ||||||||
\(991\) | − 41635.0i | − 1.33459i | −0.744793 | − | 0.667296i | \(-0.767452\pi\) | ||||
0.744793 | − | 0.667296i | \(-0.232548\pi\) | |||||||
\(992\) | 33256.2i | 1.06440i | ||||||||
\(993\) | 51965.4i | 1.66070i | ||||||||
\(994\) | 63931.7 | 2.04003 | ||||||||
\(995\) | −538.888 | −0.0171697 | ||||||||
\(996\) | 4998.07i | 0.159006i | ||||||||
\(997\) | 33986.6i | 1.07960i | 0.841792 | + | 0.539802i | \(0.181501\pi\) | ||||
−0.841792 | + | 0.539802i | \(0.818499\pi\) | |||||||
\(998\) | 50714.3i | 1.60855i | ||||||||
\(999\) | 57374.2 | 1.81706 |
(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 | 289.4.b.d.288.8 | 8 | ||
17.4 | even | 4 | 289.4.a.d.1.1 | yes | 4 | ||
17.13 | even | 4 | 289.4.a.c.1.1 | ✓ | 4 | ||
17.16 | even | 2 | inner | 289.4.b.d.288.7 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
289.4.a.c.1.1 | ✓ | 4 | 17.13 | even | 4 | ||
289.4.a.d.1.1 | yes | 4 | 17.4 | even | 4 | ||
289.4.b.d.288.7 | 8 | 17.16 | even | 2 | inner | ||
289.4.b.d.288.8 | 8 | 1.1 | even | 1 | trivial |