Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(895,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.895");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.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: | \(79.2985670477\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 672) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 895.14 | ||
Character | \(\chi\) | \(=\) | 1344.895 |
Dual form | 1344.4.b.i.895.11 |
$q$-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 \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −3.00000 | −0.577350 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.26482i | 0.202572i | 0.994857 | + | 0.101286i | \(0.0322957\pi\) | ||||
−0.994857 | + | 0.101286i | \(0.967704\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 5.56016 | − | 17.6659i | 0.300220 | − | 0.953870i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 9.00000 | 0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | − | 56.3635i | − | 1.54493i | −0.635058 | − | 0.772465i | \(-0.719024\pi\) | ||
0.635058 | − | 0.772465i | \(-0.280976\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 19.3862i | 0.413596i | 0.978384 | + | 0.206798i | \(0.0663044\pi\) | ||||
−0.978384 | + | 0.206798i | \(0.933696\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 6.79447i | − | 0.116955i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 127.174i | 1.81437i | 0.420737 | + | 0.907183i | \(0.361772\pi\) | ||||
−0.420737 | + | 0.907183i | \(0.638228\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 5.09723 | 0.0615465 | 0.0307733 | − | 0.999526i | \(-0.490203\pi\) | ||||
0.0307733 | + | 0.999526i | \(0.490203\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −16.6805 | + | 52.9978i | −0.173332 | + | 0.550717i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 94.6187i | 0.857799i | 0.903352 | + | 0.428899i | \(0.141098\pi\) | ||||
−0.903352 | + | 0.428899i | \(0.858902\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 119.871 | 0.958965 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −27.0000 | −0.192450 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 92.4931 | 0.592260 | 0.296130 | − | 0.955148i | \(-0.404304\pi\) | ||||
0.296130 | + | 0.955148i | \(0.404304\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 38.9336 | 0.225571 | 0.112785 | − | 0.993619i | \(-0.464023\pi\) | ||||
0.112785 | + | 0.993619i | \(0.464023\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 169.090i | 0.891966i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 40.0102 | + | 12.5928i | 0.193227 | + | 0.0608162i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −290.194 | −1.28940 | −0.644698 | − | 0.764437i | \(-0.723017\pi\) | ||||
−0.644698 | + | 0.764437i | \(0.723017\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 58.1585i | − | 0.238790i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 118.193i | − | 0.450212i | −0.974334 | − | 0.225106i | \(-0.927727\pi\) | ||
0.974334 | − | 0.225106i | \(-0.0722729\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 274.296i | 0.972786i | 0.873740 | + | 0.486393i | \(0.161688\pi\) | ||||
−0.873740 | + | 0.486393i | \(0.838312\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 20.3834i | 0.0675240i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 612.725 | 1.90160 | 0.950799 | − | 0.309809i | \(-0.100265\pi\) | ||||
0.950799 | + | 0.309809i | \(0.100265\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −281.169 | − | 196.451i | −0.819736 | − | 0.572742i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | − | 381.522i | − | 1.04752i | ||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −55.9875 | −0.145103 | −0.0725517 | − | 0.997365i | \(-0.523114\pi\) | ||||
−0.0725517 | + | 0.997365i | \(0.523114\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 127.653 | 0.312959 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −15.2917 | −0.0355339 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −701.109 | −1.54706 | −0.773531 | − | 0.633758i | \(-0.781511\pi\) | ||||
−0.773531 | + | 0.633758i | \(0.781511\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 655.954i | − | 1.37682i | −0.725320 | − | 0.688412i | \(-0.758308\pi\) | ||
0.725320 | − | 0.688412i | \(-0.241692\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 50.0414 | − | 158.993i | 0.100073 | − | 0.317957i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −43.9062 | −0.0837830 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 109.756i | 0.200132i | 0.994981 | + | 0.100066i | \(0.0319055\pi\) | ||||
−0.994981 | + | 0.100066i | \(0.968095\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − | 283.856i | − | 0.495250i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 478.781i | − | 0.800294i | −0.916451 | − | 0.400147i | \(-0.868959\pi\) | ||
0.916451 | − | 0.400147i | \(-0.131041\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 562.420i | 0.901729i | 0.892592 | + | 0.450865i | \(0.148884\pi\) | ||||
−0.892592 | + | 0.450865i | \(0.851116\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −359.612 | −0.553658 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −995.713 | − | 313.390i | −1.47366 | − | 0.463819i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 312.103i | − | 0.444486i | −0.974991 | − | 0.222243i | \(-0.928662\pi\) | ||
0.974991 | − | 0.222243i | \(-0.0713378\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 1038.20 | 1.37298 | 0.686488 | − | 0.727141i | \(-0.259152\pi\) | ||||
0.686488 | + | 0.727141i | \(0.259152\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −288.027 | −0.367540 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −277.479 | −0.341942 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 743.750i | 0.885813i | 0.896568 | + | 0.442906i | \(0.146053\pi\) | ||||
−0.896568 | + | 0.442906i | \(0.853947\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 342.474 | + | 107.790i | 0.394517 | + | 0.124170i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −116.801 | −0.130233 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 11.5443i | 0.0124676i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 1277.01i | 1.33671i | 0.743843 | + | 0.668354i | \(0.233001\pi\) | ||||
−0.743843 | + | 0.668354i | \(0.766999\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − | 507.271i | − | 0.514977i | ||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 1056.67i | − | 1.04101i | −0.853858 | − | 0.520507i | \(-0.825743\pi\) | ||
0.853858 | − | 0.520507i | \(-0.174257\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 1919.63 | 1.83638 | 0.918190 | − | 0.396140i | \(-0.129651\pi\) | ||||
0.918190 | + | 0.396140i | \(0.129651\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −120.031 | − | 37.7783i | −0.111560 | − | 0.0351122i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 1062.91i | 0.960331i | 0.877178 | + | 0.480165i | \(0.159423\pi\) | ||||
−0.877178 | + | 0.480165i | \(0.840577\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 1537.26 | 1.35085 | 0.675425 | − | 0.737429i | \(-0.263960\pi\) | ||||
0.675425 | + | 0.737429i | \(0.263960\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 870.583 | 0.744433 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 190.272 | 0.158401 | 0.0792003 | − | 0.996859i | \(-0.474763\pi\) | ||||
0.0792003 | + | 0.996859i | \(0.474763\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −214.295 | −0.173766 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 174.475i | 0.137865i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 2246.64 | + | 707.107i | 1.73067 | + | 0.544709i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −1845.84 | −1.38681 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 354.580i | 0.259930i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 554.589i | 0.396831i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 697.882i | − | 0.487615i | −0.969824 | − | 0.243807i | \(-0.921604\pi\) | ||
0.969824 | − | 0.243807i | \(-0.0783964\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 822.889i | − | 0.561638i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 818.426 | 0.545849 | 0.272925 | − | 0.962035i | \(-0.412009\pi\) | ||||
0.272925 | + | 0.962035i | \(0.412009\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 28.3414 | − | 90.0472i | 0.0184775 | − | 0.0587074i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 61.1502i | − | 0.0389850i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 1451.82 | 0.905380 | 0.452690 | − | 0.891668i | \(-0.350464\pi\) | ||||
0.452690 | + | 0.891668i | \(0.350464\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1515.70 | −0.924893 | −0.462446 | − | 0.886647i | \(-0.653028\pi\) | ||||
−0.462446 | + | 0.886647i | \(0.653028\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1838.17 | −1.09789 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1092.67 | 0.638977 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 209.481i | 0.119975i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 843.508 | + | 589.352i | 0.473275 | + | 0.330673i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 1971.82 | 1.08415 | 0.542074 | − | 0.840331i | \(-0.317639\pi\) | ||||
0.542074 | + | 0.840331i | \(0.317639\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 2864.69i | − | 1.54387i | −0.635699 | − | 0.771937i | \(-0.719288\pi\) | ||
0.635699 | − | 0.771937i | \(-0.280712\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 1144.57i | 0.604789i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 88.1778i | 0.0456943i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − | 323.010i | − | 0.164198i | −0.996624 | − | 0.0820988i | \(-0.973838\pi\) | ||
0.996624 | − | 0.0820988i | \(-0.0261623\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 167.963 | 0.0837755 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1671.53 | + | 526.095i | 0.818228 | + | 0.257528i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 1445.22i | − | 0.694468i | −0.937778 | − | 0.347234i | \(-0.887121\pi\) | ||
0.937778 | − | 0.347234i | \(-0.112879\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −382.960 | −0.180687 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1270.06 | 0.588505 | 0.294253 | − | 0.955728i | \(-0.404929\pi\) | ||||
0.294253 | + | 0.955728i | \(0.404929\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1821.18 | 0.828938 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 45.8750 | 0.0205155 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 264.158i | 0.116090i | 0.998314 | + | 0.0580450i | \(0.0184867\pi\) | ||||
−0.998314 | + | 0.0580450i | \(0.981513\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 666.499 | − | 2117.62i | 0.287901 | − | 0.914728i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 2103.33 | 0.893197 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | − | 3334.27i | − | 1.39226i | −0.717915 | − | 0.696131i | \(-0.754903\pi\) | ||
0.717915 | − | 0.696131i | \(-0.245097\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | − | 3466.44i | − | 1.42353i | −0.702419 | − | 0.711763i | \(-0.747897\pi\) | ||
0.702419 | − | 0.711763i | \(-0.252103\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 1967.86i | 0.794910i | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 657.239i | − | 0.261195i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 7167.97 | 2.80307 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −150.124 | + | 476.980i | −0.0577774 | + | 0.183572i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3189.84i | 1.20842i | 0.796824 | + | 0.604212i | \(0.206512\pi\) | ||||
−0.796824 | + | 0.604212i | \(0.793488\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −3521.84 | −1.31351 | −0.656756 | − | 0.754103i | \(-0.728072\pi\) | ||||
−0.656756 | + | 0.754103i | \(0.728072\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 131.719 | 0.0483722 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1263.55 | 0.456976 | 0.228488 | − | 0.973547i | \(-0.426622\pi\) | ||||
0.228488 | + | 0.973547i | \(0.426622\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2190.59 | 0.780335 | 0.390168 | − | 0.920744i | \(-0.372417\pi\) | ||||
0.390168 | + | 0.920744i | \(0.372417\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 329.269i | − | 0.115546i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 514.276 | − | 1633.98i | 0.177808 | − | 0.564939i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 267.687 | 0.0912004 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 851.569i | 0.285933i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 287.297i | − | 0.0950851i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1235.79i | 0.403201i | 0.979468 | + | 0.201601i | \(0.0646143\pi\) | ||||
−0.979468 | + | 0.201601i | \(0.935386\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 1436.34i | 0.462050i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −621.232 | −0.197059 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 216.477 | − | 687.798i | 0.0677208 | − | 0.215165i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | − | 1687.26i | − | 0.520614i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2465.41 | −0.750415 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −2757.16 | −0.827951 | −0.413976 | − | 0.910288i | \(-0.635860\pi\) | ||||
−0.413976 | + | 0.910288i | \(0.635860\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 1078.84 | 0.319655 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 33.7355 | 0.00986389 | 0.00493195 | − | 0.999988i | \(-0.498430\pi\) | ||||
0.00493195 | + | 0.999988i | \(0.498430\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 3958.87i | 1.14240i | 0.820811 | + | 0.571199i | \(0.193522\pi\) | ||||
−0.820811 | + | 0.571199i | \(0.806478\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 2987.14 | + | 940.169i | 0.850819 | + | 0.267786i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 5533.39 | 1.55581 | 0.777906 | − | 0.628381i | \(-0.216282\pi\) | ||||
0.777906 | + | 0.628381i | \(0.216282\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 1387.71i | 0.385210i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 936.310i | 0.256624i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 6534.26i | − | 1.76848i | −0.467036 | − | 0.884238i | \(-0.654678\pi\) | ||
0.467036 | − | 0.884238i | \(-0.345322\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 3981.08i | − | 1.06408i | −0.846719 | − | 0.532041i | \(-0.821425\pi\) | ||
0.846719 | − | 0.532041i | \(-0.178575\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −243.000 | −0.0641500 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 444.926 | − | 636.799i | 0.116021 | − | 0.166055i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 98.8157i | 0.0254554i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3114.59 | −0.792688 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 6393.16 | 1.60770 | 0.803850 | − | 0.594832i | \(-0.202782\pi\) | ||||
0.803850 | + | 0.594832i | \(0.202782\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5333.04 | 1.32524 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 864.080 | 0.212199 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 3544.04i | − | 0.860199i | −0.902782 | − | 0.430099i | \(-0.858479\pi\) | ||
0.902782 | − | 0.430099i | \(-0.141521\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −1613.53 | + | 5126.55i | −0.387103 | + | 1.22992i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 832.438 | 0.197420 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 2458.85i | 0.576500i | 0.957555 | + | 0.288250i | \(0.0930734\pi\) | ||||
−0.957555 | + | 0.288250i | \(0.906927\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 126.802i | − | 0.0293939i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − | 2231.25i | − | 0.511424i | ||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 6621.96i | 1.50092i | 0.660914 | + | 0.750461i | \(0.270169\pi\) | ||||
−0.660914 | + | 0.750461i | \(0.729831\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 914.675 | 0.205028 | 0.102514 | − | 0.994732i | \(-0.467311\pi\) | ||||
0.102514 | + | 0.994732i | \(0.467311\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −1027.42 | − | 323.370i | −0.227775 | − | 0.0716896i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | − | 6756.32i | − | 1.48153i | ||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −2329.10 | −0.505206 | −0.252603 | − | 0.967570i | \(-0.581287\pi\) | ||||
−0.252603 | + | 0.967570i | \(0.581287\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 350.403 | 0.0751902 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −1006.08 | −0.213586 | −0.106793 | − | 0.994281i | \(-0.534058\pi\) | ||||
−0.106793 | + | 0.994281i | \(0.534058\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 6622.25 | 1.39100 | 0.695498 | − | 0.718528i | \(-0.255184\pi\) | ||||
0.695498 | + | 0.718528i | \(0.255184\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | − | 34.6330i | − | 0.00719817i | ||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −2088.00 | − | 657.174i | −0.429444 | − | 0.135163i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −11260.2 | −2.29192 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | − | 3831.03i | − | 0.771749i | ||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 5228.26i | − | 1.04245i | −0.853419 | − | 0.521226i | \(-0.825475\pi\) | ||
0.853419 | − | 0.521226i | \(-0.174525\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 1587.89i | − | 0.313391i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1521.81i | 0.297322i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −1834.29 | −0.354782 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4845.69 | + | 1525.13i | 0.927911 | + | 0.292050i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 3170.00i | 0.601029i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 1485.62 | 0.278906 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 9966.23 | 1.85278 | 0.926389 | − | 0.376569i | \(-0.122896\pi\) | ||||
0.926389 | + | 0.376569i | \(0.122896\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −5758.90 | −1.06023 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 720.081 | 0.131293 | 0.0656463 | − | 0.997843i | \(-0.479089\pi\) | ||||
0.0656463 | + | 0.997843i | \(0.479089\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 6738.59i | 1.21689i | 0.793594 | + | 0.608447i | \(0.208207\pi\) | ||||
−0.793594 | + | 0.608447i | \(0.791793\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 360.092 | + | 113.335i | 0.0644091 | + | 0.0202721i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 6754.62 | 1.19677 | 0.598387 | − | 0.801207i | \(-0.295809\pi\) | ||||
0.598387 | + | 0.801207i | \(0.295809\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 5213.23i | − | 0.915000i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − | 3188.73i | − | 0.554447i | ||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 648.235i | 0.111668i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 2323.83i | 0.396624i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −4611.77 | −0.779913 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 3406.85 | − | 10824.3i | 0.570898 | − | 1.81388i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 9239.33i | 1.53426i | 0.641492 | + | 0.767130i | \(0.278316\pi\) | ||||
−0.641492 | + | 0.767130i | \(0.721684\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −2611.75 | −0.429799 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −248.579 | −0.0405412 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −1886.09 | −0.304871 | −0.152436 | − | 0.988313i | \(-0.548712\pi\) | ||||
−0.152436 | + | 0.988313i | \(0.548712\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −570.816 | −0.0914527 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 2194.44i | − | 0.348491i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −5033.82 | + | 3874.82i | −0.792423 | + | 0.609973i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 642.884 | 0.100324 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 6243.36i | − | 0.965883i | −0.875653 | − | 0.482941i | \(-0.839568\pi\) | ||
0.875653 | − | 0.482941i | \(-0.160432\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 5320.31i | 0.816016i | 0.912978 | + | 0.408008i | \(0.133776\pi\) | ||||
−0.912978 | + | 0.408008i | \(0.866224\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | − | 523.426i | − | 0.0795967i | ||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 7896.43i | − | 1.19061i | −0.803501 | − | 0.595304i | \(-0.797032\pi\) | ||
0.803501 | − | 0.595304i | \(-0.202968\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 1084.35 | 0.162117 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −6739.93 | − | 2121.32i | −0.999202 | − | 0.314488i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 1471.39i | − | 0.216314i | −0.994134 | − | 0.108157i | \(-0.965505\pi\) | ||
0.994134 | − | 0.108157i | \(-0.0344949\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6833.02 | −0.996212 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 5537.52 | 0.800674 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −1273.78 | −0.182665 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8200.26 | 1.16635 | 0.583175 | − | 0.812347i | \(-0.301810\pi\) | ||||
0.583175 | + | 0.812347i | \(0.301810\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − | 1063.74i | − | 0.150071i | ||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −311.299 | + | 989.071i | −0.0435630 | + | 0.138410i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −2848.05 | −0.395352 | −0.197676 | − | 0.980267i | \(-0.563339\pi\) | ||||
−0.197676 | + | 0.980267i | \(0.563339\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | − | 1663.77i | − | 0.229111i | ||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 1793.09i | 0.244957i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 99.8362i | 0.0135310i | 0.999977 | + | 0.00676549i | \(0.00215354\pi\) | ||||
−0.999977 | + | 0.00676549i | \(0.997846\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2093.65i | 0.281524i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1922.33 | −0.256466 | −0.128233 | − | 0.991744i | \(-0.540931\pi\) | ||||
−0.128233 | + | 0.991744i | \(0.540931\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 709.772 | − | 2255.11i | 0.0939567 | − | 0.298523i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 2468.67i | 0.324262i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 9766.34 | 1.27294 | 0.636470 | − | 0.771302i | \(-0.280394\pi\) | ||||
0.636470 | + | 0.771302i | \(0.280394\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −12033.0 | −1.55636 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −2455.28 | −0.315146 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 706.859 | 0.0900403 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | − | 2983.13i | − | 0.377125i | −0.982061 | − | 0.188563i | \(-0.939617\pi\) | ||
0.982061 | − | 0.188563i | \(-0.0603829\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −85.0241 | + | 270.142i | −0.0106680 | + | 0.0338947i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 1736.37 | 0.216235 | 0.108117 | − | 0.994138i | \(-0.465518\pi\) | ||||
0.108117 | + | 0.994138i | \(0.465518\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 754.774i | 0.0932952i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 183.451i | 0.0225080i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16356.4i | 1.99203i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 7946.15i | 0.960664i | 0.877087 | + | 0.480332i | \(0.159484\pi\) | ||||
−0.877087 | + | 0.480332i | \(0.840516\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −4355.45 | −0.522721 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −3898.28 | + | 12385.7i | −0.464459 | + | 1.47570i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 2351.33i | 0.278126i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 4547.10 | 0.533987 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 1132.03 | 0.131989 | 0.0659945 | − | 0.997820i | \(-0.478978\pi\) | ||||
0.0659945 | + | 0.997820i | \(0.478978\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1613.13 | 0.186744 | 0.0933719 | − | 0.995631i | \(-0.470235\pi\) | ||||
0.0933719 | + | 0.995631i | \(0.470235\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 5514.52 | 0.633866 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 15244.4i | 1.73991i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −11588.0 | − | 3647.20i | −1.31331 | − | 0.413350i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3278.01 | −0.368914 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 1769.22i | − | 0.197728i | −0.995101 | − | 0.0988638i | \(-0.968479\pi\) | ||
0.995101 | − | 0.0988638i | \(-0.0315208\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 5778.85i | 0.641372i | 0.947186 | + | 0.320686i | \(0.103913\pi\) | ||||
−0.947186 | + | 0.320686i | \(0.896087\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − | 628.442i | − | 0.0692678i | ||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 482.293i | 0.0527945i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −4620.52 | −0.502336 | −0.251168 | − | 0.967943i | \(-0.580815\pi\) | ||||
−0.251168 | + | 0.967943i | \(0.580815\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −2530.52 | − | 1768.05i | −0.273245 | − | 0.190914i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 9071.81i | 0.972945i | 0.873696 | + | 0.486473i | \(0.161717\pi\) | ||||
−0.873696 | + | 0.486473i | \(0.838283\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −1684.46 | −0.179441 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −5915.46 | −0.625933 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 15112.3 | 1.58840 | 0.794201 | − | 0.607655i | \(-0.207889\pi\) | ||||
0.794201 | + | 0.607655i | \(0.207889\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6661.79 | −0.695546 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8594.06i | 0.891356i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −244.125 | + | 775.644i | −0.0251534 | + | 0.0799181i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −16630.8 | −1.70231 | −0.851156 | − | 0.524913i | \(-0.824098\pi\) | ||||
−0.851156 | + | 0.524913i | \(0.824098\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − | 3433.70i | − | 0.349175i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 11011.6i | − | 1.11250i | −0.831016 | − | 0.556248i | \(-0.812240\pi\) | ||
0.831016 | − | 0.556248i | \(-0.187760\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 12523.9i | − | 1.25709i | −0.777773 | − | 0.628545i | \(-0.783651\pi\) | ||
0.777773 | − | 0.628545i | \(-0.216349\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 264.533i | − | 0.0263816i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −4373.03 | −0.433319 | −0.216659 | − | 0.976247i | \(-0.569516\pi\) | ||||
−0.216659 | + | 0.976247i | \(0.569516\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 1938.95 | + | 610.262i | 0.190900 | + | 0.0600838i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 969.031i | 0.0947995i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 15460.3 | 1.50289 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 611.008 | 0.0590209 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −503.888 | −0.0483678 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 4027.80 | 0.384206 | 0.192103 | − | 0.981375i | \(-0.438469\pi\) | ||||
0.192103 | + | 0.981375i | \(0.438469\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − | 5625.75i | − | 0.533290i | ||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −5014.58 | − | 1578.28i | −0.472404 | − | 0.148684i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −2892.20 | −0.270780 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | − | 4603.46i | − | 0.428342i | −0.976796 | − | 0.214171i | \(-0.931295\pi\) | ||
0.976796 | − | 0.214171i | \(-0.0687050\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4335.66i | 0.400951i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 4062.95i | − | 0.373439i | −0.982413 | − | 0.186719i | \(-0.940214\pi\) | ||
0.982413 | − | 0.186719i | \(-0.0597855\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 11762.7i | 1.07458i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1148.88 | 0.104320 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −8458.11 | − | 2662.10i | −0.763377 | − | 0.240264i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 6479.08i | − | 0.581249i | −0.956837 | − | 0.290625i | \(-0.906137\pi\) | ||
0.956837 | − | 0.290625i | \(-0.0938631\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3810.19 | −0.339774 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −4443.44 | −0.393883 | −0.196942 | − | 0.980415i | \(-0.563101\pi\) | ||||
−0.196942 | + | 0.980415i | \(0.563101\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2393.16 | 0.210880 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −5463.53 | −0.478588 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 1783.20i | 0.155282i | 0.996981 | + | 0.0776412i | \(0.0247389\pi\) | ||||
−0.996981 | + | 0.0776412i | \(0.975261\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 9935.66 | + | 3127.14i | 0.860132 | + | 0.270717i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −137.625 | −0.0118446 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 4347.63i | 0.371999i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − | 34535.3i | − | 2.93783i | ||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 792.474i | − | 0.0670245i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 2198.87i | − | 0.184902i | −0.995717 | − | 0.0924512i | \(-0.970530\pi\) | ||
0.995717 | − | 0.0924512i | \(-0.0294702\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −16655.9 | −1.39256 | −0.696282 | − | 0.717768i | \(-0.745164\pi\) | ||||
−0.696282 | + | 0.717768i | \(0.745164\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −1999.50 | + | 6352.87i | −0.166219 | + | 0.528118i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 4951.34i | 0.409267i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 3214.30 | 0.264181 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −6309.99 | −0.515687 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2291.32 | 0.186206 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −2407.30 | −0.194536 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10002.8i | 0.803823i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −11072.6 | + | 15847.7i | −0.884846 | + | 1.26643i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −16221.5 | −1.28912 | −0.644562 | − | 0.764552i | \(-0.722960\pi\) | ||||
−0.644562 | + | 0.764552i | \(0.722960\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10399.3i | 0.821873i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 3481.62i | 0.273644i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 3649.69i | 0.285282i | 0.989774 | + | 0.142641i | \(0.0455595\pi\) | ||||
−0.989774 | + | 0.142641i | \(0.954441\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | − | 5903.58i | − | 0.458941i | ||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 471.458 | 0.0364516 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −5513.59 | − | 1735.34i | −0.423981 | − | 0.133444i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 1971.72i | 0.150801i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 19277.8 | 1.46648 | 0.733238 | − | 0.679972i | \(-0.238008\pi\) | ||||
0.733238 | + | 0.679972i | \(0.238008\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −5317.55 | −0.402341 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −21503.9 | −1.61835 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −19320.9 | −1.44632 | −0.723160 | − | 0.690681i | \(-0.757311\pi\) | ||||
−0.723160 | + | 0.690681i | \(0.757311\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 430.932i | 0.0320875i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 450.373 | − | 1430.94i | 0.0333578 | − | 0.105986i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 26173.7 | 1.92840 | 0.964198 | − | 0.265183i | \(-0.0854324\pi\) | ||||
0.964198 | + | 0.265183i | \(0.0854324\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | − | 5196.24i | − | 0.380833i | −0.981703 | − | 0.190417i | \(-0.939016\pi\) | ||
0.981703 | − | 0.190417i | \(-0.0609839\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | − | 9569.53i | − | 0.697684i | ||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 11342.0i | 0.822599i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − | 11218.6i | − | 0.809421i | −0.914445 | − | 0.404711i | \(-0.867372\pi\) | ||
0.914445 | − | 0.404711i | \(-0.132628\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 10565.5 | 0.758356 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5772.54 | − | 18340.7i | 0.412195 | − | 1.30964i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3155.65i | 0.224174i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −395.156 | −0.0279277 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 3438.46 | 0.241772 | 0.120886 | − | 0.992666i | \(-0.461426\pi\) | ||||
0.120886 | + | 0.992666i | \(0.461426\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 198.454 | 0.0138831 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −3790.65 | −0.263835 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 7612.88i | − | 0.527190i | −0.964633 | − | 0.263595i | \(-0.915092\pi\) | ||
0.964633 | − | 0.263595i | \(-0.0849082\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1601.47 | + | 5088.25i | −0.110343 | + | 0.350585i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −6571.77 | −0.450527 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 16681.5i | − | 1.13788i | −0.822379 | − | 0.568940i | \(-0.807354\pi\) | ||
0.822379 | − | 0.568940i | \(-0.192646\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 5913.34i | 0.401348i | 0.979658 | + | 0.200674i | \(0.0643132\pi\) | ||||
−0.979658 | + | 0.200674i | \(0.935687\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 987.807i | 0.0667108i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | − | 4180.50i | − | 0.280928i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −26481.0 | −1.77073 | −0.885363 | − | 0.464900i | \(-0.846090\pi\) | ||||
−0.885363 | + | 0.464900i | \(0.846090\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −1542.83 | + | 4901.93i | −0.102658 | + | 0.326168i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11878.4i | 0.786494i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −25016.9 | −1.64832 | −0.824162 | − | 0.566355i | \(-0.808353\pi\) | ||||
−0.824162 | + | 0.566355i | \(0.808353\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −803.061 | −0.0526546 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 10545.5 | 0.688078 | 0.344039 | − | 0.938955i | \(-0.388205\pi\) | ||||
0.344039 | + | 0.938955i | \(0.388205\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −18079.7 | −1.17397 | −0.586984 | − | 0.809598i | \(-0.699685\pi\) | ||||
−0.586984 | + | 0.809598i | \(0.699685\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | − | 2554.71i | − | 0.165083i | ||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 13139.0 | + | 4135.37i | 0.844950 | + | 0.265939i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 13727.8 | 0.878578 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 861.892i | 0.0548974i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | − | 36905.2i | − | 2.33944i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 14856.1i | − | 0.937263i | −0.883394 | − | 0.468632i | \(-0.844747\pi\) | ||
0.883394 | − | 0.468632i | \(-0.155253\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 3707.38i | − | 0.232788i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 1580.58 | 0.0987770 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 3808.42 | − | 5450.79i | 0.236884 | − | 0.339040i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 4309.03i | − | 0.266765i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −8403.54 | −0.517815 | −0.258908 | − | 0.965902i | \(-0.583363\pi\) | ||||
−0.258908 | + | 0.965902i | \(0.583363\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −10196.8 | −0.625383 | −0.312692 | − | 0.949855i | \(-0.601231\pi\) | ||||
−0.312692 | + | 0.949855i | \(0.601231\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1863.70 | 0.113772 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7696.83 | 0.467687 | 0.233844 | − | 0.972274i | \(-0.424870\pi\) | ||||
0.233844 | + | 0.972274i | \(0.424870\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 39517.0i | 2.39010i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −649.431 | + | 2063.40i | −0.0390986 | + | 0.124226i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 16048.6 | 0.961759 | 0.480879 | − | 0.876787i | \(-0.340317\pi\) | ||||
0.480879 | + | 0.876787i | \(0.340317\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 1853.59i | 0.110574i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 5061.78i | 0.300576i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | − | 5087.65i | − | 0.300739i | −0.988630 | − | 0.150369i | \(-0.951954\pi\) | ||
0.988630 | − | 0.150369i | \(-0.0480463\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14786.6i | 0.870095i | 0.900408 | + | 0.435047i | \(0.143268\pi\) | ||||
−0.900408 | + | 0.435047i | \(0.856732\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 7396.24 | 0.433252 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 203.941 | + | 64.1882i | 0.0118925 | + | 0.00374302i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 8751.58i | 0.508040i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 8271.48 | 0.478018 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −36971.8 | −2.12710 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −11709.5 | −0.670680 | −0.335340 | − | 0.942097i | \(-0.608851\pi\) | ||||
−0.335340 | + | 0.942097i | \(0.608851\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −3236.51 | −0.184553 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 6581.03i | 0.373603i | 0.982398 | + | 0.186802i | \(0.0598122\pi\) | ||||
−0.982398 | + | 0.186802i | \(0.940188\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 22559.6 | + | 7100.37i | 1.27505 | + | 0.401307i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −101.207 | −0.00569492 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | − | 1412.04i | − | 0.0791070i | −0.999217 | − | 0.0395535i | \(-0.987406\pi\) | ||
0.999217 | − | 0.0395535i | \(-0.0125936\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3288.11i | 0.183405i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 11876.6i | − | 0.659564i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − | 1085.38i | − | 0.0600142i | ||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −5861.32 | −0.322684 | −0.161342 | − | 0.986899i | \(-0.551582\pi\) | ||||
−0.161342 | + | 0.986899i | \(0.551582\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −8961.41 | − | 2820.51i | −0.491221 | − | 0.154606i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | − | 3432.80i | − | 0.187357i | ||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 15031.1 | 0.816850 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −16600.2 | −0.898248 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 20729.3 | 1.11688 | 0.558442 | − | 0.829544i | \(-0.311399\pi\) | ||||
0.558442 | + | 0.829544i | \(0.311399\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −1479.19 | −0.0793578 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − | 4163.14i | − | 0.222401i | ||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −18667.0 | − | 5875.24i | −0.992991 | − | 0.312533i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 15204.3 | 0.805371 | 0.402685 | − | 0.915338i | \(-0.368077\pi\) | ||||
0.402685 | + | 0.915338i | \(0.368077\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 2808.93i | − | 0.148162i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 3683.85i | 0.193494i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 2474.71i | 0.129439i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 19602.8i | 1.02103i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −9047.94 | −0.469306 | −0.234653 | − | 0.972079i | \(-0.575395\pi\) | ||||
−0.234653 | + | 0.972079i | \(0.575395\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 10673.5 | − | 33912.1i | 0.551318 | − | 1.75167i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 11943.2i | 0.614348i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 11087.2 | 0.567956 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 1540.38 | 0.0785824 | 0.0392912 | − | 0.999228i | \(-0.487490\pi\) | ||||
0.0392912 | + | 0.999228i | \(0.487490\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 729.000 | 0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −34883.3 | −1.76499 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 32338.6i | 1.62954i | 0.579784 | + | 0.814770i | \(0.303137\pi\) | ||||
−0.579784 | + | 0.814770i | \(0.696863\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −1334.78 | + | 1910.40i | −0.0669850 | + | 0.0958722i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 6186.25 | 0.309190 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 23307.1i | 1.16017i | 0.814555 | + | 0.580086i | \(0.196981\pi\) | ||||
−0.814555 | + | 0.580086i | \(0.803019\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | − | 296.447i | − | 0.0146967i | ||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 537.576i | 0.0265434i | 0.999912 | + | 0.0132717i | \(0.00422464\pi\) | ||||
−0.999912 | + | 0.0132717i | \(0.995775\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4465.83i | 0.219618i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 9343.78 | 0.457658 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 18777.3 | + | 5909.94i | 0.916030 | + | 0.288311i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 8344.36i | 0.405446i | 0.979236 | + | 0.202723i | \(0.0649791\pi\) | ||||
−0.979236 | + | 0.202723i | \(0.935021\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −19179.5 | −0.928206 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 6488.01 | 0.312746 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −15987.8 | −0.767617 | −0.383808 | − | 0.923413i | \(-0.625388\pi\) | ||||
−0.383808 | + | 0.923413i | \(0.625388\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −15999.1 | −0.765127 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 30206.1i | 1.43886i | 0.694567 | + | 0.719428i | \(0.255596\pi\) | ||||
−0.694567 | + | 0.719428i | \(0.744404\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 8547.39 | − | 27157.1i | 0.405552 | − | 1.28853i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | −2592.24 | −0.122513 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | − | 13591.8i | − | 0.639859i | ||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21943.5i | 1.02900i | 0.857490 | + | 0.514501i | \(0.172023\pi\) | ||||
−0.857490 | + | 0.514501i | \(0.827977\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 10632.1i | 0.496636i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 7922.07i | 0.368612i | 0.982869 | + | 0.184306i | \(0.0590037\pi\) | ||||
−0.982869 | + | 0.184306i | \(0.940996\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 4667.00 | 0.216314 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 4840.58 | − | 15379.6i | 0.223494 | − | 0.710092i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − | 602.459i | − | 0.0277090i | ||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −26985.8 | −1.23640 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −2497.31 | −0.113981 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 731.561 | 0.0332618 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −26633.6 | −1.20634 | −0.603168 | − | 0.797614i | \(-0.706095\pi\) | ||||
−0.603168 | + | 0.797614i | \(0.706095\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | − | 7376.56i | − | 0.332842i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 1057.94 | − | 3361.33i | 0.0475551 | − | 0.151094i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12716.4 | 0.569449 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 380.405i | 0.0169706i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 12638.0i | 0.561684i | 0.959754 | + | 0.280842i | \(0.0906138\pi\) | ||||
−0.959754 | + | 0.280842i | \(0.909386\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 77922.6i | 3.45019i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 6693.75i | 0.295271i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 31699.9 | 1.39311 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −1191.51 | + | 3785.71i | −0.0521680 | + | 0.165750i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | − | 19865.9i | − | 0.866558i | ||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −3290.23 | −0.142989 | −0.0714945 | − | 0.997441i | \(-0.522777\pi\) | ||||
−0.0714945 | + | 0.997441i | \(0.522777\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 42757.5 | 1.85132 | 0.925658 | − | 0.378361i | \(-0.123512\pi\) | ||||
0.925658 | + | 0.378361i | \(0.123512\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −2744.03 | −0.118373 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 3273.17 | 0.140680 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 1398.15i | 0.0598716i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3082.27 | + | 970.111i | 0.131506 | + | 0.0413900i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 3209.29 | 0.136425 | 0.0682126 | − | 0.997671i | \(-0.478270\pi\) | ||||
0.0682126 | + | 0.997671i | \(0.478270\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 10327.4i | 0.437412i | 0.975791 | + | 0.218706i | \(0.0701836\pi\) | ||||
−0.975791 | + | 0.218706i | \(0.929816\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 20269.0i | 0.855363i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 9065.80i | 0.381195i | 0.981668 | + | 0.190598i | \(0.0610426\pi\) | ||||
−0.981668 | + | 0.190598i | \(0.938957\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 6037.66i | 0.252951i | 0.991970 | + | 0.126476i | \(0.0403666\pi\) | ||||
−0.991970 | + | 0.126476i | \(0.959633\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 6987.30 | 0.291681 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 24983.4 | − | 35757.4i | 1.03916 | − | 1.48730i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2876.47i | 0.119215i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −1051.21 | −0.0434111 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −42840.9 | −1.76285 | −0.881425 | − | 0.472323i | \(-0.843416\pi\) | ||||
−0.881425 | + | 0.472323i | \(0.843416\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −15834.0 | −0.649228 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 3018.24 | 0.123314 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4124.64i | 0.167920i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10263.2 | + | 32608.5i | −0.416348 | + | 1.32283i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −19866.8 | −0.803092 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 27457.8i | − | 1.10604i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − | 46668.7i | − | 1.87328i | −0.350296 | − | 0.936639i | \(-0.613919\pi\) | ||
0.350296 | − | 0.936639i | \(-0.386081\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 103.899i | 0.00415587i | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 23.9058i | 0.000952868i | 1.00000 | 0.000476434i | \(0.000151654\pi\) | |||||
−1.00000 | 0.000476434i | \(0.999848\pi\) | ||||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −3773.28 | −0.149875 | −0.0749375 | − | 0.997188i | \(-0.523876\pi\) | ||||
−0.0749375 | + | 0.997188i | \(0.523876\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 6263.99 | + | 1971.52i | 0.247940 | + | 0.0780363i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 26099.3i | − | 1.02947i | −0.857351 | − | 0.514733i | \(-0.827891\pi\) | ||
0.857351 | − | 0.514733i | \(-0.172109\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −598.271 | −0.0235166 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 33780.6 | 1.32324 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −17591.2 | −0.686699 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −2127.75 | −0.0827740 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 11493.1i | 0.445569i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9797.32 | + | 3083.60i | 0.378525 | + | 0.119137i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −11202.2 | −0.431324 | −0.215662 | − | 0.976468i | \(-0.569191\pi\) | ||||
−0.215662 | + | 0.976468i | \(0.569191\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 15684.8i | 0.601860i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 45579.1i | − | 1.74302i | −0.490378 | − | 0.871510i | \(-0.663141\pi\) | ||
0.490378 | − | 0.871510i | \(-0.336859\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | − | 38399.2i | − | 1.46346i | −0.681595 | − | 0.731730i | \(-0.738713\pi\) | ||
0.681595 | − | 0.731730i | \(-0.261287\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 4763.67i | 0.180937i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 20414.4 | 0.772772 | 0.386386 | − | 0.922337i | \(-0.373723\pi\) | ||||
0.386386 | + | 0.922337i | \(0.373723\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −12328.7 | − | 3880.33i | −0.465121 | − | 0.146392i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | − | 4565.44i | − | 0.171659i | ||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 3123.20 | 0.117037 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 7551.53 | 0.282033 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5502.88 | 0.204834 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 3601.09 | 0.133596 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 7120.15i | − | 0.263271i | ||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | −14537.1 | − | 4575.39i | −0.535730 | − | 0.168615i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 7850.87 | 0.288367 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 15236.6i | − | 0.557798i | −0.960320 | − | 0.278899i | \(-0.910030\pi\) | ||
0.960320 | − | 0.278899i | \(-0.0899695\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − | 9510.01i | − | 0.347004i | ||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 37590.2i | − | 1.36709i | −0.729908 | − | 0.683545i | \(-0.760437\pi\) | ||
0.729908 | − | 0.683545i | \(-0.239563\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 58516.4i | − | 2.12115i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4456.86 | −0.161026 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 4550.58 | − | 14458.3i | 0.163875 | − | 0.520669i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31369.0i | 1.12597i | 0.826466 | + | 0.562986i | \(0.190348\pi\) | ||||
−0.826466 | + | 0.562986i | \(0.809652\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −29898.7 | −1.06970 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 9281.73 | 0.330999 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −34785.8 | −1.23649 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 17276.7 | 0.612127 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 12287.4i | 0.433947i | 0.976177 | + | 0.216974i | \(0.0696186\pi\) | ||||
−0.976177 | + | 0.216974i | \(0.930381\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1433.18 | − | 1001.35i | −0.0504519 | − | 0.0352503i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −2160.24 | −0.0758019 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 16234.2i | 0.567823i | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 45545.1i | − | 1.58793i | −0.607962 | − | 0.793966i | \(-0.708013\pi\) | ||
0.607962 | − | 0.793966i | \(-0.291987\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − | 20215.8i | − | 0.702574i | ||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 40159.5i | 1.39125i | 0.718406 | + | 0.695624i | \(0.244872\pi\) | ||||
−0.718406 | + | 0.695624i | \(0.755128\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 11183.3 | 0.386192 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −1080.27 | − | 340.005i | −0.0371866 | − | 0.0117041i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 28786.1i | 0.987774i | 0.869526 | + | 0.493887i | \(0.164424\pi\) | ||||
−0.869526 | + | 0.493887i | \(0.835576\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −10903.2 | −0.372952 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −20263.9 | −0.690958 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −41034.9 | −1.39481 | −0.697404 | − | 0.716679i | \(-0.745661\pi\) | ||||
−0.697404 | + | 0.716679i | \(0.745661\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −7224.43 | −0.244793 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 15639.7i | 0.528276i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 8072.32 | − | 25647.7i | 0.271813 | − | 0.863615i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −28275.2 | −0.949118 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 9566.19i | 0.320110i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − | 7976.35i | − | 0.266081i | ||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 50246.8i | − | 1.67097i | −0.549514 | − | 0.835485i | \(-0.685187\pi\) | ||
0.549514 | − | 0.835485i | \(-0.314813\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 1944.70i | − | 0.0644715i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 9184.38 | 0.303544 | 0.151772 | − | 0.988416i | \(-0.451502\pi\) | ||||
0.151772 | + | 0.988416i | \(0.451502\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −8427.54 | + | 26776.3i | −0.277672 | + | 0.882228i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 6971.49i | − | 0.228991i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −8572.75 | −0.280723 | −0.140362 | − | 0.990100i | \(-0.544827\pi\) | ||||
−0.140362 | + | 0.990100i | \(0.544827\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 41920.3 | 1.36852 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 13835.3 | 0.450283 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −24208.5 | −0.785484 | −0.392742 | − | 0.919649i | \(-0.628473\pi\) | ||||
−0.392742 | + | 0.919649i | \(0.628473\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 2861.72i | 0.0925706i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −10220.5 | + | 32473.0i | −0.329608 | + | 1.04724i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −25953.6 | −0.834454 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 45932.1i | − | 1.47233i | −0.676801 | − | 0.736166i | \(-0.736634\pi\) | ||
0.676801 | − | 0.736166i | \(-0.263366\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − | 27718.0i | − | 0.885805i | ||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 4961.30i | 0.158074i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11888.2i | 0.377637i | 0.982012 | + | 0.188819i | \(0.0604658\pi\) | ||||
−0.982012 | + | 0.188819i | \(0.939534\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 7835.25 | 0.248144 |
(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 | 1344.4.b.i.895.14 | 24 | ||
4.3 | odd | 2 | 1344.4.b.j.895.14 | 24 | |||
7.6 | odd | 2 | 1344.4.b.j.895.11 | 24 | |||
8.3 | odd | 2 | 672.4.b.a.223.11 | ✓ | 24 | ||
8.5 | even | 2 | 672.4.b.b.223.11 | yes | 24 | ||
28.27 | even | 2 | inner | 1344.4.b.i.895.11 | 24 | ||
56.13 | odd | 2 | 672.4.b.a.223.14 | yes | 24 | ||
56.27 | even | 2 | 672.4.b.b.223.14 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
672.4.b.a.223.11 | ✓ | 24 | 8.3 | odd | 2 | ||
672.4.b.a.223.14 | yes | 24 | 56.13 | odd | 2 | ||
672.4.b.b.223.11 | yes | 24 | 8.5 | even | 2 | ||
672.4.b.b.223.14 | yes | 24 | 56.27 | even | 2 | ||
1344.4.b.i.895.11 | 24 | 28.27 | even | 2 | inner | ||
1344.4.b.i.895.14 | 24 | 1.1 | even | 1 | trivial | ||
1344.4.b.j.895.11 | 24 | 7.6 | odd | 2 | |||
1344.4.b.j.895.14 | 24 | 4.3 | odd | 2 |