Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1568,3,Mod(881,1568)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1568, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1568.881");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1568 = 2^{5} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1568.h (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: | \(42.7249054517\) |
Analytic rank: | \(0\) |
Dimension: | \(28\) |
Twist minimal: | no (minimal twist has level 56) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 881.11 | ||
Character | \(\chi\) | \(=\) | 1568.881 |
Dual form | 1568.3.h.a.881.12 |
$q$-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 \(\left(\mathbb{Z}/1568\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(1471\) | \(1473\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) |
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 | ||||||||
\(3\) | −0.910863 | −0.303621 | −0.151810 | − | 0.988410i | \(-0.548510\pi\) | ||||
−0.151810 | + | 0.988410i | \(0.548510\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −6.34503 | −1.26901 | −0.634503 | − | 0.772921i | \(-0.718795\pi\) | ||||
−0.634503 | + | 0.772921i | \(0.718795\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −8.17033 | −0.907814 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 13.2146i | 1.20133i | 0.799500 | + | 0.600666i | \(0.205098\pi\) | ||||
−0.799500 | + | 0.600666i | \(0.794902\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −19.4243 | −1.49418 | −0.747090 | − | 0.664723i | \(-0.768550\pi\) | ||||
−0.747090 | + | 0.664723i | \(0.768550\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 5.77945 | 0.385296 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 15.9268i | − 0.936869i | −0.883498 | − | 0.468434i | \(-0.844818\pi\) | ||||
0.883498 | − | 0.468434i | \(-0.155182\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −16.4545 | −0.866026 | −0.433013 | − | 0.901388i | \(-0.642550\pi\) | ||||
−0.433013 | + | 0.901388i | \(0.642550\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −23.9215 | −1.04006 | −0.520032 | − | 0.854147i | \(-0.674080\pi\) | ||||
−0.520032 | + | 0.854147i | \(0.674080\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 15.2593 | 0.610374 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 15.6398 | 0.579252 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − 16.6618i | − 0.574544i | −0.957849 | − | 0.287272i | \(-0.907252\pi\) | ||||
0.957849 | − | 0.287272i | \(-0.0927483\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 12.8588i | − 0.414799i | −0.978256 | − | 0.207400i | \(-0.933500\pi\) | ||||
0.978256 | − | 0.207400i | \(-0.0665000\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − 12.0367i | − 0.364749i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 47.5556i | 1.28529i | 0.766165 | + | 0.642644i | \(0.222162\pi\) | ||||
−0.766165 | + | 0.642644i | \(0.777838\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 17.6929 | 0.453664 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.49499i | 0.158415i | 0.996858 | + | 0.0792073i | \(0.0252389\pi\) | ||||
−0.996858 | + | 0.0792073i | \(0.974761\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 33.2928i | 0.774252i | 0.922027 | + | 0.387126i | \(0.126532\pi\) | ||||
−0.922027 | + | 0.387126i | \(0.873468\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 51.8409 | 1.15202 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 21.9062i | 0.466089i | 0.972466 | + | 0.233045i | \(0.0748688\pi\) | ||||
−0.972466 | + | 0.233045i | \(0.925131\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 14.5071i | 0.284453i | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 37.1846i | 0.701597i | 0.936451 | + | 0.350798i | \(0.114090\pi\) | ||||
−0.936451 | + | 0.350798i | \(0.885910\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 83.8473i | − 1.52450i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 14.9878 | 0.262944 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −54.6855 | −0.926874 | −0.463437 | − | 0.886130i | \(-0.653384\pi\) | ||||
−0.463437 | + | 0.886130i | \(0.653384\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 10.2468 | 0.167980 | 0.0839902 | − | 0.996467i | \(-0.473234\pi\) | ||||
0.0839902 | + | 0.996467i | \(0.473234\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 123.248 | 1.89612 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − 17.1341i | − 0.255733i | −0.991791 | − | 0.127867i | \(-0.959187\pi\) | ||||
0.991791 | − | 0.127867i | \(-0.0408129\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 21.7892 | 0.315785 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −32.0568 | −0.451505 | −0.225752 | − | 0.974185i | \(-0.572484\pi\) | ||||
−0.225752 | + | 0.974185i | \(0.572484\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | − 107.166i | − 1.46802i | −0.679137 | − | 0.734011i | \(-0.737646\pi\) | ||||
0.679137 | − | 0.734011i | \(-0.262354\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −13.8992 | −0.185322 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 58.3083 | 0.738080 | 0.369040 | − | 0.929414i | \(-0.379687\pi\) | ||||
0.369040 | + | 0.929414i | \(0.379687\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 59.2872 | 0.731941 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 36.3441 | 0.437880 | 0.218940 | − | 0.975738i | \(-0.429740\pi\) | ||||
0.218940 | + | 0.975738i | \(0.429740\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 101.056i | 1.18889i | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 15.1766i | 0.174443i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 1.07373i | 0.0120644i | 0.999982 | + | 0.00603222i | \(0.00192013\pi\) | ||||
−0.999982 | + | 0.00603222i | \(0.998080\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 11.7126i | 0.125942i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 104.404 | 1.09899 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − 169.517i | − 1.74760i | −0.486286 | − | 0.873799i | \(-0.661649\pi\) | ||||
0.486286 | − | 0.873799i | \(-0.338351\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | − 107.968i | − 1.09059i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 28.1260 | 0.278476 | 0.139238 | − | 0.990259i | \(-0.455535\pi\) | ||||
0.139238 | + | 0.990259i | \(0.455535\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 166.310i | 1.61466i | 0.590098 | + | 0.807331i | \(0.299089\pi\) | ||||
−0.590098 | + | 0.807331i | \(0.700911\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | − 197.584i | − 1.84658i | −0.384109 | − | 0.923288i | \(-0.625491\pi\) | ||||
0.384109 | − | 0.923288i | \(-0.374509\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − 11.5198i | − 0.105686i | −0.998603 | − | 0.0528431i | \(-0.983172\pi\) | ||||
0.998603 | − | 0.0528431i | \(-0.0168283\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 43.3167i | − 0.390240i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −14.7908 | −0.130892 | −0.0654460 | − | 0.997856i | \(-0.520847\pi\) | ||||
−0.0654460 | + | 0.997856i | \(0.520847\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 151.782 | 1.31985 | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 158.703 | 1.35644 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −53.6270 | −0.443198 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | − 5.91605i | − 0.0480980i | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 61.8047 | 0.494438 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 70.2656 | 0.553272 | 0.276636 | − | 0.960975i | \(-0.410780\pi\) | ||||
0.276636 | + | 0.960975i | \(0.410780\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − 30.3252i | − 0.235079i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −142.129 | −1.08496 | −0.542478 | − | 0.840070i | \(-0.682514\pi\) | ||||
−0.542478 | + | 0.840070i | \(0.682514\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −99.2350 | −0.735074 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 253.074 | 1.84725 | 0.923626 | − | 0.383295i | \(-0.125211\pi\) | ||||
0.923626 | + | 0.383295i | \(0.125211\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 49.1909 | 0.353892 | 0.176946 | − | 0.984221i | \(-0.443378\pi\) | ||||
0.176946 | + | 0.984221i | \(0.443378\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − 19.9535i | − 0.141514i | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 256.686i | − 1.79501i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 105.719i | 0.729099i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − 41.6936i | − 0.279823i | −0.990164 | − | 0.139911i | \(-0.955318\pi\) | ||||
0.990164 | − | 0.139911i | \(-0.0446818\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 97.6290 | 0.646549 | 0.323275 | − | 0.946305i | \(-0.395216\pi\) | ||||
0.323275 | + | 0.946305i | \(0.395216\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 130.127i | 0.850503i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 81.5892i | 0.526382i | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 28.1654 | 0.179397 | 0.0896986 | − | 0.995969i | \(-0.471410\pi\) | ||||
0.0896986 | + | 0.995969i | \(0.471410\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | − 33.8701i | − 0.213019i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 242.432i | 1.48731i | 0.668563 | + | 0.743655i | \(0.266910\pi\) | ||||
−0.668563 | + | 0.743655i | \(0.733090\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 76.3734i | 0.462869i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 60.1108i | 0.359945i | 0.983672 | + | 0.179972i | \(0.0576008\pi\) | ||||
−0.983672 | + | 0.179972i | \(0.942399\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 208.305 | 1.23257 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 134.439 | 0.786191 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −139.364 | −0.805573 | −0.402786 | − | 0.915294i | \(-0.631958\pi\) | ||||
−0.402786 | + | 0.915294i | \(0.631958\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 49.8110 | 0.281418 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 291.727i | 1.62976i | 0.579631 | + | 0.814879i | \(0.303197\pi\) | ||||
−0.579631 | + | 0.814879i | \(0.696803\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 166.844 | 0.921791 | 0.460895 | − | 0.887455i | \(-0.347528\pi\) | ||||
0.460895 | + | 0.887455i | \(0.347528\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −9.33343 | −0.0510024 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − 301.742i | − 1.63104i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 210.467 | 1.12549 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 131.356 | 0.687728 | 0.343864 | − | 0.939019i | \(-0.388264\pi\) | ||||
0.343864 | + | 0.939019i | \(0.388264\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −81.4392 | −0.421965 | −0.210982 | − | 0.977490i | \(-0.567666\pi\) | ||||
−0.210982 | + | 0.977490i | \(0.567666\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −112.262 | −0.575702 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − 2.09549i | − 0.0106370i | −0.999986 | − | 0.00531851i | \(-0.998307\pi\) | ||||
0.999986 | − | 0.00531851i | \(-0.00169294\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 126.944i | − 0.637911i | −0.947770 | − | 0.318955i | \(-0.896668\pi\) | ||||
0.947770 | − | 0.318955i | \(-0.103332\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 15.6068i | 0.0776459i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | − 41.2109i | − 0.201029i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 195.446 | 0.944184 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − 217.440i | − 1.04038i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − 7.16822i | − 0.0339726i | −0.999856 | − | 0.0169863i | \(-0.994593\pi\) | ||||
0.999856 | − | 0.0169863i | \(-0.00540717\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 29.1994 | 0.137086 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | − 211.244i | − 0.982530i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 97.6132i | 0.445722i | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 309.367i | 1.39985i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 279.720i | − 1.25435i | −0.778878 | − | 0.627175i | \(-0.784211\pi\) | ||||
0.778878 | − | 0.627175i | \(-0.215789\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −124.674 | −0.554106 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −304.784 | −1.34266 | −0.671330 | − | 0.741159i | \(-0.734276\pi\) | ||||
−0.671330 | + | 0.741159i | \(0.734276\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −414.688 | −1.81087 | −0.905433 | − | 0.424490i | \(-0.860453\pi\) | ||||
−0.905433 | + | 0.424490i | \(0.860453\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −164.926 | −0.707836 | −0.353918 | − | 0.935277i | \(-0.615151\pi\) | ||||
−0.353918 | + | 0.935277i | \(0.615151\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | − 138.995i | − 0.591469i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −53.1109 | −0.224097 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 19.1182 | 0.0799926 | 0.0399963 | − | 0.999200i | \(-0.487265\pi\) | ||||
0.0399963 | + | 0.999200i | \(0.487265\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 350.308i | 1.45356i | 0.686870 | + | 0.726780i | \(0.258984\pi\) | ||||
−0.686870 | + | 0.726780i | \(0.741016\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −194.761 | −0.801485 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 319.618 | 1.29400 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −33.1045 | −0.132950 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 88.3204 | 0.351874 | 0.175937 | − | 0.984401i | \(-0.443704\pi\) | ||||
0.175937 | + | 0.984401i | \(0.443704\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − 316.114i | − 1.24946i | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 92.0479i | − 0.360972i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 86.0828i | 0.334952i | 0.985876 | + | 0.167476i | \(0.0535617\pi\) | ||||
−0.985876 | + | 0.167476i | \(0.946438\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 136.132i | 0.521579i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −319.210 | −1.21373 | −0.606863 | − | 0.794806i | \(-0.707572\pi\) | ||||
−0.606863 | + | 0.794806i | \(0.707572\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 235.937i | − 0.890330i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | − 0.978025i | − 0.00366302i | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −57.4680 | −0.213636 | −0.106818 | − | 0.994279i | \(-0.534066\pi\) | ||||
−0.106818 | + | 0.994279i | \(0.534066\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − 30.8765i | − 0.113935i | −0.998376 | − | 0.0569677i | \(-0.981857\pi\) | ||||
0.998376 | − | 0.0569677i | \(-0.0181432\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 201.647i | 0.733261i | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | − 356.185i | − 1.28587i | −0.765923 | − | 0.642933i | \(-0.777718\pi\) | ||||
0.765923 | − | 0.642933i | \(-0.222282\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 105.060i | 0.376561i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −294.160 | −1.04683 | −0.523416 | − | 0.852077i | \(-0.675343\pi\) | ||||
−0.523416 | + | 0.852077i | \(0.675343\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 415.002 | 1.46644 | 0.733219 | − | 0.679993i | \(-0.238017\pi\) | ||||
0.733219 | + | 0.679993i | \(0.238017\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −95.0979 | −0.333677 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 35.3381 | 0.122277 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 154.407i | 0.530608i | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −370.564 | −1.26472 | −0.632362 | − | 0.774673i | \(-0.717915\pi\) | ||||
−0.632362 | + | 0.774673i | \(0.717915\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 346.981 | 1.17621 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 206.675i | 0.695874i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 464.658 | 1.55404 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −25.6190 | −0.0845510 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −65.0162 | −0.213168 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 160.327 | 0.522239 | 0.261120 | − | 0.965306i | \(-0.415908\pi\) | ||||
0.261120 | + | 0.965306i | \(0.415908\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | − 151.486i | − 0.490245i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 472.839i | 1.52038i | 0.649700 | + | 0.760191i | \(0.274895\pi\) | ||||
−0.649700 | + | 0.760191i | \(0.725105\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 231.013i | 0.738060i | 0.929417 | + | 0.369030i | \(0.120310\pi\) | ||||
−0.929417 | + | 0.369030i | \(0.879690\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − 225.319i | − 0.710784i | −0.934717 | − | 0.355392i | \(-0.884347\pi\) | ||||
0.934717 | − | 0.355392i | \(-0.115653\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 220.179 | 0.690218 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 179.972i | 0.560659i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 262.067i | 0.811353i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −296.403 | −0.912008 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.4930i | 0.0320885i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − 20.6988i | − 0.0625341i | −0.999511 | − | 0.0312671i | \(-0.990046\pi\) | ||||
0.999511 | − | 0.0312671i | \(-0.00995424\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − 388.545i | − 1.16680i | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 108.716i | 0.324527i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 34.9645 | 0.103752 | 0.0518762 | − | 0.998654i | \(-0.483480\pi\) | ||||
0.0518762 | + | 0.998654i | \(0.483480\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 13.4724 | 0.0397415 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 169.924 | 0.498311 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −138.253 | −0.400733 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − 438.738i | − 1.26438i | −0.774815 | − | 0.632188i | \(-0.782157\pi\) | ||||
0.774815 | − | 0.632188i | \(-0.217843\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 435.121 | 1.24677 | 0.623383 | − | 0.781917i | \(-0.285758\pi\) | ||||
0.623383 | + | 0.781917i | \(0.285758\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −303.793 | −0.865507 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 281.109i | − 0.796343i | −0.917311 | − | 0.398171i | \(-0.869645\pi\) | ||||
0.917311 | − | 0.398171i | \(-0.130355\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 203.401 | 0.572962 | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −263.930 | −0.735180 | −0.367590 | − | 0.929988i | \(-0.619817\pi\) | ||||
−0.367590 | + | 0.929988i | \(0.619817\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −90.2495 | −0.249999 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 48.8468 | 0.134564 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 679.969i | 1.86293i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 154.939i | − 0.422176i | −0.977467 | − | 0.211088i | \(-0.932299\pi\) | ||||
0.977467 | − | 0.211088i | \(-0.0677007\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | − 53.0662i | − 0.143811i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − 584.862i | − 1.56799i | −0.620765 | − | 0.783997i | \(-0.713178\pi\) | ||||
0.620765 | − | 0.783997i | \(-0.286822\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −56.2956 | −0.150122 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 323.644i | 0.858472i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 128.176i | 0.338195i | 0.985599 | + | 0.169098i | \(0.0540853\pi\) | ||||
−0.985599 | + | 0.169098i | \(0.945915\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −64.0023 | −0.167985 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 249.920i | 0.652532i | 0.945278 | + | 0.326266i | \(0.105791\pi\) | ||||
−0.945278 | + | 0.326266i | \(0.894209\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | − 272.013i | − 0.702877i | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 216.423i | 0.556358i | 0.960529 | + | 0.278179i | \(0.0897309\pi\) | ||||
−0.960529 | + | 0.278179i | \(0.910269\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 380.991i | 0.974402i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 129.460 | 0.329415 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −369.968 | −0.936627 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 699.882 | 1.76293 | 0.881463 | − | 0.472252i | \(-0.156559\pi\) | ||||
0.881463 | + | 0.472252i | \(0.156559\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −180.981 | −0.451323 | −0.225662 | − | 0.974206i | \(-0.572454\pi\) | ||||
−0.225662 | + | 0.974206i | \(0.572454\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 249.773i | 0.619785i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −376.179 | −0.928837 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −628.431 | −1.54406 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 358.843i | 0.877366i | 0.898642 | + | 0.438683i | \(0.144555\pi\) | ||||
−0.898642 | + | 0.438683i | \(0.855445\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −230.515 | −0.560864 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −230.604 | −0.555672 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −44.8062 | −0.107449 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −780.890 | −1.86370 | −0.931849 | − | 0.362846i | \(-0.881805\pi\) | ||||
−0.931849 | + | 0.362846i | \(0.881805\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 114.961i | 0.273068i | 0.990635 | + | 0.136534i | \(0.0435962\pi\) | ||||
−0.990635 | + | 0.136534i | \(0.956404\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | − 178.981i | − 0.423122i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 243.032i | − 0.571840i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 233.806i | 0.545001i | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −309.712 | −0.718590 | −0.359295 | − | 0.933224i | \(-0.616983\pi\) | ||||
−0.359295 | + | 0.933224i | \(0.616983\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 595.775i | 1.37592i | 0.725747 | + | 0.687962i | \(0.241494\pi\) | ||||
−0.725747 | + | 0.687962i | \(0.758506\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | − 96.2958i | − 0.221370i | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 393.615 | 0.900722 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − 806.900i | − 1.83804i | −0.394211 | − | 0.919020i | \(-0.628982\pi\) | ||||
0.394211 | − | 0.919020i | \(-0.371018\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | − 444.807i | − 1.00408i | −0.864845 | − | 0.502039i | \(-0.832583\pi\) | ||||
0.864845 | − | 0.502039i | \(-0.167417\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | − 6.81287i | − 0.0153098i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 37.9772i | 0.0849601i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 262.420 | 0.584455 | 0.292228 | − | 0.956349i | \(-0.405604\pi\) | ||||
0.292228 | + | 0.956349i | \(0.405604\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −85.8291 | −0.190308 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −88.9266 | −0.196306 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 389.475 | 0.852244 | 0.426122 | − | 0.904666i | \(-0.359879\pi\) | ||||
0.426122 | + | 0.904666i | \(0.359879\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | − 249.092i | − 0.542683i | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 158.714 | 0.344283 | 0.172141 | − | 0.985072i | \(-0.444931\pi\) | ||||
0.172141 | + | 0.985072i | \(0.444931\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 528.844 | 1.14221 | 0.571106 | − | 0.820877i | \(-0.306515\pi\) | ||||
0.571106 | + | 0.820877i | \(0.306515\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − 74.3166i | − 0.159821i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −436.898 | −0.935542 | −0.467771 | − | 0.883850i | \(-0.654943\pi\) | ||||
−0.467771 | + | 0.883850i | \(0.654943\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −25.6548 | −0.0544688 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −439.953 | −0.930134 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −251.085 | −0.528600 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − 303.811i | − 0.636920i | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 545.870i | 1.13960i | 0.821782 | + | 0.569802i | \(0.192980\pi\) | ||||
−0.821782 | + | 0.569802i | \(0.807020\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | − 923.737i | − 1.92045i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 1075.59i | 2.21771i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −648.230 | −1.33107 | −0.665534 | − | 0.746368i | \(-0.731796\pi\) | ||||
−0.665534 | + | 0.746368i | \(0.731796\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − 220.822i | − 0.451579i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − 732.074i | − 1.49098i | −0.666514 | − | 0.745492i | \(-0.732214\pi\) | ||||
0.666514 | − | 0.745492i | \(-0.267786\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −265.368 | −0.538272 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 685.060i | 1.38396i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − 26.7040i | − 0.0535151i | −0.999642 | − | 0.0267575i | \(-0.991482\pi\) | ||||
0.999642 | − | 0.0267575i | \(-0.00851820\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | − 54.7527i | − 0.109287i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 616.414i | 1.22548i | 0.790286 | + | 0.612738i | \(0.209932\pi\) | ||||
−0.790286 | + | 0.612738i | \(0.790068\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −178.460 | −0.353387 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −189.737 | −0.374235 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 132.753 | 0.260811 | 0.130405 | − | 0.991461i | \(-0.458372\pi\) | ||||
0.130405 | + | 0.991461i | \(0.458372\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −257.345 | −0.501648 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | − 1055.24i | − 2.04902i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −289.483 | −0.559928 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 126.942 | 0.244589 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 676.054i | 1.29761i | 0.760955 | + | 0.648804i | \(0.224731\pi\) | ||||
−0.760955 | + | 0.648804i | \(0.775269\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −372.449 | −0.712139 | −0.356069 | − | 0.934460i | \(-0.615883\pi\) | ||||
−0.356069 | + | 0.934460i | \(0.615883\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −204.799 | −0.388612 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 43.2358 | 0.0817313 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 446.799 | 0.841429 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − 126.161i | − 0.236700i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1253.67i | 2.34331i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | − 265.723i | − 0.494829i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − 69.6715i | − 0.128783i | −0.997925 | − | 0.0643914i | \(-0.979489\pi\) | ||||
0.997925 | − | 0.0643914i | \(-0.0205106\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −151.972 | −0.279875 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 73.0934i | 0.134116i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | − 466.463i | − 0.852765i | −0.904543 | − | 0.426383i | \(-0.859788\pi\) | ||||
0.904543 | − | 0.426383i | \(-0.140212\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −83.7197 | −0.152495 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 274.161i | 0.497570i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 274.845i | 0.495217i | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 137.219i | 0.246353i | 0.992385 | + | 0.123177i | \(0.0393082\pi\) | ||||
−0.992385 | + | 0.123177i | \(0.960692\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − 646.692i | − 1.15687i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −191.706 | −0.341722 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −169.126 | −0.300402 | −0.150201 | − | 0.988655i | \(-0.547992\pi\) | ||||
−0.150201 | + | 0.988655i | \(0.547992\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 93.8479 | 0.166103 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 744.931 | 1.30919 | 0.654597 | − | 0.755978i | \(-0.272838\pi\) | ||||
0.654597 | + | 0.755978i | \(0.272838\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 886.611i | 1.55273i | 0.630281 | + | 0.776367i | \(0.282940\pi\) | ||||
−0.630281 | + | 0.776367i | \(0.717060\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −119.647 | −0.208809 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −365.026 | −0.634827 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 240.062i | 0.416052i | 0.978123 | + | 0.208026i | \(0.0667038\pi\) | ||||
−0.978123 | + | 0.208026i | \(0.933296\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 74.1799 | 0.128117 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −491.382 | −0.842850 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −1006.98 | −1.72133 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −190.873 | −0.325168 | −0.162584 | − | 0.986695i | \(-0.551983\pi\) | ||||
−0.162584 | + | 0.986695i | \(0.551983\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 211.585i | 0.359227i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1.90871i | 0.00322962i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 736.177i | 1.24145i | 0.784030 | + | 0.620723i | \(0.213161\pi\) | ||||
−0.784030 | + | 0.620723i | \(0.786839\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 115.629i | 0.193683i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −1116.66 | −1.86421 | −0.932104 | − | 0.362190i | \(-0.882029\pi\) | ||||
−0.932104 | + | 0.362190i | \(0.882029\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 183.100i | − 0.304659i | −0.988330 | − | 0.152329i | \(-0.951323\pi\) | ||||
0.988330 | − | 0.152329i | \(-0.0486774\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 139.991i | 0.232158i | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 340.264 | 0.562421 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − 454.982i | − 0.749558i | −0.927114 | − | 0.374779i | \(-0.877719\pi\) | ||||
0.927114 | − | 0.374779i | \(-0.122281\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | − 425.513i | − 0.696421i | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − 268.876i | − 0.438623i | −0.975655 | − | 0.219312i | \(-0.929619\pi\) | ||||
0.975655 | − | 0.219312i | \(-0.0703811\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 37.5375i | 0.0610366i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −184.934 | −0.299731 | −0.149866 | − | 0.988706i | \(-0.547884\pi\) | ||||
−0.149866 | + | 0.988706i | \(0.547884\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −993.618 | −1.60520 | −0.802599 | − | 0.596519i | \(-0.796550\pi\) | ||||
−0.802599 | + | 0.596519i | \(0.796550\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −374.127 | −0.602459 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −773.636 | −1.23782 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 198.058i | 0.315883i | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 757.408 | 1.20415 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −805.857 | −1.27711 | −0.638555 | − | 0.769576i | \(-0.720468\pi\) | ||||
−0.638555 | + | 0.769576i | \(0.720468\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 6.52926i | 0.0103148i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −445.837 | −0.702105 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 261.915 | 0.409883 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 5.50441 | 0.00858723 | 0.00429361 | − | 0.999991i | \(-0.498633\pi\) | ||||
0.00429361 | + | 0.999991i | \(0.498633\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 1024.08 | 1.59266 | 0.796331 | − | 0.604861i | \(-0.206771\pi\) | ||||
0.796331 | + | 0.604861i | \(0.206771\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 192.414i | 0.298317i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 456.573i | 0.705677i | 0.935684 | + | 0.352839i | \(0.114784\pi\) | ||||
−0.935684 | + | 0.352839i | \(0.885216\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 722.650i | − 1.11348i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − 28.2443i | − 0.0432532i | −0.999766 | − | 0.0216266i | \(-0.993116\pi\) | ||||
0.999766 | − | 0.0216266i | \(-0.00688450\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 901.814 | 1.37681 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 875.579i | 1.33269i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 132.188i | 0.200589i | 0.994958 | + | 0.100295i | \(0.0319785\pi\) | ||||
−0.994958 | + | 0.100295i | \(0.968021\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −693.847 | −1.04969 | −0.524847 | − | 0.851197i | \(-0.675877\pi\) | ||||
−0.524847 | + | 0.851197i | \(0.675877\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 281.791i | − 0.425024i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 398.574i | 0.597562i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 254.787i | 0.380847i | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 135.408i | 0.201800i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 532.137 | 0.790694 | 0.395347 | − | 0.918532i | \(-0.370624\pi\) | ||||
0.395347 | + | 0.918532i | \(0.370624\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 238.653 | 0.353560 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 286.230 | 0.422792 | 0.211396 | − | 0.977401i | \(-0.432199\pi\) | ||||
0.211396 | + | 0.977401i | \(0.432199\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 277.616 | 0.407659 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 447.836i | 0.655690i | 0.944731 | + | 0.327845i | \(0.106322\pi\) | ||||
−0.944731 | + | 0.327845i | \(0.893678\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −1605.76 | −2.34417 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 377.724 | 0.549817 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 722.287i | − 1.04831i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 1020.73 | 1.47718 | 0.738591 | − | 0.674154i | \(-0.235492\pi\) | ||||
0.738591 | + | 0.674154i | \(0.235492\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −312.118 | −0.449090 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 103.444 | 0.148414 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 150.225 | 0.214914 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − 1311.02i | − 1.87021i | −0.354369 | − | 0.935106i | \(-0.615304\pi\) | ||||
0.354369 | − | 0.935106i | \(-0.384696\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 782.504i | − 1.11309i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 126.606i | 0.179582i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − 537.508i | − 0.758121i | −0.925372 | − | 0.379061i | \(-0.876247\pi\) | ||||
0.925372 | − | 0.379061i | \(-0.123753\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −476.398 | −0.670040 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 307.601i | 0.431417i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1628.68i | 2.27787i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −17.4141 | −0.0242874 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 269.363i | 0.374635i | 0.982299 | + | 0.187318i | \(0.0599793\pi\) | ||||
−0.982299 | + | 0.187318i | \(0.940021\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | − 319.083i | − 0.441331i | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − 254.248i | − 0.350686i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 460.316i | 0.633172i | 0.948564 | + | 0.316586i | \(0.102537\pi\) | ||||
−0.948564 | + | 0.316586i | \(0.897463\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −356.185 | −0.488594 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 530.247 | 0.725372 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 66.6821 | 0.0909715 | 0.0454857 | − | 0.998965i | \(-0.485516\pi\) | ||||
0.0454857 | + | 0.998965i | \(0.485516\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 226.421 | 0.307220 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − 933.889i | − 1.26372i | −0.775083 | − | 0.631860i | \(-0.782292\pi\) | ||||
0.775083 | − | 0.631860i | \(-0.217708\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −291.128 | −0.392885 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 1198.23 | 1.61269 | 0.806345 | − | 0.591446i | \(-0.201443\pi\) | ||||
0.806345 | + | 0.591446i | \(0.201443\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 264.547i | 0.355097i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −296.943 | −0.397514 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 168.599 | 0.224499 | 0.112249 | − | 0.993680i | \(-0.464194\pi\) | ||||
0.112249 | + | 0.993680i | \(0.464194\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −80.4478 | −0.106836 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −619.458 | −0.820474 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 209.207i | 0.276364i | 0.990407 | + | 0.138182i | \(0.0441259\pi\) | ||||
−0.990407 | + | 0.138182i | \(0.955874\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 287.936i | 0.379362i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 553.248i | 0.727002i | 0.931594 | + | 0.363501i | \(0.118419\pi\) | ||||
−0.931594 | + | 0.363501i | \(0.881581\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | − 825.659i | − 1.07929i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 1062.23 | 1.38492 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 219.524i | 0.285467i | 0.989761 | + | 0.142734i | \(0.0455892\pi\) | ||||
−0.989761 | + | 0.142734i | \(0.954411\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | − 78.4096i | − 0.101699i | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 666.674 | 0.862451 | 0.431225 | − | 0.902244i | \(-0.358081\pi\) | ||||
0.431225 | + | 0.902244i | \(0.358081\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 196.216i | − 0.253182i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | − 106.872i | − 0.137191i | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − 423.620i | − 0.542407i | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − 260.587i | − 0.332806i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −178.710 | −0.227656 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 919.865 | 1.16882 | 0.584412 | − | 0.811457i | \(-0.301325\pi\) | ||||
0.584412 | + | 0.811457i | \(0.301325\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 290.757 | 0.368513 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −199.037 | −0.250993 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 214.907i | 0.270323i | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 1016.13 | 1.27494 | 0.637470 | − | 0.770476i | \(-0.279981\pi\) | ||||
0.637470 | + | 0.770476i | \(0.279981\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 348.895 | 0.436664 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − 8.77277i | − 0.0109523i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 1416.16 | 1.76358 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 52.3454 | 0.0648642 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 1131.90 | 1.39913 | 0.699567 | − | 0.714567i | \(-0.253376\pi\) | ||||
0.699567 | + | 0.714567i | \(0.253376\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −481.066 | −0.593176 | −0.296588 | − | 0.955006i | \(-0.595849\pi\) | ||||
−0.296588 | + | 0.955006i | \(0.595849\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 28.1242i | 0.0345931i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 1538.23i | − 1.88740i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 547.817i | − 0.670523i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − 727.675i | − 0.886328i | −0.896441 | − | 0.443164i | \(-0.853856\pi\) | ||||
0.896441 | − | 0.443164i | \(-0.146144\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 626.646 | 0.761417 | 0.380709 | − | 0.924695i | \(-0.375680\pi\) | ||||
0.380709 | + | 0.924695i | \(0.375680\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − 183.673i | − 0.222633i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | − 1468.52i | − 1.77572i | −0.460116 | − | 0.887859i | \(-0.652192\pi\) | ||||
0.460116 | − | 0.887859i | \(-0.347808\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 818.704 | 0.987580 | 0.493790 | − | 0.869581i | \(-0.335611\pi\) | ||||
0.493790 | + | 0.869581i | \(0.335611\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 324.435i | 0.390416i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | − 381.404i | − 0.456772i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − 201.109i | − 0.240273i | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 1108.84i | 1.32162i | 0.750555 | + | 0.660808i | \(0.229786\pi\) | ||||
−0.750555 | + | 0.660808i | \(0.770214\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 563.386 | 0.669900 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 267.939 | 0.317840 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −1321.70 | −1.56414 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −378.010 | −0.445241 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − 1137.60i | − 1.33678i | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 610.400 | 0.715592 | 0.357796 | − | 0.933800i | \(-0.383528\pi\) | ||||
0.357796 | + | 0.933800i | \(0.383528\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −853.017 | −0.997680 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − 444.114i | − 0.518219i | −0.965848 | − | 0.259110i | \(-0.916571\pi\) | ||||
0.965848 | − | 0.259110i | \(-0.0834291\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 81.5094 | 0.0948887 | 0.0474443 | − | 0.998874i | \(-0.484892\pi\) | ||||
0.0474443 | + | 0.998874i | \(0.484892\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1051.46 | 1.21838 | 0.609189 | − | 0.793025i | \(-0.291495\pi\) | ||||
0.609189 | + | 0.793025i | \(0.291495\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 884.268 | 1.02228 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −32.1882 | −0.0371259 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 770.524i | 0.886679i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 332.819i | 0.382111i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1385.01i | 1.58650i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1559.63i | 1.77837i | 0.457551 | + | 0.889183i | \(0.348727\pi\) | ||||
−0.457551 | + | 0.889183i | \(0.651273\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 337.533 | 0.383997 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 1515.22i | − 1.71989i | −0.510389 | − | 0.859944i | \(-0.670499\pi\) | ||||
0.510389 | − | 0.859944i | \(-0.329501\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 763.828i | 0.865037i | 0.901625 | + | 0.432519i | \(0.142375\pi\) | ||||
−0.901625 | + | 0.432519i | \(0.857625\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −316.052 | −0.357121 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | − 573.371i | − 0.646416i | −0.946328 | − | 0.323208i | \(-0.895239\pi\) | ||||
0.946328 | − | 0.323208i | \(-0.104761\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 783.460i | 0.879304i | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − 360.455i | − 0.403645i | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 1851.01i | − 2.06817i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −423.240 | −0.471840 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −214.250 | −0.238320 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 592.231 | 0.657304 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −1058.63 | −1.16976 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 1021.95i | 1.12674i | 0.826205 | + | 0.563369i | \(0.190495\pi\) | ||||
−0.826205 | + | 0.563369i | \(0.809505\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −229.799 | −0.252804 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −630.111 | −0.691669 | −0.345835 | − | 0.938295i | \(-0.612404\pi\) | ||||
−0.345835 | + | 0.938295i | \(0.612404\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 480.274i | 0.526040i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 59.2208 | 0.0647222 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 842.979 | 0.917278 | 0.458639 | − | 0.888623i | \(-0.348337\pi\) | ||||
0.458639 | + | 0.888623i | \(0.348337\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −146.036 | −0.158563 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 622.683 | 0.674630 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 725.668i | 0.784506i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 1358.81i | − 1.46581i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 774.651i | 0.833855i | 0.908940 | + | 0.416927i | \(0.136893\pi\) | ||||
−0.908940 | + | 0.416927i | \(0.863107\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | − 430.691i | − 0.461620i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1335.42 | −1.42825 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 1586.27i | − 1.69293i | −0.532447 | − | 0.846463i | \(-0.678727\pi\) | ||||
0.532447 | − | 0.846463i | \(-0.321273\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | − 210.421i | − 0.224090i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −820.046 | −0.871462 | −0.435731 | − | 0.900077i | \(-0.643510\pi\) | ||||
−0.435731 | + | 0.900077i | \(0.643510\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − 155.370i | − 0.164761i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 637.335i | 0.673005i | 0.941683 | + | 0.336502i | \(0.109244\pi\) | ||||
−0.941683 | + | 0.336502i | \(0.890756\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 2081.62i | 2.19349i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 205.234i | 0.215809i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −350.626 | −0.367918 | −0.183959 | − | 0.982934i | \(-0.558891\pi\) | ||||
−0.183959 | + | 0.982934i | \(0.558891\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | −833.458 | −0.872731 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −200.553 | −0.209564 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 795.652 | 0.827942 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 1614.32i | 1.67635i | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 516.734 | 0.535475 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 649.816 | 0.671992 | 0.335996 | − | 0.941863i | \(-0.390927\pi\) | ||||
0.335996 | + | 0.941863i | \(0.390927\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − 238.707i | − 0.246344i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −970.610 | −0.999598 | −0.499799 | − | 0.866141i | \(-0.666593\pi\) | ||||
−0.499799 | + | 0.866141i | \(0.666593\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 269.982 | 0.276905 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −600.875 | −0.615020 | −0.307510 | − | 0.951545i | \(-0.599496\pi\) | ||||
−0.307510 | + | 0.951545i | \(0.599496\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −14.1890 | −0.0144934 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 94.1205i | 0.0959434i | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 1268.62i | 1.29056i | 0.763945 | + | 0.645281i | \(0.223260\pi\) | ||||
−0.763945 | + | 0.645281i | \(0.776740\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 13.2959i | 0.0134984i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − 796.413i | − 0.805271i | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1549.11 | 1.56318 | 0.781590 | − | 0.623793i | \(-0.214409\pi\) | ||||
0.781590 | + | 0.623793i | \(0.214409\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 18.8538i | 0.0189867i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 805.464i | 0.809512i | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −940.938 | −0.943769 | −0.471885 | − | 0.881660i | \(-0.656426\pi\) | ||||
−0.471885 | + | 0.881660i | \(0.656426\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 743.761i | 0.744506i |
(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 | 1568.3.h.a.881.11 | 28 | ||
4.3 | odd | 2 | 392.3.h.a.293.26 | 28 | |||
7.2 | even | 3 | 224.3.n.a.17.9 | 28 | |||
7.3 | odd | 6 | 224.3.n.a.145.6 | 28 | |||
7.6 | odd | 2 | inner | 1568.3.h.a.881.17 | 28 | ||
8.3 | odd | 2 | 392.3.h.a.293.27 | 28 | |||
8.5 | even | 2 | inner | 1568.3.h.a.881.18 | 28 | ||
28.3 | even | 6 | 56.3.j.a.5.6 | yes | 28 | ||
28.11 | odd | 6 | 392.3.j.e.117.6 | 28 | |||
28.19 | even | 6 | 392.3.j.e.325.4 | 28 | |||
28.23 | odd | 6 | 56.3.j.a.45.4 | yes | 28 | ||
28.27 | even | 2 | 392.3.h.a.293.25 | 28 | |||
56.3 | even | 6 | 56.3.j.a.5.4 | ✓ | 28 | ||
56.11 | odd | 6 | 392.3.j.e.117.4 | 28 | |||
56.13 | odd | 2 | inner | 1568.3.h.a.881.12 | 28 | ||
56.19 | even | 6 | 392.3.j.e.325.6 | 28 | |||
56.27 | even | 2 | 392.3.h.a.293.28 | 28 | |||
56.37 | even | 6 | 224.3.n.a.17.6 | 28 | |||
56.45 | odd | 6 | 224.3.n.a.145.9 | 28 | |||
56.51 | odd | 6 | 56.3.j.a.45.6 | yes | 28 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
56.3.j.a.5.4 | ✓ | 28 | 56.3 | even | 6 | ||
56.3.j.a.5.6 | yes | 28 | 28.3 | even | 6 | ||
56.3.j.a.45.4 | yes | 28 | 28.23 | odd | 6 | ||
56.3.j.a.45.6 | yes | 28 | 56.51 | odd | 6 | ||
224.3.n.a.17.6 | 28 | 56.37 | even | 6 | |||
224.3.n.a.17.9 | 28 | 7.2 | even | 3 | |||
224.3.n.a.145.6 | 28 | 7.3 | odd | 6 | |||
224.3.n.a.145.9 | 28 | 56.45 | odd | 6 | |||
392.3.h.a.293.25 | 28 | 28.27 | even | 2 | |||
392.3.h.a.293.26 | 28 | 4.3 | odd | 2 | |||
392.3.h.a.293.27 | 28 | 8.3 | odd | 2 | |||
392.3.h.a.293.28 | 28 | 56.27 | even | 2 | |||
392.3.j.e.117.4 | 28 | 56.11 | odd | 6 | |||
392.3.j.e.117.6 | 28 | 28.11 | odd | 6 | |||
392.3.j.e.325.4 | 28 | 28.19 | even | 6 | |||
392.3.j.e.325.6 | 28 | 56.19 | even | 6 | |||
1568.3.h.a.881.11 | 28 | 1.1 | even | 1 | trivial | ||
1568.3.h.a.881.12 | 28 | 56.13 | odd | 2 | inner | ||
1568.3.h.a.881.17 | 28 | 7.6 | odd | 2 | inner | ||
1568.3.h.a.881.18 | 28 | 8.5 | even | 2 | inner |