Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1568,3,Mod(97,1568)]
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, 0, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1568.97");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1568 = 2^{5} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 1568.c (of order \(2\), degree \(1\), 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: | \(16\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} + 36x^{14} + 522x^{12} + 3644x^{10} + 12219x^{8} + 15156x^{6} + 15478x^{4} - 10992x^{2} + 11025 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 2^{28} \) |
Twist minimal: | no (minimal twist has level 224) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 97.15 | ||
Root | \(-0.707107 - 3.42121i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1568.97 |
Dual form | 1568.3.c.h.97.2 |
$q$-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 | ||||||||
\(3\) | 4.83832i | 1.61277i | 0.591388 | + | 0.806387i | \(0.298580\pi\) | ||||
−0.591388 | + | 0.806387i | \(0.701420\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − 0.0515539i | − 0.0103108i | −0.999987 | − | 0.00515539i | \(-0.998359\pi\) | ||||
0.999987 | − | 0.00515539i | \(-0.00164102\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −14.4094 | −1.60104 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.78993 | 0.162721 | 0.0813604 | − | 0.996685i | \(-0.474074\pi\) | ||||
0.0813604 | + | 0.996685i | \(0.474074\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | − 5.87602i | − 0.452002i | −0.974127 | − | 0.226001i | \(-0.927435\pi\) | ||||
0.974127 | − | 0.226001i | \(-0.0725652\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0.249434 | 0.0166290 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | − 26.5867i | − 1.56392i | −0.623326 | − | 0.781962i | \(-0.714219\pi\) | ||||
0.623326 | − | 0.781962i | \(-0.285781\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 26.3426i | 1.38645i | 0.720719 | + | 0.693227i | \(0.243812\pi\) | ||||
−0.720719 | + | 0.693227i | \(0.756188\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −25.6772 | −1.11640 | −0.558199 | − | 0.829707i | \(-0.688508\pi\) | ||||
−0.558199 | + | 0.829707i | \(0.688508\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.9973 | 0.999894 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | − 26.1723i | − 0.969345i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −27.1749 | −0.937066 | −0.468533 | − | 0.883446i | \(-0.655217\pi\) | ||||
−0.468533 | + | 0.883446i | \(0.655217\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − 29.7046i | − 0.958213i | −0.877757 | − | 0.479106i | \(-0.840961\pi\) | ||||
0.877757 | − | 0.479106i | \(-0.159039\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 8.66025i | 0.262432i | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −61.7258 | −1.66826 | −0.834132 | − | 0.551565i | \(-0.814031\pi\) | ||||
−0.834132 | + | 0.551565i | \(0.814031\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 28.4301 | 0.728977 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − 65.7376i | − 1.60336i | −0.597755 | − | 0.801679i | \(-0.703941\pi\) | ||||
0.597755 | − | 0.801679i | \(-0.296059\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −9.52546 | −0.221522 | −0.110761 | − | 0.993847i | \(-0.535329\pi\) | ||||
−0.110761 | + | 0.993847i | \(0.535329\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0.742859i | 0.0165080i | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | − 70.7807i | − 1.50597i | −0.658037 | − | 0.752986i | \(-0.728613\pi\) | ||||
0.658037 | − | 0.752986i | \(-0.271387\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 128.635 | 2.52226 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 9.73110 | 0.183606 | 0.0918028 | − | 0.995777i | \(-0.470737\pi\) | ||||
0.0918028 | + | 0.995777i | \(0.470737\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | − 0.0922778i | − 0.00167778i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −127.454 | −2.23604 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | − 62.7620i | − 1.06376i | −0.846819 | − | 0.531881i | \(-0.821485\pi\) | ||||
0.846819 | − | 0.531881i | \(-0.178515\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − 76.4215i | − 1.25281i | −0.779497 | − | 0.626406i | \(-0.784525\pi\) | ||||
0.779497 | − | 0.626406i | \(-0.215475\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −0.302932 | −0.00466049 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 103.047 | 1.53802 | 0.769009 | − | 0.639238i | \(-0.220750\pi\) | ||||
0.769009 | + | 0.639238i | \(0.220750\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | − 124.234i | − 1.80050i | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 90.1681 | 1.26997 | 0.634986 | − | 0.772523i | \(-0.281006\pi\) | ||||
0.634986 | + | 0.772523i | \(0.281006\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 33.2767i | 0.455845i | 0.973679 | + | 0.227922i | \(0.0731933\pi\) | ||||
−0.973679 | + | 0.227922i | \(0.926807\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 120.945i | 1.61260i | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −64.8645 | −0.821070 | −0.410535 | − | 0.911845i | \(-0.634658\pi\) | ||||
−0.410535 | + | 0.911845i | \(0.634658\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −3.05424 | −0.0377067 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | − 29.1364i | − 0.351041i | −0.984476 | − | 0.175520i | \(-0.943839\pi\) | ||||
0.984476 | − | 0.175520i | \(-0.0561608\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −1.37065 | −0.0161253 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | − 131.481i | − 1.51128i | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 21.6725i | 0.243511i | 0.992560 | + | 0.121755i | \(0.0388523\pi\) | ||||
−0.992560 | + | 0.121755i | \(0.961148\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 143.720 | 1.54538 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1.35807 | 0.0142954 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 123.061i | 1.26867i | 0.773056 | + | 0.634337i | \(0.218727\pi\) | ||||
−0.773056 | + | 0.634337i | \(0.781273\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −25.7918 | −0.260523 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 56.5276i | 0.559679i | 0.960047 | + | 0.279840i | \(0.0902813\pi\) | ||||
−0.960047 | + | 0.279840i | \(0.909719\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 29.5675i | 0.287063i | 0.989646 | + | 0.143532i | \(0.0458459\pi\) | ||||
−0.989646 | + | 0.143532i | \(0.954154\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −29.8108 | −0.278605 | −0.139303 | − | 0.990250i | \(-0.544486\pi\) | ||||
−0.139303 | + | 0.990250i | \(0.544486\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 81.5503 | 0.748167 | 0.374084 | − | 0.927395i | \(-0.377957\pi\) | ||||
0.374084 | + | 0.927395i | \(0.377957\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − 298.649i | − 2.69053i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 43.3994 | 0.384065 | 0.192033 | − | 0.981389i | \(-0.438492\pi\) | ||||
0.192033 | + | 0.981389i | \(0.438492\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.32376i | 0.0115109i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 84.6698i | 0.723674i | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −117.796 | −0.973522 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 318.060 | 2.58585 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − 2.57756i | − 0.0206205i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −94.0304 | −0.740397 | −0.370199 | − | 0.928953i | \(-0.620710\pi\) | ||||
−0.370199 | + | 0.928953i | \(0.620710\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − 46.0873i | − 0.357266i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 125.784i | 0.960180i | 0.877219 | + | 0.480090i | \(0.159396\pi\) | ||||
−0.877219 | + | 0.480090i | \(0.840604\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.34928 | −0.00999470 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −249.856 | −1.82377 | −0.911884 | − | 0.410448i | \(-0.865372\pi\) | ||||
−0.911884 | + | 0.410448i | \(0.865372\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − 2.08301i | − 0.0149857i | −0.999972 | − | 0.00749284i | \(-0.997615\pi\) | ||||
0.999972 | − | 0.00749284i | \(-0.00238507\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 342.460 | 2.42879 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − 10.5177i | − 0.0735501i | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.40097i | 0.00966187i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −21.6244 | −0.145130 | −0.0725652 | − | 0.997364i | \(-0.523119\pi\) | ||||
−0.0725652 | + | 0.997364i | \(0.523119\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −88.0180 | −0.582900 | −0.291450 | − | 0.956586i | \(-0.594138\pi\) | ||||
−0.291450 | + | 0.956586i | \(0.594138\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 383.098i | 2.50391i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.53139 | −0.00987992 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | − 164.623i | − 1.04855i | −0.851548 | − | 0.524277i | \(-0.824336\pi\) | ||||
0.851548 | − | 0.524277i | \(-0.175664\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 47.0822i | 0.296114i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 164.884 | 1.01156 | 0.505779 | − | 0.862663i | \(-0.331205\pi\) | ||||
0.505779 | + | 0.862663i | \(0.331205\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0.446470 | 0.00270588 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 18.8929i | 0.113131i | 0.998399 | + | 0.0565655i | \(0.0180150\pi\) | ||||
−0.998399 | + | 0.0565655i | \(0.981985\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 134.472 | 0.795695 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | − 379.581i | − 2.21977i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | − 98.4856i | − 0.569281i | −0.958634 | − | 0.284641i | \(-0.908126\pi\) | ||||
0.958634 | − | 0.284641i | \(-0.0918742\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 303.663 | 1.71561 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | 70.2963 | 0.392717 | 0.196358 | − | 0.980532i | \(-0.437088\pi\) | ||||
0.196358 | + | 0.980532i | \(0.437088\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 204.167i | 1.12800i | 0.825776 | + | 0.563999i | \(0.190738\pi\) | ||||
−0.825776 | + | 0.563999i | \(0.809262\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 369.752 | 2.02050 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 3.18220i | 0.0172011i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − 47.5883i | − 0.254483i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 190.703 | 0.998447 | 0.499224 | − | 0.866473i | \(-0.333619\pi\) | ||||
0.499224 | + | 0.866473i | \(0.333619\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 85.5481 | 0.443254 | 0.221627 | − | 0.975131i | \(-0.428863\pi\) | ||||
0.221627 | + | 0.975131i | \(0.428863\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | − 1.46568i | − 0.00751631i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 275.164 | 1.39677 | 0.698386 | − | 0.715721i | \(-0.253902\pi\) | ||||
0.698386 | + | 0.715721i | \(0.253902\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | − 206.878i | − 1.03959i | −0.854292 | − | 0.519793i | \(-0.826009\pi\) | ||||
0.854292 | − | 0.519793i | \(-0.173991\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 498.576i | 2.48048i | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.38903 | −0.0165319 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 369.992 | 1.78740 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 47.1514i | 0.225605i | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 78.7325 | 0.373140 | 0.186570 | − | 0.982442i | \(-0.440263\pi\) | ||||
0.186570 | + | 0.982442i | \(0.440263\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 436.262i | 2.04818i | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.491074i | 0.00228407i | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −161.003 | −0.735175 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −156.224 | −0.706896 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | − 155.408i | − 0.696896i | −0.937328 | − | 0.348448i | \(-0.886709\pi\) | ||||
0.937328 | − | 0.348448i | \(-0.113291\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −360.196 | −1.60087 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 81.8668i | 0.360647i | 0.983607 | + | 0.180323i | \(0.0577144\pi\) | ||||
−0.983607 | + | 0.180323i | \(0.942286\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | − 410.692i | − 1.79341i | −0.442625 | − | 0.896707i | \(-0.645953\pi\) | ||||
0.442625 | − | 0.896707i | \(-0.354047\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 37.8718 | 0.162540 | 0.0812699 | − | 0.996692i | \(-0.474102\pi\) | ||||
0.0812699 | + | 0.996692i | \(0.474102\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −3.64902 | −0.0155277 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | − 313.836i | − 1.32420i | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −428.133 | −1.79135 | −0.895676 | − | 0.444707i | \(-0.853308\pi\) | ||||
−0.895676 | + | 0.444707i | \(0.853308\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − 208.025i | − 0.863174i | −0.902071 | − | 0.431587i | \(-0.857954\pi\) | ||||
0.902071 | − | 0.431587i | \(-0.142046\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − 250.328i | − 1.03016i | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 154.790 | 0.626680 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 140.971 | 0.566149 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − 375.625i | − 1.49652i | −0.663408 | − | 0.748258i | \(-0.730891\pi\) | ||||
0.663408 | − | 0.748258i | \(-0.269109\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −45.9603 | −0.181661 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | − 6.63164i | − 0.0260064i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − 72.0964i | − 0.280531i | −0.990114 | − | 0.140265i | \(-0.955204\pi\) | ||||
0.990114 | − | 0.140265i | \(-0.0447956\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 391.574 | 1.50028 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 209.100 | 0.795058 | 0.397529 | − | 0.917590i | \(-0.369868\pi\) | ||||
0.397529 | + | 0.917590i | \(0.369868\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − 0.501676i | − 0.00189312i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −104.858 | −0.392728 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 282.850i | 1.05149i | 0.850643 | + | 0.525744i | \(0.176213\pi\) | ||||
−0.850643 | + | 0.525744i | \(0.823787\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 197.927i | 0.730359i | 0.930937 | + | 0.365179i | \(0.118992\pi\) | ||||
−0.930937 | + | 0.365179i | \(0.881008\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 44.7435 | 0.162703 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −237.318 | −0.856745 | −0.428372 | − | 0.903602i | \(-0.640913\pi\) | ||||
−0.428372 | + | 0.903602i | \(0.640913\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 428.025i | 1.53414i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −239.870 | −0.853628 | −0.426814 | − | 0.904339i | \(-0.640364\pi\) | ||||
−0.426814 | + | 0.904339i | \(0.640364\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 138.174i | 0.488249i | 0.969744 | + | 0.244124i | \(0.0785005\pi\) | ||||
−0.969744 | + | 0.244124i | \(0.921499\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 6.57076i | 0.0230553i | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −417.853 | −1.44586 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −595.411 | −2.04609 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − 385.332i | − 1.31513i | −0.753400 | − | 0.657563i | \(-0.771587\pi\) | ||||
0.753400 | − | 0.657563i | \(-0.228413\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.23562 | −0.0109682 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − 46.8466i | − 0.157733i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 150.880i | 0.504614i | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −273.499 | −0.902636 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3.93983 | −0.0129175 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 222.533i | 0.724864i | 0.932010 | + | 0.362432i | \(0.118054\pi\) | ||||
−0.932010 | + | 0.362432i | \(0.881946\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −143.057 | −0.462968 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 198.425i | 0.638022i | 0.947751 | + | 0.319011i | \(0.103351\pi\) | ||||
−0.947751 | + | 0.319011i | \(0.896649\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − 379.457i | − 1.21232i | −0.795342 | − | 0.606161i | \(-0.792709\pi\) | ||||
0.795342 | − | 0.606161i | \(-0.207291\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −259.626 | −0.819010 | −0.409505 | − | 0.912308i | \(-0.634299\pi\) | ||||
−0.409505 | + | 0.912308i | \(0.634299\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −48.6411 | −0.152480 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | − 144.234i | − 0.449327i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 700.364 | 2.16831 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − 146.885i | − 0.451954i | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 394.567i | 1.20663i | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −547.177 | −1.65310 | −0.826552 | − | 0.562861i | \(-0.809701\pi\) | ||||
−0.826552 | + | 0.562861i | \(0.809701\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 889.430 | 2.67096 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − 5.31248i | − 0.0158582i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −408.705 | −1.21277 | −0.606387 | − | 0.795170i | \(-0.707382\pi\) | ||||
−0.606387 | + | 0.795170i | \(0.707382\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 209.980i | 0.619411i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − 53.1691i | − 0.155921i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −6.40477 | −0.0185645 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −267.149 | −0.769883 | −0.384941 | − | 0.922941i | \(-0.625778\pi\) | ||||
−0.384941 | + | 0.922941i | \(0.625778\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | − 466.080i | − 1.33547i | −0.744398 | − | 0.667736i | \(-0.767263\pi\) | ||||
0.744398 | − | 0.667736i | \(-0.232737\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −153.789 | −0.438146 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − 265.818i | − 0.753026i | −0.926411 | − | 0.376513i | \(-0.877123\pi\) | ||||
0.926411 | − | 0.376513i | \(-0.122877\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | − 4.64851i | − 0.0130944i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 289.805 | 0.807257 | 0.403628 | − | 0.914923i | \(-0.367749\pi\) | ||||
0.403628 | + | 0.914923i | \(0.367749\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −332.935 | −0.922257 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − 569.936i | − 1.57007i | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 1.71554 | 0.00470011 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − 7.01434i | − 0.0191126i | −0.999954 | − | 0.00955632i | \(-0.996958\pi\) | ||||
0.999954 | − | 0.00955632i | \(-0.00304192\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 947.239i | 2.56704i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −573.997 | −1.53887 | −0.769433 | − | 0.638728i | \(-0.779461\pi\) | ||||
−0.769433 | + | 0.638728i | \(0.779461\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 12.4711 | 0.0332561 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 159.680i | 0.423555i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −678.807 | −1.79105 | −0.895524 | − | 0.445014i | \(-0.853199\pi\) | ||||
−0.895524 | + | 0.445014i | \(0.853199\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | − 454.950i | − 1.19409i | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | − 413.896i | − 1.08067i | −0.841450 | − | 0.540334i | \(-0.818298\pi\) | ||||
0.841450 | − | 0.540334i | \(-0.181702\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 137.256 | 0.354667 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 138.488 | 0.356009 | 0.178005 | − | 0.984030i | \(-0.443036\pi\) | ||||
0.178005 | + | 0.984030i | \(0.443036\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 682.672i | 1.74596i | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −608.582 | −1.54855 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.34402i | 0.00846587i | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 4.18005i | 0.0105291i | 0.999986 | + | 0.00526455i | \(0.00167576\pi\) | ||||
−0.999986 | + | 0.00526455i | \(0.998324\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −602.054 | −1.50138 | −0.750690 | − | 0.660654i | \(-0.770279\pi\) | ||||
−0.750690 | + | 0.660654i | \(0.770279\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −174.545 | −0.433114 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0.157458i | 0 0.000388785i | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −110.485 | −0.271461 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 179.293i | 0.438368i | 0.975684 | + | 0.219184i | \(0.0703395\pi\) | ||||
−0.975684 | + | 0.219184i | \(0.929660\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − 1208.89i | − 2.94133i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −1.50209 | −0.00361950 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 10.0783 | 0.0241685 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 605.541i | 1.44521i | 0.691263 | + | 0.722603i | \(0.257054\pi\) | ||||
−0.691263 | + | 0.722603i | \(0.742946\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 582.852 | 1.38445 | 0.692224 | − | 0.721683i | \(-0.256631\pi\) | ||||
0.692224 | + | 0.721683i | \(0.256631\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 1019.91i | 2.41112i | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − 664.597i | − 1.56376i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 50.8878 | 0.118620 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 275.405 | 0.638990 | 0.319495 | − | 0.947588i | \(-0.396487\pi\) | ||||
0.319495 | + | 0.947588i | \(0.396487\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 27.7972i | 0.0641967i | 0.999485 | + | 0.0320984i | \(0.0102190\pi\) | ||||
−0.999485 | + | 0.0320984i | \(0.989781\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −6.77836 | −0.0155824 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | − 676.404i | − 1.54784i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 294.160i | 0.670067i | 0.942206 | + | 0.335034i | \(0.108748\pi\) | ||||
−0.942206 | + | 0.335034i | \(0.891252\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −290.890 | −0.656637 | −0.328319 | − | 0.944567i | \(-0.606482\pi\) | ||||
−0.328319 | + | 0.944567i | \(0.606482\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.11730 | 0.00251079 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − 104.626i | − 0.234063i | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 433.407 | 0.965271 | 0.482635 | − | 0.875821i | \(-0.339680\pi\) | ||||
0.482635 | + | 0.875821i | \(0.339680\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − 117.666i | − 0.260900i | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | − 425.859i | − 0.940087i | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −57.3656 | −0.125526 | −0.0627632 | − | 0.998028i | \(-0.519991\pi\) | ||||
−0.0627632 | + | 0.998028i | \(0.519991\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −695.836 | −1.51598 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − 567.060i | − 1.23007i | −0.788501 | − | 0.615033i | \(-0.789143\pi\) | ||||
0.788501 | − | 0.615033i | \(-0.210857\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −0.548177 | −0.00118397 | −0.000591984 | − | 1.00000i | \(-0.500188\pi\) | ||||
−0.000591984 | 1.00000i | \(0.500188\pi\) | ||||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − 7.40935i | − 0.0159341i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − 102.209i | − 0.218862i | −0.993994 | − | 0.109431i | \(-0.965097\pi\) | ||||
0.993994 | − | 0.109431i | \(-0.0349029\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 796.499 | 1.69108 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −17.0499 | −0.0360463 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 658.496i | 1.38631i | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −140.219 | −0.293960 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − 450.134i | − 0.939738i | −0.882736 | − | 0.469869i | \(-0.844301\pi\) | ||||
0.882736 | − | 0.469869i | \(-0.155699\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 362.702i | 0.754058i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 6.34429 | 0.0130810 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −940.772 | −1.93177 | −0.965885 | − | 0.258972i | \(-0.916616\pi\) | ||||
−0.965885 | + | 0.258972i | \(0.916616\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 797.762i | 1.63142i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 514.670 | 1.04821 | 0.524103 | − | 0.851655i | \(-0.324401\pi\) | ||||
0.524103 | + | 0.851655i | \(0.324401\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 722.492i | 1.46550i | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 1.32966i | 0.00268619i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −248.007 | −0.497008 | −0.248504 | − | 0.968631i | \(-0.579939\pi\) | ||||
−0.248504 | + | 0.968631i | \(0.579939\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −91.4099 | −0.182455 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | − 164.798i | − 0.327630i | −0.986491 | − | 0.163815i | \(-0.947620\pi\) | ||||
0.986491 | − | 0.163815i | \(-0.0523800\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 2.91422 | 0.00577073 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 650.621i | 1.28328i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 126.488i | 0.248502i | 0.992251 | + | 0.124251i | \(0.0396529\pi\) | ||||
−0.992251 | + | 0.124251i | \(0.960347\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 689.448 | 1.34395 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1.52432 | 0.00295984 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | − 126.692i | − 0.245053i | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 476.505 | 0.918122 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 51.6797i | 0.0991932i | 0.998769 | + | 0.0495966i | \(0.0157936\pi\) | ||||
−0.998769 | + | 0.0495966i | \(0.984206\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 343.615i | 0.657008i | 0.944503 | + | 0.328504i | \(0.106544\pi\) | ||||
−0.944503 | + | 0.328504i | \(0.893456\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −789.748 | −1.49857 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 130.317 | 0.246346 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 904.361i | 1.70313i | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −386.276 | −0.724720 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.53686i | 0.00287264i | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 340.116i | 0.633363i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 764.013 | 1.41222 | 0.706111 | − | 0.708101i | \(-0.250448\pi\) | ||||
0.706111 | + | 0.708101i | \(0.250448\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −987.828 | −1.81921 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − 4.20423i | − 0.00771419i | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −59.3354 | −0.108474 | −0.0542371 | − | 0.998528i | \(-0.517273\pi\) | ||||
−0.0542371 | + | 0.998528i | \(0.517273\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 1101.19i | 2.00580i | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | − 715.859i | − 1.29920i | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −15.3965 | −0.0277415 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −730.096 | −1.31076 | −0.655382 | − | 0.755298i | \(-0.727492\pi\) | ||||
−0.655382 | + | 0.755298i | \(0.727492\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 55.9718i | 0.100128i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 230.248 | 0.410424 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 476.215i | 0.845853i | 0.906164 | + | 0.422927i | \(0.138997\pi\) | ||||
−0.906164 | + | 0.422927i | \(0.861003\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | − 2.23741i | − 0.00396001i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 417.402 | 0.733570 | 0.366785 | − | 0.930306i | \(-0.380458\pi\) | ||||
0.366785 | + | 0.930306i | \(0.380458\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 984.002 | 1.72330 | 0.861648 | − | 0.507506i | \(-0.169433\pi\) | ||||
0.861648 | + | 0.507506i | \(0.169433\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 922.685i | 1.61027i | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −641.861 | −1.11628 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | − 92.7876i | − 0.160810i | −0.996762 | − | 0.0804052i | \(-0.974379\pi\) | ||||
0.996762 | − | 0.0804052i | \(-0.0256214\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 413.909i | 0.714869i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 17.4180 | 0.0298764 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 4.36506 | 0.00746163 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − 648.667i | − 1.10506i | −0.833495 | − | 0.552528i | \(-0.813663\pi\) | ||||
0.833495 | − | 0.552528i | \(-0.186337\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 782.498 | 1.32852 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 1331.33i | 2.25268i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − 523.532i | − 0.882854i | −0.897297 | − | 0.441427i | \(-0.854472\pi\) | ||||
0.897297 | − | 0.441427i | \(-0.145528\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 1000.94 | 1.67662 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −891.045 | −1.48755 | −0.743777 | − | 0.668428i | \(-0.766968\pi\) | ||||
−0.743777 | + | 0.668428i | \(0.766968\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − 502.034i | − 0.835331i | −0.908601 | − | 0.417666i | \(-0.862848\pi\) | ||||
0.908601 | − | 0.417666i | \(-0.137152\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −1484.85 | −2.46243 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.07285i | 0.0100378i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 304.423i | 0.501521i | 0.968049 | + | 0.250760i | \(0.0806806\pi\) | ||||
−0.968049 | + | 0.250760i | \(0.919319\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −415.909 | −0.680701 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −498.106 | −0.812572 | −0.406286 | − | 0.913746i | \(-0.633176\pi\) | ||||
−0.406286 | + | 0.913746i | \(0.633176\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | − 16.3972i | − 0.0266622i | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 242.250 | 0.392626 | 0.196313 | − | 0.980541i | \(-0.437103\pi\) | ||||
0.196313 | + | 0.980541i | \(0.437103\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 540.597i | 0.873339i | 0.899622 | + | 0.436669i | \(0.143842\pi\) | ||||
−0.899622 | + | 0.436669i | \(0.856158\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 672.031i | 1.08218i | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 624.801 | 0.999681 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −228.134 | −0.363850 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 1641.09i | 2.60904i | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −808.138 | −1.28073 | −0.640363 | − | 0.768073i | \(-0.721216\pi\) | ||||
−0.640363 | + | 0.768073i | \(0.721216\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 380.933i | 0.601790i | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4.84763i | 0.00763407i | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −1299.27 | −2.03328 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 310.553 | 0.484482 | 0.242241 | − | 0.970216i | \(-0.422117\pi\) | ||||
0.242241 | + | 0.970216i | \(0.422117\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 342.761i | 0.533065i | 0.963826 | + | 0.266533i | \(0.0858780\pi\) | ||||
−0.963826 | + | 0.266533i | \(0.914122\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −2.37598 | −0.00368369 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 516.908i | 0.798931i | 0.916748 | + | 0.399466i | \(0.130804\pi\) | ||||
−0.916748 | + | 0.399466i | \(0.869196\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − 112.340i | − 0.173096i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −763.553 | −1.16930 | −0.584650 | − | 0.811286i | \(-0.698768\pi\) | ||||
−0.584650 | + | 0.811286i | \(0.698768\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.48463 | 0.00990020 | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − 479.496i | − 0.729827i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 593.617 | 0.900785 | 0.450392 | − | 0.892831i | \(-0.351284\pi\) | ||||
0.450392 | + | 0.892831i | \(0.351284\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 317.730i | 0.480680i | 0.970689 | + | 0.240340i | \(0.0772590\pi\) | ||||
−0.970689 | + | 0.240340i | \(0.922741\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | − 755.863i | − 1.14006i | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 697.775 | 1.04614 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 751.914 | 1.12394 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − 136.789i | − 0.203859i | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 567.441 | 0.843152 | 0.421576 | − | 0.906793i | \(-0.361477\pi\) | ||||
0.421576 | + | 0.906793i | \(0.361477\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | − 654.238i | − 0.969242i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − 624.802i | − 0.922898i | −0.887167 | − | 0.461449i | \(-0.847330\pi\) | ||||
0.887167 | − | 0.461449i | \(-0.152670\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −396.098 | −0.581642 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −92.8849 | −0.135995 | −0.0679977 | − | 0.997685i | \(-0.521661\pi\) | ||||
−0.0679977 | + | 0.997685i | \(0.521661\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.8811i | 0.0188045i | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1987.06 | 2.89237 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | − 57.1801i | − 0.0829900i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 487.730i | 0.705832i | 0.935655 | + | 0.352916i | \(0.114810\pi\) | ||||
−0.935655 | + | 0.352916i | \(0.885190\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −0.107387 | −0.000154514 0 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −1747.75 | −2.50753 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 183.236i | 0.262140i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 548.723 | 0.782772 | 0.391386 | − | 0.920227i | \(-0.371996\pi\) | ||||
0.391386 | + | 0.920227i | \(0.371996\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − 1626.02i | − 2.31297i | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | − 17.6551i | − 0.0250427i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −251.772 | −0.355109 | −0.177555 | − | 0.984111i | \(-0.556819\pi\) | ||||
−0.177555 | + | 0.984111i | \(0.556819\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 934.658 | 1.31457 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 762.730i | 1.06975i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.542226 | −0.000758358 0 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | − 2071.45i | − 2.88905i | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − 402.578i | − 0.559914i | −0.960013 | − | 0.279957i | \(-0.909680\pi\) | ||||
0.960013 | − | 0.279957i | \(-0.0903202\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 1006.49 | 1.39210 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −679.300 | −0.936966 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 419.973i | 0.577680i | 0.957377 | + | 0.288840i | \(0.0932695\pi\) | ||||
−0.957377 | + | 0.288840i | \(0.906730\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 1183.68 | 1.62371 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 253.251i | 0.346444i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 441.727i | 0.602628i | 0.953525 | + | 0.301314i | \(0.0974253\pi\) | ||||
−0.953525 | + | 0.301314i | \(0.902575\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 184.447 | 0.250268 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −439.053 | −0.594117 | −0.297059 | − | 0.954859i | \(-0.596006\pi\) | ||||
−0.297059 | + | 0.954859i | \(0.596006\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 748.924i | 1.01069i | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 882.165 | 1.18730 | 0.593651 | − | 0.804723i | \(-0.297686\pi\) | ||||
0.593651 | + | 0.804723i | \(0.297686\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.11482i | 0.00149641i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 419.837i | 0.562031i | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 115.636 | 0.153975 | 0.0769877 | − | 0.997032i | \(-0.475470\pi\) | ||||
0.0769877 | + | 0.997032i | \(0.475470\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1817.40 | 2.41354 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.53767i | 0.00601015i | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −885.222 | −1.16938 | −0.584691 | − | 0.811256i | \(-0.698784\pi\) | ||||
−0.584691 | + | 0.811256i | \(0.698784\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | − 222.371i | − 0.292979i | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 554.033i | 0.728033i | 0.931392 | + | 0.364017i | \(0.118595\pi\) | ||||
−0.931392 | + | 0.364017i | \(0.881405\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 19.7502 | 0.0258172 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −368.791 | −0.480823 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − 502.045i | − 0.652854i | −0.945222 | − | 0.326427i | \(-0.894155\pi\) | ||||
0.945222 | − | 0.326427i | \(-0.105845\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 348.826 | 0.452433 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 1188.92i | 1.53806i | 0.639211 | + | 0.769032i | \(0.279261\pi\) | ||||
−0.639211 | + | 0.769032i | \(0.720739\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − 742.536i | − 0.958111i | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 1731.70 | 2.22298 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 161.394 | 0.206651 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 711.230i | 0.908340i | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.48695 | −0.0108114 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 283.004i | 0.359598i | 0.983703 | + | 0.179799i | \(0.0575448\pi\) | ||||
−0.983703 | + | 0.179799i | \(0.942455\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 1011.70i | 1.28225i | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −449.054 | −0.566273 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 2.42727 | 0.00305317 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − 999.015i | − 1.25347i | −0.779233 | − | 0.626735i | \(-0.784391\pi\) | ||||
0.779233 | − | 0.626735i | \(-0.215609\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1881.83 | −2.35523 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | − 312.287i | − 0.389871i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 59.5629i | 0.0741754i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −1368.52 | −1.69581 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 706.226 | 0.872962 | 0.436481 | − | 0.899713i | \(-0.356225\pi\) | ||||
0.436481 | + | 0.899713i | \(0.356225\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 357.615i | 0.440955i | 0.975392 | + | 0.220478i | \(0.0707616\pi\) | ||||
−0.975392 | + | 0.220478i | \(0.929238\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −957.636 | −1.17790 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − 8.50041i | − 0.0104299i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − 250.926i | − 0.307131i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −1337.56 | −1.62919 | −0.814594 | − | 0.580031i | \(-0.803040\pi\) | ||||
−0.814594 | + | 0.580031i | \(0.803040\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −478.600 | −0.581531 | −0.290766 | − | 0.956794i | \(-0.593910\pi\) | ||||
−0.290766 | + | 0.956794i | \(0.593910\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 216.483i | 0.262404i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −572.317 | −0.692040 | −0.346020 | − | 0.938227i | \(-0.612467\pi\) | ||||
−0.346020 | + | 0.938227i | \(0.612467\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | − 1186.46i | − 1.43119i | −0.698515 | − | 0.715596i | \(-0.746155\pi\) | ||||
0.698515 | − | 0.715596i | \(-0.253845\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − 1148.22i | − 1.38174i | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 0.974001 | 0.00116647 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −777.438 | −0.928839 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | − 979.116i | − 1.16700i | −0.812112 | − | 0.583502i | \(-0.801682\pi\) | ||||
0.812112 | − | 0.583502i | \(-0.198318\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −102.524 | −0.121908 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | − 1160.57i | − 1.37671i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | − 6.93257i | − 0.00820423i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −668.533 | −0.787435 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 1584.94 | 1.86245 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | − 683.331i | − 0.801091i | −0.916277 | − | 0.400546i | \(-0.868821\pi\) | ||||
0.916277 | − | 0.400546i | \(-0.131179\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −19.5689 | −0.0228876 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 8.13871i | 0.00949675i | 0.999989 | + | 0.00474837i | \(0.00151146\pi\) | ||||
−0.999989 | + | 0.00474837i | \(0.998489\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1052.97i | 1.22581i | 0.790156 | + | 0.612906i | \(0.210000\pi\) | ||||
−0.790156 | + | 0.612906i | \(0.790000\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1043.99 | 1.20972 | 0.604860 | − | 0.796332i | \(-0.293229\pi\) | ||||
0.604860 | + | 0.796332i | \(0.293229\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −5.07732 | −0.00586973 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | − 2021.71i | − 2.33185i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −116.103 | −0.133605 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − 605.508i | − 0.695187i | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | − 1773.24i | − 2.03120i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 807.552 | 0.920812 | 0.460406 | − | 0.887708i | \(-0.347704\pi\) | ||||
0.460406 | + | 0.887708i | \(0.347704\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 1864.36 | 2.12100 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − 681.043i | − 0.773034i | −0.922282 | − | 0.386517i | \(-0.873678\pi\) | ||||
0.922282 | − | 0.386517i | \(-0.126322\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −996.177 | −1.12817 | −0.564086 | − | 0.825716i | \(-0.690772\pi\) | ||||
−0.564086 | + | 0.825716i | \(0.690772\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | − 15.6550i | − 0.0176893i | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 273.427i | 0.308260i | 0.988051 | + | 0.154130i | \(0.0492575\pi\) | ||||
−0.988051 | + | 0.154130i | \(0.950743\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −5.46688 | −0.00613567 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 1864.55 | 2.08796 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | − 3.62405i | − 0.00404921i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −730.004 | −0.813829 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 807.220i | 0.897909i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − 258.718i | − 0.287145i | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 10.5256 | 0.0116305 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −31.9359 | −0.0352105 | −0.0176052 | − | 0.999845i | \(-0.505604\pi\) | ||||
−0.0176052 | + | 0.999845i | \(0.505604\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | − 814.527i | − 0.896070i | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 1257.16 | 1.37998 | 0.689991 | − | 0.723818i | \(-0.257615\pi\) | ||||
0.689991 | + | 0.723818i | \(0.257615\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − 52.1520i | − 0.0571216i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | − 19.0621i | − 0.0208330i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −1382.98 | −1.50488 | −0.752438 | − | 0.658663i | \(-0.771122\pi\) | ||||
−0.752438 | + | 0.658663i | \(0.771122\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −1076.69 | −1.16904 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − 529.829i | − 0.574030i | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1542.98 | −1.66809 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | − 426.049i | − 0.459600i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − 490.078i | − 0.527533i | −0.964587 | − | 0.263766i | \(-0.915035\pi\) | ||||
0.964587 | − | 0.263766i | \(-0.0849648\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −960.043 | −1.02899 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2.45336 | −0.00262392 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − 1136.61i | − 1.21303i | −0.795072 | − | 0.606515i | \(-0.792567\pi\) | ||||
0.795072 | − | 0.606515i | \(-0.207433\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1835.94 | 1.95520 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − 529.140i | − 0.562316i | −0.959661 | − | 0.281158i | \(-0.909281\pi\) | ||||
0.959661 | − | 0.281158i | \(-0.0907185\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 1687.96i | 1.78999i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −1164.16 | −1.22931 | −0.614657 | − | 0.788795i | \(-0.710705\pi\) | ||||
−0.614657 | + | 0.788795i | \(0.710705\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 195.534 | 0.206043 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − 1256.16i | − 1.32088i | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −616.861 | −0.647283 | −0.323642 | − | 0.946180i | \(-0.604907\pi\) | ||||
−0.323642 | + | 0.946180i | \(0.604907\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − 9.83150i | − 0.0102948i | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | − 235.342i | − 0.245916i | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 78.6368 | 0.0818281 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 429.554 | 0.446059 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | − 4.41034i | − 0.00457030i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −624.887 | −0.646212 | −0.323106 | − | 0.946363i | \(-0.604727\pi\) | ||||
−0.323106 | + | 0.946363i | \(0.604727\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3388.59i | 3.49700i | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 744.764i | 0.767007i | 0.923539 | + | 0.383504i | \(0.125283\pi\) | ||||
−0.923539 | + | 0.383504i | \(0.874717\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 710.677 | 0.728899 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −684.393 | −0.700504 | −0.350252 | − | 0.936655i | \(-0.613904\pi\) | ||||
−0.350252 | + | 0.936655i | \(0.613904\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 38.7922i | 0.0396243i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −1175.09 | −1.19785 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | − 909.341i | − 0.925067i | −0.886602 | − | 0.462533i | \(-0.846941\pi\) | ||||
0.886602 | − | 0.462533i | \(-0.153059\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − 14.1858i | − 0.0144018i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 244.587 | 0.247307 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −1325.02 | −1.33705 | −0.668526 | − | 0.743689i | \(-0.733074\pi\) | ||||
−0.668526 | + | 0.743689i | \(0.733074\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | − 2647.42i | − 2.66608i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −10.6653 | −0.0107189 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | − 937.109i | − 0.939928i | −0.882685 | − | 0.469964i | \(-0.844267\pi\) | ||||
0.882685 | − | 0.469964i | \(-0.155733\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 1615.51i | 1.61712i |
(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.c.h.97.15 | 16 | ||
4.3 | odd | 2 | inner | 1568.3.c.h.97.1 | 16 | ||
7.2 | even | 3 | 224.3.s.a.129.1 | yes | 16 | ||
7.3 | odd | 6 | 224.3.s.a.33.1 | ✓ | 16 | ||
7.6 | odd | 2 | inner | 1568.3.c.h.97.2 | 16 | ||
28.3 | even | 6 | 224.3.s.a.33.8 | yes | 16 | ||
28.23 | odd | 6 | 224.3.s.a.129.8 | yes | 16 | ||
28.27 | even | 2 | inner | 1568.3.c.h.97.16 | 16 | ||
56.3 | even | 6 | 448.3.s.g.257.1 | 16 | |||
56.37 | even | 6 | 448.3.s.g.129.8 | 16 | |||
56.45 | odd | 6 | 448.3.s.g.257.8 | 16 | |||
56.51 | odd | 6 | 448.3.s.g.129.1 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
224.3.s.a.33.1 | ✓ | 16 | 7.3 | odd | 6 | ||
224.3.s.a.33.8 | yes | 16 | 28.3 | even | 6 | ||
224.3.s.a.129.1 | yes | 16 | 7.2 | even | 3 | ||
224.3.s.a.129.8 | yes | 16 | 28.23 | odd | 6 | ||
448.3.s.g.129.1 | 16 | 56.51 | odd | 6 | |||
448.3.s.g.129.8 | 16 | 56.37 | even | 6 | |||
448.3.s.g.257.1 | 16 | 56.3 | even | 6 | |||
448.3.s.g.257.8 | 16 | 56.45 | odd | 6 | |||
1568.3.c.h.97.1 | 16 | 4.3 | odd | 2 | inner | ||
1568.3.c.h.97.2 | 16 | 7.6 | odd | 2 | inner | ||
1568.3.c.h.97.15 | 16 | 1.1 | even | 1 | trivial | ||
1568.3.c.h.97.16 | 16 | 28.27 | even | 2 | inner |