Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1344,4,Mod(223,1344)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1344, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1, 0, 1]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1344.223");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1344 = 2^{6} \cdot 3 \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 1344.p (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: | \(79.2985670477\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 223.13 | ||
Character | \(\chi\) | \(=\) | 1344.223 |
Dual form | 1344.4.p.d.223.14 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1344\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(449\) | \(577\) | \(1093\) |
\(\chi(n)\) | \(-1\) | \(1\) | \(-1\) | \(-1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | − | 3.00000i | − | 0.577350i | ||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −20.7003 | −1.85149 | −0.925747 | − | 0.378143i | \(-0.876563\pi\) | ||||
−0.925747 | + | 0.378143i | \(0.876563\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −11.8166 | + | 14.2607i | −0.638039 | + | 0.770004i | ||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −9.00000 | −0.333333 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 39.2814 | 1.07671 | 0.538354 | − | 0.842719i | \(-0.319046\pi\) | ||||
0.538354 | + | 0.842719i | \(0.319046\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 36.2449 | 0.773271 | 0.386636 | − | 0.922233i | \(-0.373637\pi\) | ||||
0.386636 | + | 0.922233i | \(0.373637\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 62.1010i | 1.06896i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 92.2048i | 1.31547i | 0.753251 | + | 0.657733i | \(0.228485\pi\) | ||||
−0.753251 | + | 0.657733i | \(0.771515\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | − | 87.5184i | − | 1.05674i | −0.849013 | − | 0.528371i | \(-0.822803\pi\) | ||
0.849013 | − | 0.528371i | \(-0.177197\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 42.7820 | + | 35.4499i | 0.444562 | + | 0.368372i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | − | 100.990i | − | 0.915558i | −0.889066 | − | 0.457779i | \(-0.848645\pi\) | ||
0.889066 | − | 0.457779i | \(-0.151355\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 303.504 | 2.42803 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 27.0000i | 0.192450i | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | − | 36.2034i | − | 0.231821i | −0.993260 | − | 0.115911i | \(-0.963021\pi\) | ||
0.993260 | − | 0.115911i | \(-0.0369786\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −264.306 | −1.53131 | −0.765656 | − | 0.643250i | \(-0.777586\pi\) | ||||
−0.765656 | + | 0.643250i | \(0.777586\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | − | 117.844i | − | 0.621638i | ||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 244.609 | − | 295.201i | 1.18133 | − | 1.42566i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 229.534i | 1.01987i | 0.860213 | + | 0.509936i | \(0.170331\pi\) | ||||
−0.860213 | + | 0.509936i | \(0.829669\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | − | 108.735i | − | 0.446448i | ||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 337.096i | − | 1.28404i | −0.766688 | − | 0.642019i | \(-0.778097\pi\) | ||
0.766688 | − | 0.642019i | \(-0.221903\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 368.528 | 1.30697 | 0.653487 | − | 0.756937i | \(-0.273305\pi\) | ||||
0.653487 | + | 0.756937i | \(0.273305\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 186.303 | 0.617165 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 314.672 | 0.976588 | 0.488294 | − | 0.872679i | \(-0.337619\pi\) | ||||
0.488294 | + | 0.872679i | \(0.337619\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −63.7338 | − | 337.027i | −0.185813 | − | 0.982585i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 276.614 | 0.759485 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 108.563i | 0.281362i | 0.990055 | + | 0.140681i | \(0.0449293\pi\) | ||||
−0.990055 | + | 0.140681i | \(0.955071\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −813.139 | −1.99352 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −262.555 | −0.610110 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 185.373i | 0.409043i | 0.978862 | + | 0.204521i | \(0.0655638\pi\) | ||||
−0.978862 | + | 0.204521i | \(0.934436\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 163.504 | 0.343189 | 0.171594 | − | 0.985168i | \(-0.445108\pi\) | ||||
0.171594 | + | 0.985168i | \(0.445108\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 106.350 | − | 128.346i | 0.212680 | − | 0.256668i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −750.282 | −1.43171 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 458.260 | 0.835603 | 0.417802 | − | 0.908538i | \(-0.362801\pi\) | ||||
0.417802 | + | 0.908538i | \(0.362801\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −302.969 | −0.528597 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 584.527i | − | 0.977051i | −0.872550 | − | 0.488525i | \(-0.837535\pi\) | ||
0.872550 | − | 0.488525i | \(-0.162465\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 1099.24i | 1.76241i | 0.472736 | + | 0.881204i | \(0.343266\pi\) | ||||
−0.472736 | + | 0.881204i | \(0.656734\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | − | 910.512i | − | 1.40183i | ||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −464.175 | + | 560.180i | −0.686982 | + | 0.829070i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 438.627i | 0.624676i | 0.949971 | + | 0.312338i | \(0.101112\pi\) | ||||
−0.949971 | + | 0.312338i | \(0.898888\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 81.0000 | 0.111111 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 722.114i | 0.954967i | 0.878641 | + | 0.477484i | \(0.158451\pi\) | ||||
−0.878641 | + | 0.477484i | \(0.841549\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | − | 1908.67i | − | 2.43558i | ||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −108.610 | −0.133842 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 452.334i | − | 0.538734i | −0.963038 | − | 0.269367i | \(-0.913186\pi\) | ||
0.963038 | − | 0.269367i | \(-0.0868144\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −428.293 | + | 516.877i | −0.493377 | + | 0.595422i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 792.917i | 0.884103i | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 1811.66i | 1.95655i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | − | 598.000i | − | 0.625956i | −0.949760 | − | 0.312978i | \(-0.898673\pi\) | ||
0.949760 | − | 0.312978i | \(-0.101327\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −353.533 | −0.358903 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −1415.04 | −1.39407 | −0.697037 | − | 0.717035i | \(-0.745499\pi\) | ||||
−0.697037 | + | 0.717035i | \(0.745499\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1138.86 | −1.08947 | −0.544733 | − | 0.838609i | \(-0.683369\pi\) | ||||
−0.544733 | + | 0.838609i | \(0.683369\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −885.602 | − | 733.826i | −0.823104 | − | 0.682039i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −1503.38 | −1.35829 | −0.679147 | − | 0.734002i | \(-0.737650\pi\) | ||||
−0.679147 | + | 0.734002i | \(0.737650\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 359.283i | 0.315716i | 0.987462 | + | 0.157858i | \(0.0504589\pi\) | ||||
−0.987462 | + | 0.157858i | \(0.949541\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 688.603 | 0.588823 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −2363.20 | −1.96736 | −0.983679 | − | 0.179932i | \(-0.942412\pi\) | ||||
−0.983679 | + | 0.179932i | \(0.942412\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2090.52i | 1.69515i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −326.204 | −0.257757 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1314.90 | − | 1089.55i | −1.01291 | − | 0.839319i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 212.030 | 0.159301 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −1011.29 | −0.741340 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −3695.09 | −2.64399 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 1620.69i | 1.13238i | 0.824274 | + | 0.566192i | \(0.191584\pi\) | ||||
−0.824274 | + | 0.566192i | \(0.808416\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | − | 1105.58i | − | 0.754582i | ||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 503.229i | 0.335629i | 0.985819 | + | 0.167814i | \(0.0536709\pi\) | ||||
−0.985819 | + | 0.167814i | \(0.946329\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 1248.07 | + | 1034.17i | 0.813696 | + | 0.674243i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | − | 558.909i | − | 0.356320i | ||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −577.769 | −0.360308 | −0.180154 | − | 0.983638i | \(-0.557660\pi\) | ||||
−0.180154 | + | 0.983638i | \(0.557660\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 412.449i | − | 0.251680i | −0.992051 | − | 0.125840i | \(-0.959837\pi\) | ||
0.992051 | − | 0.125840i | \(-0.0401625\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | − | 944.017i | − | 0.563834i | ||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 1423.75 | 0.832588 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 749.423i | 0.429215i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −1011.08 | + | 191.201i | −0.567296 | + | 0.107279i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 2985.68i | − | 1.64158i | −0.571227 | − | 0.820792i | \(-0.693532\pi\) | ||
0.571227 | − | 0.820792i | \(-0.306468\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 2788.11i | 1.50261i | 0.659957 | + | 0.751303i | \(0.270574\pi\) | ||||
−0.659957 | + | 0.751303i | \(0.729426\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | − | 829.843i | − | 0.438489i | ||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5471.21 | 2.83522 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −1616.65 | −0.821801 | −0.410900 | − | 0.911680i | \(-0.634786\pi\) | ||||
−0.410900 | + | 0.911680i | \(0.634786\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 325.688 | 0.162445 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 1440.18 | + | 1193.36i | 0.704983 | + | 0.584161i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 1934.76 | 0.929708 | 0.464854 | − | 0.885387i | \(-0.346107\pi\) | ||||
0.464854 | + | 0.885387i | \(0.346107\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2439.42i | 1.15096i | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −816.453 | −0.378318 | −0.189159 | − | 0.981947i | \(-0.560576\pi\) | ||||
−0.189159 | + | 0.981947i | \(0.560576\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −883.307 | −0.402051 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 787.666i | 0.352247i | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 3644.18 | 1.60151 | 0.800757 | − | 0.598989i | \(-0.204431\pi\) | ||||
0.800757 | + | 0.598989i | \(0.204431\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −3586.40 | + | 4328.17i | −1.54918 | + | 1.86959i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 556.119 | 0.236161 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −3415.80 | −1.42631 | −0.713154 | − | 0.701008i | \(-0.752734\pi\) | ||||
−0.713154 | + | 0.701008i | \(0.752734\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 3513.95 | 1.44304 | 0.721519 | − | 0.692395i | \(-0.243444\pi\) | ||||
0.721519 | + | 0.692395i | \(0.243444\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | − | 490.512i | − | 0.198140i | ||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | − | 4751.44i | − | 1.88829i | ||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3621.93i | 1.41637i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −385.038 | − | 319.049i | −0.148187 | − | 0.122791i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 3058.15i | 1.15854i | 0.815137 | + | 0.579268i | \(0.196661\pi\) | ||||
−0.815137 | + | 0.579268i | \(0.803339\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −1894.89 | −0.706721 | −0.353361 | − | 0.935487i | \(-0.614961\pi\) | ||||
−0.353361 | + | 0.935487i | \(0.614961\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 2250.85i | 0.826597i | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 109.557i | 0.0396224i | 0.999804 | + | 0.0198112i | \(0.00630651\pi\) | ||||
−0.999804 | + | 0.0198112i | \(0.993693\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1525.71 | −0.543492 | −0.271746 | − | 0.962369i | \(-0.587601\pi\) | ||||
−0.271746 | + | 0.962369i | \(0.587601\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 1374.78i | − | 0.482436i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 516.286 | + | 427.803i | 0.178503 | + | 0.147911i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 6978.01i | 2.37739i | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 908.908i | 0.305186i | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 3437.85i | − | 1.13780i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 5626.27 | 1.83568 | 0.917841 | − | 0.396949i | \(-0.129931\pi\) | ||||
0.917841 | + | 0.396949i | \(0.129931\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1753.58 | −0.564101 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7628.64 | −2.41986 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 3123.21 | − | 3769.18i | 0.977037 | − | 1.17912i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 3297.71 | 1.01753 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 3341.95i | 1.01721i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 1409.96 | 0.423398 | 0.211699 | − | 0.977335i | \(-0.432100\pi\) | ||||
0.211699 | + | 0.977335i | \(0.432100\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −2731.54 | −0.809344 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | − | 848.622i | − | 0.248128i | −0.992274 | − | 0.124064i | \(-0.960407\pi\) | ||
0.992274 | − | 0.124064i | \(-0.0395928\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −5880.63 | −1.69696 | −0.848479 | − | 0.529230i | \(-0.822481\pi\) | ||||
−0.848479 | + | 0.529230i | \(0.822481\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 1680.54 | + | 1392.52i | 0.478664 | + | 0.396629i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3101.62 | −0.872077 | −0.436038 | − | 0.899928i | \(-0.643619\pi\) | ||||
−0.436038 | + | 0.899928i | \(0.643619\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −6513.82 | −1.80815 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1315.88 | 0.360657 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 6225.18i | − | 1.68483i | −0.538831 | − | 0.842414i | \(-0.681134\pi\) | ||
0.538831 | − | 0.842414i | \(-0.318866\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 201.092i | − | 0.0537489i | −0.999639 | − | 0.0268744i | \(-0.991445\pi\) | ||
0.999639 | − | 0.0268744i | \(-0.00855543\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | − | 243.000i | − | 0.0641500i | ||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 1319.31 | + | 6976.57i | 0.344031 | + | 1.81925i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | − | 3172.10i | − | 0.817149i | ||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 2166.34 | 0.551351 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 4561.95i | − | 1.14720i | −0.819135 | − | 0.573601i | \(-0.805546\pi\) | ||
0.819135 | − | 0.573601i | \(-0.194454\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | − | 3967.02i | − | 0.985789i | ||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −5726.01 | −1.40618 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 1939.24i | − | 0.470687i | −0.971912 | − | 0.235343i | \(-0.924379\pi\) | ||
0.971912 | − | 0.235343i | \(-0.0756215\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −3273.32 | − | 2712.33i | −0.785305 | − | 0.650718i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 325.831i | 0.0772737i | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 1244.55i | 0.291796i | 0.989300 | + | 0.145898i | \(0.0466072\pi\) | ||||
−0.989300 | + | 0.145898i | \(0.953393\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | − | 2247.28i | − | 0.520941i | ||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −1357.00 | −0.311038 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −188.083 | −0.0426305 | −0.0213153 | − | 0.999773i | \(-0.506785\pi\) | ||||
−0.0213153 | + | 0.999773i | \(0.506785\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −504.590 | −0.113106 | −0.0565529 | − | 0.998400i | \(-0.518011\pi\) | ||||
−0.0565529 | + | 0.998400i | \(0.518011\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 1550.63 | + | 1284.88i | 0.343767 | + | 0.284851i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 11922.1 | 2.61428 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 4147.02i | 0.899532i | 0.893146 | + | 0.449766i | \(0.148493\pi\) | ||||
−0.893146 | + | 0.449766i | \(0.851507\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 2378.75 | 0.510437 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2018.75 | −0.428572 | −0.214286 | − | 0.976771i | \(-0.568742\pi\) | ||||
−0.214286 | + | 0.976771i | \(0.568742\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 50.2649i | − | 0.0105581i | −0.999986 | − | 0.00527905i | \(-0.998320\pi\) | ||
0.999986 | − | 0.00527905i | \(-0.00168038\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 5434.98 | 1.12962 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 4807.22 | + | 3983.35i | 0.988715 | + | 0.819267i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −3588.72 | −0.730453 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1794.00 | −0.361396 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −2247.98 | −0.448221 | −0.224110 | − | 0.974564i | \(-0.571948\pi\) | ||||
−0.224110 | + | 0.974564i | \(0.571948\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | − | 3837.29i | − | 0.757340i | ||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 1060.60i | 0.207213i | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | − | 3660.36i | − | 0.707974i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −4354.76 | + | 5255.45i | −0.833901 | + | 1.00638i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 4245.11i | 0.804869i | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −3384.59 | −0.635413 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1759.91i | 0.327177i | 0.986529 | + | 0.163588i | \(0.0523069\pi\) | ||||
−0.986529 | + | 0.163588i | \(0.947693\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3416.57i | 0.629004i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −8517.10 | −1.55293 | −0.776464 | − | 0.630162i | \(-0.782988\pi\) | ||||
−0.776464 | + | 0.630162i | \(0.782988\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 10113.5i | − | 1.82636i | −0.407556 | − | 0.913180i | \(-0.633619\pi\) | ||
0.407556 | − | 0.913180i | \(-0.366381\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −2201.48 | + | 2656.81i | −0.393775 | + | 0.475220i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 6511.01i | − | 1.15361i | −0.816882 | − | 0.576805i | \(-0.804299\pi\) | ||
0.816882 | − | 0.576805i | \(-0.195701\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 1422.12i | − | 0.249604i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 4510.15i | 0.784212i | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 8069.62 | 1.39011 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 11000.5 | 1.87753 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 1077.85 | 0.182279 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −3718.37 | + | 4487.44i | −0.623101 | + | 0.751977i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2031.11 | −0.337280 | −0.168640 | − | 0.985678i | \(-0.553938\pi\) | ||||
−0.168640 | + | 0.985678i | \(0.553938\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | − | 2065.81i | − | 0.339957i | ||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −9486.15 | −1.54712 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −9702.01 | −1.56826 | −0.784128 | − | 0.620599i | \(-0.786889\pi\) | ||||
−0.784128 | + | 0.620599i | \(0.786889\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 7089.61i | 1.13585i | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −10382.3 | −1.64878 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 5559.35 | + | 3073.64i | 0.875150 | + | 0.483851i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 6271.57 | 0.978695 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −4652.17 | −0.719716 | −0.359858 | − | 0.933007i | \(-0.617175\pi\) | ||||
−0.359858 | + | 0.933007i | \(0.617175\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −5507.67 | −0.844753 | −0.422376 | − | 0.906421i | \(-0.638804\pi\) | ||||
−0.422376 | + | 0.906421i | \(0.638804\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 978.612i | 0.148816i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 8066.25i | 1.21621i | 0.793856 | + | 0.608106i | \(0.208071\pi\) | ||||
−0.793856 | + | 0.608106i | \(0.791929\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 12099.9i | 1.80900i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −3268.65 | + | 3944.71i | −0.484581 | + | 0.584807i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | − | 2334.87i | − | 0.343258i | −0.985162 | − | 0.171629i | \(-0.945097\pi\) | ||
0.985162 | − | 0.171629i | \(-0.0549030\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −800.476 | −0.116704 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | − | 636.090i | − | 0.0919726i | ||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | − | 22754.6i | − | 3.26309i | ||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8870.84 | 1.26173 | 0.630864 | − | 0.775894i | \(-0.282701\pi\) | ||||
0.630864 | + | 0.775894i | \(0.282701\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 3033.87i | 0.428013i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −1548.17 | − | 1282.84i | −0.216650 | − | 0.179520i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | − | 8302.86i | − | 1.15256i | −0.817251 | − | 0.576281i | \(-0.804503\pi\) | ||
0.817251 | − | 0.576281i | \(-0.195497\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 11085.3i | 1.52651i | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 1312.19i | − | 0.179261i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −530.766 | −0.0719357 | −0.0359679 | − | 0.999353i | \(-0.511451\pi\) | ||||
−0.0359679 | + | 0.999353i | \(0.511451\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 4862.06 | 0.653782 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −534.478 | −0.0713069 | −0.0356535 | − | 0.999364i | \(-0.511351\pi\) | ||||
−0.0356535 | + | 0.999364i | \(0.511351\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 9608.57 | − | 11595.9i | 1.27194 | − | 1.53502i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −3316.75 | −0.435658 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 11253.1i | − | 1.46672i | −0.679842 | − | 0.733358i | \(-0.737952\pi\) | ||
0.679842 | − | 0.733358i | \(-0.262048\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9311.74 | 1.20439 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 1509.69 | 0.193775 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | − | 9079.73i | − | 1.15658i | ||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −8896.66 | −1.12471 | −0.562356 | − | 0.826895i | \(-0.690105\pi\) | ||||
−0.562356 | + | 0.826895i | \(0.690105\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 3102.52 | − | 3744.22i | 0.389274 | − | 0.469788i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 6210.10 | 0.773360 | 0.386680 | − | 0.922214i | \(-0.373622\pi\) | ||||
0.386680 | + | 0.922214i | \(0.373622\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −9579.73 | −1.18412 | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −1676.73 | −0.205722 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 9016.44i | 1.09810i | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 3899.47i | 0.471434i | 0.971822 | + | 0.235717i | \(0.0757439\pi\) | ||||
−0.971822 | + | 0.235717i | \(0.924256\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 1733.31i | 0.208024i | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −2643.54 | − | 2190.49i | −0.314965 | − | 0.260985i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 14948.0i | − | 1.76812i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −1237.35 | −0.145307 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 12136.9i | 1.41510i | 0.706663 | + | 0.707550i | \(0.250200\pi\) | ||||
−0.706663 | + | 0.707550i | \(0.749800\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 5388.65i | − | 0.623817i | −0.950112 | − | 0.311908i | \(-0.899032\pi\) | ||
0.950112 | − | 0.311908i | \(-0.100968\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −2832.05 | −0.325529 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 27984.5i | 3.19400i | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1932.07 | + | 2331.68i | −0.218968 | + | 0.264257i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | − | 4271.25i | − | 0.480695i | ||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 2284.44i | 0.255308i | 0.991819 | + | 0.127654i | \(0.0407447\pi\) | ||||
−0.991819 | + | 0.127654i | \(0.959255\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 1711.79i | 0.189985i | 0.995478 | + | 0.0949925i | \(0.0302827\pi\) | ||||
−0.995478 | + | 0.0949925i | \(0.969717\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 2248.27 | 0.247808 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −8838.47 | −0.967509 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −2820.52 | −0.306643 | −0.153322 | − | 0.988176i | \(-0.548997\pi\) | ||||
−0.153322 | + | 0.988176i | \(0.548997\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 573.604 | + | 3033.24i | 0.0619376 | + | 0.327528i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 13392.2 | 1.43630 | 0.718150 | − | 0.695888i | \(-0.244989\pi\) | ||||
0.718150 | + | 0.695888i | \(0.244989\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 9363.47i | 0.997463i | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −8957.03 | −0.947769 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −15186.9 | −1.59624 | −0.798120 | − | 0.602498i | \(-0.794172\pi\) | ||||
−0.798120 | + | 0.602498i | \(0.794172\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 13241.6i | − | 1.38254i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 8364.34 | 0.867530 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 8865.81 | − | 10699.5i | 0.913485 | − | 1.10242i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −19132.7 | −1.95840 | −0.979202 | − | 0.202888i | \(-0.934967\pi\) | ||||
−0.979202 | + | 0.202888i | \(0.934967\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −2489.53 | −0.253162 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −237.892 | −0.0240341 | −0.0120170 | − | 0.999928i | \(-0.503825\pi\) | ||||
−0.0120170 | + | 0.999928i | \(0.503825\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6527.48i | 0.655200i | 0.944816 | + | 0.327600i | \(0.106240\pi\) | ||||
−0.944816 | + | 0.327600i | \(0.893760\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | − | 16413.6i | − | 1.63691i | ||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | − | 488.599i | − | 0.0484147i | −0.999707 | − | 0.0242073i | \(-0.992294\pi\) | ||
0.999707 | − | 0.0242073i | \(-0.00770619\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −5415.10 | + | 6535.10i | −0.533147 | + | 0.643418i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 4849.95i | 0.474467i | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 14476.3 | 1.40723 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 26562.2i | − | 2.56580i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | − | 977.063i | − | 0.0937875i | ||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −5872.67 | −0.560186 | −0.280093 | − | 0.959973i | \(-0.590365\pi\) | ||||
−0.280093 | + | 0.959973i | \(0.590365\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 8319.45i | 0.788637i | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3580.08 | − | 4320.55i | 0.337266 | − | 0.407022i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 12378.8i | 1.15895i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 14307.7i | 1.33130i | 0.746263 | + | 0.665652i | \(0.231846\pi\) | ||||
−0.746263 | + | 0.665652i | \(0.768154\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | − | 5804.29i | − | 0.536767i | ||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10665.1 | −0.980264 | −0.490132 | − | 0.871648i | \(-0.663052\pi\) | ||||
−0.490132 | + | 0.871648i | \(0.663052\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 3338.13 | 0.304953 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 7318.25 | 0.664507 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 8335.75 | + | 6907.15i | 0.752333 | + | 0.623397i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −11905.8 | −1.06809 | −0.534046 | − | 0.845455i | \(-0.679329\pi\) | ||||
−0.534046 | + | 0.845455i | \(0.679329\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2449.36i | 0.218422i | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 11100.0 | 0.983941 | 0.491971 | − | 0.870612i | \(-0.336277\pi\) | ||||
0.491971 | + | 0.870612i | \(0.336277\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 29291.8 | 2.58112 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 2649.92i | 0.232125i | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 8580.71 | 0.747216 | 0.373608 | − | 0.927587i | \(-0.378120\pi\) | ||||
0.373608 | + | 0.927587i | \(0.378120\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −15675.8 | − | 12989.3i | −1.35706 | − | 1.12448i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 2363.00 | 0.203370 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 23574.7 | 2.01714 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12360.8 | 1.05150 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | − | 10932.5i | − | 0.924635i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 4351.09i | − | 0.365882i | −0.983124 | − | 0.182941i | \(-0.941438\pi\) | ||
0.983124 | − | 0.182941i | \(-0.0585618\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 3685.85i | 0.308166i | 0.988058 | + | 0.154083i | \(0.0492424\pi\) | ||||
−0.988058 | + | 0.154083i | \(0.950758\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 12984.5 | + | 10759.2i | 1.07941 | + | 0.894419i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | − | 24370.2i | − | 2.01439i | ||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 1968.06 | 0.161754 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | − | 1668.36i | − | 0.136348i | ||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 12218.0i | − | 0.992910i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 31120.5 | 2.51487 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 10247.4i | 0.823479i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −2503.55 | − | 13238.9i | −0.200066 | − | 1.05796i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 21536.0i | 1.71147i | 0.517413 | + | 0.855736i | \(0.326895\pi\) | ||||
−0.517413 | + | 0.855736i | \(0.673105\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | − | 10541.8i | − | 0.833138i | ||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 7437.28i | − | 0.584547i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 5550.29 | 0.433845 | 0.216923 | − | 0.976189i | \(-0.430398\pi\) | ||||
0.216923 | + | 0.976189i | \(0.430398\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −1471.54 | −0.114396 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −3168.47 | −0.244975 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −6255.12 | − | 5183.10i | −0.481003 | − | 0.398568i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −14254.3 | −1.09020 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 14848.3i | − | 1.12952i | −0.825256 | − | 0.564758i | \(-0.808969\pi\) | ||
0.825256 | − | 0.564758i | \(-0.191031\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 13357.2 | 1.01065 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 10865.8 | 0.817744 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | − | 1189.55i | − | 0.0890469i | −0.999008 | − | 0.0445235i | \(-0.985823\pi\) | ||
0.999008 | − | 0.0445235i | \(-0.0141769\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 48919.1 | 3.64255 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −957.148 | + | 1155.11i | −0.0708932 | + | 0.0855560i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 9572.43 | 0.705267 | 0.352634 | − | 0.935761i | \(-0.385286\pi\) | ||||
0.352634 | + | 0.935761i | \(0.385286\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −19487.5 | −1.42825 | −0.714123 | − | 0.700021i | \(-0.753174\pi\) | ||||
−0.714123 | + | 0.700021i | \(0.753174\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 9174.46 | 0.668881 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 30650.8i | − | 2.22300i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 24751.1i | 1.78579i | 0.450263 | + | 0.892896i | \(0.351330\pi\) | ||||
−0.450263 | + | 0.892896i | \(0.648670\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 5684.67i | 0.408026i | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10297.8 | − | 8532.96i | −0.735329 | − | 0.609306i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 4264.49i | 0.302945i | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 6752.54 | 0.477236 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | − | 15015.1i | − | 1.05577i | −0.849315 | − | 0.527886i | \(-0.822985\pi\) | ||
0.849315 | − | 0.527886i | \(-0.177015\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 23131.6i | 1.61820i | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 328.671 | 0.0228760 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 18080.4i | 1.25206i | 0.779799 | + | 0.626030i | \(0.215321\pi\) | ||||
−0.779799 | + | 0.626030i | \(0.784679\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 27218.9 | + | 22554.1i | 1.87541 | + | 1.55399i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 4577.13i | 0.313785i | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 18896.2i | − | 1.28894i | −0.764628 | − | 0.644472i | \(-0.777077\pi\) | ||
0.764628 | − | 0.644472i | \(-0.222923\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | − | 316.737i | − | 0.0214974i | −0.999942 | − | 0.0107487i | \(-0.996579\pi\) | ||
0.999942 | − | 0.0107487i | \(-0.00342149\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4124.34 | −0.278534 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −4389.09 | −0.294945 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −24428.2 | −1.63346 | −0.816730 | − | 0.577020i | \(-0.804216\pi\) | ||||
−0.816730 | + | 0.577020i | \(0.804216\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 1283.41 | − | 1548.86i | 0.0853964 | − | 0.103059i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 11405.3 | 0.755168 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | − | 24938.5i | − | 1.64316i | −0.570092 | − | 0.821581i | \(-0.693092\pi\) | ||
0.570092 | − | 0.821581i | \(-0.306908\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 20934.0 | 1.37259 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10603.6 | −0.691873 | −0.345936 | − | 0.938258i | \(-0.612439\pi\) | ||||
−0.345936 | + | 0.938258i | \(0.612439\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 17013.3i | − | 1.10472i | −0.833604 | − | 0.552362i | \(-0.813727\pi\) | ||
0.833604 | − | 0.552362i | \(-0.186273\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 2726.72 | 0.176199 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 6450.59 | + | 5345.07i | 0.414827 | + | 0.343733i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 38551.7 | 2.46731 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −10313.5 | −0.656911 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −21164.2 | −1.34161 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 2157.13i | 0.136092i | 0.997682 | + | 0.0680460i | \(0.0216765\pi\) | ||||
−0.997682 | + | 0.0680460i | \(0.978324\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 16878.8i | − | 1.05983i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | − | 33548.8i | − | 2.09660i | ||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −2310.02 | − | 12215.5i | −0.143684 | − | 0.759805i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 5260.75i | 0.325684i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −22030.9 | −1.35752 | −0.678758 | − | 0.734362i | \(-0.737481\pi\) | ||||
−0.678758 | + | 0.734362i | \(0.737481\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 30067.6i | 1.84409i | 0.387081 | + | 0.922046i | \(0.373483\pi\) | ||||
−0.387081 | + | 0.922046i | \(0.626517\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 22885.9i | 1.39711i | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −6954.93 | −0.422607 | −0.211303 | − | 0.977421i | \(-0.567771\pi\) | ||||
−0.211303 | + | 0.977421i | \(0.567771\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 7281.72i | 0.440420i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −11307.5 | − | 9369.62i | −0.680763 | − | 0.564092i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 1199.25i | − | 0.0718686i | −0.999354 | − | 0.0359343i | \(-0.988559\pi\) | ||
0.999354 | − | 0.0359343i | \(-0.0114407\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 10417.0i | − | 0.621415i | ||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | − | 9893.12i | − | 0.587469i | ||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −13611.9 | −0.804619 | −0.402310 | − | 0.915504i | \(-0.631792\pi\) | ||||
−0.402310 | + | 0.915504i | \(0.631792\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 30065.6 | 1.76916 | 0.884582 | − | 0.466385i | \(-0.154444\pi\) | ||||
0.884582 | + | 0.466385i | \(0.154444\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 10025.9 | 0.587288 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | −25835.5 | − | 21407.8i | −1.50655 | − | 1.24836i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −3656.18 | −0.212246 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | − | 4229.88i | − | 0.244449i | ||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 6422.67 | 0.369515 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10262.1 | 0.587777 | 0.293888 | − | 0.955840i | \(-0.405051\pi\) | ||||
0.293888 | + | 0.955840i | \(0.405051\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 8194.61i | 0.467275i | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 426.182 | 0.0241943 | 0.0120971 | − | 0.999927i | \(-0.496149\pi\) | ||||
0.0120971 | + | 0.999927i | \(0.496149\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 8527.88 | + | 7066.35i | 0.481988 | + | 0.399384i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −2545.87 | −0.143257 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −2385.48 | −0.133643 | −0.0668213 | − | 0.997765i | \(-0.521286\pi\) | ||||
−0.0668213 | + | 0.997765i | \(0.521286\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 11960.0 | 0.667108 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 17641.9i | 0.979739i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3934.84i | 0.217570i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 9485.21i | 0.522192i | 0.965313 | + | 0.261096i | \(0.0840839\pi\) | ||||
−0.965313 | + | 0.261096i | \(0.915916\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 4177.57 | − | 5041.62i | 0.228994 | − | 0.276357i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 8537.84i | 0.465984i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 31081.9 | 1.68911 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 9304.86i | 0.503494i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13463.5i | 0.725404i | 0.931905 | + | 0.362702i | \(0.118146\pi\) | ||||
−0.931905 | + | 0.362702i | \(0.881854\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 20088.5 | 1.07774 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 19541.5i | 1.04393i | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 16721.0 | − | 20179.4i | 0.889473 | − | 1.07344i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | − | 1482.11i | − | 0.0785075i | −0.999229 | − | 0.0392538i | \(-0.987502\pi\) | ||
0.999229 | − | 0.0392538i | \(-0.0124981\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | − | 3947.65i | − | 0.208225i | ||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 26692.2i | 1.40200i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −29472.1 | −1.54153 | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −18675.6 | −0.972735 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33887.8 | 1.75772 | 0.878862 | − | 0.477077i | \(-0.158304\pi\) | ||||
0.878862 | + | 0.477077i | \(0.158304\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 13457.5 | − | 16240.9i | 0.695122 | − | 0.838893i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −603.276 | −0.0310319 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 10987.9i | − | 0.562869i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 9840.41 | 0.502009 | 0.251004 | − | 0.967986i | \(-0.419239\pi\) | ||||
0.251004 | + | 0.967986i | \(0.419239\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −729.000 | −0.0370370 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 33980.0i | 1.71928i | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −13241.0 | −0.667212 | −0.333606 | − | 0.942713i | \(-0.608265\pi\) | ||||
−0.333606 | + | 0.942713i | \(0.608265\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 20929.7 | − | 3957.93i | 1.05035 | − | 0.198627i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 18001.1 | 0.899701 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −6185.80 | −0.307914 | −0.153957 | − | 0.988078i | \(-0.549202\pi\) | ||||
−0.153957 | + | 0.988078i | \(0.549202\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −9516.29 | −0.471781 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 11911.6i | 0.588148i | 0.955783 | + | 0.294074i | \(0.0950112\pi\) | ||||
−0.955783 | + | 0.294074i | \(0.904989\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 61804.5i | 3.03939i | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | − | 6499.02i | − | 0.318322i | ||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 17764.9 | − | 21439.3i | 0.866645 | − | 1.04589i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 28902.1i | 1.40433i | 0.712015 | + | 0.702165i | \(0.247783\pi\) | ||||
−0.712015 | + | 0.702165i | \(0.752217\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −13685.8 | −0.662337 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 57714.9i | − | 2.78207i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 7827.05i | − | 0.375798i | −0.982188 | − | 0.187899i | \(-0.939832\pi\) | ||
0.982188 | − | 0.187899i | \(-0.0601678\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −11901.1 | −0.569145 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 4882.67i | 0.232584i | 0.993215 | + | 0.116292i | \(0.0371008\pi\) | ||||
−0.993215 | + | 0.116292i | \(0.962899\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −5123.62 | − | 4245.52i | −0.243103 | − | 0.201439i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 17178.0i | 0.811860i | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 6718.83i | 0.316301i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 20071.4i | 0.941215i | 0.882343 | + | 0.470607i | \(0.155965\pi\) | ||||
−0.882343 | + | 0.470607i | \(0.844035\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −5817.72 | −0.271751 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −4965.70 | −0.231053 | −0.115526 | − | 0.993304i | \(-0.536855\pi\) | ||||
−0.115526 | + | 0.993304i | \(0.536855\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −80217.8 | −3.71808 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −8136.98 | + | 9819.95i | −0.375692 | + | 0.453396i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −29502.1 | −1.35690 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | − | 22961.1i | − | 1.05200i | ||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 977.493 | 0.0446140 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 33465.2 | 1.52156 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 40092.6i | 1.81594i | 0.419035 | + | 0.907970i | \(0.362369\pi\) | ||||
−0.419035 | + | 0.907970i | \(0.637631\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 3733.66 | 0.168469 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 27925.1 | − | 33700.9i | 1.25525 | − | 1.51487i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 5926.18 | 0.265378 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −6741.84 | −0.300765 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −26919.4 | −1.19640 | −0.598202 | − | 0.801345i | \(-0.704118\pi\) | ||||
−0.598202 | + | 0.801345i | \(0.704118\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 29014.3i | 1.28467i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4071.01i | 0.179578i | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 43179.5i | 1.89760i | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −29812.3 | − | 24703.0i | −1.30527 | − | 1.08157i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 564.248i | 0.0246127i | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −34737.1 | −1.50963 | −0.754815 | − | 0.655937i | \(-0.772274\pi\) | ||||
−0.754815 | + | 0.655937i | \(0.772274\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 11900.4i | 0.515265i | 0.966243 | + | 0.257632i | \(0.0829423\pi\) | ||||
−0.966243 | + | 0.257632i | \(0.917058\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 1513.77i | 0.0653017i | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −40050.3 | −1.72135 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 32252.9i | − | 1.38114i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 3854.64 | − | 4651.89i | 0.164459 | − | 0.198474i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 20274.1i | − | 0.861841i | −0.902390 | − | 0.430921i | \(-0.858189\pi\) | ||
0.902390 | − | 0.430921i | \(-0.141811\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | − | 11589.9i | − | 0.490887i | −0.969411 | − | 0.245443i | \(-0.921066\pi\) | ||
0.969411 | − | 0.245443i | \(-0.0789335\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | − | 35766.2i | − | 1.50936i | ||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −12796.5 | −0.538064 | −0.269032 | − | 0.963131i | \(-0.586704\pi\) | ||||
−0.269032 | + | 0.963131i | \(0.586704\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14976.8 | 0.627461 | 0.313730 | − | 0.949512i | \(-0.398421\pi\) | ||||
0.313730 | + | 0.949512i | \(0.398421\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 12441.1 | 0.519345 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 31075.5 | − | 5876.56i | 1.29256 | − | 0.244430i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16900.9 | 0.700453 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | − | 7136.25i | − | 0.294701i | ||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −2505.42 | −0.103095 | −0.0515476 | − | 0.998671i | \(-0.516415\pi\) | ||||
−0.0515476 | + | 0.998671i | \(0.516415\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 23078.3 | 0.946259 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 6056.25i | 0.247436i | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 18284.8 | 0.744396 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −2505.48 | + | 3023.69i | −0.101640 | + | 0.122663i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −150.795 | −0.00609572 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 23180.6 | 0.933751 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −28769.0 | −1.15479 | −0.577393 | − | 0.816467i | \(-0.695930\pi\) | ||||
−0.577393 | + | 0.816467i | \(0.695930\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | − | 16305.0i | − | 0.652184i | ||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 32617.6i | 1.30011i | 0.759887 | + | 0.650056i | \(0.225254\pi\) | ||||
−0.759887 | + | 0.650056i | \(0.774746\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 12072.8i | 0.479532i | 0.970831 | + | 0.239766i | \(0.0770708\pi\) | ||||
−0.970831 | + | 0.239766i | \(0.922929\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 11950.0 | − | 14421.7i | 0.473004 | − | 0.570835i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | − | 15773.6i | − | 0.622179i | −0.950381 | − | 0.311090i | \(-0.899306\pi\) | ||
0.950381 | − | 0.311090i | \(-0.100694\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −75435.8 | −2.96520 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 10766.2i | 0.421727i | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 17229.9i | 0.672594i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 16609.6 | 0.646148 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 5382.00i | 0.208652i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 43663.6 | − | 52694.5i | 1.68697 | − | 2.03589i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | − | 23431.2i | − | 0.902182i | −0.892478 | − | 0.451091i | \(-0.851035\pi\) | ||
0.892478 | − | 0.451091i | \(-0.148965\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 6743.95i | 0.258780i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 47521.7i | − | 1.81730i | −0.417554 | − | 0.908652i | \(-0.637113\pi\) | ||
0.417554 | − | 0.908652i | \(-0.362887\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −33236.8 | −1.26671 | −0.633357 | − | 0.773860i | \(-0.718324\pi\) | ||||
−0.633357 | + | 0.773860i | \(0.718324\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −11511.9 | −0.437251 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −16319.1 | −0.617746 | −0.308873 | − | 0.951103i | \(-0.599952\pi\) | ||||
−0.308873 | + | 0.951103i | \(0.599952\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −23112.1 | − | 19151.1i | −0.871940 | − | 0.722504i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 3181.80 | 0.119634 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 27539.6i | − | 1.03200i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 70708.3 | 2.64080 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −10981.1 | −0.408749 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 9568.77i | 0.354990i | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −10010.0 | −0.370123 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 15766.4 | + | 13064.3i | 0.581031 | + | 0.481453i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −72739.9 | −2.67178 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 40088.2 | 1.46759 | 0.733797 | − | 0.679369i | \(-0.237746\pi\) | ||||
0.733797 | + | 0.679369i | \(0.237746\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 12735.3 | 0.464691 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 47537.5i | 1.72885i | 0.502758 | + | 0.864427i | \(0.332319\pi\) | ||||
−0.502758 | + | 0.864427i | \(0.667681\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 28365.7i | 1.02822i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 10153.8i | 0.366856i | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −7176.39 | − | 5946.48i | −0.258435 | − | 0.214144i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 15740.2i | − | 0.564983i | −0.959270 | − | 0.282492i | \(-0.908839\pi\) | ||
0.959270 | − | 0.282492i | \(-0.0911610\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 5279.72 | 0.188896 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | − | 21186.1i | − | 0.755525i | ||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 69664.6i | 2.47628i | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 10249.7 | 0.363155 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 36693.6i | 1.29588i | 0.761689 | + | 0.647942i | \(0.224370\pi\) | ||||
−0.761689 | + | 0.647942i | \(0.775630\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −29496.0 | + | 5577.88i | −1.03834 | + | 0.196356i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 25551.3i | 0.896583i | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | − | 74975.3i | − | 2.62241i | ||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 31736.7i | − | 1.10650i | −0.833015 | − | 0.553251i | \(-0.813387\pi\) | ||
0.833015 | − | 0.553251i | \(-0.186613\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −30340.6 | −1.05445 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −24588.9 | −0.851835 | −0.425917 | − | 0.904762i | \(-0.640049\pi\) | ||||
−0.425917 | + | 0.904762i | \(0.640049\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −34043.3 | −1.17561 | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 7970.42 | + | 6604.43i | 0.274368 | + | 0.227346i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 6910.91 | 0.237143 | 0.118572 | − | 0.992946i | \(-0.462169\pi\) | ||||
0.118572 | + | 0.992946i | \(0.462169\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 39841.7i | 1.36282i | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −19533.0 | −0.666037 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4158.99 | 0.141367 | 0.0706835 | − | 0.997499i | \(-0.477482\pi\) | ||||
0.0706835 | + | 0.997499i | \(0.477482\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 63304.8i | − | 2.14502i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −4266.37 | −0.144109 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 6827.29 | − | 8239.38i | 0.229890 | − | 0.277438i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 40066.4 | 1.34492 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 13530.4 | 0.452765 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 39224.9 | 1.30849 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | − | 38144.8i | − | 1.26852i | −0.773121 | − | 0.634258i | \(-0.781306\pi\) | ||
0.773121 | − | 0.634258i | \(-0.218694\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 24208.8i | − | 0.802580i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 11358.8i | − | 0.375409i | −0.982226 | − | 0.187705i | \(-0.939895\pi\) | ||
0.982226 | − | 0.187705i | \(-0.0601048\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 5881.80 | + | 4873.76i | 0.193794 | + | 0.160581i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 33001.4i | − | 1.08399i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −18568.5 | −0.608043 | −0.304022 | − | 0.952665i | \(-0.598329\pi\) | ||||
−0.304022 | + | 0.952665i | \(0.598329\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | − | 17768.3i | − | 0.580059i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 3233.55i | − | 0.105239i | ||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −61176.0 | −1.98496 | −0.992479 | − | 0.122419i | \(-0.960935\pi\) | ||||
−0.992479 | + | 0.122419i | \(0.960935\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | − | 2267.86i | − | 0.0733606i | ||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 13462.3 | + | 11155.1i | 0.434154 | + | 0.359748i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 37217.5i | − | 1.19661i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 17776.3i | 0.569810i | 0.958556 | + | 0.284905i | \(0.0919621\pi\) | ||||
−0.958556 | + | 0.284905i | \(0.908038\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 6093.32i | 0.194729i | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 31582.7 | 1.00627 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 28772.7 | 0.913982 | 0.456991 | − | 0.889471i | \(-0.348927\pi\) | ||||
0.456991 | + | 0.889471i | \(0.348927\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −6197.43 | −0.196274 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 1344.4.p.d.223.13 | yes | 32 | |
4.3 | odd | 2 | inner | 1344.4.p.d.223.8 | yes | 32 | |
7.6 | odd | 2 | 1344.4.p.c.223.10 | yes | 32 | ||
8.3 | odd | 2 | 1344.4.p.c.223.9 | yes | 32 | ||
8.5 | even | 2 | 1344.4.p.c.223.6 | yes | 32 | ||
28.27 | even | 2 | 1344.4.p.c.223.5 | ✓ | 32 | ||
56.13 | odd | 2 | inner | 1344.4.p.d.223.7 | yes | 32 | |
56.27 | even | 2 | inner | 1344.4.p.d.223.14 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
1344.4.p.c.223.5 | ✓ | 32 | 28.27 | even | 2 | ||
1344.4.p.c.223.6 | yes | 32 | 8.5 | even | 2 | ||
1344.4.p.c.223.9 | yes | 32 | 8.3 | odd | 2 | ||
1344.4.p.c.223.10 | yes | 32 | 7.6 | odd | 2 | ||
1344.4.p.d.223.7 | yes | 32 | 56.13 | odd | 2 | inner | |
1344.4.p.d.223.8 | yes | 32 | 4.3 | odd | 2 | inner | |
1344.4.p.d.223.13 | yes | 32 | 1.1 | even | 1 | trivial | |
1344.4.p.d.223.14 | yes | 32 | 56.27 | even | 2 | inner |