Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [2736,2,Mod(1151,2736)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(2736, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([3, 0, 3, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("2736.1151");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 2736 = 2^{4} \cdot 3^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 2736.cg (of order \(6\), degree \(2\), 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: | \(21.8470699930\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 1151.5 | ||
Character | \(\chi\) | \(=\) | 2736.1151 |
Dual form | 2736.2.cg.a.2591.5 |
$q$-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 \(\left(\mathbb{Z}/2736\mathbb{Z}\right)^\times\).
\(n\) | \(1009\) | \(1217\) | \(1711\) | \(2053\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −1.02690 | − | 0.592883i | −0.459245 | − | 0.265145i | 0.252482 | − | 0.967602i | \(-0.418753\pi\) |
−0.711727 | + | 0.702456i | \(0.752087\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | − | 4.00663i | − | 1.51437i | −0.653203 | − | 0.757183i | \(-0.726575\pi\) | ||
0.653203 | − | 0.757183i | \(-0.273425\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.72120 | −1.12198 | −0.560992 | − | 0.827821i | \(-0.689580\pi\) | ||||
−0.560992 | + | 0.827821i | \(0.689580\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −0.163969 | − | 0.284003i | −0.0454768 | − | 0.0787681i | 0.842391 | − | 0.538867i | \(-0.181147\pi\) |
−0.887868 | + | 0.460099i | \(0.847814\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 2.92851 | + | 1.69078i | 0.710268 | + | 0.410073i | 0.811160 | − | 0.584824i | \(-0.198836\pi\) |
−0.100892 | + | 0.994897i | \(0.532170\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 3.68810 | − | 2.32335i | 0.846108 | − | 0.533012i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −1.20510 | − | 2.08730i | −0.251282 | − | 0.435232i | 0.712597 | − | 0.701573i | \(-0.247519\pi\) |
−0.963879 | + | 0.266341i | \(0.914185\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.79698 | − | 3.11246i | −0.359396 | − | 0.622492i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −0.884644 | + | 0.510749i | −0.164274 | + | 0.0948438i | −0.579883 | − | 0.814700i | \(-0.696902\pi\) |
0.415609 | + | 0.909543i | \(0.363568\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 0.252014i | − | 0.0452630i | −0.999744 | − | 0.0226315i | \(-0.992796\pi\) | ||
0.999744 | − | 0.0226315i | \(-0.00720445\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −2.37546 | + | 4.11443i | −0.401527 | + | 0.695465i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −2.26602 | −0.372532 | −0.186266 | − | 0.982499i | \(-0.559639\pi\) | ||||
−0.186266 | + | 0.982499i | \(0.559639\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.04391 | + | 3.48945i | 0.943900 | + | 0.544961i | 0.891181 | − | 0.453648i | \(-0.149878\pi\) |
0.0527193 | + | 0.998609i | \(0.483211\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.904236 | + | 0.522061i | 0.137895 | + | 0.0796135i | 0.567360 | − | 0.823470i | \(-0.307965\pi\) |
−0.429466 | + | 0.903083i | \(0.641298\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −3.48518 | − | 6.03651i | −0.508365 | − | 0.880515i | −0.999953 | − | 0.00968668i | \(-0.996917\pi\) |
0.491588 | − | 0.870828i | \(-0.336417\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −9.05312 | −1.29330 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −10.8125 | + | 6.24262i | −1.48522 | + | 0.857490i | −0.999858 | − | 0.0168248i | \(-0.994644\pi\) |
−0.485359 | + | 0.874315i | \(0.661311\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 3.82131 | + | 2.20623i | 0.515265 | + | 0.297489i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −0.581471 | + | 1.00714i | −0.0757010 | + | 0.131118i | −0.901391 | − | 0.433006i | \(-0.857453\pi\) |
0.825690 | + | 0.564124i | \(0.190786\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −4.11586 | − | 7.12888i | −0.526982 | − | 0.912759i | −0.999506 | − | 0.0314412i | \(-0.989990\pi\) |
0.472524 | − | 0.881318i | \(-0.343343\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.388857i | 0.0482318i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −8.16604 | + | 4.71466i | −0.997640 | + | 0.575988i | −0.907549 | − | 0.419946i | \(-0.862049\pi\) |
−0.0900911 | + | 0.995934i | \(0.528716\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −1.12392 | + | 1.94669i | −0.133385 | + | 0.231030i | −0.924979 | − | 0.380017i | \(-0.875918\pi\) |
0.791594 | + | 0.611047i | \(0.209251\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −1.05266 | + | 1.82325i | −0.123204 | + | 0.213395i | −0.921029 | − | 0.389493i | \(-0.872650\pi\) |
0.797826 | + | 0.602888i | \(0.205984\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 14.9095i | 1.69909i | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −5.56073 | − | 3.21049i | −0.625631 | − | 0.361208i | 0.153427 | − | 0.988160i | \(-0.450969\pi\) |
−0.779058 | + | 0.626952i | \(0.784302\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 5.14422 | 0.564651 | 0.282326 | − | 0.959319i | \(-0.408894\pi\) | ||||
0.282326 | + | 0.959319i | \(0.408894\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −2.00486 | − | 3.47253i | −0.217458 | − | 0.376648i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.86374 | + | 2.23073i | −0.409556 | + | 0.236457i | −0.690599 | − | 0.723238i | \(-0.742653\pi\) |
0.281043 | + | 0.959695i | \(0.409320\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.13789 | + | 0.656964i | −0.119284 | + | 0.0688685i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −5.16479 | + | 0.199241i | −0.529896 | + | 0.0204417i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −4.12733 | + | 7.14874i | −0.419066 | + | 0.725844i | −0.995846 | − | 0.0910556i | \(-0.970976\pi\) |
0.576779 | + | 0.816900i | \(0.304309\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −12.2411 | + | 7.06739i | −1.21803 | + | 0.703232i | −0.964497 | − | 0.264094i | \(-0.914927\pi\) |
−0.253537 | + | 0.967326i | \(0.581594\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 5.07024i | − | 0.499586i | −0.968299 | − | 0.249793i | \(-0.919637\pi\) | ||
0.968299 | − | 0.249793i | \(-0.0803626\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 0.864112 | 0.0835368 | 0.0417684 | − | 0.999127i | \(-0.486701\pi\) | ||||
0.0417684 | + | 0.999127i | \(0.486701\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −9.36177 | + | 16.2151i | −0.896695 | + | 1.55312i | −0.0650023 | + | 0.997885i | \(0.520705\pi\) |
−0.831693 | + | 0.555236i | \(0.812628\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 15.4626i | 1.45460i | 0.686320 | + | 0.727300i | \(0.259225\pi\) | ||||
−0.686320 | + | 0.727300i | \(0.740775\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 2.85794i | 0.266504i | ||||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 6.77432 | − | 11.7335i | 0.621001 | − | 1.07561i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.84732 | 0.258847 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 10.1904i | 0.911459i | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 13.0248 | − | 7.51987i | 1.15576 | − | 0.667281i | 0.205479 | − | 0.978662i | \(-0.434125\pi\) |
0.950285 | + | 0.311381i | \(0.100792\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −6.07702 | + | 10.5257i | −0.530952 | + | 0.919636i | 0.468396 | + | 0.883519i | \(0.344832\pi\) |
−0.999348 | + | 0.0361169i | \(0.988501\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −9.30880 | − | 14.7769i | −0.807175 | − | 1.28132i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 6.62454 | − | 3.82468i | 0.565973 | − | 0.326765i | −0.189567 | − | 0.981868i | \(-0.560708\pi\) |
0.755539 | + | 0.655103i | \(0.227375\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 6.50872 | − | 3.75781i | 0.552062 | − | 0.318733i | −0.197891 | − | 0.980224i | \(-0.563409\pi\) |
0.749953 | + | 0.661491i | \(0.230076\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.610161 | + | 1.05683i | 0.0510242 | + | 0.0883766i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.21126 | 0.100590 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −2.65727 | − | 1.53418i | −0.217692 | − | 0.125685i | 0.387189 | − | 0.922000i | \(-0.373446\pi\) |
−0.604881 | + | 0.796316i | \(0.706779\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 5.37855i | − | 0.437701i | −0.975758 | − | 0.218850i | \(-0.929769\pi\) | ||
0.975758 | − | 0.218850i | \(-0.0702306\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.149415 | + | 0.258794i | −0.0120013 | + | 0.0207868i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 3.92609 | − | 6.80019i | 0.313336 | − | 0.542714i | −0.665746 | − | 0.746178i | \(-0.731887\pi\) |
0.979082 | + | 0.203464i | \(0.0652200\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −8.36305 | + | 4.82841i | −0.659101 | + | 0.380532i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 11.0089i | − | 0.862286i | −0.902284 | − | 0.431143i | \(-0.858110\pi\) | ||
0.902284 | − | 0.431143i | \(-0.141890\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −10.7707 | − | 18.6555i | −0.833465 | − | 1.44360i | −0.895274 | − | 0.445516i | \(-0.853020\pi\) |
0.0618093 | − | 0.998088i | \(-0.480313\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.44623 | − | 11.1652i | 0.495864 | − | 0.858861i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 11.8493 | + | 6.84121i | 0.900888 | + | 0.520128i | 0.877488 | − | 0.479598i | \(-0.159218\pi\) |
0.0233997 | + | 0.999726i | \(0.492551\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −12.4705 | + | 7.19984i | −0.942681 | + | 0.544257i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −12.7209 | −0.950806 | −0.475403 | − | 0.879768i | \(-0.657698\pi\) | ||||
−0.475403 | + | 0.879768i | \(0.657698\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 2.80425 | + | 4.85711i | 0.208438 | + | 0.361026i | 0.951223 | − | 0.308505i | \(-0.0998286\pi\) |
−0.742784 | + | 0.669531i | \(0.766495\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 2.32699 | + | 1.34349i | 0.171083 | + | 0.0987750i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −10.8976 | − | 6.29171i | −0.796909 | − | 0.460096i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −15.3741 | −1.11243 | −0.556214 | − | 0.831039i | \(-0.687746\pi\) | ||||
−0.556214 | + | 0.831039i | \(0.687746\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −12.9663 | + | 22.4582i | −0.933332 | + | 1.61658i | −0.155749 | + | 0.987797i | \(0.549779\pi\) |
−0.777583 | + | 0.628781i | \(0.783554\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | − | 20.7134i | − | 1.47577i | −0.674929 | − | 0.737883i | \(-0.735826\pi\) | ||
0.674929 | − | 0.737883i | \(-0.264174\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 22.0917 | − | 12.7546i | 1.56604 | − | 0.904151i | 0.569412 | − | 0.822052i | \(-0.307171\pi\) |
0.996624 | − | 0.0820992i | \(-0.0261624\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 2.04639 | + | 3.54445i | 0.143628 | + | 0.248771i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.13767 | − | 7.16666i | −0.288988 | − | 0.500541i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −13.7241 | + | 8.64563i | −0.949319 | + | 0.598031i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −14.3841 | − | 8.30467i | −0.990243 | − | 0.571717i | −0.0848964 | − | 0.996390i | \(-0.527056\pi\) |
−0.905347 | + | 0.424672i | \(0.860389\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −0.619042 | − | 1.07221i | −0.0422183 | − | 0.0731242i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −1.00973 | −0.0685448 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | − | 1.10894i | − | 0.0745953i | ||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 10.1426 | + | 5.85583i | 0.679199 | + | 0.392136i | 0.799553 | − | 0.600595i | \(-0.205070\pi\) |
−0.120354 | + | 0.992731i | \(0.538403\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | −19.4717 | −1.29238 | −0.646191 | − | 0.763176i | \(-0.723639\pi\) | ||||
−0.646191 | + | 0.763176i | \(0.723639\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −1.42187 | −0.0939598 | −0.0469799 | − | 0.998896i | \(-0.514960\pi\) | ||||
−0.0469799 | + | 0.998896i | \(0.514960\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −12.8455 | − | 7.41633i | −0.841534 | − | 0.485860i | 0.0162514 | − | 0.999868i | \(-0.494827\pi\) |
−0.857785 | + | 0.514008i | \(0.828160\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 8.26521i | 0.539163i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −26.4103 | −1.70834 | −0.854169 | − | 0.519996i | \(-0.825933\pi\) | ||||
−0.854169 | + | 0.519996i | \(0.825933\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −9.04260 | − | 15.6622i | −0.582485 | − | 1.00889i | −0.995184 | − | 0.0980259i | \(-0.968747\pi\) |
0.412699 | − | 0.910867i | \(-0.364586\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 9.29668 | + | 5.36744i | 0.593943 | + | 0.342913i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −1.26457 | − | 0.666473i | −0.0804626 | − | 0.0424066i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 7.26539 | + | 12.5840i | 0.458588 | + | 0.794297i | 0.998887 | − | 0.0471760i | \(-0.0150222\pi\) |
−0.540299 | + | 0.841473i | \(0.681689\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 4.48443 | + | 7.76726i | 0.281934 | + | 0.488324i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 17.6815 | − | 10.2084i | 1.10294 | − | 0.636785i | 0.165951 | − | 0.986134i | \(-0.446931\pi\) |
0.936993 | + | 0.349349i | \(0.113597\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 9.07912i | 0.564149i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 0.386150 | − | 0.668831i | 0.0238110 | − | 0.0412419i | −0.853874 | − | 0.520479i | \(-0.825753\pi\) |
0.877685 | + | 0.479237i | \(0.159087\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 14.8046 | 0.909438 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 19.0019 | + | 10.9708i | 1.15857 | + | 0.668900i | 0.950960 | − | 0.309313i | \(-0.100099\pi\) |
0.207608 | + | 0.978212i | \(0.433432\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 2.24497 | + | 1.29614i | 0.136372 | + | 0.0787346i | 0.566634 | − | 0.823970i | \(-0.308245\pi\) |
−0.430262 | + | 0.902704i | \(0.641579\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 6.68692 | + | 11.5821i | 0.403236 | + | 0.698426i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −8.39074 | −0.504151 | −0.252075 | − | 0.967708i | \(-0.581113\pi\) | ||||
−0.252075 | + | 0.967708i | \(0.581113\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −16.4751 | + | 9.51188i | −0.982820 | + | 0.567431i | −0.903120 | − | 0.429388i | \(-0.858729\pi\) |
−0.0796995 | + | 0.996819i | \(0.525396\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 7.56151 | + | 4.36564i | 0.449485 | + | 0.259510i | 0.707613 | − | 0.706600i | \(-0.249772\pi\) |
−0.258128 | + | 0.966111i | \(0.583105\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 13.9810 | − | 24.2157i | 0.825270 | − | 1.42941i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −2.78255 | − | 4.81953i | −0.163680 | − | 0.283502i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 19.9108i | − | 1.16320i | −0.813475 | − | 0.581600i | \(-0.802427\pi\) | ||
0.813475 | − | 0.581600i | \(-0.197573\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 1.19423 | − | 0.689488i | 0.0695306 | − | 0.0401435i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −0.395199 | + | 0.684505i | −0.0228550 | + | 0.0395860i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2.09171 | − | 3.62294i | 0.120564 | − | 0.208823i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 9.76089i | 0.558907i | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −9.99756 | − | 5.77209i | −0.570591 | − | 0.329431i | 0.186794 | − | 0.982399i | \(-0.440190\pi\) |
−0.757385 | + | 0.652968i | \(0.773524\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 28.9643 | 1.64241 | 0.821207 | − | 0.570630i | \(-0.193301\pi\) | ||||
0.821207 | + | 0.570630i | \(0.193301\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −9.67318 | − | 16.7544i | −0.546760 | − | 0.947016i | −0.998494 | − | 0.0548636i | \(-0.982528\pi\) |
0.451734 | − | 0.892153i | \(-0.350806\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 18.5107 | − | 10.6871i | 1.03966 | − | 0.600249i | 0.119925 | − | 0.992783i | \(-0.461735\pi\) |
0.919738 | + | 0.392534i | \(0.128401\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.29194 | − | 1.90060i | 0.184313 | − | 0.106413i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 14.7289 | − | 0.568193i | 0.819537 | − | 0.0316151i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −0.589298 | + | 1.02069i | −0.0326884 | + | 0.0566179i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −24.1861 | + | 13.9638i | −1.33342 | + | 0.769851i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 18.2194i | 1.00143i | 0.865612 | + | 0.500715i | \(0.166930\pi\) | ||||
−0.865612 | + | 0.500715i | \(0.833070\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 11.1810 | 0.610882 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −11.5971 | + | 20.0867i | −0.631732 | + | 1.09419i | 0.355465 | + | 0.934689i | \(0.384322\pi\) |
−0.987197 | + | 0.159503i | \(0.949011\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 0.937794i | 0.0507844i | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 8.22611i | 0.444168i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 6.15774 | − | 10.6655i | 0.330565 | − | 0.572555i | −0.652058 | − | 0.758169i | \(-0.726094\pi\) |
0.982623 | + | 0.185614i | \(0.0594274\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 9.44133 | 0.505383 | 0.252691 | − | 0.967547i | \(-0.418684\pi\) | ||||
0.252691 | + | 0.967547i | \(0.418684\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | − | 4.93946i | − | 0.262901i | −0.991323 | − | 0.131451i | \(-0.958037\pi\) | ||
0.991323 | − | 0.131451i | \(-0.0419635\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 2.30832 | − | 1.33271i | 0.122513 | − | 0.0707329i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −0.994398 | + | 1.72235i | −0.0524823 | + | 0.0909020i | −0.891073 | − | 0.453860i | \(-0.850047\pi\) |
0.838591 | + | 0.544762i | \(0.183380\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 8.20413 | − | 17.1375i | 0.431796 | − | 0.901971i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 2.16195 | − | 1.24820i | 0.113162 | − | 0.0653339i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 10.0985 | − | 5.83036i | 0.527136 | − | 0.304342i | −0.212713 | − | 0.977115i | \(-0.568230\pi\) |
0.739850 | + | 0.672772i | \(0.234897\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 25.0119 | + | 43.3219i | 1.29855 | + | 2.24916i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 27.9319 | 1.44626 | 0.723129 | − | 0.690713i | \(-0.242703\pi\) | ||||
0.723129 | + | 0.690713i | \(0.242703\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 0.290108 | + | 0.167494i | 0.0149413 | + | 0.00862638i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 5.72714i | 0.294183i | 0.989123 | + | 0.147092i | \(0.0469913\pi\) | ||||
−0.989123 | + | 0.147092i | \(0.953009\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −4.59417 | + | 7.95733i | −0.234751 | + | 0.406601i | −0.959200 | − | 0.282728i | \(-0.908761\pi\) |
0.724449 | + | 0.689328i | \(0.242094\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 8.83958 | − | 15.3106i | 0.450507 | − | 0.780300i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 6.09499 | − | 3.51894i | 0.309028 | − | 0.178418i | −0.337463 | − | 0.941339i | \(-0.609569\pi\) |
0.646492 | + | 0.762921i | \(0.276236\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 8.15024i | − | 0.412175i | ||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 3.80689 | + | 6.59373i | 0.191545 | + | 0.331766i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −10.2252 | + | 17.7106i | −0.513188 | + | 0.888868i | 0.486695 | + | 0.873572i | \(0.338202\pi\) |
−0.999883 | + | 0.0152962i | \(0.995131\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 15.8453 | + | 9.14827i | 0.791275 | + | 0.456843i | 0.840411 | − | 0.541949i | \(-0.182314\pi\) |
−0.0491363 | + | 0.998792i | \(0.515647\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −0.0715726 | + | 0.0413224i | −0.00356528 | + | 0.00205842i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.43232 | 0.417974 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.49657 | + | 4.32418i | 0.123447 | + | 0.213817i | 0.921125 | − | 0.389267i | \(-0.127272\pi\) |
−0.797678 | + | 0.603084i | \(0.793938\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 4.03523 | + | 2.32974i | 0.198561 | + | 0.114639i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −5.28261 | − | 3.04992i | −0.259313 | − | 0.149715i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 32.8318 | 1.60394 | 0.801970 | − | 0.597364i | \(-0.203785\pi\) | ||||
0.801970 | + | 0.597364i | \(0.203785\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −3.85236 | + | 6.67249i | −0.187753 | + | 0.325197i | −0.944501 | − | 0.328510i | \(-0.893454\pi\) |
0.756748 | + | 0.653707i | \(0.226787\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 12.1532i | − | 0.589515i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −28.5628 | + | 16.4907i | −1.38225 | + | 0.798043i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −12.3923 | − | 21.4640i | −0.596915 | − | 1.03389i | −0.993274 | − | 0.115791i | \(-0.963060\pi\) |
0.396359 | − | 0.918096i | \(-0.370274\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 2.32776 | + | 4.03180i | 0.111865 | + | 0.193756i | 0.916522 | − | 0.399984i | \(-0.130984\pi\) |
−0.804657 | + | 0.593740i | \(0.797651\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −9.29406 | − | 4.89830i | −0.444595 | − | 0.234317i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 21.7426 | + | 12.5531i | 1.03772 | + | 0.599125i | 0.919185 | − | 0.393825i | \(-0.128848\pi\) |
0.118530 | + | 0.992950i | \(0.462182\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 5.10222 | + | 8.83731i | 0.242414 | + | 0.419873i | 0.961401 | − | 0.275150i | \(-0.0887275\pi\) |
−0.718987 | + | 0.695023i | \(0.755394\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 5.29025 | 0.250782 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 32.5901i | − | 1.53802i | −0.639236 | − | 0.769011i | \(-0.720749\pi\) | ||
0.639236 | − | 0.769011i | \(-0.279251\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −22.4906 | − | 12.9849i | −1.05904 | − | 0.611437i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 1.55801 | 0.0730406 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 2.39243 | 0.111913 | 0.0559566 | − | 0.998433i | \(-0.482179\pi\) | ||||
0.0559566 | + | 0.998433i | \(0.482179\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −24.6438 | − | 14.2281i | −1.14778 | − | 0.662669i | −0.199432 | − | 0.979912i | \(-0.563910\pi\) |
−0.948344 | + | 0.317242i | \(0.897243\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | − | 2.85291i | − | 0.132586i | −0.997800 | − | 0.0662929i | \(-0.978883\pi\) | ||
0.997800 | − | 0.0662929i | \(-0.0211172\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −18.1140 | −0.838217 | −0.419109 | − | 0.907936i | \(-0.637657\pi\) | ||||
−0.419109 | + | 0.907936i | \(0.637657\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 18.8899 | + | 32.7183i | 0.872256 | + | 1.51079i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −3.36484 | − | 1.94269i | −0.154715 | − | 0.0893250i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −13.8588 | − | 7.30405i | −0.635883 | − | 0.335133i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −6.95305 | − | 12.0430i | −0.317693 | − | 0.550260i | 0.662313 | − | 0.749227i | \(-0.269575\pi\) |
−0.980006 | + | 0.198967i | \(0.936241\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0.371557 | + | 0.643556i | 0.0169416 | + | 0.0293436i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 8.47673 | − | 4.89404i | 0.384908 | − | 0.222227i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 39.0698i | 1.77042i | 0.465189 | + | 0.885211i | \(0.345986\pi\) | ||||
−0.465189 | + | 0.885211i | \(0.654014\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −10.3322 | + | 17.8958i | −0.466284 | + | 0.807627i | −0.999258 | − | 0.0385040i | \(-0.987741\pi\) |
0.532975 | + | 0.846131i | \(0.321074\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −3.45425 | −0.155572 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 7.79969 | + | 4.50315i | 0.349864 | + | 0.201994i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 6.02993 | + | 3.48138i | 0.269937 | + | 0.155848i | 0.628859 | − | 0.777519i | \(-0.283522\pi\) |
−0.358922 | + | 0.933367i | \(0.616856\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −18.7543 | − | 32.4835i | −0.836215 | − | 1.44837i | −0.893038 | − | 0.449982i | \(-0.851430\pi\) |
0.0568230 | − | 0.998384i | \(-0.481903\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 16.7605 | 0.745835 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −17.9508 | + | 10.3639i | −0.795655 | + | 0.459372i | −0.841950 | − | 0.539556i | \(-0.818592\pi\) |
0.0462946 | + | 0.998928i | \(0.485259\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 7.30510 | + | 4.21760i | 0.323159 | + | 0.186576i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.00606 | + | 5.20665i | −0.132463 | + | 0.229432i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 12.9690 | + | 22.4630i | 0.570378 | + | 0.987923i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 38.8104i | − | 1.70032i | −0.526528 | − | 0.850158i | \(-0.676506\pi\) | ||
0.526528 | − | 0.850158i | \(-0.323494\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −30.8774 | + | 17.8271i | −1.35017 | + | 0.779524i | −0.988274 | − | 0.152693i | \(-0.951206\pi\) |
−0.361901 | + | 0.932217i | \(0.617872\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0.426099 | − | 0.738025i | 0.0185612 | − | 0.0321489i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 8.59545 | − | 14.8878i | 0.373715 | − | 0.647294i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | − | 2.28865i | − | 0.0991323i | ||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −0.887359 | − | 0.512317i | −0.0383639 | − | 0.0221494i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 33.6885 | 1.45106 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 1.71812 | + | 2.97586i | 0.0738676 | + | 0.127942i | 0.900593 | − | 0.434663i | \(-0.143132\pi\) |
−0.826726 | + | 0.562605i | \(0.809799\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 19.2273 | − | 11.1009i | 0.823606 | − | 0.475509i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 23.6262 | − | 13.6406i | 1.01018 | − | 0.583229i | 0.0989378 | − | 0.995094i | \(-0.468456\pi\) |
0.911245 | + | 0.411864i | \(0.135122\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −2.07601 | + | 3.93903i | −0.0884408 | + | 0.167808i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −12.8633 | + | 22.2798i | −0.547002 | + | 0.947434i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 22.4498 | − | 12.9614i | 0.951230 | − | 0.549193i | 0.0577675 | − | 0.998330i | \(-0.481602\pi\) |
0.893463 | + | 0.449137i | \(0.148268\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 0.342407i | − | 0.0144823i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −10.0390 | −0.423092 | −0.211546 | − | 0.977368i | \(-0.567850\pi\) | ||||
−0.211546 | + | 0.977368i | \(0.567850\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 9.16751 | − | 15.8786i | 0.385680 | − | 0.668018i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 44.2910i | − | 1.85678i | −0.371613 | − | 0.928388i | \(-0.621195\pi\) | ||
0.371613 | − | 0.928388i | \(-0.378805\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 37.2489i | 1.55882i | 0.626516 | + | 0.779409i | \(0.284480\pi\) | ||||
−0.626516 | + | 0.779409i | \(0.715520\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −4.33109 | + | 7.50168i | −0.180619 | + | 0.312842i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 38.2192 | 1.59109 | 0.795544 | − | 0.605896i | \(-0.207185\pi\) | ||||
0.795544 | + | 0.605896i | \(0.207185\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | − | 20.6110i | − | 0.855088i | ||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 40.2356 | − | 23.2300i | 1.66639 | − | 0.962090i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 17.3490 | − | 30.0493i | 0.716069 | − | 1.24027i | −0.246477 | − | 0.969149i | \(-0.579273\pi\) |
0.962546 | − | 0.271119i | \(-0.0873935\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −0.585515 | − | 0.929452i | −0.0241257 | − | 0.0382974i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 5.97148 | − | 3.44763i | 0.245219 | − | 0.141577i | −0.372354 | − | 0.928091i | \(-0.621449\pi\) |
0.617573 | + | 0.786513i | \(0.288116\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −13.9131 | + | 8.03276i | −0.570383 | + | 0.329311i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −9.70202 | − | 16.8044i | −0.396414 | − | 0.686609i | 0.596867 | − | 0.802340i | \(-0.296412\pi\) |
−0.993281 | + | 0.115731i | \(0.963079\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 1.22714 | 0.0500559 | 0.0250279 | − | 0.999687i | \(-0.492033\pi\) | ||||
0.0250279 | + | 0.999687i | \(0.492033\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2.92392 | − | 1.68813i | −0.118874 | − | 0.0686321i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 2.35663i | − | 0.0956528i | −0.998856 | − | 0.0478264i | \(-0.984771\pi\) | ||
0.998856 | − | 0.0478264i | \(-0.0152294\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −1.14292 | + | 1.97960i | −0.0462377 | + | 0.0800860i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 8.89335 | − | 15.4037i | 0.359199 | − | 0.622151i | −0.628628 | − | 0.777706i | \(-0.716383\pi\) |
0.987827 | + | 0.155555i | \(0.0497166\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 20.1208 | − | 11.6168i | 0.810034 | − | 0.467673i | −0.0369339 | − | 0.999318i | \(-0.511759\pi\) |
0.846968 | + | 0.531645i | \(0.178426\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 36.7083i | − | 1.47543i | −0.675112 | − | 0.737715i | \(-0.735905\pi\) | ||
0.675112 | − | 0.737715i | \(-0.264095\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 8.93773 | + | 15.4806i | 0.358083 | + | 0.620217i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −2.94317 | + | 5.09773i | −0.117727 | + | 0.203909i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6.63607 | − | 3.83133i | −0.264597 | − | 0.152765i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −22.1565 | + | 12.7921i | −0.882038 | + | 0.509245i | −0.871330 | − | 0.490698i | \(-0.836742\pi\) |
−0.0107083 | + | 0.999943i | \(0.503409\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −17.8336 | −0.707705 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1.48443 | + | 2.57111i | 0.0588153 | + | 0.101871i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 1.03785 | + | 0.599206i | 0.0409928 | + | 0.0236672i | 0.520356 | − | 0.853949i | \(-0.325799\pi\) |
−0.479364 | + | 0.877616i | \(0.659132\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −28.2815 | − | 16.3283i | −1.11531 | − | 0.643926i | −0.175112 | − | 0.984548i | \(-0.556029\pi\) |
−0.940200 | + | 0.340623i | \(0.889362\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 7.82161 | 0.307499 | 0.153750 | − | 0.988110i | \(-0.450865\pi\) | ||||
0.153750 | + | 0.988110i | \(0.450865\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 2.16377 | − | 3.74775i | 0.0849353 | − | 0.147112i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | − | 27.7018i | − | 1.08405i | −0.840361 | − | 0.542027i | \(-0.817657\pi\) | ||
0.840361 | − | 0.542027i | \(-0.182343\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 12.4810 | − | 7.20592i | 0.487674 | − | 0.281559i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −0.927195 | − | 1.60595i | −0.0361184 | − | 0.0625589i | 0.847401 | − | 0.530953i | \(-0.178166\pi\) |
−0.883520 | + | 0.468394i | \(0.844833\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 9.79648 | + | 16.9680i | 0.381039 | + | 0.659979i | 0.991211 | − | 0.132290i | \(-0.0422331\pi\) |
−0.610172 | + | 0.792269i | \(0.708900\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0.798286 | + | 20.6934i | 0.0309562 | + | 0.802457i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 2.13218 | + | 1.23101i | 0.0825582 | + | 0.0476650i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 15.3159 | + | 26.5280i | 0.591265 | + | 1.02410i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 29.6231 | 1.14189 | 0.570944 | − | 0.820989i | \(-0.306577\pi\) | ||||
0.570944 | + | 0.820989i | \(0.306577\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 1.81662i | 0.0698184i | 0.999390 | + | 0.0349092i | \(0.0111142\pi\) | ||||
−0.999390 | + | 0.0349092i | \(0.988886\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 28.6424 | + | 16.5367i | 1.09919 | + | 0.634620i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −21.5025 | −0.822772 | −0.411386 | − | 0.911461i | \(-0.634955\pi\) | ||||
−0.411386 | + | 0.911461i | \(0.634955\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −9.07035 | −0.346560 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 3.54584 | + | 2.04719i | 0.135086 | + | 0.0779918i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 7.92674i | − | 0.301547i | −0.988568 | − | 0.150774i | \(-0.951824\pi\) | ||
0.988568 | − | 0.150774i | \(-0.0481765\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −8.91176 | −0.338042 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 11.7998 | + | 20.4378i | 0.446948 | + | 0.774136i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −11.1463 | − | 6.43532i | −0.420990 | − | 0.243059i | 0.274511 | − | 0.961584i | \(-0.411484\pi\) |
−0.695501 | + | 0.718525i | \(0.744817\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −8.35731 | + | 5.26475i | −0.315202 | + | 0.198564i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 28.3165 | + | 49.0456i | 1.06495 | + | 1.84455i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.4038 | − | 38.8046i | −0.841394 | − | 1.45734i | −0.888716 | − | 0.458458i | \(-0.848402\pi\) |
0.0473221 | − | 0.998880i | \(-0.484931\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −0.526029 | + | 0.303703i | −0.0196999 | + | 0.0113738i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | − | 1.44702i | − | 0.0541153i | ||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −2.72709 | + | 4.72347i | −0.101703 | + | 0.176156i | −0.912387 | − | 0.409330i | \(-0.865763\pi\) |
0.810683 | + | 0.585485i | \(0.199096\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −20.3146 | −0.756556 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 3.17937 | + | 1.83561i | 0.118079 | + | 0.0681730i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.44349 | + | 1.98810i | 0.127712 | + | 0.0737346i | 0.562495 | − | 0.826801i | \(-0.309842\pi\) |
−0.434783 | + | 0.900535i | \(0.643175\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 1.76537 | + | 3.05772i | 0.0652947 | + | 0.113094i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 29.8710 | 1.10331 | 0.551654 | − | 0.834073i | \(-0.313997\pi\) | ||||
0.551654 | + | 0.834073i | \(0.313997\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 30.3874 | − | 17.5442i | 1.11934 | − | 0.646249i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −29.3695 | − | 16.9565i | −1.08038 | − | 0.623755i | −0.149378 | − | 0.988780i | \(-0.547727\pi\) |
−0.930998 | + | 0.365025i | \(0.881060\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 21.8637 | − | 37.8690i | 0.802100 | − | 1.38928i | −0.116131 | − | 0.993234i | \(-0.537049\pi\) |
0.918231 | − | 0.396045i | \(-0.129617\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 1.81917 | + | 3.15090i | 0.0666494 | + | 0.115440i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0 | 0 | ||||||||
\(749\) | − | 3.46218i | − | 0.126505i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −21.6246 | + | 12.4850i | −0.789092 | + | 0.455583i | −0.839643 | − | 0.543139i | \(-0.817236\pi\) |
0.0505507 | + | 0.998721i | \(0.483902\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −3.18885 | + | 5.52325i | −0.116054 | + | 0.201012i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 14.5980 | − | 25.2844i | 0.530572 | − | 0.918977i | −0.468792 | − | 0.883309i | \(-0.655311\pi\) |
0.999364 | − | 0.0356686i | \(-0.0113561\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 2.01476i | − | 0.0730351i | −0.999333 | − | 0.0365176i | \(-0.988374\pi\) | ||
0.999333 | − | 0.0365176i | \(-0.0116265\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 64.9678 | + | 37.5092i | 2.35199 | + | 1.35792i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 0.381372 | 0.0137706 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.5009 | + | 37.2407i | 0.775343 | + | 1.34293i | 0.934601 | + | 0.355697i | \(0.115757\pi\) |
−0.159258 | + | 0.987237i | \(0.550910\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −15.8967 | + | 9.17794i | −0.571763 | + | 0.330107i | −0.757853 | − | 0.652425i | \(-0.773752\pi\) |
0.186090 | + | 0.982533i | \(0.440418\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.784383 | + | 0.452864i | −0.0281759 | + | 0.0162674i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 30.3977 | − | 1.17265i | 1.08911 | − | 0.0420144i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 4.18234 | − | 7.24403i | 0.149656 | − | 0.259212i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −8.06343 | + | 4.65542i | −0.287796 | + | 0.166159i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | − | 5.84314i | − | 0.208286i | −0.994562 | − | 0.104143i | \(-0.966790\pi\) | ||
0.994562 | − | 0.104143i | \(-0.0332099\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 61.9530 | 2.20280 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −1.34975 | + | 2.33783i | −0.0479309 | + | 0.0830187i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 0 | 0 | ||||||||
\(797\) | − | 12.6541i | − | 0.448231i | −0.974563 | − | 0.224115i | \(-0.928051\pi\) | ||
0.974563 | − | 0.224115i | \(-0.0719493\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 23.5706i | − | 0.833868i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 3.91714 | − | 6.78468i | 0.138233 | − | 0.239426i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 11.4507 | 0.403585 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 7.52049i | − | 0.264406i | −0.991223 | − | 0.132203i | \(-0.957795\pi\) | ||
0.991223 | − | 0.132203i | \(-0.0422051\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −20.3422 | + | 11.7446i | −0.714313 | + | 0.412409i | −0.812656 | − | 0.582744i | \(-0.801979\pi\) |
0.0983431 | + | 0.995153i | \(0.468646\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −6.52701 | + | 11.3051i | −0.228631 | + | 0.396001i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 4.54784 | − | 0.175441i | 0.159109 | − | 0.00613790i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −5.32878 | + | 3.07657i | −0.185976 | + | 0.107373i | −0.590097 | − | 0.807332i | \(-0.700911\pi\) |
0.404122 | + | 0.914705i | \(0.367577\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 0.640832 | − | 0.369984i | 0.0223380 | − | 0.0128968i | −0.488789 | − | 0.872402i | \(-0.662561\pi\) |
0.511127 | + | 0.859505i | \(0.329228\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 25.3235 | + | 43.8616i | 0.880584 | + | 1.52522i | 0.850692 | + | 0.525664i | \(0.176183\pi\) |
0.0298920 | + | 0.999553i | \(0.490484\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −39.2083 | −1.36176 | −0.680880 | − | 0.732395i | \(-0.738402\pi\) | ||||
−0.680880 | + | 0.732395i | \(0.738402\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −26.5122 | − | 15.3068i | −0.918592 | − | 0.530349i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 25.5431i | 0.883957i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 13.0620 | − | 22.6241i | 0.450952 | − | 0.781071i | −0.547494 | − | 0.836810i | \(-0.684418\pi\) |
0.998445 | + | 0.0557387i | \(0.0177514\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −13.9783 | + | 24.2111i | −0.482009 | + | 0.834865i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −13.2393 | + | 7.64372i | −0.455446 | + | 0.262952i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 11.4082i | − | 0.391989i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.73079 | + | 4.72987i | 0.0936103 | + | 0.162138i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 9.06915 | − | 15.7082i | 0.310522 | − | 0.537840i | −0.667954 | − | 0.744203i | \(-0.732830\pi\) |
0.978475 | + | 0.206363i | \(0.0661629\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 45.3247 | + | 26.1683i | 1.54826 | + | 0.893890i | 0.998275 | + | 0.0587185i | \(0.0187014\pi\) |
0.549989 | + | 0.835172i | \(0.314632\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 1.74572 | − | 1.00789i | 0.0595633 | − | 0.0343889i | −0.469923 | − | 0.882708i | \(-0.655718\pi\) |
0.529486 | + | 0.848319i | \(0.322385\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | −28.2094 | −0.960260 | −0.480130 | − | 0.877197i | \(-0.659410\pi\) | ||||
−0.480130 | + | 0.877197i | \(0.659410\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.11208 | − | 14.0505i | −0.275819 | − | 0.477732i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 20.6926 | + | 11.9469i | 0.701948 | + | 0.405270i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.67795 | + | 1.54612i | 0.0907390 | + | 0.0523882i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 40.8293 | 1.38028 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 1.82642 | − | 3.16346i | 0.0616739 | − | 0.106822i | −0.833540 | − | 0.552459i | \(-0.813689\pi\) |
0.895214 | + | 0.445637i | \(0.147023\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 42.7712i | 1.44100i | 0.693456 | + | 0.720499i | \(0.256087\pi\) | ||||
−0.693456 | + | 0.720499i | \(0.743913\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −22.5134 | + | 12.9981i | −0.757636 | + | 0.437421i | −0.828446 | − | 0.560068i | \(-0.810775\pi\) |
0.0708104 | + | 0.997490i | \(0.477441\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −21.7353 | − | 37.6467i | −0.729801 | − | 1.26405i | −0.956967 | − | 0.290197i | \(-0.906279\pi\) |
0.227166 | − | 0.973856i | \(-0.427054\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −30.1294 | − | 52.1856i | −1.01051 | − | 1.75025i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −26.8786 | − | 14.1659i | −0.899457 | − | 0.474045i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 13.0632 | + | 7.54201i | 0.436653 | + | 0.252102i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 0.128716 | + | 0.222943i | 0.00429292 | + | 0.00743555i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −42.2195 | −1.40654 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | − | 6.65037i | − | 0.221066i | ||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 29.1447 | + | 16.8267i | 0.967735 | + | 0.558722i | 0.898545 | − | 0.438881i | \(-0.144625\pi\) |
0.0691900 | + | 0.997603i | \(0.477959\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −0.923995 | −0.0306133 | −0.0153067 | − | 0.999883i | \(-0.504872\pi\) | ||||
−0.0153067 | + | 0.999883i | \(0.504872\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −19.1426 | −0.633529 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 42.1727 | + | 24.3484i | 1.39266 | + | 0.804055i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 43.4679i | 1.43387i | 0.697138 | + | 0.716937i | \(0.254456\pi\) | ||||
−0.697138 | + | 0.716937i | \(0.745544\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 0.737154 | 0.0242637 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 4.07200 | + | 7.05290i | 0.133886 | + | 0.231898i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −9.17871 | − | 5.29933i | −0.301144 | − | 0.173865i | 0.341813 | − | 0.939768i | \(-0.388959\pi\) |
−0.642957 | + | 0.765903i | \(0.722292\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −33.3888 | + | 21.0335i | −1.09427 | + | 0.689346i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 7.46050 | + | 12.9220i | 0.243984 | + | 0.422593i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 23.4364 | + | 40.5930i | 0.765632 | + | 1.32611i | 0.939912 | + | 0.341418i | \(0.110907\pi\) |
−0.174279 | + | 0.984696i | \(0.555760\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −27.0848 | + | 15.6374i | −0.882941 | + | 0.509766i | −0.871627 | − | 0.490170i | \(-0.836935\pi\) |
−0.0113138 | + | 0.999936i | \(0.503601\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 16.8206i | − | 0.547754i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −25.5392 | + | 44.2352i | −0.829913 | + | 1.43745i | 0.0681937 | + | 0.997672i | \(0.478276\pi\) |
−0.898106 | + | 0.439779i | \(0.855057\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 0.690411 | 0.0224117 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 16.1394 | + | 9.31810i | 0.522807 | + | 0.301843i | 0.738082 | − | 0.674711i | \(-0.235732\pi\) |
−0.215275 | + | 0.976553i | \(0.569065\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 15.7877 | + | 9.11501i | 0.510877 | + | 0.294955i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −15.3241 | − | 26.5421i | −0.494841 | − | 0.857090i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 30.9365 | 0.997951 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 26.6302 | − | 15.3749i | 0.857256 | − | 0.494937i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −10.3838 | − | 5.99509i | −0.333920 | − | 0.192789i | 0.323660 | − | 0.946173i | \(-0.395087\pi\) |
−0.657580 | + | 0.753384i | \(0.728420\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 16.1961 | − | 28.0524i | 0.519757 | − | 0.900245i | −0.479980 | − | 0.877280i | \(-0.659356\pi\) |
0.999736 | − | 0.0229653i | \(-0.00731072\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −15.0562 | − | 26.0781i | −0.482679 | − | 0.836024i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 8.73136i | − | 0.279341i | −0.990198 | − | 0.139671i | \(-0.955396\pi\) | ||
0.990198 | − | 0.139671i | \(-0.0446043\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 14.3777 | − | 8.30100i | 0.459515 | − | 0.265301i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 12.5732 | − | 21.7774i | 0.401022 | − | 0.694591i | −0.592827 | − | 0.805329i | \(-0.701988\pi\) |
0.993850 | + | 0.110739i | \(0.0353217\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −12.2806 | + | 21.2706i | −0.391292 | + | 0.677738i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 2.51655i | − | 0.0800216i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −22.4616 | − | 12.9682i | −0.713518 | − | 0.411950i | 0.0988446 | − | 0.995103i | \(-0.468485\pi\) |
−0.812362 | + | 0.583153i | \(0.801819\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −30.2480 | −0.958926 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.44201 | − | 7.69378i | −0.140680 | − | 0.243664i | 0.787073 | − | 0.616860i | \(-0.211595\pi\) |
−0.927753 | + | 0.373195i | \(0.878262\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 0 | 0 |
(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 | 2736.2.cg.a.1151.5 | ✓ | 24 | |
3.2 | odd | 2 | inner | 2736.2.cg.a.1151.8 | yes | 24 | |
4.3 | odd | 2 | 2736.2.cg.b.1151.5 | yes | 24 | ||
12.11 | even | 2 | 2736.2.cg.b.1151.8 | yes | 24 | ||
19.7 | even | 3 | 2736.2.cg.b.2591.8 | yes | 24 | ||
57.26 | odd | 6 | 2736.2.cg.b.2591.5 | yes | 24 | ||
76.7 | odd | 6 | inner | 2736.2.cg.a.2591.8 | yes | 24 | |
228.83 | even | 6 | inner | 2736.2.cg.a.2591.5 | yes | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
2736.2.cg.a.1151.5 | ✓ | 24 | 1.1 | even | 1 | trivial | |
2736.2.cg.a.1151.8 | yes | 24 | 3.2 | odd | 2 | inner | |
2736.2.cg.a.2591.5 | yes | 24 | 228.83 | even | 6 | inner | |
2736.2.cg.a.2591.8 | yes | 24 | 76.7 | odd | 6 | inner | |
2736.2.cg.b.1151.5 | yes | 24 | 4.3 | odd | 2 | ||
2736.2.cg.b.1151.8 | yes | 24 | 12.11 | even | 2 | ||
2736.2.cg.b.2591.5 | yes | 24 | 57.26 | odd | 6 | ||
2736.2.cg.b.2591.8 | yes | 24 | 19.7 | even | 3 |