Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [128,3,Mod(31,128)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(128, base_ring=CyclotomicField(4))
chi = DirichletCharacter(H, H._module([2, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("128.31");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 128 = 2^{7} \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 128.f (of order \(4\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(3.48774738381\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(i)\) |
Coefficient field: | 6.0.399424.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 2x^{5} + 3x^{4} - 6x^{3} + 6x^{2} - 8x + 8 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{9}]\) |
Coefficient ring index: | \( 2^{6} \) |
Twist minimal: | no (minimal twist has level 16) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{4}]$ |
Embedding invariants
Embedding label | 95.3 | ||
Root | \(0.264658 - 1.38923i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 128.95 |
Dual form | 128.3.f.b.31.3 |
$q$-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 \(\left(\mathbb{Z}/128\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(127\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(-1\) |
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 | ||||||||
\(3\) | 3.24914 | − | 3.24914i | 1.08305 | − | 1.08305i | 0.0868231 | − | 0.996224i | \(-0.472329\pi\) |
0.996224 | − | 0.0868231i | \(-0.0276715\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 0.0586332 | − | 0.0586332i | 0.0117266 | − | 0.0117266i | −0.701219 | − | 0.712946i | \(-0.747361\pi\) |
0.712946 | + | 0.701219i | \(0.247361\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 4.61555 | 0.659364 | 0.329682 | − | 0.944092i | \(-0.393058\pi\) | ||||
0.329682 | + | 0.944092i | \(0.393058\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | − | 12.1138i | − | 1.34598i | ||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 5.36641 | + | 5.36641i | 0.487855 | + | 0.487855i | 0.907629 | − | 0.419774i | \(-0.137891\pi\) |
−0.419774 | + | 0.907629i | \(0.637891\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −11.0552 | − | 11.0552i | −0.850400 | − | 0.850400i | 0.139783 | − | 0.990182i | \(-0.455360\pi\) |
−0.990182 | + | 0.139783i | \(0.955360\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | − | 0.381015i | − | 0.0254010i | ||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −12.8793 | −0.757606 | −0.378803 | − | 0.925477i | \(-0.623664\pi\) | ||||
−0.378803 | + | 0.925477i | \(0.623664\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −2.63359 | + | 2.63359i | −0.138610 | + | 0.138610i | −0.773007 | − | 0.634397i | \(-0.781248\pi\) |
0.634397 | + | 0.773007i | \(0.281248\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 14.9966 | − | 14.9966i | 0.714122 | − | 0.714122i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 16.3810 | 0.712218 | 0.356109 | − | 0.934444i | \(-0.384103\pi\) | ||||
0.356109 | + | 0.934444i | \(0.384103\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 24.9931i | 0.999725i | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −10.1173 | − | 10.1173i | −0.374714 | − | 0.374714i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 26.0518 | + | 26.0518i | 0.898336 | + | 0.898336i | 0.995289 | − | 0.0969525i | \(-0.0309095\pi\) |
−0.0969525 | + | 0.995289i | \(0.530910\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | − | 20.2345i | − | 0.652727i | −0.945244 | − | 0.326363i | \(-0.894177\pi\) | ||
0.945244 | − | 0.326363i | \(-0.105823\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 34.8724 | 1.05674 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0.270624 | − | 0.270624i | 0.00773212 | − | 0.00773212i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −41.2829 | + | 41.2829i | −1.11575 | + | 1.11575i | −0.123395 | + | 0.992358i | \(0.539378\pi\) |
−0.992358 | + | 0.123395i | \(0.960622\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −71.8398 | −1.84205 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 3.29640i | − | 0.0804001i | −0.999192 | − | 0.0402000i | \(-0.987200\pi\) | ||
0.999192 | − | 0.0402000i | \(-0.0127995\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 0.786951 | + | 0.786951i | 0.0183012 | + | 0.0183012i | 0.716198 | − | 0.697897i | \(-0.245881\pi\) |
−0.697897 | + | 0.716198i | \(0.745881\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −0.710272 | − | 0.710272i | −0.0157838 | − | 0.0157838i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 79.7517i | 1.69685i | 0.529320 | + | 0.848423i | \(0.322447\pi\) | ||||
−0.529320 | + | 0.848423i | \(0.677553\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −27.6967 | −0.565239 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −41.8466 | + | 41.8466i | −0.820522 | + | 0.820522i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | −1.06207 | + | 1.06207i | −0.0200391 | + | 0.0200391i | −0.717055 | − | 0.697016i | \(-0.754511\pi\) |
0.697016 | + | 0.717055i | \(0.254511\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.629299 | 0.0114418 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 17.1138i | 0.300243i | ||||||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −32.5163 | − | 32.5163i | −0.551124 | − | 0.551124i | 0.375641 | − | 0.926765i | \(-0.377423\pi\) |
−0.926765 | + | 0.375641i | \(0.877423\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −15.2897 | − | 15.2897i | −0.250651 | − | 0.250651i | 0.570586 | − | 0.821238i | \(-0.306716\pi\) |
−0.821238 | + | 0.570586i | \(0.806716\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | − | 55.9119i | − | 0.887491i | ||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −1.29640 | −0.0199446 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 60.0631 | − | 60.0631i | 0.896465 | − | 0.896465i | −0.0986569 | − | 0.995122i | \(-0.531455\pi\) |
0.995122 | + | 0.0986569i | \(0.0314546\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 53.2242 | − | 53.2242i | 0.771365 | − | 0.771365i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 56.3535 | 0.793711 | 0.396856 | − | 0.917881i | \(-0.370101\pi\) | ||||
0.396856 | + | 0.917881i | \(0.370101\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 9.70663i | 0.132968i | 0.997788 | + | 0.0664838i | \(0.0211781\pi\) | ||||
−0.997788 | + | 0.0664838i | \(0.978822\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 81.2062 | + | 81.2062i | 1.08275 | + | 1.08275i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 24.7689 | + | 24.7689i | 0.321674 | + | 0.321674i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 84.4278i | − | 1.06871i | −0.845261 | − | 0.534353i | \(-0.820555\pi\) | ||
0.845261 | − | 0.534353i | \(-0.179445\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 43.2796 | 0.534316 | ||||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −26.7577 | + | 26.7577i | −0.322382 | + | 0.322382i | −0.849680 | − | 0.527298i | \(-0.823205\pi\) |
0.527298 | + | 0.849680i | \(0.323205\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.755154 | + | 0.755154i | −0.00888416 | + | 0.00888416i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 169.292 | 1.94588 | ||||||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 115.555i | − | 1.29838i | −0.760628 | − | 0.649188i | \(-0.775109\pi\) | ||
0.760628 | − | 0.649188i | \(-0.224891\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −51.0258 | − | 51.0258i | −0.560723 | − | 0.560723i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −65.7448 | − | 65.7448i | −0.706934 | − | 0.706934i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 0.308832i | 0.00325086i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −146.245 | −1.50768 | −0.753841 | − | 0.657056i | \(-0.771801\pi\) | ||||
−0.753841 | + | 0.657056i | \(0.771801\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 65.0077 | − | 65.0077i | 0.656644 | − | 0.656644i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 53.8554 | − | 53.8554i | 0.533222 | − | 0.533222i | −0.388308 | − | 0.921530i | \(-0.626940\pi\) |
0.921530 | + | 0.388308i | \(0.126940\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −158.184 | −1.53577 | −0.767885 | − | 0.640588i | \(-0.778691\pi\) | ||||
−0.767885 | + | 0.640588i | \(0.778691\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | − | 1.75859i | − | 0.0167485i | ||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 57.6009 | + | 57.6009i | 0.538327 | + | 0.538327i | 0.923037 | − | 0.384711i | \(-0.125699\pi\) |
−0.384711 | + | 0.923037i | \(0.625699\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −56.8795 | − | 56.8795i | −0.521830 | − | 0.521830i | 0.396294 | − | 0.918124i | \(-0.370296\pi\) |
−0.918124 | + | 0.396294i | \(0.870296\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 268.268i | 2.41683i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 135.731 | 1.20116 | 0.600580 | − | 0.799565i | \(-0.294936\pi\) | ||||
0.600580 | + | 0.799565i | \(0.294936\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 0.960471 | − | 0.960471i | 0.00835192 | − | 0.00835192i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | −133.921 | + | 133.921i | −1.14462 | + | 1.14462i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −59.4450 | −0.499538 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | − | 63.4034i | − | 0.523995i | ||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | −10.7105 | − | 10.7105i | −0.0870770 | − | 0.0870770i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 2.93125 | + | 2.93125i | 0.0234500 | + | 0.0234500i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | − | 166.552i | − | 1.31144i | −0.755006 | − | 0.655718i | \(-0.772366\pi\) | ||
0.755006 | − | 0.655718i | \(-0.227634\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 5.11383 | 0.0396421 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −22.2547 | + | 22.2547i | −0.169883 | + | 0.169883i | −0.786928 | − | 0.617045i | \(-0.788330\pi\) |
0.617045 | + | 0.786928i | \(0.288330\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.1555 | + | 12.1555i | −0.0913945 | + | 0.0913945i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −1.18641 | −0.00878826 | ||||||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 174.890i | 1.27657i | 0.769800 | + | 0.638285i | \(0.220356\pi\) | ||||
−0.769800 | + | 0.638285i | \(0.779644\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −99.8891 | − | 99.8891i | −0.718627 | − | 0.718627i | 0.249697 | − | 0.968324i | \(-0.419669\pi\) |
−0.968324 | + | 0.249697i | \(0.919669\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 259.125 | + | 259.125i | 1.83776 | + | 1.83776i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 118.653i | − | 0.829744i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 3.05499 | 0.0210689 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −89.9905 | + | 89.9905i | −0.612181 | + | 0.612181i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 74.8860 | − | 74.8860i | 0.502590 | − | 0.502590i | −0.409652 | − | 0.912242i | \(-0.634350\pi\) |
0.912242 | + | 0.409652i | \(0.134350\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 70.0357 | 0.463813 | 0.231906 | − | 0.972738i | \(-0.425504\pi\) | ||||
0.231906 | + | 0.972738i | \(0.425504\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 156.018i | 1.01972i | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1.18641 | − | 1.18641i | −0.00765429 | − | 0.00765429i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 29.5307 | + | 29.5307i | 0.188094 | + | 0.188094i | 0.794872 | − | 0.606778i | \(-0.207538\pi\) |
−0.606778 | + | 0.794872i | \(0.707538\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 6.90164i | 0.0434065i | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 75.6074 | 0.469611 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −47.7990 | + | 47.7990i | −0.293245 | + | 0.293245i | −0.838361 | − | 0.545116i | \(-0.816486\pi\) |
0.545116 | + | 0.838361i | \(0.316486\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 2.04468 | − | 2.04468i | 0.0123920 | − | 0.0123920i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −156.268 | −0.935734 | −0.467867 | − | 0.883799i | \(-0.654977\pi\) | ||||
−0.467867 | + | 0.883799i | \(0.654977\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 75.4347i | 0.446359i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 31.9029 | + | 31.9029i | 0.186567 | + | 0.186567i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −190.103 | − | 190.103i | −1.09886 | − | 1.09886i | −0.994544 | − | 0.104319i | \(-0.966734\pi\) |
−0.104319 | − | 0.994544i | \(-0.533266\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 115.357i | 0.659183i | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −211.300 | −1.19379 | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −54.2749 | + | 54.2749i | −0.303212 | + | 0.303212i | −0.842269 | − | 0.539057i | \(-0.818781\pi\) |
0.539057 | + | 0.842269i | \(0.318781\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −19.7343 | + | 19.7343i | −0.109029 | + | 0.109029i | −0.759517 | − | 0.650487i | \(-0.774565\pi\) |
0.650487 | + | 0.759517i | \(0.274565\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −99.3569 | −0.542934 | ||||||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 4.84109i | 0.0261680i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −69.1155 | − | 69.1155i | −0.369602 | − | 0.369602i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −46.6967 | − | 46.6967i | −0.247073 | − | 0.247073i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 166.552i | 0.872002i | 0.899946 | + | 0.436001i | \(0.143606\pi\) | ||||
−0.899946 | + | 0.436001i | \(0.856394\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 2.18257 | 0.0113087 | 0.00565434 | − | 0.999984i | \(-0.498200\pi\) | ||||
0.00565434 | + | 0.999984i | \(0.498200\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −4.21219 | + | 4.21219i | −0.0216010 | + | 0.0216010i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −67.4310 | + | 67.4310i | −0.342290 | + | 0.342290i | −0.857227 | − | 0.514938i | \(-0.827815\pi\) |
0.514938 | + | 0.857227i | \(0.327815\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 222.906 | 1.12013 | 0.560065 | − | 0.828449i | \(-0.310776\pi\) | ||||
0.560065 | + | 0.828449i | \(0.310776\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | − | 390.307i | − | 1.94183i | ||||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 120.243 | + | 120.243i | 0.592331 | + | 0.592331i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −0.193278 | − | 0.193278i | −0.000942822 | − | 0.000942822i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 198.437i | − | 0.958632i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −28.2659 | −0.135243 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 147.118 | − | 147.118i | 0.697240 | − | 0.697240i | −0.266574 | − | 0.963814i | \(-0.585892\pi\) |
0.963814 | + | 0.266574i | \(0.0858917\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 183.100 | − | 183.100i | 0.859627 | − | 0.859627i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 0.0922828 | 0.000429223 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 93.3934i | − | 0.430385i | ||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 31.5382 | + | 31.5382i | 0.144010 | + | 0.144010i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 142.383 | + | 142.383i | 0.644268 | + | 0.644268i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 60.7036i | 0.272213i | 0.990694 | + | 0.136107i | \(0.0434590\pi\) | ||||
−0.990694 | + | 0.136107i | \(0.956541\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 302.762 | 1.34561 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 225.526 | − | 225.526i | 0.993505 | − | 0.993505i | −0.00647371 | − | 0.999979i | \(-0.502061\pi\) |
0.999979 | + | 0.00647371i | \(0.00206066\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −227.796 | + | 227.796i | −0.994743 | + | 0.994743i | −0.999986 | − | 0.00524305i | \(-0.998331\pi\) |
0.00524305 | + | 0.999986i | \(0.498331\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 160.955 | 0.696776 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 121.053i | − | 0.519540i | −0.965671 | − | 0.259770i | \(-0.916353\pi\) | ||
0.965671 | − | 0.259770i | \(-0.0836467\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 4.67610 | + | 4.67610i | 0.0198983 | + | 0.0198983i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −274.318 | − | 274.318i | −1.15746 | − | 1.15746i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 221.393i | − | 0.926332i | −0.886271 | − | 0.463166i | \(-0.846713\pi\) | ||
0.886271 | − | 0.463166i | \(-0.153287\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 84.2667 | 0.349654 | 0.174827 | − | 0.984599i | \(-0.444063\pi\) | ||||
0.174827 | + | 0.984599i | \(0.444063\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 231.677 | − | 231.677i | 0.953403 | − | 0.953403i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | −1.62395 | + | 1.62395i | −0.00662835 | + | 0.00662835i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 58.2298 | 0.235748 | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 173.879i | 0.698310i | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 176.615 | + | 176.615i | 0.703646 | + | 0.703646i | 0.965191 | − | 0.261545i | \(-0.0842321\pi\) |
−0.261545 | + | 0.965191i | \(0.584232\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 87.9072 | + | 87.9072i | 0.347459 | + | 0.347459i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 4.90720i | 0.0192439i | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −163.001 | −0.634244 | −0.317122 | − | 0.948385i | \(-0.602717\pi\) | ||||
−0.317122 | + | 0.948385i | \(0.602717\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −190.543 | + | 190.543i | −0.735687 | + | 0.735687i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 315.587 | − | 315.587i | 1.20914 | − | 1.20914i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | 175.001 | 0.665404 | 0.332702 | − | 0.943032i | \(-0.392040\pi\) | ||||
0.332702 | + | 0.943032i | \(0.392040\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 0.124545i | 0.000469982i | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −375.456 | − | 375.456i | −1.40620 | − | 1.40620i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −29.7489 | − | 29.7489i | −0.110591 | − | 0.110591i | 0.649646 | − | 0.760237i | \(-0.274917\pi\) |
−0.760237 | + | 0.649646i | \(0.774917\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 275.891i | 1.01805i | 0.860753 | + | 0.509024i | \(0.169993\pi\) | ||||
−0.860753 | + | 0.509024i | \(0.830007\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −331.580 | −1.21458 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −134.123 | + | 134.123i | −0.487721 | + | 0.487721i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 278.337 | − | 278.337i | 1.00483 | − | 1.00483i | 0.00484003 | − | 0.999988i | \(-0.498459\pi\) |
0.999988 | − | 0.00484003i | \(-0.00154063\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −245.118 | −0.878558 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 202.356i | 0.720128i | 0.932928 | + | 0.360064i | \(0.117245\pi\) | ||||
−0.932928 | + | 0.360064i | \(0.882755\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 292.256 | + | 292.256i | 1.03271 | + | 1.03271i | 0.999447 | + | 0.0332615i | \(0.0105894\pi\) |
0.0332615 | + | 0.999447i | \(0.489411\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 1.00344 | + | 1.00344i | 0.00352083 | + | 0.00352083i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | − | 15.2147i | − | 0.0530129i | ||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −123.124 | −0.426034 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −475.171 | + | 475.171i | −1.63289 | + | 1.63289i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −331.170 | + | 331.170i | −1.13027 | + | 1.13027i | −0.140141 | + | 0.990132i | \(0.544756\pi\) |
−0.990132 | + | 0.140141i | \(0.955244\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −3.81307 | −0.0129257 | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | − | 108.587i | − | 0.365612i | ||||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −181.095 | − | 181.095i | −0.605670 | − | 0.605670i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 3.63221 | + | 3.63221i | 0.0120671 | + | 0.0120671i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 349.968i | − | 1.15501i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −1.79297 | −0.00587859 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −23.7513 | + | 23.7513i | −0.0773656 | + | 0.0773656i | −0.744731 | − | 0.667365i | \(-0.767422\pi\) |
0.667365 | + | 0.744731i | \(0.267422\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −513.963 | + | 513.963i | −1.66331 | + | 1.66331i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −157.757 | −0.507258 | −0.253629 | − | 0.967302i | \(-0.581624\pi\) | ||||
−0.253629 | + | 0.967302i | \(0.581624\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 58.5936i | 0.187200i | 0.995610 | + | 0.0936000i | \(0.0298375\pi\) | ||||
−0.995610 | + | 0.0936000i | \(0.970163\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −3.27829 | − | 3.27829i | −0.0104073 | − | 0.0104073i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −27.0040 | − | 27.0040i | −0.0851863 | − | 0.0851863i | 0.663230 | − | 0.748416i | \(-0.269185\pi\) |
−0.748416 | + | 0.663230i | \(0.769185\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 279.609i | 0.876516i | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 374.307 | 1.16607 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 33.9188 | − | 33.9188i | 0.105012 | − | 0.105012i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 276.304 | − | 276.304i | 0.850166 | − | 0.850166i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −369.619 | −1.13033 | ||||||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 368.098i | 1.11884i | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 182.195 | + | 182.195i | 0.550437 | + | 0.550437i | 0.926567 | − | 0.376130i | \(-0.122745\pi\) |
−0.376130 | + | 0.926567i | \(0.622745\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 500.093 | + | 500.093i | 1.50178 | + | 1.50178i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | − | 7.04338i | − | 0.0210250i | ||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 510.137 | 1.51376 | 0.756881 | − | 0.653553i | \(-0.226722\pi\) | ||||
0.756881 | + | 0.653553i | \(0.226722\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 441.009 | − | 441.009i | 1.30091 | − | 1.30091i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 108.587 | − | 108.587i | 0.318436 | − | 0.318436i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −353.997 | −1.03206 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | − | 6.24141i | − | 0.0180910i | ||||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −432.614 | − | 432.614i | −1.24673 | − | 1.24673i | −0.957157 | − | 0.289570i | \(-0.906488\pi\) |
−0.289570 | − | 0.957157i | \(-0.593512\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 148.839 | + | 148.839i | 0.426472 | + | 0.426472i | 0.887425 | − | 0.460953i | \(-0.152492\pi\) |
−0.460953 | + | 0.887425i | \(0.652492\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 223.697i | 0.637313i | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −268.587 | −0.760869 | −0.380434 | − | 0.924808i | \(-0.624226\pi\) | ||||
−0.380434 | + | 0.924808i | \(0.624226\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 3.30418 | − | 3.30418i | 0.00930756 | − | 0.00930756i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −193.145 | + | 193.145i | −0.541023 | + | 0.541023i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 628.520 | 1.75075 | 0.875376 | − | 0.483442i | \(-0.160614\pi\) | ||||
0.875376 | + | 0.483442i | \(0.160614\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 347.128i | 0.961574i | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −206.006 | − | 206.006i | −0.567511 | − | 0.567511i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.569131 | + | 0.569131i | 0.00155926 | + | 0.00155926i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 396.386i | − | 1.08007i | −0.841643 | − | 0.540035i | \(-0.818411\pi\) | ||
0.841643 | − | 0.540035i | \(-0.181589\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −39.9320 | −0.108217 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −4.90204 | + | 4.90204i | −0.0132130 | + | 0.0132130i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −134.275 | + | 134.275i | −0.359987 | + | 0.359987i | −0.863808 | − | 0.503821i | \(-0.831927\pi\) |
0.503821 | + | 0.863808i | \(0.331927\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 19.0481 | 0.0507950 | ||||||||
\(376\) | 0 | 0 | ||||||||
\(377\) | − | 576.015i | − | 1.52789i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 350.491 | + | 350.491i | 0.924777 | + | 0.924777i | 0.997362 | − | 0.0725851i | \(-0.0231249\pi\) |
−0.0725851 | + | 0.997362i | \(0.523125\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −541.152 | − | 541.152i | −1.42035 | − | 1.42035i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | 403.778i | 1.05425i | 0.849787 | + | 0.527126i | \(0.176730\pi\) | ||||
−0.849787 | + | 0.527126i | \(0.823270\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 2.90456 | 0.00754431 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 9.53299 | − | 9.53299i | 0.0246330 | − | 0.0246330i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 125.310 | − | 125.310i | 0.322134 | − | 0.322134i | −0.527452 | − | 0.849585i | \(-0.676852\pi\) |
0.849585 | + | 0.527452i | \(0.176852\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −210.976 | −0.539580 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 144.617i | 0.367983i | ||||||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −4.95027 | − | 4.95027i | −0.0125323 | − | 0.0125323i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 69.8722 | + | 69.8722i | 0.176001 | + | 0.176001i | 0.789610 | − | 0.613609i | \(-0.210283\pi\) |
−0.613609 | + | 0.789610i | \(0.710283\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 78.9897i | 0.197969i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 11.3010 | 0.0281821 | 0.0140911 | − | 0.999901i | \(-0.495515\pi\) | ||||
0.0140911 | + | 0.999901i | \(0.495515\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −223.697 | + | 223.697i | −0.555079 | + | 0.555079i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 2.53762 | − | 2.53762i | 0.00626573 | − | 0.00626573i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −443.081 | −1.08865 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 614.595i | − | 1.50268i | −0.659917 | − | 0.751339i | \(-0.729408\pi\) | ||
0.659917 | − | 0.751339i | \(-0.270592\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 568.242 | + | 568.242i | 1.38258 | + | 1.38258i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −150.081 | − | 150.081i | −0.363391 | − | 0.363391i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.13778i | 0.00756092i | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −649.108 | −1.55661 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −78.7092 | + | 78.7092i | −0.187850 | + | 0.187850i | −0.794766 | − | 0.606916i | \(-0.792406\pi\) |
0.606916 | + | 0.794766i | \(0.292406\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 374.618 | − | 374.618i | 0.889829 | − | 0.889829i | −0.104678 | − | 0.994506i | \(-0.533381\pi\) |
0.994506 | + | 0.104678i | \(0.0333811\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 966.099 | 2.28392 | ||||||||
\(424\) | 0 | 0 | ||||||||
\(425\) | − | 321.894i | − | 0.757397i | ||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −70.5705 | − | 70.5705i | −0.165270 | − | 0.165270i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −385.521 | − | 385.521i | −0.898651 | − | 0.898651i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 616.593i | − | 1.43061i | −0.698813 | − | 0.715305i | \(-0.746288\pi\) | ||
0.698813 | − | 0.715305i | \(-0.253712\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 219.246 | 0.506342 | 0.253171 | − | 0.967422i | \(-0.418526\pi\) | ||||
0.253171 | + | 0.967422i | \(0.418526\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 9.92610 | − | 9.92610i | 0.0228186 | − | 0.0228186i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −43.1409 | + | 43.1409i | −0.0987207 | + | 0.0987207i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 575.292 | 1.31046 | 0.655231 | − | 0.755429i | \(-0.272571\pi\) | ||||
0.655231 | + | 0.755429i | \(0.272571\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 335.513i | 0.760801i | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −371.895 | − | 371.895i | −0.839492 | − | 0.839492i | 0.149300 | − | 0.988792i | \(-0.452298\pi\) |
−0.988792 | + | 0.149300i | \(0.952298\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −6.77538 | − | 6.77538i | −0.0152256 | − | 0.0152256i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | − | 486.630i | − | 1.08866i | ||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −498.135 | −1.10943 | −0.554716 | − | 0.832040i | \(-0.687173\pi\) | ||||
−0.554716 | + | 0.832040i | \(0.687173\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 17.6898 | − | 17.6898i | 0.0392236 | − | 0.0392236i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 227.556 | − | 227.556i | 0.502331 | − | 0.502331i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | −5.98361 | −0.0131508 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 61.1711i | 0.133854i | 0.997758 | + | 0.0669268i | \(0.0213194\pi\) | ||||
−0.997758 | + | 0.0669268i | \(0.978681\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 130.303 | + | 130.303i | 0.283885 | + | 0.283885i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 443.183 | + | 443.183i | 0.961352 | + | 0.961352i | 0.999280 | − | 0.0379287i | \(-0.0120760\pi\) |
−0.0379287 | + | 0.999280i | \(0.512076\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 706.883i | 1.52675i | 0.645958 | + | 0.763373i | \(0.276458\pi\) | ||||
−0.645958 | + | 0.763373i | \(0.723542\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −7.70966 | −0.0165799 | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 406.857 | − | 406.857i | 0.871214 | − | 0.871214i | −0.121391 | − | 0.992605i | \(-0.538735\pi\) |
0.992605 | + | 0.121391i | \(0.0387355\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 277.224 | − | 277.224i | 0.591096 | − | 0.591096i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 191.899 | 0.407429 | ||||||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.44620i | 0.0178567i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −65.8217 | − | 65.8217i | −0.138572 | − | 0.138572i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 12.8657 | + | 12.8657i | 0.0269722 | + | 0.0269722i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | − | 133.063i | − | 0.277793i | −0.990307 | − | 0.138896i | \(-0.955645\pi\) | ||
0.990307 | − | 0.138896i | \(-0.0443555\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 912.780 | 1.89767 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 245.659 | − | 245.659i | 0.508611 | − | 0.508611i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −8.57482 | + | 8.57482i | −0.0176800 | + | 0.0176800i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −208.075 | −0.427259 | −0.213629 | − | 0.976915i | \(-0.568529\pi\) | ||||
−0.213629 | + | 0.976915i | \(0.568529\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 310.611i | 0.635197i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 98.9374 | + | 98.9374i | 0.201502 | + | 0.201502i | 0.800643 | − | 0.599141i | \(-0.204491\pi\) |
−0.599141 | + | 0.800643i | \(0.704491\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −335.528 | − | 335.528i | −0.680585 | − | 0.680585i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | − | 7.62322i | − | 0.0154004i | ||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 260.102 | 0.523345 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 287.076 | − | 287.076i | 0.575304 | − | 0.575304i | −0.358302 | − | 0.933606i | \(-0.616644\pi\) |
0.933606 | + | 0.358302i | \(0.116644\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −507.735 | + | 507.735i | −1.01344 | + | 1.01344i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −78.7359 | −0.156533 | −0.0782663 | − | 0.996932i | \(-0.524938\pi\) | ||||
−0.0782663 | + | 0.996932i | \(0.524938\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | − | 6.31543i | − | 0.0125058i | ||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 245.098 | + | 245.098i | 0.483428 | + | 0.483428i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 242.477 | + | 242.477i | 0.476378 | + | 0.476378i | 0.903971 | − | 0.427593i | \(-0.140638\pi\) |
−0.427593 | + | 0.903971i | \(0.640638\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 44.8014i | 0.0876740i | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 53.2895 | 0.103878 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −9.27484 | + | 9.27484i | −0.0180094 | + | 0.0180094i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −427.980 | + | 427.980i | −0.827815 | + | 0.827815i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −1235.34 | −2.38024 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 561.306i | − | 1.07736i | −0.842510 | − | 0.538681i | \(-0.818923\pi\) | ||
0.842510 | − | 0.538681i | \(-0.181077\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −396.152 | − | 396.152i | −0.757460 | − | 0.757460i | 0.218399 | − | 0.975859i | \(-0.429916\pi\) |
−0.975859 | + | 0.218399i | \(0.929916\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 374.811 | + | 374.811i | 0.713926 | + | 0.713926i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 260.607i | 0.494510i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −260.662 | −0.492745 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −393.897 | + | 393.897i | −0.741803 | + | 0.741803i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | −36.4424 | + | 36.4424i | −0.0683722 | + | 0.0683722i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 6.75465 | 0.0126255 | ||||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 352.694i | 0.656785i | ||||||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −148.632 | − | 148.632i | −0.275755 | − | 0.275755i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.5728 | + | 22.5728i | 0.0417242 | + | 0.0417242i | 0.727661 | − | 0.685937i | \(-0.240607\pi\) |
−0.685937 | + | 0.727661i | \(0.740607\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 128.239i | 0.236168i | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −6.67005 | −0.0122386 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −601.634 | + | 601.634i | −1.09988 | + | 1.09988i | −0.105456 | + | 0.994424i | \(0.533630\pi\) |
−0.994424 | + | 0.105456i | \(0.966370\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −185.217 | + | 185.217i | −0.337372 | + | 0.337372i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −137.219 | −0.249037 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | − | 389.681i | − | 0.704666i | ||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 15.7294 | + | 15.7294i | 0.0283412 | + | 0.0283412i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −502.883 | − | 502.883i | −0.902841 | − | 0.902841i | 0.0928399 | − | 0.995681i | \(-0.470406\pi\) |
−0.995681 | + | 0.0928399i | \(0.970406\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 17.3998i | − | 0.0311266i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −449.132 | −0.800592 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −655.972 | + | 655.972i | −1.16514 | + | 1.16514i | −0.181802 | + | 0.983335i | \(0.558193\pi\) |
−0.983335 | + | 0.181802i | \(0.941807\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 7.95834 | − | 7.95834i | 0.0140856 | − | 0.0140856i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 199.759 | 0.352309 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 649.911i | 1.14220i | 0.820881 | + | 0.571099i | \(0.193483\pi\) | ||||
−0.820881 | + | 0.571099i | \(0.806517\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −269.718 | − | 269.718i | −0.472360 | − | 0.472360i | 0.430317 | − | 0.902678i | \(-0.358402\pi\) |
−0.902678 | + | 0.430317i | \(0.858402\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 541.152 | + | 541.152i | 0.944419 | + | 0.944419i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 409.413i | 0.712022i | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −142.675 | −0.247271 | −0.123635 | − | 0.992328i | \(-0.539455\pi\) | ||||
−0.123635 | + | 0.992328i | \(0.539455\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.09149 | − | 7.09149i | 0.0122478 | − | 0.0122478i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −123.502 | + | 123.502i | −0.212567 | + | 0.212567i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −11.3990 | −0.0195523 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 15.7044i | 0.0268451i | ||||||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 687.876 | + | 687.876i | 1.17185 | + | 1.17185i | 0.981768 | + | 0.190082i | \(0.0608753\pi\) |
0.190082 | + | 0.981768i | \(0.439125\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 53.2895 | + | 53.2895i | 0.0904746 | + | 0.0904746i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 438.186i | 0.741431i | ||||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −58.8678 | −0.0992711 | −0.0496355 | − | 0.998767i | \(-0.515806\pi\) | ||||
−0.0496355 | + | 0.998767i | \(0.515806\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −3.48545 | + | 3.48545i | −0.00585790 | + | 0.00585790i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 724.252 | − | 724.252i | 1.21315 | − | 1.21315i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −670.449 | −1.11928 | −0.559641 | − | 0.828735i | \(-0.689061\pi\) | ||||
−0.559641 | + | 0.828735i | \(0.689061\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 910.721i | 1.51534i | 0.652636 | + | 0.757671i | \(0.273663\pi\) | ||||
−0.652636 | + | 0.757671i | \(0.726337\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −727.594 | − | 727.594i | −1.20662 | − | 1.20662i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −3.71754 | − | 3.71754i | −0.00614469 | − | 0.00614469i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 761.794i | − | 1.25501i | −0.778611 | − | 0.627507i | \(-0.784075\pi\) | ||
0.778611 | − | 0.627507i | \(-0.215925\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 781.374 | 1.28304 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 881.671 | − | 881.671i | 1.44300 | − | 1.44300i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −273.397 | + | 273.397i | −0.445999 | + | 0.445999i | −0.894022 | − | 0.448023i | \(-0.852128\pi\) |
0.448023 | + | 0.894022i | \(0.352128\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −1.25598 | −0.00204224 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 1088.68i | 1.76448i | 0.470804 | + | 0.882238i | \(0.343964\pi\) | ||||
−0.470804 | + | 0.882238i | \(0.656036\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 129.299 | + | 129.299i | 0.208884 | + | 0.208884i | 0.803793 | − | 0.594909i | \(-0.202812\pi\) |
−0.594909 | + | 0.803793i | \(0.702812\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −165.731 | − | 165.731i | −0.266878 | − | 0.266878i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 533.351i | − | 0.856102i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −624.484 | −0.999175 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −91.8398 | + | 91.8398i | −0.146475 | + | 0.146475i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 531.694 | − | 531.694i | 0.845301 | − | 0.845301i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 455.029 | 0.721123 | 0.360562 | − | 0.932735i | \(-0.382585\pi\) | ||||
0.360562 | + | 0.932735i | \(0.382585\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | − | 956.012i | − | 1.51029i | ||||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −9.76549 | − | 9.76549i | −0.0153787 | − | 0.0153787i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 306.193 | + | 306.193i | 0.480679 | + | 0.480679i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | − | 682.657i | − | 1.06832i | ||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 798.626 | 1.24591 | 0.622953 | − | 0.782259i | \(-0.285933\pi\) | ||||
0.622953 | + | 0.782259i | \(0.285933\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 305.718 | − | 305.718i | 0.475455 | − | 0.475455i | −0.428219 | − | 0.903675i | \(-0.640859\pi\) |
0.903675 | + | 0.428219i | \(0.140859\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0.299840 | − | 0.299840i | 0.000464868 | − | 0.000464868i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 1161.90 | 1.79583 | 0.897916 | − | 0.440167i | \(-0.145081\pi\) | ||||
0.897916 | + | 0.440167i | \(0.145081\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | − | 348.992i | − | 0.537738i | ||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −303.448 | − | 303.448i | −0.466127 | − | 0.466127i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −77.5410 | − | 77.5410i | −0.118746 | − | 0.118746i | 0.645237 | − | 0.763983i | \(-0.276759\pi\) |
−0.763983 | + | 0.645237i | \(0.776759\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 2.60973i | 0.00398431i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 117.584 | 0.178972 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −836.993 | + | 836.993i | −1.27010 | + | 1.27010i | −0.324059 | + | 0.946037i | \(0.605048\pi\) |
−0.946037 | + | 0.324059i | \(0.894952\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −121.071 | + | 121.071i | −0.183164 | + | 0.183164i | −0.792733 | − | 0.609569i | \(-0.791342\pi\) |
0.609569 | + | 0.792733i | \(0.291342\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 925.246 | 1.39554 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 1.42543i | 0.00214350i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 426.754 | + | 426.754i | 0.639811 | + | 0.639811i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 197.235 | + | 197.235i | 0.294820 | + | 0.294820i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | − | 164.102i | − | 0.244563i | ||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −954.371 | −1.41808 | −0.709042 | − | 0.705166i | \(-0.750872\pi\) | ||||
−0.709042 | + | 0.705166i | \(0.750872\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 252.862 | − | 252.862i | 0.374611 | − | 0.374611i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −245.475 | + | 245.475i | −0.362593 | + | 0.362593i | −0.864767 | − | 0.502174i | \(-0.832534\pi\) |
0.502174 | + | 0.864767i | \(0.332534\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −675.002 | −0.994112 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | − | 1465.53i | − | 2.15203i | ||||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 911.271 | + | 911.271i | 1.33422 | + | 1.33422i | 0.901556 | + | 0.432663i | \(0.142426\pi\) |
0.432663 | + | 0.901556i | \(0.357574\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 10.2544 | + | 10.2544i | 0.0149699 | + | 0.0149699i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1480.28i | 2.15471i | ||||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 23.4828 | 0.0340824 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 476.155 | − | 476.155i | 0.689081 | − | 0.689081i | −0.272947 | − | 0.962029i | \(-0.587999\pi\) |
0.962029 | + | 0.272947i | \(0.0879985\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 300.046 | − | 300.046i | 0.432967 | − | 0.432967i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −11.7136 | −0.0168541 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 42.4553i | 0.0609115i | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −393.317 | − | 393.317i | −0.562686 | − | 0.562686i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −934.966 | − | 934.966i | −1.33376 | − | 1.33376i | −0.901978 | − | 0.431782i | \(-0.857885\pi\) |
−0.431782 | − | 0.901978i | \(-0.642115\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 217.444i | − | 0.309309i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 30.3866 | 0.0431015 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 248.572 | − | 248.572i | 0.351587 | − | 0.351587i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −5.89548 | + | 5.89548i | −0.00831520 | + | 0.00831520i | −0.711252 | − | 0.702937i | \(-0.751872\pi\) |
0.702937 | + | 0.711252i | \(0.251872\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1022.74 | −1.43846 | ||||||||
\(712\) | 0 | 0 | ||||||||
\(713\) | − | 331.462i | − | 0.464884i | ||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.95702 | − | 6.95702i | −0.00973010 | − | 0.00973010i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −719.338 | − | 719.338i | −1.00326 | − | 1.00326i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | − | 19.5965i | − | 0.0272552i | −0.999907 | − | 0.0136276i | \(-0.995662\pi\) | ||
0.999907 | − | 0.0136276i | \(-0.00433793\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −730.107 | −1.01263 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 273.794 | − | 273.794i | 0.378692 | − | 0.378692i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −651.115 | + | 651.115i | −0.898089 | + | 0.898089i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 741.995 | 1.02063 | 0.510313 | − | 0.859989i | \(-0.329530\pi\) | ||||
0.510313 | + | 0.859989i | \(0.329530\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | − | 1115.99i | − | 1.53084i | ||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −10.1354 | − | 10.1354i | −0.0138651 | − | 0.0138651i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −349.267 | − | 349.267i | −0.476490 | − | 0.476490i | 0.427517 | − | 0.904007i | \(-0.359388\pi\) |
−0.904007 | + | 0.427517i | \(0.859388\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 10.5529i | 0.0143576i | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 644.646 | 0.874690 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 358.932 | − | 358.932i | 0.485700 | − | 0.485700i | −0.421246 | − | 0.906946i | \(-0.638407\pi\) |
0.906946 | + | 0.421246i | \(0.138407\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 189.197 | − | 189.197i | 0.255326 | − | 0.255326i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −856.214 | −1.15237 | −0.576187 | − | 0.817318i | \(-0.695460\pi\) | ||||
−0.576187 | + | 0.817318i | \(0.695460\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | − | 8.78160i | − | 0.0117874i | ||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 324.139 | + | 324.139i | 0.433921 | + | 0.433921i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 265.860 | + | 265.860i | 0.354953 | + | 0.354953i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 442.218i | 0.588839i | 0.955676 | + | 0.294420i | \(0.0951264\pi\) | ||||
−0.955676 | + | 0.294420i | \(0.904874\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 1147.69 | 1.52416 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 4.10641 | − | 4.10641i | 0.00543896 | − | 0.00543896i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −489.198 | + | 489.198i | −0.646233 | + | 0.646233i | −0.952080 | − | 0.305848i | \(-0.901060\pi\) |
0.305848 | + | 0.952080i | \(0.401060\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 571.246 | 0.752629 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 404.015i | 0.530899i | 0.964125 | + | 0.265450i | \(0.0855204\pi\) | ||||
−0.964125 | + | 0.265450i | \(0.914480\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −262.530 | − | 262.530i | −0.344076 | − | 0.344076i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 9.14780 | + | 9.14780i | 0.0119579 | + | 0.0119579i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 718.949i | 0.937352i | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −387.336 | −0.503688 | −0.251844 | − | 0.967768i | \(-0.581037\pi\) | ||||
−0.251844 | + | 0.967768i | \(0.581037\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −529.612 | + | 529.612i | −0.686916 | + | 0.686916i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 960.396 | − | 960.396i | 1.24243 | − | 1.24243i | 0.283436 | − | 0.958991i | \(-0.408526\pi\) |
0.958991 | − | 0.283436i | \(-0.0914745\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 505.724 | 0.652547 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 1238.20i | 1.59357i | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 8.68138 | + | 8.68138i | 0.0111443 | + | 0.0111443i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 302.416 | + | 302.416i | 0.387216 | + | 0.387216i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 527.145i | − | 0.673238i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 3.46296 | 0.00441141 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 298.374 | − | 298.374i | 0.379129 | − | 0.379129i | −0.491659 | − | 0.870788i | \(-0.663609\pi\) |
0.870788 | + | 0.491659i | \(0.163609\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 568.604 | − | 568.604i | 0.720664 | − | 0.720664i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 626.473 | 0.792002 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 338.062i | 0.426308i | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 0.404665 | + | 0.404665i | 0.000509012 | + | 0.000509012i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 870.093 | + | 870.093i | 1.09171 | + | 1.09171i | 0.995346 | + | 0.0963642i | \(0.0307214\pi\) |
0.0963642 | + | 0.995346i | \(0.469279\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | − | 1027.15i | − | 1.28554i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1399.82 | −1.74759 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | −52.0897 | + | 52.0897i | −0.0648689 | + | 0.0648689i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 4.43310 | − | 4.43310i | 0.00550695 | − | 0.00550695i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −193.317 | −0.239550 | ||||||||
\(808\) | 0 | 0 | ||||||||
\(809\) | − | 107.642i | − | 0.133055i | −0.997785 | − | 0.0665277i | \(-0.978808\pi\) | ||
0.997785 | − | 0.0665277i | \(-0.0211921\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −829.739 | − | 829.739i | −1.02311 | − | 1.02311i | −0.999727 | − | 0.0233795i | \(-0.992557\pi\) |
−0.0233795 | − | 0.999727i | \(-0.507443\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 896.408 | + | 896.408i | 1.10259 | + | 1.10259i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 5.60521i | 0.00687756i | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −4.14502 | −0.00507346 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −618.118 | + | 618.118i | −0.754722 | + | 0.754722i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −506.899 | + | 506.899i | −0.617416 | + | 0.617416i | −0.944868 | − | 0.327452i | \(-0.893810\pi\) |
0.327452 | + | 0.944868i | \(0.393810\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −927.304 | −1.12674 | −0.563368 | − | 0.826206i | \(-0.690495\pi\) | ||||
−0.563368 | + | 0.826206i | \(0.690495\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 871.571i | 1.05645i | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 19.4711 | + | 19.4711i | 0.0235443 | + | 0.0235443i | 0.718781 | − | 0.695237i | \(-0.244700\pi\) |
−0.695237 | + | 0.718781i | \(0.744700\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −409.028 | − | 409.028i | −0.493400 | − | 0.493400i | 0.415976 | − | 0.909376i | \(-0.363440\pi\) |
−0.909376 | + | 0.415976i | \(0.863440\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 1808.71i | − | 2.17655i | ||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 356.714 | 0.428228 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.16246 | + | 9.16246i | −0.0109730 | + | 0.0109730i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −204.718 | + | 204.718i | −0.244586 | + | 0.244586i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 634.212 | 0.755914 | 0.377957 | − | 0.925823i | \(-0.376627\pi\) | ||||
0.377957 | + | 0.925823i | \(0.376627\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 516.388i | 0.614017i | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 657.483 | + | 657.483i | 0.779933 | + | 0.779933i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 4.42297 | + | 4.42297i | 0.00523429 | + | 0.00523429i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 292.641i | − | 0.345503i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 1899.16 | 2.23694 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −676.255 | + | 676.255i | −0.794659 | + | 0.794659i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −687.203 | + | 687.203i | −0.805630 | + | 0.805630i | −0.983969 | − | 0.178339i | \(-0.942928\pi\) |
0.178339 | + | 0.983969i | \(0.442928\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 3.74114 | 0.00437560 | ||||||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 995.675i | − | 1.16181i | −0.813970 | − | 0.580907i | \(-0.802698\pi\) | ||
0.813970 | − | 0.580907i | \(-0.197302\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −430.241 | − | 430.241i | −0.500863 | − | 0.500863i | 0.410843 | − | 0.911706i | \(-0.365234\pi\) |
−0.911706 | + | 0.410843i | \(0.865234\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −49.4347 | − | 49.4347i | −0.0574154 | − | 0.0574154i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 1014.03i | 1.17501i | 0.809222 | + | 0.587503i | \(0.199889\pi\) | ||||
−0.809222 | + | 0.587503i | \(0.800111\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −22.2927 | −0.0257719 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −400.046 | + | 400.046i | −0.461414 | + | 0.461414i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 453.074 | − | 453.074i | 0.521374 | − | 0.521374i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −1328.02 | −1.52471 | ||||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 1771.59i | 2.02931i | ||||||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 13.5293 | + | 13.5293i | 0.0154621 | + | 0.0154621i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 544.315 | + | 544.315i | 0.620656 | + | 0.620656i | 0.945699 | − | 0.325043i | \(-0.105379\pi\) |
−0.325043 | + | 0.945699i | \(0.605379\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 2152.03i | 2.44828i | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −645.905 | −0.733150 | −0.366575 | − | 0.930388i | \(-0.619470\pi\) | ||||
−0.366575 | + | 0.930388i | \(0.619470\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −586.952 | + | 586.952i | −0.664725 | + | 0.664725i | −0.956490 | − | 0.291765i | \(-0.905757\pi\) |
0.291765 | + | 0.956490i | \(0.405757\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −12.3892 | + | 12.3892i | −0.0139991 | + | 0.0139991i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −1221.93 | −1.37759 | −0.688797 | − | 0.724955i | \(-0.741861\pi\) | ||||
−0.688797 | + | 0.724955i | \(0.741861\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | − | 768.730i | − | 0.864713i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 232.256 | + | 232.256i | 0.260669 | + | 0.260669i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −210.034 | − | 210.034i | −0.235200 | − | 0.235200i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 6.36462i | 0.00711131i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −1176.81 | −1.31194 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 527.145 | − | 527.145i | 0.586368 | − | 0.586368i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 13.6787 | − | 13.6787i | 0.0151817 | − | 0.0151817i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 23.6031 | 0.0261386 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 2.31417i | 0.00255710i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −310.014 | − | 310.014i | −0.341801 | − | 0.341801i | 0.515243 | − | 0.857044i | \(-0.327702\pi\) |
−0.857044 | + | 0.515243i | \(0.827702\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −652.395 | − | 652.395i | −0.717707 | − | 0.717707i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | − | 1044.12i | − | 1.14612i | −0.819513 | − | 0.573060i | \(-0.805756\pi\) | ||
0.819513 | − | 0.573060i | \(-0.194244\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −287.186 | −0.314552 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.82561 | + | 5.82561i | −0.00636679 | + | 0.00636679i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | −102.718 | + | 102.718i | −0.112015 | + | 0.112015i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 188.522 | 0.205138 | 0.102569 | − | 0.994726i | \(-0.467294\pi\) | ||||
0.102569 | + | 0.994726i | \(0.467294\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 154.342i | 0.167581i | ||||||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −622.999 | − | 622.999i | −0.674972 | − | 0.674972i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −1031.79 | − | 1031.79i | −1.11545 | − | 1.11545i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | 1916.22i | 2.06712i | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | −220.366 | −0.237208 | −0.118604 | − | 0.992942i | \(-0.537842\pi\) | ||||
−0.118604 | + | 0.992942i | \(0.537842\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 72.9419 | − | 72.9419i | 0.0783479 | − | 0.0783479i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −512.576 | + | 512.576i | −0.549384 | + | 0.549384i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −8.10493 | −0.00866837 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | − | 558.321i | − | 0.595860i | −0.954588 | − | 0.297930i | \(-0.903704\pi\) | ||
0.954588 | − | 0.297930i | \(-0.0962962\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 190.379 | + | 190.379i | 0.202746 | + | 0.202746i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 794.760 | + | 794.760i | 0.844591 | + | 0.844591i | 0.989452 | − | 0.144861i | \(-0.0462736\pi\) |
−0.144861 | + | 0.989452i | \(0.546274\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 53.9984i | − | 0.0572624i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −5.47595 | −0.00579466 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 44.9362 | − | 44.9362i | 0.0474511 | − | 0.0474511i | −0.682983 | − | 0.730434i | \(-0.739318\pi\) |
0.730434 | + | 0.682983i | \(0.239318\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 107.309 | − | 107.309i | 0.113076 | − | 0.113076i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −175.480 | −0.184521 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 304.232i | − | 0.319236i | −0.987179 | − | 0.159618i | \(-0.948974\pi\) | ||
0.987179 | − | 0.159618i | \(-0.0510262\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 9.76549 | + | 9.76549i | 0.0102256 | + | 0.0102256i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 908.488 | + | 908.488i | 0.949308 | + | 0.949308i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 807.213i | 0.841724i | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 551.564 | 0.573948 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 697.768 | − | 697.768i | 0.724577 | − | 0.724577i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 0.127971 | − | 0.127971i | 0.000132613 | − | 0.000132613i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 834.409 | 0.862884 | 0.431442 | − | 0.902141i | \(-0.358005\pi\) | ||||
0.431442 | + | 0.902141i | \(0.358005\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | − | 220.414i | − | 0.227465i | ||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −211.499 | − | 211.499i | −0.217816 | − | 0.217816i | 0.589761 | − | 0.807577i | \(-0.299222\pi\) |
−0.807577 | + | 0.589761i | \(0.799222\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −461.043 | − | 461.043i | −0.473837 | − | 0.473837i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | − | 1795.50i | − | 1.84154i | ||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 891.561 | 0.912549 | 0.456275 | − | 0.889839i | \(-0.349183\pi\) | ||||
0.456275 | + | 0.889839i | \(0.349183\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 620.117 | − | 620.117i | 0.633419 | − | 0.633419i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −689.028 | + | 689.028i | −0.702374 | + | 0.702374i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −181.589 | −0.184730 | −0.0923648 | − | 0.995725i | \(-0.529443\pi\) | ||||
−0.0923648 | + | 0.995725i | \(0.529443\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 7.90739i | 0.00802781i | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 1196.00 | + | 1196.00i | 1.21175 | + | 1.21175i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 12.8911 | + | 12.8911i | 0.0130344 | + | 0.0130344i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | − | 1140.89i | − | 1.15125i | −0.817715 | − | 0.575624i | \(-0.804759\pi\) | ||
0.817715 | − | 0.575624i | \(-0.195241\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 1183.95 | 1.19230 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 13.0697 | − | 13.0697i | 0.0131354 | − | 0.0131354i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 742.946 | − | 742.946i | 0.745182 | − | 0.745182i | −0.228388 | − | 0.973570i | \(-0.573346\pi\) |
0.973570 | + | 0.228388i | \(0.0733455\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 835.339 | 0.836175 |
(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 | 128.3.f.b.95.3 | 6 | ||
3.2 | odd | 2 | 1152.3.m.a.991.2 | 6 | |||
4.3 | odd | 2 | 128.3.f.a.95.1 | 6 | |||
8.3 | odd | 2 | 64.3.f.a.47.3 | 6 | |||
8.5 | even | 2 | 16.3.f.a.3.3 | ✓ | 6 | ||
12.11 | even | 2 | 1152.3.m.b.991.2 | 6 | |||
16.3 | odd | 4 | 16.3.f.a.11.3 | yes | 6 | ||
16.5 | even | 4 | 128.3.f.a.31.1 | 6 | |||
16.11 | odd | 4 | inner | 128.3.f.b.31.3 | 6 | ||
16.13 | even | 4 | 64.3.f.a.15.3 | 6 | |||
24.5 | odd | 2 | 144.3.m.a.19.1 | 6 | |||
24.11 | even | 2 | 576.3.m.a.559.2 | 6 | |||
32.3 | odd | 8 | 1024.3.d.k.511.2 | 12 | |||
32.5 | even | 8 | 1024.3.c.j.1023.12 | 12 | |||
32.11 | odd | 8 | 1024.3.c.j.1023.11 | 12 | |||
32.13 | even | 8 | 1024.3.d.k.511.1 | 12 | |||
32.19 | odd | 8 | 1024.3.d.k.511.11 | 12 | |||
32.21 | even | 8 | 1024.3.c.j.1023.1 | 12 | |||
32.27 | odd | 8 | 1024.3.c.j.1023.2 | 12 | |||
32.29 | even | 8 | 1024.3.d.k.511.12 | 12 | |||
40.13 | odd | 4 | 400.3.k.c.99.1 | 6 | |||
40.29 | even | 2 | 400.3.r.c.51.1 | 6 | |||
40.37 | odd | 4 | 400.3.k.d.99.3 | 6 | |||
48.5 | odd | 4 | 1152.3.m.b.415.2 | 6 | |||
48.11 | even | 4 | 1152.3.m.a.415.2 | 6 | |||
48.29 | odd | 4 | 576.3.m.a.271.2 | 6 | |||
48.35 | even | 4 | 144.3.m.a.91.1 | 6 | |||
80.3 | even | 4 | 400.3.k.d.299.3 | 6 | |||
80.19 | odd | 4 | 400.3.r.c.251.1 | 6 | |||
80.67 | even | 4 | 400.3.k.c.299.1 | 6 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
16.3.f.a.3.3 | ✓ | 6 | 8.5 | even | 2 | ||
16.3.f.a.11.3 | yes | 6 | 16.3 | odd | 4 | ||
64.3.f.a.15.3 | 6 | 16.13 | even | 4 | |||
64.3.f.a.47.3 | 6 | 8.3 | odd | 2 | |||
128.3.f.a.31.1 | 6 | 16.5 | even | 4 | |||
128.3.f.a.95.1 | 6 | 4.3 | odd | 2 | |||
128.3.f.b.31.3 | 6 | 16.11 | odd | 4 | inner | ||
128.3.f.b.95.3 | 6 | 1.1 | even | 1 | trivial | ||
144.3.m.a.19.1 | 6 | 24.5 | odd | 2 | |||
144.3.m.a.91.1 | 6 | 48.35 | even | 4 | |||
400.3.k.c.99.1 | 6 | 40.13 | odd | 4 | |||
400.3.k.c.299.1 | 6 | 80.67 | even | 4 | |||
400.3.k.d.99.3 | 6 | 40.37 | odd | 4 | |||
400.3.k.d.299.3 | 6 | 80.3 | even | 4 | |||
400.3.r.c.51.1 | 6 | 40.29 | even | 2 | |||
400.3.r.c.251.1 | 6 | 80.19 | odd | 4 | |||
576.3.m.a.271.2 | 6 | 48.29 | odd | 4 | |||
576.3.m.a.559.2 | 6 | 24.11 | even | 2 | |||
1024.3.c.j.1023.1 | 12 | 32.21 | even | 8 | |||
1024.3.c.j.1023.2 | 12 | 32.27 | odd | 8 | |||
1024.3.c.j.1023.11 | 12 | 32.11 | odd | 8 | |||
1024.3.c.j.1023.12 | 12 | 32.5 | even | 8 | |||
1024.3.d.k.511.1 | 12 | 32.13 | even | 8 | |||
1024.3.d.k.511.2 | 12 | 32.3 | odd | 8 | |||
1024.3.d.k.511.11 | 12 | 32.19 | odd | 8 | |||
1024.3.d.k.511.12 | 12 | 32.29 | even | 8 | |||
1152.3.m.a.415.2 | 6 | 48.11 | even | 4 | |||
1152.3.m.a.991.2 | 6 | 3.2 | odd | 2 | |||
1152.3.m.b.415.2 | 6 | 48.5 | odd | 4 | |||
1152.3.m.b.991.2 | 6 | 12.11 | even | 2 |