Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [475,3,Mod(474,475)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(475, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 1]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("475.474");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 475 = 5^{2} \cdot 19 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 475.d (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(12.9428125571\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Twist minimal: | no (minimal twist has level 95) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 474.20 | ||
Character | \(\chi\) | \(=\) | 475.474 |
Dual form | 475.3.d.c.474.19 |
$q$-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 \(\left(\mathbb{Z}/475\mathbb{Z}\right)^\times\).
\(n\) | \(77\) | \(401\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.36559 | 1.18279 | 0.591397 | − | 0.806381i | \(-0.298577\pi\) | ||||
0.591397 | + | 0.806381i | \(0.298577\pi\) | |||||||
\(3\) | 3.55563 | 1.18521 | 0.592605 | − | 0.805493i | \(-0.298100\pi\) | ||||
0.592605 | + | 0.805493i | \(0.298100\pi\) | |||||||
\(4\) | 1.59600 | 0.399000 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 8.41115 | 1.40186 | ||||||||
\(7\) | − | 11.0785i | − | 1.58264i | −0.611405 | − | 0.791318i | \(-0.709395\pi\) | ||
0.611405 | − | 0.791318i | \(-0.290605\pi\) | |||||||
\(8\) | −5.68687 | −0.710859 | ||||||||
\(9\) | 3.64250 | 0.404723 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 16.7704 | 1.52458 | 0.762289 | − | 0.647237i | \(-0.224076\pi\) | ||||
0.762289 | + | 0.647237i | \(0.224076\pi\) | |||||||
\(12\) | 5.67479 | 0.472899 | ||||||||
\(13\) | 14.3035 | 1.10027 | 0.550136 | − | 0.835075i | \(-0.314576\pi\) | ||||
0.550136 | + | 0.835075i | \(0.314576\pi\) | |||||||
\(14\) | − | 26.2070i | − | 1.87193i | ||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −19.8368 | −1.23980 | ||||||||
\(17\) | 20.2160i | 1.18918i | 0.804031 | + | 0.594588i | \(0.202685\pi\) | ||||
−0.804031 | + | 0.594588i | \(0.797315\pi\) | |||||||
\(18\) | 8.61666 | 0.478703 | ||||||||
\(19\) | 16.4480 | − | 9.51127i | 0.865683 | − | 0.500593i | ||||
\(20\) | 0 | 0 | ||||||||
\(21\) | − | 39.3909i | − | 1.87576i | ||||||
\(22\) | 39.6717 | 1.80326 | ||||||||
\(23\) | − | 13.5882i | − | 0.590792i | −0.955375 | − | 0.295396i | \(-0.904548\pi\) | ||
0.955375 | − | 0.295396i | \(-0.0954516\pi\) | |||||||
\(24\) | −20.2204 | −0.842517 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 33.8362 | 1.30139 | ||||||||
\(27\) | −19.0493 | −0.705529 | ||||||||
\(28\) | − | 17.6812i | − | 0.631472i | ||||||
\(29\) | − | 30.3972i | − | 1.04818i | −0.851663 | − | 0.524090i | \(-0.824406\pi\) | ||
0.851663 | − | 0.524090i | \(-0.175594\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 16.1256i | 0.520181i | 0.965584 | + | 0.260091i | \(0.0837525\pi\) | ||||
−0.965584 | + | 0.260091i | \(0.916248\pi\) | |||||||
\(32\) | −24.1782 | −0.755567 | ||||||||
\(33\) | 59.6292 | 1.80694 | ||||||||
\(34\) | 47.8227i | 1.40655i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 5.81344 | 0.161484 | ||||||||
\(37\) | −51.2678 | −1.38562 | −0.692808 | − | 0.721122i | \(-0.743627\pi\) | ||||
−0.692808 | + | 0.721122i | \(0.743627\pi\) | |||||||
\(38\) | 38.9091 | − | 22.4997i | 1.02392 | − | 0.592098i | ||||
\(39\) | 50.8580 | 1.30405 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 74.6652i | 1.82110i | 0.413395 | + | 0.910552i | \(0.364343\pi\) | ||||
−0.413395 | + | 0.910552i | \(0.635657\pi\) | |||||||
\(42\) | − | 93.1825i | − | 2.21863i | ||||||
\(43\) | 6.23197i | 0.144929i | 0.997371 | + | 0.0724647i | \(0.0230865\pi\) | ||||
−0.997371 | + | 0.0724647i | \(0.976914\pi\) | |||||||
\(44\) | 26.7655 | 0.608307 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | − | 32.1441i | − | 0.698785i | ||||||
\(47\) | 44.0252i | 0.936706i | 0.883541 | + | 0.468353i | \(0.155152\pi\) | ||||
−0.883541 | + | 0.468353i | \(0.844848\pi\) | |||||||
\(48\) | −70.5323 | −1.46942 | ||||||||
\(49\) | −73.7321 | −1.50474 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 71.8806i | 1.40942i | ||||||||
\(52\) | 22.8284 | 0.439008 | ||||||||
\(53\) | −30.8058 | −0.581241 | −0.290620 | − | 0.956838i | \(-0.593862\pi\) | ||||
−0.290620 | + | 0.956838i | \(0.593862\pi\) | |||||||
\(54\) | −45.0627 | −0.834495 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 63.0017i | 1.12503i | ||||||||
\(57\) | 58.4829 | − | 33.8185i | 1.02602 | − | 0.593308i | ||||
\(58\) | − | 71.9073i | − | 1.23978i | ||||||
\(59\) | 73.0098i | 1.23745i | 0.785606 | + | 0.618727i | \(0.212351\pi\) | ||||
−0.785606 | + | 0.618727i | \(0.787649\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −17.7828 | −0.291522 | −0.145761 | − | 0.989320i | \(-0.546563\pi\) | ||||
−0.145761 | + | 0.989320i | \(0.546563\pi\) | |||||||
\(62\) | 38.1466i | 0.615267i | ||||||||
\(63\) | − | 40.3533i | − | 0.640528i | ||||||
\(64\) | 22.1516 | 0.346119 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | 141.058 | 2.13724 | ||||||||
\(67\) | 20.5719 | 0.307044 | 0.153522 | − | 0.988145i | \(-0.450938\pi\) | ||||
0.153522 | + | 0.988145i | \(0.450938\pi\) | |||||||
\(68\) | 32.2647i | 0.474481i | ||||||||
\(69\) | − | 48.3147i | − | 0.700212i | ||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 7.48928i | 0.105483i | 0.998608 | + | 0.0527414i | \(0.0167959\pi\) | ||||
−0.998608 | + | 0.0527414i | \(0.983204\pi\) | |||||||
\(72\) | −20.7144 | −0.287700 | ||||||||
\(73\) | − | 29.2302i | − | 0.400414i | −0.979754 | − | 0.200207i | \(-0.935838\pi\) | ||
0.979754 | − | 0.200207i | \(-0.0641615\pi\) | |||||||
\(74\) | −121.278 | −1.63890 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 26.2510 | − | 15.1800i | 0.345408 | − | 0.199737i | ||||
\(77\) | − | 185.790i | − | 2.41285i | ||||||
\(78\) | 120.309 | 1.54242 | ||||||||
\(79\) | 8.78894i | 0.111252i | 0.998452 | + | 0.0556262i | \(0.0177155\pi\) | ||||
−0.998452 | + | 0.0556262i | \(0.982284\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −100.515 | −1.24092 | ||||||||
\(82\) | 176.627i | 2.15399i | ||||||||
\(83\) | − | 63.7886i | − | 0.768537i | −0.923221 | − | 0.384269i | \(-0.874454\pi\) | ||
0.923221 | − | 0.384269i | \(-0.125546\pi\) | |||||||
\(84\) | − | 62.8679i | − | 0.748427i | ||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 14.7423i | 0.171422i | ||||||||
\(87\) | − | 108.081i | − | 1.24231i | ||||||
\(88\) | −95.3708 | −1.08376 | ||||||||
\(89\) | 162.908i | 1.83043i | 0.402965 | + | 0.915215i | \(0.367980\pi\) | ||||
−0.402965 | + | 0.915215i | \(0.632020\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | − | 158.461i | − | 1.74133i | ||||||
\(92\) | − | 21.6868i | − | 0.235726i | ||||||
\(93\) | 57.3367i | 0.616524i | ||||||||
\(94\) | 104.145i | 1.10793i | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −85.9686 | −0.895506 | ||||||||
\(97\) | −75.5974 | −0.779355 | −0.389677 | − | 0.920951i | \(-0.627413\pi\) | ||||
−0.389677 | + | 0.920951i | \(0.627413\pi\) | |||||||
\(98\) | −174.420 | −1.77979 | ||||||||
\(99\) | 61.0861 | 0.617031 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 15.7692 | 0.156131 | 0.0780656 | − | 0.996948i | \(-0.475126\pi\) | ||||
0.0780656 | + | 0.996948i | \(0.475126\pi\) | |||||||
\(102\) | 170.040i | 1.66706i | ||||||||
\(103\) | −7.15141 | −0.0694312 | −0.0347156 | − | 0.999397i | \(-0.511053\pi\) | ||||
−0.0347156 | + | 0.999397i | \(0.511053\pi\) | |||||||
\(104\) | −81.3423 | −0.782137 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −72.8737 | −0.687488 | ||||||||
\(107\) | 85.9872 | 0.803619 | 0.401809 | − | 0.915723i | \(-0.368381\pi\) | ||||
0.401809 | + | 0.915723i | \(0.368381\pi\) | |||||||
\(108\) | −30.4027 | −0.281506 | ||||||||
\(109\) | − | 95.0893i | − | 0.872379i | −0.899855 | − | 0.436190i | \(-0.856328\pi\) | ||
0.899855 | − | 0.436190i | \(-0.143672\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −182.289 | −1.64225 | ||||||||
\(112\) | 219.761i | 1.96215i | ||||||||
\(113\) | −19.0355 | −0.168456 | −0.0842281 | − | 0.996447i | \(-0.526842\pi\) | ||||
−0.0842281 | + | 0.996447i | \(0.526842\pi\) | |||||||
\(114\) | 138.346 | − | 80.0007i | 1.21356 | − | 0.701761i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | − | 48.5140i | − | 0.418224i | ||||||
\(117\) | 52.1006 | 0.445304 | ||||||||
\(118\) | 172.711i | 1.46365i | ||||||||
\(119\) | 223.962 | 1.88203 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 160.245 | 1.32434 | ||||||||
\(122\) | −42.0668 | −0.344810 | ||||||||
\(123\) | 265.482i | 2.15839i | ||||||||
\(124\) | 25.7365i | 0.207552i | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | − | 95.4592i | − | 0.757613i | ||||||
\(127\) | 93.4107 | 0.735518 | 0.367759 | − | 0.929921i | \(-0.380125\pi\) | ||||
0.367759 | + | 0.929921i | \(0.380125\pi\) | |||||||
\(128\) | 149.114 | 1.16495 | ||||||||
\(129\) | 22.1586i | 0.171772i | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 126.496 | 0.965619 | 0.482810 | − | 0.875725i | \(-0.339616\pi\) | ||||
0.482810 | + | 0.875725i | \(0.339616\pi\) | |||||||
\(132\) | 95.1682 | 0.720971 | ||||||||
\(133\) | −105.370 | − | 182.218i | −0.792257 | − | 1.37006i | ||||
\(134\) | 48.6647 | 0.363170 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | − | 114.966i | − | 0.845336i | ||||||
\(137\) | − | 93.8813i | − | 0.685265i | −0.939470 | − | 0.342632i | \(-0.888681\pi\) | ||
0.939470 | − | 0.342632i | \(-0.111319\pi\) | |||||||
\(138\) | − | 114.293i | − | 0.828207i | ||||||
\(139\) | −41.0986 | −0.295673 | −0.147837 | − | 0.989012i | \(-0.547231\pi\) | ||||
−0.147837 | + | 0.989012i | \(0.547231\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 156.537i | 1.11019i | ||||||||
\(142\) | 17.7165i | 0.124764i | ||||||||
\(143\) | 239.875 | 1.67745 | ||||||||
\(144\) | −72.2555 | −0.501775 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 69.1467i | − | 0.473607i | ||||||
\(147\) | −262.164 | −1.78343 | ||||||||
\(148\) | −81.8235 | −0.552861 | ||||||||
\(149\) | −92.2911 | −0.619404 | −0.309702 | − | 0.950834i | \(-0.600229\pi\) | ||||
−0.309702 | + | 0.950834i | \(0.600229\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 7.26853i | 0.0481359i | 0.999710 | + | 0.0240680i | \(0.00766181\pi\) | ||||
−0.999710 | + | 0.0240680i | \(0.992338\pi\) | |||||||
\(152\) | −93.5375 | + | 54.0893i | −0.615378 | + | 0.355851i | ||||
\(153\) | 73.6368i | 0.481286i | ||||||||
\(154\) | − | 439.501i | − | 2.85390i | ||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 81.1695 | 0.520317 | ||||||||
\(157\) | − | 229.214i | − | 1.45996i | −0.683468 | − | 0.729981i | \(-0.739529\pi\) | ||
0.683468 | − | 0.729981i | \(-0.260471\pi\) | |||||||
\(158\) | 20.7910i | 0.131589i | ||||||||
\(159\) | −109.534 | −0.688892 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −150.536 | −0.935009 | ||||||||
\(162\) | −237.776 | −1.46775 | ||||||||
\(163\) | 34.0426i | 0.208850i | 0.994533 | + | 0.104425i | \(0.0333002\pi\) | ||||
−0.994533 | + | 0.104425i | \(0.966700\pi\) | |||||||
\(164\) | 119.166i | 0.726621i | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | − | 150.897i | − | 0.909021i | ||||||
\(167\) | 162.274 | 0.971702 | 0.485851 | − | 0.874042i | \(-0.338510\pi\) | ||||
0.485851 | + | 0.874042i | \(0.338510\pi\) | |||||||
\(168\) | 224.011i | 1.33340i | ||||||||
\(169\) | 35.5908 | 0.210597 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 59.9118 | − | 34.6448i | 0.350361 | − | 0.202601i | ||||
\(172\) | 9.94623i | 0.0578269i | ||||||||
\(173\) | −29.7956 | −0.172229 | −0.0861145 | − | 0.996285i | \(-0.527445\pi\) | ||||
−0.0861145 | + | 0.996285i | \(0.527445\pi\) | |||||||
\(174\) | − | 255.676i | − | 1.46940i | ||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −332.670 | −1.89017 | ||||||||
\(177\) | 259.596i | 1.46664i | ||||||||
\(178\) | 385.374i | 2.16502i | ||||||||
\(179\) | 59.2752i | 0.331146i | 0.986197 | + | 0.165573i | \(0.0529474\pi\) | ||||
−0.986197 | + | 0.165573i | \(0.947053\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 205.700i | 1.13647i | 0.822868 | + | 0.568233i | \(0.192373\pi\) | ||||
−0.822868 | + | 0.568233i | \(0.807627\pi\) | |||||||
\(182\) | − | 374.853i | − | 2.05963i | ||||||
\(183\) | −63.2291 | −0.345514 | ||||||||
\(184\) | 77.2744i | 0.419970i | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 135.635i | 0.729221i | ||||||||
\(187\) | 339.029i | 1.81299i | ||||||||
\(188\) | 70.2642i | 0.373746i | ||||||||
\(189\) | 211.037i | 1.11660i | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −253.682 | −1.32818 | −0.664089 | − | 0.747654i | \(-0.731180\pi\) | ||||
−0.664089 | + | 0.747654i | \(0.731180\pi\) | |||||||
\(192\) | 78.7629 | 0.410223 | ||||||||
\(193\) | 289.646 | 1.50076 | 0.750378 | − | 0.661009i | \(-0.229872\pi\) | ||||
0.750378 | + | 0.661009i | \(0.229872\pi\) | |||||||
\(194\) | −178.832 | −0.921816 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −117.676 | −0.600390 | ||||||||
\(197\) | − | 178.190i | − | 0.904515i | −0.891887 | − | 0.452258i | \(-0.850619\pi\) | ||
0.891887 | − | 0.452258i | \(-0.149381\pi\) | |||||||
\(198\) | 144.504 | 0.729820 | ||||||||
\(199\) | 154.602 | 0.776893 | 0.388446 | − | 0.921471i | \(-0.373012\pi\) | ||||
0.388446 | + | 0.921471i | \(0.373012\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 73.1462 | 0.363912 | ||||||||
\(202\) | 37.3035 | 0.184671 | ||||||||
\(203\) | −336.754 | −1.65889 | ||||||||
\(204\) | 114.721i | 0.562360i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −16.9173 | −0.0821228 | ||||||||
\(207\) | − | 49.4951i | − | 0.239107i | ||||||
\(208\) | −283.736 | −1.36412 | ||||||||
\(209\) | 275.838 | − | 159.507i | 1.31980 | − | 0.763193i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 273.846i | − | 1.29785i | −0.760854 | − | 0.648923i | \(-0.775220\pi\) | ||
0.760854 | − | 0.648923i | \(-0.224780\pi\) | |||||||
\(212\) | −49.1660 | −0.231915 | ||||||||
\(213\) | 26.6291i | 0.125019i | ||||||||
\(214\) | 203.410 | 0.950515 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | 108.331 | 0.501531 | ||||||||
\(217\) | 178.647 | 0.823258 | ||||||||
\(218\) | − | 224.942i | − | 1.03184i | ||||||
\(219\) | − | 103.932i | − | 0.474575i | ||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 289.160i | 1.30842i | ||||||||
\(222\) | −431.221 | −1.94244 | ||||||||
\(223\) | −229.796 | −1.03048 | −0.515238 | − | 0.857047i | \(-0.672296\pi\) | ||||
−0.515238 | + | 0.857047i | \(0.672296\pi\) | |||||||
\(224\) | 267.857i | 1.19579i | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −45.0302 | −0.199249 | ||||||||
\(227\) | −366.166 | −1.61306 | −0.806532 | − | 0.591190i | \(-0.798658\pi\) | ||||
−0.806532 | + | 0.591190i | \(0.798658\pi\) | |||||||
\(228\) | 93.3387 | − | 53.9744i | 0.409380 | − | 0.236730i | ||||
\(229\) | −334.098 | −1.45894 | −0.729471 | − | 0.684012i | \(-0.760234\pi\) | ||||
−0.729471 | + | 0.684012i | \(0.760234\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | − | 660.599i | − | 2.85974i | ||||||
\(232\) | 172.865i | 0.745108i | ||||||||
\(233\) | 83.9900i | 0.360472i | 0.983623 | + | 0.180236i | \(0.0576861\pi\) | ||||
−0.983623 | + | 0.180236i | \(0.942314\pi\) | |||||||
\(234\) | 123.249 | 0.526703 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | 116.524i | 0.493745i | ||||||||
\(237\) | 31.2502i | 0.131857i | ||||||||
\(238\) | 529.801 | 2.22606 | ||||||||
\(239\) | 110.020 | 0.460335 | 0.230168 | − | 0.973151i | \(-0.426073\pi\) | ||||
0.230168 | + | 0.973151i | \(0.426073\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 321.641i | 1.33461i | 0.744785 | + | 0.667305i | \(0.232552\pi\) | ||||
−0.744785 | + | 0.667305i | \(0.767448\pi\) | |||||||
\(242\) | 379.073 | 1.56642 | ||||||||
\(243\) | −185.950 | −0.765225 | ||||||||
\(244\) | −28.3814 | −0.116317 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 628.021i | 2.55293i | ||||||||
\(247\) | 235.264 | − | 136.045i | 0.952486 | − | 0.550788i | ||||
\(248\) | − | 91.7043i | − | 0.369775i | ||||||
\(249\) | − | 226.809i | − | 0.910878i | ||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 143.410 | 0.571353 | 0.285676 | − | 0.958326i | \(-0.407782\pi\) | ||||
0.285676 | + | 0.958326i | \(0.407782\pi\) | |||||||
\(252\) | − | 64.4039i | − | 0.255571i | ||||||
\(253\) | − | 227.879i | − | 0.900708i | ||||||
\(254\) | 220.971 | 0.869965 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 264.136 | 1.03178 | ||||||||
\(257\) | −171.202 | −0.666156 | −0.333078 | − | 0.942899i | \(-0.608087\pi\) | ||||
−0.333078 | + | 0.942899i | \(0.608087\pi\) | |||||||
\(258\) | 52.4180i | 0.203171i | ||||||||
\(259\) | 567.968i | 2.19293i | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | − | 110.722i | − | 0.424222i | ||||||
\(262\) | 299.238 | 1.14213 | ||||||||
\(263\) | − | 184.993i | − | 0.703395i | −0.936114 | − | 0.351697i | \(-0.885605\pi\) | ||
0.936114 | − | 0.351697i | \(-0.114395\pi\) | |||||||
\(264\) | −339.103 | −1.28448 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −249.262 | − | 431.053i | −0.937076 | − | 1.62050i | ||||
\(267\) | 579.242i | 2.16944i | ||||||||
\(268\) | 32.8328 | 0.122511 | ||||||||
\(269\) | 453.194i | 1.68473i | 0.538904 | + | 0.842367i | \(0.318839\pi\) | ||||
−0.538904 | + | 0.842367i | \(0.681161\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 336.795 | 1.24279 | 0.621393 | − | 0.783499i | \(-0.286567\pi\) | ||||
0.621393 | + | 0.783499i | \(0.286567\pi\) | |||||||
\(272\) | − | 401.020i | − | 1.47434i | ||||||
\(273\) | − | 563.428i | − | 2.06384i | ||||||
\(274\) | − | 222.084i | − | 0.810527i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | − | 77.1102i | − | 0.279385i | ||||||
\(277\) | − | 270.449i | − | 0.976351i | −0.872746 | − | 0.488175i | \(-0.837663\pi\) | ||
0.872746 | − | 0.488175i | \(-0.162337\pi\) | |||||||
\(278\) | −97.2223 | −0.349720 | ||||||||
\(279\) | 58.7376i | 0.210529i | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | − | 151.335i | − | 0.538558i | −0.963062 | − | 0.269279i | \(-0.913215\pi\) | ||
0.963062 | − | 0.269279i | \(-0.0867853\pi\) | |||||||
\(282\) | 370.303i | 1.31313i | ||||||||
\(283\) | − | 437.891i | − | 1.54732i | −0.633603 | − | 0.773658i | \(-0.718425\pi\) | ||
0.633603 | − | 0.773658i | \(-0.281575\pi\) | |||||||
\(284\) | 11.9529i | 0.0420876i | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 567.446 | 1.98408 | ||||||||
\(287\) | 827.175 | 2.88214 | ||||||||
\(288\) | −88.0690 | −0.305795 | ||||||||
\(289\) | −119.686 | −0.414139 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −268.796 | −0.923699 | ||||||||
\(292\) | − | 46.6515i | − | 0.159765i | ||||||
\(293\) | 265.247 | 0.905279 | 0.452640 | − | 0.891694i | \(-0.350482\pi\) | ||||
0.452640 | + | 0.891694i | \(0.350482\pi\) | |||||||
\(294\) | −620.172 | −2.10943 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 291.553 | 0.984977 | ||||||||
\(297\) | −319.463 | −1.07563 | ||||||||
\(298\) | −218.323 | −0.732627 | ||||||||
\(299\) | − | 194.359i | − | 0.650031i | ||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 69.0406 | 0.229371 | ||||||||
\(302\) | 17.1943i | 0.0569349i | ||||||||
\(303\) | 56.0696 | 0.185048 | ||||||||
\(304\) | −326.275 | + | 188.673i | −1.07327 | + | 0.620635i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 174.194i | 0.569262i | ||||||||
\(307\) | 405.065 | 1.31943 | 0.659714 | − | 0.751517i | \(-0.270677\pi\) | ||||
0.659714 | + | 0.751517i | \(0.270677\pi\) | |||||||
\(308\) | − | 296.520i | − | 0.962728i | ||||||
\(309\) | −25.4278 | −0.0822906 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −313.906 | −1.00934 | −0.504672 | − | 0.863311i | \(-0.668387\pi\) | ||||
−0.504672 | + | 0.863311i | \(0.668387\pi\) | |||||||
\(312\) | −289.223 | −0.926997 | ||||||||
\(313\) | 513.442i | 1.64039i | 0.572085 | + | 0.820194i | \(0.306135\pi\) | ||||
−0.572085 | + | 0.820194i | \(0.693865\pi\) | |||||||
\(314\) | − | 542.225i | − | 1.72683i | ||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 14.0271i | 0.0443897i | ||||||||
\(317\) | −25.8051 | −0.0814042 | −0.0407021 | − | 0.999171i | \(-0.512959\pi\) | ||||
−0.0407021 | + | 0.999171i | \(0.512959\pi\) | |||||||
\(318\) | −259.112 | −0.814817 | ||||||||
\(319\) | − | 509.772i | − | 1.59803i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 305.739 | 0.952457 | ||||||||
\(322\) | −356.107 | −1.10592 | ||||||||
\(323\) | 192.280 | + | 332.512i | 0.595293 | + | 1.02945i | ||||
\(324\) | −160.422 | −0.495128 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 80.5307i | 0.247027i | ||||||||
\(327\) | − | 338.102i | − | 1.03395i | ||||||
\(328\) | − | 424.611i | − | 1.29455i | ||||||
\(329\) | 487.731 | 1.48247 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 171.635i | − | 0.518534i | −0.965806 | − | 0.259267i | \(-0.916519\pi\) | ||
0.965806 | − | 0.259267i | \(-0.0834810\pi\) | |||||||
\(332\) | − | 101.807i | − | 0.306647i | ||||||
\(333\) | −186.743 | −0.560790 | ||||||||
\(334\) | 383.874 | 1.14932 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 781.388i | 2.32556i | ||||||||
\(337\) | −206.114 | −0.611613 | −0.305807 | − | 0.952094i | \(-0.598926\pi\) | ||||
−0.305807 | + | 0.952094i | \(0.598926\pi\) | |||||||
\(338\) | 84.1932 | 0.249092 | ||||||||
\(339\) | −67.6833 | −0.199656 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 270.432i | 0.793057i | ||||||||
\(342\) | 141.727 | − | 81.9553i | 0.414405 | − | 0.239635i | ||||
\(343\) | 273.994i | 0.798815i | ||||||||
\(344\) | − | 35.4404i | − | 0.103024i | ||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −70.4841 | −0.203711 | ||||||||
\(347\) | 7.91893i | 0.0228211i | 0.999935 | + | 0.0114106i | \(0.00363217\pi\) | ||||
−0.999935 | + | 0.0114106i | \(0.996368\pi\) | |||||||
\(348\) | − | 172.498i | − | 0.495683i | ||||||
\(349\) | −409.448 | −1.17320 | −0.586602 | − | 0.809876i | \(-0.699535\pi\) | ||||
−0.586602 | + | 0.809876i | \(0.699535\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −272.472 | −0.776273 | ||||||||
\(352\) | −405.476 | −1.15192 | ||||||||
\(353\) | − | 637.919i | − | 1.80714i | −0.428445 | − | 0.903568i | \(-0.640939\pi\) | ||
0.428445 | − | 0.903568i | \(-0.359061\pi\) | |||||||
\(354\) | 614.097i | 1.73474i | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | 260.002i | 0.730342i | ||||||||
\(357\) | 796.325 | 2.23060 | ||||||||
\(358\) | 140.221i | 0.391678i | ||||||||
\(359\) | 237.272 | 0.660926 | 0.330463 | − | 0.943819i | \(-0.392795\pi\) | ||||
0.330463 | + | 0.943819i | \(0.392795\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 180.072 | − | 312.882i | 0.498813 | − | 0.866710i | ||||
\(362\) | 486.602i | 1.34420i | ||||||||
\(363\) | 569.771 | 1.56962 | ||||||||
\(364\) | − | 252.904i | − | 0.694790i | ||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −149.574 | −0.408672 | ||||||||
\(367\) | − | 542.889i | − | 1.47926i | −0.673013 | − | 0.739631i | \(-0.735000\pi\) | ||
0.673013 | − | 0.739631i | \(-0.265000\pi\) | |||||||
\(368\) | 269.546i | 0.732463i | ||||||||
\(369\) | 271.968i | 0.737042i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 341.280i | 0.919892i | ||||||||
\(372\) | 91.5095i | 0.245993i | ||||||||
\(373\) | −444.746 | −1.19235 | −0.596175 | − | 0.802855i | \(-0.703313\pi\) | ||||
−0.596175 | + | 0.802855i | \(0.703313\pi\) | |||||||
\(374\) | 802.003i | 2.14439i | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | − | 250.366i | − | 0.665866i | ||||||
\(377\) | − | 434.787i | − | 1.15328i | ||||||
\(378\) | 499.225i | 1.32070i | ||||||||
\(379\) | 150.221i | 0.396362i | 0.980165 | + | 0.198181i | \(0.0635035\pi\) | ||||
−0.980165 | + | 0.198181i | \(0.936497\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 332.134 | 0.871743 | ||||||||
\(382\) | −600.106 | −1.57096 | ||||||||
\(383\) | −85.8011 | −0.224024 | −0.112012 | − | 0.993707i | \(-0.535729\pi\) | ||||
−0.112012 | + | 0.993707i | \(0.535729\pi\) | |||||||
\(384\) | 530.195 | 1.38072 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 685.182 | 1.77508 | ||||||||
\(387\) | 22.7000i | 0.0586562i | ||||||||
\(388\) | −120.654 | −0.310963 | ||||||||
\(389\) | 249.669 | 0.641822 | 0.320911 | − | 0.947109i | \(-0.396011\pi\) | ||||
0.320911 | + | 0.947109i | \(0.396011\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 274.699 | 0.702555 | ||||||||
\(392\) | 419.305 | 1.06966 | ||||||||
\(393\) | 449.773 | 1.14446 | ||||||||
\(394\) | − | 421.523i | − | 1.06985i | ||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 97.4934 | 0.246195 | ||||||||
\(397\) | 340.476i | 0.857622i | 0.903394 | + | 0.428811i | \(0.141067\pi\) | ||||
−0.903394 | + | 0.428811i | \(0.858933\pi\) | |||||||
\(398\) | 365.724 | 0.918904 | ||||||||
\(399\) | −374.657 | − | 647.900i | −0.938990 | − | 1.62381i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 491.002i | − | 1.22444i | −0.790686 | − | 0.612221i | \(-0.790276\pi\) | ||
0.790686 | − | 0.612221i | \(-0.209724\pi\) | |||||||
\(402\) | 173.034 | 0.430432 | ||||||||
\(403\) | 230.653i | 0.572341i | ||||||||
\(404\) | 25.1677 | 0.0622964 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −796.621 | −1.96212 | ||||||||
\(407\) | −859.779 | −2.11248 | ||||||||
\(408\) | − | 408.775i | − | 1.00190i | ||||||
\(409\) | 115.833i | 0.283210i | 0.989923 | + | 0.141605i | \(0.0452263\pi\) | ||||
−0.989923 | + | 0.141605i | \(0.954774\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | − | 333.807i | − | 0.812183i | ||||||
\(412\) | −11.4137 | −0.0277031 | ||||||||
\(413\) | 808.836 | 1.95844 | ||||||||
\(414\) | − | 117.085i | − | 0.282814i | ||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | −345.833 | −0.831329 | ||||||||
\(417\) | −146.131 | −0.350435 | ||||||||
\(418\) | 652.519 | − | 377.328i | 1.56105 | − | 0.902700i | ||||
\(419\) | −81.4969 | −0.194503 | −0.0972516 | − | 0.995260i | \(-0.531005\pi\) | ||||
−0.0972516 | + | 0.995260i | \(0.531005\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | − | 221.652i | − | 0.526490i | −0.964729 | − | 0.263245i | \(-0.915207\pi\) | ||
0.964729 | − | 0.263245i | \(-0.0847927\pi\) | |||||||
\(422\) | − | 647.806i | − | 1.53508i | ||||||
\(423\) | 160.362i | 0.379106i | ||||||||
\(424\) | 175.188 | 0.413180 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 62.9934i | 0.147872i | ||||||||
\(427\) | 197.006i | 0.461372i | ||||||||
\(428\) | 137.236 | 0.320644 | ||||||||
\(429\) | 852.907 | 1.98813 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 211.834i | 0.491494i | 0.969334 | + | 0.245747i | \(0.0790333\pi\) | ||||
−0.969334 | + | 0.245747i | \(0.920967\pi\) | |||||||
\(432\) | 377.876 | 0.874714 | ||||||||
\(433\) | −389.534 | −0.899616 | −0.449808 | − | 0.893125i | \(-0.648508\pi\) | ||||
−0.449808 | + | 0.893125i | \(0.648508\pi\) | |||||||
\(434\) | 422.605 | 0.973744 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | − | 151.763i | − | 0.348079i | ||||||
\(437\) | −129.241 | − | 223.499i | −0.295746 | − | 0.511438i | ||||
\(438\) | − | 245.860i | − | 0.561324i | ||||||
\(439\) | − | 465.691i | − | 1.06080i | −0.847748 | − | 0.530400i | \(-0.822042\pi\) | ||
0.847748 | − | 0.530400i | \(-0.177958\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −268.569 | −0.609001 | ||||||||
\(442\) | 684.033i | 1.54759i | ||||||||
\(443\) | − | 382.479i | − | 0.863383i | −0.902021 | − | 0.431692i | \(-0.857917\pi\) | ||
0.902021 | − | 0.431692i | \(-0.142083\pi\) | |||||||
\(444\) | −290.934 | −0.655257 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −543.603 | −1.21884 | ||||||||
\(447\) | −328.153 | −0.734123 | ||||||||
\(448\) | − | 245.406i | − | 0.547780i | ||||||
\(449\) | − | 666.393i | − | 1.48417i | −0.670305 | − | 0.742086i | \(-0.733837\pi\) | ||
0.670305 | − | 0.742086i | \(-0.266163\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1252.16i | 2.77641i | ||||||||
\(452\) | −30.3807 | −0.0672140 | ||||||||
\(453\) | 25.8442i | 0.0570512i | ||||||||
\(454\) | −866.196 | −1.90792 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −332.585 | + | 192.322i | −0.729352 | + | 0.421758i | ||||
\(457\) | 627.200i | 1.37243i | 0.727399 | + | 0.686214i | \(0.240729\pi\) | ||||
−0.727399 | + | 0.686214i | \(0.759271\pi\) | |||||||
\(458\) | −790.337 | −1.72563 | ||||||||
\(459\) | − | 385.100i | − | 0.838998i | ||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 798.338 | 1.73175 | 0.865876 | − | 0.500258i | \(-0.166762\pi\) | ||||
0.865876 | + | 0.500258i | \(0.166762\pi\) | |||||||
\(462\) | − | 1562.70i | − | 3.38248i | ||||||
\(463\) | 791.786i | 1.71012i | 0.518528 | + | 0.855061i | \(0.326480\pi\) | ||||
−0.518528 | + | 0.855061i | \(0.673520\pi\) | |||||||
\(464\) | 602.983i | 1.29953i | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 198.686i | 0.426364i | ||||||||
\(467\) | 418.723i | 0.896622i | 0.893878 | + | 0.448311i | \(0.147974\pi\) | ||||
−0.893878 | + | 0.448311i | \(0.852026\pi\) | |||||||
\(468\) | 83.1526 | 0.177677 | ||||||||
\(469\) | − | 227.905i | − | 0.485939i | ||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | − | 815.000i | − | 1.73036i | ||||||
\(472\) | − | 415.197i | − | 0.879655i | ||||||
\(473\) | 104.512i | 0.220956i | ||||||||
\(474\) | 73.9251i | 0.155960i | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 357.443 | 0.750931 | ||||||||
\(477\) | −112.210 | −0.235241 | ||||||||
\(478\) | 260.262 | 0.544481 | ||||||||
\(479\) | −63.6160 | −0.132810 | −0.0664050 | − | 0.997793i | \(-0.521153\pi\) | ||||
−0.0664050 | + | 0.997793i | \(0.521153\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −733.310 | −1.52455 | ||||||||
\(482\) | 760.869i | 1.57857i | ||||||||
\(483\) | −535.252 | −1.10818 | ||||||||
\(484\) | 255.751 | 0.528411 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −439.880 | −0.905102 | ||||||||
\(487\) | 556.997 | 1.14373 | 0.571866 | − | 0.820347i | \(-0.306220\pi\) | ||||
0.571866 | + | 0.820347i | \(0.306220\pi\) | |||||||
\(488\) | 101.129 | 0.207231 | ||||||||
\(489\) | 121.043i | 0.247531i | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 856.809 | 1.74503 | 0.872514 | − | 0.488589i | \(-0.162488\pi\) | ||||
0.872514 | + | 0.488589i | \(0.162488\pi\) | |||||||
\(492\) | 423.709i | 0.861198i | ||||||||
\(493\) | 614.510 | 1.24647 | ||||||||
\(494\) | 556.537 | − | 321.825i | 1.12659 | − | 0.651469i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 319.881i | − | 0.644920i | ||||||
\(497\) | 82.9696 | 0.166941 | ||||||||
\(498\) | − | 536.536i | − | 1.07738i | ||||||
\(499\) | −761.632 | −1.52632 | −0.763158 | − | 0.646211i | \(-0.776352\pi\) | ||||
−0.763158 | + | 0.646211i | \(0.776352\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 576.987 | 1.15167 | ||||||||
\(502\) | 339.248 | 0.675792 | ||||||||
\(503\) | − | 34.7192i | − | 0.0690242i | −0.999404 | − | 0.0345121i | \(-0.989012\pi\) | ||
0.999404 | − | 0.0345121i | \(-0.0109877\pi\) | |||||||
\(504\) | 229.484i | 0.455325i | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | − | 539.068i | − | 1.06535i | ||||||
\(507\) | 126.548 | 0.249601 | ||||||||
\(508\) | 149.084 | 0.293472 | ||||||||
\(509\) | 9.31181i | 0.0182943i | 0.999958 | + | 0.00914716i | \(0.00291167\pi\) | ||||
−0.999958 | + | 0.00914716i | \(0.997088\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −323.826 | −0.633710 | ||||||||
\(512\) | 28.3801 | 0.0554300 | ||||||||
\(513\) | −313.322 | + | 181.183i | −0.610764 | + | 0.353183i | ||||
\(514\) | −404.993 | −0.787925 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 35.3651i | 0.0685370i | ||||||||
\(517\) | 738.318i | 1.42808i | ||||||||
\(518\) | 1343.58i | 2.59378i | ||||||||
\(519\) | −105.942 | −0.204128 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | − | 88.0858i | − | 0.169071i | −0.996420 | − | 0.0845353i | \(-0.973059\pi\) | ||
0.996420 | − | 0.0845353i | \(-0.0269406\pi\) | |||||||
\(522\) | − | 261.922i | − | 0.501767i | ||||||
\(523\) | −377.616 | −0.722019 | −0.361009 | − | 0.932562i | \(-0.617568\pi\) | ||||
−0.361009 | + | 0.932562i | \(0.617568\pi\) | |||||||
\(524\) | 201.888 | 0.385282 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | − | 437.617i | − | 0.831971i | ||||||
\(527\) | −325.995 | −0.618587 | ||||||||
\(528\) | −1182.85 | −2.24025 | ||||||||
\(529\) | 344.360 | 0.650965 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 265.938i | 0.500826i | ||||||||
\(532\) | −168.171 | − | 290.820i | −0.316111 | − | 0.546654i | ||||
\(533\) | 1067.98i | 2.00371i | ||||||||
\(534\) | 1370.25i | 2.56600i | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | −116.990 | −0.218265 | ||||||||
\(537\) | 210.761i | 0.392478i | ||||||||
\(538\) | 1072.07i | 1.99269i | ||||||||
\(539\) | −1236.51 | −2.29409 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −225.756 | −0.417293 | −0.208647 | − | 0.977991i | \(-0.566906\pi\) | ||||
−0.208647 | + | 0.977991i | \(0.566906\pi\) | |||||||
\(542\) | 796.718 | 1.46996 | ||||||||
\(543\) | 731.394i | 1.34695i | ||||||||
\(544\) | − | 488.785i | − | 0.898502i | ||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | − | 1332.84i | − | 2.44110i | ||||||
\(547\) | −1050.58 | −1.92062 | −0.960309 | − | 0.278938i | \(-0.910018\pi\) | ||||
−0.960309 | + | 0.278938i | \(0.910018\pi\) | |||||||
\(548\) | − | 149.835i | − | 0.273421i | ||||||
\(549\) | −64.7739 | −0.117985 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −289.116 | − | 499.973i | −0.524712 | − | 0.907391i | ||||
\(552\) | 274.759i | 0.497752i | ||||||||
\(553\) | 97.3678 | 0.176072 | ||||||||
\(554\) | − | 639.771i | − | 1.15482i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −65.5934 | −0.117974 | ||||||||
\(557\) | − | 580.999i | − | 1.04309i | −0.853225 | − | 0.521543i | \(-0.825356\pi\) | ||
0.853225 | − | 0.521543i | \(-0.174644\pi\) | |||||||
\(558\) | 138.949i | 0.249012i | ||||||||
\(559\) | 89.1391i | 0.159462i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 1205.46i | 2.14877i | ||||||||
\(562\) | − | 357.995i | − | 0.637002i | ||||||
\(563\) | −796.409 | −1.41458 | −0.707291 | − | 0.706923i | \(-0.750083\pi\) | ||||
−0.707291 | + | 0.706923i | \(0.750083\pi\) | |||||||
\(564\) | 249.834i | 0.442967i | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 1035.87i | − | 1.83016i | ||||||
\(567\) | 1113.55i | 1.96393i | ||||||||
\(568\) | − | 42.5905i | − | 0.0749833i | ||||||
\(569\) | 171.428i | 0.301280i | 0.988589 | + | 0.150640i | \(0.0481334\pi\) | ||||
−0.988589 | + | 0.150640i | \(0.951867\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −673.960 | −1.18031 | −0.590157 | − | 0.807288i | \(-0.700934\pi\) | ||||
−0.590157 | + | 0.807288i | \(0.700934\pi\) | |||||||
\(572\) | 382.841 | 0.669302 | ||||||||
\(573\) | −901.999 | −1.57417 | ||||||||
\(574\) | 1956.76 | 3.40898 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 80.6873 | 0.140082 | ||||||||
\(577\) | 795.916i | 1.37940i | 0.724094 | + | 0.689702i | \(0.242258\pi\) | ||||
−0.724094 | + | 0.689702i | \(0.757742\pi\) | |||||||
\(578\) | −283.128 | −0.489840 | ||||||||
\(579\) | 1029.87 | 1.77871 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −706.679 | −1.21632 | ||||||||
\(582\) | −635.861 | −1.09254 | ||||||||
\(583\) | −516.623 | −0.886146 | ||||||||
\(584\) | 166.229i | 0.284638i | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 627.464 | 1.07076 | ||||||||
\(587\) | 19.6929i | 0.0335484i | 0.999859 | + | 0.0167742i | \(0.00533965\pi\) | ||||
−0.999859 | + | 0.0167742i | \(0.994660\pi\) | |||||||
\(588\) | −418.414 | −0.711589 | ||||||||
\(589\) | 153.375 | + | 265.234i | 0.260399 | + | 0.450312i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 633.576i | − | 1.07204i | ||||||
\(592\) | 1016.99 | 1.71789 | ||||||||
\(593\) | − | 636.058i | − | 1.07261i | −0.844024 | − | 0.536306i | \(-0.819819\pi\) | ||
0.844024 | − | 0.536306i | \(-0.180181\pi\) | |||||||
\(594\) | −755.718 | −1.27225 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −147.297 | −0.247142 | ||||||||
\(597\) | 549.706 | 0.920781 | ||||||||
\(598\) | − | 459.774i | − | 0.768853i | ||||||
\(599\) | 936.525i | 1.56348i | 0.623604 | + | 0.781741i | \(0.285668\pi\) | ||||
−0.623604 | + | 0.781741i | \(0.714332\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 252.090i | 0.419451i | 0.977760 | + | 0.209725i | \(0.0672570\pi\) | ||||
−0.977760 | + | 0.209725i | \(0.932743\pi\) | |||||||
\(602\) | 163.321 | 0.271298 | ||||||||
\(603\) | 74.9334 | 0.124268 | ||||||||
\(604\) | 11.6006i | 0.0192062i | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 132.638 | 0.218874 | ||||||||
\(607\) | −498.526 | −0.821295 | −0.410648 | − | 0.911794i | \(-0.634697\pi\) | ||||
−0.410648 | + | 0.911794i | \(0.634697\pi\) | |||||||
\(608\) | −397.682 | + | 229.965i | −0.654082 | + | 0.378232i | ||||
\(609\) | −1197.37 | −1.96613 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 629.715i | 1.03063i | ||||||||
\(612\) | 117.524i | 0.192033i | ||||||||
\(613\) | − | 638.709i | − | 1.04194i | −0.853575 | − | 0.520969i | \(-0.825571\pi\) | ||
0.853575 | − | 0.520969i | \(-0.174429\pi\) | |||||||
\(614\) | 958.215 | 1.56061 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 1056.56i | 1.71520i | ||||||||
\(617\) | − | 702.709i | − | 1.13891i | −0.822021 | − | 0.569457i | \(-0.807154\pi\) | ||
0.822021 | − | 0.569457i | \(-0.192846\pi\) | |||||||
\(618\) | −60.1516 | −0.0973327 | ||||||||
\(619\) | −195.693 | −0.316144 | −0.158072 | − | 0.987428i | \(-0.550528\pi\) | ||||
−0.158072 | + | 0.987428i | \(0.550528\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 258.846i | 0.416821i | ||||||||
\(622\) | −742.572 | −1.19385 | ||||||||
\(623\) | 1804.77 | 2.89691 | ||||||||
\(624\) | −1008.86 | −1.61676 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1214.59i | 1.94024i | ||||||||
\(627\) | 980.779 | − | 567.149i | 1.56424 | − | 0.904544i | ||||
\(628\) | − | 365.826i | − | 0.582525i | ||||||
\(629\) | − | 1036.43i | − | 1.64774i | ||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −1063.16 | −1.68489 | −0.842444 | − | 0.538784i | \(-0.818884\pi\) | ||||
−0.842444 | + | 0.538784i | \(0.818884\pi\) | |||||||
\(632\) | − | 49.9815i | − | 0.0790847i | ||||||
\(633\) | − | 973.694i | − | 1.53822i | ||||||
\(634\) | −61.0443 | −0.0962843 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −174.816 | −0.274868 | ||||||||
\(637\) | −1054.63 | −1.65562 | ||||||||
\(638\) | − | 1205.91i | − | 1.89014i | ||||||
\(639\) | 27.2797i | 0.0426913i | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | − | 744.630i | − | 1.16167i | −0.814021 | − | 0.580835i | \(-0.802726\pi\) | ||
0.814021 | − | 0.580835i | \(-0.197274\pi\) | |||||||
\(642\) | 723.251 | 1.12656 | ||||||||
\(643\) | 195.660i | 0.304293i | 0.988358 | + | 0.152146i | \(0.0486185\pi\) | ||||
−0.988358 | + | 0.152146i | \(0.951382\pi\) | |||||||
\(644\) | −240.256 | −0.373069 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 454.854 | + | 786.586i | 0.704109 | + | 1.21763i | ||||
\(647\) | 128.045i | 0.197906i | 0.995092 | + | 0.0989529i | \(0.0315493\pi\) | ||||
−0.995092 | + | 0.0989529i | \(0.968451\pi\) | |||||||
\(648\) | 571.614 | 0.882120 | ||||||||
\(649\) | 1224.40i | 1.88660i | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 635.202 | 0.975733 | ||||||||
\(652\) | 54.3320i | 0.0833313i | ||||||||
\(653\) | − | 717.897i | − | 1.09938i | −0.835368 | − | 0.549692i | \(-0.814745\pi\) | ||
0.835368 | − | 0.549692i | \(-0.185255\pi\) | |||||||
\(654\) | − | 799.811i | − | 1.22295i | ||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | − | 1481.12i | − | 2.25780i | ||||||
\(657\) | − | 106.471i | − | 0.162057i | ||||||
\(658\) | 1153.77 | 1.75345 | ||||||||
\(659\) | 544.617i | 0.826430i | 0.910633 | + | 0.413215i | \(0.135594\pi\) | ||||
−0.910633 | + | 0.413215i | \(0.864406\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 435.420i | 0.658729i | 0.944203 | + | 0.329365i | \(0.106835\pi\) | ||||
−0.944203 | + | 0.329365i | \(0.893165\pi\) | |||||||
\(662\) | − | 406.017i | − | 0.613319i | ||||||
\(663\) | 1028.15i | 1.55075i | ||||||||
\(664\) | 362.757i | 0.546321i | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −441.757 | −0.663299 | ||||||||
\(667\) | −413.044 | −0.619256 | ||||||||
\(668\) | 258.990 | 0.387709 | ||||||||
\(669\) | −817.070 | −1.22133 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −298.224 | −0.444447 | ||||||||
\(672\) | 952.399i | 1.41726i | ||||||||
\(673\) | 397.296 | 0.590336 | 0.295168 | − | 0.955445i | \(-0.404624\pi\) | ||||
0.295168 | + | 0.955445i | \(0.404624\pi\) | |||||||
\(674\) | −487.580 | −0.723412 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 56.8030 | 0.0840281 | ||||||||
\(677\) | 456.859 | 0.674829 | 0.337415 | − | 0.941356i | \(-0.390448\pi\) | ||||
0.337415 | + | 0.941356i | \(0.390448\pi\) | |||||||
\(678\) | −160.111 | −0.236152 | ||||||||
\(679\) | 837.502i | 1.23343i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −1301.95 | −1.91182 | ||||||||
\(682\) | 639.731i | 0.938022i | ||||||||
\(683\) | −880.553 | −1.28924 | −0.644621 | − | 0.764502i | \(-0.722985\pi\) | ||||
−0.644621 | + | 0.764502i | \(0.722985\pi\) | |||||||
\(684\) | 95.6192 | − | 55.2932i | 0.139794 | − | 0.0808379i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 648.155i | 0.944833i | ||||||||
\(687\) | −1187.93 | −1.72915 | ||||||||
\(688\) | − | 123.622i | − | 0.179683i | ||||||
\(689\) | −440.631 | −0.639522 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −34.3920 | −0.0497713 | −0.0248857 | − | 0.999690i | \(-0.507922\pi\) | ||||
−0.0248857 | + | 0.999690i | \(0.507922\pi\) | |||||||
\(692\) | −47.5538 | −0.0687194 | ||||||||
\(693\) | − | 676.739i | − | 0.976535i | ||||||
\(694\) | 18.7329i | 0.0269927i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 614.644i | 0.883109i | ||||||||
\(697\) | −1509.43 | −2.16561 | ||||||||
\(698\) | −968.585 | −1.38766 | ||||||||
\(699\) | 298.637i | 0.427235i | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 419.321 | 0.598175 | 0.299088 | − | 0.954226i | \(-0.403318\pi\) | ||||
0.299088 | + | 0.954226i | \(0.403318\pi\) | |||||||
\(702\) | −644.556 | −0.918171 | ||||||||
\(703\) | −843.251 | + | 487.622i | −1.19950 | + | 0.693630i | ||||
\(704\) | 371.490 | 0.527685 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | − | 1509.05i | − | 2.13747i | ||||||
\(707\) | − | 174.699i | − | 0.247099i | ||||||
\(708\) | 414.315i | 0.585191i | ||||||||
\(709\) | −373.670 | −0.527038 | −0.263519 | − | 0.964654i | \(-0.584883\pi\) | ||||
−0.263519 | + | 0.964654i | \(0.584883\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 32.0137i | 0.0450263i | ||||||||
\(712\) | − | 926.438i | − | 1.30118i | ||||||
\(713\) | 219.118 | 0.307319 | ||||||||
\(714\) | 1883.78 | 2.63834 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 94.6033i | 0.132127i | ||||||||
\(717\) | 391.191 | 0.545594 | ||||||||
\(718\) | 561.289 | 0.781739 | ||||||||
\(719\) | 328.089 | 0.456312 | 0.228156 | − | 0.973625i | \(-0.426730\pi\) | ||||
0.228156 | + | 0.973625i | \(0.426730\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 79.2266i | 0.109884i | ||||||||
\(722\) | 425.975 | − | 740.150i | 0.589993 | − | 1.02514i | ||||
\(723\) | 1143.64i | 1.58179i | ||||||||
\(724\) | 328.298i | 0.453450i | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1347.84 | 1.85653 | ||||||||
\(727\) | − | 1131.05i | − | 1.55578i | −0.628402 | − | 0.777889i | \(-0.716291\pi\) | ||
0.628402 | − | 0.777889i | \(-0.283709\pi\) | |||||||
\(728\) | 901.146i | 1.23784i | ||||||||
\(729\) | 243.465 | 0.333971 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −125.985 | −0.172347 | ||||||||
\(732\) | −100.914 | −0.137860 | ||||||||
\(733\) | − | 450.895i | − | 0.615137i | −0.951526 | − | 0.307568i | \(-0.900485\pi\) | ||
0.951526 | − | 0.307568i | \(-0.0995153\pi\) | |||||||
\(734\) | − | 1284.25i | − | 1.74966i | ||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 328.538i | 0.446383i | ||||||||
\(737\) | 344.999 | 0.468112 | ||||||||
\(738\) | 643.365i | 0.871768i | ||||||||
\(739\) | 195.478 | 0.264517 | 0.132258 | − | 0.991215i | \(-0.457777\pi\) | ||||
0.132258 | + | 0.991215i | \(0.457777\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 836.512 | − | 483.724i | 1.12890 | − | 0.652800i | ||||
\(742\) | 807.328i | 1.08804i | ||||||||
\(743\) | −194.450 | −0.261710 | −0.130855 | − | 0.991402i | \(-0.541772\pi\) | ||||
−0.130855 | + | 0.991402i | \(0.541772\pi\) | |||||||
\(744\) | − | 326.067i | − | 0.438262i | ||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | −1052.09 | −1.41030 | ||||||||
\(747\) | − | 232.350i | − | 0.311044i | ||||||
\(748\) | 541.091i | 0.723383i | ||||||||
\(749\) | − | 952.605i | − | 1.27184i | ||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 943.646i | 1.25652i | 0.778004 | + | 0.628259i | \(0.216232\pi\) | ||||
−0.778004 | + | 0.628259i | \(0.783768\pi\) | |||||||
\(752\) | − | 873.318i | − | 1.16133i | ||||||
\(753\) | 509.911 | 0.677173 | ||||||||
\(754\) | − | 1028.53i | − | 1.36409i | ||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 336.814i | 0.445522i | ||||||||
\(757\) | − | 891.082i | − | 1.17712i | −0.808453 | − | 0.588561i | \(-0.799695\pi\) | ||
0.808453 | − | 0.588561i | \(-0.200305\pi\) | |||||||
\(758\) | 355.362i | 0.468815i | ||||||||
\(759\) | − | 810.254i | − | 1.06753i | ||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 759.322 | 0.997795 | 0.498898 | − | 0.866661i | \(-0.333738\pi\) | ||||
0.498898 | + | 0.866661i | \(0.333738\pi\) | |||||||
\(762\) | 785.692 | 1.03109 | ||||||||
\(763\) | −1053.44 | −1.38066 | ||||||||
\(764\) | −404.876 | −0.529943 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −202.970 | −0.264974 | ||||||||
\(767\) | 1044.30i | 1.36154i | ||||||||
\(768\) | 939.170 | 1.22288 | ||||||||
\(769\) | −225.596 | −0.293363 | −0.146681 | − | 0.989184i | \(-0.546859\pi\) | ||||
−0.146681 | + | 0.989184i | \(0.546859\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −608.731 | −0.789535 | ||||||||
\(772\) | 462.275 | 0.598802 | ||||||||
\(773\) | 1189.39 | 1.53867 | 0.769337 | − | 0.638843i | \(-0.220587\pi\) | ||||
0.769337 | + | 0.638843i | \(0.220587\pi\) | |||||||
\(774\) | 53.6987i | 0.0693782i | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 429.913 | 0.554011 | ||||||||
\(777\) | 2019.48i | 2.59908i | ||||||||
\(778\) | 590.613 | 0.759143 | ||||||||
\(779\) | 710.161 | + | 1228.09i | 0.911632 | + | 1.57650i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 125.598i | 0.160817i | ||||||||
\(782\) | 649.825 | 0.830978 | ||||||||
\(783\) | 579.045i | 0.739521i | ||||||||
\(784\) | 1462.61 | 1.86557 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 1063.98 | 1.35366 | ||||||||
\(787\) | 254.533 | 0.323422 | 0.161711 | − | 0.986838i | \(-0.448299\pi\) | ||||
0.161711 | + | 0.986838i | \(0.448299\pi\) | |||||||
\(788\) | − | 284.391i | − | 0.360902i | ||||||
\(789\) | − | 657.766i | − | 0.833670i | ||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 210.884i | 0.266605i | ||||||||
\(792\) | −347.388 | −0.438622 | ||||||||
\(793\) | −254.357 | −0.320753 | ||||||||
\(794\) | 805.425i | 1.01439i | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 246.744 | 0.309980 | ||||||||
\(797\) | 719.295 | 0.902503 | 0.451251 | − | 0.892397i | \(-0.350978\pi\) | ||||
0.451251 | + | 0.892397i | \(0.350978\pi\) | |||||||
\(798\) | −886.284 | − | 1532.66i | −1.11063 | − | 1.92063i | ||||
\(799\) | −890.013 | −1.11391 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 593.394i | 0.740816i | ||||||||
\(802\) | − | 1161.51i | − | 1.44826i | ||||||
\(803\) | − | 490.202i | − | 0.610463i | ||||||
\(804\) | 116.741 | 0.145201 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 545.630i | 0.676961i | ||||||||
\(807\) | 1611.39i | 1.99676i | ||||||||
\(808\) | −89.6776 | −0.110987 | ||||||||
\(809\) | −67.3018 | −0.0831914 | −0.0415957 | − | 0.999135i | \(-0.513244\pi\) | ||||
−0.0415957 | + | 0.999135i | \(0.513244\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 401.142i | − | 0.494626i | −0.968936 | − | 0.247313i | \(-0.920452\pi\) | ||
0.968936 | − | 0.247313i | \(-0.0795477\pi\) | |||||||
\(812\) | −537.460 | −0.661896 | ||||||||
\(813\) | 1197.52 | 1.47296 | ||||||||
\(814\) | −2033.88 | −2.49863 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | − | 1425.88i | − | 1.74740i | ||||||
\(817\) | 59.2739 | + | 102.503i | 0.0725507 | + | 0.125463i | ||||
\(818\) | 274.013i | 0.334979i | ||||||||
\(819\) | − | 577.194i | − | 0.704755i | ||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −99.8212 | −0.121585 | −0.0607925 | − | 0.998150i | \(-0.519363\pi\) | ||||
−0.0607925 | + | 0.998150i | \(0.519363\pi\) | |||||||
\(822\) | − | 789.650i | − | 0.960644i | ||||||
\(823\) | − | 93.5359i | − | 0.113652i | −0.998384 | − | 0.0568262i | \(-0.981902\pi\) | ||
0.998384 | − | 0.0568262i | \(-0.0180981\pi\) | |||||||
\(824\) | 40.6692 | 0.0493558 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 1913.37 | 2.31643 | ||||||||
\(827\) | −398.725 | −0.482135 | −0.241067 | − | 0.970508i | \(-0.577497\pi\) | ||||
−0.241067 | + | 0.970508i | \(0.577497\pi\) | |||||||
\(828\) | − | 78.9942i | − | 0.0954036i | ||||||
\(829\) | 805.348i | 0.971470i | 0.874106 | + | 0.485735i | \(0.161448\pi\) | ||||
−0.874106 | + | 0.485735i | \(0.838552\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | − | 961.617i | − | 1.15718i | ||||||
\(832\) | 316.846 | 0.380825 | ||||||||
\(833\) | − | 1490.57i | − | 1.78940i | ||||||
\(834\) | −345.686 | −0.414492 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 440.238 | − | 254.574i | 0.526601 | − | 0.304514i | ||||
\(837\) | − | 307.181i | − | 0.367003i | ||||||
\(838\) | −192.788 | −0.230057 | ||||||||
\(839\) | − | 1547.08i | − | 1.84396i | −0.387235 | − | 0.921981i | \(-0.626570\pi\) | ||
0.387235 | − | 0.921981i | \(-0.373430\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −82.9912 | −0.0986815 | ||||||||
\(842\) | − | 524.338i | − | 0.622729i | ||||||
\(843\) | − | 538.090i | − | 0.638304i | ||||||
\(844\) | − | 437.058i | − | 0.517841i | ||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 379.350i | 0.448404i | ||||||||
\(847\) | − | 1775.26i | − | 2.09594i | ||||||
\(848\) | 611.087 | 0.720622 | ||||||||
\(849\) | − | 1556.98i | − | 1.83390i | ||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 696.638i | 0.818611i | ||||||||
\(852\) | 42.5001i | 0.0498827i | ||||||||
\(853\) | − | 252.303i | − | 0.295784i | −0.989004 | − | 0.147892i | \(-0.952751\pi\) | ||
0.989004 | − | 0.147892i | \(-0.0472487\pi\) | |||||||
\(854\) | 466.035i | 0.545708i | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −488.998 | −0.571259 | ||||||||
\(857\) | 1397.35 | 1.63051 | 0.815255 | − | 0.579102i | \(-0.196597\pi\) | ||||
0.815255 | + | 0.579102i | \(0.196597\pi\) | |||||||
\(858\) | 2017.63 | 2.35155 | ||||||||
\(859\) | 1472.96 | 1.71473 | 0.857366 | − | 0.514706i | \(-0.172099\pi\) | ||||
0.857366 | + | 0.514706i | \(0.172099\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 2941.13 | 3.41595 | ||||||||
\(862\) | 501.112i | 0.581336i | ||||||||
\(863\) | −63.9533 | −0.0741058 | −0.0370529 | − | 0.999313i | \(-0.511797\pi\) | ||||
−0.0370529 | + | 0.999313i | \(0.511797\pi\) | |||||||
\(864\) | 460.576 | 0.533075 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −921.476 | −1.06406 | ||||||||
\(867\) | −425.559 | −0.490841 | ||||||||
\(868\) | 285.121 | 0.328480 | ||||||||
\(869\) | 147.394i | 0.169613i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 294.251 | 0.337832 | ||||||||
\(872\) | 540.761i | 0.620138i | ||||||||
\(873\) | −275.364 | −0.315422 | ||||||||
\(874\) | −305.731 | − | 528.705i | −0.349807 | − | 0.604926i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | − | 165.875i | − | 0.189356i | ||||||
\(877\) | 399.492 | 0.455522 | 0.227761 | − | 0.973717i | \(-0.426860\pi\) | ||||
0.227761 | + | 0.973717i | \(0.426860\pi\) | |||||||
\(878\) | − | 1101.63i | − | 1.25471i | ||||||
\(879\) | 943.119 | 1.07295 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 514.180 | 0.583632 | 0.291816 | − | 0.956474i | \(-0.405740\pi\) | ||||
0.291816 | + | 0.956474i | \(0.405740\pi\) | |||||||
\(882\) | −635.324 | −0.720322 | ||||||||
\(883\) | 323.869i | 0.366783i | 0.983040 | + | 0.183392i | \(0.0587076\pi\) | ||||
−0.983040 | + | 0.183392i | \(0.941292\pi\) | |||||||
\(884\) | 461.499i | 0.522058i | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | − | 904.787i | − | 1.02120i | ||||||
\(887\) | −277.999 | −0.313415 | −0.156707 | − | 0.987645i | \(-0.550088\pi\) | ||||
−0.156707 | + | 0.987645i | \(0.550088\pi\) | |||||||
\(888\) | 1036.66 | 1.16740 | ||||||||
\(889\) | − | 1034.85i | − | 1.16406i | ||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −1685.67 | −1.89188 | ||||||||
\(892\) | −366.755 | −0.411160 | ||||||||
\(893\) | 418.735 | + | 724.125i | 0.468909 | + | 0.810890i | ||||
\(894\) | −776.275 | −0.868316 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | − | 1651.95i | − | 1.84370i | ||||||
\(897\) | − | 691.070i | − | 0.770424i | ||||||
\(898\) | − | 1576.41i | − | 1.75547i | ||||||
\(899\) | 490.174 | 0.545244 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | − | 622.769i | − | 0.691197i | ||||||
\(902\) | 2962.10i | 3.28392i | ||||||||
\(903\) | 245.483 | 0.271852 | ||||||||
\(904\) | 108.253 | 0.119749 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 61.1367i | 0.0674798i | ||||||||
\(907\) | 401.356 | 0.442509 | 0.221255 | − | 0.975216i | \(-0.428985\pi\) | ||||
0.221255 | + | 0.975216i | \(0.428985\pi\) | |||||||
\(908\) | −584.400 | −0.643613 | ||||||||
\(909\) | 57.4395 | 0.0631898 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 378.750i | 0.415752i | 0.978155 | + | 0.207876i | \(0.0666551\pi\) | ||||
−0.978155 | + | 0.207876i | \(0.933345\pi\) | |||||||
\(912\) | −1160.11 | + | 670.851i | −1.27205 | + | 0.735583i | ||||
\(913\) | − | 1069.76i | − | 1.17170i | ||||||
\(914\) | 1483.70i | 1.62330i | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −533.220 | −0.582118 | ||||||||
\(917\) | − | 1401.38i | − | 1.52822i | ||||||
\(918\) | − | 910.987i | − | 0.992361i | ||||||
\(919\) | 102.234 | 0.111244 | 0.0556222 | − | 0.998452i | \(-0.482286\pi\) | ||||
0.0556222 | + | 0.998452i | \(0.482286\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 1440.26 | 1.56380 | ||||||||
\(922\) | 1888.54 | 2.04831 | ||||||||
\(923\) | 107.123i | 0.116060i | ||||||||
\(924\) | − | 1054.32i | − | 1.14103i | ||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 1873.04i | 2.02272i | ||||||||
\(927\) | −26.0490 | −0.0281004 | ||||||||
\(928\) | 734.949i | 0.791971i | ||||||||
\(929\) | −1794.45 | −1.93160 | −0.965798 | − | 0.259295i | \(-0.916510\pi\) | ||||
−0.965798 | + | 0.259295i | \(0.916510\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −1212.74 | + | 701.286i | −1.30262 | + | 0.753261i | ||||
\(932\) | 134.048i | 0.143828i | ||||||||
\(933\) | −1116.13 | −1.19629 | ||||||||
\(934\) | 990.525i | 1.06052i | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −296.289 | −0.316549 | ||||||||
\(937\) | 823.194i | 0.878542i | 0.898355 | + | 0.439271i | \(0.144763\pi\) | ||||
−0.898355 | + | 0.439271i | \(0.855237\pi\) | |||||||
\(938\) | − | 539.130i | − | 0.574765i | ||||||
\(939\) | 1825.61i | 1.94421i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 270.097i | 0.287032i | 0.989648 | + | 0.143516i | \(0.0458409\pi\) | ||||
−0.989648 | + | 0.143516i | \(0.954159\pi\) | |||||||
\(942\) | − | 1927.95i | − | 2.04666i | ||||||
\(943\) | 1014.57 | 1.07589 | ||||||||
\(944\) | − | 1448.28i | − | 1.53420i | ||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 247.233i | 0.261346i | ||||||||
\(947\) | 1412.14i | 1.49118i | 0.666407 | + | 0.745588i | \(0.267831\pi\) | ||||
−0.666407 | + | 0.745588i | \(0.732169\pi\) | |||||||
\(948\) | 49.8753i | 0.0526111i | ||||||||
\(949\) | − | 418.096i | − | 0.440564i | ||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −91.7535 | −0.0964811 | ||||||||
\(952\) | −1273.64 | −1.33786 | ||||||||
\(953\) | 432.598 | 0.453933 | 0.226966 | − | 0.973903i | \(-0.427119\pi\) | ||||
0.226966 | + | 0.973903i | \(0.427119\pi\) | |||||||
\(954\) | −265.443 | −0.278242 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 175.592 | 0.183674 | ||||||||
\(957\) | − | 1812.56i | − | 1.89400i | ||||||
\(958\) | −150.489 | −0.157087 | ||||||||
\(959\) | −1040.06 | −1.08452 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 700.964 | 0.729411 | ||||||||
\(962\) | −1734.71 | −1.80323 | ||||||||
\(963\) | 313.209 | 0.325243 | ||||||||
\(964\) | 513.339i | 0.532509i | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −1266.18 | −1.31075 | ||||||||
\(967\) | − | 10.0222i | − | 0.0103642i | −0.999987 | − | 0.00518210i | \(-0.998350\pi\) | ||
0.999987 | − | 0.00518210i | \(-0.00164952\pi\) | |||||||
\(968\) | −911.291 | −0.941416 | ||||||||
\(969\) | 683.675 | + | 1182.29i | 0.705547 | + | 1.22011i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 339.417i | 0.349554i | 0.984608 | + | 0.174777i | \(0.0559205\pi\) | ||||
−0.984608 | + | 0.174777i | \(0.944080\pi\) | |||||||
\(972\) | −296.776 | −0.305325 | ||||||||
\(973\) | 455.309i | 0.467943i | ||||||||
\(974\) | 1317.63 | 1.35280 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 352.754 | 0.361428 | ||||||||
\(977\) | 673.762 | 0.689623 | 0.344812 | − | 0.938672i | \(-0.387943\pi\) | ||||
0.344812 | + | 0.938672i | \(0.387943\pi\) | |||||||
\(978\) | 286.337i | 0.292778i | ||||||||
\(979\) | 2732.03i | 2.79063i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | − | 346.363i | − | 0.353071i | ||||||
\(982\) | 2026.86 | 2.06401 | ||||||||
\(983\) | −428.230 | −0.435636 | −0.217818 | − | 0.975989i | \(-0.569894\pi\) | ||||
−0.217818 | + | 0.975989i | \(0.569894\pi\) | |||||||
\(984\) | − | 1509.76i | − | 1.53431i | ||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 1453.68 | 1.47432 | ||||||||
\(987\) | 1734.19 | 1.75703 | ||||||||
\(988\) | 375.481 | − | 217.127i | 0.380042 | − | 0.219765i | ||||
\(989\) | 84.6813 | 0.0856232 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 1310.89i | 1.32280i | 0.750033 | + | 0.661400i | \(0.230037\pi\) | ||||
−0.750033 | + | 0.661400i | \(0.769963\pi\) | |||||||
\(992\) | − | 389.888i | − | 0.393032i | ||||||
\(993\) | − | 610.270i | − | 0.614572i | ||||||
\(994\) | 196.272 | 0.197457 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | − | 361.987i | − | 0.363441i | ||||||
\(997\) | 690.240i | 0.692316i | 0.938176 | + | 0.346158i | \(0.112514\pi\) | ||||
−0.938176 | + | 0.346158i | \(0.887486\pi\) | |||||||
\(998\) | −1801.71 | −1.80532 | ||||||||
\(999\) | 976.615 | 0.977592 |
(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 | 475.3.d.c.474.20 | 24 | ||
5.2 | odd | 4 | 95.3.c.a.56.10 | yes | 12 | ||
5.3 | odd | 4 | 475.3.c.g.151.3 | 12 | |||
5.4 | even | 2 | inner | 475.3.d.c.474.5 | 24 | ||
15.2 | even | 4 | 855.3.e.a.721.3 | 12 | |||
19.18 | odd | 2 | inner | 475.3.d.c.474.6 | 24 | ||
20.7 | even | 4 | 1520.3.h.a.721.9 | 12 | |||
95.18 | even | 4 | 475.3.c.g.151.10 | 12 | |||
95.37 | even | 4 | 95.3.c.a.56.3 | ✓ | 12 | ||
95.94 | odd | 2 | inner | 475.3.d.c.474.19 | 24 | ||
285.227 | odd | 4 | 855.3.e.a.721.10 | 12 | |||
380.227 | odd | 4 | 1520.3.h.a.721.4 | 12 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
95.3.c.a.56.3 | ✓ | 12 | 95.37 | even | 4 | ||
95.3.c.a.56.10 | yes | 12 | 5.2 | odd | 4 | ||
475.3.c.g.151.3 | 12 | 5.3 | odd | 4 | |||
475.3.c.g.151.10 | 12 | 95.18 | even | 4 | |||
475.3.d.c.474.5 | 24 | 5.4 | even | 2 | inner | ||
475.3.d.c.474.6 | 24 | 19.18 | odd | 2 | inner | ||
475.3.d.c.474.19 | 24 | 95.94 | odd | 2 | inner | ||
475.3.d.c.474.20 | 24 | 1.1 | even | 1 | trivial | ||
855.3.e.a.721.3 | 12 | 15.2 | even | 4 | |||
855.3.e.a.721.10 | 12 | 285.227 | odd | 4 | |||
1520.3.h.a.721.4 | 12 | 380.227 | odd | 4 | |||
1520.3.h.a.721.9 | 12 | 20.7 | even | 4 |