Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [287,3,Mod(286,287)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(287, 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("287.286");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 287 = 7 \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 287.d (of order \(2\), degree \(1\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(7.82018358714\) |
Analytic rank: | \(0\) |
Dimension: | \(32\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 286.19 | ||
Character | \(\chi\) | \(=\) | 287.286 |
Dual form | 287.3.d.d.286.20 |
$q$-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 \(\left(\mathbb{Z}/287\mathbb{Z}\right)^\times\).
\(n\) | \(206\) | \(211\) |
\(\chi(n)\) | \(-1\) | \(-1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.16717 | 0.583583 | 0.291791 | − | 0.956482i | \(-0.405749\pi\) | ||||
0.291791 | + | 0.956482i | \(0.405749\pi\) | |||||||
\(3\) | 4.43412 | 1.47804 | 0.739020 | − | 0.673683i | \(-0.235289\pi\) | ||||
0.739020 | + | 0.673683i | \(0.235289\pi\) | |||||||
\(4\) | −2.63772 | −0.659431 | ||||||||
\(5\) | − | 9.05049i | − | 1.81010i | −0.425307 | − | 0.905049i | \(-0.639834\pi\) | ||
0.425307 | − | 0.905049i | \(-0.360166\pi\) | |||||||
\(6\) | 5.17535 | 0.862559 | ||||||||
\(7\) | −6.69015 | + | 2.05957i | −0.955736 | + | 0.294225i | ||||
\(8\) | −7.74732 | −0.968416 | ||||||||
\(9\) | 10.6614 | 1.18460 | ||||||||
\(10\) | − | 10.5634i | − | 1.05634i | ||||||
\(11\) | − | 15.2851i | − | 1.38956i | −0.719225 | − | 0.694778i | \(-0.755503\pi\) | ||
0.719225 | − | 0.694778i | \(-0.244497\pi\) | |||||||
\(12\) | −11.6960 | −0.974666 | ||||||||
\(13\) | 11.9347 | 0.918054 | 0.459027 | − | 0.888422i | \(-0.348198\pi\) | ||||
0.459027 | + | 0.888422i | \(0.348198\pi\) | |||||||
\(14\) | −7.80852 | + | 2.40386i | −0.557751 | + | 0.171704i | ||||
\(15\) | − | 40.1310i | − | 2.67540i | ||||||
\(16\) | 1.50849 | 0.0942804 | ||||||||
\(17\) | 17.3346 | 1.01968 | 0.509842 | − | 0.860268i | \(-0.329704\pi\) | ||||
0.509842 | + | 0.860268i | \(0.329704\pi\) | |||||||
\(18\) | 12.4437 | 0.691315 | ||||||||
\(19\) | −0.333198 | −0.0175367 | −0.00876836 | − | 0.999962i | \(-0.502791\pi\) | ||||
−0.00876836 | + | 0.999962i | \(0.502791\pi\) | |||||||
\(20\) | 23.8727i | 1.19364i | ||||||||
\(21\) | −29.6650 | + | 9.13239i | −1.41262 | + | 0.434876i | ||||
\(22\) | − | 17.8403i | − | 0.810921i | ||||||
\(23\) | 14.2064 | 0.617669 | 0.308835 | − | 0.951116i | \(-0.400061\pi\) | ||||
0.308835 | + | 0.951116i | \(0.400061\pi\) | |||||||
\(24\) | −34.3526 | −1.43136 | ||||||||
\(25\) | −56.9114 | −2.27646 | ||||||||
\(26\) | 13.9298 | 0.535761 | ||||||||
\(27\) | 7.36701 | 0.272852 | ||||||||
\(28\) | 17.6468 | − | 5.43258i | 0.630242 | − | 0.194021i | ||||
\(29\) | − | 9.15119i | − | 0.315558i | −0.987474 | − | 0.157779i | \(-0.949567\pi\) | ||
0.987474 | − | 0.157779i | \(-0.0504334\pi\) | |||||||
\(30\) | − | 46.8395i | − | 1.56132i | ||||||
\(31\) | 50.9978i | 1.64509i | 0.568700 | + | 0.822545i | \(0.307446\pi\) | ||||
−0.568700 | + | 0.822545i | \(0.692554\pi\) | |||||||
\(32\) | 32.7499 | 1.02344 | ||||||||
\(33\) | − | 67.7760i | − | 2.05382i | ||||||
\(34\) | 20.2324 | 0.595070 | ||||||||
\(35\) | 18.6401 | + | 60.5492i | 0.532575 | + | 1.72998i | ||||
\(36\) | −28.1219 | −0.781165 | ||||||||
\(37\) | 16.3960 | 0.443135 | 0.221568 | − | 0.975145i | \(-0.428883\pi\) | ||||
0.221568 | + | 0.975145i | \(0.428883\pi\) | |||||||
\(38\) | −0.388897 | −0.0102341 | ||||||||
\(39\) | 52.9199 | 1.35692 | ||||||||
\(40\) | 70.1171i | 1.75293i | ||||||||
\(41\) | −8.37067 | + | 40.1364i | −0.204163 | + | 0.978937i | ||||
\(42\) | −34.6239 | + | 10.6590i | −0.824379 | + | 0.253786i | ||||
\(43\) | −38.9612 | −0.906075 | −0.453037 | − | 0.891492i | \(-0.649660\pi\) | ||||
−0.453037 | + | 0.891492i | \(0.649660\pi\) | |||||||
\(44\) | 40.3179i | 0.916316i | ||||||||
\(45\) | − | 96.4912i | − | 2.14425i | ||||||
\(46\) | 16.5812 | 0.360461 | ||||||||
\(47\) | 79.8303 | 1.69852 | 0.849259 | − | 0.527977i | \(-0.177049\pi\) | ||||
0.849259 | + | 0.527977i | \(0.177049\pi\) | |||||||
\(48\) | 6.68881 | 0.139350 | ||||||||
\(49\) | 40.5163 | − | 27.5577i | 0.826864 | − | 0.562402i | ||||
\(50\) | −66.4250 | −1.32850 | ||||||||
\(51\) | 76.8638 | 1.50713 | ||||||||
\(52\) | −31.4805 | −0.605394 | ||||||||
\(53\) | − | 28.3291i | − | 0.534511i | −0.963626 | − | 0.267256i | \(-0.913883\pi\) | ||
0.963626 | − | 0.267256i | \(-0.0861168\pi\) | |||||||
\(54\) | 8.59852 | 0.159232 | ||||||||
\(55\) | −138.338 | −2.51523 | ||||||||
\(56\) | 51.8308 | − | 15.9562i | 0.925550 | − | 0.284932i | ||||
\(57\) | −1.47744 | −0.0259200 | ||||||||
\(58\) | − | 10.6810i | − | 0.184154i | ||||||
\(59\) | − | 89.3467i | − | 1.51435i | −0.653211 | − | 0.757176i | \(-0.726579\pi\) | ||
0.653211 | − | 0.757176i | \(-0.273421\pi\) | |||||||
\(60\) | 105.854i | 1.76424i | ||||||||
\(61\) | 35.2643i | 0.578102i | 0.957314 | + | 0.289051i | \(0.0933398\pi\) | ||||
−0.957314 | + | 0.289051i | \(0.906660\pi\) | |||||||
\(62\) | 59.5229i | 0.960046i | ||||||||
\(63\) | −71.3266 | + | 21.9580i | −1.13217 | + | 0.348540i | ||||
\(64\) | 32.1907 | 0.502979 | ||||||||
\(65\) | − | 108.015i | − | 1.66177i | ||||||
\(66\) | − | 79.1059i | − | 1.19857i | ||||||
\(67\) | 62.8702i | 0.938362i | 0.883102 | + | 0.469181i | \(0.155451\pi\) | ||||
−0.883102 | + | 0.469181i | \(0.844549\pi\) | |||||||
\(68\) | −45.7240 | −0.672411 | ||||||||
\(69\) | 62.9929 | 0.912940 | ||||||||
\(70\) | 21.7561 | + | 70.6709i | 0.310802 | + | 1.00958i | ||||
\(71\) | 30.5308i | 0.430011i | 0.976613 | + | 0.215006i | \(0.0689770\pi\) | ||||
−0.976613 | + | 0.215006i | \(0.931023\pi\) | |||||||
\(72\) | −82.5976 | −1.14719 | ||||||||
\(73\) | 19.9599i | 0.273423i | 0.990611 | + | 0.136711i | \(0.0436533\pi\) | ||||
−0.990611 | + | 0.136711i | \(0.956347\pi\) | |||||||
\(74\) | 19.1369 | 0.258606 | ||||||||
\(75\) | −252.352 | −3.36469 | ||||||||
\(76\) | 0.878884 | 0.0115643 | ||||||||
\(77\) | 31.4808 | + | 102.260i | 0.408841 | + | 1.32805i | ||||
\(78\) | 61.7663 | 0.791876 | ||||||||
\(79\) | − | 38.5638i | − | 0.488149i | −0.969756 | − | 0.244075i | \(-0.921516\pi\) | ||
0.969756 | − | 0.244075i | \(-0.0784842\pi\) | |||||||
\(80\) | − | 13.6525i | − | 0.170657i | ||||||
\(81\) | −63.2867 | −0.781318 | ||||||||
\(82\) | −9.76995 | + | 46.8458i | −0.119146 | + | 0.571291i | ||||
\(83\) | − | 113.184i | − | 1.36367i | −0.731508 | − | 0.681833i | \(-0.761183\pi\) | ||
0.731508 | − | 0.681833i | \(-0.238817\pi\) | |||||||
\(84\) | 78.2480 | − | 24.0887i | 0.931524 | − | 0.286771i | ||||
\(85\) | − | 156.887i | − | 1.84573i | ||||||
\(86\) | −45.4742 | −0.528770 | ||||||||
\(87\) | − | 40.5775i | − | 0.466408i | ||||||
\(88\) | 118.419i | 1.34567i | ||||||||
\(89\) | 141.916 | 1.59456 | 0.797281 | − | 0.603609i | \(-0.206271\pi\) | ||||
0.797281 | + | 0.603609i | \(0.206271\pi\) | |||||||
\(90\) | − | 112.621i | − | 1.25135i | ||||||
\(91\) | −79.8450 | + | 24.5804i | −0.877418 | + | 0.270114i | ||||
\(92\) | −37.4725 | −0.407310 | ||||||||
\(93\) | 226.130i | 2.43151i | ||||||||
\(94\) | 93.1752 | 0.991226 | ||||||||
\(95\) | 3.01560i | 0.0317432i | ||||||||
\(96\) | 145.217 | 1.51268 | ||||||||
\(97\) | 86.9985 | 0.896892 | 0.448446 | − | 0.893810i | \(-0.351978\pi\) | ||||
0.448446 | + | 0.893810i | \(0.351978\pi\) | |||||||
\(98\) | 47.2893 | − | 32.1644i | 0.482544 | − | 0.328208i | ||||
\(99\) | − | 162.961i | − | 1.64607i | ||||||
\(100\) | 150.117 | 1.50117 | ||||||||
\(101\) | 54.1701 | 0.536338 | 0.268169 | − | 0.963372i | \(-0.413581\pi\) | ||||
0.268169 | + | 0.963372i | \(0.413581\pi\) | |||||||
\(102\) | 89.7128 | 0.879538 | ||||||||
\(103\) | 132.145i | 1.28296i | 0.767140 | + | 0.641480i | \(0.221679\pi\) | ||||
−0.767140 | + | 0.641480i | \(0.778321\pi\) | |||||||
\(104\) | −92.4620 | −0.889058 | ||||||||
\(105\) | 82.6526 | + | 268.482i | 0.787168 | + | 2.55698i | ||||
\(106\) | − | 33.0647i | − | 0.311932i | ||||||
\(107\) | −182.443 | −1.70507 | −0.852536 | − | 0.522668i | \(-0.824937\pi\) | ||||
−0.852536 | + | 0.522668i | \(0.824937\pi\) | |||||||
\(108\) | −19.4321 | −0.179927 | ||||||||
\(109\) | − | 10.7582i | − | 0.0986987i | −0.998782 | − | 0.0493494i | \(-0.984285\pi\) | ||
0.998782 | − | 0.0493494i | \(-0.0157148\pi\) | |||||||
\(110\) | −161.463 | −1.46785 | ||||||||
\(111\) | 72.7019 | 0.654972 | ||||||||
\(112\) | −10.0920 | + | 3.10684i | −0.0901072 | + | 0.0277396i | ||||
\(113\) | 70.0377 | 0.619803 | 0.309901 | − | 0.950769i | \(-0.399704\pi\) | ||||
0.309901 | + | 0.950769i | \(0.399704\pi\) | |||||||
\(114\) | −1.72442 | −0.0151265 | ||||||||
\(115\) | − | 128.575i | − | 1.11804i | ||||||
\(116\) | 24.1383i | 0.208089i | ||||||||
\(117\) | 127.241 | 1.08753 | ||||||||
\(118\) | − | 104.282i | − | 0.883750i | ||||||
\(119\) | −115.971 | + | 35.7019i | −0.974549 | + | 0.300016i | ||||
\(120\) | 310.908i | 2.59090i | ||||||||
\(121\) | −112.635 | −0.930864 | ||||||||
\(122\) | 41.1592i | 0.337371i | ||||||||
\(123\) | −37.1165 | + | 177.970i | −0.301761 | + | 1.44691i | ||||
\(124\) | − | 134.518i | − | 1.08482i | ||||||
\(125\) | 288.814i | 2.31051i | ||||||||
\(126\) | −83.2500 | + | 25.6286i | −0.660714 | + | 0.203402i | ||||
\(127\) | −105.378 | −0.829747 | −0.414873 | − | 0.909879i | \(-0.636174\pi\) | ||||
−0.414873 | + | 0.909879i | \(0.636174\pi\) | |||||||
\(128\) | −93.4279 | −0.729906 | ||||||||
\(129\) | −172.759 | −1.33922 | ||||||||
\(130\) | − | 126.071i | − | 0.969780i | ||||||
\(131\) | 132.914i | 1.01461i | 0.861766 | + | 0.507306i | \(0.169359\pi\) | ||||
−0.861766 | + | 0.507306i | \(0.830641\pi\) | |||||||
\(132\) | 178.774i | 1.35435i | ||||||||
\(133\) | 2.22914 | − | 0.686245i | 0.0167605 | − | 0.00515973i | ||||
\(134\) | 73.3800i | 0.547612i | ||||||||
\(135\) | − | 66.6750i | − | 0.493889i | ||||||
\(136\) | −134.297 | −0.987478 | ||||||||
\(137\) | − | 28.4370i | − | 0.207569i | −0.994600 | − | 0.103785i | \(-0.966905\pi\) | ||
0.994600 | − | 0.103785i | \(-0.0330953\pi\) | |||||||
\(138\) | 73.5231 | 0.532776 | ||||||||
\(139\) | − | 2.50637i | − | 0.0180314i | −0.999959 | − | 0.00901571i | \(-0.997130\pi\) | ||
0.999959 | − | 0.00901571i | \(-0.00286983\pi\) | |||||||
\(140\) | −49.1675 | − | 159.712i | −0.351197 | − | 1.14080i | ||||
\(141\) | 353.977 | 2.51048 | ||||||||
\(142\) | 35.6345i | 0.250947i | ||||||||
\(143\) | − | 182.423i | − | 1.27569i | ||||||
\(144\) | 16.0826 | 0.111685 | ||||||||
\(145\) | −82.8228 | −0.571192 | ||||||||
\(146\) | 23.2965i | 0.159565i | ||||||||
\(147\) | 179.654 | − | 122.194i | 1.22214 | − | 0.831253i | ||||
\(148\) | −43.2481 | −0.292217 | ||||||||
\(149\) | 246.154i | 1.65204i | 0.563643 | + | 0.826019i | \(0.309399\pi\) | ||||
−0.563643 | + | 0.826019i | \(0.690601\pi\) | |||||||
\(150\) | −294.537 | −1.96358 | ||||||||
\(151\) | − | 140.536i | − | 0.930705i | −0.885126 | − | 0.465352i | \(-0.845928\pi\) | ||
0.885126 | − | 0.465352i | \(-0.154072\pi\) | |||||||
\(152\) | 2.58139 | 0.0169828 | ||||||||
\(153\) | 184.812 | 1.20792 | ||||||||
\(154\) | 36.7433 | + | 119.354i | 0.238593 | + | 0.775026i | ||||
\(155\) | 461.555 | 2.97777 | ||||||||
\(156\) | −139.588 | −0.894796 | ||||||||
\(157\) | 26.0425 | 0.165876 | 0.0829378 | − | 0.996555i | \(-0.473570\pi\) | ||||
0.0829378 | + | 0.996555i | \(0.473570\pi\) | |||||||
\(158\) | − | 45.0104i | − | 0.284876i | ||||||
\(159\) | − | 125.615i | − | 0.790029i | ||||||
\(160\) | − | 296.403i | − | 1.85252i | ||||||
\(161\) | −95.0429 | + | 29.2591i | −0.590329 | + | 0.181733i | ||||
\(162\) | −73.8661 | −0.455963 | ||||||||
\(163\) | 93.4220 | 0.573141 | 0.286571 | − | 0.958059i | \(-0.407485\pi\) | ||||
0.286571 | + | 0.958059i | \(0.407485\pi\) | |||||||
\(164\) | 22.0795 | − | 105.869i | 0.134631 | − | 0.645541i | ||||
\(165\) | −613.406 | −3.71761 | ||||||||
\(166\) | − | 132.105i | − | 0.795812i | ||||||
\(167\) | −235.762 | −1.41175 | −0.705875 | − | 0.708336i | \(-0.749446\pi\) | ||||
−0.705875 | + | 0.708336i | \(0.749446\pi\) | |||||||
\(168\) | 229.824 | − | 70.7516i | 1.36800 | − | 0.421141i | ||||
\(169\) | −26.5628 | −0.157176 | ||||||||
\(170\) | − | 183.113i | − | 1.07714i | ||||||
\(171\) | −3.55237 | −0.0207741 | ||||||||
\(172\) | 102.769 | 0.597494 | ||||||||
\(173\) | − | 226.574i | − | 1.30968i | −0.755769 | − | 0.654838i | \(-0.772737\pi\) | ||
0.755769 | − | 0.654838i | \(-0.227263\pi\) | |||||||
\(174\) | − | 47.3607i | − | 0.272188i | ||||||
\(175\) | 380.746 | − | 117.213i | 2.17569 | − | 0.669789i | ||||
\(176\) | − | 23.0574i | − | 0.131008i | ||||||
\(177\) | − | 396.174i | − | 2.23827i | ||||||
\(178\) | 165.639 | 0.930559 | ||||||||
\(179\) | − | 274.692i | − | 1.53459i | −0.641294 | − | 0.767295i | \(-0.721602\pi\) | ||
0.641294 | − | 0.767295i | \(-0.278398\pi\) | |||||||
\(180\) | 254.517i | 1.41398i | ||||||||
\(181\) | 98.0863 | 0.541913 | 0.270957 | − | 0.962592i | \(-0.412660\pi\) | ||||
0.270957 | + | 0.962592i | \(0.412660\pi\) | |||||||
\(182\) | −93.1924 | + | 28.6894i | −0.512046 | + | 0.157634i | ||||
\(183\) | 156.366i | 0.854459i | ||||||||
\(184\) | −110.061 | −0.598160 | ||||||||
\(185\) | − | 148.392i | − | 0.802118i | ||||||
\(186\) | 263.932i | 1.41899i | ||||||||
\(187\) | − | 264.962i | − | 1.41691i | ||||||
\(188\) | −210.570 | −1.12006 | ||||||||
\(189\) | −49.2864 | + | 15.1729i | −0.260775 | + | 0.0802798i | ||||
\(190\) | 3.51971i | 0.0185248i | ||||||||
\(191\) | 291.856i | 1.52804i | 0.645191 | + | 0.764022i | \(0.276778\pi\) | ||||
−0.645191 | + | 0.764022i | \(0.723222\pi\) | |||||||
\(192\) | 142.737 | 0.743424 | ||||||||
\(193\) | − | 186.353i | − | 0.965559i | −0.875742 | − | 0.482780i | \(-0.839627\pi\) | ||
0.875742 | − | 0.482780i | \(-0.160373\pi\) | |||||||
\(194\) | 101.542 | 0.523411 | ||||||||
\(195\) | − | 478.951i | − | 2.45616i | ||||||
\(196\) | −106.871 | + | 72.6896i | −0.545260 | + | 0.370866i | ||||
\(197\) | −189.225 | −0.960531 | −0.480266 | − | 0.877123i | \(-0.659460\pi\) | ||||
−0.480266 | + | 0.877123i | \(0.659460\pi\) | |||||||
\(198\) | − | 190.203i | − | 0.960620i | ||||||
\(199\) | 17.2404 | 0.0866351 | 0.0433176 | − | 0.999061i | \(-0.486207\pi\) | ||||
0.0433176 | + | 0.999061i | \(0.486207\pi\) | |||||||
\(200\) | 440.911 | 2.20455 | ||||||||
\(201\) | 278.774i | 1.38694i | ||||||||
\(202\) | 63.2255 | 0.312997 | ||||||||
\(203\) | 18.8475 | + | 61.2229i | 0.0928450 | + | 0.301591i | ||||
\(204\) | −202.746 | −0.993851 | ||||||||
\(205\) | 363.254 | + | 75.7586i | 1.77197 | + | 0.369554i | ||||
\(206\) | 154.235i | 0.748713i | ||||||||
\(207\) | 151.460 | 0.731693 | ||||||||
\(208\) | 18.0033 | 0.0865545 | ||||||||
\(209\) | 5.09296i | 0.0243682i | ||||||||
\(210\) | 96.4693 | + | 313.363i | 0.459378 | + | 1.49221i | ||||
\(211\) | 74.0767i | 0.351074i | 0.984473 | + | 0.175537i | \(0.0561662\pi\) | ||||
−0.984473 | + | 0.175537i | \(0.943834\pi\) | |||||||
\(212\) | 74.7243i | 0.352473i | ||||||||
\(213\) | 135.377i | 0.635574i | ||||||||
\(214\) | −212.941 | −0.995051 | ||||||||
\(215\) | 352.618i | 1.64008i | ||||||||
\(216\) | −57.0746 | −0.264234 | ||||||||
\(217\) | −105.034 | − | 341.183i | −0.484026 | − | 1.57227i | ||||
\(218\) | − | 12.5566i | − | 0.0575989i | ||||||
\(219\) | 88.5045i | 0.404130i | ||||||||
\(220\) | 364.897 | 1.65862 | ||||||||
\(221\) | 206.884 | 0.936125 | ||||||||
\(222\) | 84.8551 | 0.382230 | ||||||||
\(223\) | 420.599i | 1.88609i | 0.332662 | + | 0.943046i | \(0.392053\pi\) | ||||
−0.332662 | + | 0.943046i | \(0.607947\pi\) | |||||||
\(224\) | −219.102 | + | 67.4509i | −0.978135 | + | 0.301120i | ||||
\(225\) | −606.757 | −2.69670 | ||||||||
\(226\) | 81.7456 | 0.361706 | ||||||||
\(227\) | −84.3164 | −0.371438 | −0.185719 | − | 0.982603i | \(-0.559461\pi\) | ||||
−0.185719 | + | 0.982603i | \(0.559461\pi\) | |||||||
\(228\) | 3.89708 | 0.0170924 | ||||||||
\(229\) | 141.115 | 0.616224 | 0.308112 | − | 0.951350i | \(-0.400303\pi\) | ||||
0.308112 | + | 0.951350i | \(0.400303\pi\) | |||||||
\(230\) | − | 150.068i | − | 0.652470i | ||||||
\(231\) | 139.590 | + | 453.432i | 0.604284 | + | 1.96291i | ||||
\(232\) | 70.8973i | 0.305592i | ||||||||
\(233\) | − | 199.548i | − | 0.856428i | −0.903677 | − | 0.428214i | \(-0.859143\pi\) | ||
0.903677 | − | 0.428214i | \(-0.140857\pi\) | |||||||
\(234\) | 148.511 | 0.634664 | ||||||||
\(235\) | − | 722.504i | − | 3.07448i | ||||||
\(236\) | 235.672i | 0.998610i | ||||||||
\(237\) | − | 170.997i | − | 0.721505i | ||||||
\(238\) | −135.358 | + | 41.6700i | −0.568730 | + | 0.175084i | ||||
\(239\) | − | 61.1830i | − | 0.255996i | −0.991774 | − | 0.127998i | \(-0.959145\pi\) | ||
0.991774 | − | 0.127998i | \(-0.0408551\pi\) | |||||||
\(240\) | − | 60.5370i | − | 0.252238i | ||||||
\(241\) | 209.187i | 0.867996i | 0.900914 | + | 0.433998i | \(0.142898\pi\) | ||||
−0.900914 | + | 0.433998i | \(0.857102\pi\) | |||||||
\(242\) | −131.463 | −0.543236 | ||||||||
\(243\) | −346.924 | −1.42767 | ||||||||
\(244\) | − | 93.0174i | − | 0.381219i | ||||||
\(245\) | −249.411 | − | 366.693i | −1.01800 | − | 1.49670i | ||||
\(246\) | −43.3212 | + | 207.720i | −0.176102 | + | 0.844391i | ||||
\(247\) | −3.97662 | −0.0160997 | ||||||||
\(248\) | − | 395.096i | − | 1.59313i | ||||||
\(249\) | − | 501.873i | − | 2.01555i | ||||||
\(250\) | 337.094i | 1.34837i | ||||||||
\(251\) | 6.07084i | 0.0241866i | 0.999927 | + | 0.0120933i | \(0.00384952\pi\) | ||||
−0.999927 | + | 0.0120933i | \(0.996150\pi\) | |||||||
\(252\) | 188.140 | − | 57.9191i | 0.746587 | − | 0.229838i | ||||
\(253\) | − | 217.146i | − | 0.858285i | ||||||
\(254\) | −122.993 | −0.484226 | ||||||||
\(255\) | − | 695.655i | − | 2.72806i | ||||||
\(256\) | −237.809 | −0.928940 | ||||||||
\(257\) | −96.9712 | −0.377320 | −0.188660 | − | 0.982042i | \(-0.560414\pi\) | ||||
−0.188660 | + | 0.982042i | \(0.560414\pi\) | |||||||
\(258\) | −201.638 | −0.781543 | ||||||||
\(259\) | −109.692 | + | 33.7688i | −0.423520 | + | 0.130381i | ||||
\(260\) | 284.914i | 1.09582i | ||||||||
\(261\) | − | 97.5648i | − | 0.373812i | ||||||
\(262\) | 155.133i | 0.592110i | ||||||||
\(263\) | 246.414i | 0.936935i | 0.883481 | + | 0.468467i | \(0.155194\pi\) | ||||
−0.883481 | + | 0.468467i | \(0.844806\pi\) | |||||||
\(264\) | 525.083i | 1.98895i | ||||||||
\(265\) | −256.392 | −0.967518 | ||||||||
\(266\) | 2.60178 | − | 0.800961i | 0.00978113 | − | 0.00301113i | ||||
\(267\) | 629.273 | 2.35683 | ||||||||
\(268\) | − | 165.834i | − | 0.618785i | ||||||
\(269\) | − | 65.0432i | − | 0.241796i | −0.992665 | − | 0.120898i | \(-0.961423\pi\) | ||
0.992665 | − | 0.120898i | \(-0.0385775\pi\) | |||||||
\(270\) | − | 77.8208i | − | 0.288225i | ||||||
\(271\) | 259.763i | 0.958536i | 0.877669 | + | 0.479268i | \(0.159098\pi\) | ||||
−0.877669 | + | 0.479268i | \(0.840902\pi\) | |||||||
\(272\) | 26.1490 | 0.0961362 | ||||||||
\(273\) | −354.043 | + | 108.992i | −1.29686 | + | 0.399240i | ||||
\(274\) | − | 33.1907i | − | 0.121134i | ||||||
\(275\) | 869.897i | 3.16326i | ||||||||
\(276\) | −166.158 | −0.602021 | ||||||||
\(277\) | −18.1476 | −0.0655146 | −0.0327573 | − | 0.999463i | \(-0.510429\pi\) | ||||
−0.0327573 | + | 0.999463i | \(0.510429\pi\) | |||||||
\(278\) | − | 2.92535i | − | 0.0105228i | ||||||
\(279\) | 543.709i | 1.94878i | ||||||||
\(280\) | −144.411 | − | 469.094i | −0.515754 | − | 1.67534i | ||||
\(281\) | 196.222i | 0.698297i | 0.937067 | + | 0.349149i | \(0.113529\pi\) | ||||
−0.937067 | + | 0.349149i | \(0.886471\pi\) | |||||||
\(282\) | 413.150 | 1.46507 | ||||||||
\(283\) | − | 304.726i | − | 1.07677i | −0.842698 | − | 0.538386i | \(-0.819034\pi\) | ||
0.842698 | − | 0.538386i | \(-0.180966\pi\) | |||||||
\(284\) | − | 80.5318i | − | 0.283563i | ||||||
\(285\) | 13.3715i | 0.0469177i | ||||||||
\(286\) | − | 212.918i | − | 0.744469i | ||||||
\(287\) | −26.6628 | − | 285.759i | −0.0929018 | − | 0.995675i | ||||
\(288\) | 349.161 | 1.21237 | ||||||||
\(289\) | 11.4892 | 0.0397550 | ||||||||
\(290\) | −96.6679 | −0.333338 | ||||||||
\(291\) | 385.762 | 1.32564 | ||||||||
\(292\) | − | 52.6486i | − | 0.180304i | ||||||
\(293\) | 528.537 | 1.80388 | 0.901940 | − | 0.431862i | \(-0.142143\pi\) | ||||
0.901940 | + | 0.431862i | \(0.142143\pi\) | |||||||
\(294\) | 209.686 | − | 142.621i | 0.713219 | − | 0.485105i | ||||
\(295\) | −808.632 | −2.74112 | ||||||||
\(296\) | −127.025 | −0.429139 | ||||||||
\(297\) | − | 112.605i | − | 0.379143i | ||||||
\(298\) | 287.302i | 0.964101i | ||||||||
\(299\) | 169.549 | 0.567054 | ||||||||
\(300\) | 665.635 | 2.21878 | ||||||||
\(301\) | 260.656 | − | 80.2434i | 0.865968 | − | 0.266589i | ||||
\(302\) | − | 164.029i | − | 0.543143i | ||||||
\(303\) | 240.197 | 0.792729 | ||||||||
\(304\) | −0.502624 | −0.00165337 | ||||||||
\(305\) | 319.159 | 1.04642 | ||||||||
\(306\) | 215.706 | 0.704922 | ||||||||
\(307\) | − | 385.509i | − | 1.25573i | −0.778323 | − | 0.627865i | \(-0.783929\pi\) | ||
0.778323 | − | 0.627865i | \(-0.216071\pi\) | |||||||
\(308\) | −83.0376 | − | 269.733i | −0.269603 | − | 0.875756i | ||||
\(309\) | 585.946i | 1.89627i | ||||||||
\(310\) | 538.711 | 1.73778 | ||||||||
\(311\) | −370.453 | −1.19117 | −0.595584 | − | 0.803293i | \(-0.703079\pi\) | ||||
−0.595584 | + | 0.803293i | \(0.703079\pi\) | |||||||
\(312\) | −409.988 | −1.31406 | ||||||||
\(313\) | 25.9563 | 0.0829275 | 0.0414638 | − | 0.999140i | \(-0.486798\pi\) | ||||
0.0414638 | + | 0.999140i | \(0.486798\pi\) | |||||||
\(314\) | 30.3959 | 0.0968022 | ||||||||
\(315\) | 198.731 | + | 645.541i | 0.630891 | + | 2.04934i | ||||
\(316\) | 101.721i | 0.321901i | ||||||||
\(317\) | 481.625i | 1.51932i | 0.650320 | + | 0.759661i | \(0.274635\pi\) | ||||
−0.650320 | + | 0.759661i | \(0.725365\pi\) | |||||||
\(318\) | − | 146.613i | − | 0.461047i | ||||||
\(319\) | −139.877 | −0.438486 | ||||||||
\(320\) | − | 291.341i | − | 0.910442i | ||||||
\(321\) | −808.973 | −2.52017 | ||||||||
\(322\) | −110.931 | + | 34.1502i | −0.344506 | + | 0.106057i | ||||
\(323\) | −5.77586 | −0.0178819 | ||||||||
\(324\) | 166.933 | 0.515225 | ||||||||
\(325\) | −679.221 | −2.08991 | ||||||||
\(326\) | 109.039 | 0.334475 | ||||||||
\(327\) | − | 47.7030i | − | 0.145881i | ||||||
\(328\) | 64.8503 | − | 310.950i | 0.197714 | − | 0.948018i | ||||
\(329\) | −534.077 | + | 164.416i | −1.62334 | + | 0.499746i | ||||
\(330\) | −715.947 | −2.16954 | ||||||||
\(331\) | 213.502i | 0.645021i | 0.946566 | + | 0.322510i | \(0.104527\pi\) | ||||
−0.946566 | + | 0.322510i | \(0.895473\pi\) | |||||||
\(332\) | 298.549i | 0.899243i | ||||||||
\(333\) | 174.805 | 0.524940 | ||||||||
\(334\) | −275.174 | −0.823873 | ||||||||
\(335\) | 569.007 | 1.69853 | ||||||||
\(336\) | −44.7492 | + | 13.7761i | −0.133182 | + | 0.0410003i | ||||
\(337\) | 144.101 | 0.427600 | 0.213800 | − | 0.976877i | \(-0.431416\pi\) | ||||
0.213800 | + | 0.976877i | \(0.431416\pi\) | |||||||
\(338\) | −31.0032 | −0.0917254 | ||||||||
\(339\) | 310.556 | 0.916094 | ||||||||
\(340\) | 413.824i | 1.21713i | ||||||||
\(341\) | 779.507 | 2.28594 | ||||||||
\(342\) | −4.14620 | −0.0121234 | ||||||||
\(343\) | −214.303 | + | 267.812i | −0.624791 | + | 0.780792i | ||||
\(344\) | 301.845 | 0.877457 | ||||||||
\(345\) | − | 570.116i | − | 1.65251i | ||||||
\(346\) | − | 264.449i | − | 0.764305i | ||||||
\(347\) | 365.274i | 1.05266i | 0.850279 | + | 0.526332i | \(0.176433\pi\) | ||||
−0.850279 | + | 0.526332i | \(0.823567\pi\) | |||||||
\(348\) | 107.032i | 0.307564i | ||||||||
\(349\) | 161.384i | 0.462417i | 0.972904 | + | 0.231209i | \(0.0742680\pi\) | ||||
−0.972904 | + | 0.231209i | \(0.925732\pi\) | |||||||
\(350\) | 444.394 | − | 136.807i | 1.26970 | − | 0.390877i | ||||
\(351\) | 87.9230 | 0.250493 | ||||||||
\(352\) | − | 500.587i | − | 1.42212i | ||||||
\(353\) | − | 215.147i | − | 0.609481i | −0.952435 | − | 0.304740i | \(-0.901430\pi\) | ||
0.952435 | − | 0.304740i | \(-0.0985697\pi\) | |||||||
\(354\) | − | 462.401i | − | 1.30622i | ||||||
\(355\) | 276.319 | 0.778362 | ||||||||
\(356\) | −374.335 | −1.05150 | ||||||||
\(357\) | −514.231 | + | 158.307i | −1.44042 | + | 0.443436i | ||||
\(358\) | − | 320.611i | − | 0.895561i | ||||||
\(359\) | 68.7380 | 0.191471 | 0.0957354 | − | 0.995407i | \(-0.469480\pi\) | ||||
0.0957354 | + | 0.995407i | \(0.469480\pi\) | |||||||
\(360\) | 747.549i | 2.07652i | ||||||||
\(361\) | −360.889 | −0.999692 | ||||||||
\(362\) | 114.483 | 0.316251 | ||||||||
\(363\) | −499.435 | −1.37585 | ||||||||
\(364\) | 210.609 | − | 64.8363i | 0.578597 | − | 0.178122i | ||||
\(365\) | 180.647 | 0.494922 | ||||||||
\(366\) | 182.505i | 0.498648i | ||||||||
\(367\) | 255.033i | 0.694912i | 0.937696 | + | 0.347456i | \(0.112954\pi\) | ||||
−0.937696 | + | 0.347456i | \(0.887046\pi\) | |||||||
\(368\) | 21.4301 | 0.0582341 | ||||||||
\(369\) | −89.2433 | + | 427.912i | −0.241852 | + | 1.15965i | ||||
\(370\) | − | 173.198i | − | 0.468102i | ||||||
\(371\) | 58.3458 | + | 189.526i | 0.157266 | + | 0.510852i | ||||
\(372\) | − | 596.469i | − | 1.60341i | ||||||
\(373\) | 317.831 | 0.852095 | 0.426048 | − | 0.904701i | \(-0.359906\pi\) | ||||
0.426048 | + | 0.904701i | \(0.359906\pi\) | |||||||
\(374\) | − | 309.254i | − | 0.826883i | ||||||
\(375\) | 1280.64i | 3.41503i | ||||||||
\(376\) | −618.471 | −1.64487 | ||||||||
\(377\) | − | 109.217i | − | 0.289700i | ||||||
\(378\) | −57.5254 | + | 17.7093i | −0.152184 | + | 0.0468499i | ||||
\(379\) | 567.422 | 1.49716 | 0.748578 | − | 0.663047i | \(-0.230737\pi\) | ||||
0.748578 | + | 0.663047i | \(0.230737\pi\) | |||||||
\(380\) | − | 7.95433i | − | 0.0209324i | ||||||
\(381\) | −467.258 | −1.22640 | ||||||||
\(382\) | 340.645i | 0.891740i | ||||||||
\(383\) | −363.473 | −0.949016 | −0.474508 | − | 0.880251i | \(-0.657374\pi\) | ||||
−0.474508 | + | 0.880251i | \(0.657374\pi\) | |||||||
\(384\) | −414.271 | −1.07883 | ||||||||
\(385\) | 925.501 | − | 284.917i | 2.40390 | − | 0.740043i | ||||
\(386\) | − | 217.505i | − | 0.563484i | ||||||
\(387\) | −415.382 | −1.07334 | ||||||||
\(388\) | −229.478 | −0.591438 | ||||||||
\(389\) | 0.303045 | 0.000779037 | 0.000389519 | − | 1.00000i | \(-0.499876\pi\) | ||||
0.000389519 | 1.00000i | \(0.499876\pi\) | ||||||||
\(390\) | − | 559.016i | − | 1.43337i | ||||||
\(391\) | 246.262 | 0.629827 | ||||||||
\(392\) | −313.893 | + | 213.499i | −0.800748 | + | 0.544639i | ||||
\(393\) | 589.358i | 1.49964i | ||||||||
\(394\) | −220.857 | −0.560550 | ||||||||
\(395\) | −349.021 | −0.883599 | ||||||||
\(396\) | 429.847i | 1.08547i | ||||||||
\(397\) | 373.212 | 0.940081 | 0.470041 | − | 0.882645i | \(-0.344239\pi\) | ||||
0.470041 | + | 0.882645i | \(0.344239\pi\) | |||||||
\(398\) | 20.1224 | 0.0505588 | ||||||||
\(399\) | 9.88429 | − | 3.04289i | 0.0247727 | − | 0.00762630i | ||||
\(400\) | −85.8500 | −0.214625 | ||||||||
\(401\) | 172.196 | 0.429417 | 0.214709 | − | 0.976678i | \(-0.431120\pi\) | ||||
0.214709 | + | 0.976678i | \(0.431120\pi\) | |||||||
\(402\) | 325.376i | 0.809393i | ||||||||
\(403\) | 608.643i | 1.51028i | ||||||||
\(404\) | −142.886 | −0.353678 | ||||||||
\(405\) | 572.776i | 1.41426i | ||||||||
\(406\) | 21.9982 | + | 71.4573i | 0.0541828 | + | 0.176003i | ||||
\(407\) | − | 250.615i | − | 0.615761i | ||||||
\(408\) | −595.489 | −1.45953 | ||||||||
\(409\) | − | 132.063i | − | 0.322893i | −0.986881 | − | 0.161446i | \(-0.948384\pi\) | ||
0.986881 | − | 0.161446i | \(-0.0516159\pi\) | |||||||
\(410\) | 423.978 | + | 88.4229i | 1.03409 | + | 0.215666i | ||||
\(411\) | − | 126.093i | − | 0.306796i | ||||||
\(412\) | − | 348.562i | − | 0.846023i | ||||||
\(413\) | 184.016 | + | 597.743i | 0.445559 | + | 1.44732i | ||||
\(414\) | 176.779 | 0.427004 | ||||||||
\(415\) | −1024.37 | −2.46837 | ||||||||
\(416\) | 390.861 | 0.939570 | ||||||||
\(417\) | − | 11.1135i | − | 0.0266512i | ||||||
\(418\) | 5.94433i | 0.0142209i | ||||||||
\(419\) | 585.115i | 1.39646i | 0.715875 | + | 0.698228i | \(0.246028\pi\) | ||||
−0.715875 | + | 0.698228i | \(0.753972\pi\) | |||||||
\(420\) | −218.015 | − | 708.183i | −0.519083 | − | 1.68615i | ||||
\(421\) | − | 436.655i | − | 1.03718i | −0.855022 | − | 0.518592i | \(-0.826456\pi\) | ||
0.855022 | − | 0.518592i | \(-0.173544\pi\) | |||||||
\(422\) | 86.4598i | 0.204881i | ||||||||
\(423\) | 851.106 | 2.01207 | ||||||||
\(424\) | 219.475i | 0.517629i | ||||||||
\(425\) | −986.538 | −2.32126 | ||||||||
\(426\) | 158.008i | 0.370910i | ||||||||
\(427\) | −72.6293 | − | 235.923i | −0.170092 | − | 0.552514i | ||||
\(428\) | 481.234 | 1.12438 | ||||||||
\(429\) | − | 808.887i | − | 1.88552i | ||||||
\(430\) | 411.564i | 0.957125i | ||||||||
\(431\) | −110.451 | −0.256268 | −0.128134 | − | 0.991757i | \(-0.540899\pi\) | ||||
−0.128134 | + | 0.991757i | \(0.540899\pi\) | |||||||
\(432\) | 11.1130 | 0.0257246 | ||||||||
\(433\) | 70.1227i | 0.161946i | 0.996716 | + | 0.0809731i | \(0.0258028\pi\) | ||||
−0.996716 | + | 0.0809731i | \(0.974197\pi\) | |||||||
\(434\) | −122.592 | − | 398.217i | −0.282469 | − | 0.917551i | ||||
\(435\) | −367.246 | −0.844244 | ||||||||
\(436\) | 28.3771i | 0.0650850i | ||||||||
\(437\) | −4.73354 | −0.0108319 | ||||||||
\(438\) | 103.299i | 0.235843i | ||||||||
\(439\) | 640.138 | 1.45817 | 0.729086 | − | 0.684422i | \(-0.239945\pi\) | ||||
0.729086 | + | 0.684422i | \(0.239945\pi\) | |||||||
\(440\) | 1071.75 | 2.43579 | ||||||||
\(441\) | 431.962 | − | 293.805i | 0.979506 | − | 0.666224i | ||||
\(442\) | 241.467 | 0.546307 | ||||||||
\(443\) | −122.631 | −0.276820 | −0.138410 | − | 0.990375i | \(-0.544199\pi\) | ||||
−0.138410 | + | 0.990375i | \(0.544199\pi\) | |||||||
\(444\) | −191.768 | −0.431909 | ||||||||
\(445\) | − | 1284.41i | − | 2.88631i | ||||||
\(446\) | 490.908i | 1.10069i | ||||||||
\(447\) | 1091.47i | 2.44178i | ||||||||
\(448\) | −215.361 | + | 66.2990i | −0.480716 | + | 0.147989i | ||||
\(449\) | −201.374 | −0.448494 | −0.224247 | − | 0.974532i | \(-0.571992\pi\) | ||||
−0.224247 | + | 0.974532i | \(0.571992\pi\) | |||||||
\(450\) | −708.186 | −1.57375 | ||||||||
\(451\) | 613.489 | + | 127.947i | 1.36029 | + | 0.283695i | ||||
\(452\) | −184.740 | −0.408717 | ||||||||
\(453\) | − | 623.155i | − | 1.37562i | ||||||
\(454\) | −98.4112 | −0.216765 | ||||||||
\(455\) | 222.465 | + | 722.637i | 0.488933 | + | 1.58821i | ||||
\(456\) | 11.4462 | 0.0251013 | ||||||||
\(457\) | − | 3.62254i | − | 0.00792678i | −0.999992 | − | 0.00396339i | \(-0.998738\pi\) | ||
0.999992 | − | 0.00396339i | \(-0.00126159\pi\) | |||||||
\(458\) | 164.705 | 0.359618 | ||||||||
\(459\) | 127.704 | 0.278223 | ||||||||
\(460\) | 339.145i | 0.737271i | ||||||||
\(461\) | 178.971i | 0.388223i | 0.980979 | + | 0.194112i | \(0.0621824\pi\) | ||||
−0.980979 | + | 0.194112i | \(0.937818\pi\) | |||||||
\(462\) | 162.924 | + | 529.230i | 0.352650 | + | 1.14552i | ||||
\(463\) | 291.968i | 0.630600i | 0.948992 | + | 0.315300i | \(0.102105\pi\) | ||||
−0.948992 | + | 0.315300i | \(0.897895\pi\) | |||||||
\(464\) | − | 13.8044i | − | 0.0297510i | ||||||
\(465\) | 2046.59 | 4.40127 | ||||||||
\(466\) | − | 232.905i | − | 0.499797i | ||||||
\(467\) | − | 627.934i | − | 1.34461i | −0.740273 | − | 0.672306i | \(-0.765304\pi\) | ||
0.740273 | − | 0.672306i | \(-0.234696\pi\) | |||||||
\(468\) | −335.627 | −0.717151 | ||||||||
\(469\) | −129.486 | − | 420.612i | −0.276089 | − | 0.896827i | ||||
\(470\) | − | 843.282i | − | 1.79422i | ||||||
\(471\) | 115.476 | 0.245171 | ||||||||
\(472\) | 692.198i | 1.46652i | ||||||||
\(473\) | 595.526i | 1.25904i | ||||||||
\(474\) | − | 199.581i | − | 0.421058i | ||||||
\(475\) | 18.9627 | 0.0399216 | ||||||||
\(476\) | 305.900 | − | 94.1718i | 0.642648 | − | 0.197840i | ||||
\(477\) | − | 302.029i | − | 0.633184i | ||||||
\(478\) | − | 71.4107i | − | 0.149395i | ||||||
\(479\) | −301.484 | −0.629404 | −0.314702 | − | 0.949191i | \(-0.601905\pi\) | ||||
−0.314702 | + | 0.949191i | \(0.601905\pi\) | |||||||
\(480\) | − | 1314.29i | − | 2.73810i | ||||||
\(481\) | 195.681 | 0.406822 | ||||||||
\(482\) | 244.156i | 0.506548i | ||||||||
\(483\) | −421.432 | + | 129.738i | −0.872530 | + | 0.268609i | ||||
\(484\) | 297.099 | 0.613841 | ||||||||
\(485\) | − | 787.379i | − | 1.62346i | ||||||
\(486\) | −404.918 | −0.833164 | ||||||||
\(487\) | 10.6678 | 0.0219051 | 0.0109526 | − | 0.999940i | \(-0.496514\pi\) | ||||
0.0109526 | + | 0.999940i | \(0.496514\pi\) | |||||||
\(488\) | − | 273.204i | − | 0.559843i | ||||||
\(489\) | 414.244 | 0.847126 | ||||||||
\(490\) | −291.104 | − | 427.991i | −0.594089 | − | 0.873451i | ||||
\(491\) | −793.174 | −1.61543 | −0.807713 | − | 0.589576i | \(-0.799295\pi\) | ||||
−0.807713 | + | 0.589576i | \(0.799295\pi\) | |||||||
\(492\) | 97.9032 | − | 469.435i | 0.198990 | − | 0.954136i | ||||
\(493\) | − | 158.632i | − | 0.321770i | ||||||
\(494\) | −4.64137 | −0.00939549 | ||||||||
\(495\) | −1474.88 | −2.97955 | ||||||||
\(496\) | 76.9294i | 0.155100i | ||||||||
\(497\) | −62.8804 | − | 204.256i | −0.126520 | − | 0.410977i | ||||
\(498\) | − | 585.769i | − | 1.17624i | ||||||
\(499\) | 330.798i | 0.662922i | 0.943469 | + | 0.331461i | \(0.107541\pi\) | ||||
−0.943469 | + | 0.331461i | \(0.892459\pi\) | |||||||
\(500\) | − | 761.811i | − | 1.52362i | ||||||
\(501\) | −1045.40 | −2.08662 | ||||||||
\(502\) | 7.08568i | 0.0141149i | ||||||||
\(503\) | −543.482 | −1.08048 | −0.540241 | − | 0.841510i | \(-0.681667\pi\) | ||||
−0.540241 | + | 0.841510i | \(0.681667\pi\) | |||||||
\(504\) | 552.591 | − | 170.116i | 1.09641 | − | 0.337531i | ||||
\(505\) | − | 490.266i | − | 0.970824i | ||||||
\(506\) | − | 253.446i | − | 0.500881i | ||||||
\(507\) | −117.783 | −0.232313 | ||||||||
\(508\) | 277.958 | 0.547161 | ||||||||
\(509\) | 371.445 | 0.729755 | 0.364878 | − | 0.931056i | \(-0.381111\pi\) | ||||
0.364878 | + | 0.931056i | \(0.381111\pi\) | |||||||
\(510\) | − | 811.945i | − | 1.59205i | ||||||
\(511\) | −41.1088 | − | 133.535i | −0.0804477 | − | 0.261320i | ||||
\(512\) | 96.1498 | 0.187793 | ||||||||
\(513\) | −2.45467 | −0.00478493 | ||||||||
\(514\) | −113.182 | −0.220197 | ||||||||
\(515\) | 1195.98 | 2.32228 | ||||||||
\(516\) | 455.690 | 0.883120 | ||||||||
\(517\) | − | 1220.22i | − | 2.36018i | ||||||
\(518\) | −128.028 | + | 39.4137i | −0.247159 | + | 0.0760883i | ||||
\(519\) | − | 1004.66i | − | 1.93575i | ||||||
\(520\) | 836.827i | 1.60928i | ||||||||
\(521\) | 121.091 | 0.232421 | 0.116210 | − | 0.993225i | \(-0.462925\pi\) | ||||
0.116210 | + | 0.993225i | \(0.462925\pi\) | |||||||
\(522\) | − | 113.874i | − | 0.218150i | ||||||
\(523\) | 189.011i | 0.361398i | 0.983538 | + | 0.180699i | \(0.0578360\pi\) | ||||
−0.983538 | + | 0.180699i | \(0.942164\pi\) | |||||||
\(524\) | − | 350.591i | − | 0.669067i | ||||||
\(525\) | 1688.27 | − | 519.737i | 3.21576 | − | 0.989976i | ||||
\(526\) | 287.606i | 0.546779i | ||||||||
\(527\) | 884.027i | 1.67747i | ||||||||
\(528\) | − | 102.239i | − | 0.193635i | ||||||
\(529\) | −327.179 | −0.618485 | ||||||||
\(530\) | −299.252 | −0.564627 | ||||||||
\(531\) | − | 952.564i | − | 1.79391i | ||||||
\(532\) | −5.87987 | + | 1.81012i | −0.0110524 | + | 0.00340249i | ||||
\(533\) | −99.9014 | + | 479.016i | −0.187432 | + | 0.898717i | ||||
\(534\) | 734.466 | 1.37540 | ||||||||
\(535\) | 1651.20i | 3.08635i | ||||||||
\(536\) | − | 487.076i | − | 0.908724i | ||||||
\(537\) | − | 1218.02i | − | 2.26819i | ||||||
\(538\) | − | 75.9162i | − | 0.141108i | ||||||
\(539\) | −421.223 | − | 619.296i | −0.781489 | − | 1.14897i | ||||
\(540\) | 175.870i | 0.325686i | ||||||||
\(541\) | −543.204 | −1.00407 | −0.502037 | − | 0.864846i | \(-0.667416\pi\) | ||||
−0.502037 | + | 0.864846i | \(0.667416\pi\) | |||||||
\(542\) | 303.187i | 0.559385i | ||||||||
\(543\) | 434.927 | 0.800970 | ||||||||
\(544\) | 567.708 | 1.04358 | ||||||||
\(545\) | −97.3667 | −0.178654 | ||||||||
\(546\) | −413.226 | + | 127.212i | −0.756825 | + | 0.232989i | ||||
\(547\) | 389.951i | 0.712890i | 0.934316 | + | 0.356445i | \(0.116011\pi\) | ||||
−0.934316 | + | 0.356445i | \(0.883989\pi\) | |||||||
\(548\) | 75.0089i | 0.136878i | ||||||||
\(549\) | 375.968i | 0.684822i | ||||||||
\(550\) | 1015.31i | 1.84602i | ||||||||
\(551\) | 3.04916i | 0.00553386i | ||||||||
\(552\) | −488.026 | −0.884105 | ||||||||
\(553\) | 79.4249 | + | 257.998i | 0.143626 | + | 0.466542i | ||||
\(554\) | −21.1812 | −0.0382332 | ||||||||
\(555\) | − | 657.988i | − | 1.18556i | ||||||
\(556\) | 6.61111i | 0.0118905i | ||||||||
\(557\) | 871.683i | 1.56496i | 0.622675 | + | 0.782480i | \(0.286046\pi\) | ||||
−0.622675 | + | 0.782480i | \(0.713954\pi\) | |||||||
\(558\) | 634.599i | 1.13727i | ||||||||
\(559\) | −464.991 | −0.831826 | ||||||||
\(560\) | 28.1184 | + | 91.3376i | 0.0502114 | + | 0.163103i | ||||
\(561\) | − | 1174.87i | − | 2.09425i | ||||||
\(562\) | 229.023i | 0.407514i | ||||||||
\(563\) | −869.717 | −1.54479 | −0.772396 | − | 0.635142i | \(-0.780942\pi\) | ||||
−0.772396 | + | 0.635142i | \(0.780942\pi\) | |||||||
\(564\) | −933.695 | −1.65549 | ||||||||
\(565\) | − | 633.876i | − | 1.12190i | ||||||
\(566\) | − | 355.666i | − | 0.628386i | ||||||
\(567\) | 423.398 | − | 130.344i | 0.746734 | − | 0.229883i | ||||
\(568\) | − | 236.532i | − | 0.416429i | ||||||
\(569\) | −703.517 | −1.23641 | −0.618205 | − | 0.786017i | \(-0.712140\pi\) | ||||
−0.618205 | + | 0.786017i | \(0.712140\pi\) | |||||||
\(570\) | 15.6068i | 0.0273804i | ||||||||
\(571\) | − | 599.351i | − | 1.04965i | −0.851210 | − | 0.524826i | \(-0.824130\pi\) | ||
0.851210 | − | 0.524826i | \(-0.175870\pi\) | |||||||
\(572\) | 481.182i | 0.841228i | ||||||||
\(573\) | 1294.13i | 2.25851i | ||||||||
\(574\) | −31.1199 | − | 333.528i | −0.0542159 | − | 0.581059i | ||||
\(575\) | −808.505 | −1.40610 | ||||||||
\(576\) | 343.199 | 0.595831 | ||||||||
\(577\) | −344.447 | −0.596962 | −0.298481 | − | 0.954416i | \(-0.596480\pi\) | ||||
−0.298481 | + | 0.954416i | \(0.596480\pi\) | |||||||
\(578\) | 13.4098 | 0.0232003 | ||||||||
\(579\) | − | 826.311i | − | 1.42714i | ||||||
\(580\) | 218.464 | 0.376662 | ||||||||
\(581\) | 233.111 | + | 757.220i | 0.401224 | + | 1.30330i | ||||
\(582\) | 450.248 | 0.773622 | ||||||||
\(583\) | −433.013 | −0.742733 | ||||||||
\(584\) | − | 154.636i | − | 0.264787i | ||||||
\(585\) | − | 1151.59i | − | 1.96854i | ||||||
\(586\) | 616.890 | 1.05271 | ||||||||
\(587\) | 14.3452 | 0.0244382 | 0.0122191 | − | 0.999925i | \(-0.496110\pi\) | ||||
0.0122191 | + | 0.999925i | \(0.496110\pi\) | |||||||
\(588\) | −473.879 | + | 322.315i | −0.805916 | + | 0.548154i | ||||
\(589\) | − | 16.9923i | − | 0.0288495i | ||||||
\(590\) | −943.807 | −1.59967 | ||||||||
\(591\) | −839.045 | −1.41970 | ||||||||
\(592\) | 24.7331 | 0.0417790 | ||||||||
\(593\) | −835.017 | −1.40812 | −0.704061 | − | 0.710139i | \(-0.748632\pi\) | ||||
−0.704061 | + | 0.710139i | \(0.748632\pi\) | |||||||
\(594\) | − | 131.429i | − | 0.221261i | ||||||
\(595\) | 323.120 | + | 1049.60i | 0.543058 | + | 1.76403i | ||||
\(596\) | − | 649.285i | − | 1.08940i | ||||||
\(597\) | 76.4460 | 0.128050 | ||||||||
\(598\) | 197.892 | 0.330923 | ||||||||
\(599\) | 527.043 | 0.879872 | 0.439936 | − | 0.898029i | \(-0.355001\pi\) | ||||
0.439936 | + | 0.898029i | \(0.355001\pi\) | |||||||
\(600\) | 1955.05 | 3.25842 | ||||||||
\(601\) | −89.1917 | −0.148405 | −0.0742027 | − | 0.997243i | \(-0.523641\pi\) | ||||
−0.0742027 | + | 0.997243i | \(0.523641\pi\) | |||||||
\(602\) | 304.229 | − | 93.6574i | 0.505364 | − | 0.155577i | ||||
\(603\) | 670.287i | 1.11159i | ||||||||
\(604\) | 370.696i | 0.613735i | ||||||||
\(605\) | 1019.40i | 1.68495i | ||||||||
\(606\) | 280.350 | 0.462623 | ||||||||
\(607\) | 151.022i | 0.248801i | 0.992232 | + | 0.124401i | \(0.0397008\pi\) | ||||
−0.992232 | + | 0.124401i | \(0.960299\pi\) | |||||||
\(608\) | −10.9122 | −0.0179477 | ||||||||
\(609\) | 83.5723 | + | 271.470i | 0.137229 | + | 0.445763i | ||||
\(610\) | 372.511 | 0.610674 | ||||||||
\(611\) | 952.751 | 1.55933 | ||||||||
\(612\) | −487.483 | −0.796541 | ||||||||
\(613\) | −799.097 | −1.30358 | −0.651792 | − | 0.758397i | \(-0.725983\pi\) | ||||
−0.651792 | + | 0.758397i | \(0.725983\pi\) | |||||||
\(614\) | − | 449.953i | − | 0.732822i | ||||||
\(615\) | 1610.71 | + | 335.923i | 2.61905 | + | 0.546216i | ||||
\(616\) | −243.892 | − | 792.239i | −0.395928 | − | 1.28610i | ||||
\(617\) | −29.0725 | −0.0471192 | −0.0235596 | − | 0.999722i | \(-0.507500\pi\) | ||||
−0.0235596 | + | 0.999722i | \(0.507500\pi\) | |||||||
\(618\) | 683.896i | 1.10663i | ||||||||
\(619\) | 467.755i | 0.755662i | 0.925875 | + | 0.377831i | \(0.123330\pi\) | ||||
−0.925875 | + | 0.377831i | \(0.876670\pi\) | |||||||
\(620\) | −1217.45 | −1.96364 | ||||||||
\(621\) | 104.659 | 0.168532 | ||||||||
\(622\) | −432.380 | −0.695145 | ||||||||
\(623\) | −949.440 | + | 292.286i | −1.52398 | + | 0.469159i | ||||
\(624\) | 79.8290 | 0.127931 | ||||||||
\(625\) | 1191.12 | 1.90579 | ||||||||
\(626\) | 30.2953 | 0.0483951 | ||||||||
\(627\) | 22.5828i | 0.0360172i | ||||||||
\(628\) | −68.6929 | −0.109384 | ||||||||
\(629\) | 284.219 | 0.451858 | ||||||||
\(630\) | 231.952 | + | 753.453i | 0.368177 | + | 1.19596i | ||||
\(631\) | 330.433 | 0.523666 | 0.261833 | − | 0.965113i | \(-0.415673\pi\) | ||||
0.261833 | + | 0.965113i | \(0.415673\pi\) | |||||||
\(632\) | 298.766i | 0.472732i | ||||||||
\(633\) | 328.465i | 0.518902i | ||||||||
\(634\) | 562.136i | 0.886650i | ||||||||
\(635\) | 953.721i | 1.50192i | ||||||||
\(636\) | 331.337i | 0.520970i | ||||||||
\(637\) | 483.550 | − | 328.893i | 0.759106 | − | 0.516316i | ||||
\(638\) | −163.260 | −0.255893 | ||||||||
\(639\) | 325.502i | 0.509393i | ||||||||
\(640\) | 845.569i | 1.32120i | ||||||||
\(641\) | − | 603.751i | − | 0.941889i | −0.882163 | − | 0.470944i | \(-0.843913\pi\) | ||
0.882163 | − | 0.470944i | \(-0.156087\pi\) | |||||||
\(642\) | −944.206 | −1.47073 | ||||||||
\(643\) | 841.198 | 1.30824 | 0.654120 | − | 0.756391i | \(-0.273039\pi\) | ||||
0.654120 | + | 0.756391i | \(0.273039\pi\) | |||||||
\(644\) | 250.697 | − | 77.1774i | 0.389281 | − | 0.119841i | ||||
\(645\) | 1563.55i | 2.42411i | ||||||||
\(646\) | −6.74138 | −0.0104356 | ||||||||
\(647\) | 87.5245i | 0.135277i | 0.997710 | + | 0.0676387i | \(0.0215465\pi\) | ||||
−0.997710 | + | 0.0676387i | \(0.978453\pi\) | |||||||
\(648\) | 490.303 | 0.756640 | ||||||||
\(649\) | −1365.67 | −2.10427 | ||||||||
\(650\) | −792.763 | −1.21964 | ||||||||
\(651\) | −465.732 | − | 1512.85i | −0.715410 | − | 2.32388i | ||||
\(652\) | −246.421 | −0.377947 | ||||||||
\(653\) | − | 941.438i | − | 1.44171i | −0.693085 | − | 0.720856i | \(-0.743749\pi\) | ||
0.693085 | − | 0.720856i | \(-0.256251\pi\) | |||||||
\(654\) | − | 55.6773i | − | 0.0851335i | ||||||
\(655\) | 1202.94 | 1.83655 | ||||||||
\(656\) | −12.6270 | + | 60.5452i | −0.0192485 | + | 0.0922946i | ||||
\(657\) | 212.801i | 0.323898i | ||||||||
\(658\) | −623.357 | + | 191.901i | −0.947350 | + | 0.291643i | ||||
\(659\) | − | 727.209i | − | 1.10350i | −0.834008 | − | 0.551752i | \(-0.813960\pi\) | ||
0.834008 | − | 0.551752i | \(-0.186040\pi\) | |||||||
\(660\) | 1618.00 | 2.45151 | ||||||||
\(661\) | − | 1035.36i | − | 1.56635i | −0.621798 | − | 0.783177i | \(-0.713598\pi\) | ||
0.621798 | − | 0.783177i | \(-0.286402\pi\) | |||||||
\(662\) | 249.192i | 0.376423i | ||||||||
\(663\) | 917.347 | 1.38363 | ||||||||
\(664\) | 876.875i | 1.32059i | ||||||||
\(665\) | −6.21085 | − | 20.1748i | −0.00933963 | − | 0.0303381i | ||||
\(666\) | 204.026 | 0.306346 | ||||||||
\(667\) | − | 130.005i | − | 0.194911i | ||||||
\(668\) | 621.876 | 0.930952 | ||||||||
\(669\) | 1864.99i | 2.78772i | ||||||||
\(670\) | 664.125 | 0.991231 | ||||||||
\(671\) | 539.018 | 0.803305 | ||||||||
\(672\) | −971.526 | + | 299.085i | −1.44572 | + | 0.445068i | ||||
\(673\) | 1029.20i | 1.52927i | 0.644462 | + | 0.764636i | \(0.277081\pi\) | ||||
−0.644462 | + | 0.764636i | \(0.722919\pi\) | |||||||
\(674\) | 168.190 | 0.249540 | ||||||||
\(675\) | −419.267 | −0.621136 | ||||||||
\(676\) | 70.0654 | 0.103647 | ||||||||
\(677\) | − | 351.751i | − | 0.519574i | −0.965666 | − | 0.259787i | \(-0.916348\pi\) | ||
0.965666 | − | 0.259787i | \(-0.0836523\pi\) | |||||||
\(678\) | 362.470 | 0.534617 | ||||||||
\(679\) | −582.033 | + | 179.180i | −0.857192 | + | 0.263888i | ||||
\(680\) | 1215.45i | 1.78743i | ||||||||
\(681\) | −373.869 | −0.549000 | ||||||||
\(682\) | 909.813 | 1.33404 | ||||||||
\(683\) | − | 942.056i | − | 1.37929i | −0.724147 | − | 0.689646i | \(-0.757766\pi\) | ||
0.724147 | − | 0.689646i | \(-0.242234\pi\) | |||||||
\(684\) | 9.37016 | 0.0136991 | ||||||||
\(685\) | −257.369 | −0.375721 | ||||||||
\(686\) | −250.128 | + | 312.581i | −0.364617 | + | 0.455657i | ||||
\(687\) | 625.722 | 0.910804 | ||||||||
\(688\) | −58.7724 | −0.0854251 | ||||||||
\(689\) | − | 338.099i | − | 0.490710i | ||||||
\(690\) | − | 665.420i | − | 0.964377i | ||||||
\(691\) | −546.729 | −0.791214 | −0.395607 | − | 0.918420i | \(-0.629466\pi\) | ||||
−0.395607 | + | 0.918420i | \(0.629466\pi\) | |||||||
\(692\) | 597.640i | 0.863641i | ||||||||
\(693\) | 335.630 | + | 1090.24i | 0.484315 | + | 1.57321i | ||||
\(694\) | 426.336i | 0.614317i | ||||||||
\(695\) | −22.6839 | −0.0326386 | ||||||||
\(696\) | 314.367i | 0.451677i | ||||||||
\(697\) | −145.102 | + | 695.750i | −0.208181 | + | 0.998206i | ||||
\(698\) | 188.361i | 0.269859i | ||||||||
\(699\) | − | 884.819i | − | 1.26584i | ||||||
\(700\) | −1004.30 | + | 309.176i | −1.43472 | + | 0.441680i | ||||
\(701\) | 160.450 | 0.228888 | 0.114444 | − | 0.993430i | \(-0.463491\pi\) | ||||
0.114444 | + | 0.993430i | \(0.463491\pi\) | |||||||
\(702\) | 102.621 | 0.146183 | ||||||||
\(703\) | −5.46311 | −0.00777114 | ||||||||
\(704\) | − | 492.038i | − | 0.698917i | ||||||
\(705\) | − | 3203.67i | − | 4.54421i | ||||||
\(706\) | − | 251.112i | − | 0.355682i | ||||||
\(707\) | −362.406 | + | 111.567i | −0.512597 | + | 0.157804i | ||||
\(708\) | 1045.00i | 1.47599i | ||||||||
\(709\) | − | 774.322i | − | 1.09213i | −0.837742 | − | 0.546067i | \(-0.816125\pi\) | ||
0.837742 | − | 0.546067i | \(-0.183875\pi\) | |||||||
\(710\) | 322.510 | 0.454239 | ||||||||
\(711\) | − | 411.146i | − | 0.578264i | ||||||
\(712\) | −1099.47 | −1.54420 | ||||||||
\(713\) | 724.494i | 1.01612i | ||||||||
\(714\) | −600.193 | + | 184.770i | −0.840606 | + | 0.258782i | ||||
\(715\) | −1651.02 | −2.30912 | ||||||||
\(716\) | 724.561i | 1.01196i | ||||||||
\(717\) | − | 271.293i | − | 0.378372i | ||||||
\(718\) | 80.2286 | 0.111739 | ||||||||
\(719\) | −591.145 | −0.822176 | −0.411088 | − | 0.911596i | \(-0.634851\pi\) | ||||
−0.411088 | + | 0.911596i | \(0.634851\pi\) | |||||||
\(720\) | − | 145.556i | − | 0.202161i | ||||||
\(721\) | −272.162 | − | 884.069i | −0.377478 | − | 1.22617i | ||||
\(722\) | −421.217 | −0.583403 | ||||||||
\(723\) | 927.561i | 1.28293i | ||||||||
\(724\) | −258.725 | −0.357355 | ||||||||
\(725\) | 520.807i | 0.718355i | ||||||||
\(726\) | −582.924 | −0.802925 | ||||||||
\(727\) | 19.6607 | 0.0270436 | 0.0135218 | − | 0.999909i | \(-0.495696\pi\) | ||||
0.0135218 | + | 0.999909i | \(0.495696\pi\) | |||||||
\(728\) | 618.585 | − | 190.432i | 0.849705 | − | 0.261583i | ||||
\(729\) | −968.723 | −1.32884 | ||||||||
\(730\) | 210.845 | 0.288828 | ||||||||
\(731\) | −675.378 | −0.923910 | ||||||||
\(732\) | − | 412.450i | − | 0.563457i | ||||||
\(733\) | 284.356i | 0.387935i | 0.981008 | + | 0.193967i | \(0.0621356\pi\) | ||||
−0.981008 | + | 0.193967i | \(0.937864\pi\) | |||||||
\(734\) | 297.665i | 0.405539i | ||||||||
\(735\) | −1105.92 | − | 1625.96i | −1.50465 | − | 2.21219i | ||||
\(736\) | 465.259 | 0.632145 | ||||||||
\(737\) | 960.979 | 1.30391 | ||||||||
\(738\) | −104.162 | + | 499.444i | −0.141141 | + | 0.676753i | ||||
\(739\) | 105.738 | 0.143083 | 0.0715416 | − | 0.997438i | \(-0.477208\pi\) | ||||
0.0715416 | + | 0.997438i | \(0.477208\pi\) | |||||||
\(740\) | 391.417i | 0.528942i | ||||||||
\(741\) | −17.6328 | −0.0237960 | ||||||||
\(742\) | 68.0992 | + | 221.208i | 0.0917779 | + | 0.298124i | ||||
\(743\) | 1098.00 | 1.47779 | 0.738894 | − | 0.673822i | \(-0.235348\pi\) | ||||
0.738894 | + | 0.673822i | \(0.235348\pi\) | |||||||
\(744\) | − | 1751.91i | − | 2.35471i | ||||||
\(745\) | 2227.81 | 2.99035 | ||||||||
\(746\) | 370.962 | 0.497268 | ||||||||
\(747\) | − | 1206.71i | − | 1.61540i | ||||||
\(748\) | 698.896i | 0.934352i | ||||||||
\(749\) | 1220.57 | − | 375.754i | 1.62960 | − | 0.501674i | ||||
\(750\) | 1494.71i | 1.99295i | ||||||||
\(751\) | 1238.52i | 1.64916i | 0.565748 | + | 0.824578i | \(0.308588\pi\) | ||||
−0.565748 | + | 0.824578i | \(0.691412\pi\) | |||||||
\(752\) | 120.423 | 0.160137 | ||||||||
\(753\) | 26.9189i | 0.0357488i | ||||||||
\(754\) | − | 127.474i | − | 0.169064i | ||||||
\(755\) | −1271.92 | −1.68467 | ||||||||
\(756\) | 130.004 | − | 40.0219i | 0.171963 | − | 0.0529390i | ||||
\(757\) | − | 824.856i | − | 1.08964i | −0.838554 | − | 0.544819i | \(-0.816598\pi\) | ||
0.838554 | − | 0.544819i | \(-0.183402\pi\) | |||||||
\(758\) | 662.275 | 0.873714 | ||||||||
\(759\) | − | 962.853i | − | 1.26858i | ||||||
\(760\) | − | 23.3628i | − | 0.0307406i | ||||||
\(761\) | 214.329i | 0.281642i | 0.990035 | + | 0.140821i | \(0.0449741\pi\) | ||||
−0.990035 | + | 0.140821i | \(0.955026\pi\) | |||||||
\(762\) | −545.368 | −0.715706 | ||||||||
\(763\) | 22.1572 | + | 71.9738i | 0.0290396 | + | 0.0943300i | ||||
\(764\) | − | 769.836i | − | 1.00764i | ||||||
\(765\) | − | 1672.64i | − | 2.18646i | ||||||
\(766\) | −424.234 | −0.553830 | ||||||||
\(767\) | − | 1066.33i | − | 1.39026i | ||||||
\(768\) | −1054.47 | −1.37301 | ||||||||
\(769\) | − | 74.1441i | − | 0.0964163i | −0.998837 | − | 0.0482081i | \(-0.984649\pi\) | ||
0.998837 | − | 0.0482081i | \(-0.0153511\pi\) | |||||||
\(770\) | 1080.21 | − | 332.545i | 1.40287 | − | 0.431876i | ||||
\(771\) | −429.982 | −0.557694 | ||||||||
\(772\) | 491.548i | 0.636720i | ||||||||
\(773\) | 389.758 | 0.504215 | 0.252108 | − | 0.967699i | \(-0.418876\pi\) | ||||
0.252108 | + | 0.967699i | \(0.418876\pi\) | |||||||
\(774\) | −484.820 | −0.626383 | ||||||||
\(775\) | − | 2902.35i | − | 3.74497i | ||||||
\(776\) | −674.006 | −0.868564 | ||||||||
\(777\) | −486.387 | + | 149.735i | −0.625980 | + | 0.192709i | ||||
\(778\) | 0.353704 | 0.000454633 | ||||||||
\(779\) | 2.78909 | − | 13.3734i | 0.00358034 | − | 0.0171673i | ||||
\(780\) | 1263.34i | 1.61967i | ||||||||
\(781\) | 466.666 | 0.597524 | ||||||||
\(782\) | 287.429 | 0.367556 | ||||||||
\(783\) | − | 67.4169i | − | 0.0861007i | ||||||
\(784\) | 61.1183 | − | 41.5704i | 0.0779570 | − | 0.0530235i | ||||
\(785\) | − | 235.697i | − | 0.300251i | ||||||
\(786\) | 687.878i | 0.875163i | ||||||||
\(787\) | 939.917i | 1.19430i | 0.802128 | + | 0.597152i | \(0.203701\pi\) | ||||
−0.802128 | + | 0.597152i | \(0.796299\pi\) | |||||||
\(788\) | 499.123 | 0.633404 | ||||||||
\(789\) | 1092.63i | 1.38483i | ||||||||
\(790\) | −407.366 | −0.515653 | ||||||||
\(791\) | −468.563 | + | 144.248i | −0.592368 | + | 0.182361i | ||||
\(792\) | 1262.51i | 1.59408i | ||||||||
\(793\) | 420.868i | 0.530729i | ||||||||
\(794\) | 435.601 | 0.548615 | ||||||||
\(795\) | −1136.87 | −1.43003 | ||||||||
\(796\) | −45.4754 | −0.0571299 | ||||||||
\(797\) | − | 1061.91i | − | 1.33238i | −0.745781 | − | 0.666191i | \(-0.767924\pi\) | ||
0.745781 | − | 0.666191i | \(-0.232076\pi\) | |||||||
\(798\) | 11.5366 | − | 3.55156i | 0.0144569 | − | 0.00445058i | ||||
\(799\) | 1383.83 | 1.73195 | ||||||||
\(800\) | −1863.85 | −2.32981 | ||||||||
\(801\) | 1513.03 | 1.88892 | ||||||||
\(802\) | 200.982 | 0.250600 | ||||||||
\(803\) | 305.089 | 0.379936 | ||||||||
\(804\) | − | 735.330i | − | 0.914589i | ||||||
\(805\) | 264.809 | + | 860.185i | 0.328955 | + | 1.06855i | ||||
\(806\) | 710.388i | 0.881374i | ||||||||
\(807\) | − | 288.410i | − | 0.357385i | ||||||
\(808\) | −419.673 | −0.519398 | ||||||||
\(809\) | − | 527.236i | − | 0.651714i | −0.945419 | − | 0.325857i | \(-0.894347\pi\) | ||
0.945419 | − | 0.325857i | \(-0.105653\pi\) | |||||||
\(810\) | 668.524i | 0.825339i | ||||||||
\(811\) | 98.1048i | 0.120968i | 0.998169 | + | 0.0604838i | \(0.0192644\pi\) | ||||
−0.998169 | + | 0.0604838i | \(0.980736\pi\) | |||||||
\(812\) | −49.7146 | − | 161.489i | −0.0612249 | − | 0.198878i | ||||
\(813\) | 1151.82i | 1.41676i | ||||||||
\(814\) | − | 292.509i | − | 0.359348i | ||||||
\(815\) | − | 845.515i | − | 1.03744i | ||||||
\(816\) | 115.948 | 0.142093 | ||||||||
\(817\) | 12.9818 | 0.0158896 | ||||||||
\(818\) | − | 154.140i | − | 0.188435i | ||||||
\(819\) | −851.262 | + | 262.062i | −1.03939 | + | 0.319978i | ||||
\(820\) | −958.165 | − | 199.830i | −1.16849 | − | 0.243696i | ||||
\(821\) | 1035.05 | 1.26072 | 0.630358 | − | 0.776304i | \(-0.282908\pi\) | ||||
0.630358 | + | 0.776304i | \(0.282908\pi\) | |||||||
\(822\) | − | 147.171i | − | 0.179041i | ||||||
\(823\) | 1117.99i | 1.35843i | 0.733939 | + | 0.679216i | \(0.237680\pi\) | ||||
−0.733939 | + | 0.679216i | \(0.762320\pi\) | |||||||
\(824\) | − | 1023.77i | − | 1.24244i | ||||||
\(825\) | 3857.23i | 4.67543i | ||||||||
\(826\) | 214.777 | + | 697.666i | 0.260021 | + | 0.844631i | ||||
\(827\) | 1053.80i | 1.27425i | 0.770760 | + | 0.637125i | \(0.219877\pi\) | ||||
−0.770760 | + | 0.637125i | \(0.780123\pi\) | |||||||
\(828\) | −399.511 | −0.482501 | ||||||||
\(829\) | 317.668i | 0.383194i | 0.981474 | + | 0.191597i | \(0.0613666\pi\) | ||||
−0.981474 | + | 0.191597i | \(0.938633\pi\) | |||||||
\(830\) | −1195.61 | −1.44050 | ||||||||
\(831\) | −80.4685 | −0.0968333 | ||||||||
\(832\) | 384.186 | 0.461762 | ||||||||
\(833\) | 702.335 | − | 477.703i | 0.843140 | − | 0.573472i | ||||
\(834\) | − | 12.9713i | − | 0.0155532i | ||||||
\(835\) | 2133.77i | 2.55541i | ||||||||
\(836\) | − | 13.4338i | − | 0.0160692i | ||||||
\(837\) | 375.701i | 0.448866i | ||||||||
\(838\) | 682.927i | 0.814948i | ||||||||
\(839\) | 1629.21 | 1.94185 | 0.970925 | − | 0.239382i | \(-0.0769449\pi\) | ||||
0.970925 | + | 0.239382i | \(0.0769449\pi\) | |||||||
\(840\) | −640.337 | − | 2080.02i | −0.762306 | − | 2.47621i | ||||
\(841\) | 757.256 | 0.900423 | ||||||||
\(842\) | − | 509.648i | − | 0.605283i | ||||||
\(843\) | 870.070i | 1.03211i | ||||||||
\(844\) | − | 195.394i | − | 0.231509i | ||||||
\(845\) | 240.406i | 0.284505i | ||||||||
\(846\) | 993.382 | 1.17421 | ||||||||
\(847\) | 753.542 | − | 231.979i | 0.889660 | − | 0.273883i | ||||
\(848\) | − | 42.7340i | − | 0.0503939i | ||||||
\(849\) | − | 1351.19i | − | 1.59151i | ||||||
\(850\) | −1151.45 | −1.35465 | ||||||||
\(851\) | 232.928 | 0.273711 | ||||||||
\(852\) | − | 357.088i | − | 0.419117i | ||||||
\(853\) | 937.070i | 1.09856i | 0.835639 | + | 0.549279i | \(0.185098\pi\) | ||||
−0.835639 | + | 0.549279i | \(0.814902\pi\) | |||||||
\(854\) | −84.7704 | − | 275.362i | −0.0992627 | − | 0.322437i | ||||
\(855\) | 32.1507i | 0.0376031i | ||||||||
\(856\) | 1413.44 | 1.65122 | ||||||||
\(857\) | − | 497.757i | − | 0.580813i | −0.956903 | − | 0.290407i | \(-0.906209\pi\) | ||
0.956903 | − | 0.290407i | \(-0.0937905\pi\) | |||||||
\(858\) | − | 944.105i | − | 1.10036i | ||||||
\(859\) | − | 450.744i | − | 0.524731i | −0.964969 | − | 0.262365i | \(-0.915497\pi\) | ||
0.964969 | − | 0.262365i | \(-0.0845026\pi\) | |||||||
\(860\) | − | 930.109i | − | 1.08152i | ||||||
\(861\) | −118.226 | − | 1267.09i | −0.137313 | − | 1.47165i | ||||
\(862\) | −128.915 | −0.149554 | ||||||||
\(863\) | 1035.10 | 1.19942 | 0.599710 | − | 0.800218i | \(-0.295283\pi\) | ||||
0.599710 | + | 0.800218i | \(0.295283\pi\) | |||||||
\(864\) | 241.269 | 0.279247 | ||||||||
\(865\) | −2050.61 | −2.37064 | ||||||||
\(866\) | 81.8448i | 0.0945090i | ||||||||
\(867\) | 50.9445 | 0.0587595 | ||||||||
\(868\) | 277.050 | + | 899.947i | 0.319182 | + | 1.03680i | ||||
\(869\) | −589.452 | −0.678311 | ||||||||
\(870\) | −428.637 | −0.492687 | ||||||||
\(871\) | 750.338i | 0.861467i | ||||||||
\(872\) | 83.3470i | 0.0955814i | ||||||||
\(873\) | 927.529 | 1.06246 | ||||||||
\(874\) | −5.52482 | −0.00632130 | ||||||||
\(875\) | −594.833 | − | 1932.21i | −0.679809 | − | 2.20824i | ||||
\(876\) | − | 233.450i | − | 0.266496i | ||||||
\(877\) | 207.891 | 0.237048 | 0.118524 | − | 0.992951i | \(-0.462184\pi\) | ||||
0.118524 | + | 0.992951i | \(0.462184\pi\) | |||||||
\(878\) | 747.147 | 0.850965 | ||||||||
\(879\) | 2343.60 | 2.66621 | ||||||||
\(880\) | −208.681 | −0.237137 | ||||||||
\(881\) | − | 440.754i | − | 0.500288i | −0.968209 | − | 0.250144i | \(-0.919522\pi\) | ||
0.968209 | − | 0.250144i | \(-0.0804780\pi\) | |||||||
\(882\) | 504.171 | − | 342.919i | 0.571623 | − | 0.388797i | ||||
\(883\) | − | 377.705i | − | 0.427752i | −0.976861 | − | 0.213876i | \(-0.931391\pi\) | ||
0.976861 | − | 0.213876i | \(-0.0686089\pi\) | |||||||
\(884\) | −545.702 | −0.617310 | ||||||||
\(885\) | −3585.57 | −4.05149 | ||||||||
\(886\) | −143.131 | −0.161547 | ||||||||
\(887\) | 1273.12 | 1.43531 | 0.717655 | − | 0.696399i | \(-0.245216\pi\) | ||||
0.717655 | + | 0.696399i | \(0.245216\pi\) | |||||||
\(888\) | −563.245 | −0.634285 | ||||||||
\(889\) | 704.994 | − | 217.033i | 0.793019 | − | 0.244132i | ||||
\(890\) | − | 1499.12i | − | 1.68440i | ||||||
\(891\) | 967.344i | 1.08568i | ||||||||
\(892\) | − | 1109.42i | − | 1.24375i | ||||||
\(893\) | −26.5993 | −0.0297864 | ||||||||
\(894\) | 1273.93i | 1.42498i | ||||||||
\(895\) | −2486.09 | −2.77776 | ||||||||
\(896\) | 625.047 | − | 192.422i | 0.697598 | − | 0.214756i | ||||
\(897\) | 751.801 | 0.838128 | ||||||||
\(898\) | −235.037 | −0.261733 | ||||||||
\(899\) | 466.690 | 0.519122 | ||||||||
\(900\) | 1600.46 | 1.77829 | ||||||||
\(901\) | − | 491.074i | − | 0.545032i | ||||||
\(902\) | 716.044 | + | 149.335i | 0.793840 | + | 0.165560i | ||||
\(903\) | 1155.78 | − | 355.809i | 1.27994 | − | 0.394030i | ||||
\(904\) | −542.605 | −0.600227 | ||||||||
\(905\) | − | 887.730i | − | 0.980917i | ||||||
\(906\) | − | 727.326i | − | 0.802788i | ||||||
\(907\) | 1470.59 | 1.62138 | 0.810689 | − | 0.585477i | \(-0.199093\pi\) | ||||
0.810689 | + | 0.585477i | \(0.199093\pi\) | |||||||
\(908\) | 222.403 | 0.244938 | ||||||||
\(909\) | 577.531 | 0.635348 | ||||||||
\(910\) | 259.653 | + | 843.437i | 0.285333 | + | 0.926854i | ||||
\(911\) | −277.146 | −0.304222 | −0.152111 | − | 0.988363i | \(-0.548607\pi\) | ||||
−0.152111 | + | 0.988363i | \(0.548607\pi\) | |||||||
\(912\) | −2.22870 | −0.00244375 | ||||||||
\(913\) | −1730.03 | −1.89489 | ||||||||
\(914\) | − | 4.22810i | − | 0.00462594i | ||||||
\(915\) | 1415.19 | 1.54665 | ||||||||
\(916\) | −372.223 | −0.406357 | ||||||||
\(917\) | −273.746 | − | 889.216i | −0.298524 | − | 0.969702i | ||||
\(918\) | 149.052 | 0.162366 | ||||||||
\(919\) | − | 1173.84i | − | 1.27730i | −0.769496 | − | 0.638651i | \(-0.779493\pi\) | ||
0.769496 | − | 0.638651i | \(-0.220507\pi\) | |||||||
\(920\) | 996.111i | 1.08273i | ||||||||
\(921\) | − | 1709.39i | − | 1.85602i | ||||||
\(922\) | 208.889i | 0.226560i | ||||||||
\(923\) | 364.376i | 0.394773i | ||||||||
\(924\) | −368.199 | − | 1196.03i | −0.398484 | − | 1.29440i | ||||
\(925\) | −933.119 | −1.00878 | ||||||||
\(926\) | 340.775i | 0.368007i | ||||||||
\(927\) | 1408.85i | 1.51980i | ||||||||
\(928\) | − | 299.701i | − | 0.322954i | ||||||
\(929\) | 55.5029 | 0.0597448 | 0.0298724 | − | 0.999554i | \(-0.490490\pi\) | ||||
0.0298724 | + | 0.999554i | \(0.490490\pi\) | |||||||
\(930\) | 2388.71 | 2.56851 | ||||||||
\(931\) | −13.4999 | + | 9.18216i | −0.0145005 | + | 0.00986269i | ||||
\(932\) | 526.352i | 0.564755i | ||||||||
\(933\) | −1642.63 | −1.76059 | ||||||||
\(934\) | − | 732.903i | − | 0.784693i | ||||||
\(935\) | −2398.03 | −2.56474 | ||||||||
\(936\) | −985.778 | −1.05318 | ||||||||
\(937\) | −420.521 | −0.448795 | −0.224398 | − | 0.974498i | \(-0.572041\pi\) | ||||
−0.224398 | + | 0.974498i | \(0.572041\pi\) | |||||||
\(938\) | −151.131 | − | 490.923i | −0.161121 | − | 0.523373i | ||||
\(939\) | 115.093 | 0.122570 | ||||||||
\(940\) | 1905.77i | 2.02741i | ||||||||
\(941\) | 1591.40i | 1.69118i | 0.533834 | + | 0.845589i | \(0.320751\pi\) | ||||
−0.533834 | + | 0.845589i | \(0.679249\pi\) | |||||||
\(942\) | 134.779 | 0.143078 | ||||||||
\(943\) | −118.917 | + | 570.194i | −0.126105 | + | 0.604659i | ||||
\(944\) | − | 134.778i | − | 0.142774i | ||||||
\(945\) | 137.322 | + | 446.066i | 0.145314 | + | 0.472028i | ||||
\(946\) | 695.078i | 0.734755i | ||||||||
\(947\) | −742.202 | −0.783740 | −0.391870 | − | 0.920021i | \(-0.628172\pi\) | ||||
−0.391870 | + | 0.920021i | \(0.628172\pi\) | |||||||
\(948\) | 451.042i | 0.475783i | ||||||||
\(949\) | 238.215i | 0.251017i | ||||||||
\(950\) | 22.1327 | 0.0232975 | ||||||||
\(951\) | 2135.58i | 2.24562i | ||||||||
\(952\) | 898.467 | − | 276.594i | 0.943768 | − | 0.290540i | ||||
\(953\) | −721.199 | −0.756767 | −0.378384 | − | 0.925649i | \(-0.623520\pi\) | ||||
−0.378384 | + | 0.925649i | \(0.623520\pi\) | |||||||
\(954\) | − | 352.518i | − | 0.369515i | ||||||
\(955\) | 2641.44 | 2.76591 | ||||||||
\(956\) | 161.384i | 0.168812i | ||||||||
\(957\) | −620.231 | −0.648100 | ||||||||
\(958\) | −351.882 | −0.367309 | ||||||||
\(959\) | 58.5680 | + | 190.248i | 0.0610720 | + | 0.198381i | ||||
\(960\) | − | 1291.84i | − | 1.34567i | ||||||
\(961\) | −1639.77 | −1.70632 | ||||||||
\(962\) | 228.393 | 0.237414 | ||||||||
\(963\) | −1945.10 | −2.01984 | ||||||||
\(964\) | − | 551.778i | − | 0.572384i | ||||||
\(965\) | −1686.59 | −1.74776 | ||||||||
\(966\) | −491.881 | + | 151.426i | −0.509193 | + | 0.156756i | ||||
\(967\) | − | 1694.31i | − | 1.75213i | −0.482189 | − | 0.876067i | \(-0.660158\pi\) | ||
0.482189 | − | 0.876067i | \(-0.339842\pi\) | |||||||
\(968\) | 872.616 | 0.901463 | ||||||||
\(969\) | −25.6108 | −0.0264302 | ||||||||
\(970\) | − | 919.002i | − | 0.947425i | ||||||
\(971\) | 833.947 | 0.858854 | 0.429427 | − | 0.903102i | \(-0.358716\pi\) | ||||
0.429427 | + | 0.903102i | \(0.358716\pi\) | |||||||
\(972\) | 915.090 | 0.941451 | ||||||||
\(973\) | 5.16204 | + | 16.7680i | 0.00530529 | + | 0.0172333i | ||||
\(974\) | 12.4511 | 0.0127835 | ||||||||
\(975\) | −3011.75 | −3.08897 | ||||||||
\(976\) | 53.1956i | 0.0545037i | ||||||||
\(977\) | 1051.47i | 1.07623i | 0.842872 | + | 0.538114i | \(0.180863\pi\) | ||||
−0.842872 | + | 0.538114i | \(0.819137\pi\) | |||||||
\(978\) | 483.492 | 0.494368 | ||||||||
\(979\) | − | 2169.20i | − | 2.21573i | ||||||
\(980\) | 657.877 | + | 967.234i | 0.671303 | + | 0.986974i | ||||
\(981\) | − | 114.697i | − | 0.116919i | ||||||
\(982\) | −925.766 | −0.942735 | ||||||||
\(983\) | − | 983.670i | − | 1.00068i | −0.865829 | − | 0.500341i | \(-0.833208\pi\) | ||
0.865829 | − | 0.500341i | \(-0.166792\pi\) | |||||||
\(984\) | 287.554 | − | 1378.79i | 0.292230 | − | 1.40121i | ||||
\(985\) | 1712.58i | 1.73866i | ||||||||
\(986\) | − | 185.150i | − | 0.187779i | ||||||
\(987\) | −2368.16 | + | 729.042i | −2.39935 | + | 0.738644i | ||||
\(988\) | 10.4892 | 0.0106166 | ||||||||
\(989\) | −553.498 | −0.559654 | ||||||||
\(990\) | −1721.43 | −1.73882 | ||||||||
\(991\) | 1010.76i | 1.01994i | 0.860192 | + | 0.509970i | \(0.170343\pi\) | ||||
−0.860192 | + | 0.509970i | \(0.829657\pi\) | |||||||
\(992\) | 1670.17i | 1.68364i | ||||||||
\(993\) | 946.694i | 0.953367i | ||||||||
\(994\) | −73.3918 | − | 238.400i | −0.0738348 | − | 0.239839i | ||||
\(995\) | − | 156.034i | − | 0.156818i | ||||||
\(996\) | 1323.80i | 1.32912i | ||||||||
\(997\) | −1395.18 | −1.39938 | −0.699691 | − | 0.714445i | \(-0.746679\pi\) | ||||
−0.699691 | + | 0.714445i | \(0.746679\pi\) | |||||||
\(998\) | 386.096i | 0.386870i | ||||||||
\(999\) | 120.789 | 0.120910 |
(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 | 287.3.d.d.286.19 | yes | 32 | |
7.6 | odd | 2 | inner | 287.3.d.d.286.18 | yes | 32 | |
41.40 | even | 2 | inner | 287.3.d.d.286.17 | ✓ | 32 | |
287.286 | odd | 2 | inner | 287.3.d.d.286.20 | yes | 32 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
287.3.d.d.286.17 | ✓ | 32 | 41.40 | even | 2 | inner | |
287.3.d.d.286.18 | yes | 32 | 7.6 | odd | 2 | inner | |
287.3.d.d.286.19 | yes | 32 | 1.1 | even | 1 | trivial | |
287.3.d.d.286.20 | yes | 32 | 287.286 | odd | 2 | inner |