Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [256,4,Mod(33,256)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(256, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 7]))
N = Newforms(chi, 4, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("256.33");
S:= CuspForms(chi, 4);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 256 = 2^{8} \) |
Weight: | \( k \) | \(=\) | \( 4 \) |
Character orbit: | \([\chi]\) | \(=\) | 256.g (of order \(8\), degree \(4\), 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: | \(15.1044889615\) |
Analytic rank: | \(0\) |
Dimension: | \(44\) |
Relative dimension: | \(11\) over \(\Q(\zeta_{8})\) |
Twist minimal: | no (minimal twist has level 32) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 33.9 | ||
Character | \(\chi\) | \(=\) | 256.33 |
Dual form | 256.4.g.a.225.9 |
$q$-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 \(\left(\mathbb{Z}/256\mathbb{Z}\right)^\times\).
\(n\) | \(5\) | \(255\) |
\(\chi(n)\) | \(e\left(\frac{7}{8}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.94138 | − | 4.68690i | 0.373618 | − | 0.901994i | −0.619513 | − | 0.784986i | \(-0.712670\pi\) |
0.993131 | − | 0.117007i | \(-0.0373301\pi\) | |||||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −4.93338 | + | 2.04347i | −0.441255 | + | 0.182774i | −0.592239 | − | 0.805762i | \(-0.701756\pi\) |
0.150984 | + | 0.988536i | \(0.451756\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −14.0755 | + | 14.0755i | −0.760005 | + | 0.760005i | −0.976323 | − | 0.216318i | \(-0.930595\pi\) |
0.216318 | + | 0.976323i | \(0.430595\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 0.893826 | + | 0.893826i | 0.0331047 | + | 0.0331047i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −3.78733 | − | 9.14343i | −0.103811 | − | 0.250623i | 0.863436 | − | 0.504458i | \(-0.168308\pi\) |
−0.967247 | + | 0.253836i | \(0.918308\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 64.7407 | + | 26.8165i | 1.38122 | + | 0.572120i | 0.944807 | − | 0.327627i | \(-0.106249\pi\) |
0.436412 | + | 0.899747i | \(0.356249\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 27.0894i | 0.466297i | ||||||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 79.3923i | 1.13267i | 0.824174 | + | 0.566337i | \(0.191640\pi\) | ||||
−0.824174 | + | 0.566337i | \(0.808360\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 94.7756 | + | 39.2573i | 1.14437 | + | 0.474013i | 0.872642 | − | 0.488361i | \(-0.162405\pi\) |
0.271727 | + | 0.962374i | \(0.412405\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 38.6445 | + | 93.2961i | 0.401568 | + | 0.969471i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −71.6801 | − | 71.6801i | −0.649841 | − | 0.649841i | 0.303114 | − | 0.952954i | \(-0.401974\pi\) |
−0.952954 | + | 0.303114i | \(0.901974\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −68.2259 | + | 68.2259i | −0.545807 | + | 0.545807i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 132.471 | − | 54.8712i | 0.944222 | − | 0.391110i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 53.0409 | − | 128.052i | 0.339636 | − | 0.819955i | −0.658114 | − | 0.752918i | \(-0.728646\pi\) |
0.997751 | − | 0.0670366i | \(-0.0213544\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 267.650 | 1.55069 | 0.775346 | − | 0.631537i | \(-0.217576\pi\) | ||||
0.775346 | + | 0.631537i | \(0.217576\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −50.2070 | −0.264846 | ||||||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 40.6768 | − | 98.2026i | 0.196447 | − | 0.474265i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −205.678 | + | 85.1946i | −0.913872 | + | 0.378538i | −0.789537 | − | 0.613702i | \(-0.789679\pi\) |
−0.124334 | + | 0.992240i | \(0.539679\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 251.372 | − | 251.372i | 1.03210 | − | 1.03210i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 210.468 | + | 210.468i | 0.801697 | + | 0.801697i | 0.983361 | − | 0.181664i | \(-0.0581482\pi\) |
−0.181664 | + | 0.983361i | \(0.558148\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −56.9749 | − | 137.550i | −0.202060 | − | 0.487817i | 0.790072 | − | 0.613015i | \(-0.210043\pi\) |
−0.992132 | + | 0.125198i | \(0.960043\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −6.23610 | − | 2.58308i | −0.0206583 | − | 0.00855694i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 173.739i | 0.539201i | 0.962972 | + | 0.269600i | \(0.0868916\pi\) | ||||
−0.962972 | + | 0.269600i | \(0.913108\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | − | 53.2384i | − | 0.155214i | ||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 372.103 | + | 154.130i | 1.02166 | + | 0.423187i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 188.605 | + | 455.333i | 0.488810 | + | 1.18009i | 0.955319 | + | 0.295575i | \(0.0955113\pi\) |
−0.466510 | + | 0.884516i | \(0.654489\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 37.3687 | + | 37.3687i | 0.0916145 | + | 0.0916145i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 367.990 | − | 367.990i | 0.855113 | − | 0.855113i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −627.964 | + | 260.111i | −1.38566 | + | 0.573959i | −0.945989 | − | 0.324199i | \(-0.894905\pi\) |
−0.439671 | + | 0.898159i | \(0.644905\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −66.5782 | + | 160.734i | −0.139745 | + | 0.337375i | −0.978222 | − | 0.207563i | \(-0.933447\pi\) |
0.838476 | + | 0.544938i | \(0.183447\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −25.1621 | −0.0503194 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | −374.189 | −0.714038 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 211.710 | − | 511.113i | 0.386037 | − | 0.931975i | −0.604734 | − | 0.796428i | \(-0.706721\pi\) |
0.990771 | − | 0.135548i | \(-0.0432794\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −475.115 | + | 196.799i | −0.828945 | + | 0.343360i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 226.201 | − | 226.201i | 0.378100 | − | 0.378100i | −0.492316 | − | 0.870416i | \(-0.663850\pi\) |
0.870416 | + | 0.492316i | \(0.163850\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 802.290 | + | 802.290i | 1.28631 | + | 1.28631i | 0.937009 | + | 0.349305i | \(0.113582\pi\) |
0.349305 | + | 0.937009i | \(0.386418\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 187.316 | + | 452.220i | 0.288391 | + | 0.696238i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 182.007 | + | 75.3897i | 0.269371 | + | 0.111577i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 552.368i | 0.786662i | 0.919397 | + | 0.393331i | \(0.128677\pi\) | ||||
−0.919397 | + | 0.393331i | \(0.871323\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | − | 693.272i | − | 0.950991i | ||||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −137.983 | − | 57.1544i | −0.182477 | − | 0.0755845i | 0.289574 | − | 0.957156i | \(-0.406486\pi\) |
−0.472051 | + | 0.881571i | \(0.656486\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −162.236 | − | 391.672i | −0.207023 | − | 0.499798i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −497.195 | − | 497.195i | −0.612700 | − | 0.612700i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −579.803 | + | 579.803i | −0.690550 | + | 0.690550i | −0.962353 | − | 0.271803i | \(-0.912380\pi\) |
0.271803 | + | 0.962353i | \(0.412380\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1288.71 | + | 533.802i | −1.48455 | + | 0.614919i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 519.610 | − | 1254.45i | 0.579366 | − | 1.39871i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −547.785 | −0.591595 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −912.077 | −0.954716 | −0.477358 | − | 0.878709i | \(-0.658405\pi\) | ||||
−0.477358 | + | 0.878709i | \(0.658405\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 4.78742 | − | 11.5579i | 0.00486014 | − | 0.0117334i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 968.800 | − | 401.290i | 0.954447 | − | 0.395345i | 0.149547 | − | 0.988755i | \(-0.452219\pi\) |
0.804901 | + | 0.593410i | \(0.202219\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −351.683 | + | 351.683i | −0.336430 | + | 0.336430i | −0.855022 | − | 0.518592i | \(-0.826457\pi\) |
0.518592 | + | 0.855022i | \(0.326457\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | −381.296 | − | 381.296i | −0.354388 | − | 0.354388i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −95.4774 | − | 230.503i | −0.0862631 | − | 0.208257i | 0.874861 | − | 0.484374i | \(-0.160953\pi\) |
−0.961124 | + | 0.276116i | \(0.910953\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −858.330 | − | 355.532i | −0.754249 | − | 0.312420i | −0.0277749 | − | 0.999614i | \(-0.508842\pi\) |
−0.726474 | + | 0.687194i | \(0.758842\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 1129.39i | 0.965735i | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | − | 1154.63i | − | 0.961222i | −0.876934 | − | 0.480611i | \(-0.840415\pi\) | ||
0.876934 | − | 0.480611i | \(-0.159585\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 500.102 | + | 207.149i | 0.405519 | + | 0.167972i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 33.8977 | + | 81.8362i | 0.0267850 | + | 0.0646646i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | −1117.48 | − | 1117.48i | −0.860838 | − | 0.860838i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 871.901 | − | 871.901i | 0.655072 | − | 0.655072i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1395.04 | − | 577.844i | 1.02265 | − | 0.423597i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | 452.601 | − | 1092.67i | 0.323855 | − | 0.781854i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −953.091 | −0.665930 | −0.332965 | − | 0.942939i | \(-0.608049\pi\) | ||||
−0.332965 | + | 0.942939i | \(0.608049\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −755.290 | −0.515501 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 26.3943 | − | 63.7216i | 0.0176037 | − | 0.0424991i | −0.914833 | − | 0.403832i | \(-0.867678\pi\) |
0.932437 | + | 0.361333i | \(0.117678\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1886.58 | + | 781.446i | −1.22998 | + | 0.509473i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −541.401 | + | 541.401i | −0.345158 | + | 0.345158i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −1910.45 | − | 1910.45i | −1.19139 | − | 1.19139i | −0.976677 | − | 0.214713i | \(-0.931118\pi\) |
−0.214713 | − | 0.976677i | \(-0.568882\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −525.552 | − | 1268.79i | −0.320696 | − | 0.774228i | −0.999214 | − | 0.0396445i | \(-0.987377\pi\) |
0.678518 | − | 0.734584i | \(-0.262623\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 814.297 | + | 337.293i | 0.486356 | + | 0.201455i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | − | 693.516i | − | 0.405557i | ||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 740.118i | 0.423886i | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −249.523 | − | 103.356i | −0.140002 | − | 0.0579908i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −477.450 | − | 1152.67i | −0.262512 | − | 0.633759i | 0.736581 | − | 0.676349i | \(-0.236439\pi\) |
−0.999093 | + | 0.0425902i | \(0.986439\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1185.23 | + | 1185.23i | 0.638757 | + | 0.638757i | 0.950249 | − | 0.311492i | \(-0.100829\pi\) |
−0.311492 | + | 0.950249i | \(0.600829\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −70.9629 | + | 70.9629i | −0.0374968 | + | 0.0374968i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −1320.42 | + | 546.937i | −0.684250 | + | 0.283426i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −187.368 | + | 452.347i | −0.0952460 | + | 0.229944i | −0.964321 | − | 0.264737i | \(-0.914715\pi\) |
0.869075 | + | 0.494681i | \(0.164715\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 2500.25 | 1.24706 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 2017.87 | 0.987764 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −926.026 | + | 2235.62i | −0.444981 | + | 1.07428i | 0.529197 | + | 0.848499i | \(0.322493\pi\) |
−0.974178 | + | 0.225781i | \(0.927507\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 247.690 | − | 102.597i | 0.116865 | − | 0.0484069i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −753.289 | + | 753.289i | −0.349049 | + | 0.349049i | −0.859755 | − | 0.510706i | \(-0.829384\pi\) |
0.510706 | + | 0.859755i | \(0.329384\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1918.72 | + | 1918.72i | 0.873338 | + | 0.873338i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 49.6237 | + | 119.802i | 0.0221919 | + | 0.0535760i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 186.646 | + | 77.3114i | 0.0820257 | + | 0.0339762i | 0.423319 | − | 0.905981i | \(-0.360865\pi\) |
−0.341293 | + | 0.939957i | \(0.610865\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 1920.62i | − | 0.829632i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 3448.18i | 1.46430i | ||||||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −1509.31 | − | 625.176i | −0.630229 | − | 0.261049i | 0.0446216 | − | 0.999004i | \(-0.485792\pi\) |
−0.674850 | + | 0.737955i | \(0.735792\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 772.420 | + | 1864.79i | 0.317202 | + | 0.765793i | 0.999400 | + | 0.0346258i | \(0.0110239\pi\) |
−0.682199 | + | 0.731167i | \(0.738976\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 624.090 | + | 624.090i | 0.252099 | + | 0.252099i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 840.595 | − | 840.595i | 0.334064 | − | 0.334064i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 725.918 | − | 300.685i | 0.283874 | − | 0.117584i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | −1092.25 | + | 2636.93i | −0.420368 | + | 1.01486i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −1509.32 | −0.571784 | −0.285892 | − | 0.958262i | \(-0.592290\pi\) | ||||
−0.285892 | + | 0.958262i | \(0.592290\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3625.68 | 1.35224 | 0.676120 | − | 0.736791i | \(-0.263660\pi\) | ||||
0.676120 | + | 0.736791i | \(0.263660\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −726.442 | + | 1753.79i | −0.266778 | + | 0.644058i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 1764.33 | − | 730.811i | 0.638090 | − | 0.264305i | −0.0400962 | − | 0.999196i | \(-0.512766\pi\) |
0.678186 | + | 0.734890i | \(0.262766\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2008.70 | − | 2008.70i | 0.715544 | − | 0.715544i | −0.252146 | − | 0.967689i | \(-0.581136\pi\) |
0.967689 | + | 0.252146i | \(0.0811362\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −1984.52 | − | 1984.52i | −0.696406 | − | 0.696406i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 1055.82 | + | 2548.97i | 0.365044 | + | 0.881295i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1468.40 | − | 608.233i | −0.500282 | − | 0.207224i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | − | 128.139i | − | 0.0430255i | ||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 1015.25i | − | 0.336013i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1133.08 | − | 469.337i | −0.369689 | − | 0.153130i | 0.190101 | − | 0.981764i | \(-0.439118\pi\) |
−0.559790 | + | 0.828634i | \(0.689118\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −621.039 | − | 1499.32i | −0.199779 | − | 0.482309i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | 562.158 | + | 562.158i | 0.178320 | + | 0.178320i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −3767.31 | + | 3767.31i | −1.17853 | + | 1.17853i | ||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 5317.80 | − | 2202.70i | 1.64084 | − | 0.679657i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −2129.02 | + | 5139.91i | −0.648025 | + | 1.56447i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 3100.74 | 0.931125 | 0.465562 | − | 0.885015i | \(-0.345852\pi\) | ||||
0.465562 | + | 0.885015i | \(0.345852\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −121.964 | −0.0361375 | ||||||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 1661.15 | − | 4010.36i | 0.485701 | − | 1.17259i | −0.471162 | − | 0.882047i | \(-0.656165\pi\) |
0.956863 | − | 0.290539i | \(-0.0938347\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 2972.95 | − | 1231.44i | 0.857895 | − | 0.355352i | 0.0900110 | − | 0.995941i | \(-0.471310\pi\) |
0.767884 | + | 0.640589i | \(0.221310\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 706.687 | − | 706.687i | 0.201284 | − | 0.201284i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 1590.35 | + | 1590.35i | 0.447155 | + | 0.447155i | 0.894408 | − | 0.447253i | \(-0.147597\pi\) |
−0.447253 | + | 0.894408i | \(0.647597\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −355.031 | − | 857.121i | −0.0985518 | − | 0.237925i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 2588.89 | + | 1072.35i | 0.709564 | + | 0.293911i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | − | 6173.19i | − | 1.67076i | −0.549676 | − | 0.835378i | \(-0.685249\pi\) | ||
0.549676 | − | 0.835378i | \(-0.314751\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | − | 1436.00i | − | 0.383822i | −0.981412 | − | 0.191911i | \(-0.938531\pi\) | ||
0.981412 | − | 0.191911i | \(-0.0614685\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 327.413 | + | 135.619i | 0.0864344 | + | 0.0358023i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 108.791 | + | 262.646i | 0.0283691 | + | 0.0684890i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 5083.09 | + | 5083.09i | 1.30943 | + | 1.30943i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −535.754 | + | 535.754i | −0.136354 | + | 0.136354i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4781.23 | − | 1980.45i | 1.20235 | − | 0.498028i | 0.310589 | − | 0.950544i | \(-0.399474\pi\) |
0.891756 | + | 0.452516i | \(0.149474\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −383.926 | + | 926.879i | −0.0954040 | + | 0.230326i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −2150.69 | −0.528162 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −246.466 | −0.0598215 | −0.0299107 | − | 0.999553i | \(-0.509522\pi\) | ||||
−0.0299107 | + | 0.999553i | \(0.509522\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 1695.86 | − | 4094.17i | 0.406856 | − | 0.982237i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 161.866 | − | 67.0470i | 0.0383879 | − | 0.0159008i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −3454.60 | + | 3454.60i | −0.809960 | + | 0.809960i | −0.984628 | − | 0.174667i | \(-0.944115\pi\) |
0.174667 | + | 0.984628i | \(0.444115\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1860.92 | − | 1860.92i | −0.431380 | − | 0.431380i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 1591.86 | + | 3843.09i | 0.364870 | + | 0.880874i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −2611.67 | − | 1081.79i | −0.591958 | − | 0.245197i | 0.0665350 | − | 0.997784i | \(-0.478806\pi\) |
−0.658493 | + | 0.752587i | \(0.728806\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 3464.52i | 0.776585i | 0.921536 | + | 0.388292i | \(0.126935\pi\) | ||||
−0.921536 | + | 0.388292i | \(0.873065\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 7076.37i | 1.56880i | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 882.213 | + | 365.425i | 0.193453 | + | 0.0801307i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −1186.33 | − | 2864.06i | −0.257328 | − | 0.621245i | 0.741432 | − | 0.671028i | \(-0.234147\pi\) |
−0.998760 | + | 0.0497833i | \(0.984147\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 239.233 | + | 239.233i | 0.0513352 | + | 0.0513352i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3210.39 | − | 3210.39i | 0.681552 | − | 0.681552i | −0.278798 | − | 0.960350i | \(-0.589936\pi\) |
0.960350 | + | 0.278798i | \(0.0899360\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2512.41 | + | 1040.67i | −0.527729 | + | 0.218593i | −0.630608 | − | 0.776101i | \(-0.717194\pi\) |
0.102879 | + | 0.994694i | \(0.467194\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −1063.46 | + | 2567.41i | −0.221031 | + | 0.533615i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −5924.88 | −1.21859 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −1390.14 | −0.282950 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −1770.68 | + | 4274.81i | −0.356699 | + | 0.861147i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 7264.11 | − | 3008.89i | 1.44838 | − | 0.599937i | 0.486563 | − | 0.873646i | \(-0.338251\pi\) |
0.961812 | + | 0.273709i | \(0.0882506\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 2566.46 | − | 2566.46i | 0.506525 | − | 0.506525i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −1003.42 | − | 1003.42i | −0.196042 | − | 0.196042i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −2718.41 | − | 6562.83i | −0.525786 | − | 1.26936i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 2738.03 | + | 1134.13i | 0.524310 | + | 0.217176i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | − | 5319.72i | − | 1.00861i | ||||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 929.012i | − | 0.174410i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 1055.79 | + | 437.322i | 0.196277 | + | 0.0813006i | 0.478657 | − | 0.878002i | \(-0.341124\pi\) |
−0.282380 | + | 0.959303i | \(0.591124\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 965.552 | + | 2331.05i | 0.177762 | + | 0.429155i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −2154.35 | − | 2154.35i | −0.392804 | − | 0.392804i | 0.482882 | − | 0.875686i | \(-0.339590\pi\) |
−0.875686 | + | 0.482882i | \(0.839590\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3659.65 | + | 3659.65i | −0.660881 | + | 0.660881i | −0.955588 | − | 0.294706i | \(-0.904778\pi\) |
0.294706 | + | 0.955588i | \(0.404778\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 124.134 | − | 51.4180i | 0.0222037 | − | 0.00919707i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 3106.88 | − | 7500.68i | 0.550473 | − | 1.32896i | −0.366652 | − | 0.930358i | \(-0.619496\pi\) |
0.917125 | − | 0.398601i | \(-0.130504\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −1371.72 | −0.240757 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −1265.70 | −0.220076 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −3116.73 | + | 7524.45i | −0.536902 | + | 1.29620i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6246.57 | + | 2587.41i | −1.06615 | + | 0.441612i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −3332.68 | + | 3332.68i | −0.563602 | + | 0.563602i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | −2445.46 | − | 2445.46i | −0.409795 | − | 0.409795i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 2372.98 | + | 5728.87i | 0.394050 | + | 0.951321i | 0.989048 | + | 0.147594i | \(0.0471528\pi\) |
−0.594998 | + | 0.803727i | \(0.702847\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −259.990 | − | 107.691i | −0.0427848 | − | 0.0177220i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 2954.14i | 0.481796i | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | − | 5514.75i | − | 0.891418i | −0.895178 | − | 0.445709i | \(-0.852952\pi\) | ||
0.895178 | − | 0.445709i | \(-0.147048\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −5411.61 | − | 2241.56i | −0.867016 | − | 0.359130i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −1013.68 | − | 2447.24i | −0.160979 | − | 0.388638i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −4078.53 | − | 4078.53i | −0.642041 | − | 0.642041i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 1941.77 | − | 1941.77i | 0.303019 | − | 0.303019i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −9323.05 | + | 3861.74i | −1.44233 | + | 0.597432i | −0.960361 | − | 0.278758i | \(-0.910077\pi\) |
−0.481966 | + | 0.876190i | \(0.660077\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 1844.20 | − | 4452.29i | 0.282859 | − | 0.682882i | −0.717041 | − | 0.697031i | \(-0.754504\pi\) |
0.999900 | + | 0.0141493i | \(0.00450400\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 10047.7 | 1.52794 | ||||||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 7343.73 | 1.10727 | 0.553636 | − | 0.832759i | \(-0.313240\pi\) | ||||
0.553636 | + | 0.832759i | \(0.313240\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −653.700 | + | 1578.17i | −0.0977317 | + | 0.235945i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −7406.99 | + | 3068.08i | −1.09809 | + | 0.454846i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −4187.33 | + | 4187.33i | −0.615596 | + | 0.615596i | −0.944399 | − | 0.328802i | \(-0.893355\pi\) |
0.328802 | + | 0.944399i | \(0.393355\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2591.22 | + | 2591.22i | 0.377784 | + | 0.377784i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −2393.82 | − | 5779.20i | −0.346124 | − | 0.835617i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | −5597.46 | − | 2318.54i | −0.802697 | − | 0.332488i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 9231.47i | 1.31302i | 0.754317 | + | 0.656510i | \(0.227968\pi\) | ||||
−0.754317 | + | 0.656510i | \(0.772032\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 376.244i | 0.0530798i | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −9063.75 | − | 3754.33i | −1.26837 | − | 0.525377i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 117.113 | + | 282.737i | 0.0162571 | + | 0.0392481i | 0.931800 | − | 0.362973i | \(-0.118238\pi\) |
−0.915543 | + | 0.402221i | \(0.868238\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −4242.58 | − | 4242.58i | −0.584230 | − | 0.584230i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 6867.82 | − | 6867.82i | 0.938224 | − | 0.938224i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 3068.05 | − | 1270.83i | 0.415819 | − | 0.172238i | −0.164958 | − | 0.986301i | \(-0.552749\pi\) |
0.580777 | + | 0.814063i | \(0.302749\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −1850.31 | + | 4467.04i | −0.248804 | + | 0.600665i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −1379.97 | −0.184107 | −0.0920537 | − | 0.995754i | \(-0.529343\pi\) | ||||
−0.0920537 | + | 0.995754i | \(0.529343\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −1051.97 | −0.139255 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 72.0198 | − | 173.871i | 0.00945987 | − | 0.0228381i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1279.89 | + | 530.148i | −0.166820 | + | 0.0690992i | −0.464531 | − | 0.885557i | \(-0.653777\pi\) |
0.297711 | + | 0.954656i | \(0.403777\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 5690.85 | − | 5690.85i | 0.736058 | − | 0.736058i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −247.415 | − | 247.415i | −0.0317568 | − | 0.0317568i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −1128.75 | − | 2725.04i | −0.143781 | − | 0.347118i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 706.615 | + | 292.690i | 0.0893300 | + | 0.0370017i | 0.426901 | − | 0.904298i | \(-0.359605\pi\) |
−0.337571 | + | 0.941300i | \(0.609605\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 10359.3i | 1.29978i | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | − | 9680.79i | − | 1.20557i | −0.797902 | − | 0.602787i | \(-0.794057\pi\) | ||
0.797902 | − | 0.602787i | \(-0.205943\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 17327.9 | + | 7177.45i | 2.14184 | + | 0.887181i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | 1416.68 | + | 3420.18i | 0.173816 | + | 0.419630i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 1557.94 | + | 1557.94i | 0.189740 | + | 0.189740i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −1231.14 | + | 1231.14i | −0.148841 | + | 0.148841i | −0.777600 | − | 0.628759i | \(-0.783563\pi\) |
0.628759 | + | 0.777600i | \(0.283563\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −12663.0 | + | 5245.17i | −1.51975 | + | 0.629502i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 5177.71 | − | 12500.1i | 0.616896 | − | 1.48932i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 797.516 | 0.0943338 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −6967.00 | −0.818167 | ||||||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 3904.87 | − | 9427.19i | 0.455287 | − | 1.09916i | −0.514997 | − | 0.857192i | \(-0.672207\pi\) |
0.970284 | − | 0.241968i | \(-0.0777930\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10566.0 | + | 4376.59i | −1.22318 | + | 0.506656i | −0.898418 | − | 0.439141i | \(-0.855283\pi\) |
−0.324758 | + | 0.945797i | \(0.605283\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −155.292 | + | 155.292i | −0.0178501 | + | 0.0178501i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −5416.61 | − | 5416.61i | −0.618222 | − | 0.618222i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | −1325.29 | − | 3199.53i | −0.150199 | − | 0.362614i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −3250.44 | − | 1346.37i | −0.365810 | − | 0.151523i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | − | 16965.2i | − | 1.89602i | −0.318242 | − | 0.948010i | \(-0.603092\pi\) | ||
0.318242 | − | 0.948010i | \(-0.396908\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 5628.82i | − | 0.624720i | −0.949964 | − | 0.312360i | \(-0.898880\pi\) | ||
0.949964 | − | 0.312360i | \(-0.101120\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 3468.86 | + | 1436.85i | 0.382342 | + | 0.158371i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −3979.55 | − | 9607.49i | −0.435625 | − | 1.05169i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −6003.38 | − | 6003.38i | −0.652678 | − | 0.652678i | 0.300959 | − | 0.953637i | \(-0.402693\pi\) |
−0.953637 | + | 0.300959i | \(0.902693\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 47.5859 | − | 47.5859i | 0.00513831 | − | 0.00513831i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 1448.22 | − | 599.872i | 0.155321 | − | 0.0643359i | −0.303669 | − | 0.952778i | \(-0.598212\pi\) |
0.458989 | + | 0.888442i | \(0.348212\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1675.58 | − | 4045.20i | 0.178494 | − | 0.430923i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −6329.34 | −0.669726 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −12533.6 | −1.31737 | −0.658683 | − | 0.752421i | \(-0.728886\pi\) | ||||
−0.658683 | + | 0.752421i | \(0.728886\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 1127.29 | − | 2721.51i | 0.117698 | − | 0.284149i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 7856.00 | − | 3254.06i | 0.814806 | − | 0.337504i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 5266.90 | − | 5266.90i | 0.542672 | − | 0.542672i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 11661.6 | + | 11661.6i | 1.19367 | + | 1.19367i | 0.976029 | + | 0.217641i | \(0.0698361\pi\) |
0.217641 | + | 0.976029i | \(0.430164\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 4356.35 | + | 10517.2i | 0.443000 | + | 1.06950i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 8424.31 | + | 3489.46i | 0.851104 | + | 0.352539i | 0.765222 | − | 0.643766i | \(-0.222629\pi\) |
0.0858823 | + | 0.996305i | \(0.472629\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 11549.8i | 1.15932i | 0.814860 | + | 0.579658i | \(0.196814\pi\) | ||||
−0.814860 | + | 0.579658i | \(0.803186\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 7250.49i | 0.723083i | ||||||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −6314.42 | − | 2615.52i | −0.625689 | − | 0.259169i | 0.0472314 | − | 0.998884i | \(-0.484960\pi\) |
−0.672920 | + | 0.739715i | \(0.734960\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4214.24 | + | 10174.1i | 0.414916 | + | 1.00170i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 1756.35 | + | 1756.35i | 0.171823 | + | 0.171823i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −1041.89 | + | 1041.89i | −0.101282 | + | 0.101282i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −9144.51 | + | 3787.78i | −0.883324 | + | 0.365885i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −238.409 | + | 575.569i | −0.0228847 | + | 0.0552484i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 10874.6 | 1.03731 | 0.518655 | − | 0.854983i | \(-0.326433\pi\) | ||||
0.518655 | + | 0.854983i | \(0.326433\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −15600.4 | −1.47883 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 3917.43 | − | 9457.52i | 0.369046 | − | 0.890957i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 4499.62 | − | 1863.81i | 0.421273 | − | 0.174497i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −538.006 | + | 538.006i | −0.0500603 | + | 0.0500603i | −0.731694 | − | 0.681633i | \(-0.761270\pi\) |
0.681633 | + | 0.731694i | \(0.261270\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 8680.37 | + | 8680.37i | 0.802741 | + | 0.802741i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1701.48 | + | 4107.75i | 0.156389 | + | 0.377556i | 0.982582 | − | 0.185831i | \(-0.0594978\pi\) |
−0.826193 | + | 0.563387i | \(0.809498\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 10166.4 | + | 4211.04i | 0.928742 | + | 0.384697i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 66.8023i | 0.00606574i | ||||||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 6367.77i | 0.574716i | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 19571.5 | + | 8106.78i | 1.75579 | + | 0.727273i | 0.997123 | + | 0.0757967i | \(0.0241500\pi\) |
0.758669 | + | 0.651476i | \(0.225850\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 2068.17 | + | 4993.00i | 0.184429 | + | 0.445251i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 373.535 | + | 373.535i | 0.0331115 | + | 0.0331115i | 0.723469 | − | 0.690357i | \(-0.242547\pi\) |
−0.690357 | + | 0.723469i | \(0.742547\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3959.43 | + | 3959.43i | −0.348896 | + | 0.348896i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 12717.8 | − | 5267.90i | 1.11404 | − | 0.461451i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −874.883 | + | 2112.15i | −0.0761857 | + | 0.183928i | −0.957384 | − | 0.288819i | \(-0.906738\pi\) |
0.881198 | + | 0.472747i | \(0.156738\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −22585.2 | −1.95521 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 14709.1 | 1.26593 | ||||||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 1016.33 | − | 2453.64i | 0.0869609 | − | 0.209942i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 1588.57 | − | 658.008i | 0.135136 | − | 0.0559751i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 724.701 | − | 724.701i | 0.0612926 | − | 0.0612926i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 15352.0 | + | 15352.0i | 1.29095 | + | 1.29095i | 0.934203 | + | 0.356743i | \(0.116113\pi\) |
0.356743 | + | 0.934203i | \(0.383887\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −2376.45 | − | 5737.26i | −0.198690 | − | 0.479680i | 0.792860 | − | 0.609404i | \(-0.208591\pi\) |
−0.991550 | + | 0.129723i | \(0.958591\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −9001.77 | − | 3728.65i | −0.748323 | − | 0.309965i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 21249.4i | 1.75643i | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | − | 1890.92i | − | 0.155414i | ||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −793.785 | − | 328.796i | −0.0648726 | − | 0.0268711i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 7981.84 | + | 19269.9i | 0.648653 | + | 1.56599i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 942.053 | + | 942.053i | 0.0761280 | + | 0.0761280i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −5860.27 | + | 5860.27i | −0.470930 | + | 0.470930i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −486.782 | + | 201.632i | −0.0389002 | + | 0.0161130i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −2381.59 | + | 5749.66i | −0.189265 | + | 0.456926i | −0.989819 | − | 0.142335i | \(-0.954539\pi\) |
0.800553 | + | 0.599261i | \(0.204539\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | 10239.6 | 0.809252 | ||||||||
\(544\) | 0 | 0 | ||||||||
\(545\) | 4960.99 | 0.389918 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −2560.31 | + | 6181.14i | −0.200130 | + | 0.483156i | −0.991801 | − | 0.127791i | \(-0.959211\pi\) |
0.791671 | + | 0.610947i | \(0.209211\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −203.178 | + | 84.1589i | −0.0157949 | + | 0.00654247i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 10054.0 | − | 10054.0i | 0.777338 | − | 0.777338i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −7774.85 | − | 7774.85i | −0.597866 | − | 0.597866i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −2307.87 | − | 5571.69i | −0.176511 | − | 0.426135i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −10306.9 | − | 4269.27i | −0.784055 | − | 0.324766i | −0.0455041 | − | 0.998964i | \(-0.514489\pi\) |
−0.738551 | + | 0.674198i | \(0.764489\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 10432.9i | − | 0.789384i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | − | 3986.05i | − | 0.299984i | ||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −8478.56 | − | 3511.93i | −0.634687 | − | 0.262896i | 0.0420563 | − | 0.999115i | \(-0.486609\pi\) |
−0.676743 | + | 0.736219i | \(0.736609\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 2359.45 | + | 5696.21i | 0.175686 | + | 0.424144i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 9758.15 | + | 9758.15i | 0.722758 | + | 0.722758i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 304.321 | − | 304.321i | 0.0224214 | − | 0.0224214i | −0.695807 | − | 0.718229i | \(-0.744953\pi\) |
0.718229 | + | 0.695807i | \(0.244953\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 7459.96 | − | 3090.02i | 0.546742 | − | 0.226468i | −0.0921763 | − | 0.995743i | \(-0.529382\pi\) |
0.638918 | + | 0.769275i | \(0.279382\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −2930.16 | + | 7074.04i | −0.213629 | + | 0.515746i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9780.88 | 0.709376 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −11616.3 | −0.838118 | −0.419059 | − | 0.907959i | \(-0.637640\pi\) | ||||
−0.419059 | + | 0.907959i | \(0.637640\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7038.82 | − | 16993.2i | 0.505221 | − | 1.21971i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 2746.65 | − | 1137.70i | 0.196128 | − | 0.0812389i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 3449.00 | − | 3449.00i | 0.245014 | − | 0.245014i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −334.460 | − | 334.460i | −0.0236380 | − | 0.0236380i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 6654.96 | + | 16066.5i | 0.467938 | + | 1.12970i | 0.965062 | + | 0.262023i | \(0.0843897\pi\) |
−0.497123 | + | 0.867680i | \(0.665610\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 25366.7 | + | 10507.2i | 1.77456 | + | 0.735048i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | − | 9688.04i | − | 0.674302i | ||||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 9365.10i | 0.648530i | 0.945966 | + | 0.324265i | \(0.105117\pi\) | ||||
−0.945966 | + | 0.324265i | \(0.894883\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 7796.53 | + | 3229.43i | 0.537187 | + | 0.222510i | ||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −5514.93 | − | 13314.2i | −0.378076 | − | 0.912756i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −12280.1 | − | 12280.1i | −0.837647 | − | 0.837647i | 0.150902 | − | 0.988549i | \(-0.451782\pi\) |
−0.988549 | + | 0.150902i | \(0.951782\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 11681.6 | − | 11681.6i | 0.792852 | − | 0.792852i | −0.189105 | − | 0.981957i | \(-0.560559\pi\) |
0.981957 | + | 0.189105i | \(0.0605587\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 646.078 | − | 267.614i | 0.0436324 | − | 0.0180731i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | −2519.71 | + | 6083.12i | −0.169324 | + | 0.408784i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 20354.6 | 1.36107 | 0.680535 | − | 0.732716i | \(-0.261747\pi\) | ||||
0.680535 | + | 0.732716i | \(0.261747\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 13996.5 | 0.931309 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −4659.07 | + | 11248.0i | −0.308487 | + | 0.744754i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −23946.8 | + | 9919.08i | −1.57782 | + | 0.653553i | −0.988066 | − | 0.154032i | \(-0.950774\pi\) |
−0.589751 | + | 0.807585i | \(0.700774\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −5701.45 | + | 5701.45i | −0.373829 | + | 0.373829i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −17139.4 | − | 17139.4i | −1.11833 | − | 1.11833i | −0.991987 | − | 0.126340i | \(-0.959677\pi\) |
−0.126340 | − | 0.991987i | \(-0.540323\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −9612.31 | − | 23206.2i | −0.624154 | − | 1.50684i | −0.846783 | − | 0.531938i | \(-0.821464\pi\) |
0.222629 | − | 0.974903i | \(-0.428536\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −13428.7 | − | 5562.35i | −0.867753 | − | 0.359435i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | − | 16322.0i | − | 1.04964i | ||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | − | 5745.29i | − | 0.367699i | ||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −4758.39 | − | 1970.99i | −0.303081 | − | 0.125540i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −6763.80 | − | 16329.2i | −0.428760 | − | 1.03512i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −2243.98 | − | 2243.98i | −0.141571 | − | 0.141571i | 0.632769 | − | 0.774340i | \(-0.281918\pi\) |
−0.774340 | + | 0.632769i | \(0.781918\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −4399.46 | + | 4399.46i | −0.276245 | + | 0.276245i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 4701.96 | − | 1947.62i | 0.293845 | − | 0.121715i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 1427.67 | − | 3446.70i | 0.0888010 | − | 0.214385i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | 404.369 | 0.0250338 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 19815.9 | 1.22103 | 0.610515 | − | 0.792005i | \(-0.290963\pi\) | ||||
0.610515 | + | 0.792005i | \(0.290963\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −5189.74 | + | 12529.1i | −0.318295 | + | 0.768431i | 0.681050 | + | 0.732237i | \(0.261524\pi\) |
−0.999345 | + | 0.0361945i | \(0.988476\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 3726.13 | − | 1543.42i | 0.227467 | − | 0.0942200i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −18031.1 | + | 18031.1i | −1.09563 | + | 1.09563i | −0.100717 | + | 0.994915i | \(0.532114\pi\) |
−0.994915 | + | 0.100717i | \(0.967886\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 4756.62 | + | 4756.62i | 0.287694 | + | 0.287694i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10343.2 | + | 24970.8i | 0.622708 | + | 1.50335i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −4031.36 | − | 1669.85i | −0.241592 | − | 0.100071i | 0.258602 | − | 0.965984i | \(-0.416738\pi\) |
−0.500194 | + | 0.865913i | \(0.666738\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 368.299i | 0.0219704i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 1434.22i | 0.0851660i | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −16047.0 | − | 6646.88i | −0.948561 | − | 0.392907i | −0.145871 | − | 0.989304i | \(-0.546599\pi\) |
−0.802690 | + | 0.596397i | \(0.796599\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −6313.25 | − | 15241.5i | −0.371493 | − | 0.896864i | −0.993498 | − | 0.113850i | \(-0.963682\pi\) |
0.622005 | − | 0.783014i | \(-0.286318\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 19957.0 | + | 19957.0i | 1.16903 | + | 1.16903i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 7710.34 | − | 7710.34i | 0.449615 | − | 0.449615i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −12980.8 | + | 5376.81i | −0.753550 | + | 0.312131i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 6019.70 | − | 14532.8i | 0.347885 | − | 0.839869i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 1721.81 | 0.0990609 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9059.04 | 0.518871 | 0.259436 | − | 0.965760i | \(-0.416463\pi\) | ||||
0.259436 | + | 0.965760i | \(0.416463\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −5294.30 | + | 12781.6i | −0.301893 | + | 0.728834i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −1398.12 | + | 579.121i | −0.0793710 | + | 0.0328765i | −0.422016 | − | 0.906589i | \(-0.638677\pi\) |
0.342645 | + | 0.939465i | \(0.388677\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 12837.9 | − | 12837.9i | 0.725588 | − | 0.725588i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −15571.2 | − | 15571.2i | −0.876199 | − | 0.876199i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −11645.5 | − | 28114.8i | −0.652422 | − | 1.57509i | −0.809252 | − | 0.587462i | \(-0.800127\pi\) |
0.156830 | − | 0.987626i | \(-0.449873\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 13328.9 | + | 5521.01i | 0.743462 | + | 0.307952i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | − | 16324.6i | − | 0.906582i | ||||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 34536.3i | 1.90962i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −4362.78 | − | 1807.12i | −0.240185 | − | 0.0994879i | 0.259344 | − | 0.965785i | \(-0.416494\pi\) |
−0.499529 | + | 0.866297i | \(0.666494\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 95.2972 | + | 230.068i | 0.00522372 | + | 0.0126112i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 5185.49 | + | 5185.49i | 0.283017 | + | 0.283017i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −16709.5 | + | 16709.5i | −0.908061 | + | 0.908061i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 10541.3 | − | 4366.33i | 0.570396 | − | 0.236266i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −6417.56 | + | 15493.3i | −0.345774 | + | 0.834773i | 0.651335 | + | 0.758790i | \(0.274209\pi\) |
−0.997109 | + | 0.0759825i | \(0.975791\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −22837.8 | −1.22524 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −4706.48 | −0.251428 | ||||||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −7987.97 | + | 19284.7i | −0.424920 | + | 1.02585i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 17513.4 | − | 7254.29i | 0.927686 | − | 0.384260i | 0.132886 | − | 0.991131i | \(-0.457576\pi\) |
0.794800 | + | 0.606871i | \(0.207576\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −493.721 | + | 493.721i | −0.0260422 | + | 0.0260422i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −19185.2 | − | 19185.2i | −1.00770 | − | 1.00770i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1417.18 | + | 3421.38i | 0.0741252 | + | 0.178954i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −28933.1 | − | 11984.5i | −1.50701 | − | 0.624224i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 4682.98i | 0.242901i | 0.992598 | + | 0.121450i | \(0.0387545\pi\) | ||||
−0.992598 | + | 0.121450i | \(0.961245\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | − | 9900.21i | − | 0.511377i | ||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −6730.40 | − | 2787.82i | −0.346205 | − | 0.143403i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 5117.71 | + | 12355.2i | 0.262161 | + | 0.632913i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −20269.6 | − | 20269.6i | −1.03405 | − | 1.03405i | −0.999399 | − | 0.0346553i | \(-0.988967\pi\) |
−0.0346553 | − | 0.999399i | \(-0.511033\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 14507.1 | − | 14507.1i | 0.737039 | − | 0.737039i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 10920.4 | − | 4523.37i | 0.552537 | − | 0.228868i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1705.29 | + | 4116.94i | −0.0859297 | + | 0.207453i | −0.961003 | − | 0.276538i | \(-0.910813\pi\) |
0.875073 | + | 0.483990i | \(0.160813\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 1442.20 | 0.0723758 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −5475.14 | −0.273649 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −467.052 | + | 1127.56i | −0.0232487 | + | 0.0561273i | −0.935078 | − | 0.354443i | \(-0.884670\pi\) |
0.911829 | + | 0.410570i | \(0.134670\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 33692.1 | − | 13955.7i | 1.67033 | − | 0.691872i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −27671.7 | + | 27671.7i | −1.36632 | + | 1.36632i | −0.500701 | + | 0.865620i | \(0.666924\pi\) |
−0.865620 | + | 0.500701i | \(0.833076\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4710.89 | + | 4710.89i | 0.231669 | + | 0.231669i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −72.2467 | − | 174.419i | −0.00353865 | − | 0.00854305i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 4588.33 | + | 1900.55i | 0.223837 | + | 0.0927163i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 22288.5i | 1.08298i | 0.840707 | + | 0.541490i | \(0.182140\pi\) | ||||
−0.840707 | + | 0.541490i | \(0.817860\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | − | 26253.9i | − | 1.27058i | ||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −8269.15 | − | 3425.19i | −0.398603 | − | 0.165107i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −10902.9 | − | 26321.9i | −0.523478 | − | 1.26379i | −0.935730 | − | 0.352718i | \(-0.885258\pi\) |
0.412252 | − | 0.911070i | \(-0.364742\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 3598.84 | + | 3598.84i | 0.172108 | + | 0.172108i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −6249.83 | + | 6249.83i | −0.297709 | + | 0.297709i | −0.840116 | − | 0.542407i | \(-0.817513\pi\) |
0.542407 | + | 0.840116i | \(0.317513\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 17085.7 | − | 7077.13i | 0.810673 | − | 0.335792i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 205.076 | − | 495.098i | 0.00969222 | − | 0.0233991i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −47630.1 | −2.24227 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 5109.01 | 0.239578 | 0.119789 | − | 0.992799i | \(-0.461778\pi\) | ||||
0.119789 | + | 0.992799i | \(0.461778\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −478.483 | + | 1155.16i | −0.0223504 | + | 0.0539586i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −119.699 | + | 49.5811i | −0.00556958 | + | 0.00230699i | −0.385466 | − | 0.922722i | \(-0.625959\pi\) |
0.379897 | + | 0.925029i | \(0.375959\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −18260.7 | + | 18260.7i | −0.846379 | + | 0.846379i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −15896.7 | − | 15896.7i | −0.733963 | − | 0.733963i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 11684.8 | + | 28209.6i | 0.537422 | + | 1.29745i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −2924.95 | − | 1211.55i | −0.134011 | − | 0.0555094i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | − | 19873.6i | − | 0.907055i | ||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | − | 2614.48i | − | 0.118872i | ||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −24341.3 | − | 10082.5i | −1.10251 | − | 0.456674i | −0.244157 | − | 0.969736i | \(-0.578511\pi\) |
−0.858352 | + | 0.513062i | \(0.828511\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 9484.67 | + | 22898.0i | 0.427963 | + | 1.03319i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 16251.9 | + | 16251.9i | 0.730533 | + | 0.730533i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −8620.64 | + | 8620.64i | −0.386038 | + | 0.386038i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −12334.7 | + | 5109.20i | −0.550273 | + | 0.227930i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −9871.79 | + | 23832.6i | −0.438741 | + | 1.05921i | 0.537643 | + | 0.843173i | \(0.319315\pi\) |
−0.976384 | + | 0.216042i | \(0.930685\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −13793.5 | −0.610739 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −1036.49 | −0.0457209 | ||||||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 4297.14 | − | 10374.2i | 0.188845 | − | 0.455913i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −9954.90 | + | 4123.45i | −0.435856 | + | 0.180537i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −10140.5 | + | 10140.5i | −0.442332 | + | 0.442332i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 12475.0 | + | 12475.0i | 0.542147 | + | 0.542147i | 0.924158 | − | 0.382011i | \(-0.124768\pi\) |
−0.382011 | + | 0.924158i | \(0.624768\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −711.024 | − | 1716.56i | −0.0307860 | − | 0.0743239i | 0.907739 | − | 0.419536i | \(-0.137807\pi\) |
−0.938525 | + | 0.345212i | \(0.887807\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 16237.8 | + | 6725.93i | 0.700475 | + | 0.290146i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | − | 12921.5i | − | 0.555362i | ||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | − | 15273.0i | − | 0.654021i | ||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | −1629.01 | − | 674.758i | −0.0695021 | − | 0.0287887i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7001.23 | − | 16902.5i | −0.297618 | − | 0.718514i | −0.999978 | − | 0.00669143i | \(-0.997870\pi\) |
0.702359 | − | 0.711823i | \(-0.252130\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 6527.87 | + | 6527.87i | 0.276485 | + | 0.276485i | 0.831704 | − | 0.555219i | \(-0.187366\pi\) |
−0.555219 | + | 0.831704i | \(0.687366\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3425.41 | − | 3425.41i | 0.144555 | − | 0.144555i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 22099.6 | − | 9153.94i | 0.929235 | − | 0.384902i | 0.133847 | − | 0.991002i | \(-0.457267\pi\) |
0.795388 | + | 0.606100i | \(0.207267\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 13794.8 | − | 33303.5i | 0.577939 | − | 1.39527i | −0.316720 | − | 0.948519i | \(-0.602582\pi\) |
0.894659 | − | 0.446749i | \(-0.147418\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −15726.7 | −0.656501 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 4226.72 | 0.175807 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2176.93 | − | 5255.59i | 0.0902227 | − | 0.217817i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 35455.9 | − | 14686.3i | 1.46420 | − | 0.606491i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 22145.1 | − | 22145.1i | 0.911243 | − | 0.911243i | −0.0851272 | − | 0.996370i | \(-0.527130\pi\) |
0.996370 | + | 0.0851272i | \(0.0271297\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 3661.61 | + | 3661.61i | 0.150134 | + | 0.150134i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −8814.20 | − | 21279.4i | −0.360115 | − | 0.869395i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −13386.7 | − | 5544.93i | −0.544988 | − | 0.225741i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 24544.8i | 0.995715i | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 13795.7i | 0.557678i | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 20849.8 | + | 8636.26i | 0.839861 | + | 0.347882i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −9655.46 | − | 23310.3i | −0.387569 | − | 0.935675i | −0.990454 | − | 0.137847i | \(-0.955982\pi\) |
0.602884 | − | 0.797829i | \(-0.294018\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −489.625 | − | 489.625i | −0.0195846 | − | 0.0195846i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −7592.18 | + | 7592.18i | −0.302619 | + | 0.302619i | −0.842038 | − | 0.539419i | \(-0.818644\pi\) |
0.539419 | + | 0.842038i | \(0.318644\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −39825.7 | + | 16496.4i | −1.58188 | + | 0.655237i | −0.988710 | − | 0.149839i | \(-0.952124\pi\) |
−0.593171 | + | 0.805076i | \(0.702124\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −11502.4 | + | 27769.3i | −0.455286 | + | 1.09916i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 48726.7 | 1.92199 | 0.960995 | − | 0.276565i | \(-0.0891962\pi\) | ||||
0.960995 | + | 0.276565i | \(0.0891962\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −1078.78 | −0.0424042 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −2698.78 | + | 6515.42i | −0.105715 | + | 0.255219i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 5050.54 | − | 2092.00i | 0.197155 | − | 0.0816644i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 27412.5 | − | 27412.5i | 1.06640 | − | 1.06640i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −815.239 | − | 815.239i | −0.0316055 | − | 0.0316055i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 9009.35 | + | 21750.5i | 0.348082 | + | 0.840344i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −17160.7 | − | 7108.21i | −0.660749 | − | 0.273691i | 0.0270046 | − | 0.999635i | \(-0.491403\pi\) |
−0.687754 | + | 0.725944i | \(0.741403\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | − | 39887.5i | − | 1.53057i | ||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 25601.4i | 0.979039i | 0.871992 | + | 0.489520i | \(0.162828\pi\) | ||||
−0.871992 | + | 0.489520i | \(0.837172\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 2470.51 | + | 1023.32i | 0.0941555 | + | 0.0390005i | 0.429264 | − | 0.903179i | \(-0.358773\pi\) |
−0.335109 | + | 0.942180i | \(0.608773\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −7046.25 | − | 17011.2i | −0.267635 | − | 0.646129i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 3316.04 | + | 3316.04i | 0.125526 | + | 0.125526i | 0.767079 | − | 0.641553i | \(-0.221709\pi\) |
−0.641553 | + | 0.767079i | \(0.721709\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 13415.2 | − | 13415.2i | 0.506110 | − | 0.506110i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −6338.89 | + | 2625.65i | −0.238340 | + | 0.0987236i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −6820.53 | + | 16466.2i | −0.255588 | + | 0.617044i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 8723.52 | 0.325805 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −36036.8 | −1.34140 | ||||||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 14196.4 | − | 34273.2i | 0.526671 | − | 1.27150i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −36150.0 | + | 14973.8i | −1.33666 | + | 0.553662i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 10631.1 | − | 10631.1i | 0.391783 | − | 0.391783i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −7621.28 | − | 7621.28i | −0.279934 | − | 0.279934i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −2525.01 | − | 6095.91i | −0.0924382 | − | 0.223166i | 0.870897 | − | 0.491465i | \(-0.163538\pi\) |
−0.963336 | + | 0.268299i | \(0.913538\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 1224.62 | + | 507.255i | 0.0446844 | + | 0.0185089i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 4913.39i | 0.178692i | 0.996001 | + | 0.0893458i | \(0.0284776\pi\) | ||||
−0.996001 | + | 0.0893458i | \(0.971522\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 1478.10i | 0.0535794i | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −4354.18 | − | 1803.56i | −0.157317 | − | 0.0651628i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 525.399 | + | 1268.42i | 0.0189206 | + | 0.0456784i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 17562.4 | + | 17562.4i | 0.630392 | + | 0.630392i | 0.948166 | − | 0.317774i | \(-0.102935\pi\) |
−0.317774 | + | 0.948166i | \(0.602935\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 4099.37 | − | 4099.37i | 0.146665 | − | 0.146665i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 20710.3 | − | 8578.50i | 0.738557 | − | 0.305920i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 8220.09 | − | 19845.0i | 0.292189 | − | 0.705406i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −628.687 | −0.0222748 | ||||||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 4262.05 | 0.150520 | 0.0752602 | − | 0.997164i | \(-0.476021\pi\) | ||||
0.0752602 | + | 0.997164i | \(0.476021\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 2090.00 | − | 5045.70i | 0.0735735 | − | 0.177622i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −14279.6 | + | 5914.81i | −0.501065 | + | 0.207548i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −2966.79 | + | 2966.79i | −0.103769 | + | 0.103769i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 20895.1 | + | 20895.1i | 0.728511 | + | 0.728511i | 0.970323 | − | 0.241812i | \(-0.0777419\pi\) |
−0.241812 | + | 0.970323i | \(0.577742\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 10047.7 | + | 24257.2i | 0.349194 | + | 0.843028i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 16995.0 | + | 7039.57i | 0.588759 | + | 0.243872i | 0.657116 | − | 0.753789i | \(-0.271776\pi\) |
−0.0683579 | + | 0.997661i | \(0.521776\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | − | 30172.8i | − | 1.04195i | ||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | − | 15241.0i | − | 0.524644i | ||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 36843.7 | + | 15261.2i | 1.26427 | + | 0.523676i | 0.911216 | − | 0.411928i | \(-0.135144\pi\) |
0.353050 | + | 0.935604i | \(0.385144\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 30426.2 | + | 73455.4i | 1.04076 | + | 2.51261i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −29123.3 | − | 29123.3i | −0.993046 | − | 0.993046i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −9331.21 | + | 9331.21i | −0.317175 | + | 0.317175i | −0.847681 | − | 0.530506i | \(-0.822002\pi\) |
0.530506 | + | 0.847681i | \(0.322002\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 7446.06 | − | 3084.26i | 0.252303 | − | 0.104507i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −2663.02 | + | 6429.11i | −0.0899513 | + | 0.217162i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 53780.9 | 1.81092 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 41845.8 | 1.40465 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 120.689 | − | 291.370i | 0.00403859 | − | 0.00975001i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −17886.9 | + | 7408.99i | −0.596683 | + | 0.247154i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 16402.9 | − | 16402.9i | 0.545483 | − | 0.545483i | −0.379648 | − | 0.925131i | \(-0.623955\pi\) |
0.925131 | + | 0.379648i | \(0.123955\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 29215.6 | + | 29215.6i | 0.968565 | + | 0.968565i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −2483.25 | − | 5995.10i | −0.0820714 | − | 0.198138i | 0.877517 | − | 0.479546i | \(-0.159199\pi\) |
−0.959588 | + | 0.281408i | \(0.909199\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 25256.3 | + | 10461.5i | 0.832147 | + | 0.344687i | ||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 34300.2i | 1.12665i | ||||||||
\(976\) | 0 | 0 | ||||||||
\(977\) | − | 26525.8i | − | 0.868613i | −0.900765 | − | 0.434307i | \(-0.856993\pi\) | ||
0.900765 | − | 0.434307i | \(-0.143007\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 7497.30 | + | 3105.48i | 0.244754 | + | 0.101381i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −449.414 | − | 1084.98i | −0.0146266 | − | 0.0353117i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −3562.07 | − | 3562.07i | −0.115577 | − | 0.115577i | 0.646953 | − | 0.762530i | \(-0.276043\pi\) |
−0.762530 | + | 0.646953i | \(0.776043\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −7210.74 | + | 7210.74i | −0.233252 | + | 0.233252i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −16209.2 | + | 6714.06i | −0.522739 | + | 0.216526i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −5775.60 | + | 13943.5i | −0.185696 | + | 0.448310i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 10011.3 | 0.320907 | 0.160453 | − | 0.987043i | \(-0.448704\pi\) | ||||
0.160453 | + | 0.987043i | \(0.448704\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 31457.5 | 1.00531 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −5804.97 | + | 14014.4i | −0.184955 | + | 0.446520i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −19700.4 | + | 8160.16i | −0.625795 | + | 0.259213i | −0.672965 | − | 0.739674i | \(-0.734980\pi\) |
0.0471705 | + | 0.998887i | \(0.484980\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −22571.6 | + | 22571.6i | −0.714848 | + | 0.714848i |
(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 | 256.4.g.a.33.9 | 44 | ||
4.3 | odd | 2 | 256.4.g.b.33.3 | 44 | |||
8.3 | odd | 2 | 32.4.g.a.13.3 | yes | 44 | ||
8.5 | even | 2 | 128.4.g.a.17.3 | 44 | |||
32.5 | even | 8 | inner | 256.4.g.a.225.9 | 44 | ||
32.11 | odd | 8 | 32.4.g.a.5.3 | ✓ | 44 | ||
32.21 | even | 8 | 128.4.g.a.113.3 | 44 | |||
32.27 | odd | 8 | 256.4.g.b.225.3 | 44 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
32.4.g.a.5.3 | ✓ | 44 | 32.11 | odd | 8 | ||
32.4.g.a.13.3 | yes | 44 | 8.3 | odd | 2 | ||
128.4.g.a.17.3 | 44 | 8.5 | even | 2 | |||
128.4.g.a.113.3 | 44 | 32.21 | even | 8 | |||
256.4.g.a.33.9 | 44 | 1.1 | even | 1 | trivial | ||
256.4.g.a.225.9 | 44 | 32.5 | even | 8 | inner | ||
256.4.g.b.33.3 | 44 | 4.3 | odd | 2 | |||
256.4.g.b.225.3 | 44 | 32.27 | odd | 8 |