Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [864,2,Mod(49,864)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(864, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([0, 9, 14]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("864.49");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 864 = 2^{5} \cdot 3^{3} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 864.bf (of order \(18\), degree \(6\), 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: | \(6.89907473464\) |
Analytic rank: | \(0\) |
Dimension: | \(204\) |
Relative dimension: | \(34\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 216) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 49.4 | ||
Character | \(\chi\) | \(=\) | 864.49 |
Dual form | 864.2.bf.a.529.4 |
$q$-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 \(\left(\mathbb{Z}/864\mathbb{Z}\right)^\times\).
\(n\) | \(325\) | \(353\) | \(703\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{7}{9}\right)\) | \(1\) |
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 | ||||||||
\(3\) | −1.59613 | + | 0.672593i | −0.921524 | + | 0.388322i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.882298 | − | 2.42409i | −0.394576 | − | 1.08409i | −0.964888 | − | 0.262660i | \(-0.915400\pi\) |
0.570312 | − | 0.821428i | \(-0.306822\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −0.818935 | − | 4.64441i | −0.309528 | − | 1.75542i | −0.601384 | − | 0.798960i | \(-0.705384\pi\) |
0.291856 | − | 0.956462i | \(-0.405727\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.09524 | − | 2.14709i | 0.698412 | − | 0.715696i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.647163 | − | 1.77807i | 0.195127 | − | 0.536107i | −0.803086 | − | 0.595863i | \(-0.796810\pi\) |
0.998213 | + | 0.0597559i | \(0.0190322\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.09972 | + | 2.50235i | −0.582358 | + | 0.694028i | −0.974118 | − | 0.226040i | \(-0.927422\pi\) |
0.391760 | + | 0.920068i | \(0.371866\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 3.03869 | + | 3.27573i | 0.784586 | + | 0.845791i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −0.567141 | + | 0.982316i | −0.137552 | + | 0.238247i | −0.926569 | − | 0.376124i | \(-0.877257\pi\) |
0.789018 | + | 0.614371i | \(0.210590\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −4.48572 | + | 2.58983i | −1.02910 | + | 0.594148i | −0.916725 | − | 0.399518i | \(-0.869177\pi\) |
−0.112370 | + | 0.993666i | \(0.535844\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 4.43092 | + | 6.86226i | 0.966907 | + | 1.49747i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.560942 | + | 3.18126i | −0.116964 | + | 0.663338i | 0.868794 | + | 0.495173i | \(0.164895\pi\) |
−0.985759 | + | 0.168165i | \(0.946216\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −1.26756 | + | 1.06361i | −0.253513 | + | 0.212722i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.90015 | + | 4.83626i | −0.365683 | + | 0.930739i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 3.21760 | + | 3.83458i | 0.597493 | + | 0.712064i | 0.977028 | − | 0.213113i | \(-0.0683603\pi\) |
−0.379535 | + | 0.925178i | \(0.623916\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 0.775862 | − | 4.40013i | 0.139349 | − | 0.790287i | −0.832383 | − | 0.554201i | \(-0.813024\pi\) |
0.971732 | − | 0.236086i | \(-0.0758648\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.162961 | + | 3.27330i | 0.0283679 | + | 0.569808i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | −10.5359 | + | 6.08293i | −1.78090 | + | 1.02820i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.20995 | − | 3.58532i | −1.02091 | − | 0.589422i | −0.106542 | − | 0.994308i | \(-0.533978\pi\) |
−0.914367 | + | 0.404886i | \(0.867311\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 1.66836 | − | 5.40633i | 0.267151 | − | 0.865706i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.91303 | − | 2.44432i | −0.454938 | − | 0.381738i | 0.386326 | − | 0.922362i | \(-0.373744\pi\) |
−0.841265 | + | 0.540624i | \(0.818188\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.90770 | − | 5.24136i | 0.290921 | − | 0.799300i | −0.705011 | − | 0.709196i | \(-0.749058\pi\) |
0.995932 | − | 0.0901037i | \(-0.0287199\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −7.05337 | − | 3.18468i | −1.05145 | − | 0.474744i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 2.09323 | + | 11.8713i | 0.305329 | + | 1.73161i | 0.621950 | + | 0.783057i | \(0.286341\pi\) |
−0.316621 | + | 0.948552i | \(0.602548\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −14.3221 | + | 5.21280i | −2.04601 | + | 0.744686i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0.244529 | − | 1.94936i | 0.0342409 | − | 0.272964i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 3.54525i | 0.486978i | 0.969904 | + | 0.243489i | \(0.0782920\pi\) | ||||
−0.969904 | + | 0.243489i | \(0.921708\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | −4.88119 | −0.658180 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 5.41787 | − | 7.15077i | 0.717615 | − | 0.947142i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.29386 | − | 11.7973i | −0.559013 | − | 1.53588i | −0.821072 | − | 0.570824i | \(-0.806624\pi\) |
0.262059 | − | 0.965052i | \(-0.415599\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −3.67306 | + | 0.647659i | −0.470287 | + | 0.0829243i | −0.403769 | − | 0.914861i | \(-0.632300\pi\) |
−0.0665178 | + | 0.997785i | \(0.521189\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | −11.6878 | − | 7.97282i | −1.47253 | − | 1.00448i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 7.91852 | + | 2.88211i | 0.982172 | + | 0.357481i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −0.836157 | + | 0.996493i | −0.102153 | + | 0.121741i | −0.814699 | − | 0.579885i | \(-0.803098\pi\) |
0.712546 | + | 0.701626i | \(0.247542\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | −1.24436 | − | 5.45497i | −0.149803 | − | 0.656702i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 2.92491 | − | 5.06609i | 0.347123 | − | 0.601234i | −0.638614 | − | 0.769527i | \(-0.720492\pi\) |
0.985737 | + | 0.168293i | \(0.0538254\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 2.92352 | + | 5.06368i | 0.342172 | + | 0.592659i | 0.984836 | − | 0.173489i | \(-0.0555042\pi\) |
−0.642664 | + | 0.766148i | \(0.722171\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | 1.30781 | − | 2.55021i | 0.151013 | − | 0.294473i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | −8.78806 | − | 1.54957i | −1.00149 | − | 0.176590i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.80639 | + | 1.51574i | −0.203234 | + | 0.170534i | −0.738724 | − | 0.674008i | \(-0.764571\pi\) |
0.535490 | + | 0.844542i | \(0.320127\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −0.219965 | − | 8.99731i | −0.0244406 | − | 0.999701i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 8.86580 | + | 10.5658i | 0.973148 | + | 1.15975i | 0.987141 | + | 0.159850i | \(0.0511012\pi\) |
−0.0139934 | + | 0.999902i | \(0.504454\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.88162 | + | 0.508107i | 0.312555 | + | 0.0551119i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −7.71481 | − | 3.95635i | −0.827114 | − | 0.424165i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | 0.302925 | + | 0.524682i | 0.0321100 | + | 0.0556162i | 0.881634 | − | 0.471934i | \(-0.156444\pi\) |
−0.849524 | + | 0.527550i | \(0.823111\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 13.3415 | + | 7.70271i | 1.39857 | + | 0.807464i | ||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 1.72113 | + | 7.54500i | 0.178472 | + | 0.782380i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 10.2357 | + | 8.58881i | 1.05017 | + | 0.881193i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −15.8957 | − | 5.78557i | −1.61397 | − | 0.587436i | −0.631747 | − | 0.775174i | \(-0.717662\pi\) |
−0.982219 | + | 0.187739i | \(0.939884\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.46170 | − | 5.11499i | −0.247411 | − | 0.514076i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 2.63438 | − | 0.464512i | 0.262130 | − | 0.0462207i | −0.0410382 | − | 0.999158i | \(-0.513067\pi\) |
0.303169 | + | 0.952937i | \(0.401955\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −14.5813 | + | 5.30716i | −1.43674 | + | 0.522930i | −0.938854 | − | 0.344314i | \(-0.888111\pi\) |
−0.497883 | + | 0.867244i | \(0.665889\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 12.7254 | − | 16.7955i | 1.24187 | − | 1.63908i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 11.5155i | 1.11325i | 0.830764 | + | 0.556625i | \(0.187904\pi\) | ||||
−0.830764 | + | 0.556625i | \(0.812096\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | − | 15.9553i | − | 1.52824i | −0.645075 | − | 0.764119i | \(-0.723174\pi\) | ||
0.645075 | − | 0.764119i | \(-0.276826\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 12.3233 | + | 1.54585i | 1.16968 | + | 0.146725i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −0.805672 | + | 0.293240i | −0.0757912 | + | 0.0275857i | −0.379638 | − | 0.925135i | \(-0.623951\pi\) |
0.303846 | + | 0.952721i | \(0.401729\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 8.20659 | − | 1.44704i | 0.765268 | − | 0.134937i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.973351 | + | 9.75131i | 0.0899864 | + | 0.901509i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 5.02673 | + | 1.82958i | 0.460800 | + | 0.167717i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 5.68379 | + | 4.76926i | 0.516708 | + | 0.433569i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 6.29359 | + | 1.94216i | 0.567474 | + | 0.175119i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −7.47362 | − | 4.31490i | −0.668461 | − | 0.385936i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.07290 | − | 1.85831i | −0.0952042 | − | 0.164898i | 0.814490 | − | 0.580178i | \(-0.197017\pi\) |
−0.909694 | + | 0.415280i | \(0.863684\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | 0.480375 | + | 9.64898i | 0.0422947 | + | 0.849545i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 10.6350 | + | 1.87524i | 0.929187 | + | 0.163841i | 0.617704 | − | 0.786411i | \(-0.288063\pi\) |
0.311483 | + | 0.950252i | \(0.399174\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 15.7018 | + | 18.7126i | 1.36152 | + | 1.62259i | ||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 13.4001 | + | 0.339107i | 1.15329 | + | 0.0291857i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −12.7808 | + | 10.7244i | −1.09194 | + | 0.916245i | −0.996857 | − | 0.0792243i | \(-0.974756\pi\) |
−0.0950817 | + | 0.995469i | \(0.530311\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −15.7604 | − | 2.77899i | −1.33678 | − | 0.235710i | −0.540861 | − | 0.841112i | \(-0.681901\pi\) |
−0.795920 | + | 0.605402i | \(0.793012\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −11.3256 | − | 17.5402i | −0.953790 | − | 1.47715i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 3.09049 | + | 5.35288i | 0.258439 | + | 0.447630i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 6.45651 | − | 11.1830i | 0.536184 | − | 0.928698i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 19.3537 | − | 17.9532i | 1.59627 | − | 1.48076i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −1.12442 | + | 1.34003i | −0.0921157 | + | 0.109779i | −0.810133 | − | 0.586246i | \(-0.800605\pi\) |
0.718018 | + | 0.696025i | \(0.245050\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 1.88609 | + | 0.686481i | 0.153488 | + | 0.0558650i | 0.417622 | − | 0.908621i | \(-0.362864\pi\) |
−0.264134 | + | 0.964486i | \(0.585086\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.920825 | + | 3.27589i | 0.0744443 | + | 0.264840i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −11.3509 | + | 2.00147i | −0.911725 | + | 0.160762i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −2.34039 | − | 6.43016i | −0.186783 | − | 0.513182i | 0.810590 | − | 0.585614i | \(-0.199146\pi\) |
−0.997373 | + | 0.0724314i | \(0.976924\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −2.38451 | − | 5.65867i | −0.189104 | − | 0.448762i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 15.2344 | 1.20064 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 6.85942i | − | 0.537271i | −0.963242 | − | 0.268636i | \(-0.913427\pi\) | ||
0.963242 | − | 0.268636i | \(-0.0865728\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 7.79100 | − | 3.28306i | 0.606529 | − | 0.255586i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −6.78917 | + | 2.47106i | −0.525362 | + | 0.191216i | −0.591066 | − | 0.806623i | \(-0.701293\pi\) |
0.0657043 | + | 0.997839i | \(0.479071\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 0.404495 | + | 2.29401i | 0.0311150 | + | 0.176462i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.83805 | + | 15.0575i | −0.293503 | + | 1.15148i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 2.35038 | − | 6.45762i | 0.178696 | − | 0.490964i | −0.817714 | − | 0.575625i | \(-0.804759\pi\) |
0.996410 | + | 0.0846617i | \(0.0269810\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.97791 | + | 5.01606i | 0.451887 | + | 0.379178i | ||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 14.7883 | + | 15.9419i | 1.11156 | + | 1.19827i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −2.11037 | − | 1.21842i | −0.157737 | − | 0.0910693i | 0.419054 | − | 0.907961i | \(-0.362362\pi\) |
−0.576791 | + | 0.816892i | \(0.695695\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 21.1559 | − | 12.2143i | 1.57250 | − | 0.907885i | 0.576642 | − | 0.816997i | \(-0.304363\pi\) |
0.995861 | − | 0.0908887i | \(-0.0289708\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.42705 | − | 3.50422i | 0.401179 | − | 0.259039i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −3.21212 | + | 18.2168i | −0.236160 | + | 1.33933i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.37959 | + | 1.64413i | 0.100886 | + | 0.120231i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 24.0177 | + | 4.86447i | 1.74703 | + | 0.353838i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −0.483744 | + | 0.405909i | −0.0350025 | + | 0.0293706i | −0.660121 | − | 0.751159i | \(-0.729495\pi\) |
0.625119 | + | 0.780530i | \(0.285051\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 3.60135 | − | 20.4243i | 0.259231 | − | 1.47017i | −0.525744 | − | 0.850643i | \(-0.676213\pi\) |
0.784975 | − | 0.619527i | \(-0.212676\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −14.5774 | + | 0.725739i | −1.04391 | + | 0.0519712i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 8.16675 | − | 4.71508i | 0.581857 | − | 0.335935i | −0.180014 | − | 0.983664i | \(-0.557614\pi\) |
0.761871 | + | 0.647729i | \(0.224281\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −1.56260 | + | 2.70650i | −0.110770 | + | 0.191859i | −0.916081 | − | 0.400994i | \(-0.868665\pi\) |
0.805311 | + | 0.592852i | \(0.201998\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 0.664378 | − | 2.15292i | 0.0468616 | − | 0.151855i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 15.1744 | − | 18.0841i | 1.06503 | − | 1.26926i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −3.35510 | + | 9.21807i | −0.234331 | + | 0.643818i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.65513 | + | 7.86988i | 0.393059 | + | 0.546994i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 1.70190 | + | 9.65196i | 0.117723 | + | 0.667640i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −9.07630 | − | 24.9369i | −0.624838 | − | 1.71673i | −0.694823 | − | 0.719181i | \(-0.744517\pi\) |
0.0699851 | − | 0.997548i | \(-0.477705\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −1.26110 | + | 10.0534i | −0.0864095 | + | 0.688847i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −14.3887 | −0.981303 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −21.0714 | −1.43042 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.07209 | − | 6.11593i | −0.545462 | − | 0.413276i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.26726 | − | 3.48178i | −0.0852454 | − | 0.234210i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −0.840933 | − | 4.76917i | −0.0563130 | − | 0.319367i | 0.943619 | − | 0.331034i | \(-0.107397\pi\) |
−0.999932 | + | 0.0116667i | \(0.996286\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.372178 | + | 4.95009i | −0.0248119 | + | 0.330006i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 6.82487 | − | 18.7512i | 0.452982 | − | 1.24456i | −0.477633 | − | 0.878560i | \(-0.658505\pi\) |
0.930615 | − | 0.365999i | \(-0.119273\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −0.391830 | + | 0.466964i | −0.0258928 | + | 0.0308579i | −0.778835 | − | 0.627228i | \(-0.784189\pi\) |
0.752943 | + | 0.658086i | \(0.228634\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 15.0691 | − | 3.43748i | 0.991473 | − | 0.226169i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −3.02731 | + | 5.24345i | −0.198326 | + | 0.343510i | −0.947986 | − | 0.318313i | \(-0.896884\pi\) |
0.749660 | + | 0.661823i | \(0.230217\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 26.9303 | − | 15.5482i | 1.75674 | − | 1.01426i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 1.86375 | − | 3.63427i | 0.121063 | − | 0.236071i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 1.84795 | − | 10.4802i | 0.119534 | − | 0.677910i | −0.864871 | − | 0.501994i | \(-0.832600\pi\) |
0.984405 | − | 0.175916i | \(-0.0562889\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 1.94324 | − | 1.63057i | 0.125175 | − | 0.105034i | −0.578051 | − | 0.816000i | \(-0.696187\pi\) |
0.703226 | + | 0.710966i | \(0.251742\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 6.40262 | + | 14.2129i | 0.410728 | + | 0.911758i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 25.2727 | + | 30.1188i | 1.61461 | + | 1.92422i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.93810 | − | 16.6628i | 0.186947 | − | 1.06023i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −21.2575 | − | 10.9013i | −1.34714 | − | 0.690845i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | −9.74106 | + | 5.62400i | −0.614850 | + | 0.354984i | −0.774861 | − | 0.632131i | \(-0.782180\pi\) |
0.160011 | + | 0.987115i | \(0.448847\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 5.29347 | + | 3.05619i | 0.332798 | + | 0.192141i | ||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −4.94117 | + | 1.12715i | −0.309428 | + | 0.0705850i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.40395 | − | 4.53446i | −0.337089 | − | 0.282852i | 0.458492 | − | 0.888699i | \(-0.348390\pi\) |
−0.795581 | + | 0.605847i | \(0.792834\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | −11.5661 | + | 31.7777i | −0.718685 | + | 1.97457i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 14.9748 | + | 1.12590i | 0.926918 | + | 0.0696914i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.03677 | − | 28.5649i | −0.310580 | − | 1.76139i | −0.595999 | − | 0.802985i | \(-0.703244\pi\) |
0.285418 | − | 0.958403i | \(-0.407867\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 8.59403 | − | 3.12797i | 0.527927 | − | 0.192150i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −0.836405 | − | 0.633713i | −0.0511871 | − | 0.0387826i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 14.3553i | − | 0.875257i | −0.899156 | − | 0.437628i | \(-0.855819\pi\) | ||
0.899156 | − | 0.437628i | \(-0.144181\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −15.9782 | −0.970609 | −0.485305 | − | 0.874345i | \(-0.661291\pi\) | ||||
−0.485305 | + | 0.874345i | \(0.661291\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | −26.4755 | − | 3.32111i | −1.60237 | − | 0.201002i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 1.07085 | + | 2.94214i | 0.0645749 | + | 0.177418i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.40970 | + | 1.30653i | −0.445206 | + | 0.0785017i | −0.391757 | − | 0.920069i | \(-0.628133\pi\) |
−0.0534488 | + | 0.998571i | \(0.517021\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | −7.82185 | − | 10.8852i | −0.468282 | − | 0.651678i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −8.85360 | − | 3.22245i | −0.528162 | − | 0.192235i | 0.0641557 | − | 0.997940i | \(-0.479565\pi\) |
−0.592317 | + | 0.805705i | \(0.701787\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −15.8895 | + | 18.9364i | −0.944533 | + | 1.12565i | 0.0473989 | + | 0.998876i | \(0.484907\pi\) |
−0.991932 | + | 0.126774i | \(0.959538\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −22.1143 | − | 6.82433i | −1.30994 | − | 0.404239i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −8.96684 | + | 15.5310i | −0.529296 | + | 0.916768i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 7.85670 | + | 13.6082i | 0.462159 | + | 0.800483i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 29.2629 | − | 1.45686i | 1.71542 | − | 0.0854024i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −7.64101 | − | 1.34732i | −0.446392 | − | 0.0787110i | −0.0540666 | − | 0.998537i | \(-0.517218\pi\) |
−0.392326 | + | 0.919826i | \(0.628329\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −24.8093 | + | 20.8175i | −1.44445 | + | 1.21204i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 7.36950 | + | 6.50844i | 0.427622 | + | 0.377658i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −6.78281 | − | 8.08343i | −0.392260 | − | 0.467477i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −25.9053 | − | 4.56781i | −1.49316 | − | 0.263284i | ||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −3.89237 | + | 2.51328i | −0.223611 | + | 0.144384i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 4.81072 | + | 8.33241i | 0.275461 | + | 0.477112i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −11.1421 | − | 6.43289i | −0.635913 | − | 0.367145i | 0.147125 | − | 0.989118i | \(-0.452998\pi\) |
−0.783038 | + | 0.621973i | \(0.786331\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 19.7040 | − | 18.2782i | 1.12092 | − | 1.03981i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 12.4067 | + | 10.4105i | 0.703521 | + | 0.590324i | 0.922773 | − | 0.385344i | \(-0.125917\pi\) |
−0.219252 | + | 0.975668i | \(0.570362\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.04686 | − | 0.381024i | −0.0591718 | − | 0.0215368i | 0.312265 | − | 0.949995i | \(-0.398912\pi\) |
−0.371436 | + | 0.928458i | \(0.621135\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | −9.01472 | + | 35.3668i | −0.507922 | + | 1.99269i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −1.55544 | + | 0.274266i | −0.0873623 | + | 0.0154043i | −0.217158 | − | 0.976136i | \(-0.569679\pi\) |
0.129796 | + | 0.991541i | \(0.458568\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 8.90046 | − | 3.23950i | 0.498330 | − | 0.181377i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −7.74527 | − | 18.3803i | −0.432299 | − | 1.02589i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | − | 5.87520i | − | 0.326905i | ||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | − | 5.40518i | − | 0.299826i | ||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 10.7314 | + | 25.4666i | 0.593448 | + | 1.40831i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 53.4211 | − | 19.4437i | 2.94520 | − | 1.07196i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 12.2698 | − | 2.16350i | 0.674411 | − | 0.118917i | 0.174054 | − | 0.984736i | \(-0.444313\pi\) |
0.500357 | + | 0.865819i | \(0.333202\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −20.7093 | + | 5.82122i | −1.13486 | + | 0.319001i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | 3.15333 | + | 1.14772i | 0.172285 | + | 0.0627066i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.46382 | − | 2.90649i | −0.188686 | − | 0.158327i | 0.543551 | − | 0.839376i | \(-0.317079\pi\) |
−0.732237 | + | 0.681049i | \(0.761524\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 1.08872 | − | 1.00994i | 0.0591313 | − | 0.0548523i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −7.32162 | − | 4.22714i | −0.396488 | − | 0.228912i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 19.4330 | + | 33.6590i | 1.04928 | + | 1.81741i | ||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −12.1255 | + | 7.82936i | −0.652814 | + | 0.421519i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 3.23530 | + | 0.570470i | 0.173680 | + | 0.0306244i | 0.259812 | − | 0.965659i | \(-0.416340\pi\) |
−0.0861319 | + | 0.996284i | \(0.527451\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 0.513251 | + | 0.611669i | 0.0274737 | + | 0.0327419i | 0.779606 | − | 0.626270i | \(-0.215419\pi\) |
−0.752133 | + | 0.659012i | \(0.770975\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −8.11226 | − | 14.9096i | −0.433000 | − | 0.795818i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 18.2518 | − | 15.3150i | 0.971443 | − | 0.815138i | −0.0113333 | − | 0.999936i | \(-0.503608\pi\) |
0.982776 | + | 0.184798i | \(0.0591631\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −14.8613 | − | 2.62045i | −0.788757 | − | 0.139079i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | −9.25386 | + | 0.460704i | −0.489766 | + | 0.0243830i | ||||
\(358\) | 0 | 0 | ||||||||
\(359\) | −8.66171 | − | 15.0025i | −0.457148 | − | 0.791803i | 0.541661 | − | 0.840597i | \(-0.317796\pi\) |
−0.998809 | + | 0.0487939i | \(0.984462\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 3.91447 | − | 6.78006i | 0.206025 | − | 0.356845i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −12.2798 | − | 3.78947i | −0.644523 | − | 0.198896i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 9.69542 | − | 11.5546i | 0.507482 | − | 0.604793i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 15.6943 | + | 5.71227i | 0.819237 | + | 0.298178i | 0.717434 | − | 0.696627i | \(-0.245317\pi\) |
0.101803 | + | 0.994805i | \(0.467539\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −11.3516 | + | 1.13309i | −0.590943 | + | 0.0589865i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 16.4656 | − | 2.90333i | 0.854852 | − | 0.150733i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.32927 | − | 3.65215i | −0.0688272 | − | 0.189101i | 0.900510 | − | 0.434835i | \(-0.143193\pi\) |
−0.969337 | + | 0.245734i | \(0.920971\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 14.8310 | + | 1.86041i | 0.765870 | + | 0.0960714i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −16.3515 | −0.842147 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 10.9558i | − | 0.562760i | −0.959596 | − | 0.281380i | \(-0.909208\pi\) | ||
0.959596 | − | 0.281380i | \(-0.0907922\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 2.96237 | + | 2.24448i | 0.151767 | + | 0.114988i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −13.6840 | + | 4.98057i | −0.699220 | + | 0.254495i | −0.667078 | − | 0.744988i | \(-0.732455\pi\) |
−0.0321425 | + | 0.999483i | \(0.510233\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 3.99738 | + | 22.6703i | 0.203725 | + | 1.15538i | ||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −7.25658 | − | 15.0779i | −0.368873 | − | 0.766452i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −1.59337 | + | 4.37774i | −0.0807869 | + | 0.221960i | −0.973510 | − | 0.228646i | \(-0.926570\pi\) |
0.892723 | + | 0.450607i | \(0.148792\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −2.80687 | − | 2.35524i | −0.141949 | − | 0.119110i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −18.2361 | + | 4.15993i | −0.919891 | + | 0.209840i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | 5.26807 | + | 3.04152i | 0.265065 | + | 0.153035i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −2.23476 | + | 1.29024i | −0.112160 | + | 0.0647554i | −0.555030 | − | 0.831830i | \(-0.687293\pi\) |
0.442871 | + | 0.896585i | \(0.353960\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −37.6480 | − | 19.3068i | −1.88476 | − | 0.966550i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 2.06316 | − | 11.7008i | 0.103029 | − | 0.584309i | −0.888960 | − | 0.457986i | \(-0.848571\pi\) |
0.991989 | − | 0.126324i | \(-0.0403178\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.38158 | + | 11.1805i | 0.467330 | + | 0.556942i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −21.6163 | + | 8.47153i | −1.07412 | + | 0.420954i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −10.3938 | + | 8.72142i | −0.515201 | + | 0.432305i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −2.49747 | + | 14.1638i | −0.123492 | + | 0.700357i | 0.858700 | + | 0.512478i | \(0.171272\pi\) |
−0.982192 | + | 0.187879i | \(0.939839\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 13.1866 | − | 25.7137i | 0.650449 | − | 1.26837i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | −51.2751 | + | 29.6037i | −2.52308 | + | 1.45670i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 17.7903 | − | 30.8138i | 0.873293 | − | 1.51259i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 27.0247 | − | 6.16473i | 1.32341 | − | 0.301888i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −15.8793 | + | 18.9242i | −0.775755 | + | 0.924509i | −0.998733 | − | 0.0503146i | \(-0.983978\pi\) |
0.222978 | + | 0.974823i | \(0.428422\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −10.8138 | + | 29.7106i | −0.527032 | + | 1.44801i | 0.335517 | + | 0.942034i | \(0.391089\pi\) |
−0.862549 | + | 0.505974i | \(0.831133\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 29.8746 | + | 20.3789i | 1.45255 | + | 0.990854i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −0.325917 | − | 1.84837i | −0.0158093 | − | 0.0896589i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 6.01599 | + | 16.5288i | 0.291134 | + | 0.799885i | ||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.53312 | − | 6.46523i | −0.411983 | − | 0.312144i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 7.78707 | 0.375090 | 0.187545 | − | 0.982256i | \(-0.439947\pi\) | ||||
0.187545 | + | 0.982256i | \(0.439947\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 8.41002 | 0.404160 | 0.202080 | − | 0.979369i | \(-0.435230\pi\) | ||||
0.202080 | + | 0.979369i | \(0.435230\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −2.78379 | + | 22.1921i | −0.133473 | + | 1.06403i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −5.72270 | − | 15.7230i | −0.273754 | − | 0.752132i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 3.95770 | + | 22.4452i | 0.188891 | + | 1.07125i | 0.920854 | + | 0.389908i | \(0.127493\pi\) |
−0.731963 | + | 0.681344i | \(0.761396\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | −18.8158 | + | 41.6728i | −0.895989 | + | 1.98442i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −7.54668 | + | 20.7343i | −0.358554 | + | 0.985118i | 0.620978 | + | 0.783828i | \(0.286736\pi\) |
−0.979532 | + | 0.201290i | \(0.935487\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 1.00461 | − | 1.19725i | 0.0476230 | − | 0.0567549i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 0.893416 | − | 2.89512i | 0.0422571 | − | 0.136935i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −0.937600 | + | 1.62397i | −0.0442481 | + | 0.0766400i | −0.887301 | − | 0.461190i | \(-0.847423\pi\) |
0.843053 | + | 0.537830i | \(0.180756\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −6.23137 | + | 3.59768i | −0.293424 | + | 0.169408i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.47216 | + | 0.172862i | −0.163136 | + | 0.00812175i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 6.90093 | − | 39.1371i | 0.323521 | − | 1.83478i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 20.8493 | − | 17.4947i | 0.975290 | − | 0.818365i | −0.00808235 | − | 0.999967i | \(-0.502573\pi\) |
0.983372 | + | 0.181602i | \(0.0581283\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | −3.67309 | − | 4.60939i | −0.171445 | − | 0.215148i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.21149 | + | 10.9778i | 0.429022 | + | 0.511289i | 0.936640 | − | 0.350294i | \(-0.113918\pi\) |
−0.507618 | + | 0.861582i | \(0.669474\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.62893 | − | 14.9094i | 0.122177 | − | 0.692899i | −0.860768 | − | 0.508998i | \(-0.830016\pi\) |
0.982945 | − | 0.183901i | \(-0.0588727\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 16.7713 | − | 10.8291i | 0.777749 | − | 0.502188i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −8.60621 | + | 4.96880i | −0.398248 | + | 0.229929i | −0.685728 | − | 0.727858i | \(-0.740516\pi\) |
0.287480 | + | 0.957787i | \(0.407183\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 5.31288 | + | 3.06739i | 0.245326 | + | 0.141639i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 8.06043 | + | 8.68921i | 0.371405 | + | 0.400378i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | −8.08490 | − | 6.78404i | −0.371744 | − | 0.311930i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 2.93136 | − | 8.05385i | 0.134500 | − | 0.369536i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 7.61197 | + | 7.42814i | 0.348528 | + | 0.340111i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −1.57169 | − | 8.91349i | −0.0718123 | − | 0.407268i | −0.999431 | − | 0.0337386i | \(-0.989259\pi\) |
0.927618 | − | 0.373529i | \(-0.121852\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 22.0109 | − | 8.01131i | 1.00361 | − | 0.365284i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | −24.3161 | + | 10.2466i | −1.10642 | + | 0.466236i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 43.6373i | 1.98147i | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −23.7830 | −1.07771 | −0.538856 | − | 0.842398i | \(-0.681143\pi\) | ||||
−0.538856 | + | 0.842398i | \(0.681143\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 4.61360 | + | 10.9485i | 0.208634 | + | 0.495108i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −11.9837 | − | 32.9250i | −0.540818 | − | 1.48589i | −0.845786 | − | 0.533523i | \(-0.820868\pi\) |
0.304968 | − | 0.952363i | \(-0.401354\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −5.59160 | + | 0.985951i | −0.251833 | + | 0.0444050i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | −10.2273 | + | 10.4803i | −0.459681 | + | 0.471057i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | −25.9243 | − | 9.43568i | −1.16286 | − | 0.423248i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −4.72891 | + | 5.63569i | −0.211695 | + | 0.252288i | −0.861435 | − | 0.507869i | \(-0.830434\pi\) |
0.649739 | + | 0.760157i | \(0.274878\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 9.17436 | − | 8.51047i | 0.409880 | − | 0.380220i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 9.31955 | − | 16.1419i | 0.415538 | − | 0.719733i | −0.579947 | − | 0.814655i | \(-0.696927\pi\) |
0.995485 | + | 0.0949212i | \(0.0302599\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −3.45033 | − | 5.97615i | −0.153538 | − | 0.265935i | ||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −2.18856 | − | 3.38946i | −0.0971973 | − | 0.150531i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −13.2305 | − | 2.33290i | −0.586432 | − | 0.103404i | −0.127443 | − | 0.991846i | \(-0.540677\pi\) |
−0.458989 | + | 0.888442i | \(0.651788\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 21.1236 | − | 17.7248i | 0.934454 | − | 0.784100i | ||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −4.00159 | − | 26.6152i | −0.176674 | − | 1.17509i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 25.7301 | + | 30.6639i | 1.13380 | + | 1.35121i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 22.4627 | + | 3.96077i | 0.987907 | + | 0.174195i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0.591846 | + | 11.8880i | 0.0259791 | + | 0.521826i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −18.3404 | − | 31.7664i | −0.803505 | − | 1.39171i | −0.917295 | − | 0.398207i | \(-0.869632\pi\) |
0.113790 | − | 0.993505i | \(-0.463701\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 4.88996 | + | 2.82322i | 0.213823 | + | 0.123451i | 0.603087 | − | 0.797676i | \(-0.293937\pi\) |
−0.389264 | + | 0.921126i | \(0.627271\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −12.9153 | − | 3.98556i | −0.563668 | − | 0.173944i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 3.88230 | + | 3.25764i | 0.169116 | + | 0.141905i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.8072 | + | 4.29746i | 0.513356 | + | 0.186846i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −34.3265 | − | 15.4988i | −1.48964 | − | 0.672592i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 12.2331 | − | 2.15702i | 0.529874 | − | 0.0934311i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 27.9148 | − | 10.1601i | 1.20686 | − | 0.439261i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 4.18793 | + | 0.525337i | 0.180722 | + | 0.0226699i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 28.8391i | 1.24219i | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | − | 17.4866i | − | 0.751808i | −0.926659 | − | 0.375904i | \(-0.877332\pi\) | ||
0.926659 | − | 0.375904i | \(-0.122668\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −25.5522 | + | 33.7249i | −1.09655 | + | 1.44728i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −38.6771 | + | 14.0773i | −1.65674 | + | 0.603006i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 30.3035 | − | 5.34332i | 1.29568 | − | 0.228464i | 0.517056 | − | 0.855952i | \(-0.327028\pi\) |
0.778626 | + | 0.627488i | \(0.215917\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −6.30534 | + | 9.24337i | −0.269106 | + | 0.394498i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −24.3642 | − | 8.86784i | −1.03795 | − | 0.377783i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 8.51903 | + | 7.14831i | 0.362266 | + | 0.303977i | ||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −7.12557 | − | 31.2368i | −0.302464 | − | 1.32593i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | −5.65968 | − | 3.26762i | −0.239808 | − | 0.138453i | 0.375280 | − | 0.926911i | \(-0.377546\pi\) |
−0.615089 | + | 0.788458i | \(0.710880\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.11009 | + | 15.7791i | 0.385316 | + | 0.667387i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −3.30783 | − | 1.69634i | −0.139657 | − | 0.0716195i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | −25.8351 | − | 4.55543i | −1.08882 | − | 0.191989i | −0.399708 | − | 0.916642i | \(-0.630889\pi\) |
−0.689113 | + | 0.724654i | \(0.742000\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 1.42169 | + | 1.69430i | 0.0598108 | + | 0.0712797i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | −41.6071 | + | 8.38982i | −1.74733 | + | 0.352339i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | −7.81553 | + | 6.55801i | −0.327644 | + | 0.274926i | −0.791739 | − | 0.610859i | \(-0.790824\pi\) |
0.464095 | + | 0.885785i | \(0.346380\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −14.9514 | − | 2.63633i | −0.625696 | − | 0.110327i | −0.148195 | − | 0.988958i | \(-0.547346\pi\) |
−0.477501 | + | 0.878631i | \(0.658457\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 0.499105 | − | 0.973246i | 0.0208504 | − | 0.0406579i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −2.67260 | − | 4.62907i | −0.111455 | − | 0.193046i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 9.96264 | − | 17.2558i | 0.414750 | − | 0.718369i | −0.580652 | − | 0.814152i | \(-0.697202\pi\) |
0.995402 | + | 0.0957834i | \(0.0305356\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | 7.98901 | + | 35.0219i | 0.332012 | + | 1.45546i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 41.8116 | − | 49.8292i | 1.73464 | − | 2.06726i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 6.30370 | + | 2.29436i | 0.261072 | + | 0.0950226i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 22.7793 | − | 10.9631i | 0.941809 | − | 0.453267i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | 23.9630 | − | 4.22532i | 0.989057 | − | 0.174397i | 0.344362 | − | 0.938837i | \(-0.388095\pi\) |
0.644695 | + | 0.764440i | \(0.276984\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 7.91530 | + | 21.7471i | 0.326144 | + | 0.896074i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −9.86384 | + | 13.0188i | −0.405744 | + | 0.535520i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | −38.6846 | −1.58859 | −0.794294 | − | 0.607534i | \(-0.792159\pi\) | ||||
−0.794294 | + | 0.607534i | \(0.792159\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | − | 13.7995i | − | 0.565725i | ||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 0.673730 | − | 5.37090i | 0.0275739 | − | 0.219816i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −2.64435 | + | 0.962466i | −0.108045 | + | 0.0393253i | −0.395477 | − | 0.918476i | \(-0.629421\pi\) |
0.287432 | + | 0.957801i | \(0.407199\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.20959 | − | 23.8738i | −0.171713 | − | 0.973831i | −0.941870 | − | 0.335977i | \(-0.890933\pi\) |
0.770157 | − | 0.637854i | \(-0.220178\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0.387610 | + | 3.88319i | 0.0157847 | + | 0.158136i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 6.54635 | − | 17.9860i | 0.266147 | − | 0.731233i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −14.5888 | − | 12.2415i | −0.592143 | − | 0.496867i | 0.296766 | − | 0.954950i | \(-0.404092\pi\) |
−0.888909 | + | 0.458083i | \(0.848536\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −12.0570 | + | 39.0707i | −0.488573 | + | 1.58323i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −34.1014 | − | 19.6885i | −1.37960 | − | 0.796510i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −42.4123 | + | 24.4868i | −1.71302 | + | 0.989011i | −0.782586 | + | 0.622542i | \(0.786100\pi\) |
−0.930430 | + | 0.366469i | \(0.880567\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −0.844843 | − | 16.9698i | −0.0340674 | − | 0.684289i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −5.23248 | + | 29.6749i | −0.210652 | + | 1.19467i | 0.677643 | + | 0.735391i | \(0.263002\pi\) |
−0.888295 | + | 0.459274i | \(0.848110\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 0.100470 | + | 0.119735i | 0.00403821 | + | 0.00481256i | 0.768060 | − | 0.640378i | \(-0.221222\pi\) |
−0.764022 | + | 0.645191i | \(0.776778\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −14.3195 | − | 8.75772i | −0.574623 | − | 0.351435i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 2.18876 | − | 1.83659i | 0.0876909 | − | 0.0735814i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −5.30242 | + | 30.0715i | −0.212097 | + | 1.20286i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −9.20829 | − | 14.2611i | −0.367744 | − | 0.569532i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 7.04383 | − | 4.06676i | 0.280856 | − | 0.162152i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 15.3663 | − | 26.6153i | 0.611724 | − | 1.05954i | −0.379226 | − | 0.925304i | \(-0.623810\pi\) |
0.990950 | − | 0.134233i | \(-0.0428570\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 31.2593 | + | 33.6978i | 1.24245 | + | 1.33937i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −3.55811 | + | 4.24039i | −0.141199 | + | 0.168275i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 17.0281 | − | 46.7843i | 0.674677 | − | 1.85366i | ||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −4.74896 | − | 16.8947i | −0.187866 | − | 0.668343i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −4.59544 | − | 26.0620i | −0.181509 | − | 1.02939i | −0.930359 | − | 0.366649i | \(-0.880505\pi\) |
0.748850 | − | 0.662739i | \(-0.230606\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.39955 | + | 14.8351i | 0.212937 | + | 0.585040i | 0.999472 | − | 0.0325063i | \(-0.0103489\pi\) |
−0.786534 | + | 0.617547i | \(0.788127\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 22.9662 | − | 9.67775i | 0.904294 | − | 0.381061i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 20.7744 | 0.816724 | 0.408362 | − | 0.912820i | \(-0.366100\pi\) | ||||
0.408362 | + | 0.912820i | \(0.366100\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −23.7552 | −0.932473 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 33.6326 | − | 14.1725i | 1.31817 | − | 0.555463i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 3.19032 | + | 8.76533i | 0.124847 | + | 0.343014i | 0.986332 | − | 0.164768i | \(-0.0526877\pi\) |
−0.861485 | + | 0.507782i | \(0.830465\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.83750 | − | 27.4349i | −0.189017 | − | 1.07197i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | 16.9976 | + | 4.33256i | 0.663140 | + | 0.169029i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 5.15867 | − | 14.1733i | 0.200953 | − | 0.552114i | −0.797752 | − | 0.602986i | \(-0.793978\pi\) |
0.998705 | + | 0.0508713i | \(0.0161998\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −7.27008 | + | 8.66414i | −0.282773 | + | 0.336996i | −0.888670 | − | 0.458547i | \(-0.848370\pi\) |
0.605897 | + | 0.795543i | \(0.292814\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 4.36453 | + | 4.70500i | 0.169504 | + | 0.182727i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 31.5076 | − | 54.5727i | 1.22181 | − | 2.11624i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −14.0037 | + | 8.08503i | −0.542225 | + | 0.313054i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 4.54994 | + | 7.04659i | 0.175911 | + | 0.272437i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −1.22549 | + | 6.95008i | −0.0473094 | + | 0.268305i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.6114 | + | 13.0996i | −0.601777 | + | 0.504951i | −0.892016 | − | 0.452003i | \(-0.850710\pi\) |
0.290239 | + | 0.956954i | \(0.406265\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −2.73535 | − | 8.15129i | −0.105284 | − | 0.313743i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.6992 | − | 22.2848i | −0.718668 | − | 0.856475i | 0.275833 | − | 0.961206i | \(-0.411046\pi\) |
−0.994501 | + | 0.104731i | \(0.966602\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | −13.8530 | + | 78.5643i | −0.531630 | + | 3.01502i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 1.71856 | + | 34.5196i | 0.0658554 | + | 1.32279i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 19.5414 | − | 11.2822i | 0.747730 | − | 0.431702i | −0.0771431 | − | 0.997020i | \(-0.524580\pi\) |
0.824873 | + | 0.565318i | \(0.191247\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 37.2734 | + | 21.5198i | 1.42414 | + | 0.822229i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0.311332 | − | 1.00888i | 0.0118781 | − | 0.0384910i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | −8.87147 | − | 7.44405i | −0.337976 | − | 0.283596i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −7.19879 | + | 19.7785i | −0.273855 | + | 0.752410i | 0.724172 | + | 0.689620i | \(0.242222\pi\) |
−0.998027 | + | 0.0627907i | \(0.980000\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −21.7401 | + | 15.6220i | −0.825839 | + | 0.593431i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 7.16886 | + | 40.6566i | 0.271930 | + | 1.54219i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 4.05319 | − | 1.47524i | 0.153525 | − | 0.0558787i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.30526 | − | 10.4054i | 0.0493693 | − | 0.393567i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 2.33170i | − | 0.0880670i | −0.999030 | − | 0.0440335i | \(-0.985979\pi\) | ||
0.999030 | − | 0.0440335i | \(-0.0140208\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 37.1415 | 1.40082 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | −32.5266 | + | 42.9301i | −1.22502 | + | 1.61684i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | −4.31477 | − | 11.8547i | −0.162274 | − | 0.445843i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 38.0666 | − | 6.71217i | 1.42962 | − | 0.252081i | 0.595364 | − | 0.803456i | \(-0.297008\pi\) |
0.834257 | + | 0.551375i | \(0.185897\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −0.530386 | + | 7.05430i | −0.0198910 | + | 0.264557i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 13.5627 | + | 4.93643i | 0.507929 | + | 0.184871i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 10.2492 | − | 12.2145i | 0.383297 | − | 0.456795i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 4.09938 | + | 17.9707i | 0.153094 | + | 0.671128i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | −0.0699843 | + | 0.121216i | −0.00260997 | + | 0.00452061i | −0.867327 | − | 0.497738i | \(-0.834164\pi\) |
0.864717 | + | 0.502259i | \(0.167497\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 36.5898 | + | 63.3753i | 1.36267 | + | 2.36022i | ||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −2.00494 | + | 3.90960i | −0.0745646 | + | 0.145400i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | −8.15702 | − | 1.43830i | −0.302944 | − | 0.0534172i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 3.66655 | − | 3.07660i | 0.135985 | − | 0.114105i | −0.572258 | − | 0.820073i | \(-0.693933\pi\) |
0.708243 | + | 0.705969i | \(0.249488\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −19.7789 | − | 18.3792i | −0.732551 | − | 0.680712i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 4.06674 | + | 4.84655i | 0.150414 | + | 0.179256i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −46.3266 | − | 8.16862i | −1.71111 | − | 0.301715i | −0.769557 | − | 0.638578i | \(-0.779523\pi\) |
−0.941553 | + | 0.336864i | \(0.890634\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −60.5960 | − | 31.0751i | −2.23512 | − | 1.14622i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 1.23070 | + | 2.13164i | 0.0453335 | + | 0.0785199i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −12.2180 | − | 7.05405i | −0.449446 | − | 0.259487i | 0.258150 | − | 0.966105i | \(-0.416887\pi\) |
−0.707596 | + | 0.706617i | \(0.750220\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 6.51770 | + | 28.5721i | 0.239434 | + | 1.04962i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −30.5037 | − | 25.5956i | −1.11907 | − | 0.939013i | −0.120514 | − | 0.992712i | \(-0.538454\pi\) |
−0.998557 | + | 0.0536990i | \(0.982899\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 4.24042 | + | 1.54339i | 0.155357 | + | 0.0565453i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 41.2617 | + | 3.10231i | 1.50969 | + | 0.113508i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 53.4829 | − | 9.43048i | 1.95422 | − | 0.344582i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.2150 | − | 7.72164i | 0.774147 | − | 0.281766i | 0.0754172 | − | 0.997152i | \(-0.475971\pi\) |
0.698730 | + | 0.715386i | \(0.253749\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 11.7653 | − | 15.5284i | 0.428751 | − | 0.565886i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | − | 5.17774i | − | 0.188437i | ||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | − | 18.5219i | − | 0.673188i | −0.941650 | − | 0.336594i | \(-0.890725\pi\) | ||
0.941650 | − | 0.336594i | \(-0.109275\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −10.5046 | − | 1.31771i | −0.381293 | − | 0.0478297i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 44.9798 | − | 16.3713i | 1.63052 | − | 0.593460i | 0.645173 | − | 0.764037i | \(-0.276785\pi\) |
0.985344 | + | 0.170577i | \(0.0545632\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −74.1029 | + | 13.0663i | −2.68270 | + | 0.473033i | ||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 7.12862 | − | 5.12248i | 0.257736 | − | 0.185203i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | 38.5369 | + | 14.0263i | 1.39149 | + | 0.506460i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26.8445 | − | 22.5252i | −0.968039 | − | 0.812281i | 0.0142034 | − | 0.999899i | \(-0.495479\pi\) |
−0.982242 | + | 0.187618i | \(0.939923\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 11.6752 | + | 3.60290i | 0.420473 | + | 0.129755i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | 33.2570 | + | 19.2010i | 1.19617 | + | 0.690610i | 0.959700 | − | 0.281028i | \(-0.0906754\pi\) |
0.236472 | + | 0.971638i | \(0.424009\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 3.69658 | + | 6.40266i | 0.132785 | + | 0.229990i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −2.91245 | − | 58.5005i | −0.104484 | − | 2.09869i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 19.3974 | + | 3.42029i | 0.694984 | + | 0.122544i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −7.11495 | − | 8.47927i | −0.254593 | − | 0.303412i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −24.6590 | + | 8.27488i | −0.881240 | + | 0.295720i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −13.5224 | + | 11.3466i | −0.482635 | + | 0.404979i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 41.3365 | + | 7.28874i | 1.47349 | + | 0.259816i | 0.851972 | − | 0.523587i | \(-0.175406\pi\) |
0.621515 | + | 0.783402i | \(0.286518\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 27.2519 | + | 42.2055i | 0.970193 | + | 1.50256i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 2.02172 | + | 3.50173i | 0.0718842 | + | 0.124507i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 6.09173 | − | 10.5512i | 0.216324 | − | 0.374684i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −11.6133 | + | 10.7729i | −0.411881 | + | 0.382076i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | −0.294996 | + | 0.351563i | −0.0104493 | + | 0.0124530i | −0.771244 | − | 0.636540i | \(-0.780365\pi\) |
0.760794 | + | 0.648993i | \(0.224810\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −12.8485 | − | 4.67649i | −0.454549 | − | 0.165442i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 1.76124 | + | 0.448926i | 0.0622303 | + | 0.0158620i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 10.8956 | − | 1.92118i | 0.384496 | − | 0.0677970i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −13.4413 | − | 36.9297i | −0.473745 | − | 1.30160i | ||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 9.65526 | + | 22.9128i | 0.339881 | + | 0.806570i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 29.3388 | 1.03150 | 0.515749 | − | 0.856740i | \(-0.327514\pi\) | ||||
0.515749 | + | 0.856740i | \(0.327514\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 9.18827i | − | 0.322644i | −0.986902 | − | 0.161322i | \(-0.948424\pi\) | ||
0.986902 | − | 0.161322i | \(-0.0515757\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 25.5033 | − | 10.7469i | 0.894440 | − | 0.376909i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −16.6279 | + | 6.05206i | −0.582450 | + | 0.211994i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 5.01684 | + | 28.4519i | 0.175517 | + | 0.995407i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 44.4920 | − | 12.5063i | 1.55468 | − | 0.437007i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −14.5843 | + | 40.0700i | −0.508995 | + | 1.39845i | 0.373280 | + | 0.927719i | \(0.378233\pi\) |
−0.882275 | + | 0.470734i | \(0.843989\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −5.98871 | − | 5.02513i | −0.208753 | − | 0.175165i | 0.532416 | − | 0.846483i | \(-0.321284\pi\) |
−0.741170 | + | 0.671318i | \(0.765729\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −3.68808 | − | 3.97579i | −0.128403 | − | 0.138419i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 12.5094 | + | 7.22230i | 0.434994 | + | 0.251144i | 0.701472 | − | 0.712697i | \(-0.252527\pi\) |
−0.266478 | + | 0.963841i | \(0.585860\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 14.0046 | − | 8.08556i | 0.486400 | − | 0.280823i | −0.236680 | − | 0.971588i | \(-0.576059\pi\) |
0.723080 | + | 0.690765i | \(0.242726\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 10.9480 | − | 7.06910i | 0.379784 | − | 0.245224i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 3.00200 | − | 17.0252i | 0.104013 | − | 0.589888i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 11.9802 | + | 14.2774i | 0.414590 | + | 0.494089i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 19.8059 | + | 12.1132i | 0.684594 | + | 0.418692i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 41.0275 | − | 34.4262i | 1.41643 | − | 1.18852i | 0.463205 | − | 0.886251i | \(-0.346700\pi\) |
0.953222 | − | 0.302271i | \(-0.0977449\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 0.684700 | − | 3.88313i | 0.0236103 | − | 0.133901i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 16.2989 | − | 0.811439i | 0.561362 | − | 0.0279475i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 5.20400 | − | 3.00453i | 0.179023 | − | 0.103359i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 17.4958 | − | 30.3036i | 0.601162 | − | 1.04124i | ||||
\(848\) | 0 | 0 | ||||||||
\(849\) | 12.6252 | − | 40.9120i | 0.433295 | − | 1.40410i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 14.8892 | − | 17.7443i | 0.510396 | − | 0.608267i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 1.62827 | − | 4.47364i | 0.0557509 | − | 0.153174i | −0.908691 | − | 0.417469i | \(-0.862917\pi\) |
0.964442 | + | 0.264295i | \(0.0851393\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 39.8872 | − | 3.98144i | 1.36411 | − | 0.136163i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 3.69992 | + | 20.9833i | 0.126387 | + | 0.716775i | 0.980475 | + | 0.196646i | \(0.0630050\pi\) |
−0.854088 | + | 0.520129i | \(0.825884\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 0.568591 | + | 1.56219i | 0.0194001 | + | 0.0533013i | 0.949015 | − | 0.315232i | \(-0.102082\pi\) |
−0.929615 | + | 0.368533i | \(0.879860\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 3.86615 | − | 30.8205i | 0.131758 | − | 1.05036i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 4.65067 | 0.158311 | 0.0791554 | − | 0.996862i | \(-0.474778\pi\) | ||||
0.0791554 | + | 0.996862i | \(0.474778\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −17.7276 | −0.602757 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | −21.6931 | − | 16.4361i | −0.736736 | − | 0.558198i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 1.52606 | + | 4.19281i | 0.0517680 | + | 0.142231i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −0.737879 | − | 4.18472i | −0.0250021 | − | 0.141794i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −45.7274 | + | 22.0074i | −1.54764 | + | 0.744836i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | −13.9198 | + | 38.2442i | −0.470574 | + | 1.29289i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −28.6728 | + | 34.1709i | −0.968211 | + | 1.15387i | 0.0198497 | + | 0.999803i | \(0.493681\pi\) |
−0.988061 | + | 0.154066i | \(0.950763\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 13.1022 | − | 2.98880i | 0.441926 | − | 0.100810i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −11.4635 | + | 19.8554i | −0.386215 | + | 0.668944i | −0.991937 | − | 0.126732i | \(-0.959551\pi\) |
0.605722 | + | 0.795676i | \(0.292884\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 30.6898 | − | 17.7188i | 1.03279 | − | 0.596284i | 0.115010 | − | 0.993364i | \(-0.463310\pi\) |
0.917784 | + | 0.397081i | \(0.129977\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 25.5971 | − | 49.9138i | 0.860436 | − | 1.67784i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.26510 | − | 29.8598i | 0.176785 | − | 1.00260i | −0.759279 | − | 0.650765i | \(-0.774448\pi\) |
0.936064 | − | 0.351830i | \(-0.114441\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −7.75213 | + | 6.50481i | −0.259998 | + | 0.218164i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −16.1402 | − | 5.43162i | −0.540716 | − | 0.181966i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −40.1344 | − | 47.8303i | −1.34305 | − | 1.60058i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −1.09160 | + | 6.19076i | −0.0364881 | + | 0.206934i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.2631 | + | 8.34011i | 0.543008 | + | 0.278468i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 19.3691 | − | 11.1827i | 0.645995 | − | 0.372965i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.48256 | − | 2.01066i | −0.116021 | − | 0.0669847i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 44.4204 | − | 10.1329i | 1.47822 | − | 0.337203i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −48.2745 | − | 40.5071i | −1.60470 | − | 1.34650i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.25848 | − | 17.1950i | 0.207809 | − | 0.570951i | −0.791375 | − | 0.611331i | \(-0.790634\pi\) |
0.999184 | + | 0.0403795i | \(0.0128567\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | 4.52230 | − | 6.62950i | 0.149995 | − | 0.219887i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 6.84735 | + | 38.8333i | 0.226863 | + | 1.28660i | 0.859092 | + | 0.511822i | \(0.171029\pi\) |
−0.632229 | + | 0.774782i | \(0.717860\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 24.5244 | − | 8.92615i | 0.811639 | − | 0.295413i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −13.2828 | − | 10.0639i | −0.439117 | − | 0.332703i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 50.9292i | − | 1.68183i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −28.0411 | −0.924991 | −0.462496 | − | 0.886622i | \(-0.653046\pi\) | ||||
−0.462496 | + | 0.886622i | \(0.653046\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 22.1109 | + | 2.77361i | 0.728579 | + | 0.0913935i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 6.53564 | + | 17.9565i | 0.215123 | + | 0.591046i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 11.6849 | − | 2.06036i | 0.384197 | − | 0.0677443i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −19.1563 | + | 42.4271i | −0.629177 | + | 1.39349i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 48.6959 | + | 17.7239i | 1.59766 | + | 0.581501i | 0.978947 | − | 0.204115i | \(-0.0654317\pi\) |
0.618714 | + | 0.785616i | \(0.287654\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 50.7445 | − | 60.4749i | 1.66308 | − | 1.98199i | ||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −26.8047 | − | 8.27176i | −0.877547 | − | 0.270805i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 2.76832 | − | 4.79488i | 0.0905339 | − | 0.156809i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 24.4737 | + | 42.3897i | 0.799522 | + | 1.38481i | 0.919928 | + | 0.392088i | \(0.128247\pi\) |
−0.120406 | + | 0.992725i | \(0.538420\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 1.92719 | − | 0.0959452i | 0.0628914 | − | 0.00313105i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 57.1903 | + | 10.0842i | 1.86435 | + | 0.328735i | 0.988184 | − | 0.153271i | \(-0.0489808\pi\) |
0.876167 | + | 0.482007i | \(0.160092\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.41005 | − | 7.89597i | 0.306433 | − | 0.257128i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −9.39882 | − | 62.5131i | −0.305744 | − | 2.03355i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −22.0563 | − | 26.2856i | −0.716732 | − | 0.854168i | 0.277577 | − | 0.960703i | \(-0.410469\pi\) |
−0.994309 | + | 0.106535i | \(0.966024\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −18.8097 | − | 3.31665i | −0.610588 | − | 0.107663i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.29821 | − | 1.48394i | 0.0745246 | − | 0.0481202i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 5.11095 | + | 8.85243i | 0.165560 | + | 0.286758i | 0.936854 | − | 0.349721i | \(-0.113724\pi\) |
−0.771294 | + | 0.636479i | \(0.780390\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 1.41077 | + | 0.814508i | 0.0456514 | + | 0.0263569i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.0274 | + | 11.1570i | −0.388790 | + | 0.360656i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 60.2751 | + | 50.5768i | 1.94638 | + | 1.63321i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 10.3713 | + | 3.77484i | 0.334557 | + | 0.121769i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 24.7249 | + | 24.1278i | 0.796748 | + | 0.777507i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | −52.6878 | + | 9.29028i | −1.69608 | + | 0.299065i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −28.7380 | + | 10.4598i | −0.924151 | + | 0.336364i | −0.759889 | − | 0.650053i | \(-0.774747\pi\) |
−0.164262 | + | 0.986417i | \(0.552524\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 3.95162 | + | 9.37756i | 0.126944 | + | 0.301250i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | − | 47.4592i | − | 1.52304i | −0.648142 | − | 0.761519i | \(-0.724454\pi\) | ||
0.648142 | − | 0.761519i | \(-0.275546\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 75.4736i | 2.41957i | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 3.63549 | + | 8.62735i | 0.116429 | + | 0.276296i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −28.5748 | + | 10.4004i | −0.914189 | + | 0.332737i | −0.755924 | − | 0.654659i | \(-0.772812\pi\) |
−0.158264 | + | 0.987397i | \(0.550590\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 1.12896 | − | 0.199066i | 0.0360818 | − | 0.00636219i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −34.2574 | − | 33.4301i | −1.09375 | − | 1.06734i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | −50.6147 | − | 18.4222i | −1.61436 | − | 0.587578i | −0.632063 | − | 0.774917i | \(-0.717792\pi\) |
−0.982295 | + | 0.187338i | \(0.940014\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −18.6353 | − | 15.6369i | −0.593770 | − | 0.498232i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −72.1890 | + | 66.9652i | −2.29780 | + | 2.13153i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 15.6040 | + | 9.00898i | 0.496179 | + | 0.286469i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 24.8280 | + | 43.0034i | 0.788688 | + | 1.36605i | 0.926771 | + | 0.375627i | \(0.122573\pi\) |
−0.138083 | + | 0.990421i | \(0.544094\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −18.1290 | + | 11.7058i | −0.575307 | + | 0.371473i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 7.93949 | + | 1.39995i | 0.251699 | + | 0.0443813i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 11.6323 | + | 13.8628i | 0.368398 | + | 0.439040i | 0.918117 | − | 0.396310i | \(-0.129709\pi\) |
−0.549719 | + | 0.835350i | \(0.685265\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 29.1393 | − | 23.2203i | 0.921928 | − | 0.734659i |
(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 | 864.2.bf.a.49.4 | 204 | ||
4.3 | odd | 2 | 216.2.t.a.157.25 | ✓ | 204 | ||
8.3 | odd | 2 | 216.2.t.a.157.30 | yes | 204 | ||
8.5 | even | 2 | inner | 864.2.bf.a.49.31 | 204 | ||
12.11 | even | 2 | 648.2.t.a.37.10 | 204 | |||
24.11 | even | 2 | 648.2.t.a.37.5 | 204 | |||
27.16 | even | 9 | inner | 864.2.bf.a.529.31 | 204 | ||
108.11 | even | 18 | 648.2.t.a.613.5 | 204 | |||
108.43 | odd | 18 | 216.2.t.a.205.30 | yes | 204 | ||
216.11 | even | 18 | 648.2.t.a.613.10 | 204 | |||
216.43 | odd | 18 | 216.2.t.a.205.25 | yes | 204 | ||
216.205 | even | 18 | inner | 864.2.bf.a.529.4 | 204 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
216.2.t.a.157.25 | ✓ | 204 | 4.3 | odd | 2 | ||
216.2.t.a.157.30 | yes | 204 | 8.3 | odd | 2 | ||
216.2.t.a.205.25 | yes | 204 | 216.43 | odd | 18 | ||
216.2.t.a.205.30 | yes | 204 | 108.43 | odd | 18 | ||
648.2.t.a.37.5 | 204 | 24.11 | even | 2 | |||
648.2.t.a.37.10 | 204 | 12.11 | even | 2 | |||
648.2.t.a.613.5 | 204 | 108.11 | even | 18 | |||
648.2.t.a.613.10 | 204 | 216.11 | even | 18 | |||
864.2.bf.a.49.4 | 204 | 1.1 | even | 1 | trivial | ||
864.2.bf.a.49.31 | 204 | 8.5 | even | 2 | inner | ||
864.2.bf.a.529.4 | 204 | 216.205 | even | 18 | inner | ||
864.2.bf.a.529.31 | 204 | 27.16 | even | 9 | inner |