Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [405,2,Mod(19,405)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(405, base_ring=CyclotomicField(18))
chi = DirichletCharacter(H, H._module([16, 9]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("405.19");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 405 = 3^{4} \cdot 5 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 405.p (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: | \(3.23394128186\) |
Analytic rank: | \(0\) |
Dimension: | \(96\) |
Relative dimension: | \(16\) over \(\Q(\zeta_{18})\) |
Twist minimal: | no (minimal twist has level 135) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{18}]$ |
Embedding invariants
Embedding label | 289.8 | ||
Character | \(\chi\) | \(=\) | 405.289 |
Dual form | 405.2.p.a.199.8 |
$q$-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 \(\left(\mathbb{Z}/405\mathbb{Z}\right)^\times\).
\(n\) | \(82\) | \(326\) |
\(\chi(n)\) | \(-1\) | \(e\left(\frac{2}{9}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.133405 | + | 0.158986i | −0.0943314 | + | 0.112420i | −0.811145 | − | 0.584845i | \(-0.801155\pi\) |
0.716814 | + | 0.697265i | \(0.245600\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 0.339817 | + | 1.92720i | 0.169908 | + | 0.963598i | ||||
\(5\) | −1.06091 | + | 1.96837i | −0.474452 | + | 0.880282i | ||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −2.83580 | − | 0.500029i | −1.07183 | − | 0.188993i | −0.390232 | − | 0.920717i | \(-0.627605\pi\) |
−0.681602 | + | 0.731724i | \(0.738716\pi\) | |||||||
\(8\) | −0.711201 | − | 0.410612i | −0.251448 | − | 0.145173i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −0.171413 | − | 0.431259i | −0.0542054 | − | 0.136376i | ||||
\(11\) | −1.38169 | + | 0.502894i | −0.416595 | + | 0.151628i | −0.541809 | − | 0.840502i | \(-0.682260\pi\) |
0.125214 | + | 0.992130i | \(0.460038\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.55650 | − | 1.85496i | −0.431695 | − | 0.514474i | 0.505715 | − | 0.862700i | \(-0.331229\pi\) |
−0.937411 | + | 0.348226i | \(0.886784\pi\) | |||||||
\(14\) | 0.457807 | − | 0.384146i | 0.122354 | − | 0.102667i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −3.51766 | + | 1.28032i | −0.879415 | + | 0.320081i | ||||
\(17\) | −1.21975 | + | 0.704220i | −0.295832 | + | 0.170799i | −0.640569 | − | 0.767901i | \(-0.721301\pi\) |
0.344737 | + | 0.938699i | \(0.387968\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 2.34516 | − | 4.06194i | 0.538017 | − | 0.931872i | −0.460994 | − | 0.887403i | \(-0.652507\pi\) |
0.999011 | − | 0.0444689i | \(-0.0141595\pi\) | |||||||
\(20\) | −4.15395 | − | 1.37569i | −0.928851 | − | 0.307613i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.104371 | − | 0.286757i | 0.0222520 | − | 0.0611368i | ||||
\(23\) | −2.36796 | + | 0.417535i | −0.493753 | + | 0.0870620i | −0.414980 | − | 0.909831i | \(-0.636211\pi\) |
−0.0787733 | + | 0.996893i | \(0.525100\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −2.74896 | − | 4.17651i | −0.549791 | − | 0.835302i | ||||
\(26\) | 0.502557 | 0.0985595 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | − | 5.63507i | − | 1.06493i | ||||||
\(29\) | 6.73596 | + | 5.65214i | 1.25084 | + | 1.04958i | 0.996596 | + | 0.0824353i | \(0.0262698\pi\) |
0.254240 | + | 0.967141i | \(0.418175\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.00865 | + | 5.72033i | 0.181159 | + | 1.02740i | 0.930792 | + | 0.365549i | \(0.119119\pi\) |
−0.749634 | + | 0.661853i | \(0.769770\pi\) | |||||||
\(32\) | 0.827470 | − | 2.27346i | 0.146277 | − | 0.401894i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 0.0507589 | − | 0.287868i | 0.00870509 | − | 0.0493690i | ||||
\(35\) | 3.99276 | − | 5.05143i | 0.674900 | − | 0.853847i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −7.57034 | + | 4.37074i | −1.24456 | + | 0.718545i | −0.970019 | − | 0.243031i | \(-0.921858\pi\) |
−0.274538 | + | 0.961576i | \(0.588525\pi\) | |||||||
\(38\) | 0.332934 | + | 0.914728i | 0.0540090 | + | 0.148388i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.56275 | − | 0.964286i | 0.247093 | − | 0.152467i | ||||
\(41\) | −8.32538 | + | 6.98582i | −1.30021 | + | 1.09100i | −0.310096 | + | 0.950705i | \(0.600361\pi\) |
−0.990110 | + | 0.140297i | \(0.955194\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.63439 | + | 7.23793i | 0.401741 | + | 1.10377i | 0.961425 | + | 0.275068i | \(0.0887003\pi\) |
−0.559684 | + | 0.828706i | \(0.689077\pi\) | |||||||
\(44\) | −1.43870 | − | 2.49190i | −0.216892 | − | 0.375667i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 0.249515 | − | 0.432172i | 0.0367889 | − | 0.0637203i | ||||
\(47\) | 6.68918 | + | 1.17948i | 0.975717 | + | 0.172045i | 0.638702 | − | 0.769454i | \(-0.279472\pi\) |
0.337015 | + | 0.941499i | \(0.390583\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 1.21391 | + | 0.441827i | 0.173416 | + | 0.0631181i | ||||
\(50\) | 1.03073 | + | 0.120122i | 0.145767 | + | 0.0169878i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 3.04596 | − | 3.63003i | 0.422398 | − | 0.503394i | ||||
\(53\) | 5.43934i | 0.747151i | 0.927600 | + | 0.373575i | \(0.121868\pi\) | ||||
−0.927600 | + | 0.373575i | \(0.878132\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.475961 | − | 3.25320i | 0.0641786 | − | 0.438661i | ||||
\(56\) | 1.81151 | + | 1.52004i | 0.242073 | + | 0.203123i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −1.79722 | + | 0.316898i | −0.235986 | + | 0.0416108i | ||||
\(59\) | −6.83272 | − | 2.48691i | −0.889545 | − | 0.323768i | −0.143489 | − | 0.989652i | \(-0.545832\pi\) |
−0.746055 | + | 0.665884i | \(0.768055\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.03952 | + | 5.89541i | −0.133097 | + | 0.754830i | 0.843069 | + | 0.537805i | \(0.180746\pi\) |
−0.976166 | + | 0.217025i | \(0.930365\pi\) | |||||||
\(62\) | −1.04401 | − | 0.602759i | −0.132589 | − | 0.0765504i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −3.49236 | − | 6.04894i | −0.436545 | − | 0.756118i | ||||
\(65\) | 5.30255 | − | 1.09582i | 0.657701 | − | 0.135920i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 4.95280 | + | 5.90251i | 0.605081 | + | 0.721107i | 0.978429 | − | 0.206584i | \(-0.0662348\pi\) |
−0.373348 | + | 0.927691i | \(0.621790\pi\) | |||||||
\(68\) | −1.77166 | − | 2.11138i | −0.214845 | − | 0.256043i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0.270451 | + | 1.30868i | 0.0323250 | + | 0.156417i | ||||
\(71\) | −4.51802 | − | 7.82544i | −0.536190 | − | 0.928708i | −0.999105 | − | 0.0423056i | \(-0.986530\pi\) |
0.462915 | − | 0.886403i | \(-0.346804\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 10.8910 | + | 6.28791i | 1.27469 | + | 0.735944i | 0.975867 | − | 0.218364i | \(-0.0700721\pi\) |
0.298825 | + | 0.954308i | \(0.403405\pi\) | |||||||
\(74\) | 0.315035 | − | 1.78665i | 0.0366221 | − | 0.207694i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 8.62507 | + | 3.13927i | 0.989364 | + | 0.360099i | ||||
\(77\) | 4.16966 | − | 0.735224i | 0.475177 | − | 0.0837865i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −1.14861 | − | 0.963795i | −0.129228 | − | 0.108435i | 0.575883 | − | 0.817532i | \(-0.304658\pi\) |
−0.705111 | + | 0.709097i | \(0.749103\pi\) | |||||||
\(80\) | 1.21176 | − | 8.28236i | 0.135478 | − | 0.925996i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | − | 2.25556i | − | 0.249085i | ||||||
\(83\) | 7.46590 | − | 8.89751i | 0.819489 | − | 0.976629i | −0.180487 | − | 0.983577i | \(-0.557767\pi\) |
0.999976 | + | 0.00694857i | \(0.00221182\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.0921308 | − | 3.14802i | −0.00999299 | − | 0.341451i | ||||
\(86\) | −1.50217 | − | 0.546744i | −0.161983 | − | 0.0589569i | ||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 1.18915 | + | 0.209680i | 0.126764 | + | 0.0223519i | ||||
\(89\) | 5.96766 | − | 10.3363i | 0.632571 | − | 1.09564i | −0.354454 | − | 0.935074i | \(-0.615333\pi\) |
0.987024 | − | 0.160571i | \(-0.0513336\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 3.48639 | + | 6.03861i | 0.365473 | + | 0.633018i | ||||
\(92\) | −1.60934 | − | 4.42164i | −0.167786 | − | 0.460987i | ||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −1.07989 | + | 0.906134i | −0.111382 | + | 0.0934606i | ||||
\(95\) | 5.50740 | + | 8.92547i | 0.565047 | + | 0.915734i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −1.92260 | − | 5.28231i | −0.195211 | − | 0.536337i | 0.803010 | − | 0.595966i | \(-0.203231\pi\) |
−0.998221 | + | 0.0596285i | \(0.981008\pi\) | |||||||
\(98\) | −0.232185 | + | 0.134052i | −0.0234543 | + | 0.0135413i | ||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 7.11481 | − | 6.71703i | 0.711481 | − | 0.671703i | ||||
\(101\) | −1.86284 | + | 10.5647i | −0.185360 | + | 1.05123i | 0.740133 | + | 0.672461i | \(0.234763\pi\) |
−0.925492 | + | 0.378766i | \(0.876348\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −0.183395 | + | 0.503873i | −0.0180704 | + | 0.0496480i | −0.948400 | − | 0.317077i | \(-0.897299\pi\) |
0.930329 | + | 0.366725i | \(0.119521\pi\) | |||||||
\(104\) | 0.345313 | + | 1.95837i | 0.0338608 | + | 0.192034i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −0.864777 | − | 0.725634i | −0.0839945 | − | 0.0704798i | ||||
\(107\) | − | 2.82482i | − | 0.273086i | −0.990634 | − | 0.136543i | \(-0.956401\pi\) | ||
0.990634 | − | 0.136543i | \(-0.0435992\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −0.479801 | −0.0459566 | −0.0229783 | − | 0.999736i | \(-0.507315\pi\) | ||||
−0.0229783 | + | 0.999736i | \(0.507315\pi\) | |||||||
\(110\) | 0.453716 | + | 0.509663i | 0.0432601 | + | 0.0485945i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 10.6156 | − | 1.87182i | 1.00308 | − | 0.176870i | ||||
\(113\) | 1.45557 | − | 3.99915i | 0.136928 | − | 0.376208i | −0.852209 | − | 0.523202i | \(-0.824737\pi\) |
0.989137 | + | 0.146994i | \(0.0469597\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | 1.69032 | − | 5.10398i | 0.157623 | − | 0.475949i | ||||
\(116\) | −8.60380 | + | 14.9022i | −0.798843 | + | 1.38364i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 1.30690 | − | 0.754539i | 0.120310 | − | 0.0694609i | ||||
\(119\) | 3.81109 | − | 1.38712i | 0.349362 | − | 0.127157i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −6.77033 | + | 5.68098i | −0.615484 | + | 0.516453i | ||||
\(122\) | −0.798608 | − | 0.951744i | −0.0723026 | − | 0.0861669i | ||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −10.6814 | + | 3.88773i | −0.959222 | + | 0.349128i | ||||
\(125\) | 11.1373 | − | 0.980081i | 0.996150 | − | 0.0876611i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 10.4667 | + | 6.04293i | 0.928765 | + | 0.536223i | 0.886421 | − | 0.462880i | \(-0.153184\pi\) |
0.0423444 | + | 0.999103i | \(0.486517\pi\) | |||||||
\(128\) | 6.19280 | + | 1.09196i | 0.547371 | + | 0.0965164i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −0.533166 | + | 0.989218i | −0.0467617 | + | 0.0867601i | ||||
\(131\) | −0.0451328 | − | 0.255961i | −0.00394327 | − | 0.0223634i | 0.982773 | − | 0.184819i | \(-0.0591698\pi\) |
−0.986716 | + | 0.162455i | \(0.948059\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −8.68150 | + | 10.3462i | −0.752781 | + | 0.897130i | ||||
\(134\) | −1.59914 | −0.138145 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.15665 | 0.0991816 | ||||||||
\(137\) | −12.0038 | + | 14.3056i | −1.02555 | + | 1.22221i | −0.0508517 | + | 0.998706i | \(0.516194\pi\) |
−0.974703 | + | 0.223503i | \(0.928251\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.20743 | − | 6.84769i | −0.102413 | − | 0.580813i | −0.992222 | − | 0.124480i | \(-0.960274\pi\) |
0.889809 | − | 0.456333i | \(-0.150837\pi\) | |||||||
\(140\) | 11.0919 | + | 5.97828i | 0.937437 | + | 0.505257i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 1.84686 | + | 0.325651i | 0.154985 | + | 0.0273280i | ||||
\(143\) | 3.08345 | + | 1.78023i | 0.257851 | + | 0.148870i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | −18.2717 | + | 7.26247i | −1.51738 | + | 0.603115i | ||||
\(146\) | −2.45259 | + | 0.892671i | −0.202978 | + | 0.0738780i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −10.9958 | − | 13.1043i | −0.903850 | − | 1.07717i | ||||
\(149\) | 6.29367 | − | 5.28102i | 0.515598 | − | 0.432638i | −0.347496 | − | 0.937681i | \(-0.612968\pi\) |
0.863094 | + | 0.505044i | \(0.168524\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.32039 | − | 3.02837i | 0.677103 | − | 0.246445i | 0.0195001 | − | 0.999810i | \(-0.493793\pi\) |
0.657603 | + | 0.753364i | \(0.271570\pi\) | |||||||
\(152\) | −3.33576 | + | 1.92590i | −0.270566 | + | 0.156211i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | −0.439363 | + | 0.760998i | −0.0354049 | + | 0.0613230i | ||||
\(155\) | −12.3298 | − | 4.08334i | −0.990354 | − | 0.327982i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 2.12942 | − | 5.85053i | 0.169946 | − | 0.466923i | −0.825256 | − | 0.564758i | \(-0.808969\pi\) |
0.995203 | + | 0.0978347i | \(0.0311917\pi\) | |||||||
\(158\) | 0.306459 | − | 0.0540370i | 0.0243806 | − | 0.00429895i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 3.59713 | + | 4.04069i | 0.284378 | + | 0.319445i | ||||
\(161\) | 6.92384 | 0.545675 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | − | 20.6617i | − | 1.61835i | −0.587569 | − | 0.809174i | \(-0.699915\pi\) | ||
0.587569 | − | 0.809174i | \(-0.300085\pi\) | |||||||
\(164\) | −16.2922 | − | 13.6707i | −1.27220 | − | 1.06751i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 0.418590 | + | 2.37394i | 0.0324889 | + | 0.184254i | ||||
\(167\) | −2.14444 | + | 5.89179i | −0.165942 | + | 0.455921i | −0.994594 | − | 0.103843i | \(-0.966886\pi\) |
0.828652 | + | 0.559764i | \(0.189108\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 1.23923 | − | 7.02800i | 0.0953251 | − | 0.540615i | ||||
\(170\) | 0.512781 | + | 0.405314i | 0.0393285 | + | 0.0310861i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −13.0537 | + | 7.53656i | −0.995336 | + | 0.574657i | ||||
\(173\) | 1.35761 | + | 3.72999i | 0.103217 | + | 0.283586i | 0.980542 | − | 0.196311i | \(-0.0628963\pi\) |
−0.877325 | + | 0.479897i | \(0.840674\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 5.70713 | + | 13.2183i | 0.431419 | + | 0.999211i | ||||
\(176\) | 4.21645 | − | 3.53802i | 0.317827 | − | 0.266688i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 0.847207 | + | 2.32768i | 0.0635008 | + | 0.174467i | ||||
\(179\) | 7.02005 | + | 12.1591i | 0.524703 | + | 0.908813i | 0.999586 | + | 0.0287637i | \(0.00915704\pi\) |
−0.474883 | + | 0.880049i | \(0.657510\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −3.31514 | + | 5.74198i | −0.246412 | + | 0.426798i | −0.962528 | − | 0.271183i | \(-0.912585\pi\) |
0.716116 | + | 0.697982i | \(0.245918\pi\) | |||||||
\(182\) | −1.42515 | − | 0.251293i | −0.105639 | − | 0.0186271i | ||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 1.85554 | + | 0.675361i | 0.136792 | + | 0.0497883i | ||||
\(185\) | −0.571809 | − | 19.5382i | −0.0420403 | − | 1.43648i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 1.33116 | − | 1.58642i | 0.0973441 | − | 0.116010i | ||||
\(188\) | 13.2922i | 0.969431i | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −2.15373 | − | 0.315104i | −0.156248 | − | 0.0228600i | ||||
\(191\) | −7.50310 | − | 6.29585i | −0.542905 | − | 0.455552i | 0.329625 | − | 0.944112i | \(-0.393078\pi\) |
−0.872530 | + | 0.488560i | \(0.837522\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −19.1316 | + | 3.37342i | −1.37712 | + | 0.242824i | −0.812710 | − | 0.582668i | \(-0.802009\pi\) |
−0.564414 | + | 0.825492i | \(0.690898\pi\) | |||||||
\(194\) | 1.09630 | + | 0.399019i | 0.0787094 | + | 0.0286479i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −0.438980 | + | 2.48958i | −0.0313557 | + | 0.177827i | ||||
\(197\) | −5.60720 | − | 3.23732i | −0.399497 | − | 0.230649i | 0.286770 | − | 0.957999i | \(-0.407418\pi\) |
−0.686267 | + | 0.727350i | \(0.740752\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 8.61414 | + | 14.9201i | 0.610640 | + | 1.05766i | 0.991133 | + | 0.132875i | \(0.0424210\pi\) |
−0.380493 | + | 0.924784i | \(0.624246\pi\) | |||||||
\(200\) | 0.240136 | + | 4.09909i | 0.0169802 | + | 0.289850i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −1.43112 | − | 1.70555i | −0.100693 | − | 0.120002i | ||||
\(203\) | −16.2756 | − | 19.3965i | −1.14233 | − | 1.36137i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.91824 | − | 23.7987i | −0.343504 | − | 1.66217i | ||||
\(206\) | −0.0556428 | − | 0.0963761i | −0.00387681 | − | 0.00671484i | ||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 7.85019 | + | 4.53231i | 0.544313 | + | 0.314259i | ||||
\(209\) | −1.19756 | + | 6.79170i | −0.0828369 | + | 0.469792i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −18.9632 | − | 6.90203i | −1.30548 | − | 0.475156i | −0.406702 | − | 0.913561i | \(-0.633321\pi\) |
−0.898777 | + | 0.438405i | \(0.855543\pi\) | |||||||
\(212\) | −10.4827 | + | 1.84838i | −0.719953 | + | 0.126947i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 0.449106 | + | 0.376845i | 0.0307003 | + | 0.0257606i | ||||
\(215\) | −17.0418 | − | 2.49331i | −1.16224 | − | 0.170042i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | − | 16.7261i | − | 1.13544i | ||||||
\(218\) | 0.0640078 | − | 0.0762815i | 0.00433515 | − | 0.00516644i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 6.43129 | − | 0.188220i | 0.433598 | − | 0.0126898i | ||||
\(221\) | 3.20484 | + | 1.16647i | 0.215581 | + | 0.0784649i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 9.20020 | + | 1.62224i | 0.616091 | + | 0.108633i | 0.472980 | − | 0.881073i | \(-0.343178\pi\) |
0.143111 | + | 0.989707i | \(0.454289\pi\) | |||||||
\(224\) | −3.48334 | + | 6.03332i | −0.232740 | + | 0.403118i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 0.441627 | + | 0.764920i | 0.0293766 | + | 0.0508817i | ||||
\(227\) | −2.68962 | − | 7.38967i | −0.178516 | − | 0.490470i | 0.817870 | − | 0.575403i | \(-0.195155\pi\) |
−0.996387 | + | 0.0849329i | \(0.972932\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 12.7733 | − | 10.7181i | 0.844086 | − | 0.708272i | −0.114393 | − | 0.993436i | \(-0.536492\pi\) |
0.958479 | + | 0.285163i | \(0.0920478\pi\) | |||||||
\(230\) | 0.585963 | + | 0.949631i | 0.0386373 | + | 0.0626168i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.46978 | − | 6.78568i | −0.162149 | − | 0.445502i | ||||
\(233\) | −25.8565 | + | 14.9283i | −1.69391 | + | 0.977982i | −0.742613 | + | 0.669720i | \(0.766414\pi\) |
−0.951302 | + | 0.308262i | \(0.900253\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −9.41825 | + | 11.9155i | −0.614379 | + | 0.777279i | ||||
\(236\) | 2.47089 | − | 14.0131i | 0.160841 | − | 0.912174i | ||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −0.287885 | + | 0.790957i | −0.0186608 | + | 0.0512701i | ||||
\(239\) | 4.19886 | + | 23.8129i | 0.271602 | + | 1.54033i | 0.749554 | + | 0.661943i | \(0.230268\pi\) |
−0.477952 | + | 0.878386i | \(0.658621\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 11.3477 | + | 9.52183i | 0.730968 | + | 0.613355i | 0.930395 | − | 0.366558i | \(-0.119464\pi\) |
−0.199427 | + | 0.979913i | \(0.563908\pi\) | |||||||
\(242\) | − | 1.83425i | − | 0.117910i | ||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | −11.7149 | −0.749967 | ||||||||
\(245\) | −2.15752 | + | 1.92069i | −0.137839 | + | 0.122708i | ||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −11.1850 | + | 1.97221i | −0.711683 | + | 0.125489i | ||||
\(248\) | 1.63149 | − | 4.48247i | 0.103599 | − | 0.284637i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −1.32995 | + | 1.90142i | −0.0841134 | + | 0.120256i | ||||
\(251\) | −3.98405 | + | 6.90057i | −0.251471 | + | 0.435560i | −0.963931 | − | 0.266152i | \(-0.914248\pi\) |
0.712460 | + | 0.701712i | \(0.247581\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 3.06181 | − | 1.76773i | 0.192494 | − | 0.111137i | ||||
\(254\) | −2.35704 | + | 0.857892i | −0.147894 | + | 0.0538289i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 9.70145 | − | 8.14048i | 0.606341 | − | 0.508780i | ||||
\(257\) | 13.0075 | + | 15.5017i | 0.811386 | + | 0.966972i | 0.999886 | − | 0.0151015i | \(-0.00480713\pi\) |
−0.188500 | + | 0.982073i | \(0.560363\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 23.6535 | − | 8.60917i | 1.46976 | − | 0.534948i | ||||
\(260\) | 3.91377 | + | 9.84668i | 0.242721 | + | 0.610665i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 0.0467150 | + | 0.0269709i | 0.00288606 | + | 0.00166627i | ||||
\(263\) | 21.4662 | + | 3.78508i | 1.32367 | + | 0.233398i | 0.790421 | − | 0.612563i | \(-0.209862\pi\) |
0.533244 | + | 0.845961i | \(0.320973\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −10.7066 | − | 5.77063i | −0.657703 | − | 0.354487i | ||||
\(266\) | −0.486745 | − | 2.76047i | −0.0298442 | − | 0.169255i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −9.69226 | + | 11.5508i | −0.592049 | + | 0.705577i | ||||
\(269\) | 4.34109 | 0.264681 | 0.132341 | − | 0.991204i | \(-0.457751\pi\) | ||||
0.132341 | + | 0.991204i | \(0.457751\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −13.1672 | −0.799852 | −0.399926 | − | 0.916547i | \(-0.630964\pi\) | ||||
−0.399926 | + | 0.916547i | \(0.630964\pi\) | |||||||
\(272\) | 3.38902 | − | 4.03888i | 0.205490 | − | 0.244893i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.673017 | − | 3.81687i | −0.0406584 | − | 0.230585i | ||||
\(275\) | 5.89855 | + | 4.38820i | 0.355696 | + | 0.264619i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 0.500044 | + | 0.0881712i | 0.0300447 | + | 0.00529770i | 0.188650 | − | 0.982044i | \(-0.439589\pi\) |
−0.158606 | + | 0.987342i | \(0.550700\pi\) | |||||||
\(278\) | 1.24976 | + | 0.721550i | 0.0749557 | + | 0.0432757i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | −4.91383 | + | 1.95310i | −0.293658 | + | 0.116720i | ||||
\(281\) | 0.459552 | − | 0.167263i | 0.0274146 | − | 0.00997809i | −0.328276 | − | 0.944582i | \(-0.606468\pi\) |
0.355691 | + | 0.934604i | \(0.384246\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −2.70977 | − | 3.22938i | −0.161079 | − | 0.191967i | 0.679468 | − | 0.733705i | \(-0.262211\pi\) |
−0.840547 | + | 0.541739i | \(0.817766\pi\) | |||||||
\(284\) | 13.5459 | − | 11.3663i | 0.803799 | − | 0.674467i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −0.694377 | + | 0.252733i | −0.0410594 | + | 0.0149444i | ||||
\(287\) | 27.1023 | − | 15.6475i | 1.59980 | − | 0.923642i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −7.50815 | + | 13.0045i | −0.441656 | + | 0.764970i | ||||
\(290\) | 1.28291 | − | 3.87379i | 0.0753349 | − | 0.227477i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −8.41710 | + | 23.1258i | −0.492573 | + | 1.35333i | ||||
\(293\) | −22.7756 | + | 4.01595i | −1.33056 | + | 0.234614i | −0.793315 | − | 0.608811i | \(-0.791647\pi\) |
−0.537247 | + | 0.843425i | \(0.680536\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.1440 | − | 10.8109i | 0.707053 | − | 0.629438i | ||||
\(296\) | 7.17872 | 0.417254 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 1.70512i | 0.0987747i | ||||||||
\(299\) | 4.46024 | + | 3.74258i | 0.257942 | + | 0.216439i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −3.85144 | − | 21.8426i | −0.221994 | − | 1.25899i | ||||
\(302\) | −0.628511 | + | 1.72682i | −0.0361668 | + | 0.0993674i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −3.04888 | + | 17.2911i | −0.174865 | + | 0.991711i | ||||
\(305\) | −10.5015 | − | 8.30063i | −0.601315 | − | 0.475293i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 2.88589 | − | 1.66617i | 0.164706 | − | 0.0950932i | −0.415381 | − | 0.909648i | \(-0.636352\pi\) |
0.580087 | + | 0.814554i | \(0.303018\pi\) | |||||||
\(308\) | 2.83384 | + | 7.78592i | 0.161473 | + | 0.443644i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 2.29405 | − | 1.41552i | 0.130293 | − | 0.0803964i | ||||
\(311\) | 8.46844 | − | 7.10587i | 0.480201 | − | 0.402937i | −0.370298 | − | 0.928913i | \(-0.620744\pi\) |
0.850499 | + | 0.525976i | \(0.176300\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 3.19684 | + | 8.78326i | 0.180696 | + | 0.496459i | 0.996662 | − | 0.0816417i | \(-0.0260163\pi\) |
−0.815965 | + | 0.578101i | \(0.803794\pi\) | |||||||
\(314\) | 0.646076 | + | 1.11904i | 0.0364602 | + | 0.0631509i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.46711 | − | 2.54110i | 0.0825312 | − | 0.142948i | ||||
\(317\) | −26.8303 | − | 4.73090i | −1.50694 | − | 0.265714i | −0.641654 | − | 0.766994i | \(-0.721752\pi\) |
−0.865285 | + | 0.501280i | \(0.832863\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −12.1494 | − | 4.42203i | −0.680238 | − | 0.247586i | ||||
\(320\) | 15.6116 | − | 0.456894i | 0.872716 | − | 0.0255411i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −0.923674 | + | 1.10079i | −0.0514743 | + | 0.0613447i | ||||
\(323\) | 6.60604i | 0.367570i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −3.46852 | + | 11.6000i | −0.192399 | + | 0.643450i | ||||
\(326\) | 3.28491 | + | 2.75637i | 0.181934 | + | 0.152661i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | 8.78948 | − | 1.54982i | 0.485318 | − | 0.0855746i | ||||
\(329\) | −18.3794 | − | 6.68956i | −1.01329 | − | 0.368808i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.40921 | − | 25.0059i | 0.242352 | − | 1.37445i | −0.584210 | − | 0.811602i | \(-0.698596\pi\) |
0.826562 | − | 0.562845i | \(-0.190293\pi\) | |||||||
\(332\) | 19.6843 | + | 11.3647i | 1.08032 | + | 0.623721i | ||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −0.650632 | − | 1.12693i | −0.0356010 | − | 0.0616628i | ||||
\(335\) | −16.8728 | + | 3.48692i | −0.921859 | + | 0.190511i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.09214 | − | 3.68507i | −0.168440 | − | 0.200739i | 0.675221 | − | 0.737616i | \(-0.264048\pi\) |
−0.843661 | + | 0.536877i | \(0.819604\pi\) | |||||||
\(338\) | 0.952032 | + | 1.13459i | 0.0517837 | + | 0.0617134i | ||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 6.03555 | − | 1.24730i | 0.327324 | − | 0.0676446i | ||||
\(341\) | −4.27036 | − | 7.39648i | −0.231253 | − | 0.400542i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 14.2349 | + | 8.21851i | 0.768611 | + | 0.443758i | ||||
\(344\) | 1.09840 | − | 6.22934i | 0.0592218 | − | 0.335863i | ||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −0.774126 | − | 0.281759i | −0.0416173 | − | 0.0151474i | ||||
\(347\) | 23.4852 | − | 4.14108i | 1.26075 | − | 0.222305i | 0.496964 | − | 0.867771i | \(-0.334448\pi\) |
0.763789 | + | 0.645466i | \(0.223337\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 10.1403 | + | 8.50874i | 0.542799 | + | 0.455462i | 0.872494 | − | 0.488625i | \(-0.162501\pi\) |
−0.329695 | + | 0.944087i | \(0.606946\pi\) | |||||||
\(350\) | −2.86288 | − | 0.856035i | −0.153027 | − | 0.0457570i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 3.55734i | 0.189607i | ||||||||
\(353\) | 12.6452 | − | 15.0700i | 0.673036 | − | 0.802093i | −0.316158 | − | 0.948707i | \(-0.602393\pi\) |
0.989194 | + | 0.146614i | \(0.0468375\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.1965 | − | 0.591077i | 1.07192 | − | 0.0313711i | ||||
\(356\) | 21.9480 | + | 7.98841i | 1.16324 | + | 0.423385i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −2.86963 | − | 0.505993i | −0.151665 | − | 0.0267425i | ||||
\(359\) | −5.85683 | + | 10.1443i | −0.309112 | + | 0.535397i | −0.978168 | − | 0.207814i | \(-0.933365\pi\) |
0.669057 | + | 0.743211i | \(0.266698\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −1.49955 | − | 2.59729i | −0.0789236 | − | 0.136700i | ||||
\(362\) | −0.470638 | − | 1.29307i | −0.0247362 | − | 0.0679621i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −10.4529 | + | 8.77098i | −0.547878 | + | 0.459724i | ||||
\(365\) | −23.9312 | + | 14.7666i | −1.25262 | + | 0.772918i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 8.09527 | + | 22.2416i | 0.422569 | + | 1.16100i | 0.950231 | + | 0.311546i | \(0.100847\pi\) |
−0.527662 | + | 0.849455i | \(0.676931\pi\) | |||||||
\(368\) | 7.79509 | − | 4.50050i | 0.406347 | − | 0.234605i | ||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 3.18257 | + | 2.51558i | 0.165454 | + | 0.130779i | ||||
\(371\) | 2.71983 | − | 15.4249i | 0.141206 | − | 0.800821i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 7.08072 | − | 19.4541i | 0.366626 | − | 1.00730i | −0.610010 | − | 0.792394i | \(-0.708834\pi\) |
0.976636 | − | 0.214902i | \(-0.0689434\pi\) | |||||||
\(374\) | 0.0746341 | + | 0.423271i | 0.00385924 | + | 0.0218868i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.27304 | − | 3.58551i | −0.220365 | − | 0.184908i | ||||
\(377\) | − | 21.2925i | − | 1.09662i | ||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 14.1618 | 0.727442 | 0.363721 | − | 0.931508i | \(-0.381506\pi\) | ||||
0.363721 | + | 0.931508i | \(0.381506\pi\) | |||||||
\(380\) | −15.3296 | + | 13.6469i | −0.786394 | + | 0.700069i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 2.00190 | − | 0.352989i | 0.102426 | − | 0.0180605i | ||||
\(383\) | 6.96733 | − | 19.1426i | 0.356014 | − | 0.978140i | −0.624385 | − | 0.781117i | \(-0.714650\pi\) |
0.980399 | − | 0.197023i | \(-0.0631274\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −2.97643 | + | 8.98744i | −0.151693 | + | 0.458042i | ||||
\(386\) | 2.01592 | − | 3.49168i | 0.102608 | − | 0.177722i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 9.52672 | − | 5.50025i | 0.483646 | − | 0.279233i | ||||
\(389\) | −10.7321 | + | 3.90618i | −0.544141 | + | 0.198051i | −0.599441 | − | 0.800419i | \(-0.704611\pi\) |
0.0553005 | + | 0.998470i | \(0.482388\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 2.59427 | − | 2.17685i | 0.131198 | − | 0.110088i | ||||
\(392\) | −0.681914 | − | 0.812674i | −0.0344419 | − | 0.0410462i | ||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 1.26271 | − | 0.459590i | 0.0636146 | − | 0.0231538i | ||||
\(395\) | 3.11567 | − | 1.23839i | 0.156766 | − | 0.0623099i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 2.93301 | + | 1.69337i | 0.147204 | + | 0.0849880i | 0.571793 | − | 0.820398i | \(-0.306248\pi\) |
−0.424589 | + | 0.905386i | \(0.639581\pi\) | |||||||
\(398\) | −3.52125 | − | 0.620891i | −0.176504 | − | 0.0311225i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 15.0172 | + | 11.1720i | 0.750859 | + | 0.558599i | ||||
\(401\) | −3.73348 | − | 21.1736i | −0.186441 | − | 1.05736i | −0.924090 | − | 0.382175i | \(-0.875175\pi\) |
0.737649 | − | 0.675184i | \(-0.235936\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 9.04105 | − | 10.7747i | 0.450367 | − | 0.536726i | ||||
\(404\) | −20.9933 | −1.04445 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 5.25502 | 0.260802 | ||||||||
\(407\) | 8.26184 | − | 9.84608i | 0.409524 | − | 0.488052i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 2.13010 | + | 12.0804i | 0.105327 | + | 0.597338i | 0.991089 | + | 0.133199i | \(0.0425250\pi\) |
−0.885762 | + | 0.464139i | \(0.846364\pi\) | |||||||
\(410\) | 4.43977 | + | 2.39293i | 0.219265 | + | 0.118179i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.03338 | − | 0.182213i | −0.0509111 | − | 0.00897700i | ||||
\(413\) | 18.1327 | + | 10.4689i | 0.892254 | + | 0.515143i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 9.59298 | + | 24.1351i | 0.470901 | + | 1.18474i | ||||
\(416\) | −5.50513 | + | 2.00370i | −0.269911 | + | 0.0982397i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.920022 | − | 1.09644i | −0.0449998 | − | 0.0536286i | ||||
\(419\) | 23.2229 | − | 19.4864i | 1.13451 | − | 0.951971i | 0.135269 | − | 0.990809i | \(-0.456810\pi\) |
0.999246 | + | 0.0388381i | \(0.0123657\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −8.53967 | + | 3.10819i | −0.416198 | + | 0.151484i | −0.541627 | − | 0.840619i | \(-0.682191\pi\) |
0.125429 | + | 0.992103i | \(0.459969\pi\) | |||||||
\(422\) | 3.62710 | − | 2.09411i | 0.176565 | − | 0.101940i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 2.23346 | − | 3.86847i | 0.108466 | − | 0.187869i | ||||
\(425\) | 6.29421 | + | 3.15841i | 0.305314 | + | 0.153205i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 5.89575 | − | 16.1984i | 0.285315 | − | 0.783897i | ||||
\(428\) | 5.44399 | − | 0.959922i | 0.263145 | − | 0.0463996i | ||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 2.66985 | − | 2.37678i | 0.128752 | − | 0.114618i | ||||
\(431\) | 17.7056 | 0.852847 | 0.426424 | − | 0.904524i | \(-0.359773\pi\) | ||||
0.426424 | + | 0.904524i | \(0.359773\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | − | 6.74677i | − | 0.324229i | −0.986772 | − | 0.162114i | \(-0.948169\pi\) | ||
0.986772 | − | 0.162114i | \(-0.0518314\pi\) | |||||||
\(434\) | 2.65921 | + | 2.23134i | 0.127646 | + | 0.107108i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −0.163045 | − | 0.924672i | −0.00780842 | − | 0.0442837i | ||||
\(437\) | −3.85724 | + | 10.5977i | −0.184517 | + | 0.506956i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 0.774036 | − | 4.38977i | 0.0369427 | − | 0.209512i | −0.960749 | − | 0.277419i | \(-0.910521\pi\) |
0.997692 | + | 0.0679067i | \(0.0216320\pi\) | |||||||
\(440\) | −1.67431 | + | 2.11824i | −0.0798195 | + | 0.100983i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −0.612991 | + | 0.353911i | −0.0291570 | + | 0.0168338i | ||||
\(443\) | −2.74386 | − | 7.53869i | −0.130365 | − | 0.358174i | 0.857287 | − | 0.514838i | \(-0.172148\pi\) |
−0.987652 | + | 0.156665i | \(0.949926\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 14.0145 | + | 22.7124i | 0.664352 | + | 1.07667i | ||||
\(446\) | −1.48526 | + | 1.24628i | −0.0703293 | + | 0.0590133i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 6.87900 | + | 18.8999i | 0.325002 | + | 0.892936i | ||||
\(449\) | −2.62606 | − | 4.54847i | −0.123931 | − | 0.214655i | 0.797383 | − | 0.603473i | \(-0.206217\pi\) |
−0.921315 | + | 0.388818i | \(0.872884\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.98996 | − | 13.8390i | 0.376232 | − | 0.651654i | ||||
\(452\) | 8.20177 | + | 1.44619i | 0.385779 | + | 0.0680232i | ||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 1.53366 | + | 0.558206i | 0.0719782 | + | 0.0261979i | ||||
\(455\) | −15.5849 | + | 0.456113i | −0.730634 | + | 0.0213829i | ||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 1.94777 | − | 2.32127i | 0.0911130 | − | 0.108584i | −0.718562 | − | 0.695463i | \(-0.755199\pi\) |
0.809675 | + | 0.586879i | \(0.199644\pi\) | |||||||
\(458\) | 3.46062i | 0.161704i | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 10.4108 | + | 1.52316i | 0.485405 | + | 0.0710175i | ||||
\(461\) | 2.25112 | + | 1.88892i | 0.104845 | + | 0.0879757i | 0.693703 | − | 0.720261i | \(-0.255978\pi\) |
−0.588858 | + | 0.808236i | \(0.700422\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −18.1798 | + | 3.20559i | −0.844886 | + | 0.148976i | −0.579304 | − | 0.815112i | \(-0.696675\pi\) |
−0.265583 | + | 0.964088i | \(0.585564\pi\) | |||||||
\(464\) | −30.9314 | − | 11.2581i | −1.43595 | − | 0.522644i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.07600 | − | 6.10231i | 0.0498448 | − | 0.282684i | ||||
\(467\) | −18.7117 | − | 10.8032i | −0.865875 | − | 0.499913i | 9.99457e−5 | − | 1.00000i | \(-0.499968\pi\) |
−0.865975 | + | 0.500087i | \(0.833302\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −11.0937 | − | 19.2149i | −0.512261 | − | 0.887263i | ||||
\(470\) | −0.637947 | − | 3.08694i | −0.0294263 | − | 0.142390i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | 3.83828 | + | 4.57429i | 0.176671 | + | 0.210549i | ||||
\(473\) | −7.27982 | − | 8.67575i | −0.334726 | − | 0.398911i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −23.4115 | + | 1.37151i | −1.07419 | + | 0.0629290i | ||||
\(476\) | 3.96833 | + | 6.87335i | 0.181888 | + | 0.315040i | ||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −4.34606 | − | 2.50920i | −0.198784 | − | 0.114768i | ||||
\(479\) | −0.173381 | + | 0.983295i | −0.00792200 | + | 0.0449279i | −0.988513 | − | 0.151139i | \(-0.951706\pi\) |
0.980591 | + | 0.196067i | \(0.0628170\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 19.8908 | + | 7.23966i | 0.906942 | + | 0.330100i | ||||
\(482\) | −3.02767 | + | 0.533859i | −0.137906 | + | 0.0243166i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −13.2490 | − | 11.1173i | −0.602229 | − | 0.505330i | ||||
\(485\) | 12.4372 | + | 1.81964i | 0.564746 | + | 0.0826255i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.3516i | 0.831589i | 0.909459 | + | 0.415794i | \(0.136496\pi\) | ||||
−0.909459 | + | 0.415794i | \(0.863504\pi\) | |||||||
\(488\) | 3.16003 | − | 3.76598i | 0.143048 | − | 0.170478i | ||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −0.0175376 | − | 0.599243i | −0.000792269 | − | 0.0270711i | ||||
\(491\) | 10.2329 | + | 3.72447i | 0.461805 | + | 0.168083i | 0.562436 | − | 0.826841i | \(-0.309864\pi\) |
−0.100632 | + | 0.994924i | \(0.532086\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −12.1965 | − | 2.15057i | −0.549303 | − | 0.0968570i | ||||
\(494\) | 1.17858 | − | 2.04135i | 0.0530266 | − | 0.0918449i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −10.8720 | − | 18.8308i | −0.488165 | − | 0.845527i | ||||
\(497\) | 8.89927 | + | 24.4505i | 0.399187 | + | 1.09676i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −22.2753 | + | 18.6912i | −0.997180 | + | 0.836733i | −0.986591 | − | 0.163211i | \(-0.947815\pi\) |
−0.0105884 | + | 0.999944i | \(0.503370\pi\) | |||||||
\(500\) | 5.67345 | + | 21.1307i | 0.253724 | + | 0.944994i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −0.565600 | − | 1.55397i | −0.0252440 | − | 0.0693573i | ||||
\(503\) | −16.5027 | + | 9.52781i | −0.735817 | + | 0.424824i | −0.820546 | − | 0.571580i | \(-0.806331\pi\) |
0.0847294 | + | 0.996404i | \(0.472997\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −18.8189 | − | 14.8749i | −0.837432 | − | 0.661925i | ||||
\(506\) | −0.127415 | + | 0.722607i | −0.00566429 | + | 0.0321238i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −8.08916 | + | 22.2248i | −0.358898 | + | 0.986065i | ||||
\(509\) | 6.00851 | + | 34.0759i | 0.266322 | + | 1.51039i | 0.765243 | + | 0.643741i | \(0.222619\pi\) |
−0.498921 | + | 0.866648i | \(0.666270\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −27.7405 | − | 23.2771i | −1.22717 | − | 1.02972i | ||||
\(512\) | 15.2050i | 0.671974i | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | −4.19981 | −0.185246 | ||||||||
\(515\) | −0.797243 | − | 0.895550i | −0.0351307 | − | 0.0394626i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −9.83552 | + | 1.73427i | −0.432566 | + | 0.0762730i | ||||
\(518\) | −1.78676 | + | 4.90907i | −0.0785055 | + | 0.215692i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −4.22114 | − | 1.39794i | −0.185109 | − | 0.0613038i | ||||
\(521\) | 10.0641 | − | 17.4315i | 0.440915 | − | 0.763686i | −0.556843 | − | 0.830618i | \(-0.687988\pi\) |
0.997758 | + | 0.0669313i | \(0.0213208\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.9232 | − | 9.19327i | 0.696274 | − | 0.401994i | −0.109684 | − | 0.993966i | \(-0.534984\pi\) |
0.805958 | + | 0.591973i | \(0.201651\pi\) | |||||||
\(524\) | 0.477950 | − | 0.173960i | 0.0208793 | − | 0.00759946i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −3.46547 | + | 2.90788i | −0.151102 | + | 0.126789i | ||||
\(527\) | −5.25867 | − | 6.26704i | −0.229071 | − | 0.272996i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | −16.1800 | + | 5.88905i | −0.703480 | + | 0.256046i | ||||
\(530\) | 2.34576 | − | 0.932371i | 0.101893 | − | 0.0404996i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −22.8893 | − | 13.2151i | −0.992377 | − | 0.572949i | ||||
\(533\) | 25.9169 | + | 4.56985i | 1.12259 | + | 0.197942i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 5.56030 | + | 2.99687i | 0.240393 | + | 0.129566i | ||||
\(536\) | −1.09879 | − | 6.23155i | −0.0474605 | − | 0.269162i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −0.579122 | + | 0.690171i | −0.0249677 | + | 0.0297554i | ||||
\(539\) | −1.89944 | −0.0818146 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 4.17044 | 0.179301 | 0.0896506 | − | 0.995973i | \(-0.471425\pi\) | ||||
0.0896506 | + | 0.995973i | \(0.471425\pi\) | |||||||
\(542\) | 1.75657 | − | 2.09340i | 0.0754512 | − | 0.0899192i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 0.591711 | + | 3.35576i | 0.0253694 | + | 0.143877i | ||||
\(545\) | 0.509024 | − | 0.944427i | 0.0218042 | − | 0.0404548i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −23.2507 | − | 4.09973i | −0.994128 | − | 0.175292i | −0.347158 | − | 0.937807i | \(-0.612853\pi\) |
−0.646970 | + | 0.762515i | \(0.723964\pi\) | |||||||
\(548\) | −31.6488 | − | 18.2724i | −1.35197 | − | 0.780560i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −1.48456 | + | 0.352376i | −0.0633016 | + | 0.0150254i | ||||
\(551\) | 38.7555 | − | 14.1059i | 1.65104 | − | 0.600930i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 2.77530 | + | 3.30747i | 0.118018 | + | 0.140648i | ||||
\(554\) | −0.0807262 | + | 0.0677373i | −0.00342973 | + | 0.00287788i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12.7865 | − | 4.65392i | 0.542270 | − | 0.197370i | ||||
\(557\) | −23.3763 | + | 13.4963i | −0.990484 | + | 0.571856i | −0.905419 | − | 0.424519i | \(-0.860443\pi\) |
−0.0850648 | + | 0.996375i | \(0.527110\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 9.32567 | − | 16.1525i | 0.394434 | − | 0.683179i | ||||
\(560\) | −7.57772 | + | 22.8812i | −0.320217 | + | 0.966909i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −0.0347140 | + | 0.0953759i | −0.00146432 | + | 0.00402319i | ||||
\(563\) | 13.8182 | − | 2.43652i | 0.582366 | − | 0.102687i | 0.125299 | − | 0.992119i | \(-0.460011\pi\) |
0.457067 | + | 0.889432i | \(0.348900\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 6.32757 | + | 7.10782i | 0.266203 | + | 0.299028i | ||||
\(566\) | 0.874921 | 0.0367757 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 7.42061i | 0.311362i | ||||||||
\(569\) | 17.5672 | + | 14.7406i | 0.736454 | + | 0.617958i | 0.931883 | − | 0.362760i | \(-0.118165\pi\) |
−0.195429 | + | 0.980718i | \(0.562610\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 0.200726 | + | 1.13838i | 0.00840013 | + | 0.0476395i | 0.988720 | − | 0.149778i | \(-0.0478558\pi\) |
−0.980320 | + | 0.197417i | \(0.936745\pi\) | |||||||
\(572\) | −2.38305 | + | 6.54736i | −0.0996401 | + | 0.273759i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.12784 | + | 6.39632i | −0.0470753 | + | 0.266977i | ||||
\(575\) | 8.25325 | + | 8.74201i | 0.344184 | + | 0.364567i | ||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 22.9770 | − | 13.2658i | 0.956544 | − | 0.552261i | 0.0614366 | − | 0.998111i | \(-0.480432\pi\) |
0.895108 | + | 0.445850i | \(0.147098\pi\) | |||||||
\(578\) | −1.06590 | − | 2.92855i | −0.0443358 | − | 0.121812i | ||||
\(579\) | 0 | 0 | ||||||||
\(580\) | −20.2052 | − | 32.7453i | −0.838977 | − | 1.35967i | ||||
\(581\) | −25.6208 | + | 21.4984i | −1.06293 | + | 0.891906i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.73541 | − | 7.51548i | −0.113289 | − | 0.311259i | ||||
\(584\) | −5.16378 | − | 8.94393i | −0.213679 | − | 0.370102i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 2.39989 | − | 4.15673i | 0.0991385 | − | 0.171713i | ||||
\(587\) | −31.2941 | − | 5.51799i | −1.29165 | − | 0.227752i | −0.514728 | − | 0.857354i | \(-0.672107\pi\) |
−0.776918 | + | 0.629602i | \(0.783218\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 25.6011 | + | 9.31802i | 1.05487 | + | 0.383942i | ||||
\(590\) | 0.0987138 | + | 3.37296i | 0.00406398 | + | 0.138862i | ||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 21.0339 | − | 25.0673i | 0.864489 | − | 1.03026i | ||||
\(593\) | 10.3324i | 0.424303i | 0.977237 | + | 0.212151i | \(0.0680470\pi\) | ||||
−0.977237 | + | 0.212151i | \(0.931953\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | −1.31284 | + | 8.97324i | −0.0538210 | + | 0.367867i | ||||
\(596\) | 12.3163 | + | 10.3346i | 0.504494 | + | 0.423320i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −1.19003 | + | 0.209835i | −0.0486641 | + | 0.00858079i | ||||
\(599\) | −30.6411 | − | 11.1524i | −1.25196 | − | 0.455677i | −0.370897 | − | 0.928674i | \(-0.620950\pi\) |
−0.881064 | + | 0.472997i | \(0.843172\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −4.69496 | + | 26.6264i | −0.191511 | + | 1.08611i | 0.725789 | + | 0.687918i | \(0.241475\pi\) |
−0.917300 | + | 0.398197i | \(0.869636\pi\) | |||||||
\(602\) | 3.98646 | + | 2.30159i | 0.162476 | + | 0.0938056i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 8.66368 | + | 15.0059i | 0.352520 | + | 0.610583i | ||||
\(605\) | −3.99959 | − | 19.3535i | −0.162606 | − | 0.786831i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.08135 | + | 4.86396i | 0.165657 | + | 0.197422i | 0.842486 | − | 0.538718i | \(-0.181091\pi\) |
−0.676830 | + | 0.736140i | \(0.736647\pi\) | |||||||
\(608\) | −7.29408 | − | 8.69275i | −0.295814 | − | 0.352537i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 2.72063 | − | 0.562245i | 0.110155 | − | 0.0227646i | ||||
\(611\) | −8.22381 | − | 14.2440i | −0.332700 | − | 0.576253i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −33.0811 | − | 19.0994i | −1.33613 | − | 0.771416i | −0.349900 | − | 0.936787i | \(-0.613784\pi\) |
−0.986231 | + | 0.165371i | \(0.947118\pi\) | |||||||
\(614\) | −0.120094 | + | 0.681089i | −0.00484661 | + | 0.0274865i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −3.26736 | − | 1.18922i | −0.131646 | − | 0.0479151i | ||||
\(617\) | −16.9692 | + | 2.99213i | −0.683155 | + | 0.120459i | −0.504446 | − | 0.863443i | \(-0.668303\pi\) |
−0.178709 | + | 0.983902i | \(0.557192\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 3.05553 | + | 2.56390i | 0.122812 | + | 0.103052i | 0.702125 | − | 0.712053i | \(-0.252235\pi\) |
−0.579313 | + | 0.815105i | \(0.696679\pi\) | |||||||
\(620\) | 3.67952 | − | 25.1495i | 0.147773 | − | 1.01003i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 2.29432i | 0.0919937i | ||||||||
\(623\) | −22.0916 | + | 26.3277i | −0.885080 | + | 1.05480i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −9.88647 | + | 22.9621i | −0.395459 | + | 0.918484i | ||||
\(626\) | −1.82289 | − | 0.663476i | −0.0728571 | − | 0.0265178i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 11.9987 | + | 2.11570i | 0.478802 | + | 0.0844257i | ||||
\(629\) | 6.15593 | − | 10.6624i | 0.245453 | − | 0.425137i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −3.17235 | − | 5.49468i | −0.126289 | − | 0.218740i | 0.795947 | − | 0.605367i | \(-0.206973\pi\) |
−0.922236 | + | 0.386627i | \(0.873640\pi\) | |||||||
\(632\) | 0.421144 | + | 1.15708i | 0.0167522 | + | 0.0460263i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 4.33143 | − | 3.63450i | 0.172023 | − | 0.144345i | ||||
\(635\) | −22.9988 | + | 14.1913i | −0.912681 | + | 0.563163i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −1.06988 | − | 2.93946i | −0.0423900 | − | 0.116466i | ||||
\(638\) | 2.32383 | − | 1.34166i | 0.0920014 | − | 0.0531170i | ||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −8.71936 | + | 11.0313i | −0.344663 | + | 0.436049i | ||||
\(641\) | −5.63430 | + | 31.9537i | −0.222542 | + | 1.26210i | 0.644788 | + | 0.764362i | \(0.276946\pi\) |
−0.867329 | + | 0.497734i | \(0.834165\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 5.98189 | − | 16.4351i | 0.235903 | − | 0.648137i | −0.764093 | − | 0.645106i | \(-0.776813\pi\) |
0.999995 | − | 0.00303079i | \(-0.000964731\pi\) | |||||||
\(644\) | 2.35284 | + | 13.3436i | 0.0927148 | + | 0.525812i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.05026 | − | 0.881277i | −0.0413221 | − | 0.0346734i | ||||
\(647\) | 3.69757i | 0.145367i | 0.997355 | + | 0.0726833i | \(0.0231562\pi\) | ||||
−0.997355 | + | 0.0726833i | \(0.976844\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.6913 | 0.419672 | ||||||||
\(650\) | −1.38151 | − | 2.09893i | −0.0541872 | − | 0.0823270i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 39.8191 | − | 7.02118i | 1.55944 | − | 0.274971i | ||||
\(653\) | −9.02248 | + | 24.7891i | −0.353077 | + | 0.970071i | 0.628299 | + | 0.777972i | \(0.283752\pi\) |
−0.981376 | + | 0.192099i | \(0.938471\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.551707 | + | 0.182712i | 0.0215570 | + | 0.00713916i | ||||
\(656\) | 20.3417 | − | 35.2329i | 0.794211 | − | 1.37561i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 3.51545 | − | 2.02964i | 0.137046 | − | 0.0791238i | ||||
\(659\) | 14.2209 | − | 5.17599i | 0.553968 | − | 0.201628i | −0.0498407 | − | 0.998757i | \(-0.515871\pi\) |
0.603809 | + | 0.797129i | \(0.293649\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 14.8757 | − | 12.4822i | 0.578598 | − | 0.485501i | −0.305889 | − | 0.952067i | \(-0.598953\pi\) |
0.884486 | + | 0.466566i | \(0.154509\pi\) | |||||||
\(662\) | 3.38736 | + | 4.03690i | 0.131654 | + | 0.156899i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −8.96318 | + | 3.26233i | −0.347839 | + | 0.126603i | ||||
\(665\) | −11.1549 | − | 28.0648i | −0.432569 | − | 1.08830i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −18.3104 | − | 10.5715i | −0.708983 | − | 0.409332i | ||||
\(668\) | −12.0834 | − | 2.13062i | −0.467519 | − | 0.0824363i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 1.69654 | − | 3.14770i | 0.0655430 | − | 0.121606i | ||||
\(671\) | −1.52847 | − | 8.66839i | −0.0590060 | − | 0.334640i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −15.8772 | + | 18.9217i | −0.612021 | + | 0.729378i | −0.979677 | − | 0.200584i | \(-0.935716\pi\) |
0.367656 | + | 0.929962i | \(0.380161\pi\) | |||||||
\(674\) | 0.998381 | 0.0384562 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 13.9654 | 0.537133 | ||||||||
\(677\) | −6.58819 | + | 7.85150i | −0.253205 | + | 0.301758i | −0.877641 | − | 0.479318i | \(-0.840884\pi\) |
0.624437 | + | 0.781075i | \(0.285329\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 2.81082 | + | 15.9410i | 0.107869 | + | 0.611758i | ||||
\(680\) | −1.22709 | + | 2.27671i | −0.0470568 | + | 0.0873077i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1.74562 | + | 0.307800i | 0.0668432 | + | 0.0117863i | ||||
\(683\) | 12.1386 | + | 7.00820i | 0.464469 | + | 0.268161i | 0.713921 | − | 0.700226i | \(-0.246917\pi\) |
−0.249453 | + | 0.968387i | \(0.580251\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −15.4238 | − | 38.8048i | −0.589312 | − | 1.48266i | ||||
\(686\) | −3.20562 | + | 1.16675i | −0.122391 | + | 0.0445468i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −18.5338 | − | 22.0877i | −0.706594 | − | 0.842086i | ||||
\(689\) | 10.0898 | − | 8.46633i | 0.384390 | − | 0.322542i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −15.6160 | + | 5.68375i | −0.594060 | + | 0.216220i | −0.621514 | − | 0.783403i | \(-0.713482\pi\) |
0.0274543 | + | 0.999623i | \(0.491260\pi\) | |||||||
\(692\) | −6.72709 | + | 3.88389i | −0.255725 | + | 0.147643i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.47467 | + | 4.28625i | −0.0939372 | + | 0.162704i | ||||
\(695\) | 14.7597 | + | 4.88808i | 0.559869 | + | 0.185415i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 5.23528 | − | 14.3838i | 0.198301 | − | 0.544826i | ||||
\(698\) | −2.70553 | + | 0.477058i | −0.102406 | + | 0.0180569i | ||||
\(699\) | 0 | 0 | ||||||||
\(700\) | −23.5349 | + | 15.4906i | −0.889537 | + | 0.585489i | ||||
\(701\) | −23.2471 | −0.878029 | −0.439015 | − | 0.898480i | \(-0.644672\pi\) | ||||
−0.439015 | + | 0.898480i | \(0.644672\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | 41.0003i | 1.54636i | ||||||||
\(704\) | 7.86733 | + | 6.60147i | 0.296511 | + | 0.248802i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 0.708977 | + | 4.02081i | 0.0266827 | + | 0.151325i | ||||
\(707\) | 10.5653 | − | 29.0280i | 0.397349 | − | 1.09171i | ||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 0.376750 | − | 2.13666i | 0.0141492 | − | 0.0802438i | −0.976916 | − | 0.213626i | \(-0.931473\pi\) |
0.991065 | + | 0.133382i | \(0.0425837\pi\) | |||||||
\(710\) | −2.60034 | + | 3.28981i | −0.0975891 | + | 0.123464i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8.48841 | + | 4.90079i | −0.318117 | + | 0.183665i | ||||
\(713\) | −4.77688 | − | 13.1244i | −0.178895 | − | 0.491511i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −6.77540 | + | 4.18071i | −0.253386 | + | 0.156350i | ||||
\(716\) | −21.0474 | + | 17.6609i | −0.786579 | + | 0.660018i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −0.831472 | − | 2.28445i | −0.0310303 | − | 0.0852550i | ||||
\(719\) | −2.14999 | − | 3.72389i | −0.0801810 | − | 0.138878i | 0.823147 | − | 0.567829i | \(-0.192217\pi\) |
−0.903328 | + | 0.428951i | \(0.858883\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.772022 | − | 1.33718i | 0.0287516 | − | 0.0497992i | ||||
\(722\) | 0.612979 | + | 0.108085i | 0.0228127 | + | 0.00402250i | ||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −12.1925 | − | 4.43770i | −0.453130 | − | 0.164926i | ||||
\(725\) | 5.08936 | − | 43.6703i | 0.189014 | − | 1.62187i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.7760 | + | 17.6094i | −0.548011 | + | 0.653095i | −0.966964 | − | 0.254914i | \(-0.917953\pi\) |
0.418952 | + | 0.908008i | \(0.362397\pi\) | |||||||
\(728\) | − | 5.72622i | − | 0.212228i | ||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 0.844864 | − | 5.77465i | 0.0312698 | − | 0.213729i | ||||
\(731\) | −8.31038 | − | 6.97324i | −0.307371 | − | 0.257915i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −1.93062 | + | 0.340421i | −0.0713092 | + | 0.0125737i | −0.209189 | − | 0.977875i | \(-0.567082\pi\) |
0.137880 | + | 0.990449i | \(0.455971\pi\) | |||||||
\(734\) | −4.61603 | − | 1.68010i | −0.170381 | − | 0.0620136i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −1.01017 | + | 5.72894i | −0.0372353 | + | 0.211172i | ||||
\(737\) | −9.81157 | − | 5.66471i | −0.361414 | − | 0.208662i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 2.11839 | + | 3.66916i | 0.0779263 | + | 0.134972i | 0.902355 | − | 0.430993i | \(-0.141837\pi\) |
−0.824429 | + | 0.565966i | \(0.808503\pi\) | |||||||
\(740\) | 37.4596 | − | 7.74139i | 1.37704 | − | 0.284579i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 2.08950 | + | 2.49017i | 0.0767080 | + | 0.0914170i | ||||
\(743\) | 26.6003 | + | 31.7011i | 0.975872 | + | 1.16300i | 0.986617 | + | 0.163057i | \(0.0521353\pi\) |
−0.0107448 | + | 0.999942i | \(0.503420\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 3.71800 | + | 17.9909i | 0.136217 | + | 0.659137i | ||||
\(746\) | 2.14832 | + | 3.72101i | 0.0786557 | + | 0.136236i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 3.50969 | + | 2.02632i | 0.128327 | + | 0.0740895i | ||||
\(749\) | −1.41249 | + | 8.01065i | −0.0516114 | + | 0.292703i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −16.4803 | − | 5.99834i | −0.601375 | − | 0.218883i | 0.0233500 | − | 0.999727i | \(-0.492567\pi\) |
−0.624725 | + | 0.780845i | \(0.714789\pi\) | |||||||
\(752\) | −25.0404 | + | 4.41529i | −0.913129 | + | 0.161009i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 3.38520 | + | 2.84052i | 0.123282 | + | 0.103446i | ||||
\(755\) | −2.86619 | + | 19.5904i | −0.104311 | + | 0.712968i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 31.2786i | 1.13684i | 0.822739 | + | 0.568420i | \(0.192445\pi\) | ||||
−0.822739 | + | 0.568420i | \(0.807555\pi\) | |||||||
\(758\) | −1.88925 | + | 2.25152i | −0.0686206 | + | 0.0817789i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −0.251959 | − | 8.60921i | −0.00913953 | − | 0.312289i | ||||
\(761\) | −12.3465 | − | 4.49377i | −0.447561 | − | 0.162899i | 0.108400 | − | 0.994107i | \(-0.465427\pi\) |
−0.555961 | + | 0.831208i | \(0.687650\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 1.36062 | + | 0.239915i | 0.0492579 | + | 0.00868549i | ||||
\(764\) | 9.58366 | − | 16.5994i | 0.346725 | − | 0.600545i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.11392 | + | 3.66141i | 0.0763790 | + | 0.132292i | ||||
\(767\) | 6.02200 | + | 16.5453i | 0.217442 | + | 0.597417i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 36.6235 | − | 30.7307i | 1.32068 | − | 1.10818i | 0.334514 | − | 0.942391i | \(-0.391428\pi\) |
0.986161 | − | 0.165788i | \(-0.0530166\pi\) | |||||||
\(770\) | −1.03180 | − | 1.67218i | −0.0371836 | − | 0.0602610i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −13.0025 | − | 35.7240i | −0.467970 | − | 1.28574i | ||||
\(773\) | 45.6728 | − | 26.3692i | 1.64274 | − | 0.948434i | 0.662881 | − | 0.748725i | \(-0.269333\pi\) |
0.979855 | − | 0.199710i | \(-0.0639999\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 21.1183 | − | 19.9376i | 0.758591 | − | 0.716179i | ||||
\(776\) | −0.801623 | + | 4.54623i | −0.0287766 | + | 0.163200i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0.810692 | − | 2.22736i | 0.0290647 | − | 0.0798546i | ||||
\(779\) | 8.85162 | + | 50.2000i | 0.317142 | + | 1.79860i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 10.1779 | + | 8.54024i | 0.364192 | + | 0.305594i | ||||
\(782\) | 0.702854i | 0.0251340i | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −4.83580 | −0.172707 | ||||||||
\(785\) | 9.25690 | + | 10.3984i | 0.330393 | + | 0.371133i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −8.67001 | + | 1.52876i | −0.309053 | + | 0.0544943i | −0.326023 | − | 0.945362i | \(-0.605709\pi\) |
0.0169709 | + | 0.999856i | \(0.494598\pi\) | |||||||
\(788\) | 4.33353 | − | 11.9063i | 0.154376 | − | 0.424144i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −0.218759 | + | 0.660553i | −0.00778311 | + | 0.0235014i | ||||
\(791\) | −6.12740 | + | 10.6130i | −0.217865 | + | 0.377354i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 12.5538 | − | 7.24793i | 0.445798 | − | 0.257382i | ||||
\(794\) | −0.660500 | + | 0.240402i | −0.0234403 | + | 0.00853156i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −25.8268 | + | 21.6712i | −0.915406 | + | 0.768117i | ||||
\(797\) | 5.59255 | + | 6.66494i | 0.198098 | + | 0.236084i | 0.855944 | − | 0.517068i | \(-0.172977\pi\) |
−0.657846 | + | 0.753153i | \(0.728532\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −8.98971 | + | 3.27199i | −0.318033 | + | 0.115755i | ||||
\(800\) | −11.7698 | + | 2.79370i | −0.416125 | + | 0.0987720i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 3.86436 | + | 2.23109i | 0.136455 | + | 0.0787825i | ||||
\(803\) | −18.2101 | − | 3.21093i | −0.642620 | − | 0.113311i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −7.34555 | + | 13.6287i | −0.258897 | + | 0.480348i | ||||
\(806\) | 0.506903 | + | 2.87479i | 0.0178549 | + | 0.101260i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 5.66285 | − | 6.74872i | 0.199218 | − | 0.237419i | ||||
\(809\) | 37.8226 | 1.32977 | 0.664886 | − | 0.746945i | \(-0.268480\pi\) | ||||
0.664886 | + | 0.746945i | \(0.268480\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −0.322691 | −0.0113312 | −0.00566561 | − | 0.999984i | \(-0.501803\pi\) | ||||
−0.00566561 | + | 0.999984i | \(0.501803\pi\) | |||||||
\(812\) | 31.8502 | − | 37.9576i | 1.11772 | − | 1.33205i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 0.463216 | + | 2.62703i | 0.0162357 | + | 0.0920773i | ||||
\(815\) | 40.6698 | + | 21.9201i | 1.42460 | + | 0.767827i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 35.5781 | + | 6.27337i | 1.24472 | + | 0.219478i | ||||
\(818\) | −2.20478 | − | 1.27293i | −0.0770883 | − | 0.0445069i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 44.1935 | − | 17.5656i | 1.54330 | − | 0.613418i | ||||
\(821\) | 0.715925 | − | 0.260575i | 0.0249859 | − | 0.00909414i | −0.329497 | − | 0.944157i | \(-0.606879\pi\) |
0.354483 | + | 0.935063i | \(0.384657\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 34.5795 | + | 41.2102i | 1.20537 | + | 1.43650i | 0.869033 | + | 0.494755i | \(0.164742\pi\) |
0.336332 | + | 0.941743i | \(0.390813\pi\) | |||||||
\(824\) | 0.337327 | − | 0.283051i | 0.0117513 | − | 0.00986054i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −4.08340 | + | 1.48624i | −0.142080 | + | 0.0517128i | ||||
\(827\) | −15.4598 | + | 8.92572i | −0.537590 | + | 0.310378i | −0.744102 | − | 0.668066i | \(-0.767122\pi\) |
0.206512 | + | 0.978444i | \(0.433789\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.49405 | − | 6.05188i | 0.121354 | − | 0.210190i | −0.798948 | − | 0.601400i | \(-0.794610\pi\) |
0.920302 | + | 0.391209i | \(0.127943\pi\) | |||||||
\(830\) | −5.11688 | − | 1.69459i | −0.177609 | − | 0.0588200i | ||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −5.78471 | + | 15.8934i | −0.200549 | + | 0.551003i | ||||
\(833\) | −1.79180 | + | 0.315943i | −0.0620823 | + | 0.0109468i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −9.32218 | − | 10.4717i | −0.322607 | − | 0.362388i | ||||
\(836\) | −13.4959 | −0.466765 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 6.29168i | 0.217343i | ||||||||
\(839\) | −34.2020 | − | 28.6989i | −1.18078 | − | 0.990795i | −0.999974 | − | 0.00727705i | \(-0.997684\pi\) |
−0.180810 | − | 0.983518i | \(-0.557872\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 8.39066 | + | 47.5858i | 0.289333 | + | 1.64089i | ||||
\(842\) | 0.645076 | − | 1.77233i | 0.0222308 | − | 0.0610786i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | 6.85757 | − | 38.8912i | 0.236047 | − | 1.33869i | ||||
\(845\) | 12.5190 | + | 9.89530i | 0.430667 | + | 0.340409i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 22.0400 | − | 12.7248i | 0.757302 | − | 0.437229i | ||||
\(848\) | −6.96412 | − | 19.1338i | −0.239149 | − | 0.657056i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −1.34182 | + | 0.579342i | −0.0460240 | + | 0.0198713i | ||||
\(851\) | 16.1013 | − | 13.5106i | 0.551946 | − | 0.463138i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −6.47405 | − | 17.7873i | −0.221667 | − | 0.609026i | 0.778151 | − | 0.628077i | \(-0.216158\pi\) |
−0.999819 | + | 0.0190511i | \(0.993935\pi\) | |||||||
\(854\) | 1.78880 | + | 3.09829i | 0.0612114 | + | 0.106021i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −1.15991 | + | 2.00902i | −0.0396448 | + | 0.0686668i | ||||
\(857\) | 55.0204 | + | 9.70158i | 1.87946 | + | 0.331400i | 0.991665 | − | 0.128840i | \(-0.0411252\pi\) |
0.887795 | + | 0.460239i | \(0.152236\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | 5.69311 | + | 2.07212i | 0.194246 | + | 0.0706999i | 0.437312 | − | 0.899310i | \(-0.355931\pi\) |
−0.243065 | + | 0.970010i | \(0.578153\pi\) | |||||||
\(860\) | −0.985983 | − | 33.6901i | −0.0336217 | − | 1.14882i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.36201 | + | 2.81493i | −0.0804503 | + | 0.0958769i | ||||
\(863\) | − | 31.2067i | − | 1.06229i | −0.847281 | − | 0.531145i | \(-0.821762\pi\) | ||
0.847281 | − | 0.531145i | \(-0.178238\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −8.78229 | − | 1.28490i | −0.298607 | − | 0.0436879i | ||||
\(866\) | 1.07264 | + | 0.900051i | 0.0364497 | + | 0.0305850i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 32.2345 | − | 5.68381i | 1.09411 | − | 0.192921i | ||||
\(869\) | 2.07170 | + | 0.754038i | 0.0702777 | + | 0.0255790i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.23992 | − | 18.3745i | 0.109781 | − | 0.622597i | ||||
\(872\) | 0.341235 | + | 0.197012i | 0.0115557 | + | 0.00667168i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −1.17030 | − | 2.02703i | −0.0395861 | − | 0.0685652i | ||||
\(875\) | −32.0733 | − | 2.78965i | −1.08427 | − | 0.0943075i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 0.574169 | + | 0.684268i | 0.0193883 | + | 0.0231061i | 0.775651 | − | 0.631161i | \(-0.217421\pi\) |
−0.756263 | + | 0.654268i | \(0.772977\pi\) | |||||||
\(878\) | 0.594651 | + | 0.708677i | 0.0200685 | + | 0.0239167i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 2.49088 | + | 12.0530i | 0.0839674 | + | 0.406308i | ||||
\(881\) | 28.2154 | + | 48.8706i | 0.950602 | + | 1.64649i | 0.744126 | + | 0.668039i | \(0.232866\pi\) |
0.206476 | + | 0.978452i | \(0.433801\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −45.6611 | − | 26.3625i | −1.53662 | − | 0.887168i | −0.999033 | − | 0.0439585i | \(-0.986003\pi\) |
−0.537586 | − | 0.843209i | \(-0.680664\pi\) | |||||||
\(884\) | −1.15895 | + | 6.57273i | −0.0389797 | + | 0.221065i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1.56459 | + | 0.569463i | 0.0525633 | + | 0.0191315i | ||||
\(887\) | 51.5601 | − | 9.09144i | 1.73122 | − | 0.305261i | 0.782799 | − | 0.622275i | \(-0.213792\pi\) |
0.948421 | + | 0.317015i | \(0.102680\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −26.6597 | − | 22.3702i | −0.894139 | − | 0.750272i | ||||
\(890\) | −5.48055 | − | 0.801835i | −0.183708 | − | 0.0268776i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 18.2819i | 0.612122i | ||||||||
\(893\) | 20.4782 | − | 24.4049i | 0.685276 | − | 0.816680i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −31.3812 | + | 0.918410i | −1.04896 | + | 0.0306991i | ||||
\(896\) | −17.0156 | − | 6.19316i | −0.568450 | − | 0.206899i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1.07347 | + | 0.189282i | 0.0358221 | + | 0.00631641i | ||||
\(899\) | −25.5379 | + | 44.2330i | −0.851737 | + | 1.47525i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −3.83049 | − | 6.63461i | −0.127612 | − | 0.221031i | ||||
\(902\) | 1.13431 | + | 3.11648i | 0.0377682 | + | 0.103767i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −2.67730 | + | 2.24652i | −0.0890457 | + | 0.0747182i | ||||
\(905\) | −7.78530 | − | 12.6171i | −0.258792 | − | 0.419407i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 6.80568 | + | 18.6984i | 0.225979 | + | 0.620872i | 0.999923 | − | 0.0123817i | \(-0.00394131\pi\) |
−0.773945 | + | 0.633253i | \(0.781719\pi\) | |||||||
\(908\) | 13.3274 | − | 7.69456i | 0.442284 | − | 0.255353i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 2.00659 | − | 2.53863i | 0.0665178 | − | 0.0841548i | ||||
\(911\) | 2.63013 | − | 14.9162i | 0.0871400 | − | 0.494195i | −0.909734 | − | 0.415191i | \(-0.863715\pi\) |
0.996874 | − | 0.0790044i | \(-0.0251741\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −5.84105 | + | 16.0482i | −0.193311 | + | 0.531116i | ||||
\(914\) | 0.109206 | + | 0.619336i | 0.00361220 | + | 0.0204858i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 24.9965 | + | 20.9746i | 0.825907 | + | 0.693019i | ||||
\(917\) | 0.748423i | 0.0247151i | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 31.1704 | 1.02822 | 0.514109 | − | 0.857725i | \(-0.328123\pi\) | ||||
0.514109 | + | 0.857725i | \(0.328123\pi\) | |||||||
\(920\) | −3.29791 | + | 2.93589i | −0.108729 | + | 0.0967935i | ||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −0.600621 | + | 0.105906i | −0.0197804 | + | 0.00348782i | ||||
\(923\) | −7.48361 | + | 20.5610i | −0.246326 | + | 0.676775i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 39.0650 | + | 19.6026i | 1.28445 | + | 0.644531i | ||||
\(926\) | 1.91563 | − | 3.31796i | 0.0629514 | − | 0.109035i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 18.4237 | − | 10.6369i | 0.604788 | − | 0.349174i | ||||
\(929\) | −9.60870 | + | 3.49728i | −0.315251 | + | 0.114742i | −0.494800 | − | 0.869007i | \(-0.664759\pi\) |
0.179548 | + | 0.983749i | \(0.442536\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 4.64148 | − | 3.89467i | 0.152118 | − | 0.127643i | ||||
\(932\) | −37.5561 | − | 44.7577i | −1.23019 | − | 1.46609i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 4.21379 | − | 1.53369i | 0.137879 | − | 0.0501840i | ||||
\(935\) | 1.71042 | + | 4.30326i | 0.0559366 | + | 0.140731i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 0.758718 | + | 0.438046i | 0.0247862 | + | 0.0143103i | 0.512342 | − | 0.858782i | \(-0.328778\pi\) |
−0.487556 | + | 0.873092i | \(0.662111\pi\) | |||||||
\(938\) | 4.53485 | + | 0.799617i | 0.148068 | + | 0.0261084i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −26.1639 | − | 14.1017i | −0.853373 | − | 0.459948i | ||||
\(941\) | −0.921099 | − | 5.22381i | −0.0300270 | − | 0.170291i | 0.966107 | − | 0.258144i | \(-0.0831108\pi\) |
−0.996134 | + | 0.0878522i | \(0.972000\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 16.7973 | − | 20.0183i | 0.546996 | − | 0.651884i | ||||
\(944\) | 27.2192 | 0.885911 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 2.35048 | 0.0764208 | ||||||||
\(947\) | −14.4581 | + | 17.2305i | −0.469825 | + | 0.559916i | −0.947968 | − | 0.318366i | \(-0.896866\pi\) |
0.478143 | + | 0.878282i | \(0.341310\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −5.28795 | − | 29.9895i | −0.171654 | − | 0.973500i | ||||
\(950\) | 2.90515 | − | 3.90505i | 0.0942555 | − | 0.126697i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | −3.28002 | − | 0.578356i | −0.106306 | − | 0.0187446i | ||||
\(953\) | −3.69060 | − | 2.13077i | −0.119550 | − | 0.0690223i | 0.439032 | − | 0.898471i | \(-0.355321\pi\) |
−0.558583 | + | 0.829449i | \(0.688655\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 20.3526 | − | 8.08957i | 0.658596 | − | 0.261772i | ||||
\(956\) | −44.4653 | + | 16.1840i | −1.43811 | + | 0.523430i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −0.133200 | − | 0.158741i | −0.00430349 | − | 0.00512870i | ||||
\(959\) | 41.1937 | − | 34.5656i | 1.33021 | − | 1.11618i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −2.57434 | + | 0.936985i | −0.0830434 | + | 0.0302253i | ||||
\(962\) | −3.80453 | + | 2.19655i | −0.122663 | + | 0.0708195i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −14.4943 | + | 25.1049i | −0.466830 | + | 0.808573i | ||||
\(965\) | 13.6567 | − | 41.2370i | 0.439625 | − | 1.32747i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −1.30770 | + | 3.59289i | −0.0420529 | + | 0.115539i | −0.958942 | − | 0.283604i | \(-0.908470\pi\) |
0.916889 | + | 0.399143i | \(0.130692\pi\) | |||||||
\(968\) | 7.14774 | − | 1.26034i | 0.229737 | − | 0.0405089i | ||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −1.94848 | + | 1.73459i | −0.0625620 | + | 0.0556944i | ||||
\(971\) | −57.0974 | −1.83234 | −0.916171 | − | 0.400787i | \(-0.868737\pi\) | ||||
−0.916171 | + | 0.400787i | \(0.868737\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.0225i | 0.641890i | ||||||||
\(974\) | −2.91763 | − | 2.44819i | −0.0934870 | − | 0.0784449i | ||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.89136 | − | 22.0690i | −0.124559 | − | 0.706411i | ||||
\(977\) | 9.83942 | − | 27.0336i | 0.314791 | − | 0.864881i | −0.676881 | − | 0.736092i | \(-0.736669\pi\) |
0.991672 | − | 0.128789i | \(-0.0411089\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −3.04740 | + | 17.2826i | −0.0973952 | + | 0.552356i | ||||
\(980\) | −4.43470 | − | 3.50529i | −0.141661 | − | 0.111972i | ||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1.95726 | + | 1.13002i | −0.0624586 | + | 0.0360605i | ||||
\(983\) | 14.8222 | + | 40.7237i | 0.472756 | + | 1.29889i | 0.915529 | + | 0.402252i | \(0.131772\pi\) |
−0.442773 | + | 0.896634i | \(0.646005\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 12.3210 | − | 7.60255i | 0.392578 | − | 0.242238i | ||||
\(986\) | 1.96898 | − | 1.65217i | 0.0627052 | − | 0.0526159i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.60169 | − | 20.8855i | −0.241842 | − | 0.664455i | ||||
\(989\) | −9.26022 | − | 16.0392i | −0.294458 | − | 0.510016i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −23.9951 | + | 41.5607i | −0.762230 | + | 1.32022i | 0.179469 | + | 0.983764i | \(0.442562\pi\) |
−0.941699 | + | 0.336457i | \(0.890771\pi\) | |||||||
\(992\) | 13.8395 | + | 2.44028i | 0.439406 | + | 0.0774791i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −5.07449 | − | 1.84696i | −0.160953 | − | 0.0585821i | ||||
\(995\) | −38.5071 | + | 1.12696i | −1.22076 | + | 0.0357270i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −21.4919 | + | 25.6130i | −0.680655 | + | 0.811173i | −0.990192 | − | 0.139715i | \(-0.955382\pi\) |
0.309537 | + | 0.950887i | \(0.399826\pi\) | |||||||
\(998\) | − | 6.03495i | − | 0.191033i | ||||||
\(999\) | 0 | 0 |
(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 | 405.2.p.a.289.8 | 96 | ||
3.2 | odd | 2 | 135.2.p.a.124.9 | yes | 96 | ||
5.4 | even | 2 | inner | 405.2.p.a.289.9 | 96 | ||
15.2 | even | 4 | 675.2.l.h.151.9 | 96 | |||
15.8 | even | 4 | 675.2.l.h.151.8 | 96 | |||
15.14 | odd | 2 | 135.2.p.a.124.8 | yes | 96 | ||
27.5 | odd | 18 | 135.2.p.a.49.8 | ✓ | 96 | ||
27.22 | even | 9 | inner | 405.2.p.a.199.9 | 96 | ||
135.32 | even | 36 | 675.2.l.h.76.9 | 96 | |||
135.49 | even | 18 | inner | 405.2.p.a.199.8 | 96 | ||
135.59 | odd | 18 | 135.2.p.a.49.9 | yes | 96 | ||
135.113 | even | 36 | 675.2.l.h.76.8 | 96 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
135.2.p.a.49.8 | ✓ | 96 | 27.5 | odd | 18 | ||
135.2.p.a.49.9 | yes | 96 | 135.59 | odd | 18 | ||
135.2.p.a.124.8 | yes | 96 | 15.14 | odd | 2 | ||
135.2.p.a.124.9 | yes | 96 | 3.2 | odd | 2 | ||
405.2.p.a.199.8 | 96 | 135.49 | even | 18 | inner | ||
405.2.p.a.199.9 | 96 | 27.22 | even | 9 | inner | ||
405.2.p.a.289.8 | 96 | 1.1 | even | 1 | trivial | ||
405.2.p.a.289.9 | 96 | 5.4 | even | 2 | inner | ||
675.2.l.h.76.8 | 96 | 135.113 | even | 36 | |||
675.2.l.h.76.9 | 96 | 135.32 | even | 36 | |||
675.2.l.h.151.8 | 96 | 15.8 | even | 4 | |||
675.2.l.h.151.9 | 96 | 15.2 | even | 4 |