Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [525,2,Mod(32,525)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(525, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([6, 3, 8]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("525.32");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 525 = 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 525.bf (of order \(12\), degree \(4\), 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: | \(4.19214610612\) |
Analytic rank: | \(0\) |
Dimension: | \(80\) |
Relative dimension: | \(20\) over \(\Q(\zeta_{12})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 32.5 | ||
Character | \(\chi\) | \(=\) | 525.32 |
Dual form | 525.2.bf.g.443.5 |
$q$-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 \(\left(\mathbb{Z}/525\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(176\) | \(451\) |
\(\chi(n)\) | \(e\left(\frac{1}{4}\right)\) | \(-1\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −1.78672 | − | 0.478751i | −1.26340 | − | 0.338528i | −0.435904 | − | 0.899993i | \(-0.643571\pi\) |
−0.827500 | + | 0.561465i | \(0.810238\pi\) | |||||||
\(3\) | 0.293073 | − | 1.70708i | 0.169206 | − | 0.985581i | ||||
\(4\) | 1.23113 | + | 0.710791i | 0.615563 | + | 0.355395i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −1.34091 | + | 2.90976i | −0.547422 | + | 1.18791i | ||||
\(7\) | 0.585067 | − | 2.58025i | 0.221134 | − | 0.975243i | ||||
\(8\) | 0.756555 | + | 0.756555i | 0.267482 | + | 0.267482i | ||||
\(9\) | −2.82822 | − | 1.00060i | −0.942739 | − | 0.333532i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 4.61054 | + | 2.66189i | 1.39013 | + | 0.802591i | 0.993329 | − | 0.115314i | \(-0.0367874\pi\) |
0.396800 | + | 0.917905i | \(0.370121\pi\) | |||||||
\(12\) | 1.57418 | − | 1.89331i | 0.454428 | − | 0.546552i | ||||
\(13\) | 3.44938 | − | 3.44938i | 0.956686 | − | 0.956686i | −0.0424138 | − | 0.999100i | \(-0.513505\pi\) |
0.999100 | + | 0.0424138i | \(0.0135048\pi\) | |||||||
\(14\) | −2.28065 | + | 4.33009i | −0.609529 | + | 1.15727i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −2.41113 | − | 4.17621i | −0.602784 | − | 1.04405i | ||||
\(17\) | −1.13091 | − | 4.22062i | −0.274286 | − | 1.02365i | −0.956318 | − | 0.292328i | \(-0.905570\pi\) |
0.682032 | − | 0.731322i | \(-0.261096\pi\) | |||||||
\(18\) | 4.57420 | + | 3.14180i | 1.07815 | + | 0.740529i | ||||
\(19\) | 2.14466 | − | 1.23822i | 0.492018 | − | 0.284067i | −0.233393 | − | 0.972382i | \(-0.574983\pi\) |
0.725411 | + | 0.688316i | \(0.241650\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −4.23322 | − | 1.75496i | −0.923764 | − | 0.382963i | ||||
\(22\) | −6.96337 | − | 6.96337i | −1.48459 | − | 1.48459i | ||||
\(23\) | −0.533436 | + | 1.99081i | −0.111229 | + | 0.415113i | −0.998977 | − | 0.0452168i | \(-0.985602\pi\) |
0.887748 | + | 0.460330i | \(0.152269\pi\) | |||||||
\(24\) | 1.51322 | − | 1.06977i | 0.308885 | − | 0.218366i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | −7.81448 | + | 4.51169i | −1.53255 | + | 0.884816i | ||||
\(27\) | −2.53697 | + | 4.53473i | −0.488240 | + | 0.872709i | ||||
\(28\) | 2.55431 | − | 2.76075i | 0.482719 | − | 0.521734i | ||||
\(29\) | 2.05014 | 0.380701 | 0.190350 | − | 0.981716i | \(-0.439038\pi\) | ||||
0.190350 | + | 0.981716i | \(0.439038\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 1.18652 | − | 2.05512i | 0.213106 | − | 0.369110i | −0.739579 | − | 0.673069i | \(-0.764975\pi\) |
0.952685 | + | 0.303960i | \(0.0983088\pi\) | |||||||
\(32\) | 1.75483 | + | 6.54911i | 0.310213 | + | 1.15773i | ||||
\(33\) | 5.89528 | − | 7.09041i | 1.02624 | − | 1.23428i | ||||
\(34\) | 8.08250i | 1.38614i | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −2.77068 | − | 3.24213i | −0.461779 | − | 0.540355i | ||||
\(37\) | −1.26256 | + | 4.71194i | −0.207564 | + | 0.774639i | 0.781089 | + | 0.624420i | \(0.214665\pi\) |
−0.988653 | + | 0.150219i | \(0.952002\pi\) | |||||||
\(38\) | −4.42470 | + | 1.18560i | −0.717782 | + | 0.192329i | ||||
\(39\) | −4.87743 | − | 6.89928i | −0.781015 | − | 1.10477i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | − | 4.06556i | − | 0.634934i | −0.948269 | − | 0.317467i | \(-0.897168\pi\) | ||
0.948269 | − | 0.317467i | \(-0.102832\pi\) | |||||||
\(42\) | 6.72340 | + | 5.16228i | 1.03744 | + | 0.796557i | ||||
\(43\) | 0.254109 | − | 0.254109i | 0.0387513 | − | 0.0387513i | −0.687466 | − | 0.726217i | \(-0.741277\pi\) |
0.726217 | + | 0.687466i | \(0.241277\pi\) | |||||||
\(44\) | 3.78410 | + | 6.55425i | 0.570475 | + | 0.988091i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 1.90621 | − | 3.30165i | 0.281055 | − | 0.486801i | ||||
\(47\) | −8.31648 | − | 2.22839i | −1.21308 | − | 0.325045i | −0.405112 | − | 0.914267i | \(-0.632768\pi\) |
−0.807971 | + | 0.589222i | \(0.799434\pi\) | |||||||
\(48\) | −7.83574 | + | 2.89205i | −1.13099 | + | 0.417432i | ||||
\(49\) | −6.31539 | − | 3.01924i | −0.902199 | − | 0.431320i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −7.53635 | + | 0.693601i | −1.05530 | + | 0.0971235i | ||||
\(52\) | 6.69841 | − | 1.79483i | 0.928903 | − | 0.248899i | ||||
\(53\) | −11.8899 | + | 3.18590i | −1.63321 | + | 0.437616i | −0.954843 | − | 0.297110i | \(-0.903977\pi\) |
−0.678364 | + | 0.734726i | \(0.737311\pi\) | |||||||
\(54\) | 6.70387 | − | 6.88773i | 0.912281 | − | 0.937302i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.39474 | − | 1.50947i | 0.320010 | − | 0.201711i | ||||
\(57\) | −1.48519 | − | 4.02398i | −0.196718 | − | 0.532989i | ||||
\(58\) | −3.66302 | − | 0.981504i | −0.480979 | − | 0.128878i | ||||
\(59\) | −1.70041 | + | 2.94520i | −0.221375 | + | 0.383433i | −0.955226 | − | 0.295878i | \(-0.904388\pi\) |
0.733851 | + | 0.679311i | \(0.237721\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 3.95741 | + | 6.85444i | 0.506695 | + | 0.877621i | 0.999970 | + | 0.00774794i | \(0.00246627\pi\) |
−0.493275 | + | 0.869873i | \(0.664200\pi\) | |||||||
\(62\) | −3.10387 | + | 3.10387i | −0.394193 | + | 0.394193i | ||||
\(63\) | −4.23649 | + | 6.71209i | −0.533747 | + | 0.845644i | ||||
\(64\) | − | 2.89704i | − | 0.362130i | ||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −13.9278 | + | 9.84622i | −1.71439 | + | 1.21199i | ||||
\(67\) | 2.76544 | − | 0.740997i | 0.337852 | − | 0.0905272i | −0.0859043 | − | 0.996303i | \(-0.527378\pi\) |
0.423756 | + | 0.905776i | \(0.360711\pi\) | |||||||
\(68\) | 1.60768 | − | 5.99995i | 0.194960 | − | 0.727601i | ||||
\(69\) | 3.24213 | + | 1.49407i | 0.390307 | + | 0.179865i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 14.7384i | − | 1.74913i | −0.484910 | − | 0.874564i | \(-0.661148\pi\) | ||
0.484910 | − | 0.874564i | \(-0.338852\pi\) | |||||||
\(72\) | −1.38269 | − | 2.89671i | −0.162952 | − | 0.341380i | ||||
\(73\) | −2.84465 | − | 10.6164i | −0.332941 | − | 1.24255i | −0.906084 | − | 0.423098i | \(-0.860943\pi\) |
0.573143 | − | 0.819456i | \(-0.305724\pi\) | |||||||
\(74\) | 4.51169 | − | 7.81448i | 0.524474 | − | 0.908415i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.52046 | 0.403824 | ||||||||
\(77\) | 9.56583 | − | 10.3390i | 1.09013 | − | 1.17823i | ||||
\(78\) | 5.41159 | + | 14.6622i | 0.612742 | + | 1.66016i | ||||
\(79\) | −5.48749 | + | 3.16820i | −0.617391 | + | 0.356451i | −0.775853 | − | 0.630914i | \(-0.782680\pi\) |
0.158462 | + | 0.987365i | \(0.449347\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 6.99761 | + | 5.65981i | 0.777513 | + | 0.628867i | ||||
\(82\) | −1.94639 | + | 7.26404i | −0.214943 | + | 0.802179i | ||||
\(83\) | −1.57660 | − | 1.57660i | −0.173054 | − | 0.173054i | 0.615266 | − | 0.788320i | \(-0.289049\pi\) |
−0.788320 | + | 0.615266i | \(0.789049\pi\) | |||||||
\(84\) | −3.96422 | − | 5.16950i | −0.432532 | − | 0.564039i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | −0.575678 | + | 0.332368i | −0.0620770 | + | 0.0358402i | ||||
\(87\) | 0.600840 | − | 3.49974i | 0.0644168 | − | 0.375211i | ||||
\(88\) | 1.47425 | + | 5.50199i | 0.157156 | + | 0.586514i | ||||
\(89\) | −4.07820 | − | 7.06365i | −0.432289 | − | 0.748746i | 0.564781 | − | 0.825241i | \(-0.308960\pi\) |
−0.997070 | + | 0.0764948i | \(0.975627\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −6.88215 | − | 10.9184i | −0.721446 | − | 1.14456i | ||||
\(92\) | −2.07178 | + | 2.07178i | −0.215998 | + | 0.215998i | ||||
\(93\) | −3.16050 | − | 2.62778i | −0.327729 | − | 0.272488i | ||||
\(94\) | 13.7924 | + | 7.96305i | 1.42258 | + | 0.821326i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 11.6941 | − | 1.07626i | 1.19353 | − | 0.109845i | ||||
\(97\) | 7.54172 | + | 7.54172i | 0.765746 | + | 0.765746i | 0.977354 | − | 0.211609i | \(-0.0678702\pi\) |
−0.211609 | + | 0.977354i | \(0.567870\pi\) | |||||||
\(98\) | 9.83840 | + | 8.41804i | 0.993828 | + | 0.850351i | ||||
\(99\) | −10.3761 | − | 12.1417i | −1.04284 | − | 1.22029i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 9.23839 | + | 5.33378i | 0.919254 | + | 0.530731i | 0.883397 | − | 0.468626i | \(-0.155251\pi\) |
0.0358568 | + | 0.999357i | \(0.488584\pi\) | |||||||
\(102\) | 13.7974 | + | 2.36876i | 1.36615 | + | 0.234543i | ||||
\(103\) | −2.37835 | − | 0.637278i | −0.234346 | − | 0.0627928i | 0.139735 | − | 0.990189i | \(-0.455375\pi\) |
−0.374081 | + | 0.927396i | \(0.622042\pi\) | |||||||
\(104\) | 5.21929 | 0.511794 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 22.7693 | 2.21155 | ||||||||
\(107\) | 11.9953 | + | 3.21414i | 1.15963 | + | 0.310722i | 0.786819 | − | 0.617184i | \(-0.211727\pi\) |
0.372813 | + | 0.927907i | \(0.378393\pi\) | |||||||
\(108\) | −6.34657 | + | 3.77957i | −0.610699 | + | 0.363689i | ||||
\(109\) | 15.8009 | + | 9.12263i | 1.51345 | + | 0.873789i | 0.999876 | + | 0.0157428i | \(0.00501130\pi\) |
0.513572 | + | 0.858047i | \(0.328322\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.67362 | + | 3.53623i | 0.728348 | + | 0.335644i | ||||
\(112\) | −12.1863 | + | 3.77797i | −1.15150 | + | 0.356985i | ||||
\(113\) | 3.89017 | + | 3.89017i | 0.365956 | + | 0.365956i | 0.866000 | − | 0.500044i | \(-0.166683\pi\) |
−0.500044 | + | 0.866000i | \(0.666683\pi\) | |||||||
\(114\) | 0.727140 | + | 7.90077i | 0.0681029 | + | 0.739975i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 2.52398 | + | 1.45722i | 0.234345 | + | 0.135299i | ||||
\(117\) | −13.2070 | + | 6.30416i | −1.22099 | + | 0.582820i | ||||
\(118\) | 4.44819 | − | 4.44819i | 0.409489 | − | 0.409489i | ||||
\(119\) | −11.5519 | + | 0.448692i | −1.05896 | + | 0.0411315i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 8.67136 | + | 15.0192i | 0.788306 | + | 1.36539i | ||||
\(122\) | −3.78923 | − | 14.1416i | −0.343061 | − | 1.28032i | ||||
\(123\) | −6.94022 | − | 1.19151i | −0.625779 | − | 0.107435i | ||||
\(124\) | 2.92152 | − | 1.68674i | 0.262360 | − | 0.151474i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | 10.7828 | − | 9.96443i | 0.960612 | − | 0.887702i | ||||
\(127\) | −2.80299 | − | 2.80299i | −0.248725 | − | 0.248725i | 0.571722 | − | 0.820447i | \(-0.306276\pi\) |
−0.820447 | + | 0.571722i | \(0.806276\pi\) | |||||||
\(128\) | 2.12270 | − | 7.92202i | 0.187622 | − | 0.700214i | ||||
\(129\) | −0.359311 | − | 0.508257i | −0.0316356 | − | 0.0447495i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −10.1898 | + | 5.88311i | −0.890291 | + | 0.514010i | −0.874038 | − | 0.485858i | \(-0.838507\pi\) |
−0.0162535 | + | 0.999868i | \(0.505174\pi\) | |||||||
\(132\) | 12.2976 | − | 4.53887i | 1.07037 | − | 0.395058i | ||||
\(133\) | −1.94015 | − | 6.25819i | −0.168232 | − | 0.542654i | ||||
\(134\) | −5.29583 | −0.457490 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 2.33753 | − | 4.04872i | 0.200442 | − | 0.347175i | ||||
\(137\) | 4.71026 | + | 17.5789i | 0.402425 | + | 1.50187i | 0.808756 | + | 0.588144i | \(0.200141\pi\) |
−0.406331 | + | 0.913726i | \(0.633192\pi\) | |||||||
\(138\) | −5.07750 | − | 4.22166i | −0.432226 | − | 0.359372i | ||||
\(139\) | − | 18.0947i | − | 1.53478i | −0.641183 | − | 0.767388i | \(-0.721556\pi\) | ||
0.641183 | − | 0.767388i | \(-0.278444\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −6.24138 | + | 13.5438i | −0.525619 | + | 1.14059i | ||||
\(142\) | −7.05603 | + | 26.3335i | −0.592129 | + | 2.20986i | ||||
\(143\) | 25.0854 | − | 6.72161i | 2.09775 | − | 0.562089i | ||||
\(144\) | 2.64051 | + | 14.2238i | 0.220043 | + | 1.18532i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 20.3304i | 1.68256i | ||||||||
\(147\) | −7.00494 | + | 9.89600i | −0.577758 | + | 0.816208i | ||||
\(148\) | −4.90358 | + | 4.90358i | −0.403072 | + | 0.403072i | ||||
\(149\) | −1.27294 | − | 2.20479i | −0.104283 | − | 0.180623i | 0.809162 | − | 0.587586i | \(-0.199921\pi\) |
−0.913445 | + | 0.406962i | \(0.866588\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 3.21101 | − | 5.56163i | 0.261308 | − | 0.452599i | −0.705282 | − | 0.708927i | \(-0.749179\pi\) |
0.966590 | + | 0.256328i | \(0.0825128\pi\) | |||||||
\(152\) | 2.55933 | + | 0.685770i | 0.207589 | + | 0.0556233i | ||||
\(153\) | −1.02467 | + | 13.0684i | −0.0828400 | + | 1.05652i | ||||
\(154\) | −22.0413 | + | 13.8932i | −1.77614 | + | 1.11955i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.10079 | − | 11.9607i | −0.0881340 | − | 0.957624i | ||||
\(157\) | 17.5121 | − | 4.69234i | 1.39761 | − | 0.374490i | 0.520127 | − | 0.854089i | \(-0.325885\pi\) |
0.877487 | + | 0.479600i | \(0.159218\pi\) | |||||||
\(158\) | 11.3214 | − | 3.03356i | 0.900683 | − | 0.241337i | ||||
\(159\) | 1.95395 | + | 21.2307i | 0.154958 | + | 1.68370i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 4.82470 | + | 2.54116i | 0.380240 | + | 0.200271i | ||||
\(162\) | −9.79316 | − | 13.4626i | −0.769423 | − | 1.05772i | ||||
\(163\) | 4.94341 | + | 1.32458i | 0.387198 | + | 0.103749i | 0.447166 | − | 0.894451i | \(-0.352433\pi\) |
−0.0599682 | + | 0.998200i | \(0.519100\pi\) | |||||||
\(164\) | 2.88977 | − | 5.00522i | 0.225653 | − | 0.390842i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 2.06214 | + | 3.57174i | 0.160053 | + | 0.277221i | ||||
\(167\) | 7.80577 | − | 7.80577i | 0.604028 | − | 0.604028i | −0.337351 | − | 0.941379i | \(-0.609531\pi\) |
0.941379 | + | 0.337351i | \(0.109531\pi\) | |||||||
\(168\) | −1.87494 | − | 4.53038i | −0.144655 | − | 0.349526i | ||||
\(169\) | − | 10.7965i | − | 0.830498i | ||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −7.30451 | + | 1.35601i | −0.558590 | + | 0.103697i | ||||
\(172\) | 0.493460 | − | 0.132222i | 0.0376259 | − | 0.0100818i | ||||
\(173\) | −5.26428 | + | 19.6466i | −0.400236 | + | 1.49370i | 0.412440 | + | 0.910985i | \(0.364677\pi\) |
−0.812676 | + | 0.582716i | \(0.801990\pi\) | |||||||
\(174\) | −2.74904 | + | 5.96541i | −0.208404 | + | 0.452236i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | − | 25.6727i | − | 1.93516i | ||||||
\(177\) | 4.52934 | + | 3.76589i | 0.340446 | + | 0.283062i | ||||
\(178\) | 3.90489 | + | 14.5732i | 0.292684 | + | 1.09231i | ||||
\(179\) | −3.30836 | + | 5.73025i | −0.247279 | + | 0.428299i | −0.962770 | − | 0.270323i | \(-0.912870\pi\) |
0.715491 | + | 0.698622i | \(0.246203\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.70804 | −0.647264 | −0.323632 | − | 0.946183i | \(-0.604904\pi\) | ||||
−0.323632 | + | 0.946183i | \(0.604904\pi\) | |||||||
\(182\) | 7.06931 | + | 22.8030i | 0.524012 | + | 1.69027i | ||||
\(183\) | 12.8609 | − | 4.74675i | 0.950702 | − | 0.350890i | ||||
\(184\) | −1.90973 | + | 1.10258i | −0.140787 | + | 0.0812836i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 4.38889 | + | 6.20821i | 0.321809 | + | 0.455208i | ||||
\(187\) | 6.02073 | − | 22.4697i | 0.440279 | − | 1.64314i | ||||
\(188\) | −8.65471 | − | 8.65471i | −0.631210 | − | 0.631210i | ||||
\(189\) | 10.2165 | + | 9.19914i | 0.743137 | + | 0.669139i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 0.256493 | − | 0.148087i | 0.0185592 | − | 0.0107152i | −0.490692 | − | 0.871333i | \(-0.663256\pi\) |
0.509251 | + | 0.860618i | \(0.329923\pi\) | |||||||
\(192\) | −4.94547 | − | 0.849045i | −0.356908 | − | 0.0612745i | ||||
\(193\) | −2.78610 | − | 10.3979i | −0.200548 | − | 0.748456i | −0.990761 | − | 0.135623i | \(-0.956696\pi\) |
0.790212 | − | 0.612833i | \(-0.209970\pi\) | |||||||
\(194\) | −9.86436 | − | 17.0856i | −0.708220 | − | 1.22667i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −5.62900 | − | 8.20599i | −0.402071 | − | 0.586142i | ||||
\(197\) | −0.160785 | + | 0.160785i | −0.0114555 | + | 0.0114555i | −0.712811 | − | 0.701356i | \(-0.752578\pi\) |
0.701356 | + | 0.712811i | \(0.252578\pi\) | |||||||
\(198\) | 12.7264 | + | 26.6614i | 0.904425 | + | 1.89475i | ||||
\(199\) | 5.92757 | + | 3.42229i | 0.420195 | + | 0.242599i | 0.695161 | − | 0.718854i | \(-0.255333\pi\) |
−0.274966 | + | 0.961454i | \(0.588667\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −0.454462 | − | 4.93798i | −0.0320553 | − | 0.348298i | ||||
\(202\) | −13.9529 | − | 13.9529i | −0.981721 | − | 0.981721i | ||||
\(203\) | 1.19947 | − | 5.28987i | 0.0841860 | − | 0.371276i | ||||
\(204\) | −9.77120 | − | 4.50286i | −0.684121 | − | 0.315263i | ||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 3.94436 | + | 2.27728i | 0.274817 | + | 0.158665i | ||||
\(207\) | 3.50067 | − | 5.09669i | 0.243314 | − | 0.354245i | ||||
\(208\) | −22.7223 | − | 6.08841i | −1.57550 | − | 0.422155i | ||||
\(209\) | 13.1840 | 0.911958 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −6.49776 | −0.447324 | −0.223662 | − | 0.974667i | \(-0.571801\pi\) | ||||
−0.223662 | + | 0.974667i | \(0.571801\pi\) | |||||||
\(212\) | −16.9025 | − | 4.52901i | −1.16087 | − | 0.311054i | ||||
\(213\) | −25.1596 | − | 4.31944i | −1.72391 | − | 0.295963i | ||||
\(214\) | −19.8935 | − | 11.4855i | −1.35989 | − | 0.785136i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −5.35013 | + | 1.51142i | −0.364030 | + | 0.102839i | ||||
\(217\) | −4.60852 | − | 4.26390i | −0.312847 | − | 0.289453i | ||||
\(218\) | −23.8643 | − | 23.8643i | −1.61629 | − | 1.61629i | ||||
\(219\) | −18.9567 | + | 1.74466i | −1.28097 | + | 0.117893i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −18.4595 | − | 10.6576i | −1.24172 | − | 0.716906i | ||||
\(222\) | −12.0177 | − | 9.99202i | −0.806573 | − | 0.670621i | ||||
\(223\) | 0.832465 | − | 0.832465i | 0.0557460 | − | 0.0557460i | −0.678684 | − | 0.734430i | \(-0.737449\pi\) |
0.734430 | + | 0.678684i | \(0.237449\pi\) | |||||||
\(224\) | 17.9250 | − | 0.696234i | 1.19767 | − | 0.0465191i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −5.08823 | − | 8.81308i | −0.338464 | − | 0.586237i | ||||
\(227\) | 4.01248 | + | 14.9748i | 0.266318 | + | 0.993912i | 0.961439 | + | 0.275019i | \(0.0886842\pi\) |
−0.695121 | + | 0.718893i | \(0.744649\pi\) | |||||||
\(228\) | 1.03175 | − | 6.00969i | 0.0683294 | − | 0.398001i | ||||
\(229\) | 9.74226 | − | 5.62470i | 0.643787 | − | 0.371690i | −0.142285 | − | 0.989826i | \(-0.545445\pi\) |
0.786072 | + | 0.618135i | \(0.212112\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −14.8459 | − | 19.3597i | −0.976788 | − | 1.27377i | ||||
\(232\) | 1.55104 | + | 1.55104i | 0.101831 | + | 0.101831i | ||||
\(233\) | 6.74201 | − | 25.1615i | 0.441684 | − | 1.64839i | −0.282863 | − | 0.959160i | \(-0.591284\pi\) |
0.724547 | − | 0.689226i | \(-0.242049\pi\) | |||||||
\(234\) | 26.6154 | − | 4.94090i | 1.73991 | − | 0.322997i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −4.18685 | + | 2.41728i | −0.272540 | + | 0.157351i | ||||
\(237\) | 3.80013 | + | 10.2961i | 0.246845 | + | 0.668802i | ||||
\(238\) | 20.8549 | + | 4.72880i | 1.35182 | + | 0.306523i | ||||
\(239\) | −1.44722 | −0.0936127 | −0.0468063 | − | 0.998904i | \(-0.514904\pi\) | ||||
−0.0468063 | + | 0.998904i | \(0.514904\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −11.8069 | + | 20.4502i | −0.760550 | + | 1.31731i | 0.182017 | + | 0.983295i | \(0.441737\pi\) |
−0.942567 | + | 0.334016i | \(0.891596\pi\) | |||||||
\(242\) | −8.30285 | − | 30.9866i | −0.533727 | − | 1.99190i | ||||
\(243\) | 11.7125 | − | 10.2867i | 0.751359 | − | 0.659893i | ||||
\(244\) | 11.2516i | 0.720308i | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 11.8298 | + | 5.45153i | 0.754242 | + | 0.347577i | ||||
\(247\) | 3.12665 | − | 11.6688i | 0.198944 | − | 0.742469i | ||||
\(248\) | 2.45248 | − | 0.657139i | 0.155732 | − | 0.0417284i | ||||
\(249\) | −3.15343 | + | 2.22931i | −0.199840 | + | 0.141277i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | − | 14.3739i | − | 0.907273i | −0.891187 | − | 0.453637i | \(-0.850126\pi\) | ||
0.891187 | − | 0.453637i | \(-0.149874\pi\) | |||||||
\(252\) | −9.98654 | + | 5.25218i | −0.629093 | + | 0.330856i | ||||
\(253\) | −7.75876 | + | 7.75876i | −0.487789 | + | 0.487789i | ||||
\(254\) | 3.66624 | + | 6.35011i | 0.230040 | + | 0.398441i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −10.4824 | + | 18.1560i | −0.655149 | + | 1.13475i | ||||
\(257\) | 7.36234 | + | 1.97273i | 0.459250 | + | 0.123056i | 0.481025 | − | 0.876707i | \(-0.340265\pi\) |
−0.0217741 | + | 0.999763i | \(0.506931\pi\) | |||||||
\(258\) | 0.398662 | + | 1.08014i | 0.0248196 | + | 0.0672463i | ||||
\(259\) | 11.4193 | + | 6.01453i | 0.709562 | + | 0.373724i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −5.79823 | − | 2.05136i | −0.358901 | − | 0.126976i | ||||
\(262\) | 21.0230 | − | 5.63309i | 1.29880 | − | 0.348014i | ||||
\(263\) | −19.4637 | + | 5.21527i | −1.20018 | + | 0.321588i | −0.802902 | − | 0.596110i | \(-0.796712\pi\) |
−0.397279 | + | 0.917698i | \(0.630045\pi\) | |||||||
\(264\) | 9.82438 | − | 0.904177i | 0.604649 | − | 0.0556483i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 0.470389 | + | 12.1105i | 0.0288414 | + | 0.742543i | ||||
\(267\) | −13.2534 | + | 4.89163i | −0.811095 | + | 0.299363i | ||||
\(268\) | 3.93130 | + | 1.05339i | 0.240142 | + | 0.0643459i | ||||
\(269\) | 7.88383 | − | 13.6552i | 0.480686 | − | 0.832572i | −0.519069 | − | 0.854732i | \(-0.673721\pi\) |
0.999754 | + | 0.0221606i | \(0.00705452\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 0.445532 | + | 0.771684i | 0.0270641 | + | 0.0468765i | 0.879240 | − | 0.476379i | \(-0.158051\pi\) |
−0.852176 | + | 0.523255i | \(0.824717\pi\) | |||||||
\(272\) | −14.8994 | + | 14.8994i | −0.903408 | + | 0.903408i | ||||
\(273\) | −20.6555 | + | 8.54847i | −1.25013 | + | 0.517377i | ||||
\(274\) | − | 33.6637i | − | 2.03370i | ||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 2.92950 | + | 4.14387i | 0.176335 | + | 0.249431i | ||||
\(277\) | −20.4274 | + | 5.47349i | −1.22736 | + | 0.328870i | −0.813551 | − | 0.581493i | \(-0.802469\pi\) |
−0.413809 | + | 0.910364i | \(0.635802\pi\) | |||||||
\(278\) | −8.66287 | + | 32.3303i | −0.519565 | + | 1.93904i | ||||
\(279\) | −5.41208 | + | 4.62508i | −0.324013 | + | 0.276896i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 15.1742i | 0.905215i | 0.891710 | + | 0.452608i | \(0.149506\pi\) | ||||
−0.891710 | + | 0.452608i | \(0.850494\pi\) | |||||||
\(282\) | 17.6357 | − | 21.2109i | 1.05019 | − | 1.26309i | ||||
\(283\) | 7.34572 | + | 27.4146i | 0.436658 | + | 1.62963i | 0.737068 | + | 0.675819i | \(0.236210\pi\) |
−0.300410 | + | 0.953810i | \(0.597123\pi\) | |||||||
\(284\) | 10.4759 | − | 18.1449i | 0.621632 | − | 1.07670i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −48.0386 | −2.84058 | ||||||||
\(287\) | −10.4902 | − | 2.37863i | −0.619215 | − | 0.140406i | ||||
\(288\) | 1.58998 | − | 20.2782i | 0.0936906 | − | 1.19490i | ||||
\(289\) | −1.81221 | + | 1.04628i | −0.106601 | + | 0.0615458i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 15.0846 | − | 10.6640i | 0.884273 | − | 0.625136i | ||||
\(292\) | 4.04390 | − | 15.0921i | 0.236652 | − | 0.883196i | ||||
\(293\) | 9.07274 | + | 9.07274i | 0.530035 | + | 0.530035i | 0.920583 | − | 0.390548i | \(-0.127714\pi\) |
−0.390548 | + | 0.920583i | \(0.627714\pi\) | |||||||
\(294\) | 17.2536 | − | 14.3278i | 1.00625 | − | 0.835614i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −4.52004 | + | 2.60965i | −0.262722 | + | 0.151683i | ||||
\(297\) | −23.7678 | + | 14.1544i | −1.37915 | + | 0.821322i | ||||
\(298\) | 1.21884 | + | 4.54877i | 0.0706055 | + | 0.263503i | ||||
\(299\) | 5.02704 | + | 8.70710i | 0.290721 | + | 0.503544i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −0.506995 | − | 0.804337i | −0.0292227 | − | 0.0463612i | ||||
\(302\) | −8.39982 | + | 8.39982i | −0.483355 | + | 0.483355i | ||||
\(303\) | 11.8127 | − | 14.2074i | 0.678622 | − | 0.816196i | ||||
\(304\) | −10.3421 | − | 5.97102i | −0.593161 | − | 0.342461i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 8.08732 | − | 22.8590i | 0.462321 | − | 1.30676i | ||||
\(307\) | 5.35299 | + | 5.35299i | 0.305511 | + | 0.305511i | 0.843165 | − | 0.537654i | \(-0.180689\pi\) |
−0.537654 | + | 0.843165i | \(0.680689\pi\) | |||||||
\(308\) | 19.1256 | − | 5.92926i | 1.08978 | − | 0.337851i | ||||
\(309\) | −1.78491 | + | 3.87326i | −0.101540 | + | 0.220342i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 1.32067 | + | 0.762488i | 0.0748883 | + | 0.0432368i | 0.536977 | − | 0.843597i | \(-0.319566\pi\) |
−0.462088 | + | 0.886834i | \(0.652900\pi\) | |||||||
\(312\) | 1.52963 | − | 8.90973i | 0.0865985 | − | 0.504414i | ||||
\(313\) | 22.0134 | + | 5.89848i | 1.24427 | + | 0.333402i | 0.820121 | − | 0.572190i | \(-0.193906\pi\) |
0.424151 | + | 0.905592i | \(0.360573\pi\) | |||||||
\(314\) | −33.5357 | −1.89253 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −9.00773 | −0.506724 | ||||||||
\(317\) | 9.10844 | + | 2.44060i | 0.511581 | + | 0.137078i | 0.505370 | − | 0.862903i | \(-0.331356\pi\) |
0.00621145 | + | 0.999981i | \(0.498023\pi\) | |||||||
\(318\) | 6.67306 | − | 38.8688i | 0.374207 | − | 2.17966i | ||||
\(319\) | 9.45222 | + | 5.45724i | 0.529223 | + | 0.305547i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 9.00228 | − | 19.5349i | 0.502458 | − | 1.09033i | ||||
\(322\) | −7.40382 | − | 6.85017i | −0.412599 | − | 0.381745i | ||||
\(323\) | −7.65146 | − | 7.65146i | −0.425738 | − | 0.425738i | ||||
\(324\) | 4.59200 | + | 11.9418i | 0.255111 | + | 0.663432i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −8.19836 | − | 4.73333i | −0.454065 | − | 0.262155i | ||||
\(327\) | 20.2038 | − | 24.2997i | 1.11727 | − | 1.34377i | ||||
\(328\) | 3.07582 | − | 3.07582i | 0.169834 | − | 0.169834i | ||||
\(329\) | −10.6155 | + | 20.1548i | −0.585252 | + | 1.11117i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −2.28471 | − | 3.95724i | −0.125579 | − | 0.217510i | 0.796380 | − | 0.604797i | \(-0.206746\pi\) |
−0.921959 | + | 0.387287i | \(0.873412\pi\) | |||||||
\(332\) | −0.820358 | − | 3.06162i | −0.0450230 | − | 0.168028i | ||||
\(333\) | 8.28555 | − | 12.0631i | 0.454045 | − | 0.661053i | ||||
\(334\) | −17.6838 | + | 10.2097i | −0.967612 | + | 0.558651i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | 2.87780 | + | 21.9102i | 0.156997 | + | 1.19530i | ||||
\(337\) | −7.88524 | − | 7.88524i | −0.429537 | − | 0.429537i | 0.458934 | − | 0.888470i | \(-0.348232\pi\) |
−0.888470 | + | 0.458934i | \(0.848232\pi\) | |||||||
\(338\) | −5.16882 | + | 19.2903i | −0.281147 | + | 1.04925i | ||||
\(339\) | 7.78092 | − | 5.50071i | 0.422601 | − | 0.298758i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | 10.9410 | − | 6.31679i | 0.592489 | − | 0.342073i | ||||
\(342\) | 13.7003 | + | 1.07422i | 0.740829 | + | 0.0580873i | ||||
\(343\) | −11.4853 | + | 14.5288i | −0.620149 | + | 0.784484i | ||||
\(344\) | 0.384495 | 0.0207306 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 18.8116 | − | 32.5827i | 1.01132 | − | 1.75166i | ||||
\(347\) | −8.58998 | − | 32.0582i | −0.461134 | − | 1.72098i | −0.669399 | − | 0.742903i | \(-0.733448\pi\) |
0.208265 | − | 0.978072i | \(-0.433218\pi\) | |||||||
\(348\) | 3.22729 | − | 3.88155i | 0.173001 | − | 0.208073i | ||||
\(349\) | 31.6736i | 1.69545i | 0.530437 | + | 0.847724i | \(0.322028\pi\) | ||||
−0.530437 | + | 0.847724i | \(0.677972\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 6.89105 | + | 24.3930i | 0.367817 | + | 1.30200i | ||||
\(352\) | −9.34234 | + | 34.8661i | −0.497948 | + | 1.85837i | ||||
\(353\) | −3.43985 | + | 0.921705i | −0.183085 | + | 0.0490574i | −0.349196 | − | 0.937050i | \(-0.613545\pi\) |
0.166112 | + | 0.986107i | \(0.446879\pi\) | |||||||
\(354\) | −6.28975 | − | 8.89704i | −0.334296 | − | 0.472872i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 11.5950i | − | 0.614534i | ||||||
\(357\) | −2.61960 | + | 19.8515i | −0.138644 | + | 1.05065i | ||||
\(358\) | 8.65449 | − | 8.65449i | 0.457404 | − | 0.457404i | ||||
\(359\) | 3.21386 | + | 5.56657i | 0.169621 | + | 0.293792i | 0.938287 | − | 0.345859i | \(-0.112412\pi\) |
−0.768666 | + | 0.639651i | \(0.779079\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −6.43363 | + | 11.1434i | −0.338612 | + | 0.586494i | ||||
\(362\) | 15.5589 | + | 4.16898i | 0.817756 | + | 0.219117i | ||||
\(363\) | 28.1803 | − | 10.4009i | 1.47908 | − | 0.545908i | ||||
\(364\) | −0.712106 | − | 18.3337i | −0.0373245 | − | 0.960946i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −25.2513 | + | 2.32398i | −1.31991 | + | 0.121476i | ||||
\(367\) | 16.8145 | − | 4.50544i | 0.877712 | − | 0.235182i | 0.208292 | − | 0.978067i | \(-0.433210\pi\) |
0.669420 | + | 0.742884i | \(0.266543\pi\) | |||||||
\(368\) | 9.60023 | − | 2.57237i | 0.500447 | − | 0.134094i | ||||
\(369\) | −4.06799 | + | 11.4983i | −0.211771 | + | 0.598577i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 1.26401 | + | 32.5430i | 0.0656243 | + | 1.68955i | ||||
\(372\) | −2.02317 | − | 5.48159i | −0.104897 | − | 0.284207i | ||||
\(373\) | −16.4184 | − | 4.39929i | −0.850111 | − | 0.227787i | −0.192643 | − | 0.981269i | \(-0.561706\pi\) |
−0.657468 | + | 0.753482i | \(0.728373\pi\) | |||||||
\(374\) | −21.5148 | + | 37.2646i | −1.11250 | + | 1.92691i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −4.60597 | − | 7.97777i | −0.237535 | − | 0.411422i | ||||
\(377\) | 7.07170 | − | 7.07170i | 0.364211 | − | 0.364211i | ||||
\(378\) | −13.8499 | − | 21.3274i | −0.712361 | − | 1.09697i | ||||
\(379\) | 0.345401i | 0.0177420i | 0.999961 | + | 0.00887102i | \(0.00282377\pi\) | ||||
−0.999961 | + | 0.00887102i | \(0.997176\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −5.60640 | + | 3.96344i | −0.287225 | + | 0.203053i | ||||
\(382\) | −0.529179 | + | 0.141793i | −0.0270752 | + | 0.00725477i | ||||
\(383\) | −2.21949 | + | 8.28324i | −0.113411 | + | 0.423254i | −0.999163 | − | 0.0409038i | \(-0.986976\pi\) |
0.885753 | + | 0.464158i | \(0.153643\pi\) | |||||||
\(384\) | −12.9014 | − | 5.94534i | −0.658371 | − | 0.303397i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 19.9120i | 1.01349i | ||||||||
\(387\) | −0.972938 | + | 0.464416i | −0.0494572 | + | 0.0236076i | ||||
\(388\) | 3.92422 | + | 14.6454i | 0.199222 | + | 0.743507i | ||||
\(389\) | −9.20300 | + | 15.9401i | −0.466611 | + | 0.808193i | −0.999273 | − | 0.0381349i | \(-0.987858\pi\) |
0.532662 | + | 0.846328i | \(0.321192\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 9.00572 | 0.455439 | ||||||||
\(392\) | −2.49372 | − | 7.06216i | −0.125952 | − | 0.356693i | ||||
\(393\) | 7.05655 | + | 19.1190i | 0.355956 | + | 0.964427i | ||||
\(394\) | 0.364254 | − | 0.210302i | 0.0183509 | − | 0.0105949i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −4.14409 | − | 22.3232i | −0.208248 | − | 1.12178i | ||||
\(397\) | −6.02986 | + | 22.5038i | −0.302630 | + | 1.12943i | 0.632336 | + | 0.774694i | \(0.282096\pi\) |
−0.934966 | + | 0.354737i | \(0.884570\pi\) | |||||||
\(398\) | −8.95251 | − | 8.95251i | −0.448749 | − | 0.448749i | ||||
\(399\) | −11.2518 | + | 1.47787i | −0.563295 | + | 0.0739860i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 28.1317 | − | 16.2419i | 1.40483 | − | 0.811080i | 0.409949 | − | 0.912109i | \(-0.365547\pi\) |
0.994884 | + | 0.101028i | \(0.0322133\pi\) | |||||||
\(402\) | −1.55206 | + | 9.04038i | −0.0774099 | + | 0.450893i | ||||
\(403\) | −2.99611 | − | 11.1816i | −0.149247 | − | 0.556997i | ||||
\(404\) | 7.58241 | + | 13.1331i | 0.377239 | + | 0.653397i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −4.67564 | + | 8.87728i | −0.232048 | + | 0.440572i | ||||
\(407\) | −18.3638 | + | 18.3638i | −0.910259 | + | 0.910259i | ||||
\(408\) | −6.22641 | − | 5.17692i | −0.308253 | − | 0.256295i | ||||
\(409\) | −3.74989 | − | 2.16500i | −0.185420 | − | 0.107052i | 0.404417 | − | 0.914575i | \(-0.367475\pi\) |
−0.589837 | + | 0.807523i | \(0.700808\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 31.3890 | − | 2.88886i | 1.54831 | − | 0.142497i | ||||
\(412\) | −2.47508 | − | 2.47508i | −0.121938 | − | 0.121938i | ||||
\(413\) | 6.60451 | + | 6.11063i | 0.324987 | + | 0.300685i | ||||
\(414\) | −8.69478 | + | 7.43043i | −0.427325 | + | 0.365186i | ||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 28.6435 | + | 16.5373i | 1.40436 | + | 0.810808i | ||||
\(417\) | −30.8891 | − | 5.30308i | −1.51265 | − | 0.259693i | ||||
\(418\) | −23.5562 | − | 6.31186i | −1.15217 | − | 0.308723i | ||||
\(419\) | 33.4081 | 1.63209 | 0.816046 | − | 0.577986i | \(-0.196161\pi\) | ||||
0.816046 | + | 0.577986i | \(0.196161\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 17.3681 | 0.846471 | 0.423236 | − | 0.906020i | \(-0.360894\pi\) | ||||
0.423236 | + | 0.906020i | \(0.360894\pi\) | |||||||
\(422\) | 11.6097 | + | 3.11081i | 0.565152 | + | 0.151432i | ||||
\(423\) | 21.2911 | + | 14.6238i | 1.03521 | + | 0.711035i | ||||
\(424\) | −11.4057 | − | 6.58507i | −0.553909 | − | 0.319800i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 42.8853 | + | 19.7628i | 2.07780 | + | 0.957512i | ||||
\(427\) | 20.0015 | − | 6.20082i | 0.967942 | − | 0.300079i | ||||
\(428\) | 12.4832 | + | 12.4832i | 0.603397 | + | 0.603397i | ||||
\(429\) | −4.12244 | − | 44.7926i | −0.199033 | − | 2.16261i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −19.4574 | − | 11.2337i | −0.937228 | − | 0.541109i | −0.0481375 | − | 0.998841i | \(-0.515329\pi\) |
−0.889090 | + | 0.457732i | \(0.848662\pi\) | |||||||
\(432\) | 25.0550 | − | 0.338941i | 1.20546 | − | 0.0163073i | ||||
\(433\) | 7.76189 | − | 7.76189i | 0.373013 | − | 0.373013i | −0.495561 | − | 0.868573i | \(-0.665037\pi\) |
0.868573 | + | 0.495561i | \(0.165037\pi\) | |||||||
\(434\) | 6.19280 | + | 9.82475i | 0.297264 | + | 0.471603i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 12.9686 | + | 22.4622i | 0.621082 | + | 1.07575i | ||||
\(437\) | 1.32102 | + | 4.93012i | 0.0631930 | + | 0.235839i | ||||
\(438\) | 34.7056 | + | 5.95830i | 1.65830 | + | 0.284699i | ||||
\(439\) | −4.35444 | + | 2.51404i | −0.207826 | + | 0.119988i | −0.600301 | − | 0.799774i | \(-0.704952\pi\) |
0.392475 | + | 0.919763i | \(0.371619\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 14.8403 | + | 14.8582i | 0.706679 | + | 0.707534i | ||||
\(442\) | 27.8796 | + | 27.8796i | 1.32610 | + | 1.32610i | ||||
\(443\) | −2.56800 | + | 9.58391i | −0.122009 | + | 0.455345i | −0.999715 | − | 0.0238542i | \(-0.992406\pi\) |
0.877706 | + | 0.479199i | \(0.159073\pi\) | |||||||
\(444\) | 6.93367 | + | 9.80789i | 0.329058 | + | 0.465462i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | −1.88593 | + | 1.08884i | −0.0893013 | + | 0.0515581i | ||||
\(447\) | −4.13681 | + | 1.52683i | −0.195664 | + | 0.0722168i | ||||
\(448\) | −7.47509 | − | 1.69496i | −0.353165 | − | 0.0800794i | ||||
\(449\) | 3.59510 | 0.169663 | 0.0848317 | − | 0.996395i | \(-0.472965\pi\) | ||||
0.0848317 | + | 0.996395i | \(0.472965\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 10.8221 | − | 18.7444i | 0.509593 | − | 0.882641i | ||||
\(452\) | 2.02419 | + | 7.55439i | 0.0952100 | + | 0.355328i | ||||
\(453\) | −8.55306 | − | 7.11140i | −0.401858 | − | 0.334123i | ||||
\(454\) | − | 28.6768i | − | 1.34587i | ||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 1.92073 | − | 4.16799i | 0.0899465 | − | 0.195184i | ||||
\(457\) | −1.77045 | + | 6.60740i | −0.0828181 | + | 0.309081i | −0.994892 | − | 0.100944i | \(-0.967814\pi\) |
0.912074 | + | 0.410026i | \(0.134480\pi\) | |||||||
\(458\) | −20.0996 | + | 5.38566i | −0.939190 | + | 0.251655i | ||||
\(459\) | 22.0084 | + | 5.57919i | 1.02727 | + | 0.260414i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 2.00072i | − | 0.0931829i | −0.998914 | − | 0.0465915i | \(-0.985164\pi\) | ||
0.998914 | − | 0.0465915i | \(-0.0148359\pi\) | |||||||
\(462\) | 17.2570 | + | 41.6978i | 0.802870 | + | 1.93996i | ||||
\(463\) | −29.2416 | + | 29.2416i | −1.35897 | + | 1.35897i | −0.483786 | + | 0.875186i | \(0.660739\pi\) |
−0.875186 | + | 0.483786i | \(0.839261\pi\) | |||||||
\(464\) | −4.94315 | − | 8.56179i | −0.229480 | − | 0.397471i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −24.0922 | + | 41.7289i | −1.11605 | + | 1.93306i | ||||
\(467\) | −13.6417 | − | 3.65529i | −0.631265 | − | 0.169147i | −0.0710212 | − | 0.997475i | \(-0.522626\pi\) |
−0.560244 | + | 0.828328i | \(0.689292\pi\) | |||||||
\(468\) | −20.7405 | − | 1.62623i | −0.958728 | − | 0.0751725i | ||||
\(469\) | −0.293993 | − | 7.56906i | −0.0135753 | − | 0.349507i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −2.87787 | − | 31.2696i | −0.132605 | − | 1.44083i | ||||
\(472\) | −3.51466 | + | 0.941751i | −0.161775 | + | 0.0433476i | ||||
\(473\) | 1.84799 | − | 0.495168i | 0.0849708 | − | 0.0227679i | ||||
\(474\) | −1.86052 | − | 20.2156i | −0.0854565 | − | 0.928531i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −14.5408 | − | 7.65860i | −0.666476 | − | 0.351031i | ||||
\(477\) | 36.8151 | + | 2.88662i | 1.68565 | + | 0.132169i | ||||
\(478\) | 2.58578 | + | 0.692856i | 0.118271 | + | 0.0316905i | ||||
\(479\) | 8.02039 | − | 13.8917i | 0.366461 | − | 0.634729i | −0.622548 | − | 0.782581i | \(-0.713903\pi\) |
0.989009 | + | 0.147852i | \(0.0472360\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 11.8982 | + | 20.6083i | 0.542513 | + | 0.939660i | ||||
\(482\) | 30.8862 | − | 30.8862i | 1.40683 | − | 1.40683i | ||||
\(483\) | 5.75194 | − | 7.49138i | 0.261722 | − | 0.340870i | ||||
\(484\) | 24.6541i | 1.12064i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −25.8518 | + | 12.7721i | −1.17266 | + | 0.579356i | ||||
\(487\) | −4.68754 | + | 1.25602i | −0.212413 | + | 0.0569158i | −0.363456 | − | 0.931611i | \(-0.618403\pi\) |
0.151044 | + | 0.988527i | \(0.451737\pi\) | |||||||
\(488\) | −2.19176 | + | 8.17976i | −0.0992163 | + | 0.370280i | ||||
\(489\) | 3.70995 | − | 8.05058i | 0.167770 | − | 0.364060i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | − | 15.9243i | − | 0.718652i | −0.933212 | − | 0.359326i | \(-0.883007\pi\) | ||
0.933212 | − | 0.359326i | \(-0.116993\pi\) | |||||||
\(492\) | −7.69738 | − | 6.39995i | −0.347025 | − | 0.288532i | ||||
\(493\) | −2.31852 | − | 8.65284i | −0.104421 | − | 0.389704i | ||||
\(494\) | −11.1729 | + | 19.3521i | −0.502694 | + | 0.870691i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −11.4435 | −0.513826 | ||||||||
\(497\) | −38.0288 | − | 8.62296i | −1.70583 | − | 0.386793i | ||||
\(498\) | 6.70159 | − | 2.47345i | 0.300305 | − | 0.110838i | ||||
\(499\) | 9.09769 | − | 5.25255i | 0.407268 | − | 0.235137i | −0.282347 | − | 0.959312i | \(-0.591113\pi\) |
0.689615 | + | 0.724176i | \(0.257780\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −11.0374 | − | 15.6127i | −0.493114 | − | 0.697524i | ||||
\(502\) | −6.88153 | + | 25.6822i | −0.307138 | + | 1.14625i | ||||
\(503\) | 9.84893 | + | 9.84893i | 0.439142 | + | 0.439142i | 0.891723 | − | 0.452581i | \(-0.149497\pi\) |
−0.452581 | + | 0.891723i | \(0.649497\pi\) | |||||||
\(504\) | −8.28320 | + | 1.87293i | −0.368963 | + | 0.0834270i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 17.5773 | − | 10.1482i | 0.781405 | − | 0.451144i | ||||
\(507\) | −18.4304 | − | 3.16416i | −0.818522 | − | 0.140525i | ||||
\(508\) | −1.45850 | − | 5.44318i | −0.0647103 | − | 0.241502i | ||||
\(509\) | −12.0330 | − | 20.8417i | −0.533352 | − | 0.923793i | −0.999241 | − | 0.0389500i | \(-0.987599\pi\) |
0.465889 | − | 0.884843i | \(-0.345735\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −29.0572 | + | 1.12862i | −1.28542 | + | 0.0499274i | ||||
\(512\) | 15.8227 | − | 15.8227i | 0.699271 | − | 0.699271i | ||||
\(513\) | 0.174060 | + | 12.8668i | 0.00768494 | + | 0.568081i | ||||
\(514\) | −12.2100 | − | 7.04946i | −0.538561 | − | 0.310938i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | −0.0810934 | − | 0.881124i | −0.00356994 | − | 0.0387893i | ||||
\(517\) | −32.4117 | − | 32.4117i | −1.42546 | − | 1.42546i | ||||
\(518\) | −17.5237 | − | 16.2133i | −0.769947 | − | 0.712372i | ||||
\(519\) | 31.9954 | + | 14.7444i | 1.40444 | + | 0.647208i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 0.396615 | + | 0.228986i | 0.0173760 | + | 0.0100320i | 0.508663 | − | 0.860966i | \(-0.330140\pi\) |
−0.491287 | + | 0.870998i | \(0.663473\pi\) | |||||||
\(522\) | 9.37774 | + | 6.44112i | 0.410452 | + | 0.281920i | ||||
\(523\) | 38.0113 | + | 10.1851i | 1.66212 | + | 0.445364i | 0.962969 | − | 0.269611i | \(-0.0868951\pi\) |
0.699150 | + | 0.714975i | \(0.253562\pi\) | |||||||
\(524\) | −16.7267 | −0.730707 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 37.2730 | 1.62518 | ||||||||
\(527\) | −10.0157 | − | 2.68370i | −0.436291 | − | 0.116904i | ||||
\(528\) | −43.8253 | − | 7.52399i | −1.90725 | − | 0.327440i | ||||
\(529\) | 16.2398 | + | 9.37606i | 0.706079 | + | 0.407655i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 7.75610 | − | 6.62824i | 0.336586 | − | 0.287641i | ||||
\(532\) | 2.05970 | − | 9.08366i | 0.0892994 | − | 0.393827i | ||||
\(533\) | −14.0237 | − | 14.0237i | −0.607433 | − | 0.607433i | ||||
\(534\) | 26.0220 | − | 2.39491i | 1.12608 | − | 0.103638i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.65281 | + | 1.53160i | 0.114584 | + | 0.0661551i | ||||
\(537\) | 8.81238 | + | 7.32701i | 0.380282 | + | 0.316184i | ||||
\(538\) | −20.6237 | + | 20.6237i | −0.889149 | + | 0.889149i | ||||
\(539\) | −21.0805 | − | 30.7312i | −0.908000 | − | 1.32369i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 12.8403 | + | 22.2400i | 0.552046 | + | 0.956172i | 0.998127 | + | 0.0611795i | \(0.0194862\pi\) |
−0.446080 | + | 0.894993i | \(0.647180\pi\) | |||||||
\(542\) | −0.426598 | − | 1.59208i | −0.0183239 | − | 0.0683859i | ||||
\(543\) | −2.55209 | + | 14.8653i | −0.109521 | + | 0.637931i | ||||
\(544\) | 25.6567 | − | 14.8129i | 1.10002 | − | 0.635099i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 40.9982 | − | 5.38491i | 1.75456 | − | 0.230453i | ||||
\(547\) | 23.9536 | + | 23.9536i | 1.02418 | + | 1.02418i | 0.999700 | + | 0.0244811i | \(0.00779337\pi\) |
0.0244811 | + | 0.999700i | \(0.492207\pi\) | |||||||
\(548\) | −6.69602 | + | 24.9899i | −0.286040 | + | 1.06752i | ||||
\(549\) | −4.33389 | − | 23.3456i | −0.184966 | − | 0.996367i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 4.39684 | − | 2.53851i | 0.187312 | − | 0.108144i | ||||
\(552\) | 1.32250 | + | 3.58320i | 0.0562895 | + | 0.152511i | ||||
\(553\) | 4.96422 | + | 16.0127i | 0.211100 | + | 0.680930i | ||||
\(554\) | 39.1185 | 1.66198 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 12.8616 | − | 22.2769i | 0.545452 | − | 0.944751i | ||||
\(557\) | 7.02893 | + | 26.2323i | 0.297825 | + | 1.11150i | 0.938947 | + | 0.344061i | \(0.111803\pi\) |
−0.641122 | + | 0.767439i | \(0.721531\pi\) | |||||||
\(558\) | 11.8842 | − | 5.67270i | 0.503096 | − | 0.240145i | ||||
\(559\) | − | 1.75304i | − | 0.0741457i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −36.5929 | − | 16.8631i | −1.54495 | − | 0.711961i | ||||
\(562\) | 7.26465 | − | 27.1120i | 0.306441 | − | 1.14365i | ||||
\(563\) | −1.54034 | + | 0.412734i | −0.0649177 | + | 0.0173947i | −0.291132 | − | 0.956683i | \(-0.594032\pi\) |
0.226214 | + | 0.974078i | \(0.427365\pi\) | |||||||
\(564\) | −17.3107 | + | 12.2378i | −0.728913 | + | 0.515304i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | − | 52.4991i | − | 2.20670i | ||||||
\(567\) | 18.6978 | − | 14.7442i | 0.785234 | − | 0.619200i | ||||
\(568\) | 11.1504 | − | 11.1504i | 0.467861 | − | 0.467861i | ||||
\(569\) | −6.46955 | − | 11.2056i | −0.271218 | − | 0.469763i | 0.697956 | − | 0.716140i | \(-0.254093\pi\) |
−0.969174 | + | 0.246378i | \(0.920760\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 3.63645 | − | 6.29852i | 0.152181 | − | 0.263585i | −0.779848 | − | 0.625969i | \(-0.784704\pi\) |
0.932029 | + | 0.362384i | \(0.118037\pi\) | |||||||
\(572\) | 35.6609 | + | 9.55532i | 1.49106 | + | 0.399528i | ||||
\(573\) | −0.177624 | − | 0.481254i | −0.00742033 | − | 0.0201047i | ||||
\(574\) | 17.6043 | + | 9.27213i | 0.734788 | + | 0.387011i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −2.89877 | + | 8.19346i | −0.120782 | + | 0.341394i | ||||
\(577\) | 17.6275 | − | 4.72328i | 0.733843 | − | 0.196633i | 0.127503 | − | 0.991838i | \(-0.459304\pi\) |
0.606340 | + | 0.795206i | \(0.292637\pi\) | |||||||
\(578\) | 3.73882 | − | 1.00181i | 0.155515 | − | 0.0416700i | ||||
\(579\) | −18.5665 | + | 1.70875i | −0.771598 | + | 0.0710132i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −4.99043 | + | 3.14560i | −0.207038 | + | 0.130501i | ||||
\(582\) | −32.0574 | + | 11.8319i | −1.32882 | + | 0.490448i | ||||
\(583\) | −63.2995 | − | 16.9610i | −2.62160 | − | 0.702454i | ||||
\(584\) | 5.87974 | − | 10.1840i | 0.243305 | − | 0.421417i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −11.8669 | − | 20.5541i | −0.490217 | − | 0.849080i | ||||
\(587\) | 5.12734 | − | 5.12734i | 0.211628 | − | 0.211628i | −0.593331 | − | 0.804959i | \(-0.702187\pi\) |
0.804959 | + | 0.593331i | \(0.202187\pi\) | |||||||
\(588\) | −15.6580 | + | 7.20417i | −0.645723 | + | 0.297095i | ||||
\(589\) | − | 5.87669i | − | 0.242145i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 0.227350 | + | 0.321594i | 0.00935195 | + | 0.0132286i | ||||
\(592\) | 22.7223 | − | 6.08841i | 0.933879 | − | 0.250232i | ||||
\(593\) | 3.03836 | − | 11.3393i | 0.124770 | − | 0.465650i | −0.875061 | − | 0.484013i | \(-0.839179\pi\) |
0.999831 | + | 0.0183632i | \(0.00584550\pi\) | |||||||
\(594\) | 49.2428 | − | 13.9112i | 2.02046 | − | 0.570782i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | − | 3.61917i | − | 0.148247i | ||||||
\(597\) | 7.57932 | − | 9.11584i | 0.310201 | − | 0.373086i | ||||
\(598\) | −4.81340 | − | 17.9639i | −0.196835 | − | 0.734597i | ||||
\(599\) | 4.87896 | − | 8.45060i | 0.199349 | − | 0.345282i | −0.748969 | − | 0.662605i | \(-0.769451\pi\) |
0.948317 | + | 0.317323i | \(0.102784\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 37.0872 | 1.51282 | 0.756408 | − | 0.654100i | \(-0.226952\pi\) | ||||
0.756408 | + | 0.654100i | \(0.226952\pi\) | |||||||
\(602\) | 0.520783 | + | 1.67985i | 0.0212255 | + | 0.0684657i | ||||
\(603\) | −8.56270 | − | 0.671388i | −0.348700 | − | 0.0273410i | ||||
\(604\) | 7.90631 | − | 4.56471i | 0.321703 | − | 0.185735i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −27.9078 | + | 19.7294i | −1.13368 | + | 0.801453i | ||||
\(607\) | −4.36982 | + | 16.3084i | −0.177366 | + | 0.661937i | 0.818771 | + | 0.574120i | \(0.194656\pi\) |
−0.996137 | + | 0.0878171i | \(0.972011\pi\) | |||||||
\(608\) | 11.8727 | + | 11.8727i | 0.481503 | + | 0.481503i | ||||
\(609\) | −8.67867 | − | 3.59790i | −0.351677 | − | 0.145794i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −36.3733 | + | 21.0001i | −1.47151 | + | 0.849574i | ||||
\(612\) | −10.5504 | + | 15.3605i | −0.426475 | + | 0.620912i | ||||
\(613\) | 2.74436 | + | 10.2421i | 0.110844 | + | 0.413674i | 0.998942 | − | 0.0459784i | \(-0.0146405\pi\) |
−0.888099 | + | 0.459653i | \(0.847974\pi\) | |||||||
\(614\) | −7.00156 | − | 12.1271i | −0.282560 | − | 0.489408i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 15.0591 | − | 0.584914i | 0.606747 | − | 0.0235669i | ||||
\(617\) | −18.4282 | + | 18.4282i | −0.741892 | + | 0.741892i | −0.972942 | − | 0.231050i | \(-0.925784\pi\) |
0.231050 | + | 0.972942i | \(0.425784\pi\) | |||||||
\(618\) | 5.04347 | − | 6.06591i | 0.202878 | − | 0.244007i | ||||
\(619\) | −27.8270 | − | 16.0659i | −1.11846 | − | 0.645745i | −0.177455 | − | 0.984129i | \(-0.556786\pi\) |
−0.941008 | + | 0.338384i | \(0.890120\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −7.67449 | − | 7.46962i | −0.307967 | − | 0.299745i | ||||
\(622\) | −1.99463 | − | 1.99463i | −0.0799773 | − | 0.0799773i | ||||
\(623\) | −20.6120 | + | 6.39008i | −0.825803 | + | 0.256013i | ||||
\(624\) | −17.0527 | + | 37.0043i | −0.682653 | + | 1.48136i | ||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −36.5080 | − | 21.0779i | −1.45915 | − | 0.842442i | ||||
\(627\) | 3.86388 | − | 22.5061i | 0.154309 | − | 0.898808i | ||||
\(628\) | 24.8948 | + | 6.67055i | 0.993411 | + | 0.266184i | ||||
\(629\) | 21.3151 | 0.849891 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −33.8314 | −1.34681 | −0.673404 | − | 0.739274i | \(-0.735169\pi\) | ||||
−0.673404 | + | 0.739274i | \(0.735169\pi\) | |||||||
\(632\) | −6.54851 | − | 1.75467i | −0.260486 | − | 0.0697969i | ||||
\(633\) | −1.90432 | + | 11.0922i | −0.0756899 | + | 0.440874i | ||||
\(634\) | −15.1058 | − | 8.72135i | −0.599929 | − | 0.346369i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −12.6850 | + | 27.5265i | −0.502995 | + | 1.09150i | ||||
\(637\) | −32.1987 | + | 11.3697i | −1.27576 | + | 0.450484i | ||||
\(638\) | −14.2758 | − | 14.2758i | −0.565186 | − | 0.565186i | ||||
\(639\) | −14.7472 | + | 41.6834i | −0.583391 | + | 1.64897i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 16.3821 | + | 9.45823i | 0.647055 | + | 0.373577i | 0.787327 | − | 0.616536i | \(-0.211464\pi\) |
−0.140272 | + | 0.990113i | \(0.544798\pi\) | |||||||
\(642\) | −25.4370 | + | 30.5937i | −1.00392 | + | 1.20744i | ||||
\(643\) | −2.39355 | + | 2.39355i | −0.0943926 | + | 0.0943926i | −0.752726 | − | 0.658334i | \(-0.771262\pi\) |
0.658334 | + | 0.752726i | \(0.271262\pi\) | |||||||
\(644\) | 4.13358 | + | 6.55784i | 0.162886 | + | 0.258415i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 10.0079 | + | 17.3342i | 0.393755 | + | 0.682004i | ||||
\(647\) | 0.609034 | + | 2.27295i | 0.0239436 | + | 0.0893588i | 0.976864 | − | 0.213863i | \(-0.0686045\pi\) |
−0.952920 | + | 0.303221i | \(0.901938\pi\) | |||||||
\(648\) | 1.01212 | + | 9.57603i | 0.0397600 | + | 0.376182i | ||||
\(649\) | −15.6796 | + | 9.05264i | −0.615480 | + | 0.355347i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −8.62944 | + | 6.61746i | −0.338215 | + | 0.259359i | ||||
\(652\) | 5.14446 | + | 5.14446i | 0.201473 | + | 0.201473i | ||||
\(653\) | 6.42731 | − | 23.9871i | 0.251520 | − | 0.938686i | −0.718473 | − | 0.695555i | \(-0.755159\pi\) |
0.969993 | − | 0.243132i | \(-0.0781747\pi\) | |||||||
\(654\) | −47.7321 | + | 33.7442i | −1.86647 | + | 1.31950i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | −16.9786 | + | 9.80262i | −0.662904 | + | 0.382728i | ||||
\(657\) | −2.57743 | + | 32.8718i | −0.100555 | + | 1.28245i | ||||
\(658\) | 28.6161 | − | 30.9289i | 1.11557 | − | 1.20574i | ||||
\(659\) | 10.2106 | 0.397748 | 0.198874 | − | 0.980025i | \(-0.436271\pi\) | ||||
0.198874 | + | 0.980025i | \(0.436271\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.16075 | + | 2.01047i | −0.0451478 | + | 0.0781982i | −0.887716 | − | 0.460391i | \(-0.847709\pi\) |
0.842568 | + | 0.538589i | \(0.181043\pi\) | |||||||
\(662\) | 2.18762 | + | 8.16430i | 0.0850242 | + | 0.317315i | ||||
\(663\) | −23.6033 | + | 28.3882i | −0.916675 | + | 1.10251i | ||||
\(664\) | − | 2.38556i | − | 0.0925778i | ||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −20.5792 | + | 17.5867i | −0.797428 | + | 0.681469i | ||||
\(667\) | −1.09362 | + | 4.08143i | −0.0423450 | + | 0.158034i | ||||
\(668\) | 15.1582 | − | 4.06161i | 0.586487 | − | 0.157149i | ||||
\(669\) | −1.17711 | − | 1.66505i | −0.0455096 | − | 0.0643747i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 42.1369i | 1.62668i | ||||||||
\(672\) | 4.06483 | − | 30.8035i | 0.156804 | − | 1.18827i | ||||
\(673\) | 1.14714 | − | 1.14714i | 0.0442189 | − | 0.0442189i | −0.684652 | − | 0.728870i | \(-0.740046\pi\) |
0.728870 | + | 0.684652i | \(0.240046\pi\) | |||||||
\(674\) | 10.3137 | + | 17.8638i | 0.397268 | + | 0.688089i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 7.67403 | − | 13.2918i | 0.295155 | − | 0.511224i | ||||
\(677\) | −2.42261 | − | 0.649136i | −0.0931084 | − | 0.0249483i | 0.211964 | − | 0.977277i | \(-0.432014\pi\) |
−0.305072 | + | 0.952329i | \(0.598681\pi\) | |||||||
\(678\) | −16.5358 | + | 6.10312i | −0.635054 | + | 0.234389i | ||||
\(679\) | 23.8719 | − | 15.0471i | 0.916121 | − | 0.577456i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 26.7391 | − | 2.46090i | 1.02464 | − | 0.0943020i | ||||
\(682\) | −22.5727 | + | 6.04834i | −0.864354 | + | 0.231603i | ||||
\(683\) | 26.8414 | − | 7.19213i | 1.02706 | − | 0.275199i | 0.294317 | − | 0.955708i | \(-0.404908\pi\) |
0.732740 | + | 0.680509i | \(0.238241\pi\) | |||||||
\(684\) | −9.95661 | − | 3.52256i | −0.380701 | − | 0.134688i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | 27.4768 | − | 20.4604i | 1.04907 | − | 0.781182i | ||||
\(687\) | −6.74659 | − | 18.2792i | −0.257398 | − | 0.697396i | ||||
\(688\) | −1.67391 | − | 0.448522i | −0.0638171 | − | 0.0170997i | ||||
\(689\) | −30.0235 | + | 52.0023i | −1.14381 | + | 1.98113i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −21.0048 | − | 36.3813i | −0.799059 | − | 1.38401i | −0.920230 | − | 0.391379i | \(-0.871998\pi\) |
0.121171 | − | 0.992632i | \(-0.461335\pi\) | |||||||
\(692\) | −20.4456 | + | 20.4456i | −0.777225 | + | 0.777225i | ||||
\(693\) | −37.3994 | + | 19.6693i | −1.42068 | + | 0.747174i | ||||
\(694\) | 61.3916i | 2.33039i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 3.10231 | − | 2.19317i | 0.117593 | − | 0.0831321i | ||||
\(697\) | −17.1592 | + | 4.59779i | −0.649950 | + | 0.174154i | ||||
\(698\) | 15.1638 | − | 56.5919i | 0.573957 | − | 2.14204i | ||||
\(699\) | −40.9767 | − | 18.8833i | −1.54988 | − | 0.714232i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 12.5905i | 0.475538i | 0.971322 | + | 0.237769i | \(0.0764161\pi\) | ||||
−0.971322 | + | 0.237769i | \(0.923584\pi\) | |||||||
\(702\) | −0.634223 | − | 46.8826i | −0.0239372 | − | 1.76947i | ||||
\(703\) | 3.12665 | + | 11.6688i | 0.117924 | + | 0.440098i | ||||
\(704\) | 7.71162 | − | 13.3569i | 0.290642 | − | 0.503407i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 6.58733 | 0.247917 | ||||||||
\(707\) | 19.1676 | − | 20.7167i | 0.720871 | − | 0.779133i | ||||
\(708\) | 2.89942 | + | 7.85570i | 0.108967 | + | 0.295235i | ||||
\(709\) | 13.5078 | − | 7.79873i | 0.507296 | − | 0.292887i | −0.224426 | − | 0.974491i | \(-0.572051\pi\) |
0.731721 | + | 0.681604i | \(0.238717\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 18.6899 | − | 3.46960i | 0.700926 | − | 0.130120i | ||||
\(712\) | 2.25866 | − | 8.42942i | 0.0846468 | − | 0.315906i | ||||
\(713\) | 3.45842 | + | 3.45842i | 0.129519 | + | 0.129519i | ||||
\(714\) | 14.1844 | − | 34.2150i | 0.530839 | − | 1.28046i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | −8.14602 | + | 4.70311i | −0.304431 | + | 0.175763i | ||||
\(717\) | −0.424140 | + | 2.47051i | −0.0158398 | + | 0.0922628i | ||||
\(718\) | −3.07728 | − | 11.4846i | −0.114843 | − | 0.428600i | ||||
\(719\) | 0.580808 | + | 1.00599i | 0.0216605 | + | 0.0375171i | 0.876652 | − | 0.481124i | \(-0.159771\pi\) |
−0.854992 | + | 0.518641i | \(0.826438\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −3.03583 | + | 5.76390i | −0.113060 | + | 0.214659i | ||||
\(722\) | 16.8300 | − | 16.8300i | 0.626349 | − | 0.626349i | ||||
\(723\) | 31.4497 | + | 26.1487i | 1.16963 | + | 0.972481i | ||||
\(724\) | −10.7207 | − | 6.18960i | −0.398432 | − | 0.230035i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | −55.3299 | + | 5.09223i | −2.05349 | + | 0.188990i | ||||
\(727\) | −29.8756 | − | 29.8756i | −1.10803 | − | 1.10803i | −0.993410 | − | 0.114616i | \(-0.963436\pi\) |
−0.114616 | − | 0.993410i | \(-0.536564\pi\) | |||||||
\(728\) | 3.05363 | − | 13.4671i | 0.113175 | − | 0.499123i | ||||
\(729\) | −14.1276 | − | 23.0089i | −0.523244 | − | 0.852183i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.35987 | − | 0.785123i | −0.0502967 | − | 0.0290388i | ||||
\(732\) | 19.2073 | + | 3.29754i | 0.709922 | + | 0.121880i | ||||
\(733\) | 10.9604 | + | 2.93683i | 0.404831 | + | 0.108474i | 0.455488 | − | 0.890242i | \(-0.349465\pi\) |
−0.0506569 | + | 0.998716i | \(0.516131\pi\) | |||||||
\(734\) | −32.1999 | −1.18852 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −13.9741 | −0.515094 | ||||||||
\(737\) | 14.7226 | + | 3.94491i | 0.542314 | + | 0.145313i | ||||
\(738\) | 12.7732 | − | 18.5967i | 0.470188 | − | 0.684554i | ||||
\(739\) | 13.2799 | + | 7.66718i | 0.488511 | + | 0.282042i | 0.723956 | − | 0.689846i | \(-0.242322\pi\) |
−0.235446 | + | 0.971888i | \(0.575655\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −19.0032 | − | 8.75725i | −0.698101 | − | 0.321706i | ||||
\(742\) | 13.3215 | − | 58.7504i | 0.489049 | − | 2.15680i | ||||
\(743\) | 29.6061 | + | 29.6061i | 1.08614 | + | 1.08614i | 0.995922 | + | 0.0902205i | \(0.0287572\pi\) |
0.0902205 | + | 0.995922i | \(0.471243\pi\) | |||||||
\(744\) | −0.403031 | − | 4.37915i | −0.0147758 | − | 0.160548i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 27.2289 | + | 15.7206i | 0.996922 | + | 0.575573i | ||||
\(747\) | 2.88142 | + | 6.03649i | 0.105426 | + | 0.220864i | ||||
\(748\) | 23.3835 | − | 23.3835i | 0.854986 | − | 0.854986i | ||||
\(749\) | 15.3113 | − | 29.0705i | 0.559464 | − | 1.06221i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −5.18864 | − | 8.98698i | −0.189336 | − | 0.327940i | 0.755693 | − | 0.654926i | \(-0.227300\pi\) |
−0.945029 | + | 0.326986i | \(0.893967\pi\) | |||||||
\(752\) | 10.7459 | + | 40.1043i | 0.391863 | + | 1.46245i | ||||
\(753\) | −24.5374 | − | 4.21261i | −0.894191 | − | 0.153516i | ||||
\(754\) | −16.0208 | + | 9.24959i | −0.583441 | + | 0.336850i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 6.03908 | + | 18.5871i | 0.219639 | + | 0.676005i | ||||
\(757\) | −1.14687 | − | 1.14687i | −0.0416838 | − | 0.0416838i | 0.685958 | − | 0.727641i | \(-0.259384\pi\) |
−0.727641 | + | 0.685958i | \(0.759384\pi\) | |||||||
\(758\) | 0.165361 | − | 0.617135i | 0.00600618 | − | 0.0224154i | ||||
\(759\) | 10.9709 | + | 15.5187i | 0.398219 | + | 0.563292i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.5360 | − | 6.66031i | 0.418180 | − | 0.241436i | −0.276119 | − | 0.961124i | \(-0.589048\pi\) |
0.694298 | + | 0.719687i | \(0.255715\pi\) | |||||||
\(762\) | 11.9146 | − | 4.39750i | 0.431620 | − | 0.159304i | ||||
\(763\) | 32.7832 | − | 35.4328i | 1.18683 | − | 1.28275i | ||||
\(764\) | 0.421034 | 0.0152325 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 7.93122 | − | 13.7373i | 0.286567 | − | 0.496348i | ||||
\(767\) | 4.29375 | + | 16.0245i | 0.155038 | + | 0.578611i | ||||
\(768\) | 27.9216 | + | 23.2153i | 1.00753 | + | 0.837709i | ||||
\(769\) | 47.7620i | 1.72234i | 0.508315 | + | 0.861171i | \(0.330269\pi\) | ||||
−0.508315 | + | 0.861171i | \(0.669731\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 5.52531 | − | 11.9899i | 0.198989 | − | 0.431807i | ||||
\(772\) | 3.96067 | − | 14.7814i | 0.142548 | − | 0.531996i | ||||
\(773\) | 4.71423 | − | 1.26317i | 0.169559 | − | 0.0454332i | −0.173041 | − | 0.984915i | \(-0.555359\pi\) |
0.342600 | + | 0.939481i | \(0.388693\pi\) | |||||||
\(774\) | 1.96071 | − | 0.363987i | 0.0704762 | − | 0.0130832i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 11.4115i | 0.409647i | ||||||||
\(777\) | 13.6139 | − | 17.7309i | 0.488398 | − | 0.636094i | ||||
\(778\) | 24.0745 | − | 24.0745i | 0.863114 | − | 0.863114i | ||||
\(779\) | −5.03405 | − | 8.71924i | −0.180364 | − | 0.312399i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 39.2321 | − | 67.9520i | 1.40384 | − | 2.43151i | ||||
\(782\) | −16.0907 | − | 4.31150i | −0.575403 | − | 0.154179i | ||||
\(783\) | −5.20113 | + | 9.29681i | −0.185873 | + | 0.332241i | ||||
\(784\) | 2.61830 | + | 33.6542i | 0.0935107 | + | 1.20194i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | −3.45484 | − | 37.5387i | −0.123230 | − | 1.33896i | ||||
\(787\) | −5.59964 | + | 1.50042i | −0.199606 | + | 0.0534842i | −0.357237 | − | 0.934014i | \(-0.616281\pi\) |
0.157631 | + | 0.987498i | \(0.449614\pi\) | |||||||
\(788\) | −0.312231 | + | 0.0836621i | −0.0111228 | + | 0.00298034i | ||||
\(789\) | 3.19859 | + | 34.7544i | 0.113873 | + | 1.23729i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.3136 | − | 7.76161i | 0.437822 | − | 0.275971i | ||||
\(792\) | 1.33576 | − | 17.0360i | 0.0474643 | − | 0.605346i | ||||
\(793\) | 37.2942 | + | 9.99295i | 1.32436 | + | 0.354860i | ||||
\(794\) | 21.5474 | − | 37.3212i | 0.764688 | − | 1.32448i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 4.86506 | + | 8.42653i | 0.172438 | + | 0.298671i | ||||
\(797\) | −25.7650 | + | 25.7650i | −0.912644 | + | 0.912644i | −0.996480 | − | 0.0838353i | \(-0.973283\pi\) |
0.0838353 | + | 0.996480i | \(0.473283\pi\) | |||||||
\(798\) | 20.8114 | + | 2.74628i | 0.736716 | + | 0.0972171i | ||||
\(799\) | 37.6208i | 1.33093i | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 4.46617 | + | 24.0582i | 0.157804 | + | 0.850054i | ||||
\(802\) | −58.0394 | + | 15.5516i | −2.04944 | + | 0.549147i | ||||
\(803\) | 15.1443 | − | 56.5194i | 0.534432 | − | 1.99453i | ||||
\(804\) | 2.95037 | − | 6.40230i | 0.104052 | − | 0.225792i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 21.4129i | 0.754237i | ||||||||
\(807\) | −20.9999 | − | 17.4603i | −0.739232 | − | 0.614630i | ||||
\(808\) | 2.95404 | + | 11.0246i | 0.103923 | + | 0.387846i | ||||
\(809\) | 13.1923 | − | 22.8498i | 0.463818 | − | 0.803356i | −0.535330 | − | 0.844643i | \(-0.679813\pi\) |
0.999147 | + | 0.0412873i | \(0.0131459\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −21.9075 | −0.769276 | −0.384638 | − | 0.923067i | \(-0.625674\pi\) | ||||
−0.384638 | + | 0.923067i | \(0.625674\pi\) | |||||||
\(812\) | 5.23668 | − | 5.65992i | 0.183772 | − | 0.198624i | ||||
\(813\) | 1.44790 | − | 0.534397i | 0.0507799 | − | 0.0187421i | ||||
\(814\) | 41.6027 | − | 24.0193i | 1.45817 | − | 0.841876i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 21.0678 | + | 29.8010i | 0.737520 | + | 1.04324i | ||||
\(817\) | 0.230335 | − | 0.859620i | 0.00805839 | − | 0.0300743i | ||||
\(818\) | 5.66352 | + | 5.66352i | 0.198020 | + | 0.198020i | ||||
\(819\) | 8.53931 | + | 37.7658i | 0.298388 | + | 1.31964i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −29.6181 | + | 17.1000i | −1.03368 | + | 0.596794i | −0.918036 | − | 0.396497i | \(-0.870226\pi\) |
−0.115642 | + | 0.993291i | \(0.536893\pi\) | |||||||
\(822\) | −57.4665 | − | 9.86594i | −2.00438 | − | 0.344114i | ||||
\(823\) | −10.4901 | − | 39.1497i | −0.365663 | − | 1.36467i | −0.866520 | − | 0.499142i | \(-0.833649\pi\) |
0.500858 | − | 0.865530i | \(-0.333018\pi\) | |||||||
\(824\) | −1.31722 | − | 2.28149i | −0.0458875 | − | 0.0794795i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −8.87495 | − | 14.0799i | −0.308799 | − | 0.489903i | ||||
\(827\) | 33.6571 | − | 33.6571i | 1.17037 | − | 1.17037i | 0.188249 | − | 0.982121i | \(-0.439719\pi\) |
0.982121 | − | 0.188249i | \(-0.0602812\pi\) | |||||||
\(828\) | 7.93245 | − | 3.78642i | 0.275672 | − | 0.131587i | ||||
\(829\) | −14.9735 | − | 8.64496i | −0.520051 | − | 0.300252i | 0.216904 | − | 0.976193i | \(-0.430404\pi\) |
−0.736956 | + | 0.675941i | \(0.763737\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 3.35696 | + | 36.4752i | 0.116452 | + | 1.26531i | ||||
\(832\) | −9.99300 | − | 9.99300i | −0.346445 | − | 0.346445i | ||||
\(833\) | −5.60090 | + | 30.0693i | −0.194060 | + | 1.04184i | ||||
\(834\) | 52.6514 | + | 24.2633i | 1.82317 | + | 0.840170i | ||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 16.2312 | + | 9.37108i | 0.561367 | + | 0.324106i | ||||
\(837\) | 6.30923 | + | 10.5943i | 0.218079 | + | 0.366193i | ||||
\(838\) | −59.6910 | − | 15.9942i | −2.06199 | − | 0.552509i | ||||
\(839\) | −29.2813 | −1.01090 | −0.505452 | − | 0.862855i | \(-0.668674\pi\) | ||||
−0.505452 | + | 0.862855i | \(0.668674\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −24.7969 | −0.855067 | ||||||||
\(842\) | −31.0321 | − | 8.31501i | −1.06944 | − | 0.286554i | ||||
\(843\) | 25.9035 | + | 4.44714i | 0.892162 | + | 0.153168i | ||||
\(844\) | −7.99957 | − | 4.61855i | −0.275356 | − | 0.158977i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −31.0401 | − | 36.3218i | −1.06718 | − | 1.24877i | ||||
\(847\) | 43.8267 | − | 13.5870i | 1.50590 | − | 0.466856i | ||||
\(848\) | 41.9732 | + | 41.9732i | 1.44136 | + | 1.44136i | ||||
\(849\) | 48.9516 | − | 4.50522i | 1.68002 | − | 0.154619i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.70710 | − | 5.02704i | −0.298475 | − | 0.172325i | ||||
\(852\) | −27.9044 | − | 23.2010i | −0.955990 | − | 0.794853i | ||||
\(853\) | 16.2493 | − | 16.2493i | 0.556365 | − | 0.556365i | −0.371905 | − | 0.928271i | \(-0.621295\pi\) |
0.928271 | + | 0.371905i | \(0.121295\pi\) | |||||||
\(854\) | −38.7058 | + | 1.50339i | −1.32449 | + | 0.0514449i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 6.64345 | + | 11.5068i | 0.227068 | + | 0.393294i | ||||
\(857\) | −9.04935 | − | 33.7726i | −0.309120 | − | 1.15365i | −0.929341 | − | 0.369224i | \(-0.879624\pi\) |
0.620221 | − | 0.784427i | \(-0.287043\pi\) | |||||||
\(858\) | −14.0788 | + | 82.0056i | −0.480643 | + | 2.79962i | ||||
\(859\) | 47.9023 | − | 27.6564i | 1.63441 | − | 0.943625i | 0.651695 | − | 0.758481i | \(-0.274058\pi\) |
0.982712 | − | 0.185143i | \(-0.0592750\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −7.13488 | + | 17.2104i | −0.243156 | + | 0.586529i | ||||
\(862\) | 29.3868 | + | 29.3868i | 1.00092 | + | 1.00092i | ||||
\(863\) | 8.09450 | − | 30.2091i | 0.275540 | − | 1.02833i | −0.679939 | − | 0.733269i | \(-0.737994\pi\) |
0.955479 | − | 0.295060i | \(-0.0953397\pi\) | |||||||
\(864\) | −34.1504 | − | 8.65721i | −1.16182 | − | 0.294524i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | −17.5844 | + | 10.1523i | −0.597541 | + | 0.344991i | ||||
\(867\) | 1.25497 | + | 3.40021i | 0.0426210 | + | 0.115477i | ||||
\(868\) | −2.64293 | − | 8.52510i | −0.0897068 | − | 0.289361i | ||||
\(869\) | −33.7337 | −1.14434 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 6.98307 | − | 12.0950i | 0.236612 | − | 0.409825i | ||||
\(872\) | 5.05245 | + | 18.8560i | 0.171097 | + | 0.638544i | ||||
\(873\) | −13.7834 | − | 28.8758i | −0.466497 | − | 0.977299i | ||||
\(874\) | − | 9.44119i | − | 0.319353i | ||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −24.5781 | − | 11.3263i | −0.830418 | − | 0.382681i | ||||
\(877\) | 5.81291 | − | 21.6941i | 0.196288 | − | 0.732556i | −0.795642 | − | 0.605767i | \(-0.792866\pi\) |
0.991930 | − | 0.126789i | \(-0.0404671\pi\) | |||||||
\(878\) | 8.98378 | − | 2.40720i | 0.303188 | − | 0.0812389i | ||||
\(879\) | 18.1468 | − | 12.8289i | 0.612078 | − | 0.432707i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 47.2694i | 1.59254i | 0.604938 | + | 0.796272i | \(0.293198\pi\) | ||||
−0.604938 | + | 0.796272i | \(0.706802\pi\) | |||||||
\(882\) | −19.4020 | − | 33.6523i | −0.653301 | − | 1.13313i | ||||
\(883\) | −2.23535 | + | 2.23535i | −0.0752257 | + | 0.0752257i | −0.743719 | − | 0.668493i | \(-0.766940\pi\) |
0.668493 | + | 0.743719i | \(0.266940\pi\) | |||||||
\(884\) | −15.1506 | − | 26.2416i | −0.509570 | − | 0.882602i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 9.17661 | − | 15.8944i | 0.308294 | − | 0.533981i | ||||
\(887\) | −40.3902 | − | 10.8225i | −1.35617 | − | 0.363384i | −0.493761 | − | 0.869598i | \(-0.664378\pi\) |
−0.862408 | + | 0.506213i | \(0.831045\pi\) | |||||||
\(888\) | 3.13016 | + | 8.48087i | 0.105041 | + | 0.284599i | ||||
\(889\) | −8.87236 | + | 5.59249i | −0.297569 | + | 0.187566i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 17.1969 | + | 44.7216i | 0.576119 | + | 1.49823i | ||||
\(892\) | 1.61658 | − | 0.433161i | 0.0541270 | − | 0.0145033i | ||||
\(893\) | −20.5952 | + | 5.51847i | −0.689193 | + | 0.184669i | ||||
\(894\) | 8.12230 | − | 0.747528i | 0.271650 | − | 0.0250011i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −19.1989 | − | 10.1120i | −0.641389 | − | 0.337818i | ||||
\(897\) | 16.3370 | − | 6.02973i | 0.545475 | − | 0.201327i | ||||
\(898\) | −6.42346 | − | 1.72116i | −0.214354 | − | 0.0574358i | ||||
\(899\) | 2.43253 | − | 4.21327i | 0.0811294 | − | 0.140520i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 26.8929 | + | 46.5798i | 0.895932 | + | 1.55180i | ||||
\(902\) | −28.3100 | + | 28.3100i | −0.942620 | + | 0.942620i | ||||
\(903\) | −1.52165 | + | 0.629750i | −0.0506374 | + | 0.0209568i | ||||
\(904\) | 5.88625i | 0.195774i | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 11.8774 | + | 16.8009i | 0.394599 | + | 0.558172i | ||||
\(907\) | 40.3556 | − | 10.8133i | 1.33999 | − | 0.359048i | 0.483557 | − | 0.875313i | \(-0.339345\pi\) |
0.856429 | + | 0.516265i | \(0.172678\pi\) | |||||||
\(908\) | −5.70408 | + | 21.2879i | −0.189296 | + | 0.706464i | ||||
\(909\) | −20.7912 | − | 24.3290i | −0.689600 | − | 0.806942i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 14.8509i | 0.492031i | 0.969266 | + | 0.246016i | \(0.0791215\pi\) | ||||
−0.969266 | + | 0.246016i | \(0.920879\pi\) | |||||||
\(912\) | −13.2240 | + | 15.9048i | −0.437890 | + | 0.526661i | ||||
\(913\) | −3.07222 | − | 11.4657i | −0.101676 | − | 0.379459i | ||||
\(914\) | 6.32660 | − | 10.9580i | 0.209265 | − | 0.362458i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 15.9919 | 0.528388 | ||||||||
\(917\) | 9.21817 | + | 29.7344i | 0.304411 | + | 0.981916i | ||||
\(918\) | −36.6520 | − | 20.5050i | −1.20969 | − | 0.676767i | ||||
\(919\) | −48.8849 | + | 28.2237i | −1.61257 | + | 0.931015i | −0.623792 | + | 0.781590i | \(0.714409\pi\) |
−0.988773 | + | 0.149425i | \(0.952258\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 10.7068 | − | 7.56914i | 0.352800 | − | 0.249412i | ||||
\(922\) | −0.957848 | + | 3.57474i | −0.0315450 | + | 0.117728i | ||||
\(923\) | −50.8384 | − | 50.8384i | −1.67337 | − | 1.67337i | ||||
\(924\) | −4.51649 | − | 34.3865i | −0.148582 | − | 1.13123i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | 66.2461 | − | 38.2472i | 2.17698 | − | 1.25688i | ||||
\(927\) | 6.08884 | + | 4.18213i | 0.199984 | + | 0.137359i | ||||
\(928\) | 3.59764 | + | 13.4266i | 0.118098 | + | 0.440749i | ||||
\(929\) | 26.8842 | + | 46.5647i | 0.882041 | + | 1.52774i | 0.849068 | + | 0.528283i | \(0.177164\pi\) |
0.0329723 | + | 0.999456i | \(0.489503\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | −17.2828 | + | 1.34461i | −0.566422 | + | 0.0440677i | ||||
\(932\) | 26.1848 | − | 26.1848i | 0.857713 | − | 0.857713i | ||||
\(933\) | 1.68868 | − | 2.03102i | 0.0552848 | − | 0.0664925i | ||||
\(934\) | 22.6240 | + | 13.0620i | 0.740281 | + | 0.427402i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −14.7613 | − | 5.22240i | −0.482488 | − | 0.170700i | ||||
\(937\) | 29.0463 | + | 29.0463i | 0.948901 | + | 0.948901i | 0.998756 | − | 0.0498553i | \(-0.0158760\pi\) |
−0.0498553 | + | 0.998756i | \(0.515876\pi\) | |||||||
\(938\) | −3.09841 | + | 13.6646i | −0.101167 | + | 0.446164i | ||||
\(939\) | 16.5207 | − | 35.8499i | 0.539132 | − | 1.16992i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −41.3850 | − | 23.8937i | −1.34911 | − | 0.778911i | −0.360989 | − | 0.932570i | \(-0.617561\pi\) |
−0.988124 | + | 0.153659i | \(0.950894\pi\) | |||||||
\(942\) | −9.82840 | + | 57.2479i | −0.320227 | + | 1.86524i | ||||
\(943\) | 8.09377 | + | 2.16872i | 0.263569 | + | 0.0706232i | ||||
\(944\) | 16.3997 | 0.533765 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −3.53892 | −0.115060 | ||||||||
\(947\) | 4.63306 | + | 1.24142i | 0.150554 | + | 0.0403409i | 0.333309 | − | 0.942818i | \(-0.391835\pi\) |
−0.182755 | + | 0.983159i | \(0.558501\pi\) | |||||||
\(948\) | −2.63992 | + | 15.3769i | −0.0857407 | + | 0.499418i | ||||
\(949\) | −46.4322 | − | 26.8077i | −1.50725 | − | 0.870214i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 6.83573 | − | 14.8335i | 0.221664 | − | 0.481010i | ||||
\(952\) | −9.07911 | − | 8.40019i | −0.294256 | − | 0.272252i | ||||
\(953\) | 3.13902 | + | 3.13902i | 0.101683 | + | 0.101683i | 0.756118 | − | 0.654435i | \(-0.227094\pi\) |
−0.654435 | + | 0.756118i | \(0.727094\pi\) | |||||||
\(954\) | −64.3964 | − | 22.7828i | −2.08491 | − | 0.737622i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −1.78171 | − | 1.02867i | −0.0576245 | − | 0.0332695i | ||||
\(957\) | 12.0861 | − | 14.5363i | 0.390689 | − | 0.469892i | ||||
\(958\) | −20.9809 | + | 20.9809i | −0.677862 | + | 0.677862i | ||||
\(959\) | 48.1139 | − | 1.86881i | 1.55368 | − | 0.0603470i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 12.6843 | + | 21.9699i | 0.409172 | + | 0.708707i | ||||
\(962\) | −11.3926 | − | 42.5177i | −0.367312 | − | 1.37083i | ||||
\(963\) | −30.7093 | − | 21.0928i | −0.989594 | − | 0.679704i | ||||
\(964\) | −29.0716 | + | 16.7845i | −0.936333 | + | 0.540592i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −13.8636 | + | 10.6313i | −0.446055 | + | 0.342056i | ||||
\(967\) | −17.3509 | − | 17.3509i | −0.557968 | − | 0.557968i | 0.370760 | − | 0.928729i | \(-0.379097\pi\) |
−0.928729 | + | 0.370760i | \(0.879097\pi\) | |||||||
\(968\) | −4.80252 | + | 17.9232i | −0.154359 | + | 0.576075i | ||||
\(969\) | −15.3041 | + | 10.8192i | −0.491637 | + | 0.347562i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 2.99257 | − | 1.72776i | 0.0960363 | − | 0.0554466i | −0.451213 | − | 0.892416i | \(-0.649008\pi\) |
0.547249 | + | 0.836970i | \(0.315675\pi\) | |||||||
\(972\) | 21.7313 | − | 4.33909i | 0.697032 | − | 0.139176i | ||||
\(973\) | −46.6890 | − | 10.5866i | −1.49678 | − | 0.339392i | ||||
\(974\) | 8.97665 | 0.287630 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 19.0837 | − | 33.0540i | 0.610855 | − | 1.05803i | ||||
\(977\) | 1.13275 | + | 4.22749i | 0.0362399 | + | 0.135249i | 0.981676 | − | 0.190559i | \(-0.0610302\pi\) |
−0.945436 | + | 0.325809i | \(0.894363\pi\) | |||||||
\(978\) | −10.4829 | + | 12.6080i | −0.335205 | + | 0.403160i | ||||
\(979\) | − | 43.4230i | − | 1.38780i | ||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −35.5602 | − | 41.6111i | −1.13535 | − | 1.32854i | ||||
\(982\) | −7.62375 | + | 28.4522i | −0.243284 | + | 0.907947i | ||||
\(983\) | −25.7749 | + | 6.90637i | −0.822093 | + | 0.220279i | −0.645261 | − | 0.763962i | \(-0.723251\pi\) |
−0.176831 | + | 0.984241i | \(0.556585\pi\) | |||||||
\(984\) | −4.34922 | − | 6.15210i | −0.138648 | − | 0.196122i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | 16.5702i | 0.527703i | ||||||||
\(987\) | 31.2947 | + | 24.0283i | 0.996122 | + | 0.764830i | ||||
\(988\) | 12.1434 | − | 12.1434i | 0.386333 | − | 0.386333i | ||||
\(989\) | 0.370333 | + | 0.641435i | 0.0117759 | + | 0.0203965i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −4.20000 | + | 7.27461i | −0.133417 | + | 0.231086i | −0.924992 | − | 0.379987i | \(-0.875928\pi\) |
0.791574 | + | 0.611073i | \(0.209262\pi\) | |||||||
\(992\) | 15.5413 | + | 4.16429i | 0.493438 | + | 0.132216i | ||||
\(993\) | −7.42490 | + | 2.74042i | −0.235622 | + | 0.0869645i | ||||
\(994\) | 63.8187 | + | 33.6132i | 2.02421 | + | 1.06615i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −5.46684 | + | 0.503135i | −0.173223 | + | 0.0159425i | ||||
\(997\) | −18.5787 | + | 4.97815i | −0.588393 | + | 0.157659i | −0.540719 | − | 0.841203i | \(-0.681848\pi\) |
−0.0476744 | + | 0.998863i | \(0.515181\pi\) | |||||||
\(998\) | −18.7697 | + | 5.02933i | −0.594145 | + | 0.159201i | ||||
\(999\) | −18.1643 | − | 17.6794i | −0.574694 | − | 0.559352i |
(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 | 525.2.bf.g.32.5 | ✓ | 80 | |
3.2 | odd | 2 | inner | 525.2.bf.g.32.15 | yes | 80 | |
5.2 | odd | 4 | inner | 525.2.bf.g.368.15 | yes | 80 | |
5.3 | odd | 4 | inner | 525.2.bf.g.368.6 | yes | 80 | |
5.4 | even | 2 | inner | 525.2.bf.g.32.16 | yes | 80 | |
7.2 | even | 3 | inner | 525.2.bf.g.107.16 | yes | 80 | |
15.2 | even | 4 | inner | 525.2.bf.g.368.5 | yes | 80 | |
15.8 | even | 4 | inner | 525.2.bf.g.368.16 | yes | 80 | |
15.14 | odd | 2 | inner | 525.2.bf.g.32.6 | yes | 80 | |
21.2 | odd | 6 | inner | 525.2.bf.g.107.6 | yes | 80 | |
35.2 | odd | 12 | inner | 525.2.bf.g.443.6 | yes | 80 | |
35.9 | even | 6 | inner | 525.2.bf.g.107.5 | yes | 80 | |
35.23 | odd | 12 | inner | 525.2.bf.g.443.15 | yes | 80 | |
105.2 | even | 12 | inner | 525.2.bf.g.443.16 | yes | 80 | |
105.23 | even | 12 | inner | 525.2.bf.g.443.5 | yes | 80 | |
105.44 | odd | 6 | inner | 525.2.bf.g.107.15 | yes | 80 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
525.2.bf.g.32.5 | ✓ | 80 | 1.1 | even | 1 | trivial | |
525.2.bf.g.32.6 | yes | 80 | 15.14 | odd | 2 | inner | |
525.2.bf.g.32.15 | yes | 80 | 3.2 | odd | 2 | inner | |
525.2.bf.g.32.16 | yes | 80 | 5.4 | even | 2 | inner | |
525.2.bf.g.107.5 | yes | 80 | 35.9 | even | 6 | inner | |
525.2.bf.g.107.6 | yes | 80 | 21.2 | odd | 6 | inner | |
525.2.bf.g.107.15 | yes | 80 | 105.44 | odd | 6 | inner | |
525.2.bf.g.107.16 | yes | 80 | 7.2 | even | 3 | inner | |
525.2.bf.g.368.5 | yes | 80 | 15.2 | even | 4 | inner | |
525.2.bf.g.368.6 | yes | 80 | 5.3 | odd | 4 | inner | |
525.2.bf.g.368.15 | yes | 80 | 5.2 | odd | 4 | inner | |
525.2.bf.g.368.16 | yes | 80 | 15.8 | even | 4 | inner | |
525.2.bf.g.443.5 | yes | 80 | 105.23 | even | 12 | inner | |
525.2.bf.g.443.6 | yes | 80 | 35.2 | odd | 12 | inner | |
525.2.bf.g.443.15 | yes | 80 | 35.23 | odd | 12 | inner | |
525.2.bf.g.443.16 | yes | 80 | 105.2 | even | 12 | inner |