Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [403,2,Mod(218,403)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(403, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([5, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("403.218");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 403 = 13 \cdot 31 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 403.r (of order \(6\), degree \(2\), 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: | \(3.21797120146\) |
Analytic rank: | \(0\) |
Dimension: | \(68\) |
Relative dimension: | \(34\) over \(\Q(\zeta_{6})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 218.21 | ||
Character | \(\chi\) | \(=\) | 403.218 |
Dual form | 403.2.r.a.342.21 |
$q$-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 \(\left(\mathbb{Z}/403\mathbb{Z}\right)^\times\).
\(n\) | \(249\) | \(313\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.519051 | − | 0.299674i | 0.367025 | − | 0.211902i | −0.305133 | − | 0.952310i | \(-0.598701\pi\) |
0.672158 | + | 0.740408i | \(0.265368\pi\) | |||||||
\(3\) | 0.801804 | + | 1.38877i | 0.462922 | + | 0.801804i | 0.999105 | − | 0.0422975i | \(-0.0134677\pi\) |
−0.536183 | + | 0.844102i | \(0.680134\pi\) | |||||||
\(4\) | −0.820391 | + | 1.42096i | −0.410195 | + | 0.710479i | ||||
\(5\) | − | 0.195832i | − | 0.0875787i | −0.999041 | − | 0.0437893i | \(-0.986057\pi\) | ||
0.999041 | − | 0.0437893i | \(-0.0139430\pi\) | |||||||
\(6\) | 0.832355 | + | 0.480560i | 0.339807 | + | 0.196188i | ||||
\(7\) | 2.33812 | + | 1.34992i | 0.883727 | + | 0.510220i | 0.871886 | − | 0.489710i | \(-0.162897\pi\) |
0.0118418 | + | 0.999930i | \(0.496231\pi\) | |||||||
\(8\) | 2.18210i | 0.771488i | ||||||||
\(9\) | 0.214221 | − | 0.371041i | 0.0714068 | − | 0.123680i | ||||
\(10\) | −0.0586858 | − | 0.101647i | −0.0185581 | − | 0.0321435i | ||||
\(11\) | 0.499279 | − | 0.288259i | 0.150538 | − | 0.0869133i | −0.422839 | − | 0.906205i | \(-0.638966\pi\) |
0.573377 | + | 0.819292i | \(0.305633\pi\) | |||||||
\(12\) | −2.63117 | −0.759553 | ||||||||
\(13\) | −3.39340 | + | 1.21853i | −0.941161 | + | 0.337960i | ||||
\(14\) | 1.61814 | 0.432466 | ||||||||
\(15\) | 0.271965 | − | 0.157019i | 0.0702210 | − | 0.0405421i | ||||
\(16\) | −0.986863 | − | 1.70930i | −0.246716 | − | 0.427324i | ||||
\(17\) | −1.81374 | + | 3.14150i | −0.439898 | + | 0.761925i | −0.997681 | − | 0.0680614i | \(-0.978319\pi\) |
0.557783 | + | 0.829986i | \(0.311652\pi\) | |||||||
\(18\) | − | 0.256786i | − | 0.0605249i | ||||||
\(19\) | −1.74940 | − | 1.01002i | −0.401341 | − | 0.231714i | 0.285722 | − | 0.958313i | \(-0.407767\pi\) |
−0.687062 | + | 0.726599i | \(0.741100\pi\) | |||||||
\(20\) | 0.278269 | + | 0.160659i | 0.0622228 | + | 0.0359244i | ||||
\(21\) | 4.32947i | 0.944768i | ||||||||
\(22\) | 0.172768 | − | 0.299242i | 0.0368342 | − | 0.0637986i | ||||
\(23\) | 1.32064 | + | 2.28742i | 0.275372 | + | 0.476959i | 0.970229 | − | 0.242189i | \(-0.0778655\pi\) |
−0.694857 | + | 0.719148i | \(0.744532\pi\) | |||||||
\(24\) | −3.03042 | + | 1.74961i | −0.618582 | + | 0.357139i | ||||
\(25\) | 4.96165 | 0.992330 | ||||||||
\(26\) | −1.39619 | + | 1.64940i | −0.273815 | + | 0.323473i | ||||
\(27\) | 5.49788 | 1.05807 | ||||||||
\(28\) | −3.83635 | + | 2.21492i | −0.725002 | + | 0.418580i | ||||
\(29\) | 1.15635 | + | 2.00286i | 0.214729 | + | 0.371921i | 0.953189 | − | 0.302376i | \(-0.0977799\pi\) |
−0.738460 | + | 0.674297i | \(0.764447\pi\) | |||||||
\(30\) | 0.0941090 | − | 0.163002i | 0.0171819 | − | 0.0297599i | ||||
\(31\) | − | 1.00000i | − | 0.179605i | ||||||
\(32\) | −4.80397 | − | 2.77357i | −0.849230 | − | 0.490303i | ||||
\(33\) | 0.800648 | + | 0.462254i | 0.139375 | + | 0.0804681i | ||||
\(34\) | 2.17413i | 0.372860i | ||||||||
\(35\) | 0.264357 | − | 0.457879i | 0.0446844 | − | 0.0773957i | ||||
\(36\) | 0.351489 | + | 0.608797i | 0.0585815 | + | 0.101466i | ||||
\(37\) | 6.65790 | − | 3.84394i | 1.09455 | − | 0.631940i | 0.159767 | − | 0.987155i | \(-0.448926\pi\) |
0.934785 | + | 0.355215i | \(0.115592\pi\) | |||||||
\(38\) | −1.21071 | −0.196402 | ||||||||
\(39\) | −4.41310 | − | 3.73562i | −0.706661 | − | 0.598177i | ||||
\(40\) | 0.427324 | 0.0675659 | ||||||||
\(41\) | −7.10424 | + | 4.10164i | −1.10950 | + | 0.640568i | −0.938699 | − | 0.344738i | \(-0.887968\pi\) |
−0.170797 | + | 0.985306i | \(0.554634\pi\) | |||||||
\(42\) | 1.29743 | + | 2.24722i | 0.200198 | + | 0.346753i | ||||
\(43\) | 2.73090 | − | 4.73006i | 0.416459 | − | 0.721328i | −0.579122 | − | 0.815241i | \(-0.696604\pi\) |
0.995580 | + | 0.0939136i | \(0.0299377\pi\) | |||||||
\(44\) | 0.945939i | 0.142606i | ||||||||
\(45\) | −0.0726616 | − | 0.0419512i | −0.0108318 | − | 0.00625372i | ||||
\(46\) | 1.37096 | + | 0.791524i | 0.202137 | + | 0.116704i | ||||
\(47\) | − | 9.19538i | − | 1.34128i | −0.741781 | − | 0.670642i | \(-0.766019\pi\) | ||
0.741781 | − | 0.670642i | \(-0.233981\pi\) | |||||||
\(48\) | 1.58254 | − | 2.74104i | 0.228420 | − | 0.395635i | ||||
\(49\) | 0.144545 | + | 0.250360i | 0.0206493 | + | 0.0357657i | ||||
\(50\) | 2.57535 | − | 1.48688i | 0.364210 | − | 0.210276i | ||||
\(51\) | −5.81707 | −0.814553 | ||||||||
\(52\) | 1.05243 | − | 5.82156i | 0.145946 | − | 0.807304i | ||||
\(53\) | 5.67619 | 0.779684 | 0.389842 | − | 0.920882i | \(-0.372530\pi\) | ||||
0.389842 | + | 0.920882i | \(0.372530\pi\) | |||||||
\(54\) | 2.85368 | − | 1.64757i | 0.388336 | − | 0.224206i | ||||
\(55\) | −0.0564503 | − | 0.0977747i | −0.00761175 | − | 0.0131839i | ||||
\(56\) | −2.94565 | + | 5.10201i | −0.393629 | + | 0.681785i | ||||
\(57\) | − | 3.23935i | − | 0.429062i | ||||||
\(58\) | 1.20041 | + | 0.693057i | 0.157621 | + | 0.0910028i | ||||
\(59\) | −7.50447 | − | 4.33271i | −0.976999 | − | 0.564071i | −0.0756365 | − | 0.997135i | \(-0.524099\pi\) |
−0.901363 | + | 0.433065i | \(0.857432\pi\) | |||||||
\(60\) | 0.515267i | 0.0665207i | ||||||||
\(61\) | 2.54128 | − | 4.40162i | 0.325377 | − | 0.563570i | −0.656211 | − | 0.754577i | \(-0.727842\pi\) |
0.981589 | + | 0.191007i | \(0.0611753\pi\) | |||||||
\(62\) | −0.299674 | − | 0.519051i | −0.0380587 | − | 0.0659196i | ||||
\(63\) | 1.00175 | − | 0.578359i | 0.126208 | − | 0.0728664i | ||||
\(64\) | 0.622777 | 0.0778472 | ||||||||
\(65\) | 0.238627 | + | 0.664537i | 0.0295981 | + | 0.0824256i | ||||
\(66\) | 0.554103 | 0.0682053 | ||||||||
\(67\) | 5.44159 | − | 3.14171i | 0.664796 | − | 0.383820i | −0.129306 | − | 0.991605i | \(-0.541275\pi\) |
0.794102 | + | 0.607784i | \(0.207942\pi\) | |||||||
\(68\) | −2.97596 | − | 5.15451i | −0.360888 | − | 0.625076i | ||||
\(69\) | −2.11779 | + | 3.66812i | −0.254952 | + | 0.441589i | ||||
\(70\) | − | 0.316884i | − | 0.0378748i | ||||||
\(71\) | 3.45618 | + | 1.99543i | 0.410173 | + | 0.236814i | 0.690864 | − | 0.722985i | \(-0.257230\pi\) |
−0.280691 | + | 0.959798i | \(0.590564\pi\) | |||||||
\(72\) | 0.809647 | + | 0.467450i | 0.0954178 | + | 0.0550895i | ||||
\(73\) | − | 3.07081i | − | 0.359412i | −0.983720 | − | 0.179706i | \(-0.942485\pi\) | ||
0.983720 | − | 0.179706i | \(-0.0575146\pi\) | |||||||
\(74\) | 2.30386 | − | 3.99040i | 0.267818 | − | 0.463875i | ||||
\(75\) | 3.97827 | + | 6.89057i | 0.459371 | + | 0.795654i | ||||
\(76\) | 2.87039 | − | 1.65722i | 0.329256 | − | 0.190096i | ||||
\(77\) | 1.55650 | 0.177380 | ||||||||
\(78\) | −3.41009 | − | 0.616484i | −0.386117 | − | 0.0698030i | ||||
\(79\) | 2.16052 | 0.243077 | 0.121538 | − | 0.992587i | \(-0.461217\pi\) | ||||
0.121538 | + | 0.992587i | \(0.461217\pi\) | |||||||
\(80\) | −0.334735 | + | 0.193259i | −0.0374245 | + | 0.0216070i | ||||
\(81\) | 3.76556 | + | 6.52214i | 0.418395 | + | 0.724682i | ||||
\(82\) | −2.45831 | + | 4.25792i | −0.271475 | + | 0.470208i | ||||
\(83\) | 6.83048i | 0.749743i | 0.927077 | + | 0.374871i | \(0.122313\pi\) | ||||
−0.927077 | + | 0.374871i | \(0.877687\pi\) | |||||||
\(84\) | −6.15200 | − | 3.55186i | −0.671238 | − | 0.387539i | ||||
\(85\) | 0.615205 | + | 0.355189i | 0.0667284 | + | 0.0385257i | ||||
\(86\) | − | 3.27352i | − | 0.352993i | ||||||
\(87\) | −1.85433 | + | 3.21180i | −0.198805 | + | 0.344341i | ||||
\(88\) | 0.629009 | + | 1.08948i | 0.0670526 | + | 0.116138i | ||||
\(89\) | 11.6309 | − | 6.71512i | 1.23288 | − | 0.711801i | 0.265247 | − | 0.964180i | \(-0.414546\pi\) |
0.967628 | + | 0.252379i | \(0.0812130\pi\) | |||||||
\(90\) | −0.0502868 | −0.00530070 | ||||||||
\(91\) | −9.57911 | − | 1.73173i | −1.00416 | − | 0.181535i | ||||
\(92\) | −4.33376 | −0.451826 | ||||||||
\(93\) | 1.38877 | − | 0.801804i | 0.144008 | − | 0.0831432i | ||||
\(94\) | −2.75562 | − | 4.77287i | −0.284221 | − | 0.492284i | ||||
\(95\) | −0.197794 | + | 0.342589i | −0.0202932 | + | 0.0351489i | ||||
\(96\) | − | 8.89545i | − | 0.907888i | ||||||
\(97\) | 10.7426 | + | 6.20224i | 1.09074 | + | 0.629742i | 0.933775 | − | 0.357861i | \(-0.116494\pi\) |
0.156970 | + | 0.987603i | \(0.449827\pi\) | |||||||
\(98\) | 0.150053 | + | 0.0866331i | 0.0151576 | + | 0.00875126i | ||||
\(99\) | − | 0.247004i | − | 0.0248248i | ||||||
\(100\) | −4.07049 | + | 7.05030i | −0.407049 | + | 0.705030i | ||||
\(101\) | −2.96541 | − | 5.13624i | −0.295069 | − | 0.511075i | 0.679932 | − | 0.733275i | \(-0.262009\pi\) |
−0.975001 | + | 0.222200i | \(0.928676\pi\) | |||||||
\(102\) | −3.01936 | + | 1.74323i | −0.298961 | + | 0.172605i | ||||
\(103\) | −12.8209 | −1.26328 | −0.631641 | − | 0.775261i | \(-0.717618\pi\) | ||||
−0.631641 | + | 0.775261i | \(0.717618\pi\) | |||||||
\(104\) | −2.65895 | − | 7.40473i | −0.260732 | − | 0.726094i | ||||
\(105\) | 0.847849 | 0.0827416 | ||||||||
\(106\) | 2.94623 | − | 1.70101i | 0.286163 | − | 0.165216i | ||||
\(107\) | −4.57423 | − | 7.92280i | −0.442208 | − | 0.765926i | 0.555645 | − | 0.831419i | \(-0.312471\pi\) |
−0.997853 | + | 0.0654932i | \(0.979138\pi\) | |||||||
\(108\) | −4.51041 | + | 7.81225i | −0.434014 | + | 0.751734i | ||||
\(109\) | − | 12.0868i | − | 1.15770i | −0.815432 | − | 0.578852i | \(-0.803501\pi\) | ||
0.815432 | − | 0.578852i | \(-0.196499\pi\) | |||||||
\(110\) | −0.0586012 | − | 0.0338334i | −0.00558740 | − | 0.00322589i | ||||
\(111\) | 10.6767 | + | 6.16417i | 1.01338 | + | 0.585078i | ||||
\(112\) | − | 5.32873i | − | 0.503517i | ||||||
\(113\) | −8.84571 | + | 15.3212i | −0.832134 | + | 1.44130i | 0.0642085 | + | 0.997937i | \(0.479548\pi\) |
−0.896343 | + | 0.443362i | \(0.853786\pi\) | |||||||
\(114\) | −0.970749 | − | 1.68139i | −0.0909190 | − | 0.157476i | ||||
\(115\) | 0.447949 | − | 0.258623i | 0.0417714 | − | 0.0241168i | ||||
\(116\) | −3.79463 | −0.352323 | ||||||||
\(117\) | −0.274812 | + | 1.52013i | −0.0254063 | + | 0.140536i | ||||
\(118\) | −5.19361 | −0.478110 | ||||||||
\(119\) | −8.48151 | + | 4.89680i | −0.777499 | + | 0.448889i | ||||
\(120\) | 0.342630 | + | 0.593453i | 0.0312777 | + | 0.0541746i | ||||
\(121\) | −5.33381 | + | 9.23844i | −0.484892 | + | 0.839858i | ||||
\(122\) | − | 3.04622i | − | 0.275792i | ||||||
\(123\) | −11.3924 | − | 6.57742i | −1.02722 | − | 0.593066i | ||||
\(124\) | 1.42096 | + | 0.820391i | 0.127606 | + | 0.0736733i | ||||
\(125\) | − | 1.95081i | − | 0.174486i | ||||||
\(126\) | 0.346639 | − | 0.600396i | 0.0308810 | − | 0.0534875i | ||||
\(127\) | −3.45110 | − | 5.97748i | −0.306235 | − | 0.530415i | 0.671300 | − | 0.741185i | \(-0.265736\pi\) |
−0.977536 | + | 0.210770i | \(0.932403\pi\) | |||||||
\(128\) | 9.93119 | − | 5.73377i | 0.877801 | − | 0.506799i | ||||
\(129\) | 8.75859 | 0.771151 | ||||||||
\(130\) | 0.323004 | + | 0.273418i | 0.0283294 | + | 0.0239803i | ||||
\(131\) | 4.63123 | 0.404633 | 0.202316 | − | 0.979320i | \(-0.435153\pi\) | ||||
0.202316 | + | 0.979320i | \(0.435153\pi\) | |||||||
\(132\) | −1.31369 | + | 0.758458i | −0.114342 | + | 0.0660153i | ||||
\(133\) | −2.72688 | − | 4.72309i | −0.236450 | − | 0.409544i | ||||
\(134\) | 1.88298 | − | 3.26141i | 0.162664 | − | 0.281743i | ||||
\(135\) | − | 1.07666i | − | 0.0926641i | ||||||
\(136\) | −6.85505 | − | 3.95777i | −0.587816 | − | 0.339376i | ||||
\(137\) | 1.45803 | + | 0.841794i | 0.124568 | + | 0.0719193i | 0.560989 | − | 0.827823i | \(-0.310421\pi\) |
−0.436421 | + | 0.899742i | \(0.643754\pi\) | |||||||
\(138\) | 2.53859i | 0.216099i | ||||||||
\(139\) | −4.10838 | + | 7.11593i | −0.348469 | + | 0.603565i | −0.985978 | − | 0.166878i | \(-0.946632\pi\) |
0.637509 | + | 0.770443i | \(0.279965\pi\) | |||||||
\(140\) | 0.433751 | + | 0.751279i | 0.0366587 | + | 0.0634947i | ||||
\(141\) | 12.7702 | − | 7.37290i | 1.07545 | − | 0.620910i | ||||
\(142\) | 2.39191 | 0.200725 | ||||||||
\(143\) | −1.34300 | + | 1.58657i | −0.112307 | + | 0.132675i | ||||
\(144\) | −0.845625 | −0.0704688 | ||||||||
\(145\) | 0.392223 | − | 0.226450i | 0.0325724 | − | 0.0188057i | ||||
\(146\) | −0.920244 | − | 1.59391i | −0.0761600 | − | 0.131913i | ||||
\(147\) | −0.231794 | + | 0.401479i | −0.0191181 | + | 0.0331134i | ||||
\(148\) | 12.6141i | 1.03688i | ||||||||
\(149\) | −16.8568 | − | 9.73230i | −1.38097 | − | 0.797301i | −0.388692 | − | 0.921368i | \(-0.627073\pi\) |
−0.992274 | + | 0.124067i | \(0.960406\pi\) | |||||||
\(150\) | 4.12985 | + | 2.38437i | 0.337201 | + | 0.194683i | ||||
\(151\) | − | 5.65804i | − | 0.460445i | −0.973138 | − | 0.230222i | \(-0.926055\pi\) | ||
0.973138 | − | 0.230222i | \(-0.0739454\pi\) | |||||||
\(152\) | 2.20396 | − | 3.81737i | 0.178765 | − | 0.309629i | ||||
\(153\) | 0.777083 | + | 1.34595i | 0.0628234 | + | 0.108813i | ||||
\(154\) | 0.807903 | − | 0.466443i | 0.0651027 | − | 0.0375871i | ||||
\(155\) | −0.195832 | −0.0157296 | ||||||||
\(156\) | 8.92862 | − | 3.20616i | 0.714862 | − | 0.256699i | ||||
\(157\) | 16.9567 | 1.35330 | 0.676648 | − | 0.736307i | \(-0.263432\pi\) | ||||
0.676648 | + | 0.736307i | \(0.263432\pi\) | |||||||
\(158\) | 1.12142 | − | 0.647451i | 0.0892152 | − | 0.0515084i | ||||
\(159\) | 4.55119 | + | 7.88289i | 0.360933 | + | 0.625154i | ||||
\(160\) | −0.543154 | + | 0.940770i | −0.0429401 | + | 0.0743744i | ||||
\(161\) | 7.13101i | 0.562002i | ||||||||
\(162\) | 3.90903 | + | 2.25688i | 0.307123 | + | 0.177317i | ||||
\(163\) | 8.51007 | + | 4.91329i | 0.666560 | + | 0.384838i | 0.794772 | − | 0.606908i | \(-0.207590\pi\) |
−0.128212 | + | 0.991747i | \(0.540924\pi\) | |||||||
\(164\) | − | 13.4598i | − | 1.05103i | ||||||
\(165\) | 0.0905241 | − | 0.156792i | 0.00704729 | − | 0.0122063i | ||||
\(166\) | 2.04692 | + | 3.54537i | 0.158872 | + | 0.275174i | ||||
\(167\) | −7.08097 | + | 4.08820i | −0.547942 | + | 0.316354i | −0.748291 | − | 0.663370i | \(-0.769125\pi\) |
0.200350 | + | 0.979724i | \(0.435792\pi\) | |||||||
\(168\) | −9.44733 | −0.728877 | ||||||||
\(169\) | 10.0304 | − | 8.26994i | 0.771566 | − | 0.636149i | ||||
\(170\) | 0.425764 | 0.0326546 | ||||||||
\(171\) | −0.749516 | + | 0.432733i | −0.0573169 | + | 0.0330919i | ||||
\(172\) | 4.48081 | + | 7.76100i | 0.341659 | + | 0.591770i | ||||
\(173\) | −3.60133 | + | 6.23769i | −0.273804 | + | 0.474243i | −0.969833 | − | 0.243771i | \(-0.921615\pi\) |
0.696029 | + | 0.718014i | \(0.254949\pi\) | |||||||
\(174\) | 2.22278i | 0.168509i | ||||||||
\(175\) | 11.6009 | + | 6.69781i | 0.876949 | + | 0.506307i | ||||
\(176\) | −0.985439 | − | 0.568944i | −0.0742803 | − | 0.0428857i | ||||
\(177\) | − | 13.8959i | − | 1.04448i | ||||||
\(178\) | 4.02470 | − | 6.97098i | 0.301664 | − | 0.522497i | ||||
\(179\) | 0.277728 | + | 0.481040i | 0.0207584 | + | 0.0359546i | 0.876218 | − | 0.481915i | \(-0.160059\pi\) |
−0.855460 | + | 0.517870i | \(0.826725\pi\) | |||||||
\(180\) | 0.119222 | − | 0.0688328i | 0.00888627 | − | 0.00513049i | ||||
\(181\) | −10.3418 | −0.768698 | −0.384349 | − | 0.923188i | \(-0.625574\pi\) | ||||
−0.384349 | + | 0.923188i | \(0.625574\pi\) | |||||||
\(182\) | −5.49100 | + | 1.97176i | −0.407020 | + | 0.146156i | ||||
\(183\) | 8.15043 | 0.602497 | ||||||||
\(184\) | −4.99136 | + | 2.88176i | −0.367968 | + | 0.212446i | ||||
\(185\) | −0.752766 | − | 1.30383i | −0.0553445 | − | 0.0958594i | ||||
\(186\) | 0.480560 | − | 0.832355i | 0.0352364 | − | 0.0610312i | ||||
\(187\) | 2.09131i | 0.152932i | ||||||||
\(188\) | 13.0663 | + | 7.54381i | 0.952955 | + | 0.550189i | ||||
\(189\) | 12.8547 | + | 7.42167i | 0.935042 | + | 0.539847i | ||||
\(190\) | 0.237095i | 0.0172007i | ||||||||
\(191\) | −12.6976 | + | 21.9929i | −0.918765 | + | 1.59135i | −0.117472 | + | 0.993076i | \(0.537479\pi\) |
−0.801293 | + | 0.598272i | \(0.795854\pi\) | |||||||
\(192\) | 0.499345 | + | 0.864892i | 0.0360372 | + | 0.0624182i | ||||
\(193\) | −12.3763 | + | 7.14546i | −0.890865 | + | 0.514341i | −0.874225 | − | 0.485520i | \(-0.838630\pi\) |
−0.0166398 | + | 0.999862i | \(0.505297\pi\) | |||||||
\(194\) | 7.43461 | 0.533774 | ||||||||
\(195\) | −0.731553 | + | 0.864225i | −0.0523876 | + | 0.0618885i | ||||
\(196\) | −0.474335 | −0.0338810 | ||||||||
\(197\) | 8.93985 | − | 5.16143i | 0.636938 | − | 0.367736i | −0.146496 | − | 0.989211i | \(-0.546800\pi\) |
0.783434 | + | 0.621475i | \(0.213466\pi\) | |||||||
\(198\) | −0.0740207 | − | 0.128208i | −0.00526042 | − | 0.00911132i | ||||
\(199\) | −7.28802 | + | 12.6232i | −0.516634 | + | 0.894837i | 0.483179 | + | 0.875522i | \(0.339482\pi\) |
−0.999813 | + | 0.0193153i | \(0.993851\pi\) | |||||||
\(200\) | 10.8268i | 0.765571i | ||||||||
\(201\) | 8.72618 | + | 5.03806i | 0.615497 | + | 0.355358i | ||||
\(202\) | −3.07840 | − | 1.77731i | −0.216595 | − | 0.125051i | ||||
\(203\) | 6.24390i | 0.438236i | ||||||||
\(204\) | 4.77227 | − | 8.26581i | 0.334126 | − | 0.578723i | ||||
\(205\) | 0.803231 | + | 1.39124i | 0.0561001 | + | 0.0971682i | ||||
\(206\) | −6.65471 | + | 3.84210i | −0.463655 | + | 0.267692i | ||||
\(207\) | 1.13163 | 0.0786539 | ||||||||
\(208\) | 5.43165 | + | 4.59781i | 0.376617 | + | 0.318801i | ||||
\(209\) | −1.16459 | −0.0805561 | ||||||||
\(210\) | 0.440077 | − | 0.254079i | 0.0303682 | − | 0.0175331i | ||||
\(211\) | 9.26921 | + | 16.0547i | 0.638119 | + | 1.10525i | 0.985845 | + | 0.167658i | \(0.0536205\pi\) |
−0.347726 | + | 0.937596i | \(0.613046\pi\) | |||||||
\(212\) | −4.65669 | + | 8.06562i | −0.319823 | + | 0.553949i | ||||
\(213\) | 6.39977i | 0.438505i | ||||||||
\(214\) | −4.74852 | − | 2.74156i | −0.324602 | − | 0.187409i | ||||
\(215\) | −0.926297 | − | 0.534798i | −0.0631729 | − | 0.0364729i | ||||
\(216\) | 11.9969i | 0.816286i | ||||||||
\(217\) | 1.34992 | − | 2.33812i | 0.0916383 | − | 0.158722i | ||||
\(218\) | −3.62210 | − | 6.27366i | −0.245320 | − | 0.424906i | ||||
\(219\) | 4.26464 | − | 2.46219i | 0.288178 | − | 0.166379i | ||||
\(220\) | 0.185245 | 0.0124892 | ||||||||
\(221\) | 2.32675 | − | 12.8705i | 0.156514 | − | 0.865762i | ||||
\(222\) | 7.38898 | 0.495916 | ||||||||
\(223\) | −6.26714 | + | 3.61833i | −0.419679 | + | 0.242302i | −0.694940 | − | 0.719068i | \(-0.744569\pi\) |
0.275261 | + | 0.961369i | \(0.411236\pi\) | |||||||
\(224\) | −7.48818 | − | 12.9699i | −0.500325 | − | 0.866588i | ||||
\(225\) | 1.06289 | − | 1.84097i | 0.0708592 | − | 0.122732i | ||||
\(226\) | 10.6033i | 0.705323i | ||||||||
\(227\) | −21.3029 | − | 12.2993i | −1.41393 | − | 0.816330i | −0.418170 | − | 0.908369i | \(-0.637328\pi\) |
−0.995755 | + | 0.0920386i | \(0.970662\pi\) | |||||||
\(228\) | 4.60298 | + | 2.65753i | 0.304840 | + | 0.175999i | ||||
\(229\) | − | 26.3489i | − | 1.74118i | −0.492006 | − | 0.870592i | \(-0.663736\pi\) | ||
0.492006 | − | 0.870592i | \(-0.336264\pi\) | |||||||
\(230\) | 0.155006 | − | 0.268478i | 0.0102208 | − | 0.0177029i | ||||
\(231\) | 1.24801 | + | 2.16161i | 0.0821129 | + | 0.142224i | ||||
\(232\) | −4.37043 | + | 2.52327i | −0.286933 | + | 0.165661i | ||||
\(233\) | −20.7814 | −1.36144 | −0.680719 | − | 0.732545i | \(-0.738333\pi\) | ||||
−0.680719 | + | 0.732545i | \(0.738333\pi\) | |||||||
\(234\) | 0.312901 | + | 0.871377i | 0.0204550 | + | 0.0569637i | ||||
\(235\) | −1.80075 | −0.117468 | ||||||||
\(236\) | 12.3132 | − | 7.10903i | 0.801521 | − | 0.462758i | ||||
\(237\) | 1.73231 | + | 3.00045i | 0.112526 | + | 0.194900i | ||||
\(238\) | −2.93489 | + | 5.08338i | −0.190241 | + | 0.329507i | ||||
\(239\) | 2.75636i | 0.178294i | 0.996018 | + | 0.0891471i | \(0.0284141\pi\) | ||||
−0.996018 | + | 0.0891471i | \(0.971586\pi\) | |||||||
\(240\) | −0.536783 | − | 0.309912i | −0.0346492 | − | 0.0200047i | ||||
\(241\) | 22.0705 | + | 12.7424i | 1.42168 | + | 0.820809i | 0.996443 | − | 0.0842710i | \(-0.0268561\pi\) |
0.425241 | + | 0.905080i | \(0.360189\pi\) | |||||||
\(242\) | 6.39363i | 0.410998i | ||||||||
\(243\) | 2.20834 | − | 3.82495i | 0.141665 | − | 0.245371i | ||||
\(244\) | 4.16968 | + | 7.22210i | 0.266937 | + | 0.462348i | ||||
\(245\) | 0.0490285 | − | 0.0283066i | 0.00313231 | − | 0.00180844i | ||||
\(246\) | −7.88433 | −0.502687 | ||||||||
\(247\) | 7.16717 | + | 1.29570i | 0.456036 | + | 0.0824432i | ||||
\(248\) | 2.18210 | 0.138563 | ||||||||
\(249\) | −9.48594 | + | 5.47671i | −0.601147 | + | 0.347072i | ||||
\(250\) | −0.584607 | − | 1.01257i | −0.0369738 | − | 0.0640405i | ||||
\(251\) | 0.742182 | − | 1.28550i | 0.0468461 | − | 0.0811398i | −0.841652 | − | 0.540021i | \(-0.818416\pi\) |
0.888498 | + | 0.458881i | \(0.151750\pi\) | |||||||
\(252\) | 1.89792i | 0.119558i | ||||||||
\(253\) | 1.31874 | + | 0.761372i | 0.0829082 | + | 0.0478670i | ||||
\(254\) | −3.58259 | − | 2.06841i | −0.224792 | − | 0.129784i | ||||
\(255\) | 1.13917i | 0.0713375i | ||||||||
\(256\) | 2.81375 | − | 4.87356i | 0.175860 | − | 0.304598i | ||||
\(257\) | −10.5142 | − | 18.2111i | −0.655858 | − | 1.13598i | −0.981678 | − | 0.190548i | \(-0.938974\pi\) |
0.325820 | − | 0.945432i | \(-0.394360\pi\) | |||||||
\(258\) | 4.54616 | − | 2.62473i | 0.283031 | − | 0.163408i | ||||
\(259\) | 20.7560 | 1.28971 | ||||||||
\(260\) | −1.14005 | − | 0.206100i | −0.0707027 | − | 0.0127818i | ||||
\(261\) | 0.990855 | 0.0613324 | ||||||||
\(262\) | 2.40385 | − | 1.38786i | 0.148510 | − | 0.0857423i | ||||
\(263\) | −9.42616 | − | 16.3266i | −0.581242 | − | 1.00674i | −0.995333 | − | 0.0965045i | \(-0.969234\pi\) |
0.414091 | − | 0.910236i | \(-0.364100\pi\) | |||||||
\(264\) | −1.00868 | + | 1.74709i | −0.0620802 | + | 0.107526i | ||||
\(265\) | − | 1.11158i | − | 0.0682837i | ||||||
\(266\) | −2.83078 | − | 1.63435i | −0.173566 | − | 0.100209i | ||||
\(267\) | 18.6514 | + | 10.7684i | 1.14145 | + | 0.659017i | ||||
\(268\) | 10.3097i | 0.629765i | ||||||||
\(269\) | −8.89209 | + | 15.4015i | −0.542160 | + | 0.939049i | 0.456620 | + | 0.889662i | \(0.349060\pi\) |
−0.998780 | + | 0.0493869i | \(0.984273\pi\) | |||||||
\(270\) | −0.322647 | − | 0.558841i | −0.0196357 | − | 0.0340100i | ||||
\(271\) | −6.57678 | + | 3.79711i | −0.399511 | + | 0.230658i | −0.686273 | − | 0.727344i | \(-0.740754\pi\) |
0.286762 | + | 0.958002i | \(0.407421\pi\) | |||||||
\(272\) | 7.15967 | 0.434119 | ||||||||
\(273\) | −5.27560 | − | 14.6916i | −0.319294 | − | 0.889179i | ||||
\(274\) | 1.00906 | 0.0609593 | ||||||||
\(275\) | 2.47725 | − | 1.43024i | 0.149384 | − | 0.0862467i | ||||
\(276\) | −3.47483 | − | 6.01858i | −0.209160 | − | 0.362276i | ||||
\(277\) | −14.6643 | + | 25.3992i | −0.881090 | + | 1.52609i | −0.0309587 | + | 0.999521i | \(0.509856\pi\) |
−0.850131 | + | 0.526571i | \(0.823477\pi\) | |||||||
\(278\) | 4.92471i | 0.295364i | ||||||||
\(279\) | −0.371041 | − | 0.214221i | −0.0222136 | − | 0.0128250i | ||||
\(280\) | 0.999137 | + | 0.576852i | 0.0597098 | + | 0.0344735i | ||||
\(281\) | − | 6.40035i | − | 0.381813i | −0.981608 | − | 0.190907i | \(-0.938857\pi\) | ||
0.981608 | − | 0.190907i | \(-0.0611428\pi\) | |||||||
\(282\) | 4.41894 | − | 7.65382i | 0.263144 | − | 0.455778i | ||||
\(283\) | −3.24959 | − | 5.62846i | −0.193168 | − | 0.334577i | 0.753130 | − | 0.657872i | \(-0.228543\pi\) |
−0.946299 | + | 0.323294i | \(0.895210\pi\) | |||||||
\(284\) | −5.67084 | + | 3.27406i | −0.336502 | + | 0.194280i | ||||
\(285\) | −0.634368 | −0.0375767 | ||||||||
\(286\) | −0.221634 | + | 1.22597i | −0.0131055 | + | 0.0724932i | ||||
\(287\) | −22.1475 | −1.30732 | ||||||||
\(288\) | −2.05822 | + | 1.18831i | −0.121282 | + | 0.0700220i | ||||
\(289\) | 1.92066 | + | 3.32668i | 0.112980 | + | 0.195687i | ||||
\(290\) | 0.135723 | − | 0.235078i | 0.00796991 | − | 0.0138043i | ||||
\(291\) | 19.8919i | 1.16608i | ||||||||
\(292\) | 4.36350 | + | 2.51927i | 0.255354 | + | 0.147429i | ||||
\(293\) | 5.07672 | + | 2.93105i | 0.296585 | + | 0.171234i | 0.640908 | − | 0.767618i | \(-0.278558\pi\) |
−0.344323 | + | 0.938851i | \(0.611891\pi\) | |||||||
\(294\) | 0.277851i | 0.0162046i | ||||||||
\(295\) | −0.848483 | + | 1.46962i | −0.0494006 | + | 0.0855643i | ||||
\(296\) | 8.38785 | + | 14.5282i | 0.487534 | + | 0.844434i | ||||
\(297\) | 2.74497 | − | 1.58481i | 0.159280 | − | 0.0919601i | ||||
\(298\) | −11.6661 | −0.675798 | ||||||||
\(299\) | −7.26875 | − | 6.15288i | −0.420363 | − | 0.355830i | ||||
\(300\) | −13.0549 | −0.753728 | ||||||||
\(301\) | 12.7704 | − | 7.37298i | 0.736072 | − | 0.424971i | ||||
\(302\) | −1.69557 | − | 2.93681i | −0.0975691 | − | 0.168995i | ||||
\(303\) | 4.75536 | − | 8.23652i | 0.273188 | − | 0.473176i | ||||
\(304\) | 3.98700i | 0.228670i | ||||||||
\(305\) | −0.861978 | − | 0.497663i | −0.0493567 | − | 0.0284961i | ||||
\(306\) | 0.806691 | + | 0.465743i | 0.0461155 | + | 0.0266248i | ||||
\(307\) | − | 1.68315i | − | 0.0960625i | −0.998846 | − | 0.0480312i | \(-0.984705\pi\) | ||
0.998846 | − | 0.0480312i | \(-0.0152947\pi\) | |||||||
\(308\) | −1.27694 | + | 2.21172i | −0.0727603 | + | 0.126025i | ||||
\(309\) | −10.2799 | − | 17.8052i | −0.584800 | − | 1.01290i | ||||
\(310\) | −0.101647 | + | 0.0586858i | −0.00577315 | + | 0.00333313i | ||||
\(311\) | −26.7569 | −1.51724 | −0.758622 | − | 0.651531i | \(-0.774127\pi\) | ||||
−0.758622 | + | 0.651531i | \(0.774127\pi\) | |||||||
\(312\) | 8.15148 | − | 9.62981i | 0.461487 | − | 0.545181i | ||||
\(313\) | 31.1093 | 1.75840 | 0.879200 | − | 0.476453i | \(-0.158078\pi\) | ||||
0.879200 | + | 0.476453i | \(0.158078\pi\) | |||||||
\(314\) | 8.80142 | − | 5.08150i | 0.496693 | − | 0.286766i | ||||
\(315\) | −0.113261 | − | 0.196174i | −0.00638155 | − | 0.0110532i | ||||
\(316\) | −1.77247 | + | 3.07000i | −0.0997090 | + | 0.172701i | ||||
\(317\) | 1.57405i | 0.0884076i | 0.999023 | + | 0.0442038i | \(0.0140751\pi\) | ||||
−0.999023 | + | 0.0442038i | \(0.985925\pi\) | |||||||
\(318\) | 4.72460 | + | 2.72775i | 0.264942 | + | 0.152965i | ||||
\(319\) | 1.15468 | + | 0.666656i | 0.0646498 | + | 0.0373256i | ||||
\(320\) | − | 0.121960i | − | 0.00681775i | ||||||
\(321\) | 7.33528 | − | 12.7051i | 0.409415 | − | 0.709128i | ||||
\(322\) | 2.13698 | + | 3.70136i | 0.119089 | + | 0.206269i | ||||
\(323\) | 6.34594 | − | 3.66383i | 0.353098 | − | 0.203861i | ||||
\(324\) | −12.3569 | −0.686495 | ||||||||
\(325\) | −16.8369 | + | 6.04593i | −0.933942 | + | 0.335368i | ||||
\(326\) | 5.88955 | 0.326192 | ||||||||
\(327\) | 16.7857 | − | 9.69124i | 0.928252 | − | 0.535927i | ||||
\(328\) | −8.95017 | − | 15.5021i | −0.494190 | − | 0.855963i | ||||
\(329\) | 12.4130 | − | 21.4999i | 0.684350 | − | 1.18533i | ||||
\(330\) | − | 0.108511i | − | 0.00597333i | ||||||
\(331\) | −8.67786 | − | 5.01016i | −0.476978 | − | 0.275383i | 0.242178 | − | 0.970232i | \(-0.422138\pi\) |
−0.719156 | + | 0.694848i | \(0.755471\pi\) | |||||||
\(332\) | −9.70583 | − | 5.60366i | −0.532677 | − | 0.307541i | ||||
\(333\) | − | 3.29380i | − | 0.180499i | ||||||
\(334\) | −2.45026 | + | 4.24397i | −0.134072 | + | 0.232220i | ||||
\(335\) | −0.615246 | − | 1.06564i | −0.0336145 | − | 0.0582220i | ||||
\(336\) | 7.40035 | − | 4.27259i | 0.403722 | − | 0.233089i | ||||
\(337\) | 12.0323 | 0.655441 | 0.327721 | − | 0.944775i | \(-0.393720\pi\) | ||||
0.327721 | + | 0.944775i | \(0.393720\pi\) | |||||||
\(338\) | 2.72798 | − | 7.29836i | 0.148383 | − | 0.396979i | ||||
\(339\) | −28.3701 | −1.54085 | ||||||||
\(340\) | −1.00942 | + | 0.582788i | −0.0547434 | + | 0.0316061i | ||||
\(341\) | −0.288259 | − | 0.499279i | −0.0156101 | − | 0.0270375i | ||||
\(342\) | −0.259358 | + | 0.449221i | −0.0140245 | + | 0.0242911i | ||||
\(343\) | − | 18.1183i | − | 0.978298i | ||||||
\(344\) | 10.3215 | + | 5.95909i | 0.556495 | + | 0.321293i | ||||
\(345\) | 0.718334 | + | 0.414731i | 0.0386738 | + | 0.0223283i | ||||
\(346\) | 4.31690i | 0.232078i | ||||||||
\(347\) | −1.63299 | + | 2.82841i | −0.0876633 | + | 0.151837i | −0.906523 | − | 0.422156i | \(-0.861273\pi\) |
0.818860 | + | 0.573994i | \(0.194607\pi\) | |||||||
\(348\) | −3.04255 | − | 5.26986i | −0.163098 | − | 0.282494i | ||||
\(349\) | −7.03372 | + | 4.06092i | −0.376506 | + | 0.217376i | −0.676297 | − | 0.736629i | \(-0.736416\pi\) |
0.299791 | + | 0.954005i | \(0.403083\pi\) | |||||||
\(350\) | 8.02865 | 0.429149 | ||||||||
\(351\) | −18.6565 | + | 6.69934i | −0.995811 | + | 0.357584i | ||||
\(352\) | −3.19803 | −0.170455 | ||||||||
\(353\) | 15.2510 | − | 8.80516i | 0.811728 | − | 0.468651i | −0.0358275 | − | 0.999358i | \(-0.511407\pi\) |
0.847556 | + | 0.530707i | \(0.178073\pi\) | |||||||
\(354\) | −4.16426 | − | 7.21270i | −0.221328 | − | 0.383351i | ||||
\(355\) | 0.390768 | − | 0.676831i | 0.0207398 | − | 0.0359224i | ||||
\(356\) | 22.0361i | 1.16791i | ||||||||
\(357\) | −13.6010 | − | 7.85256i | −0.719843 | − | 0.415601i | ||||
\(358\) | 0.288310 | + | 0.166456i | 0.0152377 | + | 0.00879748i | ||||
\(359\) | 27.2273i | 1.43700i | 0.695525 | + | 0.718501i | \(0.255172\pi\) | ||||
−0.695525 | + | 0.718501i | \(0.744828\pi\) | |||||||
\(360\) | 0.0915416 | − | 0.158555i | 0.00482467 | − | 0.00835657i | ||||
\(361\) | −7.45973 | − | 12.9206i | −0.392617 | − | 0.680033i | ||||
\(362\) | −5.36791 | + | 3.09916i | −0.282131 | + | 0.162888i | ||||
\(363\) | −17.1067 | −0.897869 | ||||||||
\(364\) | 10.3193 | − | 12.1908i | 0.540880 | − | 0.638972i | ||||
\(365\) | −0.601363 | −0.0314768 | ||||||||
\(366\) | 4.23049 | − | 2.44247i | 0.221131 | − | 0.127670i | ||||
\(367\) | −10.6172 | − | 18.3896i | −0.554214 | − | 0.959927i | −0.997964 | − | 0.0637764i | \(-0.979686\pi\) |
0.443750 | − | 0.896151i | \(-0.353648\pi\) | |||||||
\(368\) | 2.60658 | − | 4.51473i | 0.135877 | − | 0.235347i | ||||
\(369\) | 3.51462i | 0.182964i | ||||||||
\(370\) | −0.781448 | − | 0.451169i | −0.0406256 | − | 0.0234552i | ||||
\(371\) | 13.2716 | + | 7.66237i | 0.689028 | + | 0.397811i | ||||
\(372\) | 2.63117i | 0.136420i | ||||||||
\(373\) | 9.99793 | − | 17.3169i | 0.517673 | − | 0.896636i | −0.482116 | − | 0.876107i | \(-0.660132\pi\) |
0.999789 | − | 0.0205288i | \(-0.00653499\pi\) | |||||||
\(374\) | 0.626712 | + | 1.08550i | 0.0324065 | + | 0.0561297i | ||||
\(375\) | 2.70922 | − | 1.56417i | 0.139903 | − | 0.0807732i | ||||
\(376\) | 20.0652 | 1.03478 | ||||||||
\(377\) | −6.36450 | − | 5.38745i | −0.327789 | − | 0.277468i | ||||
\(378\) | 8.89634 | 0.457578 | ||||||||
\(379\) | 1.98960 | − | 1.14869i | 0.102199 | − | 0.0590044i | −0.448030 | − | 0.894019i | \(-0.647874\pi\) |
0.550228 | + | 0.835014i | \(0.314541\pi\) | |||||||
\(380\) | −0.324536 | − | 0.562114i | −0.0166484 | − | 0.0288358i | ||||
\(381\) | 5.53421 | − | 9.58553i | 0.283526 | − | 0.491081i | ||||
\(382\) | 15.2206i | 0.778752i | ||||||||
\(383\) | −11.7268 | − | 6.77047i | −0.599212 | − | 0.345955i | 0.169520 | − | 0.985527i | \(-0.445778\pi\) |
−0.768731 | + | 0.639572i | \(0.779112\pi\) | |||||||
\(384\) | 15.9257 | + | 9.19473i | 0.812707 | + | 0.469216i | ||||
\(385\) | − | 0.304812i | − | 0.0155347i | ||||||
\(386\) | −4.28262 | + | 7.41772i | −0.217980 | + | 0.377552i | ||||
\(387\) | −1.17003 | − | 2.02655i | −0.0594760 | − | 0.103015i | ||||
\(388\) | −17.6262 | + | 10.1765i | −0.894837 | + | 0.516634i | ||||
\(389\) | 25.6713 | 1.30159 | 0.650794 | − | 0.759254i | \(-0.274436\pi\) | ||||
0.650794 | + | 0.759254i | \(0.274436\pi\) | |||||||
\(390\) | −0.120727 | + | 0.667805i | −0.00611326 | + | 0.0338156i | ||||
\(391\) | −9.58121 | −0.484543 | ||||||||
\(392\) | −0.546310 | + | 0.315412i | −0.0275928 | + | 0.0159307i | ||||
\(393\) | 3.71334 | + | 6.43169i | 0.187313 | + | 0.324436i | ||||
\(394\) | 3.09349 | − | 5.35809i | 0.155848 | − | 0.269937i | ||||
\(395\) | − | 0.423098i | − | 0.0212884i | ||||||
\(396\) | 0.350982 | + | 0.202640i | 0.0176375 | + | 0.0101830i | ||||
\(397\) | −19.9855 | − | 11.5386i | −1.00304 | − | 0.579107i | −0.0938953 | − | 0.995582i | \(-0.529932\pi\) |
−0.909147 | + | 0.416475i | \(0.863265\pi\) | |||||||
\(398\) | 8.73613i | 0.437903i | ||||||||
\(399\) | 4.37285 | − | 7.57399i | 0.218916 | − | 0.379174i | ||||
\(400\) | −4.89647 | − | 8.48093i | −0.244823 | − | 0.424046i | ||||
\(401\) | −21.8180 | + | 12.5966i | −1.08954 | + | 0.629045i | −0.933453 | − | 0.358699i | \(-0.883220\pi\) |
−0.156084 | + | 0.987744i | \(0.549887\pi\) | |||||||
\(402\) | 6.03911 | 0.301204 | ||||||||
\(403\) | 1.21853 | + | 3.39340i | 0.0606994 | + | 0.169037i | ||||
\(404\) | 9.73118 | 0.484144 | ||||||||
\(405\) | 1.27724 | − | 0.737416i | 0.0634667 | − | 0.0366425i | ||||
\(406\) | 1.87114 | + | 3.24090i | 0.0928629 | + | 0.160843i | ||||
\(407\) | 2.21610 | − | 3.83840i | 0.109848 | − | 0.190262i | ||||
\(408\) | − | 12.6934i | − | 0.628418i | ||||||
\(409\) | 5.17040 | + | 2.98513i | 0.255660 | + | 0.147605i | 0.622353 | − | 0.782737i | \(-0.286177\pi\) |
−0.366693 | + | 0.930342i | \(0.619510\pi\) | |||||||
\(410\) | 0.833836 | + | 0.481416i | 0.0411802 | + | 0.0237754i | ||||
\(411\) | 2.69981i | 0.133172i | ||||||||
\(412\) | 10.5181 | − | 18.2180i | 0.518192 | − | 0.897535i | ||||
\(413\) | −11.6976 | − | 20.2608i | −0.575601 | − | 0.996970i | ||||
\(414\) | 0.587375 | − | 0.339121i | 0.0288679 | − | 0.0166669i | ||||
\(415\) | 1.33763 | 0.0656615 | ||||||||
\(416\) | 19.6815 | + | 3.55806i | 0.964964 | + | 0.174448i | ||||
\(417\) | −13.1765 | −0.645255 | ||||||||
\(418\) | −0.604480 | + | 0.348997i | −0.0295661 | + | 0.0170700i | ||||
\(419\) | 6.43004 | + | 11.1372i | 0.314128 | + | 0.544086i | 0.979252 | − | 0.202647i | \(-0.0649545\pi\) |
−0.665124 | + | 0.746733i | \(0.731621\pi\) | |||||||
\(420\) | −0.695567 | + | 1.20476i | −0.0339402 | + | 0.0587862i | ||||
\(421\) | − | 9.00187i | − | 0.438724i | −0.975644 | − | 0.219362i | \(-0.929602\pi\) | ||
0.975644 | − | 0.219362i | \(-0.0703976\pi\) | |||||||
\(422\) | 9.62239 | + | 5.55549i | 0.468411 | + | 0.270437i | ||||
\(423\) | −3.41186 | − | 1.96984i | −0.165890 | − | 0.0957769i | ||||
\(424\) | 12.3860i | 0.601517i | ||||||||
\(425\) | −8.99916 | + | 15.5870i | −0.436524 | + | 0.756081i | ||||
\(426\) | 1.91785 | + | 3.32181i | 0.0929199 | + | 0.160942i | ||||
\(427\) | 11.8836 | − | 6.86102i | 0.575090 | − | 0.332028i | ||||
\(428\) | 15.0106 | 0.725566 | ||||||||
\(429\) | −3.28019 | − | 0.593000i | −0.158369 | − | 0.0286303i | ||||
\(430\) | −0.641061 | −0.0309147 | ||||||||
\(431\) | 4.74542 | − | 2.73977i | 0.228579 | − | 0.131970i | −0.381337 | − | 0.924436i | \(-0.624536\pi\) |
0.609916 | + | 0.792466i | \(0.291203\pi\) | |||||||
\(432\) | −5.42565 | − | 9.39750i | −0.261042 | − | 0.452137i | ||||
\(433\) | −8.01983 | + | 13.8908i | −0.385409 | + | 0.667547i | −0.991826 | − | 0.127599i | \(-0.959273\pi\) |
0.606417 | + | 0.795147i | \(0.292606\pi\) | |||||||
\(434\) | − | 1.61814i | − | 0.0776732i | ||||||
\(435\) | 0.628972 | + | 0.363137i | 0.0301569 | + | 0.0174111i | ||||
\(436\) | 17.1748 | + | 9.91589i | 0.822525 | + | 0.474885i | ||||
\(437\) | − | 5.33548i | − | 0.255231i | ||||||
\(438\) | 1.47571 | − | 2.55601i | 0.0705122 | − | 0.122131i | ||||
\(439\) | −3.04264 | − | 5.27001i | −0.145217 | − | 0.251524i | 0.784237 | − | 0.620462i | \(-0.213055\pi\) |
−0.929454 | + | 0.368938i | \(0.879721\pi\) | |||||||
\(440\) | 0.213354 | − | 0.123180i | 0.0101713 | − | 0.00587238i | ||||
\(441\) | 0.123858 | 0.00589802 | ||||||||
\(442\) | −2.64925 | − | 7.37770i | −0.126012 | − | 0.350921i | ||||
\(443\) | 25.6498 | 1.21866 | 0.609330 | − | 0.792917i | \(-0.291438\pi\) | ||||
0.609330 | + | 0.792917i | \(0.291438\pi\) | |||||||
\(444\) | −17.5181 | + | 10.1141i | −0.831371 | + | 0.479992i | ||||
\(445\) | −1.31503 | − | 2.27771i | −0.0623386 | − | 0.107974i | ||||
\(446\) | −2.16864 | + | 3.75620i | −0.102688 | + | 0.177861i | ||||
\(447\) | − | 31.2136i | − | 1.47635i | ||||||
\(448\) | 1.45613 | + | 0.840697i | 0.0687957 | + | 0.0397192i | ||||
\(449\) | −19.7645 | − | 11.4111i | −0.932746 | − | 0.538521i | −0.0450672 | − | 0.998984i | \(-0.514350\pi\) |
−0.887679 | + | 0.460463i | \(0.847684\pi\) | |||||||
\(450\) | − | 1.27408i | − | 0.0600607i | ||||||
\(451\) | −2.36467 | + | 4.09572i | −0.111348 | + | 0.192860i | ||||
\(452\) | −14.5139 | − | 25.1388i | −0.682675 | − | 1.18243i | ||||
\(453\) | 7.85769 | − | 4.53664i | 0.369187 | − | 0.213150i | ||||
\(454\) | −14.7431 | −0.691927 | ||||||||
\(455\) | −0.339128 | + | 1.87589i | −0.0158986 | + | 0.0879433i | ||||
\(456\) | 7.06857 | 0.331016 | ||||||||
\(457\) | 21.2235 | − | 12.2534i | 0.992793 | − | 0.573189i | 0.0866848 | − | 0.996236i | \(-0.472373\pi\) |
0.906108 | + | 0.423047i | \(0.139039\pi\) | |||||||
\(458\) | −7.89608 | − | 13.6764i | −0.368960 | − | 0.639057i | ||||
\(459\) | −9.97174 | + | 17.2716i | −0.465441 | + | 0.806168i | ||||
\(460\) | 0.848689i | 0.0395703i | ||||||||
\(461\) | −5.66788 | − | 3.27235i | −0.263980 | − | 0.152409i | 0.362169 | − | 0.932112i | \(-0.382036\pi\) |
−0.626149 | + | 0.779704i | \(0.715370\pi\) | |||||||
\(462\) | 1.29556 | + | 0.747992i | 0.0602749 | + | 0.0347997i | ||||
\(463\) | − | 3.26046i | − | 0.151527i | −0.997126 | − | 0.0757633i | \(-0.975861\pi\) | ||
0.997126 | − | 0.0757633i | \(-0.0241393\pi\) | |||||||
\(464\) | 2.28232 | − | 3.95309i | 0.105954 | − | 0.183518i | ||||
\(465\) | −0.157019 | − | 0.271965i | −0.00728157 | − | 0.0126121i | ||||
\(466\) | −10.7866 | + | 6.22767i | −0.499681 | + | 0.288491i | ||||
\(467\) | −2.75854 | −0.127650 | −0.0638249 | − | 0.997961i | \(-0.520330\pi\) | ||||
−0.0638249 | + | 0.997961i | \(0.520330\pi\) | |||||||
\(468\) | −1.93458 | − | 1.63759i | −0.0894261 | − | 0.0756977i | ||||
\(469\) | 16.9641 | 0.783332 | ||||||||
\(470\) | −0.934681 | + | 0.539638i | −0.0431136 | + | 0.0248917i | ||||
\(471\) | 13.5960 | + | 23.5489i | 0.626470 | + | 1.08508i | ||||
\(472\) | 9.45440 | − | 16.3755i | 0.435174 | − | 0.753743i | ||||
\(473\) | − | 3.14883i | − | 0.144783i | ||||||
\(474\) | 1.79832 | + | 1.03826i | 0.0825993 | + | 0.0476888i | ||||
\(475\) | −8.67993 | − | 5.01136i | −0.398262 | − | 0.229937i | ||||
\(476\) | − | 16.0692i | − | 0.736529i | ||||||
\(477\) | 1.21596 | − | 2.10610i | 0.0556748 | − | 0.0964316i | ||||
\(478\) | 0.826011 | + | 1.43069i | 0.0377809 | + | 0.0654384i | ||||
\(479\) | −19.5289 | + | 11.2750i | −0.892300 | + | 0.515170i | −0.874694 | − | 0.484675i | \(-0.838938\pi\) |
−0.0176061 | + | 0.999845i | \(0.505604\pi\) | |||||||
\(480\) | −1.74201 | −0.0795116 | ||||||||
\(481\) | −17.9090 | + | 21.1569i | −0.816579 | + | 0.964672i | ||||
\(482\) | 15.2743 | 0.695724 | ||||||||
\(483\) | −9.90330 | + | 5.71767i | −0.450616 | + | 0.260163i | ||||
\(484\) | −8.75162 | − | 15.1583i | −0.397801 | − | 0.689011i | ||||
\(485\) | 1.21460 | − | 2.10374i | 0.0551520 | − | 0.0955260i | ||||
\(486\) | − | 2.64713i | − | 0.120076i | ||||||
\(487\) | −28.7558 | − | 16.6021i | −1.30305 | − | 0.752315i | −0.322122 | − | 0.946698i | \(-0.604396\pi\) |
−0.980926 | + | 0.194383i | \(0.937730\pi\) | |||||||
\(488\) | 9.60477 | + | 5.54532i | 0.434787 | + | 0.251025i | ||||
\(489\) | 15.7580i | 0.712600i | ||||||||
\(490\) | 0.0169655 | − | 0.0293851i | 0.000766424 | − | 0.00132749i | ||||
\(491\) | 9.20114 | + | 15.9368i | 0.415242 | + | 0.719219i | 0.995454 | − | 0.0952459i | \(-0.0303637\pi\) |
−0.580212 | + | 0.814465i | \(0.697030\pi\) | |||||||
\(492\) | 18.6925 | − | 10.7921i | 0.842722 | − | 0.486545i | ||||
\(493\) | −8.38929 | −0.377835 | ||||||||
\(494\) | 4.10841 | − | 1.47528i | 0.184846 | − | 0.0663762i | ||||
\(495\) | −0.0483712 | −0.00217413 | ||||||||
\(496\) | −1.70930 | + | 0.986863i | −0.0767497 | + | 0.0443114i | ||||
\(497\) | 5.38732 | + | 9.33111i | 0.241654 | + | 0.418557i | ||||
\(498\) | −3.28246 | + | 5.68538i | −0.147090 | + | 0.254768i | ||||
\(499\) | 2.08493i | 0.0933342i | 0.998910 | + | 0.0466671i | \(0.0148600\pi\) | ||||
−0.998910 | + | 0.0466671i | \(0.985140\pi\) | |||||||
\(500\) | 2.77202 | + | 1.60043i | 0.123968 | + | 0.0715732i | ||||
\(501\) | −11.3551 | − | 6.55587i | −0.507308 | − | 0.292895i | ||||
\(502\) | − | 0.889651i | − | 0.0397071i | ||||||
\(503\) | −15.5086 | + | 26.8617i | −0.691495 | + | 1.19771i | 0.279852 | + | 0.960043i | \(0.409714\pi\) |
−0.971348 | + | 0.237662i | \(0.923619\pi\) | |||||||
\(504\) | 1.26204 | + | 2.18591i | 0.0562156 | + | 0.0973682i | ||||
\(505\) | −1.00584 | + | 0.580722i | −0.0447593 | + | 0.0258418i | ||||
\(506\) | 0.912655 | 0.0405724 | ||||||||
\(507\) | 19.5274 | + | 7.29895i | 0.867242 | + | 0.324158i | ||||
\(508\) | 11.3250 | 0.502465 | ||||||||
\(509\) | 26.7560 | − | 15.4476i | 1.18594 | − | 0.684701i | 0.228557 | − | 0.973531i | \(-0.426599\pi\) |
0.957381 | + | 0.288829i | \(0.0932660\pi\) | |||||||
\(510\) | 0.341379 | + | 0.591286i | 0.0151165 | + | 0.0261826i | ||||
\(511\) | 4.14534 | − | 7.17994i | 0.183379 | − | 0.317622i | ||||
\(512\) | 19.5623i | 0.864538i | ||||||||
\(513\) | −9.61800 | − | 5.55296i | −0.424645 | − | 0.245169i | ||||
\(514\) | −10.9148 | − | 6.30167i | −0.481432 | − | 0.277955i | ||||
\(515\) | 2.51074i | 0.110637i | ||||||||
\(516\) | −7.18547 | + | 12.4456i | −0.316323 | + | 0.547887i | ||||
\(517\) | −2.65065 | − | 4.59106i | −0.116575 | − | 0.201915i | ||||
\(518\) | 10.7734 | − | 6.22004i | 0.473357 | − | 0.273293i | ||||
\(519\) | −11.5502 | −0.506999 | ||||||||
\(520\) | −1.45008 | + | 0.520708i | −0.0635904 | + | 0.0228346i | ||||
\(521\) | 6.79917 | 0.297877 | 0.148939 | − | 0.988846i | \(-0.452414\pi\) | ||||
0.148939 | + | 0.988846i | \(0.452414\pi\) | |||||||
\(522\) | 0.514305 | − | 0.296934i | 0.0225105 | − | 0.0129964i | ||||
\(523\) | 5.65669 | + | 9.79767i | 0.247350 | + | 0.428422i | 0.962790 | − | 0.270252i | \(-0.0871070\pi\) |
−0.715440 | + | 0.698674i | \(0.753774\pi\) | |||||||
\(524\) | −3.79942 | + | 6.58079i | −0.165978 | + | 0.287483i | ||||
\(525\) | 21.4813i | 0.937522i | ||||||||
\(526\) | −9.78531 | − | 5.64955i | −0.426660 | − | 0.246332i | ||||
\(527\) | 3.14150 | + | 1.81374i | 0.136846 | + | 0.0790079i | ||||
\(528\) | − | 1.82473i | − | 0.0794110i | ||||||
\(529\) | 8.01182 | − | 13.8769i | 0.348340 | − | 0.603343i | ||||
\(530\) | −0.333111 | − | 0.576966i | −0.0144694 | − | 0.0250618i | ||||
\(531\) | −3.21523 | + | 1.85631i | −0.139529 | + | 0.0805570i | ||||
\(532\) | 8.94843 | 0.387963 | ||||||||
\(533\) | 19.1096 | − | 22.5752i | 0.827728 | − | 0.977842i | ||||
\(534\) | 12.9081 | 0.558587 | ||||||||
\(535\) | −1.55154 | + | 0.895781i | −0.0670788 | + | 0.0387280i | ||||
\(536\) | 6.85551 | + | 11.8741i | 0.296113 | + | 0.512882i | ||||
\(537\) | −0.445368 | + | 0.771399i | −0.0192190 | + | 0.0332883i | ||||
\(538\) | 10.6589i | 0.459539i | ||||||||
\(539\) | 0.144337 | + | 0.0833330i | 0.00621703 | + | 0.00358940i | ||||
\(540\) | 1.52989 | + | 0.883281i | 0.0658359 | + | 0.0380104i | ||||
\(541\) | − | 17.8415i | − | 0.767068i | −0.923527 | − | 0.383534i | \(-0.874707\pi\) | ||
0.923527 | − | 0.383534i | \(-0.125293\pi\) | |||||||
\(542\) | −2.27579 | + | 3.94179i | −0.0977536 | + | 0.169314i | ||||
\(543\) | −8.29207 | − | 14.3623i | −0.355847 | − | 0.616345i | ||||
\(544\) | 17.4263 | − | 10.0611i | 0.747148 | − | 0.431366i | ||||
\(545\) | −2.36698 | −0.101390 | ||||||||
\(546\) | −7.14101 | − | 6.04475i | −0.305607 | − | 0.258691i | ||||
\(547\) | −10.4631 | −0.447368 | −0.223684 | − | 0.974662i | \(-0.571808\pi\) | ||||
−0.223684 | + | 0.974662i | \(0.571808\pi\) | |||||||
\(548\) | −2.39231 | + | 1.38120i | −0.102194 | + | 0.0590019i | ||||
\(549\) | −1.08879 | − | 1.88584i | −0.0464683 | − | 0.0804855i | ||||
\(550\) | 0.857212 | − | 1.48473i | 0.0365516 | − | 0.0633093i | ||||
\(551\) | − | 4.67174i | − | 0.199023i | ||||||
\(552\) | −8.00419 | − | 4.62122i | −0.340681 | − | 0.196692i | ||||
\(553\) | 5.05155 | + | 2.91651i | 0.214814 | + | 0.124023i | ||||
\(554\) | 17.5780i | 0.746818i | ||||||||
\(555\) | 1.20714 | − | 2.09083i | 0.0512403 | − | 0.0887508i | ||||
\(556\) | −6.74096 | − | 11.6757i | −0.285880 | − | 0.495159i | ||||
\(557\) | 9.37522 | − | 5.41278i | 0.397241 | − | 0.229347i | −0.288052 | − | 0.957615i | \(-0.593008\pi\) |
0.685293 | + | 0.728268i | \(0.259674\pi\) | |||||||
\(558\) | −0.256786 | −0.0108706 | ||||||||
\(559\) | −3.50332 | + | 19.3787i | −0.148175 | + | 0.819631i | ||||
\(560\) | −1.04353 | −0.0440974 | ||||||||
\(561\) | −2.90434 | + | 1.67682i | −0.122621 | + | 0.0707955i | ||||
\(562\) | −1.91802 | − | 3.32211i | −0.0809069 | − | 0.140135i | ||||
\(563\) | −3.91169 | + | 6.77525i | −0.164858 | + | 0.285543i | −0.936605 | − | 0.350387i | \(-0.886050\pi\) |
0.771747 | + | 0.635930i | \(0.219383\pi\) | |||||||
\(564\) | 24.1946i | 1.01878i | ||||||||
\(565\) | 3.00038 | + | 1.73227i | 0.126227 | + | 0.0728772i | ||||
\(566\) | −3.37341 | − | 1.94764i | −0.141795 | − | 0.0818654i | ||||
\(567\) | 20.3327i | 0.853895i | ||||||||
\(568\) | −4.35422 | + | 7.54173i | −0.182699 | + | 0.316444i | ||||
\(569\) | 4.74605 | + | 8.22040i | 0.198965 | + | 0.344617i | 0.948193 | − | 0.317695i | \(-0.102909\pi\) |
−0.749228 | + | 0.662312i | \(0.769575\pi\) | |||||||
\(570\) | −0.329269 | + | 0.190104i | −0.0137916 | + | 0.00796257i | ||||
\(571\) | −13.0424 | −0.545808 | −0.272904 | − | 0.962041i | \(-0.587984\pi\) | ||||
−0.272904 | + | 0.962041i | \(0.587984\pi\) | |||||||
\(572\) | −1.15266 | − | 3.20995i | −0.0481950 | − | 0.134215i | ||||
\(573\) | −40.7239 | −1.70127 | ||||||||
\(574\) | −11.4957 | + | 6.63702i | −0.479820 | + | 0.277024i | ||||
\(575\) | 6.55255 | + | 11.3494i | 0.273260 | + | 0.473301i | ||||
\(576\) | 0.133412 | − | 0.231076i | 0.00555882 | − | 0.00962816i | ||||
\(577\) | 26.3767i | 1.09808i | 0.835797 | + | 0.549039i | \(0.185006\pi\) | ||||
−0.835797 | + | 0.549039i | \(0.814994\pi\) | |||||||
\(578\) | 1.99384 | + | 1.15115i | 0.0829330 | + | 0.0478814i | ||||
\(579\) | −19.8467 | − | 11.4585i | −0.824802 | − | 0.476200i | ||||
\(580\) | 0.743110i | 0.0308560i | ||||||||
\(581\) | −9.22058 | + | 15.9705i | −0.382534 | + | 0.662568i | ||||
\(582\) | 5.96110 | + | 10.3249i | 0.247095 | + | 0.427982i | ||||
\(583\) | 2.83400 | − | 1.63621i | 0.117372 | − | 0.0677649i | ||||
\(584\) | 6.70082 | 0.277282 | ||||||||
\(585\) | 0.297689 | + | 0.0538169i | 0.0123079 | + | 0.00222505i | ||||
\(586\) | 3.51344 | 0.145139 | ||||||||
\(587\) | −3.07815 | + | 1.77717i | −0.127049 | + | 0.0733517i | −0.562178 | − | 0.827017i | \(-0.690036\pi\) |
0.435129 | + | 0.900368i | \(0.356703\pi\) | |||||||
\(588\) | −0.380323 | − | 0.658740i | −0.0156843 | − | 0.0271660i | ||||
\(589\) | −1.01002 | + | 1.74940i | −0.0416171 | + | 0.0720829i | ||||
\(590\) | 1.01707i | 0.0418723i | ||||||||
\(591\) | 14.3360 | + | 8.27690i | 0.589705 | + | 0.340466i | ||||
\(592\) | −13.1409 | − | 7.58688i | −0.540086 | − | 0.311819i | ||||
\(593\) | − | 7.79544i | − | 0.320121i | −0.987107 | − | 0.160060i | \(-0.948831\pi\) | ||
0.987107 | − | 0.160060i | \(-0.0511689\pi\) | |||||||
\(594\) | 0.949854 | − | 1.64520i | 0.0389730 | − | 0.0675032i | ||||
\(595\) | 0.958951 | + | 1.66095i | 0.0393131 | + | 0.0680924i | ||||
\(596\) | 27.6584 | − | 15.9686i | 1.13293 | − | 0.654098i | ||||
\(597\) | −23.3743 | −0.956645 | ||||||||
\(598\) | −5.61671 | − | 1.01540i | −0.229684 | − | 0.0415228i | ||||
\(599\) | −21.8161 | −0.891382 | −0.445691 | − | 0.895187i | \(-0.647042\pi\) | ||||
−0.445691 | + | 0.895187i | \(0.647042\pi\) | |||||||
\(600\) | −15.0359 | + | 8.68097i | −0.613838 | + | 0.354399i | ||||
\(601\) | 17.5245 | + | 30.3534i | 0.714840 | + | 1.23814i | 0.963021 | + | 0.269425i | \(0.0868338\pi\) |
−0.248181 | + | 0.968714i | \(0.579833\pi\) | |||||||
\(602\) | 4.41898 | − | 7.65390i | 0.180104 | − | 0.311950i | ||||
\(603\) | − | 2.69207i | − | 0.109630i | ||||||
\(604\) | 8.03984 | + | 4.64180i | 0.327137 | + | 0.188872i | ||||
\(605\) | 1.80918 | + | 1.04453i | 0.0735537 | + | 0.0424662i | ||||
\(606\) | − | 5.70023i | − | 0.231556i | ||||||
\(607\) | −13.7173 | + | 23.7591i | −0.556768 | + | 0.964351i | 0.440995 | + | 0.897509i | \(0.354626\pi\) |
−0.997764 | + | 0.0668415i | \(0.978708\pi\) | |||||||
\(608\) | 5.60272 | + | 9.70419i | 0.227220 | + | 0.393557i | ||||
\(609\) | −8.67131 | + | 5.00638i | −0.351379 | + | 0.202869i | ||||
\(610\) | −0.596548 | −0.0241535 | ||||||||
\(611\) | 11.2049 | + | 31.2036i | 0.453300 | + | 1.26236i | ||||
\(612\) | −2.55005 | −0.103079 | ||||||||
\(613\) | 21.3319 | − | 12.3160i | 0.861587 | − | 0.497437i | −0.00295642 | − | 0.999996i | \(-0.500941\pi\) |
0.864543 | + | 0.502558i | \(0.167608\pi\) | |||||||
\(614\) | −0.504397 | − | 0.873641i | −0.0203558 | − | 0.0352573i | ||||
\(615\) | −1.28807 | + | 2.23100i | −0.0519399 | + | 0.0899626i | ||||
\(616\) | 3.39644i | 0.136846i | ||||||||
\(617\) | 6.40738 | + | 3.69930i | 0.257951 | + | 0.148928i | 0.623400 | − | 0.781903i | \(-0.285751\pi\) |
−0.365448 | + | 0.930832i | \(0.619084\pi\) | |||||||
\(618\) | −10.6715 | − | 6.16122i | −0.429272 | − | 0.247840i | ||||
\(619\) | 2.38292i | 0.0957777i | 0.998853 | + | 0.0478888i | \(0.0152493\pi\) | ||||
−0.998853 | + | 0.0478888i | \(0.984751\pi\) | |||||||
\(620\) | 0.160659 | − | 0.278269i | 0.00645221 | − | 0.0111756i | ||||
\(621\) | 7.26071 | + | 12.5759i | 0.291362 | + | 0.504654i | ||||
\(622\) | −13.8882 | + | 8.01836i | −0.556866 | + | 0.321507i | ||||
\(623\) | 36.2594 | 1.45270 | ||||||||
\(624\) | −2.03015 | + | 11.2298i | −0.0812712 | + | 0.449553i | ||||
\(625\) | 24.4262 | 0.977049 | ||||||||
\(626\) | 16.1473 | − | 9.32265i | 0.645376 | − | 0.372608i | ||||
\(627\) | −0.933770 | − | 1.61734i | −0.0372912 | − | 0.0645902i | ||||
\(628\) | −13.9112 | + | 24.0948i | −0.555115 | + | 0.961488i | ||||
\(629\) | 27.8877i | 1.11196i | ||||||||
\(630\) | −0.117577 | − | 0.0678830i | −0.00468437 | − | 0.00270452i | ||||
\(631\) | 21.3020 | + | 12.2987i | 0.848020 | + | 0.489605i | 0.859982 | − | 0.510324i | \(-0.170474\pi\) |
−0.0119620 | + | 0.999928i | \(0.503808\pi\) | |||||||
\(632\) | 4.71445i | 0.187531i | ||||||||
\(633\) | −14.8642 | + | 25.7455i | −0.590798 | + | 1.02329i | ||||
\(634\) | 0.471703 | + | 0.817014i | 0.0187337 | + | 0.0324478i | ||||
\(635\) | −1.17058 | + | 0.675835i | −0.0464531 | + | 0.0268197i | ||||
\(636\) | −14.9350 | −0.592212 | ||||||||
\(637\) | −0.795572 | − | 0.673439i | −0.0315217 | − | 0.0266826i | ||||
\(638\) | 0.799119 | 0.0316374 | ||||||||
\(639\) | 1.48077 | − | 0.854923i | 0.0585784 | − | 0.0338202i | ||||
\(640\) | −1.12286 | − | 1.94484i | −0.0443848 | − | 0.0768767i | ||||
\(641\) | −9.98187 | + | 17.2891i | −0.394260 | + | 0.682879i | −0.993006 | − | 0.118060i | \(-0.962332\pi\) |
0.598746 | + | 0.800939i | \(0.295666\pi\) | |||||||
\(642\) | − | 8.79278i | − | 0.347023i | ||||||
\(643\) | 28.6055 | + | 16.5154i | 1.12809 | + | 0.651304i | 0.943454 | − | 0.331503i | \(-0.107556\pi\) |
0.184637 | + | 0.982807i | \(0.440889\pi\) | |||||||
\(644\) | −10.1329 | − | 5.85021i | −0.399291 | − | 0.230531i | ||||
\(645\) | − | 1.71521i | − | 0.0675364i | ||||||
\(646\) | 2.19591 | − | 3.80343i | 0.0863970 | − | 0.149644i | ||||
\(647\) | −13.2429 | − | 22.9374i | −0.520633 | − | 0.901763i | −0.999712 | − | 0.0239914i | \(-0.992363\pi\) |
0.479079 | − | 0.877772i | \(-0.340971\pi\) | |||||||
\(648\) | −14.2319 | + | 8.21681i | −0.559083 | + | 0.322787i | ||||
\(649\) | −4.99577 | −0.196101 | ||||||||
\(650\) | −6.92739 | + | 8.18372i | −0.271715 | + | 0.320992i | ||||
\(651\) | 4.32947 | 0.169685 | ||||||||
\(652\) | −13.9632 | + | 8.06163i | −0.546839 | + | 0.315718i | ||||
\(653\) | 12.7092 | + | 22.0130i | 0.497351 | + | 0.861437i | 0.999995 | − | 0.00305614i | \(-0.000972800\pi\) |
−0.502644 | + | 0.864493i | \(0.667639\pi\) | |||||||
\(654\) | 5.80843 | − | 10.0605i | 0.227128 | − | 0.393397i | ||||
\(655\) | − | 0.906943i | − | 0.0354372i | ||||||
\(656\) | 14.0218 | + | 8.09550i | 0.547460 | + | 0.316076i | ||||
\(657\) | −1.13940 | − | 0.657831i | −0.0444521 | − | 0.0256645i | ||||
\(658\) | − | 14.8794i | − | 0.580060i | ||||||
\(659\) | 17.8086 | − | 30.8453i | 0.693723 | − | 1.20156i | −0.276886 | − | 0.960903i | \(-0.589302\pi\) |
0.970609 | − | 0.240661i | \(-0.0773642\pi\) | |||||||
\(660\) | 0.148530 | + | 0.257262i | 0.00578153 | + | 0.0100139i | ||||
\(661\) | 20.0318 | − | 11.5654i | 0.779148 | − | 0.449842i | −0.0569800 | − | 0.998375i | \(-0.518147\pi\) |
0.836128 | + | 0.548534i | \(0.184814\pi\) | |||||||
\(662\) | −6.00567 | −0.233417 | ||||||||
\(663\) | 19.7397 | − | 7.08828i | 0.766625 | − | 0.275286i | ||||
\(664\) | −14.9048 | −0.578418 | ||||||||
\(665\) | −0.924933 | + | 0.534010i | −0.0358673 | + | 0.0207080i | ||||
\(666\) | −0.987069 | − | 1.70965i | −0.0382481 | − | 0.0662477i | ||||
\(667\) | −3.05424 | + | 5.29010i | −0.118261 | + | 0.204834i | ||||
\(668\) | − | 13.4157i | − | 0.519068i | ||||||
\(669\) | −10.0500 | − | 5.80239i | −0.388557 | − | 0.224333i | ||||
\(670\) | −0.638688 | − | 0.368747i | −0.0246747 | − | 0.0142459i | ||||
\(671\) | − | 2.93018i | − | 0.113118i | ||||||
\(672\) | 12.0081 | − | 20.7986i | 0.463223 | − | 0.802325i | ||||
\(673\) | 21.2871 | + | 36.8703i | 0.820556 | + | 1.42124i | 0.905269 | + | 0.424839i | \(0.139669\pi\) |
−0.0847131 | + | 0.996405i | \(0.526997\pi\) | |||||||
\(674\) | 6.24538 | − | 3.60577i | 0.240563 | − | 0.138889i | ||||
\(675\) | 27.2785 | 1.04995 | ||||||||
\(676\) | 3.52242 | + | 21.0373i | 0.135478 | + | 0.809127i | ||||
\(677\) | −25.8793 | −0.994623 | −0.497312 | − | 0.867572i | \(-0.665679\pi\) | ||||
−0.497312 | + | 0.867572i | \(0.665679\pi\) | |||||||
\(678\) | −14.7255 | + | 8.50179i | −0.565531 | + | 0.326509i | ||||
\(679\) | 16.7450 | + | 29.0032i | 0.642614 | + | 1.11304i | ||||
\(680\) | −0.775057 | + | 1.34244i | −0.0297221 | + | 0.0514802i | ||||
\(681\) | − | 39.4464i | − | 1.51159i | ||||||
\(682\) | −0.299242 | − | 0.172768i | −0.0114586 | − | 0.00661561i | ||||
\(683\) | 21.4977 | + | 12.4117i | 0.822586 | + | 0.474920i | 0.851307 | − | 0.524667i | \(-0.175810\pi\) |
−0.0287214 | + | 0.999587i | \(0.509144\pi\) | |||||||
\(684\) | − | 1.42004i | − | 0.0542966i | ||||||
\(685\) | 0.164850 | − | 0.285529i | 0.00629860 | − | 0.0109095i | ||||
\(686\) | −5.42960 | − | 9.40434i | −0.207303 | − | 0.359059i | ||||
\(687\) | 36.5924 | − | 21.1266i | 1.39609 | − | 0.806032i | ||||
\(688\) | −10.7801 | −0.410987 | ||||||||
\(689\) | −19.2616 | + | 6.91661i | −0.733808 | + | 0.263502i | ||||
\(690\) | 0.497136 | 0.0189257 | ||||||||
\(691\) | −22.4256 | + | 12.9474i | −0.853110 | + | 0.492543i | −0.861699 | − | 0.507420i | \(-0.830599\pi\) |
0.00858925 | + | 0.999963i | \(0.497266\pi\) | |||||||
\(692\) | −5.90900 | − | 10.2347i | −0.224626 | − | 0.389064i | ||||
\(693\) | 0.333434 | − | 0.577525i | 0.0126661 | − | 0.0219384i | ||||
\(694\) | 1.95746i | 0.0743040i | ||||||||
\(695\) | 1.39353 | + | 0.804553i | 0.0528595 | + | 0.0305184i | ||||
\(696\) | −7.00845 | − | 4.04633i | −0.265655 | − | 0.153376i | ||||
\(697\) | − | 29.7573i | − | 1.12714i | ||||||
\(698\) | −2.43391 | + | 4.21565i | −0.0921247 | + | 0.159565i | ||||
\(699\) | −16.6626 | − | 28.8606i | −0.630239 | − | 1.09161i | ||||
\(700\) | −19.0346 | + | 10.9896i | −0.719441 | + | 0.415369i | ||||
\(701\) | 41.4487 | 1.56550 | 0.782748 | − | 0.622339i | \(-0.213817\pi\) | ||||
0.782748 | + | 0.622339i | \(0.213817\pi\) | |||||||
\(702\) | −7.67606 | + | 9.06817i | −0.289714 | + | 0.342256i | ||||
\(703\) | −15.5298 | −0.585718 | ||||||||
\(704\) | 0.310940 | − | 0.179521i | 0.0117190 | − | 0.00676595i | ||||
\(705\) | −1.44385 | − | 2.50082i | −0.0543785 | − | 0.0941863i | ||||
\(706\) | 5.27736 | − | 9.14066i | 0.198616 | − | 0.344013i | ||||
\(707\) | − | 16.0122i | − | 0.602201i | ||||||
\(708\) | 19.7455 | + | 11.4001i | 0.742083 | + | 0.428442i | ||||
\(709\) | 3.29463 | + | 1.90215i | 0.123732 | + | 0.0714369i | 0.560589 | − | 0.828094i | \(-0.310575\pi\) |
−0.436856 | + | 0.899531i | \(0.643908\pi\) | |||||||
\(710\) | − | 0.468413i | − | 0.0175792i | ||||||
\(711\) | 0.462827 | − | 0.801640i | 0.0173574 | − | 0.0300638i | ||||
\(712\) | 14.6530 | + | 25.3798i | 0.549146 | + | 0.951149i | ||||
\(713\) | 2.28742 | − | 1.32064i | 0.0856644 | − | 0.0494583i | ||||
\(714\) | −9.41284 | −0.352267 | ||||||||
\(715\) | 0.310700 | + | 0.263003i | 0.0116195 | + | 0.00983574i | ||||
\(716\) | −0.911383 | −0.0340600 | ||||||||
\(717\) | −3.82794 | + | 2.21006i | −0.142957 | + | 0.0825363i | ||||
\(718\) | 8.15933 | + | 14.1324i | 0.304503 | + | 0.527415i | ||||
\(719\) | 21.3385 | − | 36.9593i | 0.795791 | − | 1.37835i | −0.126545 | − | 0.991961i | \(-0.540389\pi\) |
0.922336 | − | 0.386389i | \(-0.126278\pi\) | |||||||
\(720\) | 0.165600i | 0.00617156i | ||||||||
\(721\) | −29.9768 | − | 17.3071i | −1.11640 | − | 0.644552i | ||||
\(722\) | −7.74396 | − | 4.47098i | −0.288200 | − | 0.166393i | ||||
\(723\) | 40.8676i | 1.51988i | ||||||||
\(724\) | 8.48429 | − | 14.6952i | 0.315316 | − | 0.546144i | ||||
\(725\) | 5.73740 | + | 9.93747i | 0.213082 | + | 0.369068i | ||||
\(726\) | −8.87925 | + | 5.12644i | −0.329540 | + | 0.190260i | ||||
\(727\) | −11.2466 | −0.417115 | −0.208557 | − | 0.978010i | \(-0.566877\pi\) | ||||
−0.208557 | + | 0.978010i | \(0.566877\pi\) | |||||||
\(728\) | 3.77881 | − | 20.9025i | 0.140052 | − | 0.774700i | ||||
\(729\) | 29.6760 | 1.09911 | ||||||||
\(730\) | −0.312138 | + | 0.180213i | −0.0115528 | + | 0.00666999i | ||||
\(731\) | 9.90632 | + | 17.1582i | 0.366398 | + | 0.634621i | ||||
\(732\) | −6.68654 | + | 11.5814i | −0.247141 | + | 0.428062i | ||||
\(733\) | − | 42.2746i | − | 1.56145i | −0.624876 | − | 0.780724i | \(-0.714850\pi\) | ||
0.624876 | − | 0.780724i | \(-0.285150\pi\) | |||||||
\(734\) | −11.0218 | − | 6.36341i | −0.406820 | − | 0.234878i | ||||
\(735\) | 0.0786224 | + | 0.0453927i | 0.00290003 | + | 0.00167433i | ||||
\(736\) | − | 14.6516i | − | 0.540064i | ||||||
\(737\) | 1.81125 | − | 3.13717i | 0.0667182 | − | 0.115559i | ||||
\(738\) | 1.05324 | + | 1.82427i | 0.0387703 | + | 0.0671522i | ||||
\(739\) | 14.2378 | − | 8.22017i | 0.523744 | − | 0.302384i | −0.214721 | − | 0.976675i | \(-0.568884\pi\) |
0.738465 | + | 0.674292i | \(0.235551\pi\) | |||||||
\(740\) | 2.47025 | 0.0908082 | ||||||||
\(741\) | 3.94725 | + | 10.9924i | 0.145006 | + | 0.403816i | ||||
\(742\) | 9.18487 | 0.337187 | ||||||||
\(743\) | 23.3723 | − | 13.4940i | 0.857447 | − | 0.495047i | −0.00570973 | − | 0.999984i | \(-0.501817\pi\) |
0.863156 | + | 0.504937i | \(0.168484\pi\) | |||||||
\(744\) | 1.74961 | + | 3.03042i | 0.0641440 | + | 0.111101i | ||||
\(745\) | −1.90589 | + | 3.30111i | −0.0698266 | + | 0.120943i | ||||
\(746\) | − | 11.9845i | − | 0.438783i | ||||||
\(747\) | 2.53439 | + | 1.46323i | 0.0927284 | + | 0.0535368i | ||||
\(748\) | −2.97167 | − | 1.71569i | −0.108655 | − | 0.0627319i | ||||
\(749\) | − | 24.6993i | − | 0.902493i | ||||||
\(750\) | 0.937481 | − | 1.62376i | 0.0342320 | − | 0.0592915i | ||||
\(751\) | 3.23975 | + | 5.61142i | 0.118220 | + | 0.204764i | 0.919062 | − | 0.394112i | \(-0.128948\pi\) |
−0.800842 | + | 0.598875i | \(0.795614\pi\) | |||||||
\(752\) | −15.7176 | + | 9.07458i | −0.573163 | + | 0.330916i | ||||
\(753\) | 2.38034 | 0.0867443 | ||||||||
\(754\) | −4.91798 | − | 0.889083i | −0.179102 | − | 0.0323785i | ||||
\(755\) | −1.10803 | −0.0403252 | ||||||||
\(756\) | −21.0918 | + | 12.1773i | −0.767100 | + | 0.442885i | ||||
\(757\) | −21.6818 | − | 37.5539i | −0.788037 | − | 1.36492i | −0.927168 | − | 0.374647i | \(-0.877764\pi\) |
0.139130 | − | 0.990274i | \(-0.455569\pi\) | |||||||
\(758\) | 0.688468 | − | 1.19246i | 0.0250063 | − | 0.0433122i | ||||
\(759\) | 2.44188i | 0.0886348i | ||||||||
\(760\) | −0.747562 | − | 0.431605i | −0.0271169 | − | 0.0156560i | ||||
\(761\) | 22.4048 | + | 12.9354i | 0.812173 | + | 0.468909i | 0.847710 | − | 0.530460i | \(-0.177981\pi\) |
−0.0355367 | + | 0.999368i | \(0.511314\pi\) | |||||||
\(762\) | − | 6.63384i | − | 0.240319i | ||||||
\(763\) | 16.3162 | − | 28.2604i | 0.590684 | − | 1.02310i | ||||
\(764\) | −20.8340 | − | 36.0855i | −0.753746 | − | 1.30553i | ||||
\(765\) | 0.263579 | − | 0.152178i | 0.00952973 | − | 0.00550199i | ||||
\(766\) | −8.11575 | −0.293234 | ||||||||
\(767\) | 30.7452 | + | 5.55819i | 1.11015 | + | 0.200695i | ||||
\(768\) | 9.02431 | 0.325637 | ||||||||
\(769\) | −26.7510 | + | 15.4447i | −0.964666 | + | 0.556950i | −0.897606 | − | 0.440799i | \(-0.854695\pi\) |
−0.0670602 | + | 0.997749i | \(0.521362\pi\) | |||||||
\(770\) | −0.0913445 | − | 0.158213i | −0.00329183 | − | 0.00570161i | ||||
\(771\) | 16.8607 | − | 29.2035i | 0.607222 | − | 1.05174i | ||||
\(772\) | − | 23.4483i | − | 0.843921i | ||||||
\(773\) | 5.62635 | + | 3.24837i | 0.202366 | + | 0.116836i | 0.597758 | − | 0.801676i | \(-0.296058\pi\) |
−0.395393 | + | 0.918512i | \(0.629392\pi\) | |||||||
\(774\) | −1.21461 | − | 0.701256i | −0.0436583 | − | 0.0252061i | ||||
\(775\) | − | 4.96165i | − | 0.178228i | ||||||
\(776\) | −13.5339 | + | 23.4414i | −0.485838 | + | 0.841497i | ||||
\(777\) | 16.6422 | + | 28.8252i | 0.597037 | + | 1.03410i | ||||
\(778\) | 13.3247 | − | 7.69304i | 0.477715 | − | 0.275809i | ||||
\(779\) | 16.5709 | 0.593714 | ||||||||
\(780\) | −0.627869 | − | 1.74851i | −0.0224813 | − | 0.0626066i | ||||
\(781\) | 2.30080 | 0.0823290 | ||||||||
\(782\) | −4.97314 | + | 2.87124i | −0.177839 | + | 0.102675i | ||||
\(783\) | 6.35747 | + | 11.0115i | 0.227197 | + | 0.393517i | ||||
\(784\) | 0.285293 | − | 0.494142i | 0.0101890 | − | 0.0176479i | ||||
\(785\) | − | 3.32067i | − | 0.118520i | ||||||
\(786\) | 3.85483 | + | 2.22559i | 0.137497 | + | 0.0793840i | ||||
\(787\) | −44.5917 | − | 25.7450i | −1.58952 | − | 0.917712i | −0.993385 | − | 0.114830i | \(-0.963368\pi\) |
−0.596138 | − | 0.802882i | \(-0.703299\pi\) | |||||||
\(788\) | 16.9375i | 0.603375i | ||||||||
\(789\) | 15.1159 | − | 26.1814i | 0.538139 | − | 0.932084i | ||||
\(790\) | −0.126792 | − | 0.219609i | −0.00451104 | − | 0.00781335i | ||||
\(791\) | −41.3647 | + | 23.8819i | −1.47076 | + | 0.849143i | ||||
\(792\) | 0.538986 | 0.0191520 | ||||||||
\(793\) | −3.26006 | + | 18.0331i | −0.115768 | + | 0.640374i | ||||
\(794\) | −13.8313 | −0.490855 | ||||||||
\(795\) | 1.54372 | − | 0.891268i | 0.0547502 | − | 0.0316100i | ||||
\(796\) | −11.9581 | − | 20.7120i | −0.423842 | − | 0.734116i | ||||
\(797\) | −15.1760 | + | 26.2856i | −0.537562 | + | 0.931085i | 0.461472 | + | 0.887155i | \(0.347321\pi\) |
−0.999035 | + | 0.0439306i | \(0.986012\pi\) | |||||||
\(798\) | − | 5.24172i | − | 0.185555i | ||||||
\(799\) | 28.8873 | + | 16.6781i | 1.02196 | + | 0.590028i | ||||
\(800\) | −23.8356 | − | 13.7615i | −0.842716 | − | 0.486542i | ||||
\(801\) | − | 5.75407i | − | 0.203310i | ||||||
\(802\) | −7.54976 | + | 13.0766i | −0.266591 | + | 0.461750i | ||||
\(803\) | −0.885189 | − | 1.53319i | −0.0312376 | − | 0.0541052i | ||||
\(804\) | −14.3178 | + | 8.26636i | −0.504948 | + | 0.291532i | ||||
\(805\) | 1.39648 | 0.0492194 | ||||||||
\(806\) | 1.64940 | + | 1.39619i | 0.0580975 | + | 0.0491786i | ||||
\(807\) | −28.5188 | −1.00391 | ||||||||
\(808\) | 11.2078 | − | 6.47081i | 0.394288 | − | 0.227642i | ||||
\(809\) | 15.6314 | + | 27.0743i | 0.549570 | + | 0.951883i | 0.998304 | + | 0.0582177i | \(0.0185418\pi\) |
−0.448734 | + | 0.893665i | \(0.648125\pi\) | |||||||
\(810\) | 0.441969 | − | 0.765514i | 0.0155292 | − | 0.0268974i | ||||
\(811\) | − | 50.9155i | − | 1.78788i | −0.448183 | − | 0.893942i | \(-0.647929\pi\) | ||
0.448183 | − | 0.893942i | \(-0.352071\pi\) | |||||||
\(812\) | −8.87232 | − | 5.12244i | −0.311357 | − | 0.179762i | ||||
\(813\) | −10.5466 | − | 6.08907i | −0.369885 | − | 0.213553i | ||||
\(814\) | − | 2.65643i | − | 0.0931079i | ||||||
\(815\) | 0.962179 | − | 1.66654i | 0.0337037 | − | 0.0583764i | ||||
\(816\) | 5.74065 | + | 9.94310i | 0.200963 | + | 0.348078i | ||||
\(817\) | −9.55490 | + | 5.51652i | −0.334284 | + | 0.192999i | ||||
\(818\) | 3.57827 | 0.125111 | ||||||||
\(819\) | −2.69458 | + | 3.18327i | −0.0941564 | + | 0.111232i | ||||
\(820\) | −2.63585 | −0.0920480 | ||||||||
\(821\) | −12.3596 | + | 7.13584i | −0.431354 | + | 0.249043i | −0.699923 | − | 0.714218i | \(-0.746783\pi\) |
0.268569 | + | 0.963260i | \(0.413449\pi\) | |||||||
\(822\) | 0.809065 | + | 1.40134i | 0.0282194 | + | 0.0488774i | ||||
\(823\) | 24.4887 | − | 42.4157i | 0.853623 | − | 1.47852i | −0.0242940 | − | 0.999705i | \(-0.507734\pi\) |
0.877917 | − | 0.478813i | \(-0.158933\pi\) | |||||||
\(824\) | − | 27.9765i | − | 0.974606i | ||||||
\(825\) | 3.97253 | + | 2.29354i | 0.138306 | + | 0.0798509i | ||||
\(826\) | −12.1433 | − | 7.01093i | −0.422519 | − | 0.243942i | ||||
\(827\) | 2.42778i | 0.0844223i | 0.999109 | + | 0.0422112i | \(0.0134402\pi\) | ||||
−0.999109 | + | 0.0422112i | \(0.986560\pi\) | |||||||
\(828\) | −0.928381 | + | 1.60800i | −0.0322635 | + | 0.0558820i | ||||
\(829\) | 10.5850 | + | 18.3338i | 0.367634 | + | 0.636760i | 0.989195 | − | 0.146605i | \(-0.0468347\pi\) |
−0.621561 | + | 0.783365i | \(0.713501\pi\) | |||||||
\(830\) | 0.694297 | − | 0.400852i | 0.0240994 | − | 0.0139138i | ||||
\(831\) | −47.0314 | −1.63150 | ||||||||
\(832\) | −2.11333 | + | 0.758874i | −0.0732667 | + | 0.0263092i | ||||
\(833\) | −1.04867 | −0.0363344 | ||||||||
\(834\) | −6.83926 | + | 3.94865i | −0.236824 | + | 0.136731i | ||||
\(835\) | 0.800600 | + | 1.38668i | 0.0277059 | + | 0.0479880i | ||||
\(836\) | 0.955416 | − | 1.65483i | 0.0330438 | − | 0.0572335i | ||||
\(837\) | − | 5.49788i | − | 0.190034i | ||||||
\(838\) | 6.67504 | + | 3.85384i | 0.230586 | + | 0.133129i | ||||
\(839\) | −17.2568 | − | 9.96319i | −0.595769 | − | 0.343968i | 0.171606 | − | 0.985166i | \(-0.445104\pi\) |
−0.767375 | + | 0.641198i | \(0.778438\pi\) | |||||||
\(840\) | 1.85009i | 0.0638341i | ||||||||
\(841\) | 11.8257 | − | 20.4827i | 0.407783 | − | 0.706301i | ||||
\(842\) | −2.69763 | − | 4.67243i | −0.0929665 | − | 0.161023i | ||||
\(843\) | 8.88859 | − | 5.13183i | 0.306139 | − | 0.176750i | ||||
\(844\) | −30.4175 | −1.04701 | ||||||||
\(845\) | −1.61952 | − | 1.96426i | −0.0557131 | − | 0.0675728i | ||||
\(846\) | −2.36124 | −0.0811812 | ||||||||
\(847\) | −24.9422 | + | 14.4004i | −0.857025 | + | 0.494804i | ||||
\(848\) | −5.60162 | − | 9.70228i | −0.192360 | − | 0.333178i | ||||
\(849\) | 5.21108 | − | 9.02585i | 0.178844 | − | 0.309766i | ||||
\(850\) | 10.7873i | 0.370000i | ||||||||
\(851\) | 17.5854 | + | 10.1529i | 0.602819 | + | 0.348038i | ||||
\(852\) | −9.09380 | − | 5.25031i | −0.311549 | − | 0.179873i | ||||
\(853\) | − | 31.9736i | − | 1.09476i | −0.836886 | − | 0.547378i | \(-0.815626\pi\) | ||
0.836886 | − | 0.547378i | \(-0.184374\pi\) | |||||||
\(854\) | 4.11215 | − | 7.12244i | 0.140715 | − | 0.243725i | ||||
\(855\) | 0.0847430 | + | 0.146779i | 0.00289815 | + | 0.00501974i | ||||
\(856\) | 17.2883 | − | 9.98142i | 0.590903 | − | 0.341158i | ||||
\(857\) | 43.5978 | 1.48927 | 0.744636 | − | 0.667471i | \(-0.232623\pi\) | ||||
0.744636 | + | 0.667471i | \(0.232623\pi\) | |||||||
\(858\) | −1.88029 | + | 0.675192i | −0.0641922 | + | 0.0230507i | ||||
\(859\) | 3.20313 | 0.109289 | 0.0546446 | − | 0.998506i | \(-0.482597\pi\) | ||||
0.0546446 | + | 0.998506i | \(0.482597\pi\) | |||||||
\(860\) | 1.51985 | − | 0.877486i | 0.0518265 | − | 0.0299220i | ||||
\(861\) | −17.7579 | − | 30.7576i | −0.605188 | − | 1.04822i | ||||
\(862\) | 1.64208 | − | 2.84416i | 0.0559294 | − | 0.0968726i | ||||
\(863\) | − | 24.8623i | − | 0.846322i | −0.906055 | − | 0.423161i | \(-0.860921\pi\) | ||
0.906055 | − | 0.423161i | \(-0.139079\pi\) | |||||||
\(864\) | −26.4116 | − | 15.2488i | −0.898542 | − | 0.518773i | ||||
\(865\) | 1.22154 | + | 0.705255i | 0.0415335 | + | 0.0239794i | ||||
\(866\) | 9.61335i | 0.326675i | ||||||||
\(867\) | −3.07999 | + | 5.33470i | −0.104602 | + | 0.181176i | ||||
\(868\) | 2.21492 | + | 3.83635i | 0.0751792 | + | 0.130214i | ||||
\(869\) | 1.07870 | − | 0.622788i | 0.0365924 | − | 0.0211266i | ||||
\(870\) | 0.435292 | 0.0147578 | ||||||||
\(871\) | −14.6372 | + | 17.2918i | −0.495964 | + | 0.585911i | ||||
\(872\) | 26.3746 | 0.893155 | ||||||||
\(873\) | 4.60257 | − | 2.65729i | 0.155773 | − | 0.0899358i | ||||
\(874\) | −1.59891 | − | 2.76939i | −0.0540838 | − | 0.0936759i | ||||
\(875\) | 2.63343 | − | 4.56123i | 0.0890261 | − | 0.154198i | ||||
\(876\) | 8.07983i | 0.272992i | ||||||||
\(877\) | −17.1660 | − | 9.91082i | −0.579656 | − | 0.334665i | 0.181341 | − | 0.983420i | \(-0.441956\pi\) |
−0.760997 | + | 0.648756i | \(0.775290\pi\) | |||||||
\(878\) | −3.15857 | − | 1.82360i | −0.106597 | − | 0.0615436i | ||||
\(879\) | 9.40050i | 0.317071i | ||||||||
\(880\) | −0.111417 | + | 0.192980i | −0.00375588 | + | 0.00650537i | ||||
\(881\) | 2.52473 | + | 4.37296i | 0.0850602 | + | 0.147329i | 0.905417 | − | 0.424524i | \(-0.139558\pi\) |
−0.820357 | + | 0.571852i | \(0.806225\pi\) | |||||||
\(882\) | 0.0642888 | − | 0.0371172i | 0.00216472 | − | 0.00124980i | ||||
\(883\) | −43.1671 | −1.45269 | −0.726345 | − | 0.687331i | \(-0.758782\pi\) | ||||
−0.726345 | + | 0.687331i | \(0.758782\pi\) | |||||||
\(884\) | 16.3796 | + | 13.8650i | 0.550904 | + | 0.466331i | ||||
\(885\) | −2.72127 | −0.0914744 | ||||||||
\(886\) | 13.3136 | − | 7.68659i | 0.447278 | − | 0.258236i | ||||
\(887\) | −25.9238 | − | 44.9014i | −0.870437 | − | 1.50764i | −0.861546 | − | 0.507680i | \(-0.830503\pi\) |
−0.00889128 | − | 0.999960i | \(-0.502830\pi\) | |||||||
\(888\) | −13.4508 | + | 23.2975i | −0.451380 | + | 0.781814i | ||||
\(889\) | − | 18.6348i | − | 0.624990i | ||||||
\(890\) | −1.36514 | − | 0.788164i | −0.0457596 | − | 0.0264193i | ||||
\(891\) | 3.76013 | + | 2.17091i | 0.125969 | + | 0.0727282i | ||||
\(892\) | − | 11.8738i | − | 0.397564i | ||||||
\(893\) | −9.28751 | + | 16.0864i | −0.310795 | + | 0.538312i | ||||
\(894\) | −9.35391 | − | 16.2015i | −0.312842 | − | 0.541858i | ||||
\(895\) | 0.0942029 | − | 0.0543881i | 0.00314886 | − | 0.00181799i | ||||
\(896\) | 30.9605 | 1.03432 | ||||||||
\(897\) | 2.71679 | − | 15.0280i | 0.0907110 | − | 0.501770i | ||||
\(898\) | −13.6784 | −0.456454 | ||||||||
\(899\) | 2.00286 | − | 1.15635i | 0.0667990 | − | 0.0385664i | ||||
\(900\) | 1.74397 | + | 3.02064i | 0.0581322 | + | 0.100688i | ||||
\(901\) | −10.2952 | + | 17.8317i | −0.342981 | + | 0.594061i | ||||
\(902\) | 2.83452i | 0.0943791i | ||||||||
\(903\) | 20.4787 | + | 11.8234i | 0.681487 | + | 0.393457i | ||||
\(904\) | −33.4324 | − | 19.3022i | −1.11194 | − | 0.641981i | ||||
\(905\) | 2.02525i | 0.0673216i | ||||||||
\(906\) | 2.71903 | − | 4.70950i | 0.0903337 | − | 0.156463i | ||||
\(907\) | 19.8240 | + | 34.3362i | 0.658245 | + | 1.14011i | 0.981070 | + | 0.193655i | \(0.0620343\pi\) |
−0.322825 | + | 0.946459i | \(0.604632\pi\) | |||||||
\(908\) | 34.9535 | − | 20.1804i | 1.15997 | − | 0.669710i | ||||
\(909\) | −2.54101 | −0.0842799 | ||||||||
\(910\) | 0.386133 | + | 1.07531i | 0.0128002 | + | 0.0356463i | ||||
\(911\) | −37.0140 | −1.22633 | −0.613164 | − | 0.789956i | \(-0.710103\pi\) | ||||
−0.613164 | + | 0.789956i | \(0.710103\pi\) | |||||||
\(912\) | −5.53700 | + | 3.19679i | −0.183349 | + | 0.105856i | ||||
\(913\) | 1.96895 | + | 3.41032i | 0.0651626 | + | 0.112865i | ||||
\(914\) | 7.34405 | − | 12.7203i | 0.242920 | − | 0.420749i | ||||
\(915\) | − | 1.59611i | − | 0.0527659i | ||||||
\(916\) | 37.4407 | + | 21.6164i | 1.23707 | + | 0.714225i | ||||
\(917\) | 10.8284 | + | 6.25177i | 0.357585 | + | 0.206452i | ||||
\(918\) | 11.9531i | 0.394511i | ||||||||
\(919\) | 3.09173 | − | 5.35504i | 0.101987 | − | 0.176647i | −0.810516 | − | 0.585716i | \(-0.800813\pi\) |
0.912503 | + | 0.409070i | \(0.134147\pi\) | |||||||
\(920\) | 0.564341 | + | 0.977468i | 0.0186058 | + | 0.0322262i | ||||
\(921\) | 2.33750 | − | 1.34956i | 0.0770233 | − | 0.0444694i | ||||
\(922\) | −3.92256 | −0.129183 | ||||||||
\(923\) | −14.1597 | − | 2.55982i | −0.466072 | − | 0.0842576i | ||||
\(924\) | −4.09542 | −0.134729 | ||||||||
\(925\) | 33.0342 | − | 19.0723i | 1.08616 | − | 0.627093i | ||||
\(926\) | −0.977077 | − | 1.69235i | −0.0321087 | − | 0.0556140i | ||||
\(927\) | −2.74650 | + | 4.75708i | −0.0902069 | + | 0.156243i | ||||
\(928\) | − | 12.8289i | − | 0.421129i | ||||||
\(929\) | 29.6815 | + | 17.1366i | 0.973819 | + | 0.562235i | 0.900398 | − | 0.435067i | \(-0.143275\pi\) |
0.0734205 | + | 0.997301i | \(0.476608\pi\) | |||||||
\(930\) | −0.163002 | − | 0.0941090i | −0.00534503 | − | 0.00308596i | ||||
\(931\) | − | 0.583974i | − | 0.0191390i | ||||||
\(932\) | 17.0489 | − | 29.5296i | 0.558455 | − | 0.967273i | ||||
\(933\) | −21.4538 | − | 37.1591i | −0.702366 | − | 1.21653i | ||||
\(934\) | −1.43182 | + | 0.826662i | −0.0468506 | + | 0.0270492i | ||||
\(935\) | 0.409545 | 0.0133936 | ||||||||
\(936\) | −3.31706 | − | 0.599665i | −0.108422 | − | 0.0196007i | ||||
\(937\) | −28.3177 | −0.925099 | −0.462550 | − | 0.886593i | \(-0.653065\pi\) | ||||
−0.462550 | + | 0.886593i | \(0.653065\pi\) | |||||||
\(938\) | 8.80526 | − | 5.08372i | 0.287502 | − | 0.165989i | ||||
\(939\) | 24.9435 | + | 43.2035i | 0.814001 | + | 1.40989i | ||||
\(940\) | 1.47732 | − | 2.55879i | 0.0481848 | − | 0.0834585i | ||||
\(941\) | 45.1723i | 1.47257i | 0.676669 | + | 0.736287i | \(0.263423\pi\) | ||||
−0.676669 | + | 0.736287i | \(0.736577\pi\) | |||||||
\(942\) | 14.1140 | + | 8.14873i | 0.459860 | + | 0.265500i | ||||
\(943\) | −18.7643 | − | 10.8336i | −0.611049 | − | 0.352789i | ||||
\(944\) | 17.1032i | 0.556660i | ||||||||
\(945\) | 1.45340 | − | 2.51736i | 0.0472791 | − | 0.0818898i | ||||
\(946\) | −0.943622 | − | 1.63440i | −0.0306798 | − | 0.0531390i | ||||
\(947\) | 32.9978 | − | 19.0513i | 1.07228 | − | 0.619084i | 0.143479 | − | 0.989653i | \(-0.454171\pi\) |
0.928805 | + | 0.370570i | \(0.120838\pi\) | |||||||
\(948\) | −5.68468 | −0.184630 | ||||||||
\(949\) | 3.74188 | + | 10.4205i | 0.121467 | + | 0.338264i | ||||
\(950\) | −6.00710 | −0.194896 | ||||||||
\(951\) | −2.18599 | + | 1.26208i | −0.0708855 | + | 0.0409258i | ||||
\(952\) | −10.6853 | − | 18.5075i | −0.346313 | − | 0.599831i | ||||
\(953\) | 4.40361 | − | 7.62727i | 0.142647 | − | 0.247071i | −0.785846 | − | 0.618423i | \(-0.787772\pi\) |
0.928493 | + | 0.371351i | \(0.121105\pi\) | |||||||
\(954\) | − | 1.45756i | − | 0.0471903i | ||||||
\(955\) | 4.30691 | + | 2.48659i | 0.139368 | + | 0.0804643i | ||||
\(956\) | −3.91667 | − | 2.26129i | −0.126674 | − | 0.0731354i | ||||
\(957\) | 2.13811i | 0.0691153i | ||||||||
\(958\) | −6.75768 | + | 11.7046i | −0.218331 | + | 0.378160i | ||||
\(959\) | 2.27270 | + | 3.93643i | 0.0733894 | + | 0.127114i | ||||
\(960\) | 0.169373 | − | 0.0977878i | 0.00546650 | − | 0.00315609i | ||||
\(961\) | −1.00000 | −0.0322581 | ||||||||
\(962\) | −2.95549 | + | 16.3484i | −0.0952889 | + | 0.527093i | ||||
\(963\) | −3.91958 | −0.126307 | ||||||||
\(964\) | −36.2128 | + | 20.9075i | −1.16634 | + | 0.673384i | ||||
\(965\) | 1.39931 | + | 2.42367i | 0.0450453 | + | 0.0780208i | ||||
\(966\) | −3.42688 | + | 5.93553i | −0.110258 | + | 0.190973i | ||||
\(967\) | − | 46.1127i | − | 1.48288i | −0.671017 | − | 0.741442i | \(-0.734142\pi\) | ||
0.671017 | − | 0.741442i | \(-0.265858\pi\) | |||||||
\(968\) | −20.1592 | − | 11.6389i | −0.647940 | − | 0.374088i | ||||
\(969\) | 10.1764 | + | 5.87535i | 0.326913 | + | 0.188743i | ||||
\(970\) | − | 1.45593i | − | 0.0467472i | ||||||
\(971\) | −6.07861 | + | 10.5285i | −0.195072 | + | 0.337875i | −0.946924 | − | 0.321457i | \(-0.895827\pi\) |
0.751852 | + | 0.659332i | \(0.229161\pi\) | |||||||
\(972\) | 3.62340 | + | 6.27590i | 0.116220 | + | 0.201300i | ||||
\(973\) | −19.2118 | + | 11.0919i | −0.615902 | + | 0.355591i | ||||
\(974\) | −19.9010 | −0.637668 | ||||||||
\(975\) | −21.8962 | − | 18.5348i | −0.701241 | − | 0.593589i | ||||
\(976\) | −10.0316 | −0.321103 | ||||||||
\(977\) | −35.9405 | + | 20.7502i | −1.14984 | + | 0.663859i | −0.948848 | − | 0.315734i | \(-0.897749\pi\) |
−0.200990 | + | 0.979593i | \(0.564416\pi\) | |||||||
\(978\) | 4.72226 | + | 8.17920i | 0.151001 | + | 0.261542i | ||||
\(979\) | 3.87138 | − | 6.70543i | 0.123730 | − | 0.214307i | ||||
\(980\) | 0.0928899i | 0.00296726i | ||||||||
\(981\) | −4.48469 | − | 2.58924i | −0.143185 | − | 0.0826681i | ||||
\(982\) | 9.55172 | + | 5.51469i | 0.304808 | + | 0.175981i | ||||
\(983\) | 35.5530i | 1.13396i | 0.823730 | + | 0.566982i | \(0.191889\pi\) | ||||
−0.823730 | + | 0.566982i | \(0.808111\pi\) | |||||||
\(984\) | 14.3526 | − | 24.8594i | 0.457543 | − | 0.792488i | ||||
\(985\) | −1.01077 | − | 1.75071i | −0.0322059 | − | 0.0557822i | ||||
\(986\) | −4.35447 | + | 2.51406i | −0.138675 | + | 0.0800638i | ||||
\(987\) | 39.8112 | 1.26720 | ||||||||
\(988\) | −7.72101 | + | 9.12127i | −0.245638 | + | 0.290186i | ||||
\(989\) | 14.4262 | 0.458725 | ||||||||
\(990\) | −0.0251071 | + | 0.0144956i | −0.000797957 | + | 0.000460701i | ||||
\(991\) | 19.1309 | + | 33.1357i | 0.607713 | + | 1.05259i | 0.991616 | + | 0.129216i | \(0.0412462\pi\) |
−0.383904 | + | 0.923373i | \(0.625421\pi\) | |||||||
\(992\) | −2.77357 | + | 4.80397i | −0.0880610 | + | 0.152526i | ||||
\(993\) | − | 16.0687i | − | 0.509924i | ||||||
\(994\) | 5.59259 | + | 3.22888i | 0.177386 | + | 0.102414i | ||||
\(995\) | 2.47203 | + | 1.42723i | 0.0783686 | + | 0.0452462i | ||||
\(996\) | − | 17.9722i | − | 0.569470i | ||||||
\(997\) | 6.76457 | − | 11.7166i | 0.214236 | − | 0.371068i | −0.738800 | − | 0.673925i | \(-0.764607\pi\) |
0.953036 | + | 0.302857i | \(0.0979405\pi\) | |||||||
\(998\) | 0.624799 | + | 1.08218i | 0.0197777 | + | 0.0342559i | ||||
\(999\) | 36.6043 | − | 21.1335i | 1.15811 | − | 0.668635i |
(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 | 403.2.r.a.218.21 | ✓ | 68 | |
13.2 | odd | 12 | 5239.2.a.r.1.19 | 34 | |||
13.4 | even | 6 | inner | 403.2.r.a.342.21 | yes | 68 | |
13.11 | odd | 12 | 5239.2.a.q.1.16 | 34 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
403.2.r.a.218.21 | ✓ | 68 | 1.1 | even | 1 | trivial | |
403.2.r.a.342.21 | yes | 68 | 13.4 | even | 6 | inner | |
5239.2.a.q.1.16 | 34 | 13.11 | odd | 12 | |||
5239.2.a.r.1.19 | 34 | 13.2 | odd | 12 |