Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [637,2,Mod(165,637)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(637, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([4, 4]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("637.165");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 637 = 7^{2} \cdot 13 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 637.h (of order \(3\), degree \(2\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(5.08647060876\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Relative dimension: | \(2\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\Q(\sqrt{2}, \sqrt{-3})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 2x^{2} + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 165.2 | ||
Root | \(-0.707107 + 1.22474i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 637.165 |
Dual form | 637.2.h.c.471.2 |
$q$-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 \(\left(\mathbb{Z}/637\mathbb{Z}\right)^\times\).
\(n\) | \(197\) | \(248\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(e\left(\frac{2}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.414214 | 0.292893 | 0.146447 | − | 0.989219i | \(-0.453216\pi\) | ||||
0.146447 | + | 0.989219i | \(0.453216\pi\) | |||||||
\(3\) | 0.707107 | + | 1.22474i | 0.408248 | + | 0.707107i | 0.994694 | − | 0.102882i | \(-0.0328064\pi\) |
−0.586445 | + | 0.809989i | \(0.699473\pi\) | |||||||
\(4\) | −1.82843 | −0.914214 | ||||||||
\(5\) | −0.914214 | − | 1.58346i | −0.408849 | − | 0.708147i | 0.585912 | − | 0.810374i | \(-0.300736\pi\) |
−0.994761 | + | 0.102228i | \(0.967403\pi\) | |||||||
\(6\) | 0.292893 | + | 0.507306i | 0.119573 | + | 0.207107i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | −1.58579 | −0.560660 | ||||||||
\(9\) | 0.500000 | − | 0.866025i | 0.166667 | − | 0.288675i | ||||
\(10\) | −0.378680 | − | 0.655892i | −0.119749 | − | 0.207411i | ||||
\(11\) | −0.292893 | − | 0.507306i | −0.0883106 | − | 0.152958i | 0.818487 | − | 0.574526i | \(-0.194813\pi\) |
−0.906797 | + | 0.421567i | \(0.861480\pi\) | |||||||
\(12\) | −1.29289 | − | 2.23936i | −0.373226 | − | 0.646447i | ||||
\(13\) | 3.50000 | + | 0.866025i | 0.970725 | + | 0.240192i | ||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 1.29289 | − | 2.23936i | 0.333824 | − | 0.578199i | ||||
\(16\) | 3.00000 | 0.750000 | ||||||||
\(17\) | 5.82843 | 1.41360 | 0.706801 | − | 0.707413i | \(-0.250138\pi\) | ||||
0.706801 | + | 0.707413i | \(0.250138\pi\) | |||||||
\(18\) | 0.207107 | − | 0.358719i | 0.0488155 | − | 0.0845510i | ||||
\(19\) | 3.00000 | − | 5.19615i | 0.688247 | − | 1.19208i | −0.284157 | − | 0.958778i | \(-0.591714\pi\) |
0.972404 | − | 0.233301i | \(-0.0749529\pi\) | |||||||
\(20\) | 1.67157 | + | 2.89525i | 0.373775 | + | 0.647397i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −0.121320 | − | 0.210133i | −0.0258656 | − | 0.0448005i | ||||
\(23\) | −1.41421 | −0.294884 | −0.147442 | − | 0.989071i | \(-0.547104\pi\) | ||||
−0.147442 | + | 0.989071i | \(0.547104\pi\) | |||||||
\(24\) | −1.12132 | − | 1.94218i | −0.228889 | − | 0.396447i | ||||
\(25\) | 0.828427 | − | 1.43488i | 0.165685 | − | 0.286976i | ||||
\(26\) | 1.44975 | + | 0.358719i | 0.284319 | + | 0.0703507i | ||||
\(27\) | 5.65685 | 1.08866 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.08579 | + | 3.61269i | −0.387321 | + | 0.670859i | −0.992088 | − | 0.125543i | \(-0.959933\pi\) |
0.604767 | + | 0.796402i | \(0.293266\pi\) | |||||||
\(30\) | 0.535534 | − | 0.927572i | 0.0977747 | − | 0.169351i | ||||
\(31\) | 1.29289 | − | 2.23936i | 0.232210 | − | 0.402200i | −0.726248 | − | 0.687433i | \(-0.758738\pi\) |
0.958458 | + | 0.285233i | \(0.0920709\pi\) | |||||||
\(32\) | 4.41421 | 0.780330 | ||||||||
\(33\) | 0.414214 | − | 0.717439i | 0.0721053 | − | 0.124890i | ||||
\(34\) | 2.41421 | 0.414034 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −0.914214 | + | 1.58346i | −0.152369 | + | 0.263911i | ||||
\(37\) | −9.48528 | −1.55937 | −0.779685 | − | 0.626172i | \(-0.784621\pi\) | ||||
−0.779685 | + | 0.626172i | \(0.784621\pi\) | |||||||
\(38\) | 1.24264 | − | 2.15232i | 0.201583 | − | 0.349152i | ||||
\(39\) | 1.41421 | + | 4.89898i | 0.226455 | + | 0.784465i | ||||
\(40\) | 1.44975 | + | 2.51104i | 0.229225 | + | 0.397030i | ||||
\(41\) | 0.0857864 | − | 0.148586i | 0.0133976 | − | 0.0232053i | −0.859249 | − | 0.511558i | \(-0.829069\pi\) |
0.872646 | + | 0.488352i | \(0.162402\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −1.70711 | − | 2.95680i | −0.260331 | − | 0.450907i | 0.705999 | − | 0.708213i | \(-0.250498\pi\) |
−0.966330 | + | 0.257306i | \(0.917165\pi\) | |||||||
\(44\) | 0.535534 | + | 0.927572i | 0.0807348 | + | 0.139837i | ||||
\(45\) | −1.82843 | −0.272566 | ||||||||
\(46\) | −0.585786 | −0.0863695 | ||||||||
\(47\) | −1.82843 | − | 3.16693i | −0.266704 | − | 0.461944i | 0.701305 | − | 0.712861i | \(-0.252601\pi\) |
−0.968009 | + | 0.250917i | \(0.919268\pi\) | |||||||
\(48\) | 2.12132 | + | 3.67423i | 0.306186 | + | 0.530330i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0.343146 | − | 0.594346i | 0.0485281 | − | 0.0840532i | ||||
\(51\) | 4.12132 | + | 7.13834i | 0.577100 | + | 0.999567i | ||||
\(52\) | −6.39949 | − | 1.58346i | −0.887450 | − | 0.219587i | ||||
\(53\) | 1.50000 | − | 2.59808i | 0.206041 | − | 0.356873i | −0.744423 | − | 0.667708i | \(-0.767275\pi\) |
0.950464 | + | 0.310835i | \(0.100609\pi\) | |||||||
\(54\) | 2.34315 | 0.318862 | ||||||||
\(55\) | −0.535534 | + | 0.927572i | −0.0722114 | + | 0.125074i | ||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 8.48528 | 1.12390 | ||||||||
\(58\) | −0.863961 | + | 1.49642i | −0.113444 | + | 0.196490i | ||||
\(59\) | 10.2426 | 1.33348 | 0.666739 | − | 0.745291i | \(-0.267690\pi\) | ||||
0.666739 | + | 0.745291i | \(0.267690\pi\) | |||||||
\(60\) | −2.36396 | + | 4.09450i | −0.305186 | + | 0.528598i | ||||
\(61\) | 2.08579 | − | 3.61269i | 0.267058 | − | 0.462557i | −0.701043 | − | 0.713119i | \(-0.747282\pi\) |
0.968101 | + | 0.250562i | \(0.0806153\pi\) | |||||||
\(62\) | 0.535534 | − | 0.927572i | 0.0680129 | − | 0.117802i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | −4.17157 | −0.521447 | ||||||||
\(65\) | −1.82843 | − | 6.33386i | −0.226788 | − | 0.785618i | ||||
\(66\) | 0.171573 | − | 0.297173i | 0.0211192 | − | 0.0365795i | ||||
\(67\) | −2.12132 | − | 3.67423i | −0.259161 | − | 0.448879i | 0.706857 | − | 0.707357i | \(-0.250113\pi\) |
−0.966017 | + | 0.258478i | \(0.916779\pi\) | |||||||
\(68\) | −10.6569 | −1.29233 | ||||||||
\(69\) | −1.00000 | − | 1.73205i | −0.120386 | − | 0.208514i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 5.82843 | + | 10.0951i | 0.691707 | + | 1.19807i | 0.971278 | + | 0.237947i | \(0.0764744\pi\) |
−0.279571 | + | 0.960125i | \(0.590192\pi\) | |||||||
\(72\) | −0.792893 | + | 1.37333i | −0.0934434 | + | 0.161849i | ||||
\(73\) | −5.32843 | + | 9.22911i | −0.623645 | + | 1.08019i | 0.365156 | + | 0.930946i | \(0.381016\pi\) |
−0.988801 | + | 0.149239i | \(0.952318\pi\) | |||||||
\(74\) | −3.92893 | −0.456729 | ||||||||
\(75\) | 2.34315 | 0.270563 | ||||||||
\(76\) | −5.48528 | + | 9.50079i | −0.629205 | + | 1.08981i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0.585786 | + | 2.02922i | 0.0663273 | + | 0.229764i | ||||
\(79\) | −0.878680 | − | 1.52192i | −0.0988592 | − | 0.171229i | 0.812354 | − | 0.583165i | \(-0.198186\pi\) |
−0.911213 | + | 0.411936i | \(0.864853\pi\) | |||||||
\(80\) | −2.74264 | − | 4.75039i | −0.306637 | − | 0.531110i | ||||
\(81\) | 2.50000 | + | 4.33013i | 0.277778 | + | 0.481125i | ||||
\(82\) | 0.0355339 | − | 0.0615465i | 0.00392406 | − | 0.00679668i | ||||
\(83\) | −1.07107 | −0.117565 | −0.0587825 | − | 0.998271i | \(-0.518722\pi\) | ||||
−0.0587825 | + | 0.998271i | \(0.518722\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −5.32843 | − | 9.22911i | −0.577949 | − | 1.00104i | ||||
\(86\) | −0.707107 | − | 1.22474i | −0.0762493 | − | 0.132068i | ||||
\(87\) | −5.89949 | −0.632492 | ||||||||
\(88\) | 0.464466 | + | 0.804479i | 0.0495123 | + | 0.0857577i | ||||
\(89\) | −15.3137 | −1.62325 | −0.811625 | − | 0.584179i | \(-0.801417\pi\) | ||||
−0.811625 | + | 0.584179i | \(0.801417\pi\) | |||||||
\(90\) | −0.757359 | −0.0798327 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 2.58579 | 0.269587 | ||||||||
\(93\) | 3.65685 | 0.379198 | ||||||||
\(94\) | −0.757359 | − | 1.31178i | −0.0781156 | − | 0.135300i | ||||
\(95\) | −10.9706 | −1.12556 | ||||||||
\(96\) | 3.12132 | + | 5.40629i | 0.318568 | + | 0.551777i | ||||
\(97\) | −5.41421 | − | 9.37769i | −0.549730 | − | 0.952160i | −0.998293 | − | 0.0584091i | \(-0.981397\pi\) |
0.448563 | − | 0.893751i | \(-0.351936\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −0.585786 | −0.0588738 | ||||||||
\(100\) | −1.51472 | + | 2.62357i | −0.151472 | + | 0.262357i | ||||
\(101\) | 7.32843 | + | 12.6932i | 0.729206 | + | 1.26302i | 0.957219 | + | 0.289363i | \(0.0934436\pi\) |
−0.228014 | + | 0.973658i | \(0.573223\pi\) | |||||||
\(102\) | 1.70711 | + | 2.95680i | 0.169029 | + | 0.292766i | ||||
\(103\) | 7.00000 | + | 12.1244i | 0.689730 | + | 1.19465i | 0.971925 | + | 0.235291i | \(0.0756043\pi\) |
−0.282194 | + | 0.959357i | \(0.591062\pi\) | |||||||
\(104\) | −5.55025 | − | 1.37333i | −0.544247 | − | 0.134666i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0.621320 | − | 1.07616i | 0.0603480 | − | 0.104526i | ||||
\(107\) | 17.3137 | 1.67378 | 0.836890 | − | 0.547372i | \(-0.184372\pi\) | ||||
0.836890 | + | 0.547372i | \(0.184372\pi\) | |||||||
\(108\) | −10.3431 | −0.995270 | ||||||||
\(109\) | 6.82843 | − | 11.8272i | 0.654045 | − | 1.13284i | −0.328088 | − | 0.944647i | \(-0.606404\pi\) |
0.982132 | − | 0.188191i | \(-0.0602625\pi\) | |||||||
\(110\) | −0.221825 | + | 0.384213i | −0.0211502 | + | 0.0366333i | ||||
\(111\) | −6.70711 | − | 11.6170i | −0.636610 | − | 1.10264i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −10.1569 | − | 17.5922i | −0.955476 | − | 1.65493i | −0.733274 | − | 0.679933i | \(-0.762009\pi\) |
−0.222202 | − | 0.975001i | \(-0.571325\pi\) | |||||||
\(114\) | 3.51472 | 0.329184 | ||||||||
\(115\) | 1.29289 | + | 2.23936i | 0.120563 | + | 0.208821i | ||||
\(116\) | 3.81371 | − | 6.60554i | 0.354094 | − | 0.613309i | ||||
\(117\) | 2.50000 | − | 2.59808i | 0.231125 | − | 0.240192i | ||||
\(118\) | 4.24264 | 0.390567 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −2.05025 | + | 3.55114i | −0.187162 | + | 0.324173i | ||||
\(121\) | 5.32843 | − | 9.22911i | 0.484402 | − | 0.839010i | ||||
\(122\) | 0.863961 | − | 1.49642i | 0.0782194 | − | 0.135480i | ||||
\(123\) | 0.242641 | 0.0218782 | ||||||||
\(124\) | −2.36396 | + | 4.09450i | −0.212290 | + | 0.367697i | ||||
\(125\) | −12.1716 | −1.08866 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −6.65685 | + | 11.5300i | −0.590700 | + | 1.02312i | 0.403438 | + | 0.915007i | \(0.367815\pi\) |
−0.994138 | + | 0.108116i | \(0.965518\pi\) | |||||||
\(128\) | −10.5563 | −0.933058 | ||||||||
\(129\) | 2.41421 | − | 4.18154i | 0.212560 | − | 0.368164i | ||||
\(130\) | −0.757359 | − | 2.62357i | −0.0664248 | − | 0.230102i | ||||
\(131\) | 10.6569 | + | 18.4582i | 0.931094 | + | 1.61270i | 0.781456 | + | 0.623961i | \(0.214477\pi\) |
0.149638 | + | 0.988741i | \(0.452189\pi\) | |||||||
\(132\) | −0.757359 | + | 1.31178i | −0.0659197 | + | 0.114176i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −0.878680 | − | 1.52192i | −0.0759064 | − | 0.131474i | ||||
\(135\) | −5.17157 | − | 8.95743i | −0.445098 | − | 0.770933i | ||||
\(136\) | −9.24264 | −0.792550 | ||||||||
\(137\) | −0.171573 | −0.0146585 | −0.00732923 | − | 0.999973i | \(-0.502333\pi\) | ||||
−0.00732923 | + | 0.999973i | \(0.502333\pi\) | |||||||
\(138\) | −0.414214 | − | 0.717439i | −0.0352602 | − | 0.0610725i | ||||
\(139\) | −5.94975 | − | 10.3053i | −0.504651 | − | 0.874081i | −0.999986 | − | 0.00537886i | \(-0.998288\pi\) |
0.495335 | − | 0.868702i | \(-0.335045\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 2.58579 | − | 4.47871i | 0.217763 | − | 0.377176i | ||||
\(142\) | 2.41421 | + | 4.18154i | 0.202596 | + | 0.350907i | ||||
\(143\) | −0.585786 | − | 2.02922i | −0.0489859 | − | 0.169692i | ||||
\(144\) | 1.50000 | − | 2.59808i | 0.125000 | − | 0.216506i | ||||
\(145\) | 7.62742 | 0.633423 | ||||||||
\(146\) | −2.20711 | + | 3.82282i | −0.182661 | + | 0.316379i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 17.3431 | 1.42560 | ||||||||
\(149\) | −1.50000 | + | 2.59808i | −0.122885 | + | 0.212843i | −0.920904 | − | 0.389789i | \(-0.872548\pi\) |
0.798019 | + | 0.602632i | \(0.205881\pi\) | |||||||
\(150\) | 0.970563 | 0.0792461 | ||||||||
\(151\) | −7.48528 | + | 12.9649i | −0.609144 | + | 1.05507i | 0.382238 | + | 0.924064i | \(0.375153\pi\) |
−0.991382 | + | 0.131004i | \(0.958180\pi\) | |||||||
\(152\) | −4.75736 | + | 8.23999i | −0.385873 | + | 0.668351i | ||||
\(153\) | 2.91421 | − | 5.04757i | 0.235600 | − | 0.408072i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −4.72792 | −0.379756 | ||||||||
\(156\) | −2.58579 | − | 8.95743i | −0.207029 | − | 0.717168i | ||||
\(157\) | 2.74264 | − | 4.75039i | 0.218887 | − | 0.379123i | −0.735581 | − | 0.677436i | \(-0.763091\pi\) |
0.954468 | + | 0.298314i | \(0.0964242\pi\) | |||||||
\(158\) | −0.363961 | − | 0.630399i | −0.0289552 | − | 0.0501519i | ||||
\(159\) | 4.24264 | 0.336463 | ||||||||
\(160\) | −4.03553 | − | 6.98975i | −0.319037 | − | 0.552588i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 1.03553 | + | 1.79360i | 0.0813592 | + | 0.140918i | ||||
\(163\) | −6.29289 | + | 10.8996i | −0.492897 | + | 0.853723i | −0.999967 | − | 0.00818201i | \(-0.997396\pi\) |
0.507069 | + | 0.861905i | \(0.330729\pi\) | |||||||
\(164\) | −0.156854 | + | 0.271680i | −0.0122483 | + | 0.0212146i | ||||
\(165\) | −1.51472 | −0.117921 | ||||||||
\(166\) | −0.443651 | −0.0344340 | ||||||||
\(167\) | 3.36396 | − | 5.82655i | 0.260311 | − | 0.450872i | −0.706013 | − | 0.708198i | \(-0.749508\pi\) |
0.966325 | + | 0.257326i | \(0.0828415\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 11.5000 | + | 6.06218i | 0.884615 | + | 0.466321i | ||||
\(170\) | −2.20711 | − | 3.82282i | −0.169277 | − | 0.293197i | ||||
\(171\) | −3.00000 | − | 5.19615i | −0.229416 | − | 0.397360i | ||||
\(172\) | 3.12132 | + | 5.40629i | 0.237998 | + | 0.412225i | ||||
\(173\) | −5.07107 | + | 8.78335i | −0.385546 | + | 0.667786i | −0.991845 | − | 0.127452i | \(-0.959320\pi\) |
0.606299 | + | 0.795237i | \(0.292654\pi\) | |||||||
\(174\) | −2.44365 | −0.185253 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −0.878680 | − | 1.52192i | −0.0662330 | − | 0.114719i | ||||
\(177\) | 7.24264 | + | 12.5446i | 0.544390 | + | 0.942912i | ||||
\(178\) | −6.34315 | −0.475439 | ||||||||
\(179\) | 2.82843 | + | 4.89898i | 0.211407 | + | 0.366167i | 0.952155 | − | 0.305616i | \(-0.0988623\pi\) |
−0.740748 | + | 0.671783i | \(0.765529\pi\) | |||||||
\(180\) | 3.34315 | 0.249183 | ||||||||
\(181\) | −9.14214 | −0.679530 | −0.339765 | − | 0.940510i | \(-0.610347\pi\) | ||||
−0.339765 | + | 0.940510i | \(0.610347\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 5.89949 | 0.436103 | ||||||||
\(184\) | 2.24264 | 0.165330 | ||||||||
\(185\) | 8.67157 | + | 15.0196i | 0.637547 | + | 1.10426i | ||||
\(186\) | 1.51472 | 0.111065 | ||||||||
\(187\) | −1.70711 | − | 2.95680i | −0.124836 | − | 0.216222i | ||||
\(188\) | 3.34315 | + | 5.79050i | 0.243824 | + | 0.422315i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −4.54416 | −0.329668 | ||||||||
\(191\) | −8.12132 | + | 14.0665i | −0.587638 | + | 1.01782i | 0.406903 | + | 0.913471i | \(0.366609\pi\) |
−0.994541 | + | 0.104348i | \(0.966725\pi\) | |||||||
\(192\) | −2.94975 | − | 5.10911i | −0.212880 | − | 0.368718i | ||||
\(193\) | −3.57107 | − | 6.18527i | −0.257051 | − | 0.445226i | 0.708400 | − | 0.705812i | \(-0.249418\pi\) |
−0.965451 | + | 0.260586i | \(0.916084\pi\) | |||||||
\(194\) | −2.24264 | − | 3.88437i | −0.161012 | − | 0.278881i | ||||
\(195\) | 6.46447 | − | 6.71807i | 0.462930 | − | 0.481091i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −7.41421 | + | 12.8418i | −0.528241 | + | 0.914940i | 0.471217 | + | 0.882017i | \(0.343815\pi\) |
−0.999458 | + | 0.0329227i | \(0.989518\pi\) | |||||||
\(198\) | −0.242641 | −0.0172437 | ||||||||
\(199\) | 14.9706 | 1.06124 | 0.530618 | − | 0.847611i | \(-0.321960\pi\) | ||||
0.530618 | + | 0.847611i | \(0.321960\pi\) | |||||||
\(200\) | −1.31371 | + | 2.27541i | −0.0928932 | + | 0.160896i | ||||
\(201\) | 3.00000 | − | 5.19615i | 0.211604 | − | 0.366508i | ||||
\(202\) | 3.03553 | + | 5.25770i | 0.213579 | + | 0.369930i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | −7.53553 | − | 13.0519i | −0.527593 | − | 0.913818i | ||||
\(205\) | −0.313708 | −0.0219104 | ||||||||
\(206\) | 2.89949 | + | 5.02207i | 0.202017 | + | 0.349904i | ||||
\(207\) | −0.707107 | + | 1.22474i | −0.0491473 | + | 0.0851257i | ||||
\(208\) | 10.5000 | + | 2.59808i | 0.728044 | + | 0.180144i | ||||
\(209\) | −3.51472 | −0.243118 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −12.3640 | + | 21.4150i | −0.851170 | + | 1.47427i | 0.0289828 | + | 0.999580i | \(0.490773\pi\) |
−0.880153 | + | 0.474690i | \(0.842560\pi\) | |||||||
\(212\) | −2.74264 | + | 4.75039i | −0.188365 | + | 0.326258i | ||||
\(213\) | −8.24264 | + | 14.2767i | −0.564776 | + | 0.978221i | ||||
\(214\) | 7.17157 | 0.490239 | ||||||||
\(215\) | −3.12132 | + | 5.40629i | −0.212872 | + | 0.368706i | ||||
\(216\) | −8.97056 | −0.610369 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 2.82843 | − | 4.89898i | 0.191565 | − | 0.331801i | ||||
\(219\) | −15.0711 | −1.01841 | ||||||||
\(220\) | 0.979185 | − | 1.69600i | 0.0660166 | − | 0.114344i | ||||
\(221\) | 20.3995 | + | 5.04757i | 1.37222 | + | 0.339536i | ||||
\(222\) | −2.77817 | − | 4.81194i | −0.186459 | − | 0.322956i | ||||
\(223\) | 1.00000 | − | 1.73205i | 0.0669650 | − | 0.115987i | −0.830599 | − | 0.556871i | \(-0.812002\pi\) |
0.897564 | + | 0.440884i | \(0.145335\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.828427 | − | 1.43488i | −0.0552285 | − | 0.0956585i | ||||
\(226\) | −4.20711 | − | 7.28692i | −0.279853 | − | 0.484719i | ||||
\(227\) | −5.89949 | −0.391563 | −0.195782 | − | 0.980648i | \(-0.562724\pi\) | ||||
−0.195782 | + | 0.980648i | \(0.562724\pi\) | |||||||
\(228\) | −15.5147 | −1.02749 | ||||||||
\(229\) | −6.24264 | − | 10.8126i | −0.412525 | − | 0.714515i | 0.582640 | − | 0.812730i | \(-0.302020\pi\) |
−0.995165 | + | 0.0982157i | \(0.968686\pi\) | |||||||
\(230\) | 0.535534 | + | 0.927572i | 0.0353121 | + | 0.0611623i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 3.30761 | − | 5.72895i | 0.217155 | − | 0.376124i | ||||
\(233\) | −1.41421 | − | 2.44949i | −0.0926482 | − | 0.160471i | 0.815976 | − | 0.578085i | \(-0.196200\pi\) |
−0.908625 | + | 0.417614i | \(0.862867\pi\) | |||||||
\(234\) | 1.03553 | − | 1.07616i | 0.0676950 | − | 0.0703507i | ||||
\(235\) | −3.34315 | + | 5.79050i | −0.218083 | + | 0.377730i | ||||
\(236\) | −18.7279 | −1.21908 | ||||||||
\(237\) | 1.24264 | − | 2.15232i | 0.0807182 | − | 0.139808i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 24.3848 | 1.57732 | 0.788660 | − | 0.614830i | \(-0.210775\pi\) | ||||
0.788660 | + | 0.614830i | \(0.210775\pi\) | |||||||
\(240\) | 3.87868 | − | 6.71807i | 0.250368 | − | 0.433650i | ||||
\(241\) | −15.4853 | −0.997495 | −0.498747 | − | 0.866747i | \(-0.666206\pi\) | ||||
−0.498747 | + | 0.866747i | \(0.666206\pi\) | |||||||
\(242\) | 2.20711 | − | 3.82282i | 0.141878 | − | 0.245740i | ||||
\(243\) | 4.94975 | − | 8.57321i | 0.317526 | − | 0.549972i | ||||
\(244\) | −3.81371 | + | 6.60554i | −0.244148 | + | 0.422876i | ||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0.100505 | 0.00640797 | ||||||||
\(247\) | 15.0000 | − | 15.5885i | 0.954427 | − | 0.991870i | ||||
\(248\) | −2.05025 | + | 3.55114i | −0.130191 | + | 0.225498i | ||||
\(249\) | −0.757359 | − | 1.31178i | −0.0479957 | − | 0.0831310i | ||||
\(250\) | −5.04163 | −0.318861 | ||||||||
\(251\) | 11.4853 | + | 19.8931i | 0.724945 | + | 1.25564i | 0.958997 | + | 0.283417i | \(0.0914680\pi\) |
−0.234052 | + | 0.972224i | \(0.575199\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 0.414214 | + | 0.717439i | 0.0260414 | + | 0.0451050i | ||||
\(254\) | −2.75736 | + | 4.77589i | −0.173012 | + | 0.299666i | ||||
\(255\) | 7.53553 | − | 13.0519i | 0.471893 | − | 0.817343i | ||||
\(256\) | 3.97056 | 0.248160 | ||||||||
\(257\) | −15.0000 | −0.935674 | −0.467837 | − | 0.883815i | \(-0.654967\pi\) | ||||
−0.467837 | + | 0.883815i | \(0.654967\pi\) | |||||||
\(258\) | 1.00000 | − | 1.73205i | 0.0622573 | − | 0.107833i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 3.34315 | + | 11.5810i | 0.207333 | + | 0.718223i | ||||
\(261\) | 2.08579 | + | 3.61269i | 0.129107 | + | 0.223620i | ||||
\(262\) | 4.41421 | + | 7.64564i | 0.272711 | + | 0.472349i | ||||
\(263\) | 3.36396 | + | 5.82655i | 0.207431 | + | 0.359281i | 0.950904 | − | 0.309485i | \(-0.100157\pi\) |
−0.743474 | + | 0.668765i | \(0.766823\pi\) | |||||||
\(264\) | −0.656854 | + | 1.13770i | −0.0404266 | + | 0.0700209i | ||||
\(265\) | −5.48528 | −0.336958 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −10.8284 | − | 18.7554i | −0.662689 | − | 1.14781i | ||||
\(268\) | 3.87868 | + | 6.71807i | 0.236928 | + | 0.410371i | ||||
\(269\) | 18.0000 | 1.09748 | 0.548740 | − | 0.835993i | \(-0.315108\pi\) | ||||
0.548740 | + | 0.835993i | \(0.315108\pi\) | |||||||
\(270\) | −2.14214 | − | 3.71029i | −0.130366 | − | 0.225801i | ||||
\(271\) | 21.0711 | 1.27998 | 0.639988 | − | 0.768385i | \(-0.278939\pi\) | ||||
0.639988 | + | 0.768385i | \(0.278939\pi\) | |||||||
\(272\) | 17.4853 | 1.06020 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −0.0710678 | −0.00429336 | ||||||||
\(275\) | −0.970563 | −0.0585271 | ||||||||
\(276\) | 1.82843 | + | 3.16693i | 0.110058 | + | 0.190627i | ||||
\(277\) | 1.97056 | 0.118400 | 0.0591998 | − | 0.998246i | \(-0.481145\pi\) | ||||
0.0591998 | + | 0.998246i | \(0.481145\pi\) | |||||||
\(278\) | −2.46447 | − | 4.26858i | −0.147809 | − | 0.256012i | ||||
\(279\) | −1.29289 | − | 2.23936i | −0.0774035 | − | 0.134067i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −17.4853 | −1.04308 | −0.521542 | − | 0.853225i | \(-0.674643\pi\) | ||||
−0.521542 | + | 0.853225i | \(0.674643\pi\) | |||||||
\(282\) | 1.07107 | − | 1.85514i | 0.0637812 | − | 0.110472i | ||||
\(283\) | −9.94975 | − | 17.2335i | −0.591451 | − | 1.02442i | −0.994037 | − | 0.109041i | \(-0.965222\pi\) |
0.402586 | − | 0.915382i | \(-0.368111\pi\) | |||||||
\(284\) | −10.6569 | − | 18.4582i | −0.632368 | − | 1.09529i | ||||
\(285\) | −7.75736 | − | 13.4361i | −0.459506 | − | 0.795888i | ||||
\(286\) | −0.242641 | − | 0.840532i | −0.0143476 | − | 0.0497017i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 2.20711 | − | 3.82282i | 0.130055 | − | 0.225262i | ||||
\(289\) | 16.9706 | 0.998268 | ||||||||
\(290\) | 3.15938 | 0.185525 | ||||||||
\(291\) | 7.65685 | − | 13.2621i | 0.448853 | − | 0.777436i | ||||
\(292\) | 9.74264 | − | 16.8747i | 0.570145 | − | 0.987520i | ||||
\(293\) | 14.2279 | + | 24.6435i | 0.831204 | + | 1.43969i | 0.897084 | + | 0.441860i | \(0.145681\pi\) |
−0.0658799 | + | 0.997828i | \(0.520985\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.36396 | − | 16.2189i | −0.545191 | − | 0.944298i | ||||
\(296\) | 15.0416 | 0.874277 | ||||||||
\(297\) | −1.65685 | − | 2.86976i | −0.0961404 | − | 0.166520i | ||||
\(298\) | −0.621320 | + | 1.07616i | −0.0359921 | + | 0.0623402i | ||||
\(299\) | −4.94975 | − | 1.22474i | −0.286251 | − | 0.0708288i | ||||
\(300\) | −4.28427 | −0.247353 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −3.10051 | + | 5.37023i | −0.178414 | + | 0.309022i | ||||
\(303\) | −10.3640 | + | 17.9509i | −0.595394 | + | 1.03125i | ||||
\(304\) | 9.00000 | − | 15.5885i | 0.516185 | − | 0.894059i | ||||
\(305\) | −7.62742 | −0.436745 | ||||||||
\(306\) | 1.20711 | − | 2.09077i | 0.0690057 | − | 0.119521i | ||||
\(307\) | 32.7279 | 1.86788 | 0.933941 | − | 0.357428i | \(-0.116346\pi\) | ||||
0.933941 | + | 0.357428i | \(0.116346\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −9.89949 | + | 17.1464i | −0.563163 | + | 0.975426i | ||||
\(310\) | −1.95837 | −0.111228 | ||||||||
\(311\) | −6.46447 | + | 11.1968i | −0.366566 | + | 0.634911i | −0.989026 | − | 0.147740i | \(-0.952800\pi\) |
0.622460 | + | 0.782652i | \(0.286133\pi\) | |||||||
\(312\) | −2.24264 | − | 7.76874i | −0.126965 | − | 0.439818i | ||||
\(313\) | −7.00000 | − | 12.1244i | −0.395663 | − | 0.685309i | 0.597522 | − | 0.801852i | \(-0.296152\pi\) |
−0.993186 | + | 0.116543i | \(0.962819\pi\) | |||||||
\(314\) | 1.13604 | − | 1.96768i | 0.0641104 | − | 0.111042i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 1.60660 | + | 2.78272i | 0.0903784 | + | 0.156540i | ||||
\(317\) | −16.3284 | − | 28.2817i | −0.917096 | − | 1.58846i | −0.803804 | − | 0.594895i | \(-0.797194\pi\) |
−0.113292 | − | 0.993562i | \(-0.536140\pi\) | |||||||
\(318\) | 1.75736 | 0.0985478 | ||||||||
\(319\) | 2.44365 | 0.136818 | ||||||||
\(320\) | 3.81371 | + | 6.60554i | 0.213193 | + | 0.369261i | ||||
\(321\) | 12.2426 | + | 21.2049i | 0.683318 | + | 1.18354i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 17.4853 | − | 30.2854i | 0.972907 | − | 1.68512i | ||||
\(324\) | −4.57107 | − | 7.91732i | −0.253948 | − | 0.439851i | ||||
\(325\) | 4.14214 | − | 4.30463i | 0.229764 | − | 0.238778i | ||||
\(326\) | −2.60660 | + | 4.51477i | −0.144366 | + | 0.250050i | ||||
\(327\) | 19.3137 | 1.06805 | ||||||||
\(328\) | −0.136039 | + | 0.235626i | −0.00751150 | + | 0.0130103i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | −0.627417 | −0.0345382 | ||||||||
\(331\) | 12.4350 | − | 21.5381i | 0.683491 | − | 1.18384i | −0.290417 | − | 0.956900i | \(-0.593794\pi\) |
0.973908 | − | 0.226941i | \(-0.0728725\pi\) | |||||||
\(332\) | 1.95837 | 0.107479 | ||||||||
\(333\) | −4.74264 | + | 8.21449i | −0.259895 | + | 0.450152i | ||||
\(334\) | 1.39340 | − | 2.41344i | 0.0762434 | − | 0.132057i | ||||
\(335\) | −3.87868 | + | 6.71807i | −0.211915 | + | 0.367047i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −3.48528 | −0.189855 | −0.0949277 | − | 0.995484i | \(-0.530262\pi\) | ||||
−0.0949277 | + | 0.995484i | \(0.530262\pi\) | |||||||
\(338\) | 4.76346 | + | 2.51104i | 0.259098 | + | 0.136582i | ||||
\(339\) | 14.3640 | − | 24.8791i | 0.780143 | − | 1.35125i | ||||
\(340\) | 9.74264 | + | 16.8747i | 0.528369 | + | 0.915162i | ||||
\(341\) | −1.51472 | −0.0820266 | ||||||||
\(342\) | −1.24264 | − | 2.15232i | −0.0671943 | − | 0.116384i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 2.70711 | + | 4.68885i | 0.145957 | + | 0.252806i | ||||
\(345\) | −1.82843 | + | 3.16693i | −0.0984392 | + | 0.170502i | ||||
\(346\) | −2.10051 | + | 3.63818i | −0.112924 | + | 0.195590i | ||||
\(347\) | −6.10051 | −0.327492 | −0.163746 | − | 0.986503i | \(-0.552358\pi\) | ||||
−0.163746 | + | 0.986503i | \(0.552358\pi\) | |||||||
\(348\) | 10.7868 | 0.578233 | ||||||||
\(349\) | 4.65685 | − | 8.06591i | 0.249276 | − | 0.431758i | −0.714049 | − | 0.700095i | \(-0.753141\pi\) |
0.963325 | + | 0.268337i | \(0.0864741\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 19.7990 | + | 4.89898i | 1.05679 | + | 0.261488i | ||||
\(352\) | −1.29289 | − | 2.23936i | −0.0689114 | − | 0.119358i | ||||
\(353\) | 2.91421 | + | 5.04757i | 0.155108 | + | 0.268655i | 0.933098 | − | 0.359621i | \(-0.117094\pi\) |
−0.777990 | + | 0.628276i | \(0.783761\pi\) | |||||||
\(354\) | 3.00000 | + | 5.19615i | 0.159448 | + | 0.276172i | ||||
\(355\) | 10.6569 | − | 18.4582i | 0.565607 | − | 0.979660i | ||||
\(356\) | 28.0000 | 1.48400 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 1.17157 | + | 2.02922i | 0.0619196 | + | 0.107248i | ||||
\(359\) | 8.48528 | + | 14.6969i | 0.447836 | + | 0.775675i | 0.998245 | − | 0.0592205i | \(-0.0188615\pi\) |
−0.550409 | + | 0.834895i | \(0.685528\pi\) | |||||||
\(360\) | 2.89949 | 0.152817 | ||||||||
\(361\) | −8.50000 | − | 14.7224i | −0.447368 | − | 0.774865i | ||||
\(362\) | −3.78680 | −0.199030 | ||||||||
\(363\) | 15.0711 | 0.791026 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 19.4853 | 1.01991 | ||||||||
\(366\) | 2.44365 | 0.127732 | ||||||||
\(367\) | −14.3640 | − | 24.8791i | −0.749793 | − | 1.29868i | −0.947922 | − | 0.318503i | \(-0.896820\pi\) |
0.198129 | − | 0.980176i | \(-0.436513\pi\) | |||||||
\(368\) | −4.24264 | −0.221163 | ||||||||
\(369\) | −0.0857864 | − | 0.148586i | −0.00446586 | − | 0.00773510i | ||||
\(370\) | 3.59188 | + | 6.22132i | 0.186733 | + | 0.323431i | ||||
\(371\) | 0 | 0 | ||||||||
\(372\) | −6.68629 | −0.346668 | ||||||||
\(373\) | −13.2279 | + | 22.9114i | −0.684916 | + | 1.18631i | 0.288547 | + | 0.957466i | \(0.406828\pi\) |
−0.973463 | + | 0.228843i | \(0.926506\pi\) | |||||||
\(374\) | −0.707107 | − | 1.22474i | −0.0365636 | − | 0.0633300i | ||||
\(375\) | −8.60660 | − | 14.9071i | −0.444443 | − | 0.769798i | ||||
\(376\) | 2.89949 | + | 5.02207i | 0.149530 | + | 0.258994i | ||||
\(377\) | −10.4289 | + | 10.8381i | −0.537117 | + | 0.558189i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 0.121320 | − | 0.210133i | 0.00623181 | − | 0.0107938i | −0.862893 | − | 0.505387i | \(-0.831350\pi\) |
0.869124 | + | 0.494593i | \(0.164683\pi\) | |||||||
\(380\) | 20.0589 | 1.02900 | ||||||||
\(381\) | −18.8284 | −0.964610 | ||||||||
\(382\) | −3.36396 | + | 5.82655i | −0.172115 | + | 0.298112i | ||||
\(383\) | −17.0208 | + | 29.4809i | −0.869723 | + | 1.50640i | −0.00744324 | + | 0.999972i | \(0.502369\pi\) |
−0.862280 | + | 0.506432i | \(0.830964\pi\) | |||||||
\(384\) | −7.46447 | − | 12.9288i | −0.380919 | − | 0.659772i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −1.47918 | − | 2.56202i | −0.0752885 | − | 0.130404i | ||||
\(387\) | −3.41421 | −0.173554 | ||||||||
\(388\) | 9.89949 | + | 17.1464i | 0.502571 | + | 0.870478i | ||||
\(389\) | −13.5711 | + | 23.5058i | −0.688080 | + | 1.19179i | 0.284378 | + | 0.958712i | \(0.408213\pi\) |
−0.972458 | + | 0.233078i | \(0.925120\pi\) | |||||||
\(390\) | 2.67767 | − | 2.78272i | 0.135589 | − | 0.140908i | ||||
\(391\) | −8.24264 | −0.416848 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −15.0711 | + | 26.1039i | −0.760235 | + | 1.31677i | ||||
\(394\) | −3.07107 | + | 5.31925i | −0.154718 | + | 0.267980i | ||||
\(395\) | −1.60660 | + | 2.78272i | −0.0808369 | + | 0.140014i | ||||
\(396\) | 1.07107 | 0.0538232 | ||||||||
\(397\) | 3.31371 | − | 5.73951i | 0.166310 | − | 0.288058i | −0.770810 | − | 0.637066i | \(-0.780148\pi\) |
0.937120 | + | 0.349008i | \(0.113481\pi\) | |||||||
\(398\) | 6.20101 | 0.310829 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 2.48528 | − | 4.30463i | 0.124264 | − | 0.215232i | ||||
\(401\) | 8.79899 | 0.439401 | 0.219700 | − | 0.975567i | \(-0.429492\pi\) | ||||
0.219700 | + | 0.975567i | \(0.429492\pi\) | |||||||
\(402\) | 1.24264 | − | 2.15232i | 0.0619773 | − | 0.107348i | ||||
\(403\) | 6.46447 | − | 6.71807i | 0.322018 | − | 0.334651i | ||||
\(404\) | −13.3995 | − | 23.2086i | −0.666650 | − | 1.15467i | ||||
\(405\) | 4.57107 | − | 7.91732i | 0.227138 | − | 0.393415i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 2.77817 | + | 4.81194i | 0.137709 | + | 0.238519i | ||||
\(408\) | −6.53553 | − | 11.3199i | −0.323557 | − | 0.560417i | ||||
\(409\) | 21.9706 | 1.08637 | 0.543187 | − | 0.839612i | \(-0.317217\pi\) | ||||
0.543187 | + | 0.839612i | \(0.317217\pi\) | |||||||
\(410\) | −0.129942 | −0.00641739 | ||||||||
\(411\) | −0.121320 | − | 0.210133i | −0.00598429 | − | 0.0103651i | ||||
\(412\) | −12.7990 | − | 22.1685i | −0.630561 | − | 1.09216i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | −0.292893 | + | 0.507306i | −0.0143949 | + | 0.0249327i | ||||
\(415\) | 0.979185 | + | 1.69600i | 0.0480663 | + | 0.0832533i | ||||
\(416\) | 15.4497 | + | 3.82282i | 0.757486 | + | 0.187429i | ||||
\(417\) | 8.41421 | − | 14.5738i | 0.412046 | − | 0.713684i | ||||
\(418\) | −1.45584 | −0.0712077 | ||||||||
\(419\) | −5.77817 | + | 10.0081i | −0.282282 | + | 0.488927i | −0.971946 | − | 0.235202i | \(-0.924425\pi\) |
0.689664 | + | 0.724129i | \(0.257758\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 21.4853 | 1.04713 | 0.523564 | − | 0.851986i | \(-0.324602\pi\) | ||||
0.523564 | + | 0.851986i | \(0.324602\pi\) | |||||||
\(422\) | −5.12132 | + | 8.87039i | −0.249302 | + | 0.431804i | ||||
\(423\) | −3.65685 | −0.177802 | ||||||||
\(424\) | −2.37868 | + | 4.11999i | −0.115519 | + | 0.200085i | ||||
\(425\) | 4.82843 | − | 8.36308i | 0.234213 | − | 0.405669i | ||||
\(426\) | −3.41421 | + | 5.91359i | −0.165419 | + | 0.286514i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −31.6569 | −1.53019 | ||||||||
\(429\) | 2.07107 | − | 2.15232i | 0.0999921 | − | 0.103915i | ||||
\(430\) | −1.29289 | + | 2.23936i | −0.0623488 | + | 0.107991i | ||||
\(431\) | −6.00000 | − | 10.3923i | −0.289010 | − | 0.500580i | 0.684564 | − | 0.728953i | \(-0.259993\pi\) |
−0.973574 | + | 0.228373i | \(0.926659\pi\) | |||||||
\(432\) | 16.9706 | 0.816497 | ||||||||
\(433\) | 8.74264 | + | 15.1427i | 0.420144 | + | 0.727712i | 0.995953 | − | 0.0898728i | \(-0.0286461\pi\) |
−0.575809 | + | 0.817584i | \(0.695313\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 5.39340 | + | 9.34164i | 0.258594 | + | 0.447897i | ||||
\(436\) | −12.4853 | + | 21.6251i | −0.597937 | + | 1.03566i | ||||
\(437\) | −4.24264 | + | 7.34847i | −0.202953 | + | 0.351525i | ||||
\(438\) | −6.24264 | −0.298285 | ||||||||
\(439\) | 1.27208 | 0.0607130 | 0.0303565 | − | 0.999539i | \(-0.490336\pi\) | ||||
0.0303565 | + | 0.999539i | \(0.490336\pi\) | |||||||
\(440\) | 0.849242 | − | 1.47093i | 0.0404860 | − | 0.0701239i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 8.44975 | + | 2.09077i | 0.401914 | + | 0.0994478i | ||||
\(443\) | −12.8284 | − | 22.2195i | −0.609497 | − | 1.05568i | −0.991323 | − | 0.131446i | \(-0.958038\pi\) |
0.381826 | − | 0.924234i | \(-0.375295\pi\) | |||||||
\(444\) | 12.2635 | + | 21.2409i | 0.581998 | + | 1.00805i | ||||
\(445\) | 14.0000 | + | 24.2487i | 0.663664 | + | 1.14950i | ||||
\(446\) | 0.414214 | − | 0.717439i | 0.0196136 | − | 0.0339717i | ||||
\(447\) | −4.24264 | −0.200670 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −16.2426 | − | 28.1331i | −0.766538 | − | 1.32768i | −0.939430 | − | 0.342741i | \(-0.888645\pi\) |
0.172892 | − | 0.984941i | \(-0.444689\pi\) | |||||||
\(450\) | −0.343146 | − | 0.594346i | −0.0161760 | − | 0.0280177i | ||||
\(451\) | −0.100505 | −0.00473260 | ||||||||
\(452\) | 18.5711 | + | 32.1660i | 0.873510 | + | 1.51296i | ||||
\(453\) | −21.1716 | −0.994727 | ||||||||
\(454\) | −2.44365 | −0.114686 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −13.4558 | −0.630128 | ||||||||
\(457\) | −25.0000 | −1.16945 | −0.584725 | − | 0.811231i | \(-0.698798\pi\) | ||||
−0.584725 | + | 0.811231i | \(0.698798\pi\) | |||||||
\(458\) | −2.58579 | − | 4.47871i | −0.120826 | − | 0.209277i | ||||
\(459\) | 32.9706 | 1.53893 | ||||||||
\(460\) | −2.36396 | − | 4.09450i | −0.110220 | − | 0.190907i | ||||
\(461\) | 0.671573 | + | 1.16320i | 0.0312783 | + | 0.0541755i | 0.881241 | − | 0.472668i | \(-0.156709\pi\) |
−0.849963 | + | 0.526843i | \(0.823376\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 6.72792 | 0.312673 | 0.156337 | − | 0.987704i | \(-0.450032\pi\) | ||||
0.156337 | + | 0.987704i | \(0.450032\pi\) | |||||||
\(464\) | −6.25736 | + | 10.8381i | −0.290491 | + | 0.503145i | ||||
\(465\) | −3.34315 | − | 5.79050i | −0.155035 | − | 0.268528i | ||||
\(466\) | −0.585786 | − | 1.01461i | −0.0271360 | − | 0.0470010i | ||||
\(467\) | 5.70711 | + | 9.88500i | 0.264093 | + | 0.457423i | 0.967326 | − | 0.253537i | \(-0.0815939\pi\) |
−0.703232 | + | 0.710960i | \(0.748261\pi\) | |||||||
\(468\) | −4.57107 | + | 4.75039i | −0.211298 | + | 0.219587i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −1.38478 | + | 2.39850i | −0.0638750 | + | 0.110635i | ||||
\(471\) | 7.75736 | 0.357440 | ||||||||
\(472\) | −16.2426 | −0.747628 | ||||||||
\(473\) | −1.00000 | + | 1.73205i | −0.0459800 | + | 0.0796398i | ||||
\(474\) | 0.514719 | − | 0.891519i | 0.0236418 | − | 0.0409488i | ||||
\(475\) | −4.97056 | − | 8.60927i | −0.228065 | − | 0.395020i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −1.50000 | − | 2.59808i | −0.0686803 | − | 0.118958i | ||||
\(478\) | 10.1005 | 0.461986 | ||||||||
\(479\) | −0.807612 | − | 1.39882i | −0.0369007 | − | 0.0639139i | 0.846985 | − | 0.531616i | \(-0.178415\pi\) |
−0.883886 | + | 0.467703i | \(0.845082\pi\) | |||||||
\(480\) | 5.70711 | − | 9.88500i | 0.260493 | − | 0.451186i | ||||
\(481\) | −33.1985 | − | 8.21449i | −1.51372 | − | 0.374549i | ||||
\(482\) | −6.41421 | −0.292159 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −9.74264 | + | 16.8747i | −0.442847 | + | 0.767034i | ||||
\(485\) | −9.89949 | + | 17.1464i | −0.449513 | + | 0.778579i | ||||
\(486\) | 2.05025 | − | 3.55114i | 0.0930013 | − | 0.161083i | ||||
\(487\) | −12.9706 | −0.587752 | −0.293876 | − | 0.955844i | \(-0.594945\pi\) | ||||
−0.293876 | + | 0.955844i | \(0.594945\pi\) | |||||||
\(488\) | −3.30761 | + | 5.72895i | −0.149729 | + | 0.259337i | ||||
\(489\) | −17.7990 | −0.804898 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −6.34315 | + | 10.9867i | −0.286262 | + | 0.495821i | −0.972914 | − | 0.231165i | \(-0.925746\pi\) |
0.686652 | + | 0.726986i | \(0.259079\pi\) | |||||||
\(492\) | −0.443651 | −0.0200013 | ||||||||
\(493\) | −12.1569 | + | 21.0563i | −0.547517 | + | 0.948328i | ||||
\(494\) | 6.21320 | − | 6.45695i | 0.279545 | − | 0.290512i | ||||
\(495\) | 0.535534 | + | 0.927572i | 0.0240705 | + | 0.0416913i | ||||
\(496\) | 3.87868 | − | 6.71807i | 0.174158 | − | 0.301650i | ||||
\(497\) | 0 | 0 | ||||||||
\(498\) | −0.313708 | − | 0.543359i | −0.0140576 | − | 0.0243485i | ||||
\(499\) | −10.0208 | − | 17.3566i | −0.448593 | − | 0.776986i | 0.549701 | − | 0.835361i | \(-0.314741\pi\) |
−0.998295 | + | 0.0583748i | \(0.981408\pi\) | |||||||
\(500\) | 22.2548 | 0.995266 | ||||||||
\(501\) | 9.51472 | 0.425086 | ||||||||
\(502\) | 4.75736 | + | 8.23999i | 0.212331 | + | 0.367769i | ||||
\(503\) | −1.22183 | − | 2.11626i | −0.0544785 | − | 0.0943595i | 0.837500 | − | 0.546437i | \(-0.184016\pi\) |
−0.891979 | + | 0.452078i | \(0.850683\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 13.3995 | − | 23.2086i | 0.596270 | − | 1.03277i | ||||
\(506\) | 0.171573 | + | 0.297173i | 0.00762734 | + | 0.0132109i | ||||
\(507\) | 0.707107 | + | 18.3712i | 0.0314037 | + | 0.815892i | ||||
\(508\) | 12.1716 | − | 21.0818i | 0.540026 | − | 0.935353i | ||||
\(509\) | −4.65685 | −0.206411 | −0.103206 | − | 0.994660i | \(-0.532910\pi\) | ||||
−0.103206 | + | 0.994660i | \(0.532910\pi\) | |||||||
\(510\) | 3.12132 | − | 5.40629i | 0.138214 | − | 0.239394i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 22.7574 | 1.00574 | ||||||||
\(513\) | 16.9706 | − | 29.3939i | 0.749269 | − | 1.29777i | ||||
\(514\) | −6.21320 | −0.274053 | ||||||||
\(515\) | 12.7990 | − | 22.1685i | 0.563991 | − | 0.976861i | ||||
\(516\) | −4.41421 | + | 7.64564i | −0.194325 | + | 0.336581i | ||||
\(517\) | −1.07107 | + | 1.85514i | −0.0471055 | + | 0.0815891i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | −14.3431 | −0.629594 | ||||||||
\(520\) | 2.89949 | + | 10.0441i | 0.127151 | + | 0.440465i | ||||
\(521\) | −12.3284 | + | 21.3535i | −0.540118 | + | 0.935512i | 0.458779 | + | 0.888551i | \(0.348287\pi\) |
−0.998897 | + | 0.0469615i | \(0.985046\pi\) | |||||||
\(522\) | 0.863961 | + | 1.49642i | 0.0378145 | + | 0.0654967i | ||||
\(523\) | 16.9706 | 0.742071 | 0.371035 | − | 0.928619i | \(-0.379003\pi\) | ||||
0.371035 | + | 0.928619i | \(0.379003\pi\) | |||||||
\(524\) | −19.4853 | − | 33.7495i | −0.851218 | − | 1.47435i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 1.39340 | + | 2.41344i | 0.0607551 | + | 0.105231i | ||||
\(527\) | 7.53553 | − | 13.0519i | 0.328253 | − | 0.568551i | ||||
\(528\) | 1.24264 | − | 2.15232i | 0.0540790 | − | 0.0936676i | ||||
\(529\) | −21.0000 | −0.913043 | ||||||||
\(530\) | −2.27208 | −0.0986928 | ||||||||
\(531\) | 5.12132 | − | 8.87039i | 0.222246 | − | 0.384942i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 0.428932 | − | 0.445759i | 0.0185791 | − | 0.0193080i | ||||
\(534\) | −4.48528 | − | 7.76874i | −0.194097 | − | 0.336186i | ||||
\(535\) | −15.8284 | − | 27.4156i | −0.684323 | − | 1.18528i | ||||
\(536\) | 3.36396 | + | 5.82655i | 0.145301 | + | 0.251669i | ||||
\(537\) | −4.00000 | + | 6.92820i | −0.172613 | + | 0.298974i | ||||
\(538\) | 7.45584 | 0.321444 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 9.45584 | + | 16.3780i | 0.406915 | + | 0.704797i | ||||
\(541\) | 5.74264 | + | 9.94655i | 0.246895 | + | 0.427635i | 0.962663 | − | 0.270703i | \(-0.0872563\pi\) |
−0.715767 | + | 0.698339i | \(0.753923\pi\) | |||||||
\(542\) | 8.72792 | 0.374896 | ||||||||
\(543\) | −6.46447 | − | 11.1968i | −0.277417 | − | 0.480500i | ||||
\(544\) | 25.7279 | 1.10308 | ||||||||
\(545\) | −24.9706 | −1.06962 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 0.928932 | 0.0397183 | 0.0198591 | − | 0.999803i | \(-0.493678\pi\) | ||||
0.0198591 | + | 0.999803i | \(0.493678\pi\) | |||||||
\(548\) | 0.313708 | 0.0134010 | ||||||||
\(549\) | −2.08579 | − | 3.61269i | −0.0890192 | − | 0.154186i | ||||
\(550\) | −0.402020 | −0.0171422 | ||||||||
\(551\) | 12.5147 | + | 21.6761i | 0.533145 | + | 0.923434i | ||||
\(552\) | 1.58579 | + | 2.74666i | 0.0674956 | + | 0.116906i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0.816234 | 0.0346785 | ||||||||
\(555\) | −12.2635 | + | 21.2409i | −0.520555 | + | 0.901627i | ||||
\(556\) | 10.8787 | + | 18.8424i | 0.461359 | + | 0.799097i | ||||
\(557\) | −6.15685 | − | 10.6640i | −0.260874 | − | 0.451848i | 0.705600 | − | 0.708610i | \(-0.250677\pi\) |
−0.966474 | + | 0.256763i | \(0.917344\pi\) | |||||||
\(558\) | −0.535534 | − | 0.927572i | −0.0226710 | − | 0.0392673i | ||||
\(559\) | −3.41421 | − | 11.8272i | −0.144406 | − | 0.500237i | ||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 2.41421 | − | 4.18154i | 0.101928 | − | 0.176545i | ||||
\(562\) | −7.24264 | −0.305512 | ||||||||
\(563\) | −0.100505 | −0.00423578 | −0.00211789 | − | 0.999998i | \(-0.500674\pi\) | ||||
−0.00211789 | + | 0.999998i | \(0.500674\pi\) | |||||||
\(564\) | −4.72792 | + | 8.18900i | −0.199081 | + | 0.344819i | ||||
\(565\) | −18.5711 | + | 32.1660i | −0.781291 | + | 1.35324i | ||||
\(566\) | −4.12132 | − | 7.13834i | −0.173232 | − | 0.300047i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −9.24264 | − | 16.0087i | −0.387813 | − | 0.671711i | ||||
\(569\) | 18.8284 | 0.789329 | 0.394664 | − | 0.918825i | \(-0.370861\pi\) | ||||
0.394664 | + | 0.918825i | \(0.370861\pi\) | |||||||
\(570\) | −3.21320 | − | 5.56543i | −0.134586 | − | 0.233110i | ||||
\(571\) | −14.4853 | + | 25.0892i | −0.606190 | + | 1.04995i | 0.385672 | + | 0.922636i | \(0.373970\pi\) |
−0.991862 | + | 0.127316i | \(0.959364\pi\) | |||||||
\(572\) | 1.07107 | + | 3.71029i | 0.0447836 | + | 0.155135i | ||||
\(573\) | −22.9706 | −0.959609 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.17157 | + | 2.02922i | −0.0488580 | + | 0.0846245i | ||||
\(576\) | −2.08579 | + | 3.61269i | −0.0869078 | + | 0.150529i | ||||
\(577\) | −6.84315 | + | 11.8527i | −0.284884 | + | 0.493433i | −0.972581 | − | 0.232564i | \(-0.925288\pi\) |
0.687697 | + | 0.725998i | \(0.258622\pi\) | |||||||
\(578\) | 7.02944 | 0.292386 | ||||||||
\(579\) | 5.05025 | − | 8.74729i | 0.209881 | − | 0.363525i | ||||
\(580\) | −13.9462 | −0.579083 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 3.17157 | − | 5.49333i | 0.131466 | − | 0.227706i | ||||
\(583\) | −1.75736 | −0.0727824 | ||||||||
\(584\) | 8.44975 | − | 14.6354i | 0.349653 | − | 0.605617i | ||||
\(585\) | −6.39949 | − | 1.58346i | −0.264587 | − | 0.0654682i | ||||
\(586\) | 5.89340 | + | 10.2077i | 0.243454 | + | 0.421675i | ||||
\(587\) | −14.8284 | + | 25.6836i | −0.612035 | + | 1.06008i | 0.378862 | + | 0.925453i | \(0.376315\pi\) |
−0.990897 | + | 0.134622i | \(0.957018\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −7.75736 | − | 13.4361i | −0.319636 | − | 0.553627i | ||||
\(590\) | −3.87868 | − | 6.71807i | −0.159683 | − | 0.276579i | ||||
\(591\) | −20.9706 | −0.862614 | ||||||||
\(592\) | −28.4558 | −1.16953 | ||||||||
\(593\) | 12.6421 | + | 21.8968i | 0.519150 | + | 0.899195i | 0.999752 | + | 0.0222559i | \(0.00708484\pi\) |
−0.480602 | + | 0.876939i | \(0.659582\pi\) | |||||||
\(594\) | −0.686292 | − | 1.18869i | −0.0281589 | − | 0.0487726i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 2.74264 | − | 4.75039i | 0.112343 | − | 0.194584i | ||||
\(597\) | 10.5858 | + | 18.3351i | 0.433247 | + | 0.750407i | ||||
\(598\) | −2.05025 | − | 0.507306i | −0.0838411 | − | 0.0207453i | ||||
\(599\) | −14.1716 | + | 24.5459i | −0.579035 | + | 1.00292i | 0.416556 | + | 0.909110i | \(0.363237\pi\) |
−0.995590 | + | 0.0938074i | \(0.970096\pi\) | |||||||
\(600\) | −3.71573 | −0.151694 | ||||||||
\(601\) | 15.4706 | − | 26.7958i | 0.631057 | − | 1.09302i | −0.356278 | − | 0.934380i | \(-0.615955\pi\) |
0.987336 | − | 0.158644i | \(-0.0507121\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −4.24264 | −0.172774 | ||||||||
\(604\) | 13.6863 | − | 23.7054i | 0.556887 | − | 0.964557i | ||||
\(605\) | −19.4853 | −0.792189 | ||||||||
\(606\) | −4.29289 | + | 7.43551i | −0.174387 | + | 0.302047i | ||||
\(607\) | −16.1716 | + | 28.0100i | −0.656384 | + | 1.13689i | 0.325161 | + | 0.945659i | \(0.394581\pi\) |
−0.981545 | + | 0.191232i | \(0.938752\pi\) | |||||||
\(608\) | 13.2426 | − | 22.9369i | 0.537060 | − | 0.930215i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −3.15938 | −0.127920 | ||||||||
\(611\) | −3.65685 | − | 12.6677i | −0.147940 | − | 0.512481i | ||||
\(612\) | −5.32843 | + | 9.22911i | −0.215389 | + | 0.373065i | ||||
\(613\) | 7.39949 | + | 12.8163i | 0.298863 | + | 0.517646i | 0.975876 | − | 0.218325i | \(-0.0700594\pi\) |
−0.677013 | + | 0.735971i | \(0.736726\pi\) | |||||||
\(614\) | 13.5563 | 0.547090 | ||||||||
\(615\) | −0.221825 | − | 0.384213i | −0.00894486 | − | 0.0154930i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.5711 | + | 26.9699i | 0.626868 | + | 1.08577i | 0.988177 | + | 0.153320i | \(0.0489966\pi\) |
−0.361309 | + | 0.932446i | \(0.617670\pi\) | |||||||
\(618\) | −4.10051 | + | 7.10228i | −0.164947 | + | 0.285696i | ||||
\(619\) | 20.7782 | − | 35.9889i | 0.835145 | − | 1.44651i | −0.0587667 | − | 0.998272i | \(-0.518717\pi\) |
0.893912 | − | 0.448242i | \(-0.147950\pi\) | |||||||
\(620\) | 8.64466 | 0.347178 | ||||||||
\(621\) | −8.00000 | −0.321029 | ||||||||
\(622\) | −2.67767 | + | 4.63786i | −0.107365 | + | 0.185961i | ||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 4.24264 | + | 14.6969i | 0.169842 | + | 0.588348i | ||||
\(625\) | 6.98528 | + | 12.0989i | 0.279411 | + | 0.483954i | ||||
\(626\) | −2.89949 | − | 5.02207i | −0.115887 | − | 0.200722i | ||||
\(627\) | −2.48528 | − | 4.30463i | −0.0992526 | − | 0.171911i | ||||
\(628\) | −5.01472 | + | 8.68575i | −0.200109 | + | 0.346599i | ||||
\(629\) | −55.2843 | −2.20433 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −12.1421 | − | 21.0308i | −0.483371 | − | 0.837223i | 0.516447 | − | 0.856319i | \(-0.327254\pi\) |
−0.999818 | + | 0.0190965i | \(0.993921\pi\) | |||||||
\(632\) | 1.39340 | + | 2.41344i | 0.0554264 | + | 0.0960014i | ||||
\(633\) | −34.9706 | −1.38996 | ||||||||
\(634\) | −6.76346 | − | 11.7146i | −0.268611 | − | 0.465248i | ||||
\(635\) | 24.3431 | 0.966028 | ||||||||
\(636\) | −7.75736 | −0.307599 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 1.01219 | 0.0400731 | ||||||||
\(639\) | 11.6569 | 0.461138 | ||||||||
\(640\) | 9.65076 | + | 16.7156i | 0.381480 | + | 0.660742i | ||||
\(641\) | −14.7990 | −0.584525 | −0.292262 | − | 0.956338i | \(-0.594408\pi\) | ||||
−0.292262 | + | 0.956338i | \(0.594408\pi\) | |||||||
\(642\) | 5.07107 | + | 8.78335i | 0.200139 | + | 0.346651i | ||||
\(643\) | 7.51472 | + | 13.0159i | 0.296352 | + | 0.513296i | 0.975298 | − | 0.220891i | \(-0.0708967\pi\) |
−0.678947 | + | 0.734187i | \(0.737563\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.82843 | −0.347619 | ||||||||
\(646\) | 7.24264 | − | 12.5446i | 0.284958 | − | 0.493562i | ||||
\(647\) | −8.65685 | − | 14.9941i | −0.340336 | − | 0.589479i | 0.644159 | − | 0.764892i | \(-0.277207\pi\) |
−0.984495 | + | 0.175412i | \(0.943874\pi\) | |||||||
\(648\) | −3.96447 | − | 6.86666i | −0.155739 | − | 0.269748i | ||||
\(649\) | −3.00000 | − | 5.19615i | −0.117760 | − | 0.203967i | ||||
\(650\) | 1.71573 | − | 1.78304i | 0.0672964 | − | 0.0699365i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 11.5061 | − | 19.9291i | 0.450614 | − | 0.780486i | ||||
\(653\) | 26.1421 | 1.02302 | 0.511510 | − | 0.859277i | \(-0.329086\pi\) | ||||
0.511510 | + | 0.859277i | \(0.329086\pi\) | |||||||
\(654\) | 8.00000 | 0.312825 | ||||||||
\(655\) | 19.4853 | − | 33.7495i | 0.761353 | − | 1.31870i | ||||
\(656\) | 0.257359 | − | 0.445759i | 0.0100482 | − | 0.0174040i | ||||
\(657\) | 5.32843 | + | 9.22911i | 0.207882 | + | 0.360062i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 7.65685 | + | 13.2621i | 0.298269 | + | 0.516617i | 0.975740 | − | 0.218933i | \(-0.0702575\pi\) |
−0.677471 | + | 0.735549i | \(0.736924\pi\) | |||||||
\(660\) | 2.76955 | 0.107805 | ||||||||
\(661\) | −16.5711 | − | 28.7019i | −0.644540 | − | 1.11638i | −0.984408 | − | 0.175903i | \(-0.943716\pi\) |
0.339868 | − | 0.940473i | \(-0.389618\pi\) | |||||||
\(662\) | 5.15076 | − | 8.92137i | 0.200190 | − | 0.346739i | ||||
\(663\) | 8.24264 | + | 28.5533i | 0.320118 | + | 1.10892i | ||||
\(664\) | 1.69848 | 0.0659140 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −1.96447 | + | 3.40256i | −0.0761215 | + | 0.131846i | ||||
\(667\) | 2.94975 | − | 5.10911i | 0.114215 | − | 0.197826i | ||||
\(668\) | −6.15076 | + | 10.6534i | −0.237980 | + | 0.412193i | ||||
\(669\) | 2.82843 | 0.109353 | ||||||||
\(670\) | −1.60660 | + | 2.78272i | −0.0620684 | + | 0.107506i | ||||
\(671\) | −2.44365 | −0.0943361 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −7.25736 | + | 12.5701i | −0.279751 | + | 0.484542i | −0.971323 | − | 0.237765i | \(-0.923585\pi\) |
0.691572 | + | 0.722308i | \(0.256918\pi\) | |||||||
\(674\) | −1.44365 | −0.0556074 | ||||||||
\(675\) | 4.68629 | − | 8.11689i | 0.180375 | − | 0.312419i | ||||
\(676\) | −21.0269 | − | 11.0843i | −0.808727 | − | 0.426317i | ||||
\(677\) | −8.82843 | − | 15.2913i | −0.339304 | − | 0.587692i | 0.644998 | − | 0.764184i | \(-0.276858\pi\) |
−0.984302 | + | 0.176492i | \(0.943525\pi\) | |||||||
\(678\) | 5.94975 | − | 10.3053i | 0.228499 | − | 0.395771i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 8.44975 | + | 14.6354i | 0.324033 | + | 0.561242i | ||||
\(681\) | −4.17157 | − | 7.22538i | −0.159855 | − | 0.276877i | ||||
\(682\) | −0.627417 | −0.0240250 | ||||||||
\(683\) | 5.31371 | 0.203323 | 0.101662 | − | 0.994819i | \(-0.467584\pi\) | ||||
0.101662 | + | 0.994819i | \(0.467584\pi\) | |||||||
\(684\) | 5.48528 | + | 9.50079i | 0.209735 | + | 0.363272i | ||||
\(685\) | 0.156854 | + | 0.271680i | 0.00599309 | + | 0.0103803i | ||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 8.82843 | − | 15.2913i | 0.336826 | − | 0.583399i | ||||
\(688\) | −5.12132 | − | 8.87039i | −0.195249 | − | 0.338180i | ||||
\(689\) | 7.50000 | − | 7.79423i | 0.285727 | − | 0.296936i | ||||
\(690\) | −0.757359 | + | 1.31178i | −0.0288322 | + | 0.0499388i | ||||
\(691\) | −29.9411 | −1.13901 | −0.569507 | − | 0.821986i | \(-0.692866\pi\) | ||||
−0.569507 | + | 0.821986i | \(0.692866\pi\) | |||||||
\(692\) | 9.27208 | − | 16.0597i | 0.352472 | − | 0.610499i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −2.52691 | −0.0959203 | ||||||||
\(695\) | −10.8787 | + | 18.8424i | −0.412652 | + | 0.714734i | ||||
\(696\) | 9.35534 | 0.354613 | ||||||||
\(697\) | 0.500000 | − | 0.866025i | 0.0189389 | − | 0.0328031i | ||||
\(698\) | 1.92893 | − | 3.34101i | 0.0730112 | − | 0.126459i | ||||
\(699\) | 2.00000 | − | 3.46410i | 0.0756469 | − | 0.131024i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 13.8579 | 0.523404 | 0.261702 | − | 0.965149i | \(-0.415716\pi\) | ||||
0.261702 | + | 0.965149i | \(0.415716\pi\) | |||||||
\(702\) | 8.20101 | + | 2.02922i | 0.309527 | + | 0.0765881i | ||||
\(703\) | −28.4558 | + | 49.2870i | −1.07323 | + | 1.85889i | ||||
\(704\) | 1.22183 | + | 2.11626i | 0.0460493 | + | 0.0797597i | ||||
\(705\) | −9.45584 | −0.356128 | ||||||||
\(706\) | 1.20711 | + | 2.09077i | 0.0454301 | + | 0.0786872i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | −13.2426 | − | 22.9369i | −0.497689 | − | 0.862022i | ||||
\(709\) | −8.81371 | + | 15.2658i | −0.331006 | + | 0.573319i | −0.982709 | − | 0.185155i | \(-0.940721\pi\) |
0.651704 | + | 0.758474i | \(0.274055\pi\) | |||||||
\(710\) | 4.41421 | − | 7.64564i | 0.165662 | − | 0.286936i | ||||
\(711\) | −1.75736 | −0.0659061 | ||||||||
\(712\) | 24.2843 | 0.910092 | ||||||||
\(713\) | −1.82843 | + | 3.16693i | −0.0684751 | + | 0.118602i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.67767 | + | 2.78272i | −0.100139 | + | 0.104068i | ||||
\(716\) | −5.17157 | − | 8.95743i | −0.193271 | − | 0.334755i | ||||
\(717\) | 17.2426 | + | 29.8651i | 0.643938 | + | 1.11533i | ||||
\(718\) | 3.51472 | + | 6.08767i | 0.131168 | + | 0.227190i | ||||
\(719\) | 0.192388 | − | 0.333226i | 0.00717487 | − | 0.0124272i | −0.862416 | − | 0.506201i | \(-0.831049\pi\) |
0.869591 | + | 0.493774i | \(0.164383\pi\) | |||||||
\(720\) | −5.48528 | −0.204424 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −3.52082 | − | 6.09823i | −0.131031 | − | 0.226953i | ||||
\(723\) | −10.9497 | − | 18.9655i | −0.407225 | − | 0.705335i | ||||
\(724\) | 16.7157 | 0.621235 | ||||||||
\(725\) | 3.45584 | + | 5.98570i | 0.128347 | + | 0.222303i | ||||
\(726\) | 6.24264 | 0.231686 | ||||||||
\(727\) | −24.9706 | −0.926107 | −0.463053 | − | 0.886330i | \(-0.653246\pi\) | ||||
−0.463053 | + | 0.886330i | \(0.653246\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 29.0000 | 1.07407 | ||||||||
\(730\) | 8.07107 | 0.298724 | ||||||||
\(731\) | −9.94975 | − | 17.2335i | −0.368005 | − | 0.637403i | ||||
\(732\) | −10.7868 | −0.398691 | ||||||||
\(733\) | −10.5000 | − | 18.1865i | −0.387826 | − | 0.671735i | 0.604331 | − | 0.796734i | \(-0.293441\pi\) |
−0.992157 | + | 0.124999i | \(0.960107\pi\) | |||||||
\(734\) | −5.94975 | − | 10.3053i | −0.219609 | − | 0.380374i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −6.24264 | −0.230107 | ||||||||
\(737\) | −1.24264 | + | 2.15232i | −0.0457733 | + | 0.0792816i | ||||
\(738\) | −0.0355339 | − | 0.0615465i | −0.00130802 | − | 0.00226556i | ||||
\(739\) | 10.1421 | + | 17.5667i | 0.373084 | + | 0.646201i | 0.990038 | − | 0.140798i | \(-0.0449668\pi\) |
−0.616954 | + | 0.786999i | \(0.711633\pi\) | |||||||
\(740\) | −15.8553 | − | 27.4623i | −0.582854 | − | 1.00953i | ||||
\(741\) | 29.6985 | + | 7.34847i | 1.09100 | + | 0.269953i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −15.7990 | + | 27.3647i | −0.579609 | + | 1.00391i | 0.415915 | + | 0.909403i | \(0.363461\pi\) |
−0.995524 | + | 0.0945084i | \(0.969872\pi\) | |||||||
\(744\) | −5.79899 | −0.212601 | ||||||||
\(745\) | 5.48528 | 0.200965 | ||||||||
\(746\) | −5.47918 | + | 9.49023i | −0.200607 | + | 0.347462i | ||||
\(747\) | −0.535534 | + | 0.927572i | −0.0195942 | + | 0.0339381i | ||||
\(748\) | 3.12132 | + | 5.40629i | 0.114127 | + | 0.197673i | ||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −3.56497 | − | 6.17471i | −0.130174 | − | 0.225469i | ||||
\(751\) | −17.5563 | −0.640640 | −0.320320 | − | 0.947309i | \(-0.603790\pi\) | ||||
−0.320320 | + | 0.947309i | \(0.603790\pi\) | |||||||
\(752\) | −5.48528 | − | 9.50079i | −0.200028 | − | 0.346458i | ||||
\(753\) | −16.2426 | + | 28.1331i | −0.591915 | + | 1.02523i | ||||
\(754\) | −4.31981 | + | 4.48927i | −0.157318 | + | 0.163490i | ||||
\(755\) | 27.3726 | 0.996190 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −14.7279 | + | 25.5095i | −0.535295 | + | 0.927159i | 0.463854 | + | 0.885912i | \(0.346466\pi\) |
−0.999149 | + | 0.0412470i | \(0.986867\pi\) | |||||||
\(758\) | 0.0502525 | − | 0.0870399i | 0.00182525 | − | 0.00316143i | ||||
\(759\) | −0.585786 | + | 1.01461i | −0.0212627 | + | 0.0368281i | ||||
\(760\) | 17.3970 | 0.631054 | ||||||||
\(761\) | 8.92893 | − | 15.4654i | 0.323674 | − | 0.560619i | −0.657569 | − | 0.753394i | \(-0.728415\pi\) |
0.981243 | + | 0.192775i | \(0.0617487\pi\) | |||||||
\(762\) | −7.79899 | −0.282528 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 14.8492 | − | 25.7196i | 0.537227 | − | 0.930504i | ||||
\(765\) | −10.6569 | −0.385299 | ||||||||
\(766\) | −7.05025 | + | 12.2114i | −0.254736 | + | 0.441216i | ||||
\(767\) | 35.8492 | + | 8.87039i | 1.29444 | + | 0.320291i | ||||
\(768\) | 2.80761 | + | 4.86293i | 0.101311 | + | 0.175476i | ||||
\(769\) | −24.7279 | + | 42.8300i | −0.891712 | + | 1.54449i | −0.0538894 | + | 0.998547i | \(0.517162\pi\) |
−0.837822 | + | 0.545943i | \(0.816172\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −10.6066 | − | 18.3712i | −0.381987 | − | 0.661622i | ||||
\(772\) | 6.52944 | + | 11.3093i | 0.235000 | + | 0.407031i | ||||
\(773\) | −6.34315 | −0.228147 | −0.114074 | − | 0.993472i | \(-0.536390\pi\) | ||||
−0.114074 | + | 0.993472i | \(0.536390\pi\) | |||||||
\(774\) | −1.41421 | −0.0508329 | ||||||||
\(775\) | −2.14214 | − | 3.71029i | −0.0769478 | − | 0.133277i | ||||
\(776\) | 8.58579 | + | 14.8710i | 0.308212 | + | 0.533838i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −5.62132 | + | 9.73641i | −0.201534 | + | 0.349067i | ||||
\(779\) | −0.514719 | − | 0.891519i | −0.0184417 | − | 0.0319420i | ||||
\(780\) | −11.8198 | + | 12.2835i | −0.423217 | + | 0.439820i | ||||
\(781\) | 3.41421 | − | 5.91359i | 0.122170 | − | 0.211605i | ||||
\(782\) | −3.41421 | −0.122092 | ||||||||
\(783\) | −11.7990 | + | 20.4364i | −0.421661 | + | 0.730339i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −10.0294 | −0.357966 | ||||||||
\(786\) | −6.24264 | + | 10.8126i | −0.222668 | + | 0.385672i | ||||
\(787\) | 13.8995 | 0.495463 | 0.247732 | − | 0.968829i | \(-0.420315\pi\) | ||||
0.247732 | + | 0.968829i | \(0.420315\pi\) | |||||||
\(788\) | 13.5563 | − | 23.4803i | 0.482925 | − | 0.836451i | ||||
\(789\) | −4.75736 | + | 8.23999i | −0.169366 | + | 0.293351i | ||||
\(790\) | −0.665476 | + | 1.15264i | −0.0236766 | + | 0.0410090i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0.928932 | 0.0330082 | ||||||||
\(793\) | 10.4289 | − | 10.8381i | 0.370342 | − | 0.384871i | ||||
\(794\) | 1.37258 | − | 2.37738i | 0.0487111 | − | 0.0843702i | ||||
\(795\) | −3.87868 | − | 6.71807i | −0.137563 | − | 0.238265i | ||||
\(796\) | −27.3726 | −0.970195 | ||||||||
\(797\) | −9.07107 | − | 15.7116i | −0.321314 | − | 0.556532i | 0.659446 | − | 0.751752i | \(-0.270791\pi\) |
−0.980759 | + | 0.195221i | \(0.937458\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −10.6569 | − | 18.4582i | −0.377012 | − | 0.653005i | ||||
\(800\) | 3.65685 | − | 6.33386i | 0.129289 | − | 0.223936i | ||||
\(801\) | −7.65685 | + | 13.2621i | −0.270542 | + | 0.468592i | ||||
\(802\) | 3.64466 | 0.128697 | ||||||||
\(803\) | 6.24264 | 0.220298 | ||||||||
\(804\) | −5.48528 | + | 9.50079i | −0.193451 | + | 0.335067i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 2.67767 | − | 2.78272i | 0.0943169 | − | 0.0980170i | ||||
\(807\) | 12.7279 | + | 22.0454i | 0.448044 | + | 0.776035i | ||||
\(808\) | −11.6213 | − | 20.1287i | −0.408837 | − | 0.708126i | ||||
\(809\) | −17.5711 | − | 30.4340i | −0.617766 | − | 1.07000i | −0.989892 | − | 0.141820i | \(-0.954705\pi\) |
0.372127 | − | 0.928182i | \(-0.378629\pi\) | |||||||
\(810\) | 1.89340 | − | 3.27946i | 0.0665272 | − | 0.115229i | ||||
\(811\) | 42.1838 | 1.48127 | 0.740636 | − | 0.671906i | \(-0.234524\pi\) | ||||
0.740636 | + | 0.671906i | \(0.234524\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 14.8995 | + | 25.8067i | 0.522548 | + | 0.905080i | ||||
\(814\) | 1.15076 | + | 1.99317i | 0.0403340 | + | 0.0698606i | ||||
\(815\) | 23.0122 | 0.806082 | ||||||||
\(816\) | 12.3640 | + | 21.4150i | 0.432825 | + | 0.749675i | ||||
\(817\) | −20.4853 | −0.716689 | ||||||||
\(818\) | 9.10051 | 0.318192 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.573593 | 0.0200307 | ||||||||
\(821\) | −39.9411 | −1.39395 | −0.696977 | − | 0.717093i | \(-0.745472\pi\) | ||||
−0.696977 | + | 0.717093i | \(0.745472\pi\) | |||||||
\(822\) | −0.0502525 | − | 0.0870399i | −0.00175276 | − | 0.00303587i | ||||
\(823\) | 19.3137 | 0.673234 | 0.336617 | − | 0.941642i | \(-0.390717\pi\) | ||||
0.336617 | + | 0.941642i | \(0.390717\pi\) | |||||||
\(824\) | −11.1005 | − | 19.2266i | −0.386704 | − | 0.669792i | ||||
\(825\) | −0.686292 | − | 1.18869i | −0.0238936 | − | 0.0413849i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −52.6690 | −1.83148 | −0.915741 | − | 0.401769i | \(-0.868396\pi\) | ||||
−0.915741 | + | 0.401769i | \(0.868396\pi\) | |||||||
\(828\) | 1.29289 | − | 2.23936i | 0.0449311 | − | 0.0778230i | ||||
\(829\) | 23.1569 | + | 40.1088i | 0.804271 | + | 1.39304i | 0.916782 | + | 0.399387i | \(0.130777\pi\) |
−0.112511 | + | 0.993650i | \(0.535889\pi\) | |||||||
\(830\) | 0.405592 | + | 0.702505i | 0.0140783 | + | 0.0243843i | ||||
\(831\) | 1.39340 | + | 2.41344i | 0.0483365 | + | 0.0837212i | ||||
\(832\) | −14.6005 | − | 3.61269i | −0.506181 | − | 0.125247i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 3.48528 | − | 6.03668i | 0.120685 | − | 0.209033i | ||||
\(835\) | −12.3015 | −0.425711 | ||||||||
\(836\) | 6.42641 | 0.222262 | ||||||||
\(837\) | 7.31371 | − | 12.6677i | 0.252799 | − | 0.437860i | ||||
\(838\) | −2.39340 | + | 4.14549i | −0.0826786 | + | 0.143203i | ||||
\(839\) | −20.7990 | − | 36.0249i | −0.718061 | − | 1.24372i | −0.961767 | − | 0.273869i | \(-0.911697\pi\) |
0.243706 | − | 0.969849i | \(-0.421637\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 5.79899 | + | 10.0441i | 0.199965 | + | 0.346350i | ||||
\(842\) | 8.89949 | 0.306697 | ||||||||
\(843\) | −12.3640 | − | 21.4150i | −0.425837 | − | 0.737572i | ||||
\(844\) | 22.6066 | − | 39.1558i | 0.778151 | − | 1.34780i | ||||
\(845\) | −0.914214 | − | 23.7520i | −0.0314499 | − | 0.817092i | ||||
\(846\) | −1.51472 | −0.0520771 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 4.50000 | − | 7.79423i | 0.154531 | − | 0.267655i | ||||
\(849\) | 14.0711 | − | 24.3718i | 0.482918 | − | 0.836438i | ||||
\(850\) | 2.00000 | − | 3.46410i | 0.0685994 | − | 0.118818i | ||||
\(851\) | 13.4142 | 0.459833 | ||||||||
\(852\) | 15.0711 | − | 26.1039i | 0.516326 | − | 0.894303i | ||||
\(853\) | 35.0000 | 1.19838 | 0.599189 | − | 0.800608i | \(-0.295490\pi\) | ||||
0.599189 | + | 0.800608i | \(0.295490\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −5.48528 | + | 9.50079i | −0.187593 | + | 0.324920i | ||||
\(856\) | −27.4558 | −0.938421 | ||||||||
\(857\) | 0.600505 | − | 1.04011i | 0.0205129 | − | 0.0355293i | −0.855587 | − | 0.517659i | \(-0.826803\pi\) |
0.876100 | + | 0.482130i | \(0.160137\pi\) | |||||||
\(858\) | 0.857864 | − | 0.891519i | 0.0292870 | − | 0.0304360i | ||||
\(859\) | −6.46447 | − | 11.1968i | −0.220565 | − | 0.382029i | 0.734415 | − | 0.678701i | \(-0.237457\pi\) |
−0.954980 | + | 0.296672i | \(0.904123\pi\) | |||||||
\(860\) | 5.70711 | − | 9.88500i | 0.194611 | − | 0.337076i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −2.48528 | − | 4.30463i | −0.0846490 | − | 0.146616i | ||||
\(863\) | 10.0919 | + | 17.4797i | 0.343532 | + | 0.595014i | 0.985086 | − | 0.172063i | \(-0.0550434\pi\) |
−0.641554 | + | 0.767078i | \(0.721710\pi\) | |||||||
\(864\) | 24.9706 | 0.849516 | ||||||||
\(865\) | 18.5442 | 0.630520 | ||||||||
\(866\) | 3.62132 | + | 6.27231i | 0.123057 | + | 0.213142i | ||||
\(867\) | 12.0000 | + | 20.7846i | 0.407541 | + | 0.705882i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −0.514719 | + | 0.891519i | −0.0174606 | + | 0.0302427i | ||||
\(870\) | 2.23402 | + | 3.86943i | 0.0757403 | + | 0.131186i | ||||
\(871\) | −4.24264 | − | 14.6969i | −0.143756 | − | 0.497987i | ||||
\(872\) | −10.8284 | + | 18.7554i | −0.366697 | + | 0.635138i | ||||
\(873\) | −10.8284 | −0.366487 | ||||||||
\(874\) | −1.75736 | + | 3.04384i | −0.0594436 | + | 0.102959i | ||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 27.5563 | 0.931043 | ||||||||
\(877\) | −8.50000 | + | 14.7224i | −0.287025 | + | 0.497141i | −0.973098 | − | 0.230391i | \(-0.925999\pi\) |
0.686074 | + | 0.727532i | \(0.259333\pi\) | |||||||
\(878\) | 0.526912 | 0.0177824 | ||||||||
\(879\) | −20.1213 | + | 34.8511i | −0.678675 | + | 1.17550i | ||||
\(880\) | −1.60660 | + | 2.78272i | −0.0541585 | + | 0.0938053i | ||||
\(881\) | 2.22792 | − | 3.85887i | 0.0750606 | − | 0.130009i | −0.826052 | − | 0.563594i | \(-0.809418\pi\) |
0.901113 | + | 0.433585i | \(0.142752\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 56.0416 | 1.88595 | 0.942976 | − | 0.332862i | \(-0.108014\pi\) | ||||
0.942976 | + | 0.332862i | \(0.108014\pi\) | |||||||
\(884\) | −37.2990 | − | 9.22911i | −1.25450 | − | 0.310408i | ||||
\(885\) | 13.2426 | − | 22.9369i | 0.445146 | − | 0.771016i | ||||
\(886\) | −5.31371 | − | 9.20361i | −0.178518 | − | 0.309201i | ||||
\(887\) | 34.6274 | 1.16267 | 0.581337 | − | 0.813663i | \(-0.302530\pi\) | ||||
0.581337 | + | 0.813663i | \(0.302530\pi\) | |||||||
\(888\) | 10.6360 | + | 18.4222i | 0.356922 | + | 0.618207i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 5.79899 | + | 10.0441i | 0.194383 | + | 0.336681i | ||||
\(891\) | 1.46447 | − | 2.53653i | 0.0490615 | − | 0.0849769i | ||||
\(892\) | −1.82843 | + | 3.16693i | −0.0612203 | + | 0.106037i | ||||
\(893\) | −21.9411 | −0.734232 | ||||||||
\(894\) | −1.75736 | −0.0587749 | ||||||||
\(895\) | 5.17157 | − | 8.95743i | 0.172867 | − | 0.299414i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −2.00000 | − | 6.92820i | −0.0667781 | − | 0.231326i | ||||
\(898\) | −6.72792 | − | 11.6531i | −0.224514 | − | 0.388869i | ||||
\(899\) | 5.39340 | + | 9.34164i | 0.179880 | + | 0.311561i | ||||
\(900\) | 1.51472 | + | 2.62357i | 0.0504906 | + | 0.0874523i | ||||
\(901\) | 8.74264 | − | 15.1427i | 0.291260 | − | 0.504476i | ||||
\(902\) | −0.0416306 | −0.00138615 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 16.1066 | + | 27.8975i | 0.535698 | + | 0.927855i | ||||
\(905\) | 8.35786 | + | 14.4762i | 0.277825 | + | 0.481207i | ||||
\(906\) | −8.76955 | −0.291349 | ||||||||
\(907\) | 3.36396 | + | 5.82655i | 0.111698 | + | 0.193467i | 0.916455 | − | 0.400137i | \(-0.131038\pi\) |
−0.804757 | + | 0.593605i | \(0.797704\pi\) | |||||||
\(908\) | 10.7868 | 0.357972 | ||||||||
\(909\) | 14.6569 | 0.486137 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −29.6569 | −0.982575 | −0.491288 | − | 0.870997i | \(-0.663474\pi\) | ||||
−0.491288 | + | 0.870997i | \(0.663474\pi\) | |||||||
\(912\) | 25.4558 | 0.842927 | ||||||||
\(913\) | 0.313708 | + | 0.543359i | 0.0103822 | + | 0.0179826i | ||||
\(914\) | −10.3553 | −0.342524 | ||||||||
\(915\) | −5.39340 | − | 9.34164i | −0.178300 | − | 0.308825i | ||||
\(916\) | 11.4142 | + | 19.7700i | 0.377136 | + | 0.653219i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 13.6569 | 0.450743 | ||||||||
\(919\) | −1.34315 | + | 2.32640i | −0.0443063 | + | 0.0767407i | −0.887328 | − | 0.461139i | \(-0.847441\pi\) |
0.843022 | + | 0.537879i | \(0.180774\pi\) | |||||||
\(920\) | −2.05025 | − | 3.55114i | −0.0675948 | − | 0.117078i | ||||
\(921\) | 23.1421 | + | 40.0834i | 0.762559 | + | 1.32079i | ||||
\(922\) | 0.278175 | + | 0.481813i | 0.00916119 | + | 0.0158677i | ||||
\(923\) | 11.6569 | + | 40.3805i | 0.383690 | + | 1.32914i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.85786 | + | 13.6102i | −0.258365 | + | 0.447501i | ||||
\(926\) | 2.78680 | 0.0915798 | ||||||||
\(927\) | 14.0000 | 0.459820 | ||||||||
\(928\) | −9.20711 | + | 15.9472i | −0.302238 | + | 0.523492i | ||||
\(929\) | 24.4706 | − | 42.3843i | 0.802853 | − | 1.39058i | −0.114878 | − | 0.993380i | \(-0.536648\pi\) |
0.917731 | − | 0.397203i | \(-0.130019\pi\) | |||||||
\(930\) | −1.38478 | − | 2.39850i | −0.0454086 | − | 0.0786500i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 2.58579 | + | 4.47871i | 0.0847003 | + | 0.146705i | ||||
\(933\) | −18.2843 | −0.598600 | ||||||||
\(934\) | 2.36396 | + | 4.09450i | 0.0773512 | + | 0.133976i | ||||
\(935\) | −3.12132 | + | 5.40629i | −0.102078 | + | 0.176804i | ||||
\(936\) | −3.96447 | + | 4.11999i | −0.129583 | + | 0.134666i | ||||
\(937\) | 37.1421 | 1.21338 | 0.606690 | − | 0.794938i | \(-0.292497\pi\) | ||||
0.606690 | + | 0.794938i | \(0.292497\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 9.89949 | − | 17.1464i | 0.323058 | − | 0.559553i | ||||
\(940\) | 6.11270 | − | 10.5875i | 0.199374 | − | 0.345326i | ||||
\(941\) | 26.4853 | − | 45.8739i | 0.863395 | − | 1.49544i | −0.00523607 | − | 0.999986i | \(-0.501667\pi\) |
0.868632 | − | 0.495459i | \(-0.165000\pi\) | |||||||
\(942\) | 3.21320 | 0.104692 | ||||||||
\(943\) | −0.121320 | + | 0.210133i | −0.00395073 | + | 0.00684287i | ||||
\(944\) | 30.7279 | 1.00011 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −0.414214 | + | 0.717439i | −0.0134672 | + | 0.0233260i | ||||
\(947\) | 21.4142 | 0.695868 | 0.347934 | − | 0.937519i | \(-0.386883\pi\) | ||||
0.347934 | + | 0.937519i | \(0.386883\pi\) | |||||||
\(948\) | −2.27208 | + | 3.93535i | −0.0737937 | + | 0.127814i | ||||
\(949\) | −26.6421 | + | 27.6873i | −0.864840 | + | 0.898768i | ||||
\(950\) | −2.05887 | − | 3.56608i | −0.0667987 | − | 0.115699i | ||||
\(951\) | 23.0919 | − | 39.9963i | 0.748806 | − | 1.29697i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −3.31371 | − | 5.73951i | −0.107342 | − | 0.185921i | 0.807351 | − | 0.590072i | \(-0.200900\pi\) |
−0.914692 | + | 0.404151i | \(0.867567\pi\) | |||||||
\(954\) | −0.621320 | − | 1.07616i | −0.0201160 | − | 0.0348419i | ||||
\(955\) | 29.6985 | 0.961020 | ||||||||
\(956\) | −44.5858 | −1.44201 | ||||||||
\(957\) | 1.72792 | + | 2.99285i | 0.0558558 | + | 0.0967451i | ||||
\(958\) | −0.334524 | − | 0.579412i | −0.0108080 | − | 0.0187200i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −5.39340 | + | 9.34164i | −0.174071 | + | 0.301500i | ||||
\(961\) | 12.1569 | + | 21.0563i | 0.392157 | + | 0.679235i | ||||
\(962\) | −13.7513 | − | 3.40256i | −0.443359 | − | 0.109703i | ||||
\(963\) | 8.65685 | − | 14.9941i | 0.278963 | − | 0.483178i | ||||
\(964\) | 28.3137 | 0.911923 | ||||||||
\(965\) | −6.52944 | + | 11.3093i | −0.210190 | + | 0.364060i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −19.7574 | −0.635354 | −0.317677 | − | 0.948199i | \(-0.602903\pi\) | ||||
−0.317677 | + | 0.948199i | \(0.602903\pi\) | |||||||
\(968\) | −8.44975 | + | 14.6354i | −0.271585 | + | 0.470399i | ||||
\(969\) | 49.4558 | 1.58875 | ||||||||
\(970\) | −4.10051 | + | 7.10228i | −0.131659 | + | 0.228041i | ||||
\(971\) | 25.8284 | − | 44.7361i | 0.828874 | − | 1.43565i | −0.0700488 | − | 0.997544i | \(-0.522315\pi\) |
0.898922 | − | 0.438108i | \(-0.144351\pi\) | |||||||
\(972\) | −9.05025 | + | 15.6755i | −0.290287 | + | 0.502792i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −5.37258 | −0.172149 | ||||||||
\(975\) | 8.20101 | + | 2.02922i | 0.262643 | + | 0.0649872i | ||||
\(976\) | 6.25736 | − | 10.8381i | 0.200293 | − | 0.346918i | ||||
\(977\) | −15.2990 | − | 26.4986i | −0.489458 | − | 0.847766i | 0.510468 | − | 0.859897i | \(-0.329472\pi\) |
−0.999926 | + | 0.0121303i | \(0.996139\pi\) | |||||||
\(978\) | −7.37258 | −0.235749 | ||||||||
\(979\) | 4.48528 | + | 7.76874i | 0.143350 | + | 0.248290i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −6.82843 | − | 11.8272i | −0.218015 | − | 0.377613i | ||||
\(982\) | −2.62742 | + | 4.55082i | −0.0838442 | + | 0.145222i | ||||
\(983\) | −21.0000 | + | 36.3731i | −0.669796 | + | 1.16012i | 0.308165 | + | 0.951333i | \(0.400285\pi\) |
−0.977961 | + | 0.208788i | \(0.933048\pi\) | |||||||
\(984\) | −0.384776 | −0.0122662 | ||||||||
\(985\) | 27.1127 | 0.863882 | ||||||||
\(986\) | −5.03553 | + | 8.72180i | −0.160364 | + | 0.277759i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −27.4264 | + | 28.5024i | −0.872550 | + | 0.906781i | ||||
\(989\) | 2.41421 | + | 4.18154i | 0.0767675 | + | 0.132965i | ||||
\(990\) | 0.221825 | + | 0.384213i | 0.00705007 | + | 0.0122111i | ||||
\(991\) | −9.87868 | − | 17.1104i | −0.313807 | − | 0.543529i | 0.665376 | − | 0.746508i | \(-0.268271\pi\) |
−0.979183 | + | 0.202979i | \(0.934938\pi\) | |||||||
\(992\) | 5.70711 | − | 9.88500i | 0.181201 | − | 0.313849i | ||||
\(993\) | 35.1716 | 1.11614 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −13.6863 | − | 23.7054i | −0.433885 | − | 0.751510i | ||||
\(996\) | 1.38478 | + | 2.39850i | 0.0438783 | + | 0.0759995i | ||||
\(997\) | −13.9706 | −0.442452 | −0.221226 | − | 0.975223i | \(-0.571006\pi\) | ||||
−0.221226 | + | 0.975223i | \(0.571006\pi\) | |||||||
\(998\) | −4.15076 | − | 7.18932i | −0.131390 | − | 0.227574i | ||||
\(999\) | −53.6569 | −1.69763 |
(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 | 637.2.h.c.165.2 | 4 | ||
7.2 | even | 3 | 637.2.g.g.373.1 | 4 | |||
7.3 | odd | 6 | 637.2.f.f.295.1 | yes | 4 | ||
7.4 | even | 3 | 637.2.f.e.295.1 | ✓ | 4 | ||
7.5 | odd | 6 | 637.2.g.f.373.1 | 4 | |||
7.6 | odd | 2 | 637.2.h.b.165.2 | 4 | |||
13.3 | even | 3 | 637.2.g.g.263.1 | 4 | |||
91.3 | odd | 6 | 637.2.f.f.393.1 | yes | 4 | ||
91.4 | even | 6 | 8281.2.a.y.1.1 | 2 | |||
91.16 | even | 3 | inner | 637.2.h.c.471.2 | 4 | ||
91.17 | odd | 6 | 8281.2.a.x.1.1 | 2 | |||
91.55 | odd | 6 | 637.2.g.f.263.1 | 4 | |||
91.68 | odd | 6 | 637.2.h.b.471.2 | 4 | |||
91.74 | even | 3 | 8281.2.a.o.1.2 | 2 | |||
91.81 | even | 3 | 637.2.f.e.393.1 | yes | 4 | ||
91.87 | odd | 6 | 8281.2.a.p.1.2 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
637.2.f.e.295.1 | ✓ | 4 | 7.4 | even | 3 | ||
637.2.f.e.393.1 | yes | 4 | 91.81 | even | 3 | ||
637.2.f.f.295.1 | yes | 4 | 7.3 | odd | 6 | ||
637.2.f.f.393.1 | yes | 4 | 91.3 | odd | 6 | ||
637.2.g.f.263.1 | 4 | 91.55 | odd | 6 | |||
637.2.g.f.373.1 | 4 | 7.5 | odd | 6 | |||
637.2.g.g.263.1 | 4 | 13.3 | even | 3 | |||
637.2.g.g.373.1 | 4 | 7.2 | even | 3 | |||
637.2.h.b.165.2 | 4 | 7.6 | odd | 2 | |||
637.2.h.b.471.2 | 4 | 91.68 | odd | 6 | |||
637.2.h.c.165.2 | 4 | 1.1 | even | 1 | trivial | ||
637.2.h.c.471.2 | 4 | 91.16 | even | 3 | inner | ||
8281.2.a.o.1.2 | 2 | 91.74 | even | 3 | |||
8281.2.a.p.1.2 | 2 | 91.87 | odd | 6 | |||
8281.2.a.x.1.1 | 2 | 91.17 | odd | 6 | |||
8281.2.a.y.1.1 | 2 | 91.4 | even | 6 |