Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [441,2,Mod(148,441)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(441, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("441.148");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 441 = 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 441.f (of order \(3\), 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: | \(3.52140272914\) |
Analytic rank: | \(0\) |
Dimension: | \(24\) |
Relative dimension: | \(12\) over \(\Q(\zeta_{3})\) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 148.7 | ||
Character | \(\chi\) | \(=\) | 441.148 |
Dual form | 441.2.f.h.295.7 |
$q$-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 \(\left(\mathbb{Z}/441\mathbb{Z}\right)^\times\).
\(n\) | \(199\) | \(344\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0.551407 | + | 0.955065i | 0.389903 | + | 0.675333i | 0.992436 | − | 0.122762i | \(-0.0391750\pi\) |
−0.602533 | + | 0.798094i | \(0.705842\pi\) | |||||||
\(3\) | −1.67475 | + | 0.441824i | −0.966918 | + | 0.255087i | ||||
\(4\) | 0.391901 | − | 0.678793i | 0.195951 | − | 0.339396i | ||||
\(5\) | 0.0527330 | − | 0.0913363i | 0.0235829 | − | 0.0408468i | −0.853993 | − | 0.520284i | \(-0.825826\pi\) |
0.877576 | + | 0.479438i | \(0.159159\pi\) | |||||||
\(6\) | −1.34544 | − | 1.35587i | −0.549273 | − | 0.553532i | ||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 3.07001 | 1.08541 | ||||||||
\(9\) | 2.60958 | − | 1.47989i | 0.869861 | − | 0.493297i | ||||
\(10\) | 0.116309 | 0.0367803 | ||||||||
\(11\) | −1.66866 | − | 2.89020i | −0.503119 | − | 0.871428i | −0.999994 | − | 0.00360543i | \(-0.998852\pi\) |
0.496874 | − | 0.867822i | \(-0.334481\pi\) | |||||||
\(12\) | −0.356430 | + | 1.30996i | −0.102892 | + | 0.378153i | ||||
\(13\) | 1.23997 | − | 2.14770i | 0.343907 | − | 0.595664i | −0.641248 | − | 0.767334i | \(-0.721583\pi\) |
0.985155 | + | 0.171670i | \(0.0549162\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −0.0479602 | + | 0.176264i | −0.0123833 | + | 0.0455113i | ||||
\(16\) | 0.909025 | + | 1.57448i | 0.227256 | + | 0.393619i | ||||
\(17\) | −1.61319 | −0.391255 | −0.195628 | − | 0.980678i | \(-0.562674\pi\) | ||||
−0.195628 | + | 0.980678i | \(0.562674\pi\) | |||||||
\(18\) | 2.85233 | + | 1.67630i | 0.672301 | + | 0.395107i | ||||
\(19\) | 7.68266 | 1.76252 | 0.881262 | − | 0.472629i | \(-0.156695\pi\) | ||||
0.881262 | + | 0.472629i | \(0.156695\pi\) | |||||||
\(20\) | −0.0413323 | − | 0.0715896i | −0.00924218 | − | 0.0160079i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 1.84022 | − | 3.18735i | 0.392336 | − | 0.679546i | ||||
\(23\) | 0.948593 | − | 1.64301i | 0.197795 | − | 0.342592i | −0.750018 | − | 0.661417i | \(-0.769955\pi\) |
0.947813 | + | 0.318826i | \(0.103289\pi\) | |||||||
\(24\) | −5.14151 | + | 1.35641i | −1.04951 | + | 0.276875i | ||||
\(25\) | 2.49444 | + | 4.32049i | 0.498888 | + | 0.864099i | ||||
\(26\) | 2.73492 | 0.536362 | ||||||||
\(27\) | −3.71655 | + | 3.63142i | −0.715251 | + | 0.698868i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 4.64521 | + | 8.04574i | 0.862594 | + | 1.49406i | 0.869416 | + | 0.494080i | \(0.164495\pi\) |
−0.00682200 | + | 0.999977i | \(0.502172\pi\) | |||||||
\(30\) | −0.194789 | + | 0.0513883i | −0.0355635 | + | 0.00938218i | ||||
\(31\) | 4.63081 | − | 8.02080i | 0.831718 | − | 1.44058i | −0.0649574 | − | 0.997888i | \(-0.520691\pi\) |
0.896675 | − | 0.442689i | \(-0.145976\pi\) | |||||||
\(32\) | 2.06753 | − | 3.58107i | 0.365491 | − | 0.633049i | ||||
\(33\) | 4.07155 | + | 4.10311i | 0.708765 | + | 0.714260i | ||||
\(34\) | −0.889523 | − | 1.54070i | −0.152552 | − | 0.264228i | ||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0.0181599 | − | 2.35134i | 0.00302665 | − | 0.391889i | ||||
\(37\) | −1.98254 | −0.325927 | −0.162963 | − | 0.986632i | \(-0.552105\pi\) | ||||
−0.162963 | + | 0.986632i | \(0.552105\pi\) | |||||||
\(38\) | 4.23627 | + | 7.33744i | 0.687214 | + | 1.19029i | ||||
\(39\) | −1.12774 | + | 4.14471i | −0.180583 | + | 0.663684i | ||||
\(40\) | 0.161891 | − | 0.280404i | 0.0255973 | − | 0.0443357i | ||||
\(41\) | −3.74268 | + | 6.48252i | −0.584509 | + | 1.01240i | 0.410427 | + | 0.911893i | \(0.365379\pi\) |
−0.994936 | + | 0.100506i | \(0.967954\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −3.77388 | − | 6.53655i | −0.575512 | − | 0.996815i | −0.995986 | − | 0.0895108i | \(-0.971470\pi\) |
0.420474 | − | 0.907304i | \(-0.361864\pi\) | |||||||
\(44\) | −2.61579 | −0.394346 | ||||||||
\(45\) | 0.00244354 | − | 0.316389i | 0.000364262 | − | 0.0471645i | ||||
\(46\) | 2.09224 | 0.308484 | ||||||||
\(47\) | −1.59780 | − | 2.76747i | −0.233063 | − | 0.403677i | 0.725645 | − | 0.688070i | \(-0.241542\pi\) |
−0.958708 | + | 0.284392i | \(0.908208\pi\) | |||||||
\(48\) | −2.21803 | − | 2.23523i | −0.320145 | − | 0.322627i | ||||
\(49\) | 0 | 0 | ||||||||
\(50\) | −2.75090 | + | 4.76470i | −0.389036 | + | 0.673830i | ||||
\(51\) | 2.70169 | − | 0.712745i | 0.378312 | − | 0.0998042i | ||||
\(52\) | −0.971894 | − | 1.68337i | −0.134777 | − | 0.233441i | ||||
\(53\) | −9.97679 | −1.37042 | −0.685209 | − | 0.728347i | \(-0.740289\pi\) | ||||
−0.685209 | + | 0.728347i | \(0.740289\pi\) | |||||||
\(54\) | −5.51758 | − | 1.54715i | −0.750847 | − | 0.210541i | ||||
\(55\) | −0.351974 | −0.0474601 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −12.8665 | + | 3.39438i | −1.70422 | + | 0.449597i | ||||
\(58\) | −5.12280 | + | 8.87296i | −0.672657 | + | 1.16508i | ||||
\(59\) | 2.22993 | − | 3.86235i | 0.290312 | − | 0.502836i | −0.683571 | − | 0.729884i | \(-0.739574\pi\) |
0.973884 | + | 0.227048i | \(0.0729075\pi\) | |||||||
\(60\) | 0.100851 | + | 0.101633i | 0.0130198 | + | 0.0131208i | ||||
\(61\) | −2.83550 | − | 4.91123i | −0.363048 | − | 0.628818i | 0.625413 | − | 0.780294i | \(-0.284931\pi\) |
−0.988461 | + | 0.151476i | \(0.951597\pi\) | |||||||
\(62\) | 10.2138 | 1.29716 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 8.19630 | 1.02454 | ||||||||
\(65\) | −0.130775 | − | 0.226509i | −0.0162207 | − | 0.0280950i | ||||
\(66\) | −1.67366 | + | 6.15107i | −0.206013 | + | 0.757145i | ||||
\(67\) | −4.98571 | + | 8.63550i | −0.609101 | + | 1.05499i | 0.382288 | + | 0.924043i | \(0.375136\pi\) |
−0.991389 | + | 0.130951i | \(0.958197\pi\) | |||||||
\(68\) | −0.632210 | + | 1.09502i | −0.0766667 | + | 0.132791i | ||||
\(69\) | −0.862736 | + | 3.17075i | −0.103861 | + | 0.381713i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | 3.29042 | 0.390502 | 0.195251 | − | 0.980753i | \(-0.437448\pi\) | ||||
0.195251 | + | 0.980753i | \(0.437448\pi\) | |||||||
\(72\) | 8.01146 | − | 4.54329i | 0.944160 | − | 0.535431i | ||||
\(73\) | 4.72378 | 0.552877 | 0.276438 | − | 0.961032i | \(-0.410846\pi\) | ||||
0.276438 | + | 0.961032i | \(0.410846\pi\) | |||||||
\(74\) | −1.09318 | − | 1.89345i | −0.127080 | − | 0.220109i | ||||
\(75\) | −6.08646 | − | 6.13365i | −0.702804 | − | 0.708253i | ||||
\(76\) | 3.01084 | − | 5.21493i | 0.345367 | − | 0.598194i | ||||
\(77\) | 0 | 0 | ||||||||
\(78\) | −4.58031 | + | 1.20835i | −0.518618 | + | 0.136819i | ||||
\(79\) | −3.84705 | − | 6.66328i | −0.432827 | − | 0.749678i | 0.564289 | − | 0.825577i | \(-0.309150\pi\) |
−0.997115 | + | 0.0758997i | \(0.975817\pi\) | |||||||
\(80\) | 0.191743 | 0.0214375 | ||||||||
\(81\) | 4.61985 | − | 7.72379i | 0.513317 | − | 0.858199i | ||||
\(82\) | −8.25496 | −0.911608 | ||||||||
\(83\) | 0.584428 | + | 1.01226i | 0.0641493 | + | 0.111110i | 0.896316 | − | 0.443415i | \(-0.146233\pi\) |
−0.832167 | + | 0.554525i | \(0.812900\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.0850683 | + | 0.147343i | −0.00922695 | + | 0.0159815i | ||||
\(86\) | 4.16189 | − | 7.20860i | 0.448788 | − | 0.777323i | ||||
\(87\) | −11.3344 | − | 11.4223i | −1.21517 | − | 1.22459i | ||||
\(88\) | −5.12280 | − | 8.87296i | −0.546093 | − | 0.945860i | ||||
\(89\) | −6.02954 | −0.639130 | −0.319565 | − | 0.947564i | \(-0.603537\pi\) | ||||
−0.319565 | + | 0.947564i | \(0.603537\pi\) | |||||||
\(90\) | 0.303519 | − | 0.172125i | 0.0319937 | − | 0.0181436i | ||||
\(91\) | 0 | 0 | ||||||||
\(92\) | −0.743509 | − | 1.28780i | −0.0775162 | − | 0.134262i | ||||
\(93\) | −4.21167 | + | 15.4788i | −0.436730 | + | 1.60508i | ||||
\(94\) | 1.76208 | − | 3.05201i | 0.181744 | − | 0.314791i | ||||
\(95\) | 0.405130 | − | 0.701706i | 0.0415655 | − | 0.0719935i | ||||
\(96\) | −1.88040 | + | 6.91088i | −0.191917 | + | 0.705339i | ||||
\(97\) | 1.90127 | + | 3.29310i | 0.193045 | + | 0.334364i | 0.946258 | − | 0.323413i | \(-0.104830\pi\) |
−0.753213 | + | 0.657777i | \(0.771497\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −8.63168 | − | 5.07279i | −0.867516 | − | 0.509834i | ||||
\(100\) | 3.91029 | 0.391029 | ||||||||
\(101\) | 8.73512 | + | 15.1297i | 0.869177 | + | 1.50546i | 0.862839 | + | 0.505479i | \(0.168684\pi\) |
0.00633771 | + | 0.999980i | \(0.497983\pi\) | |||||||
\(102\) | 2.17045 | + | 2.18727i | 0.214906 | + | 0.216572i | ||||
\(103\) | −4.36602 | + | 7.56217i | −0.430197 | + | 0.745123i | −0.996890 | − | 0.0788062i | \(-0.974889\pi\) |
0.566693 | + | 0.823929i | \(0.308223\pi\) | |||||||
\(104\) | 3.80674 | − | 6.59346i | 0.373281 | − | 0.646542i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.50127 | − | 9.52848i | −0.534330 | − | 0.925487i | ||||
\(107\) | −18.1463 | −1.75427 | −0.877135 | − | 0.480244i | \(-0.840548\pi\) | ||||
−0.877135 | + | 0.480244i | \(0.840548\pi\) | |||||||
\(108\) | 1.00846 | + | 3.94593i | 0.0970394 | + | 0.379697i | ||||
\(109\) | −4.22248 | −0.404440 | −0.202220 | − | 0.979340i | \(-0.564816\pi\) | ||||
−0.202220 | + | 0.979340i | \(0.564816\pi\) | |||||||
\(110\) | −0.194081 | − | 0.336157i | −0.0185049 | − | 0.0320514i | ||||
\(111\) | 3.32025 | − | 0.875932i | 0.315145 | − | 0.0831398i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 1.02824 | − | 1.78096i | 0.0967285 | − | 0.167539i | −0.813600 | − | 0.581425i | \(-0.802495\pi\) |
0.910329 | + | 0.413886i | \(0.135829\pi\) | |||||||
\(114\) | −10.3366 | − | 10.4167i | −0.968107 | − | 0.975613i | ||||
\(115\) | −0.100044 | − | 0.173282i | −0.00932919 | − | 0.0161586i | ||||
\(116\) | 7.28186 | 0.676103 | ||||||||
\(117\) | 0.0574579 | − | 7.43962i | 0.00531198 | − | 0.687793i | ||||
\(118\) | 4.91840 | 0.452775 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | −0.147238 | + | 0.541134i | −0.0134410 | + | 0.0493986i | ||||
\(121\) | −0.0688352 | + | 0.119226i | −0.00625774 | + | 0.0108387i | ||||
\(122\) | 3.12703 | − | 5.41617i | 0.283108 | − | 0.490357i | ||||
\(123\) | 3.40393 | − | 12.5102i | 0.306922 | − | 1.12801i | ||||
\(124\) | −3.62964 | − | 6.28672i | −0.325951 | − | 0.564564i | ||||
\(125\) | 1.05349 | 0.0942268 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 0.317159 | 0.0281433 | 0.0140717 | − | 0.999901i | \(-0.495521\pi\) | ||||
0.0140717 | + | 0.999901i | \(0.495521\pi\) | |||||||
\(128\) | 0.384435 | + | 0.665862i | 0.0339796 | + | 0.0588544i | ||||
\(129\) | 9.20832 | + | 9.27971i | 0.810747 | + | 0.817033i | ||||
\(130\) | 0.144221 | − | 0.249797i | 0.0126490 | − | 0.0219087i | ||||
\(131\) | −7.47816 | + | 12.9525i | −0.653370 | + | 1.13167i | 0.328930 | + | 0.944354i | \(0.393312\pi\) |
−0.982300 | + | 0.187315i | \(0.940021\pi\) | |||||||
\(132\) | 4.38081 | − | 1.15572i | 0.381300 | − | 0.100593i | ||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −10.9966 | −0.949962 | ||||||||
\(135\) | 0.135696 | + | 0.530952i | 0.0116788 | + | 0.0456971i | ||||
\(136\) | −4.95251 | −0.424674 | ||||||||
\(137\) | 7.62367 | + | 13.2046i | 0.651334 | + | 1.12814i | 0.982799 | + | 0.184676i | \(0.0591235\pi\) |
−0.331466 | + | 0.943467i | \(0.607543\pi\) | |||||||
\(138\) | −3.50399 | + | 0.924403i | −0.298279 | + | 0.0786904i | ||||
\(139\) | 4.05943 | − | 7.03114i | 0.344316 | − | 0.596374i | −0.640913 | − | 0.767614i | \(-0.721444\pi\) |
0.985229 | + | 0.171240i | \(0.0547774\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 3.89866 | + | 3.92888i | 0.328326 | + | 0.330872i | ||||
\(142\) | 1.81436 | + | 3.14257i | 0.152258 | + | 0.263718i | ||||
\(143\) | −8.27636 | −0.692104 | ||||||||
\(144\) | 4.70223 | + | 2.76347i | 0.391852 | + | 0.230289i | ||||
\(145\) | 0.979825 | 0.0813700 | ||||||||
\(146\) | 2.60473 | + | 4.51152i | 0.215569 | + | 0.373376i | ||||
\(147\) | 0 | 0 | ||||||||
\(148\) | −0.776958 | + | 1.34573i | −0.0638656 | + | 0.110618i | ||||
\(149\) | 5.57430 | − | 9.65497i | 0.456664 | − | 0.790966i | −0.542118 | − | 0.840303i | \(-0.682377\pi\) |
0.998782 | + | 0.0493365i | \(0.0157107\pi\) | |||||||
\(150\) | 2.50192 | − | 9.19510i | 0.204281 | − | 0.750777i | ||||
\(151\) | 5.63676 | + | 9.76315i | 0.458713 | + | 0.794514i | 0.998893 | − | 0.0470354i | \(-0.0149774\pi\) |
−0.540180 | + | 0.841549i | \(0.681644\pi\) | |||||||
\(152\) | 23.5859 | 1.91307 | ||||||||
\(153\) | −4.20975 | + | 2.38734i | −0.340338 | + | 0.193005i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −0.488393 | − | 0.845922i | −0.0392287 | − | 0.0679461i | ||||
\(156\) | 2.37143 | + | 2.38982i | 0.189867 | + | 0.191339i | ||||
\(157\) | −6.10318 | + | 10.5710i | −0.487087 | + | 0.843659i | −0.999890 | − | 0.0148476i | \(-0.995274\pi\) |
0.512803 | + | 0.858506i | \(0.328607\pi\) | |||||||
\(158\) | 4.24258 | − | 7.34836i | 0.337521 | − | 0.584604i | ||||
\(159\) | 16.7086 | − | 4.40798i | 1.32508 | − | 0.349576i | ||||
\(160\) | −0.218054 | − | 0.377681i | −0.0172387 | − | 0.0298583i | ||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 9.92414 | + | 0.153302i | 0.779714 | + | 0.0120445i | ||||
\(163\) | 8.96264 | 0.702008 | 0.351004 | − | 0.936374i | \(-0.385840\pi\) | ||||
0.351004 | + | 0.936374i | \(0.385840\pi\) | |||||||
\(164\) | 2.93352 | + | 5.08101i | 0.229070 | + | 0.396760i | ||||
\(165\) | 0.589468 | − | 0.155510i | 0.0458900 | − | 0.0121065i | ||||
\(166\) | −0.644515 | + | 1.11633i | −0.0500240 | + | 0.0866442i | ||||
\(167\) | −8.70833 | + | 15.0833i | −0.673871 | + | 1.16718i | 0.302927 | + | 0.953014i | \(0.402036\pi\) |
−0.976798 | + | 0.214165i | \(0.931297\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 3.42493 | + | 5.93216i | 0.263456 | + | 0.456320i | ||||
\(170\) | −0.187629 | −0.0143905 | ||||||||
\(171\) | 20.0485 | − | 11.3695i | 1.53315 | − | 0.869447i | ||||
\(172\) | −5.91595 | −0.451087 | ||||||||
\(173\) | −1.41466 | − | 2.45027i | −0.107555 | − | 0.186291i | 0.807224 | − | 0.590245i | \(-0.200969\pi\) |
−0.914779 | + | 0.403954i | \(0.867635\pi\) | |||||||
\(174\) | 4.65914 | − | 17.1234i | 0.353208 | − | 1.29812i | ||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 3.03370 | − | 5.25453i | 0.228674 | − | 0.396075i | ||||
\(177\) | −2.02810 | + | 7.45372i | −0.152441 | + | 0.560256i | ||||
\(178\) | −3.32473 | − | 5.75860i | −0.249199 | − | 0.431625i | ||||
\(179\) | −10.1627 | −0.759595 | −0.379798 | − | 0.925070i | \(-0.624006\pi\) | ||||
−0.379798 | + | 0.925070i | \(0.624006\pi\) | |||||||
\(180\) | −0.213805 | − | 0.125652i | −0.0159361 | − | 0.00936553i | ||||
\(181\) | −17.0870 | −1.27006 | −0.635032 | − | 0.772486i | \(-0.719013\pi\) | ||||
−0.635032 | + | 0.772486i | \(0.719013\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 6.91865 | + | 6.97229i | 0.511441 | + | 0.515407i | ||||
\(184\) | 2.91220 | − | 5.04407i | 0.214690 | − | 0.371854i | ||||
\(185\) | −0.104545 | + | 0.181078i | −0.00768631 | + | 0.0133131i | ||||
\(186\) | −17.1056 | + | 4.51272i | −1.25425 | + | 0.330888i | ||||
\(187\) | 2.69186 | + | 4.66243i | 0.196848 | + | 0.340951i | ||||
\(188\) | −2.50472 | −0.182676 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0.893566 | 0.0648261 | ||||||||
\(191\) | 11.2000 | + | 19.3990i | 0.810404 | + | 1.40366i | 0.912582 | + | 0.408894i | \(0.134086\pi\) |
−0.102178 | + | 0.994766i | \(0.532581\pi\) | |||||||
\(192\) | −13.7268 | + | 3.62132i | −0.990644 | + | 0.261346i | ||||
\(193\) | 0.128393 | − | 0.222383i | 0.00924194 | − | 0.0160075i | −0.861367 | − | 0.507982i | \(-0.830391\pi\) |
0.870609 | + | 0.491975i | \(0.163725\pi\) | |||||||
\(194\) | −2.09675 | + | 3.63168i | −0.150538 | + | 0.260739i | ||||
\(195\) | 0.319093 | + | 0.321567i | 0.0228507 | + | 0.0230279i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −0.763370 | −0.0543878 | −0.0271939 | − | 0.999630i | \(-0.508657\pi\) | ||||
−0.0271939 | + | 0.999630i | \(0.508657\pi\) | |||||||
\(198\) | 0.0852720 | − | 11.0410i | 0.00606002 | − | 0.784648i | ||||
\(199\) | −5.03121 | −0.356653 | −0.178327 | − | 0.983971i | \(-0.557068\pi\) | ||||
−0.178327 | + | 0.983971i | \(0.557068\pi\) | |||||||
\(200\) | 7.65796 | + | 13.2640i | 0.541500 | + | 0.937905i | ||||
\(201\) | 4.53445 | − | 16.6651i | 0.319835 | − | 1.17547i | ||||
\(202\) | −9.63321 | + | 16.6852i | −0.677790 | + | 1.17397i | ||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0.574988 | − | 2.11321i | 0.0402572 | − | 0.147954i | ||||
\(205\) | 0.394726 | + | 0.683686i | 0.0275689 | + | 0.0477507i | ||||
\(206\) | −9.62981 | −0.670941 | ||||||||
\(207\) | 0.0439559 | − | 5.69139i | 0.00305515 | − | 0.395579i | ||||
\(208\) | 4.50867 | 0.312620 | ||||||||
\(209\) | −12.8197 | − | 22.2044i | −0.886759 | − | 1.53591i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −3.60537 | + | 6.24468i | −0.248204 | + | 0.429901i | −0.963027 | − | 0.269403i | \(-0.913174\pi\) |
0.714824 | + | 0.699305i | \(0.246507\pi\) | |||||||
\(212\) | −3.90991 | + | 6.77217i | −0.268534 | + | 0.465114i | ||||
\(213\) | −5.51064 | + | 1.45379i | −0.377583 | + | 0.0996119i | ||||
\(214\) | −10.0060 | − | 17.3309i | −0.683996 | − | 1.18472i | ||||
\(215\) | −0.796033 | −0.0542890 | ||||||||
\(216\) | −11.4099 | + | 11.1485i | −0.776343 | + | 0.758561i | ||||
\(217\) | 0 | 0 | ||||||||
\(218\) | −2.32831 | − | 4.03274i | −0.157693 | − | 0.273132i | ||||
\(219\) | −7.91116 | + | 2.08708i | −0.534587 | + | 0.141032i | ||||
\(220\) | −0.137939 | + | 0.238917i | −0.00929983 | + | 0.0161078i | ||||
\(221\) | −2.00031 | + | 3.46464i | −0.134555 | + | 0.233057i | ||||
\(222\) | 2.66738 | + | 2.68806i | 0.179023 | + | 0.180411i | ||||
\(223\) | 5.59106 | + | 9.68400i | 0.374405 | + | 0.648488i | 0.990238 | − | 0.139388i | \(-0.0445137\pi\) |
−0.615833 | + | 0.787877i | \(0.711180\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 12.9033 | + | 7.58319i | 0.860220 | + | 0.505546i | ||||
\(226\) | 2.26791 | 0.150859 | ||||||||
\(227\) | −11.8853 | − | 20.5860i | −0.788857 | − | 1.36634i | −0.926668 | − | 0.375881i | \(-0.877340\pi\) |
0.137811 | − | 0.990459i | \(-0.455993\pi\) | |||||||
\(228\) | −2.73833 | + | 10.0640i | −0.181350 | + | 0.666503i | ||||
\(229\) | 0.952737 | − | 1.65019i | 0.0629586 | − | 0.109048i | −0.832828 | − | 0.553532i | \(-0.813280\pi\) |
0.895787 | + | 0.444484i | \(0.146613\pi\) | |||||||
\(230\) | 0.110330 | − | 0.191098i | 0.00727497 | − | 0.0126006i | ||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 14.2609 | + | 24.7006i | 0.936272 | + | 1.62167i | ||||
\(233\) | 6.54184 | 0.428570 | 0.214285 | − | 0.976771i | \(-0.431258\pi\) | ||||
0.214285 | + | 0.976771i | \(0.431258\pi\) | |||||||
\(234\) | 7.13700 | − | 4.04738i | 0.466560 | − | 0.264586i | ||||
\(235\) | −0.337028 | −0.0219853 | ||||||||
\(236\) | −1.74782 | − | 3.02732i | −0.113774 | − | 0.197062i | ||||
\(237\) | 9.38684 | + | 9.45962i | 0.609741 | + | 0.614468i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 10.6735 | − | 18.4870i | 0.690409 | − | 1.19582i | −0.281295 | − | 0.959621i | \(-0.590764\pi\) |
0.971704 | − | 0.236202i | \(-0.0759028\pi\) | |||||||
\(240\) | −0.321121 | + | 0.0847165i | −0.0207283 | + | 0.00546842i | ||||
\(241\) | 10.0331 | + | 17.3778i | 0.646288 | + | 1.11940i | 0.984003 | + | 0.178155i | \(0.0570127\pi\) |
−0.337715 | + | 0.941248i | \(0.609654\pi\) | |||||||
\(242\) | −0.151825 | −0.00975967 | ||||||||
\(243\) | −4.32454 | + | 14.9766i | −0.277419 | + | 0.960749i | ||||
\(244\) | −4.44494 | −0.284558 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 13.8250 | − | 3.64724i | 0.881451 | − | 0.232540i | ||||
\(247\) | 9.52629 | − | 16.5000i | 0.606144 | − | 1.04987i | ||||
\(248\) | 14.2167 | − | 24.6240i | 0.902758 | − | 1.56362i | ||||
\(249\) | −1.42601 | − | 1.43707i | −0.0903698 | − | 0.0910704i | ||||
\(250\) | 0.580900 | + | 1.00615i | 0.0367394 | + | 0.0636344i | ||||
\(251\) | −6.81467 | −0.430138 | −0.215069 | − | 0.976599i | \(-0.568998\pi\) | ||||
−0.215069 | + | 0.976599i | \(0.568998\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −6.33151 | −0.398059 | ||||||||
\(254\) | 0.174884 | + | 0.302907i | 0.0109732 | + | 0.0190061i | ||||
\(255\) | 0.0773687 | − | 0.284347i | 0.00484502 | − | 0.0178065i | ||||
\(256\) | 7.77234 | − | 13.4621i | 0.485771 | − | 0.841380i | ||||
\(257\) | 7.19415 | − | 12.4606i | 0.448759 | − | 0.777273i | −0.549546 | − | 0.835463i | \(-0.685199\pi\) |
0.998306 | + | 0.0581897i | \(0.0185328\pi\) | |||||||
\(258\) | −3.78519 | + | 13.9114i | −0.235656 | + | 0.866088i | ||||
\(259\) | 0 | 0 | ||||||||
\(260\) | −0.205004 | −0.0127138 | ||||||||
\(261\) | 24.0289 | + | 14.1216i | 1.48735 | + | 0.874107i | ||||
\(262\) | −16.4940 | −1.01900 | ||||||||
\(263\) | 0.769503 | + | 1.33282i | 0.0474496 | + | 0.0821851i | 0.888775 | − | 0.458344i | \(-0.151557\pi\) |
−0.841325 | + | 0.540529i | \(0.818224\pi\) | |||||||
\(264\) | 12.4997 | + | 12.5966i | 0.769304 | + | 0.775268i | ||||
\(265\) | −0.526106 | + | 0.911243i | −0.0323185 | + | 0.0559772i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 10.0980 | − | 2.66399i | 0.617986 | − | 0.163034i | ||||
\(268\) | 3.90781 | + | 6.76852i | 0.238707 | + | 0.413453i | ||||
\(269\) | −26.2571 | −1.60092 | −0.800461 | − | 0.599385i | \(-0.795412\pi\) | ||||
−0.800461 | + | 0.599385i | \(0.795412\pi\) | |||||||
\(270\) | −0.432270 | + | 0.422369i | −0.0263071 | + | 0.0257046i | ||||
\(271\) | 17.9335 | 1.08938 | 0.544690 | − | 0.838637i | \(-0.316647\pi\) | ||||
0.544690 | + | 0.838637i | \(0.316647\pi\) | |||||||
\(272\) | −1.46643 | − | 2.53993i | −0.0889152 | − | 0.154006i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −8.40748 | + | 14.5622i | −0.507915 | + | 0.879734i | ||||
\(275\) | 8.32473 | − | 14.4188i | 0.502000 | − | 0.869489i | ||||
\(276\) | 1.81417 | + | 1.82824i | 0.109200 | + | 0.110047i | ||||
\(277\) | 9.43563 | + | 16.3430i | 0.566932 | + | 0.981955i | 0.996867 | + | 0.0790954i | \(0.0252032\pi\) |
−0.429935 | + | 0.902860i | \(0.641463\pi\) | |||||||
\(278\) | 8.95359 | 0.537001 | ||||||||
\(279\) | 0.214582 | − | 27.7840i | 0.0128467 | − | 1.66339i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −2.49578 | − | 4.32283i | −0.148886 | − | 0.257878i | 0.781930 | − | 0.623366i | \(-0.214235\pi\) |
−0.930816 | + | 0.365488i | \(0.880902\pi\) | |||||||
\(282\) | −1.60259 | + | 5.88988i | −0.0954329 | + | 0.350737i | ||||
\(283\) | −7.69634 | + | 13.3304i | −0.457500 | + | 0.792413i | −0.998828 | − | 0.0483984i | \(-0.984588\pi\) |
0.541328 | + | 0.840811i | \(0.317922\pi\) | |||||||
\(284\) | 1.28952 | − | 2.23352i | 0.0765190 | − | 0.132535i | ||||
\(285\) | −0.368462 | + | 1.35418i | −0.0218258 | + | 0.0802146i | ||||
\(286\) | −4.56364 | − | 7.90446i | −0.269854 | − | 0.467401i | ||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0.0958052 | − | 12.4048i | 0.00564537 | − | 0.730960i | ||||
\(289\) | −14.3976 | −0.846919 | ||||||||
\(290\) | 0.540282 | + | 0.935796i | 0.0317265 | + | 0.0549518i | ||||
\(291\) | −4.63913 | − | 4.67510i | −0.271951 | − | 0.274059i | ||||
\(292\) | 1.85126 | − | 3.20647i | 0.108337 | − | 0.187644i | ||||
\(293\) | 12.9013 | − | 22.3456i | 0.753700 | − | 1.30545i | −0.192318 | − | 0.981333i | \(-0.561601\pi\) |
0.946018 | − | 0.324114i | \(-0.105066\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −0.235182 | − | 0.407347i | −0.0136928 | − | 0.0237167i | ||||
\(296\) | −6.08642 | −0.353766 | ||||||||
\(297\) | 16.6972 | + | 4.68197i | 0.968869 | + | 0.271676i | ||||
\(298\) | 12.2948 | 0.712220 | ||||||||
\(299\) | −2.35246 | − | 4.07458i | −0.136046 | − | 0.235639i | ||||
\(300\) | −6.54877 | + | 1.72766i | −0.378093 | + | 0.0997465i | ||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −6.21629 | + | 10.7669i | −0.357707 | + | 0.619567i | ||||
\(303\) | −21.3138 | − | 21.4790i | −1.22445 | − | 1.23394i | ||||
\(304\) | 6.98373 | + | 12.0962i | 0.400544 | + | 0.693763i | ||||
\(305\) | −0.598098 | −0.0342470 | ||||||||
\(306\) | −4.60135 | − | 2.70418i | −0.263042 | − | 0.154588i | ||||
\(307\) | 22.2914 | 1.27224 | 0.636120 | − | 0.771590i | \(-0.280538\pi\) | ||||
0.636120 | + | 0.771590i | \(0.280538\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 3.97085 | − | 14.5938i | 0.225894 | − | 0.830210i | ||||
\(310\) | 0.538607 | − | 0.932894i | 0.0305908 | − | 0.0529848i | ||||
\(311\) | −0.654931 | + | 1.13437i | −0.0371377 | + | 0.0643245i | −0.883997 | − | 0.467493i | \(-0.845157\pi\) |
0.846859 | + | 0.531817i | \(0.178491\pi\) | |||||||
\(312\) | −3.46219 | + | 12.7243i | −0.196008 | + | 0.720373i | ||||
\(313\) | 10.7885 | + | 18.6862i | 0.609802 | + | 1.05621i | 0.991273 | + | 0.131827i | \(0.0420843\pi\) |
−0.381471 | + | 0.924381i | \(0.624582\pi\) | |||||||
\(314\) | −13.4613 | −0.759667 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −6.03065 | −0.339250 | ||||||||
\(317\) | 12.3910 | + | 21.4618i | 0.695946 | + | 1.20541i | 0.969861 | + | 0.243660i | \(0.0783480\pi\) |
−0.273915 | + | 0.961754i | \(0.588319\pi\) | |||||||
\(318\) | 13.4232 | + | 13.5272i | 0.752734 | + | 0.758570i | ||||
\(319\) | 15.5025 | − | 26.8512i | 0.867975 | − | 1.50338i | ||||
\(320\) | 0.432216 | − | 0.748620i | 0.0241616 | − | 0.0418491i | ||||
\(321\) | 30.3906 | − | 8.01748i | 1.69624 | − | 0.447492i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −12.3936 | −0.689597 | ||||||||
\(324\) | −3.43233 | − | 6.16288i | −0.190685 | − | 0.342382i | ||||
\(325\) | 12.3722 | 0.686283 | ||||||||
\(326\) | 4.94206 | + | 8.55990i | 0.273715 | + | 0.474089i | ||||
\(327\) | 7.07161 | − | 1.86559i | 0.391061 | − | 0.103168i | ||||
\(328\) | −11.4901 | + | 19.9014i | −0.634434 | + | 1.09887i | ||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0.473559 | + | 0.477231i | 0.0260686 | + | 0.0262707i | ||||
\(331\) | −6.92256 | − | 11.9902i | −0.380498 | − | 0.659042i | 0.610635 | − | 0.791912i | \(-0.290914\pi\) |
−0.991133 | + | 0.132870i | \(0.957581\pi\) | |||||||
\(332\) | 0.916151 | 0.0502803 | ||||||||
\(333\) | −5.17359 | + | 2.93394i | −0.283511 | + | 0.160779i | ||||
\(334\) | −19.2073 | −1.05098 | ||||||||
\(335\) | 0.525823 | + | 0.910752i | 0.0287288 | + | 0.0497597i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 1.69444 | − | 2.93485i | 0.0923018 | − | 0.159871i | −0.816178 | − | 0.577801i | \(-0.803911\pi\) |
0.908479 | + | 0.417930i | \(0.137244\pi\) | |||||||
\(338\) | −3.77706 | + | 6.54206i | −0.205445 | + | 0.355841i | ||||
\(339\) | −0.935172 | + | 3.43697i | −0.0507916 | + | 0.186670i | ||||
\(340\) | 0.0666767 | + | 0.115487i | 0.00361605 | + | 0.00626319i | ||||
\(341\) | −30.9089 | −1.67381 | ||||||||
\(342\) | 21.9135 | + | 12.8784i | 1.18495 | + | 0.696386i | ||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −11.5859 | − | 20.0673i | −0.624668 | − | 1.08196i | ||||
\(345\) | 0.244110 | + | 0.246002i | 0.0131424 | + | 0.0132443i | ||||
\(346\) | 1.56011 | − | 2.70219i | 0.0838720 | − | 0.145271i | ||||
\(347\) | 7.25739 | − | 12.5702i | 0.389597 | − | 0.674802i | −0.602798 | − | 0.797894i | \(-0.705948\pi\) |
0.992395 | + | 0.123091i | \(0.0392809\pi\) | |||||||
\(348\) | −12.1953 | + | 3.21730i | −0.653736 | + | 0.172465i | ||||
\(349\) | −7.86412 | − | 13.6211i | −0.420957 | − | 0.729119i | 0.575076 | − | 0.818100i | \(-0.304972\pi\) |
−0.996033 | + | 0.0889810i | \(0.971639\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.19077 | + | 12.4849i | 0.170311 | + | 0.666395i | ||||
\(352\) | −13.8000 | −0.735542 | ||||||||
\(353\) | −2.07211 | − | 3.58900i | −0.110287 | − | 0.191023i | 0.805599 | − | 0.592462i | \(-0.201844\pi\) |
−0.915886 | + | 0.401438i | \(0.868510\pi\) | |||||||
\(354\) | −8.23709 | + | 2.17307i | −0.437796 | + | 0.115497i | ||||
\(355\) | 0.173514 | − | 0.300535i | 0.00920917 | − | 0.0159508i | ||||
\(356\) | −2.36298 | + | 4.09281i | −0.125238 | + | 0.216918i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −5.60378 | − | 9.70603i | −0.296169 | − | 0.512979i | ||||
\(359\) | 7.93988 | 0.419051 | 0.209525 | − | 0.977803i | \(-0.432808\pi\) | ||||
0.209525 | + | 0.977803i | \(0.432808\pi\) | |||||||
\(360\) | 0.00750171 | − | 0.971318i | 0.000395375 | − | 0.0511930i | ||||
\(361\) | 40.0233 | 2.10649 | ||||||||
\(362\) | −9.42187 | − | 16.3192i | −0.495202 | − | 0.857716i | ||||
\(363\) | 0.0626049 | − | 0.230087i | 0.00328590 | − | 0.0120764i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0.249099 | − | 0.431453i | 0.0130385 | − | 0.0225833i | ||||
\(366\) | −2.84400 | + | 10.4523i | −0.148658 | + | 0.546352i | ||||
\(367\) | −6.57455 | − | 11.3875i | −0.343189 | − | 0.594420i | 0.641834 | − | 0.766843i | \(-0.278174\pi\) |
−0.985023 | + | 0.172423i | \(0.944840\pi\) | |||||||
\(368\) | 3.44918 | 0.179801 | ||||||||
\(369\) | −0.173428 | + | 22.4554i | −0.00902832 | + | 1.16898i | ||||
\(370\) | −0.230588 | −0.0119877 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 8.85636 | + | 8.92503i | 0.459181 | + | 0.462741i | ||||
\(373\) | −3.90543 | + | 6.76441i | −0.202216 | + | 0.350248i | −0.949242 | − | 0.314547i | \(-0.898147\pi\) |
0.747026 | + | 0.664794i | \(0.231481\pi\) | |||||||
\(374\) | −2.96862 | + | 5.14180i | −0.153504 | + | 0.265876i | ||||
\(375\) | −1.76433 | + | 0.465456i | −0.0911096 | + | 0.0240361i | ||||
\(376\) | −4.90527 | − | 8.49618i | −0.252970 | − | 0.438157i | ||||
\(377\) | 23.0398 | 1.18661 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −31.6147 | −1.62394 | −0.811968 | − | 0.583702i | \(-0.801604\pi\) | ||||
−0.811968 | + | 0.583702i | \(0.801604\pi\) | |||||||
\(380\) | −0.317542 | − | 0.549999i | −0.0162896 | − | 0.0282143i | ||||
\(381\) | −0.531163 | + | 0.140128i | −0.0272123 | + | 0.00717900i | ||||
\(382\) | −12.3515 | + | 21.3934i | −0.631958 | + | 1.09458i | ||||
\(383\) | −5.36593 | + | 9.29407i | −0.274186 | + | 0.474905i | −0.969930 | − | 0.243386i | \(-0.921742\pi\) |
0.695743 | + | 0.718291i | \(0.255075\pi\) | |||||||
\(384\) | −0.938027 | − | 0.945300i | −0.0478685 | − | 0.0482396i | ||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0.283187 | 0.0144139 | ||||||||
\(387\) | −19.5216 | − | 11.4728i | −0.992341 | − | 0.583193i | ||||
\(388\) | 2.98045 | 0.151309 | ||||||||
\(389\) | −12.0734 | − | 20.9118i | −0.612147 | − | 1.06027i | −0.990878 | − | 0.134763i | \(-0.956973\pi\) |
0.378731 | − | 0.925507i | \(-0.376361\pi\) | |||||||
\(390\) | −0.131167 | + | 0.482069i | −0.00664191 | + | 0.0244105i | ||||
\(391\) | −1.53026 | + | 2.65049i | −0.0773885 | + | 0.134041i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 6.80131 | − | 24.9963i | 0.343081 | − | 1.26090i | ||||
\(394\) | −0.420927 | − | 0.729067i | −0.0212060 | − | 0.0367299i | ||||
\(395\) | −0.811466 | −0.0408293 | ||||||||
\(396\) | −6.82613 | + | 3.87109i | −0.343026 | + | 0.194530i | ||||
\(397\) | −24.0569 | −1.20738 | −0.603691 | − | 0.797218i | \(-0.706304\pi\) | ||||
−0.603691 | + | 0.797218i | \(0.706304\pi\) | |||||||
\(398\) | −2.77424 | − | 4.80513i | −0.139060 | − | 0.240860i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | −4.53501 | + | 7.85487i | −0.226751 | + | 0.392744i | ||||
\(401\) | 0.781158 | − | 1.35301i | 0.0390092 | − | 0.0675659i | −0.845862 | − | 0.533402i | \(-0.820913\pi\) |
0.884871 | + | 0.465836i | \(0.154247\pi\) | |||||||
\(402\) | 18.4166 | − | 4.85857i | 0.918536 | − | 0.242323i | ||||
\(403\) | −11.4842 | − | 19.8911i | −0.572067 | − | 0.990849i | ||||
\(404\) | 13.6932 | 0.681263 | ||||||||
\(405\) | −0.461844 | − | 0.829259i | −0.0229492 | − | 0.0412062i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 3.30817 | + | 5.72992i | 0.163980 | + | 0.284022i | ||||
\(408\) | 8.29422 | − | 2.18814i | 0.410625 | − | 0.108329i | ||||
\(409\) | −11.1728 | + | 19.3519i | −0.552460 | + | 0.956889i | 0.445636 | + | 0.895214i | \(0.352977\pi\) |
−0.998096 | + | 0.0616748i | \(0.980356\pi\) | |||||||
\(410\) | −0.435309 | + | 0.753978i | −0.0214984 | + | 0.0372363i | ||||
\(411\) | −18.6018 | − | 18.7461i | −0.917561 | − | 0.924675i | ||||
\(412\) | 3.42210 | + | 5.92725i | 0.168595 | + | 0.292014i | ||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 5.45988 | − | 3.09629i | 0.268339 | − | 0.152174i | ||||
\(415\) | 0.123275 | 0.00605131 | ||||||||
\(416\) | −5.12736 | − | 8.88086i | −0.251390 | − | 0.435420i | ||||
\(417\) | −3.69201 | + | 13.5690i | −0.180799 | + | 0.664475i | ||||
\(418\) | 14.1378 | − | 24.4873i | 0.691501 | − | 1.19771i | ||||
\(419\) | −2.98648 | + | 5.17273i | −0.145899 | + | 0.252704i | −0.929708 | − | 0.368298i | \(-0.879941\pi\) |
0.783809 | + | 0.621002i | \(0.213274\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 7.31594 | + | 12.6716i | 0.356557 | + | 0.617575i | 0.987383 | − | 0.158349i | \(-0.0506172\pi\) |
−0.630826 | + | 0.775924i | \(0.717284\pi\) | |||||||
\(422\) | −7.95210 | −0.387102 | ||||||||
\(423\) | −8.26515 | − | 4.85738i | −0.401865 | − | 0.236174i | ||||
\(424\) | −30.6289 | −1.48747 | ||||||||
\(425\) | −4.02400 | − | 6.96977i | −0.195193 | − | 0.338083i | ||||
\(426\) | −4.42707 | − | 4.46139i | −0.214492 | − | 0.216155i | ||||
\(427\) | 0 | 0 | ||||||||
\(428\) | −7.11156 | + | 12.3176i | −0.343750 | + | 0.595393i | ||||
\(429\) | 13.8609 | − | 3.65670i | 0.669208 | − | 0.176547i | ||||
\(430\) | −0.438938 | − | 0.760263i | −0.0211675 | − | 0.0366631i | ||||
\(431\) | −19.4034 | −0.934628 | −0.467314 | − | 0.884091i | \(-0.654778\pi\) | ||||
−0.467314 | + | 0.884091i | \(0.654778\pi\) | |||||||
\(432\) | −9.09603 | − | 2.55057i | −0.437633 | − | 0.122714i | ||||
\(433\) | −1.35217 | −0.0649810 | −0.0324905 | − | 0.999472i | \(-0.510344\pi\) | ||||
−0.0324905 | + | 0.999472i | \(0.510344\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −1.64096 | + | 0.432910i | −0.0786781 | + | 0.0207564i | ||||
\(436\) | −1.65480 | + | 2.86619i | −0.0792503 | + | 0.137266i | ||||
\(437\) | 7.28772 | − | 12.6227i | 0.348619 | − | 0.603826i | ||||
\(438\) | −6.35556 | − | 6.40484i | −0.303681 | − | 0.306035i | ||||
\(439\) | 8.67059 | + | 15.0179i | 0.413825 | + | 0.716766i | 0.995304 | − | 0.0967954i | \(-0.0308592\pi\) |
−0.581479 | + | 0.813561i | \(0.697526\pi\) | |||||||
\(440\) | −1.08056 | −0.0515139 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −4.41194 | −0.209854 | ||||||||
\(443\) | −9.80499 | − | 16.9827i | −0.465849 | − | 0.806874i | 0.533390 | − | 0.845869i | \(-0.320918\pi\) |
−0.999239 | + | 0.0389949i | \(0.987584\pi\) | |||||||
\(444\) | 0.706635 | − | 2.59704i | 0.0335354 | − | 0.123250i | ||||
\(445\) | −0.317956 | + | 0.550716i | −0.0150726 | + | 0.0261064i | ||||
\(446\) | −6.16590 | + | 10.6796i | −0.291964 | + | 0.505696i | ||||
\(447\) | −5.06977 | + | 18.6325i | −0.239792 | + | 0.881289i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −17.7345 | −0.836942 | −0.418471 | − | 0.908230i | \(-0.637434\pi\) | ||||
−0.418471 | + | 0.908230i | \(0.637434\pi\) | |||||||
\(450\) | −0.127471 | + | 16.5049i | −0.00600905 | + | 0.778049i | ||||
\(451\) | 24.9810 | 1.17631 | ||||||||
\(452\) | −0.805935 | − | 1.39592i | −0.0379080 | − | 0.0656586i | ||||
\(453\) | −13.7538 | − | 13.8604i | −0.646208 | − | 0.651218i | ||||
\(454\) | 13.1073 | − | 22.7025i | 0.615156 | − | 1.06548i | ||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −39.5005 | + | 10.4208i | −1.84978 | + | 0.487999i | ||||
\(457\) | −0.242725 | − | 0.420413i | −0.0113542 | − | 0.0196661i | 0.860292 | − | 0.509801i | \(-0.170281\pi\) |
−0.871647 | + | 0.490135i | \(0.836948\pi\) | |||||||
\(458\) | 2.10138 | 0.0981912 | ||||||||
\(459\) | 5.99549 | − | 5.85817i | 0.279846 | − | 0.273436i | ||||
\(460\) | −0.156830 | −0.00731224 | ||||||||
\(461\) | −3.99687 | − | 6.92279i | −0.186153 | − | 0.322426i | 0.757811 | − | 0.652474i | \(-0.226269\pi\) |
−0.943964 | + | 0.330047i | \(0.892935\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 5.24280 | − | 9.08080i | 0.243654 | − | 0.422021i | −0.718098 | − | 0.695942i | \(-0.754987\pi\) |
0.961752 | + | 0.273921i | \(0.0883206\pi\) | |||||||
\(464\) | −8.44523 | + | 14.6276i | −0.392060 | + | 0.679068i | ||||
\(465\) | 1.19169 | + | 1.20092i | 0.0552631 | + | 0.0556916i | ||||
\(466\) | 3.60721 | + | 6.24788i | 0.167101 | + | 0.289427i | ||||
\(467\) | −21.8977 | −1.01331 | −0.506653 | − | 0.862150i | \(-0.669117\pi\) | ||||
−0.506653 | + | 0.862150i | \(0.669117\pi\) | |||||||
\(468\) | −5.02744 | − | 2.95460i | −0.232394 | − | 0.136576i | ||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −0.185839 | − | 0.321883i | −0.00857213 | − | 0.0148474i | ||||
\(471\) | 5.55078 | − | 20.4003i | 0.255766 | − | 0.939998i | ||||
\(472\) | 6.84592 | − | 11.8575i | 0.315109 | − | 0.545785i | ||||
\(473\) | −12.5946 | + | 21.8145i | −0.579102 | + | 1.00303i | ||||
\(474\) | −3.85858 | + | 14.1811i | −0.177230 | + | 0.651361i | ||||
\(475\) | 19.1639 | + | 33.1929i | 0.879301 | + | 1.52299i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −26.0353 | + | 14.7645i | −1.19207 | + | 0.676022i | ||||
\(478\) | 23.5417 | 1.07677 | ||||||||
\(479\) | 2.00085 | + | 3.46557i | 0.0914210 | + | 0.158346i | 0.908109 | − | 0.418733i | \(-0.137526\pi\) |
−0.816688 | + | 0.577079i | \(0.804192\pi\) | |||||||
\(480\) | 0.532055 | + | 0.536180i | 0.0242849 | + | 0.0244732i | ||||
\(481\) | −2.45829 | + | 4.25789i | −0.112088 | + | 0.194143i | ||||
\(482\) | −11.0646 | + | 19.1645i | −0.503980 | + | 0.872918i | ||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0.0539532 | + | 0.0934496i | 0.00245242 | + | 0.00424771i | ||||
\(485\) | 0.401040 | 0.0182103 | ||||||||
\(486\) | −16.6882 | + | 4.12798i | −0.756992 | + | 0.187249i | ||||
\(487\) | −26.4755 | −1.19972 | −0.599859 | − | 0.800106i | \(-0.704777\pi\) | ||||
−0.599859 | + | 0.800106i | \(0.704777\pi\) | |||||||
\(488\) | −8.70502 | − | 15.0775i | −0.394058 | − | 0.682528i | ||||
\(489\) | −15.0102 | + | 3.95991i | −0.678784 | + | 0.179073i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 14.2149 | − | 24.6210i | 0.641511 | − | 1.11113i | −0.343584 | − | 0.939122i | \(-0.611641\pi\) |
0.985096 | − | 0.172008i | \(-0.0550255\pi\) | |||||||
\(492\) | −7.15783 | − | 7.21333i | −0.322700 | − | 0.325202i | ||||
\(493\) | −7.49360 | − | 12.9793i | −0.337495 | − | 0.584558i | ||||
\(494\) | 21.0115 | 0.945350 | ||||||||
\(495\) | −0.918504 | + | 0.520882i | −0.0412837 | + | 0.0234119i | ||||
\(496\) | 16.8381 | 0.756052 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0.586179 | − | 2.15434i | 0.0262673 | − | 0.0965383i | ||||
\(499\) | 3.71559 | − | 6.43559i | 0.166333 | − | 0.288097i | −0.770795 | − | 0.637083i | \(-0.780141\pi\) |
0.937128 | + | 0.348986i | \(0.113474\pi\) | |||||||
\(500\) | 0.412863 | − | 0.715100i | 0.0184638 | − | 0.0319802i | ||||
\(501\) | 7.92014 | − | 29.1083i | 0.353846 | − | 1.30046i | ||||
\(502\) | −3.75765 | − | 6.50845i | −0.167712 | − | 0.290486i | ||||
\(503\) | 10.1610 | 0.453057 | 0.226529 | − | 0.974004i | \(-0.427262\pi\) | ||||
0.226529 | + | 0.974004i | \(0.427262\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.84252 | 0.0819910 | ||||||||
\(506\) | −3.49124 | − | 6.04700i | −0.155204 | − | 0.268822i | ||||
\(507\) | −8.35688 | − | 8.42167i | −0.371142 | − | 0.374019i | ||||
\(508\) | 0.124295 | − | 0.215285i | 0.00551470 | − | 0.00955174i | ||||
\(509\) | 14.4532 | − | 25.0336i | 0.640625 | − | 1.10960i | −0.344668 | − | 0.938725i | \(-0.612009\pi\) |
0.985293 | − | 0.170871i | \(-0.0546581\pi\) | |||||||
\(510\) | 0.314232 | − | 0.0828990i | 0.0139144 | − | 0.00367083i | ||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 18.6806 | 0.825575 | ||||||||
\(513\) | −28.5530 | + | 27.8990i | −1.26065 | + | 1.23177i | ||||
\(514\) | 15.8676 | 0.699891 | ||||||||
\(515\) | 0.460467 | + | 0.797553i | 0.0202906 | + | 0.0351444i | ||||
\(516\) | 9.90775 | − | 2.61381i | 0.436164 | − | 0.115067i | ||||
\(517\) | −5.33237 | + | 9.23593i | −0.234517 | + | 0.406196i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 3.45180 | + | 3.47856i | 0.151517 | + | 0.152692i | ||||
\(520\) | −0.401482 | − | 0.695387i | −0.0176061 | − | 0.0304947i | ||||
\(521\) | 33.7990 | 1.48076 | 0.740381 | − | 0.672187i | \(-0.234645\pi\) | ||||
0.740381 | + | 0.672187i | \(0.234645\pi\) | |||||||
\(522\) | −0.237380 | + | 30.7359i | −0.0103899 | + | 1.34527i | ||||
\(523\) | −14.3779 | −0.628701 | −0.314351 | − | 0.949307i | \(-0.601787\pi\) | ||||
−0.314351 | + | 0.949307i | \(0.601787\pi\) | |||||||
\(524\) | 5.86140 | + | 10.1522i | 0.256056 | + | 0.443502i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −0.848618 | + | 1.46985i | −0.0370015 | + | 0.0640885i | ||||
\(527\) | −7.47036 | + | 12.9390i | −0.325414 | + | 0.563634i | ||||
\(528\) | −2.75912 | + | 10.1404i | −0.120075 | + | 0.441304i | ||||
\(529\) | 9.70034 | + | 16.8015i | 0.421754 | + | 0.730499i | ||||
\(530\) | −1.16039 | −0.0504043 | ||||||||
\(531\) | 0.103331 | − | 13.3792i | 0.00448416 | − | 0.580607i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 9.28166 | + | 16.0763i | 0.402033 | + | 0.696342i | ||||
\(534\) | 8.11238 | + | 8.17528i | 0.351057 | + | 0.353779i | ||||
\(535\) | −0.956910 | + | 1.65742i | −0.0413708 | + | 0.0716564i | ||||
\(536\) | −15.3062 | + | 26.5111i | −0.661127 | + | 1.14511i | ||||
\(537\) | 17.0200 | − | 4.49012i | 0.734466 | − | 0.193763i | ||||
\(538\) | −14.4783 | − | 25.0772i | −0.624205 | − | 1.08116i | ||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0.413586 | + | 0.115971i | 0.0177979 | + | 0.00499062i | ||||
\(541\) | −25.1764 | −1.08242 | −0.541210 | − | 0.840888i | \(-0.682034\pi\) | ||||
−0.541210 | + | 0.840888i | \(0.682034\pi\) | |||||||
\(542\) | 9.88863 | + | 17.1276i | 0.424753 | + | 0.735694i | ||||
\(543\) | 28.6164 | − | 7.54943i | 1.22805 | − | 0.323977i | ||||
\(544\) | −3.33531 | + | 5.77693i | −0.143000 | + | 0.247684i | ||||
\(545\) | −0.222664 | + | 0.385666i | −0.00953789 | + | 0.0165201i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 1.59011 | + | 2.75416i | 0.0679883 | + | 0.117759i | 0.898016 | − | 0.439963i | \(-0.145009\pi\) |
−0.830027 | + | 0.557723i | \(0.811675\pi\) | |||||||
\(548\) | 11.9509 | 0.510517 | ||||||||
\(549\) | −14.6675 | − | 8.62003i | −0.625996 | − | 0.367894i | ||||
\(550\) | 18.3612 | 0.782926 | ||||||||
\(551\) | 35.6876 | + | 61.8127i | 1.52034 | + | 2.63331i | ||||
\(552\) | −2.64861 | + | 9.73424i | −0.112732 | + | 0.414317i | ||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −10.4057 | + | 18.0233i | −0.442098 | + | 0.765736i | ||||
\(555\) | 0.0950828 | − | 0.349450i | 0.00403604 | − | 0.0148333i | ||||
\(556\) | −3.18179 | − | 5.51102i | −0.134938 | − | 0.233719i | ||||
\(557\) | 20.0459 | 0.849371 | 0.424686 | − | 0.905341i | \(-0.360385\pi\) | ||||
0.424686 | + | 0.905341i | \(0.360385\pi\) | |||||||
\(558\) | 26.6539 | − | 15.1154i | 1.12835 | − | 0.639884i | ||||
\(559\) | −18.7181 | −0.791689 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −6.56817 | − | 6.61909i | −0.277308 | − | 0.279458i | ||||
\(562\) | 2.75238 | − | 4.76727i | 0.116102 | − | 0.201095i | ||||
\(563\) | −19.9007 | + | 34.4690i | −0.838713 | + | 1.45269i | 0.0522584 | + | 0.998634i | \(0.483358\pi\) |
−0.890971 | + | 0.454060i | \(0.849975\pi\) | |||||||
\(564\) | 4.19478 | − | 1.10665i | 0.176632 | − | 0.0465982i | ||||
\(565\) | −0.108444 | − | 0.187831i | −0.00456228 | − | 0.00790211i | ||||
\(566\) | −16.9753 | −0.713523 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 10.1017 | 0.423856 | ||||||||
\(569\) | −6.90797 | − | 11.9649i | −0.289597 | − | 0.501597i | 0.684117 | − | 0.729373i | \(-0.260188\pi\) |
−0.973714 | + | 0.227776i | \(0.926855\pi\) | |||||||
\(570\) | −1.49650 | + | 0.394799i | −0.0626815 | + | 0.0165363i | ||||
\(571\) | −5.21935 | + | 9.04019i | −0.218423 | + | 0.378320i | −0.954326 | − | 0.298767i | \(-0.903425\pi\) |
0.735903 | + | 0.677087i | \(0.236758\pi\) | |||||||
\(572\) | −3.24352 | + | 5.61793i | −0.135618 | + | 0.234898i | ||||
\(573\) | −27.3281 | − | 27.5400i | −1.14165 | − | 1.15050i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 9.46483 | 0.394711 | ||||||||
\(576\) | 21.3889 | − | 12.1296i | 0.891205 | − | 0.505401i | ||||
\(577\) | −25.4923 | −1.06126 | −0.530628 | − | 0.847605i | \(-0.678044\pi\) | ||||
−0.530628 | + | 0.847605i | \(0.678044\pi\) | |||||||
\(578\) | −7.93895 | − | 13.7507i | −0.330217 | − | 0.571952i | ||||
\(579\) | −0.116772 | + | 0.429164i | −0.00485289 | + | 0.0178354i | ||||
\(580\) | 0.383994 | − | 0.665098i | 0.0159445 | − | 0.0276167i | ||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 1.90697 | − | 7.00855i | 0.0790466 | − | 0.290514i | ||||
\(583\) | 16.6478 | + | 28.8349i | 0.689483 | + | 1.19422i | ||||
\(584\) | 14.5021 | 0.600100 | ||||||||
\(585\) | −0.676477 | − | 0.397562i | −0.0279689 | − | 0.0164372i | ||||
\(586\) | 28.4554 | 1.17548 | ||||||||
\(587\) | 17.5168 | + | 30.3401i | 0.722998 | + | 1.25227i | 0.959793 | + | 0.280709i | \(0.0905697\pi\) |
−0.236795 | + | 0.971560i | \(0.576097\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 35.5769 | − | 61.6210i | 1.46592 | − | 2.53905i | ||||
\(590\) | 0.259362 | − | 0.449228i | 0.0106778 | − | 0.0184944i | ||||
\(591\) | 1.27845 | − | 0.337275i | 0.0525886 | − | 0.0138736i | ||||
\(592\) | −1.80217 | − | 3.12146i | −0.0740689 | − | 0.128291i | ||||
\(593\) | 36.1292 | 1.48365 | 0.741824 | − | 0.670594i | \(-0.233961\pi\) | ||||
0.741824 | + | 0.670594i | \(0.233961\pi\) | |||||||
\(594\) | 4.73536 | + | 18.5286i | 0.194294 | + | 0.760236i | ||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −4.36915 | − | 7.56759i | −0.178967 | − | 0.309980i | ||||
\(597\) | 8.42603 | − | 2.22291i | 0.344854 | − | 0.0909777i | ||||
\(598\) | 2.59433 | − | 4.49350i | 0.106090 | − | 0.183753i | ||||
\(599\) | 20.4742 | − | 35.4623i | 0.836552 | − | 1.44895i | −0.0562080 | − | 0.998419i | \(-0.517901\pi\) |
0.892760 | − | 0.450532i | \(-0.148766\pi\) | |||||||
\(600\) | −18.6855 | − | 18.8304i | −0.762833 | − | 0.768748i | ||||
\(601\) | −12.8547 | − | 22.2650i | −0.524354 | − | 0.908207i | −0.999598 | − | 0.0283533i | \(-0.990974\pi\) |
0.475244 | − | 0.879854i | \(-0.342360\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −0.231028 | + | 29.9133i | −0.00940817 | + | 1.21817i | ||||
\(604\) | 8.83620 | 0.359540 | ||||||||
\(605\) | 0.00725978 | + | 0.0125743i | 0.000295152 | + | 0.000511218i | ||||
\(606\) | 8.76130 | − | 32.1998i | 0.355904 | − | 1.30803i | ||||
\(607\) | 3.42258 | − | 5.92808i | 0.138918 | − | 0.240613i | −0.788169 | − | 0.615459i | \(-0.788971\pi\) |
0.927087 | + | 0.374845i | \(0.122304\pi\) | |||||||
\(608\) | 15.8841 | − | 27.5121i | 0.644187 | − | 1.11576i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −0.329795 | − | 0.571222i | −0.0133530 | − | 0.0231281i | ||||
\(611\) | −7.92493 | −0.320608 | ||||||||
\(612\) | −0.0292953 | + | 3.79315i | −0.00118419 | + | 0.153329i | ||||
\(613\) | −29.1297 | −1.17654 | −0.588269 | − | 0.808666i | \(-0.700190\pi\) | ||||
−0.588269 | + | 0.808666i | \(0.700190\pi\) | |||||||
\(614\) | 12.2917 | + | 21.2898i | 0.496051 | + | 0.859185i | ||||
\(615\) | −0.963137 | − | 0.970604i | −0.0388374 | − | 0.0391385i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −10.3395 | + | 17.9085i | −0.416252 | + | 0.720969i | −0.995559 | − | 0.0941404i | \(-0.969990\pi\) |
0.579307 | + | 0.815109i | \(0.303323\pi\) | |||||||
\(618\) | 16.1275 | − | 4.25468i | 0.648745 | − | 0.171148i | ||||
\(619\) | −4.43178 | − | 7.67606i | −0.178128 | − | 0.308527i | 0.763111 | − | 0.646267i | \(-0.223671\pi\) |
−0.941239 | + | 0.337740i | \(0.890337\pi\) | |||||||
\(620\) | −0.765607 | −0.0307475 | ||||||||
\(621\) | 2.44098 | + | 9.55108i | 0.0979530 | + | 0.383272i | ||||
\(622\) | −1.44453 | −0.0579205 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | −7.55090 | + | 1.99204i | −0.302278 | + | 0.0797453i | ||||
\(625\) | −12.4166 | + | 21.5062i | −0.496666 | + | 0.860250i | ||||
\(626\) | −11.8977 | + | 20.6074i | −0.475528 | + | 0.823638i | ||||
\(627\) | 31.2803 | + | 31.5228i | 1.24921 | + | 1.25890i | ||||
\(628\) | 4.78368 | + | 8.28558i | 0.190890 | + | 0.330631i | ||||
\(629\) | 3.19820 | 0.127521 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 26.4661 | 1.05360 | 0.526799 | − | 0.849990i | \(-0.323392\pi\) | ||||
0.526799 | + | 0.849990i | \(0.323392\pi\) | |||||||
\(632\) | −11.8105 | − | 20.4564i | −0.469796 | − | 0.813711i | ||||
\(633\) | 3.27904 | − | 12.0512i | 0.130330 | − | 0.478993i | ||||
\(634\) | −13.6649 | + | 23.6683i | −0.542704 | + | 0.939990i | ||||
\(635\) | 0.0167248 | − | 0.0289681i | 0.000663702 | − | 0.00114957i | ||||
\(636\) | 3.55603 | − | 13.0692i | 0.141006 | − | 0.518227i | ||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 34.1928 | 1.35371 | ||||||||
\(639\) | 8.58664 | − | 4.86947i | 0.339682 | − | 0.192633i | ||||
\(640\) | 0.0810898 | 0.00320536 | ||||||||
\(641\) | 8.26595 | + | 14.3171i | 0.326486 | + | 0.565489i | 0.981812 | − | 0.189856i | \(-0.0608022\pi\) |
−0.655326 | + | 0.755346i | \(0.727469\pi\) | |||||||
\(642\) | 24.4148 | + | 24.6041i | 0.963574 | + | 0.971045i | ||||
\(643\) | 15.4460 | − | 26.7532i | 0.609130 | − | 1.05504i | −0.382254 | − | 0.924057i | \(-0.624852\pi\) |
0.991384 | − | 0.130987i | \(-0.0418147\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 1.33316 | − | 0.351706i | 0.0524930 | − | 0.0138484i | ||||
\(646\) | −6.83390 | − | 11.8367i | −0.268876 | − | 0.465707i | ||||
\(647\) | 1.29981 | 0.0511007 | 0.0255503 | − | 0.999674i | \(-0.491866\pi\) | ||||
0.0255503 | + | 0.999674i | \(0.491866\pi\) | |||||||
\(648\) | 14.1830 | − | 23.7122i | 0.557161 | − | 0.931502i | ||||
\(649\) | −14.8840 | −0.584247 | ||||||||
\(650\) | 6.82209 | + | 11.8162i | 0.267584 | + | 0.463470i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 3.51247 | − | 6.08377i | 0.137559 | − | 0.238259i | ||||
\(653\) | 22.4435 | − | 38.8733i | 0.878281 | − | 1.52123i | 0.0250558 | − | 0.999686i | \(-0.492024\pi\) |
0.853226 | − | 0.521542i | \(-0.174643\pi\) | |||||||
\(654\) | 5.68109 | + | 5.72514i | 0.222148 | + | 0.223871i | ||||
\(655\) | 0.788692 | + | 1.36605i | 0.0308167 | + | 0.0533762i | ||||
\(656\) | −13.6088 | −0.531333 | ||||||||
\(657\) | 12.3271 | − | 6.99068i | 0.480926 | − | 0.272732i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 8.96167 | + | 15.5221i | 0.349097 | + | 0.604654i | 0.986089 | − | 0.166216i | \(-0.0531549\pi\) |
−0.636992 | + | 0.770870i | \(0.719822\pi\) | |||||||
\(660\) | 0.125454 | − | 0.461071i | 0.00488329 | − | 0.0179472i | ||||
\(661\) | 16.5128 | − | 28.6010i | 0.642274 | − | 1.11245i | −0.342649 | − | 0.939463i | \(-0.611324\pi\) |
0.984924 | − | 0.172989i | \(-0.0553424\pi\) | |||||||
\(662\) | 7.63429 | − | 13.2230i | 0.296715 | − | 0.513925i | ||||
\(663\) | 1.81926 | − | 6.68619i | 0.0706542 | − | 0.259670i | ||||
\(664\) | 1.79420 | + | 3.10765i | 0.0696285 | + | 0.120600i | ||||
\(665\) | 0 | 0 | ||||||||
\(666\) | −5.65485 | − | 3.32332i | −0.219121 | − | 0.128776i | ||||
\(667\) | 17.6257 | 0.682469 | ||||||||
\(668\) | 6.82561 | + | 11.8223i | 0.264091 | + | 0.457419i | ||||
\(669\) | −13.6423 | − | 13.7480i | −0.527440 | − | 0.531529i | ||||
\(670\) | −0.579885 | + | 1.00439i | −0.0224029 | + | 0.0388030i | ||||
\(671\) | −9.46295 | + | 16.3903i | −0.365313 | + | 0.632741i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −10.6758 | − | 18.4909i | −0.411520 | − | 0.712774i | 0.583536 | − | 0.812087i | \(-0.301669\pi\) |
−0.995056 | + | 0.0993135i | \(0.968335\pi\) | |||||||
\(674\) | 3.73729 | 0.143955 | ||||||||
\(675\) | −24.9603 | − | 6.99898i | −0.960721 | − | 0.269391i | ||||
\(676\) | 5.36894 | 0.206498 | ||||||||
\(677\) | 4.15084 | + | 7.18946i | 0.159530 | + | 0.276313i | 0.934699 | − | 0.355440i | \(-0.115669\pi\) |
−0.775170 | + | 0.631753i | \(0.782336\pi\) | |||||||
\(678\) | −3.79818 | + | 1.00202i | −0.145868 | + | 0.0384822i | ||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −0.261161 | + | 0.452344i | −0.0100151 | + | 0.0173466i | ||||
\(681\) | 29.0003 | + | 29.2252i | 1.11130 | + | 1.11991i | ||||
\(682\) | −17.0434 | − | 29.5200i | −0.652625 | − | 1.13038i | ||||
\(683\) | 2.49456 | 0.0954518 | 0.0477259 | − | 0.998860i | \(-0.484803\pi\) | ||||
0.0477259 | + | 0.998860i | \(0.484803\pi\) | |||||||
\(684\) | 0.139516 | − | 18.0645i | 0.00533454 | − | 0.690714i | ||||
\(685\) | 1.60808 | 0.0614414 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −0.866505 | + | 3.18460i | −0.0330592 | + | 0.121500i | ||||
\(688\) | 6.86110 | − | 11.8838i | 0.261577 | − | 0.453065i | ||||
\(689\) | −12.3710 | + | 21.4271i | −0.471296 | + | 0.816308i | ||||
\(690\) | −0.100344 | + | 0.368788i | −0.00382004 | + | 0.0140395i | ||||
\(691\) | −8.43455 | − | 14.6091i | −0.320865 | − | 0.555755i | 0.659801 | − | 0.751440i | \(-0.270640\pi\) |
−0.980667 | + | 0.195685i | \(0.937307\pi\) | |||||||
\(692\) | −2.21763 | −0.0843017 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 16.0071 | 0.607621 | ||||||||
\(695\) | −0.428132 | − | 0.741547i | −0.0162400 | − | 0.0281285i | ||||
\(696\) | −34.7967 | − | 35.0665i | −1.31897 | − | 1.32919i | ||||
\(697\) | 6.03765 | − | 10.4575i | 0.228692 | − | 0.396107i | ||||
\(698\) | 8.67266 | − | 15.0215i | 0.328265 | − | 0.568572i | ||||
\(699\) | −10.9559 | + | 2.89034i | −0.414392 | + | 0.109323i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 16.4806 | 0.622465 | 0.311232 | − | 0.950334i | \(-0.399258\pi\) | ||||
0.311232 | + | 0.950334i | \(0.399258\pi\) | |||||||
\(702\) | −10.1645 | + | 9.93165i | −0.383633 | + | 0.374846i | ||||
\(703\) | −15.2312 | −0.574454 | ||||||||
\(704\) | −13.6768 | − | 23.6889i | −0.515464 | − | 0.892811i | ||||
\(705\) | 0.564438 | − | 0.148907i | 0.0212580 | − | 0.00560816i | ||||
\(706\) | 2.28515 | − | 3.95800i | 0.0860029 | − | 0.148961i | ||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 4.26472 | + | 4.29778i | 0.160278 | + | 0.161520i | ||||
\(709\) | 14.7462 | + | 25.5412i | 0.553807 | + | 0.959222i | 0.997995 | + | 0.0632882i | \(0.0201587\pi\) |
−0.444188 | + | 0.895933i | \(0.646508\pi\) | |||||||
\(710\) | 0.382707 | 0.0143628 | ||||||||
\(711\) | −19.9001 | − | 11.6952i | −0.746313 | − | 0.438604i | ||||
\(712\) | −18.5108 | −0.693721 | ||||||||
\(713\) | −8.78551 | − | 15.2169i | −0.329020 | − | 0.569879i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −0.436438 | + | 0.755933i | −0.0163219 | + | 0.0282703i | ||||
\(716\) | −3.98277 | + | 6.89836i | −0.148843 | + | 0.257804i | ||||
\(717\) | −9.70741 | + | 35.6769i | −0.362530 | + | 1.33238i | ||||
\(718\) | 4.37810 | + | 7.58310i | 0.163389 | + | 0.282999i | ||||
\(719\) | 0.434622 | 0.0162087 | 0.00810433 | − | 0.999967i | \(-0.497420\pi\) | ||||
0.00810433 | + | 0.999967i | \(0.497420\pi\) | |||||||
\(720\) | 0.500368 | − | 0.283758i | 0.0186476 | − | 0.0105750i | ||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 22.0691 | + | 38.2248i | 0.821327 | + | 1.42258i | ||||
\(723\) | −24.4808 | − | 24.6707i | −0.910453 | − | 0.917511i | ||||
\(724\) | −6.69640 | + | 11.5985i | −0.248870 | + | 0.431055i | ||||
\(725\) | −23.1744 | + | 40.1392i | −0.860675 | + | 1.49073i | ||||
\(726\) | 0.254269 | − | 0.0670798i | 0.00943680 | − | 0.00248957i | ||||
\(727\) | −13.5839 | − | 23.5280i | −0.503799 | − | 0.872605i | −0.999990 | − | 0.00439187i | \(-0.998602\pi\) |
0.496192 | − | 0.868213i | \(-0.334731\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0.625513 | − | 26.9928i | 0.0231672 | − | 0.999732i | ||||
\(730\) | 0.549420 | 0.0203350 | ||||||||
\(731\) | 6.08798 | + | 10.5447i | 0.225172 | + | 0.390009i | ||||
\(732\) | 7.44417 | − | 1.96388i | 0.275144 | − | 0.0725871i | ||||
\(733\) | −2.83307 | + | 4.90702i | −0.104642 | + | 0.181245i | −0.913592 | − | 0.406632i | \(-0.866703\pi\) |
0.808950 | + | 0.587878i | \(0.200036\pi\) | |||||||
\(734\) | 7.25050 | − | 12.5582i | 0.267621 | − | 0.463533i | ||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −3.92249 | − | 6.79395i | −0.144585 | − | 0.250428i | ||||
\(737\) | 33.2777 | 1.22580 | ||||||||
\(738\) | −21.5420 | + | 12.2164i | −0.792973 | + | 0.449693i | ||||
\(739\) | −13.6108 | −0.500681 | −0.250341 | − | 0.968158i | \(-0.580543\pi\) | ||||
−0.250341 | + | 0.968158i | \(0.580543\pi\) | |||||||
\(740\) | 0.0819427 | + | 0.141929i | 0.00301227 | + | 0.00521741i | ||||
\(741\) | −8.66407 | + | 31.8424i | −0.318282 | + | 1.16976i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −6.33421 | + | 10.9712i | −0.232380 | + | 0.402493i | −0.958508 | − | 0.285066i | \(-0.907985\pi\) |
0.726128 | + | 0.687559i | \(0.241318\pi\) | |||||||
\(744\) | −12.9299 | + | 47.5203i | −0.474033 | + | 1.74218i | ||||
\(745\) | −0.587900 | − | 1.01827i | −0.0215390 | − | 0.0373066i | ||||
\(746\) | −8.61393 | −0.315378 | ||||||||
\(747\) | 3.02314 | + | 1.77668i | 0.110611 | + | 0.0650055i | ||||
\(748\) | 4.21977 | 0.154290 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | −1.41740 | − | 1.42839i | −0.0517563 | − | 0.0521576i | ||||
\(751\) | 3.57269 | − | 6.18808i | 0.130369 | − | 0.225806i | −0.793450 | − | 0.608636i | \(-0.791717\pi\) |
0.923819 | + | 0.382830i | \(0.125050\pi\) | |||||||
\(752\) | 2.90488 | − | 5.03140i | 0.105930 | − | 0.183476i | ||||
\(753\) | 11.4129 | − | 3.01088i | 0.415908 | − | 0.109723i | ||||
\(754\) | 12.7043 | + | 22.0045i | 0.462663 | + | 0.801355i | ||||
\(755\) | 1.18897 | 0.0432712 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 37.6446 | 1.36822 | 0.684108 | − | 0.729381i | \(-0.260192\pi\) | ||||
0.684108 | + | 0.729381i | \(0.260192\pi\) | |||||||
\(758\) | −17.4325 | − | 30.1940i | −0.633178 | − | 1.09670i | ||||
\(759\) | 10.6037 | − | 2.79741i | 0.384890 | − | 0.101540i | ||||
\(760\) | 1.24376 | − | 2.15425i | 0.0451157 | − | 0.0781428i | ||||
\(761\) | 5.02358 | − | 8.70109i | 0.182104 | − | 0.315414i | −0.760493 | − | 0.649347i | \(-0.775042\pi\) |
0.942597 | + | 0.333933i | \(0.108376\pi\) | |||||||
\(762\) | −0.426718 | − | 0.430027i | −0.0154584 | − | 0.0155782i | ||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 17.5572 | 0.635196 | ||||||||
\(765\) | −0.00394189 | + | 0.510395i | −0.000142519 | + | 0.0184534i | ||||
\(766\) | −11.8352 | −0.427625 | ||||||||
\(767\) | −5.53011 | − | 9.57843i | −0.199681 | − | 0.345857i | ||||
\(768\) | −7.06886 | + | 25.9797i | −0.255076 | + | 0.937460i | ||||
\(769\) | −16.1463 | + | 27.9663i | −0.582252 | + | 1.00849i | 0.412960 | + | 0.910749i | \(0.364495\pi\) |
−0.995212 | + | 0.0977407i | \(0.968838\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −6.54301 | + | 24.0470i | −0.235641 | + | 0.866032i | ||||
\(772\) | −0.100635 | − | 0.174305i | −0.00362192 | − | 0.00627336i | ||||
\(773\) | 48.5878 | 1.74758 | 0.873792 | − | 0.486300i | \(-0.161654\pi\) | ||||
0.873792 | + | 0.486300i | \(0.161654\pi\) | |||||||
\(774\) | 0.192853 | − | 24.9706i | 0.00693198 | − | 0.897549i | ||||
\(775\) | 46.2051 | 1.65973 | ||||||||
\(776\) | 5.83694 | + | 10.1099i | 0.209534 | + | 0.362923i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 13.3147 | − | 23.0618i | 0.477356 | − | 0.826806i | ||||
\(779\) | −28.7538 | + | 49.8030i | −1.03021 | + | 1.78438i | ||||
\(780\) | 0.343330 | − | 0.0905755i | 0.0122932 | − | 0.00324312i | ||||
\(781\) | −5.49059 | − | 9.50998i | −0.196469 | − | 0.340294i | ||||
\(782\) | −3.37518 | −0.120696 | ||||||||
\(783\) | −46.4817 | − | 13.0337i | −1.66112 | − | 0.465786i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 0.643678 | + | 1.11488i | 0.0229739 | + | 0.0397919i | ||||
\(786\) | 27.6234 | − | 7.28746i | 0.985294 | − | 0.259935i | ||||
\(787\) | 24.4776 | − | 42.3964i | 0.872531 | − | 1.51127i | 0.0131602 | − | 0.999913i | \(-0.495811\pi\) |
0.859370 | − | 0.511354i | \(-0.170856\pi\) | |||||||
\(788\) | −0.299165 | + | 0.518170i | −0.0106573 | + | 0.0184590i | ||||
\(789\) | −1.87760 | − | 1.89215i | −0.0668442 | − | 0.0673625i | ||||
\(790\) | −0.447448 | − | 0.775003i | −0.0159195 | − | 0.0275734i | ||||
\(791\) | 0 | 0 | ||||||||
\(792\) | −26.4994 | − | 15.5735i | −0.941615 | − | 0.553381i | ||||
\(793\) | −14.0638 | −0.499419 | ||||||||
\(794\) | −13.2652 | − | 22.9759i | −0.470763 | − | 0.815385i | ||||
\(795\) | 0.478488 | − | 1.75855i | 0.0169702 | − | 0.0623694i | ||||
\(796\) | −1.97174 | + | 3.41515i | −0.0698864 | + | 0.121047i | ||||
\(797\) | −1.44417 | + | 2.50137i | −0.0511550 | + | 0.0886030i | −0.890469 | − | 0.455044i | \(-0.849624\pi\) |
0.839314 | + | 0.543647i | \(0.182957\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 2.57755 | + | 4.46445i | 0.0911873 | + | 0.157941i | ||||
\(800\) | 20.6293 | 0.729356 | ||||||||
\(801\) | −15.7346 | + | 8.92306i | −0.555954 | + | 0.315281i | ||||
\(802\) | 1.72294 | 0.0608393 | ||||||||
\(803\) | −7.88237 | − | 13.6527i | −0.278163 | − | 0.481792i | ||||
\(804\) | −9.53510 | − | 9.60903i | −0.336277 | − | 0.338884i | ||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 12.6649 | − | 21.9362i | 0.446102 | − | 0.772671i | ||||
\(807\) | 43.9741 | − | 11.6010i | 1.54796 | − | 0.408375i | ||||
\(808\) | 26.8169 | + | 46.4483i | 0.943417 | + | 1.63405i | ||||
\(809\) | 11.6974 | 0.411258 | 0.205629 | − | 0.978630i | \(-0.434076\pi\) | ||||
0.205629 | + | 0.978630i | \(0.434076\pi\) | |||||||
\(810\) | 0.537332 | − | 0.898350i | 0.0188799 | − | 0.0315648i | ||||
\(811\) | 17.1780 | 0.603199 | 0.301600 | − | 0.953435i | \(-0.402479\pi\) | ||||
0.301600 | + | 0.953435i | \(0.402479\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −30.0341 | + | 7.92343i | −1.05334 | + | 0.277887i | ||||
\(814\) | −3.64830 | + | 6.31904i | −0.127873 | + | 0.221482i | ||||
\(815\) | 0.472627 | − | 0.818614i | 0.0165554 | − | 0.0286748i | ||||
\(816\) | 3.57810 | + | 3.60584i | 0.125259 | + | 0.126230i | ||||
\(817\) | −28.9934 | − | 50.2181i | −1.01435 | − | 1.75691i | ||||
\(818\) | −24.6431 | −0.861624 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0.618775 | 0.0216085 | ||||||||
\(821\) | −17.0068 | − | 29.4567i | −0.593543 | − | 1.02805i | −0.993751 | − | 0.111622i | \(-0.964396\pi\) |
0.400208 | − | 0.916424i | \(-0.368938\pi\) | |||||||
\(822\) | 7.64652 | − | 28.1027i | 0.266703 | − | 0.980193i | ||||
\(823\) | −21.6890 | + | 37.5664i | −0.756031 | + | 1.30948i | 0.188829 | + | 0.982010i | \(0.439531\pi\) |
−0.944860 | + | 0.327474i | \(0.893803\pi\) | |||||||
\(824\) | −13.4037 | + | 23.2160i | −0.466942 | + | 0.808767i | ||||
\(825\) | −7.57125 | + | 27.8260i | −0.263597 | + | 0.968779i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −34.0909 | −1.18546 | −0.592728 | − | 0.805403i | \(-0.701949\pi\) | ||||
−0.592728 | + | 0.805403i | \(0.701949\pi\) | |||||||
\(828\) | −3.84605 | − | 2.26030i | −0.133659 | − | 0.0785508i | ||||
\(829\) | 16.9167 | 0.587540 | 0.293770 | − | 0.955876i | \(-0.405090\pi\) | ||||
0.293770 | + | 0.955876i | \(0.405090\pi\) | |||||||
\(830\) | 0.0679744 | + | 0.117735i | 0.00235943 | + | 0.00408665i | ||||
\(831\) | −23.0231 | − | 23.2016i | −0.798661 | − | 0.804853i | ||||
\(832\) | 10.1632 | − | 17.6032i | 0.352345 | − | 0.610280i | ||||
\(833\) | 0 | 0 | ||||||||
\(834\) | −14.9950 | + | 3.95591i | −0.519236 | + | 0.136982i | ||||
\(835\) | 0.918434 | + | 1.59077i | 0.0317837 | + | 0.0550510i | ||||
\(836\) | −20.0963 | −0.695044 | ||||||||
\(837\) | 11.9163 | + | 46.6261i | 0.411887 | + | 1.61163i | ||||
\(838\) | −6.58705 | −0.227546 | ||||||||
\(839\) | 8.16244 | + | 14.1378i | 0.281799 | + | 0.488089i | 0.971828 | − | 0.235692i | \(-0.0757357\pi\) |
−0.690029 | + | 0.723782i | \(0.742402\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −28.6560 | + | 49.6336i | −0.988138 | + | 1.71150i | ||||
\(842\) | −8.06812 | + | 13.9744i | −0.278046 | + | 0.481589i | ||||
\(843\) | 6.08975 | + | 6.13696i | 0.209742 | + | 0.211368i | ||||
\(844\) | 2.82590 | + | 4.89459i | 0.0972713 | + | 0.168479i | ||||
\(845\) | 0.722428 | 0.0248523 | ||||||||
\(846\) | 0.0816511 | − | 10.5721i | 0.00280722 | − | 0.363478i | ||||
\(847\) | 0 | 0 | ||||||||
\(848\) | −9.06915 | − | 15.7082i | −0.311436 | − | 0.539423i | ||||
\(849\) | 6.99974 | − | 25.7256i | 0.240230 | − | 0.882901i | ||||
\(850\) | 4.43772 | − | 7.68635i | 0.152212 | − | 0.263640i | ||||
\(851\) | −1.88062 | + | 3.25733i | −0.0644668 | + | 0.111660i | ||||
\(852\) | −1.17281 | + | 4.31032i | −0.0401797 | + | 0.147669i | ||||
\(853\) | 14.4524 | + | 25.0323i | 0.494841 | + | 0.857089i | 0.999982 | − | 0.00594733i | \(-0.00189311\pi\) |
−0.505142 | + | 0.863036i | \(0.668560\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0.0187729 | − | 2.43071i | 0.000642020 | − | 0.0831285i | ||||
\(856\) | −55.7095 | −1.90411 | ||||||||
\(857\) | −14.5284 | − | 25.1639i | −0.496280 | − | 0.859582i | 0.503711 | − | 0.863872i | \(-0.331968\pi\) |
−0.999991 | + | 0.00429061i | \(0.998634\pi\) | |||||||
\(858\) | 11.1353 | + | 11.2217i | 0.380154 | + | 0.383102i | ||||
\(859\) | −6.29820 | + | 10.9088i | −0.214892 | + | 0.372203i | −0.953239 | − | 0.302217i | \(-0.902273\pi\) |
0.738347 | + | 0.674421i | \(0.235607\pi\) | |||||||
\(860\) | −0.311966 | + | 0.540341i | −0.0106380 | + | 0.0184255i | ||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −10.6992 | − | 18.5315i | −0.364415 | − | 0.631185i | ||||
\(863\) | −14.6662 | −0.499243 | −0.249621 | − | 0.968344i | \(-0.580306\pi\) | ||||
−0.249621 | + | 0.968344i | \(0.580306\pi\) | |||||||
\(864\) | 5.32029 | + | 20.8173i | 0.181000 | + | 0.708219i | ||||
\(865\) | −0.298398 | −0.0101458 | ||||||||
\(866\) | −0.745594 | − | 1.29141i | −0.0253363 | − | 0.0438838i | ||||
\(867\) | 24.1124 | − | 6.36122i | 0.818901 | − | 0.216038i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −12.8388 | + | 22.2375i | −0.435527 | + | 0.754354i | ||||
\(870\) | −1.31829 | − | 1.32852i | −0.0446944 | − | 0.0450409i | ||||
\(871\) | 12.3643 | + | 21.4156i | 0.418948 | + | 0.725639i | ||||
\(872\) | −12.9631 | −0.438985 | ||||||||
\(873\) | 9.83497 | + | 5.77995i | 0.332863 | + | 0.195622i | ||||
\(874\) | 16.0740 | 0.543711 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | −1.68370 | + | 6.18797i | −0.0568869 | + | 0.209072i | ||||
\(877\) | −16.5951 | + | 28.7435i | −0.560376 | + | 0.970600i | 0.437087 | + | 0.899419i | \(0.356010\pi\) |
−0.997463 | + | 0.0711811i | \(0.977323\pi\) | |||||||
\(878\) | −9.56205 | + | 16.5620i | −0.322704 | + | 0.558939i | ||||
\(879\) | −11.7336 | + | 43.1235i | −0.395763 | + | 1.45452i | ||||
\(880\) | −0.319953 | − | 0.554174i | −0.0107856 | − | 0.0186812i | ||||
\(881\) | 31.7179 | 1.06860 | 0.534301 | − | 0.845294i | \(-0.320575\pi\) | ||||
0.534301 | + | 0.845294i | \(0.320575\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −39.5231 | −1.33006 | −0.665029 | − | 0.746818i | \(-0.731581\pi\) | ||||
−0.665029 | + | 0.746818i | \(0.731581\pi\) | |||||||
\(884\) | 1.56785 | + | 2.71559i | 0.0527324 | + | 0.0913352i | ||||
\(885\) | 0.573847 | + | 0.578296i | 0.0192897 | + | 0.0194392i | ||||
\(886\) | 10.8131 | − | 18.7288i | 0.363272 | − | 0.629206i | ||||
\(887\) | 24.9513 | − | 43.2169i | 0.837782 | − | 1.45108i | −0.0539627 | − | 0.998543i | \(-0.517185\pi\) |
0.891745 | − | 0.452538i | \(-0.149481\pi\) | |||||||
\(888\) | 10.1932 | − | 2.68912i | 0.342062 | − | 0.0902411i | ||||
\(889\) | 0 | 0 | ||||||||
\(890\) | −0.701292 | −0.0235074 | ||||||||
\(891\) | −30.0323 | − | 0.463920i | −1.00612 | − | 0.0155419i | ||||
\(892\) | 8.76457 | 0.293459 | ||||||||
\(893\) | −12.2754 | − | 21.2616i | −0.410779 | − | 0.711491i | ||||
\(894\) | −20.5908 | + | 5.43215i | −0.688659 | + | 0.181678i | ||||
\(895\) | −0.535910 | + | 0.928223i | −0.0179135 | + | 0.0310271i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.74003 | + | 5.78454i | 0.191654 | + | 0.193140i | ||||
\(898\) | −9.77891 | − | 16.9376i | −0.326326 | − | 0.565214i | ||||
\(899\) | 86.0443 | 2.86974 | ||||||||
\(900\) | 10.2042 | − | 5.78680i | 0.340141 | − | 0.192893i | ||||
\(901\) | 16.0944 | 0.536183 | ||||||||
\(902\) | 13.7747 | + | 23.8585i | 0.458648 | + | 0.794401i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 3.15671 | − | 5.46757i | 0.104990 | − | 0.181849i | ||||
\(905\) | −0.901048 | + | 1.56066i | −0.0299518 | + | 0.0518781i | ||||
\(906\) | 5.65365 | − | 20.7784i | 0.187830 | − | 0.690317i | ||||
\(907\) | 6.96080 | + | 12.0565i | 0.231129 | + | 0.400328i | 0.958141 | − | 0.286298i | \(-0.0924246\pi\) |
−0.727011 | + | 0.686625i | \(0.759091\pi\) | |||||||
\(908\) | −18.6315 | −0.618308 | ||||||||
\(909\) | 45.1853 | + | 26.5551i | 1.49870 | + | 0.880778i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 2.70428 | + | 4.68394i | 0.0895967 | + | 0.155186i | 0.907341 | − | 0.420396i | \(-0.138109\pi\) |
−0.817744 | + | 0.575582i | \(0.804776\pi\) | |||||||
\(912\) | −17.0404 | − | 17.1725i | −0.564264 | − | 0.568638i | ||||
\(913\) | 1.95042 | − | 3.37822i | 0.0645494 | − | 0.111803i | ||||
\(914\) | 0.267681 | − | 0.463637i | 0.00885409 | − | 0.0153357i | ||||
\(915\) | 1.00166 | − | 0.264254i | 0.0331140 | − | 0.00873596i | ||||
\(916\) | −0.746758 | − | 1.29342i | −0.0246736 | − | 0.0427359i | ||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 8.90089 | + | 2.49585i | 0.293773 | + | 0.0823754i | ||||
\(919\) | 34.0283 | 1.12249 | 0.561245 | − | 0.827649i | \(-0.310322\pi\) | ||||
0.561245 | + | 0.827649i | \(0.310322\pi\) | |||||||
\(920\) | −0.307138 | − | 0.531978i | −0.0101260 | − | 0.0175388i | ||||
\(921\) | −37.3326 | + | 9.84889i | −1.23015 | + | 0.324532i | ||||
\(922\) | 4.40781 | − | 7.63455i | 0.145163 | − | 0.251430i | ||||
\(923\) | 4.08004 | − | 7.06683i | 0.134296 | − | 0.232608i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −4.94531 | − | 8.56554i | −0.162601 | − | 0.281633i | ||||
\(926\) | 11.5637 | 0.380006 | ||||||||
\(927\) | −0.202313 | + | 26.1953i | −0.00664482 | + | 0.860368i | ||||
\(928\) | 38.4165 | 1.26108 | ||||||||
\(929\) | 5.31646 | + | 9.20837i | 0.174427 | + | 0.302117i | 0.939963 | − | 0.341277i | \(-0.110859\pi\) |
−0.765536 | + | 0.643393i | \(0.777526\pi\) | |||||||
\(930\) | −0.489857 | + | 1.80033i | −0.0160631 | + | 0.0590353i | ||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 2.56375 | − | 4.44055i | 0.0839785 | − | 0.145455i | ||||
\(933\) | 0.595653 | − | 2.18916i | 0.0195008 | − | 0.0716698i | ||||
\(934\) | −12.0746 | − | 20.9137i | −0.395092 | − | 0.684319i | ||||
\(935\) | 0.567799 | 0.0185690 | ||||||||
\(936\) | 0.176397 | − | 22.8397i | 0.00576570 | − | 0.746540i | ||||
\(937\) | −52.6692 | −1.72063 | −0.860314 | − | 0.509765i | \(-0.829732\pi\) | ||||
−0.860314 | + | 0.509765i | \(0.829732\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | −26.3241 | − | 26.5282i | −0.859053 | − | 0.865714i | ||||
\(940\) | −0.132082 | + | 0.228772i | −0.00430802 | + | 0.00746172i | ||||
\(941\) | −17.1828 | + | 29.7615i | −0.560143 | + | 0.970197i | 0.437340 | + | 0.899296i | \(0.355921\pi\) |
−0.997483 | + | 0.0709006i | \(0.977413\pi\) | |||||||
\(942\) | 22.5444 | − | 5.94754i | 0.734536 | − | 0.193781i | ||||
\(943\) | 7.10057 | + | 12.2985i | 0.231226 | + | 0.400496i | ||||
\(944\) | 8.10825 | 0.263901 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | −27.7791 | −0.903175 | ||||||||
\(947\) | 20.2920 | + | 35.1468i | 0.659401 | + | 1.14212i | 0.980771 | + | 0.195162i | \(0.0625234\pi\) |
−0.321370 | + | 0.946954i | \(0.604143\pi\) | |||||||
\(948\) | 10.0998 | − | 2.66448i | 0.328027 | − | 0.0865384i | ||||
\(949\) | 5.85736 | − | 10.1453i | 0.190138 | − | 0.329329i | ||||
\(950\) | −21.1342 | + | 36.6056i | −0.685685 | + | 1.18764i | ||||
\(951\) | −30.2341 | − | 30.4685i | −0.980408 | − | 0.988009i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | −22.6904 | −0.735013 | −0.367507 | − | 0.930021i | \(-0.619789\pi\) | ||||
−0.367507 | + | 0.930021i | \(0.619789\pi\) | |||||||
\(954\) | −28.4571 | − | 16.7241i | −0.921333 | − | 0.541462i | ||||
\(955\) | 2.36244 | 0.0764468 | ||||||||
\(956\) | −8.36589 | − | 14.4901i | −0.270572 | − | 0.468645i | ||||
\(957\) | −14.0994 | + | 51.8184i | −0.455769 | + | 1.67505i | ||||
\(958\) | −2.20656 | + | 3.82187i | −0.0712907 | + | 0.123479i | ||||
\(959\) | 0 | 0 | ||||||||
\(960\) | −0.393096 | + | 1.44472i | −0.0126871 | + | 0.0466280i | ||||
\(961\) | −27.3888 | − | 47.4387i | −0.883509 | − | 1.53028i | ||||
\(962\) | −5.42208 | −0.174815 | ||||||||
\(963\) | −47.3543 | + | 26.8546i | −1.52597 | + | 0.865376i | ||||
\(964\) | 15.7279 | 0.506562 | ||||||||
\(965\) | −0.0135411 | − | 0.0234539i | −0.000435904 | − | 0.000755008i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | −12.1388 | + | 21.0250i | −0.390357 | + | 0.676118i | −0.992497 | − | 0.122273i | \(-0.960982\pi\) |
0.602139 | + | 0.798391i | \(0.294315\pi\) | |||||||
\(968\) | −0.211325 | + | 0.366026i | −0.00679224 | + | 0.0117645i | ||||
\(969\) | 20.7561 | − | 5.47578i | 0.666784 | − | 0.175907i | ||||
\(970\) | 0.221136 | + | 0.383019i | 0.00710025 | + | 0.0122980i | ||||
\(971\) | −45.5771 | −1.46264 | −0.731319 | − | 0.682035i | \(-0.761095\pi\) | ||||
−0.731319 | + | 0.682035i | \(0.761095\pi\) | |||||||
\(972\) | 8.47121 | + | 8.80481i | 0.271714 | + | 0.282414i | ||||
\(973\) | 0 | 0 | ||||||||
\(974\) | −14.5988 | − | 25.2858i | −0.467774 | − | 0.810209i | ||||
\(975\) | −20.7203 | + | 5.46631i | −0.663580 | + | 0.175062i | ||||
\(976\) | 5.15508 | − | 8.92885i | 0.165010 | − | 0.285806i | ||||
\(977\) | 7.34481 | − | 12.7216i | 0.234981 | − | 0.407000i | −0.724286 | − | 0.689500i | \(-0.757830\pi\) |
0.959267 | + | 0.282500i | \(0.0911637\pi\) | |||||||
\(978\) | −12.0587 | − | 12.1522i | −0.385594 | − | 0.388584i | ||||
\(979\) | 10.0612 | + | 17.4266i | 0.321558 | + | 0.556956i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −11.0189 | + | 6.24881i | −0.351807 | + | 0.199509i | ||||
\(982\) | 31.3528 | 1.00051 | ||||||||
\(983\) | −22.2955 | − | 38.6169i | −0.711115 | − | 1.23169i | −0.964439 | − | 0.264305i | \(-0.914857\pi\) |
0.253324 | − | 0.967381i | \(-0.418476\pi\) | |||||||
\(984\) | 10.4501 | − | 38.4065i | 0.333138 | − | 1.22436i | ||||
\(985\) | −0.0402548 | + | 0.0697234i | −0.00128262 | + | 0.00222157i | ||||
\(986\) | 8.26404 | − | 14.3137i | 0.263181 | − | 0.455842i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | −7.46673 | − | 12.9328i | −0.237548 | − | 0.411446i | ||||
\(989\) | −14.3195 | −0.455334 | ||||||||
\(990\) | −1.00395 | − | 0.590013i | −0.0319075 | − | 0.0187518i | ||||
\(991\) | 24.1829 | 0.768196 | 0.384098 | − | 0.923292i | \(-0.374512\pi\) | ||||
0.384098 | + | 0.923292i | \(0.374512\pi\) | |||||||
\(992\) | −19.1487 | − | 33.1665i | −0.607971 | − | 1.05304i | ||||
\(993\) | 16.8911 | + | 17.0221i | 0.536024 | + | 0.540179i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | −0.265311 | + | 0.459532i | −0.00841093 | + | 0.0145682i | ||||
\(996\) | −1.53433 | + | 0.404778i | −0.0486170 | + | 0.0128259i | ||||
\(997\) | −5.43262 | − | 9.40957i | −0.172053 | − | 0.298004i | 0.767085 | − | 0.641546i | \(-0.221707\pi\) |
−0.939137 | + | 0.343542i | \(0.888373\pi\) | |||||||
\(998\) | 8.19521 | 0.259415 | ||||||||
\(999\) | 7.36820 | − | 7.19943i | 0.233119 | − | 0.227780i |
(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 | 441.2.f.h.148.7 | ✓ | 24 | |
3.2 | odd | 2 | 1323.2.f.h.442.6 | 24 | |||
7.2 | even | 3 | 441.2.g.h.67.8 | 24 | |||
7.3 | odd | 6 | 441.2.h.h.373.5 | 24 | |||
7.4 | even | 3 | 441.2.h.h.373.6 | 24 | |||
7.5 | odd | 6 | 441.2.g.h.67.7 | 24 | |||
7.6 | odd | 2 | inner | 441.2.f.h.148.8 | yes | 24 | |
9.2 | odd | 6 | 1323.2.f.h.883.6 | 24 | |||
9.4 | even | 3 | 3969.2.a.bh.1.5 | 12 | |||
9.5 | odd | 6 | 3969.2.a.bi.1.8 | 12 | |||
9.7 | even | 3 | inner | 441.2.f.h.295.7 | yes | 24 | |
21.2 | odd | 6 | 1323.2.g.h.361.6 | 24 | |||
21.5 | even | 6 | 1323.2.g.h.361.5 | 24 | |||
21.11 | odd | 6 | 1323.2.h.h.226.7 | 24 | |||
21.17 | even | 6 | 1323.2.h.h.226.8 | 24 | |||
21.20 | even | 2 | 1323.2.f.h.442.5 | 24 | |||
63.2 | odd | 6 | 1323.2.h.h.802.7 | 24 | |||
63.11 | odd | 6 | 1323.2.g.h.667.6 | 24 | |||
63.13 | odd | 6 | 3969.2.a.bh.1.6 | 12 | |||
63.16 | even | 3 | 441.2.h.h.214.6 | 24 | |||
63.20 | even | 6 | 1323.2.f.h.883.5 | 24 | |||
63.25 | even | 3 | 441.2.g.h.79.8 | 24 | |||
63.34 | odd | 6 | inner | 441.2.f.h.295.8 | yes | 24 | |
63.38 | even | 6 | 1323.2.g.h.667.5 | 24 | |||
63.41 | even | 6 | 3969.2.a.bi.1.7 | 12 | |||
63.47 | even | 6 | 1323.2.h.h.802.8 | 24 | |||
63.52 | odd | 6 | 441.2.g.h.79.7 | 24 | |||
63.61 | odd | 6 | 441.2.h.h.214.5 | 24 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
441.2.f.h.148.7 | ✓ | 24 | 1.1 | even | 1 | trivial | |
441.2.f.h.148.8 | yes | 24 | 7.6 | odd | 2 | inner | |
441.2.f.h.295.7 | yes | 24 | 9.7 | even | 3 | inner | |
441.2.f.h.295.8 | yes | 24 | 63.34 | odd | 6 | inner | |
441.2.g.h.67.7 | 24 | 7.5 | odd | 6 | |||
441.2.g.h.67.8 | 24 | 7.2 | even | 3 | |||
441.2.g.h.79.7 | 24 | 63.52 | odd | 6 | |||
441.2.g.h.79.8 | 24 | 63.25 | even | 3 | |||
441.2.h.h.214.5 | 24 | 63.61 | odd | 6 | |||
441.2.h.h.214.6 | 24 | 63.16 | even | 3 | |||
441.2.h.h.373.5 | 24 | 7.3 | odd | 6 | |||
441.2.h.h.373.6 | 24 | 7.4 | even | 3 | |||
1323.2.f.h.442.5 | 24 | 21.20 | even | 2 | |||
1323.2.f.h.442.6 | 24 | 3.2 | odd | 2 | |||
1323.2.f.h.883.5 | 24 | 63.20 | even | 6 | |||
1323.2.f.h.883.6 | 24 | 9.2 | odd | 6 | |||
1323.2.g.h.361.5 | 24 | 21.5 | even | 6 | |||
1323.2.g.h.361.6 | 24 | 21.2 | odd | 6 | |||
1323.2.g.h.667.5 | 24 | 63.38 | even | 6 | |||
1323.2.g.h.667.6 | 24 | 63.11 | odd | 6 | |||
1323.2.h.h.226.7 | 24 | 21.11 | odd | 6 | |||
1323.2.h.h.226.8 | 24 | 21.17 | even | 6 | |||
1323.2.h.h.802.7 | 24 | 63.2 | odd | 6 | |||
1323.2.h.h.802.8 | 24 | 63.47 | even | 6 | |||
3969.2.a.bh.1.5 | 12 | 9.4 | even | 3 | |||
3969.2.a.bh.1.6 | 12 | 63.13 | odd | 6 | |||
3969.2.a.bi.1.7 | 12 | 63.41 | even | 6 | |||
3969.2.a.bi.1.8 | 12 | 9.5 | odd | 6 |