Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1050,2,Mod(157,1050)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1050, base_ring=CyclotomicField(12))
chi = DirichletCharacter(H, H._module([0, 3, 2]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1050.157");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1050 = 2 \cdot 3 \cdot 5^{2} \cdot 7 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1050.bc (of order \(12\), degree \(4\), minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(8.38429221223\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(4\) over \(\Q(\zeta_{12})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 4 x^{15} + 12 x^{14} - 48 x^{13} + 67 x^{12} - 24 x^{11} + 118 x^{10} - 176 x^{9} + 351 x^{8} + \cdots + 4 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 210) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{12}]$ |
Embedding invariants
Embedding label | 943.2 | ||
Root | \(0.117630 - 0.893490i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1050.943 |
Dual form | 1050.2.bc.h.157.2 |
$q$-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 \(\left(\mathbb{Z}/1050\mathbb{Z}\right)^\times\).
\(n\) | \(127\) | \(451\) | \(701\) |
\(\chi(n)\) | \(e\left(\frac{3}{4}\right)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.258819 | − | 0.965926i | −0.183013 | − | 0.683013i | ||||
\(3\) | −0.965926 | − | 0.258819i | −0.557678 | − | 0.149429i | ||||
\(4\) | −0.866025 | + | 0.500000i | −0.433013 | + | 0.250000i | ||||
\(5\) | 0 | 0 | ||||||||
\(6\) | 1.00000i | 0.408248i | ||||||||
\(7\) | 2.55046 | − | 0.703686i | 0.963982 | − | 0.265968i | ||||
\(8\) | 0.707107 | + | 0.707107i | 0.250000 | + | 0.250000i | ||||
\(9\) | 0.866025 | + | 0.500000i | 0.288675 | + | 0.166667i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 0.989376 | + | 1.71365i | 0.298308 | + | 0.516685i | 0.975749 | − | 0.218892i | \(-0.0702443\pi\) |
−0.677441 | + | 0.735577i | \(0.736911\pi\) | |||||||
\(12\) | 0.965926 | − | 0.258819i | 0.278839 | − | 0.0747146i | ||||
\(13\) | −2.19222 | + | 2.19222i | −0.608011 | + | 0.608011i | −0.942426 | − | 0.334415i | \(-0.891461\pi\) |
0.334415 | + | 0.942426i | \(0.391461\pi\) | |||||||
\(14\) | −1.33981 | − | 2.28142i | −0.358081 | − | 0.609736i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 0.500000 | − | 0.866025i | 0.125000 | − | 0.216506i | ||||
\(17\) | −1.19130 | + | 4.44599i | −0.288932 | + | 1.07831i | 0.656985 | + | 0.753903i | \(0.271831\pi\) |
−0.945918 | + | 0.324407i | \(0.894835\pi\) | |||||||
\(18\) | 0.258819 | − | 0.965926i | 0.0610042 | − | 0.227671i | ||||
\(19\) | −2.10939 | + | 3.65357i | −0.483928 | + | 0.838188i | −0.999830 | − | 0.0184602i | \(-0.994124\pi\) |
0.515902 | + | 0.856648i | \(0.327457\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −2.64568 | + | 0.0196015i | −0.577334 | + | 0.00427740i | ||||
\(22\) | 1.39919 | − | 1.39919i | 0.298308 | − | 0.298308i | ||||
\(23\) | −5.68202 | + | 1.52249i | −1.18478 | + | 0.317462i | −0.796822 | − | 0.604214i | \(-0.793487\pi\) |
−0.387961 | + | 0.921676i | \(0.626821\pi\) | |||||||
\(24\) | −0.500000 | − | 0.866025i | −0.102062 | − | 0.176777i | ||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 2.68491 | + | 1.55013i | 0.526553 | + | 0.304006i | ||||
\(27\) | −0.707107 | − | 0.707107i | −0.136083 | − | 0.136083i | ||||
\(28\) | −1.85692 | + | 1.88464i | −0.350924 | + | 0.356163i | ||||
\(29\) | − | 8.94996i | − | 1.66197i | −0.556298 | − | 0.830983i | \(-0.687779\pi\) | ||
0.556298 | − | 0.830983i | \(-0.312221\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −1.50157 | + | 0.866930i | −0.269689 | + | 0.155705i | −0.628747 | − | 0.777610i | \(-0.716432\pi\) |
0.359057 | + | 0.933316i | \(0.383098\pi\) | |||||||
\(32\) | −0.965926 | − | 0.258819i | −0.170753 | − | 0.0457532i | ||||
\(33\) | −0.512139 | − | 1.91133i | −0.0891519 | − | 0.332720i | ||||
\(34\) | 4.60282 | 0.789378 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | −1.00000 | −0.166667 | ||||||||
\(37\) | 0.717425 | + | 2.67747i | 0.117944 | + | 0.440173i | 0.999490 | − | 0.0319248i | \(-0.0101637\pi\) |
−0.881546 | + | 0.472097i | \(0.843497\pi\) | |||||||
\(38\) | 4.07503 | + | 1.09190i | 0.661058 | + | 0.177130i | ||||
\(39\) | 2.68491 | − | 1.55013i | 0.429929 | − | 0.248220i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 6.55691i | 1.02402i | 0.858980 | + | 0.512008i | \(0.171098\pi\) | ||||
−0.858980 | + | 0.512008i | \(0.828902\pi\) | |||||||
\(42\) | 0.703686 | + | 2.55046i | 0.108581 | + | 0.393544i | ||||
\(43\) | 6.33724 | + | 6.33724i | 0.966421 | + | 0.966421i | 0.999454 | − | 0.0330335i | \(-0.0105168\pi\) |
−0.0330335 | + | 0.999454i | \(0.510517\pi\) | |||||||
\(44\) | −1.71365 | − | 0.989376i | −0.258342 | − | 0.149154i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.94123 | + | 5.09436i | 0.433661 | + | 0.751122i | ||||
\(47\) | −5.87298 | + | 1.57366i | −0.856663 | + | 0.229542i | −0.660312 | − | 0.750992i | \(-0.729576\pi\) |
−0.196351 | + | 0.980534i | \(0.562909\pi\) | |||||||
\(48\) | −0.707107 | + | 0.707107i | −0.102062 | + | 0.102062i | ||||
\(49\) | 6.00965 | − | 3.58944i | 0.858522 | − | 0.512777i | ||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 2.30141 | − | 3.98616i | 0.322262 | − | 0.558174i | ||||
\(52\) | 0.802407 | − | 2.99462i | 0.111274 | − | 0.415280i | ||||
\(53\) | −2.95926 | + | 11.0441i | −0.406485 | + | 1.51702i | 0.394814 | + | 0.918761i | \(0.370809\pi\) |
−0.801300 | + | 0.598263i | \(0.795858\pi\) | |||||||
\(54\) | −0.500000 | + | 0.866025i | −0.0680414 | + | 0.117851i | ||||
\(55\) | 0 | 0 | ||||||||
\(56\) | 2.30103 | + | 1.30586i | 0.307487 | + | 0.174503i | ||||
\(57\) | 2.98313 | − | 2.98313i | 0.395125 | − | 0.395125i | ||||
\(58\) | −8.64500 | + | 2.31642i | −1.13514 | + | 0.304161i | ||||
\(59\) | 2.10351 | + | 3.64339i | 0.273854 | + | 0.474329i | 0.969845 | − | 0.243721i | \(-0.0783682\pi\) |
−0.695991 | + | 0.718050i | \(0.745035\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 9.63018 | + | 5.55999i | 1.23302 | + | 0.711883i | 0.967658 | − | 0.252266i | \(-0.0811759\pi\) |
0.265360 | + | 0.964149i | \(0.414509\pi\) | |||||||
\(62\) | 1.22602 | + | 1.22602i | 0.155705 | + | 0.155705i | ||||
\(63\) | 2.56060 | + | 0.665818i | 0.322606 | + | 0.0838852i | ||||
\(64\) | 1.00000i | 0.125000i | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.71365 | + | 0.989376i | −0.210936 | + | 0.121784i | ||||
\(67\) | 5.32434 | + | 1.42665i | 0.650472 | + | 0.174294i | 0.568942 | − | 0.822377i | \(-0.307353\pi\) |
0.0815298 | + | 0.996671i | \(0.474019\pi\) | |||||||
\(68\) | −1.19130 | − | 4.44599i | −0.144466 | − | 0.539155i | ||||
\(69\) | 5.88246 | 0.708165 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −3.86002 | −0.458100 | −0.229050 | − | 0.973415i | \(-0.573562\pi\) | ||||
−0.229050 | + | 0.973415i | \(0.573562\pi\) | |||||||
\(72\) | 0.258819 | + | 0.965926i | 0.0305021 | + | 0.113835i | ||||
\(73\) | 14.7013 | + | 3.93920i | 1.72066 | + | 0.461048i | 0.977997 | − | 0.208621i | \(-0.0668974\pi\) |
0.742660 | + | 0.669669i | \(0.233564\pi\) | |||||||
\(74\) | 2.40055 | − | 1.38596i | 0.279058 | − | 0.161114i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | − | 4.21878i | − | 0.483928i | ||||||
\(77\) | 3.72923 | + | 3.67438i | 0.424985 | + | 0.418734i | ||||
\(78\) | −2.19222 | − | 2.19222i | −0.248220 | − | 0.248220i | ||||
\(79\) | −2.21282 | − | 1.27757i | −0.248962 | − | 0.143738i | 0.370327 | − | 0.928901i | \(-0.379246\pi\) |
−0.619289 | + | 0.785163i | \(0.712579\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 0.500000 | + | 0.866025i | 0.0555556 | + | 0.0962250i | ||||
\(82\) | 6.33349 | − | 1.69705i | 0.699416 | − | 0.187408i | ||||
\(83\) | 9.52969 | − | 9.52969i | 1.04602 | − | 1.04602i | 0.0471311 | − | 0.998889i | \(-0.484992\pi\) |
0.998889 | − | 0.0471311i | \(-0.0150078\pi\) | |||||||
\(84\) | 2.28142 | − | 1.33981i | 0.248924 | − | 0.146186i | ||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.48111 | − | 7.76151i | 0.483210 | − | 0.836945i | ||||
\(87\) | −2.31642 | + | 8.64500i | −0.248346 | + | 0.926841i | ||||
\(88\) | −0.512139 | + | 1.91133i | −0.0545942 | + | 0.203748i | ||||
\(89\) | −3.09593 | + | 5.36231i | −0.328168 | + | 0.568404i | −0.982148 | − | 0.188108i | \(-0.939765\pi\) |
0.653980 | + | 0.756512i | \(0.273098\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −4.04852 | + | 7.13378i | −0.424400 | + | 0.747824i | ||||
\(92\) | 4.15953 | − | 4.15953i | 0.433661 | − | 0.433661i | ||||
\(93\) | 1.67478 | − | 0.448756i | 0.173667 | − | 0.0465339i | ||||
\(94\) | 3.04008 | + | 5.26557i | 0.313560 | + | 0.543102i | ||||
\(95\) | 0 | 0 | ||||||||
\(96\) | 0.866025 | + | 0.500000i | 0.0883883 | + | 0.0510310i | ||||
\(97\) | −1.48031 | − | 1.48031i | −0.150303 | − | 0.150303i | 0.627951 | − | 0.778253i | \(-0.283894\pi\) |
−0.778253 | + | 0.627951i | \(0.783894\pi\) | |||||||
\(98\) | −5.02254 | − | 4.87586i | −0.507354 | − | 0.492537i | ||||
\(99\) | 1.97875i | 0.198872i | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −8.70112 | + | 5.02360i | −0.865794 | + | 0.499866i | −0.865948 | − | 0.500134i | \(-0.833284\pi\) |
0.000154194 | 1.00000i | \(0.499951\pi\) | ||||||||
\(102\) | −4.44599 | − | 1.19130i | −0.440218 | − | 0.117956i | ||||
\(103\) | −1.29095 | − | 4.81790i | −0.127201 | − | 0.474722i | 0.872707 | − | 0.488244i | \(-0.162362\pi\) |
−0.999909 | + | 0.0135219i | \(0.995696\pi\) | |||||||
\(104\) | −3.10026 | −0.304006 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 11.4337 | 1.11054 | ||||||||
\(107\) | −1.56576 | − | 5.84351i | −0.151368 | − | 0.564913i | −0.999389 | − | 0.0349507i | \(-0.988873\pi\) |
0.848021 | − | 0.529963i | \(-0.177794\pi\) | |||||||
\(108\) | 0.965926 | + | 0.258819i | 0.0929463 | + | 0.0249049i | ||||
\(109\) | −8.44287 | + | 4.87449i | −0.808680 | + | 0.466892i | −0.846497 | − | 0.532393i | \(-0.821293\pi\) |
0.0378171 | + | 0.999285i | \(0.487960\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | − | 2.77192i | − | 0.263099i | ||||||
\(112\) | 0.665818 | − | 2.56060i | 0.0629139 | − | 0.241954i | ||||
\(113\) | −6.02504 | − | 6.02504i | −0.566788 | − | 0.566788i | 0.364439 | − | 0.931227i | \(-0.381261\pi\) |
−0.931227 | + | 0.364439i | \(0.881261\pi\) | |||||||
\(114\) | −3.65357 | − | 2.10939i | −0.342189 | − | 0.197563i | ||||
\(115\) | 0 | 0 | ||||||||
\(116\) | 4.47498 | + | 7.75089i | 0.415491 | + | 0.719652i | ||||
\(117\) | −2.99462 | + | 0.802407i | −0.276853 | + | 0.0741826i | ||||
\(118\) | 2.97481 | − | 2.97481i | 0.273854 | − | 0.273854i | ||||
\(119\) | 0.0902224 | + | 12.1776i | 0.00827067 | + | 1.11632i | ||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 3.54227 | − | 6.13539i | 0.322024 | − | 0.557763i | ||||
\(122\) | 2.87806 | − | 10.7411i | 0.260567 | − | 0.972451i | ||||
\(123\) | 1.69705 | − | 6.33349i | 0.153018 | − | 0.571071i | ||||
\(124\) | 0.866930 | − | 1.50157i | 0.0778527 | − | 0.134845i | ||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −0.0196015 | − | 2.64568i | −0.00174624 | − | 0.235696i | ||||
\(127\) | 8.92770 | − | 8.92770i | 0.792205 | − | 0.792205i | −0.189647 | − | 0.981852i | \(-0.560734\pi\) |
0.981852 | + | 0.189647i | \(0.0607345\pi\) | |||||||
\(128\) | 0.965926 | − | 0.258819i | 0.0853766 | − | 0.0228766i | ||||
\(129\) | −4.48111 | − | 7.76151i | −0.394540 | − | 0.683363i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −4.43543 | − | 2.56080i | −0.387526 | − | 0.223738i | 0.293562 | − | 0.955940i | \(-0.405159\pi\) |
−0.681087 | + | 0.732202i | \(0.738493\pi\) | |||||||
\(132\) | 1.39919 | + | 1.39919i | 0.121784 | + | 0.121784i | ||||
\(133\) | −2.80894 | + | 10.8026i | −0.243566 | + | 0.936707i | ||||
\(134\) | − | 5.51217i | − | 0.476179i | ||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −3.98616 | + | 2.30141i | −0.341811 | + | 0.197344i | ||||
\(137\) | −11.1877 | − | 2.99773i | −0.955829 | − | 0.256114i | −0.252995 | − | 0.967468i | \(-0.581416\pi\) |
−0.702834 | + | 0.711354i | \(0.748082\pi\) | |||||||
\(138\) | −1.52249 | − | 5.68202i | −0.129603 | − | 0.483686i | ||||
\(139\) | −2.87054 | −0.243476 | −0.121738 | − | 0.992562i | \(-0.538847\pi\) | ||||
−0.121738 | + | 0.992562i | \(0.538847\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 6.08016 | 0.512042 | ||||||||
\(142\) | 0.999046 | + | 3.72849i | 0.0838381 | + | 0.312888i | ||||
\(143\) | −5.92562 | − | 1.58776i | −0.495525 | − | 0.132776i | ||||
\(144\) | 0.866025 | − | 0.500000i | 0.0721688 | − | 0.0416667i | ||||
\(145\) | 0 | 0 | ||||||||
\(146\) | − | 15.2199i | − | 1.25961i | ||||||
\(147\) | −6.73389 | + | 1.91172i | −0.555402 | + | 0.157676i | ||||
\(148\) | −1.96004 | − | 1.96004i | −0.161114 | − | 0.161114i | ||||
\(149\) | 13.4924 | + | 7.78982i | 1.10534 | + | 0.638167i | 0.937618 | − | 0.347668i | \(-0.113026\pi\) |
0.167720 | + | 0.985835i | \(0.446360\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −10.5953 | − | 18.3516i | −0.862232 | − | 1.49343i | −0.869769 | − | 0.493459i | \(-0.835732\pi\) |
0.00753703 | − | 0.999972i | \(-0.497601\pi\) | |||||||
\(152\) | −4.07503 | + | 1.09190i | −0.330529 | + | 0.0885649i | ||||
\(153\) | −3.25469 | + | 3.25469i | −0.263126 | + | 0.263126i | ||||
\(154\) | 2.58398 | − | 4.55316i | 0.208223 | − | 0.366904i | ||||
\(155\) | 0 | 0 | ||||||||
\(156\) | −1.55013 | + | 2.68491i | −0.124110 | + | 0.214965i | ||||
\(157\) | −3.92974 | + | 14.6660i | −0.313627 | + | 1.17047i | 0.611633 | + | 0.791141i | \(0.290513\pi\) |
−0.925261 | + | 0.379332i | \(0.876154\pi\) | |||||||
\(158\) | −0.661320 | + | 2.46808i | −0.0526118 | + | 0.196350i | ||||
\(159\) | 5.71685 | − | 9.90187i | 0.453375 | − | 0.785269i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | −13.4204 | + | 7.88141i | −1.05767 | + | 0.621142i | ||||
\(162\) | 0.707107 | − | 0.707107i | 0.0555556 | − | 0.0555556i | ||||
\(163\) | 21.5624 | − | 5.77762i | 1.68890 | − | 0.452538i | 0.718792 | − | 0.695225i | \(-0.244695\pi\) |
0.970105 | + | 0.242687i | \(0.0780288\pi\) | |||||||
\(164\) | −3.27845 | − | 5.67845i | −0.256004 | − | 0.443412i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −11.6714 | − | 6.73851i | −0.905880 | − | 0.523010i | ||||
\(167\) | −6.91224 | − | 6.91224i | −0.534885 | − | 0.534885i | 0.387137 | − | 0.922022i | \(-0.373464\pi\) |
−0.922022 | + | 0.387137i | \(0.873464\pi\) | |||||||
\(168\) | −1.88464 | − | 1.85692i | −0.145403 | − | 0.143264i | ||||
\(169\) | 3.38837i | 0.260644i | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | −3.65357 | + | 2.10939i | −0.279396 | + | 0.161309i | ||||
\(172\) | −8.65684 | − | 2.31959i | −0.660078 | − | 0.176867i | ||||
\(173\) | 1.17183 | + | 4.37334i | 0.0890928 | + | 0.332499i | 0.996058 | − | 0.0887072i | \(-0.0282735\pi\) |
−0.906965 | + | 0.421206i | \(0.861607\pi\) | |||||||
\(174\) | 8.94996 | 0.678495 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 1.97875 | 0.149154 | ||||||||
\(177\) | −1.08886 | − | 4.06367i | −0.0818436 | − | 0.305444i | ||||
\(178\) | 5.98088 | + | 1.60257i | 0.448286 | + | 0.120118i | ||||
\(179\) | −1.79084 | + | 1.03394i | −0.133853 | + | 0.0772803i | −0.565431 | − | 0.824795i | \(-0.691290\pi\) |
0.431578 | + | 0.902076i | \(0.357957\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 6.13199i | 0.455787i | 0.973686 | + | 0.227894i | \(0.0731839\pi\) | ||||
−0.973686 | + | 0.227894i | \(0.926816\pi\) | |||||||
\(182\) | 7.93854 | + | 2.06421i | 0.588444 | + | 0.153010i | ||||
\(183\) | −7.86301 | − | 7.86301i | −0.581250 | − | 0.581250i | ||||
\(184\) | −5.09436 | − | 2.94123i | −0.375561 | − | 0.216830i | ||||
\(185\) | 0 | 0 | ||||||||
\(186\) | −0.866930 | − | 1.50157i | −0.0635664 | − | 0.110100i | ||||
\(187\) | −8.79751 | + | 2.35728i | −0.643337 | + | 0.172382i | ||||
\(188\) | 4.29932 | − | 4.29932i | 0.313560 | − | 0.313560i | ||||
\(189\) | −2.30103 | − | 1.30586i | −0.167375 | − | 0.0949876i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 8.08306 | − | 14.0003i | 0.584869 | − | 1.01302i | −0.410022 | − | 0.912075i | \(-0.634479\pi\) |
0.994892 | − | 0.100948i | \(-0.0321876\pi\) | |||||||
\(192\) | 0.258819 | − | 0.965926i | 0.0186787 | − | 0.0697097i | ||||
\(193\) | −5.63991 | + | 21.0484i | −0.405969 | + | 1.51510i | 0.396292 | + | 0.918125i | \(0.370297\pi\) |
−0.802261 | + | 0.596973i | \(0.796370\pi\) | |||||||
\(194\) | −1.04674 | + | 1.81300i | −0.0751514 | + | 0.130166i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −3.40979 | + | 6.11337i | −0.243557 | + | 0.436669i | ||||
\(197\) | 0.628120 | − | 0.628120i | 0.0447517 | − | 0.0447517i | −0.684377 | − | 0.729129i | \(-0.739926\pi\) |
0.729129 | + | 0.684377i | \(0.239926\pi\) | |||||||
\(198\) | 1.91133 | − | 0.512139i | 0.135832 | − | 0.0363961i | ||||
\(199\) | 4.81248 | + | 8.33546i | 0.341147 | + | 0.590885i | 0.984646 | − | 0.174563i | \(-0.0558511\pi\) |
−0.643499 | + | 0.765447i | \(0.722518\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −4.77368 | − | 2.75608i | −0.336709 | − | 0.194399i | ||||
\(202\) | 7.10444 | + | 7.10444i | 0.499866 | + | 0.499866i | ||||
\(203\) | −6.29796 | − | 22.8265i | −0.442030 | − | 1.60210i | ||||
\(204\) | 4.60282i | 0.322262i | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | −4.31961 | + | 2.49393i | −0.300962 | + | 0.173760i | ||||
\(207\) | −5.68202 | − | 1.52249i | −0.394928 | − | 0.105821i | ||||
\(208\) | 0.802407 | + | 2.99462i | 0.0556369 | + | 0.207640i | ||||
\(209\) | −8.34793 | −0.577439 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 11.2669 | 0.775648 | 0.387824 | − | 0.921733i | \(-0.373227\pi\) | ||||
0.387824 | + | 0.921733i | \(0.373227\pi\) | |||||||
\(212\) | −2.95926 | − | 11.0441i | −0.203243 | − | 0.758512i | ||||
\(213\) | 3.72849 | + | 0.999046i | 0.255472 | + | 0.0684535i | ||||
\(214\) | −5.23915 | + | 3.02482i | −0.358141 | + | 0.206773i | ||||
\(215\) | 0 | 0 | ||||||||
\(216\) | − | 1.00000i | − | 0.0680414i | ||||||
\(217\) | −3.21964 | + | 3.26770i | −0.218563 | + | 0.221826i | ||||
\(218\) | 6.89357 | + | 6.89357i | 0.466892 | + | 0.466892i | ||||
\(219\) | −13.1808 | − | 7.60995i | −0.890677 | − | 0.514233i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −7.13498 | − | 12.3581i | −0.479951 | − | 0.831299i | ||||
\(222\) | −2.67747 | + | 0.717425i | −0.179700 | + | 0.0481504i | ||||
\(223\) | −13.1718 | + | 13.1718i | −0.882048 | + | 0.882048i | −0.993743 | − | 0.111694i | \(-0.964372\pi\) |
0.111694 | + | 0.993743i | \(0.464372\pi\) | |||||||
\(224\) | −2.64568 | + | 0.0196015i | −0.176772 | + | 0.00130968i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −4.26035 | + | 7.37914i | −0.283394 | + | 0.490853i | ||||
\(227\) | −6.96589 | + | 25.9971i | −0.462343 | + | 1.72549i | 0.203210 | + | 0.979135i | \(0.434863\pi\) |
−0.665552 | + | 0.746351i | \(0.731804\pi\) | |||||||
\(228\) | −1.09190 | + | 4.07503i | −0.0723130 | + | 0.269876i | ||||
\(229\) | −13.4452 | + | 23.2878i | −0.888486 | + | 1.53890i | −0.0468199 | + | 0.998903i | \(0.514909\pi\) |
−0.841666 | + | 0.539999i | \(0.818425\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −2.65116 | − | 4.51437i | −0.174434 | − | 0.297024i | ||||
\(232\) | 6.32858 | − | 6.32858i | 0.415491 | − | 0.415491i | ||||
\(233\) | −0.889853 | + | 0.238436i | −0.0582962 | + | 0.0156204i | −0.287849 | − | 0.957676i | \(-0.592940\pi\) |
0.229553 | + | 0.973296i | \(0.426274\pi\) | |||||||
\(234\) | 1.55013 | + | 2.68491i | 0.101335 | + | 0.175518i | ||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −3.64339 | − | 2.10351i | −0.237164 | − | 0.136927i | ||||
\(237\) | 1.80676 | + | 1.80676i | 0.117362 | + | 0.117362i | ||||
\(238\) | 11.7393 | − | 3.23894i | 0.760946 | − | 0.209949i | ||||
\(239\) | − | 25.3432i | − | 1.63931i | −0.572856 | − | 0.819656i | \(-0.694164\pi\) | ||
0.572856 | − | 0.819656i | \(-0.305836\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 18.2905 | − | 10.5600i | 1.17819 | − | 0.680230i | 0.222597 | − | 0.974911i | \(-0.428547\pi\) |
0.955596 | + | 0.294681i | \(0.0952134\pi\) | |||||||
\(242\) | −6.84314 | − | 1.83361i | −0.439894 | − | 0.117869i | ||||
\(243\) | −0.258819 | − | 0.965926i | −0.0166032 | − | 0.0619642i | ||||
\(244\) | −11.1200 | −0.711883 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −6.55691 | −0.418053 | ||||||||
\(247\) | −3.38518 | − | 12.6337i | −0.215394 | − | 0.803861i | ||||
\(248\) | −1.67478 | − | 0.448756i | −0.106349 | − | 0.0284960i | ||||
\(249\) | −11.6714 | + | 6.73851i | −0.739648 | + | 0.427036i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.70623i | 0.170816i | 0.996346 | + | 0.0854078i | \(0.0272193\pi\) | ||||
−0.996346 | + | 0.0854078i | \(0.972781\pi\) | |||||||
\(252\) | −2.55046 | + | 0.703686i | −0.160664 | + | 0.0443280i | ||||
\(253\) | −8.23068 | − | 8.23068i | −0.517458 | − | 0.517458i | ||||
\(254\) | −10.9342 | − | 6.31283i | −0.686070 | − | 0.396102i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −0.500000 | − | 0.866025i | −0.0312500 | − | 0.0541266i | ||||
\(257\) | 23.2035 | − | 6.21737i | 1.44740 | − | 0.387829i | 0.552279 | − | 0.833660i | \(-0.313758\pi\) |
0.895117 | + | 0.445831i | \(0.147092\pi\) | |||||||
\(258\) | −6.33724 | + | 6.33724i | −0.394540 | + | 0.394540i | ||||
\(259\) | 3.71385 | + | 6.32392i | 0.230768 | + | 0.392949i | ||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 4.47498 | − | 7.75089i | 0.276994 | − | 0.479768i | ||||
\(262\) | −1.32557 | + | 4.94708i | −0.0818938 | + | 0.305632i | ||||
\(263\) | −0.220080 | + | 0.821351i | −0.0135707 | + | 0.0506467i | −0.972379 | − | 0.233407i | \(-0.925013\pi\) |
0.958808 | + | 0.284053i | \(0.0916793\pi\) | |||||||
\(264\) | 0.989376 | − | 1.71365i | 0.0608919 | − | 0.105468i | ||||
\(265\) | 0 | 0 | ||||||||
\(266\) | 11.1615 | − | 0.0826946i | 0.684359 | − | 0.00507033i | ||||
\(267\) | 4.37831 | − | 4.37831i | 0.267948 | − | 0.267948i | ||||
\(268\) | −5.32434 | + | 1.42665i | −0.325236 | + | 0.0871468i | ||||
\(269\) | 5.82171 | + | 10.0835i | 0.354956 | + | 0.614802i | 0.987110 | − | 0.160041i | \(-0.0511625\pi\) |
−0.632154 | + | 0.774842i | \(0.717829\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −20.2171 | − | 11.6724i | −1.22810 | − | 0.709046i | −0.261471 | − | 0.965211i | \(-0.584208\pi\) |
−0.966633 | + | 0.256165i | \(0.917541\pi\) | |||||||
\(272\) | 3.25469 | + | 3.25469i | 0.197344 | + | 0.197344i | ||||
\(273\) | 5.75693 | − | 5.84287i | 0.348425 | − | 0.353627i | ||||
\(274\) | 11.5824i | 0.699715i | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | −5.09436 | + | 2.94123i | −0.306644 | + | 0.177041i | ||||
\(277\) | 9.12775 | + | 2.44577i | 0.548433 | + | 0.146952i | 0.522387 | − | 0.852708i | \(-0.325042\pi\) |
0.0260462 | + | 0.999661i | \(0.491708\pi\) | |||||||
\(278\) | 0.742949 | + | 2.77273i | 0.0445591 | + | 0.166297i | ||||
\(279\) | −1.73386 | −0.103804 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −11.7320 | −0.699871 | −0.349935 | − | 0.936774i | \(-0.613796\pi\) | ||||
−0.349935 | + | 0.936774i | \(0.613796\pi\) | |||||||
\(282\) | −1.57366 | − | 5.87298i | −0.0937101 | − | 0.349731i | ||||
\(283\) | −3.52349 | − | 0.944117i | −0.209450 | − | 0.0561219i | 0.152568 | − | 0.988293i | \(-0.451246\pi\) |
−0.362018 | + | 0.932171i | \(0.617912\pi\) | |||||||
\(284\) | 3.34287 | − | 1.93001i | 0.198363 | − | 0.114525i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 6.13465i | 0.362750i | ||||||||
\(287\) | 4.61400 | + | 16.7231i | 0.272356 | + | 0.987133i | ||||
\(288\) | −0.707107 | − | 0.707107i | −0.0416667 | − | 0.0416667i | ||||
\(289\) | −3.62517 | − | 2.09299i | −0.213245 | − | 0.123117i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 1.04674 | + | 1.81300i | 0.0613609 | + | 0.106280i | ||||
\(292\) | −14.7013 | + | 3.93920i | −0.860328 | + | 0.230524i | ||||
\(293\) | 8.62354 | − | 8.62354i | 0.503793 | − | 0.503793i | −0.408822 | − | 0.912614i | \(-0.634060\pi\) |
0.912614 | + | 0.408822i | \(0.134060\pi\) | |||||||
\(294\) | 3.58944 | + | 6.00965i | 0.209340 | + | 0.350490i | ||||
\(295\) | 0 | 0 | ||||||||
\(296\) | −1.38596 | + | 2.40055i | −0.0805572 | + | 0.139529i | ||||
\(297\) | 0.512139 | − | 1.91133i | 0.0297173 | − | 0.110907i | ||||
\(298\) | 4.03231 | − | 15.0488i | 0.233585 | − | 0.871752i | ||||
\(299\) | 9.11859 | − | 15.7939i | 0.527341 | − | 0.913382i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 20.6223 | + | 11.7034i | 1.18865 | + | 0.674575i | ||||
\(302\) | −14.9840 | + | 14.9840i | −0.862232 | + | 0.862232i | ||||
\(303\) | 9.70484 | − | 2.60040i | 0.557529 | − | 0.149389i | ||||
\(304\) | 2.10939 | + | 3.65357i | 0.120982 | + | 0.209547i | ||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 3.98616 | + | 2.30141i | 0.227874 | + | 0.131563i | ||||
\(307\) | −15.9933 | − | 15.9933i | −0.912785 | − | 0.912785i | 0.0837060 | − | 0.996490i | \(-0.473324\pi\) |
−0.996490 | + | 0.0837060i | \(0.973324\pi\) | |||||||
\(308\) | −5.06680 | − | 1.31749i | −0.288708 | − | 0.0750710i | ||||
\(309\) | 4.98786i | 0.283750i | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 6.70522 | − | 3.87126i | 0.380218 | − | 0.219519i | −0.297695 | − | 0.954661i | \(-0.596218\pi\) |
0.677913 | + | 0.735142i | \(0.262885\pi\) | |||||||
\(312\) | 2.99462 | + | 0.802407i | 0.169537 | + | 0.0454273i | ||||
\(313\) | −5.18810 | − | 19.3623i | −0.293249 | − | 1.09442i | −0.942598 | − | 0.333929i | \(-0.891625\pi\) |
0.649349 | − | 0.760490i | \(-0.275041\pi\) | |||||||
\(314\) | 15.1833 | 0.856846 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 2.55514 | 0.143738 | ||||||||
\(317\) | 0.771364 | + | 2.87877i | 0.0433241 | + | 0.161688i | 0.984199 | − | 0.177067i | \(-0.0566609\pi\) |
−0.940875 | + | 0.338755i | \(0.889994\pi\) | |||||||
\(318\) | −11.0441 | − | 2.95926i | −0.619322 | − | 0.165947i | ||||
\(319\) | 15.3371 | − | 8.85488i | 0.858713 | − | 0.495778i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 6.04965i | 0.337658i | ||||||||
\(322\) | 11.0863 | + | 10.9232i | 0.617816 | + | 0.608728i | ||||
\(323\) | −13.7308 | − | 13.7308i | −0.764004 | − | 0.764004i | ||||
\(324\) | −0.866025 | − | 0.500000i | −0.0481125 | − | 0.0277778i | ||||
\(325\) | 0 | 0 | ||||||||
\(326\) | −11.1615 | − | 19.3323i | −0.618179 | − | 1.07072i | ||||
\(327\) | 9.41680 | − | 2.52322i | 0.520750 | − | 0.139535i | ||||
\(328\) | −4.63643 | + | 4.63643i | −0.256004 | + | 0.256004i | ||||
\(329\) | −13.8714 | + | 8.14629i | −0.764756 | + | 0.449119i | ||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −13.9186 | + | 24.1077i | −0.765035 | + | 1.32508i | 0.175194 | + | 0.984534i | \(0.443945\pi\) |
−0.940228 | + | 0.340545i | \(0.889388\pi\) | |||||||
\(332\) | −3.48811 | + | 13.0178i | −0.191435 | + | 0.714445i | ||||
\(333\) | −0.717425 | + | 2.67747i | −0.0393146 | + | 0.146724i | ||||
\(334\) | −4.88769 | + | 8.46573i | −0.267442 | + | 0.463224i | ||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −1.30586 | + | 2.30103i | −0.0712407 | + | 0.125531i | ||||
\(337\) | 17.1567 | − | 17.1567i | 0.934583 | − | 0.934583i | −0.0634051 | − | 0.997988i | \(-0.520196\pi\) |
0.997988 | + | 0.0634051i | \(0.0201960\pi\) | |||||||
\(338\) | 3.27292 | − | 0.876975i | 0.178023 | − | 0.0477012i | ||||
\(339\) | 4.26035 | + | 7.37914i | 0.231390 | + | 0.400780i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −2.97123 | − | 1.71544i | −0.160901 | − | 0.0928963i | ||||
\(342\) | 2.98313 | + | 2.98313i | 0.161309 | + | 0.161309i | ||||
\(343\) | 12.8015 | − | 13.3836i | 0.691217 | − | 0.722647i | ||||
\(344\) | 8.96222i | 0.483210i | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 3.92103 | − | 2.26381i | 0.210796 | − | 0.121703i | ||||
\(347\) | −24.1895 | − | 6.48156i | −1.29856 | − | 0.347948i | −0.457655 | − | 0.889130i | \(-0.651311\pi\) |
−0.840906 | + | 0.541181i | \(0.817977\pi\) | |||||||
\(348\) | −2.31642 | − | 8.64500i | −0.124173 | − | 0.463421i | ||||
\(349\) | −18.0130 | −0.964212 | −0.482106 | − | 0.876113i | \(-0.660128\pi\) | ||||
−0.482106 | + | 0.876113i | \(0.660128\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.10026 | 0.165480 | ||||||||
\(352\) | −0.512139 | − | 1.91133i | −0.0272971 | − | 0.101874i | ||||
\(353\) | −7.33911 | − | 1.96651i | −0.390621 | − | 0.104667i | 0.0581623 | − | 0.998307i | \(-0.481476\pi\) |
−0.448784 | + | 0.893641i | \(0.648143\pi\) | |||||||
\(354\) | −3.64339 | + | 2.10351i | −0.193644 | + | 0.111800i | ||||
\(355\) | 0 | 0 | ||||||||
\(356\) | − | 6.19187i | − | 0.328168i | ||||||
\(357\) | 3.06464 | − | 11.7860i | 0.162198 | − | 0.623781i | ||||
\(358\) | 1.46221 | + | 1.46221i | 0.0772803 | + | 0.0772803i | ||||
\(359\) | −2.84638 | − | 1.64336i | −0.150226 | − | 0.0867332i | 0.423003 | − | 0.906128i | \(-0.360976\pi\) |
−0.573229 | + | 0.819395i | \(0.694309\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 0.600927 | + | 1.04084i | 0.0316277 | + | 0.0547808i | ||||
\(362\) | 5.92305 | − | 1.58708i | 0.311309 | − | 0.0834149i | ||||
\(363\) | −5.00952 | + | 5.00952i | −0.262932 | + | 0.262932i | ||||
\(364\) | −0.0607699 | − | 8.20230i | −0.00318521 | − | 0.429917i | ||||
\(365\) | 0 | 0 | ||||||||
\(366\) | −5.55999 | + | 9.63018i | −0.290625 | + | 0.503377i | ||||
\(367\) | 0.840538 | − | 3.13693i | 0.0438757 | − | 0.163746i | −0.940512 | − | 0.339761i | \(-0.889654\pi\) |
0.984388 | + | 0.176014i | \(0.0563205\pi\) | |||||||
\(368\) | −1.52249 | + | 5.68202i | −0.0793654 | + | 0.296196i | ||||
\(369\) | −3.27845 | + | 5.67845i | −0.170669 | + | 0.295608i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0.224118 | + | 30.2499i | 0.0116356 | + | 1.57050i | ||||
\(372\) | −1.22602 | + | 1.22602i | −0.0635664 | + | 0.0635664i | ||||
\(373\) | −15.2290 | + | 4.08060i | −0.788529 | + | 0.211286i | −0.630542 | − | 0.776156i | \(-0.717167\pi\) |
−0.157987 | + | 0.987441i | \(0.550500\pi\) | |||||||
\(374\) | 4.55392 | + | 7.88763i | 0.235478 | + | 0.407860i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −5.26557 | − | 3.04008i | −0.271551 | − | 0.156780i | ||||
\(377\) | 19.6203 | + | 19.6203i | 1.01049 | + | 1.01049i | ||||
\(378\) | −0.665818 | + | 2.56060i | −0.0342460 | + | 0.131703i | ||||
\(379\) | − | 21.7428i | − | 1.11685i | −0.829555 | − | 0.558426i | \(-0.811406\pi\) | ||
0.829555 | − | 0.558426i | \(-0.188594\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −10.9342 | + | 6.31283i | −0.560174 | + | 0.323416i | ||||
\(382\) | −15.6153 | − | 4.18410i | −0.798946 | − | 0.214077i | ||||
\(383\) | 4.62973 | + | 17.2784i | 0.236568 | + | 0.882883i | 0.977436 | + | 0.211233i | \(0.0677478\pi\) |
−0.740868 | + | 0.671651i | \(0.765586\pi\) | |||||||
\(384\) | −1.00000 | −0.0510310 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 21.7909 | 1.10913 | ||||||||
\(387\) | 2.31959 | + | 8.65684i | 0.117912 | + | 0.440052i | ||||
\(388\) | 2.02214 | + | 0.541831i | 0.102659 | + | 0.0275073i | ||||
\(389\) | 4.36130 | − | 2.51800i | 0.221127 | − | 0.127667i | −0.385345 | − | 0.922772i | \(-0.625918\pi\) |
0.606472 | + | 0.795105i | \(0.292584\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | − | 27.0759i | − | 1.36929i | ||||||
\(392\) | 6.78758 | + | 1.71135i | 0.342825 | + | 0.0864362i | ||||
\(393\) | 3.62152 | + | 3.62152i | 0.182681 | + | 0.182681i | ||||
\(394\) | −0.769287 | − | 0.444148i | −0.0387561 | − | 0.0223759i | ||||
\(395\) | 0 | 0 | ||||||||
\(396\) | −0.989376 | − | 1.71365i | −0.0497180 | − | 0.0861142i | ||||
\(397\) | 14.2520 | − | 3.81880i | 0.715285 | − | 0.191660i | 0.117218 | − | 0.993106i | \(-0.462602\pi\) |
0.598067 | + | 0.801446i | \(0.295936\pi\) | |||||||
\(398\) | 6.80587 | − | 6.80587i | 0.341147 | − | 0.341147i | ||||
\(399\) | 5.50916 | − | 9.70753i | 0.275803 | − | 0.485984i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 4.34686 | − | 7.52897i | 0.217072 | − | 0.375979i | −0.736840 | − | 0.676067i | \(-0.763683\pi\) |
0.953911 | + | 0.300088i | \(0.0970162\pi\) | |||||||
\(402\) | −1.42665 | + | 5.32434i | −0.0711550 | + | 0.265554i | ||||
\(403\) | 1.39126 | − | 5.19226i | 0.0693037 | − | 0.258645i | ||||
\(404\) | 5.02360 | − | 8.70112i | 0.249933 | − | 0.432897i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | −20.4187 | + | 11.9913i | −1.01336 | + | 0.595118i | ||||
\(407\) | −3.87844 | + | 3.87844i | −0.192247 | + | 0.192247i | ||||
\(408\) | 4.44599 | − | 1.19130i | 0.220109 | − | 0.0589781i | ||||
\(409\) | −9.49095 | − | 16.4388i | −0.469297 | − | 0.812847i | 0.530087 | − | 0.847944i | \(-0.322159\pi\) |
−0.999384 | + | 0.0350966i | \(0.988826\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.0306 | + | 5.79118i | 0.494774 | + | 0.285658i | ||||
\(412\) | 3.52695 | + | 3.52695i | 0.173760 | + | 0.173760i | ||||
\(413\) | 7.92871 | + | 7.81209i | 0.390147 | + | 0.384408i | ||||
\(414\) | 5.88246i | 0.289107i | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 2.68491 | − | 1.55013i | 0.131638 | − | 0.0760014i | ||||
\(417\) | 2.77273 | + | 0.742949i | 0.135781 | + | 0.0363824i | ||||
\(418\) | 2.16060 | + | 8.06348i | 0.105679 | + | 0.394398i | ||||
\(419\) | 11.9171 | 0.582188 | 0.291094 | − | 0.956695i | \(-0.405981\pi\) | ||||
0.291094 | + | 0.956695i | \(0.405981\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 6.95263 | 0.338850 | 0.169425 | − | 0.985543i | \(-0.445809\pi\) | ||||
0.169425 | + | 0.985543i | \(0.445809\pi\) | |||||||
\(422\) | −2.91610 | − | 10.8830i | −0.141953 | − | 0.529778i | ||||
\(423\) | −5.87298 | − | 1.57366i | −0.285554 | − | 0.0765140i | ||||
\(424\) | −9.90187 | + | 5.71685i | −0.480877 | + | 0.277635i | ||||
\(425\) | 0 | 0 | ||||||||
\(426\) | − | 3.86002i | − | 0.187018i | ||||||
\(427\) | 28.4738 | + | 7.40388i | 1.37795 | + | 0.358299i | ||||
\(428\) | 4.27775 | + | 4.27775i | 0.206773 | + | 0.206773i | ||||
\(429\) | 5.31277 | + | 3.06733i | 0.256503 | + | 0.148092i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −3.12392 | − | 5.41078i | −0.150474 | − | 0.260628i | 0.780928 | − | 0.624621i | \(-0.214747\pi\) |
−0.931402 | + | 0.363993i | \(0.881413\pi\) | |||||||
\(432\) | −0.965926 | + | 0.258819i | −0.0464731 | + | 0.0124524i | ||||
\(433\) | −15.1544 | + | 15.1544i | −0.728274 | + | 0.728274i | −0.970276 | − | 0.242002i | \(-0.922196\pi\) |
0.242002 | + | 0.970276i | \(0.422196\pi\) | |||||||
\(434\) | 3.98966 | + | 2.26419i | 0.191510 | + | 0.108684i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 4.87449 | − | 8.44287i | 0.233446 | − | 0.404340i | ||||
\(437\) | 6.42307 | − | 23.9712i | 0.307257 | − | 1.14670i | ||||
\(438\) | −3.93920 | + | 14.7013i | −0.188222 | + | 0.702455i | ||||
\(439\) | 16.3729 | − | 28.3588i | 0.781438 | − | 1.35349i | −0.149666 | − | 0.988737i | \(-0.547820\pi\) |
0.931104 | − | 0.364753i | \(-0.118847\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 6.99923 | − | 0.103719i | 0.333297 | − | 0.00493899i | ||||
\(442\) | −10.0904 | + | 10.0904i | −0.479951 | + | 0.479951i | ||||
\(443\) | 29.7032 | − | 7.95895i | 1.41124 | − | 0.378141i | 0.528874 | − | 0.848701i | \(-0.322615\pi\) |
0.882368 | + | 0.470559i | \(0.155948\pi\) | |||||||
\(444\) | 1.38596 | + | 2.40055i | 0.0657747 | + | 0.113925i | ||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 16.1321 | + | 9.31386i | 0.763876 | + | 0.441024i | ||||
\(447\) | −11.0165 | − | 11.0165i | −0.521061 | − | 0.521061i | ||||
\(448\) | 0.703686 | + | 2.55046i | 0.0332460 | + | 0.120498i | ||||
\(449\) | − | 16.8713i | − | 0.796207i | −0.917341 | − | 0.398103i | \(-0.869669\pi\) | ||
0.917341 | − | 0.398103i | \(-0.130331\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −11.2362 | + | 6.48725i | −0.529094 | + | 0.305473i | ||||
\(452\) | 8.23036 | + | 2.20532i | 0.387123 | + | 0.103729i | ||||
\(453\) | 5.48452 | + | 20.4685i | 0.257685 | + | 0.961695i | ||||
\(454\) | 26.9142 | 1.26314 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 4.21878 | 0.197563 | ||||||||
\(457\) | −5.13696 | − | 19.1714i | −0.240297 | − | 0.896800i | −0.975689 | − | 0.219158i | \(-0.929669\pi\) |
0.735393 | − | 0.677641i | \(-0.236998\pi\) | |||||||
\(458\) | 25.9742 | + | 6.95976i | 1.21369 | + | 0.325208i | ||||
\(459\) | 3.98616 | − | 2.30141i | 0.186058 | − | 0.107421i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 15.7775i | 0.734830i | 0.930057 | + | 0.367415i | \(0.119757\pi\) | ||||
−0.930057 | + | 0.367415i | \(0.880243\pi\) | |||||||
\(462\) | −3.67438 | + | 3.72923i | −0.170948 | + | 0.173500i | ||||
\(463\) | −4.48617 | − | 4.48617i | −0.208490 | − | 0.208490i | 0.595135 | − | 0.803625i | \(-0.297098\pi\) |
−0.803625 | + | 0.595135i | \(0.797098\pi\) | |||||||
\(464\) | −7.75089 | − | 4.47498i | −0.359826 | − | 0.207746i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 0.460622 | + | 0.797821i | 0.0213379 | + | 0.0369583i | ||||
\(467\) | 16.8554 | − | 4.51639i | 0.779975 | − | 0.208994i | 0.153201 | − | 0.988195i | \(-0.451042\pi\) |
0.626774 | + | 0.779201i | \(0.284375\pi\) | |||||||
\(468\) | 2.19222 | − | 2.19222i | 0.101335 | − | 0.101335i | ||||
\(469\) | 14.5834 | − | 0.108047i | 0.673400 | − | 0.00498914i | ||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 7.59167 | − | 13.1492i | 0.349806 | − | 0.605881i | ||||
\(472\) | −1.08886 | + | 4.06367i | −0.0501187 | + | 0.187046i | ||||
\(473\) | −4.58990 | + | 17.1297i | −0.211044 | + | 0.787626i | ||||
\(474\) | 1.27757 | − | 2.21282i | 0.0586808 | − | 0.101638i | ||||
\(475\) | 0 | 0 | ||||||||
\(476\) | −6.16693 | − | 10.5010i | −0.282661 | − | 0.481312i | ||||
\(477\) | −8.08484 | + | 8.08484i | −0.370180 | + | 0.370180i | ||||
\(478\) | −24.4796 | + | 6.55929i | −1.11967 | + | 0.300015i | ||||
\(479\) | 15.8748 | + | 27.4960i | 0.725339 | + | 1.25632i | 0.958834 | + | 0.283966i | \(0.0916503\pi\) |
−0.233495 | + | 0.972358i | \(0.575016\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.44233 | − | 4.29683i | −0.339341 | − | 0.195919i | ||||
\(482\) | −14.9341 | − | 14.9341i | −0.680230 | − | 0.680230i | ||||
\(483\) | 15.0030 | − | 4.13940i | 0.682658 | − | 0.188349i | ||||
\(484\) | 7.08454i | 0.322024i | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −0.866025 | + | 0.500000i | −0.0392837 | + | 0.0226805i | ||||
\(487\) | −28.8890 | − | 7.74077i | −1.30908 | − | 0.350768i | −0.464206 | − | 0.885727i | \(-0.653660\pi\) |
−0.844878 | + | 0.534960i | \(0.820327\pi\) | |||||||
\(488\) | 2.87806 | + | 10.7411i | 0.130284 | + | 0.486225i | ||||
\(489\) | −22.3230 | −1.00948 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 1.57179 | 0.0709340 | 0.0354670 | − | 0.999371i | \(-0.488708\pi\) | ||||
0.0354670 | + | 0.999371i | \(0.488708\pi\) | |||||||
\(492\) | 1.69705 | + | 6.33349i | 0.0765090 | + | 0.285536i | ||||
\(493\) | 39.7914 | + | 10.6621i | 1.79211 | + | 0.480196i | ||||
\(494\) | −11.3270 | + | 6.53967i | −0.509628 | + | 0.294234i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | 1.73386i | 0.0778527i | ||||||||
\(497\) | −9.84480 | + | 2.71624i | −0.441600 | + | 0.121840i | ||||
\(498\) | 9.52969 | + | 9.52969i | 0.427036 | + | 0.427036i | ||||
\(499\) | 12.3491 | + | 7.12977i | 0.552823 | + | 0.319172i | 0.750260 | − | 0.661143i | \(-0.229928\pi\) |
−0.197437 | + | 0.980316i | \(0.563262\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | 4.88769 | + | 8.46573i | 0.218366 | + | 0.378221i | ||||
\(502\) | 2.61401 | − | 0.700423i | 0.116669 | − | 0.0312614i | ||||
\(503\) | −28.7896 | + | 28.7896i | −1.28367 | + | 1.28367i | −0.345100 | + | 0.938566i | \(0.612155\pi\) |
−0.938566 | + | 0.345100i | \(0.887845\pi\) | |||||||
\(504\) | 1.33981 | + | 2.28142i | 0.0596801 | + | 0.101623i | ||||
\(505\) | 0 | 0 | ||||||||
\(506\) | −5.81997 | + | 10.0805i | −0.258729 | + | 0.448132i | ||||
\(507\) | 0.876975 | − | 3.27292i | 0.0389478 | − | 0.145355i | ||||
\(508\) | −3.26776 | + | 12.1955i | −0.144984 | + | 0.541086i | ||||
\(509\) | 7.30942 | − | 12.6603i | 0.323984 | − | 0.561157i | −0.657322 | − | 0.753610i | \(-0.728311\pi\) |
0.981306 | + | 0.192453i | \(0.0616442\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 40.2670 | − | 0.298333i | 1.78131 | − | 0.0131975i | ||||
\(512\) | −0.707107 | + | 0.707107i | −0.0312500 | + | 0.0312500i | ||||
\(513\) | 4.07503 | − | 1.09190i | 0.179917 | − | 0.0482086i | ||||
\(514\) | −12.0110 | − | 20.8037i | −0.529784 | − | 0.917612i | ||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 7.76151 | + | 4.48111i | 0.341681 | + | 0.197270i | ||||
\(517\) | −8.50729 | − | 8.50729i | −0.374150 | − | 0.374150i | ||||
\(518\) | 5.14722 | − | 5.22406i | 0.226156 | − | 0.229532i | ||||
\(519\) | − | 4.52762i | − | 0.198740i | ||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −13.3153 | + | 7.68757i | −0.583352 | + | 0.336798i | −0.762464 | − | 0.647030i | \(-0.776011\pi\) |
0.179112 | + | 0.983829i | \(0.442677\pi\) | |||||||
\(522\) | −8.64500 | − | 2.31642i | −0.378381 | − | 0.101387i | ||||
\(523\) | −6.06041 | − | 22.6178i | −0.265003 | − | 0.989006i | −0.962248 | − | 0.272173i | \(-0.912258\pi\) |
0.697245 | − | 0.716833i | \(-0.254409\pi\) | |||||||
\(524\) | 5.12160 | 0.223738 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0.850325 | 0.0370759 | ||||||||
\(527\) | −2.06555 | − | 7.70872i | −0.0899766 | − | 0.335797i | ||||
\(528\) | −1.91133 | − | 0.512139i | −0.0831799 | − | 0.0222880i | ||||
\(529\) | 10.0488 | − | 5.80167i | 0.436904 | − | 0.252247i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 4.20702i | 0.182569i | ||||||||
\(532\) | −2.96870 | − | 10.7598i | −0.128709 | − | 0.466498i | ||||
\(533\) | −14.3742 | − | 14.3742i | −0.622614 | − | 0.622614i | ||||
\(534\) | −5.36231 | − | 3.09593i | −0.232050 | − | 0.133974i | ||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 2.75608 | + | 4.77368i | 0.119045 | + | 0.206191i | ||||
\(537\) | 1.99742 | − | 0.535206i | 0.0861949 | − | 0.0230959i | ||||
\(538\) | 8.23314 | − | 8.23314i | 0.354956 | − | 0.354956i | ||||
\(539\) | 12.0969 | + | 6.74714i | 0.521048 | + | 0.290620i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −3.98437 | + | 6.90113i | −0.171301 | + | 0.296703i | −0.938875 | − | 0.344258i | \(-0.888131\pi\) |
0.767574 | + | 0.640961i | \(0.221464\pi\) | |||||||
\(542\) | −6.04206 | + | 22.5493i | −0.259529 | + | 0.968575i | ||||
\(543\) | 1.58708 | − | 5.92305i | 0.0681080 | − | 0.254182i | ||||
\(544\) | 2.30141 | − | 3.98616i | 0.0986722 | − | 0.170905i | ||||
\(545\) | 0 | 0 | ||||||||
\(546\) | −7.13378 | − | 4.04852i | −0.305298 | − | 0.173261i | ||||
\(547\) | 5.88082 | − | 5.88082i | 0.251446 | − | 0.251446i | −0.570117 | − | 0.821563i | \(-0.693102\pi\) |
0.821563 | + | 0.570117i | \(0.193102\pi\) | |||||||
\(548\) | 11.1877 | − | 2.99773i | 0.477915 | − | 0.128057i | ||||
\(549\) | 5.55999 | + | 9.63018i | 0.237294 | + | 0.411006i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 32.6994 | + | 18.8790i | 1.39304 | + | 0.804272i | ||||
\(552\) | 4.15953 | + | 4.15953i | 0.177041 | + | 0.177041i | ||||
\(553\) | −6.54271 | − | 1.70126i | −0.278224 | − | 0.0723450i | ||||
\(554\) | − | 9.44974i | − | 0.401481i | ||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 2.48596 | − | 1.43527i | 0.105428 | − | 0.0608689i | ||||
\(557\) | 25.3198 | + | 6.78443i | 1.07284 | + | 0.287466i | 0.751658 | − | 0.659553i | \(-0.229254\pi\) |
0.321178 | + | 0.947019i | \(0.395921\pi\) | |||||||
\(558\) | 0.448756 | + | 1.67478i | 0.0189974 | + | 0.0708991i | ||||
\(559\) | −27.7852 | −1.17519 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 9.10785 | 0.384534 | ||||||||
\(562\) | 3.03646 | + | 11.3322i | 0.128085 | + | 0.478020i | ||||
\(563\) | −0.844624 | − | 0.226316i | −0.0355967 | − | 0.00953810i | 0.240977 | − | 0.970531i | \(-0.422532\pi\) |
−0.276573 | + | 0.960993i | \(0.589199\pi\) | |||||||
\(564\) | −5.26557 | + | 3.04008i | −0.221721 | + | 0.128010i | ||||
\(565\) | 0 | 0 | ||||||||
\(566\) | 3.64779i | 0.153328i | ||||||||
\(567\) | 1.88464 | + | 1.85692i | 0.0791473 | + | 0.0779832i | ||||
\(568\) | −2.72944 | − | 2.72944i | −0.114525 | − | 0.114525i | ||||
\(569\) | 28.5877 | + | 16.5051i | 1.19846 | + | 0.691929i | 0.960211 | − | 0.279275i | \(-0.0900943\pi\) |
0.238246 | + | 0.971205i | \(0.423428\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −2.39594 | − | 4.14989i | −0.100267 | − | 0.173668i | 0.811528 | − | 0.584314i | \(-0.198636\pi\) |
−0.911795 | + | 0.410646i | \(0.865303\pi\) | |||||||
\(572\) | 5.92562 | − | 1.58776i | 0.247763 | − | 0.0663878i | ||||
\(573\) | −11.4312 | + | 11.4312i | −0.477544 | + | 0.477544i | ||||
\(574\) | 14.9591 | − | 8.78504i | 0.624380 | − | 0.366680i | ||||
\(575\) | 0 | 0 | ||||||||
\(576\) | −0.500000 | + | 0.866025i | −0.0208333 | + | 0.0360844i | ||||
\(577\) | −8.45046 | + | 31.5375i | −0.351797 | + | 1.31293i | 0.532670 | + | 0.846323i | \(0.321189\pi\) |
−0.884467 | + | 0.466602i | \(0.845478\pi\) | |||||||
\(578\) | −1.08341 | + | 4.04335i | −0.0450640 | + | 0.168181i | ||||
\(579\) | 10.8955 | − | 18.8715i | 0.452800 | − | 0.784272i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 17.5992 | − | 31.0110i | 0.730136 | − | 1.28655i | ||||
\(582\) | 1.48031 | − | 1.48031i | 0.0613609 | − | 0.0613609i | ||||
\(583\) | −21.8535 | + | 5.85564i | −0.905081 | + | 0.242516i | ||||
\(584\) | 7.60995 | + | 13.1808i | 0.314902 | + | 0.545426i | ||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −10.5616 | − | 6.09777i | −0.436297 | − | 0.251896i | ||||
\(587\) | −6.03856 | − | 6.03856i | −0.249238 | − | 0.249238i | 0.571420 | − | 0.820658i | \(-0.306393\pi\) |
−0.820658 | + | 0.571420i | \(0.806393\pi\) | |||||||
\(588\) | 4.87586 | − | 5.02254i | 0.201077 | − | 0.207126i | ||||
\(589\) | − | 7.31479i | − | 0.301401i | ||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −0.769287 | + | 0.444148i | −0.0316442 | + | 0.0182698i | ||||
\(592\) | 2.67747 | + | 0.717425i | 0.110043 | + | 0.0294860i | ||||
\(593\) | −1.05350 | − | 3.93171i | −0.0432620 | − | 0.161456i | 0.940915 | − | 0.338642i | \(-0.109967\pi\) |
−0.984177 | + | 0.177186i | \(0.943301\pi\) | |||||||
\(594\) | −1.97875 | −0.0811892 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | −15.5796 | −0.638167 | ||||||||
\(597\) | −2.49112 | − | 9.29699i | −0.101955 | − | 0.380501i | ||||
\(598\) | −17.6158 | − | 4.72013i | −0.720362 | − | 0.193020i | ||||
\(599\) | −29.5547 | + | 17.0634i | −1.20757 | + | 0.697193i | −0.962229 | − | 0.272243i | \(-0.912235\pi\) |
−0.245345 | + | 0.969436i | \(0.578901\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 9.99405i | 0.407666i | 0.979006 | + | 0.203833i | \(0.0653399\pi\) | ||||
−0.979006 | + | 0.203833i | \(0.934660\pi\) | |||||||
\(602\) | 5.96721 | − | 22.9487i | 0.243205 | − | 0.935318i | ||||
\(603\) | 3.89769 | + | 3.89769i | 0.158726 | + | 0.158726i | ||||
\(604\) | 18.3516 | + | 10.5953i | 0.746715 | + | 0.431116i | ||||
\(605\) | 0 | 0 | ||||||||
\(606\) | −5.02360 | − | 8.70112i | −0.204070 | − | 0.353459i | ||||
\(607\) | −17.6567 | + | 4.73109i | −0.716662 | + | 0.192029i | −0.598682 | − | 0.800987i | \(-0.704309\pi\) |
−0.117980 | + | 0.993016i | \(0.537642\pi\) | |||||||
\(608\) | 2.98313 | − | 2.98313i | 0.120982 | − | 0.120982i | ||||
\(609\) | 0.175433 | + | 23.6787i | 0.00710890 | + | 0.959510i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 9.42504 | − | 16.3247i | 0.381296 | − | 0.660425i | ||||
\(612\) | 1.19130 | − | 4.44599i | 0.0481554 | − | 0.179718i | ||||
\(613\) | 7.72109 | − | 28.8155i | 0.311852 | − | 1.16385i | −0.615033 | − | 0.788501i | \(-0.710857\pi\) |
0.926885 | − | 0.375346i | \(-0.122476\pi\) | |||||||
\(614\) | −11.3090 | + | 19.5877i | −0.456392 | + | 0.790495i | ||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.0387866 | + | 5.23514i | 0.00156276 | + | 0.210930i | ||||
\(617\) | 35.0246 | − | 35.0246i | 1.41004 | − | 1.41004i | 0.650721 | − | 0.759317i | \(-0.274467\pi\) |
0.759317 | − | 0.650721i | \(-0.225533\pi\) | |||||||
\(618\) | 4.81790 | − | 1.29095i | 0.193805 | − | 0.0519298i | ||||
\(619\) | −5.75770 | − | 9.97263i | −0.231422 | − | 0.400834i | 0.726805 | − | 0.686844i | \(-0.241004\pi\) |
−0.958227 | + | 0.286010i | \(0.907671\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 5.09436 | + | 2.94123i | 0.204430 | + | 0.118028i | ||||
\(622\) | −5.47479 | − | 5.47479i | −0.219519 | − | 0.219519i | ||||
\(623\) | −4.12266 | + | 15.8549i | −0.165171 | + | 0.635214i | ||||
\(624\) | − | 3.10026i | − | 0.124110i | ||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | −17.3597 | + | 10.0226i | −0.693834 | + | 0.400585i | ||||
\(627\) | 8.06348 | + | 2.16060i | 0.322024 | + | 0.0862862i | ||||
\(628\) | −3.92974 | − | 14.6660i | −0.156814 | − | 0.585237i | ||||
\(629\) | −12.7586 | −0.508720 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 18.4477 | 0.734390 | 0.367195 | − | 0.930144i | \(-0.380318\pi\) | ||||
0.367195 | + | 0.930144i | \(0.380318\pi\) | |||||||
\(632\) | −0.661320 | − | 2.46808i | −0.0263059 | − | 0.0981749i | ||||
\(633\) | −10.8830 | − | 2.91610i | −0.432562 | − | 0.115905i | ||||
\(634\) | 2.58104 | − | 1.49016i | 0.102506 | − | 0.0591819i | ||||
\(635\) | 0 | 0 | ||||||||
\(636\) | 11.4337i | 0.453375i | ||||||||
\(637\) | −5.30563 | + | 21.0433i | −0.210217 | + | 0.833765i | ||||
\(638\) | −12.5227 | − | 12.5227i | −0.495778 | − | 0.495778i | ||||
\(639\) | −3.34287 | − | 1.93001i | −0.132242 | − | 0.0763499i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 9.74229 | + | 16.8741i | 0.384797 | + | 0.666488i | 0.991741 | − | 0.128256i | \(-0.0409380\pi\) |
−0.606944 | + | 0.794745i | \(0.707605\pi\) | |||||||
\(642\) | 5.84351 | − | 1.56576i | 0.230625 | − | 0.0617958i | ||||
\(643\) | 28.2707 | − | 28.2707i | 1.11489 | − | 1.11489i | 0.122408 | − | 0.992480i | \(-0.460938\pi\) |
0.992480 | − | 0.122408i | \(-0.0390615\pi\) | |||||||
\(644\) | 7.68169 | − | 13.5357i | 0.302701 | − | 0.533381i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −9.70916 | + | 16.8168i | −0.382002 | + | 0.661647i | ||||
\(647\) | 6.45214 | − | 24.0797i | 0.253660 | − | 0.946672i | −0.715171 | − | 0.698949i | \(-0.753651\pi\) |
0.968831 | − | 0.247722i | \(-0.0796821\pi\) | |||||||
\(648\) | −0.258819 | + | 0.965926i | −0.0101674 | + | 0.0379452i | ||||
\(649\) | −4.16233 | + | 7.20937i | −0.163386 | + | 0.282992i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 3.95567 | − | 2.32305i | 0.155035 | − | 0.0910476i | ||||
\(652\) | −15.7848 | + | 15.7848i | −0.618179 | + | 0.618179i | ||||
\(653\) | −48.0477 | + | 12.8743i | −1.88025 | + | 0.503812i | −0.880705 | + | 0.473666i | \(0.842930\pi\) |
−0.999546 | + | 0.0301458i | \(0.990403\pi\) | |||||||
\(654\) | −4.87449 | − | 8.44287i | −0.190608 | − | 0.330142i | ||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 5.67845 | + | 3.27845i | 0.221706 | + | 0.128002i | ||||
\(657\) | 10.7621 | + | 10.7621i | 0.419869 | + | 0.419869i | ||||
\(658\) | 11.4589 | + | 11.2903i | 0.446714 | + | 0.440144i | ||||
\(659\) | 39.5644i | 1.54121i | 0.637312 | + | 0.770606i | \(0.280046\pi\) | ||||
−0.637312 | + | 0.770606i | \(0.719954\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −1.74995 | + | 1.01033i | −0.0680651 | + | 0.0392974i | −0.533646 | − | 0.845708i | \(-0.679179\pi\) |
0.465581 | + | 0.885005i | \(0.345845\pi\) | |||||||
\(662\) | 26.8886 | + | 7.20479i | 1.04506 | + | 0.280022i | ||||
\(663\) | 3.69334 | + | 13.7837i | 0.143437 | + | 0.535315i | ||||
\(664\) | 13.4770 | 0.523010 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 2.77192 | 0.107410 | ||||||||
\(667\) | 13.6263 | + | 50.8539i | 0.527611 | + | 1.96907i | ||||
\(668\) | 9.44229 | + | 2.53005i | 0.365333 | + | 0.0978907i | ||||
\(669\) | 16.1321 | − | 9.31386i | 0.623702 | − | 0.360095i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 22.0037i | 0.849442i | ||||||||
\(672\) | 2.56060 | + | 0.665818i | 0.0987774 | + | 0.0256845i | ||||
\(673\) | 19.7775 | + | 19.7775i | 0.762366 | + | 0.762366i | 0.976750 | − | 0.214383i | \(-0.0687742\pi\) |
−0.214383 | + | 0.976750i | \(0.568774\pi\) | |||||||
\(674\) | −21.0125 | − | 12.1316i | −0.809372 | − | 0.467291i | ||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −1.69419 | − | 2.93442i | −0.0651610 | − | 0.112862i | ||||
\(677\) | 16.5748 | − | 4.44120i | 0.637021 | − | 0.170689i | 0.0741672 | − | 0.997246i | \(-0.476370\pi\) |
0.562854 | + | 0.826557i | \(0.309703\pi\) | |||||||
\(678\) | 6.02504 | − | 6.02504i | 0.231390 | − | 0.231390i | ||||
\(679\) | −4.81714 | − | 2.73379i | −0.184865 | − | 0.104913i | ||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 13.4571 | − | 23.3083i | 0.515676 | − | 0.893177i | ||||
\(682\) | −0.887978 | + | 3.31398i | −0.0340024 | + | 0.126899i | ||||
\(683\) | −0.130540 | + | 0.487181i | −0.00499496 | + | 0.0186414i | −0.968378 | − | 0.249486i | \(-0.919738\pi\) |
0.963383 | + | 0.268128i | \(0.0864049\pi\) | |||||||
\(684\) | 2.10939 | − | 3.65357i | 0.0806546 | − | 0.139698i | ||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −16.2409 | − | 8.90138i | −0.620079 | − | 0.339856i | ||||
\(687\) | 19.0144 | − | 19.0144i | 0.725445 | − | 0.725445i | ||||
\(688\) | 8.65684 | − | 2.31959i | 0.330039 | − | 0.0884336i | ||||
\(689\) | −17.7237 | − | 30.6984i | −0.675220 | − | 1.16952i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 13.5396 | + | 7.81710i | 0.515071 | + | 0.297376i | 0.734916 | − | 0.678158i | \(-0.237222\pi\) |
−0.219845 | + | 0.975535i | \(0.570555\pi\) | |||||||
\(692\) | −3.20151 | − | 3.20151i | −0.121703 | − | 0.121703i | ||||
\(693\) | 1.39242 | + | 5.04672i | 0.0528937 | + | 0.191709i | ||||
\(694\) | 25.0428i | 0.950613i | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | −7.75089 | + | 4.47498i | −0.293797 | + | 0.169624i | ||||
\(697\) | −29.1519 | − | 7.81123i | −1.10421 | − | 0.295871i | ||||
\(698\) | 4.66210 | + | 17.3992i | 0.176463 | + | 0.658569i | ||||
\(699\) | 0.921244 | 0.0348447 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 8.02724 | 0.303185 | 0.151592 | − | 0.988443i | \(-0.451560\pi\) | ||||
0.151592 | + | 0.988443i | \(0.451560\pi\) | |||||||
\(702\) | −0.802407 | − | 2.99462i | −0.0302849 | − | 0.113025i | ||||
\(703\) | −11.2956 | − | 3.02666i | −0.426023 | − | 0.114153i | ||||
\(704\) | −1.71365 | + | 0.989376i | −0.0645856 | + | 0.0372885i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.59800i | 0.285955i | ||||||||
\(707\) | −18.6568 | + | 18.9353i | −0.701661 | + | 0.712136i | ||||
\(708\) | 2.97481 | + | 2.97481i | 0.111800 | + | 0.111800i | ||||
\(709\) | 11.8457 | + | 6.83914i | 0.444876 | + | 0.256849i | 0.705664 | − | 0.708547i | \(-0.250649\pi\) |
−0.260788 | + | 0.965396i | \(0.583982\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −1.27757 | − | 2.21282i | −0.0479127 | − | 0.0829872i | ||||
\(712\) | −5.98088 | + | 1.60257i | −0.224143 | + | 0.0600590i | ||||
\(713\) | 7.21204 | − | 7.21204i | 0.270093 | − | 0.270093i | ||||
\(714\) | −12.1776 | + | 0.0902224i | −0.455735 | + | 0.00337649i | ||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 1.03394 | − | 1.79084i | 0.0386401 | − | 0.0669267i | ||||
\(717\) | −6.55929 | + | 24.4796i | −0.244961 | + | 0.914208i | ||||
\(718\) | −0.850665 | + | 3.17473i | −0.0317465 | + | 0.118480i | ||||
\(719\) | −10.5235 | + | 18.2273i | −0.392462 | + | 0.679764i | −0.992774 | − | 0.120002i | \(-0.961710\pi\) |
0.600312 | + | 0.799766i | \(0.295043\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −6.68281 | − | 11.3794i | −0.248881 | − | 0.423792i | ||||
\(722\) | 0.849839 | − | 0.849839i | 0.0316277 | − | 0.0316277i | ||||
\(723\) | −20.4004 | + | 5.46626i | −0.758698 | + | 0.203292i | ||||
\(724\) | −3.06600 | − | 5.31046i | −0.113947 | − | 0.197362i | ||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 6.13539 | + | 3.54227i | 0.227706 | + | 0.131466i | ||||
\(727\) | 11.2251 | + | 11.2251i | 0.416317 | + | 0.416317i | 0.883932 | − | 0.467615i | \(-0.154887\pi\) |
−0.467615 | + | 0.883932i | \(0.654887\pi\) | |||||||
\(728\) | −7.90708 | + | 2.18161i | −0.293056 | + | 0.0808559i | ||||
\(729\) | 1.00000i | 0.0370370i | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −35.7248 | + | 20.6258i | −1.32133 | + | 0.762871i | ||||
\(732\) | 10.7411 | + | 2.87806i | 0.397001 | + | 0.106376i | ||||
\(733\) | −7.44145 | − | 27.7719i | −0.274856 | − | 1.02578i | −0.955938 | − | 0.293570i | \(-0.905157\pi\) |
0.681081 | − | 0.732208i | \(-0.261510\pi\) | |||||||
\(734\) | −3.24759 | −0.119871 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 5.88246 | 0.216830 | ||||||||
\(737\) | 2.82300 | + | 10.5356i | 0.103986 | + | 0.388082i | ||||
\(738\) | 6.33349 | + | 1.69705i | 0.233139 | + | 0.0624694i | ||||
\(739\) | 36.3593 | − | 20.9921i | 1.33750 | − | 0.772205i | 0.351063 | − | 0.936352i | \(-0.385820\pi\) |
0.986436 | + | 0.164147i | \(0.0524871\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 13.0793i | 0.480482i | ||||||||
\(742\) | 29.1611 | − | 8.04573i | 1.07054 | − | 0.295368i | ||||
\(743\) | −8.63799 | − | 8.63799i | −0.316897 | − | 0.316897i | 0.530677 | − | 0.847574i | \(-0.321938\pi\) |
−0.847574 | + | 0.530677i | \(0.821938\pi\) | |||||||
\(744\) | 1.50157 | + | 0.866930i | 0.0550501 | + | 0.0317832i | ||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 7.88312 | + | 13.6540i | 0.288622 | + | 0.499907i | ||||
\(747\) | 13.0178 | − | 3.48811i | 0.476297 | − | 0.127623i | ||||
\(748\) | 6.44022 | − | 6.44022i | 0.235478 | − | 0.235478i | ||||
\(749\) | −8.10541 | − | 13.8018i | −0.296165 | − | 0.504307i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −15.8723 | + | 27.4916i | −0.579188 | + | 1.00318i | 0.416384 | + | 0.909189i | \(0.363297\pi\) |
−0.995573 | + | 0.0939948i | \(0.970036\pi\) | |||||||
\(752\) | −1.57366 | + | 5.87298i | −0.0573855 | + | 0.214166i | ||||
\(753\) | 0.700423 | − | 2.61401i | 0.0255248 | − | 0.0952600i | ||||
\(754\) | 13.8736 | − | 24.0298i | 0.505247 | − | 0.875114i | ||||
\(755\) | 0 | 0 | ||||||||
\(756\) | 2.64568 | − | 0.0196015i | 0.0962224 | − | 0.000712901i | ||||
\(757\) | 9.81959 | − | 9.81959i | 0.356899 | − | 0.356899i | −0.505770 | − | 0.862669i | \(-0.668791\pi\) |
0.862669 | + | 0.505770i | \(0.168791\pi\) | |||||||
\(758\) | −21.0019 | + | 5.62744i | −0.762824 | + | 0.204398i | ||||
\(759\) | 5.81997 | + | 10.0805i | 0.211251 | + | 0.365898i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 27.6636 | + | 15.9716i | 1.00280 | + | 0.578970i | 0.909077 | − | 0.416628i | \(-0.136788\pi\) |
0.0937278 | + | 0.995598i | \(0.470122\pi\) | |||||||
\(762\) | 8.92770 | + | 8.92770i | 0.323416 | + | 0.323416i | ||||
\(763\) | −18.1031 | + | 18.3733i | −0.655375 | + | 0.665158i | ||||
\(764\) | 16.1661i | 0.584869i | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 15.4914 | − | 8.94394i | 0.559726 | − | 0.323158i | ||||
\(767\) | −12.5985 | − | 3.37574i | −0.454904 | − | 0.121891i | ||||
\(768\) | 0.258819 | + | 0.965926i | 0.00933933 | + | 0.0348548i | ||||
\(769\) | −26.3715 | −0.950981 | −0.475490 | − | 0.879721i | \(-0.657729\pi\) | ||||
−0.475490 | + | 0.879721i | \(0.657729\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −24.0221 | −0.865133 | ||||||||
\(772\) | −5.63991 | − | 21.0484i | −0.202985 | − | 0.757549i | ||||
\(773\) | 44.4561 | + | 11.9120i | 1.59898 | + | 0.428444i | 0.944733 | − | 0.327841i | \(-0.106321\pi\) |
0.654242 | + | 0.756285i | \(0.272988\pi\) | |||||||
\(774\) | 7.76151 | − | 4.48111i | 0.278982 | − | 0.161070i | ||||
\(775\) | 0 | 0 | ||||||||
\(776\) | − | 2.09348i | − | 0.0751514i | ||||||
\(777\) | −1.95056 | − | 7.06965i | −0.0699759 | − | 0.253622i | ||||
\(778\) | −3.56098 | − | 3.56098i | −0.127667 | − | 0.127667i | ||||
\(779\) | −23.9561 | − | 13.8311i | −0.858318 | − | 0.495550i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −3.81901 | − | 6.61472i | −0.136655 | − | 0.236693i | ||||
\(782\) | −26.1533 | + | 7.00777i | −0.935241 | + | 0.250597i | ||||
\(783\) | −6.32858 | + | 6.32858i | −0.226165 | + | 0.226165i | ||||
\(784\) | −0.103719 | − | 6.99923i | −0.00370424 | − | 0.249973i | ||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 2.56080 | − | 4.43543i | 0.0913407 | − | 0.158207i | ||||
\(787\) | 2.93226 | − | 10.9433i | 0.104524 | − | 0.390088i | −0.893767 | − | 0.448532i | \(-0.851947\pi\) |
0.998291 | + | 0.0584437i | \(0.0186138\pi\) | |||||||
\(788\) | −0.229908 | + | 0.858028i | −0.00819013 | + | 0.0305660i | ||||
\(789\) | 0.425163 | − | 0.736403i | 0.0151362 | − | 0.0262167i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −19.6063 | − | 11.1269i | −0.697121 | − | 0.395626i | ||||
\(792\) | −1.39919 | + | 1.39919i | −0.0497180 | + | 0.0497180i | ||||
\(793\) | −33.3001 | + | 8.92274i | −1.18252 | + | 0.316856i | ||||
\(794\) | −7.37735 | − | 12.7780i | −0.261813 | − | 0.453473i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −8.33546 | − | 4.81248i | −0.295442 | − | 0.170574i | ||||
\(797\) | −24.7239 | − | 24.7239i | −0.875767 | − | 0.875767i | 0.117327 | − | 0.993093i | \(-0.462568\pi\) |
−0.993093 | + | 0.117327i | \(0.962568\pi\) | |||||||
\(798\) | −10.8026 | − | 2.80894i | −0.382409 | − | 0.0994356i | ||||
\(799\) | − | 27.9859i | − | 0.990070i | ||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −5.36231 | + | 3.09593i | −0.189468 | + | 0.109389i | ||||
\(802\) | −8.39748 | − | 2.25010i | −0.296525 | − | 0.0794537i | ||||
\(803\) | 7.79470 | + | 29.0902i | 0.275069 | + | 1.02657i | ||||
\(804\) | 5.51217 | 0.194399 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | −5.37542 | −0.189341 | ||||||||
\(807\) | −3.01354 | − | 11.2467i | −0.106082 | − | 0.395902i | ||||
\(808\) | −9.70484 | − | 2.60040i | −0.341415 | − | 0.0914819i | ||||
\(809\) | 5.02215 | − | 2.89954i | 0.176569 | − | 0.101942i | −0.409110 | − | 0.912485i | \(-0.634161\pi\) |
0.585680 | + | 0.810542i | \(0.300828\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 28.8064i | − | 1.01153i | −0.862671 | − | 0.505765i | \(-0.831210\pi\) | ||
0.862671 | − | 0.505765i | \(-0.168790\pi\) | |||||||
\(812\) | 16.8674 | + | 16.6193i | 0.591931 | + | 0.583224i | ||||
\(813\) | 16.5072 | + | 16.5072i | 0.578934 | + | 0.578934i | ||||
\(814\) | 4.75009 | + | 2.74247i | 0.166491 | + | 0.0961235i | ||||
\(815\) | 0 | 0 | ||||||||
\(816\) | −2.30141 | − | 3.98616i | −0.0805655 | − | 0.139544i | ||||
\(817\) | −36.5213 | + | 9.78586i | −1.27772 | + | 0.342364i | ||||
\(818\) | −13.4222 | + | 13.4222i | −0.469297 | + | 0.469297i | ||||
\(819\) | −7.07301 | + | 4.15378i | −0.247151 | + | 0.145145i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −2.25899 | + | 3.91269i | −0.0788395 | + | 0.136554i | −0.902749 | − | 0.430167i | \(-0.858455\pi\) |
0.823910 | + | 0.566721i | \(0.191788\pi\) | |||||||
\(822\) | 2.99773 | − | 11.1877i | 0.104558 | − | 0.390216i | ||||
\(823\) | 5.79271 | − | 21.6187i | 0.201921 | − | 0.753580i | −0.788445 | − | 0.615105i | \(-0.789113\pi\) |
0.990366 | − | 0.138474i | \(-0.0442199\pi\) | |||||||
\(824\) | 2.49393 | − | 4.31961i | 0.0868802 | − | 0.150481i | ||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 5.49380 | − | 9.68047i | 0.191154 | − | 0.336827i | ||||
\(827\) | −22.5410 | + | 22.5410i | −0.783826 | + | 0.783826i | −0.980474 | − | 0.196648i | \(-0.936994\pi\) |
0.196648 | + | 0.980474i | \(0.436994\pi\) | |||||||
\(828\) | 5.68202 | − | 1.52249i | 0.197464 | − | 0.0529103i | ||||
\(829\) | 3.61347 | + | 6.25871i | 0.125501 | + | 0.217374i | 0.921929 | − | 0.387360i | \(-0.126613\pi\) |
−0.796428 | + | 0.604734i | \(0.793280\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | −8.18372 | − | 4.72487i | −0.283890 | − | 0.163904i | ||||
\(832\) | −2.19222 | − | 2.19222i | −0.0760014 | − | 0.0760014i | ||||
\(833\) | 8.79930 | + | 30.9949i | 0.304878 | + | 1.07391i | ||||
\(834\) | − | 2.87054i | − | 0.0993985i | ||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 7.22952 | − | 4.17397i | 0.250038 | − | 0.144360i | ||||
\(837\) | 1.67478 | + | 0.448756i | 0.0578889 | + | 0.0155113i | ||||
\(838\) | −3.08437 | − | 11.5110i | −0.106548 | − | 0.397642i | ||||
\(839\) | 5.52622 | 0.190786 | 0.0953932 | − | 0.995440i | \(-0.469589\pi\) | ||||
0.0953932 | + | 0.995440i | \(0.469589\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −51.1018 | −1.76213 | ||||||||
\(842\) | −1.79947 | − | 6.71572i | −0.0620139 | − | 0.231439i | ||||
\(843\) | 11.3322 | + | 3.03646i | 0.390302 | + | 0.104581i | ||||
\(844\) | −9.75746 | + | 5.63347i | −0.335866 | + | 0.193912i | ||||
\(845\) | 0 | 0 | ||||||||
\(846\) | 6.08016i | 0.209040i | ||||||||
\(847\) | 4.71702 | − | 18.1407i | 0.162079 | − | 0.623321i | ||||
\(848\) | 8.08484 | + | 8.08484i | 0.277635 | + | 0.277635i | ||||
\(849\) | 3.15908 | + | 1.82389i | 0.108419 | + | 0.0625959i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −8.15284 | − | 14.1211i | −0.279476 | − | 0.484066i | ||||
\(852\) | −3.72849 | + | 0.999046i | −0.127736 | + | 0.0342267i | ||||
\(853\) | 10.4649 | − | 10.4649i | 0.358313 | − | 0.358313i | −0.504878 | − | 0.863191i | \(-0.668462\pi\) |
0.863191 | + | 0.504878i | \(0.168462\pi\) | |||||||
\(854\) | −0.217968 | − | 29.4199i | −0.00745873 | − | 1.00673i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 3.02482 | − | 5.23915i | 0.103386 | − | 0.179070i | ||||
\(857\) | −0.556370 | + | 2.07640i | −0.0190053 | + | 0.0709286i | −0.974777 | − | 0.223180i | \(-0.928356\pi\) |
0.955772 | + | 0.294109i | \(0.0950228\pi\) | |||||||
\(858\) | 1.58776 | − | 5.92562i | 0.0542054 | − | 0.202297i | ||||
\(859\) | −3.59455 | + | 6.22594i | −0.122644 | + | 0.212426i | −0.920810 | − | 0.390012i | \(-0.872471\pi\) |
0.798165 | + | 0.602439i | \(0.205804\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −0.128525 | − | 17.3475i | −0.00438013 | − | 0.591200i | ||||
\(862\) | −4.41788 | + | 4.41788i | −0.150474 | + | 0.150474i | ||||
\(863\) | 39.1589 | − | 10.4926i | 1.33298 | − | 0.357172i | 0.479157 | − | 0.877729i | \(-0.340943\pi\) |
0.853827 | + | 0.520557i | \(0.174276\pi\) | |||||||
\(864\) | 0.500000 | + | 0.866025i | 0.0170103 | + | 0.0294628i | ||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 18.5603 | + | 10.7158i | 0.630704 | + | 0.364137i | ||||
\(867\) | 2.95994 | + | 2.95994i | 0.100525 | + | 0.100525i | ||||
\(868\) | 1.15444 | − | 4.43973i | 0.0391841 | − | 0.150694i | ||||
\(869\) | − | 5.05600i | − | 0.171513i | ||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −14.7997 | + | 8.54458i | −0.501467 | + | 0.289522i | ||||
\(872\) | −9.41680 | − | 2.52322i | −0.318893 | − | 0.0854471i | ||||
\(873\) | −0.541831 | − | 2.02214i | −0.0183382 | − | 0.0684391i | ||||
\(874\) | −24.8168 | −0.839442 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 15.2199 | 0.514233 | ||||||||
\(877\) | 13.2237 | + | 49.3516i | 0.446533 | + | 1.66648i | 0.711857 | + | 0.702325i | \(0.247855\pi\) |
−0.265324 | + | 0.964159i | \(0.585479\pi\) | |||||||
\(878\) | −31.6301 | − | 8.47526i | −1.06746 | − | 0.286026i | ||||
\(879\) | −10.5616 | + | 6.09777i | −0.356235 | + | 0.205673i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 27.9972i | − | 0.943251i | −0.881799 | − | 0.471625i | \(-0.843667\pi\) | ||
0.881799 | − | 0.471625i | \(-0.156333\pi\) | |||||||
\(882\) | −1.91172 | − | 6.73389i | −0.0643709 | − | 0.226742i | ||||
\(883\) | −4.66131 | − | 4.66131i | −0.156865 | − | 0.156865i | 0.624311 | − | 0.781176i | \(-0.285380\pi\) |
−0.781176 | + | 0.624311i | \(0.785380\pi\) | |||||||
\(884\) | 12.3581 | + | 7.13498i | 0.415650 | + | 0.239975i | ||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.3755 | − | 26.6312i | −0.516550 | − | 0.894692i | ||||
\(887\) | 13.4547 | − | 3.60517i | 0.451763 | − | 0.121050i | −0.0257610 | − | 0.999668i | \(-0.508201\pi\) |
0.477524 | + | 0.878619i | \(0.341534\pi\) | |||||||
\(888\) | 1.96004 | − | 1.96004i | 0.0657747 | − | 0.0657747i | ||||
\(889\) | 16.4874 | − | 29.0520i | 0.552970 | − | 0.974372i | ||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −0.989376 | + | 1.71365i | −0.0331454 | + | 0.0574094i | ||||
\(892\) | 4.82121 | − | 17.9930i | 0.161426 | − | 0.602450i | ||||
\(893\) | 6.63894 | − | 24.7768i | 0.222164 | − | 0.829126i | ||||
\(894\) | −7.78982 | + | 13.4924i | −0.260531 | + | 0.451252i | ||||
\(895\) | 0 | 0 | ||||||||
\(896\) | 2.28142 | − | 1.33981i | 0.0762170 | − | 0.0447601i | ||||
\(897\) | −12.8956 | + | 12.8956i | −0.430573 | + | 0.430573i | ||||
\(898\) | −16.2964 | + | 4.36662i | −0.543819 | + | 0.145716i | ||||
\(899\) | 7.75899 | + | 13.4390i | 0.258777 | + | 0.448215i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −45.5766 | − | 26.3136i | −1.51838 | − | 0.876634i | ||||
\(902\) | 9.17435 | + | 9.17435i | 0.305473 | + | 0.305473i | ||||
\(903\) | −16.8905 | − | 16.6421i | −0.562082 | − | 0.553814i | ||||
\(904\) | − | 8.52069i | − | 0.283394i | ||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 18.3516 | − | 10.5953i | 0.609690 | − | 0.352005i | ||||
\(907\) | 26.0691 | + | 6.98519i | 0.865610 | + | 0.231939i | 0.664188 | − | 0.747565i | \(-0.268777\pi\) |
0.201421 | + | 0.979505i | \(0.435444\pi\) | |||||||
\(908\) | −6.96589 | − | 25.9971i | −0.231171 | − | 0.862743i | ||||
\(909\) | −10.0472 | −0.333244 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −15.5364 | −0.514744 | −0.257372 | − | 0.966312i | \(-0.582857\pi\) | ||||
−0.257372 | + | 0.966312i | \(0.582857\pi\) | |||||||
\(912\) | −1.09190 | − | 4.07503i | −0.0361565 | − | 0.134938i | ||||
\(913\) | 25.7590 | + | 6.90211i | 0.852499 | + | 0.228426i | ||||
\(914\) | −17.1886 | + | 9.92384i | −0.568548 | + | 0.328251i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | − | 26.8905i | − | 0.888486i | ||||||
\(917\) | −13.1144 | − | 3.41005i | −0.433075 | − | 0.112610i | ||||
\(918\) | −3.25469 | − | 3.25469i | −0.107421 | − | 0.107421i | ||||
\(919\) | 32.7915 | + | 18.9322i | 1.08169 | + | 0.624515i | 0.931352 | − | 0.364120i | \(-0.118630\pi\) |
0.150339 | + | 0.988634i | \(0.451963\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 11.3090 | + | 19.5877i | 0.372643 | + | 0.645436i | ||||
\(922\) | 15.2399 | − | 4.08351i | 0.501898 | − | 0.134483i | ||||
\(923\) | 8.46199 | − | 8.46199i | 0.278530 | − | 0.278530i | ||||
\(924\) | 4.55316 | + | 2.58398i | 0.149788 | + | 0.0850068i | ||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −3.17220 | + | 5.49441i | −0.104245 | + | 0.180558i | ||||
\(927\) | 1.29095 | − | 4.81790i | 0.0424005 | − | 0.158241i | ||||
\(928\) | −2.31642 | + | 8.64500i | −0.0760402 | + | 0.283786i | ||||
\(929\) | 8.75685 | − | 15.1673i | 0.287303 | − | 0.497624i | −0.685862 | − | 0.727732i | \(-0.740575\pi\) |
0.973165 | + | 0.230108i | \(0.0739080\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0.437567 | + | 29.5283i | 0.0143407 | + | 0.967749i | ||||
\(932\) | 0.651418 | − | 0.651418i | 0.0213379 | − | 0.0213379i | ||||
\(933\) | −7.47870 | + | 2.00391i | −0.244842 | + | 0.0656051i | ||||
\(934\) | −8.72500 | − | 15.1121i | −0.285491 | − | 0.494484i | ||||
\(935\) | 0 | 0 | ||||||||
\(936\) | −2.68491 | − | 1.55013i | −0.0877589 | − | 0.0506676i | ||||
\(937\) | −2.68964 | − | 2.68964i | −0.0878666 | − | 0.0878666i | 0.661807 | − | 0.749674i | \(-0.269790\pi\) |
−0.749674 | + | 0.661807i | \(0.769790\pi\) | |||||||
\(938\) | −3.87883 | − | 14.0585i | −0.126648 | − | 0.459028i | ||||
\(939\) | 20.0453i | 0.654153i | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 28.0634 | − | 16.2024i | 0.914839 | − | 0.528183i | 0.0328543 | − | 0.999460i | \(-0.489540\pi\) |
0.881985 | + | 0.471277i | \(0.156207\pi\) | |||||||
\(942\) | −14.6660 | − | 3.92974i | −0.477844 | − | 0.128038i | ||||
\(943\) | −9.98284 | − | 37.2565i | −0.325086 | − | 1.21324i | ||||
\(944\) | 4.20702 | 0.136927 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 17.7340 | 0.576582 | ||||||||
\(947\) | 9.93164 | + | 37.0654i | 0.322735 | + | 1.20446i | 0.916569 | + | 0.399876i | \(0.130947\pi\) |
−0.593834 | + | 0.804587i | \(0.702386\pi\) | |||||||
\(948\) | −2.46808 | − | 0.661320i | −0.0801595 | − | 0.0214787i | ||||
\(949\) | −40.8640 | + | 23.5928i | −1.32650 | + | 0.765856i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | − | 2.98032i | − | 0.0966436i | ||||||
\(952\) | −8.54706 | + | 8.67465i | −0.277012 | + | 0.281147i | ||||
\(953\) | −12.2232 | − | 12.2232i | −0.395949 | − | 0.395949i | 0.480853 | − | 0.876801i | \(-0.340327\pi\) |
−0.876801 | + | 0.480853i | \(0.840327\pi\) | |||||||
\(954\) | 9.90187 | + | 5.71685i | 0.320585 | + | 0.185090i | ||||
\(955\) | 0 | 0 | ||||||||
\(956\) | 12.6716 | + | 21.9478i | 0.409828 | + | 0.709843i | ||||
\(957\) | −17.1063 | + | 4.58362i | −0.552969 | + | 0.148167i | ||||
\(958\) | 22.4504 | − | 22.4504i | 0.725339 | − | 0.725339i | ||||
\(959\) | −30.6432 | + | 0.227032i | −0.989520 | + | 0.00733124i | ||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −13.9969 | + | 24.2433i | −0.451512 | + | 0.782041i | ||||
\(962\) | −2.22420 | + | 8.30084i | −0.0717112 | + | 0.267630i | ||||
\(963\) | 1.56576 | − | 5.84351i | 0.0504560 | − | 0.188304i | ||||
\(964\) | −10.5600 | + | 18.2905i | −0.340115 | + | 0.589096i | ||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −7.88141 | − | 13.4204i | −0.253580 | − | 0.431794i | ||||
\(967\) | −24.7551 | + | 24.7551i | −0.796071 | + | 0.796071i | −0.982474 | − | 0.186402i | \(-0.940317\pi\) |
0.186402 | + | 0.982474i | \(0.440317\pi\) | |||||||
\(968\) | 6.84314 | − | 1.83361i | 0.219947 | − | 0.0589346i | ||||
\(969\) | 9.70916 | + | 16.8168i | 0.311903 | + | 0.540232i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 8.84412 | + | 5.10615i | 0.283821 | + | 0.163864i | 0.635152 | − | 0.772387i | \(-0.280937\pi\) |
−0.351331 | + | 0.936251i | \(0.614271\pi\) | |||||||
\(972\) | 0.707107 | + | 0.707107i | 0.0226805 | + | 0.0226805i | ||||
\(973\) | −7.32118 | + | 2.01996i | −0.234706 | + | 0.0647568i | ||||
\(974\) | 29.9080i | 0.958316i | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 9.63018 | − | 5.55999i | 0.308254 | − | 0.177971i | ||||
\(977\) | −15.4715 | − | 4.14558i | −0.494977 | − | 0.132629i | 0.00269080 | − | 0.999996i | \(-0.499143\pi\) |
−0.497668 | + | 0.867368i | \(0.665810\pi\) | |||||||
\(978\) | 5.77762 | + | 21.5624i | 0.184748 | + | 0.689489i | ||||
\(979\) | −12.2522 | −0.391581 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | −9.74899 | −0.311261 | ||||||||
\(982\) | −0.406810 | − | 1.51824i | −0.0129818 | − | 0.0484488i | ||||
\(983\) | −7.36683 | − | 1.97394i | −0.234965 | − | 0.0629588i | 0.139415 | − | 0.990234i | \(-0.455478\pi\) |
−0.374380 | + | 0.927275i | \(0.622145\pi\) | |||||||
\(984\) | 5.67845 | − | 3.27845i | 0.181022 | − | 0.104513i | ||||
\(985\) | 0 | 0 | ||||||||
\(986\) | − | 41.1951i | − | 1.31192i | ||||||
\(987\) | 15.5072 | − | 4.27852i | 0.493599 | − | 0.136187i | ||||
\(988\) | 9.24849 | + | 9.24849i | 0.294234 | + | 0.294234i | ||||
\(989\) | −45.6568 | − | 26.3599i | −1.45180 | − | 0.838198i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −25.4379 | − | 44.0597i | −0.808060 | − | 1.39960i | −0.914206 | − | 0.405251i | \(-0.867184\pi\) |
0.106145 | − | 0.994351i | \(-0.466149\pi\) | |||||||
\(992\) | 1.67478 | − | 0.448756i | 0.0531743 | − | 0.0142480i | ||||
\(993\) | 19.6839 | − | 19.6839i | 0.624648 | − | 0.624648i | ||||
\(994\) | 5.17171 | + | 8.80633i | 0.164037 | + | 0.279320i | ||||
\(995\) | 0 | 0 | ||||||||
\(996\) | 6.73851 | − | 11.6714i | 0.213518 | − | 0.369824i | ||||
\(997\) | 10.5401 | − | 39.3361i | 0.333808 | − | 1.24579i | −0.571348 | − | 0.820708i | \(-0.693579\pi\) |
0.905156 | − | 0.425080i | \(-0.139754\pi\) | |||||||
\(998\) | 3.69064 | − | 13.7737i | 0.116825 | − | 0.435997i | ||||
\(999\) | 1.38596 | − | 2.40055i | 0.0438498 | − | 0.0759500i |
(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 | 1050.2.bc.h.943.2 | 16 | ||
5.2 | odd | 4 | 1050.2.bc.g.607.4 | 16 | |||
5.3 | odd | 4 | 210.2.u.b.187.2 | yes | 16 | ||
5.4 | even | 2 | 210.2.u.a.103.3 | ✓ | 16 | ||
7.3 | odd | 6 | 1050.2.bc.g.493.4 | 16 | |||
15.8 | even | 4 | 630.2.bv.b.397.3 | 16 | |||
15.14 | odd | 2 | 630.2.bv.a.523.2 | 16 | |||
35.3 | even | 12 | 210.2.u.a.157.3 | yes | 16 | ||
35.9 | even | 6 | 1470.2.m.d.1273.7 | 16 | |||
35.17 | even | 12 | inner | 1050.2.bc.h.157.2 | 16 | ||
35.19 | odd | 6 | 1470.2.m.e.1273.6 | 16 | |||
35.23 | odd | 12 | 1470.2.m.e.97.6 | 16 | |||
35.24 | odd | 6 | 210.2.u.b.73.2 | yes | 16 | ||
35.33 | even | 12 | 1470.2.m.d.97.7 | 16 | |||
105.38 | odd | 12 | 630.2.bv.a.577.2 | 16 | |||
105.59 | even | 6 | 630.2.bv.b.73.3 | 16 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
210.2.u.a.103.3 | ✓ | 16 | 5.4 | even | 2 | ||
210.2.u.a.157.3 | yes | 16 | 35.3 | even | 12 | ||
210.2.u.b.73.2 | yes | 16 | 35.24 | odd | 6 | ||
210.2.u.b.187.2 | yes | 16 | 5.3 | odd | 4 | ||
630.2.bv.a.523.2 | 16 | 15.14 | odd | 2 | |||
630.2.bv.a.577.2 | 16 | 105.38 | odd | 12 | |||
630.2.bv.b.73.3 | 16 | 105.59 | even | 6 | |||
630.2.bv.b.397.3 | 16 | 15.8 | even | 4 | |||
1050.2.bc.g.493.4 | 16 | 7.3 | odd | 6 | |||
1050.2.bc.g.607.4 | 16 | 5.2 | odd | 4 | |||
1050.2.bc.h.157.2 | 16 | 35.17 | even | 12 | inner | ||
1050.2.bc.h.943.2 | 16 | 1.1 | even | 1 | trivial | ||
1470.2.m.d.97.7 | 16 | 35.33 | even | 12 | |||
1470.2.m.d.1273.7 | 16 | 35.9 | even | 6 | |||
1470.2.m.e.97.6 | 16 | 35.23 | odd | 12 | |||
1470.2.m.e.1273.6 | 16 | 35.19 | odd | 6 |