Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [483,2,Mod(277,483)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(483, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 4, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("483.277");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 483 = 3 \cdot 7 \cdot 23 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 483.i (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: | \(3.85677441763\) |
Analytic rank: | \(0\) |
Dimension: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{3})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - x^{15} + 16 x^{14} - 7 x^{13} + 161 x^{12} - 50 x^{11} + 929 x^{10} - 47 x^{9} + 3741 x^{8} - 158 x^{7} + 8993 x^{6} + 265 x^{5} + 15176 x^{4} + 383 x^{3} + 12649 x^{2} + \cdots + 6400 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 3 \) |
Twist minimal: | yes |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 415.4 | ||
Root | \(0.595971 + 1.03225i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 483.415 |
Dual form | 483.2.i.g.277.4 |
$q$-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 \(\left(\mathbb{Z}/483\mathbb{Z}\right)^\times\).
\(n\) | \(323\) | \(346\) | \(442\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{3}\right)\) | \(1\) |
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.595971 | + | 1.03225i | −0.421415 | + | 0.729913i | −0.996078 | − | 0.0884776i | \(-0.971800\pi\) |
0.574663 | + | 0.818390i | \(0.305133\pi\) | |||||||
\(3\) | −0.500000 | − | 0.866025i | −0.288675 | − | 0.500000i | ||||
\(4\) | 0.289637 | + | 0.501666i | 0.144818 | + | 0.250833i | ||||
\(5\) | 1.89410 | − | 3.28068i | 0.847068 | − | 1.46717i | −0.0367448 | − | 0.999325i | \(-0.511699\pi\) |
0.883813 | − | 0.467840i | \(-0.154968\pi\) | |||||||
\(6\) | 1.19194 | 0.486608 | ||||||||
\(7\) | 2.62328 | − | 0.344130i | 0.991505 | − | 0.130069i | ||||
\(8\) | −3.07435 | −1.08695 | ||||||||
\(9\) | −0.500000 | + | 0.866025i | −0.166667 | + | 0.288675i | ||||
\(10\) | 2.25766 | + | 3.91038i | 0.713935 | + | 1.23657i | ||||
\(11\) | 0.745201 | + | 1.29073i | 0.224686 | + | 0.389168i | 0.956225 | − | 0.292631i | \(-0.0945309\pi\) |
−0.731539 | + | 0.681800i | \(0.761198\pi\) | |||||||
\(12\) | 0.289637 | − | 0.501666i | 0.0836110 | − | 0.144818i | ||||
\(13\) | −0.460711 | −0.127778 | −0.0638892 | − | 0.997957i | \(-0.520350\pi\) | ||||
−0.0638892 | + | 0.997957i | \(0.520350\pi\) | |||||||
\(14\) | −1.20817 | + | 2.91297i | −0.322896 | + | 0.778525i | ||||
\(15\) | −3.78820 | −0.978110 | ||||||||
\(16\) | 1.25295 | − | 2.17017i | 0.313237 | − | 0.542542i | ||||
\(17\) | −3.02964 | − | 5.24749i | −0.734796 | − | 1.27270i | −0.954813 | − | 0.297207i | \(-0.903945\pi\) |
0.220017 | − | 0.975496i | \(-0.429389\pi\) | |||||||
\(18\) | −0.595971 | − | 1.03225i | −0.140472 | − | 0.243304i | ||||
\(19\) | 2.95317 | − | 5.11504i | 0.677504 | − | 1.17347i | −0.298227 | − | 0.954495i | \(-0.596395\pi\) |
0.975730 | − | 0.218976i | \(-0.0702715\pi\) | |||||||
\(20\) | 2.19441 | 0.490684 | ||||||||
\(21\) | −1.60966 | − | 2.09976i | −0.351257 | − | 0.458205i | ||||
\(22\) | −1.77647 | −0.378745 | ||||||||
\(23\) | 0.500000 | − | 0.866025i | 0.104257 | − | 0.180579i | ||||
\(24\) | 1.53717 | + | 2.66246i | 0.313774 | + | 0.543473i | ||||
\(25\) | −4.67524 | − | 8.09776i | −0.935049 | − | 1.61955i | ||||
\(26\) | 0.274571 | − | 0.475570i | 0.0538477 | − | 0.0932670i | ||||
\(27\) | 1.00000 | 0.192450 | ||||||||
\(28\) | 0.932436 | + | 1.21633i | 0.176214 | + | 0.229866i | ||||
\(29\) | 2.10833 | 0.391506 | 0.195753 | − | 0.980653i | \(-0.437285\pi\) | ||||
0.195753 | + | 0.980653i | \(0.437285\pi\) | |||||||
\(30\) | 2.25766 | − | 3.91038i | 0.412190 | − | 0.713935i | ||||
\(31\) | 4.03574 | + | 6.99011i | 0.724841 | + | 1.25546i | 0.959040 | + | 0.283272i | \(0.0914200\pi\) |
−0.234199 | + | 0.972189i | \(0.575247\pi\) | |||||||
\(32\) | −1.58090 | − | 2.73821i | −0.279467 | − | 0.484051i | ||||
\(33\) | 0.745201 | − | 1.29073i | 0.129723 | − | 0.224686i | ||||
\(34\) | 7.22231 | 1.23862 | ||||||||
\(35\) | 3.83977 | − | 9.25795i | 0.649040 | − | 1.56488i | ||||
\(36\) | −0.579274 | −0.0965456 | ||||||||
\(37\) | −5.65171 | + | 9.78904i | −0.929135 | + | 1.60931i | −0.144362 | + | 0.989525i | \(0.546113\pi\) |
−0.784773 | + | 0.619784i | \(0.787220\pi\) | |||||||
\(38\) | 3.52001 | + | 6.09683i | 0.571021 | + | 0.989037i | ||||
\(39\) | 0.230356 | + | 0.398988i | 0.0368864 | + | 0.0638892i | ||||
\(40\) | −5.82312 | + | 10.0859i | −0.920717 | + | 1.59473i | ||||
\(41\) | 5.23193 | 0.817090 | 0.408545 | − | 0.912738i | \(-0.366036\pi\) | ||||
0.408545 | + | 0.912738i | \(0.366036\pi\) | |||||||
\(42\) | 3.12679 | − | 0.410183i | 0.482475 | − | 0.0632926i | ||||
\(43\) | 4.64064 | 0.707691 | 0.353845 | − | 0.935304i | \(-0.384874\pi\) | ||||
0.353845 | + | 0.935304i | \(0.384874\pi\) | |||||||
\(44\) | −0.431675 | + | 0.747683i | −0.0650775 | + | 0.112718i | ||||
\(45\) | 1.89410 | + | 3.28068i | 0.282356 | + | 0.489055i | ||||
\(46\) | 0.595971 | + | 1.03225i | 0.0878711 | + | 0.152197i | ||||
\(47\) | 2.30279 | − | 3.98854i | 0.335896 | − | 0.581789i | −0.647760 | − | 0.761844i | \(-0.724294\pi\) |
0.983657 | + | 0.180055i | \(0.0576276\pi\) | |||||||
\(48\) | −2.50589 | −0.361695 | ||||||||
\(49\) | 6.76315 | − | 1.80550i | 0.966164 | − | 0.257928i | ||||
\(50\) | 11.1452 | 1.57618 | ||||||||
\(51\) | −3.02964 | + | 5.24749i | −0.424234 | + | 0.734796i | ||||
\(52\) | −0.133439 | − | 0.231123i | −0.0185047 | − | 0.0320510i | ||||
\(53\) | 2.66141 | + | 4.60970i | 0.365573 | + | 0.633191i | 0.988868 | − | 0.148796i | \(-0.0475397\pi\) |
−0.623295 | + | 0.781987i | \(0.714206\pi\) | |||||||
\(54\) | −0.595971 | + | 1.03225i | −0.0811014 | + | 0.140472i | ||||
\(55\) | 5.64594 | 0.761299 | ||||||||
\(56\) | −8.06485 | + | 1.05797i | −1.07771 | + | 0.141378i | ||||
\(57\) | −5.90634 | −0.782314 | ||||||||
\(58\) | −1.25650 | + | 2.17632i | −0.164987 | + | 0.285765i | ||||
\(59\) | −6.14546 | − | 10.6443i | −0.800071 | − | 1.38576i | −0.919569 | − | 0.392929i | \(-0.871462\pi\) |
0.119498 | − | 0.992834i | \(-0.461872\pi\) | |||||||
\(60\) | −1.09720 | − | 1.90041i | −0.141648 | − | 0.245342i | ||||
\(61\) | −0.205912 | + | 0.356650i | −0.0263643 | + | 0.0456644i | −0.878907 | − | 0.476994i | \(-0.841726\pi\) |
0.852542 | + | 0.522658i | \(0.175060\pi\) | |||||||
\(62\) | −9.62074 | −1.22184 | ||||||||
\(63\) | −1.01361 | + | 2.44389i | −0.127703 | + | 0.307901i | ||||
\(64\) | 8.78048 | 1.09756 | ||||||||
\(65\) | −0.872634 | + | 1.51145i | −0.108237 | + | 0.187472i | ||||
\(66\) | 0.888236 | + | 1.53847i | 0.109334 | + | 0.189373i | ||||
\(67\) | −7.56042 | − | 13.0950i | −0.923652 | − | 1.59981i | −0.793715 | − | 0.608290i | \(-0.791856\pi\) |
−0.129937 | − | 0.991522i | \(-0.541478\pi\) | |||||||
\(68\) | 1.75499 | − | 3.03973i | 0.212824 | − | 0.368622i | ||||
\(69\) | −1.00000 | −0.120386 | ||||||||
\(70\) | 7.26814 | + | 9.48108i | 0.868709 | + | 1.13321i | ||||
\(71\) | 6.85490 | 0.813527 | 0.406764 | − | 0.913533i | \(-0.366657\pi\) | ||||
0.406764 | + | 0.913533i | \(0.366657\pi\) | |||||||
\(72\) | 1.53717 | − | 2.66246i | 0.181158 | − | 0.313774i | ||||
\(73\) | 6.07119 | + | 10.5156i | 0.710579 | + | 1.23076i | 0.964640 | + | 0.263571i | \(0.0849003\pi\) |
−0.254061 | + | 0.967188i | \(0.581766\pi\) | |||||||
\(74\) | −6.73651 | − | 11.6680i | −0.783103 | − | 1.35637i | ||||
\(75\) | −4.67524 | + | 8.09776i | −0.539851 | + | 0.935049i | ||||
\(76\) | 3.42139 | 0.392460 | ||||||||
\(77\) | 2.39904 | + | 3.12948i | 0.273396 | + | 0.356638i | ||||
\(78\) | −0.549141 | −0.0621780 | ||||||||
\(79\) | −3.23685 | + | 5.60638i | −0.364174 | + | 0.630767i | −0.988643 | − | 0.150282i | \(-0.951982\pi\) |
0.624470 | + | 0.781049i | \(0.285315\pi\) | |||||||
\(80\) | −4.74642 | − | 8.22104i | −0.530666 | − | 0.919140i | ||||
\(81\) | −0.500000 | − | 0.866025i | −0.0555556 | − | 0.0962250i | ||||
\(82\) | −3.11808 | + | 5.40067i | −0.344334 | + | 0.596404i | ||||
\(83\) | −4.68019 | −0.513717 | −0.256859 | − | 0.966449i | \(-0.582687\pi\) | ||||
−0.256859 | + | 0.966449i | \(0.582687\pi\) | |||||||
\(84\) | 0.587159 | − | 1.41568i | 0.0640643 | − | 0.154463i | ||||
\(85\) | −22.9538 | −2.48969 | ||||||||
\(86\) | −2.76569 | + | 4.79031i | −0.298232 | + | 0.516552i | ||||
\(87\) | −1.05416 | − | 1.82586i | −0.113018 | − | 0.195753i | ||||
\(88\) | −2.29100 | − | 3.96814i | −0.244222 | − | 0.423005i | ||||
\(89\) | −8.14048 | + | 14.0997i | −0.862889 | + | 1.49457i | 0.00623959 | + | 0.999981i | \(0.498014\pi\) |
−0.869128 | + | 0.494587i | \(0.835319\pi\) | |||||||
\(90\) | −4.51532 | −0.475957 | ||||||||
\(91\) | −1.20857 | + | 0.158545i | −0.126693 | + | 0.0166200i | ||||
\(92\) | 0.579274 | 0.0603935 | ||||||||
\(93\) | 4.03574 | − | 6.99011i | 0.418487 | − | 0.724841i | ||||
\(94\) | 2.74479 | + | 4.75412i | 0.283103 | + | 0.490350i | ||||
\(95\) | −11.1872 | − | 19.3768i | −1.14778 | − | 1.98802i | ||||
\(96\) | −1.58090 | + | 2.73821i | −0.161350 | + | 0.279467i | ||||
\(97\) | −6.78248 | −0.688656 | −0.344328 | − | 0.938849i | \(-0.611893\pi\) | ||||
−0.344328 | + | 0.938849i | \(0.611893\pi\) | |||||||
\(98\) | −2.16691 | + | 8.05730i | −0.218891 | + | 0.813910i | ||||
\(99\) | −1.49040 | −0.149791 | ||||||||
\(100\) | 2.70825 | − | 4.69082i | 0.270825 | − | 0.469082i | ||||
\(101\) | 1.21872 | + | 2.11089i | 0.121267 | + | 0.210041i | 0.920268 | − | 0.391289i | \(-0.127971\pi\) |
−0.799000 | + | 0.601330i | \(0.794638\pi\) | |||||||
\(102\) | −3.61116 | − | 6.25470i | −0.357558 | − | 0.619308i | ||||
\(103\) | −2.90373 | + | 5.02940i | −0.286113 | + | 0.495562i | −0.972878 | − | 0.231317i | \(-0.925697\pi\) |
0.686766 | + | 0.726879i | \(0.259030\pi\) | |||||||
\(104\) | 1.41639 | 0.138888 | ||||||||
\(105\) | −9.93750 | + | 1.30364i | −0.969801 | + | 0.127222i | ||||
\(106\) | −6.34450 | −0.616232 | ||||||||
\(107\) | −6.12909 | + | 10.6159i | −0.592521 | + | 1.02628i | 0.401371 | + | 0.915916i | \(0.368534\pi\) |
−0.993892 | + | 0.110361i | \(0.964799\pi\) | |||||||
\(108\) | 0.289637 | + | 0.501666i | 0.0278703 | + | 0.0482728i | ||||
\(109\) | 4.49419 | + | 7.78417i | 0.430465 | + | 0.745588i | 0.996913 | − | 0.0785096i | \(-0.0250161\pi\) |
−0.566448 | + | 0.824097i | \(0.691683\pi\) | |||||||
\(110\) | −3.36482 | + | 5.82804i | −0.320823 | + | 0.555682i | ||||
\(111\) | 11.3034 | 1.07287 | ||||||||
\(112\) | 2.54001 | − | 6.12413i | 0.240008 | − | 0.578675i | ||||
\(113\) | 6.08150 | 0.572099 | 0.286050 | − | 0.958215i | \(-0.407658\pi\) | ||||
0.286050 | + | 0.958215i | \(0.407658\pi\) | |||||||
\(114\) | 3.52001 | − | 6.09683i | 0.329679 | − | 0.571021i | ||||
\(115\) | −1.89410 | − | 3.28068i | −0.176626 | − | 0.305925i | ||||
\(116\) | 0.610649 | + | 1.05768i | 0.0566973 | + | 0.0982027i | ||||
\(117\) | 0.230356 | − | 0.398988i | 0.0212964 | − | 0.0368864i | ||||
\(118\) | 14.6501 | 1.34865 | ||||||||
\(119\) | −9.75340 | − | 12.7230i | −0.894093 | − | 1.16632i | ||||
\(120\) | 11.6462 | 1.06315 | ||||||||
\(121\) | 4.38935 | − | 7.60258i | 0.399032 | − | 0.691144i | ||||
\(122\) | −0.245435 | − | 0.425106i | −0.0222207 | − | 0.0384873i | ||||
\(123\) | −2.61596 | − | 4.53098i | −0.235874 | − | 0.408545i | ||||
\(124\) | −2.33780 | + | 4.04919i | −0.209941 | + | 0.363628i | ||||
\(125\) | −16.4805 | −1.47406 | ||||||||
\(126\) | −1.91863 | − | 2.50279i | −0.170925 | − | 0.222966i | ||||
\(127\) | 2.84429 | 0.252390 | 0.126195 | − | 0.992005i | \(-0.459724\pi\) | ||||
0.126195 | + | 0.992005i | \(0.459724\pi\) | |||||||
\(128\) | −2.07110 | + | 3.58726i | −0.183061 | + | 0.317072i | ||||
\(129\) | −2.32032 | − | 4.01891i | −0.204293 | − | 0.353845i | ||||
\(130\) | −1.04013 | − | 1.80156i | −0.0912254 | − | 0.158007i | ||||
\(131\) | −4.96443 | + | 8.59865i | −0.433745 | + | 0.751268i | −0.997192 | − | 0.0748841i | \(-0.976141\pi\) |
0.563448 | + | 0.826152i | \(0.309475\pi\) | |||||||
\(132\) | 0.863350 | 0.0751450 | ||||||||
\(133\) | 5.98674 | − | 14.4344i | 0.519116 | − | 1.25162i | ||||
\(134\) | 18.0232 | 1.55696 | ||||||||
\(135\) | 1.89410 | − | 3.28068i | 0.163018 | − | 0.282356i | ||||
\(136\) | 9.31416 | + | 16.1326i | 0.798682 | + | 1.38336i | ||||
\(137\) | 6.02046 | + | 10.4278i | 0.514363 | + | 0.890903i | 0.999861 | + | 0.0166652i | \(0.00530494\pi\) |
−0.485498 | + | 0.874238i | \(0.661362\pi\) | |||||||
\(138\) | 0.595971 | − | 1.03225i | 0.0507324 | − | 0.0878711i | ||||
\(139\) | −1.51537 | −0.128532 | −0.0642659 | − | 0.997933i | \(-0.520471\pi\) | ||||
−0.0642659 | + | 0.997933i | \(0.520471\pi\) | |||||||
\(140\) | 5.75654 | − | 0.755162i | 0.486516 | − | 0.0638228i | ||||
\(141\) | −4.60558 | −0.387859 | ||||||||
\(142\) | −4.08532 | + | 7.07599i | −0.342833 | + | 0.593804i | ||||
\(143\) | −0.343322 | − | 0.594652i | −0.0287101 | − | 0.0497273i | ||||
\(144\) | 1.25295 | + | 2.17017i | 0.104412 | + | 0.180847i | ||||
\(145\) | 3.99338 | − | 6.91674i | 0.331633 | − | 0.574404i | ||||
\(146\) | −14.4730 | −1.19780 | ||||||||
\(147\) | −4.94518 | − | 4.95431i | −0.407872 | − | 0.408625i | ||||
\(148\) | −6.54777 | −0.538223 | ||||||||
\(149\) | −9.12604 | + | 15.8068i | −0.747635 | + | 1.29494i | 0.201319 | + | 0.979526i | \(0.435477\pi\) |
−0.948954 | + | 0.315415i | \(0.897856\pi\) | |||||||
\(150\) | −5.57262 | − | 9.65206i | −0.455003 | − | 0.788088i | ||||
\(151\) | 1.46583 | + | 2.53889i | 0.119287 | + | 0.206612i | 0.919485 | − | 0.393124i | \(-0.128606\pi\) |
−0.800198 | + | 0.599736i | \(0.795272\pi\) | |||||||
\(152\) | −9.07906 | + | 15.7254i | −0.736409 | + | 1.27550i | ||||
\(153\) | 6.05928 | 0.489864 | ||||||||
\(154\) | −4.66018 | + | 0.611338i | −0.375528 | + | 0.0492630i | ||||
\(155\) | 30.5764 | 2.45596 | ||||||||
\(156\) | −0.133439 | + | 0.231123i | −0.0106837 | + | 0.0185047i | ||||
\(157\) | −8.39877 | − | 14.5471i | −0.670295 | − | 1.16098i | −0.977820 | − | 0.209445i | \(-0.932834\pi\) |
0.307526 | − | 0.951540i | \(-0.400499\pi\) | |||||||
\(158\) | −3.85813 | − | 6.68248i | −0.306937 | − | 0.531630i | ||||
\(159\) | 2.66141 | − | 4.60970i | 0.211064 | − | 0.365573i | ||||
\(160\) | −11.9776 | −0.946911 | ||||||||
\(161\) | 1.01361 | − | 2.44389i | 0.0798838 | − | 0.192605i | ||||
\(162\) | 1.19194 | 0.0936478 | ||||||||
\(163\) | 1.82489 | − | 3.16081i | 0.142937 | − | 0.247574i | −0.785665 | − | 0.618653i | \(-0.787679\pi\) |
0.928601 | + | 0.371079i | \(0.121012\pi\) | |||||||
\(164\) | 1.51536 | + | 2.62468i | 0.118330 | + | 0.204953i | ||||
\(165\) | −2.82297 | − | 4.88953i | −0.219768 | − | 0.380649i | ||||
\(166\) | 2.78926 | − | 4.83113i | 0.216488 | − | 0.374969i | ||||
\(167\) | −15.2399 | −1.17930 | −0.589649 | − | 0.807660i | \(-0.700734\pi\) | ||||
−0.589649 | + | 0.807660i | \(0.700734\pi\) | |||||||
\(168\) | 4.94866 | + | 6.45538i | 0.381797 | + | 0.498044i | ||||
\(169\) | −12.7877 | −0.983673 | ||||||||
\(170\) | 13.6798 | − | 23.6941i | 1.04919 | − | 1.81725i | ||||
\(171\) | 2.95317 | + | 5.11504i | 0.225835 | + | 0.391157i | ||||
\(172\) | 1.34410 | + | 2.32805i | 0.102487 | + | 0.177512i | ||||
\(173\) | −1.09316 | + | 1.89341i | −0.0831113 | + | 0.143953i | −0.904585 | − | 0.426294i | \(-0.859819\pi\) |
0.821474 | + | 0.570247i | \(0.193152\pi\) | |||||||
\(174\) | 2.51300 | 0.190510 | ||||||||
\(175\) | −15.0511 | − | 19.6338i | −1.13776 | − | 1.48417i | ||||
\(176\) | 3.73479 | 0.281520 | ||||||||
\(177\) | −6.14546 | + | 10.6443i | −0.461921 | + | 0.800071i | ||||
\(178\) | −9.70298 | − | 16.8060i | −0.727269 | − | 1.25967i | ||||
\(179\) | 0.930522 | + | 1.61171i | 0.0695505 | + | 0.120465i | 0.898704 | − | 0.438557i | \(-0.144510\pi\) |
−0.829153 | + | 0.559022i | \(0.811177\pi\) | |||||||
\(180\) | −1.09720 | + | 1.90041i | −0.0817807 | + | 0.141648i | ||||
\(181\) | −14.4867 | −1.07679 | −0.538394 | − | 0.842693i | \(-0.680969\pi\) | ||||
−0.538394 | + | 0.842693i | \(0.680969\pi\) | |||||||
\(182\) | 0.556616 | − | 1.34204i | 0.0412592 | − | 0.0994786i | ||||
\(183\) | 0.411824 | 0.0304429 | ||||||||
\(184\) | −1.53717 | + | 2.66246i | −0.113322 | + | 0.196279i | ||||
\(185\) | 21.4098 | + | 37.0829i | 1.57408 | + | 2.72639i | ||||
\(186\) | 4.81037 | + | 8.33181i | 0.352714 | + | 0.610918i | ||||
\(187\) | 4.51538 | − | 7.82087i | 0.330197 | − | 0.571918i | ||||
\(188\) | 2.66789 | 0.194576 | ||||||||
\(189\) | 2.62328 | − | 0.344130i | 0.190815 | − | 0.0250318i | ||||
\(190\) | 26.6690 | 1.93477 | ||||||||
\(191\) | −9.92673 | + | 17.1936i | −0.718273 | + | 1.24409i | 0.243411 | + | 0.969923i | \(0.421734\pi\) |
−0.961684 | + | 0.274162i | \(0.911600\pi\) | |||||||
\(192\) | −4.39024 | − | 7.60412i | −0.316838 | − | 0.548780i | ||||
\(193\) | −0.779443 | − | 1.35003i | −0.0561055 | − | 0.0971776i | 0.836609 | − | 0.547801i | \(-0.184535\pi\) |
−0.892714 | + | 0.450624i | \(0.851202\pi\) | |||||||
\(194\) | 4.04216 | − | 7.00123i | 0.290210 | − | 0.502659i | ||||
\(195\) | 1.74527 | 0.124981 | ||||||||
\(196\) | 2.86461 | + | 2.86990i | 0.204615 | + | 0.204993i | ||||
\(197\) | −2.48101 | −0.176764 | −0.0883822 | − | 0.996087i | \(-0.528170\pi\) | ||||
−0.0883822 | + | 0.996087i | \(0.528170\pi\) | |||||||
\(198\) | 0.888236 | − | 1.53847i | 0.0631242 | − | 0.109334i | ||||
\(199\) | 2.64623 | + | 4.58340i | 0.187586 | + | 0.324909i | 0.944445 | − | 0.328670i | \(-0.106600\pi\) |
−0.756859 | + | 0.653578i | \(0.773267\pi\) | |||||||
\(200\) | 14.3733 | + | 24.8953i | 1.01635 | + | 1.76036i | ||||
\(201\) | −7.56042 | + | 13.0950i | −0.533271 | + | 0.923652i | ||||
\(202\) | −2.90529 | −0.204415 | ||||||||
\(203\) | 5.53072 | − | 0.725538i | 0.388180 | − | 0.0509228i | ||||
\(204\) | −3.50998 | −0.245748 | ||||||||
\(205\) | 9.90980 | − | 17.1643i | 0.692131 | − | 1.19881i | ||||
\(206\) | −3.46108 | − | 5.99476i | −0.241145 | − | 0.417675i | ||||
\(207\) | 0.500000 | + | 0.866025i | 0.0347524 | + | 0.0601929i | ||||
\(208\) | −0.577247 | + | 0.999821i | −0.0400249 | + | 0.0693251i | ||||
\(209\) | 8.80282 | 0.608904 | ||||||||
\(210\) | 4.57678 | − | 11.0349i | 0.315828 | − | 0.761483i | ||||
\(211\) | 27.0118 | 1.85957 | 0.929784 | − | 0.368105i | \(-0.119993\pi\) | ||||
0.929784 | + | 0.368105i | \(0.119993\pi\) | |||||||
\(212\) | −1.54169 | + | 2.67028i | −0.105883 | + | 0.183395i | ||||
\(213\) | −3.42745 | − | 5.93652i | −0.234845 | − | 0.406764i | ||||
\(214\) | −7.30551 | − | 12.6535i | −0.499395 | − | 0.864977i | ||||
\(215\) | 8.78984 | − | 15.2245i | 0.599462 | − | 1.03830i | ||||
\(216\) | −3.07435 | −0.209183 | ||||||||
\(217\) | 12.9924 | + | 16.9482i | 0.881980 | + | 1.15052i | ||||
\(218\) | −10.7136 | −0.725619 | ||||||||
\(219\) | 6.07119 | − | 10.5156i | 0.410253 | − | 0.710579i | ||||
\(220\) | 1.63527 | + | 2.83238i | 0.110250 | + | 0.190959i | ||||
\(221\) | 1.39579 | + | 2.41758i | 0.0938909 | + | 0.162624i | ||||
\(222\) | −6.73651 | + | 11.6680i | −0.452125 | + | 0.783103i | ||||
\(223\) | −4.93735 | −0.330630 | −0.165315 | − | 0.986241i | \(-0.552864\pi\) | ||||
−0.165315 | + | 0.986241i | \(0.552864\pi\) | |||||||
\(224\) | −5.08945 | − | 6.63904i | −0.340053 | − | 0.443589i | ||||
\(225\) | 9.35049 | 0.623366 | ||||||||
\(226\) | −3.62440 | + | 6.27764i | −0.241091 | + | 0.417582i | ||||
\(227\) | −5.72866 | − | 9.92233i | −0.380224 | − | 0.658568i | 0.610870 | − | 0.791731i | \(-0.290820\pi\) |
−0.991094 | + | 0.133163i | \(0.957487\pi\) | |||||||
\(228\) | −1.71069 | − | 2.96301i | −0.113293 | − | 0.196230i | ||||
\(229\) | 4.85646 | − | 8.41164i | 0.320924 | − | 0.555857i | −0.659755 | − | 0.751481i | \(-0.729340\pi\) |
0.980679 | + | 0.195624i | \(0.0626732\pi\) | |||||||
\(230\) | 4.51532 | 0.297731 | ||||||||
\(231\) | 1.51069 | − | 3.64237i | 0.0993961 | − | 0.239651i | ||||
\(232\) | −6.48172 | −0.425546 | ||||||||
\(233\) | −4.46345 | + | 7.73092i | −0.292410 | + | 0.506470i | −0.974379 | − | 0.224912i | \(-0.927791\pi\) |
0.681969 | + | 0.731381i | \(0.261124\pi\) | |||||||
\(234\) | 0.274571 | + | 0.475570i | 0.0179492 | + | 0.0310890i | ||||
\(235\) | −8.72343 | − | 15.1094i | −0.569054 | − | 0.985630i | ||||
\(236\) | 3.55991 | − | 6.16594i | 0.231730 | − | 0.401368i | ||||
\(237\) | 6.47369 | 0.420511 | ||||||||
\(238\) | 18.9461 | − | 2.48541i | 1.22809 | − | 0.161105i | ||||
\(239\) | 14.7250 | 0.952480 | 0.476240 | − | 0.879315i | \(-0.341999\pi\) | ||||
0.476240 | + | 0.879315i | \(0.341999\pi\) | |||||||
\(240\) | −4.74642 | + | 8.22104i | −0.306380 | + | 0.530666i | ||||
\(241\) | 12.2335 | + | 21.1890i | 0.788027 | + | 1.36490i | 0.927174 | + | 0.374631i | \(0.122231\pi\) |
−0.139147 | + | 0.990272i | \(0.544436\pi\) | |||||||
\(242\) | 5.23185 | + | 9.06184i | 0.336316 | + | 0.582517i | ||||
\(243\) | −0.500000 | + | 0.866025i | −0.0320750 | + | 0.0555556i | ||||
\(244\) | −0.238559 | −0.0152722 | ||||||||
\(245\) | 6.88684 | − | 25.6075i | 0.439984 | − | 1.63600i | ||||
\(246\) | 6.23615 | 0.397603 | ||||||||
\(247\) | −1.36056 | + | 2.35656i | −0.0865703 | + | 0.149944i | ||||
\(248\) | −12.4073 | − | 21.4900i | −0.787862 | − | 1.36462i | ||||
\(249\) | 2.34009 | + | 4.05316i | 0.148297 | + | 0.256859i | ||||
\(250\) | 9.82193 | − | 17.0121i | 0.621193 | − | 1.07594i | ||||
\(251\) | −2.61433 | −0.165015 | −0.0825076 | − | 0.996590i | \(-0.526293\pi\) | ||||
−0.0825076 | + | 0.996590i | \(0.526293\pi\) | |||||||
\(252\) | −1.51959 | + | 0.199346i | −0.0957255 | + | 0.0125576i | ||||
\(253\) | 1.49040 | 0.0937007 | ||||||||
\(254\) | −1.69511 | + | 2.93602i | −0.106361 | + | 0.184222i | ||||
\(255\) | 11.4769 | + | 19.8786i | 0.718711 | + | 1.24484i | ||||
\(256\) | 6.31185 | + | 10.9324i | 0.394490 | + | 0.683277i | ||||
\(257\) | 0.509978 | − | 0.883308i | 0.0318116 | − | 0.0550993i | −0.849681 | − | 0.527297i | \(-0.823206\pi\) |
0.881493 | + | 0.472197i | \(0.156539\pi\) | |||||||
\(258\) | 5.53137 | 0.344368 | ||||||||
\(259\) | −11.4573 | + | 27.6243i | −0.711921 | + | 1.71649i | ||||
\(260\) | −1.01099 | −0.0626988 | ||||||||
\(261\) | −1.05416 | + | 1.82586i | −0.0652510 | + | 0.113018i | ||||
\(262\) | −5.91732 | − | 10.2491i | −0.365573 | − | 0.633191i | ||||
\(263\) | −4.46901 | − | 7.74054i | −0.275571 | − | 0.477302i | 0.694708 | − | 0.719292i | \(-0.255533\pi\) |
−0.970279 | + | 0.241989i | \(0.922200\pi\) | |||||||
\(264\) | −2.29100 | + | 3.96814i | −0.141002 | + | 0.244222i | ||||
\(265\) | 20.1639 | 1.23866 | ||||||||
\(266\) | 11.3321 | + | 14.7823i | 0.694813 | + | 0.906363i | ||||
\(267\) | 16.2810 | 0.996378 | ||||||||
\(268\) | 4.37955 | − | 7.58561i | 0.267524 | − | 0.463365i | ||||
\(269\) | 6.84056 | + | 11.8482i | 0.417076 | + | 0.722397i | 0.995644 | − | 0.0932372i | \(-0.0297215\pi\) |
−0.578568 | + | 0.815634i | \(0.696388\pi\) | |||||||
\(270\) | 2.25766 | + | 3.91038i | 0.137397 | + | 0.237978i | ||||
\(271\) | 1.98691 | − | 3.44144i | 0.120696 | − | 0.209052i | −0.799346 | − | 0.600871i | \(-0.794821\pi\) |
0.920043 | + | 0.391819i | \(0.128154\pi\) | |||||||
\(272\) | −15.1839 | −0.920660 | ||||||||
\(273\) | 0.741590 | + | 0.967382i | 0.0448831 | + | 0.0585486i | ||||
\(274\) | −14.3521 | −0.867042 | ||||||||
\(275\) | 6.96799 | − | 12.0689i | 0.420186 | − | 0.727783i | ||||
\(276\) | −0.289637 | − | 0.501666i | −0.0174341 | − | 0.0301967i | ||||
\(277\) | 5.00728 | + | 8.67286i | 0.300858 | + | 0.521101i | 0.976331 | − | 0.216284i | \(-0.0693936\pi\) |
−0.675472 | + | 0.737385i | \(0.736060\pi\) | |||||||
\(278\) | 0.903115 | − | 1.56424i | 0.0541652 | − | 0.0938169i | ||||
\(279\) | −8.07148 | −0.483227 | ||||||||
\(280\) | −11.8048 | + | 28.4621i | −0.705471 | + | 1.70094i | ||||
\(281\) | −21.3379 | −1.27291 | −0.636456 | − | 0.771313i | \(-0.719600\pi\) | ||||
−0.636456 | + | 0.771313i | \(0.719600\pi\) | |||||||
\(282\) | 2.74479 | − | 4.75412i | 0.163450 | − | 0.283103i | ||||
\(283\) | −7.24152 | − | 12.5427i | −0.430463 | − | 0.745585i | 0.566450 | − | 0.824096i | \(-0.308317\pi\) |
−0.996913 | + | 0.0785118i | \(0.974983\pi\) | |||||||
\(284\) | 1.98543 | + | 3.43887i | 0.117814 | + | 0.204059i | ||||
\(285\) | −11.1872 | + | 19.3768i | −0.662673 | + | 1.14778i | ||||
\(286\) | 0.818441 | 0.0483954 | ||||||||
\(287\) | 13.7248 | − | 1.80046i | 0.810149 | − | 0.106278i | ||||
\(288\) | 3.16181 | 0.186311 | ||||||||
\(289\) | −9.85743 | + | 17.0736i | −0.579849 | + | 1.00433i | ||||
\(290\) | 4.75988 | + | 8.24436i | 0.279510 | + | 0.484125i | ||||
\(291\) | 3.39124 | + | 5.87380i | 0.198798 | + | 0.344328i | ||||
\(292\) | −3.51688 | + | 6.09142i | −0.205810 | + | 0.356473i | ||||
\(293\) | 33.1986 | 1.93948 | 0.969741 | − | 0.244134i | \(-0.0785038\pi\) | ||||
0.969741 | + | 0.244134i | \(0.0785038\pi\) | |||||||
\(294\) | 8.06128 | − | 2.15205i | 0.470144 | − | 0.125510i | ||||
\(295\) | −46.5605 | −2.71086 | ||||||||
\(296\) | 17.3753 | − | 30.0949i | 1.00992 | − | 1.74923i | ||||
\(297\) | 0.745201 | + | 1.29073i | 0.0432409 | + | 0.0748955i | ||||
\(298\) | −10.8777 | − | 18.8408i | −0.630129 | − | 1.09142i | ||||
\(299\) | −0.230356 | + | 0.398988i | −0.0133218 | + | 0.0230741i | ||||
\(300\) | −5.41649 | −0.312721 | ||||||||
\(301\) | 12.1737 | − | 1.59698i | 0.701679 | − | 0.0920486i | ||||
\(302\) | −3.49436 | −0.201078 | ||||||||
\(303\) | 1.21872 | − | 2.11089i | 0.0700137 | − | 0.121267i | ||||
\(304\) | −7.40033 | − | 12.8178i | −0.424438 | − | 0.735148i | ||||
\(305\) | 0.780037 | + | 1.35106i | 0.0446648 | + | 0.0773616i | ||||
\(306\) | −3.61116 | + | 6.25470i | −0.206436 | + | 0.357558i | ||||
\(307\) | 31.4823 | 1.79679 | 0.898396 | − | 0.439187i | \(-0.144733\pi\) | ||||
0.898396 | + | 0.439187i | \(0.144733\pi\) | |||||||
\(308\) | −0.875103 | + | 2.10993i | −0.0498636 | + | 0.120225i | ||||
\(309\) | 5.80746 | 0.330375 | ||||||||
\(310\) | −18.2227 | + | 31.5626i | −1.03498 | + | 1.79263i | ||||
\(311\) | 9.10379 | + | 15.7682i | 0.516229 | + | 0.894135i | 0.999822 | + | 0.0188419i | \(0.00599793\pi\) |
−0.483594 | + | 0.875293i | \(0.660669\pi\) | |||||||
\(312\) | −0.708193 | − | 1.22663i | −0.0400935 | − | 0.0694440i | ||||
\(313\) | −10.7276 | + | 18.5807i | −0.606359 | + | 1.05025i | 0.385476 | + | 0.922718i | \(0.374037\pi\) |
−0.991835 | + | 0.127527i | \(0.959296\pi\) | |||||||
\(314\) | 20.0217 | 1.12989 | ||||||||
\(315\) | 6.09773 | + | 7.95431i | 0.343568 | + | 0.448175i | ||||
\(316\) | −3.75004 | −0.210956 | ||||||||
\(317\) | 1.40432 | − | 2.43236i | 0.0788747 | − | 0.136615i | −0.823890 | − | 0.566750i | \(-0.808201\pi\) |
0.902765 | + | 0.430135i | \(0.141534\pi\) | |||||||
\(318\) | 3.17225 | + | 5.49450i | 0.177891 | + | 0.308116i | ||||
\(319\) | 1.57113 | + | 2.72127i | 0.0879662 | + | 0.152362i | ||||
\(320\) | 16.6311 | − | 28.8060i | 0.929708 | − | 1.61030i | ||||
\(321\) | 12.2582 | 0.684184 | ||||||||
\(322\) | 1.91863 | + | 2.50279i | 0.106921 | + | 0.139475i | ||||
\(323\) | −35.7882 | −1.99131 | ||||||||
\(324\) | 0.289637 | − | 0.501666i | 0.0160909 | − | 0.0278703i | ||||
\(325\) | 2.15394 | + | 3.73073i | 0.119479 | + | 0.206944i | ||||
\(326\) | 2.17517 | + | 3.76750i | 0.120471 | + | 0.208663i | ||||
\(327\) | 4.49419 | − | 7.78417i | 0.248529 | − | 0.430465i | ||||
\(328\) | −16.0848 | −0.888132 | ||||||||
\(329\) | 4.66827 | − | 11.2555i | 0.257370 | − | 0.620536i | ||||
\(330\) | 6.72964 | 0.370454 | ||||||||
\(331\) | 13.5491 | − | 23.4678i | 0.744727 | − | 1.28991i | −0.205595 | − | 0.978637i | \(-0.565913\pi\) |
0.950322 | − | 0.311268i | \(-0.100754\pi\) | |||||||
\(332\) | −1.35556 | − | 2.34789i | −0.0743957 | − | 0.128857i | ||||
\(333\) | −5.65171 | − | 9.78904i | −0.309712 | − | 0.536436i | ||||
\(334\) | 9.08253 | − | 15.7314i | 0.496974 | − | 0.860784i | ||||
\(335\) | −57.2808 | −3.12959 | ||||||||
\(336\) | −6.57365 | + | 0.862354i | −0.358622 | + | 0.0470452i | ||||
\(337\) | 8.21670 | 0.447592 | 0.223796 | − | 0.974636i | \(-0.428155\pi\) | ||||
0.223796 | + | 0.974636i | \(0.428155\pi\) | |||||||
\(338\) | 7.62113 | − | 13.2002i | 0.414535 | − | 0.717995i | ||||
\(339\) | −3.04075 | − | 5.26673i | −0.165151 | − | 0.286050i | ||||
\(340\) | −6.64826 | − | 11.5151i | −0.360553 | − | 0.624496i | ||||
\(341\) | −6.01488 | + | 10.4181i | −0.325724 | + | 0.564170i | ||||
\(342\) | −7.04002 | −0.380680 | ||||||||
\(343\) | 17.1203 | − | 7.06372i | 0.924408 | − | 0.381405i | ||||
\(344\) | −14.2669 | −0.769221 | ||||||||
\(345\) | −1.89410 | + | 3.28068i | −0.101975 | + | 0.176626i | ||||
\(346\) | −1.30298 | − | 2.25683i | −0.0700487 | − | 0.121328i | ||||
\(347\) | −1.30625 | − | 2.26249i | −0.0701230 | − | 0.121457i | 0.828832 | − | 0.559497i | \(-0.189006\pi\) |
−0.898955 | + | 0.438041i | \(0.855673\pi\) | |||||||
\(348\) | 0.610649 | − | 1.05768i | 0.0327342 | − | 0.0566973i | ||||
\(349\) | −16.3975 | −0.877740 | −0.438870 | − | 0.898551i | \(-0.644621\pi\) | ||||
−0.438870 | + | 0.898551i | \(0.644621\pi\) | |||||||
\(350\) | 29.2370 | − | 3.83541i | 1.56279 | − | 0.205011i | ||||
\(351\) | −0.460711 | −0.0245910 | ||||||||
\(352\) | 2.35618 | − | 4.08103i | 0.125585 | − | 0.217520i | ||||
\(353\) | −14.5072 | − | 25.1273i | −0.772142 | − | 1.33739i | −0.936387 | − | 0.350969i | \(-0.885852\pi\) |
0.164245 | − | 0.986420i | \(-0.447481\pi\) | |||||||
\(354\) | −7.32503 | − | 12.6873i | −0.389321 | − | 0.674324i | ||||
\(355\) | 12.9839 | − | 22.4887i | 0.689113 | − | 1.19358i | ||||
\(356\) | −9.43113 | −0.499849 | ||||||||
\(357\) | −6.14176 | + | 14.8082i | −0.325056 | + | 0.783733i | ||||
\(358\) | −2.21826 | −0.117239 | ||||||||
\(359\) | 15.0803 | − | 26.1199i | 0.795910 | − | 1.37856i | −0.126349 | − | 0.991986i | \(-0.540326\pi\) |
0.922259 | − | 0.386571i | \(-0.126341\pi\) | |||||||
\(360\) | −5.82312 | − | 10.0859i | −0.306906 | − | 0.531576i | ||||
\(361\) | −7.94243 | − | 13.7567i | −0.418022 | − | 0.724036i | ||||
\(362\) | 8.63365 | − | 14.9539i | 0.453775 | − | 0.785961i | ||||
\(363\) | −8.77870 | −0.460762 | ||||||||
\(364\) | −0.429584 | − | 0.560379i | −0.0225163 | − | 0.0293719i | ||||
\(365\) | 45.9978 | 2.40764 | ||||||||
\(366\) | −0.245435 | + | 0.425106i | −0.0128291 | + | 0.0222207i | ||||
\(367\) | −4.35916 | − | 7.55029i | −0.227546 | − | 0.394122i | 0.729534 | − | 0.683945i | \(-0.239737\pi\) |
−0.957080 | + | 0.289823i | \(0.906404\pi\) | |||||||
\(368\) | −1.25295 | − | 2.17017i | −0.0653144 | − | 0.113128i | ||||
\(369\) | −2.61596 | + | 4.53098i | −0.136182 | + | 0.235874i | ||||
\(370\) | −51.0385 | −2.65337 | ||||||||
\(371\) | 8.56795 | + | 11.1766i | 0.444826 | + | 0.580262i | ||||
\(372\) | 4.67560 | 0.242419 | ||||||||
\(373\) | 5.45347 | − | 9.44568i | 0.282370 | − | 0.489079i | −0.689598 | − | 0.724192i | \(-0.742213\pi\) |
0.971968 | + | 0.235113i | \(0.0755461\pi\) | |||||||
\(374\) | 5.38207 | + | 9.32202i | 0.278300 | + | 0.482030i | ||||
\(375\) | 8.24027 | + | 14.2726i | 0.425526 | + | 0.737032i | ||||
\(376\) | −7.07956 | + | 12.2622i | −0.365101 | + | 0.632373i | ||||
\(377\) | −0.971330 | −0.0500260 | ||||||||
\(378\) | −1.20817 | + | 2.91297i | −0.0621414 | + | 0.149827i | ||||
\(379\) | −11.5747 | −0.594551 | −0.297275 | − | 0.954792i | \(-0.596078\pi\) | ||||
−0.297275 | + | 0.954792i | \(0.596078\pi\) | |||||||
\(380\) | 6.48046 | − | 11.2245i | 0.332440 | − | 0.575804i | ||||
\(381\) | −1.42214 | − | 2.46322i | −0.0728586 | − | 0.126195i | ||||
\(382\) | −11.8321 | − | 20.4938i | −0.605382 | − | 1.04855i | ||||
\(383\) | −12.1224 | + | 20.9967i | −0.619428 | + | 1.07288i | 0.370163 | + | 0.928967i | \(0.379302\pi\) |
−0.989590 | + | 0.143913i | \(0.954031\pi\) | |||||||
\(384\) | 4.14221 | 0.211381 | ||||||||
\(385\) | 14.8109 | − | 1.94294i | 0.754832 | − | 0.0990214i | ||||
\(386\) | 1.85810 | 0.0945748 | ||||||||
\(387\) | −2.32032 | + | 4.01891i | −0.117948 | + | 0.204293i | ||||
\(388\) | −1.96446 | − | 3.40254i | −0.0997301 | − | 0.172738i | ||||
\(389\) | −2.90240 | − | 5.02710i | −0.147157 | − | 0.254884i | 0.783018 | − | 0.621999i | \(-0.213679\pi\) |
−0.930176 | + | 0.367115i | \(0.880346\pi\) | |||||||
\(390\) | −1.04013 | + | 1.80156i | −0.0526690 | + | 0.0912254i | ||||
\(391\) | −6.05928 | −0.306431 | ||||||||
\(392\) | −20.7923 | + | 5.55072i | −1.05017 | + | 0.280354i | ||||
\(393\) | 9.92887 | 0.500845 | ||||||||
\(394\) | 1.47861 | − | 2.56103i | 0.0744912 | − | 0.129023i | ||||
\(395\) | 12.2618 | + | 21.2381i | 0.616960 | + | 1.06861i | ||||
\(396\) | −0.431675 | − | 0.747683i | −0.0216925 | − | 0.0375725i | ||||
\(397\) | 6.60091 | − | 11.4331i | 0.331290 | − | 0.573812i | −0.651475 | − | 0.758670i | \(-0.725849\pi\) |
0.982765 | + | 0.184859i | \(0.0591827\pi\) | |||||||
\(398\) | −6.30830 | −0.316207 | ||||||||
\(399\) | −15.4940 | + | 2.03255i | −0.775668 | + | 0.101755i | ||||
\(400\) | −23.4313 | −1.17157 | ||||||||
\(401\) | −11.7994 | + | 20.4372i | −0.589236 | + | 1.02059i | 0.405097 | + | 0.914274i | \(0.367238\pi\) |
−0.994333 | + | 0.106313i | \(0.966095\pi\) | |||||||
\(402\) | −9.01158 | − | 15.6085i | −0.449457 | − | 0.778482i | ||||
\(403\) | −1.85931 | − | 3.22042i | −0.0926189 | − | 0.160421i | ||||
\(404\) | −0.705973 | + | 1.22278i | −0.0351235 | + | 0.0608356i | ||||
\(405\) | −3.78820 | −0.188237 | ||||||||
\(406\) | −2.54721 | + | 6.14150i | −0.126416 | + | 0.304797i | ||||
\(407\) | −16.8466 | −0.835056 | ||||||||
\(408\) | 9.31416 | − | 16.1326i | 0.461120 | − | 0.798682i | ||||
\(409\) | −4.32065 | − | 7.48358i | −0.213642 | − | 0.370039i | 0.739209 | − | 0.673476i | \(-0.235199\pi\) |
−0.952852 | + | 0.303436i | \(0.901866\pi\) | |||||||
\(410\) | 11.8119 | + | 20.4588i | 0.583349 | + | 1.01039i | ||||
\(411\) | 6.02046 | − | 10.4278i | 0.296968 | − | 0.514363i | ||||
\(412\) | −3.36411 | −0.165738 | ||||||||
\(413\) | −19.7842 | − | 25.8080i | −0.973519 | − | 1.26993i | ||||
\(414\) | −1.19194 | −0.0585808 | ||||||||
\(415\) | −8.86475 | + | 15.3542i | −0.435154 | + | 0.753708i | ||||
\(416\) | 0.728341 | + | 1.26152i | 0.0357098 | + | 0.0618513i | ||||
\(417\) | 0.757684 | + | 1.31235i | 0.0371039 | + | 0.0642659i | ||||
\(418\) | −5.24622 | + | 9.08673i | −0.256601 | + | 0.444446i | ||||
\(419\) | 30.0603 | 1.46854 | 0.734270 | − | 0.678858i | \(-0.237525\pi\) | ||||
0.734270 | + | 0.678858i | \(0.237525\pi\) | |||||||
\(420\) | −3.53226 | − | 4.60773i | −0.172356 | − | 0.224834i | ||||
\(421\) | −24.7510 | −1.20629 | −0.603144 | − | 0.797632i | \(-0.706085\pi\) | ||||
−0.603144 | + | 0.797632i | \(0.706085\pi\) | |||||||
\(422\) | −16.0982 | + | 27.8830i | −0.783650 | + | 1.35732i | ||||
\(423\) | 2.30279 | + | 3.98854i | 0.111965 | + | 0.193930i | ||||
\(424\) | −8.18210 | − | 14.1718i | −0.397358 | − | 0.688244i | ||||
\(425\) | −28.3286 | + | 49.0666i | −1.37414 | + | 2.38008i | ||||
\(426\) | 8.17065 | 0.395869 | ||||||||
\(427\) | −0.417430 | + | 1.00645i | −0.0202008 | + | 0.0487056i | ||||
\(428\) | −7.10084 | −0.343232 | ||||||||
\(429\) | −0.343322 | + | 0.594652i | −0.0165758 | + | 0.0287101i | ||||
\(430\) | 10.4770 | + | 18.1467i | 0.505245 | + | 0.875110i | ||||
\(431\) | 7.82692 | + | 13.5566i | 0.377010 | + | 0.653000i | 0.990626 | − | 0.136605i | \(-0.0436191\pi\) |
−0.613616 | + | 0.789605i | \(0.710286\pi\) | |||||||
\(432\) | 1.25295 | − | 2.17017i | 0.0602824 | − | 0.104412i | ||||
\(433\) | −0.941683 | −0.0452544 | −0.0226272 | − | 0.999744i | \(-0.507203\pi\) | ||||
−0.0226272 | + | 0.999744i | \(0.507203\pi\) | |||||||
\(434\) | −25.2379 | + | 3.31079i | −1.21146 | + | 0.158923i | ||||
\(435\) | −7.98677 | −0.382936 | ||||||||
\(436\) | −2.60337 | + | 4.50916i | −0.124679 | + | 0.215950i | ||||
\(437\) | −2.95317 | − | 5.11504i | −0.141269 | − | 0.244686i | ||||
\(438\) | 7.23651 | + | 12.5340i | 0.345774 | + | 0.598898i | ||||
\(439\) | 9.42204 | − | 16.3194i | 0.449689 | − | 0.778885i | −0.548676 | − | 0.836035i | \(-0.684868\pi\) |
0.998366 | + | 0.0571502i | \(0.0182014\pi\) | |||||||
\(440\) | −17.3576 | −0.827490 | ||||||||
\(441\) | −1.81797 | + | 6.75981i | −0.0865699 | + | 0.321896i | ||||
\(442\) | −3.32740 | −0.158268 | ||||||||
\(443\) | 1.26840 | − | 2.19693i | 0.0602634 | − | 0.104379i | −0.834320 | − | 0.551281i | \(-0.814139\pi\) |
0.894583 | + | 0.446902i | \(0.147473\pi\) | |||||||
\(444\) | 3.27389 | + | 5.67054i | 0.155372 | + | 0.269112i | ||||
\(445\) | 30.8378 | + | 53.4126i | 1.46185 | + | 2.53200i | ||||
\(446\) | 2.94252 | − | 5.09659i | 0.139332 | − | 0.241331i | ||||
\(447\) | 18.2521 | 0.863294 | ||||||||
\(448\) | 23.0336 | − | 3.02163i | 1.08824 | − | 0.142759i | ||||
\(449\) | −34.2788 | −1.61772 | −0.808859 | − | 0.588003i | \(-0.799914\pi\) | ||||
−0.808859 | + | 0.588003i | \(0.799914\pi\) | |||||||
\(450\) | −5.57262 | + | 9.65206i | −0.262696 | + | 0.455003i | ||||
\(451\) | 3.89884 | + | 6.75298i | 0.183589 | + | 0.317985i | ||||
\(452\) | 1.76143 | + | 3.05088i | 0.0828505 | + | 0.143501i | ||||
\(453\) | 1.46583 | − | 2.53889i | 0.0688706 | − | 0.119287i | ||||
\(454\) | 13.6565 | 0.640929 | ||||||||
\(455\) | −1.76903 | + | 4.26524i | −0.0829332 | + | 0.199958i | ||||
\(456\) | 18.1581 | 0.850332 | ||||||||
\(457\) | 7.54327 | − | 13.0653i | 0.352859 | − | 0.611170i | −0.633890 | − | 0.773423i | \(-0.718543\pi\) |
0.986749 | + | 0.162253i | \(0.0518762\pi\) | |||||||
\(458\) | 5.78862 | + | 10.0262i | 0.270485 | + | 0.468493i | ||||
\(459\) | −3.02964 | − | 5.24749i | −0.141411 | − | 0.244932i | ||||
\(460\) | 1.09720 | − | 1.90041i | 0.0511574 | − | 0.0886072i | ||||
\(461\) | 15.6065 | 0.726865 | 0.363433 | − | 0.931621i | \(-0.381605\pi\) | ||||
0.363433 | + | 0.931621i | \(0.381605\pi\) | |||||||
\(462\) | 2.85952 | + | 3.73016i | 0.133037 | + | 0.173543i | ||||
\(463\) | 6.25815 | 0.290841 | 0.145420 | − | 0.989370i | \(-0.453547\pi\) | ||||
0.145420 | + | 0.989370i | \(0.453547\pi\) | |||||||
\(464\) | 2.64162 | − | 4.57542i | 0.122634 | − | 0.212409i | ||||
\(465\) | −15.2882 | − | 26.4800i | −0.708974 | − | 1.22798i | ||||
\(466\) | −5.32018 | − | 9.21481i | −0.246452 | − | 0.426868i | ||||
\(467\) | −4.38154 | + | 7.58905i | −0.202753 | + | 0.351179i | −0.949415 | − | 0.314025i | \(-0.898322\pi\) |
0.746661 | + | 0.665205i | \(0.231656\pi\) | |||||||
\(468\) | 0.266878 | 0.0123364 | ||||||||
\(469\) | −24.3395 | − | 31.7501i | −1.12389 | − | 1.46608i | ||||
\(470\) | 20.7956 | 0.959232 | ||||||||
\(471\) | −8.39877 | + | 14.5471i | −0.386995 | + | 0.670295i | ||||
\(472\) | 18.8933 | + | 32.7241i | 0.869633 | + | 1.50625i | ||||
\(473\) | 3.45821 | + | 5.98979i | 0.159009 | + | 0.275411i | ||||
\(474\) | −3.85813 | + | 6.68248i | −0.177210 | + | 0.306937i | ||||
\(475\) | −55.2272 | −2.53400 | ||||||||
\(476\) | 3.55776 | − | 8.57800i | 0.163070 | − | 0.393172i | ||||
\(477\) | −5.32282 | −0.243715 | ||||||||
\(478\) | −8.77567 | + | 15.1999i | −0.401390 | + | 0.695227i | ||||
\(479\) | 7.88811 | + | 13.6626i | 0.360417 | + | 0.624260i | 0.988029 | − | 0.154266i | \(-0.0493012\pi\) |
−0.627613 | + | 0.778526i | \(0.715968\pi\) | |||||||
\(480\) | 5.98879 | + | 10.3729i | 0.273350 | + | 0.473455i | ||||
\(481\) | 2.60380 | − | 4.50992i | 0.118723 | − | 0.205635i | ||||
\(482\) | −29.1632 | −1.32835 | ||||||||
\(483\) | −2.62328 | + | 0.344130i | −0.119363 | + | 0.0156585i | ||||
\(484\) | 5.08527 | 0.231149 | ||||||||
\(485\) | −12.8467 | + | 22.2511i | −0.583339 | + | 1.01037i | ||||
\(486\) | −0.595971 | − | 1.03225i | −0.0270338 | − | 0.0468239i | ||||
\(487\) | −20.2877 | − | 35.1393i | −0.919323 | − | 1.59231i | −0.800446 | − | 0.599405i | \(-0.795404\pi\) |
−0.118877 | − | 0.992909i | \(-0.537929\pi\) | |||||||
\(488\) | 0.633045 | − | 1.09647i | 0.0286566 | − | 0.0496347i | ||||
\(489\) | −3.64979 | −0.165049 | ||||||||
\(490\) | 22.3291 | + | 22.3703i | 1.00872 | + | 1.01059i | ||||
\(491\) | 9.38984 | 0.423757 | 0.211879 | − | 0.977296i | \(-0.432042\pi\) | ||||
0.211879 | + | 0.977296i | \(0.432042\pi\) | |||||||
\(492\) | 1.51536 | − | 2.62468i | 0.0683177 | − | 0.118330i | ||||
\(493\) | −6.38747 | − | 11.0634i | −0.287677 | − | 0.498271i | ||||
\(494\) | −1.62171 | − | 2.80888i | −0.0729641 | − | 0.126377i | ||||
\(495\) | −2.82297 | + | 4.88953i | −0.126883 | + | 0.219768i | ||||
\(496\) | 20.2263 | 0.908187 | ||||||||
\(497\) | 17.9823 | − | 2.35898i | 0.806616 | − | 0.105815i | ||||
\(498\) | −5.57851 | −0.249979 | ||||||||
\(499\) | −9.53902 | + | 16.5221i | −0.427025 | + | 0.739629i | −0.996607 | − | 0.0823054i | \(-0.973772\pi\) |
0.569582 | + | 0.821934i | \(0.307105\pi\) | |||||||
\(500\) | −4.77337 | − | 8.26773i | −0.213472 | − | 0.369744i | ||||
\(501\) | 7.61994 | + | 13.1981i | 0.340434 | + | 0.589649i | ||||
\(502\) | 1.55807 | − | 2.69865i | 0.0695399 | − | 0.120447i | ||||
\(503\) | 30.4559 | 1.35796 | 0.678982 | − | 0.734155i | \(-0.262422\pi\) | ||||
0.678982 | + | 0.734155i | \(0.262422\pi\) | |||||||
\(504\) | 3.11619 | − | 7.51336i | 0.138806 | − | 0.334671i | ||||
\(505\) | 9.23353 | 0.410887 | ||||||||
\(506\) | −0.888236 | + | 1.53847i | −0.0394869 | + | 0.0683933i | ||||
\(507\) | 6.39387 | + | 11.0745i | 0.283962 | + | 0.491836i | ||||
\(508\) | 0.823810 | + | 1.42688i | 0.0365507 | + | 0.0633076i | ||||
\(509\) | 11.1695 | − | 19.3462i | 0.495082 | − | 0.857506i | −0.504902 | − | 0.863176i | \(-0.668472\pi\) |
0.999984 | + | 0.00567004i | \(0.00180484\pi\) | |||||||
\(510\) | −27.3596 | −1.21150 | ||||||||
\(511\) | 19.5451 | + | 25.4961i | 0.864626 | + | 1.12788i | ||||
\(512\) | −23.3311 | −1.03110 | ||||||||
\(513\) | 2.95317 | − | 5.11504i | 0.130386 | − | 0.225835i | ||||
\(514\) | 0.607865 | + | 1.05285i | 0.0268118 | + | 0.0464393i | ||||
\(515\) | 10.9999 | + | 19.0524i | 0.484714 | + | 0.839549i | ||||
\(516\) | 1.34410 | − | 2.32805i | 0.0591707 | − | 0.102487i | ||||
\(517\) | 6.86416 | 0.301885 | ||||||||
\(518\) | −21.6870 | − | 28.2901i | −0.952873 | − | 1.24299i | ||||
\(519\) | 2.18632 | 0.0959687 | ||||||||
\(520\) | 2.68278 | − | 4.64671i | 0.117648 | − | 0.203772i | ||||
\(521\) | 7.92935 | + | 13.7340i | 0.347391 | + | 0.601699i | 0.985785 | − | 0.168010i | \(-0.0537342\pi\) |
−0.638394 | + | 0.769710i | \(0.720401\pi\) | |||||||
\(522\) | −1.25650 | − | 2.17632i | −0.0549956 | − | 0.0952551i | ||||
\(523\) | 9.36555 | − | 16.2216i | 0.409527 | − | 0.709321i | −0.585310 | − | 0.810810i | \(-0.699027\pi\) |
0.994837 | + | 0.101489i | \(0.0323605\pi\) | |||||||
\(524\) | −5.75153 | −0.251257 | ||||||||
\(525\) | −9.47777 | + | 22.8516i | −0.413644 | + | 0.997324i | ||||
\(526\) | 10.6536 | 0.464519 | ||||||||
\(527\) | 24.4537 | − | 42.3550i | 1.06522 | − | 1.84501i | ||||
\(528\) | −1.86739 | − | 3.23442i | −0.0812679 | − | 0.140760i | ||||
\(529\) | −0.500000 | − | 0.866025i | −0.0217391 | − | 0.0376533i | ||||
\(530\) | −12.0171 | + | 20.8143i | −0.521991 | + | 0.904114i | ||||
\(531\) | 12.2909 | 0.533381 | ||||||||
\(532\) | 8.97524 | − | 1.17740i | 0.389126 | − | 0.0510469i | ||||
\(533\) | −2.41041 | −0.104406 | ||||||||
\(534\) | −9.70298 | + | 16.8060i | −0.419889 | + | 0.727269i | ||||
\(535\) | 23.2182 | + | 40.2151i | 1.00381 | + | 1.73865i | ||||
\(536\) | 23.2433 | + | 40.2586i | 1.00396 | + | 1.73891i | ||||
\(537\) | 0.930522 | − | 1.61171i | 0.0401550 | − | 0.0695505i | ||||
\(538\) | −16.3071 | −0.703049 | ||||||||
\(539\) | 7.37030 | + | 7.38391i | 0.317461 | + | 0.318048i | ||||
\(540\) | 2.19441 | 0.0944323 | ||||||||
\(541\) | 10.1229 | − | 17.5333i | 0.435217 | − | 0.753817i | −0.562097 | − | 0.827071i | \(-0.690005\pi\) |
0.997313 | + | 0.0732543i | \(0.0233385\pi\) | |||||||
\(542\) | 2.36829 | + | 4.10199i | 0.101727 | + | 0.176196i | ||||
\(543\) | 7.24335 | + | 12.5458i | 0.310842 | + | 0.538394i | ||||
\(544\) | −9.57914 | + | 16.5916i | −0.410702 | + | 0.711357i | ||||
\(545\) | 34.0498 | 1.45853 | ||||||||
\(546\) | −1.44055 | + | 0.188976i | −0.0616498 | + | 0.00808743i | ||||
\(547\) | −11.9031 | −0.508940 | −0.254470 | − | 0.967081i | \(-0.581901\pi\) | ||||
−0.254470 | + | 0.967081i | \(0.581901\pi\) | |||||||
\(548\) | −3.48750 | + | 6.04052i | −0.148979 | + | 0.258038i | ||||
\(549\) | −0.205912 | − | 0.356650i | −0.00878811 | − | 0.0152215i | ||||
\(550\) | 8.30544 | + | 14.3854i | 0.354145 | + | 0.613398i | ||||
\(551\) | 6.22624 | − | 10.7842i | 0.265247 | − | 0.459421i | ||||
\(552\) | 3.07435 | 0.130853 | ||||||||
\(553\) | −6.56181 | + | 15.8210i | −0.279037 | + | 0.672776i | ||||
\(554\) | −11.9368 | −0.507145 | ||||||||
\(555\) | 21.4098 | − | 37.0829i | 0.908796 | − | 1.57408i | ||||
\(556\) | −0.438906 | − | 0.760208i | −0.0186138 | − | 0.0322400i | ||||
\(557\) | −7.78105 | − | 13.4772i | −0.329694 | − | 0.571046i | 0.652757 | − | 0.757567i | \(-0.273612\pi\) |
−0.982451 | + | 0.186521i | \(0.940279\pi\) | |||||||
\(558\) | 4.81037 | − | 8.33181i | 0.203639 | − | 0.352714i | ||||
\(559\) | −2.13799 | −0.0904275 | ||||||||
\(560\) | −15.2803 | − | 19.9327i | −0.645709 | − | 0.842309i | ||||
\(561\) | −9.03076 | −0.381279 | ||||||||
\(562\) | 12.7168 | − | 22.0261i | 0.536424 | − | 0.929114i | ||||
\(563\) | −10.0431 | − | 17.3951i | −0.423264 | − | 0.733115i | 0.572992 | − | 0.819561i | \(-0.305782\pi\) |
−0.996257 | + | 0.0864456i | \(0.972449\pi\) | |||||||
\(564\) | −1.33394 | − | 2.31046i | −0.0561692 | − | 0.0972879i | ||||
\(565\) | 11.5190 | − | 19.9514i | 0.484607 | − | 0.839364i | ||||
\(566\) | 17.2629 | 0.725615 | ||||||||
\(567\) | −1.60966 | − | 2.09976i | −0.0675995 | − | 0.0881816i | ||||
\(568\) | −21.0743 | −0.884259 | ||||||||
\(569\) | −7.55265 | + | 13.0816i | −0.316623 | + | 0.548408i | −0.979781 | − | 0.200072i | \(-0.935882\pi\) |
0.663158 | + | 0.748480i | \(0.269216\pi\) | |||||||
\(570\) | −13.3345 | − | 23.0960i | −0.558521 | − | 0.967387i | ||||
\(571\) | −12.1016 | − | 20.9605i | −0.506435 | − | 0.877170i | −0.999972 | − | 0.00744602i | \(-0.997630\pi\) |
0.493538 | − | 0.869724i | \(-0.335703\pi\) | |||||||
\(572\) | 0.198878 | − | 0.344466i | 0.00831549 | − | 0.0144029i | ||||
\(573\) | 19.8535 | 0.829390 | ||||||||
\(574\) | −6.32104 | + | 15.2405i | −0.263835 | + | 0.636125i | ||||
\(575\) | −9.35049 | −0.389942 | ||||||||
\(576\) | −4.39024 | + | 7.60412i | −0.182927 | + | 0.316838i | ||||
\(577\) | −1.17864 | − | 2.04146i | −0.0490673 | − | 0.0849871i | 0.840449 | − | 0.541891i | \(-0.182292\pi\) |
−0.889516 | + | 0.456904i | \(0.848958\pi\) | |||||||
\(578\) | −11.7495 | − | 20.3507i | −0.488714 | − | 0.846478i | ||||
\(579\) | −0.779443 | + | 1.35003i | −0.0323925 | + | 0.0561055i | ||||
\(580\) | 4.62653 | 0.192106 | ||||||||
\(581\) | −12.2774 | + | 1.61059i | −0.509353 | + | 0.0668187i | ||||
\(582\) | −8.08432 | −0.335106 | ||||||||
\(583\) | −3.96657 | + | 6.87030i | −0.164279 | + | 0.284539i | ||||
\(584\) | −18.6649 | − | 32.3286i | −0.772361 | − | 1.33777i | ||||
\(585\) | −0.872634 | − | 1.51145i | −0.0360790 | − | 0.0624906i | ||||
\(586\) | −19.7854 | + | 34.2693i | −0.817328 | + | 1.41565i | ||||
\(587\) | −3.74241 | −0.154466 | −0.0772329 | − | 0.997013i | \(-0.524608\pi\) | ||||
−0.0772329 | + | 0.997013i | \(0.524608\pi\) | |||||||
\(588\) | 1.05310 | − | 3.91578i | 0.0434292 | − | 0.161484i | ||||
\(589\) | 47.6729 | 1.96433 | ||||||||
\(590\) | 27.7487 | − | 48.0622i | 1.14240 | − | 1.97869i | ||||
\(591\) | 1.24050 | + | 2.14862i | 0.0510275 | + | 0.0883822i | ||||
\(592\) | 14.1626 | + | 24.5303i | 0.582078 | + | 1.00819i | ||||
\(593\) | −2.26864 | + | 3.92941i | −0.0931621 | + | 0.161361i | −0.908840 | − | 0.417145i | \(-0.863031\pi\) |
0.815678 | + | 0.578506i | \(0.196364\pi\) | |||||||
\(594\) | −1.77647 | −0.0728895 | ||||||||
\(595\) | −60.2141 | + | 7.89909i | −2.46854 | + | 0.323831i | ||||
\(596\) | −10.5730 | −0.433085 | ||||||||
\(597\) | 2.64623 | − | 4.58340i | 0.108303 | − | 0.187586i | ||||
\(598\) | −0.274571 | − | 0.475570i | −0.0112280 | − | 0.0194475i | ||||
\(599\) | −17.6106 | − | 30.5025i | −0.719551 | − | 1.24630i | −0.961178 | − | 0.275930i | \(-0.911014\pi\) |
0.241626 | − | 0.970369i | \(-0.422319\pi\) | |||||||
\(600\) | 14.3733 | − | 24.8953i | 0.586788 | − | 1.01635i | ||||
\(601\) | 29.5802 | 1.20660 | 0.603302 | − | 0.797513i | \(-0.293852\pi\) | ||||
0.603302 | + | 0.797513i | \(0.293852\pi\) | |||||||
\(602\) | −5.60667 | + | 13.5181i | −0.228511 | + | 0.550955i | ||||
\(603\) | 15.1208 | 0.615768 | ||||||||
\(604\) | −0.849115 | + | 1.47071i | −0.0345500 | + | 0.0598424i | ||||
\(605\) | −16.6278 | − | 28.8001i | −0.676015 | − | 1.17089i | ||||
\(606\) | 1.45264 | + | 2.51605i | 0.0590097 | + | 0.102208i | ||||
\(607\) | −10.8420 | + | 18.7789i | −0.440062 | + | 0.762210i | −0.997694 | − | 0.0678785i | \(-0.978377\pi\) |
0.557631 | + | 0.830089i | \(0.311710\pi\) | |||||||
\(608\) | −18.6747 | −0.757360 | ||||||||
\(609\) | −3.39369 | − | 4.42697i | −0.137519 | − | 0.179390i | ||||
\(610\) | −1.85952 | −0.0752896 | ||||||||
\(611\) | −1.06092 | + | 1.83757i | −0.0429202 | + | 0.0743400i | ||||
\(612\) | 1.75499 | + | 3.03973i | 0.0709413 | + | 0.122874i | ||||
\(613\) | 12.4937 | + | 21.6398i | 0.504617 | + | 0.874023i | 0.999986 | + | 0.00533991i | \(0.00169975\pi\) |
−0.495368 | + | 0.868683i | \(0.664967\pi\) | |||||||
\(614\) | −18.7626 | + | 32.4977i | −0.757195 | + | 1.31150i | ||||
\(615\) | −19.8196 | −0.799204 | ||||||||
\(616\) | −7.37549 | − | 9.62111i | −0.297167 | − | 0.387646i | ||||
\(617\) | −15.3643 | −0.618542 | −0.309271 | − | 0.950974i | \(-0.600085\pi\) | ||||
−0.309271 | + | 0.950974i | \(0.600085\pi\) | |||||||
\(618\) | −3.46108 | + | 5.99476i | −0.139225 | + | 0.241145i | ||||
\(619\) | −11.8444 | − | 20.5151i | −0.476067 | − | 0.824572i | 0.523557 | − | 0.851991i | \(-0.324605\pi\) |
−0.999624 | + | 0.0274185i | \(0.991271\pi\) | |||||||
\(620\) | 8.85606 | + | 15.3392i | 0.355668 | + | 0.616035i | ||||
\(621\) | 0.500000 | − | 0.866025i | 0.0200643 | − | 0.0347524i | ||||
\(622\) | −21.7024 | −0.870187 | ||||||||
\(623\) | −16.5026 | + | 39.7888i | −0.661162 | + | 1.59411i | ||||
\(624\) | 1.15449 | 0.0462167 | ||||||||
\(625\) | −7.83961 | + | 13.5786i | −0.313584 | + | 0.543144i | ||||
\(626\) | −12.7867 | − | 22.1472i | −0.511058 | − | 0.885179i | ||||
\(627\) | −4.40141 | − | 7.62346i | −0.175775 | − | 0.304452i | ||||
\(628\) | 4.86519 | − | 8.42675i | 0.194142 | − | 0.336264i | ||||
\(629\) | 68.4905 | 2.73090 | ||||||||
\(630\) | −11.8449 | + | 1.55386i | −0.471913 | + | 0.0619072i | ||||
\(631\) | 12.2965 | 0.489515 | 0.244758 | − | 0.969584i | \(-0.421292\pi\) | ||||
0.244758 | + | 0.969584i | \(0.421292\pi\) | |||||||
\(632\) | 9.95118 | − | 17.2360i | 0.395837 | − | 0.685609i | ||||
\(633\) | −13.5059 | − | 23.3929i | −0.536811 | − | 0.929784i | ||||
\(634\) | 1.67387 | + | 2.89923i | 0.0664780 | + | 0.115143i | ||||
\(635\) | 5.38737 | − | 9.33119i | 0.213791 | − | 0.370297i | ||||
\(636\) | 3.08337 | 0.122264 | ||||||||
\(637\) | −3.11586 | + | 0.831813i | −0.123455 | + | 0.0329576i | ||||
\(638\) | −3.74538 | −0.148281 | ||||||||
\(639\) | −3.42745 | + | 5.93652i | −0.135588 | + | 0.234845i | ||||
\(640\) | 7.84577 | + | 13.5893i | 0.310131 | + | 0.537163i | ||||
\(641\) | −1.55282 | − | 2.68956i | −0.0613326 | − | 0.106231i | 0.833729 | − | 0.552174i | \(-0.186202\pi\) |
−0.895061 | + | 0.445943i | \(0.852868\pi\) | |||||||
\(642\) | −7.30551 | + | 12.6535i | −0.288326 | + | 0.499395i | ||||
\(643\) | 44.2523 | 1.74514 | 0.872570 | − | 0.488489i | \(-0.162452\pi\) | ||||
0.872570 | + | 0.488489i | \(0.162452\pi\) | |||||||
\(644\) | 1.51959 | − | 0.199346i | 0.0598804 | − | 0.00785532i | ||||
\(645\) | −17.5797 | −0.692199 | ||||||||
\(646\) | 21.3287 | − | 36.9424i | 0.839167 | − | 1.45348i | ||||
\(647\) | −14.2931 | − | 24.7564i | −0.561919 | − | 0.973273i | −0.997329 | − | 0.0730404i | \(-0.976730\pi\) |
0.435410 | − | 0.900232i | \(-0.356604\pi\) | |||||||
\(648\) | 1.53717 | + | 2.66246i | 0.0603858 | + | 0.104591i | ||||
\(649\) | 9.15920 | − | 15.8642i | 0.359530 | − | 0.622725i | ||||
\(650\) | −5.13474 | −0.201401 | ||||||||
\(651\) | 8.18136 | − | 19.7258i | 0.320653 | − | 0.773115i | ||||
\(652\) | 2.11423 | 0.0827995 | ||||||||
\(653\) | −4.85971 | + | 8.41727i | −0.190175 | + | 0.329393i | −0.945308 | − | 0.326179i | \(-0.894239\pi\) |
0.755133 | + | 0.655572i | \(0.227572\pi\) | |||||||
\(654\) | 5.35681 | + | 9.27828i | 0.209468 | + | 0.362809i | ||||
\(655\) | 18.8063 | + | 32.5734i | 0.734822 | + | 1.27275i | ||||
\(656\) | 6.55533 | − | 11.3542i | 0.255943 | − | 0.443306i | ||||
\(657\) | −12.1424 | −0.473719 | ||||||||
\(658\) | 8.83637 | + | 11.5268i | 0.344478 | + | 0.449361i | ||||
\(659\) | 29.8923 | 1.16444 | 0.582220 | − | 0.813031i | \(-0.302184\pi\) | ||||
0.582220 | + | 0.813031i | \(0.302184\pi\) | |||||||
\(660\) | 1.63527 | − | 2.83238i | 0.0636529 | − | 0.110250i | ||||
\(661\) | −21.5812 | − | 37.3797i | −0.839411 | − | 1.45390i | −0.890388 | − | 0.455202i | \(-0.849567\pi\) |
0.0509778 | − | 0.998700i | \(-0.483766\pi\) | |||||||
\(662\) | 16.1498 | + | 27.9722i | 0.627679 | + | 1.08717i | ||||
\(663\) | 1.39579 | − | 2.41758i | 0.0542080 | − | 0.0938909i | ||||
\(664\) | 14.3885 | 0.558383 | ||||||||
\(665\) | −36.0153 | − | 46.9809i | −1.39661 | − | 1.82184i | ||||
\(666\) | 13.4730 | 0.522069 | ||||||||
\(667\) | 1.05416 | − | 1.82586i | 0.0408174 | − | 0.0706977i | ||||
\(668\) | −4.41403 | − | 7.64533i | −0.170784 | − | 0.295807i | ||||
\(669\) | 2.46868 | + | 4.27587i | 0.0954446 | + | 0.165315i | ||||
\(670\) | 34.1377 | − | 59.1282i | 1.31885 | − | 2.28432i | ||||
\(671\) | −0.613783 | −0.0236948 | ||||||||
\(672\) | −3.20485 | + | 7.72711i | −0.123630 | + | 0.298080i | ||||
\(673\) | 2.93645 | 0.113192 | 0.0565959 | − | 0.998397i | \(-0.481975\pi\) | ||||
0.0565959 | + | 0.998397i | \(0.481975\pi\) | |||||||
\(674\) | −4.89692 | + | 8.48171i | −0.188622 | + | 0.326703i | ||||
\(675\) | −4.67524 | − | 8.09776i | −0.179950 | − | 0.311683i | ||||
\(676\) | −3.70380 | − | 6.41518i | −0.142454 | − | 0.246738i | ||||
\(677\) | −19.2810 | + | 33.3956i | −0.741028 | + | 1.28350i | 0.211000 | + | 0.977486i | \(0.432328\pi\) |
−0.952028 | + | 0.306012i | \(0.901005\pi\) | |||||||
\(678\) | 7.24879 | 0.278388 | ||||||||
\(679\) | −17.7923 | + | 2.33405i | −0.682806 | + | 0.0895728i | ||||
\(680\) | 70.5679 | 2.70615 | ||||||||
\(681\) | −5.72866 | + | 9.92233i | −0.219523 | + | 0.380224i | ||||
\(682\) | −7.16938 | − | 12.4177i | −0.274530 | − | 0.475500i | ||||
\(683\) | 7.12801 | + | 12.3461i | 0.272746 | + | 0.472409i | 0.969564 | − | 0.244839i | \(-0.0787350\pi\) |
−0.696818 | + | 0.717248i | \(0.745402\pi\) | |||||||
\(684\) | −1.71069 | + | 2.96301i | −0.0654100 | + | 0.113293i | ||||
\(685\) | 45.6135 | 1.74280 | ||||||||
\(686\) | −2.91165 | + | 21.8822i | −0.111167 | + | 0.835467i | ||||
\(687\) | −9.71293 | −0.370571 | ||||||||
\(688\) | 5.81447 | − | 10.0710i | 0.221675 | − | 0.383952i | ||||
\(689\) | −1.22614 | − | 2.12374i | −0.0467123 | − | 0.0809081i | ||||
\(690\) | −2.25766 | − | 3.91038i | −0.0859477 | − | 0.148866i | ||||
\(691\) | −0.731849 | + | 1.26760i | −0.0278408 | + | 0.0482217i | −0.879610 | − | 0.475695i | \(-0.842196\pi\) |
0.851769 | + | 0.523917i | \(0.175530\pi\) | |||||||
\(692\) | −1.26648 | −0.0481442 | ||||||||
\(693\) | −3.90973 | + | 0.512892i | −0.148518 | + | 0.0194832i | ||||
\(694\) | 3.11394 | 0.118204 | ||||||||
\(695\) | −2.87026 | + | 4.97144i | −0.108875 | + | 0.188577i | ||||
\(696\) | 3.24086 | + | 5.61334i | 0.122845 | + | 0.212773i | ||||
\(697\) | −15.8509 | − | 27.4545i | −0.600394 | − | 1.03991i | ||||
\(698\) | 9.77246 | − | 16.9264i | 0.369893 | − | 0.640674i | ||||
\(699\) | 8.92690 | 0.337646 | ||||||||
\(700\) | 5.49023 | − | 13.2373i | 0.207511 | − | 0.500323i | ||||
\(701\) | −26.8881 | −1.01555 | −0.507775 | − | 0.861490i | \(-0.669532\pi\) | ||||
−0.507775 | + | 0.861490i | \(0.669532\pi\) | |||||||
\(702\) | 0.274571 | − | 0.475570i | 0.0103630 | − | 0.0179492i | ||||
\(703\) | 33.3809 | + | 57.8174i | 1.25898 | + | 2.18062i | ||||
\(704\) | 6.54322 | + | 11.3332i | 0.246607 | + | 0.427136i | ||||
\(705\) | −8.72343 | + | 15.1094i | −0.328543 | + | 0.569054i | ||||
\(706\) | 34.5835 | 1.30157 | ||||||||
\(707\) | 3.92346 | + | 5.11804i | 0.147557 | + | 0.192484i | ||||
\(708\) | −7.11981 | −0.267579 | ||||||||
\(709\) | −1.83576 | + | 3.17963i | −0.0689435 | + | 0.119414i | −0.898437 | − | 0.439103i | \(-0.855296\pi\) |
0.829493 | + | 0.558517i | \(0.188629\pi\) | |||||||
\(710\) | 15.4760 | + | 26.8053i | 0.580805 | + | 1.00598i | ||||
\(711\) | −3.23685 | − | 5.60638i | −0.121391 | − | 0.210256i | ||||
\(712\) | 25.0266 | − | 43.3474i | 0.937913 | − | 1.62451i | ||||
\(713\) | 8.07148 | 0.302279 | ||||||||
\(714\) | −11.6255 | − | 15.1651i | −0.435073 | − | 0.567540i | ||||
\(715\) | −2.60115 | −0.0972775 | ||||||||
\(716\) | −0.539027 | + | 0.933622i | −0.0201444 | + | 0.0348911i | ||||
\(717\) | −7.36249 | − | 12.7522i | −0.274957 | − | 0.476240i | ||||
\(718\) | 17.9749 | + | 31.1334i | 0.670817 | + | 1.16189i | ||||
\(719\) | 9.29585 | − | 16.1009i | 0.346677 | − | 0.600462i | −0.638980 | − | 0.769223i | \(-0.720643\pi\) |
0.985657 | + | 0.168761i | \(0.0539767\pi\) | |||||||
\(720\) | 9.49284 | 0.353777 | ||||||||
\(721\) | −5.88651 | + | 14.1928i | −0.219225 | + | 0.528566i | ||||
\(722\) | 18.9338 | 0.704644 | ||||||||
\(723\) | 12.2335 | − | 21.1890i | 0.454968 | − | 0.788027i | ||||
\(724\) | −4.19588 | − | 7.26748i | −0.155939 | − | 0.270094i | ||||
\(725\) | −9.85694 | − | 17.0727i | −0.366078 | − | 0.634065i | ||||
\(726\) | 5.23185 | − | 9.06184i | 0.194172 | − | 0.336316i | ||||
\(727\) | 16.8322 | 0.624273 | 0.312136 | − | 0.950037i | \(-0.398955\pi\) | ||||
0.312136 | + | 0.950037i | \(0.398955\pi\) | |||||||
\(728\) | 3.71557 | − | 0.487421i | 0.137708 | − | 0.0180650i | ||||
\(729\) | 1.00000 | 0.0370370 | ||||||||
\(730\) | −27.4134 | + | 47.4814i | −1.01461 | + | 1.75736i | ||||
\(731\) | −14.0595 | − | 24.3517i | −0.520008 | − | 0.900680i | ||||
\(732\) | 0.119279 | + | 0.206598i | 0.00440869 | + | 0.00763608i | ||||
\(733\) | −9.42942 | + | 16.3322i | −0.348284 | + | 0.603245i | −0.985945 | − | 0.167072i | \(-0.946569\pi\) |
0.637661 | + | 0.770317i | \(0.279902\pi\) | |||||||
\(734\) | 10.3917 | 0.383566 | ||||||||
\(735\) | −25.6202 | + | 6.83959i | −0.945015 | + | 0.252282i | ||||
\(736\) | −3.16181 | −0.116546 | ||||||||
\(737\) | 11.2681 | − | 19.5168i | 0.415064 | − | 0.718912i | ||||
\(738\) | −3.11808 | − | 5.40067i | −0.114778 | − | 0.198801i | ||||
\(739\) | −22.3548 | − | 38.7196i | −0.822333 | − | 1.42432i | −0.903940 | − | 0.427659i | \(-0.859339\pi\) |
0.0816069 | − | 0.996665i | \(-0.473995\pi\) | |||||||
\(740\) | −12.4021 | + | 21.4811i | −0.455912 | + | 0.789663i | ||||
\(741\) | 2.72112 | 0.0999628 | ||||||||
\(742\) | −16.6434 | + | 2.18333i | −0.610997 | + | 0.0801527i | ||||
\(743\) | 49.0083 | 1.79794 | 0.898970 | − | 0.438011i | \(-0.144317\pi\) | ||||
0.898970 | + | 0.438011i | \(0.144317\pi\) | |||||||
\(744\) | −12.4073 | + | 21.4900i | −0.454872 | + | 0.787862i | ||||
\(745\) | 34.5713 | + | 59.8793i | 1.26659 | + | 2.19381i | ||||
\(746\) | 6.50022 | + | 11.2587i | 0.237990 | + | 0.412211i | ||||
\(747\) | 2.34009 | − | 4.05316i | 0.0856196 | − | 0.148297i | ||||
\(748\) | 5.23128 | 0.191275 | ||||||||
\(749\) | −12.4250 | + | 29.9576i | −0.454001 | + | 1.09463i | ||||
\(750\) | −19.6439 | −0.717292 | ||||||||
\(751\) | −5.85462 | + | 10.1405i | −0.213638 | + | 0.370032i | −0.952850 | − | 0.303440i | \(-0.901865\pi\) |
0.739212 | + | 0.673472i | \(0.235198\pi\) | |||||||
\(752\) | −5.77054 | − | 9.99487i | −0.210430 | − | 0.364475i | ||||
\(753\) | 1.30717 | + | 2.26408i | 0.0476358 | + | 0.0825076i | ||||
\(754\) | 0.578884 | − | 1.00266i | 0.0210817 | − | 0.0365146i | ||||
\(755\) | 11.1057 | 0.404178 | ||||||||
\(756\) | 0.932436 | + | 1.21633i | 0.0339124 | + | 0.0442377i | ||||
\(757\) | −24.2422 | −0.881096 | −0.440548 | − | 0.897729i | \(-0.645216\pi\) | ||||
−0.440548 | + | 0.897729i | \(0.645216\pi\) | |||||||
\(758\) | 6.89817 | − | 11.9480i | 0.250553 | − | 0.433970i | ||||
\(759\) | −0.745201 | − | 1.29073i | −0.0270491 | − | 0.0468504i | ||||
\(760\) | 34.3933 | + | 59.5710i | 1.24758 | + | 2.16087i | ||||
\(761\) | −15.3628 | + | 26.6091i | −0.556900 | + | 0.964579i | 0.440853 | + | 0.897579i | \(0.354676\pi\) |
−0.997753 | + | 0.0669997i | \(0.978657\pi\) | |||||||
\(762\) | 3.39022 | 0.122815 | ||||||||
\(763\) | 14.4683 | + | 18.8734i | 0.523786 | + | 0.683264i | ||||
\(764\) | −11.5006 | −0.416077 | ||||||||
\(765\) | 11.4769 | − | 19.8786i | 0.414948 | − | 0.718711i | ||||
\(766\) | −14.4492 | − | 25.0268i | −0.522072 | − | 0.904256i | ||||
\(767\) | 2.83128 | + | 4.90393i | 0.102232 | + | 0.177071i | ||||
\(768\) | 6.31185 | − | 10.9324i | 0.227759 | − | 0.394490i | ||||
\(769\) | −39.0901 | −1.40963 | −0.704813 | − | 0.709393i | \(-0.748969\pi\) | ||||
−0.704813 | + | 0.709393i | \(0.748969\pi\) | |||||||
\(770\) | −6.82125 | + | 16.4465i | −0.245821 | + | 0.592690i | ||||
\(771\) | −1.01996 | −0.0367328 | ||||||||
\(772\) | 0.451511 | − | 0.782039i | 0.0162502 | − | 0.0281462i | ||||
\(773\) | −0.437496 | − | 0.757766i | −0.0157356 | − | 0.0272549i | 0.858050 | − | 0.513566i | \(-0.171676\pi\) |
−0.873786 | + | 0.486311i | \(0.838342\pi\) | |||||||
\(774\) | −2.76569 | − | 4.79031i | −0.0994105 | − | 0.172184i | ||||
\(775\) | 37.7362 | − | 65.3610i | 1.35552 | − | 2.34783i | ||||
\(776\) | 20.8517 | 0.748532 | ||||||||
\(777\) | 29.6520 | − | 3.88984i | 1.06376 | − | 0.139547i | ||||
\(778\) | 6.91898 | 0.248057 | ||||||||
\(779\) | 15.4508 | − | 26.7615i | 0.553581 | − | 0.958831i | ||||
\(780\) | 0.505494 | + | 0.875542i | 0.0180996 | + | 0.0313494i | ||||
\(781\) | 5.10828 | + | 8.84780i | 0.182789 | + | 0.316599i | ||||
\(782\) | 3.61116 | − | 6.25470i | 0.129135 | − | 0.223668i | ||||
\(783\) | 2.10833 | 0.0753454 | ||||||||
\(784\) | 4.55564 | − | 16.9394i | 0.162701 | − | 0.604977i | ||||
\(785\) | −63.6325 | −2.27114 | ||||||||
\(786\) | −5.91732 | + | 10.2491i | −0.211064 | + | 0.365573i | ||||
\(787\) | −6.16206 | − | 10.6730i | −0.219654 | − | 0.380452i | 0.735048 | − | 0.678015i | \(-0.237159\pi\) |
−0.954702 | + | 0.297563i | \(0.903826\pi\) | |||||||
\(788\) | −0.718591 | − | 1.24464i | −0.0255988 | − | 0.0443384i | ||||
\(789\) | −4.46901 | + | 7.74054i | −0.159101 | + | 0.275571i | ||||
\(790\) | −29.2308 | −1.03998 | ||||||||
\(791\) | 15.9534 | − | 2.09283i | 0.567239 | − | 0.0744123i | ||||
\(792\) | 4.58201 | 0.162815 | ||||||||
\(793\) | 0.0948660 | − | 0.164313i | 0.00336879 | − | 0.00583492i | ||||
\(794\) | 7.86791 | + | 13.6276i | 0.279222 | + | 0.483626i | ||||
\(795\) | −10.0820 | − | 17.4625i | −0.357571 | − | 0.619330i | ||||
\(796\) | −1.53289 | + | 2.65504i | −0.0543319 | + | 0.0941056i | ||||
\(797\) | −33.6866 | −1.19324 | −0.596621 | − | 0.802524i | \(-0.703490\pi\) | ||||
−0.596621 | + | 0.802524i | \(0.703490\pi\) | |||||||
\(798\) | 7.13585 | − | 17.2050i | 0.252606 | − | 0.609051i | ||||
\(799\) | −27.9065 | −0.987260 | ||||||||
\(800\) | −14.7822 | + | 25.6036i | −0.522631 | + | 0.905223i | ||||
\(801\) | −8.14048 | − | 14.0997i | −0.287630 | − | 0.498189i | ||||
\(802\) | −14.0643 | − | 24.3600i | −0.496626 | − | 0.860181i | ||||
\(803\) | −9.04851 | + | 15.6725i | −0.319315 | + | 0.553070i | ||||
\(804\) | −8.75911 | −0.308910 | ||||||||
\(805\) | −6.09773 | − | 7.95431i | −0.214917 | − | 0.280353i | ||||
\(806\) | 4.43238 | 0.156124 | ||||||||
\(807\) | 6.84056 | − | 11.8482i | 0.240799 | − | 0.417076i | ||||
\(808\) | −3.74677 | − | 6.48959i | −0.131811 | − | 0.228303i | ||||
\(809\) | 2.94113 | + | 5.09419i | 0.103405 | + | 0.179102i | 0.913085 | − | 0.407769i | \(-0.133693\pi\) |
−0.809681 | + | 0.586871i | \(0.800360\pi\) | |||||||
\(810\) | 2.25766 | − | 3.91038i | 0.0793261 | − | 0.137397i | ||||
\(811\) | 13.3036 | 0.467152 | 0.233576 | − | 0.972339i | \(-0.424957\pi\) | ||||
0.233576 | + | 0.972339i | \(0.424957\pi\) | |||||||
\(812\) | 1.96588 | + | 2.56443i | 0.0689888 | + | 0.0899939i | ||||
\(813\) | −3.97383 | −0.139368 | ||||||||
\(814\) | 10.0401 | − | 17.3900i | 0.351905 | − | 0.609518i | ||||
\(815\) | −6.91307 | − | 11.9738i | −0.242154 | − | 0.419424i | ||||
\(816\) | 7.59196 | + | 13.1497i | 0.265772 | + | 0.460330i | ||||
\(817\) | 13.7046 | − | 23.7371i | 0.479463 | − | 0.830454i | ||||
\(818\) | 10.2999 | 0.360128 | ||||||||
\(819\) | 0.466983 | − | 1.12593i | 0.0163177 | − | 0.0393431i | ||||
\(820\) | 11.4810 | 0.400933 | ||||||||
\(821\) | −19.5406 | + | 33.8454i | −0.681973 | + | 1.18121i | 0.292405 | + | 0.956295i | \(0.405545\pi\) |
−0.974378 | + | 0.224917i | \(0.927789\pi\) | |||||||
\(822\) | 7.17605 | + | 12.4293i | 0.250293 | + | 0.433521i | ||||
\(823\) | 9.50351 | + | 16.4606i | 0.331272 | + | 0.573779i | 0.982761 | − | 0.184878i | \(-0.0591890\pi\) |
−0.651490 | + | 0.758657i | \(0.725856\pi\) | |||||||
\(824\) | 8.92706 | − | 15.4621i | 0.310989 | − | 0.538649i | ||||
\(825\) | −13.9360 | −0.485189 | ||||||||
\(826\) | 38.4312 | − | 5.04153i | 1.33719 | − | 0.175417i | ||||
\(827\) | 35.8180 | 1.24551 | 0.622757 | − | 0.782415i | \(-0.286012\pi\) | ||||
0.622757 | + | 0.782415i | \(0.286012\pi\) | |||||||
\(828\) | −0.289637 | + | 0.501666i | −0.0100656 | + | 0.0174341i | ||||
\(829\) | 13.5527 | + | 23.4740i | 0.470706 | + | 0.815287i | 0.999439 | − | 0.0335018i | \(-0.0106659\pi\) |
−0.528733 | + | 0.848788i | \(0.677333\pi\) | |||||||
\(830\) | −10.5663 | − | 18.3013i | −0.366761 | − | 0.635248i | ||||
\(831\) | 5.00728 | − | 8.67286i | 0.173700 | − | 0.300858i | ||||
\(832\) | −4.04527 | −0.140244 | ||||||||
\(833\) | −29.9642 | − | 30.0196i | −1.03820 | − | 1.04012i | ||||
\(834\) | −1.80623 | −0.0625446 | ||||||||
\(835\) | −28.8659 | + | 49.9972i | −0.998945 | + | 1.73022i | ||||
\(836\) | 2.54962 | + | 4.41607i | 0.0881805 | + | 0.152733i | ||||
\(837\) | 4.03574 | + | 6.99011i | 0.139496 | + | 0.241614i | ||||
\(838\) | −17.9150 | + | 31.0298i | −0.618865 | + | 1.07191i | ||||
\(839\) | 25.7997 | 0.890704 | 0.445352 | − | 0.895356i | \(-0.353079\pi\) | ||||
0.445352 | + | 0.895356i | \(0.353079\pi\) | |||||||
\(840\) | 30.5513 | − | 4.00782i | 1.05412 | − | 0.138283i | ||||
\(841\) | −24.5550 | −0.846723 | ||||||||
\(842\) | 14.7509 | − | 25.5492i | 0.508348 | − | 0.880484i | ||||
\(843\) | 10.6689 | + | 18.4791i | 0.367458 | + | 0.636456i | ||||
\(844\) | 7.82361 | + | 13.5509i | 0.269300 | + | 0.466441i | ||||
\(845\) | −24.2213 | + | 41.9525i | −0.833238 | + | 1.44321i | ||||
\(846\) | −5.48958 | −0.188736 | ||||||||
\(847\) | 8.89820 | − | 21.4542i | 0.305746 | − | 0.737174i | ||||
\(848\) | 13.3384 | 0.458044 | ||||||||
\(849\) | −7.24152 | + | 12.5427i | −0.248528 | + | 0.430463i | ||||
\(850\) | −33.7661 | − | 58.4845i | −1.15817 | − | 2.00600i | ||||
\(851\) | 5.65171 | + | 9.78904i | 0.193738 | + | 0.335564i | ||||
\(852\) | 1.98543 | − | 3.43887i | 0.0680198 | − | 0.117814i | ||||
\(853\) | −6.24250 | −0.213739 | −0.106870 | − | 0.994273i | \(-0.534083\pi\) | ||||
−0.106870 | + | 0.994273i | \(0.534083\pi\) | |||||||
\(854\) | −0.790136 | − | 1.03071i | −0.0270379 | − | 0.0352701i | ||||
\(855\) | 22.3744 | 0.765189 | ||||||||
\(856\) | 18.8429 | − | 32.6369i | 0.644038 | − | 1.11551i | ||||
\(857\) | −10.9852 | − | 19.0270i | −0.375249 | − | 0.649950i | 0.615115 | − | 0.788437i | \(-0.289109\pi\) |
−0.990364 | + | 0.138487i | \(0.955776\pi\) | |||||||
\(858\) | −0.409220 | − | 0.708791i | −0.0139706 | − | 0.0241977i | ||||
\(859\) | −10.1658 | + | 17.6078i | −0.346854 | + | 0.600769i | −0.985689 | − | 0.168575i | \(-0.946083\pi\) |
0.638835 | + | 0.769344i | \(0.279417\pi\) | |||||||
\(860\) | 10.1835 | 0.347253 | ||||||||
\(861\) | −8.42164 | − | 10.9858i | −0.287009 | − | 0.374394i | ||||
\(862\) | −18.6585 | −0.635510 | ||||||||
\(863\) | −13.8855 | + | 24.0503i | −0.472667 | + | 0.818683i | −0.999511 | − | 0.0312790i | \(-0.990042\pi\) |
0.526844 | + | 0.849962i | \(0.323375\pi\) | |||||||
\(864\) | −1.58090 | − | 2.73821i | −0.0537835 | − | 0.0931557i | ||||
\(865\) | 4.14111 | + | 7.17261i | 0.140802 | + | 0.243876i | ||||
\(866\) | 0.561216 | − | 0.972054i | 0.0190709 | − | 0.0330317i | ||||
\(867\) | 19.7149 | 0.669552 | ||||||||
\(868\) | −4.73925 | + | 11.4266i | −0.160860 | + | 0.387846i | ||||
\(869\) | −9.64840 | −0.327300 | ||||||||
\(870\) | 4.75988 | − | 8.24436i | 0.161375 | − | 0.279510i | ||||
\(871\) | 3.48317 | + | 6.03303i | 0.118023 | + | 0.204421i | ||||
\(872\) | −13.8167 | − | 23.9312i | −0.467892 | − | 0.810413i | ||||
\(873\) | 3.39124 | − | 5.87380i | 0.114776 | − | 0.198798i | ||||
\(874\) | 7.04002 | 0.238132 | ||||||||
\(875\) | −43.2330 | + | 5.67145i | −1.46154 | + | 0.191730i | ||||
\(876\) | 7.03376 | 0.237649 | ||||||||
\(877\) | −16.2656 | + | 28.1729i | −0.549251 | + | 0.951331i | 0.449075 | + | 0.893494i | \(0.351754\pi\) |
−0.998326 | + | 0.0578367i | \(0.981580\pi\) | |||||||
\(878\) | 11.2305 | + | 19.4518i | 0.379012 | + | 0.656468i | ||||
\(879\) | −16.5993 | − | 28.7508i | −0.559880 | − | 0.969741i | ||||
\(880\) | 7.07407 | − | 12.2526i | 0.238467 | − | 0.413037i | ||||
\(881\) | 3.88986 | 0.131053 | 0.0655263 | − | 0.997851i | \(-0.479127\pi\) | ||||
0.0655263 | + | 0.997851i | \(0.479127\pi\) | |||||||
\(882\) | −5.89437 | − | 5.90525i | −0.198474 | − | 0.198840i | ||||
\(883\) | −35.6597 | −1.20004 | −0.600022 | − | 0.799984i | \(-0.704841\pi\) | ||||
−0.600022 | + | 0.799984i | \(0.704841\pi\) | |||||||
\(884\) | −0.808544 | + | 1.40044i | −0.0271943 | + | 0.0471019i | ||||
\(885\) | 23.2803 | + | 40.3226i | 0.782557 | + | 1.35543i | ||||
\(886\) | 1.51186 | + | 2.61861i | 0.0507918 | + | 0.0879740i | ||||
\(887\) | 23.8635 | − | 41.3328i | 0.801259 | − | 1.38782i | −0.117529 | − | 0.993069i | \(-0.537497\pi\) |
0.918788 | − | 0.394752i | \(-0.129169\pi\) | |||||||
\(888\) | −34.7506 | −1.16615 | ||||||||
\(889\) | 7.46134 | − | 0.978804i | 0.250245 | − | 0.0328280i | ||||
\(890\) | −73.5137 | −2.46419 | ||||||||
\(891\) | 0.745201 | − | 1.29073i | 0.0249652 | − | 0.0432409i | ||||
\(892\) | −1.43004 | − | 2.47690i | −0.0478813 | − | 0.0829328i | ||||
\(893\) | −13.6010 | − | 23.5577i | −0.455142 | − | 0.788328i | ||||
\(894\) | −10.8777 | + | 18.8408i | −0.363805 | + | 0.630129i | ||||
\(895\) | 7.05002 | 0.235656 | ||||||||
\(896\) | −4.19859 | + | 10.1231i | −0.140265 | + | 0.338189i | ||||
\(897\) | 0.460711 | 0.0153827 | ||||||||
\(898\) | 20.4292 | − | 35.3844i | 0.681731 | − | 1.18079i | ||||
\(899\) | 8.50866 | + | 14.7374i | 0.283780 | + | 0.491521i | ||||
\(900\) | 2.70825 | + | 4.69082i | 0.0902749 | + | 0.156361i | ||||
\(901\) | 16.1262 | − | 27.9315i | 0.537243 | − | 0.930532i | ||||
\(902\) | −9.29437 | −0.309469 | ||||||||
\(903\) | −7.46987 | − | 9.74422i | −0.248582 | − | 0.324267i | ||||
\(904\) | −18.6966 | −0.621840 | ||||||||
\(905\) | −27.4393 | + | 47.5262i | −0.912113 | + | 1.57983i | ||||
\(906\) | 1.74718 | + | 3.02621i | 0.0580462 | + | 0.100539i | ||||
\(907\) | 4.94034 | + | 8.55693i | 0.164041 | + | 0.284128i | 0.936314 | − | 0.351163i | \(-0.114214\pi\) |
−0.772273 | + | 0.635291i | \(0.780880\pi\) | |||||||
\(908\) | 3.31846 | − | 5.74774i | 0.110127 | − | 0.190746i | ||||
\(909\) | −2.43744 | −0.0808448 | ||||||||
\(910\) | −3.34852 | − | 4.36804i | −0.111002 | − | 0.144799i | ||||
\(911\) | −22.5568 | −0.747339 | −0.373669 | − | 0.927562i | \(-0.621901\pi\) | ||||
−0.373669 | + | 0.927562i | \(0.621901\pi\) | |||||||
\(912\) | −7.40033 | + | 12.8178i | −0.245049 | + | 0.424438i | ||||
\(913\) | −3.48768 | − | 6.04084i | −0.115425 | − | 0.199923i | ||||
\(914\) | 8.99114 | + | 15.5731i | 0.297400 | + | 0.515113i | ||||
\(915\) | 0.780037 | − | 1.35106i | 0.0257872 | − | 0.0446648i | ||||
\(916\) | 5.62644 | 0.185903 | ||||||||
\(917\) | −10.0640 | + | 24.2650i | −0.332343 | + | 0.801302i | ||||
\(918\) | 7.22231 | 0.238372 | ||||||||
\(919\) | −17.5510 | + | 30.3992i | −0.578954 | + | 1.00278i | 0.416646 | + | 0.909069i | \(0.363206\pi\) |
−0.995600 | + | 0.0937089i | \(0.970128\pi\) | |||||||
\(920\) | 5.82312 | + | 10.0859i | 0.191983 | + | 0.332524i | ||||
\(921\) | −15.7412 | − | 27.2645i | −0.518689 | − | 0.898396i | ||||
\(922\) | −9.30100 | + | 16.1098i | −0.306312 | + | 0.530548i | ||||
\(923\) | −3.15813 | −0.103951 | ||||||||
\(924\) | 2.26481 | − | 0.297105i | 0.0745067 | − | 0.00977403i | ||||
\(925\) | 105.692 | 3.47515 | ||||||||
\(926\) | −3.72968 | + | 6.45999i | −0.122565 | + | 0.212288i | ||||
\(927\) | −2.90373 | − | 5.02940i | −0.0953709 | − | 0.165187i | ||||
\(928\) | −3.33306 | − | 5.77303i | −0.109413 | − | 0.189509i | ||||
\(929\) | 23.8750 | − | 41.3527i | 0.783314 | − | 1.35674i | −0.146688 | − | 0.989183i | \(-0.546861\pi\) |
0.930001 | − | 0.367556i | \(-0.119805\pi\) | |||||||
\(930\) | 36.4453 | 1.19509 | ||||||||
\(931\) | 10.7375 | − | 39.9257i | 0.351909 | − | 1.30851i | ||||
\(932\) | −5.17112 | −0.169386 | ||||||||
\(933\) | 9.10379 | − | 15.7682i | 0.298045 | − | 0.516229i | ||||
\(934\) | −5.22254 | − | 9.04571i | −0.170887 | − | 0.295985i | ||||
\(935\) | −17.1052 | − | 29.6270i | −0.559399 | − | 0.968908i | ||||
\(936\) | −0.708193 | + | 1.22663i | −0.0231480 | + | 0.0400935i | ||||
\(937\) | 16.1702 | 0.528258 | 0.264129 | − | 0.964487i | \(-0.414916\pi\) | ||||
0.264129 | + | 0.964487i | \(0.414916\pi\) | |||||||
\(938\) | 47.2797 | − | 6.20231i | 1.54374 | − | 0.202513i | ||||
\(939\) | 21.4552 | 0.700164 | ||||||||
\(940\) | 5.05325 | − | 8.75249i | 0.164819 | − | 0.285475i | ||||
\(941\) | 23.8793 | + | 41.3601i | 0.778441 | + | 1.34830i | 0.932840 | + | 0.360291i | \(0.117323\pi\) |
−0.154398 | + | 0.988009i | \(0.549344\pi\) | |||||||
\(942\) | −10.0108 | − | 17.3393i | −0.326171 | − | 0.564945i | ||||
\(943\) | 2.61596 | − | 4.53098i | 0.0851875 | − | 0.147549i | ||||
\(944\) | −30.7998 | −1.00245 | ||||||||
\(945\) | 3.83977 | − | 9.25795i | 0.124908 | − | 0.301161i | ||||
\(946\) | −8.24397 | −0.268034 | ||||||||
\(947\) | −2.44092 | + | 4.22780i | −0.0793192 | + | 0.137385i | −0.902956 | − | 0.429732i | \(-0.858608\pi\) |
0.823637 | + | 0.567117i | \(0.191941\pi\) | |||||||
\(948\) | 1.87502 | + | 3.24763i | 0.0608978 | + | 0.105478i | ||||
\(949\) | −2.79707 | − | 4.84466i | −0.0907966 | − | 0.157264i | ||||
\(950\) | 32.9138 | − | 57.0084i | 1.06786 | − | 1.84960i | ||||
\(951\) | −2.80865 | −0.0910767 | ||||||||
\(952\) | 29.9853 | + | 39.1150i | 0.971830 | + | 1.26772i | ||||
\(953\) | 17.0472 | 0.552212 | 0.276106 | − | 0.961127i | \(-0.410956\pi\) | ||||
0.276106 | + | 0.961127i | \(0.410956\pi\) | |||||||
\(954\) | 3.17225 | − | 5.49450i | 0.102705 | − | 0.177891i | ||||
\(955\) | 37.6045 | + | 65.1329i | 1.21685 | + | 2.10765i | ||||
\(956\) | 4.26490 | + | 7.38702i | 0.137937 | + | 0.238913i | ||||
\(957\) | 1.57113 | − | 2.72127i | 0.0507873 | − | 0.0879662i | ||||
\(958\) | −18.8043 | −0.607540 | ||||||||
\(959\) | 19.3818 | + | 25.2830i | 0.625872 | + | 0.816432i | ||||
\(960\) | −33.2623 | −1.07353 | ||||||||
\(961\) | −17.0744 | + | 29.5738i | −0.550788 | + | 0.953993i | ||||
\(962\) | 3.10358 | + | 5.37557i | 0.100064 | + | 0.173315i | ||||
\(963\) | −6.12909 | − | 10.6159i | −0.197507 | − | 0.342092i | ||||
\(964\) | −7.08653 | + | 12.2742i | −0.228242 | + | 0.395326i | ||||
\(965\) | −5.90538 | −0.190101 | ||||||||
\(966\) | 1.20817 | − | 2.91297i | 0.0388721 | − | 0.0937234i | ||||
\(967\) | 23.3640 | 0.751335 | 0.375667 | − | 0.926755i | \(-0.377413\pi\) | ||||
0.375667 | + | 0.926755i | \(0.377413\pi\) | |||||||
\(968\) | −13.4944 | + | 23.3730i | −0.433726 | + | 0.751235i | ||||
\(969\) | 17.8941 | + | 30.9935i | 0.574841 | + | 0.995653i | ||||
\(970\) | −15.3125 | − | 26.5221i | −0.491656 | − | 0.851573i | ||||
\(971\) | −18.4523 | + | 31.9603i | −0.592162 | + | 1.02565i | 0.401779 | + | 0.915737i | \(0.368392\pi\) |
−0.993941 | + | 0.109918i | \(0.964941\pi\) | |||||||
\(972\) | −0.579274 | −0.0185802 | ||||||||
\(973\) | −3.97523 | + | 0.521483i | −0.127440 | + | 0.0167180i | ||||
\(974\) | 48.3635 | 1.54967 | ||||||||
\(975\) | 2.15394 | − | 3.73073i | 0.0689812 | − | 0.119479i | ||||
\(976\) | 0.515994 | + | 0.893727i | 0.0165166 | + | 0.0286075i | ||||
\(977\) | −0.274426 | − | 0.475320i | −0.00877967 | − | 0.0152068i | 0.861602 | − | 0.507584i | \(-0.169461\pi\) |
−0.870382 | + | 0.492377i | \(0.836128\pi\) | |||||||
\(978\) | 2.17517 | − | 3.76750i | 0.0695542 | − | 0.120471i | ||||
\(979\) | −24.2652 | −0.775518 | ||||||||
\(980\) | 14.8411 | − | 3.96199i | 0.474082 | − | 0.126561i | ||||
\(981\) | −8.98838 | −0.286977 | ||||||||
\(982\) | −5.59607 | + | 9.69268i | −0.178578 | + | 0.309306i | ||||
\(983\) | −3.48677 | − | 6.03926i | −0.111211 | − | 0.192623i | 0.805048 | − | 0.593210i | \(-0.202140\pi\) |
−0.916259 | + | 0.400587i | \(0.868806\pi\) | |||||||
\(984\) | 8.04238 | + | 13.9298i | 0.256382 | + | 0.444066i | ||||
\(985\) | −4.69928 | + | 8.13940i | −0.149732 | + | 0.259343i | ||||
\(986\) | 15.2270 | 0.484926 | ||||||||
\(987\) | −12.0817 | + | 1.58492i | −0.384565 | + | 0.0504485i | ||||
\(988\) | −1.57627 | −0.0501479 | ||||||||
\(989\) | 2.32032 | − | 4.01891i | 0.0737819 | − | 0.127794i | ||||
\(990\) | −3.36482 | − | 5.82804i | −0.106941 | − | 0.185227i | ||||
\(991\) | 15.6563 | + | 27.1174i | 0.497337 | + | 0.861413i | 0.999995 | − | 0.00307193i | \(-0.000977828\pi\) |
−0.502658 | + | 0.864485i | \(0.667644\pi\) | |||||||
\(992\) | 12.7602 | − | 22.1014i | 0.405138 | − | 0.701720i | ||||
\(993\) | −27.0983 | −0.859937 | ||||||||
\(994\) | −8.28187 | + | 19.9681i | −0.262685 | + | 0.633351i | ||||
\(995\) | 20.0489 | 0.635593 | ||||||||
\(996\) | −1.35556 | + | 2.34789i | −0.0429524 | + | 0.0743957i | ||||
\(997\) | −22.6062 | − | 39.1551i | −0.715947 | − | 1.24006i | −0.962593 | − | 0.270950i | \(-0.912662\pi\) |
0.246647 | − | 0.969105i | \(-0.420671\pi\) | |||||||
\(998\) | −11.3700 | − | 19.6933i | −0.359910 | − | 0.623382i | ||||
\(999\) | −5.65171 | + | 9.78904i | −0.178812 | + | 0.309712i |
(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 | 483.2.i.g.415.4 | yes | 16 | |
7.2 | even | 3 | 3381.2.a.bf.1.5 | 8 | |||
7.4 | even | 3 | inner | 483.2.i.g.277.4 | ✓ | 16 | |
7.5 | odd | 6 | 3381.2.a.be.1.5 | 8 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
483.2.i.g.277.4 | ✓ | 16 | 7.4 | even | 3 | inner | |
483.2.i.g.415.4 | yes | 16 | 1.1 | even | 1 | trivial | |
3381.2.a.be.1.5 | 8 | 7.5 | odd | 6 | |||
3381.2.a.bf.1.5 | 8 | 7.2 | even | 3 |