Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [369,3,Mod(55,369)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(369, base_ring=CyclotomicField(8))
chi = DirichletCharacter(H, H._module([0, 5]))
N = Newforms(chi, 3, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("369.55");
S:= CuspForms(chi, 3);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 369 = 3^{2} \cdot 41 \) |
Weight: | \( k \) | \(=\) | \( 3 \) |
Character orbit: | \([\chi]\) | \(=\) | 369.l (of order \(8\), 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: | \(10.0545217549\) |
Analytic rank: | \(0\) |
Dimension: | \(20\) |
Relative dimension: | \(5\) over \(\Q(\zeta_{8})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{20} + \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{20} + 66 x^{18} + 1853 x^{16} + 28868 x^{14} + 272678 x^{12} + 1600296 x^{10} + 5739482 x^{8} + \cdots + 776161 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 41) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{8}]$ |
Embedding invariants
Embedding label | 109.5 | ||
Root | \(3.37131i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 369.109 |
Dual form | 369.3.l.b.325.5 |
$q$-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 \(\left(\mathbb{Z}/369\mathbb{Z}\right)^\times\).
\(n\) | \(83\) | \(334\) |
\(\chi(n)\) | \(1\) | \(e\left(\frac{1}{8}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 2.38388 | + | 2.38388i | 1.19194 | + | 1.19194i | 0.976522 | + | 0.215418i | \(0.0691112\pi\) |
0.215418 | + | 0.976522i | \(0.430889\pi\) | |||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 7.36576i | 1.84144i | ||||||||
\(5\) | −2.78016 | + | 2.78016i | −0.556032 | + | 0.556032i | −0.928175 | − | 0.372144i | \(-0.878623\pi\) |
0.372144 | + | 0.928175i | \(0.378623\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | −9.79337 | + | 4.05655i | −1.39905 | + | 0.579506i | −0.949506 | − | 0.313750i | \(-0.898415\pi\) |
−0.449547 | + | 0.893257i | \(0.648415\pi\) | |||||||
\(8\) | −8.02356 | + | 8.02356i | −1.00295 | + | 1.00295i | ||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −13.2551 | −1.32551 | ||||||||
\(11\) | −4.61148 | − | 11.1331i | −0.419225 | − | 1.01210i | −0.982573 | − | 0.185879i | \(-0.940487\pi\) |
0.563347 | − | 0.826220i | \(-0.309513\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.11730 | + | 0.877014i | −0.162869 | + | 0.0674626i | −0.462628 | − | 0.886552i | \(-0.653094\pi\) |
0.299759 | + | 0.954015i | \(0.403094\pi\) | |||||||
\(14\) | −33.0165 | − | 13.6759i | −2.35832 | − | 0.976849i | ||||
\(15\) | 0 | 0 | ||||||||
\(16\) | −8.79138 | −0.549461 | ||||||||
\(17\) | 2.83394 | + | 1.17386i | 0.166702 | + | 0.0690504i | 0.464474 | − | 0.885587i | \(-0.346243\pi\) |
−0.297772 | + | 0.954637i | \(0.596243\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 8.73721 | + | 3.61907i | 0.459853 | + | 0.190477i | 0.600569 | − | 0.799573i | \(-0.294941\pi\) |
−0.140716 | + | 0.990050i | \(0.544941\pi\) | |||||||
\(20\) | −20.4780 | − | 20.4780i | −1.02390 | − | 1.02390i | ||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 15.5467 | − | 37.5332i | 0.706670 | − | 1.70605i | ||||
\(23\) | 20.5237i | 0.892336i | 0.894949 | + | 0.446168i | \(0.147212\pi\) | ||||
−0.894949 | + | 0.446168i | \(0.852788\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 9.54144i | 0.381658i | ||||||||
\(26\) | −7.13808 | − | 2.95669i | −0.274541 | − | 0.113719i | ||||
\(27\) | 0 | 0 | ||||||||
\(28\) | −29.8795 | − | 72.1356i | −1.06713 | − | 2.57627i | ||||
\(29\) | −8.67290 | + | 3.59243i | −0.299066 | + | 0.123877i | −0.527171 | − | 0.849760i | \(-0.676747\pi\) |
0.228105 | + | 0.973637i | \(0.426747\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 33.7758i | 1.08954i | 0.838585 | + | 0.544771i | \(0.183383\pi\) | ||||
−0.838585 | + | 0.544771i | \(0.816617\pi\) | |||||||
\(32\) | 11.1367 | + | 11.1367i | 0.348021 | + | 0.348021i | ||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 3.95744 | + | 9.55410i | 0.116395 | + | 0.281003i | ||||
\(35\) | 15.9493 | − | 38.5049i | 0.455693 | − | 1.10014i | ||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −60.1877 | −1.62669 | −0.813347 | − | 0.581778i | \(-0.802357\pi\) | ||||
−0.813347 | + | 0.581778i | \(0.802357\pi\) | |||||||
\(38\) | 12.2010 | + | 29.4559i | 0.321079 | + | 0.775154i | ||||
\(39\) | 0 | 0 | ||||||||
\(40\) | − | 44.6136i | − | 1.11534i | ||||||
\(41\) | 6.99603 | + | 40.3987i | 0.170635 | + | 0.985334i | ||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 6.83594 | + | 6.83594i | 0.158975 | + | 0.158975i | 0.782112 | − | 0.623137i | \(-0.214142\pi\) |
−0.623137 | + | 0.782112i | \(0.714142\pi\) | |||||||
\(44\) | 82.0037 | − | 33.9670i | 1.86372 | − | 0.771978i | ||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −48.9261 | + | 48.9261i | −1.06361 | + | 1.06361i | ||||
\(47\) | −0.199100 | − | 0.0824700i | −0.00423618 | − | 0.00175468i | 0.380564 | − | 0.924754i | \(-0.375730\pi\) |
−0.384801 | + | 0.923000i | \(0.625730\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 44.8062 | − | 44.8062i | 0.914413 | − | 0.914413i | ||||
\(50\) | −22.7456 | + | 22.7456i | −0.454913 | + | 0.454913i | ||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −6.45987 | − | 15.5955i | −0.124228 | − | 0.299914i | ||||
\(53\) | 6.93524 | + | 16.7431i | 0.130854 | + | 0.315908i | 0.975704 | − | 0.219095i | \(-0.0703104\pi\) |
−0.844850 | + | 0.535003i | \(0.820310\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 43.7724 | + | 18.1311i | 0.795862 | + | 0.329657i | ||||
\(56\) | 46.0298 | − | 111.126i | 0.821960 | − | 1.98439i | ||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −29.2391 | − | 12.1112i | −0.504122 | − | 0.208814i | ||||
\(59\) | 36.2067 | 0.613673 | 0.306836 | − | 0.951762i | \(-0.400730\pi\) | ||||
0.306836 | + | 0.951762i | \(0.400730\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −81.0896 | − | 81.0896i | −1.32934 | − | 1.32934i | −0.905947 | − | 0.423391i | \(-0.860840\pi\) |
−0.423391 | − | 0.905947i | \(-0.639160\pi\) | |||||||
\(62\) | −80.5174 | + | 80.5174i | −1.29867 | + | 1.29867i | ||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 88.2625i | 1.37910i | ||||||||
\(65\) | 3.44819 | − | 8.32466i | 0.0530490 | − | 0.128072i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | 49.6077 | + | 20.5482i | 0.740413 | + | 0.306689i | 0.720823 | − | 0.693119i | \(-0.243764\pi\) |
0.0195897 | + | 0.999808i | \(0.493764\pi\) | |||||||
\(68\) | −8.64634 | + | 20.8741i | −0.127152 | + | 0.306972i | ||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 129.812 | − | 53.7700i | 1.85446 | − | 0.768143i | ||||
\(71\) | 13.8205 | − | 5.72464i | 0.194655 | − | 0.0806287i | −0.283227 | − | 0.959053i | \(-0.591405\pi\) |
0.477881 | + | 0.878424i | \(0.341405\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 47.3455 | + | 47.3455i | 0.648569 | + | 0.648569i | 0.952647 | − | 0.304078i | \(-0.0983484\pi\) |
−0.304078 | + | 0.952647i | \(0.598348\pi\) | |||||||
\(74\) | −143.480 | − | 143.480i | −1.93892 | − | 1.93892i | ||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −26.6572 | + | 64.3562i | −0.350753 | + | 0.846792i | ||||
\(77\) | 90.3238 | + | 90.3238i | 1.17304 | + | 1.17304i | ||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 14.7604 | + | 35.6349i | 0.186841 | + | 0.451074i | 0.989348 | − | 0.145568i | \(-0.0465010\pi\) |
−0.802507 | + | 0.596643i | \(0.796501\pi\) | |||||||
\(80\) | 24.4414 | − | 24.4414i | 0.305518 | − | 0.305518i | ||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −79.6280 | + | 112.983i | −0.971073 | + | 1.37785i | ||||
\(83\) | 99.1394 | 1.19445 | 0.597225 | − | 0.802073i | \(-0.296270\pi\) | ||||
0.597225 | + | 0.802073i | \(0.296270\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −11.1423 | + | 4.61529i | −0.131086 | + | 0.0542976i | ||||
\(86\) | 32.5921i | 0.378978i | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 126.328 | + | 52.3266i | 1.43554 | + | 0.594620i | ||||
\(89\) | 40.3183 | − | 16.7004i | 0.453015 | − | 0.187645i | −0.144497 | − | 0.989505i | \(-0.546156\pi\) |
0.597511 | + | 0.801860i | \(0.296156\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 17.1778 | − | 17.1778i | 0.188767 | − | 0.188767i | ||||
\(92\) | −151.173 | −1.64318 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | −0.278032 | − | 0.671230i | −0.00295779 | − | 0.00714074i | ||||
\(95\) | −34.3524 | + | 14.2292i | −0.361604 | + | 0.149781i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 50.8068 | − | 122.659i | 0.523782 | − | 1.26452i | −0.411756 | − | 0.911294i | \(-0.635084\pi\) |
0.935538 | − | 0.353227i | \(-0.114916\pi\) | |||||||
\(98\) | 213.625 | 2.17985 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | −70.2800 | −0.702800 | ||||||||
\(101\) | −137.221 | − | 56.8388i | −1.35862 | − | 0.562761i | −0.419944 | − | 0.907550i | \(-0.637950\pi\) |
−0.938680 | + | 0.344789i | \(0.887950\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 127.979 | − | 127.979i | 1.24252 | − | 1.24252i | 0.283565 | − | 0.958953i | \(-0.408483\pi\) |
0.958953 | − | 0.283565i | \(-0.0915170\pi\) | |||||||
\(104\) | 9.95150 | − | 24.0251i | 0.0956875 | − | 0.231010i | ||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −23.3809 | + | 56.4464i | −0.220574 | + | 0.532513i | ||||
\(107\) | − | 69.5523i | − | 0.650022i | −0.945710 | − | 0.325011i | \(-0.894632\pi\) | ||
0.945710 | − | 0.325011i | \(-0.105368\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 10.0089 | − | 24.1636i | 0.0918247 | − | 0.221684i | −0.871294 | − | 0.490762i | \(-0.836719\pi\) |
0.963119 | + | 0.269077i | \(0.0867186\pi\) | |||||||
\(110\) | 61.1257 | + | 147.571i | 0.555688 | + | 1.34155i | ||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 86.0972 | − | 35.6626i | 0.768725 | − | 0.318416i | ||||
\(113\) | 183.205i | 1.62129i | 0.585541 | + | 0.810643i | \(0.300882\pi\) | ||||
−0.585541 | + | 0.810643i | \(0.699118\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −57.0592 | − | 57.0592i | −0.496167 | − | 0.496167i | ||||
\(116\) | −26.4610 | − | 63.8825i | −0.228112 | − | 0.550711i | ||||
\(117\) | 0 | 0 | ||||||||
\(118\) | 86.3124 | + | 86.3124i | 0.731461 | + | 0.731461i | ||||
\(119\) | −32.5156 | −0.273240 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −17.1201 | + | 17.1201i | −0.141489 | + | 0.141489i | ||||
\(122\) | − | 386.616i | − | 3.16898i | ||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −248.784 | −2.00633 | ||||||||
\(125\) | −96.0307 | − | 96.0307i | −0.768245 | − | 0.768245i | ||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 147.141i | 1.15859i | 0.815119 | + | 0.579294i | \(0.196672\pi\) | ||||
−0.815119 | + | 0.579294i | \(0.803328\pi\) | |||||||
\(128\) | −165.860 | + | 165.860i | −1.29578 | + | 1.29578i | ||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 28.0650 | − | 11.6249i | 0.215885 | − | 0.0894225i | ||||
\(131\) | −94.0344 | + | 94.0344i | −0.717820 | + | 0.717820i | −0.968158 | − | 0.250338i | \(-0.919458\pi\) |
0.250338 | + | 0.968158i | \(0.419458\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −100.248 | −0.753741 | ||||||||
\(134\) | 69.2743 | + | 167.243i | 0.516973 | + | 1.24808i | ||||
\(135\) | 0 | 0 | ||||||||
\(136\) | −32.1568 | + | 13.3198i | −0.236447 | + | 0.0979396i | ||||
\(137\) | 103.079 | + | 42.6969i | 0.752405 | + | 0.311656i | 0.725722 | − | 0.687988i | \(-0.241506\pi\) |
0.0266823 | + | 0.999644i | \(0.491506\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 106.826 | 0.768535 | 0.384268 | − | 0.923222i | \(-0.374454\pi\) | ||||
0.384268 | + | 0.923222i | \(0.374454\pi\) | |||||||
\(140\) | 283.618 | + | 117.478i | 2.02584 | + | 0.839132i | ||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 46.5932 | + | 19.2995i | 0.328121 | + | 0.135912i | ||||
\(143\) | 19.5278 | + | 19.5278i | 0.136558 | + | 0.136558i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 14.1245 | − | 34.0996i | 0.0974104 | − | 0.235170i | ||||
\(146\) | 225.732i | 1.54611i | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | − | 443.328i | − | 2.99546i | ||||||
\(149\) | 88.6747 | + | 36.7303i | 0.595132 | + | 0.246512i | 0.659857 | − | 0.751391i | \(-0.270617\pi\) |
−0.0647247 | + | 0.997903i | \(0.520617\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −15.5155 | − | 37.4578i | −0.102752 | − | 0.248065i | 0.864140 | − | 0.503252i | \(-0.167863\pi\) |
−0.966892 | + | 0.255187i | \(0.917863\pi\) | |||||||
\(152\) | −99.1414 | + | 41.0657i | −0.652246 | + | 0.270169i | ||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 430.642i | 2.79638i | ||||||||
\(155\) | −93.9021 | − | 93.9021i | −0.605820 | − | 0.605820i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 7.16318 | + | 17.2934i | 0.0456253 | + | 0.110149i | 0.945049 | − | 0.326928i | \(-0.106014\pi\) |
−0.899424 | + | 0.437078i | \(0.856014\pi\) | |||||||
\(158\) | −49.7621 | + | 120.136i | −0.314950 | + | 0.760357i | ||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −61.9234 | −0.387022 | ||||||||
\(161\) | −83.2555 | − | 200.996i | −0.517115 | − | 1.24843i | ||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 135.937i | 0.833972i | 0.908913 | + | 0.416986i | \(0.136914\pi\) | ||||
−0.908913 | + | 0.416986i | \(0.863086\pi\) | |||||||
\(164\) | −297.567 | + | 51.5311i | −1.81443 | + | 0.314214i | ||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 236.336 | + | 236.336i | 1.42371 | + | 1.42371i | ||||
\(167\) | −218.746 | + | 90.6077i | −1.30986 | + | 0.542561i | −0.924843 | − | 0.380350i | \(-0.875804\pi\) |
−0.385015 | + | 0.922910i | \(0.625804\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −115.787 | + | 115.787i | −0.685132 | + | 0.685132i | ||||
\(170\) | −37.5642 | − | 15.5596i | −0.220966 | − | 0.0915271i | ||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −50.3519 | + | 50.3519i | −0.292743 | + | 0.292743i | ||||
\(173\) | 36.3303 | − | 36.3303i | 0.210002 | − | 0.210002i | −0.594267 | − | 0.804268i | \(-0.702558\pi\) |
0.804268 | + | 0.594267i | \(0.202558\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | −38.7053 | − | 93.4428i | −0.221173 | − | 0.533959i | ||||
\(176\) | 40.5412 | + | 97.8752i | 0.230348 | + | 0.556109i | ||||
\(177\) | 0 | 0 | ||||||||
\(178\) | 135.926 | + | 56.3023i | 0.763627 | + | 0.316305i | ||||
\(179\) | −27.8175 | + | 67.1573i | −0.155405 | + | 0.375181i | −0.982337 | − | 0.187122i | \(-0.940084\pi\) |
0.826932 | + | 0.562302i | \(0.190084\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −80.9954 | − | 33.5494i | −0.447488 | − | 0.185356i | 0.147548 | − | 0.989055i | \(-0.452862\pi\) |
−0.595036 | + | 0.803699i | \(0.702862\pi\) | |||||||
\(182\) | 81.8998 | 0.449999 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −164.674 | − | 164.674i | −0.894965 | − | 0.894965i | ||||
\(185\) | 167.331 | − | 167.331i | 0.904494 | − | 0.904494i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | − | 36.9637i | − | 0.197667i | ||||||
\(188\) | 0.607454 | − | 1.46652i | 0.00323114 | − | 0.00780066i | ||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −115.813 | − | 47.9712i | −0.609541 | − | 0.252480i | ||||
\(191\) | 118.697 | − | 286.560i | 0.621451 | − | 1.50032i | −0.228549 | − | 0.973532i | \(-0.573398\pi\) |
0.850000 | − | 0.526783i | \(-0.176602\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 271.296 | − | 112.375i | 1.40568 | − | 0.582252i | 0.454460 | − | 0.890767i | \(-0.349832\pi\) |
0.951219 | + | 0.308515i | \(0.0998322\pi\) | |||||||
\(194\) | 413.520 | − | 171.286i | 2.13155 | − | 0.882916i | ||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 330.032 | + | 330.032i | 1.68384 | + | 1.68384i | ||||
\(197\) | −5.26587 | − | 5.26587i | −0.0267303 | − | 0.0267303i | 0.693615 | − | 0.720346i | \(-0.256017\pi\) |
−0.720346 | + | 0.693615i | \(0.756017\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −25.2153 | + | 60.8750i | −0.126710 | + | 0.305905i | −0.974486 | − | 0.224450i | \(-0.927941\pi\) |
0.847776 | + | 0.530355i | \(0.177941\pi\) | |||||||
\(200\) | −76.5564 | − | 76.5564i | −0.382782 | − | 0.382782i | ||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −191.622 | − | 462.615i | −0.948621 | − | 2.29017i | ||||
\(203\) | 70.3641 | − | 70.3641i | 0.346621 | − | 0.346621i | ||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −131.765 | − | 92.8647i | −0.642755 | − | 0.452999i | ||||
\(206\) | 610.174 | 2.96201 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | 18.6140 | − | 7.71016i | 0.0894902 | − | 0.0370681i | ||||
\(209\) | − | 113.961i | − | 0.545270i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 188.285 | + | 77.9903i | 0.892347 | + | 0.369622i | 0.781273 | − | 0.624190i | \(-0.214571\pi\) |
0.111074 | + | 0.993812i | \(0.464571\pi\) | |||||||
\(212\) | −123.326 | + | 51.0833i | −0.581726 | + | 0.240959i | ||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 165.804 | − | 165.804i | 0.774787 | − | 0.774787i | ||||
\(215\) | −38.0100 | −0.176791 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −137.013 | − | 330.779i | −0.631397 | − | 1.52433i | ||||
\(218\) | 81.4631 | − | 33.7431i | 0.373684 | − | 0.154785i | ||||
\(219\) | 0 | 0 | ||||||||
\(220\) | −133.549 | + | 322.417i | −0.607043 | + | 1.46553i | ||||
\(221\) | −7.02978 | −0.0318090 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −32.4398 | −0.145470 | −0.0727350 | − | 0.997351i | \(-0.523173\pi\) | ||||
−0.0727350 | + | 0.997351i | \(0.523173\pi\) | |||||||
\(224\) | −154.242 | − | 63.8891i | −0.688580 | − | 0.285219i | ||||
\(225\) | 0 | 0 | ||||||||
\(226\) | −436.739 | + | 436.739i | −1.93248 | + | 1.93248i | ||||
\(227\) | 51.2534 | − | 123.737i | 0.225786 | − | 0.545095i | −0.769871 | − | 0.638200i | \(-0.779679\pi\) |
0.995656 | + | 0.0931051i | \(0.0296793\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 43.8595 | − | 105.886i | 0.191526 | − | 0.462385i | −0.798722 | − | 0.601700i | \(-0.794490\pi\) |
0.990248 | + | 0.139315i | \(0.0444901\pi\) | |||||||
\(230\) | − | 272.045i | − | 1.18280i | ||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 40.7635 | − | 98.4117i | 0.175705 | − | 0.424188i | ||||
\(233\) | 55.5861 | + | 134.197i | 0.238567 | + | 0.575951i | 0.997135 | − | 0.0756424i | \(-0.0241008\pi\) |
−0.758568 | + | 0.651594i | \(0.774101\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0.782810 | − | 0.324250i | 0.00333111 | − | 0.00137979i | ||||
\(236\) | 266.690i | 1.13004i | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | −77.5133 | − | 77.5133i | −0.325686 | − | 0.325686i | ||||
\(239\) | −106.730 | − | 257.669i | −0.446568 | − | 1.07811i | −0.973599 | − | 0.228265i | \(-0.926695\pi\) |
0.527031 | − | 0.849846i | \(-0.323305\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −28.2681 | − | 28.2681i | −0.117295 | − | 0.117295i | 0.646023 | − | 0.763318i | \(-0.276431\pi\) |
−0.763318 | + | 0.646023i | \(0.776431\pi\) | |||||||
\(242\) | −81.6246 | −0.337292 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 597.287 | − | 597.287i | 2.44790 | − | 2.44790i | ||||
\(245\) | 249.137i | 1.01689i | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | −21.6732 | −0.0877459 | ||||||||
\(248\) | −271.002 | − | 271.002i | −1.09275 | − | 1.09275i | ||||
\(249\) | 0 | 0 | ||||||||
\(250\) | − | 457.851i | − | 1.83140i | ||||||
\(251\) | −90.3600 | + | 90.3600i | −0.360000 | + | 0.360000i | −0.863813 | − | 0.503813i | \(-0.831930\pi\) |
0.503813 | + | 0.863813i | \(0.331930\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 228.493 | − | 94.6448i | 0.903133 | − | 0.374090i | ||||
\(254\) | −350.766 | + | 350.766i | −1.38097 | + | 1.38097i | ||||
\(255\) | 0 | 0 | ||||||||
\(256\) | −437.732 | −1.70989 | ||||||||
\(257\) | −84.5632 | − | 204.154i | −0.329040 | − | 0.794372i | −0.998664 | − | 0.0516720i | \(-0.983545\pi\) |
0.669625 | − | 0.742700i | \(-0.266455\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 589.440 | − | 244.154i | 2.27583 | − | 0.942680i | ||||
\(260\) | 61.3175 | + | 25.3985i | 0.235836 | + | 0.0976866i | ||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −448.334 | −1.71120 | ||||||||
\(263\) | 435.904 | + | 180.557i | 1.65743 | + | 0.686530i | 0.997877 | − | 0.0651277i | \(-0.0207455\pi\) |
0.659553 | + | 0.751658i | \(0.270745\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −65.8296 | − | 27.2675i | −0.248414 | − | 0.102896i | ||||
\(266\) | −238.978 | − | 238.978i | −0.898414 | − | 0.898414i | ||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −151.353 | + | 365.398i | −0.564749 | + | 1.36343i | ||||
\(269\) | 38.3082i | 0.142410i | 0.997462 | + | 0.0712048i | \(0.0226844\pi\) | ||||
−0.997462 | + | 0.0712048i | \(0.977316\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | − | 66.2839i | − | 0.244590i | −0.992494 | − | 0.122295i | \(-0.960975\pi\) | ||
0.992494 | − | 0.122295i | \(-0.0390254\pi\) | |||||||
\(272\) | −24.9142 | − | 10.3198i | −0.0915964 | − | 0.0379405i | ||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 143.945 | + | 347.513i | 0.525345 | + | 1.26830i | ||||
\(275\) | 106.226 | − | 44.0002i | 0.386276 | − | 0.160001i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 330.119i | 1.19176i | 0.803072 | + | 0.595882i | \(0.203198\pi\) | ||||
−0.803072 | + | 0.595882i | \(0.796802\pi\) | |||||||
\(278\) | 254.661 | + | 254.661i | 0.916047 | + | 0.916047i | ||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 180.977 | + | 436.917i | 0.646346 | + | 1.56042i | ||||
\(281\) | −168.265 | + | 406.227i | −0.598807 | + | 1.44565i | 0.275991 | + | 0.961160i | \(0.410994\pi\) |
−0.874798 | + | 0.484488i | \(0.839006\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −127.048 | −0.448933 | −0.224467 | − | 0.974482i | \(-0.572064\pi\) | ||||
−0.224467 | + | 0.974482i | \(0.572064\pi\) | |||||||
\(284\) | 42.1663 | + | 101.798i | 0.148473 | + | 0.358445i | ||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 93.1036i | 0.325537i | ||||||||
\(287\) | −232.394 | − | 367.260i | −0.809735 | − | 1.27965i | ||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −197.701 | − | 197.701i | −0.684085 | − | 0.684085i | ||||
\(290\) | 114.960 | − | 47.6182i | 0.396415 | − | 0.164201i | ||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −348.736 | + | 348.736i | −1.19430 | + | 1.19430i | ||||
\(293\) | −393.156 | − | 162.851i | −1.34183 | − | 0.555804i | −0.407823 | − | 0.913061i | \(-0.633712\pi\) |
−0.934006 | + | 0.357257i | \(0.883712\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −100.660 | + | 100.660i | −0.341221 | + | 0.341221i | ||||
\(296\) | 482.920 | − | 482.920i | 1.63149 | − | 1.63149i | ||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 123.829 | + | 298.950i | 0.415534 | + | 1.00319i | ||||
\(299\) | −17.9996 | − | 43.4549i | −0.0601993 | − | 0.145334i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | −94.6771 | − | 39.2165i | −0.314542 | − | 0.130288i | ||||
\(302\) | 52.3077 | − | 126.282i | 0.173204 | − | 0.418152i | ||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −76.8121 | − | 31.8166i | −0.252671 | − | 0.104660i | ||||
\(305\) | 450.884 | 1.47831 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −327.066 | − | 327.066i | −1.06536 | − | 1.06536i | −0.997709 | − | 0.0676533i | \(-0.978449\pi\) |
−0.0676533 | − | 0.997709i | \(-0.521551\pi\) | |||||||
\(308\) | −665.303 | + | 665.303i | −2.16008 | + | 2.16008i | ||||
\(309\) | 0 | 0 | ||||||||
\(310\) | − | 447.702i | − | 1.44420i | ||||||
\(311\) | −43.4851 | + | 104.982i | −0.139823 | + | 0.337564i | −0.978243 | − | 0.207461i | \(-0.933480\pi\) |
0.838420 | + | 0.545025i | \(0.183480\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 353.499 | + | 146.424i | 1.12939 | + | 0.467808i | 0.867573 | − | 0.497309i | \(-0.165679\pi\) |
0.261816 | + | 0.965118i | \(0.415679\pi\) | |||||||
\(314\) | −24.1493 | + | 58.3016i | −0.0769087 | + | 0.185674i | ||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −262.478 | + | 108.722i | −0.830626 | + | 0.344057i | ||||
\(317\) | −346.574 | + | 143.556i | −1.09329 | + | 0.452857i | −0.855154 | − | 0.518374i | \(-0.826537\pi\) |
−0.238139 | + | 0.971231i | \(0.576537\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 79.9898 | + | 79.9898i | 0.250752 | + | 0.250752i | ||||
\(320\) | −245.384 | − | 245.384i | −0.766824 | − | 0.766824i | ||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 280.680 | − | 677.622i | 0.871678 | − | 2.10442i | ||||
\(323\) | 20.5124 | + | 20.5124i | 0.0635060 | + | 0.0635060i | ||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −8.36798 | − | 20.2021i | −0.0257476 | − | 0.0621602i | ||||
\(326\) | −324.058 | + | 324.058i | −0.994044 | + | 0.994044i | ||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −380.275 | − | 268.009i | −1.15937 | − | 0.817099i | ||||
\(329\) | 2.28441 | 0.00694348 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −284.193 | + | 117.717i | −0.858589 | + | 0.355639i | −0.768155 | − | 0.640263i | \(-0.778825\pi\) |
−0.0904333 | + | 0.995903i | \(0.528825\pi\) | |||||||
\(332\) | 730.237i | 2.19951i | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | −737.462 | − | 305.467i | −2.20797 | − | 0.914571i | ||||
\(335\) | −195.044 | + | 80.7900i | −0.582222 | + | 0.241164i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −440.163 | + | 440.163i | −1.30612 | + | 1.30612i | −0.381928 | + | 0.924192i | \(0.624740\pi\) |
−0.924192 | + | 0.381928i | \(0.875260\pi\) | |||||||
\(338\) | −552.046 | −1.63327 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −33.9951 | − | 82.0715i | −0.0999857 | − | 0.241387i | ||||
\(341\) | 376.029 | − | 155.756i | 1.10272 | − | 0.456764i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −58.2747 | + | 140.688i | −0.169897 | + | 0.410168i | ||||
\(344\) | −109.697 | −0.318887 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 173.214 | 0.500618 | ||||||||
\(347\) | 363.094 | + | 150.398i | 1.04638 | + | 0.433425i | 0.838598 | − | 0.544751i | \(-0.183376\pi\) |
0.207782 | + | 0.978175i | \(0.433376\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −65.9189 | + | 65.9189i | −0.188879 | + | 0.188879i | −0.795212 | − | 0.606332i | \(-0.792640\pi\) |
0.606332 | + | 0.795212i | \(0.292640\pi\) | |||||||
\(350\) | 130.488 | − | 315.025i | 0.372822 | − | 0.900072i | ||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 72.6291 | − | 175.342i | 0.206333 | − | 0.498131i | ||||
\(353\) | − | 548.467i | − | 1.55373i | −0.629667 | − | 0.776865i | \(-0.716809\pi\) | ||
0.629667 | − | 0.776865i | \(-0.283191\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | −22.5078 | + | 54.3385i | −0.0634022 | + | 0.153066i | ||||
\(356\) | 123.011 | + | 296.975i | 0.345537 | + | 0.834199i | ||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −226.408 | + | 93.7814i | −0.632426 | + | 0.261959i | ||||
\(359\) | 204.799i | 0.570470i | 0.958458 | + | 0.285235i | \(0.0920717\pi\) | ||||
−0.958458 | + | 0.285235i | \(0.907928\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −192.024 | − | 192.024i | −0.531924 | − | 0.531924i | ||||
\(362\) | −113.105 | − | 273.061i | −0.312446 | − | 0.754312i | ||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 126.528 | + | 126.528i | 0.347604 | + | 0.347604i | ||||
\(365\) | −263.256 | −0.721249 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −387.267 | + | 387.267i | −1.05522 | + | 1.05522i | −0.0568391 | + | 0.998383i | \(0.518102\pi\) |
−0.998383 | + | 0.0568391i | \(0.981898\pi\) | |||||||
\(368\) | − | 180.432i | − | 0.490304i | ||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 797.795 | 2.15620 | ||||||||
\(371\) | −135.839 | − | 135.839i | −0.366142 | − | 0.366142i | ||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.5539i | 0.0390186i | 0.999810 | + | 0.0195093i | \(0.00621040\pi\) | ||||
−0.999810 | + | 0.0195093i | \(0.993790\pi\) | |||||||
\(374\) | 88.1171 | − | 88.1171i | 0.235607 | − | 0.235607i | ||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 2.25920 | − | 0.935790i | 0.00600850 | − | 0.00248880i | ||||
\(377\) | 15.2125 | − | 15.2125i | 0.0403515 | − | 0.0403515i | ||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 589.750 | 1.55607 | 0.778034 | − | 0.628222i | \(-0.216217\pi\) | ||||
0.778034 | + | 0.628222i | \(0.216217\pi\) | |||||||
\(380\) | −104.809 | − | 253.032i | −0.275813 | − | 0.665872i | ||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 966.085 | − | 400.165i | 2.52902 | − | 1.04755i | ||||
\(383\) | 363.597 | + | 150.607i | 0.949340 | + | 0.393229i | 0.802983 | − | 0.596002i | \(-0.203245\pi\) |
0.146357 | + | 0.989232i | \(0.453245\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −502.229 | −1.30449 | ||||||||
\(386\) | 914.625 | + | 378.850i | 2.36949 | + | 0.981476i | ||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 903.473 | + | 374.231i | 2.32854 | + | 0.964512i | ||||
\(389\) | −353.165 | − | 353.165i | −0.907879 | − | 0.907879i | 0.0882215 | − | 0.996101i | \(-0.471882\pi\) |
−0.996101 | + | 0.0882215i | \(0.971882\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −24.0919 | + | 58.1630i | −0.0616161 | + | 0.148755i | ||||
\(392\) | 719.012i | 1.83421i | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | − | 25.1064i | − | 0.0637219i | ||||||
\(395\) | −140.107 | − | 58.0342i | −0.354701 | − | 0.146922i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −70.4174 | − | 170.003i | −0.177374 | − | 0.428218i | 0.810040 | − | 0.586374i | \(-0.199445\pi\) |
−0.987414 | + | 0.158156i | \(0.949445\pi\) | |||||||
\(398\) | −205.229 | + | 85.0086i | −0.515651 | + | 0.213589i | ||||
\(399\) | 0 | 0 | ||||||||
\(400\) | − | 83.8824i | − | 0.209706i | ||||||
\(401\) | 95.8849 | + | 95.8849i | 0.239114 | + | 0.239114i | 0.816483 | − | 0.577369i | \(-0.195921\pi\) |
−0.577369 | + | 0.816483i | \(0.695921\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −29.6218 | − | 71.5134i | −0.0735033 | − | 0.177453i | ||||
\(404\) | 418.661 | − | 1010.74i | 1.03629 | − | 2.50182i | ||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 335.479 | 0.826302 | ||||||||
\(407\) | 277.554 | + | 670.075i | 0.681952 | + | 1.64638i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | − | 108.593i | − | 0.265509i | −0.991149 | − | 0.132755i | \(-0.957618\pi\) | ||
0.991149 | − | 0.132755i | \(-0.0423822\pi\) | |||||||
\(410\) | −92.7332 | − | 535.490i | −0.226179 | − | 1.30607i | ||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 942.665 | + | 942.665i | 2.28802 | + | 2.28802i | ||||
\(413\) | −354.585 | + | 146.874i | −0.858560 | + | 0.355627i | ||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −275.623 | + | 275.623i | −0.664152 | + | 0.664152i | ||||
\(416\) | −33.3467 | − | 13.8126i | −0.0801603 | − | 0.0332035i | ||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 271.670 | − | 271.670i | 0.649929 | − | 0.649929i | ||||
\(419\) | 201.190 | − | 201.190i | 0.480167 | − | 0.480167i | −0.425018 | − | 0.905185i | \(-0.639732\pi\) |
0.905185 | + | 0.425018i | \(0.139732\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 26.2486 | + | 63.3697i | 0.0623482 | + | 0.150522i | 0.951983 | − | 0.306151i | \(-0.0990411\pi\) |
−0.889635 | + | 0.456673i | \(0.849041\pi\) | |||||||
\(422\) | 262.930 | + | 634.769i | 0.623056 | + | 1.50419i | ||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −189.985 | − | 78.6944i | −0.448078 | − | 0.185600i | ||||
\(425\) | −11.2003 | + | 27.0399i | −0.0263536 | + | 0.0636232i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 1123.08 | + | 465.197i | 2.63017 | + | 1.08945i | ||||
\(428\) | 512.306 | 1.19698 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | −90.6112 | − | 90.6112i | −0.210724 | − | 0.210724i | ||||
\(431\) | −75.2035 | + | 75.2035i | −0.174486 | + | 0.174486i | −0.788947 | − | 0.614461i | \(-0.789373\pi\) |
0.614461 | + | 0.788947i | \(0.289373\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 725.948i | 1.67655i | 0.545245 | + | 0.838277i | \(0.316437\pi\) | ||||
−0.545245 | + | 0.838277i | \(0.683563\pi\) | |||||||
\(434\) | 461.914 | − | 1115.16i | 1.06432 | − | 2.56949i | ||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 177.983 | + | 73.7231i | 0.408219 | + | 0.169090i | ||||
\(437\) | −74.2768 | + | 179.320i | −0.169970 | + | 0.410344i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 368.226 | − | 152.524i | 0.838784 | − | 0.347436i | 0.0784103 | − | 0.996921i | \(-0.475016\pi\) |
0.760374 | + | 0.649485i | \(0.225016\pi\) | |||||||
\(440\) | −496.687 | + | 205.734i | −1.12883 | + | 0.467578i | ||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −16.7582 | − | 16.7582i | −0.0379144 | − | 0.0379144i | ||||
\(443\) | 256.839 | + | 256.839i | 0.579772 | + | 0.579772i | 0.934840 | − | 0.355069i | \(-0.115542\pi\) |
−0.355069 | + | 0.934840i | \(0.615542\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −65.6615 | + | 158.521i | −0.147554 | + | 0.356227i | ||||
\(446\) | −77.3326 | − | 77.3326i | −0.173391 | − | 0.173391i | ||||
\(447\) | 0 | 0 | ||||||||
\(448\) | −358.041 | − | 864.387i | −0.799198 | − | 1.92944i | ||||
\(449\) | 326.223 | − | 326.223i | 0.726555 | − | 0.726555i | −0.243377 | − | 0.969932i | \(-0.578255\pi\) |
0.969932 | + | 0.243377i | \(0.0782551\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 417.501 | − | 264.185i | 0.925722 | − | 0.585777i | ||||
\(452\) | −1349.45 | −2.98550 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 417.155 | − | 172.791i | 0.918843 | − | 0.380597i | ||||
\(455\) | 95.5142i | 0.209921i | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −454.419 | − | 188.227i | −0.994353 | − | 0.411875i | −0.174630 | − | 0.984634i | \(-0.555873\pi\) |
−0.819723 | + | 0.572760i | \(0.805873\pi\) | |||||||
\(458\) | 356.976 | − | 147.864i | 0.779423 | − | 0.322848i | ||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 420.285 | − | 420.285i | 0.913662 | − | 0.913662i | ||||
\(461\) | 37.6854 | 0.0817471 | 0.0408735 | − | 0.999164i | \(-0.486986\pi\) | ||||
0.0408735 | + | 0.999164i | \(0.486986\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 306.369 | + | 739.640i | 0.661704 | + | 1.59750i | 0.795132 | + | 0.606437i | \(0.207402\pi\) |
−0.133427 | + | 0.991059i | \(0.542598\pi\) | |||||||
\(464\) | 76.2468 | − | 31.5824i | 0.164325 | − | 0.0680656i | ||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −187.398 | + | 452.419i | −0.402142 | + | 0.970856i | ||||
\(467\) | 258.503 | 0.553539 | 0.276769 | − | 0.960936i | \(-0.410736\pi\) | ||||
0.276769 | + | 0.960936i | \(0.410736\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −569.181 | −1.21360 | ||||||||
\(470\) | 2.63910 | + | 1.09315i | 0.00561510 | + | 0.00232585i | ||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −290.507 | + | 290.507i | −0.615480 | + | 0.615480i | ||||
\(473\) | 44.5813 | − | 107.629i | 0.0942523 | − | 0.227545i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −34.5311 | + | 83.3656i | −0.0726971 | + | 0.175506i | ||||
\(476\) | − | 239.502i | − | 0.503156i | ||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 359.820 | − | 868.681i | 0.752761 | − | 1.81733i | ||||
\(479\) | 60.1434 | + | 145.199i | 0.125560 | + | 0.303130i | 0.974143 | − | 0.225934i | \(-0.0725433\pi\) |
−0.848582 | + | 0.529064i | \(0.822543\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 127.435 | − | 52.7854i | 0.264938 | − | 0.109741i | ||||
\(482\) | − | 134.776i | − | 0.279617i | ||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −126.103 | − | 126.103i | −0.260543 | − | 0.260543i | ||||
\(485\) | 199.759 | + | 482.261i | 0.411874 | + | 0.994353i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −73.4726 | − | 73.4726i | −0.150868 | − | 0.150868i | 0.627638 | − | 0.778506i | \(-0.284022\pi\) |
−0.778506 | + | 0.627638i | \(0.784022\pi\) | |||||||
\(488\) | 1301.26 | 2.66651 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −593.912 | + | 593.912i | −1.21207 | + | 1.21207i | ||||
\(491\) | 637.590i | 1.29855i | 0.760552 | + | 0.649277i | \(0.224928\pi\) | ||||
−0.760552 | + | 0.649277i | \(0.775072\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −28.7955 | −0.0584087 | ||||||||
\(494\) | −51.6664 | − | 51.6664i | −0.104588 | − | 0.104588i | ||||
\(495\) | 0 | 0 | ||||||||
\(496\) | − | 296.936i | − | 0.598661i | ||||||
\(497\) | −112.127 | + | 112.127i | −0.225607 | + | 0.225607i | ||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −401.985 | + | 166.508i | −0.805581 | + | 0.333683i | −0.747190 | − | 0.664611i | \(-0.768597\pi\) |
−0.0583919 | + | 0.998294i | \(0.518597\pi\) | |||||||
\(500\) | 707.339 | − | 707.339i | 1.41468 | − | 1.41468i | ||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −430.814 | −0.858196 | ||||||||
\(503\) | −116.671 | − | 281.668i | −0.231949 | − | 0.559975i | 0.764457 | − | 0.644675i | \(-0.223007\pi\) |
−0.996407 | + | 0.0846991i | \(0.973007\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 539.517 | − | 223.475i | 1.06835 | − | 0.442525i | ||||
\(506\) | 770.321 | + | 319.077i | 1.52237 | + | 0.630587i | ||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −1083.80 | −2.13347 | ||||||||
\(509\) | −52.4461 | − | 21.7239i | −0.103038 | − | 0.0426796i | 0.330569 | − | 0.943782i | \(-0.392759\pi\) |
−0.433607 | + | 0.901102i | \(0.642759\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −655.731 | − | 271.613i | −1.28323 | − | 0.531532i | ||||
\(512\) | −380.059 | − | 380.059i | −0.742304 | − | 0.742304i | ||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 285.089 | − | 688.266i | 0.554648 | − | 1.33904i | ||||
\(515\) | 711.606i | 1.38176i | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 2.59691i | 0.00502304i | ||||||||
\(518\) | 1987.19 | + | 823.120i | 3.83627 | + | 1.58904i | ||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 39.1267 | + | 94.4602i | 0.0752436 | + | 0.181654i | ||||
\(521\) | 206.145 | − | 85.3882i | 0.395673 | − | 0.163893i | −0.175970 | − | 0.984395i | \(-0.556306\pi\) |
0.571643 | + | 0.820503i | \(0.306306\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 940.733i | 1.79872i | 0.437204 | + | 0.899362i | \(0.355969\pi\) | ||||
−0.437204 | + | 0.899362i | \(0.644031\pi\) | |||||||
\(524\) | −692.635 | − | 692.635i | −1.32182 | − | 1.32182i | ||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 608.716 | + | 1469.57i | 1.15725 | + | 2.79386i | ||||
\(527\) | −39.6479 | + | 95.7186i | −0.0752333 | + | 0.181629i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 107.776 | 0.203736 | ||||||||
\(530\) | −91.9274 | − | 221.932i | −0.173448 | − | 0.418740i | ||||
\(531\) | 0 | 0 | ||||||||
\(532\) | − | 738.400i | − | 1.38797i | ||||||
\(533\) | −50.2429 | − | 79.4005i | −0.0942643 | − | 0.148969i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 193.366 | + | 193.366i | 0.361433 | + | 0.361433i | ||||
\(536\) | −562.900 | + | 233.161i | −1.05019 | + | 0.435001i | ||||
\(537\) | 0 | 0 | ||||||||
\(538\) | −91.3221 | + | 91.3221i | −0.169744 | + | 0.169744i | ||||
\(539\) | −705.455 | − | 292.209i | −1.30882 | − | 0.542132i | ||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 295.995 | − | 295.995i | 0.547126 | − | 0.547126i | −0.378483 | − | 0.925608i | \(-0.623554\pi\) |
0.925608 | + | 0.378483i | \(0.123554\pi\) | |||||||
\(542\) | 158.013 | − | 158.013i | 0.291537 | − | 0.291537i | ||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 18.4878 | + | 44.6335i | 0.0339849 | + | 0.0820469i | ||||
\(545\) | 39.3523 | + | 95.0049i | 0.0722061 | + | 0.174321i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −1.25534 | − | 0.519979i | −0.00229496 | − | 0.000950602i | 0.381536 | − | 0.924354i | \(-0.375395\pi\) |
−0.383831 | + | 0.923404i | \(0.625395\pi\) | |||||||
\(548\) | −314.495 | + | 759.258i | −0.573896 | + | 1.38551i | ||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 358.120 | + | 148.338i | 0.651128 | + | 0.269706i | ||||
\(551\) | −88.7782 | −0.161122 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −289.109 | − | 289.109i | −0.522801 | − | 0.522801i | ||||
\(554\) | −786.963 | + | 786.963i | −1.42051 | + | 1.42051i | ||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 786.857i | 1.41521i | ||||||||
\(557\) | −199.594 | + | 481.864i | −0.358338 | + | 0.865105i | 0.637196 | + | 0.770702i | \(0.280094\pi\) |
−0.995534 | + | 0.0944032i | \(0.969906\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −20.4689 | − | 8.47851i | −0.0366170 | − | 0.0151673i | ||||
\(560\) | −140.216 | + | 338.511i | −0.250386 | + | 0.604485i | ||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1369.52 | + | 567.273i | −2.43687 | + | 1.00938i | ||||
\(563\) | 507.071 | − | 210.036i | 0.900658 | − | 0.373065i | 0.116185 | − | 0.993228i | \(-0.462933\pi\) |
0.784473 | + | 0.620163i | \(0.212933\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −509.340 | − | 509.340i | −0.901486 | − | 0.901486i | ||||
\(566\) | −302.867 | − | 302.867i | −0.535101 | − | 0.535101i | ||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −64.9576 | + | 156.822i | −0.114362 | + | 0.276094i | ||||
\(569\) | −59.4295 | − | 59.4295i | −0.104446 | − | 0.104446i | 0.652953 | − | 0.757399i | \(-0.273530\pi\) |
−0.757399 | + | 0.652953i | \(0.773530\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −34.3134 | − | 82.8400i | −0.0600936 | − | 0.145079i | 0.890981 | − | 0.454041i | \(-0.150018\pi\) |
−0.951074 | + | 0.308963i | \(0.900018\pi\) | |||||||
\(572\) | −143.837 | + | 143.837i | −0.251463 | + | 0.251463i | ||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 321.504 | − | 1429.50i | 0.560111 | − | 2.49042i | ||||
\(575\) | −195.826 | −0.340567 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 526.602 | − | 218.126i | 0.912655 | − | 0.378034i | 0.123583 | − | 0.992334i | \(-0.460562\pi\) |
0.789072 | + | 0.614300i | \(0.210562\pi\) | |||||||
\(578\) | − | 942.589i | − | 1.63078i | ||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 251.169 | + | 104.038i | 0.433051 | + | 0.179375i | ||||
\(581\) | −970.909 | + | 402.164i | −1.67110 | + | 0.692192i | ||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 154.421 | − | 154.421i | 0.264874 | − | 0.264874i | ||||
\(584\) | −759.760 | −1.30096 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −549.020 | − | 1325.45i | −0.936895 | − | 2.26186i | ||||
\(587\) | 723.205 | − | 299.561i | 1.23204 | − | 0.510326i | 0.330819 | − | 0.943694i | \(-0.392675\pi\) |
0.901217 | + | 0.433369i | \(0.142675\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −122.237 | + | 295.106i | −0.207533 | + | 0.501029i | ||||
\(590\) | −479.924 | −0.813431 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 529.133 | 0.893805 | ||||||||
\(593\) | −1047.87 | − | 434.042i | −1.76706 | − | 0.731942i | −0.995388 | − | 0.0959268i | \(-0.969419\pi\) |
−0.771676 | − | 0.636015i | \(-0.780581\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 90.3985 | − | 90.3985i | 0.151930 | − | 0.151930i | ||||
\(596\) | −270.546 | + | 653.156i | −0.453937 | + | 1.09590i | ||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 60.6823 | − | 146.500i | 0.101475 | − | 0.244983i | ||||
\(599\) | 275.740i | 0.460334i | 0.973151 | + | 0.230167i | \(0.0739272\pi\) | ||||
−0.973151 | + | 0.230167i | \(0.926073\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −148.724 | + | 359.051i | −0.247460 | + | 0.597422i | −0.997987 | − | 0.0634178i | \(-0.979800\pi\) |
0.750527 | + | 0.660840i | \(0.229800\pi\) | |||||||
\(602\) | −132.211 | − | 319.186i | −0.219620 | − | 0.530210i | ||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 275.905 | − | 114.284i | 0.456797 | − | 0.189211i | ||||
\(605\) | − | 95.1933i | − | 0.157344i | ||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 434.438 | + | 434.438i | 0.715713 | + | 0.715713i | 0.967724 | − | 0.252011i | \(-0.0810921\pi\) |
−0.252011 | + | 0.967724i | \(0.581092\pi\) | |||||||
\(608\) | 56.9990 | + | 137.608i | 0.0937484 | + | 0.226329i | ||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 1074.85 | + | 1074.85i | 1.76205 | + | 1.76205i | ||||
\(611\) | 0.493882 | 0.000808317 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 554.163 | − | 554.163i | 0.904017 | − | 0.904017i | −0.0917637 | − | 0.995781i | \(-0.529250\pi\) |
0.995781 | + | 0.0917637i | \(0.0292504\pi\) | |||||||
\(614\) | − | 1559.37i | − | 2.53969i | ||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −1449.44 | −2.35298 | ||||||||
\(617\) | 550.758 | + | 550.758i | 0.892639 | + | 0.892639i | 0.994771 | − | 0.102132i | \(-0.0325663\pi\) |
−0.102132 | + | 0.994771i | \(0.532566\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 590.942i | − | 0.954671i | −0.878721 | − | 0.477336i | \(-0.841603\pi\) | ||
0.878721 | − | 0.477336i | \(-0.158397\pi\) | |||||||
\(620\) | 691.660 | − | 691.660i | 1.11558 | − | 1.11558i | ||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −353.928 | + | 146.602i | −0.569017 | + | 0.235694i | ||||
\(623\) | −327.106 | + | 327.106i | −0.525050 | + | 0.525050i | ||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 295.425 | 0.472680 | ||||||||
\(626\) | 493.641 | + | 1191.76i | 0.788564 | + | 1.90376i | ||||
\(627\) | 0 | 0 | ||||||||
\(628\) | −127.379 | + | 52.7623i | −0.202833 | + | 0.0840163i | ||||
\(629\) | −170.568 | − | 70.6517i | −0.271174 | − | 0.112324i | ||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 330.673 | 0.524047 | 0.262023 | − | 0.965062i | \(-0.415610\pi\) | ||||
0.262023 | + | 0.965062i | \(0.415610\pi\) | |||||||
\(632\) | −404.350 | − | 167.487i | −0.639794 | − | 0.265012i | ||||
\(633\) | 0 | 0 | ||||||||
\(634\) | −1168.41 | − | 483.971i | −1.84292 | − | 0.763361i | ||||
\(635\) | −409.074 | − | 409.074i | −0.644212 | − | 0.644212i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | −55.5725 | + | 134.164i | −0.0872410 | + | 0.210618i | ||||
\(638\) | 381.372i | 0.597762i | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | − | 922.236i | − | 1.44099i | ||||||
\(641\) | −616.324 | − | 255.290i | −0.961504 | − | 0.398268i | −0.153961 | − | 0.988077i | \(-0.549203\pi\) |
−0.807543 | + | 0.589809i | \(0.799203\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 31.2194 | + | 75.3704i | 0.0485528 | + | 0.117217i | 0.946295 | − | 0.323304i | \(-0.104794\pi\) |
−0.897742 | + | 0.440521i | \(0.854794\pi\) | |||||||
\(644\) | 1480.49 | − | 613.240i | 2.29890 | − | 0.952236i | ||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 97.7984i | 0.151391i | ||||||||
\(647\) | 756.871 | + | 756.871i | 1.16982 | + | 1.16982i | 0.982252 | + | 0.187564i | \(0.0600592\pi\) |
0.187564 | + | 0.982252i | \(0.439941\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −166.966 | − | 403.092i | −0.257267 | − | 0.621098i | ||||
\(650\) | 28.2111 | − | 68.1076i | 0.0434017 | − | 0.104781i | ||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −1001.28 | −1.53571 | ||||||||
\(653\) | −104.193 | − | 251.545i | −0.159561 | − | 0.385215i | 0.823799 | − | 0.566882i | \(-0.191851\pi\) |
−0.983360 | + | 0.181668i | \(0.941851\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | − | 522.861i | − | 0.798261i | ||||||
\(656\) | −61.5047 | − | 355.160i | −0.0937572 | − | 0.541403i | ||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 5.44575 | + | 5.44575i | 0.00827621 | + | 0.00827621i | ||||
\(659\) | −114.144 | + | 47.2801i | −0.173208 | + | 0.0717452i | −0.467603 | − | 0.883939i | \(-0.654882\pi\) |
0.294394 | + | 0.955684i | \(0.404882\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −49.1306 | + | 49.1306i | −0.0743277 | + | 0.0743277i | −0.743293 | − | 0.668966i | \(-0.766737\pi\) |
0.668966 | + | 0.743293i | \(0.266737\pi\) | |||||||
\(662\) | −958.103 | − | 396.859i | −1.44729 | − | 0.599486i | ||||
\(663\) | 0 | 0 | ||||||||
\(664\) | −795.451 | + | 795.451i | −1.19797 | + | 1.19797i | ||||
\(665\) | 278.704 | − | 278.704i | 0.419104 | − | 0.419104i | ||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −73.7302 | − | 178.000i | −0.110540 | − | 0.266867i | ||||
\(668\) | −667.394 | − | 1611.23i | −0.999093 | − | 2.41202i | ||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −657.556 | − | 272.368i | −0.981426 | − | 0.406520i | ||||
\(671\) | −528.835 | + | 1276.72i | −0.788130 | + | 1.90271i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | −897.045 | − | 371.568i | −1.33290 | − | 0.552107i | −0.401422 | − | 0.915893i | \(-0.631484\pi\) |
−0.931482 | + | 0.363786i | \(0.881484\pi\) | |||||||
\(674\) | −2098.59 | −3.11363 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −852.861 | − | 852.861i | −1.26163 | − | 1.26163i | ||||
\(677\) | 739.405 | − | 739.405i | 1.09218 | − | 1.09218i | 0.0968826 | − | 0.995296i | \(-0.469113\pi\) |
0.995296 | − | 0.0968826i | \(-0.0308871\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 1407.34i | 2.07267i | ||||||||
\(680\) | 52.3699 | − | 126.432i | 0.0770145 | − | 0.185930i | ||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 1267.71 | + | 525.104i | 1.85882 | + | 0.769947i | ||||
\(683\) | −364.618 | + | 880.266i | −0.533848 | + | 1.28882i | 0.395109 | + | 0.918634i | \(0.370707\pi\) |
−0.928957 | + | 0.370189i | \(0.879293\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −405.281 | + | 167.873i | −0.591651 | + | 0.245070i | ||||
\(686\) | −474.302 | + | 196.462i | −0.691402 | + | 0.286388i | ||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −60.0973 | − | 60.0973i | −0.0873507 | − | 0.0873507i | ||||
\(689\) | −29.3679 | − | 29.3679i | −0.0426240 | − | 0.0426240i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −84.8429 | + | 204.829i | −0.122783 | + | 0.296424i | −0.973305 | − | 0.229515i | \(-0.926286\pi\) |
0.850522 | + | 0.525939i | \(0.176286\pi\) | |||||||
\(692\) | 267.600 | + | 267.600i | 0.386705 | + | 0.386705i | ||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 507.040 | + | 1224.10i | 0.730605 | + | 1.76384i | ||||
\(695\) | −296.994 | + | 296.994i | −0.427330 | + | 0.427330i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −27.5960 | + | 122.700i | −0.0395925 | + | 0.176040i | ||||
\(698\) | −314.285 | −0.450266 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 688.278 | − | 285.094i | 0.983254 | − | 0.407277i | ||||
\(701\) | 284.354i | 0.405641i | 0.979216 | + | 0.202820i | \(0.0650107\pi\) | ||||
−0.979216 | + | 0.202820i | \(0.934989\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −525.872 | − | 217.824i | −0.748040 | − | 0.309849i | ||||
\(704\) | 982.635 | − | 407.021i | 1.39579 | − | 0.578154i | ||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 1307.48 | − | 1307.48i | 1.85195 | − | 1.85195i | ||||
\(707\) | 1574.43 | 2.22691 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −144.375 | − | 348.553i | −0.203632 | − | 0.491612i | 0.788764 | − | 0.614696i | \(-0.210721\pi\) |
−0.992396 | + | 0.123084i | \(0.960721\pi\) | |||||||
\(710\) | −183.192 | + | 75.8807i | −0.258017 | + | 0.106874i | ||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −189.500 | + | 457.493i | −0.266151 | + | 0.642547i | ||||
\(713\) | −693.206 | −0.972238 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −108.580 | −0.151861 | ||||||||
\(716\) | −494.665 | − | 204.897i | −0.690872 | − | 0.286169i | ||||
\(717\) | 0 | 0 | ||||||||
\(718\) | −488.216 | + | 488.216i | −0.679966 | + | 0.679966i | ||||
\(719\) | 161.288 | − | 389.383i | 0.224322 | − | 0.541562i | −0.771146 | − | 0.636659i | \(-0.780316\pi\) |
0.995468 | + | 0.0950965i | \(0.0303160\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | −734.195 | + | 1772.50i | −1.01830 | + | 2.45839i | ||||
\(722\) | − | 915.526i | − | 1.26804i | ||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | 247.117 | − | 596.592i | 0.341321 | − | 0.824023i | ||||
\(725\) | −34.2770 | − | 82.7520i | −0.0472786 | − | 0.114141i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 759.674 | − | 314.667i | 1.04494 | − | 0.432830i | 0.206859 | − | 0.978371i | \(-0.433676\pi\) |
0.838084 | + | 0.545541i | \(0.183676\pi\) | |||||||
\(728\) | 275.655i | 0.378647i | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −627.571 | − | 627.571i | −0.859686 | − | 0.859686i | ||||
\(731\) | 11.3482 | + | 27.3970i | 0.0155242 | + | 0.0374788i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −122.432 | − | 122.432i | −0.167028 | − | 0.167028i | 0.618643 | − | 0.785672i | \(-0.287683\pi\) |
−0.785672 | + | 0.618643i | \(0.787683\pi\) | |||||||
\(734\) | −1846.39 | −2.51552 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −228.566 | + | 228.566i | −0.310552 | + | 0.310552i | ||||
\(737\) | − | 647.044i | − | 0.877943i | ||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −1046.70 | −1.41637 | −0.708185 | − | 0.706027i | \(-0.750486\pi\) | ||||
−0.708185 | + | 0.706027i | \(0.750486\pi\) | |||||||
\(740\) | 1232.52 | + | 1232.52i | 1.66557 | + | 1.66557i | ||||
\(741\) | 0 | 0 | ||||||||
\(742\) | − | 647.646i | − | 0.872838i | ||||||
\(743\) | 187.656 | − | 187.656i | 0.252566 | − | 0.252566i | −0.569456 | − | 0.822022i | \(-0.692846\pi\) |
0.822022 | + | 0.569456i | \(0.192846\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −348.646 | + | 144.414i | −0.467981 | + | 0.193844i | ||||
\(746\) | −34.6948 | + | 34.6948i | −0.0465078 | + | 0.0465078i | ||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 272.266 | 0.363992 | ||||||||
\(749\) | 282.142 | + | 681.151i | 0.376692 | + | 0.909414i | ||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 638.232 | − | 264.364i | 0.849843 | − | 0.352017i | 0.0851162 | − | 0.996371i | \(-0.472874\pi\) |
0.764727 | + | 0.644354i | \(0.222874\pi\) | |||||||
\(752\) | 1.75037 | + | 0.725025i | 0.00232761 | + | 0.000964129i | ||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 72.5296 | 0.0961931 | ||||||||
\(755\) | 147.274 | + | 61.0030i | 0.195065 | + | 0.0807987i | ||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 721.384 | + | 298.807i | 0.952951 | + | 0.394725i | 0.804339 | − | 0.594170i | \(-0.202520\pi\) |
0.148612 | + | 0.988896i | \(0.452520\pi\) | |||||||
\(758\) | 1405.89 | + | 1405.89i | 1.85474 | + | 1.85474i | ||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 161.460 | − | 389.798i | 0.212447 | − | 0.512892i | ||||
\(761\) | − | 1084.11i | − | 1.42459i | −0.701882 | − | 0.712294i | \(-0.747656\pi\) | ||
0.701882 | − | 0.712294i | \(-0.252344\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 277.245i | 0.363361i | ||||||||
\(764\) | 2110.73 | + | 874.295i | 2.76274 | + | 1.14436i | ||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 507.743 | + | 1225.80i | 0.662850 | + | 1.60026i | ||||
\(767\) | −76.6604 | + | 31.7538i | −0.0999483 | + | 0.0414000i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | − | 122.901i | − | 0.159820i | −0.996802 | − | 0.0799098i | \(-0.974537\pi\) | ||
0.996802 | − | 0.0799098i | \(-0.0254632\pi\) | |||||||
\(770\) | −1197.25 | − | 1197.25i | −1.55487 | − | 1.55487i | ||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 827.724 | + | 1998.30i | 1.07218 | + | 2.58847i | ||||
\(773\) | 15.6507 | − | 37.7841i | 0.0202467 | − | 0.0488799i | −0.913433 | − | 0.406989i | \(-0.866579\pi\) |
0.933680 | + | 0.358110i | \(0.116579\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −322.270 | −0.415832 | ||||||||
\(776\) | 576.507 | + | 1391.81i | 0.742921 | + | 1.79357i | ||||
\(777\) | 0 | 0 | ||||||||
\(778\) | − | 1683.81i | − | 2.16427i | ||||||
\(779\) | −85.0800 | + | 378.291i | −0.109217 | + | 0.485611i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −127.466 | − | 127.466i | −0.163208 | − | 0.163208i | ||||
\(782\) | −196.086 | + | 81.2214i | −0.250749 | + | 0.103864i | ||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −393.909 | + | 393.909i | −0.502434 | + | 0.502434i | ||||
\(785\) | −67.9933 | − | 28.1637i | −0.0866156 | − | 0.0358774i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 707.611 | − | 707.611i | 0.899124 | − | 0.899124i | −0.0962346 | − | 0.995359i | \(-0.530680\pi\) |
0.995359 | + | 0.0962346i | \(0.0306799\pi\) | |||||||
\(788\) | 38.7872 | − | 38.7872i | 0.0492223 | − | 0.0492223i | ||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −195.652 | − | 472.345i | −0.247660 | − | 0.597904i | ||||
\(791\) | −743.181 | − | 1794.20i | −0.939546 | − | 2.26826i | ||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 242.808 | + | 100.574i | 0.306189 | + | 0.126828i | ||||
\(794\) | 237.399 | − | 573.133i | 0.298992 | − | 0.721829i | ||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −448.391 | − | 185.730i | −0.563305 | − | 0.233329i | ||||
\(797\) | 671.933 | 0.843078 | 0.421539 | − | 0.906810i | \(-0.361490\pi\) | ||||
0.421539 | + | 0.906810i | \(0.361490\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −0.467430 | − | 0.467430i | −0.000585019 | − | 0.000585019i | ||||
\(800\) | −106.260 | + | 106.260i | −0.132825 | + | 0.132825i | ||||
\(801\) | 0 | 0 | ||||||||
\(802\) | 457.156i | 0.570020i | ||||||||
\(803\) | 308.769 | − | 745.435i | 0.384520 | − | 0.928313i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 790.265 | + | 327.339i | 0.981696 | + | 0.406632i | ||||
\(806\) | 99.8645 | − | 241.094i | 0.123901 | − | 0.299124i | ||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1557.05 | − | 644.952i | 1.92704 | − | 0.798208i | ||||
\(809\) | 706.243 | − | 292.535i | 0.872983 | − | 0.361601i | 0.0992114 | − | 0.995066i | \(-0.468368\pi\) |
0.773771 | + | 0.633465i | \(0.218368\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −770.751 | − | 770.751i | −0.950371 | − | 0.950371i | 0.0484543 | − | 0.998825i | \(-0.484570\pi\) |
−0.998825 | + | 0.0484543i | \(0.984570\pi\) | |||||||
\(812\) | 518.285 | + | 518.285i | 0.638282 | + | 0.638282i | ||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −935.723 | + | 2259.03i | −1.14954 | + | 2.77523i | ||||
\(815\) | −377.927 | − | 377.927i | −0.463715 | − | 0.463715i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 34.9873 | + | 84.4667i | 0.0428241 | + | 0.103386i | ||||
\(818\) | 258.873 | − | 258.873i | 0.316471 | − | 0.316471i | ||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 684.019 | − | 970.548i | 0.834170 | − | 1.18360i | ||||
\(821\) | −623.500 | −0.759440 | −0.379720 | − | 0.925102i | \(-0.623980\pi\) | ||||
−0.379720 | + | 0.925102i | \(0.623980\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 558.248 | − | 231.234i | 0.678308 | − | 0.280964i | −0.0168113 | − | 0.999859i | \(-0.505351\pi\) |
0.695119 | + | 0.718894i | \(0.255351\pi\) | |||||||
\(824\) | 2053.70i | 2.49236i | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1195.42 | − | 495.159i | −1.44724 | − | 0.599466i | ||||
\(827\) | 929.687 | − | 385.089i | 1.12417 | − | 0.465646i | 0.258374 | − | 0.966045i | \(-0.416813\pi\) |
0.865795 | + | 0.500399i | \(0.166813\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 600.020 | − | 600.020i | 0.723788 | − | 0.723788i | −0.245587 | − | 0.969375i | \(-0.578981\pi\) |
0.969375 | + | 0.245587i | \(0.0789806\pi\) | |||||||
\(830\) | −1314.10 | −1.58326 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −77.4074 | − | 186.878i | −0.0930378 | − | 0.224613i | ||||
\(833\) | 179.574 | − | 74.3821i | 0.215575 | − | 0.0892942i | ||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 356.245 | − | 860.053i | 0.426641 | − | 1.03000i | ||||
\(836\) | 839.412 | 1.00408 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | 959.226 | 1.14466 | ||||||||
\(839\) | 927.665 | + | 384.251i | 1.10568 | + | 0.457987i | 0.859448 | − | 0.511224i | \(-0.170808\pi\) |
0.246231 | + | 0.969211i | \(0.420808\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −532.363 | + | 532.363i | −0.633012 | + | 0.633012i | ||||
\(842\) | −88.4923 | + | 213.639i | −0.105098 | + | 0.253728i | ||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −574.458 | + | 1386.86i | −0.680637 | + | 1.64320i | ||||
\(845\) | − | 643.814i | − | 0.761910i | ||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 98.2151 | − | 237.112i | 0.115956 | − | 0.279944i | ||||
\(848\) | −60.9703 | − | 147.195i | −0.0718989 | − | 0.173579i | ||||
\(849\) | 0 | 0 | ||||||||
\(850\) | −91.1599 | + | 37.7597i | −0.107247 | + | 0.0444231i | ||||
\(851\) | − | 1235.28i | − | 1.45156i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 694.593 | + | 694.593i | 0.814295 | + | 0.814295i | 0.985275 | − | 0.170980i | \(-0.0546933\pi\) |
−0.170980 | + | 0.985275i | \(0.554693\pi\) | |||||||
\(854\) | 1568.32 | + | 3786.27i | 1.83645 | + | 4.43357i | ||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 558.058 | + | 558.058i | 0.651936 | + | 0.651936i | ||||
\(857\) | −290.882 | −0.339419 | −0.169710 | − | 0.985494i | \(-0.554283\pi\) | ||||
−0.169710 | + | 0.985494i | \(0.554283\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −67.0806 | + | 67.0806i | −0.0780915 | + | 0.0780915i | −0.745074 | − | 0.666982i | \(-0.767586\pi\) |
0.666982 | + | 0.745074i | \(0.267586\pi\) | |||||||
\(860\) | − | 279.972i | − | 0.325549i | ||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | −358.552 | −0.415954 | ||||||||
\(863\) | −1122.84 | − | 1122.84i | −1.30109 | − | 1.30109i | −0.927658 | − | 0.373431i | \(-0.878181\pi\) |
−0.373431 | − | 0.927658i | \(-0.621819\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 202.008i | 0.233535i | ||||||||
\(866\) | −1730.57 | + | 1730.57i | −1.99835 | + | 1.99835i | ||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 2436.44 | − | 1009.21i | 2.80696 | − | 1.16268i | ||||
\(869\) | 328.659 | − | 328.659i | 0.378204 | − | 0.378204i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −123.055 | −0.141280 | ||||||||
\(872\) | 113.571 | + | 274.185i | 0.130242 | + | 0.314433i | ||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −604.545 | + | 250.411i | −0.691699 | + | 0.286511i | ||||
\(875\) | 1330.02 | + | 550.911i | 1.52002 | + | 0.629612i | ||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 883.264 | 1.00714 | 0.503571 | − | 0.863954i | \(-0.332019\pi\) | ||||
0.503571 | + | 0.863954i | \(0.332019\pi\) | |||||||
\(878\) | 1241.41 | + | 514.208i | 1.41390 | + | 0.585658i | ||||
\(879\) | 0 | 0 | ||||||||
\(880\) | −384.820 | − | 159.398i | −0.437295 | − | 0.181134i | ||||
\(881\) | 189.394 | + | 189.394i | 0.214976 | + | 0.214976i | 0.806377 | − | 0.591401i | \(-0.201425\pi\) |
−0.591401 | + | 0.806377i | \(0.701425\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 495.140 | − | 1195.37i | 0.560748 | − | 1.35377i | −0.348421 | − | 0.937338i | \(-0.613282\pi\) |
0.909169 | − | 0.416427i | \(-0.136718\pi\) | |||||||
\(884\) | − | 51.7797i | − | 0.0585743i | ||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | 1224.55i | 1.38211i | ||||||||
\(887\) | −152.020 | − | 62.9686i | −0.171386 | − | 0.0709905i | 0.295341 | − | 0.955392i | \(-0.404567\pi\) |
−0.466727 | + | 0.884402i | \(0.654567\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −596.883 | − | 1441.00i | −0.671409 | − | 1.62093i | ||||
\(890\) | −534.424 | + | 221.366i | −0.600476 | + | 0.248725i | ||||
\(891\) | 0 | 0 | ||||||||
\(892\) | − | 238.944i | − | 0.267874i | ||||||
\(893\) | −1.44112 | − | 1.44112i | −0.00161379 | − | 0.00161379i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −109.371 | − | 264.045i | −0.122202 | − | 0.295022i | ||||
\(896\) | 951.512 | − | 2297.15i | 1.06195 | − | 2.56379i | ||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 1555.35 | 1.73202 | ||||||||
\(899\) | −121.337 | − | 292.934i | −0.134969 | − | 0.325845i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 55.5900i | 0.0616981i | ||||||||
\(902\) | 1625.06 | + | 365.485i | 1.80161 | + | 0.405194i | ||||
\(903\) | 0 | 0 | ||||||||
\(904\) | −1469.96 | − | 1469.96i | −1.62606 | − | 1.62606i | ||||
\(905\) | 318.452 | − | 131.907i | 0.351881 | − | 0.145754i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −181.264 | + | 181.264i | −0.199850 | + | 0.199850i | −0.799936 | − | 0.600086i | \(-0.795133\pi\) |
0.600086 | + | 0.799936i | \(0.295133\pi\) | |||||||
\(908\) | 911.414 | + | 377.520i | 1.00376 | + | 0.415771i | ||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −227.694 | + | 227.694i | −0.250213 | + | 0.250213i | ||||
\(911\) | 395.125 | − | 395.125i | 0.433727 | − | 0.433727i | −0.456167 | − | 0.889894i | \(-0.650778\pi\) |
0.889894 | + | 0.456167i | \(0.150778\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −457.179 | − | 1103.73i | −0.500744 | − | 1.20890i | ||||
\(914\) | −634.571 | − | 1531.99i | −0.694279 | − | 1.67614i | ||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 779.933 | + | 323.059i | 0.851455 | + | 0.352684i | ||||
\(917\) | 539.459 | − | 1302.37i | 0.588287 | − | 1.42025i | ||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −250.905 | − | 103.928i | −0.273020 | − | 0.113089i | 0.241973 | − | 0.970283i | \(-0.422205\pi\) |
−0.514993 | + | 0.857194i | \(0.672205\pi\) | |||||||
\(920\) | 915.637 | 0.995257 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | 89.8375 | + | 89.8375i | 0.0974376 | + | 0.0974376i | ||||
\(923\) | −24.2415 | + | 24.2415i | −0.0262638 | + | 0.0262638i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | − | 574.278i | − | 0.620841i | ||||||
\(926\) | −1032.87 | + | 2493.56i | −1.11541 | + | 2.69283i | ||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −136.595 | − | 56.5795i | −0.147193 | − | 0.0609693i | ||||
\(929\) | −17.5523 | + | 42.3751i | −0.0188938 | + | 0.0456137i | −0.933045 | − | 0.359760i | \(-0.882859\pi\) |
0.914151 | + | 0.405374i | \(0.132859\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 553.638 | − | 229.324i | 0.594671 | − | 0.246321i | ||||
\(932\) | −988.460 | + | 409.434i | −1.06058 | + | 0.439306i | ||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 616.239 | + | 616.239i | 0.659785 | + | 0.659785i | ||||
\(935\) | 102.765 | + | 102.765i | 0.109909 | + | 0.109909i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −471.850 | + | 1139.15i | −0.503575 | + | 1.21574i | 0.443949 | + | 0.896052i | \(0.353577\pi\) |
−0.947524 | + | 0.319686i | \(0.896423\pi\) | |||||||
\(938\) | −1356.86 | − | 1356.86i | −1.44654 | − | 1.44654i | ||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 2.38835 | + | 5.76599i | 0.00254080 | + | 0.00613403i | ||||
\(941\) | −784.033 | + | 784.033i | −0.833192 | + | 0.833192i | −0.987952 | − | 0.154760i | \(-0.950539\pi\) |
0.154760 | + | 0.987952i | \(0.450539\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −829.132 | + | 143.585i | −0.879250 | + | 0.152264i | ||||
\(944\) | −318.307 | −0.337189 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 362.851 | − | 150.298i | 0.383563 | − | 0.158877i | ||||
\(947\) | − | 945.504i | − | 0.998420i | −0.866481 | − | 0.499210i | \(-0.833624\pi\) | ||
0.866481 | − | 0.499210i | \(-0.166376\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −141.767 | − | 58.7219i | −0.149386 | − | 0.0618777i | ||||
\(950\) | −281.051 | + | 116.415i | −0.295844 | + | 0.122542i | ||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 260.891 | − | 260.891i | 0.274045 | − | 0.274045i | ||||
\(953\) | −410.140 | −0.430368 | −0.215184 | − | 0.976574i | \(-0.569035\pi\) | ||||
−0.215184 | + | 0.976574i | \(0.569035\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 466.686 | + | 1126.68i | 0.488676 | + | 1.17977i | ||||
\(956\) | 1897.92 | − | 786.146i | 1.98528 | − | 0.822328i | ||||
\(957\) | 0 | 0 | ||||||||
\(958\) | −202.762 | + | 489.512i | −0.211652 | + | 0.510973i | ||||
\(959\) | −1182.70 | −1.23326 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −179.805 | −0.187102 | ||||||||
\(962\) | 429.625 | + | 177.956i | 0.446595 | + | 0.184986i | ||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 208.216 | − | 208.216i | 0.215992 | − | 0.215992i | ||||
\(965\) | −441.827 | + | 1066.67i | −0.457852 | + | 1.10535i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 10.4433 | − | 25.2123i | 0.0107997 | − | 0.0260727i | −0.918388 | − | 0.395682i | \(-0.870508\pi\) |
0.929187 | + | 0.369609i | \(0.120508\pi\) | |||||||
\(968\) | − | 274.729i | − | 0.283811i | ||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | −673.451 | + | 1625.85i | −0.694279 | + | 1.67614i | ||||
\(971\) | −250.318 | − | 604.320i | −0.257794 | − | 0.622369i | 0.740998 | − | 0.671507i | \(-0.234353\pi\) |
−0.998792 | + | 0.0491378i | \(0.984353\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −1046.19 | + | 433.346i | −1.07522 | + | 0.445371i | ||||
\(974\) | − | 350.300i | − | 0.359651i | ||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 712.889 | + | 712.889i | 0.730420 | + | 0.730420i | ||||
\(977\) | 243.204 | + | 587.145i | 0.248929 | + | 0.600967i | 0.998114 | − | 0.0613936i | \(-0.0195545\pi\) |
−0.749185 | + | 0.662361i | \(0.769554\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −371.854 | − | 371.854i | −0.379830 | − | 0.379830i | ||||
\(980\) | −1835.08 | −1.87253 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −1519.94 | + | 1519.94i | −1.54780 | + | 1.54780i | ||||
\(983\) | − | 94.7811i | − | 0.0964202i | −0.998837 | − | 0.0482101i | \(-0.984648\pi\) | ||
0.998837 | − | 0.0482101i | \(-0.0153517\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 29.2799 | 0.0297258 | ||||||||
\(986\) | −68.6450 | − | 68.6450i | −0.0696196 | − | 0.0696196i | ||||
\(987\) | 0 | 0 | ||||||||
\(988\) | − | 159.640i | − | 0.161579i | ||||||
\(989\) | −140.299 | + | 140.299i | −0.141859 | + | 0.141859i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −159.074 | + | 65.8906i | −0.160519 | + | 0.0664890i | −0.461496 | − | 0.887142i | \(-0.652687\pi\) |
0.300977 | + | 0.953631i | \(0.402687\pi\) | |||||||
\(992\) | −376.150 | + | 376.150i | −0.379184 | + | 0.379184i | ||||
\(993\) | 0 | 0 | ||||||||
\(994\) | −534.594 | −0.537821 | ||||||||
\(995\) | −99.1398 | − | 239.345i | −0.0996380 | − | 0.240547i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 933.834 | − | 386.807i | 0.936644 | − | 0.387971i | 0.138449 | − | 0.990370i | \(-0.455788\pi\) |
0.798195 | + | 0.602399i | \(0.205788\pi\) | |||||||
\(998\) | −1355.22 | − | 561.350i | −1.35793 | − | 0.562475i | ||||
\(999\) | 0 | 0 |
(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 | 369.3.l.b.109.5 | 20 | ||
3.2 | odd | 2 | 41.3.e.b.27.1 | ✓ | 20 | ||
41.38 | odd | 8 | inner | 369.3.l.b.325.5 | 20 | ||
123.38 | even | 8 | 41.3.e.b.38.1 | yes | 20 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
41.3.e.b.27.1 | ✓ | 20 | 3.2 | odd | 2 | ||
41.3.e.b.38.1 | yes | 20 | 123.38 | even | 8 | ||
369.3.l.b.109.5 | 20 | 1.1 | even | 1 | trivial | ||
369.3.l.b.325.5 | 20 | 41.38 | odd | 8 | inner |