Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(589,1764)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(1764, base_ring=CyclotomicField(6))
chi = DirichletCharacter(H, H._module([0, 2, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.589");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 1764 = 2^{2} \cdot 3^{2} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 1764.j (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: | \(14.0856109166\) |
Analytic rank: | \(0\) |
Dimension: | \(6\) |
Relative dimension: | \(3\) over \(\Q(\zeta_{3})\) |
Coefficient field: | 6.0.309123.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{6} - 3x^{5} + 10x^{4} - 15x^{3} + 19x^{2} - 12x + 3 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{3}]$ |
Embedding invariants
Embedding label | 1177.1 | ||
Root | \(0.500000 - 0.224437i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.1177 |
Dual form | 1764.2.j.e.589.1 |
$q$-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 \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{2}{3}\right)\) | \(1\) | \(1\) |
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 | 0 | ||||||||
\(3\) | −1.64400 | + | 0.545231i | −0.949162 | + | 0.314789i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | −0.849814 | − | 1.47192i | −0.380048 | − | 0.658263i | 0.611020 | − | 0.791615i | \(-0.290759\pi\) |
−0.991069 | + | 0.133352i | \(0.957426\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 2.40545 | − | 1.79272i | 0.801815 | − | 0.597572i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −1.23855 | + | 2.14523i | −0.373437 | + | 0.646812i | −0.990092 | − | 0.140422i | \(-0.955154\pi\) |
0.616655 | + | 0.787234i | \(0.288487\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.388736 | + | 0.673310i | 0.107816 | + | 0.186743i | 0.914885 | − | 0.403714i | \(-0.132281\pi\) |
−0.807069 | + | 0.590457i | \(0.798948\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 2.19963 | + | 1.95649i | 0.567942 | + | 0.505163i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | −2.81089 | −0.681742 | −0.340871 | − | 0.940110i | \(-0.610722\pi\) | ||||
−0.340871 | + | 0.940110i | \(0.610722\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.98762 | 1.14424 | 0.572119 | − | 0.820170i | \(-0.306121\pi\) | ||||
0.572119 | + | 0.820170i | \(0.306121\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −0.356004 | − | 0.616617i | −0.0742320 | − | 0.128574i | 0.826520 | − | 0.562907i | \(-0.190317\pi\) |
−0.900752 | + | 0.434334i | \(0.856984\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.05563 | − | 1.82841i | 0.211126 | − | 0.365682i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −2.97710 | + | 4.25874i | −0.572943 | + | 0.819595i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.25526 | + | 3.90623i | −0.418791 | + | 0.725368i | −0.995818 | − | 0.0913573i | \(-0.970879\pi\) |
0.577027 | + | 0.816725i | \(0.304213\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.54944 | + | 4.41576i | 0.457893 | + | 0.793095i | 0.998849 | − | 0.0479563i | \(-0.0152708\pi\) |
−0.540956 | + | 0.841051i | \(0.681937\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | 0.866524 | − | 4.20205i | 0.150843 | − | 0.731483i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.87636 | −1.13047 | −0.565233 | − | 0.824931i | \(-0.691214\pi\) | ||||
−0.565233 | + | 0.824931i | \(0.691214\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.00619 | − | 0.894969i | −0.161119 | − | 0.143310i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | −2.93818 | − | 5.08907i | −0.458866 | − | 0.794780i | 0.540035 | − | 0.841643i | \(-0.318411\pi\) |
−0.998901 | + | 0.0468628i | \(0.985078\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 2.32691 | − | 4.03033i | 0.354851 | − | 0.614620i | −0.632241 | − | 0.774771i | \(-0.717865\pi\) |
0.987092 | + | 0.160151i | \(0.0511982\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −4.68292 | − | 2.01715i | −0.698088 | − | 0.300699i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | 6.49381 | − | 11.2476i | 0.947220 | − | 1.64063i | 0.195975 | − | 0.980609i | \(-0.437213\pi\) |
0.751245 | − | 0.660023i | \(-0.229454\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.62110 | − | 1.53259i | 0.647083 | − | 0.214605i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 1.88874 | 0.259438 | 0.129719 | − | 0.991551i | \(-0.458593\pi\) | ||||
0.129719 | + | 0.991551i | \(0.458593\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 4.21015 | 0.567696 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −8.19963 | + | 2.71941i | −1.08607 | + | 0.360194i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | 7.14400 | + | 12.3738i | 0.930069 | + | 1.61093i | 0.783199 | + | 0.621771i | \(0.213587\pi\) |
0.146870 | + | 0.989156i | \(0.453080\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 7.15452 | − | 12.3920i | 0.916042 | − | 1.58663i | 0.110673 | − | 0.993857i | \(-0.464699\pi\) |
0.805369 | − | 0.592774i | \(-0.201967\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 0.660706 | − | 1.14438i | 0.0819505 | − | 0.141942i | ||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −3.99381 | − | 6.91748i | −0.487922 | − | 0.845105i | 0.511982 | − | 0.858996i | \(-0.328911\pi\) |
−0.999904 | + | 0.0138913i | \(0.995578\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 0.921468 | + | 0.819611i | 0.110932 | + | 0.0986696i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −10.2632 | −1.21802 | −0.609011 | − | 0.793162i | \(-0.708433\pi\) | ||||
−0.609011 | + | 0.793162i | \(0.708433\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −4.98762 | −0.583757 | −0.291878 | − | 0.956455i | \(-0.594280\pi\) | ||||
−0.291878 | + | 0.956455i | \(0.594280\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −0.738550 | + | 3.58146i | −0.0852804 | + | 0.413551i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 4.60507 | − | 7.97622i | 0.518111 | − | 0.897395i | −0.481667 | − | 0.876354i | \(-0.659969\pi\) |
0.999779 | − | 0.0210410i | \(-0.00669805\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 2.57234 | − | 8.62456i | 0.285816 | − | 0.958285i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 4.40545 | − | 7.63046i | 0.483561 | − | 0.837551i | −0.516261 | − | 0.856431i | \(-0.672677\pi\) |
0.999822 | + | 0.0188798i | \(0.00600997\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 2.38874 | + | 4.13741i | 0.259095 | + | 0.448765i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 1.57784 | − | 7.65146i | 0.169163 | − | 0.820322i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −9.65383 | −1.02330 | −0.511652 | − | 0.859193i | \(-0.670966\pi\) | ||||
−0.511652 | + | 0.859193i | \(0.670966\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −6.59888 | − | 5.86946i | −0.684272 | − | 0.608635i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | −4.23855 | − | 7.34138i | −0.434866 | − | 0.753210i | ||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 4.32072 | − | 7.48371i | 0.438703 | − | 0.759856i | −0.558887 | − | 0.829244i | \(-0.688771\pi\) |
0.997590 | + | 0.0693880i | \(0.0221047\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0.866524 | + | 7.38061i | 0.0870890 | + | 0.741779i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 1.20582 | − | 2.08854i | 0.119983 | − | 0.207817i | −0.799777 | − | 0.600297i | \(-0.795049\pi\) |
0.919761 | + | 0.392479i | \(0.128383\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −2.16690 | − | 3.75317i | −0.213511 | − | 0.369811i | 0.739300 | − | 0.673376i | \(-0.235156\pi\) |
−0.952811 | + | 0.303565i | \(0.901823\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 19.1978 | 1.85592 | 0.927959 | − | 0.372682i | \(-0.121562\pi\) | ||||
0.927959 | + | 0.372682i | \(0.121562\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.9629 | 1.81631 | 0.908156 | − | 0.418631i | \(-0.137490\pi\) | ||||
0.908156 | + | 0.418631i | \(0.137490\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 11.3047 | − | 3.74920i | 1.07299 | − | 0.355859i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | −6.46472 | − | 11.1972i | −0.608150 | − | 1.05335i | −0.991545 | − | 0.129762i | \(-0.958579\pi\) |
0.383395 | − | 0.923584i | \(-0.374755\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −0.605074 | + | 1.04802i | −0.0564235 | + | 0.0977283i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.14214 | + | 0.922719i | 0.198041 | + | 0.0853054i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | 2.43199 | + | 4.21233i | 0.221090 | + | 0.382939i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 7.60507 | + | 6.76443i | 0.685726 | + | 0.609928i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −12.0865 | −1.08105 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 17.6291 | 1.56433 | 0.782163 | − | 0.623073i | \(-0.214116\pi\) | ||||
0.782163 | + | 0.623073i | \(0.214116\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −1.62797 | + | 7.89456i | −0.143335 | + | 0.695077i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −2.84362 | − | 4.92530i | −0.248449 | − | 0.430326i | 0.714647 | − | 0.699485i | \(-0.246587\pi\) |
−0.963096 | + | 0.269160i | \(0.913254\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 8.79851 | + | 0.762918i | 0.757255 | + | 0.0656615i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 9.72617 | − | 16.8462i | 0.830963 | − | 1.43927i | −0.0663128 | − | 0.997799i | \(-0.521124\pi\) |
0.897276 | − | 0.441471i | \(-0.145543\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −1.49381 | − | 2.58736i | −0.126703 | − | 0.219457i | 0.795694 | − | 0.605699i | \(-0.207106\pi\) |
−0.922397 | + | 0.386242i | \(0.873773\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −4.54325 | + | 22.0317i | −0.382611 | + | 1.85540i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −1.92587 | −0.161050 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 7.66621 | 0.636644 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | −4.04944 | − | 7.01384i | −0.331743 | − | 0.574596i | 0.651111 | − | 0.758983i | \(-0.274303\pi\) |
−0.982854 | + | 0.184387i | \(0.940970\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 4.43199 | − | 7.67643i | 0.360670 | − | 0.624699i | −0.627401 | − | 0.778696i | \(-0.715881\pi\) |
0.988071 | + | 0.153997i | \(0.0492147\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | −6.76145 | + | 5.03913i | −0.546631 | + | 0.407390i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 4.33310 | − | 7.50516i | 0.348043 | − | 0.602829i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −4.38255 | − | 7.59079i | −0.349765 | − | 0.605811i | 0.636442 | − | 0.771324i | \(-0.280405\pi\) |
−0.986208 | + | 0.165513i | \(0.947072\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −3.10507 | + | 1.02980i | −0.246248 | + | 0.0816683i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.98762 | −0.155682 | −0.0778412 | − | 0.996966i | \(-0.524803\pi\) | ||||
−0.0778412 | + | 0.996966i | \(0.524803\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −6.92147 | + | 2.29550i | −0.538836 | + | 0.178705i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | 1.31089 | + | 2.27053i | 0.101440 | + | 0.175699i | 0.912278 | − | 0.409571i | \(-0.134322\pi\) |
−0.810838 | + | 0.585270i | \(0.800988\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | 6.19777 | − | 10.7349i | 0.476751 | − | 0.825758i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 11.9975 | − | 8.94138i | 0.917468 | − | 0.683765i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −2.61491 | + | 4.52915i | −0.198808 | + | 0.344345i | −0.948142 | − | 0.317847i | \(-0.897040\pi\) |
0.749334 | + | 0.662192i | \(0.230374\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −18.4913 | − | 16.4473i | −1.38989 | − | 1.23625i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −4.76509 | −0.356160 | −0.178080 | − | 0.984016i | \(-0.556989\pi\) | ||||
−0.178080 | + | 0.984016i | \(0.556989\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 10.4313 | 0.775352 | 0.387676 | − | 0.921796i | \(-0.373278\pi\) | ||||
0.387676 | + | 0.921796i | \(0.373278\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −5.00550 | + | 24.2732i | −0.370017 | + | 1.79433i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 5.84362 | + | 10.1215i | 0.429632 | + | 0.744144i | ||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 3.48143 | − | 6.03001i | 0.254587 | − | 0.440958i | ||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −6.66071 | + | 11.5367i | −0.481952 | + | 0.834765i | −0.999785 | − | 0.0207164i | \(-0.993405\pi\) |
0.517834 | + | 0.855481i | \(0.326739\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 7.32072 | + | 12.6799i | 0.526957 | + | 0.912717i | 0.999507 | + | 0.0314125i | \(0.0100005\pi\) |
−0.472549 | + | 0.881304i | \(0.656666\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −0.462249 | + | 2.24159i | −0.0331023 | + | 0.160524i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | −18.4858 | −1.31706 | −0.658528 | − | 0.752556i | \(-0.728821\pi\) | ||||
−0.658528 | + | 0.752556i | \(0.728821\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −23.6167 | −1.67414 | −0.837071 | − | 0.547094i | \(-0.815734\pi\) | ||||
−0.837071 | + | 0.547094i | \(0.815734\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.3374 | + | 9.19476i | 0.729146 | + | 0.648549i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −4.99381 | + | 8.64953i | −0.348783 | + | 0.604110i | ||||
\(206\) | 0 | 0 | ||||||||
\(207\) | −1.96177 | − | 0.845025i | −0.136352 | − | 0.0587333i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −6.17742 | + | 10.6996i | −0.427301 | + | 0.740107i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 7.27747 | + | 12.6050i | 0.501002 | + | 0.867761i | 0.999999 | + | 0.00115718i | \(0.000368342\pi\) |
−0.498998 | + | 0.866603i | \(0.666298\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 16.8727 | − | 5.59583i | 1.15610 | − | 0.383420i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −7.90978 | −0.539442 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | 8.19963 | − | 2.71941i | 0.554080 | − | 0.183760i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | −1.09269 | − | 1.89260i | −0.0735026 | − | 0.127310i | ||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 4.72253 | − | 8.17966i | 0.316244 | − | 0.547750i | −0.663457 | − | 0.748214i | \(-0.730912\pi\) |
0.979701 | + | 0.200464i | \(0.0642449\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −0.738550 | − | 6.29059i | −0.0492367 | − | 0.419372i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 9.55563 | − | 16.5508i | 0.634230 | − | 1.09852i | −0.352448 | − | 0.935831i | \(-0.614651\pi\) |
0.986678 | − | 0.162687i | \(-0.0520159\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 5.72253 | + | 9.91171i | 0.378155 | + | 0.654984i | 0.990794 | − | 0.135379i | \(-0.0432252\pi\) |
−0.612639 | + | 0.790363i | \(0.709892\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | −1.19049 | −0.0779913 | −0.0389956 | − | 0.999239i | \(-0.512416\pi\) | ||||
−0.0389956 | + | 0.999239i | \(0.512416\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −22.0741 | −1.43996 | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −3.22184 | + | 15.6237i | −0.209281 | + | 1.01487i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −12.1414 | − | 21.0296i | −0.785365 | − | 1.36029i | −0.928781 | − | 0.370630i | \(-0.879142\pi\) |
0.143416 | − | 0.989663i | \(-0.454191\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −10.7095 | + | 18.5493i | −0.689857 | + | 1.19487i | 0.282027 | + | 0.959406i | \(0.408993\pi\) |
−0.971884 | + | 0.235461i | \(0.924340\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 0.473458 | + | 15.5813i | 0.0303723 | + | 0.999539i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.93887 | + | 3.35822i | 0.123367 | + | 0.213678i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | −3.08217 | + | 14.9464i | −0.195325 | + | 0.947191i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 2.67996 | 0.169158 | 0.0845789 | − | 0.996417i | \(-0.473045\pi\) | ||||
0.0845789 | + | 0.996417i | \(0.473045\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | 1.76371 | 0.110884 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −6.18292 | − | 5.49948i | −0.387189 | − | 0.344391i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | −5.54256 | − | 9.60000i | −0.345736 | − | 0.598832i | 0.639752 | − | 0.768582i | \(-0.279037\pi\) |
−0.985487 | + | 0.169750i | \(0.945704\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 1.57784 | + | 13.4393i | 0.0976661 | + | 0.831869i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −6.70396 | + | 11.6116i | −0.413384 | + | 0.716002i | −0.995257 | − | 0.0972776i | \(-0.968987\pi\) |
0.581873 | + | 0.813279i | \(0.302320\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −1.60507 | − | 2.78007i | −0.0985989 | − | 0.170778i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 15.8709 | − | 5.26357i | 0.971281 | − | 0.322125i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | −4.09022 | −0.249385 | −0.124693 | − | 0.992195i | \(-0.539794\pi\) | ||||
−0.124693 | + | 0.992195i | \(0.539794\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −6.12364 | −0.371985 | −0.185992 | − | 0.982551i | \(-0.559550\pi\) | ||||
−0.185992 | + | 0.982551i | \(0.559550\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 2.61491 | + | 4.52915i | 0.157685 | + | 0.273118i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −7.88255 | + | 13.6530i | −0.473616 | + | 0.820327i | −0.999544 | − | 0.0302019i | \(-0.990385\pi\) |
0.525928 | + | 0.850529i | \(0.323718\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 14.0488 | + | 6.05146i | 0.841077 | + | 0.362291i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 10.5946 | − | 18.3503i | 0.632018 | − | 1.09469i | −0.355120 | − | 0.934821i | \(-0.615560\pi\) |
0.987139 | − | 0.159867i | \(-0.0511065\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 3.43818 | + | 5.95510i | 0.204378 | + | 0.353994i | 0.949935 | − | 0.312449i | \(-0.101149\pi\) |
−0.745556 | + | 0.666443i | \(0.767816\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 10.9709 | + | 9.75822i | 0.649861 | + | 0.578027i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −9.09888 | −0.535228 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −3.02290 | + | 14.6590i | −0.177206 | + | 0.859325i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −13.7534 | − | 23.8216i | −0.803482 | − | 1.39167i | −0.917311 | − | 0.398172i | \(-0.869645\pi\) |
0.113829 | − | 0.993500i | \(-0.463689\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 12.1421 | − | 21.0308i | 0.706943 | − | 1.22446i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | −5.44870 | − | 11.6612i | −0.316166 | − | 0.676653i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 0.276783 | − | 0.479402i | 0.0160068 | − | 0.0277245i | ||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −0.843624 | + | 4.09100i | −0.0484649 | + | 0.235022i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | −24.3200 | −1.39256 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 21.5178 | 1.22809 | 0.614043 | − | 0.789273i | \(-0.289542\pi\) | ||||
0.614043 | + | 0.789273i | \(0.289542\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 5.60872 | + | 4.98874i | 0.319069 | + | 0.283800i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 9.19275 | + | 15.9223i | 0.521273 | + | 0.902871i | 0.999694 | + | 0.0247407i | \(0.00787601\pi\) |
−0.478421 | + | 0.878131i | \(0.658791\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −0.000688709 | 0.00119288i | −3.89281e−5 | 6.74255e-5i | −0.866045 | − | 0.499966i | \(-0.833346\pi\) | ||
0.866006 | + | 0.500034i | \(0.166679\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | −7.04944 | + | 12.2100i | −0.395936 | + | 0.685781i | −0.993220 | − | 0.116248i | \(-0.962913\pi\) |
0.597284 | + | 0.802030i | \(0.296247\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | −5.58650 | − | 9.67611i | −0.312784 | − | 0.541758i | ||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −31.5611 | + | 10.4672i | −1.76157 | + | 0.584223i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −14.0197 | −0.780075 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | 1.64145 | 0.0910512 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −31.1749 | + | 10.3391i | −1.72397 | + | 0.571756i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −6.98143 | + | 12.0922i | −0.383734 | + | 0.664647i | −0.991593 | − | 0.129398i | \(-0.958695\pi\) |
0.607859 | + | 0.794045i | \(0.292029\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −16.5407 | + | 12.3274i | −0.906425 | + | 0.675535i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −6.78799 | + | 11.7571i | −0.370868 | + | 0.642362i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −12.0982 | − | 20.9547i | −0.659031 | − | 1.14147i | −0.980867 | − | 0.194679i | \(-0.937633\pi\) |
0.321836 | − | 0.946795i | \(-0.395700\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 16.7330 | + | 14.8834i | 0.908814 | + | 0.808357i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −12.6304 | −0.683977 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 0.423327 | − | 2.05285i | 0.0227912 | − | 0.110521i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | 16.3578 | + | 28.3325i | 0.878132 | + | 1.52097i | 0.853389 | + | 0.521275i | \(0.174544\pi\) |
0.0247435 | + | 0.999694i | \(0.492123\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −11.8887 | + | 20.5919i | −0.636389 | + | 1.10226i | 0.349830 | + | 0.936813i | \(0.386240\pi\) |
−0.986219 | + | 0.165445i | \(0.947094\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −4.02476 | − | 0.348986i | −0.214826 | − | 0.0186275i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 10.0309 | − | 17.3740i | 0.533889 | − | 0.924724i | −0.465327 | − | 0.885139i | \(-0.654063\pi\) |
0.999216 | − | 0.0395847i | \(-0.0126035\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 8.72184 | + | 15.1067i | 0.462907 | + | 0.801779i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 8.30175 | 0.438150 | 0.219075 | − | 0.975708i | \(-0.429696\pi\) | ||||
0.219075 | + | 0.975708i | \(0.429696\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 5.87636 | 0.309282 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −6.29487 | − | 5.59905i | −0.330395 | − | 0.293874i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 4.23855 | + | 7.34138i | 0.221856 | + | 0.384266i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 5.77197 | − | 9.99735i | 0.301294 | − | 0.521857i | −0.675135 | − | 0.737694i | \(-0.735915\pi\) |
0.976429 | + | 0.215837i | \(0.0692480\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −16.1909 | − | 6.97418i | −0.842864 | − | 0.363061i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | −1.42580 | − | 2.46956i | −0.0738250 | − | 0.127869i | 0.826750 | − | 0.562570i | \(-0.190187\pi\) |
−0.900575 | + | 0.434701i | \(0.856854\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 19.8702 | − | 6.58994i | 1.02609 | − | 0.340303i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | −3.50680 | −0.180609 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 35.9519 | 1.84672 | 0.923361 | − | 0.383932i | \(-0.125430\pi\) | ||||
0.923361 | + | 0.383932i | \(0.125430\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −28.9821 | + | 9.61192i | −1.48480 | + | 0.492433i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.915278 | − | 1.58531i | −0.0467685 | − | 0.0810054i | 0.841694 | − | 0.539956i | \(-0.181559\pi\) |
−0.888462 | + | 0.458950i | \(0.848226\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −1.62797 | − | 13.8662i | −0.0827546 | − | 0.704861i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | 5.69530 | − | 9.86454i | 0.288763 | − | 0.500152i | −0.684752 | − | 0.728776i | \(-0.740089\pi\) |
0.973515 | + | 0.228624i | \(0.0734227\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 1.00069 | + | 1.73324i | 0.0506070 | + | 0.0876539i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 7.36033 | + | 6.54674i | 0.371280 | + | 0.330240i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −15.6538 | −0.787630 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 10.4313 | 0.523532 | 0.261766 | − | 0.965131i | \(-0.415695\pi\) | ||||
0.261766 | + | 0.965131i | \(0.415695\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 17.0371 | + | 29.5091i | 0.850790 | + | 1.47361i | 0.880496 | + | 0.474053i | \(0.157210\pi\) |
−0.0297058 | + | 0.999559i | \(0.509457\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −1.98212 | + | 3.43313i | −0.0987364 | + | 0.171016i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −14.8807 | + | 3.54299i | −0.739427 | + | 0.176053i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 8.51671 | − | 14.7514i | 0.422158 | − | 0.731199i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 1.98762 | + | 3.44266i | 0.0982815 | + | 0.170229i | 0.910973 | − | 0.412465i | \(-0.135332\pi\) |
−0.812692 | + | 0.582694i | \(0.801999\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | −6.80470 | + | 32.9981i | −0.335651 | + | 1.62768i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −14.9752 | −0.735106 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | 3.86652 | + | 3.43913i | 0.189345 | + | 0.168415i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | −4.72184 | − | 8.17847i | −0.230677 | − | 0.399544i | 0.727331 | − | 0.686287i | \(-0.240761\pi\) |
−0.958008 | + | 0.286743i | \(0.907427\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 3.16002 | − | 5.47331i | 0.154010 | − | 0.266753i | −0.778688 | − | 0.627411i | \(-0.784115\pi\) |
0.932698 | + | 0.360658i | \(0.117448\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −4.54325 | − | 38.6971i | −0.220900 | − | 1.88152i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −2.96727 | + | 5.13946i | −0.143934 | + | 0.249300i | ||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | 3.16613 | − | 1.05005i | 0.152862 | − | 0.0506967i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | −27.7541 | −1.33687 | −0.668434 | − | 0.743772i | \(-0.733035\pi\) | ||||
−0.668434 | + | 0.743772i | \(0.733035\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −11.2473 | −0.540510 | −0.270255 | − | 0.962789i | \(-0.587108\pi\) | ||||
−0.270255 | + | 0.962789i | \(0.587108\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −12.6032 | + | 4.17985i | −0.604278 | + | 0.200409i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −1.77561 | − | 3.07545i | −0.0849391 | − | 0.147119i | ||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −7.54325 | + | 13.0653i | −0.360020 | + | 0.623573i | −0.987964 | − | 0.154686i | \(-0.950563\pi\) |
0.627944 | + | 0.778259i | \(0.283897\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −3.96658 | + | 6.87032i | −0.188458 | + | 0.326419i | −0.944736 | − | 0.327831i | \(-0.893682\pi\) |
0.756278 | + | 0.654250i | \(0.227016\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 8.20396 | + | 14.2097i | 0.388905 | + | 0.673603i | ||||
\(446\) | 0 | 0 | ||||||||
\(447\) | 10.4814 | + | 9.32284i | 0.495755 | + | 0.440955i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | −32.5636 | −1.53677 | −0.768386 | − | 0.639987i | \(-0.778940\pi\) | ||||
−0.768386 | + | 0.639987i | \(0.778940\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 14.5563 | 0.685430 | ||||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −3.10074 | + | 15.0365i | −0.145686 | + | 0.706475i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −5.70396 | + | 9.87955i | −0.266820 | + | 0.462146i | −0.968039 | − | 0.250800i | \(-0.919306\pi\) |
0.701219 | + | 0.712946i | \(0.252640\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 8.36831 | − | 11.9709i | 0.390599 | − | 0.558752i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 2.45853 | − | 4.25830i | 0.114505 | − | 0.198329i | −0.803077 | − | 0.595876i | \(-0.796805\pi\) |
0.917582 | + | 0.397547i | \(0.130138\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.59957 | − | 13.1628i | −0.353182 | − | 0.611729i | 0.633623 | − | 0.773642i | \(-0.281567\pi\) |
−0.986805 | + | 0.161913i | \(0.948234\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | −3.03156 | + | 14.7010i | −0.140585 | + | 0.681742i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −23.7810 | −1.10046 | −0.550228 | − | 0.835015i | \(-0.685459\pi\) | ||||
−0.550228 | + | 0.835015i | \(0.685459\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 11.3436 | + | 10.0897i | 0.522687 | + | 0.464910i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.76400 | + | 9.98354i | 0.265029 | + | 0.459044i | ||||
\(474\) | 0 | 0 | ||||||||
\(475\) | 5.26509 | − | 9.11941i | 0.241579 | − | 0.418427i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 4.54325 | − | 3.38597i | 0.208021 | − | 0.155033i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | 3.02909 | − | 5.24654i | 0.138403 | − | 0.239720i | −0.788489 | − | 0.615048i | \(-0.789137\pi\) |
0.926892 | + | 0.375328i | \(0.122470\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.67309 | − | 4.62992i | −0.121882 | − | 0.211106i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | −14.6872 | −0.666914 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 1.13602 | 0.0514781 | 0.0257391 | − | 0.999669i | \(-0.491806\pi\) | ||||
0.0257391 | + | 0.999669i | \(0.491806\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 3.26764 | − | 1.08371i | 0.147768 | − | 0.0490072i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 16.4382 | + | 28.4718i | 0.741845 | + | 1.28491i | 0.951655 | + | 0.307170i | \(0.0993821\pi\) |
−0.209810 | + | 0.977742i | \(0.567285\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 6.33929 | − | 10.9800i | 0.285507 | − | 0.494513i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 10.1273 | − | 7.54760i | 0.455188 | − | 0.339239i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −13.0989 | − | 22.6879i | −0.586387 | − | 1.01565i | −0.994701 | − | 0.102810i | \(-0.967217\pi\) |
0.408314 | − | 0.912841i | \(-0.366117\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −3.39307 | − | 3.01801i | −0.151591 | − | 0.134835i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 25.8516 | 1.15267 | 0.576333 | − | 0.817215i | \(-0.304483\pi\) | ||||
0.576333 | + | 0.817215i | \(0.304483\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −4.09888 | −0.182398 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −4.33613 | + | 21.0273i | −0.192574 | + | 0.933854i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 17.5858 | + | 30.4595i | 0.779478 | + | 1.35009i | 0.932243 | + | 0.361832i | \(0.117849\pi\) |
−0.152766 | + | 0.988262i | \(0.548818\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | −14.8486 | + | 21.2410i | −0.655584 | + | 0.937812i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −3.68292 | + | 6.37900i | −0.162289 | + | 0.281092i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 16.0858 | + | 27.8615i | 0.707453 | + | 1.22535i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 1.82946 | − | 8.87163i | 0.0803045 | − | 0.389421i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 17.8626 | 0.782575 | 0.391287 | − | 0.920269i | \(-0.372030\pi\) | ||||
0.391287 | + | 0.920269i | \(0.372030\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 22.8640 | 0.999772 | 0.499886 | − | 0.866091i | \(-0.333375\pi\) | ||||
0.499886 | + | 0.866091i | \(0.333375\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −7.16621 | − | 12.4122i | −0.312165 | − | 0.540685i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 11.2465 | − | 19.4795i | 0.488979 | − | 0.846937i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 39.3671 | + | 16.9573i | 1.70839 | + | 0.735883i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 2.28435 | − | 3.95661i | 0.0989462 | − | 0.171380i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −16.3145 | − | 28.2576i | −0.705339 | − | 1.22168i | ||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 7.83379 | − | 2.59808i | 0.338053 | − | 0.112115i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 22.3077 | 0.959081 | 0.479541 | − | 0.877520i | \(-0.340803\pi\) | ||||
0.479541 | + | 0.877520i | \(0.340803\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −17.1490 | + | 5.68747i | −0.735935 | + | 0.244073i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −16.1149 | − | 27.9118i | −0.690287 | − | 1.19561i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −10.8083 | + | 18.7206i | −0.462131 | + | 0.800435i | −0.999067 | − | 0.0431882i | \(-0.986249\pi\) |
0.536936 | + | 0.843623i | \(0.319582\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −5.00550 | − | 42.6343i | −0.213630 | − | 1.81959i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −11.2484 | + | 19.4828i | −0.479197 | + | 0.829994i | ||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | −15.1254 | − | 13.4535i | −0.642039 | − | 0.571069i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 3.17535 | 0.134544 | 0.0672720 | − | 0.997735i | \(-0.478570\pi\) | ||||
0.0672720 | + | 0.997735i | \(0.478570\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 3.61822 | 0.153034 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −2.43571 | + | 11.8115i | −0.102836 | + | 0.498682i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 21.8814 | + | 37.8997i | 0.922190 | + | 1.59728i | 0.796019 | + | 0.605271i | \(0.206935\pi\) |
0.126171 | + | 0.992009i | \(0.459731\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −10.9876 | + | 19.0311i | −0.462253 | + | 0.800645i | ||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 11.9313 | − | 20.6656i | 0.500186 | − | 0.866348i | −0.499814 | − | 0.866133i | \(-0.666598\pi\) |
1.00000 | 0.000214897i | \(-6.84039e-5\pi\) | ||||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −5.11058 | − | 8.85178i | −0.213871 | − | 0.370435i | 0.739052 | − | 0.673649i | \(-0.235274\pi\) |
−0.952923 | + | 0.303213i | \(0.901941\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 4.66002 | − | 22.5979i | 0.194675 | − | 0.944040i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −1.50324 | −0.0626893 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 36.0370 | 1.50024 | 0.750120 | − | 0.661302i | \(-0.229996\pi\) | ||||
0.750120 | + | 0.661302i | \(0.229996\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −18.9487 | − | 16.8542i | −0.787481 | − | 0.700435i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −2.33929 | + | 4.05178i | −0.0968836 | + | 0.167807i | ||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −0.462249 | − | 3.93720i | −0.0191116 | − | 0.162783i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −10.5142 | + | 18.2111i | −0.433966 | + | 0.751651i | −0.997211 | − | 0.0746391i | \(-0.976220\pi\) |
0.563245 | + | 0.826290i | \(0.309553\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 12.7156 | + | 22.0242i | 0.523939 | + | 0.907489i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 30.3905 | − | 10.0790i | 1.25010 | − | 0.414595i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 25.1606 | 1.03322 | 0.516612 | − | 0.856220i | \(-0.327193\pi\) | ||||
0.516612 | + | 0.856220i | \(0.327193\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 38.8257 | − | 12.8766i | 1.58903 | − | 0.527002i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 1.11126 | + | 1.92477i | 0.0454050 | + | 0.0786438i | 0.887835 | − | 0.460162i | \(-0.152209\pi\) |
−0.842430 | + | 0.538806i | \(0.818875\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 14.0494 | − | 24.3343i | 0.573089 | − | 0.992619i | −0.423158 | − | 0.906056i | \(-0.639078\pi\) |
0.996246 | − | 0.0865627i | \(-0.0275883\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −22.0080 | − | 9.47987i | −0.896234 | − | 0.386050i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 4.13348 | − | 7.15939i | 0.168050 | − | 0.291071i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | −3.26509 | − | 5.65531i | −0.132526 | − | 0.229542i | 0.792124 | − | 0.610361i | \(-0.208975\pi\) |
−0.924650 | + | 0.380819i | \(0.875642\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 10.0975 | 0.408501 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 10.7280 | 0.433298 | 0.216649 | − | 0.976250i | \(-0.430487\pi\) | ||||
0.216649 | + | 0.976250i | \(0.430487\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 3.49381 | − | 16.9426i | 0.140884 | − | 0.683191i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 15.5265 | + | 26.8928i | 0.625075 | + | 1.08266i | 0.988526 | + | 0.151049i | \(0.0482650\pi\) |
−0.363451 | + | 0.931613i | \(0.618402\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.723217 | + | 1.25265i | −0.0290685 | + | 0.0503482i | −0.880194 | − | 0.474615i | \(-0.842587\pi\) |
0.851125 | + | 0.524963i | \(0.175921\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 3.68587 | + | 0.319601i | 0.147909 | + | 0.0128252i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 4.99312 | + | 8.64834i | 0.199725 | + | 0.345934i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | 4.32189 | − | 20.9582i | 0.172600 | − | 0.836991i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 19.3287 | 0.770686 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | 0.0741250 | 0.00295087 | 0.00147544 | − | 0.999999i | \(-0.499530\pi\) | ||||
0.00147544 | + | 0.999999i | \(0.499530\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −18.8367 | − | 16.7546i | −0.748693 | − | 0.665935i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −14.9814 | − | 25.9486i | −0.594520 | − | 1.02974i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −24.6877 | + | 18.3991i | −0.976628 | + | 0.727855i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 23.5204 | − | 40.7384i | 0.928998 | − | 1.60907i | 0.143996 | − | 0.989578i | \(-0.454005\pi\) |
0.785002 | − | 0.619494i | \(-0.212662\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | −16.8647 | − | 29.2105i | −0.665077 | − | 1.15195i | −0.979264 | − | 0.202587i | \(-0.935065\pi\) |
0.314187 | − | 0.949361i | \(-0.398268\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 13.0036 | − | 4.31266i | 0.512018 | − | 0.169811i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | −44.9629 | −1.76767 | −0.883836 | − | 0.467796i | \(-0.845048\pi\) | ||||
−0.883836 | + | 0.467796i | \(0.845048\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −35.3928 | −1.38929 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | −20.8578 | − | 36.1267i | −0.816228 | − | 1.41375i | −0.908443 | − | 0.418010i | \(-0.862728\pi\) |
0.0922143 | − | 0.995739i | \(-0.470606\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −4.83310 | + | 8.37118i | −0.188845 | + | 0.327089i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −11.9975 | + | 8.94138i | −0.468065 | + | 0.348837i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 10.5259 | − | 18.2313i | 0.410029 | − | 0.710191i | −0.584863 | − | 0.811132i | \(-0.698852\pi\) |
0.994892 | + | 0.100941i | \(0.0321852\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 11.2218 | + | 19.4368i | 0.436479 | + | 0.756004i | 0.997415 | − | 0.0718553i | \(-0.0228920\pi\) |
−0.560936 | + | 0.827859i | \(0.689559\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 2.82829 | + | 2.51566i | 0.109842 | + | 0.0977001i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 3.21153 | 0.124351 | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | −3.30401 | + | 16.0222i | −0.127741 | + | 0.619454i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 17.7225 | + | 30.6962i | 0.684168 | + | 1.18501i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 5.83929 | − | 10.1140i | 0.225088 | − | 0.389864i | −0.731258 | − | 0.682101i | \(-0.761066\pi\) |
0.956346 | + | 0.292237i | \(0.0943996\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.64400 | + | 9.93902i | 0.178747 | + | 0.382553i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | 5.23422 | − | 9.06593i | 0.201167 | − | 0.348432i | −0.747737 | − | 0.663995i | \(-0.768860\pi\) |
0.948905 | + | 0.315562i | \(0.102193\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −6.68539 | + | 32.4195i | −0.256185 | + | 1.24232i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 32.8158 | 1.25566 | 0.627832 | − | 0.778349i | \(-0.283943\pi\) | ||||
0.627832 | + | 0.778349i | \(0.283943\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | −33.0617 | −1.26322 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | −14.8120 | − | 13.1747i | −0.565113 | − | 0.502647i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 0.734219 | + | 1.27171i | 0.0279715 | + | 0.0484481i | ||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 2.95056 | − | 5.11052i | 0.112245 | − | 0.194413i | −0.804430 | − | 0.594047i | \(-0.797529\pi\) |
0.916675 | + | 0.399634i | \(0.130863\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −2.53892 | + | 4.39754i | −0.0963068 | + | 0.166808i | ||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 8.25890 | + | 14.3048i | 0.312828 | + | 0.541834i | ||||
\(698\) | 0 | 0 | ||||||||
\(699\) | 1.95715 | − | 0.649089i | 0.0740263 | − | 0.0245508i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −12.3782 | −0.467519 | −0.233759 | − | 0.972294i | \(-0.575103\pi\) | ||||
−0.233759 | + | 0.972294i | \(0.575103\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −34.2967 | −1.29352 | ||||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 36.2898 | − | 12.0355i | 1.36675 | − | 0.453283i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 6.64145 | − | 11.5033i | 0.249425 | − | 0.432016i | −0.713942 | − | 0.700205i | \(-0.753092\pi\) |
0.963366 | + | 0.268189i | \(0.0864251\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −3.22184 | − | 27.4420i | −0.120828 | − | 1.02915i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 1.81522 | − | 3.14406i | 0.0679806 | − | 0.117746i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 1.63664 | + | 2.83474i | 0.0612067 | + | 0.106013i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | 31.4265 | + | 27.9527i | 1.17364 | + | 1.04391i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 24.3694 | 0.908825 | 0.454413 | − | 0.890791i | \(-0.349849\pi\) | ||||
0.454413 | + | 0.890791i | \(0.349849\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 7.49264 | − | 36.3342i | 0.278654 | − | 1.35128i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 4.76145 | + | 8.24707i | 0.176836 | + | 0.306289i | ||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −7.99450 | + | 13.8469i | −0.296500 | + | 0.513552i | −0.975333 | − | 0.220740i | \(-0.929153\pi\) |
0.678833 | + | 0.734293i | \(0.262486\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −9.27375 | − | 25.3574i | −0.343472 | − | 0.939163i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −6.54070 | + | 11.3288i | −0.241917 | + | 0.419012i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −21.1414 | − | 36.6181i | −0.780877 | − | 1.35252i | −0.931431 | − | 0.363917i | \(-0.881439\pi\) |
0.150554 | − | 0.988602i | \(-0.451894\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 19.7861 | 0.728832 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −3.08650 | −0.113539 | −0.0567695 | − | 0.998387i | \(-0.518080\pi\) | ||||
−0.0567695 | + | 0.998387i | \(0.518080\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −5.01849 | − | 4.46376i | −0.184359 | − | 0.163980i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −3.31522 | − | 5.74213i | −0.121624 | − | 0.210658i | 0.798784 | − | 0.601617i | \(-0.205477\pi\) |
−0.920408 | + | 0.390959i | \(0.872143\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −6.88255 | + | 11.9209i | −0.252157 | + | 0.436749i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −3.08217 | − | 26.2524i | −0.112771 | − | 0.960524i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 21.3702 | + | 37.0142i | 0.779808 | + | 1.35067i | 0.932052 | + | 0.362325i | \(0.118017\pi\) |
−0.152243 | + | 0.988343i | \(0.548650\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.40585 | + | 1.46120i | −0.160558 | + | 0.0532491i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −15.0655 | −0.548288 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −31.0232 | −1.12756 | −0.563779 | − | 0.825926i | \(-0.690653\pi\) | ||||
−0.563779 | + | 0.825926i | \(0.690653\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −2.89954 | + | 0.961632i | −0.105247 | + | 0.0349050i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | 11.8182 | + | 20.4697i | 0.428409 | + | 0.742025i | 0.996732 | − | 0.0807799i | \(-0.0257411\pi\) |
−0.568323 | + | 0.822805i | \(0.692408\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 13.1632 | + | 5.67000i | 0.475916 | + | 0.204999i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.55425 | + | 9.62025i | −0.200553 | + | 0.347367i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −1.73422 | − | 3.00376i | −0.0625375 | − | 0.108318i | 0.833061 | − | 0.553180i | \(-0.186586\pi\) |
−0.895599 | + | 0.444862i | \(0.853253\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 14.3462 | + | 12.7604i | 0.516665 | + | 0.459554i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −34.5970 | −1.24437 | −0.622184 | − | 0.782871i | \(-0.713755\pi\) | ||||
−0.622184 | + | 0.782871i | \(0.713755\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | 10.7651 | 0.386694 | ||||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −14.6545 | − | 25.3824i | −0.525053 | − | 0.909418i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 12.7115 | − | 22.0170i | 0.454854 | − | 0.787831i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | −9.92147 | − | 21.2338i | −0.354564 | − | 0.758834i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −7.44870 | + | 12.9015i | −0.265855 | + | 0.460475i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | −6.07963 | − | 10.5302i | −0.216715 | − | 0.375362i | 0.737087 | − | 0.675798i | \(-0.236201\pi\) |
−0.953802 | + | 0.300437i | \(0.902868\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 4.69028 | − | 22.7446i | 0.166978 | − | 0.809730i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 11.1249 | 0.395056 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 4.15452 | + | 3.69529i | 0.147346 | + | 0.131058i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.89493 | + | 5.01416i | 0.102544 | + | 0.177611i | 0.912732 | − | 0.408559i | \(-0.133969\pi\) |
−0.810188 | + | 0.586170i | \(0.800635\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −18.2534 | + | 31.6158i | −0.645759 | + | 1.11849i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −23.2218 | + | 17.3066i | −0.820501 | + | 0.611497i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 6.17742 | − | 10.6996i | 0.217996 | − | 0.377581i | ||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | 6.72431 | − | 2.23012i | 0.236707 | − | 0.0785038i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −49.1817 | −1.72914 | −0.864568 | − | 0.502516i | \(-0.832408\pi\) | ||||
−0.864568 | + | 0.502516i | \(0.832408\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −40.7266 | −1.43010 | −0.715052 | − | 0.699072i | \(-0.753597\pi\) | ||||
−0.715052 | + | 0.699072i | \(0.753597\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 10.0672 | − | 3.33880i | 0.353074 | − | 0.117097i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 1.68911 | + | 2.92562i | 0.0591669 | + | 0.102480i | ||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 11.6058 | − | 20.1018i | 0.406034 | − | 0.703272i | ||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | −7.54689 | + | 13.0716i | −0.263388 | + | 0.456202i | −0.967140 | − | 0.254244i | \(-0.918173\pi\) |
0.703752 | + | 0.710446i | \(0.251507\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | −8.00000 | − | 13.8564i | −0.278862 | − | 0.483004i | 0.692240 | − | 0.721668i | \(-0.256624\pi\) |
−0.971102 | + | 0.238664i | \(0.923291\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | −6.76833 | − | 6.02018i | −0.235643 | − | 0.209596i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 35.2348 | 1.22523 | 0.612616 | − | 0.790381i | \(-0.290117\pi\) | ||||
0.612616 | + | 0.790381i | \(0.290117\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.23491 | 0.112353 | 0.0561765 | − | 0.998421i | \(-0.482109\pi\) | ||||
0.0561765 | + | 0.998421i | \(0.482109\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 5.51485 | − | 26.7432i | 0.191308 | − | 0.927713i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 2.22803 | − | 3.85906i | 0.0771041 | − | 0.133548i | ||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −26.3955 | − | 2.28875i | −0.912363 | − | 0.0791109i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | −15.5197 | + | 26.8808i | −0.535798 | + | 0.928030i | 0.463326 | + | 0.886188i | \(0.346656\pi\) |
−0.999124 | + | 0.0418419i | \(0.986677\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 4.32760 | + | 7.49563i | 0.149228 | + | 0.258470i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | −7.41225 | + | 35.9443i | −0.255291 | + | 1.23799i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | −21.0678 | −0.724755 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −8.89926 | − | 7.91556i | −0.305422 | − | 0.271661i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | 2.44801 | + | 4.24008i | 0.0839167 | + | 0.145348i | ||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −8.03637 | + | 13.9194i | −0.275160 | + | 0.476591i | −0.970176 | − | 0.242403i | \(-0.922064\pi\) |
0.695015 | + | 0.718995i | \(0.255398\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | −23.3566 | − | 10.0608i | −0.798779 | − | 0.344072i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | 9.61058 | − | 16.6460i | 0.328291 | − | 0.568617i | −0.653882 | − | 0.756597i | \(-0.726861\pi\) |
0.982173 | + | 0.187980i | \(0.0601940\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −7.40112 | − | 12.8191i | −0.252523 | − | 0.437382i | 0.711697 | − | 0.702487i | \(-0.247927\pi\) |
−0.964220 | + | 0.265104i | \(0.914594\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 14.7688 | 0.502736 | 0.251368 | − | 0.967892i | \(-0.419120\pi\) | ||||
0.251368 | + | 0.967892i | \(0.419120\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 8.88874 | 0.302226 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 14.9585 | − | 4.96099i | 0.508018 | − | 0.168484i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 11.4072 | + | 19.7579i | 0.386964 | + | 0.670241i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 3.10507 | − | 5.37815i | 0.105211 | − | 0.182232i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −3.02290 | − | 25.7475i | −0.102310 | − | 0.871421i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −26.1916 | − | 45.3651i | −0.884427 | − | 1.53187i | −0.846369 | − | 0.532597i | \(-0.821216\pi\) |
−0.0380575 | − | 0.999276i | \(-0.512117\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | 35.5988 | + | 31.6638i | 1.20072 | + | 1.06799i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | 31.3214 | 1.05525 | 0.527623 | − | 0.849479i | \(-0.323084\pi\) | ||||
0.527623 | + | 0.849479i | \(0.323084\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −43.0494 | −1.44873 | −0.724363 | − | 0.689419i | \(-0.757866\pi\) | ||||
−0.724363 | + | 0.689419i | \(0.757866\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | −8.49498 | + | 41.1948i | −0.285556 | + | 1.38475i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −7.48831 | − | 12.9701i | −0.251433 | − | 0.435494i | 0.712488 | − | 0.701685i | \(-0.247568\pi\) |
−0.963921 | + | 0.266190i | \(0.914235\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 15.3157 | + | 16.2002i | 0.513095 | + | 0.542728i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | 32.3887 | − | 56.0988i | 1.08385 | − | 1.87727i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 4.04944 | + | 7.01384i | 0.135358 | + | 0.234447i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | −0.193645 | + | 0.939046i | −0.00646562 | + | 0.0313538i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −22.9986 | −0.767047 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −5.30903 | −0.176870 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −8.86467 | − | 15.3541i | −0.294671 | − | 0.510386i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −15.2280 | + | 26.3756i | −0.505636 | + | 0.875787i | 0.494343 | + | 0.869267i | \(0.335409\pi\) |
−0.999979 | + | 0.00652002i | \(0.997925\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −0.843624 | − | 7.18555i | −0.0279812 | − | 0.238330i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 9.97593 | − | 17.2788i | 0.330517 | − | 0.572473i | −0.652096 | − | 0.758136i | \(-0.726110\pi\) |
0.982613 | + | 0.185664i | \(0.0594435\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 10.9127 | + | 18.9014i | 0.361159 | + | 0.625545i | ||||
\(914\) | 0 | 0 | ||||||||
\(915\) | 39.9820 | − | 13.2600i | 1.32177 | − | 0.438363i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 45.6291 | 1.50516 | 0.752582 | − | 0.658498i | \(-0.228808\pi\) | ||||
0.752582 | + | 0.658498i | \(0.228808\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −35.3752 | + | 11.7322i | −1.16565 | + | 0.386588i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −3.98969 | − | 6.91034i | −0.131322 | − | 0.227457i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −7.25890 | + | 12.5728i | −0.238671 | + | 0.413391i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −11.9407 | − | 5.14343i | −0.392185 | − | 0.168932i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 28.1861 | − | 48.8197i | 0.924755 | − | 1.60172i | 0.132801 | − | 0.991143i | \(-0.457603\pi\) |
0.791954 | − | 0.610580i | \(-0.209064\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −23.7942 | − | 21.1640i | −0.778987 | − | 0.692880i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −11.8343 | −0.387022 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 36.8530 | 1.20393 | 0.601967 | − | 0.798521i | \(-0.294384\pi\) | ||||
0.601967 | + | 0.798521i | \(0.294384\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0.000481840 | − | 0.00233659i | 1.57243e−5 | − | 7.62519e-5i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −4.38000 | − | 7.58638i | −0.142784 | − | 0.247309i | 0.785760 | − | 0.618531i | \(-0.212272\pi\) |
−0.928544 | + | 0.371223i | \(0.878939\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −2.09201 | + | 3.62346i | −0.0681251 | + | 0.117996i | ||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | −13.3226 | + | 23.0754i | −0.432926 | + | 0.749849i | −0.997124 | − | 0.0757901i | \(-0.975852\pi\) |
0.564198 | + | 0.825640i | \(0.309185\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −1.93887 | − | 3.35822i | −0.0629383 | − | 0.109012i | ||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 4.93199 | − | 23.9168i | 0.159931 | − | 0.775554i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 24.3039 | 0.787282 | 0.393641 | − | 0.919264i | \(-0.371215\pi\) | ||||
0.393641 | + | 0.919264i | \(0.371215\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 22.6414 | 0.732660 | ||||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | 14.4599 | + | 12.8616i | 0.467422 | + | 0.415755i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 2.50069 | − | 4.33132i | 0.0806674 | − | 0.139720i | ||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 46.1792 | − | 34.4161i | 1.48810 | − | 1.10904i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 12.4425 | − | 21.5511i | 0.400539 | − | 0.693753i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 5.22872 | + | 9.05641i | 0.168144 | + | 0.291234i | 0.937767 | − | 0.347264i | \(-0.112889\pi\) |
−0.769623 | + | 0.638498i | \(0.779556\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 23.0483 | − | 7.64396i | 0.740417 | − | 0.245559i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 41.7156 | 1.33872 | 0.669358 | − | 0.742940i | \(-0.266569\pi\) | ||||
0.669358 | + | 0.742940i | \(0.266569\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −2.69853 | + | 0.894969i | −0.0864223 | + | 0.0286619i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | −2.94506 | − | 5.10099i | −0.0942207 | − | 0.163195i | 0.815062 | − | 0.579373i | \(-0.196703\pi\) |
−0.909283 | + | 0.416178i | \(0.863369\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 11.9567 | − | 20.7097i | 0.382139 | − | 0.661885i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 45.6141 | − | 33.9950i | 1.45635 | − | 1.08538i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 20.9196 | − | 36.2338i | 0.667232 | − | 1.15568i | −0.311443 | − | 0.950265i | \(-0.600812\pi\) |
0.978675 | − | 0.205415i | \(-0.0658543\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 15.7095 | + | 27.2096i | 0.500545 | + | 0.866969i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −3.31356 | −0.105365 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −54.7156 | −1.73810 | −0.869049 | − | 0.494726i | \(-0.835268\pi\) | ||||
−0.869049 | + | 0.494726i | \(0.835268\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | 4.88441 | − | 23.6860i | 0.155002 | − | 0.751653i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.0698 | + | 34.7619i | 0.636255 | + | 1.10203i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −9.02476 | + | 15.6313i | −0.285817 | + | 0.495050i | −0.972807 | − | 0.231617i | \(-0.925598\pi\) |
0.686990 | + | 0.726667i | \(0.258932\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 20.4716 | − | 29.2846i | 0.647693 | − | 0.926524i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))