Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [1764,2,Mod(509,1764)]
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, 5, 5]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("1764.509");
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.w (of order \(6\), degree \(2\), not 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: | \(16\) |
Relative dimension: | \(8\) over \(\Q(\zeta_{6})\) |
Coefficient field: | \(\mathbb{Q}[x]/(x^{16} - \cdots)\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{16} - 3x^{14} - 9x^{12} - 9x^{10} + 225x^{8} - 81x^{6} - 729x^{4} - 2187x^{2} + 6561 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{13}]\) |
Coefficient ring index: | \( 2^{2}\cdot 3^{4} \) |
Twist minimal: | no (minimal twist has level 252) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{6}]$ |
Embedding invariants
Embedding label | 509.2 | ||
Root | \(-1.71965 + 0.206851i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 1764.509 |
Dual form | 1764.2.w.a.1109.2 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/1764\mathbb{Z}\right)^\times\).
\(n\) | \(785\) | \(883\) | \(1081\) |
\(\chi(n)\) | \(e\left(\frac{5}{6}\right)\) | \(1\) | \(e\left(\frac{5}{6}\right)\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | −1.03897 | + | 1.38584i | −0.599847 | + | 0.800115i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | 2.09336 | + | 3.62580i | 0.936177 | + | 1.62151i | 0.772521 | + | 0.634989i | \(0.218995\pi\) |
0.163656 | + | 0.986518i | \(0.447671\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | −0.841101 | − | 2.87968i | −0.280367 | − | 0.959893i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 1.23222 | + | 0.711425i | 0.371529 | + | 0.214503i | 0.674126 | − | 0.738616i | \(-0.264520\pi\) |
−0.302597 | + | 0.953119i | \(0.597854\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 0.850739 | + | 0.491174i | 0.235952 | + | 0.136227i | 0.613315 | − | 0.789838i | \(-0.289836\pi\) |
−0.377363 | + | 0.926066i | \(0.623169\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −7.19970 | − | 0.866025i | −1.85895 | − | 0.223607i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0.185474 | + | 0.321250i | 0.0449840 | + | 0.0779145i | 0.887641 | − | 0.460537i | \(-0.152343\pi\) |
−0.842657 | + | 0.538451i | \(0.819010\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 4.30823 | + | 2.48736i | 0.988375 | + | 0.570638i | 0.904788 | − | 0.425862i | \(-0.140029\pi\) |
0.0835867 | + | 0.996501i | \(0.473362\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0 | 0 | ||||||||
\(23\) | −4.98775 | + | 2.87968i | −1.04002 | + | 0.600455i | −0.919838 | − | 0.392298i | \(-0.871680\pi\) |
−0.120179 | + | 0.992752i | \(0.538347\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −6.26427 | + | 10.8500i | −1.25285 | + | 2.17001i | ||||
\(26\) | 0 | 0 | ||||||||
\(27\) | 4.86465 | + | 1.82626i | 0.936202 | + | 0.351463i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 7.31732 | − | 4.22466i | 1.35879 | − | 0.784499i | 0.369332 | − | 0.929298i | \(-0.379587\pi\) |
0.989461 | + | 0.144798i | \(0.0462534\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 7.25160i | 1.30243i | 0.758895 | + | 0.651213i | \(0.225739\pi\) | ||||
−0.758895 | + | 0.651213i | \(0.774261\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −2.26616 | + | 0.968518i | −0.394488 | + | 0.168597i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −1.73222 | + | 3.00030i | −0.284776 | + | 0.493246i | −0.972555 | − | 0.232674i | \(-0.925252\pi\) |
0.687779 | + | 0.725920i | \(0.258586\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | −1.56458 | + | 0.668674i | −0.250533 | + | 0.107074i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 1.06981 | − | 1.85297i | 0.167077 | − | 0.289386i | −0.770314 | − | 0.637665i | \(-0.779901\pi\) |
0.937391 | + | 0.348279i | \(0.113234\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 3.00875 | + | 5.21130i | 0.458830 | + | 0.794716i | 0.998899 | − | 0.0469039i | \(-0.0149354\pi\) |
−0.540070 | + | 0.841620i | \(0.681602\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | 8.68041 | − | 9.07785i | 1.29400 | − | 1.35325i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −8.27085 | −1.20643 | −0.603213 | − | 0.797580i | \(-0.706113\pi\) | ||||
−0.603213 | + | 0.797580i | \(0.706113\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | −0.637901 | − | 0.0767308i | −0.0893240 | − | 0.0107445i | ||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 4.30627 | − | 2.48623i | 0.591512 | − | 0.341509i | −0.174183 | − | 0.984713i | \(-0.555729\pi\) |
0.765695 | + | 0.643204i | \(0.222395\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.95706i | 0.803250i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | −7.92317 | + | 3.38623i | −1.04945 | + | 0.448517i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −4.55766 | −0.593357 | −0.296678 | − | 0.954977i | \(-0.595879\pi\) | ||||
−0.296678 | + | 0.954977i | \(0.595879\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | − | 7.51035i | − | 0.961602i | −0.876830 | − | 0.480801i | \(-0.840346\pi\) | ||
0.876830 | − | 0.480801i | \(-0.159654\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 0 | 0 | ||||||||
\(65\) | 4.11281i | 0.510131i | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −10.0641 | −1.22953 | −0.614763 | − | 0.788712i | \(-0.710748\pi\) | ||||
−0.614763 | + | 0.788712i | \(0.710748\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 1.19133 | − | 9.90411i | 0.143419 | − | 1.19231i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | − | 10.9555i | − | 1.30018i | −0.759857 | − | 0.650090i | \(-0.774731\pi\) | ||
0.759857 | − | 0.650090i | \(-0.225269\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | 8.25191 | − | 4.76424i | 0.965813 | − | 0.557612i | 0.0678555 | − | 0.997695i | \(-0.478384\pi\) |
0.897957 | + | 0.440083i | \(0.145051\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −8.52805 | − | 19.9541i | −0.984734 | − | 2.30410i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.51105 | −0.957568 | −0.478784 | − | 0.877933i | \(-0.658922\pi\) | ||||
−0.478784 | + | 0.877933i | \(0.658922\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.58510 | + | 4.84420i | −0.842789 | + | 0.538244i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | −0.972254 | − | 1.68399i | −0.106719 | − | 0.184842i | 0.807720 | − | 0.589566i | \(-0.200701\pi\) |
−0.914439 | + | 0.404724i | \(0.867368\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −0.776524 | + | 1.34498i | −0.0842259 | + | 0.145884i | ||||
\(86\) | 0 | 0 | ||||||||
\(87\) | −1.74775 | + | 14.5299i | −0.187378 | + | 1.55777i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | −3.90368 | + | 6.76137i | −0.413789 | + | 0.716703i | −0.995300 | − | 0.0968347i | \(-0.969128\pi\) |
0.581512 | + | 0.813538i | \(0.302462\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | −10.0495 | − | 7.53416i | −1.04209 | − | 0.781256i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 20.8277i | 2.13687i | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 3.34099 | − | 1.92892i | 0.339226 | − | 0.195852i | −0.320704 | − | 0.947180i | \(-0.603919\pi\) |
0.659930 | + | 0.751327i | \(0.270586\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 1.01225 | − | 4.14679i | 0.101735 | − | 0.416768i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | 4.50637 | − | 7.80526i | 0.448401 | − | 0.776653i | −0.549882 | − | 0.835243i | \(-0.685327\pi\) |
0.998282 | + | 0.0585901i | \(0.0186605\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 5.96343 | − | 3.44299i | 0.587594 | − | 0.339248i | −0.176551 | − | 0.984291i | \(-0.556494\pi\) |
0.764146 | + | 0.645044i | \(0.223161\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 0 | 0 | ||||||||
\(107\) | −9.84062 | − | 5.68149i | −0.951329 | − | 0.549250i | −0.0578356 | − | 0.998326i | \(-0.518420\pi\) |
−0.893494 | + | 0.449076i | \(0.851753\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 7.99650 | + | 13.8503i | 0.765926 | + | 1.32662i | 0.939756 | + | 0.341846i | \(0.111052\pi\) |
−0.173830 | + | 0.984776i | \(0.555614\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −2.35821 | − | 5.51779i | −0.223832 | − | 0.523726i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 2.17043 | + | 1.25310i | 0.204177 | + | 0.117881i | 0.598602 | − | 0.801046i | \(-0.295723\pi\) |
−0.394426 | + | 0.918928i | \(0.629056\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −20.8823 | − | 12.0564i | −1.94728 | − | 1.12426i | ||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 0.698867 | − | 2.86298i | 0.0646103 | − | 0.264683i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.48775 | − | 7.77301i | −0.407977 | − | 0.706637i | ||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 1.45642 | + | 3.40776i | 0.131321 | + | 0.307268i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | −31.5199 | −2.81922 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −1.91140 | −0.169609 | −0.0848046 | − | 0.996398i | \(-0.527027\pi\) | ||||
−0.0848046 | + | 0.996398i | \(0.527027\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −10.3480 | − | 1.24473i | −0.911092 | − | 0.109592i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | 4.32591 | + | 7.49270i | 0.377957 | + | 0.654640i | 0.990765 | − | 0.135592i | \(-0.0432935\pi\) |
−0.612808 | + | 0.790232i | \(0.709960\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | 3.56180 | + | 21.4612i | 0.306551 | + | 1.84709i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | −10.0973 | − | 5.82971i | −0.862675 | − | 0.498065i | 0.00223233 | − | 0.999998i | \(-0.499289\pi\) |
−0.864907 | + | 0.501932i | \(0.832623\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | 4.82663 | + | 2.78666i | 0.409390 | + | 0.236361i | 0.690528 | − | 0.723306i | \(-0.257378\pi\) |
−0.281138 | + | 0.959667i | \(0.590712\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 8.59312 | − | 11.4621i | 0.723672 | − | 0.965280i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | 0.698867 | + | 1.21047i | 0.0584422 | + | 0.101225i | ||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 30.6355 | + | 17.6874i | 2.54414 | + | 1.46886i | ||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 0 | 0 | ||||||||
\(149\) | 13.4024 | − | 7.73789i | 1.09797 | − | 0.633913i | 0.162282 | − | 0.986744i | \(-0.448114\pi\) |
0.935687 | + | 0.352832i | \(0.114781\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 8.31732 | − | 14.4060i | 0.676854 | − | 1.17235i | −0.299069 | − | 0.954231i | \(-0.596676\pi\) |
0.975923 | − | 0.218114i | \(-0.0699905\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0.769094 | − | 0.804308i | 0.0621776 | − | 0.0650244i | ||||
\(154\) | 0 | 0 | ||||||||
\(155\) | −26.2928 | + | 15.1802i | −2.11189 | + | 1.21930i | ||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 16.8077i | 1.34140i | 0.741727 | + | 0.670702i | \(0.234007\pi\) | ||||
−0.741727 | + | 0.670702i | \(0.765993\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | −1.02856 | + | 8.55090i | −0.0815699 | + | 0.678131i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −1.75553 | + | 3.04066i | −0.137503 | + | 0.238163i | −0.926551 | − | 0.376169i | \(-0.877241\pi\) |
0.789048 | + | 0.614332i | \(0.210574\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | −8.25553 | − | 6.18918i | −0.642692 | − | 0.481827i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −4.05253 | + | 7.01918i | −0.313594 | + | 0.543160i | −0.979138 | − | 0.203198i | \(-0.934866\pi\) |
0.665544 | + | 0.746359i | \(0.268200\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −6.01750 | − | 10.4226i | −0.462884 | − | 0.801739i | ||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.53913 | − | 14.4984i | 0.270644 | − | 1.10872i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | −13.0969 | −0.995737 | −0.497868 | − | 0.867253i | \(-0.665884\pi\) | ||||
−0.497868 | + | 0.867253i | \(0.665884\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | 4.73525 | − | 6.31618i | 0.355923 | − | 0.474753i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −11.0140 | + | 6.35893i | −0.823225 | + | 0.475289i | −0.851527 | − | 0.524310i | \(-0.824323\pi\) |
0.0283026 | + | 0.999599i | \(0.490990\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | 26.5518i | 1.97358i | 0.161998 | + | 0.986791i | \(0.448206\pi\) | ||||
−0.161998 | + | 0.986791i | \(0.551794\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 10.4081 | + | 7.80300i | 0.769392 | + | 0.576814i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | −14.5046 | −1.06640 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.527802i | 0.0385967i | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | − | 1.26711i | − | 0.0916848i | −0.998949 | − | 0.0458424i | \(-0.985403\pi\) | ||
0.998949 | − | 0.0458424i | \(-0.0145972\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 18.6346 | 1.34135 | 0.670676 | − | 0.741751i | \(-0.266004\pi\) | ||||
0.670676 | + | 0.741751i | \(0.266004\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.69969 | − | 4.27307i | −0.408163 | − | 0.306001i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 5.94312i | 0.423430i | 0.977331 | + | 0.211715i | \(0.0679049\pi\) | ||||
−0.977331 | + | 0.211715i | \(0.932095\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 4.87291 | − | 2.81337i | 0.345431 | − | 0.199435i | −0.317240 | − | 0.948345i | \(-0.602756\pi\) |
0.662671 | + | 0.748910i | \(0.269423\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 10.4563 | − | 13.9472i | 0.737527 | − | 0.983761i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 8.95800 | 0.625654 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 12.4877 | + | 11.9410i | 0.867959 | + | 0.829958i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | 3.53913 | + | 6.12996i | 0.244807 | + | 0.424018i | ||||
\(210\) | 0 | 0 | ||||||||
\(211\) | 1.05305 | − | 1.82393i | 0.0724948 | − | 0.125565i | −0.827499 | − | 0.561467i | \(-0.810237\pi\) |
0.899994 | + | 0.435902i | \(0.143571\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | 15.1826 | + | 11.3824i | 1.04029 | + | 0.779909i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −12.5968 | + | 21.8182i | −0.859092 | + | 1.48799i | ||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −1.97098 | + | 16.3857i | −0.133186 | + | 1.10724i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0.364399i | 0.0245121i | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −5.52351 | + | 3.18900i | −0.369882 | + | 0.213551i | −0.673407 | − | 0.739272i | \(-0.735170\pi\) |
0.303525 | + | 0.952823i | \(0.401836\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 36.5135 | + | 8.91312i | 2.43423 | + | 0.594208i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 5.72365 | − | 9.91365i | 0.379892 | − | 0.657992i | −0.611154 | − | 0.791511i | \(-0.709295\pi\) |
0.991046 | + | 0.133520i | \(0.0426279\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −4.88696 | + | 2.82149i | −0.322940 | + | 0.186449i | −0.652702 | − | 0.757615i | \(-0.726365\pi\) |
0.329762 | + | 0.944064i | \(0.393031\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 0 | 0 | ||||||||
\(233\) | 10.7788 | + | 6.22316i | 0.706145 | + | 0.407693i | 0.809632 | − | 0.586938i | \(-0.199667\pi\) |
−0.103487 | + | 0.994631i | \(0.533000\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −17.3138 | − | 29.9884i | −1.12943 | − | 1.95623i | ||||
\(236\) | 0 | 0 | ||||||||
\(237\) | 8.84269 | − | 11.7950i | 0.574394 | − | 0.766164i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | 3.52450 | + | 2.03487i | 0.227981 | + | 0.131625i | 0.609640 | − | 0.792678i | \(-0.291314\pi\) |
−0.381659 | + | 0.924303i | \(0.624647\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 4.26195 | + | 2.46064i | 0.274537 | + | 0.158504i | 0.630947 | − | 0.775826i | \(-0.282666\pi\) |
−0.356411 | + | 0.934329i | \(0.616000\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | 1.16737 | − | 15.5447i | 0.0748871 | − | 0.997192i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.44345 | + | 4.23218i | 0.155473 | + | 0.269287i | ||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 3.34388 | + | 0.402223i | 0.211910 | + | 0.0254899i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 4.65020 | 0.293518 | 0.146759 | − | 0.989172i | \(-0.453116\pi\) | ||||
0.146759 | + | 0.989172i | \(0.453116\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −8.19470 | −0.515196 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | −1.05714 | − | 2.47353i | −0.0662009 | − | 0.154898i | ||||
\(256\) | 0 | 0 | ||||||||
\(257\) | 5.44701 | + | 9.43450i | 0.339775 | + | 0.588508i | 0.984390 | − | 0.175999i | \(-0.0563156\pi\) |
−0.644615 | + | 0.764507i | \(0.722982\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −18.3203 | − | 17.5182i | −1.13400 | − | 1.08435i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −15.6489 | − | 9.03488i | −0.964951 | − | 0.557114i | −0.0672574 | − | 0.997736i | \(-0.521425\pi\) |
−0.897693 | + | 0.440621i | \(0.854758\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 18.0291 | + | 10.4091i | 1.10752 | + | 0.639427i | ||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −5.31438 | − | 12.4347i | −0.325235 | − | 0.760991i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | 1.49205 | + | 2.58430i | 0.0909718 | + | 0.157568i | 0.907920 | − | 0.419143i | \(-0.137669\pi\) |
−0.816948 | + | 0.576711i | \(0.804336\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.97274 | + | 5.18041i | 0.545055 | + | 0.314688i | 0.747125 | − | 0.664683i | \(-0.231434\pi\) |
−0.202070 | + | 0.979371i | \(0.564767\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 0 | 0 | ||||||||
\(275\) | −15.4380 | + | 8.91312i | −0.930945 | + | 0.537481i | ||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 5.94345 | − | 10.2944i | 0.357107 | − | 0.618528i | −0.630369 | − | 0.776296i | \(-0.717096\pi\) |
0.987476 | + | 0.157768i | \(0.0504297\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 20.8823 | − | 6.09932i | 1.25019 | − | 0.365157i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.0740 | + | 6.97095i | −0.720277 | + | 0.415852i | −0.814855 | − | 0.579665i | \(-0.803183\pi\) |
0.0945775 | + | 0.995518i | \(0.469850\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 2.53564i | 0.150728i | 0.997156 | + | 0.0753642i | \(0.0240119\pi\) | ||||
−0.997156 | + | 0.0753642i | \(0.975988\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | −28.8638 | − | 21.6392i | −1.70974 | − | 1.28180i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 8.43120 | − | 14.6033i | 0.495953 | − | 0.859016i | ||||
\(290\) | 0 | 0 | ||||||||
\(291\) | −0.797998 | + | 6.63415i | −0.0467795 | + | 0.388901i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | −3.95496 | + | 6.85020i | −0.231052 | + | 0.400193i | −0.958118 | − | 0.286374i | \(-0.907550\pi\) |
0.727066 | + | 0.686567i | \(0.240883\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −9.54080 | − | 16.5251i | −0.555487 | − | 0.962131i | ||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.69509 | + | 5.71119i | 0.272437 | + | 0.331397i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | −5.65769 | −0.327193 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | 6.13487 | + | 14.3545i | 0.352439 | + | 0.824645i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | 27.2310 | − | 15.7218i | 1.55924 | − | 0.900230i | ||||
\(306\) | 0 | 0 | ||||||||
\(307\) | − | 13.9676i | − | 0.797170i | −0.917131 | − | 0.398585i | \(-0.869501\pi\) | ||
0.917131 | − | 0.398585i | \(-0.130499\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −1.42437 | + | 11.8415i | −0.0810296 | + | 0.673640i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 32.6327 | 1.85043 | 0.925215 | − | 0.379443i | \(-0.123884\pi\) | ||||
0.925215 | + | 0.379443i | \(0.123884\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | − | 15.7166i | − | 0.888357i | −0.895938 | − | 0.444178i | \(-0.853496\pi\) | ||
0.895938 | − | 0.444178i | \(-0.146504\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 0 | 0 | ||||||||
\(317\) | − | 29.0253i | − | 1.63022i | −0.579305 | − | 0.815111i | \(-0.696676\pi\) | ||
0.579305 | − | 0.815111i | \(-0.303324\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 12.0221 | 0.673109 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 18.0977 | − | 7.73465i | 1.01012 | − | 0.431706i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 1.84535i | 0.102678i | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −10.6585 | + | 6.15370i | −0.591228 | + | 0.341346i | ||||
\(326\) | 0 | 0 | ||||||||
\(327\) | −27.5024 | − | 3.30817i | −1.52089 | − | 0.182942i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 13.1702 | 0.723900 | 0.361950 | − | 0.932198i | \(-0.382111\pi\) | ||||
0.361950 | + | 0.932198i | \(0.382111\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | 10.0969 | + | 2.46469i | 0.553305 | + | 0.135064i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −21.0677 | − | 36.4904i | −1.15105 | − | 1.99368i | ||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 8.31732 | − | 14.4060i | 0.453073 | − | 0.784746i | −0.545502 | − | 0.838110i | \(-0.683661\pi\) |
0.998575 | + | 0.0533635i | \(0.0169942\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −3.99159 | + | 1.70594i | −0.216793 | + | 0.0926539i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −5.15896 | + | 8.93559i | −0.279374 | + | 0.483889i | ||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | 38.4042 | − | 16.4133i | 2.06761 | − | 0.883662i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | − | 24.7120i | − | 1.32661i | −0.748349 | − | 0.663305i | \(-0.769153\pi\) | ||
0.748349 | − | 0.663305i | \(-0.230847\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 26.7994 | − | 15.4727i | 1.43454 | − | 0.828232i | 0.437078 | − | 0.899424i | \(-0.356013\pi\) |
0.997463 | + | 0.0711915i | \(0.0226802\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 3.24153 | + | 3.94306i | 0.173020 | + | 0.210465i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | −11.6758 | + | 20.2231i | −0.621440 | + | 1.07637i | 0.367778 | + | 0.929914i | \(0.380119\pi\) |
−0.989218 | + | 0.146452i | \(0.953215\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 39.7225 | − | 22.9338i | 2.10825 | − | 1.21720i | ||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 18.3902 | + | 10.6176i | 0.970596 | + | 0.560374i | 0.899418 | − | 0.437090i | \(-0.143991\pi\) |
0.0711782 | + | 0.997464i | \(0.477324\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | 2.87387 | + | 4.97769i | 0.151256 | + | 0.261984i | ||||
\(362\) | 0 | 0 | ||||||||
\(363\) | 15.4348 | + | 1.85659i | 0.810115 | + | 0.0974458i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 34.5483 | + | 19.9465i | 1.80834 | + | 1.04405i | ||||
\(366\) | 0 | 0 | ||||||||
\(367\) | 12.0178 | + | 6.93846i | 0.627322 | + | 0.362185i | 0.779714 | − | 0.626135i | \(-0.215364\pi\) |
−0.152392 | + | 0.988320i | \(0.548698\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | −6.23579 | − | 1.52218i | −0.324622 | − | 0.0792417i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 16.0728 | + | 27.8390i | 0.832221 | + | 1.44145i | 0.896273 | + | 0.443502i | \(0.146264\pi\) |
−0.0640529 | + | 0.997947i | \(0.520403\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | 32.7480 | − | 43.6815i | 1.69110 | − | 2.25570i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 8.30017 | 0.427481 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 1.95340 | 0.100339 | 0.0501696 | − | 0.998741i | \(-0.484024\pi\) | ||||
0.0501696 | + | 0.998741i | \(0.484024\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 1.98588 | − | 2.64889i | 0.101740 | − | 0.135707i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −0.788167 | − | 1.36514i | −0.0402734 | − | 0.0697557i | 0.845186 | − | 0.534472i | \(-0.179490\pi\) |
−0.885460 | + | 0.464717i | \(0.846156\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | 12.4762 | − | 13.0475i | 0.634202 | − | 0.663240i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | −9.74447 | − | 5.62597i | −0.494064 | − | 0.285248i | 0.232195 | − | 0.972669i | \(-0.425409\pi\) |
−0.726259 | + | 0.687421i | \(0.758743\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −1.85019 | − | 1.06821i | −0.0935682 | − | 0.0540216i | ||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −14.8782 | − | 1.78964i | −0.750503 | − | 0.0902753i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −17.8167 | − | 30.8594i | −0.896453 | − | 1.55270i | ||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −0.548160 | − | 0.316480i | −0.0275114 | − | 0.0158837i | 0.486181 | − | 0.873858i | \(-0.338389\pi\) |
−0.513693 | + | 0.857974i | \(0.671723\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | −7.38032 | + | 4.26103i | −0.368555 | + | 0.212786i | −0.672827 | − | 0.739800i | \(-0.734920\pi\) |
0.304272 | + | 0.952585i | \(0.401587\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | −3.56180 | + | 6.16921i | −0.177426 | + | 0.307310i | ||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −33.4424 | − | 17.3614i | −1.66177 | − | 0.862695i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.26897 | + | 2.46469i | −0.211605 | + | 0.122170i | ||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 14.0668i | 0.695557i | 0.937577 | + | 0.347778i | \(0.113064\pi\) | ||||
−0.937577 | + | 0.347778i | \(0.886936\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 18.5698 | − | 7.93644i | 0.915982 | − | 0.391476i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 4.07054 | − | 7.05039i | 0.199815 | − | 0.346090i | ||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −8.87657 | + | 3.79370i | −0.434687 | + | 0.185778i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 10.9339 | − | 18.9381i | 0.534156 | − | 0.925185i | −0.465048 | − | 0.885286i | \(-0.653963\pi\) |
0.999204 | − | 0.0398995i | \(-0.0127038\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 13.3616 | + | 23.1430i | 0.651206 | + | 1.12792i | 0.982831 | + | 0.184510i | \(0.0590698\pi\) |
−0.331625 | + | 0.943411i | \(0.607597\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | 6.95662 | + | 23.8174i | 0.338242 | + | 1.15804i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | −4.64743 | −0.225433 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −2.40362 | − | 0.289123i | −0.116048 | − | 0.0139590i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 17.2686 | − | 9.97000i | 0.831797 | − | 0.480238i | −0.0226706 | − | 0.999743i | \(-0.507217\pi\) |
0.854468 | + | 0.519505i | \(0.173884\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 20.2826i | 0.974719i | 0.873201 | + | 0.487359i | \(0.162040\pi\) | ||||
−0.873201 | + | 0.487359i | \(0.837960\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | −56.3412 | + | 24.0793i | −2.70135 | + | 1.15451i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | −28.6511 | −1.37057 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 28.3982i | 1.35537i | 0.735350 | + | 0.677687i | \(0.237018\pi\) | ||||
−0.735350 | + | 0.677687i | \(0.762982\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 12.3056i | 0.584658i | 0.956318 | + | 0.292329i | \(0.0944302\pi\) | ||||
−0.956318 | + | 0.292329i | \(0.905570\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −32.6871 | −1.54952 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −3.20118 | + | 26.6130i | −0.151411 | + | 1.25875i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | − | 36.1924i | − | 1.70803i | −0.520251 | − | 0.854013i | \(-0.674162\pi\) | ||
0.520251 | − | 0.854013i | \(-0.325838\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 2.63650 | − | 1.52218i | 0.124148 | − | 0.0716769i | ||||
\(452\) | 0 | 0 | ||||||||
\(453\) | 11.3230 | + | 26.4938i | 0.532002 | + | 1.24479i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −8.41784 | −0.393770 | −0.196885 | − | 0.980427i | \(-0.563083\pi\) | ||||
−0.196885 | + | 0.980427i | \(0.563083\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0.315579 | + | 1.90149i | 0.0147300 | + | 0.0887539i | ||||
\(460\) | 0 | 0 | ||||||||
\(461\) | 9.07730 | + | 15.7224i | 0.422772 | + | 0.732263i | 0.996209 | − | 0.0869865i | \(-0.0277237\pi\) |
−0.573437 | + | 0.819249i | \(0.694390\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | −7.64690 | + | 13.2448i | −0.355381 | + | 0.615539i | −0.987183 | − | 0.159591i | \(-0.948982\pi\) |
0.631802 | + | 0.775130i | \(0.282316\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 6.28007 | − | 52.2093i | 0.291231 | − | 2.42115i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | −13.3932 | + | 23.1977i | −0.619763 | + | 1.07346i | 0.369766 | + | 0.929125i | \(0.379438\pi\) |
−0.989529 | + | 0.144336i | \(0.953896\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −23.2928 | − | 17.4627i | −1.07328 | − | 0.804637i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 8.56199i | 0.393681i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −53.9758 | + | 31.1630i | −2.47658 | + | 1.42985i | ||||
\(476\) | 0 | 0 | ||||||||
\(477\) | −10.7815 | − | 10.3095i | −0.493653 | − | 0.472040i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −14.2775 | + | 24.7294i | −0.652357 | + | 1.12992i | 0.330193 | + | 0.943914i | \(0.392886\pi\) |
−0.982549 | + | 0.186002i | \(0.940447\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −2.94734 | + | 1.70165i | −0.134387 | + | 0.0775884i | ||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | 0 | 0 | ||||||||
\(485\) | 13.9877 | + | 8.07583i | 0.635151 | + | 0.366705i | ||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 6.57635 | + | 11.3906i | 0.298003 | + | 0.516156i | 0.975679 | − | 0.219204i | \(-0.0703462\pi\) |
−0.677676 | + | 0.735361i | \(0.737013\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | −2.38994 | − | 5.59202i | −0.108077 | − | 0.252880i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 28.6854 | + | 16.5615i | 1.29455 | + | 0.747411i | 0.979458 | − | 0.201649i | \(-0.0646301\pi\) |
0.315096 | + | 0.949060i | \(0.397963\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 2.71434 | + | 1.56712i | 0.122248 | + | 0.0705798i | ||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 17.1544 | − | 5.01049i | 0.771034 | − | 0.225205i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | 3.27652 | + | 5.67511i | 0.146677 | + | 0.254053i | 0.929997 | − | 0.367566i | \(-0.119809\pi\) |
−0.783320 | + | 0.621619i | \(0.786475\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −5.51702 | − | 12.9088i | −0.246482 | − | 0.576724i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | −12.4969 | −0.557210 | −0.278605 | − | 0.960406i | \(-0.589872\pi\) | ||||
−0.278605 | + | 0.960406i | \(0.589872\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 37.7337 | 1.67913 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | 20.6960 | + | 2.48945i | 0.919143 | + | 0.110560i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | −3.30237 | − | 5.71987i | −0.146375 | − | 0.253529i | 0.783510 | − | 0.621379i | \(-0.213427\pi\) |
−0.929885 | + | 0.367850i | \(0.880094\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 16.4154 | + | 19.9680i | 0.724760 | + | 0.881610i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | 24.9672 | + | 14.4148i | 1.10018 | + | 0.635192i | ||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.1915 | − | 5.88408i | −0.448223 | − | 0.258782i | ||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 13.6072 | − | 18.1502i | 0.597290 | − | 0.796704i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | −7.98920 | − | 13.8377i | −0.350013 | − | 0.606241i | 0.636238 | − | 0.771493i | \(-0.280490\pi\) |
−0.986251 | + | 0.165252i | \(0.947156\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | −10.1857 | − | 5.88074i | −0.445391 | − | 0.257147i | 0.260491 | − | 0.965476i | \(-0.416116\pi\) |
−0.705882 | + | 0.708330i | \(0.749449\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 0 | 0 | ||||||||
\(527\) | −2.32957 | + | 1.34498i | −0.101478 | + | 0.0585882i | ||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 5.08510 | − | 8.80765i | 0.221091 | − | 0.382941i | ||||
\(530\) | 0 | 0 | ||||||||
\(531\) | 3.83345 | + | 13.1246i | 0.166358 | + | 0.569559i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 1.82026 | − | 1.05093i | 0.0788444 | − | 0.0455208i | ||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 47.5735i | − | 2.05678i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | 2.63070 | − | 21.8703i | 0.113523 | − | 0.943775i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 0.205980 | − | 0.356768i | 0.00885576 | − | 0.0153386i | −0.861564 | − | 0.507650i | \(-0.830514\pi\) |
0.870419 | + | 0.492311i | \(0.163848\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −36.7966 | − | 27.5864i | −1.57909 | − | 1.18385i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | −33.4790 | + | 57.9874i | −1.43408 | + | 2.48391i | ||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 11.9166 | + | 20.6402i | 0.509519 | + | 0.882513i | 0.999939 | + | 0.0110266i | \(0.00350995\pi\) |
−0.490420 | + | 0.871486i | \(0.663157\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | −21.6274 | + | 6.31696i | −0.923035 | + | 0.269601i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | 42.0329 | 1.79066 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 15.0698 | − | 20.1011i | 0.639678 | − | 0.853244i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | 37.1935 | − | 21.4737i | 1.57594 | − | 0.909869i | 0.580522 | − | 0.814245i | \(-0.302849\pi\) |
0.995418 | − | 0.0956241i | \(-0.0304847\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 5.91128i | 0.250020i | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | −0.731449 | − | 0.548368i | −0.0308818 | − | 0.0231521i | ||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 31.8908 | 1.34404 | 0.672019 | − | 0.740534i | \(-0.265428\pi\) | ||||
0.672019 | + | 0.740534i | \(0.265428\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 10.4927i | 0.441432i | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 0 | 0 | ||||||||
\(569\) | 0.495245i | 0.0207618i | 0.999946 | + | 0.0103809i | \(0.00330440\pi\) | ||||
−0.999946 | + | 0.0103809i | \(0.996696\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 2.68365 | 0.112307 | 0.0561535 | − | 0.998422i | \(-0.482116\pi\) | ||||
0.0561535 | + | 0.998422i | \(0.482116\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 1.75601 | + | 1.31648i | 0.0733584 | + | 0.0549969i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | − | 72.1564i | − | 3.00913i | ||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −36.3955 | + | 21.0130i | −1.51517 | + | 0.874781i | −0.515324 | + | 0.856995i | \(0.672328\pi\) |
−0.999842 | + | 0.0177861i | \(0.994338\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −19.3608 | + | 25.8246i | −0.804606 | + | 1.07323i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | 7.07505 | 0.293019 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 11.8436 | − | 3.45929i | 0.489671 | − | 0.143024i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −1.71916 | − | 2.97768i | −0.0709575 | − | 0.122902i | 0.828364 | − | 0.560191i | \(-0.189272\pi\) |
−0.899321 | + | 0.437289i | \(0.855939\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −18.0373 | + | 31.2415i | −0.743214 | + | 1.28728i | ||||
\(590\) | 0 | 0 | ||||||||
\(591\) | −8.23621 | − | 6.17470i | −0.338793 | − | 0.253993i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | 4.55126 | − | 7.88301i | 0.186898 | − | 0.323716i | −0.757317 | − | 0.653048i | \(-0.773490\pi\) |
0.944214 | + | 0.329332i | \(0.106823\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | −1.16390 | + | 9.67606i | −0.0476352 | + | 0.396015i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | − | 7.75019i | − | 0.316664i | −0.987386 | − | 0.158332i | \(-0.949388\pi\) | ||
0.987386 | − | 0.158332i | \(-0.0506117\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 22.0034 | − | 12.7037i | 0.897536 | − | 0.518193i | 0.0211361 | − | 0.999777i | \(-0.493272\pi\) |
0.876400 | + | 0.481584i | \(0.159938\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 8.46492 | + | 28.9814i | 0.344718 | + | 1.18021i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 18.7889 | − | 32.5433i | 0.763878 | − | 1.32308i | ||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 11.7094 | − | 6.76042i | 0.475270 | − | 0.274397i | −0.243173 | − | 0.969983i | \(-0.578188\pi\) |
0.718443 | + | 0.695586i | \(0.244855\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −7.03633 | − | 4.06243i | −0.284659 | − | 0.164348i | ||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −2.41817 | − | 4.18840i | −0.0976691 | − | 0.169168i | 0.813050 | − | 0.582193i | \(-0.197805\pi\) |
−0.910719 | + | 0.413026i | \(0.864472\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | −9.30706 | + | 12.4144i | −0.375297 | + | 0.500595i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | 5.30333 | + | 3.06188i | 0.213504 | + | 0.123267i | 0.602939 | − | 0.797787i | \(-0.293996\pi\) |
−0.389435 | + | 0.921054i | \(0.627330\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 4.94313 | + | 2.85392i | 0.198681 | + | 0.114709i | 0.596040 | − | 0.802955i | \(-0.296740\pi\) |
−0.397359 | + | 0.917663i | \(0.630073\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −29.5227 | + | 4.89971i | −1.18470 | + | 0.196618i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −34.6609 | − | 60.0344i | −1.38644 | − | 2.40138i | ||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −12.1722 | − | 1.46415i | −0.486110 | − | 0.0584724i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | −1.28513 | −0.0512414 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −19.0525 | −0.758468 | −0.379234 | − | 0.925301i | \(-0.623812\pi\) | ||||
−0.379234 | + | 0.925301i | \(0.623812\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | 1.43360 | + | 3.35436i | 0.0569804 | + | 0.133324i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | −4.00124 | − | 6.93035i | −0.158784 | − | 0.275022i | ||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −31.5483 | + | 9.21469i | −1.24803 | + | 0.364527i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −13.2820 | − | 7.66837i | −0.524607 | − | 0.302882i | 0.214210 | − | 0.976788i | \(-0.431282\pi\) |
−0.738818 | + | 0.673905i | \(0.764616\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 11.3209 | + | 6.53612i | 0.446453 | + | 0.257759i | 0.706331 | − | 0.707882i | \(-0.250349\pi\) |
−0.259878 | + | 0.965641i | \(0.583682\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −17.1490 | − | 40.1255i | −0.675239 | − | 1.57994i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 17.8533 | + | 30.9228i | 0.701885 | + | 1.21570i | 0.967804 | + | 0.251705i | \(0.0809913\pi\) |
−0.265919 | + | 0.963995i | \(0.585675\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −5.61605 | − | 3.24243i | −0.220449 | − | 0.127277i | ||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 23.6131 | − | 13.6330i | 0.924051 | − | 0.533501i | 0.0391261 | − | 0.999234i | \(-0.487543\pi\) |
0.884925 | + | 0.465733i | \(0.154209\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | −18.1113 | + | 31.3698i | −0.707669 | + | 1.22572i | ||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −20.6602 | − | 19.7556i | −0.806030 | − | 0.770741i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −14.7911 | + | 8.53963i | −0.576179 | + | 0.332657i | −0.759613 | − | 0.650375i | \(-0.774612\pi\) |
0.183435 | + | 0.983032i | \(0.441278\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | − | 46.9568i | − | 1.82641i | −0.407505 | − | 0.913203i | \(-0.633601\pi\) | ||
0.407505 | − | 0.913203i | \(-0.366399\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | −0.504999 | − | 0.378598i | −0.0196125 | − | 0.0147035i | ||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −24.3313 | + | 42.1431i | −0.942112 | + | 1.63179i | ||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 1.31930 | − | 10.9680i | 0.0510069 | − | 0.424046i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | 5.34305 | − | 9.25444i | 0.206266 | − | 0.357264i | ||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 7.76077 | + | 13.4421i | 0.299156 | + | 0.518153i | 0.975943 | − | 0.218026i | \(-0.0699616\pi\) |
−0.676787 | + | 0.736179i | \(0.736628\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | −50.2884 | + | 41.3414i | −1.93560 | + | 1.59123i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −18.1574 | −0.697845 | −0.348922 | − | 0.937152i | \(-0.613452\pi\) | ||||
−0.348922 | + | 0.937152i | \(0.613452\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 7.79205 | + | 18.2320i | 0.298592 | + | 0.698651i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | −17.4866 | + | 10.0959i | −0.669104 | + | 0.386308i | −0.795737 | − | 0.605642i | \(-0.792916\pi\) |
0.126633 | + | 0.991950i | \(0.459583\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | − | 48.8146i | − | 1.86511i | ||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 1.16726 | − | 9.70398i | 0.0445336 | − | 0.370230i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 4.88468 | 0.186092 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 0.0803432i | 0.00305640i | 0.999999 | + | 0.00152820i | \(0.000486441\pi\) | ||||
−0.999999 | + | 0.00152820i | \(0.999514\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | 0 | 0 | ||||||||
\(695\) | 23.3339i | 0.885104i | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0.793689 | 0.0300631 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −19.8231 | + | 8.47207i | −0.749780 | + | 0.320443i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | − | 35.1490i | − | 1.32756i | −0.747928 | − | 0.663780i | \(-0.768951\pi\) | ||
0.747928 | − | 0.663780i | \(-0.231049\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −14.9256 | + | 8.61731i | −0.562930 | + | 0.325008i | ||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 59.5476 | + | 7.16276i | 2.24269 | + | 0.269765i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | 1.56594 | 0.0588100 | 0.0294050 | − | 0.999568i | \(-0.490639\pi\) | ||||
0.0294050 | + | 0.999568i | \(0.490639\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 7.15865 | + | 24.5091i | 0.268470 | + | 0.919163i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | −20.8823 | − | 36.1691i | −0.782047 | − | 1.35455i | ||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −2.92595 | + | 5.06790i | −0.109424 | + | 0.189529i | ||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −6.48184 | + | 2.77023i | −0.242069 | + | 0.103456i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 12.9393 | − | 22.4116i | 0.482556 | − | 0.835811i | −0.517243 | − | 0.855838i | \(-0.673042\pi\) |
0.999799 | + | 0.0200268i | \(0.00637517\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | −7.83807 | + | 3.34986i | −0.291501 | + | 0.124583i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | 105.858i | 3.93146i | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −0.990545 | + | 0.571891i | −0.0367373 | + | 0.0212103i | −0.518256 | − | 0.855225i | \(-0.673419\pi\) |
0.481519 | + | 0.876436i | \(0.340085\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 20.3296 | + | 17.7682i | 0.752947 | + | 0.658081i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −1.11609 | + | 1.93312i | −0.0412800 | + | 0.0714990i | ||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −20.1408 | + | 11.6283i | −0.743916 | + | 0.429500i | −0.823491 | − | 0.567329i | \(-0.807977\pi\) |
0.0795755 | + | 0.996829i | \(0.474644\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 0 | 0 | ||||||||
\(737\) | −12.4012 | − | 7.15985i | −0.456805 | − | 0.263736i | ||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 18.0758 | + | 31.3082i | 0.664929 | + | 1.15169i | 0.979305 | + | 0.202392i | \(0.0648714\pi\) |
−0.314376 | + | 0.949299i | \(0.601795\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | −8.40378 | − | 1.01086i | −0.308721 | − | 0.0371349i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | 6.43940 | + | 3.71779i | 0.236239 | + | 0.136392i | 0.613447 | − | 0.789736i | \(-0.289783\pi\) |
−0.377208 | + | 0.926129i | \(0.623116\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | 56.1121 | + | 32.3963i | 2.05579 | + | 1.18691i | ||||
\(746\) | 0 | 0 | ||||||||
\(747\) | −4.03159 | + | 4.21619i | −0.147508 | + | 0.154262i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −3.67798 | − | 6.37044i | −0.134211 | − | 0.232461i | 0.791085 | − | 0.611707i | \(-0.209517\pi\) |
−0.925296 | + | 0.379246i | \(0.876183\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | −4.83140 | + | 6.44443i | −0.176066 | + | 0.234848i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 69.6445 | 2.53462 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 7.65326 | 0.278163 | 0.139081 | − | 0.990281i | \(-0.455585\pi\) | ||||
0.139081 | + | 0.990281i | \(0.455585\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | 8.51401 | − | 11.3565i | 0.309039 | − | 0.412216i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −21.7203 | − | 37.6207i | −0.787362 | − | 1.36375i | −0.927578 | − | 0.373629i | \(-0.878113\pi\) |
0.140217 | − | 0.990121i | \(-0.455220\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 4.52624 | + | 1.10488i | 0.163647 | + | 0.0399469i | ||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −3.87738 | − | 2.23860i | −0.140004 | − | 0.0808313i | ||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 18.8491 | + | 10.8825i | 0.679716 | + | 0.392434i | 0.799748 | − | 0.600336i | \(-0.204966\pi\) |
−0.120032 | + | 0.992770i | \(0.538300\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −18.7340 | − | 2.25344i | −0.674687 | − | 0.0811557i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | −7.25734 | − | 12.5701i | −0.261028 | − | 0.452114i | 0.705487 | − | 0.708723i | \(-0.250728\pi\) |
−0.966515 | + | 0.256609i | \(0.917395\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −78.6801 | − | 45.4260i | −2.82627 | − | 1.63175i | ||||
\(776\) | 0 | 0 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 0 | 0 | ||||||||
\(779\) | 9.21800 | − | 5.32202i | 0.330269 | − | 0.190681i | ||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 7.79402 | − | 13.4996i | 0.278892 | − | 0.483055i | ||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 43.3115 | − | 7.18816i | 1.54783 | − | 0.256884i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −60.9415 | + | 35.1846i | −2.17509 | + | 1.25579i | ||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 13.1972i | 0.470430i | 0.971943 | + | 0.235215i | \(0.0755795\pi\) | ||||
−0.971943 | + | 0.235215i | \(0.924421\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | 28.7795 | − | 12.2999i | 1.02458 | − | 0.437888i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 3.68889 | − | 6.38935i | 0.130996 | − | 0.226892i | ||||
\(794\) | 0 | 0 | ||||||||
\(795\) | −33.1570 | + | 14.1707i | −1.17596 | + | 0.502584i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 24.8899 | − | 43.1106i | 0.881646 | − | 1.52706i | 0.0321352 | − | 0.999484i | \(-0.489769\pi\) |
0.849511 | − | 0.527572i | \(-0.176897\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | −1.53402 | − | 2.65701i | −0.0542698 | − | 0.0939981i | ||||
\(800\) | 0 | 0 | ||||||||
\(801\) | 22.7539 | + | 5.55434i | 0.803971 | + | 0.196253i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 13.5576 | 0.478437 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −5.13162 | − | 0.617264i | −0.180642 | − | 0.0217287i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | −24.4123 | + | 14.0944i | −0.858290 | + | 0.495534i | −0.863439 | − | 0.504453i | \(-0.831694\pi\) |
0.00514934 | + | 0.999987i | \(0.498361\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | − | 33.5981i | − | 1.17979i | −0.807480 | − | 0.589894i | \(-0.799169\pi\) | ||
0.807480 | − | 0.589894i | \(-0.200831\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | −16.5016 | + | 7.05250i | −0.578736 | + | 0.247342i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | −14.6998 | −0.514910 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 29.9353i | 1.04730i | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 54.1696i | − | 1.89053i | −0.326299 | − | 0.945267i | \(-0.605802\pi\) | ||
0.326299 | − | 0.945267i | \(-0.394198\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 28.5390 | 0.994808 | 0.497404 | − | 0.867519i | \(-0.334287\pi\) | ||||
0.497404 | + | 0.867519i | \(0.334287\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 3.68738 | − | 30.6550i | 0.128378 | − | 1.06727i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 37.2062i | 1.29379i | 0.762581 | + | 0.646893i | \(0.223932\pi\) | ||||
−0.762581 | + | 0.646893i | \(0.776068\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −1.92557 | + | 1.11173i | −0.0668777 | + | 0.0386119i | −0.533066 | − | 0.846074i | \(-0.678960\pi\) |
0.466188 | + | 0.884686i | \(0.345627\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 8.09128 | + | 18.9321i | 0.280684 | + | 0.656749i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −33.9335 | −1.17432 | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | −13.2433 | + | 35.2765i | −0.457755 | + | 1.21933i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 27.8383 | + | 48.2173i | 0.961084 | + | 1.66465i | 0.719787 | + | 0.694195i | \(0.244240\pi\) |
0.241297 | + | 0.970451i | \(0.422427\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.1955 | − | 36.7116i | 0.730878 | − | 1.26592i | ||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 2.88390 | − | 23.9753i | 0.0993267 | − | 0.825752i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 25.1935 | − | 43.6364i | 0.866683 | − | 1.50114i | ||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −3.51399 | − | 2.63445i | −0.120600 | − | 0.0904140i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | − | 19.9530i | − | 0.683980i | ||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 16.2574 | − | 9.38622i | 0.556643 | − | 0.321378i | −0.195154 | − | 0.980773i | \(-0.562521\pi\) |
0.751797 | + | 0.659395i | \(0.229187\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 59.9770 | − | 17.5182i | 2.05117 | − | 0.599109i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | −11.8516 | + | 20.5276i | −0.404844 | + | 0.701210i | −0.994303 | − | 0.106588i | \(-0.966007\pi\) |
0.589460 | + | 0.807798i | \(0.299341\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −14.5237 | + | 8.38527i | −0.495543 | + | 0.286102i | −0.726871 | − | 0.686774i | \(-0.759026\pi\) |
0.231328 | + | 0.972876i | \(0.425693\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 29.2235 | + | 16.8722i | 0.994778 | + | 0.574335i | 0.906699 | − | 0.421778i | \(-0.138594\pi\) |
0.0880791 | + | 0.996113i | \(0.471927\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | −27.4164 | − | 47.4866i | −0.932186 | − | 1.61459i | ||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 11.4781 | + | 26.8566i | 0.389815 | + | 0.912097i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −10.4875 | − | 6.05497i | −0.355765 | − | 0.205401i | ||||
\(870\) | 0 | 0 | ||||||||
\(871\) | −8.56192 | − | 4.94323i | −0.290110 | − | 0.167495i | ||||
\(872\) | 0 | 0 | ||||||||
\(873\) | −8.36478 | − | 7.99855i | −0.283105 | − | 0.270710i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 19.7087 | + | 34.1365i | 0.665515 | + | 1.15271i | 0.979145 | + | 0.203161i | \(0.0651215\pi\) |
−0.313630 | + | 0.949545i | \(0.601545\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −5.38420 | − | 12.5981i | −0.181605 | − | 0.424922i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −26.2496 | −0.884372 | −0.442186 | − | 0.896923i | \(-0.645797\pi\) | ||||
−0.442186 | + | 0.896923i | \(0.645797\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −43.5087 | −1.46418 | −0.732091 | − | 0.681206i | \(-0.761456\pi\) | ||||
−0.732091 | + | 0.681206i | \(0.761456\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 32.8138 | + | 3.94705i | 1.10302 | + | 0.132679i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | −2.83888 | − | 4.91708i | −0.0953202 | − | 0.165099i | 0.814422 | − | 0.580273i | \(-0.197054\pi\) |
−0.909742 | + | 0.415174i | \(0.863721\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | −12.7928 | + | 0.572912i | −0.428576 | + | 0.0191933i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | −35.6327 | − | 20.5725i | −1.19240 | − | 0.688434i | ||||
\(894\) | 0 | 0 | ||||||||
\(895\) | −46.1124 | − | 26.6230i | −1.54137 | − | 0.889909i | ||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 5.87815 | − | 7.84066i | 0.196266 | − | 0.261792i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | 30.6355 | + | 53.0623i | 1.02175 | + | 1.76973i | ||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 1.59740 | + | 0.922259i | 0.0532171 | + | 0.0307249i | ||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 0 | 0 | ||||||||
\(905\) | −96.2716 | + | 55.5824i | −3.20018 | + | 1.84762i | ||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −7.32741 | + | 12.6914i | −0.243303 | + | 0.421412i | −0.961653 | − | 0.274269i | \(-0.911564\pi\) |
0.718350 | + | 0.695681i | \(0.244897\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −26.2670 | − | 6.41189i | −0.871220 | − | 0.212669i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 7.19133 | − | 4.15192i | 0.238260 | − | 0.137559i | −0.376117 | − | 0.926572i | \(-0.622741\pi\) |
0.614377 | + | 0.789013i | \(0.289408\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | − | 2.76674i | − | 0.0915658i | ||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −6.50416 | + | 54.0723i | −0.215021 | + | 1.78757i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | 18.5554 | − | 32.1388i | 0.612085 | − | 1.06016i | −0.378804 | − | 0.925477i | \(-0.623665\pi\) |
0.990889 | − | 0.134685i | \(-0.0430021\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 19.3568 | + | 14.5118i | 0.637828 | + | 0.478180i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | 5.38106 | − | 9.32027i | 0.177120 | − | 0.306781i | ||||
\(924\) | 0 | 0 | ||||||||
\(925\) | −21.7022 | − | 37.5894i | −0.713566 | − | 1.23593i | ||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −14.9305 | − | 14.2769i | −0.490383 | − | 0.468914i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | 7.88987 | 0.258858 | 0.129429 | − | 0.991589i | \(-0.458686\pi\) | ||||
0.129429 | + | 0.991589i | \(0.458686\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | −33.9042 | + | 45.2237i | −1.10998 | + | 1.48056i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | −1.91370 | + | 1.10488i | −0.0625848 | + | 0.0361333i | ||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 13.2688i | 0.433472i | 0.976230 | + | 0.216736i | \(0.0695411\pi\) | ||||
−0.976230 | + | 0.216736i | \(0.930459\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 21.7807 | + | 16.3290i | 0.710787 | + | 0.532878i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | −7.92922 | −0.258485 | −0.129243 | − | 0.991613i | \(-0.541255\pi\) | ||||
−0.129243 | + | 0.991613i | \(0.541255\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 12.3229i | 0.401288i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0 | 0 | ||||||||
\(947\) | − | 30.9635i | − | 1.00618i | −0.864235 | − | 0.503089i | \(-0.832197\pi\) | ||
0.864235 | − | 0.503089i | \(-0.167803\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 9.36029 | 0.303848 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 40.2244 | + | 30.1563i | 1.30436 | + | 0.977884i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 34.1087i | 1.10489i | 0.833549 | + | 0.552445i | \(0.186305\pi\) | ||||
−0.833549 | + | 0.552445i | \(0.813695\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 4.59428 | − | 2.65251i | 0.148668 | − | 0.0858332i | ||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −12.4906 | + | 16.6607i | −0.403762 | + | 0.538564i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −21.5856 | −0.696311 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | −8.08390 | + | 33.1165i | −0.260500 | + | 1.06717i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 39.0089 | + | 67.5655i | 1.25574 | + | 2.17501i | ||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 29.1066 | − | 50.4142i | 0.936007 | − | 1.62121i | 0.163177 | − | 0.986597i | \(-0.447826\pi\) |
0.772829 | − | 0.634614i | \(-0.218841\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | −2.55737 | − | 1.91726i | −0.0821544 | − | 0.0615913i | ||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 4.91896 | − | 8.51988i | 0.157857 | − | 0.273416i | −0.776239 | − | 0.630439i | \(-0.782875\pi\) |
0.934096 | + | 0.357023i | \(0.116208\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | 2.54580 | − | 21.1645i | 0.0815308 | − | 0.677806i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 33.5274i | 1.07264i | 0.844016 | + | 0.536318i | \(0.180185\pi\) | ||||
−0.844016 | + | 0.536318i | \(0.819815\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −9.62041 | + | 5.55434i | −0.307470 | + | 0.177518i | ||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 33.1587 | − | 34.6769i | 1.05867 | − | 1.10715i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 24.2359 | − | 41.9779i | 0.773006 | − | 1.33889i | −0.162902 | − | 0.986642i | \(-0.552086\pi\) |
0.935908 | − | 0.352243i | \(-0.114581\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −21.5486 | + | 12.4411i | −0.686594 | + | 0.396405i | ||||
\(986\) | 0 | 0 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | −30.0138 | − | 17.3285i | −0.954382 | − | 0.551013i | ||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 26.5005 | + | 45.9003i | 0.841818 | + | 1.45807i | 0.888357 | + | 0.459154i | \(0.151848\pi\) |
−0.0465389 | + | 0.998916i | \(0.514819\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −13.6834 | + | 18.2518i | −0.434229 | + | 0.579203i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 20.4015 | + | 11.7788i | 0.646770 | + | 0.373413i | ||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −7.57384 | − | 4.37276i | −0.239866 | − | 0.138487i | 0.375249 | − | 0.926924i | \(-0.377557\pi\) |
−0.615115 | + | 0.788437i | \(0.710890\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | −13.9060 | + | 11.4319i | −0.439966 | + | 0.361690i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))