Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [4225,2,Mod(1,4225)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(4225, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 0]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("4225.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 4225 = 5^{2} \cdot 13^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 4225.a (trivial) |
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: | yes |
Analytic conductor: | \(33.7367948540\) |
Analytic rank: | \(1\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\sqrt{3}, \sqrt{7})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} - 5x^{2} + 1 \) |
Coefficient ring: | \(\Z[a_1, a_2]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 65) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(2.18890\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 4225.1 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | −0.456850 | −0.323042 | −0.161521 | − | 0.986869i | \(-0.551640\pi\) | ||||
−0.161521 | + | 0.986869i | \(0.551640\pi\) | |||||||
\(3\) | 1.00000 | 0.577350 | 0.288675 | − | 0.957427i | \(-0.406785\pi\) | ||||
0.288675 | + | 0.957427i | \(0.406785\pi\) | |||||||
\(4\) | −1.79129 | −0.895644 | ||||||||
\(5\) | 0 | 0 | ||||||||
\(6\) | −0.456850 | −0.186508 | ||||||||
\(7\) | −1.73205 | −0.654654 | −0.327327 | − | 0.944911i | \(-0.606148\pi\) | ||||
−0.327327 | + | 0.944911i | \(0.606148\pi\) | |||||||
\(8\) | 1.73205 | 0.612372 | ||||||||
\(9\) | −2.00000 | −0.666667 | ||||||||
\(10\) | 0 | 0 | ||||||||
\(11\) | 2.64575 | 0.797724 | 0.398862 | − | 0.917011i | \(-0.369405\pi\) | ||||
0.398862 | + | 0.917011i | \(0.369405\pi\) | |||||||
\(12\) | −1.79129 | −0.517100 | ||||||||
\(13\) | 0 | 0 | ||||||||
\(14\) | 0.791288 | 0.211481 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 2.79129 | 0.697822 | ||||||||
\(17\) | 4.58258 | 1.11144 | 0.555719 | − | 0.831370i | \(-0.312443\pi\) | ||||
0.555719 | + | 0.831370i | \(0.312443\pi\) | |||||||
\(18\) | 0.913701 | 0.215361 | ||||||||
\(19\) | −1.73205 | −0.397360 | −0.198680 | − | 0.980064i | \(-0.563665\pi\) | ||||
−0.198680 | + | 0.980064i | \(0.563665\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | −1.73205 | −0.377964 | ||||||||
\(22\) | −1.20871 | −0.257698 | ||||||||
\(23\) | −4.58258 | −0.955533 | −0.477767 | − | 0.878487i | \(-0.658554\pi\) | ||||
−0.477767 | + | 0.878487i | \(0.658554\pi\) | |||||||
\(24\) | 1.73205 | 0.353553 | ||||||||
\(25\) | 0 | 0 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −5.00000 | −0.962250 | ||||||||
\(28\) | 3.10260 | 0.586337 | ||||||||
\(29\) | 4.58258 | 0.850963 | 0.425481 | − | 0.904967i | \(-0.360105\pi\) | ||||
0.425481 | + | 0.904967i | \(0.360105\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.20520 | −1.11449 | −0.557244 | − | 0.830349i | \(-0.688141\pi\) | ||||
−0.557244 | + | 0.830349i | \(0.688141\pi\) | |||||||
\(32\) | −4.73930 | −0.837798 | ||||||||
\(33\) | 2.64575 | 0.460566 | ||||||||
\(34\) | −2.09355 | −0.359041 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 3.58258 | 0.597096 | ||||||||
\(37\) | 7.93725 | 1.30488 | 0.652438 | − | 0.757842i | \(-0.273746\pi\) | ||||
0.652438 | + | 0.757842i | \(0.273746\pi\) | |||||||
\(38\) | 0.791288 | 0.128364 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 2.64575 | 0.413197 | 0.206598 | − | 0.978426i | \(-0.433761\pi\) | ||||
0.206598 | + | 0.978426i | \(0.433761\pi\) | |||||||
\(42\) | 0.791288 | 0.122098 | ||||||||
\(43\) | −10.5826 | −1.61383 | −0.806914 | − | 0.590669i | \(-0.798864\pi\) | ||||
−0.806914 | + | 0.590669i | \(0.798864\pi\) | |||||||
\(44\) | −4.73930 | −0.714477 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 2.09355 | 0.308677 | ||||||||
\(47\) | −1.82740 | −0.266554 | −0.133277 | − | 0.991079i | \(-0.542550\pi\) | ||||
−0.133277 | + | 0.991079i | \(0.542550\pi\) | |||||||
\(48\) | 2.79129 | 0.402888 | ||||||||
\(49\) | −4.00000 | −0.571429 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 4.58258 | 0.641689 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 7.58258 | 1.04155 | 0.520773 | − | 0.853695i | \(-0.325644\pi\) | ||||
0.520773 | + | 0.853695i | \(0.325644\pi\) | |||||||
\(54\) | 2.28425 | 0.310847 | ||||||||
\(55\) | 0 | 0 | ||||||||
\(56\) | −3.00000 | −0.400892 | ||||||||
\(57\) | −1.73205 | −0.229416 | ||||||||
\(58\) | −2.09355 | −0.274897 | ||||||||
\(59\) | 13.9518 | 1.81636 | 0.908182 | − | 0.418576i | \(-0.137470\pi\) | ||||
0.908182 | + | 0.418576i | \(0.137470\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | −1.41742 | −0.181483 | −0.0907413 | − | 0.995874i | \(-0.528924\pi\) | ||||
−0.0907413 | + | 0.995874i | \(0.528924\pi\) | |||||||
\(62\) | 2.83485 | 0.360026 | ||||||||
\(63\) | 3.46410 | 0.436436 | ||||||||
\(64\) | −3.41742 | −0.427178 | ||||||||
\(65\) | 0 | 0 | ||||||||
\(66\) | −1.20871 | −0.148782 | ||||||||
\(67\) | 1.00905 | 0.123275 | 0.0616376 | − | 0.998099i | \(-0.480368\pi\) | ||||
0.0616376 | + | 0.998099i | \(0.480368\pi\) | |||||||
\(68\) | −8.20871 | −0.995453 | ||||||||
\(69\) | −4.58258 | −0.551677 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −7.02355 | −0.833542 | −0.416771 | − | 0.909011i | \(-0.636838\pi\) | ||||
−0.416771 | + | 0.909011i | \(0.636838\pi\) | |||||||
\(72\) | −3.46410 | −0.408248 | ||||||||
\(73\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(74\) | −3.62614 | −0.421530 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | 3.10260 | 0.355893 | ||||||||
\(77\) | −4.58258 | −0.522233 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −6.00000 | −0.675053 | −0.337526 | − | 0.941316i | \(-0.609590\pi\) | ||||
−0.337526 | + | 0.941316i | \(0.609590\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | 1.00000 | 0.111111 | ||||||||
\(82\) | −1.20871 | −0.133480 | ||||||||
\(83\) | 6.01450 | 0.660177 | 0.330089 | − | 0.943950i | \(-0.392921\pi\) | ||||
0.330089 | + | 0.943950i | \(0.392921\pi\) | |||||||
\(84\) | 3.10260 | 0.338522 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 4.83465 | 0.521334 | ||||||||
\(87\) | 4.58258 | 0.491304 | ||||||||
\(88\) | 4.58258 | 0.488504 | ||||||||
\(89\) | 9.57395 | 1.01484 | 0.507419 | − | 0.861700i | \(-0.330600\pi\) | ||||
0.507419 | + | 0.861700i | \(0.330600\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 8.20871 | 0.855817 | ||||||||
\(93\) | −6.20520 | −0.643450 | ||||||||
\(94\) | 0.834849 | 0.0861081 | ||||||||
\(95\) | 0 | 0 | ||||||||
\(96\) | −4.73930 | −0.483703 | ||||||||
\(97\) | 11.4014 | 1.15763 | 0.578816 | − | 0.815458i | \(-0.303515\pi\) | ||||
0.578816 | + | 0.815458i | \(0.303515\pi\) | |||||||
\(98\) | 1.82740 | 0.184595 | ||||||||
\(99\) | −5.29150 | −0.531816 | ||||||||
\(100\) | 0 | 0 | ||||||||
\(101\) | −9.00000 | −0.895533 | −0.447767 | − | 0.894150i | \(-0.647781\pi\) | ||||
−0.447767 | + | 0.894150i | \(0.647781\pi\) | |||||||
\(102\) | −2.09355 | −0.207292 | ||||||||
\(103\) | −3.16515 | −0.311872 | −0.155936 | − | 0.987767i | \(-0.549839\pi\) | ||||
−0.155936 | + | 0.987767i | \(0.549839\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −3.46410 | −0.336463 | ||||||||
\(107\) | −10.5826 | −1.02306 | −0.511528 | − | 0.859267i | \(-0.670920\pi\) | ||||
−0.511528 | + | 0.859267i | \(0.670920\pi\) | |||||||
\(108\) | 8.95644 | 0.861834 | ||||||||
\(109\) | −13.1334 | −1.25795 | −0.628976 | − | 0.777425i | \(-0.716526\pi\) | ||||
−0.628976 | + | 0.777425i | \(0.716526\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | 7.93725 | 0.753371 | ||||||||
\(112\) | −4.83465 | −0.456832 | ||||||||
\(113\) | −7.41742 | −0.697773 | −0.348886 | − | 0.937165i | \(-0.613440\pi\) | ||||
−0.348886 | + | 0.937165i | \(0.613440\pi\) | |||||||
\(114\) | 0.791288 | 0.0741109 | ||||||||
\(115\) | 0 | 0 | ||||||||
\(116\) | −8.20871 | −0.762160 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.37386 | −0.586762 | ||||||||
\(119\) | −7.93725 | −0.727607 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −4.00000 | −0.363636 | ||||||||
\(122\) | 0.647551 | 0.0586265 | ||||||||
\(123\) | 2.64575 | 0.238559 | ||||||||
\(124\) | 11.1153 | 0.998184 | ||||||||
\(125\) | 0 | 0 | ||||||||
\(126\) | −1.58258 | −0.140987 | ||||||||
\(127\) | −17.7477 | −1.57486 | −0.787428 | − | 0.616407i | \(-0.788588\pi\) | ||||
−0.787428 | + | 0.616407i | \(0.788588\pi\) | |||||||
\(128\) | 11.0399 | 0.975795 | ||||||||
\(129\) | −10.5826 | −0.931744 | ||||||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −7.58258 | −0.662493 | −0.331246 | − | 0.943544i | \(-0.607469\pi\) | ||||
−0.331246 | + | 0.943544i | \(0.607469\pi\) | |||||||
\(132\) | −4.73930 | −0.412503 | ||||||||
\(133\) | 3.00000 | 0.260133 | ||||||||
\(134\) | −0.460985 | −0.0398230 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 7.93725 | 0.680614 | ||||||||
\(137\) | 10.4877 | 0.896021 | 0.448010 | − | 0.894028i | \(-0.352133\pi\) | ||||
0.448010 | + | 0.894028i | \(0.352133\pi\) | |||||||
\(138\) | 2.09355 | 0.178215 | ||||||||
\(139\) | −21.7477 | −1.84462 | −0.922309 | − | 0.386453i | \(-0.873700\pi\) | ||||
−0.922309 | + | 0.386453i | \(0.873700\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −1.82740 | −0.153895 | ||||||||
\(142\) | 3.20871 | 0.269269 | ||||||||
\(143\) | 0 | 0 | ||||||||
\(144\) | −5.58258 | −0.465215 | ||||||||
\(145\) | 0 | 0 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | −4.00000 | −0.329914 | ||||||||
\(148\) | −14.2179 | −1.16870 | ||||||||
\(149\) | −16.6929 | −1.36753 | −0.683766 | − | 0.729701i | \(-0.739659\pi\) | ||||
−0.683766 | + | 0.729701i | \(0.739659\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −9.66930 | −0.786877 | −0.393438 | − | 0.919351i | \(-0.628715\pi\) | ||||
−0.393438 | + | 0.919351i | \(0.628715\pi\) | |||||||
\(152\) | −3.00000 | −0.243332 | ||||||||
\(153\) | −9.16515 | −0.740959 | ||||||||
\(154\) | 2.09355 | 0.168703 | ||||||||
\(155\) | 0 | 0 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 9.16515 | 0.731459 | 0.365729 | − | 0.930721i | \(-0.380820\pi\) | ||||
0.365729 | + | 0.930721i | \(0.380820\pi\) | |||||||
\(158\) | 2.74110 | 0.218070 | ||||||||
\(159\) | 7.58258 | 0.601337 | ||||||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 7.93725 | 0.625543 | ||||||||
\(162\) | −0.456850 | −0.0358935 | ||||||||
\(163\) | −21.0707 | −1.65038 | −0.825191 | − | 0.564854i | \(-0.808932\pi\) | ||||
−0.825191 | + | 0.564854i | \(0.808932\pi\) | |||||||
\(164\) | −4.73930 | −0.370077 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | −2.74773 | −0.213265 | ||||||||
\(167\) | −9.57395 | −0.740855 | −0.370427 | − | 0.928861i | \(-0.620789\pi\) | ||||
−0.370427 | + | 0.928861i | \(0.620789\pi\) | |||||||
\(168\) | −3.00000 | −0.231455 | ||||||||
\(169\) | 0 | 0 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 3.46410 | 0.264906 | ||||||||
\(172\) | 18.9564 | 1.44541 | ||||||||
\(173\) | 16.5826 | 1.26075 | 0.630375 | − | 0.776291i | \(-0.282901\pi\) | ||||
0.630375 | + | 0.776291i | \(0.282901\pi\) | |||||||
\(174\) | −2.09355 | −0.158712 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | 7.38505 | 0.556669 | ||||||||
\(177\) | 13.9518 | 1.04868 | ||||||||
\(178\) | −4.37386 | −0.327835 | ||||||||
\(179\) | −18.1652 | −1.35773 | −0.678864 | − | 0.734264i | \(-0.737527\pi\) | ||||
−0.678864 | + | 0.734264i | \(0.737527\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −8.74773 | −0.650213 | −0.325107 | − | 0.945677i | \(-0.605400\pi\) | ||||
−0.325107 | + | 0.945677i | \(0.605400\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | −1.41742 | −0.104779 | ||||||||
\(184\) | −7.93725 | −0.585142 | ||||||||
\(185\) | 0 | 0 | ||||||||
\(186\) | 2.83485 | 0.207861 | ||||||||
\(187\) | 12.1244 | 0.886621 | ||||||||
\(188\) | 3.27340 | 0.238737 | ||||||||
\(189\) | 8.66025 | 0.629941 | ||||||||
\(190\) | 0 | 0 | ||||||||
\(191\) | −16.5826 | −1.19987 | −0.599937 | − | 0.800048i | \(-0.704808\pi\) | ||||
−0.599937 | + | 0.800048i | \(0.704808\pi\) | |||||||
\(192\) | −3.41742 | −0.246631 | ||||||||
\(193\) | −14.8655 | −1.07004 | −0.535020 | − | 0.844840i | \(-0.679696\pi\) | ||||
−0.535020 | + | 0.844840i | \(0.679696\pi\) | |||||||
\(194\) | −5.20871 | −0.373964 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 7.16515 | 0.511797 | ||||||||
\(197\) | 14.6748 | 1.04553 | 0.522767 | − | 0.852476i | \(-0.324900\pi\) | ||||
0.522767 | + | 0.852476i | \(0.324900\pi\) | |||||||
\(198\) | 2.41742 | 0.171799 | ||||||||
\(199\) | −10.5826 | −0.750179 | −0.375089 | − | 0.926989i | \(-0.622388\pi\) | ||||
−0.375089 | + | 0.926989i | \(0.622388\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | 1.00905 | 0.0711729 | ||||||||
\(202\) | 4.11165 | 0.289295 | ||||||||
\(203\) | −7.93725 | −0.557086 | ||||||||
\(204\) | −8.20871 | −0.574725 | ||||||||
\(205\) | 0 | 0 | ||||||||
\(206\) | 1.44600 | 0.100748 | ||||||||
\(207\) | 9.16515 | 0.637022 | ||||||||
\(208\) | 0 | 0 | ||||||||
\(209\) | −4.58258 | −0.316983 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −0.165151 | −0.0113695 | −0.00568475 | − | 0.999984i | \(-0.501810\pi\) | ||||
−0.00568475 | + | 0.999984i | \(0.501810\pi\) | |||||||
\(212\) | −13.5826 | −0.932855 | ||||||||
\(213\) | −7.02355 | −0.481246 | ||||||||
\(214\) | 4.83465 | 0.330490 | ||||||||
\(215\) | 0 | 0 | ||||||||
\(216\) | −8.66025 | −0.589256 | ||||||||
\(217\) | 10.7477 | 0.729603 | ||||||||
\(218\) | 6.00000 | 0.406371 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | −3.62614 | −0.243370 | ||||||||
\(223\) | −8.66025 | −0.579934 | −0.289967 | − | 0.957037i | \(-0.593644\pi\) | ||||
−0.289967 | + | 0.957037i | \(0.593644\pi\) | |||||||
\(224\) | 8.20871 | 0.548468 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 3.38865 | 0.225410 | ||||||||
\(227\) | −0.818350 | −0.0543158 | −0.0271579 | − | 0.999631i | \(-0.508646\pi\) | ||||
−0.0271579 | + | 0.999631i | \(0.508646\pi\) | |||||||
\(228\) | 3.10260 | 0.205475 | ||||||||
\(229\) | −26.2668 | −1.73576 | −0.867880 | − | 0.496774i | \(-0.834518\pi\) | ||||
−0.867880 | + | 0.496774i | \(0.834518\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −4.58258 | −0.301511 | ||||||||
\(232\) | 7.93725 | 0.521106 | ||||||||
\(233\) | −2.83485 | −0.185717 | −0.0928586 | − | 0.995679i | \(-0.529600\pi\) | ||||
−0.0928586 | + | 0.995679i | \(0.529600\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 0 | 0 | ||||||||
\(236\) | −24.9916 | −1.62682 | ||||||||
\(237\) | −6.00000 | −0.389742 | ||||||||
\(238\) | 3.62614 | 0.235048 | ||||||||
\(239\) | 0.190700 | 0.0123354 | 0.00616769 | − | 0.999981i | \(-0.498037\pi\) | ||||
0.00616769 | + | 0.999981i | \(0.498037\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −1.73205 | −0.111571 | −0.0557856 | − | 0.998443i | \(-0.517766\pi\) | ||||
−0.0557856 | + | 0.998443i | \(0.517766\pi\) | |||||||
\(242\) | 1.82740 | 0.117470 | ||||||||
\(243\) | 16.0000 | 1.02640 | ||||||||
\(244\) | 2.53901 | 0.162544 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | −1.20871 | −0.0770647 | ||||||||
\(247\) | 0 | 0 | ||||||||
\(248\) | −10.7477 | −0.682481 | ||||||||
\(249\) | 6.01450 | 0.381154 | ||||||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 0.165151 | 0.0104243 | 0.00521213 | − | 0.999986i | \(-0.498341\pi\) | ||||
0.00521213 | + | 0.999986i | \(0.498341\pi\) | |||||||
\(252\) | −6.20520 | −0.390891 | ||||||||
\(253\) | −12.1244 | −0.762252 | ||||||||
\(254\) | 8.10805 | 0.508745 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.79129 | 0.111955 | ||||||||
\(257\) | 18.1652 | 1.13311 | 0.566556 | − | 0.824024i | \(-0.308276\pi\) | ||||
0.566556 | + | 0.824024i | \(0.308276\pi\) | |||||||
\(258\) | 4.83465 | 0.300992 | ||||||||
\(259\) | −13.7477 | −0.854242 | ||||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | −9.16515 | −0.567309 | ||||||||
\(262\) | 3.46410 | 0.214013 | ||||||||
\(263\) | 9.00000 | 0.554964 | 0.277482 | − | 0.960731i | \(-0.410500\pi\) | ||||
0.277482 | + | 0.960731i | \(0.410500\pi\) | |||||||
\(264\) | 4.58258 | 0.282038 | ||||||||
\(265\) | 0 | 0 | ||||||||
\(266\) | −1.37055 | −0.0840339 | ||||||||
\(267\) | 9.57395 | 0.585917 | ||||||||
\(268\) | −1.80750 | −0.110411 | ||||||||
\(269\) | −15.0000 | −0.914566 | −0.457283 | − | 0.889321i | \(-0.651177\pi\) | ||||
−0.457283 | + | 0.889321i | \(0.651177\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −8.66025 | −0.526073 | −0.263036 | − | 0.964786i | \(-0.584724\pi\) | ||||
−0.263036 | + | 0.964786i | \(0.584724\pi\) | |||||||
\(272\) | 12.7913 | 0.775586 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −4.79129 | −0.289452 | ||||||||
\(275\) | 0 | 0 | ||||||||
\(276\) | 8.20871 | 0.494106 | ||||||||
\(277\) | 7.41742 | 0.445670 | 0.222835 | − | 0.974856i | \(-0.428469\pi\) | ||||
0.222835 | + | 0.974856i | \(0.428469\pi\) | |||||||
\(278\) | 9.93545 | 0.595889 | ||||||||
\(279\) | 12.4104 | 0.742992 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 3.65480 | 0.218027 | 0.109014 | − | 0.994040i | \(-0.465231\pi\) | ||||
0.109014 | + | 0.994040i | \(0.465231\pi\) | |||||||
\(282\) | 0.834849 | 0.0497145 | ||||||||
\(283\) | 27.7477 | 1.64943 | 0.824716 | − | 0.565548i | \(-0.191335\pi\) | ||||
0.824716 | + | 0.565548i | \(0.191335\pi\) | |||||||
\(284\) | 12.5812 | 0.746557 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −4.58258 | −0.270501 | ||||||||
\(288\) | 9.47860 | 0.558532 | ||||||||
\(289\) | 4.00000 | 0.235294 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 11.4014 | 0.668359 | ||||||||
\(292\) | 0 | 0 | ||||||||
\(293\) | 18.1389 | 1.05968 | 0.529842 | − | 0.848097i | \(-0.322251\pi\) | ||||
0.529842 | + | 0.848097i | \(0.322251\pi\) | |||||||
\(294\) | 1.82740 | 0.106576 | ||||||||
\(295\) | 0 | 0 | ||||||||
\(296\) | 13.7477 | 0.799070 | ||||||||
\(297\) | −13.2288 | −0.767610 | ||||||||
\(298\) | 7.62614 | 0.441770 | ||||||||
\(299\) | 0 | 0 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 18.3296 | 1.05650 | ||||||||
\(302\) | 4.41742 | 0.254194 | ||||||||
\(303\) | −9.00000 | −0.517036 | ||||||||
\(304\) | −4.83465 | −0.277286 | ||||||||
\(305\) | 0 | 0 | ||||||||
\(306\) | 4.18710 | 0.239361 | ||||||||
\(307\) | −24.2487 | −1.38395 | −0.691974 | − | 0.721923i | \(-0.743259\pi\) | ||||
−0.691974 | + | 0.721923i | \(0.743259\pi\) | |||||||
\(308\) | 8.20871 | 0.467735 | ||||||||
\(309\) | −3.16515 | −0.180059 | ||||||||
\(310\) | 0 | 0 | ||||||||
\(311\) | −7.58258 | −0.429968 | −0.214984 | − | 0.976618i | \(-0.568970\pi\) | ||||
−0.214984 | + | 0.976618i | \(0.568970\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −3.25227 | −0.183829 | −0.0919147 | − | 0.995767i | \(-0.529299\pi\) | ||||
−0.0919147 | + | 0.995767i | \(0.529299\pi\) | |||||||
\(314\) | −4.18710 | −0.236292 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 10.7477 | 0.604607 | ||||||||
\(317\) | −0.190700 | −0.0107108 | −0.00535540 | − | 0.999986i | \(-0.501705\pi\) | ||||
−0.00535540 | + | 0.999986i | \(0.501705\pi\) | |||||||
\(318\) | −3.46410 | −0.194257 | ||||||||
\(319\) | 12.1244 | 0.678834 | ||||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | −10.5826 | −0.590662 | ||||||||
\(322\) | −3.62614 | −0.202077 | ||||||||
\(323\) | −7.93725 | −0.441641 | ||||||||
\(324\) | −1.79129 | −0.0995160 | ||||||||
\(325\) | 0 | 0 | ||||||||
\(326\) | 9.62614 | 0.533142 | ||||||||
\(327\) | −13.1334 | −0.726279 | ||||||||
\(328\) | 4.58258 | 0.253030 | ||||||||
\(329\) | 3.16515 | 0.174500 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 4.47315 | 0.245867 | 0.122933 | − | 0.992415i | \(-0.460770\pi\) | ||||
0.122933 | + | 0.992415i | \(0.460770\pi\) | |||||||
\(332\) | −10.7737 | −0.591284 | ||||||||
\(333\) | −15.8745 | −0.869918 | ||||||||
\(334\) | 4.37386 | 0.239327 | ||||||||
\(335\) | 0 | 0 | ||||||||
\(336\) | −4.83465 | −0.263752 | ||||||||
\(337\) | −30.7477 | −1.67494 | −0.837468 | − | 0.546487i | \(-0.815965\pi\) | ||||
−0.837468 | + | 0.546487i | \(0.815965\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | −7.41742 | −0.402859 | ||||||||
\(340\) | 0 | 0 | ||||||||
\(341\) | −16.4174 | −0.889053 | ||||||||
\(342\) | −1.58258 | −0.0855759 | ||||||||
\(343\) | 19.0526 | 1.02874 | ||||||||
\(344\) | −18.3296 | −0.988264 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −7.57575 | −0.407275 | ||||||||
\(347\) | −21.3303 | −1.14507 | −0.572535 | − | 0.819880i | \(-0.694040\pi\) | ||||
−0.572535 | + | 0.819880i | \(0.694040\pi\) | |||||||
\(348\) | −8.20871 | −0.440033 | ||||||||
\(349\) | 2.45505 | 0.131416 | 0.0657079 | − | 0.997839i | \(-0.479069\pi\) | ||||
0.0657079 | + | 0.997839i | \(0.479069\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −12.5390 | −0.668332 | ||||||||
\(353\) | 6.83285 | 0.363676 | 0.181838 | − | 0.983328i | \(-0.441795\pi\) | ||||
0.181838 | + | 0.983328i | \(0.441795\pi\) | |||||||
\(354\) | −6.37386 | −0.338767 | ||||||||
\(355\) | 0 | 0 | ||||||||
\(356\) | −17.1497 | −0.908933 | ||||||||
\(357\) | −7.93725 | −0.420084 | ||||||||
\(358\) | 8.29875 | 0.438603 | ||||||||
\(359\) | 19.5293 | 1.03072 | 0.515359 | − | 0.856975i | \(-0.327659\pi\) | ||||
0.515359 | + | 0.856975i | \(0.327659\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −16.0000 | −0.842105 | ||||||||
\(362\) | 3.99640 | 0.210046 | ||||||||
\(363\) | −4.00000 | −0.209946 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 0 | 0 | ||||||||
\(366\) | 0.647551 | 0.0338480 | ||||||||
\(367\) | −1.74773 | −0.0912306 | −0.0456153 | − | 0.998959i | \(-0.514525\pi\) | ||||
−0.0456153 | + | 0.998959i | \(0.514525\pi\) | |||||||
\(368\) | −12.7913 | −0.666792 | ||||||||
\(369\) | −5.29150 | −0.275465 | ||||||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −13.1334 | −0.681852 | ||||||||
\(372\) | 11.1153 | 0.576302 | ||||||||
\(373\) | −13.0000 | −0.673114 | −0.336557 | − | 0.941663i | \(-0.609263\pi\) | ||||
−0.336557 | + | 0.941663i | \(0.609263\pi\) | |||||||
\(374\) | −5.53901 | −0.286416 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | −3.16515 | −0.163230 | ||||||||
\(377\) | 0 | 0 | ||||||||
\(378\) | −3.95644 | −0.203497 | ||||||||
\(379\) | 10.6784 | 0.548510 | 0.274255 | − | 0.961657i | \(-0.411569\pi\) | ||||
0.274255 | + | 0.961657i | \(0.411569\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | −17.7477 | −0.909244 | ||||||||
\(382\) | 7.57575 | 0.387609 | ||||||||
\(383\) | 23.6211 | 1.20698 | 0.603490 | − | 0.797371i | \(-0.293776\pi\) | ||||
0.603490 | + | 0.797371i | \(0.293776\pi\) | |||||||
\(384\) | 11.0399 | 0.563375 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | 6.79129 | 0.345667 | ||||||||
\(387\) | 21.1652 | 1.07589 | ||||||||
\(388\) | −20.4231 | −1.03683 | ||||||||
\(389\) | 3.16515 | 0.160480 | 0.0802398 | − | 0.996776i | \(-0.474431\pi\) | ||||
0.0802398 | + | 0.996776i | \(0.474431\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −21.0000 | −1.06202 | ||||||||
\(392\) | −6.92820 | −0.349927 | ||||||||
\(393\) | −7.58258 | −0.382490 | ||||||||
\(394\) | −6.70417 | −0.337751 | ||||||||
\(395\) | 0 | 0 | ||||||||
\(396\) | 9.47860 | 0.476318 | ||||||||
\(397\) | −20.3477 | −1.02122 | −0.510610 | − | 0.859812i | \(-0.670580\pi\) | ||||
−0.510610 | + | 0.859812i | \(0.670580\pi\) | |||||||
\(398\) | 4.83465 | 0.242339 | ||||||||
\(399\) | 3.00000 | 0.150188 | ||||||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 29.8263 | 1.48945 | 0.744726 | − | 0.667370i | \(-0.232580\pi\) | ||||
0.744726 | + | 0.667370i | \(0.232580\pi\) | |||||||
\(402\) | −0.460985 | −0.0229918 | ||||||||
\(403\) | 0 | 0 | ||||||||
\(404\) | 16.1216 | 0.802079 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 3.62614 | 0.179962 | ||||||||
\(407\) | 21.0000 | 1.04093 | ||||||||
\(408\) | 7.93725 | 0.392953 | ||||||||
\(409\) | 8.66025 | 0.428222 | 0.214111 | − | 0.976809i | \(-0.431315\pi\) | ||||
0.214111 | + | 0.976809i | \(0.431315\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 10.4877 | 0.517318 | ||||||||
\(412\) | 5.66970 | 0.279326 | ||||||||
\(413\) | −24.1652 | −1.18909 | ||||||||
\(414\) | −4.18710 | −0.205785 | ||||||||
\(415\) | 0 | 0 | ||||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −21.7477 | −1.06499 | ||||||||
\(418\) | 2.09355 | 0.102399 | ||||||||
\(419\) | −5.83485 | −0.285051 | −0.142526 | − | 0.989791i | \(-0.545522\pi\) | ||||
−0.142526 | + | 0.989791i | \(0.545522\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −5.48220 | −0.267186 | −0.133593 | − | 0.991036i | \(-0.542652\pi\) | ||||
−0.133593 | + | 0.991036i | \(0.542652\pi\) | |||||||
\(422\) | 0.0754495 | 0.00367282 | ||||||||
\(423\) | 3.65480 | 0.177703 | ||||||||
\(424\) | 13.1334 | 0.637815 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 3.20871 | 0.155463 | ||||||||
\(427\) | 2.45505 | 0.118808 | ||||||||
\(428\) | 18.9564 | 0.916294 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 8.46955 | 0.407964 | 0.203982 | − | 0.978975i | \(-0.434612\pi\) | ||||
0.203982 | + | 0.978975i | \(0.434612\pi\) | |||||||
\(432\) | −13.9564 | −0.671479 | ||||||||
\(433\) | −9.74773 | −0.468446 | −0.234223 | − | 0.972183i | \(-0.575255\pi\) | ||||
−0.234223 | + | 0.972183i | \(0.575255\pi\) | |||||||
\(434\) | −4.91010 | −0.235692 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 23.5257 | 1.12668 | ||||||||
\(437\) | 7.93725 | 0.379690 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 14.4955 | 0.691830 | 0.345915 | − | 0.938266i | \(-0.387569\pi\) | ||||
0.345915 | + | 0.938266i | \(0.387569\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 8.00000 | 0.380952 | ||||||||
\(442\) | 0 | 0 | ||||||||
\(443\) | 19.9129 | 0.946089 | 0.473045 | − | 0.881038i | \(-0.343155\pi\) | ||||
0.473045 | + | 0.881038i | \(0.343155\pi\) | |||||||
\(444\) | −14.2179 | −0.674752 | ||||||||
\(445\) | 0 | 0 | ||||||||
\(446\) | 3.95644 | 0.187343 | ||||||||
\(447\) | −16.6929 | −0.789545 | ||||||||
\(448\) | 5.91915 | 0.279654 | ||||||||
\(449\) | −11.0200 | −0.520064 | −0.260032 | − | 0.965600i | \(-0.583733\pi\) | ||||
−0.260032 | + | 0.965600i | \(0.583733\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 7.00000 | 0.329617 | ||||||||
\(452\) | 13.2867 | 0.624956 | ||||||||
\(453\) | −9.66930 | −0.454304 | ||||||||
\(454\) | 0.373864 | 0.0175463 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | −3.00000 | −0.140488 | ||||||||
\(457\) | −1.73205 | −0.0810219 | −0.0405110 | − | 0.999179i | \(-0.512899\pi\) | ||||
−0.0405110 | + | 0.999179i | \(0.512899\pi\) | |||||||
\(458\) | 12.0000 | 0.560723 | ||||||||
\(459\) | −22.9129 | −1.06948 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | −35.8408 | −1.66927 | −0.834635 | − | 0.550803i | \(-0.814322\pi\) | ||||
−0.834635 | + | 0.550803i | \(0.814322\pi\) | |||||||
\(462\) | 2.09355 | 0.0974008 | ||||||||
\(463\) | 39.4002 | 1.83108 | 0.915542 | − | 0.402223i | \(-0.131762\pi\) | ||||
0.915542 | + | 0.402223i | \(0.131762\pi\) | |||||||
\(464\) | 12.7913 | 0.593821 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 1.29510 | 0.0599944 | ||||||||
\(467\) | 24.3303 | 1.12587 | 0.562936 | − | 0.826500i | \(-0.309672\pi\) | ||||
0.562936 | + | 0.826500i | \(0.309672\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.74773 | −0.0807025 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | 9.16515 | 0.422308 | ||||||||
\(472\) | 24.1652 | 1.11229 | ||||||||
\(473\) | −27.9989 | −1.28739 | ||||||||
\(474\) | 2.74110 | 0.125903 | ||||||||
\(475\) | 0 | 0 | ||||||||
\(476\) | 14.2179 | 0.651677 | ||||||||
\(477\) | −15.1652 | −0.694365 | ||||||||
\(478\) | −0.0871215 | −0.00398485 | ||||||||
\(479\) | 4.66385 | 0.213097 | 0.106548 | − | 0.994308i | \(-0.466020\pi\) | ||||
0.106548 | + | 0.994308i | \(0.466020\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | 0 | 0 | ||||||||
\(482\) | 0.791288 | 0.0360422 | ||||||||
\(483\) | 7.93725 | 0.361158 | ||||||||
\(484\) | 7.16515 | 0.325689 | ||||||||
\(485\) | 0 | 0 | ||||||||
\(486\) | −7.30960 | −0.331570 | ||||||||
\(487\) | −10.6784 | −0.483882 | −0.241941 | − | 0.970291i | \(-0.577784\pi\) | ||||
−0.241941 | + | 0.970291i | \(0.577784\pi\) | |||||||
\(488\) | −2.45505 | −0.111135 | ||||||||
\(489\) | −21.0707 | −0.952848 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −19.4174 | −0.876296 | −0.438148 | − | 0.898903i | \(-0.644365\pi\) | ||||
−0.438148 | + | 0.898903i | \(0.644365\pi\) | |||||||
\(492\) | −4.73930 | −0.213664 | ||||||||
\(493\) | 21.0000 | 0.945792 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −17.3205 | −0.777714 | ||||||||
\(497\) | 12.1652 | 0.545682 | ||||||||
\(498\) | −2.74773 | −0.123129 | ||||||||
\(499\) | 0.723000 | 0.0323659 | 0.0161830 | − | 0.999869i | \(-0.494849\pi\) | ||||
0.0161830 | + | 0.999869i | \(0.494849\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −9.57395 | −0.427733 | ||||||||
\(502\) | −0.0754495 | −0.00336747 | ||||||||
\(503\) | 0.165151 | 0.00736374 | 0.00368187 | − | 0.999993i | \(-0.498828\pi\) | ||||
0.00368187 | + | 0.999993i | \(0.498828\pi\) | |||||||
\(504\) | 6.00000 | 0.267261 | ||||||||
\(505\) | 0 | 0 | ||||||||
\(506\) | 5.53901 | 0.246239 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 31.7913 | 1.41051 | ||||||||
\(509\) | 8.46955 | 0.375406 | 0.187703 | − | 0.982226i | \(-0.439896\pi\) | ||||
0.187703 | + | 0.982226i | \(0.439896\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | −22.8981 | −1.01196 | ||||||||
\(513\) | 8.66025 | 0.382360 | ||||||||
\(514\) | −8.29875 | −0.366042 | ||||||||
\(515\) | 0 | 0 | ||||||||
\(516\) | 18.9564 | 0.834511 | ||||||||
\(517\) | −4.83485 | −0.212636 | ||||||||
\(518\) | 6.28065 | 0.275956 | ||||||||
\(519\) | 16.5826 | 0.727894 | ||||||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 27.4955 | 1.20460 | 0.602299 | − | 0.798271i | \(-0.294252\pi\) | ||||
0.602299 | + | 0.798271i | \(0.294252\pi\) | |||||||
\(522\) | 4.18710 | 0.183264 | ||||||||
\(523\) | 0.165151 | 0.00722157 | 0.00361078 | − | 0.999993i | \(-0.498851\pi\) | ||||
0.00361078 | + | 0.999993i | \(0.498851\pi\) | |||||||
\(524\) | 13.5826 | 0.593358 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −4.11165 | −0.179277 | ||||||||
\(527\) | −28.4358 | −1.23868 | ||||||||
\(528\) | 7.38505 | 0.321393 | ||||||||
\(529\) | −2.00000 | −0.0869565 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −27.9035 | −1.21091 | ||||||||
\(532\) | −5.37386 | −0.232987 | ||||||||
\(533\) | 0 | 0 | ||||||||
\(534\) | −4.37386 | −0.189276 | ||||||||
\(535\) | 0 | 0 | ||||||||
\(536\) | 1.74773 | 0.0754903 | ||||||||
\(537\) | −18.1652 | −0.783884 | ||||||||
\(538\) | 6.85275 | 0.295443 | ||||||||
\(539\) | −10.5830 | −0.455842 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | −10.3923 | −0.446800 | −0.223400 | − | 0.974727i | \(-0.571716\pi\) | ||||
−0.223400 | + | 0.974727i | \(0.571716\pi\) | |||||||
\(542\) | 3.95644 | 0.169944 | ||||||||
\(543\) | −8.74773 | −0.375401 | ||||||||
\(544\) | −21.7182 | −0.931161 | ||||||||
\(545\) | 0 | 0 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 28.7477 | 1.22916 | 0.614582 | − | 0.788853i | \(-0.289325\pi\) | ||||
0.614582 | + | 0.788853i | \(0.289325\pi\) | |||||||
\(548\) | −18.7864 | −0.802516 | ||||||||
\(549\) | 2.83485 | 0.120988 | ||||||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −7.93725 | −0.338138 | ||||||||
\(552\) | −7.93725 | −0.337832 | ||||||||
\(553\) | 10.3923 | 0.441926 | ||||||||
\(554\) | −3.38865 | −0.143970 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | 38.9564 | 1.65212 | ||||||||
\(557\) | 7.74655 | 0.328232 | 0.164116 | − | 0.986441i | \(-0.447523\pi\) | ||||
0.164116 | + | 0.986441i | \(0.447523\pi\) | |||||||
\(558\) | −5.66970 | −0.240017 | ||||||||
\(559\) | 0 | 0 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 12.1244 | 0.511891 | ||||||||
\(562\) | −1.66970 | −0.0704319 | ||||||||
\(563\) | 9.00000 | 0.379305 | 0.189652 | − | 0.981851i | \(-0.439264\pi\) | ||||
0.189652 | + | 0.981851i | \(0.439264\pi\) | |||||||
\(564\) | 3.27340 | 0.137835 | ||||||||
\(565\) | 0 | 0 | ||||||||
\(566\) | −12.6766 | −0.532835 | ||||||||
\(567\) | −1.73205 | −0.0727393 | ||||||||
\(568\) | −12.1652 | −0.510438 | ||||||||
\(569\) | −7.74773 | −0.324802 | −0.162401 | − | 0.986725i | \(-0.551924\pi\) | ||||
−0.162401 | + | 0.986725i | \(0.551924\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 35.0780 | 1.46797 | 0.733985 | − | 0.679166i | \(-0.237658\pi\) | ||||
0.733985 | + | 0.679166i | \(0.237658\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | −16.5826 | −0.692747 | ||||||||
\(574\) | 2.09355 | 0.0873831 | ||||||||
\(575\) | 0 | 0 | ||||||||
\(576\) | 6.83485 | 0.284785 | ||||||||
\(577\) | −6.92820 | −0.288425 | −0.144212 | − | 0.989547i | \(-0.546065\pi\) | ||||
−0.144212 | + | 0.989547i | \(0.546065\pi\) | |||||||
\(578\) | −1.82740 | −0.0760099 | ||||||||
\(579\) | −14.8655 | −0.617787 | ||||||||
\(580\) | 0 | 0 | ||||||||
\(581\) | −10.4174 | −0.432188 | ||||||||
\(582\) | −5.20871 | −0.215908 | ||||||||
\(583\) | 20.0616 | 0.830867 | ||||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | −8.28674 | −0.342322 | ||||||||
\(587\) | −39.4956 | −1.63016 | −0.815078 | − | 0.579351i | \(-0.803306\pi\) | ||||
−0.815078 | + | 0.579351i | \(0.803306\pi\) | |||||||
\(588\) | 7.16515 | 0.295486 | ||||||||
\(589\) | 10.7477 | 0.442852 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 14.6748 | 0.603639 | ||||||||
\(592\) | 22.1552 | 0.910571 | ||||||||
\(593\) | −21.1660 | −0.869184 | −0.434592 | − | 0.900627i | \(-0.643107\pi\) | ||||
−0.434592 | + | 0.900627i | \(0.643107\pi\) | |||||||
\(594\) | 6.04356 | 0.247970 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 29.9017 | 1.22482 | ||||||||
\(597\) | −10.5826 | −0.433116 | ||||||||
\(598\) | 0 | 0 | ||||||||
\(599\) | 15.4955 | 0.633127 | 0.316564 | − | 0.948571i | \(-0.397471\pi\) | ||||
0.316564 | + | 0.948571i | \(0.397471\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 16.9129 | 0.689891 | 0.344945 | − | 0.938623i | \(-0.387897\pi\) | ||||
0.344945 | + | 0.938623i | \(0.387897\pi\) | |||||||
\(602\) | −8.37386 | −0.341293 | ||||||||
\(603\) | −2.01810 | −0.0821834 | ||||||||
\(604\) | 17.3205 | 0.704761 | ||||||||
\(605\) | 0 | 0 | ||||||||
\(606\) | 4.11165 | 0.167024 | ||||||||
\(607\) | 7.74773 | 0.314471 | 0.157235 | − | 0.987561i | \(-0.449742\pi\) | ||||
0.157235 | + | 0.987561i | \(0.449742\pi\) | |||||||
\(608\) | 8.20871 | 0.332907 | ||||||||
\(609\) | −7.93725 | −0.321634 | ||||||||
\(610\) | 0 | 0 | ||||||||
\(611\) | 0 | 0 | ||||||||
\(612\) | 16.4174 | 0.663635 | ||||||||
\(613\) | −5.91915 | −0.239072 | −0.119536 | − | 0.992830i | \(-0.538141\pi\) | ||||
−0.119536 | + | 0.992830i | \(0.538141\pi\) | |||||||
\(614\) | 11.0780 | 0.447073 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | −7.93725 | −0.319801 | ||||||||
\(617\) | 13.9518 | 0.561677 | 0.280838 | − | 0.959755i | \(-0.409388\pi\) | ||||
0.280838 | + | 0.959755i | \(0.409388\pi\) | |||||||
\(618\) | 1.44600 | 0.0581667 | ||||||||
\(619\) | 29.7309 | 1.19499 | 0.597493 | − | 0.801874i | \(-0.296164\pi\) | ||||
0.597493 | + | 0.801874i | \(0.296164\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | 22.9129 | 0.919462 | ||||||||
\(622\) | 3.46410 | 0.138898 | ||||||||
\(623\) | −16.5826 | −0.664367 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 0 | 0 | ||||||||
\(626\) | 1.48580 | 0.0593846 | ||||||||
\(627\) | −4.58258 | −0.183010 | ||||||||
\(628\) | −16.4174 | −0.655127 | ||||||||
\(629\) | 36.3731 | 1.45029 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −5.91915 | −0.235638 | −0.117819 | − | 0.993035i | \(-0.537590\pi\) | ||||
−0.117819 | + | 0.993035i | \(0.537590\pi\) | |||||||
\(632\) | −10.3923 | −0.413384 | ||||||||
\(633\) | −0.165151 | −0.00656418 | ||||||||
\(634\) | 0.0871215 | 0.00346004 | ||||||||
\(635\) | 0 | 0 | ||||||||
\(636\) | −13.5826 | −0.538584 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | −5.53901 | −0.219292 | ||||||||
\(639\) | 14.0471 | 0.555695 | ||||||||
\(640\) | 0 | 0 | ||||||||
\(641\) | −18.1652 | −0.717480 | −0.358740 | − | 0.933437i | \(-0.616794\pi\) | ||||
−0.358740 | + | 0.933437i | \(0.616794\pi\) | |||||||
\(642\) | 4.83465 | 0.190809 | ||||||||
\(643\) | −21.7937 | −0.859458 | −0.429729 | − | 0.902958i | \(-0.641391\pi\) | ||||
−0.429729 | + | 0.902958i | \(0.641391\pi\) | |||||||
\(644\) | −14.2179 | −0.560264 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | 3.62614 | 0.142668 | ||||||||
\(647\) | −27.0000 | −1.06148 | −0.530740 | − | 0.847535i | \(-0.678086\pi\) | ||||
−0.530740 | + | 0.847535i | \(0.678086\pi\) | |||||||
\(648\) | 1.73205 | 0.0680414 | ||||||||
\(649\) | 36.9129 | 1.44896 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | 10.7477 | 0.421237 | ||||||||
\(652\) | 37.7436 | 1.47815 | ||||||||
\(653\) | −42.8258 | −1.67590 | −0.837951 | − | 0.545746i | \(-0.816246\pi\) | ||||
−0.837951 | + | 0.545746i | \(0.816246\pi\) | |||||||
\(654\) | 6.00000 | 0.234619 | ||||||||
\(655\) | 0 | 0 | ||||||||
\(656\) | 7.38505 | 0.288338 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | −1.44600 | −0.0563710 | ||||||||
\(659\) | 30.4955 | 1.18793 | 0.593967 | − | 0.804489i | \(-0.297561\pi\) | ||||
0.593967 | + | 0.804489i | \(0.297561\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −18.3296 | −0.712937 | −0.356469 | − | 0.934307i | \(-0.616019\pi\) | ||||
−0.356469 | + | 0.934307i | \(0.616019\pi\) | |||||||
\(662\) | −2.04356 | −0.0794252 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 10.4174 | 0.404274 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 7.25227 | 0.281020 | ||||||||
\(667\) | −21.0000 | −0.813123 | ||||||||
\(668\) | 17.1497 | 0.663542 | ||||||||
\(669\) | −8.66025 | −0.334825 | ||||||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −3.75015 | −0.144773 | ||||||||
\(672\) | 8.20871 | 0.316658 | ||||||||
\(673\) | 24.1652 | 0.931498 | 0.465749 | − | 0.884917i | \(-0.345785\pi\) | ||||
0.465749 | + | 0.884917i | \(0.345785\pi\) | |||||||
\(674\) | 14.0471 | 0.541074 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | 0 | 0 | ||||||||
\(677\) | −2.83485 | −0.108952 | −0.0544760 | − | 0.998515i | \(-0.517349\pi\) | ||||
−0.0544760 | + | 0.998515i | \(0.517349\pi\) | |||||||
\(678\) | 3.38865 | 0.130140 | ||||||||
\(679\) | −19.7477 | −0.757848 | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | −0.818350 | −0.0313593 | ||||||||
\(682\) | 7.50030 | 0.287202 | ||||||||
\(683\) | −33.0997 | −1.26652 | −0.633262 | − | 0.773938i | \(-0.718284\pi\) | ||||
−0.633262 | + | 0.773938i | \(0.718284\pi\) | |||||||
\(684\) | −6.20520 | −0.237262 | ||||||||
\(685\) | 0 | 0 | ||||||||
\(686\) | −8.70417 | −0.332327 | ||||||||
\(687\) | −26.2668 | −1.00214 | ||||||||
\(688\) | −29.5390 | −1.12616 | ||||||||
\(689\) | 0 | 0 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 19.7756 | 0.752298 | 0.376149 | − | 0.926559i | \(-0.377248\pi\) | ||||
0.376149 | + | 0.926559i | \(0.377248\pi\) | |||||||
\(692\) | −29.7042 | −1.12918 | ||||||||
\(693\) | 9.16515 | 0.348155 | ||||||||
\(694\) | 9.74475 | 0.369906 | ||||||||
\(695\) | 0 | 0 | ||||||||
\(696\) | 7.93725 | 0.300861 | ||||||||
\(697\) | 12.1244 | 0.459243 | ||||||||
\(698\) | −1.12159 | −0.0424528 | ||||||||
\(699\) | −2.83485 | −0.107224 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 21.1652 | 0.799397 | 0.399698 | − | 0.916647i | \(-0.369115\pi\) | ||||
0.399698 | + | 0.916647i | \(0.369115\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −13.7477 | −0.518505 | ||||||||
\(704\) | −9.04165 | −0.340770 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −3.12159 | −0.117483 | ||||||||
\(707\) | 15.5885 | 0.586264 | ||||||||
\(708\) | −24.9916 | −0.939242 | ||||||||
\(709\) | −36.3731 | −1.36602 | −0.683010 | − | 0.730409i | \(-0.739329\pi\) | ||||
−0.683010 | + | 0.730409i | \(0.739329\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | 12.0000 | 0.450035 | ||||||||
\(712\) | 16.5826 | 0.621458 | ||||||||
\(713\) | 28.4358 | 1.06493 | ||||||||
\(714\) | 3.62614 | 0.135705 | ||||||||
\(715\) | 0 | 0 | ||||||||
\(716\) | 32.5390 | 1.21604 | ||||||||
\(717\) | 0.190700 | 0.00712184 | ||||||||
\(718\) | −8.92197 | −0.332965 | ||||||||
\(719\) | 24.4955 | 0.913526 | 0.456763 | − | 0.889588i | \(-0.349009\pi\) | ||||
0.456763 | + | 0.889588i | \(0.349009\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 5.48220 | 0.204168 | ||||||||
\(722\) | 7.30960 | 0.272035 | ||||||||
\(723\) | −1.73205 | −0.0644157 | ||||||||
\(724\) | 15.6697 | 0.582360 | ||||||||
\(725\) | 0 | 0 | ||||||||
\(726\) | 1.82740 | 0.0678212 | ||||||||
\(727\) | 15.2523 | 0.565675 | 0.282838 | − | 0.959168i | \(-0.408724\pi\) | ||||
0.282838 | + | 0.959168i | \(0.408724\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 13.0000 | 0.481481 | ||||||||
\(730\) | 0 | 0 | ||||||||
\(731\) | −48.4955 | −1.79367 | ||||||||
\(732\) | 2.53901 | 0.0938447 | ||||||||
\(733\) | −22.8027 | −0.842237 | −0.421119 | − | 0.907006i | \(-0.638362\pi\) | ||||
−0.421119 | + | 0.907006i | \(0.638362\pi\) | |||||||
\(734\) | 0.798450 | 0.0294713 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 21.7182 | 0.800544 | ||||||||
\(737\) | 2.66970 | 0.0983396 | ||||||||
\(738\) | 2.41742 | 0.0889866 | ||||||||
\(739\) | −17.0345 | −0.626623 | −0.313311 | − | 0.949650i | \(-0.601438\pi\) | ||||
−0.313311 | + | 0.949650i | \(0.601438\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 6.00000 | 0.220267 | ||||||||
\(743\) | 5.72845 | 0.210157 | 0.105078 | − | 0.994464i | \(-0.466491\pi\) | ||||
0.105078 | + | 0.994464i | \(0.466491\pi\) | |||||||
\(744\) | −10.7477 | −0.394031 | ||||||||
\(745\) | 0 | 0 | ||||||||
\(746\) | 5.93905 | 0.217444 | ||||||||
\(747\) | −12.0290 | −0.440118 | ||||||||
\(748\) | −21.7182 | −0.794096 | ||||||||
\(749\) | 18.3296 | 0.669748 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −11.7477 | −0.428681 | −0.214340 | − | 0.976759i | \(-0.568760\pi\) | ||||
−0.214340 | + | 0.976759i | \(0.568760\pi\) | |||||||
\(752\) | −5.10080 | −0.186007 | ||||||||
\(753\) | 0.165151 | 0.00601845 | ||||||||
\(754\) | 0 | 0 | ||||||||
\(755\) | 0 | 0 | ||||||||
\(756\) | −15.5130 | −0.564203 | ||||||||
\(757\) | 9.74773 | 0.354287 | 0.177144 | − | 0.984185i | \(-0.443314\pi\) | ||||
0.177144 | + | 0.984185i | \(0.443314\pi\) | |||||||
\(758\) | −4.87841 | −0.177192 | ||||||||
\(759\) | −12.1244 | −0.440086 | ||||||||
\(760\) | 0 | 0 | ||||||||
\(761\) | −35.4594 | −1.28540 | −0.642701 | − | 0.766118i | \(-0.722186\pi\) | ||||
−0.642701 | + | 0.766118i | \(0.722186\pi\) | |||||||
\(762\) | 8.10805 | 0.293724 | ||||||||
\(763\) | 22.7477 | 0.823523 | ||||||||
\(764\) | 29.7042 | 1.07466 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −10.7913 | −0.389905 | ||||||||
\(767\) | 0 | 0 | ||||||||
\(768\) | 1.79129 | 0.0646375 | ||||||||
\(769\) | 15.5885 | 0.562134 | 0.281067 | − | 0.959688i | \(-0.409312\pi\) | ||||
0.281067 | + | 0.959688i | \(0.409312\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 18.1652 | 0.654202 | ||||||||
\(772\) | 26.6283 | 0.958374 | ||||||||
\(773\) | −24.1534 | −0.868736 | −0.434368 | − | 0.900735i | \(-0.643028\pi\) | ||||
−0.434368 | + | 0.900735i | \(0.643028\pi\) | |||||||
\(774\) | −9.66930 | −0.347556 | ||||||||
\(775\) | 0 | 0 | ||||||||
\(776\) | 19.7477 | 0.708902 | ||||||||
\(777\) | −13.7477 | −0.493197 | ||||||||
\(778\) | −1.44600 | −0.0518416 | ||||||||
\(779\) | −4.58258 | −0.164188 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | −18.5826 | −0.664937 | ||||||||
\(782\) | 9.59386 | 0.343076 | ||||||||
\(783\) | −22.9129 | −0.818839 | ||||||||
\(784\) | −11.1652 | −0.398755 | ||||||||
\(785\) | 0 | 0 | ||||||||
\(786\) | 3.46410 | 0.123560 | ||||||||
\(787\) | 16.3115 | 0.581441 | 0.290720 | − | 0.956808i | \(-0.406105\pi\) | ||||
0.290720 | + | 0.956808i | \(0.406105\pi\) | |||||||
\(788\) | −26.2867 | −0.936425 | ||||||||
\(789\) | 9.00000 | 0.320408 | ||||||||
\(790\) | 0 | 0 | ||||||||
\(791\) | 12.8474 | 0.456799 | ||||||||
\(792\) | −9.16515 | −0.325669 | ||||||||
\(793\) | 0 | 0 | ||||||||
\(794\) | 9.29583 | 0.329897 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | 18.9564 | 0.671893 | ||||||||
\(797\) | −44.0780 | −1.56132 | −0.780662 | − | 0.624954i | \(-0.785118\pi\) | ||||
−0.780662 | + | 0.624954i | \(0.785118\pi\) | |||||||
\(798\) | −1.37055 | −0.0485170 | ||||||||
\(799\) | −8.37420 | −0.296258 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −19.1479 | −0.676558 | ||||||||
\(802\) | −13.6261 | −0.481156 | ||||||||
\(803\) | 0 | 0 | ||||||||
\(804\) | −1.80750 | −0.0637456 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −15.0000 | −0.528025 | ||||||||
\(808\) | −15.5885 | −0.548400 | ||||||||
\(809\) | −54.8258 | −1.92757 | −0.963785 | − | 0.266679i | \(-0.914074\pi\) | ||||
−0.963785 | + | 0.266679i | \(0.914074\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 50.5155 | 1.77384 | 0.886920 | − | 0.461923i | \(-0.152840\pi\) | ||||
0.886920 | + | 0.461923i | \(0.152840\pi\) | |||||||
\(812\) | 14.2179 | 0.498951 | ||||||||
\(813\) | −8.66025 | −0.303728 | ||||||||
\(814\) | −9.59386 | −0.336264 | ||||||||
\(815\) | 0 | 0 | ||||||||
\(816\) | 12.7913 | 0.447785 | ||||||||
\(817\) | 18.3296 | 0.641270 | ||||||||
\(818\) | −3.95644 | −0.138334 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 0 | 0 | ||||||||
\(821\) | 18.1389 | 0.633051 | 0.316525 | − | 0.948584i | \(-0.397484\pi\) | ||||
0.316525 | + | 0.948584i | \(0.397484\pi\) | |||||||
\(822\) | −4.79129 | −0.167115 | ||||||||
\(823\) | 31.4174 | 1.09514 | 0.547571 | − | 0.836759i | \(-0.315552\pi\) | ||||
0.547571 | + | 0.836759i | \(0.315552\pi\) | |||||||
\(824\) | −5.48220 | −0.190982 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 11.0399 | 0.384126 | ||||||||
\(827\) | −10.7737 | −0.374638 | −0.187319 | − | 0.982299i | \(-0.559980\pi\) | ||||
−0.187319 | + | 0.982299i | \(0.559980\pi\) | |||||||
\(828\) | −16.4174 | −0.570545 | ||||||||
\(829\) | 33.3303 | 1.15761 | 0.578805 | − | 0.815466i | \(-0.303519\pi\) | ||||
0.578805 | + | 0.815466i | \(0.303519\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 7.41742 | 0.257308 | ||||||||
\(832\) | 0 | 0 | ||||||||
\(833\) | −18.3303 | −0.635107 | ||||||||
\(834\) | 9.93545 | 0.344037 | ||||||||
\(835\) | 0 | 0 | ||||||||
\(836\) | 8.20871 | 0.283904 | ||||||||
\(837\) | 31.0260 | 1.07242 | ||||||||
\(838\) | 2.66565 | 0.0920834 | ||||||||
\(839\) | −43.6827 | −1.50809 | −0.754047 | − | 0.656821i | \(-0.771901\pi\) | ||||
−0.754047 | + | 0.656821i | \(0.771901\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −8.00000 | −0.275862 | ||||||||
\(842\) | 2.50455 | 0.0863123 | ||||||||
\(843\) | 3.65480 | 0.125878 | ||||||||
\(844\) | 0.295834 | 0.0101830 | ||||||||
\(845\) | 0 | 0 | ||||||||
\(846\) | −1.66970 | −0.0574054 | ||||||||
\(847\) | 6.92820 | 0.238056 | ||||||||
\(848\) | 21.1652 | 0.726814 | ||||||||
\(849\) | 27.7477 | 0.952300 | ||||||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −36.3731 | −1.24685 | ||||||||
\(852\) | 12.5812 | 0.431025 | ||||||||
\(853\) | −5.63310 | −0.192874 | −0.0964369 | − | 0.995339i | \(-0.530745\pi\) | ||||
−0.0964369 | + | 0.995339i | \(0.530745\pi\) | |||||||
\(854\) | −1.12159 | −0.0383800 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | −18.3296 | −0.626491 | ||||||||
\(857\) | 4.74773 | 0.162179 | 0.0810896 | − | 0.996707i | \(-0.474160\pi\) | ||||
0.0810896 | + | 0.996707i | \(0.474160\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −44.2432 | −1.50956 | −0.754779 | − | 0.655979i | \(-0.772256\pi\) | ||||
−0.754779 | + | 0.655979i | \(0.772256\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −4.58258 | −0.156174 | ||||||||
\(862\) | −3.86932 | −0.131789 | ||||||||
\(863\) | −13.6657 | −0.465186 | −0.232593 | − | 0.972574i | \(-0.574721\pi\) | ||||
−0.232593 | + | 0.972574i | \(0.574721\pi\) | |||||||
\(864\) | 23.6965 | 0.806172 | ||||||||
\(865\) | 0 | 0 | ||||||||
\(866\) | 4.45325 | 0.151328 | ||||||||
\(867\) | 4.00000 | 0.135847 | ||||||||
\(868\) | −19.2523 | −0.653465 | ||||||||
\(869\) | −15.8745 | −0.538506 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 0 | 0 | ||||||||
\(872\) | −22.7477 | −0.770335 | ||||||||
\(873\) | −22.8027 | −0.771755 | ||||||||
\(874\) | −3.62614 | −0.122656 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 7.93725 | 0.268022 | 0.134011 | − | 0.990980i | \(-0.457214\pi\) | ||||
0.134011 | + | 0.990980i | \(0.457214\pi\) | |||||||
\(878\) | −6.62225 | −0.223490 | ||||||||
\(879\) | 18.1389 | 0.611809 | ||||||||
\(880\) | 0 | 0 | ||||||||
\(881\) | −36.4955 | −1.22956 | −0.614782 | − | 0.788697i | \(-0.710756\pi\) | ||||
−0.614782 | + | 0.788697i | \(0.710756\pi\) | |||||||
\(882\) | −3.65480 | −0.123064 | ||||||||
\(883\) | −36.2432 | −1.21968 | −0.609840 | − | 0.792524i | \(-0.708766\pi\) | ||||
−0.609840 | + | 0.792524i | \(0.708766\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9.09720 | −0.305627 | ||||||||
\(887\) | 54.4955 | 1.82978 | 0.914889 | − | 0.403705i | \(-0.132278\pi\) | ||||
0.914889 | + | 0.403705i | \(0.132278\pi\) | |||||||
\(888\) | 13.7477 | 0.461344 | ||||||||
\(889\) | 30.7400 | 1.03099 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 2.64575 | 0.0886360 | ||||||||
\(892\) | 15.5130 | 0.519414 | ||||||||
\(893\) | 3.16515 | 0.105918 | ||||||||
\(894\) | 7.62614 | 0.255056 | ||||||||
\(895\) | 0 | 0 | ||||||||
\(896\) | −19.1216 | −0.638808 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 5.03447 | 0.168002 | ||||||||
\(899\) | −28.4358 | −0.948387 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 34.7477 | 1.15761 | ||||||||
\(902\) | −3.19795 | −0.106480 | ||||||||
\(903\) | 18.3296 | 0.609970 | ||||||||
\(904\) | −12.8474 | −0.427297 | ||||||||
\(905\) | 0 | 0 | ||||||||
\(906\) | 4.41742 | 0.146759 | ||||||||
\(907\) | 6.25227 | 0.207603 | 0.103802 | − | 0.994598i | \(-0.466899\pi\) | ||||
0.103802 | + | 0.994598i | \(0.466899\pi\) | |||||||
\(908\) | 1.46590 | 0.0486476 | ||||||||
\(909\) | 18.0000 | 0.597022 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | −7.91288 | −0.262165 | −0.131083 | − | 0.991371i | \(-0.541845\pi\) | ||||
−0.131083 | + | 0.991371i | \(0.541845\pi\) | |||||||
\(912\) | −4.83465 | −0.160091 | ||||||||
\(913\) | 15.9129 | 0.526639 | ||||||||
\(914\) | 0.791288 | 0.0261735 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 47.0514 | 1.55462 | ||||||||
\(917\) | 13.1334 | 0.433703 | ||||||||
\(918\) | 10.4678 | 0.345487 | ||||||||
\(919\) | 54.1652 | 1.78674 | 0.893372 | − | 0.449318i | \(-0.148333\pi\) | ||||
0.893372 | + | 0.449318i | \(0.148333\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | −24.2487 | −0.799022 | ||||||||
\(922\) | 16.3739 | 0.539244 | ||||||||
\(923\) | 0 | 0 | ||||||||
\(924\) | 8.20871 | 0.270047 | ||||||||
\(925\) | 0 | 0 | ||||||||
\(926\) | −18.0000 | −0.591517 | ||||||||
\(927\) | 6.33030 | 0.207914 | ||||||||
\(928\) | −21.7182 | −0.712935 | ||||||||
\(929\) | 26.3622 | 0.864915 | 0.432457 | − | 0.901654i | \(-0.357647\pi\) | ||||
0.432457 | + | 0.901654i | \(0.357647\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.92820 | 0.227063 | ||||||||
\(932\) | 5.07803 | 0.166336 | ||||||||
\(933\) | −7.58258 | −0.248242 | ||||||||
\(934\) | −11.1153 | −0.363704 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 31.4955 | 1.02891 | 0.514456 | − | 0.857517i | \(-0.327994\pi\) | ||||
0.514456 | + | 0.857517i | \(0.327994\pi\) | |||||||
\(938\) | 0.798450 | 0.0260703 | ||||||||
\(939\) | −3.25227 | −0.106134 | ||||||||
\(940\) | 0 | 0 | ||||||||
\(941\) | 26.4575 | 0.862490 | 0.431245 | − | 0.902235i | \(-0.358074\pi\) | ||||
0.431245 | + | 0.902235i | \(0.358074\pi\) | |||||||
\(942\) | −4.18710 | −0.136423 | ||||||||
\(943\) | −12.1244 | −0.394823 | ||||||||
\(944\) | 38.9434 | 1.26750 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 12.7913 | 0.415881 | ||||||||
\(947\) | 14.3332 | 0.465765 | 0.232883 | − | 0.972505i | \(-0.425184\pi\) | ||||
0.232883 | + | 0.972505i | \(0.425184\pi\) | |||||||
\(948\) | 10.7477 | 0.349070 | ||||||||
\(949\) | 0 | 0 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | −0.190700 | −0.00618388 | ||||||||
\(952\) | −13.7477 | −0.445566 | ||||||||
\(953\) | 8.07803 | 0.261673 | 0.130837 | − | 0.991404i | \(-0.458234\pi\) | ||||
0.130837 | + | 0.991404i | \(0.458234\pi\) | |||||||
\(954\) | 6.92820 | 0.224309 | ||||||||
\(955\) | 0 | 0 | ||||||||
\(956\) | −0.341599 | −0.0110481 | ||||||||
\(957\) | 12.1244 | 0.391925 | ||||||||
\(958\) | −2.13068 | −0.0688392 | ||||||||
\(959\) | −18.1652 | −0.586583 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 7.50455 | 0.242082 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 21.1652 | 0.682037 | ||||||||
\(964\) | 3.10260 | 0.0999281 | ||||||||
\(965\) | 0 | 0 | ||||||||
\(966\) | −3.62614 | −0.116669 | ||||||||
\(967\) | −37.3821 | −1.20213 | −0.601064 | − | 0.799201i | \(-0.705256\pi\) | ||||
−0.601064 | + | 0.799201i | \(0.705256\pi\) | |||||||
\(968\) | −6.92820 | −0.222681 | ||||||||
\(969\) | −7.93725 | −0.254981 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | −18.4955 | −0.593547 | −0.296774 | − | 0.954948i | \(-0.595911\pi\) | ||||
−0.296774 | + | 0.954948i | \(0.595911\pi\) | |||||||
\(972\) | −28.6606 | −0.919289 | ||||||||
\(973\) | 37.6682 | 1.20759 | ||||||||
\(974\) | 4.87841 | 0.156314 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | −3.95644 | −0.126643 | ||||||||
\(977\) | 35.3085 | 1.12962 | 0.564809 | − | 0.825222i | \(-0.308950\pi\) | ||||
0.564809 | + | 0.825222i | \(0.308950\pi\) | |||||||
\(978\) | 9.62614 | 0.307810 | ||||||||
\(979\) | 25.3303 | 0.809560 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 26.2668 | 0.838635 | ||||||||
\(982\) | 8.87086 | 0.283080 | ||||||||
\(983\) | 55.0840 | 1.75691 | 0.878454 | − | 0.477827i | \(-0.158576\pi\) | ||||
0.878454 | + | 0.477827i | \(0.158576\pi\) | |||||||
\(984\) | 4.58258 | 0.146087 | ||||||||
\(985\) | 0 | 0 | ||||||||
\(986\) | −9.59386 | −0.305531 | ||||||||
\(987\) | 3.16515 | 0.100748 | ||||||||
\(988\) | 0 | 0 | ||||||||
\(989\) | 48.4955 | 1.54207 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | −13.0000 | −0.412959 | −0.206479 | − | 0.978451i | \(-0.566201\pi\) | ||||
−0.206479 | + | 0.978451i | \(0.566201\pi\) | |||||||
\(992\) | 29.4083 | 0.933715 | ||||||||
\(993\) | 4.47315 | 0.141951 | ||||||||
\(994\) | −5.55765 | −0.176278 | ||||||||
\(995\) | 0 | 0 | ||||||||
\(996\) | −10.7737 | −0.341378 | ||||||||
\(997\) | 0.165151 | 0.00523040 | 0.00261520 | − | 0.999997i | \(-0.499168\pi\) | ||||
0.00261520 | + | 0.999997i | \(0.499168\pi\) | |||||||
\(998\) | −0.330303 | −0.0104556 | ||||||||
\(999\) | −39.6863 | −1.25562 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))