Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [7938,2,Mod(1,7938)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(7938, 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("7938.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 7938 = 2 \cdot 3^{4} \cdot 7^{2} \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 7938.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: | \(63.3852491245\) |
Analytic rank: | \(1\) |
Dimension: | \(3\) |
Coefficient field: | 3.3.321.1 |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{3} - x^{2} - 4x + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{5}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 126) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.1 | ||
Root | \(-1.69963\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 7938.1 |
$q$-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 \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 1.00000 | 0.707107 | ||||||||
\(3\) | 0 | 0 | ||||||||
\(4\) | 1.00000 | 0.500000 | ||||||||
\(5\) | −3.69963 | −1.65452 | −0.827262 | − | 0.561816i | \(-0.810103\pi\) | ||||
−0.827262 | + | 0.561816i | \(0.810103\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 0 | 0 | ||||||||
\(8\) | 1.00000 | 0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | −3.69963 | −1.16993 | ||||||||
\(11\) | −1.47710 | −0.445362 | −0.222681 | − | 0.974891i | \(-0.571481\pi\) | ||||
−0.222681 | + | 0.974891i | \(0.571481\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −2.69963 | −0.748742 | −0.374371 | − | 0.927279i | \(-0.622141\pi\) | ||||
−0.374371 | + | 0.927279i | \(0.622141\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | 6.57598 | 1.59491 | 0.797455 | − | 0.603378i | \(-0.206179\pi\) | ||||
0.797455 | + | 0.603378i | \(0.206179\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −0.888736 | −0.203890 | −0.101945 | − | 0.994790i | \(-0.532507\pi\) | ||||
−0.101945 | + | 0.994790i | \(0.532507\pi\) | |||||||
\(20\) | −3.69963 | −0.827262 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | −1.47710 | −0.314919 | ||||||||
\(23\) | 6.28799 | 1.31114 | 0.655568 | − | 0.755136i | \(-0.272429\pi\) | ||||
0.655568 | + | 0.755136i | \(0.272429\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 8.68725 | 1.73745 | ||||||||
\(26\) | −2.69963 | −0.529441 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 0 | 0 | ||||||||
\(29\) | −2.51052 | −0.466192 | −0.233096 | − | 0.972454i | \(-0.574886\pi\) | ||||
−0.233096 | + | 0.972454i | \(0.574886\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −6.81089 | −1.22327 | −0.611636 | − | 0.791139i | \(-0.709488\pi\) | ||||
−0.611636 | + | 0.791139i | \(0.709488\pi\) | |||||||
\(32\) | 1.00000 | 0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 6.57598 | 1.12777 | ||||||||
\(35\) | 0 | 0 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.77747 | 0.456614 | 0.228307 | − | 0.973589i | \(-0.426681\pi\) | ||||
0.228307 | + | 0.973589i | \(0.426681\pi\) | |||||||
\(38\) | −0.888736 | −0.144172 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | −3.69963 | −0.584963 | ||||||||
\(41\) | −4.11126 | −0.642072 | −0.321036 | − | 0.947067i | \(-0.604031\pi\) | ||||
−0.321036 | + | 0.947067i | \(0.604031\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | −0.0123797 | −0.00188789 | −0.000943944 | − | 1.00000i | \(-0.500300\pi\) | ||||
−0.000943944 | 1.00000i | \(0.500300\pi\) | ||||||||
\(44\) | −1.47710 | −0.222681 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | 6.28799 | 0.927114 | ||||||||
\(47\) | 6.98762 | 1.01925 | 0.509625 | − | 0.860397i | \(-0.329784\pi\) | ||||
0.509625 | + | 0.860397i | \(0.329784\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 0 | 0 | ||||||||
\(50\) | 8.68725 | 1.22856 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −2.69963 | −0.374371 | ||||||||
\(53\) | 3.21015 | 0.440948 | 0.220474 | − | 0.975393i | \(-0.429240\pi\) | ||||
0.220474 | + | 0.975393i | \(0.429240\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 5.46472 | 0.736863 | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | −2.51052 | −0.329647 | ||||||||
\(59\) | −6.90978 | −0.899576 | −0.449788 | − | 0.893135i | \(-0.648501\pi\) | ||||
−0.449788 | + | 0.893135i | \(0.648501\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 5.73305 | 0.734042 | 0.367021 | − | 0.930213i | \(-0.380378\pi\) | ||||
0.367021 | + | 0.930213i | \(0.380378\pi\) | |||||||
\(62\) | −6.81089 | −0.864984 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 9.98762 | 1.23881 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −9.46472 | −1.15630 | −0.578150 | − | 0.815931i | \(-0.696225\pi\) | ||||
−0.578150 | + | 0.815931i | \(0.696225\pi\) | |||||||
\(68\) | 6.57598 | 0.797455 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.46472 | −0.648543 | −0.324271 | − | 0.945964i | \(-0.605119\pi\) | ||||
−0.324271 | + | 0.945964i | \(0.605119\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −12.0655 | −1.41216 | −0.706078 | − | 0.708134i | \(-0.749537\pi\) | ||||
−0.706078 | + | 0.708134i | \(0.749537\pi\) | |||||||
\(74\) | 2.77747 | 0.322875 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −0.888736 | −0.101945 | ||||||||
\(77\) | 0 | 0 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | 11.4523 | 1.28849 | 0.644244 | − | 0.764820i | \(-0.277172\pi\) | ||||
0.644244 | + | 0.764820i | \(0.277172\pi\) | |||||||
\(80\) | −3.69963 | −0.413631 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −4.11126 | −0.454013 | ||||||||
\(83\) | 4.47710 | 0.491426 | 0.245713 | − | 0.969343i | \(-0.420978\pi\) | ||||
0.245713 | + | 0.969343i | \(0.420978\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | −24.3287 | −2.63882 | ||||||||
\(86\) | −0.0123797 | −0.00133494 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | −1.47710 | −0.157459 | ||||||||
\(89\) | −8.87636 | −0.940892 | −0.470446 | − | 0.882429i | \(-0.655907\pi\) | ||||
−0.470446 | + | 0.882429i | \(0.655907\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 0 | 0 | ||||||||
\(92\) | 6.28799 | 0.655568 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 6.98762 | 0.720718 | ||||||||
\(95\) | 3.28799 | 0.337341 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | −13.1767 | −1.33789 | −0.668947 | − | 0.743310i | \(-0.733255\pi\) | ||||
−0.668947 | + | 0.743310i | \(0.733255\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 8.68725 | 0.868725 | ||||||||
\(101\) | −5.25457 | −0.522849 | −0.261425 | − | 0.965224i | \(-0.584192\pi\) | ||||
−0.261425 | + | 0.965224i | \(0.584192\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | −1.66621 | −0.164176 | −0.0820882 | − | 0.996625i | \(-0.526159\pi\) | ||||
−0.0820882 | + | 0.996625i | \(0.526159\pi\) | |||||||
\(104\) | −2.69963 | −0.264720 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | 3.21015 | 0.311797 | ||||||||
\(107\) | 10.7651 | 1.04070 | 0.520350 | − | 0.853953i | \(-0.325801\pi\) | ||||
0.520350 | + | 0.853953i | \(0.325801\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 0.189108 | 0.0181132 | 0.00905662 | − | 0.999959i | \(-0.497117\pi\) | ||||
0.00905662 | + | 0.999959i | \(0.497117\pi\) | |||||||
\(110\) | 5.46472 | 0.521041 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 13.5636 | 1.27596 | 0.637978 | − | 0.770054i | \(-0.279771\pi\) | ||||
0.637978 | + | 0.770054i | \(0.279771\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −23.2632 | −2.16931 | ||||||||
\(116\) | −2.51052 | −0.233096 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −6.90978 | −0.636097 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −8.81818 | −0.801652 | ||||||||
\(122\) | 5.73305 | 0.519046 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −6.81089 | −0.611636 | ||||||||
\(125\) | −13.6414 | −1.22013 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | −2.85669 | −0.253490 | −0.126745 | − | 0.991935i | \(-0.540453\pi\) | ||||
−0.126745 | + | 0.991935i | \(0.540453\pi\) | |||||||
\(128\) | 1.00000 | 0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | 9.98762 | 0.875972 | ||||||||
\(131\) | −0.155687 | −0.0136024 | −0.00680122 | − | 0.999977i | \(-0.502165\pi\) | ||||
−0.00680122 | + | 0.999977i | \(0.502165\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | 0 | 0 | ||||||||
\(134\) | −9.46472 | −0.817627 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 6.57598 | 0.563886 | ||||||||
\(137\) | −3.41164 | −0.291476 | −0.145738 | − | 0.989323i | \(-0.546556\pi\) | ||||
−0.145738 | + | 0.989323i | \(0.546556\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −13.5105 | −1.14595 | −0.572974 | − | 0.819574i | \(-0.694210\pi\) | ||||
−0.572974 | + | 0.819574i | \(0.694210\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | −5.46472 | −0.458589 | ||||||||
\(143\) | 3.98762 | 0.333462 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 9.28799 | 0.771326 | ||||||||
\(146\) | −12.0655 | −0.998545 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.77747 | 0.228307 | ||||||||
\(149\) | 0.333792 | 0.0273453 | 0.0136727 | − | 0.999907i | \(-0.495648\pi\) | ||||
0.0136727 | + | 0.999907i | \(0.495648\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | −19.9098 | −1.62023 | −0.810117 | − | 0.586268i | \(-0.800597\pi\) | ||||
−0.810117 | + | 0.586268i | \(0.800597\pi\) | |||||||
\(152\) | −0.888736 | −0.0720860 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 25.1978 | 2.02393 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 6.96286 | 0.555697 | 0.277848 | − | 0.960625i | \(-0.410379\pi\) | ||||
0.277848 | + | 0.960625i | \(0.410379\pi\) | |||||||
\(158\) | 11.4523 | 0.911099 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | −3.69963 | −0.292481 | ||||||||
\(161\) | 0 | 0 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | −8.07413 | −0.632414 | −0.316207 | − | 0.948690i | \(-0.602409\pi\) | ||||
−0.316207 | + | 0.948690i | \(0.602409\pi\) | |||||||
\(164\) | −4.11126 | −0.321036 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 4.47710 | 0.347490 | ||||||||
\(167\) | 19.4858 | 1.50785 | 0.753927 | − | 0.656959i | \(-0.228157\pi\) | ||||
0.753927 | + | 0.656959i | \(0.228157\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −5.71201 | −0.439385 | ||||||||
\(170\) | −24.3287 | −1.86593 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | −0.0123797 | −0.000943944 0 | ||||||||
\(173\) | −22.5636 | −1.71548 | −0.857740 | − | 0.514085i | \(-0.828132\pi\) | ||||
−0.857740 | + | 0.514085i | \(0.828132\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 0 | 0 | ||||||||
\(176\) | −1.47710 | −0.111341 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −8.87636 | −0.665311 | ||||||||
\(179\) | −0.333792 | −0.0249488 | −0.0124744 | − | 0.999922i | \(-0.503971\pi\) | ||||
−0.0124744 | + | 0.999922i | \(0.503971\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −23.2422 | −1.72758 | −0.863789 | − | 0.503853i | \(-0.831915\pi\) | ||||
−0.863789 | + | 0.503853i | \(0.831915\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | 6.28799 | 0.463557 | ||||||||
\(185\) | −10.2756 | −0.755478 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | −9.71339 | −0.710313 | ||||||||
\(188\) | 6.98762 | 0.509625 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | 3.28799 | 0.238536 | ||||||||
\(191\) | −16.3214 | −1.18098 | −0.590488 | − | 0.807046i | \(-0.701065\pi\) | ||||
−0.590488 | + | 0.807046i | \(0.701065\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.3214 | −1.03088 | −0.515439 | − | 0.856926i | \(-0.672371\pi\) | ||||
−0.515439 | + | 0.856926i | \(0.672371\pi\) | |||||||
\(194\) | −13.1767 | −0.946034 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 2.42402 | 0.172704 | 0.0863520 | − | 0.996265i | \(-0.472479\pi\) | ||||
0.0863520 | + | 0.996265i | \(0.472479\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −6.11126 | −0.433216 | −0.216608 | − | 0.976259i | \(-0.569499\pi\) | ||||
−0.216608 | + | 0.976259i | \(0.569499\pi\) | |||||||
\(200\) | 8.68725 | 0.614281 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | −5.25457 | −0.369710 | ||||||||
\(203\) | 0 | 0 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 15.2101 | 1.06232 | ||||||||
\(206\) | −1.66621 | −0.116090 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −2.69963 | −0.187186 | ||||||||
\(209\) | 1.31275 | 0.0908049 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −11.4451 | −0.787910 | −0.393955 | − | 0.919130i | \(-0.628893\pi\) | ||||
−0.393955 | + | 0.919130i | \(0.628893\pi\) | |||||||
\(212\) | 3.21015 | 0.220474 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 10.7651 | 0.735887 | ||||||||
\(215\) | 0.0458003 | 0.00312356 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | 0 | 0 | ||||||||
\(218\) | 0.189108 | 0.0128080 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 5.46472 | 0.368431 | ||||||||
\(221\) | −17.7527 | −1.19418 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | −7.22253 | −0.483656 | −0.241828 | − | 0.970319i | \(-0.577747\pi\) | ||||
−0.241828 | + | 0.970319i | \(0.577747\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 13.5636 | 0.902238 | ||||||||
\(227\) | −13.6552 | −0.906328 | −0.453164 | − | 0.891427i | \(-0.649705\pi\) | ||||
−0.453164 | + | 0.891427i | \(0.649705\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | −17.3745 | −1.14814 | −0.574070 | − | 0.818807i | \(-0.694636\pi\) | ||||
−0.574070 | + | 0.818807i | \(0.694636\pi\) | |||||||
\(230\) | −23.2632 | −1.53393 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | −2.51052 | −0.164824 | ||||||||
\(233\) | −15.2422 | −0.998549 | −0.499275 | − | 0.866444i | \(-0.666400\pi\) | ||||
−0.499275 | + | 0.866444i | \(0.666400\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | −25.8516 | −1.68637 | ||||||||
\(236\) | −6.90978 | −0.449788 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −18.9505 | −1.22580 | −0.612902 | − | 0.790159i | \(-0.709998\pi\) | ||||
−0.612902 | + | 0.790159i | \(0.709998\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 24.5054 | 1.57853 | 0.789267 | − | 0.614051i | \(-0.210461\pi\) | ||||
0.789267 | + | 0.614051i | \(0.210461\pi\) | |||||||
\(242\) | −8.81818 | −0.566854 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 5.73305 | 0.367021 | ||||||||
\(245\) | 0 | 0 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 2.39926 | 0.152661 | ||||||||
\(248\) | −6.81089 | −0.432492 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | −13.6414 | −0.862761 | ||||||||
\(251\) | 12.1236 | 0.765238 | 0.382619 | − | 0.923906i | \(-0.375022\pi\) | ||||
0.382619 | + | 0.923906i | \(0.375022\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −9.28799 | −0.583931 | ||||||||
\(254\) | −2.85669 | −0.179245 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | 8.20877 | 0.512049 | 0.256025 | − | 0.966670i | \(-0.417587\pi\) | ||||
0.256025 | + | 0.966670i | \(0.417587\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 0 | 0 | ||||||||
\(260\) | 9.98762 | 0.619406 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | −0.155687 | −0.00961838 | ||||||||
\(263\) | −5.34617 | −0.329659 | −0.164830 | − | 0.986322i | \(-0.552707\pi\) | ||||
−0.164830 | + | 0.986322i | \(0.552707\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −11.8764 | −0.729559 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −9.46472 | −0.578150 | ||||||||
\(269\) | 18.4844 | 1.12701 | 0.563506 | − | 0.826112i | \(-0.309452\pi\) | ||||
0.563506 | + | 0.826112i | \(0.309452\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | −7.35483 | −0.446774 | −0.223387 | − | 0.974730i | \(-0.571711\pi\) | ||||
−0.223387 | + | 0.974730i | \(0.571711\pi\) | |||||||
\(272\) | 6.57598 | 0.398728 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | −3.41164 | −0.206104 | ||||||||
\(275\) | −12.8319 | −0.773795 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −9.09888 | −0.546699 | −0.273349 | − | 0.961915i | \(-0.588132\pi\) | ||||
−0.273349 | + | 0.961915i | \(0.588132\pi\) | |||||||
\(278\) | −13.5105 | −0.810307 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 0 | 0 | ||||||||
\(281\) | −12.0087 | −0.716377 | −0.358188 | − | 0.933649i | \(-0.616605\pi\) | ||||
−0.358188 | + | 0.933649i | \(0.616605\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | −9.84294 | −0.585102 | −0.292551 | − | 0.956250i | \(-0.594504\pi\) | ||||
−0.292551 | + | 0.956250i | \(0.594504\pi\) | |||||||
\(284\) | −5.46472 | −0.324271 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | 3.98762 | 0.235793 | ||||||||
\(287\) | 0 | 0 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 26.2436 | 1.54374 | ||||||||
\(290\) | 9.28799 | 0.545410 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −12.0655 | −0.706078 | ||||||||
\(293\) | 21.4203 | 1.25139 | 0.625694 | − | 0.780069i | \(-0.284816\pi\) | ||||
0.625694 | + | 0.780069i | \(0.284816\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 25.5636 | 1.48837 | ||||||||
\(296\) | 2.77747 | 0.161437 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | 0.333792 | 0.0193361 | ||||||||
\(299\) | −16.9752 | −0.981704 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 0 | 0 | ||||||||
\(302\) | −19.9098 | −1.14568 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −0.888736 | −0.0509725 | ||||||||
\(305\) | −21.2101 | −1.21449 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 5.68725 | 0.324588 | 0.162294 | − | 0.986742i | \(-0.448111\pi\) | ||||
0.162294 | + | 0.986742i | \(0.448111\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | 25.1978 | 1.43114 | ||||||||
\(311\) | 11.7207 | 0.664618 | 0.332309 | − | 0.943171i | \(-0.392172\pi\) | ||||
0.332309 | + | 0.943171i | \(0.392172\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 26.7738 | 1.51334 | 0.756671 | − | 0.653796i | \(-0.226824\pi\) | ||||
0.756671 | + | 0.653796i | \(0.226824\pi\) | |||||||
\(314\) | 6.96286 | 0.392937 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | 11.4523 | 0.644244 | ||||||||
\(317\) | 1.90249 | 0.106855 | 0.0534273 | − | 0.998572i | \(-0.482985\pi\) | ||||
0.0534273 | + | 0.998572i | \(0.482985\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 3.70829 | 0.207624 | ||||||||
\(320\) | −3.69963 | −0.206816 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | 0 | 0 | ||||||||
\(323\) | −5.84431 | −0.325186 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −23.4523 | −1.30090 | ||||||||
\(326\) | −8.07413 | −0.447184 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −4.11126 | −0.227007 | ||||||||
\(329\) | 0 | 0 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | 5.56732 | 0.306008 | 0.153004 | − | 0.988226i | \(-0.451105\pi\) | ||||
0.153004 | + | 0.988226i | \(0.451105\pi\) | |||||||
\(332\) | 4.47710 | 0.245713 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 19.4858 | 1.06621 | ||||||||
\(335\) | 35.0159 | 1.91313 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | 33.7738 | 1.83977 | 0.919887 | − | 0.392184i | \(-0.128280\pi\) | ||||
0.919887 | + | 0.392184i | \(0.128280\pi\) | |||||||
\(338\) | −5.71201 | −0.310692 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | −24.3287 | −1.31941 | ||||||||
\(341\) | 10.0604 | 0.544799 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 0 | 0 | ||||||||
\(344\) | −0.0123797 | −0.000667469 0 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | −22.5636 | −1.21303 | ||||||||
\(347\) | −30.4065 | −1.63231 | −0.816154 | − | 0.577834i | \(-0.803898\pi\) | ||||
−0.816154 | + | 0.577834i | \(0.803898\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −12.5956 | −0.674230 | −0.337115 | − | 0.941464i | \(-0.609451\pi\) | ||||
−0.337115 | + | 0.941464i | \(0.609451\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | −1.47710 | −0.0787297 | ||||||||
\(353\) | 7.53156 | 0.400865 | 0.200432 | − | 0.979708i | \(-0.435765\pi\) | ||||
0.200432 | + | 0.979708i | \(0.435765\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 20.2174 | 1.07303 | ||||||||
\(356\) | −8.87636 | −0.470446 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | −0.333792 | −0.0176415 | ||||||||
\(359\) | 6.89602 | 0.363958 | 0.181979 | − | 0.983302i | \(-0.441750\pi\) | ||||
0.181979 | + | 0.983302i | \(0.441750\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.2101 | −0.958429 | ||||||||
\(362\) | −23.2422 | −1.22158 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 44.6377 | 2.33645 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −23.1236 | −1.20704 | −0.603522 | − | 0.797346i | \(-0.706237\pi\) | ||||
−0.603522 | + | 0.797346i | \(0.706237\pi\) | |||||||
\(368\) | 6.28799 | 0.327784 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | −10.2756 | −0.534204 | ||||||||
\(371\) | 0 | 0 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 29.1643 | 1.51007 | 0.755036 | − | 0.655683i | \(-0.227619\pi\) | ||||
0.755036 | + | 0.655683i | \(0.227619\pi\) | |||||||
\(374\) | −9.71339 | −0.502267 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 6.98762 | 0.360359 | ||||||||
\(377\) | 6.77747 | 0.349058 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | −13.5622 | −0.696645 | −0.348322 | − | 0.937375i | \(-0.613249\pi\) | ||||
−0.348322 | + | 0.937375i | \(0.613249\pi\) | |||||||
\(380\) | 3.28799 | 0.168670 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | −16.3214 | −0.835076 | ||||||||
\(383\) | 2.83565 | 0.144895 | 0.0724475 | − | 0.997372i | \(-0.476919\pi\) | ||||
0.0724475 | + | 0.997372i | \(0.476919\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0 | 0 | ||||||||
\(386\) | −14.3214 | −0.728941 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | −13.1767 | −0.668947 | ||||||||
\(389\) | −18.6080 | −0.943464 | −0.471732 | − | 0.881742i | \(-0.656371\pi\) | ||||
−0.471732 | + | 0.881742i | \(0.656371\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 41.3497 | 2.09115 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 2.42402 | 0.122120 | ||||||||
\(395\) | −42.3694 | −2.13184 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.5760 | −1.03268 | −0.516340 | − | 0.856384i | \(-0.672706\pi\) | ||||
−0.516340 | + | 0.856384i | \(0.672706\pi\) | |||||||
\(398\) | −6.11126 | −0.306330 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 8.68725 | 0.434362 | ||||||||
\(401\) | −6.75409 | −0.337283 | −0.168642 | − | 0.985677i | \(-0.553938\pi\) | ||||
−0.168642 | + | 0.985677i | \(0.553938\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 18.3869 | 0.915916 | ||||||||
\(404\) | −5.25457 | −0.261425 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 0 | 0 | ||||||||
\(407\) | −4.10260 | −0.203358 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −15.3214 | −0.757595 | −0.378798 | − | 0.925480i | \(-0.623662\pi\) | ||||
−0.378798 | + | 0.925480i | \(0.623662\pi\) | |||||||
\(410\) | 15.2101 | 0.751176 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | −1.66621 | −0.0820882 | ||||||||
\(413\) | 0 | 0 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | −16.5636 | −0.813075 | ||||||||
\(416\) | −2.69963 | −0.132360 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | 1.31275 | 0.0642088 | ||||||||
\(419\) | −8.64283 | −0.422230 | −0.211115 | − | 0.977461i | \(-0.567709\pi\) | ||||
−0.211115 | + | 0.977461i | \(0.567709\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −37.1272 | −1.80947 | −0.904735 | − | 0.425975i | \(-0.859931\pi\) | ||||
−0.904735 | + | 0.425975i | \(0.859931\pi\) | |||||||
\(422\) | −11.4451 | −0.557137 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | 3.21015 | 0.155899 | ||||||||
\(425\) | 57.1272 | 2.77108 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0 | 0 | ||||||||
\(428\) | 10.7651 | 0.520350 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 0.0458003 | 0.00220869 | ||||||||
\(431\) | 9.42030 | 0.453760 | 0.226880 | − | 0.973923i | \(-0.427148\pi\) | ||||
0.226880 | + | 0.973923i | \(0.427148\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | 0.208771 | 0.0100329 | 0.00501645 | − | 0.999987i | \(-0.498403\pi\) | ||||
0.00501645 | + | 0.999987i | \(0.498403\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | 0.189108 | 0.00905662 | ||||||||
\(437\) | −5.58836 | −0.267328 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | 9.96796 | 0.475745 | 0.237872 | − | 0.971296i | \(-0.423550\pi\) | ||||
0.237872 | + | 0.971296i | \(0.423550\pi\) | |||||||
\(440\) | 5.46472 | 0.260520 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −17.7527 | −0.844410 | ||||||||
\(443\) | −15.6996 | −0.745912 | −0.372956 | − | 0.927849i | \(-0.621656\pi\) | ||||
−0.372956 | + | 0.927849i | \(0.621656\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | 32.8392 | 1.55673 | ||||||||
\(446\) | −7.22253 | −0.341997 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.6253 | 1.58688 | 0.793439 | − | 0.608650i | \(-0.208288\pi\) | ||||
0.793439 | + | 0.608650i | \(0.208288\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | 6.07275 | 0.285955 | ||||||||
\(452\) | 13.5636 | 0.637978 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | −13.6552 | −0.640871 | ||||||||
\(455\) | 0 | 0 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 32.7083 | 1.53003 | 0.765015 | − | 0.644013i | \(-0.222732\pi\) | ||||
0.765015 | + | 0.644013i | \(0.222732\pi\) | |||||||
\(458\) | −17.3745 | −0.811857 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −23.2632 | −1.08465 | ||||||||
\(461\) | −4.14331 | −0.192973 | −0.0964865 | − | 0.995334i | \(-0.530760\pi\) | ||||
−0.0964865 | + | 0.995334i | \(0.530760\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 16.6835 | 0.775349 | 0.387675 | − | 0.921796i | \(-0.373278\pi\) | ||||
0.387675 | + | 0.921796i | \(0.373278\pi\) | |||||||
\(464\) | −2.51052 | −0.116548 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | −15.2422 | −0.706081 | ||||||||
\(467\) | 29.9171 | 1.38440 | 0.692198 | − | 0.721707i | \(-0.256642\pi\) | ||||
0.692198 | + | 0.721707i | \(0.256642\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 0 | 0 | ||||||||
\(470\) | −25.8516 | −1.19245 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −6.90978 | −0.318048 | ||||||||
\(473\) | 0.0182861 | 0.000840794 0 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −7.72067 | −0.354249 | ||||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | −18.9505 | −0.866775 | ||||||||
\(479\) | 2.95930 | 0.135214 | 0.0676068 | − | 0.997712i | \(-0.478464\pi\) | ||||
0.0676068 | + | 0.997712i | \(0.478464\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −7.49814 | −0.341886 | ||||||||
\(482\) | 24.5054 | 1.11619 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −8.81818 | −0.400826 | ||||||||
\(485\) | 48.7490 | 2.21358 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 28.0617 | 1.27160 | 0.635800 | − | 0.771854i | \(-0.280671\pi\) | ||||
0.635800 | + | 0.771854i | \(0.280671\pi\) | |||||||
\(488\) | 5.73305 | 0.259523 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | 0 | 0 | ||||||||
\(491\) | −34.1469 | −1.54103 | −0.770513 | − | 0.637424i | \(-0.780000\pi\) | ||||
−0.770513 | + | 0.637424i | \(0.780000\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | −16.5091 | −0.743534 | ||||||||
\(494\) | 2.39926 | 0.107948 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −6.81089 | −0.305818 | ||||||||
\(497\) | 0 | 0 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −2.28071 | −0.102099 | −0.0510493 | − | 0.998696i | \(-0.516257\pi\) | ||||
−0.0510493 | + | 0.998696i | \(0.516257\pi\) | |||||||
\(500\) | −13.6414 | −0.610064 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | 12.1236 | 0.541105 | ||||||||
\(503\) | −13.9890 | −0.623739 | −0.311869 | − | 0.950125i | \(-0.600955\pi\) | ||||
−0.311869 | + | 0.950125i | \(0.600955\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 19.4400 | 0.865067 | ||||||||
\(506\) | −9.28799 | −0.412902 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | −2.85669 | −0.126745 | ||||||||
\(509\) | −25.6181 | −1.13550 | −0.567750 | − | 0.823201i | \(-0.692186\pi\) | ||||
−0.567750 | + | 0.823201i | \(0.692186\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | 0 | 0 | ||||||||
\(512\) | 1.00000 | 0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8.20877 | 0.362073 | ||||||||
\(515\) | 6.16435 | 0.271634 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | −10.3214 | −0.453935 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | 9.98762 | 0.437986 | ||||||||
\(521\) | −41.8255 | −1.83241 | −0.916203 | − | 0.400714i | \(-0.868762\pi\) | ||||
−0.916203 | + | 0.400714i | \(0.868762\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 15.7665 | 0.689420 | 0.344710 | − | 0.938709i | \(-0.387977\pi\) | ||||
0.344710 | + | 0.938709i | \(0.387977\pi\) | |||||||
\(524\) | −0.155687 | −0.00680122 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | −5.34617 | −0.233104 | ||||||||
\(527\) | −44.7883 | −1.95101 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 16.5388 | 0.719080 | ||||||||
\(530\) | −11.8764 | −0.515876 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.0989 | 0.480746 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | −39.8268 | −1.72186 | ||||||||
\(536\) | −9.46472 | −0.408814 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 18.4844 | 0.796918 | ||||||||
\(539\) | 0 | 0 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 42.1927 | 1.81400 | 0.907002 | − | 0.421126i | \(-0.138365\pi\) | ||||
0.907002 | + | 0.421126i | \(0.138365\pi\) | |||||||
\(542\) | −7.35483 | −0.315917 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 6.57598 | 0.281943 | ||||||||
\(545\) | −0.699628 | −0.0299688 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −40.6712 | −1.73897 | −0.869486 | − | 0.493957i | \(-0.835550\pi\) | ||||
−0.869486 | + | 0.493957i | \(0.835550\pi\) | |||||||
\(548\) | −3.41164 | −0.145738 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | −12.8319 | −0.547155 | ||||||||
\(551\) | 2.23119 | 0.0950519 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 0 | 0 | ||||||||
\(554\) | −9.09888 | −0.386575 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −13.5105 | −0.572974 | ||||||||
\(557\) | −13.3759 | −0.566754 | −0.283377 | − | 0.959009i | \(-0.591455\pi\) | ||||
−0.283377 | + | 0.959009i | \(0.591455\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | 0.0334206 | 0.00141354 | ||||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −12.0087 | −0.506555 | ||||||||
\(563\) | 32.7614 | 1.38073 | 0.690364 | − | 0.723463i | \(-0.257451\pi\) | ||||
0.690364 | + | 0.723463i | \(0.257451\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | −50.1803 | −2.11110 | ||||||||
\(566\) | −9.84294 | −0.413729 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | −5.46472 | −0.229295 | ||||||||
\(569\) | −16.7280 | −0.701272 | −0.350636 | − | 0.936512i | \(-0.614035\pi\) | ||||
−0.350636 | + | 0.936512i | \(0.614035\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | −27.4734 | −1.14973 | −0.574863 | − | 0.818250i | \(-0.694945\pi\) | ||||
−0.574863 | + | 0.818250i | \(0.694945\pi\) | |||||||
\(572\) | 3.98762 | 0.166731 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | 0 | 0 | ||||||||
\(575\) | 54.6253 | 2.27803 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | 2.83427 | 0.117992 | 0.0589962 | − | 0.998258i | \(-0.481210\pi\) | ||||
0.0589962 | + | 0.998258i | \(0.481210\pi\) | |||||||
\(578\) | 26.2436 | 1.09159 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 9.28799 | 0.385663 | ||||||||
\(581\) | 0 | 0 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −4.74171 | −0.196382 | ||||||||
\(584\) | −12.0655 | −0.499272 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 21.4203 | 0.884864 | ||||||||
\(587\) | −4.69591 | −0.193821 | −0.0969105 | − | 0.995293i | \(-0.530896\pi\) | ||||
−0.0969105 | + | 0.995293i | \(0.530896\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 6.05308 | 0.249413 | ||||||||
\(590\) | 25.5636 | 1.05244 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.77747 | 0.114153 | ||||||||
\(593\) | 1.27205 | 0.0522367 | 0.0261184 | − | 0.999659i | \(-0.491685\pi\) | ||||
0.0261184 | + | 0.999659i | \(0.491685\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0.333792 | 0.0136727 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | −16.9752 | −0.694169 | ||||||||
\(599\) | 43.8516 | 1.79173 | 0.895864 | − | 0.444329i | \(-0.146558\pi\) | ||||
0.895864 | + | 0.444329i | \(0.146558\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −13.4327 | −0.547930 | −0.273965 | − | 0.961740i | \(-0.588335\pi\) | ||||
−0.273965 | + | 0.961740i | \(0.588335\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | −19.9098 | −0.810117 | ||||||||
\(605\) | 32.6240 | 1.32635 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 4.58465 | 0.186085 | 0.0930425 | − | 0.995662i | \(-0.470341\pi\) | ||||
0.0930425 | + | 0.995662i | \(0.470341\pi\) | |||||||
\(608\) | −0.888736 | −0.0360430 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | −21.2101 | −0.858774 | ||||||||
\(611\) | −18.8640 | −0.763155 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 22.1075 | 0.892915 | 0.446458 | − | 0.894805i | \(-0.352685\pi\) | ||||
0.446458 | + | 0.894805i | \(0.352685\pi\) | |||||||
\(614\) | 5.68725 | 0.229519 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0 | 0 | ||||||||
\(617\) | −12.0087 | −0.483450 | −0.241725 | − | 0.970345i | \(-0.577713\pi\) | ||||
−0.241725 | + | 0.970345i | \(0.577713\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | 17.5636 | 0.705941 | 0.352970 | − | 0.935634i | \(-0.385172\pi\) | ||||
0.352970 | + | 0.935634i | \(0.385172\pi\) | |||||||
\(620\) | 25.1978 | 1.01197 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | 11.7207 | 0.469956 | ||||||||
\(623\) | 0 | 0 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 7.03204 | 0.281282 | ||||||||
\(626\) | 26.7738 | 1.07009 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 6.96286 | 0.277848 | ||||||||
\(629\) | 18.2646 | 0.728258 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −44.9381 | −1.78896 | −0.894479 | − | 0.447110i | \(-0.852453\pi\) | ||||
−0.894479 | + | 0.447110i | \(0.852453\pi\) | |||||||
\(632\) | 11.4523 | 0.455550 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 1.90249 | 0.0755576 | ||||||||
\(635\) | 10.5687 | 0.419406 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 0 | 0 | ||||||||
\(638\) | 3.70829 | 0.146813 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | −3.69963 | −0.146241 | ||||||||
\(641\) | −28.9839 | −1.14480 | −0.572398 | − | 0.819976i | \(-0.693987\pi\) | ||||
−0.572398 | + | 0.819976i | \(0.693987\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 12.0617 | 0.475669 | 0.237834 | − | 0.971306i | \(-0.423562\pi\) | ||||
0.237834 | + | 0.971306i | \(0.423562\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −5.84431 | −0.229941 | ||||||||
\(647\) | 37.7651 | 1.48470 | 0.742349 | − | 0.670013i | \(-0.233711\pi\) | ||||
0.742349 | + | 0.670013i | \(0.233711\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 10.2064 | 0.400637 | ||||||||
\(650\) | −23.4523 | −0.919876 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | −8.07413 | −0.316207 | ||||||||
\(653\) | 37.4079 | 1.46388 | 0.731942 | − | 0.681366i | \(-0.238614\pi\) | ||||
0.731942 | + | 0.681366i | \(0.238614\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 0.575984 | 0.0225056 | ||||||||
\(656\) | −4.11126 | −0.160518 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 0 | 0 | ||||||||
\(659\) | −29.8713 | −1.16362 | −0.581810 | − | 0.813325i | \(-0.697655\pi\) | ||||
−0.581810 | + | 0.813325i | \(0.697655\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | −5.60803 | −0.218127 | −0.109063 | − | 0.994035i | \(-0.534785\pi\) | ||||
−0.109063 | + | 0.994035i | \(0.534785\pi\) | |||||||
\(662\) | 5.56732 | 0.216380 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 4.47710 | 0.173745 | ||||||||
\(665\) | 0 | 0 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −15.7861 | −0.611242 | ||||||||
\(668\) | 19.4858 | 0.753927 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | 35.0159 | 1.35278 | ||||||||
\(671\) | −8.46829 | −0.326915 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 9.44506 | 0.364080 | 0.182040 | − | 0.983291i | \(-0.441730\pi\) | ||||
0.182040 | + | 0.983291i | \(0.441730\pi\) | |||||||
\(674\) | 33.7738 | 1.30092 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −5.71201 | −0.219693 | ||||||||
\(677\) | −11.0617 | −0.425137 | −0.212569 | − | 0.977146i | \(-0.568183\pi\) | ||||
−0.212569 | + | 0.977146i | \(0.568183\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 0 | 0 | ||||||||
\(680\) | −24.3287 | −0.932963 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | 10.0604 | 0.385231 | ||||||||
\(683\) | 8.83922 | 0.338223 | 0.169112 | − | 0.985597i | \(-0.445910\pi\) | ||||
0.169112 | + | 0.985597i | \(0.445910\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 12.6218 | 0.482254 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | −0.0123797 | −0.000471972 0 | ||||||||
\(689\) | −8.66621 | −0.330156 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | −25.0617 | −0.953394 | −0.476697 | − | 0.879068i | \(-0.658166\pi\) | ||||
−0.476697 | + | 0.879068i | \(0.658166\pi\) | |||||||
\(692\) | −22.5636 | −0.857740 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −30.4065 | −1.15422 | ||||||||
\(695\) | 49.9839 | 1.89600 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −27.0356 | −1.02405 | ||||||||
\(698\) | −12.5956 | −0.476752 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 0 | 0 | ||||||||
\(701\) | −43.4858 | −1.64243 | −0.821217 | − | 0.570616i | \(-0.806705\pi\) | ||||
−0.821217 | + | 0.570616i | \(0.806705\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.46844 | −0.0930989 | ||||||||
\(704\) | −1.47710 | −0.0556703 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | 7.53156 | 0.283454 | ||||||||
\(707\) | 0 | 0 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −22.7403 | −0.854031 | −0.427016 | − | 0.904244i | \(-0.640435\pi\) | ||||
−0.427016 | + | 0.904244i | \(0.640435\pi\) | |||||||
\(710\) | 20.2174 | 0.758747 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −8.87636 | −0.332656 | ||||||||
\(713\) | −42.8268 | −1.60388 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −14.7527 | −0.551720 | ||||||||
\(716\) | −0.333792 | −0.0124744 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 6.89602 | 0.257357 | ||||||||
\(719\) | 12.1236 | 0.452136 | 0.226068 | − | 0.974112i | \(-0.427413\pi\) | ||||
0.226068 | + | 0.974112i | \(0.427413\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0 | 0 | ||||||||
\(722\) | −18.2101 | −0.677712 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −23.2422 | −0.863789 | ||||||||
\(725\) | −21.8095 | −0.809985 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 46.1817 | 1.71278 | 0.856392 | − | 0.516327i | \(-0.172701\pi\) | ||||
0.856392 | + | 0.516327i | \(0.172701\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | 44.6377 | 1.65212 | ||||||||
\(731\) | −0.0814088 | −0.00301101 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 36.0297 | 1.33079 | 0.665394 | − | 0.746493i | \(-0.268264\pi\) | ||||
0.665394 | + | 0.746493i | \(0.268264\pi\) | |||||||
\(734\) | −23.1236 | −0.853509 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | 6.28799 | 0.231778 | ||||||||
\(737\) | 13.9803 | 0.514972 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | −46.4239 | −1.70773 | −0.853865 | − | 0.520495i | \(-0.825747\pi\) | ||||
−0.853865 | + | 0.520495i | \(0.825747\pi\) | |||||||
\(740\) | −10.2756 | −0.377739 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −1.19777 | −0.0439419 | −0.0219709 | − | 0.999759i | \(-0.506994\pi\) | ||||
−0.0219709 | + | 0.999759i | \(0.506994\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −1.23491 | −0.0452435 | ||||||||
\(746\) | 29.1643 | 1.06778 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | −9.71339 | −0.355157 | ||||||||
\(749\) | 0 | 0 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 48.1199 | 1.75592 | 0.877961 | − | 0.478733i | \(-0.158904\pi\) | ||||
0.877961 | + | 0.478733i | \(0.158904\pi\) | |||||||
\(752\) | 6.98762 | 0.254812 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | 6.77747 | 0.246821 | ||||||||
\(755\) | 73.6588 | 2.68072 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 49.6006 | 1.80276 | 0.901382 | − | 0.433025i | \(-0.142554\pi\) | ||||
0.901382 | + | 0.433025i | \(0.142554\pi\) | |||||||
\(758\) | −13.5622 | −0.492602 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | 3.28799 | 0.119268 | ||||||||
\(761\) | 37.5402 | 1.36083 | 0.680416 | − | 0.732826i | \(-0.261799\pi\) | ||||
0.680416 | + | 0.732826i | \(0.261799\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 0 | 0 | ||||||||
\(764\) | −16.3214 | −0.590488 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 2.83565 | 0.102456 | ||||||||
\(767\) | 18.6538 | 0.673551 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −26.9184 | −0.970704 | −0.485352 | − | 0.874319i | \(-0.661308\pi\) | ||||
−0.485352 | + | 0.874319i | \(0.661308\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | −14.3214 | −0.515439 | ||||||||
\(773\) | 50.2261 | 1.80651 | 0.903254 | − | 0.429107i | \(-0.141172\pi\) | ||||
0.903254 | + | 0.429107i | \(0.141172\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −59.1679 | −2.12537 | ||||||||
\(776\) | −13.1767 | −0.473017 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | −18.6080 | −0.667130 | ||||||||
\(779\) | 3.65383 | 0.130912 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 8.07194 | 0.288837 | ||||||||
\(782\) | 41.3497 | 1.47866 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | 0 | 0 | ||||||||
\(785\) | −25.7600 | −0.919414 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 1.65892 | 0.0591342 | 0.0295671 | − | 0.999563i | \(-0.490587\pi\) | ||||
0.0295671 | + | 0.999563i | \(0.490587\pi\) | |||||||
\(788\) | 2.42402 | 0.0863520 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −42.3694 | −1.50744 | ||||||||
\(791\) | 0 | 0 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −15.4771 | −0.549608 | ||||||||
\(794\) | −20.5760 | −0.730214 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −6.11126 | −0.216608 | ||||||||
\(797\) | −30.7403 | −1.08888 | −0.544439 | − | 0.838800i | \(-0.683258\pi\) | ||||
−0.544439 | + | 0.838800i | \(0.683258\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 45.9505 | 1.62561 | ||||||||
\(800\) | 8.68725 | 0.307141 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −6.75409 | −0.238495 | ||||||||
\(803\) | 17.8219 | 0.628921 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 0 | 0 | ||||||||
\(806\) | 18.3869 | 0.647650 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | −5.25457 | −0.184855 | ||||||||
\(809\) | 2.88502 | 0.101432 | 0.0507159 | − | 0.998713i | \(-0.483850\pi\) | ||||
0.0507159 | + | 0.998713i | \(0.483850\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −28.5461 | −1.00239 | −0.501195 | − | 0.865334i | \(-0.667106\pi\) | ||||
−0.501195 | + | 0.865334i | \(0.667106\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | −4.10260 | −0.143796 | ||||||||
\(815\) | 29.8713 | 1.04634 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 0.0110023 | 0.000384922 0 | ||||||||
\(818\) | −15.3214 | −0.535701 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | 15.2101 | 0.531161 | ||||||||
\(821\) | 7.96658 | 0.278036 | 0.139018 | − | 0.990290i | \(-0.455605\pi\) | ||||
0.139018 | + | 0.990290i | \(0.455605\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 40.5461 | 1.41335 | 0.706675 | − | 0.707539i | \(-0.250194\pi\) | ||||
0.706675 | + | 0.707539i | \(0.250194\pi\) | |||||||
\(824\) | −1.66621 | −0.0580451 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | 0 | 0 | ||||||||
\(827\) | 1.22115 | 0.0424636 | 0.0212318 | − | 0.999775i | \(-0.493241\pi\) | ||||
0.0212318 | + | 0.999775i | \(0.493241\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | −14.1506 | −0.491470 | −0.245735 | − | 0.969337i | \(-0.579029\pi\) | ||||
−0.245735 | + | 0.969337i | \(0.579029\pi\) | |||||||
\(830\) | −16.5636 | −0.574931 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −2.69963 | −0.0935928 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | −72.0901 | −2.49478 | ||||||||
\(836\) | 1.31275 | 0.0454025 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −8.64283 | −0.298561 | ||||||||
\(839\) | 2.39197 | 0.0825801 | 0.0412900 | − | 0.999147i | \(-0.486853\pi\) | ||||
0.0412900 | + | 0.999147i | \(0.486853\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −22.6973 | −0.782665 | ||||||||
\(842\) | −37.1272 | −1.27949 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −11.4451 | −0.393955 | ||||||||
\(845\) | 21.1323 | 0.726973 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | 0 | 0 | ||||||||
\(848\) | 3.21015 | 0.110237 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 57.1272 | 1.95945 | ||||||||
\(851\) | 17.4647 | 0.598683 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −16.6800 | −0.571111 | −0.285556 | − | 0.958362i | \(-0.592178\pi\) | ||||
−0.285556 | + | 0.958362i | \(0.592178\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 10.7651 | 0.367943 | ||||||||
\(857\) | 13.8516 | 0.473162 | 0.236581 | − | 0.971612i | \(-0.423973\pi\) | ||||
0.236581 | + | 0.971612i | \(0.423973\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −48.4944 | −1.65461 | −0.827304 | − | 0.561754i | \(-0.810127\pi\) | ||||
−0.827304 | + | 0.561754i | \(0.810127\pi\) | |||||||
\(860\) | 0.0458003 | 0.00156178 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 9.42030 | 0.320857 | ||||||||
\(863\) | −5.93082 | −0.201887 | −0.100944 | − | 0.994892i | \(-0.532186\pi\) | ||||
−0.100944 | + | 0.994892i | \(0.532186\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 83.4769 | 2.83830 | ||||||||
\(866\) | 0.208771 | 0.00709433 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | 0 | 0 | ||||||||
\(869\) | −16.9163 | −0.573844 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 25.5512 | 0.865770 | ||||||||
\(872\) | 0.189108 | 0.00640399 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | −5.58836 | −0.189029 | ||||||||
\(875\) | 0 | 0 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 3.92944 | 0.132688 | 0.0663439 | − | 0.997797i | \(-0.478867\pi\) | ||||
0.0663439 | + | 0.997797i | \(0.478867\pi\) | |||||||
\(878\) | 9.96796 | 0.336402 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 5.46472 | 0.184216 | ||||||||
\(881\) | −37.6552 | −1.26864 | −0.634318 | − | 0.773072i | \(-0.718719\pi\) | ||||
−0.634318 | + | 0.773072i | \(0.718719\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | −53.2334 | −1.79145 | −0.895723 | − | 0.444613i | \(-0.853341\pi\) | ||||
−0.895723 | + | 0.444613i | \(0.853341\pi\) | |||||||
\(884\) | −17.7527 | −0.597088 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −15.6996 | −0.527439 | ||||||||
\(887\) | 36.9876 | 1.24192 | 0.620961 | − | 0.783841i | \(-0.286742\pi\) | ||||
0.620961 | + | 0.783841i | \(0.286742\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 0 | 0 | ||||||||
\(890\) | 32.8392 | 1.10077 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | −7.22253 | −0.241828 | ||||||||
\(893\) | −6.21015 | −0.207815 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 1.23491 | 0.0412784 | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 33.6253 | 1.12209 | ||||||||
\(899\) | 17.0989 | 0.570280 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 21.1099 | 0.703272 | ||||||||
\(902\) | 6.07275 | 0.202200 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 13.5636 | 0.451119 | ||||||||
\(905\) | 85.9875 | 2.85832 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | −39.0159 | −1.29550 | −0.647752 | − | 0.761852i | \(-0.724291\pi\) | ||||
−0.647752 | + | 0.761852i | \(0.724291\pi\) | |||||||
\(908\) | −13.6552 | −0.453164 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 25.6181 | 0.848764 | 0.424382 | − | 0.905483i | \(-0.360491\pi\) | ||||
0.424382 | + | 0.905483i | \(0.360491\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −6.61312 | −0.218862 | ||||||||
\(914\) | 32.7083 | 1.08189 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | −17.3745 | −0.574070 | ||||||||
\(917\) | 0 | 0 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −20.6735 | −0.681956 | −0.340978 | − | 0.940071i | \(-0.610758\pi\) | ||||
−0.340978 | + | 0.940071i | \(0.610758\pi\) | |||||||
\(920\) | −23.2632 | −0.766966 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −4.14331 | −0.136453 | ||||||||
\(923\) | 14.7527 | 0.485591 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 24.1286 | 0.793343 | ||||||||
\(926\) | 16.6835 | 0.548255 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | −2.51052 | −0.0824119 | ||||||||
\(929\) | 3.74033 | 0.122716 | 0.0613582 | − | 0.998116i | \(-0.480457\pi\) | ||||
0.0613582 | + | 0.998116i | \(0.480457\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 0 | 0 | ||||||||
\(932\) | −15.2422 | −0.499275 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | 29.9171 | 0.978916 | ||||||||
\(935\) | 35.9359 | 1.17523 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | 27.1345 | 0.886445 | 0.443223 | − | 0.896412i | \(-0.353835\pi\) | ||||
0.443223 | + | 0.896412i | \(0.353835\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | −25.8516 | −0.843186 | ||||||||
\(941\) | −6.32870 | −0.206310 | −0.103155 | − | 0.994665i | \(-0.532894\pi\) | ||||
−0.103155 | + | 0.994665i | \(0.532894\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | −25.8516 | −0.841844 | ||||||||
\(944\) | −6.90978 | −0.224894 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.0182861 | 0.000594531 0 | ||||||||
\(947\) | 31.2792 | 1.01644 | 0.508218 | − | 0.861228i | \(-0.330304\pi\) | ||||
0.508218 | + | 0.861228i | \(0.330304\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 32.5723 | 1.05734 | ||||||||
\(950\) | −7.72067 | −0.250492 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 0 | 0 | ||||||||
\(953\) | 4.28937 | 0.138946 | 0.0694732 | − | 0.997584i | \(-0.477868\pi\) | ||||
0.0694732 | + | 0.997584i | \(0.477868\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 60.3832 | 1.95395 | ||||||||
\(956\) | −18.9505 | −0.612902 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 2.95930 | 0.0956105 | ||||||||
\(959\) | 0 | 0 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 15.3883 | 0.496395 | ||||||||
\(962\) | −7.49814 | −0.241750 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | 24.5054 | 0.789267 | ||||||||
\(965\) | 52.9839 | 1.70561 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 15.1840 | 0.488285 | 0.244142 | − | 0.969739i | \(-0.421494\pi\) | ||||
0.244142 | + | 0.969739i | \(0.421494\pi\) | |||||||
\(968\) | −8.81818 | −0.283427 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 48.7490 | 1.56524 | ||||||||
\(971\) | 3.24729 | 0.104210 | 0.0521052 | − | 0.998642i | \(-0.483407\pi\) | ||||
0.0521052 | + | 0.998642i | \(0.483407\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 0 | 0 | ||||||||
\(974\) | 28.0617 | 0.899156 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 5.73305 | 0.183510 | ||||||||
\(977\) | 15.5439 | 0.497295 | 0.248647 | − | 0.968594i | \(-0.420014\pi\) | ||||
0.248647 | + | 0.968594i | \(0.420014\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 13.1113 | 0.419038 | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | −34.1469 | −1.08967 | ||||||||
\(983\) | −12.3832 | −0.394961 | −0.197481 | − | 0.980307i | \(-0.563276\pi\) | ||||
−0.197481 | + | 0.980307i | \(0.563276\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | −8.96796 | −0.285743 | ||||||||
\(986\) | −16.5091 | −0.525758 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 2.39926 | 0.0763305 | ||||||||
\(989\) | −0.0778435 | −0.00247528 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 6.65521 | 0.211410 | 0.105705 | − | 0.994398i | \(-0.466290\pi\) | ||||
0.105705 | + | 0.994398i | \(0.466290\pi\) | |||||||
\(992\) | −6.81089 | −0.216246 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 22.6094 | 0.716766 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −4.80208 | −0.152083 | −0.0760417 | − | 0.997105i | \(-0.524228\pi\) | ||||
−0.0760417 | + | 0.997105i | \(0.524228\pi\) | |||||||
\(998\) | −2.28071 | −0.0721946 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))