Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [3870,2,Mod(1,3870)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(3870, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([0, 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("3870.1");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 3870 = 2 \cdot 3^{2} \cdot 5 \cdot 43 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 3870.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: | \(30.9021055822\) |
Analytic rank: | \(1\) |
Dimension: | \(2\) |
Coefficient field: | \(\Q(\zeta_{8})^+\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{2} - 2 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{11}]\) |
Coefficient ring index: | \( 1 \) |
Twist minimal: | no (minimal twist has level 430) |
Fricke sign: | \(1\) |
Sato-Tate group: | $\mathrm{SU}(2)$ |
Embedding invariants
Embedding label | 1.2 | ||
Root | \(-1.41421\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 3870.1 |
$q$-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 | ||||||||
\(5\) | −1.00000 | −0.447214 | ||||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 1.00000 | 0.377964 | 0.188982 | − | 0.981981i | \(-0.439481\pi\) | ||||
0.188982 | + | 0.981981i | \(0.439481\pi\) | |||||||
\(8\) | −1.00000 | −0.353553 | ||||||||
\(9\) | 0 | 0 | ||||||||
\(10\) | 1.00000 | 0.316228 | ||||||||
\(11\) | −0.585786 | −0.176621 | −0.0883106 | − | 0.996093i | \(-0.528147\pi\) | ||||
−0.0883106 | + | 0.996093i | \(0.528147\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | −1.82843 | −0.507114 | −0.253557 | − | 0.967320i | \(-0.581601\pi\) | ||||
−0.253557 | + | 0.967320i | \(0.581601\pi\) | |||||||
\(14\) | −1.00000 | −0.267261 | ||||||||
\(15\) | 0 | 0 | ||||||||
\(16\) | 1.00000 | 0.250000 | ||||||||
\(17\) | −1.41421 | −0.342997 | −0.171499 | − | 0.985184i | \(-0.554861\pi\) | ||||
−0.171499 | + | 0.985184i | \(0.554861\pi\) | |||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | −1.00000 | −0.229416 | −0.114708 | − | 0.993399i | \(-0.536593\pi\) | ||||
−0.114708 | + | 0.993399i | \(0.536593\pi\) | |||||||
\(20\) | −1.00000 | −0.223607 | ||||||||
\(21\) | 0 | 0 | ||||||||
\(22\) | 0.585786 | 0.124890 | ||||||||
\(23\) | 5.07107 | 1.05739 | 0.528695 | − | 0.848812i | \(-0.322681\pi\) | ||||
0.528695 | + | 0.848812i | \(0.322681\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | 1.00000 | 0.200000 | ||||||||
\(26\) | 1.82843 | 0.358584 | ||||||||
\(27\) | 0 | 0 | ||||||||
\(28\) | 1.00000 | 0.188982 | ||||||||
\(29\) | −1.24264 | −0.230753 | −0.115376 | − | 0.993322i | \(-0.536807\pi\) | ||||
−0.115376 | + | 0.993322i | \(0.536807\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | −0.414214 | −0.0743950 | −0.0371975 | − | 0.999308i | \(-0.511843\pi\) | ||||
−0.0371975 | + | 0.999308i | \(0.511843\pi\) | |||||||
\(32\) | −1.00000 | −0.176777 | ||||||||
\(33\) | 0 | 0 | ||||||||
\(34\) | 1.41421 | 0.242536 | ||||||||
\(35\) | −1.00000 | −0.169031 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | 2.24264 | 0.368688 | 0.184344 | − | 0.982862i | \(-0.440984\pi\) | ||||
0.184344 | + | 0.982862i | \(0.440984\pi\) | |||||||
\(38\) | 1.00000 | 0.162221 | ||||||||
\(39\) | 0 | 0 | ||||||||
\(40\) | 1.00000 | 0.158114 | ||||||||
\(41\) | 1.82843 | 0.285552 | 0.142776 | − | 0.989755i | \(-0.454397\pi\) | ||||
0.142776 | + | 0.989755i | \(0.454397\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | 1.00000 | 0.152499 | ||||||||
\(44\) | −0.585786 | −0.0883106 | ||||||||
\(45\) | 0 | 0 | ||||||||
\(46\) | −5.07107 | −0.747688 | ||||||||
\(47\) | −7.07107 | −1.03142 | −0.515711 | − | 0.856763i | \(-0.672472\pi\) | ||||
−0.515711 | + | 0.856763i | \(0.672472\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | −6.00000 | −0.857143 | ||||||||
\(50\) | −1.00000 | −0.141421 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | −1.82843 | −0.253557 | ||||||||
\(53\) | 5.65685 | 0.777029 | 0.388514 | − | 0.921443i | \(-0.372988\pi\) | ||||
0.388514 | + | 0.921443i | \(0.372988\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 0.585786 | 0.0789874 | ||||||||
\(56\) | −1.00000 | −0.133631 | ||||||||
\(57\) | 0 | 0 | ||||||||
\(58\) | 1.24264 | 0.163167 | ||||||||
\(59\) | 1.17157 | 0.152526 | 0.0762629 | − | 0.997088i | \(-0.475701\pi\) | ||||
0.0762629 | + | 0.997088i | \(0.475701\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 0.0710678 | 0.00909930 | 0.00454965 | − | 0.999990i | \(-0.498552\pi\) | ||||
0.00454965 | + | 0.999990i | \(0.498552\pi\) | |||||||
\(62\) | 0.414214 | 0.0526052 | ||||||||
\(63\) | 0 | 0 | ||||||||
\(64\) | 1.00000 | 0.125000 | ||||||||
\(65\) | 1.82843 | 0.226788 | ||||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | −1.24264 | −0.151813 | −0.0759064 | − | 0.997115i | \(-0.524185\pi\) | ||||
−0.0759064 | + | 0.997115i | \(0.524185\pi\) | |||||||
\(68\) | −1.41421 | −0.171499 | ||||||||
\(69\) | 0 | 0 | ||||||||
\(70\) | 1.00000 | 0.119523 | ||||||||
\(71\) | −11.8995 | −1.41221 | −0.706105 | − | 0.708107i | \(-0.749549\pi\) | ||||
−0.706105 | + | 0.708107i | \(0.749549\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −9.24264 | −1.08177 | −0.540885 | − | 0.841097i | \(-0.681910\pi\) | ||||
−0.540885 | + | 0.841097i | \(0.681910\pi\) | |||||||
\(74\) | −2.24264 | −0.260702 | ||||||||
\(75\) | 0 | 0 | ||||||||
\(76\) | −1.00000 | −0.114708 | ||||||||
\(77\) | −0.585786 | −0.0667566 | ||||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | −8.41421 | −0.946673 | −0.473336 | − | 0.880882i | \(-0.656951\pi\) | ||||
−0.473336 | + | 0.880882i | \(0.656951\pi\) | |||||||
\(80\) | −1.00000 | −0.111803 | ||||||||
\(81\) | 0 | 0 | ||||||||
\(82\) | −1.82843 | −0.201916 | ||||||||
\(83\) | −3.65685 | −0.401392 | −0.200696 | − | 0.979654i | \(-0.564320\pi\) | ||||
−0.200696 | + | 0.979654i | \(0.564320\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 1.41421 | 0.153393 | ||||||||
\(86\) | −1.00000 | −0.107833 | ||||||||
\(87\) | 0 | 0 | ||||||||
\(88\) | 0.585786 | 0.0624450 | ||||||||
\(89\) | 9.07107 | 0.961531 | 0.480766 | − | 0.876849i | \(-0.340359\pi\) | ||||
0.480766 | + | 0.876849i | \(0.340359\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | −1.82843 | −0.191671 | ||||||||
\(92\) | 5.07107 | 0.528695 | ||||||||
\(93\) | 0 | 0 | ||||||||
\(94\) | 7.07107 | 0.729325 | ||||||||
\(95\) | 1.00000 | 0.102598 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 13.5563 | 1.37644 | 0.688219 | − | 0.725503i | \(-0.258393\pi\) | ||||
0.688219 | + | 0.725503i | \(0.258393\pi\) | |||||||
\(98\) | 6.00000 | 0.606092 | ||||||||
\(99\) | 0 | 0 | ||||||||
\(100\) | 1.00000 | 0.100000 | ||||||||
\(101\) | −1.41421 | −0.140720 | −0.0703598 | − | 0.997522i | \(-0.522415\pi\) | ||||
−0.0703598 | + | 0.997522i | \(0.522415\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | 0.828427 | 0.0816274 | 0.0408137 | − | 0.999167i | \(-0.487005\pi\) | ||||
0.0408137 | + | 0.999167i | \(0.487005\pi\) | |||||||
\(104\) | 1.82843 | 0.179292 | ||||||||
\(105\) | 0 | 0 | ||||||||
\(106\) | −5.65685 | −0.549442 | ||||||||
\(107\) | −1.92893 | −0.186477 | −0.0932385 | − | 0.995644i | \(-0.529722\pi\) | ||||
−0.0932385 | + | 0.995644i | \(0.529722\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | −10.8284 | −1.03718 | −0.518588 | − | 0.855024i | \(-0.673542\pi\) | ||||
−0.518588 | + | 0.855024i | \(0.673542\pi\) | |||||||
\(110\) | −0.585786 | −0.0558525 | ||||||||
\(111\) | 0 | 0 | ||||||||
\(112\) | 1.00000 | 0.0944911 | ||||||||
\(113\) | −4.89949 | −0.460906 | −0.230453 | − | 0.973083i | \(-0.574021\pi\) | ||||
−0.230453 | + | 0.973083i | \(0.574021\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | −5.07107 | −0.472880 | ||||||||
\(116\) | −1.24264 | −0.115376 | ||||||||
\(117\) | 0 | 0 | ||||||||
\(118\) | −1.17157 | −0.107852 | ||||||||
\(119\) | −1.41421 | −0.129641 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −10.6569 | −0.968805 | ||||||||
\(122\) | −0.0710678 | −0.00643418 | ||||||||
\(123\) | 0 | 0 | ||||||||
\(124\) | −0.414214 | −0.0371975 | ||||||||
\(125\) | −1.00000 | −0.0894427 | ||||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 3.51472 | 0.311881 | 0.155940 | − | 0.987766i | \(-0.450159\pi\) | ||||
0.155940 | + | 0.987766i | \(0.450159\pi\) | |||||||
\(128\) | −1.00000 | −0.0883883 | ||||||||
\(129\) | 0 | 0 | ||||||||
\(130\) | −1.82843 | −0.160364 | ||||||||
\(131\) | −6.00000 | −0.524222 | −0.262111 | − | 0.965038i | \(-0.584419\pi\) | ||||
−0.262111 | + | 0.965038i | \(0.584419\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −1.00000 | −0.0867110 | ||||||||
\(134\) | 1.24264 | 0.107348 | ||||||||
\(135\) | 0 | 0 | ||||||||
\(136\) | 1.41421 | 0.121268 | ||||||||
\(137\) | −3.92893 | −0.335671 | −0.167836 | − | 0.985815i | \(-0.553678\pi\) | ||||
−0.167836 | + | 0.985815i | \(0.553678\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | −6.24264 | −0.529494 | −0.264747 | − | 0.964318i | \(-0.585288\pi\) | ||||
−0.264747 | + | 0.964318i | \(0.585288\pi\) | |||||||
\(140\) | −1.00000 | −0.0845154 | ||||||||
\(141\) | 0 | 0 | ||||||||
\(142\) | 11.8995 | 0.998583 | ||||||||
\(143\) | 1.07107 | 0.0895672 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 1.24264 | 0.103196 | ||||||||
\(146\) | 9.24264 | 0.764926 | ||||||||
\(147\) | 0 | 0 | ||||||||
\(148\) | 2.24264 | 0.184344 | ||||||||
\(149\) | 10.5563 | 0.864810 | 0.432405 | − | 0.901680i | \(-0.357665\pi\) | ||||
0.432405 | + | 0.901680i | \(0.357665\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | 10.4853 | 0.853280 | 0.426640 | − | 0.904422i | \(-0.359697\pi\) | ||||
0.426640 | + | 0.904422i | \(0.359697\pi\) | |||||||
\(152\) | 1.00000 | 0.0811107 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0.585786 | 0.0472040 | ||||||||
\(155\) | 0.414214 | 0.0332704 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | 10.2426 | 0.817452 | 0.408726 | − | 0.912657i | \(-0.365973\pi\) | ||||
0.408726 | + | 0.912657i | \(0.365973\pi\) | |||||||
\(158\) | 8.41421 | 0.669399 | ||||||||
\(159\) | 0 | 0 | ||||||||
\(160\) | 1.00000 | 0.0790569 | ||||||||
\(161\) | 5.07107 | 0.399656 | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 13.6569 | 1.06969 | 0.534844 | − | 0.844951i | \(-0.320370\pi\) | ||||
0.534844 | + | 0.844951i | \(0.320370\pi\) | |||||||
\(164\) | 1.82843 | 0.142776 | ||||||||
\(165\) | 0 | 0 | ||||||||
\(166\) | 3.65685 | 0.283827 | ||||||||
\(167\) | −13.5563 | −1.04902 | −0.524511 | − | 0.851404i | \(-0.675752\pi\) | ||||
−0.524511 | + | 0.851404i | \(0.675752\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.65685 | −0.742835 | ||||||||
\(170\) | −1.41421 | −0.108465 | ||||||||
\(171\) | 0 | 0 | ||||||||
\(172\) | 1.00000 | 0.0762493 | ||||||||
\(173\) | −0.514719 | −0.0391333 | −0.0195667 | − | 0.999809i | \(-0.506229\pi\) | ||||
−0.0195667 | + | 0.999809i | \(0.506229\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | 1.00000 | 0.0755929 | ||||||||
\(176\) | −0.585786 | −0.0441553 | ||||||||
\(177\) | 0 | 0 | ||||||||
\(178\) | −9.07107 | −0.679905 | ||||||||
\(179\) | −17.4853 | −1.30691 | −0.653456 | − | 0.756965i | \(-0.726681\pi\) | ||||
−0.653456 | + | 0.756965i | \(0.726681\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −15.0711 | −1.12022 | −0.560112 | − | 0.828417i | \(-0.689242\pi\) | ||||
−0.560112 | + | 0.828417i | \(0.689242\pi\) | |||||||
\(182\) | 1.82843 | 0.135532 | ||||||||
\(183\) | 0 | 0 | ||||||||
\(184\) | −5.07107 | −0.373844 | ||||||||
\(185\) | −2.24264 | −0.164882 | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0.828427 | 0.0605806 | ||||||||
\(188\) | −7.07107 | −0.515711 | ||||||||
\(189\) | 0 | 0 | ||||||||
\(190\) | −1.00000 | −0.0725476 | ||||||||
\(191\) | −19.8995 | −1.43988 | −0.719938 | − | 0.694038i | \(-0.755830\pi\) | ||||
−0.719938 | + | 0.694038i | \(0.755830\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | 6.82843 | 0.491521 | 0.245760 | − | 0.969331i | \(-0.420962\pi\) | ||||
0.245760 | + | 0.969331i | \(0.420962\pi\) | |||||||
\(194\) | −13.5563 | −0.973289 | ||||||||
\(195\) | 0 | 0 | ||||||||
\(196\) | −6.00000 | −0.428571 | ||||||||
\(197\) | −25.1421 | −1.79130 | −0.895651 | − | 0.444757i | \(-0.853290\pi\) | ||||
−0.895651 | + | 0.444757i | \(0.853290\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | −0.100505 | −0.00712462 | −0.00356231 | − | 0.999994i | \(-0.501134\pi\) | ||||
−0.00356231 | + | 0.999994i | \(0.501134\pi\) | |||||||
\(200\) | −1.00000 | −0.0707107 | ||||||||
\(201\) | 0 | 0 | ||||||||
\(202\) | 1.41421 | 0.0995037 | ||||||||
\(203\) | −1.24264 | −0.0872163 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | −1.82843 | −0.127703 | ||||||||
\(206\) | −0.828427 | −0.0577193 | ||||||||
\(207\) | 0 | 0 | ||||||||
\(208\) | −1.82843 | −0.126779 | ||||||||
\(209\) | 0.585786 | 0.0405197 | ||||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | −1.65685 | −0.114063 | −0.0570313 | − | 0.998372i | \(-0.518163\pi\) | ||||
−0.0570313 | + | 0.998372i | \(0.518163\pi\) | |||||||
\(212\) | 5.65685 | 0.388514 | ||||||||
\(213\) | 0 | 0 | ||||||||
\(214\) | 1.92893 | 0.131859 | ||||||||
\(215\) | −1.00000 | −0.0681994 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −0.414214 | −0.0281186 | ||||||||
\(218\) | 10.8284 | 0.733394 | ||||||||
\(219\) | 0 | 0 | ||||||||
\(220\) | 0.585786 | 0.0394937 | ||||||||
\(221\) | 2.58579 | 0.173939 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 16.1421 | 1.08096 | 0.540479 | − | 0.841358i | \(-0.318243\pi\) | ||||
0.540479 | + | 0.841358i | \(0.318243\pi\) | |||||||
\(224\) | −1.00000 | −0.0668153 | ||||||||
\(225\) | 0 | 0 | ||||||||
\(226\) | 4.89949 | 0.325910 | ||||||||
\(227\) | −9.17157 | −0.608739 | −0.304369 | − | 0.952554i | \(-0.598446\pi\) | ||||
−0.304369 | + | 0.952554i | \(0.598446\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 0.828427 | 0.0547440 | 0.0273720 | − | 0.999625i | \(-0.491286\pi\) | ||||
0.0273720 | + | 0.999625i | \(0.491286\pi\) | |||||||
\(230\) | 5.07107 | 0.334376 | ||||||||
\(231\) | 0 | 0 | ||||||||
\(232\) | 1.24264 | 0.0815834 | ||||||||
\(233\) | −8.48528 | −0.555889 | −0.277945 | − | 0.960597i | \(-0.589653\pi\) | ||||
−0.277945 | + | 0.960597i | \(0.589653\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 7.07107 | 0.461266 | ||||||||
\(236\) | 1.17157 | 0.0762629 | ||||||||
\(237\) | 0 | 0 | ||||||||
\(238\) | 1.41421 | 0.0916698 | ||||||||
\(239\) | −11.5858 | −0.749422 | −0.374711 | − | 0.927142i | \(-0.622258\pi\) | ||||
−0.374711 | + | 0.927142i | \(0.622258\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | −21.4142 | −1.37941 | −0.689705 | − | 0.724090i | \(-0.742260\pi\) | ||||
−0.689705 | + | 0.724090i | \(0.742260\pi\) | |||||||
\(242\) | 10.6569 | 0.685049 | ||||||||
\(243\) | 0 | 0 | ||||||||
\(244\) | 0.0710678 | 0.00454965 | ||||||||
\(245\) | 6.00000 | 0.383326 | ||||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 1.82843 | 0.116340 | ||||||||
\(248\) | 0.414214 | 0.0263026 | ||||||||
\(249\) | 0 | 0 | ||||||||
\(250\) | 1.00000 | 0.0632456 | ||||||||
\(251\) | 10.9706 | 0.692456 | 0.346228 | − | 0.938150i | \(-0.387462\pi\) | ||||
0.346228 | + | 0.938150i | \(0.387462\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −2.97056 | −0.186758 | ||||||||
\(254\) | −3.51472 | −0.220533 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 1.00000 | 0.0625000 | ||||||||
\(257\) | −8.89949 | −0.555135 | −0.277568 | − | 0.960706i | \(-0.589528\pi\) | ||||
−0.277568 | + | 0.960706i | \(0.589528\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | 2.24264 | 0.139351 | ||||||||
\(260\) | 1.82843 | 0.113394 | ||||||||
\(261\) | 0 | 0 | ||||||||
\(262\) | 6.00000 | 0.370681 | ||||||||
\(263\) | −17.4853 | −1.07819 | −0.539094 | − | 0.842245i | \(-0.681233\pi\) | ||||
−0.539094 | + | 0.842245i | \(0.681233\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | −5.65685 | −0.347498 | ||||||||
\(266\) | 1.00000 | 0.0613139 | ||||||||
\(267\) | 0 | 0 | ||||||||
\(268\) | −1.24264 | −0.0759064 | ||||||||
\(269\) | −9.17157 | −0.559201 | −0.279600 | − | 0.960116i | \(-0.590202\pi\) | ||||
−0.279600 | + | 0.960116i | \(0.590202\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 8.89949 | 0.540606 | 0.270303 | − | 0.962775i | \(-0.412876\pi\) | ||||
0.270303 | + | 0.962775i | \(0.412876\pi\) | |||||||
\(272\) | −1.41421 | −0.0857493 | ||||||||
\(273\) | 0 | 0 | ||||||||
\(274\) | 3.92893 | 0.237355 | ||||||||
\(275\) | −0.585786 | −0.0353243 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | −0.485281 | −0.0291577 | −0.0145789 | − | 0.999894i | \(-0.504641\pi\) | ||||
−0.0145789 | + | 0.999894i | \(0.504641\pi\) | |||||||
\(278\) | 6.24264 | 0.374409 | ||||||||
\(279\) | 0 | 0 | ||||||||
\(280\) | 1.00000 | 0.0597614 | ||||||||
\(281\) | 1.34315 | 0.0801254 | 0.0400627 | − | 0.999197i | \(-0.487244\pi\) | ||||
0.0400627 | + | 0.999197i | \(0.487244\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | 18.7574 | 1.11501 | 0.557505 | − | 0.830174i | \(-0.311759\pi\) | ||||
0.557505 | + | 0.830174i | \(0.311759\pi\) | |||||||
\(284\) | −11.8995 | −0.706105 | ||||||||
\(285\) | 0 | 0 | ||||||||
\(286\) | −1.07107 | −0.0633336 | ||||||||
\(287\) | 1.82843 | 0.107929 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | −15.0000 | −0.882353 | ||||||||
\(290\) | −1.24264 | −0.0729704 | ||||||||
\(291\) | 0 | 0 | ||||||||
\(292\) | −9.24264 | −0.540885 | ||||||||
\(293\) | −10.9706 | −0.640907 | −0.320454 | − | 0.947264i | \(-0.603835\pi\) | ||||
−0.320454 | + | 0.947264i | \(0.603835\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | −1.17157 | −0.0682116 | ||||||||
\(296\) | −2.24264 | −0.130351 | ||||||||
\(297\) | 0 | 0 | ||||||||
\(298\) | −10.5563 | −0.611513 | ||||||||
\(299\) | −9.27208 | −0.536218 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 1.00000 | 0.0576390 | ||||||||
\(302\) | −10.4853 | −0.603360 | ||||||||
\(303\) | 0 | 0 | ||||||||
\(304\) | −1.00000 | −0.0573539 | ||||||||
\(305\) | −0.0710678 | −0.00406933 | ||||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | −5.92893 | −0.338382 | −0.169191 | − | 0.985583i | \(-0.554115\pi\) | ||||
−0.169191 | + | 0.985583i | \(0.554115\pi\) | |||||||
\(308\) | −0.585786 | −0.0333783 | ||||||||
\(309\) | 0 | 0 | ||||||||
\(310\) | −0.414214 | −0.0235257 | ||||||||
\(311\) | 4.07107 | 0.230849 | 0.115425 | − | 0.993316i | \(-0.463177\pi\) | ||||
0.115425 | + | 0.993316i | \(0.463177\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | −1.31371 | −0.0742552 | −0.0371276 | − | 0.999311i | \(-0.511821\pi\) | ||||
−0.0371276 | + | 0.999311i | \(0.511821\pi\) | |||||||
\(314\) | −10.2426 | −0.578026 | ||||||||
\(315\) | 0 | 0 | ||||||||
\(316\) | −8.41421 | −0.473336 | ||||||||
\(317\) | −0.857864 | −0.0481825 | −0.0240912 | − | 0.999710i | \(-0.507669\pi\) | ||||
−0.0240912 | + | 0.999710i | \(0.507669\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | 0.727922 | 0.0407558 | ||||||||
\(320\) | −1.00000 | −0.0559017 | ||||||||
\(321\) | 0 | 0 | ||||||||
\(322\) | −5.07107 | −0.282600 | ||||||||
\(323\) | 1.41421 | 0.0786889 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −1.82843 | −0.101423 | ||||||||
\(326\) | −13.6569 | −0.756383 | ||||||||
\(327\) | 0 | 0 | ||||||||
\(328\) | −1.82843 | −0.100958 | ||||||||
\(329\) | −7.07107 | −0.389841 | ||||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | −25.3137 | −1.39137 | −0.695684 | − | 0.718348i | \(-0.744898\pi\) | ||||
−0.695684 | + | 0.718348i | \(0.744898\pi\) | |||||||
\(332\) | −3.65685 | −0.200696 | ||||||||
\(333\) | 0 | 0 | ||||||||
\(334\) | 13.5563 | 0.741770 | ||||||||
\(335\) | 1.24264 | 0.0678927 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −8.34315 | −0.454480 | −0.227240 | − | 0.973839i | \(-0.572970\pi\) | ||||
−0.227240 | + | 0.973839i | \(0.572970\pi\) | |||||||
\(338\) | 9.65685 | 0.525264 | ||||||||
\(339\) | 0 | 0 | ||||||||
\(340\) | 1.41421 | 0.0766965 | ||||||||
\(341\) | 0.242641 | 0.0131397 | ||||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | −13.0000 | −0.701934 | ||||||||
\(344\) | −1.00000 | −0.0539164 | ||||||||
\(345\) | 0 | 0 | ||||||||
\(346\) | 0.514719 | 0.0276714 | ||||||||
\(347\) | 22.2426 | 1.19405 | 0.597024 | − | 0.802224i | \(-0.296350\pi\) | ||||
0.597024 | + | 0.802224i | \(0.296350\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | 23.4558 | 1.25556 | 0.627781 | − | 0.778390i | \(-0.283963\pi\) | ||||
0.627781 | + | 0.778390i | \(0.283963\pi\) | |||||||
\(350\) | −1.00000 | −0.0534522 | ||||||||
\(351\) | 0 | 0 | ||||||||
\(352\) | 0.585786 | 0.0312225 | ||||||||
\(353\) | 32.3848 | 1.72367 | 0.861834 | − | 0.507191i | \(-0.169316\pi\) | ||||
0.861834 | + | 0.507191i | \(0.169316\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 11.8995 | 0.631560 | ||||||||
\(356\) | 9.07107 | 0.480766 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 17.4853 | 0.924126 | ||||||||
\(359\) | −27.5269 | −1.45281 | −0.726407 | − | 0.687264i | \(-0.758811\pi\) | ||||
−0.726407 | + | 0.687264i | \(0.758811\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −18.0000 | −0.947368 | ||||||||
\(362\) | 15.0711 | 0.792118 | ||||||||
\(363\) | 0 | 0 | ||||||||
\(364\) | −1.82843 | −0.0958356 | ||||||||
\(365\) | 9.24264 | 0.483782 | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | −31.3137 | −1.63456 | −0.817281 | − | 0.576239i | \(-0.804520\pi\) | ||||
−0.817281 | + | 0.576239i | \(0.804520\pi\) | |||||||
\(368\) | 5.07107 | 0.264348 | ||||||||
\(369\) | 0 | 0 | ||||||||
\(370\) | 2.24264 | 0.116589 | ||||||||
\(371\) | 5.65685 | 0.293689 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 14.7279 | 0.762583 | 0.381291 | − | 0.924455i | \(-0.375479\pi\) | ||||
0.381291 | + | 0.924455i | \(0.375479\pi\) | |||||||
\(374\) | −0.828427 | −0.0428369 | ||||||||
\(375\) | 0 | 0 | ||||||||
\(376\) | 7.07107 | 0.364662 | ||||||||
\(377\) | 2.27208 | 0.117018 | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | 4.14214 | 0.212767 | 0.106384 | − | 0.994325i | \(-0.466073\pi\) | ||||
0.106384 | + | 0.994325i | \(0.466073\pi\) | |||||||
\(380\) | 1.00000 | 0.0512989 | ||||||||
\(381\) | 0 | 0 | ||||||||
\(382\) | 19.8995 | 1.01815 | ||||||||
\(383\) | 8.31371 | 0.424811 | 0.212405 | − | 0.977182i | \(-0.431870\pi\) | ||||
0.212405 | + | 0.977182i | \(0.431870\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | 0.585786 | 0.0298544 | ||||||||
\(386\) | −6.82843 | −0.347558 | ||||||||
\(387\) | 0 | 0 | ||||||||
\(388\) | 13.5563 | 0.688219 | ||||||||
\(389\) | −20.8284 | −1.05604 | −0.528022 | − | 0.849231i | \(-0.677066\pi\) | ||||
−0.528022 | + | 0.849231i | \(0.677066\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | −7.17157 | −0.362682 | ||||||||
\(392\) | 6.00000 | 0.303046 | ||||||||
\(393\) | 0 | 0 | ||||||||
\(394\) | 25.1421 | 1.26664 | ||||||||
\(395\) | 8.41421 | 0.423365 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | −20.4853 | −1.02813 | −0.514063 | − | 0.857752i | \(-0.671860\pi\) | ||||
−0.514063 | + | 0.857752i | \(0.671860\pi\) | |||||||
\(398\) | 0.100505 | 0.00503786 | ||||||||
\(399\) | 0 | 0 | ||||||||
\(400\) | 1.00000 | 0.0500000 | ||||||||
\(401\) | 24.1127 | 1.20413 | 0.602065 | − | 0.798447i | \(-0.294345\pi\) | ||||
0.602065 | + | 0.798447i | \(0.294345\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 0.757359 | 0.0377268 | ||||||||
\(404\) | −1.41421 | −0.0703598 | ||||||||
\(405\) | 0 | 0 | ||||||||
\(406\) | 1.24264 | 0.0616712 | ||||||||
\(407\) | −1.31371 | −0.0651181 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | −27.2132 | −1.34561 | −0.672803 | − | 0.739822i | \(-0.734910\pi\) | ||||
−0.672803 | + | 0.739822i | \(0.734910\pi\) | |||||||
\(410\) | 1.82843 | 0.0902996 | ||||||||
\(411\) | 0 | 0 | ||||||||
\(412\) | 0.828427 | 0.0408137 | ||||||||
\(413\) | 1.17157 | 0.0576493 | ||||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | 3.65685 | 0.179508 | ||||||||
\(416\) | 1.82843 | 0.0896460 | ||||||||
\(417\) | 0 | 0 | ||||||||
\(418\) | −0.585786 | −0.0286518 | ||||||||
\(419\) | 12.7990 | 0.625272 | 0.312636 | − | 0.949873i | \(-0.398788\pi\) | ||||
0.312636 | + | 0.949873i | \(0.398788\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | 1.24264 | 0.0605626 | 0.0302813 | − | 0.999541i | \(-0.490360\pi\) | ||||
0.0302813 | + | 0.999541i | \(0.490360\pi\) | |||||||
\(422\) | 1.65685 | 0.0806544 | ||||||||
\(423\) | 0 | 0 | ||||||||
\(424\) | −5.65685 | −0.274721 | ||||||||
\(425\) | −1.41421 | −0.0685994 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 0.0710678 | 0.00343921 | ||||||||
\(428\) | −1.92893 | −0.0932385 | ||||||||
\(429\) | 0 | 0 | ||||||||
\(430\) | 1.00000 | 0.0482243 | ||||||||
\(431\) | −1.02944 | −0.0495862 | −0.0247931 | − | 0.999693i | \(-0.507893\pi\) | ||||
−0.0247931 | + | 0.999693i | \(0.507893\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −36.0711 | −1.73346 | −0.866732 | − | 0.498773i | \(-0.833784\pi\) | ||||
−0.866732 | + | 0.498773i | \(0.833784\pi\) | |||||||
\(434\) | 0.414214 | 0.0198829 | ||||||||
\(435\) | 0 | 0 | ||||||||
\(436\) | −10.8284 | −0.518588 | ||||||||
\(437\) | −5.07107 | −0.242582 | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | −15.3137 | −0.730883 | −0.365442 | − | 0.930834i | \(-0.619082\pi\) | ||||
−0.365442 | + | 0.930834i | \(0.619082\pi\) | |||||||
\(440\) | −0.585786 | −0.0279263 | ||||||||
\(441\) | 0 | 0 | ||||||||
\(442\) | −2.58579 | −0.122993 | ||||||||
\(443\) | 9.92893 | 0.471738 | 0.235869 | − | 0.971785i | \(-0.424206\pi\) | ||||
0.235869 | + | 0.971785i | \(0.424206\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −9.07107 | −0.430010 | ||||||||
\(446\) | −16.1421 | −0.764352 | ||||||||
\(447\) | 0 | 0 | ||||||||
\(448\) | 1.00000 | 0.0472456 | ||||||||
\(449\) | −22.2426 | −1.04970 | −0.524848 | − | 0.851196i | \(-0.675878\pi\) | ||||
−0.524848 | + | 0.851196i | \(0.675878\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | −1.07107 | −0.0504346 | ||||||||
\(452\) | −4.89949 | −0.230453 | ||||||||
\(453\) | 0 | 0 | ||||||||
\(454\) | 9.17157 | 0.430443 | ||||||||
\(455\) | 1.82843 | 0.0857180 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | −30.4853 | −1.42604 | −0.713021 | − | 0.701143i | \(-0.752673\pi\) | ||||
−0.713021 | + | 0.701143i | \(0.752673\pi\) | |||||||
\(458\) | −0.828427 | −0.0387099 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | −5.07107 | −0.236440 | ||||||||
\(461\) | 15.0711 | 0.701930 | 0.350965 | − | 0.936389i | \(-0.385854\pi\) | ||||
0.350965 | + | 0.936389i | \(0.385854\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 30.3137 | 1.40880 | 0.704399 | − | 0.709804i | \(-0.251217\pi\) | ||||
0.704399 | + | 0.709804i | \(0.251217\pi\) | |||||||
\(464\) | −1.24264 | −0.0576881 | ||||||||
\(465\) | 0 | 0 | ||||||||
\(466\) | 8.48528 | 0.393073 | ||||||||
\(467\) | 20.9289 | 0.968475 | 0.484238 | − | 0.874936i | \(-0.339097\pi\) | ||||
0.484238 | + | 0.874936i | \(0.339097\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | −1.24264 | −0.0573798 | ||||||||
\(470\) | −7.07107 | −0.326164 | ||||||||
\(471\) | 0 | 0 | ||||||||
\(472\) | −1.17157 | −0.0539260 | ||||||||
\(473\) | −0.585786 | −0.0269345 | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | −1.00000 | −0.0458831 | ||||||||
\(476\) | −1.41421 | −0.0648204 | ||||||||
\(477\) | 0 | 0 | ||||||||
\(478\) | 11.5858 | 0.529922 | ||||||||
\(479\) | −9.17157 | −0.419060 | −0.209530 | − | 0.977802i | \(-0.567193\pi\) | ||||
−0.209530 | + | 0.977802i | \(0.567193\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −4.10051 | −0.186967 | ||||||||
\(482\) | 21.4142 | 0.975391 | ||||||||
\(483\) | 0 | 0 | ||||||||
\(484\) | −10.6569 | −0.484402 | ||||||||
\(485\) | −13.5563 | −0.615562 | ||||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | −33.2132 | −1.50503 | −0.752517 | − | 0.658573i | \(-0.771160\pi\) | ||||
−0.752517 | + | 0.658573i | \(0.771160\pi\) | |||||||
\(488\) | −0.0710678 | −0.00321709 | ||||||||
\(489\) | 0 | 0 | ||||||||
\(490\) | −6.00000 | −0.271052 | ||||||||
\(491\) | −16.6274 | −0.750385 | −0.375192 | − | 0.926947i | \(-0.622423\pi\) | ||||
−0.375192 | + | 0.926947i | \(0.622423\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 1.75736 | 0.0791475 | ||||||||
\(494\) | −1.82843 | −0.0822648 | ||||||||
\(495\) | 0 | 0 | ||||||||
\(496\) | −0.414214 | −0.0185987 | ||||||||
\(497\) | −11.8995 | −0.533765 | ||||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | −34.4558 | −1.54246 | −0.771228 | − | 0.636559i | \(-0.780357\pi\) | ||||
−0.771228 | + | 0.636559i | \(0.780357\pi\) | |||||||
\(500\) | −1.00000 | −0.0447214 | ||||||||
\(501\) | 0 | 0 | ||||||||
\(502\) | −10.9706 | −0.489640 | ||||||||
\(503\) | 31.6569 | 1.41151 | 0.705755 | − | 0.708456i | \(-0.250608\pi\) | ||||
0.705755 | + | 0.708456i | \(0.250608\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | 1.41421 | 0.0629317 | ||||||||
\(506\) | 2.97056 | 0.132058 | ||||||||
\(507\) | 0 | 0 | ||||||||
\(508\) | 3.51472 | 0.155940 | ||||||||
\(509\) | 20.4853 | 0.907994 | 0.453997 | − | 0.891003i | \(-0.349998\pi\) | ||||
0.453997 | + | 0.891003i | \(0.349998\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | −9.24264 | −0.408870 | ||||||||
\(512\) | −1.00000 | −0.0441942 | ||||||||
\(513\) | 0 | 0 | ||||||||
\(514\) | 8.89949 | 0.392540 | ||||||||
\(515\) | −0.828427 | −0.0365049 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 4.14214 | 0.182171 | ||||||||
\(518\) | −2.24264 | −0.0985360 | ||||||||
\(519\) | 0 | 0 | ||||||||
\(520\) | −1.82843 | −0.0801818 | ||||||||
\(521\) | 11.0711 | 0.485032 | 0.242516 | − | 0.970147i | \(-0.422027\pi\) | ||||
0.242516 | + | 0.970147i | \(0.422027\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | 10.7279 | 0.469099 | 0.234550 | − | 0.972104i | \(-0.424638\pi\) | ||||
0.234550 | + | 0.972104i | \(0.424638\pi\) | |||||||
\(524\) | −6.00000 | −0.262111 | ||||||||
\(525\) | 0 | 0 | ||||||||
\(526\) | 17.4853 | 0.762394 | ||||||||
\(527\) | 0.585786 | 0.0255173 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 2.71573 | 0.118075 | ||||||||
\(530\) | 5.65685 | 0.245718 | ||||||||
\(531\) | 0 | 0 | ||||||||
\(532\) | −1.00000 | −0.0433555 | ||||||||
\(533\) | −3.34315 | −0.144808 | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | 1.92893 | 0.0833950 | ||||||||
\(536\) | 1.24264 | 0.0536739 | ||||||||
\(537\) | 0 | 0 | ||||||||
\(538\) | 9.17157 | 0.395415 | ||||||||
\(539\) | 3.51472 | 0.151390 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 7.85786 | 0.337836 | 0.168918 | − | 0.985630i | \(-0.445973\pi\) | ||||
0.168918 | + | 0.985630i | \(0.445973\pi\) | |||||||
\(542\) | −8.89949 | −0.382266 | ||||||||
\(543\) | 0 | 0 | ||||||||
\(544\) | 1.41421 | 0.0606339 | ||||||||
\(545\) | 10.8284 | 0.463839 | ||||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | −12.0000 | −0.513083 | −0.256541 | − | 0.966533i | \(-0.582583\pi\) | ||||
−0.256541 | + | 0.966533i | \(0.582583\pi\) | |||||||
\(548\) | −3.92893 | −0.167836 | ||||||||
\(549\) | 0 | 0 | ||||||||
\(550\) | 0.585786 | 0.0249780 | ||||||||
\(551\) | 1.24264 | 0.0529383 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | −8.41421 | −0.357809 | ||||||||
\(554\) | 0.485281 | 0.0206176 | ||||||||
\(555\) | 0 | 0 | ||||||||
\(556\) | −6.24264 | −0.264747 | ||||||||
\(557\) | −41.8284 | −1.77233 | −0.886164 | − | 0.463372i | \(-0.846639\pi\) | ||||
−0.886164 | + | 0.463372i | \(0.846639\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | −1.82843 | −0.0773342 | ||||||||
\(560\) | −1.00000 | −0.0422577 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | −1.34315 | −0.0566572 | ||||||||
\(563\) | 1.92893 | 0.0812948 | 0.0406474 | − | 0.999174i | \(-0.487058\pi\) | ||||
0.0406474 | + | 0.999174i | \(0.487058\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 4.89949 | 0.206123 | ||||||||
\(566\) | −18.7574 | −0.788431 | ||||||||
\(567\) | 0 | 0 | ||||||||
\(568\) | 11.8995 | 0.499292 | ||||||||
\(569\) | −22.7990 | −0.955783 | −0.477892 | − | 0.878419i | \(-0.658599\pi\) | ||||
−0.477892 | + | 0.878419i | \(0.658599\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 33.0000 | 1.38101 | 0.690504 | − | 0.723329i | \(-0.257389\pi\) | ||||
0.690504 | + | 0.723329i | \(0.257389\pi\) | |||||||
\(572\) | 1.07107 | 0.0447836 | ||||||||
\(573\) | 0 | 0 | ||||||||
\(574\) | −1.82843 | −0.0763171 | ||||||||
\(575\) | 5.07107 | 0.211478 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −5.58579 | −0.232539 | −0.116270 | − | 0.993218i | \(-0.537094\pi\) | ||||
−0.116270 | + | 0.993218i | \(0.537094\pi\) | |||||||
\(578\) | 15.0000 | 0.623918 | ||||||||
\(579\) | 0 | 0 | ||||||||
\(580\) | 1.24264 | 0.0515978 | ||||||||
\(581\) | −3.65685 | −0.151712 | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | −3.31371 | −0.137240 | ||||||||
\(584\) | 9.24264 | 0.382463 | ||||||||
\(585\) | 0 | 0 | ||||||||
\(586\) | 10.9706 | 0.453190 | ||||||||
\(587\) | 27.5563 | 1.13737 | 0.568686 | − | 0.822555i | \(-0.307452\pi\) | ||||
0.568686 | + | 0.822555i | \(0.307452\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | 0.414214 | 0.0170674 | ||||||||
\(590\) | 1.17157 | 0.0482329 | ||||||||
\(591\) | 0 | 0 | ||||||||
\(592\) | 2.24264 | 0.0921720 | ||||||||
\(593\) | 7.24264 | 0.297420 | 0.148710 | − | 0.988881i | \(-0.452488\pi\) | ||||
0.148710 | + | 0.988881i | \(0.452488\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 1.41421 | 0.0579771 | ||||||||
\(596\) | 10.5563 | 0.432405 | ||||||||
\(597\) | 0 | 0 | ||||||||
\(598\) | 9.27208 | 0.379163 | ||||||||
\(599\) | −9.85786 | −0.402781 | −0.201391 | − | 0.979511i | \(-0.564546\pi\) | ||||
−0.201391 | + | 0.979511i | \(0.564546\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | −28.0000 | −1.14214 | −0.571072 | − | 0.820900i | \(-0.693472\pi\) | ||||
−0.571072 | + | 0.820900i | \(0.693472\pi\) | |||||||
\(602\) | −1.00000 | −0.0407570 | ||||||||
\(603\) | 0 | 0 | ||||||||
\(604\) | 10.4853 | 0.426640 | ||||||||
\(605\) | 10.6569 | 0.433263 | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | 6.00000 | 0.243532 | 0.121766 | − | 0.992559i | \(-0.461144\pi\) | ||||
0.121766 | + | 0.992559i | \(0.461144\pi\) | |||||||
\(608\) | 1.00000 | 0.0405554 | ||||||||
\(609\) | 0 | 0 | ||||||||
\(610\) | 0.0710678 | 0.00287745 | ||||||||
\(611\) | 12.9289 | 0.523049 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | 38.1716 | 1.54174 | 0.770868 | − | 0.636995i | \(-0.219823\pi\) | ||||
0.770868 | + | 0.636995i | \(0.219823\pi\) | |||||||
\(614\) | 5.92893 | 0.239272 | ||||||||
\(615\) | 0 | 0 | ||||||||
\(616\) | 0.585786 | 0.0236020 | ||||||||
\(617\) | 16.2843 | 0.655580 | 0.327790 | − | 0.944751i | \(-0.393696\pi\) | ||||
0.327790 | + | 0.944751i | \(0.393696\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | −0.100505 | −0.00403964 | −0.00201982 | − | 0.999998i | \(-0.500643\pi\) | ||||
−0.00201982 | + | 0.999998i | \(0.500643\pi\) | |||||||
\(620\) | 0.414214 | 0.0166352 | ||||||||
\(621\) | 0 | 0 | ||||||||
\(622\) | −4.07107 | −0.163235 | ||||||||
\(623\) | 9.07107 | 0.363425 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | 1.00000 | 0.0400000 | ||||||||
\(626\) | 1.31371 | 0.0525064 | ||||||||
\(627\) | 0 | 0 | ||||||||
\(628\) | 10.2426 | 0.408726 | ||||||||
\(629\) | −3.17157 | −0.126459 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | −13.6985 | −0.545328 | −0.272664 | − | 0.962109i | \(-0.587905\pi\) | ||||
−0.272664 | + | 0.962109i | \(0.587905\pi\) | |||||||
\(632\) | 8.41421 | 0.334699 | ||||||||
\(633\) | 0 | 0 | ||||||||
\(634\) | 0.857864 | 0.0340701 | ||||||||
\(635\) | −3.51472 | −0.139477 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 10.9706 | 0.434670 | ||||||||
\(638\) | −0.727922 | −0.0288187 | ||||||||
\(639\) | 0 | 0 | ||||||||
\(640\) | 1.00000 | 0.0395285 | ||||||||
\(641\) | −42.7696 | −1.68930 | −0.844648 | − | 0.535322i | \(-0.820190\pi\) | ||||
−0.844648 | + | 0.535322i | \(0.820190\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | 39.7279 | 1.56672 | 0.783358 | − | 0.621571i | \(-0.213505\pi\) | ||||
0.783358 | + | 0.621571i | \(0.213505\pi\) | |||||||
\(644\) | 5.07107 | 0.199828 | ||||||||
\(645\) | 0 | 0 | ||||||||
\(646\) | −1.41421 | −0.0556415 | ||||||||
\(647\) | −5.20101 | −0.204473 | −0.102236 | − | 0.994760i | \(-0.532600\pi\) | ||||
−0.102236 | + | 0.994760i | \(0.532600\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | −0.686292 | −0.0269393 | ||||||||
\(650\) | 1.82843 | 0.0717168 | ||||||||
\(651\) | 0 | 0 | ||||||||
\(652\) | 13.6569 | 0.534844 | ||||||||
\(653\) | 6.58579 | 0.257722 | 0.128861 | − | 0.991663i | \(-0.458868\pi\) | ||||
0.128861 | + | 0.991663i | \(0.458868\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 6.00000 | 0.234439 | ||||||||
\(656\) | 1.82843 | 0.0713881 | ||||||||
\(657\) | 0 | 0 | ||||||||
\(658\) | 7.07107 | 0.275659 | ||||||||
\(659\) | −24.3848 | −0.949896 | −0.474948 | − | 0.880014i | \(-0.657533\pi\) | ||||
−0.474948 | + | 0.880014i | \(0.657533\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 24.8701 | 0.967333 | 0.483667 | − | 0.875252i | \(-0.339305\pi\) | ||||
0.483667 | + | 0.875252i | \(0.339305\pi\) | |||||||
\(662\) | 25.3137 | 0.983845 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 3.65685 | 0.141913 | ||||||||
\(665\) | 1.00000 | 0.0387783 | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | −6.30152 | −0.243996 | ||||||||
\(668\) | −13.5563 | −0.524511 | ||||||||
\(669\) | 0 | 0 | ||||||||
\(670\) | −1.24264 | −0.0480074 | ||||||||
\(671\) | −0.0416306 | −0.00160713 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 20.4142 | 0.786910 | 0.393455 | − | 0.919344i | \(-0.371280\pi\) | ||||
0.393455 | + | 0.919344i | \(0.371280\pi\) | |||||||
\(674\) | 8.34315 | 0.321366 | ||||||||
\(675\) | 0 | 0 | ||||||||
\(676\) | −9.65685 | −0.371417 | ||||||||
\(677\) | −43.4558 | −1.67014 | −0.835072 | − | 0.550141i | \(-0.814574\pi\) | ||||
−0.835072 | + | 0.550141i | \(0.814574\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 13.5563 | 0.520245 | ||||||||
\(680\) | −1.41421 | −0.0542326 | ||||||||
\(681\) | 0 | 0 | ||||||||
\(682\) | −0.242641 | −0.00929119 | ||||||||
\(683\) | 3.51472 | 0.134487 | 0.0672435 | − | 0.997737i | \(-0.478580\pi\) | ||||
0.0672435 | + | 0.997737i | \(0.478580\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 3.92893 | 0.150117 | ||||||||
\(686\) | 13.0000 | 0.496342 | ||||||||
\(687\) | 0 | 0 | ||||||||
\(688\) | 1.00000 | 0.0381246 | ||||||||
\(689\) | −10.3431 | −0.394042 | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | 18.4853 | 0.703213 | 0.351607 | − | 0.936148i | \(-0.385635\pi\) | ||||
0.351607 | + | 0.936148i | \(0.385635\pi\) | |||||||
\(692\) | −0.514719 | −0.0195667 | ||||||||
\(693\) | 0 | 0 | ||||||||
\(694\) | −22.2426 | −0.844319 | ||||||||
\(695\) | 6.24264 | 0.236797 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | −2.58579 | −0.0979436 | ||||||||
\(698\) | −23.4558 | −0.887817 | ||||||||
\(699\) | 0 | 0 | ||||||||
\(700\) | 1.00000 | 0.0377964 | ||||||||
\(701\) | −11.2721 | −0.425741 | −0.212870 | − | 0.977080i | \(-0.568281\pi\) | ||||
−0.212870 | + | 0.977080i | \(0.568281\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | −2.24264 | −0.0845828 | ||||||||
\(704\) | −0.585786 | −0.0220777 | ||||||||
\(705\) | 0 | 0 | ||||||||
\(706\) | −32.3848 | −1.21882 | ||||||||
\(707\) | −1.41421 | −0.0531870 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −7.21320 | −0.270898 | −0.135449 | − | 0.990784i | \(-0.543248\pi\) | ||||
−0.135449 | + | 0.990784i | \(0.543248\pi\) | |||||||
\(710\) | −11.8995 | −0.446580 | ||||||||
\(711\) | 0 | 0 | ||||||||
\(712\) | −9.07107 | −0.339953 | ||||||||
\(713\) | −2.10051 | −0.0786645 | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | −1.07107 | −0.0400557 | ||||||||
\(716\) | −17.4853 | −0.653456 | ||||||||
\(717\) | 0 | 0 | ||||||||
\(718\) | 27.5269 | 1.02730 | ||||||||
\(719\) | 36.6274 | 1.36597 | 0.682986 | − | 0.730431i | \(-0.260681\pi\) | ||||
0.682986 | + | 0.730431i | \(0.260681\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 0.828427 | 0.0308522 | ||||||||
\(722\) | 18.0000 | 0.669891 | ||||||||
\(723\) | 0 | 0 | ||||||||
\(724\) | −15.0711 | −0.560112 | ||||||||
\(725\) | −1.24264 | −0.0461505 | ||||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | −14.0000 | −0.519231 | −0.259616 | − | 0.965712i | \(-0.583596\pi\) | ||||
−0.259616 | + | 0.965712i | \(0.583596\pi\) | |||||||
\(728\) | 1.82843 | 0.0677660 | ||||||||
\(729\) | 0 | 0 | ||||||||
\(730\) | −9.24264 | −0.342085 | ||||||||
\(731\) | −1.41421 | −0.0523066 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | 27.7574 | 1.02524 | 0.512621 | − | 0.858615i | \(-0.328675\pi\) | ||||
0.512621 | + | 0.858615i | \(0.328675\pi\) | |||||||
\(734\) | 31.3137 | 1.15581 | ||||||||
\(735\) | 0 | 0 | ||||||||
\(736\) | −5.07107 | −0.186922 | ||||||||
\(737\) | 0.727922 | 0.0268134 | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | 8.02944 | 0.295368 | 0.147684 | − | 0.989035i | \(-0.452818\pi\) | ||||
0.147684 | + | 0.989035i | \(0.452818\pi\) | |||||||
\(740\) | −2.24264 | −0.0824411 | ||||||||
\(741\) | 0 | 0 | ||||||||
\(742\) | −5.65685 | −0.207670 | ||||||||
\(743\) | −2.31371 | −0.0848817 | −0.0424409 | − | 0.999099i | \(-0.513513\pi\) | ||||
−0.0424409 | + | 0.999099i | \(0.513513\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −10.5563 | −0.386755 | ||||||||
\(746\) | −14.7279 | −0.539228 | ||||||||
\(747\) | 0 | 0 | ||||||||
\(748\) | 0.828427 | 0.0302903 | ||||||||
\(749\) | −1.92893 | −0.0704816 | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | −8.72792 | −0.318486 | −0.159243 | − | 0.987239i | \(-0.550905\pi\) | ||||
−0.159243 | + | 0.987239i | \(0.550905\pi\) | |||||||
\(752\) | −7.07107 | −0.257855 | ||||||||
\(753\) | 0 | 0 | ||||||||
\(754\) | −2.27208 | −0.0827442 | ||||||||
\(755\) | −10.4853 | −0.381598 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | 36.4264 | 1.32394 | 0.661970 | − | 0.749530i | \(-0.269721\pi\) | ||||
0.661970 | + | 0.749530i | \(0.269721\pi\) | |||||||
\(758\) | −4.14214 | −0.150449 | ||||||||
\(759\) | 0 | 0 | ||||||||
\(760\) | −1.00000 | −0.0362738 | ||||||||
\(761\) | 44.8284 | 1.62503 | 0.812515 | − | 0.582941i | \(-0.198098\pi\) | ||||
0.812515 | + | 0.582941i | \(0.198098\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | −10.8284 | −0.392015 | ||||||||
\(764\) | −19.8995 | −0.719938 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | −8.31371 | −0.300386 | ||||||||
\(767\) | −2.14214 | −0.0773480 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | 21.0000 | 0.757279 | 0.378640 | − | 0.925544i | \(-0.376392\pi\) | ||||
0.378640 | + | 0.925544i | \(0.376392\pi\) | |||||||
\(770\) | −0.585786 | −0.0211103 | ||||||||
\(771\) | 0 | 0 | ||||||||
\(772\) | 6.82843 | 0.245760 | ||||||||
\(773\) | 25.0711 | 0.901744 | 0.450872 | − | 0.892589i | \(-0.351113\pi\) | ||||
0.450872 | + | 0.892589i | \(0.351113\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | −0.414214 | −0.0148790 | ||||||||
\(776\) | −13.5563 | −0.486645 | ||||||||
\(777\) | 0 | 0 | ||||||||
\(778\) | 20.8284 | 0.746735 | ||||||||
\(779\) | −1.82843 | −0.0655102 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 6.97056 | 0.249426 | ||||||||
\(782\) | 7.17157 | 0.256455 | ||||||||
\(783\) | 0 | 0 | ||||||||
\(784\) | −6.00000 | −0.214286 | ||||||||
\(785\) | −10.2426 | −0.365576 | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 31.2426 | 1.11368 | 0.556840 | − | 0.830620i | \(-0.312014\pi\) | ||||
0.556840 | + | 0.830620i | \(0.312014\pi\) | |||||||
\(788\) | −25.1421 | −0.895651 | ||||||||
\(789\) | 0 | 0 | ||||||||
\(790\) | −8.41421 | −0.299364 | ||||||||
\(791\) | −4.89949 | −0.174206 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | −0.129942 | −0.00461439 | ||||||||
\(794\) | 20.4853 | 0.726995 | ||||||||
\(795\) | 0 | 0 | ||||||||
\(796\) | −0.100505 | −0.00356231 | ||||||||
\(797\) | 42.9411 | 1.52105 | 0.760526 | − | 0.649307i | \(-0.224941\pi\) | ||||
0.760526 | + | 0.649307i | \(0.224941\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 10.0000 | 0.353775 | ||||||||
\(800\) | −1.00000 | −0.0353553 | ||||||||
\(801\) | 0 | 0 | ||||||||
\(802\) | −24.1127 | −0.851449 | ||||||||
\(803\) | 5.41421 | 0.191063 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | −5.07107 | −0.178732 | ||||||||
\(806\) | −0.757359 | −0.0266768 | ||||||||
\(807\) | 0 | 0 | ||||||||
\(808\) | 1.41421 | 0.0497519 | ||||||||
\(809\) | 28.7990 | 1.01252 | 0.506259 | − | 0.862381i | \(-0.331028\pi\) | ||||
0.506259 | + | 0.862381i | \(0.331028\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | −48.1127 | −1.68947 | −0.844733 | − | 0.535188i | \(-0.820241\pi\) | ||||
−0.844733 | + | 0.535188i | \(0.820241\pi\) | |||||||
\(812\) | −1.24264 | −0.0436081 | ||||||||
\(813\) | 0 | 0 | ||||||||
\(814\) | 1.31371 | 0.0460455 | ||||||||
\(815\) | −13.6569 | −0.478379 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | −1.00000 | −0.0349856 | ||||||||
\(818\) | 27.2132 | 0.951487 | ||||||||
\(819\) | 0 | 0 | ||||||||
\(820\) | −1.82843 | −0.0638514 | ||||||||
\(821\) | 20.1421 | 0.702965 | 0.351483 | − | 0.936194i | \(-0.385678\pi\) | ||||
0.351483 | + | 0.936194i | \(0.385678\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 13.5147 | 0.471093 | 0.235547 | − | 0.971863i | \(-0.424312\pi\) | ||||
0.235547 | + | 0.971863i | \(0.424312\pi\) | |||||||
\(824\) | −0.828427 | −0.0288596 | ||||||||
\(825\) | 0 | 0 | ||||||||
\(826\) | −1.17157 | −0.0407642 | ||||||||
\(827\) | 43.5269 | 1.51358 | 0.756790 | − | 0.653659i | \(-0.226767\pi\) | ||||
0.756790 | + | 0.653659i | \(0.226767\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 3.24264 | 0.112622 | 0.0563108 | − | 0.998413i | \(-0.482066\pi\) | ||||
0.0563108 | + | 0.998413i | \(0.482066\pi\) | |||||||
\(830\) | −3.65685 | −0.126931 | ||||||||
\(831\) | 0 | 0 | ||||||||
\(832\) | −1.82843 | −0.0633893 | ||||||||
\(833\) | 8.48528 | 0.293998 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 13.5563 | 0.469137 | ||||||||
\(836\) | 0.585786 | 0.0202598 | ||||||||
\(837\) | 0 | 0 | ||||||||
\(838\) | −12.7990 | −0.442134 | ||||||||
\(839\) | 51.0122 | 1.76114 | 0.880568 | − | 0.473919i | \(-0.157161\pi\) | ||||
0.880568 | + | 0.473919i | \(0.157161\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | −27.4558 | −0.946753 | ||||||||
\(842\) | −1.24264 | −0.0428242 | ||||||||
\(843\) | 0 | 0 | ||||||||
\(844\) | −1.65685 | −0.0570313 | ||||||||
\(845\) | 9.65685 | 0.332206 | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | −10.6569 | −0.366174 | ||||||||
\(848\) | 5.65685 | 0.194257 | ||||||||
\(849\) | 0 | 0 | ||||||||
\(850\) | 1.41421 | 0.0485071 | ||||||||
\(851\) | 11.3726 | 0.389847 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | −35.9411 | −1.23060 | −0.615300 | − | 0.788293i | \(-0.710965\pi\) | ||||
−0.615300 | + | 0.788293i | \(0.710965\pi\) | |||||||
\(854\) | −0.0710678 | −0.00243189 | ||||||||
\(855\) | 0 | 0 | ||||||||
\(856\) | 1.92893 | 0.0659295 | ||||||||
\(857\) | −47.0711 | −1.60792 | −0.803959 | − | 0.594685i | \(-0.797277\pi\) | ||||
−0.803959 | + | 0.594685i | \(0.797277\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | −16.5147 | −0.563475 | −0.281737 | − | 0.959492i | \(-0.590911\pi\) | ||||
−0.281737 | + | 0.959492i | \(0.590911\pi\) | |||||||
\(860\) | −1.00000 | −0.0340997 | ||||||||
\(861\) | 0 | 0 | ||||||||
\(862\) | 1.02944 | 0.0350628 | ||||||||
\(863\) | 40.8284 | 1.38982 | 0.694908 | − | 0.719099i | \(-0.255445\pi\) | ||||
0.694908 | + | 0.719099i | \(0.255445\pi\) | |||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 0.514719 | 0.0175010 | ||||||||
\(866\) | 36.0711 | 1.22574 | ||||||||
\(867\) | 0 | 0 | ||||||||
\(868\) | −0.414214 | −0.0140593 | ||||||||
\(869\) | 4.92893 | 0.167203 | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | 2.27208 | 0.0769864 | ||||||||
\(872\) | 10.8284 | 0.366697 | ||||||||
\(873\) | 0 | 0 | ||||||||
\(874\) | 5.07107 | 0.171531 | ||||||||
\(875\) | −1.00000 | −0.0338062 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | −18.6274 | −0.629003 | −0.314502 | − | 0.949257i | \(-0.601837\pi\) | ||||
−0.314502 | + | 0.949257i | \(0.601837\pi\) | |||||||
\(878\) | 15.3137 | 0.516813 | ||||||||
\(879\) | 0 | 0 | ||||||||
\(880\) | 0.585786 | 0.0197469 | ||||||||
\(881\) | 1.20101 | 0.0404631 | 0.0202315 | − | 0.999795i | \(-0.493560\pi\) | ||||
0.0202315 | + | 0.999795i | \(0.493560\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 26.2132 | 0.882145 | 0.441072 | − | 0.897472i | \(-0.354598\pi\) | ||||
0.441072 | + | 0.897472i | \(0.354598\pi\) | |||||||
\(884\) | 2.58579 | 0.0869694 | ||||||||
\(885\) | 0 | 0 | ||||||||
\(886\) | −9.92893 | −0.333569 | ||||||||
\(887\) | 56.1127 | 1.88408 | 0.942040 | − | 0.335501i | \(-0.108905\pi\) | ||||
0.942040 | + | 0.335501i | \(0.108905\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | 3.51472 | 0.117880 | ||||||||
\(890\) | 9.07107 | 0.304063 | ||||||||
\(891\) | 0 | 0 | ||||||||
\(892\) | 16.1421 | 0.540479 | ||||||||
\(893\) | 7.07107 | 0.236624 | ||||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 17.4853 | 0.584468 | ||||||||
\(896\) | −1.00000 | −0.0334077 | ||||||||
\(897\) | 0 | 0 | ||||||||
\(898\) | 22.2426 | 0.742247 | ||||||||
\(899\) | 0.514719 | 0.0171668 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | −8.00000 | −0.266519 | ||||||||
\(902\) | 1.07107 | 0.0356627 | ||||||||
\(903\) | 0 | 0 | ||||||||
\(904\) | 4.89949 | 0.162955 | ||||||||
\(905\) | 15.0711 | 0.500979 | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | 14.8995 | 0.494730 | 0.247365 | − | 0.968922i | \(-0.420435\pi\) | ||||
0.247365 | + | 0.968922i | \(0.420435\pi\) | |||||||
\(908\) | −9.17157 | −0.304369 | ||||||||
\(909\) | 0 | 0 | ||||||||
\(910\) | −1.82843 | −0.0606118 | ||||||||
\(911\) | 20.3848 | 0.675378 | 0.337689 | − | 0.941258i | \(-0.390355\pi\) | ||||
0.337689 | + | 0.941258i | \(0.390355\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | 2.14214 | 0.0708943 | ||||||||
\(914\) | 30.4853 | 1.00836 | ||||||||
\(915\) | 0 | 0 | ||||||||
\(916\) | 0.828427 | 0.0273720 | ||||||||
\(917\) | −6.00000 | −0.198137 | ||||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | −34.8995 | −1.15123 | −0.575614 | − | 0.817722i | \(-0.695237\pi\) | ||||
−0.575614 | + | 0.817722i | \(0.695237\pi\) | |||||||
\(920\) | 5.07107 | 0.167188 | ||||||||
\(921\) | 0 | 0 | ||||||||
\(922\) | −15.0711 | −0.496339 | ||||||||
\(923\) | 21.7574 | 0.716152 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 2.24264 | 0.0737376 | ||||||||
\(926\) | −30.3137 | −0.996170 | ||||||||
\(927\) | 0 | 0 | ||||||||
\(928\) | 1.24264 | 0.0407917 | ||||||||
\(929\) | 13.7990 | 0.452730 | 0.226365 | − | 0.974043i | \(-0.427316\pi\) | ||||
0.226365 | + | 0.974043i | \(0.427316\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 6.00000 | 0.196642 | ||||||||
\(932\) | −8.48528 | −0.277945 | ||||||||
\(933\) | 0 | 0 | ||||||||
\(934\) | −20.9289 | −0.684816 | ||||||||
\(935\) | −0.828427 | −0.0270925 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −34.4264 | −1.12466 | −0.562331 | − | 0.826912i | \(-0.690095\pi\) | ||||
−0.562331 | + | 0.826912i | \(0.690095\pi\) | |||||||
\(938\) | 1.24264 | 0.0405737 | ||||||||
\(939\) | 0 | 0 | ||||||||
\(940\) | 7.07107 | 0.230633 | ||||||||
\(941\) | 53.0711 | 1.73007 | 0.865034 | − | 0.501714i | \(-0.167297\pi\) | ||||
0.865034 | + | 0.501714i | \(0.167297\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 9.27208 | 0.301940 | ||||||||
\(944\) | 1.17157 | 0.0381314 | ||||||||
\(945\) | 0 | 0 | ||||||||
\(946\) | 0.585786 | 0.0190456 | ||||||||
\(947\) | −59.1838 | −1.92321 | −0.961607 | − | 0.274430i | \(-0.911511\pi\) | ||||
−0.961607 | + | 0.274430i | \(0.911511\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | 16.8995 | 0.548581 | ||||||||
\(950\) | 1.00000 | 0.0324443 | ||||||||
\(951\) | 0 | 0 | ||||||||
\(952\) | 1.41421 | 0.0458349 | ||||||||
\(953\) | 9.10051 | 0.294794 | 0.147397 | − | 0.989077i | \(-0.452910\pi\) | ||||
0.147397 | + | 0.989077i | \(0.452910\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | 19.8995 | 0.643933 | ||||||||
\(956\) | −11.5858 | −0.374711 | ||||||||
\(957\) | 0 | 0 | ||||||||
\(958\) | 9.17157 | 0.296320 | ||||||||
\(959\) | −3.92893 | −0.126872 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | −30.8284 | −0.994465 | ||||||||
\(962\) | 4.10051 | 0.132206 | ||||||||
\(963\) | 0 | 0 | ||||||||
\(964\) | −21.4142 | −0.689705 | ||||||||
\(965\) | −6.82843 | −0.219815 | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 36.2426 | 1.16548 | 0.582742 | − | 0.812657i | \(-0.301980\pi\) | ||||
0.582742 | + | 0.812657i | \(0.301980\pi\) | |||||||
\(968\) | 10.6569 | 0.342524 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 13.5563 | 0.435268 | ||||||||
\(971\) | −21.0711 | −0.676203 | −0.338101 | − | 0.941110i | \(-0.609785\pi\) | ||||
−0.338101 | + | 0.941110i | \(0.609785\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | −6.24264 | −0.200130 | ||||||||
\(974\) | 33.2132 | 1.06422 | ||||||||
\(975\) | 0 | 0 | ||||||||
\(976\) | 0.0710678 | 0.00227483 | ||||||||
\(977\) | 17.0711 | 0.546152 | 0.273076 | − | 0.961992i | \(-0.411959\pi\) | ||||
0.273076 | + | 0.961992i | \(0.411959\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | −5.31371 | −0.169827 | ||||||||
\(980\) | 6.00000 | 0.191663 | ||||||||
\(981\) | 0 | 0 | ||||||||
\(982\) | 16.6274 | 0.530602 | ||||||||
\(983\) | 27.3431 | 0.872111 | 0.436055 | − | 0.899920i | \(-0.356375\pi\) | ||||
0.436055 | + | 0.899920i | \(0.356375\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 25.1421 | 0.801095 | ||||||||
\(986\) | −1.75736 | −0.0559657 | ||||||||
\(987\) | 0 | 0 | ||||||||
\(988\) | 1.82843 | 0.0581700 | ||||||||
\(989\) | 5.07107 | 0.161251 | ||||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 41.2548 | 1.31050 | 0.655251 | − | 0.755411i | \(-0.272563\pi\) | ||||
0.655251 | + | 0.755411i | \(0.272563\pi\) | |||||||
\(992\) | 0.414214 | 0.0131513 | ||||||||
\(993\) | 0 | 0 | ||||||||
\(994\) | 11.8995 | 0.377429 | ||||||||
\(995\) | 0.100505 | 0.00318622 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | 37.1716 | 1.17724 | 0.588618 | − | 0.808411i | \(-0.299672\pi\) | ||||
0.588618 | + | 0.808411i | \(0.299672\pi\) | |||||||
\(998\) | 34.4558 | 1.09068 | ||||||||
\(999\) | 0 | 0 |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
Twists
By twisting character | |||||||
---|---|---|---|---|---|---|---|
Char | Parity | Ord | Type | Twist | Min | Dim | |
1.1 | even | 1 | trivial | 3870.2.a.bc.1.2 | 2 | ||
3.2 | odd | 2 | 430.2.a.g.1.2 | ✓ | 2 | ||
12.11 | even | 2 | 3440.2.a.j.1.1 | 2 | |||
15.2 | even | 4 | 2150.2.b.o.1549.3 | 4 | |||
15.8 | even | 4 | 2150.2.b.o.1549.2 | 4 | |||
15.14 | odd | 2 | 2150.2.a.v.1.1 | 2 |
By twisted newform | |||||||
---|---|---|---|---|---|---|---|
Twist | Min | Dim | Char | Parity | Ord | Type | |
430.2.a.g.1.2 | ✓ | 2 | 3.2 | odd | 2 | ||
2150.2.a.v.1.1 | 2 | 15.14 | odd | 2 | |||
2150.2.b.o.1549.2 | 4 | 15.8 | even | 4 | |||
2150.2.b.o.1549.3 | 4 | 15.2 | even | 4 | |||
3440.2.a.j.1.1 | 2 | 12.11 | even | 2 | |||
3870.2.a.bc.1.2 | 2 | 1.1 | even | 1 | trivial |