Newspace parameters
comment: Compute space of new eigenforms
[N,k,chi] = [192,2,Mod(191,192)]
mf = mfinit([N,k,chi],0)
lf = mfeigenbasis(mf)
from sage.modular.dirichlet import DirichletCharacter
H = DirichletGroup(192, base_ring=CyclotomicField(2))
chi = DirichletCharacter(H, H._module([1, 0, 1]))
N = Newforms(chi, 2, names="a")
//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code
chi := DirichletCharacter("192.191");
S:= CuspForms(chi, 2);
N := Newforms(S);
Level: | \( N \) | \(=\) | \( 192 = 2^{6} \cdot 3 \) |
Weight: | \( k \) | \(=\) | \( 2 \) |
Character orbit: | \([\chi]\) | \(=\) | 192.c (of order \(2\), degree \(1\), not minimal) |
Newform invariants
comment: select newform
sage: f = N[0] # Warning: the index may be different
gp: f = lf[1] \\ Warning: the index may be different
Self dual: | no |
Analytic conductor: | \(1.53312771881\) |
Analytic rank: | \(0\) |
Dimension: | \(4\) |
Coefficient field: | \(\Q(\zeta_{8})\) |
comment: defining polynomial
gp: f.mod \\ as an extension of the character field
|
|
Defining polynomial: | \( x^{4} + 1 \) |
Coefficient ring: | \(\Z[a_1, \ldots, a_{7}]\) |
Coefficient ring index: | \( 2^{3} \) |
Twist minimal: | no (minimal twist has level 96) |
Sato-Tate group: | $\mathrm{SU}(2)[C_{2}]$ |
Embedding invariants
Embedding label | 191.3 | ||
Root | \(-0.707107 + 0.707107i\) of defining polynomial | ||
Character | \(\chi\) | \(=\) | 192.191 |
Dual form | 192.2.c.b.191.4 |
$q$-expansion
comment: q-expansion
sage: f.q_expansion() # note that sage often uses an isomorphic number field
gp: mfcoefs(f, 20)
Character values
We give the values of \(\chi\) on generators for \(\left(\mathbb{Z}/192\mathbb{Z}\right)^\times\).
\(n\) | \(65\) | \(127\) | \(133\) |
\(\chi(n)\) | \(-1\) | \(-1\) | \(1\) |
Coefficient data
For each \(n\) we display the coefficients of the \(q\)-expansion \(a_n\), the Satake parameters \(\alpha_p\), and the Satake angles \(\theta_p = \textrm{Arg}(\alpha_p)\).
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))
\(n\) | \(a_n\) | \(a_n / n^{(k-1)/2}\) | \( \alpha_n \) | \( \theta_n \) | ||||||
---|---|---|---|---|---|---|---|---|---|---|
\(p\) | \(a_p\) | \(a_p / p^{(k-1)/2}\) | \( \alpha_p\) | \( \theta_p \) | ||||||
\(2\) | 0 | 0 | ||||||||
\(3\) | 1.41421 | − | 1.00000i | 0.816497 | − | 0.577350i | ||||
\(4\) | 0 | 0 | ||||||||
\(5\) | − | 2.82843i | − | 1.26491i | −0.774597 | − | 0.632456i | \(-0.782047\pi\) | ||
0.774597 | − | 0.632456i | \(-0.217953\pi\) | |||||||
\(6\) | 0 | 0 | ||||||||
\(7\) | 2.00000i | 0.755929i | 0.925820 | + | 0.377964i | \(0.123376\pi\) | ||||
−0.925820 | + | 0.377964i | \(0.876624\pi\) | |||||||
\(8\) | 0 | 0 | ||||||||
\(9\) | 1.00000 | − | 2.82843i | 0.333333 | − | 0.942809i | ||||
\(10\) | 0 | 0 | ||||||||
\(11\) | −2.82843 | −0.852803 | −0.426401 | − | 0.904534i | \(-0.640219\pi\) | ||||
−0.426401 | + | 0.904534i | \(0.640219\pi\) | |||||||
\(12\) | 0 | 0 | ||||||||
\(13\) | 2.00000 | 0.554700 | 0.277350 | − | 0.960769i | \(-0.410544\pi\) | ||||
0.277350 | + | 0.960769i | \(0.410544\pi\) | |||||||
\(14\) | 0 | 0 | ||||||||
\(15\) | −2.82843 | − | 4.00000i | −0.730297 | − | 1.03280i | ||||
\(16\) | 0 | 0 | ||||||||
\(17\) | 0 | 0 | 1.00000 | \(0\) | ||||||
−1.00000 | \(\pi\) | |||||||||
\(18\) | 0 | 0 | ||||||||
\(19\) | 6.00000i | 1.37649i | 0.725476 | + | 0.688247i | \(0.241620\pi\) | ||||
−0.725476 | + | 0.688247i | \(0.758380\pi\) | |||||||
\(20\) | 0 | 0 | ||||||||
\(21\) | 2.00000 | + | 2.82843i | 0.436436 | + | 0.617213i | ||||
\(22\) | 0 | 0 | ||||||||
\(23\) | 5.65685 | 1.17954 | 0.589768 | − | 0.807573i | \(-0.299219\pi\) | ||||
0.589768 | + | 0.807573i | \(0.299219\pi\) | |||||||
\(24\) | 0 | 0 | ||||||||
\(25\) | −3.00000 | −0.600000 | ||||||||
\(26\) | 0 | 0 | ||||||||
\(27\) | −1.41421 | − | 5.00000i | −0.272166 | − | 0.962250i | ||||
\(28\) | 0 | 0 | ||||||||
\(29\) | 2.82843i | 0.525226i | 0.964901 | + | 0.262613i | \(0.0845842\pi\) | ||||
−0.964901 | + | 0.262613i | \(0.915416\pi\) | |||||||
\(30\) | 0 | 0 | ||||||||
\(31\) | 2.00000i | 0.359211i | 0.983739 | + | 0.179605i | \(0.0574821\pi\) | ||||
−0.983739 | + | 0.179605i | \(0.942518\pi\) | |||||||
\(32\) | 0 | 0 | ||||||||
\(33\) | −4.00000 | + | 2.82843i | −0.696311 | + | 0.492366i | ||||
\(34\) | 0 | 0 | ||||||||
\(35\) | 5.65685 | 0.956183 | ||||||||
\(36\) | 0 | 0 | ||||||||
\(37\) | −6.00000 | −0.986394 | −0.493197 | − | 0.869918i | \(-0.664172\pi\) | ||||
−0.493197 | + | 0.869918i | \(0.664172\pi\) | |||||||
\(38\) | 0 | 0 | ||||||||
\(39\) | 2.82843 | − | 2.00000i | 0.452911 | − | 0.320256i | ||||
\(40\) | 0 | 0 | ||||||||
\(41\) | 5.65685i | 0.883452i | 0.897150 | + | 0.441726i | \(0.145634\pi\) | ||||
−0.897150 | + | 0.441726i | \(0.854366\pi\) | |||||||
\(42\) | 0 | 0 | ||||||||
\(43\) | − | 2.00000i | − | 0.304997i | −0.988304 | − | 0.152499i | \(-0.951268\pi\) | ||
0.988304 | − | 0.152499i | \(-0.0487319\pi\) | |||||||
\(44\) | 0 | 0 | ||||||||
\(45\) | −8.00000 | − | 2.82843i | −1.19257 | − | 0.421637i | ||||
\(46\) | 0 | 0 | ||||||||
\(47\) | −11.3137 | −1.65027 | −0.825137 | − | 0.564933i | \(-0.808902\pi\) | ||||
−0.825137 | + | 0.564933i | \(0.808902\pi\) | |||||||
\(48\) | 0 | 0 | ||||||||
\(49\) | 3.00000 | 0.428571 | ||||||||
\(50\) | 0 | 0 | ||||||||
\(51\) | 0 | 0 | ||||||||
\(52\) | 0 | 0 | ||||||||
\(53\) | 8.48528i | 1.16554i | 0.812636 | + | 0.582772i | \(0.198032\pi\) | ||||
−0.812636 | + | 0.582772i | \(0.801968\pi\) | |||||||
\(54\) | 0 | 0 | ||||||||
\(55\) | 8.00000i | 1.07872i | ||||||||
\(56\) | 0 | 0 | ||||||||
\(57\) | 6.00000 | + | 8.48528i | 0.794719 | + | 1.12390i | ||||
\(58\) | 0 | 0 | ||||||||
\(59\) | −2.82843 | −0.368230 | −0.184115 | − | 0.982905i | \(-0.558942\pi\) | ||||
−0.184115 | + | 0.982905i | \(0.558942\pi\) | |||||||
\(60\) | 0 | 0 | ||||||||
\(61\) | 2.00000 | 0.256074 | 0.128037 | − | 0.991769i | \(-0.459132\pi\) | ||||
0.128037 | + | 0.991769i | \(0.459132\pi\) | |||||||
\(62\) | 0 | 0 | ||||||||
\(63\) | 5.65685 | + | 2.00000i | 0.712697 | + | 0.251976i | ||||
\(64\) | 0 | 0 | ||||||||
\(65\) | − | 5.65685i | − | 0.701646i | ||||||
\(66\) | 0 | 0 | ||||||||
\(67\) | − | 2.00000i | − | 0.244339i | −0.992509 | − | 0.122169i | \(-0.961015\pi\) | ||
0.992509 | − | 0.122169i | \(-0.0389851\pi\) | |||||||
\(68\) | 0 | 0 | ||||||||
\(69\) | 8.00000 | − | 5.65685i | 0.963087 | − | 0.681005i | ||||
\(70\) | 0 | 0 | ||||||||
\(71\) | −5.65685 | −0.671345 | −0.335673 | − | 0.941979i | \(-0.608964\pi\) | ||||
−0.335673 | + | 0.941979i | \(0.608964\pi\) | |||||||
\(72\) | 0 | 0 | ||||||||
\(73\) | −6.00000 | −0.702247 | −0.351123 | − | 0.936329i | \(-0.614200\pi\) | ||||
−0.351123 | + | 0.936329i | \(0.614200\pi\) | |||||||
\(74\) | 0 | 0 | ||||||||
\(75\) | −4.24264 | + | 3.00000i | −0.489898 | + | 0.346410i | ||||
\(76\) | 0 | 0 | ||||||||
\(77\) | − | 5.65685i | − | 0.644658i | ||||||
\(78\) | 0 | 0 | ||||||||
\(79\) | − | 14.0000i | − | 1.57512i | −0.616236 | − | 0.787562i | \(-0.711343\pi\) | ||
0.616236 | − | 0.787562i | \(-0.288657\pi\) | |||||||
\(80\) | 0 | 0 | ||||||||
\(81\) | −7.00000 | − | 5.65685i | −0.777778 | − | 0.628539i | ||||
\(82\) | 0 | 0 | ||||||||
\(83\) | 2.82843 | 0.310460 | 0.155230 | − | 0.987878i | \(-0.450388\pi\) | ||||
0.155230 | + | 0.987878i | \(0.450388\pi\) | |||||||
\(84\) | 0 | 0 | ||||||||
\(85\) | 0 | 0 | ||||||||
\(86\) | 0 | 0 | ||||||||
\(87\) | 2.82843 | + | 4.00000i | 0.303239 | + | 0.428845i | ||||
\(88\) | 0 | 0 | ||||||||
\(89\) | − | 16.9706i | − | 1.79888i | −0.437048 | − | 0.899438i | \(-0.643976\pi\) | ||
0.437048 | − | 0.899438i | \(-0.356024\pi\) | |||||||
\(90\) | 0 | 0 | ||||||||
\(91\) | 4.00000i | 0.419314i | ||||||||
\(92\) | 0 | 0 | ||||||||
\(93\) | 2.00000 | + | 2.82843i | 0.207390 | + | 0.293294i | ||||
\(94\) | 0 | 0 | ||||||||
\(95\) | 16.9706 | 1.74114 | ||||||||
\(96\) | 0 | 0 | ||||||||
\(97\) | 10.0000 | 1.01535 | 0.507673 | − | 0.861550i | \(-0.330506\pi\) | ||||
0.507673 | + | 0.861550i | \(0.330506\pi\) | |||||||
\(98\) | 0 | 0 | ||||||||
\(99\) | −2.82843 | + | 8.00000i | −0.284268 | + | 0.804030i | ||||
\(100\) | 0 | 0 | ||||||||
\(101\) | − | 2.82843i | − | 0.281439i | −0.990050 | − | 0.140720i | \(-0.955058\pi\) | ||
0.990050 | − | 0.140720i | \(-0.0449416\pi\) | |||||||
\(102\) | 0 | 0 | ||||||||
\(103\) | − | 14.0000i | − | 1.37946i | −0.724066 | − | 0.689730i | \(-0.757729\pi\) | ||
0.724066 | − | 0.689730i | \(-0.242271\pi\) | |||||||
\(104\) | 0 | 0 | ||||||||
\(105\) | 8.00000 | − | 5.65685i | 0.780720 | − | 0.552052i | ||||
\(106\) | 0 | 0 | ||||||||
\(107\) | 8.48528 | 0.820303 | 0.410152 | − | 0.912017i | \(-0.365476\pi\) | ||||
0.410152 | + | 0.912017i | \(0.365476\pi\) | |||||||
\(108\) | 0 | 0 | ||||||||
\(109\) | 18.0000 | 1.72409 | 0.862044 | − | 0.506834i | \(-0.169184\pi\) | ||||
0.862044 | + | 0.506834i | \(0.169184\pi\) | |||||||
\(110\) | 0 | 0 | ||||||||
\(111\) | −8.48528 | + | 6.00000i | −0.805387 | + | 0.569495i | ||||
\(112\) | 0 | 0 | ||||||||
\(113\) | 11.3137i | 1.06430i | 0.846649 | + | 0.532152i | \(0.178617\pi\) | ||||
−0.846649 | + | 0.532152i | \(0.821383\pi\) | |||||||
\(114\) | 0 | 0 | ||||||||
\(115\) | − | 16.0000i | − | 1.49201i | ||||||
\(116\) | 0 | 0 | ||||||||
\(117\) | 2.00000 | − | 5.65685i | 0.184900 | − | 0.522976i | ||||
\(118\) | 0 | 0 | ||||||||
\(119\) | 0 | 0 | ||||||||
\(120\) | 0 | 0 | ||||||||
\(121\) | −3.00000 | −0.272727 | ||||||||
\(122\) | 0 | 0 | ||||||||
\(123\) | 5.65685 | + | 8.00000i | 0.510061 | + | 0.721336i | ||||
\(124\) | 0 | 0 | ||||||||
\(125\) | − | 5.65685i | − | 0.505964i | ||||||
\(126\) | 0 | 0 | ||||||||
\(127\) | 18.0000i | 1.59724i | 0.601834 | + | 0.798621i | \(0.294437\pi\) | ||||
−0.601834 | + | 0.798621i | \(0.705563\pi\) | |||||||
\(128\) | 0 | 0 | ||||||||
\(129\) | −2.00000 | − | 2.82843i | −0.176090 | − | 0.249029i | ||||
\(130\) | 0 | 0 | ||||||||
\(131\) | −19.7990 | −1.72985 | −0.864923 | − | 0.501905i | \(-0.832633\pi\) | ||||
−0.864923 | + | 0.501905i | \(0.832633\pi\) | |||||||
\(132\) | 0 | 0 | ||||||||
\(133\) | −12.0000 | −1.04053 | ||||||||
\(134\) | 0 | 0 | ||||||||
\(135\) | −14.1421 | + | 4.00000i | −1.21716 | + | 0.344265i | ||||
\(136\) | 0 | 0 | ||||||||
\(137\) | 5.65685i | 0.483298i | 0.970364 | + | 0.241649i | \(0.0776882\pi\) | ||||
−0.970364 | + | 0.241649i | \(0.922312\pi\) | |||||||
\(138\) | 0 | 0 | ||||||||
\(139\) | − | 10.0000i | − | 0.848189i | −0.905618 | − | 0.424094i | \(-0.860592\pi\) | ||
0.905618 | − | 0.424094i | \(-0.139408\pi\) | |||||||
\(140\) | 0 | 0 | ||||||||
\(141\) | −16.0000 | + | 11.3137i | −1.34744 | + | 0.952786i | ||||
\(142\) | 0 | 0 | ||||||||
\(143\) | −5.65685 | −0.473050 | ||||||||
\(144\) | 0 | 0 | ||||||||
\(145\) | 8.00000 | 0.664364 | ||||||||
\(146\) | 0 | 0 | ||||||||
\(147\) | 4.24264 | − | 3.00000i | 0.349927 | − | 0.247436i | ||||
\(148\) | 0 | 0 | ||||||||
\(149\) | − | 14.1421i | − | 1.15857i | −0.815125 | − | 0.579284i | \(-0.803332\pi\) | ||
0.815125 | − | 0.579284i | \(-0.196668\pi\) | |||||||
\(150\) | 0 | 0 | ||||||||
\(151\) | − | 14.0000i | − | 1.13930i | −0.821886 | − | 0.569652i | \(-0.807078\pi\) | ||
0.821886 | − | 0.569652i | \(-0.192922\pi\) | |||||||
\(152\) | 0 | 0 | ||||||||
\(153\) | 0 | 0 | ||||||||
\(154\) | 0 | 0 | ||||||||
\(155\) | 5.65685 | 0.454369 | ||||||||
\(156\) | 0 | 0 | ||||||||
\(157\) | −14.0000 | −1.11732 | −0.558661 | − | 0.829396i | \(-0.688685\pi\) | ||||
−0.558661 | + | 0.829396i | \(0.688685\pi\) | |||||||
\(158\) | 0 | 0 | ||||||||
\(159\) | 8.48528 | + | 12.0000i | 0.672927 | + | 0.951662i | ||||
\(160\) | 0 | 0 | ||||||||
\(161\) | 11.3137i | 0.891645i | ||||||||
\(162\) | 0 | 0 | ||||||||
\(163\) | 6.00000i | 0.469956i | 0.972001 | + | 0.234978i | \(0.0755019\pi\) | ||||
−0.972001 | + | 0.234978i | \(0.924498\pi\) | |||||||
\(164\) | 0 | 0 | ||||||||
\(165\) | 8.00000 | + | 11.3137i | 0.622799 | + | 0.880771i | ||||
\(166\) | 0 | 0 | ||||||||
\(167\) | −5.65685 | −0.437741 | −0.218870 | − | 0.975754i | \(-0.570237\pi\) | ||||
−0.218870 | + | 0.975754i | \(0.570237\pi\) | |||||||
\(168\) | 0 | 0 | ||||||||
\(169\) | −9.00000 | −0.692308 | ||||||||
\(170\) | 0 | 0 | ||||||||
\(171\) | 16.9706 | + | 6.00000i | 1.29777 | + | 0.458831i | ||||
\(172\) | 0 | 0 | ||||||||
\(173\) | 14.1421i | 1.07521i | 0.843198 | + | 0.537603i | \(0.180670\pi\) | ||||
−0.843198 | + | 0.537603i | \(0.819330\pi\) | |||||||
\(174\) | 0 | 0 | ||||||||
\(175\) | − | 6.00000i | − | 0.453557i | ||||||
\(176\) | 0 | 0 | ||||||||
\(177\) | −4.00000 | + | 2.82843i | −0.300658 | + | 0.212598i | ||||
\(178\) | 0 | 0 | ||||||||
\(179\) | −8.48528 | −0.634220 | −0.317110 | − | 0.948389i | \(-0.602712\pi\) | ||||
−0.317110 | + | 0.948389i | \(0.602712\pi\) | |||||||
\(180\) | 0 | 0 | ||||||||
\(181\) | −6.00000 | −0.445976 | −0.222988 | − | 0.974821i | \(-0.571581\pi\) | ||||
−0.222988 | + | 0.974821i | \(0.571581\pi\) | |||||||
\(182\) | 0 | 0 | ||||||||
\(183\) | 2.82843 | − | 2.00000i | 0.209083 | − | 0.147844i | ||||
\(184\) | 0 | 0 | ||||||||
\(185\) | 16.9706i | 1.24770i | ||||||||
\(186\) | 0 | 0 | ||||||||
\(187\) | 0 | 0 | ||||||||
\(188\) | 0 | 0 | ||||||||
\(189\) | 10.0000 | − | 2.82843i | 0.727393 | − | 0.205738i | ||||
\(190\) | 0 | 0 | ||||||||
\(191\) | 22.6274 | 1.63726 | 0.818631 | − | 0.574320i | \(-0.194733\pi\) | ||||
0.818631 | + | 0.574320i | \(0.194733\pi\) | |||||||
\(192\) | 0 | 0 | ||||||||
\(193\) | −14.0000 | −1.00774 | −0.503871 | − | 0.863779i | \(-0.668091\pi\) | ||||
−0.503871 | + | 0.863779i | \(0.668091\pi\) | |||||||
\(194\) | 0 | 0 | ||||||||
\(195\) | −5.65685 | − | 8.00000i | −0.405096 | − | 0.572892i | ||||
\(196\) | 0 | 0 | ||||||||
\(197\) | 19.7990i | 1.41062i | 0.708899 | + | 0.705310i | \(0.249192\pi\) | ||||
−0.708899 | + | 0.705310i | \(0.750808\pi\) | |||||||
\(198\) | 0 | 0 | ||||||||
\(199\) | 2.00000i | 0.141776i | 0.997484 | + | 0.0708881i | \(0.0225833\pi\) | ||||
−0.997484 | + | 0.0708881i | \(0.977417\pi\) | |||||||
\(200\) | 0 | 0 | ||||||||
\(201\) | −2.00000 | − | 2.82843i | −0.141069 | − | 0.199502i | ||||
\(202\) | 0 | 0 | ||||||||
\(203\) | −5.65685 | −0.397033 | ||||||||
\(204\) | 0 | 0 | ||||||||
\(205\) | 16.0000 | 1.11749 | ||||||||
\(206\) | 0 | 0 | ||||||||
\(207\) | 5.65685 | − | 16.0000i | 0.393179 | − | 1.11208i | ||||
\(208\) | 0 | 0 | ||||||||
\(209\) | − | 16.9706i | − | 1.17388i | ||||||
\(210\) | 0 | 0 | ||||||||
\(211\) | − | 2.00000i | − | 0.137686i | −0.997628 | − | 0.0688428i | \(-0.978069\pi\) | ||
0.997628 | − | 0.0688428i | \(-0.0219307\pi\) | |||||||
\(212\) | 0 | 0 | ||||||||
\(213\) | −8.00000 | + | 5.65685i | −0.548151 | + | 0.387601i | ||||
\(214\) | 0 | 0 | ||||||||
\(215\) | −5.65685 | −0.385794 | ||||||||
\(216\) | 0 | 0 | ||||||||
\(217\) | −4.00000 | −0.271538 | ||||||||
\(218\) | 0 | 0 | ||||||||
\(219\) | −8.48528 | + | 6.00000i | −0.573382 | + | 0.405442i | ||||
\(220\) | 0 | 0 | ||||||||
\(221\) | 0 | 0 | ||||||||
\(222\) | 0 | 0 | ||||||||
\(223\) | 2.00000i | 0.133930i | 0.997755 | + | 0.0669650i | \(0.0213316\pi\) | ||||
−0.997755 | + | 0.0669650i | \(0.978668\pi\) | |||||||
\(224\) | 0 | 0 | ||||||||
\(225\) | −3.00000 | + | 8.48528i | −0.200000 | + | 0.565685i | ||||
\(226\) | 0 | 0 | ||||||||
\(227\) | 14.1421 | 0.938647 | 0.469323 | − | 0.883026i | \(-0.344498\pi\) | ||||
0.469323 | + | 0.883026i | \(0.344498\pi\) | |||||||
\(228\) | 0 | 0 | ||||||||
\(229\) | 10.0000 | 0.660819 | 0.330409 | − | 0.943838i | \(-0.392813\pi\) | ||||
0.330409 | + | 0.943838i | \(0.392813\pi\) | |||||||
\(230\) | 0 | 0 | ||||||||
\(231\) | −5.65685 | − | 8.00000i | −0.372194 | − | 0.526361i | ||||
\(232\) | 0 | 0 | ||||||||
\(233\) | − | 5.65685i | − | 0.370593i | −0.982683 | − | 0.185296i | \(-0.940675\pi\) | ||
0.982683 | − | 0.185296i | \(-0.0593245\pi\) | |||||||
\(234\) | 0 | 0 | ||||||||
\(235\) | 32.0000i | 2.08745i | ||||||||
\(236\) | 0 | 0 | ||||||||
\(237\) | −14.0000 | − | 19.7990i | −0.909398 | − | 1.28608i | ||||
\(238\) | 0 | 0 | ||||||||
\(239\) | −11.3137 | −0.731823 | −0.365911 | − | 0.930650i | \(-0.619243\pi\) | ||||
−0.365911 | + | 0.930650i | \(0.619243\pi\) | |||||||
\(240\) | 0 | 0 | ||||||||
\(241\) | 2.00000 | 0.128831 | 0.0644157 | − | 0.997923i | \(-0.479482\pi\) | ||||
0.0644157 | + | 0.997923i | \(0.479482\pi\) | |||||||
\(242\) | 0 | 0 | ||||||||
\(243\) | −15.5563 | − | 1.00000i | −0.997940 | − | 0.0641500i | ||||
\(244\) | 0 | 0 | ||||||||
\(245\) | − | 8.48528i | − | 0.542105i | ||||||
\(246\) | 0 | 0 | ||||||||
\(247\) | 12.0000i | 0.763542i | ||||||||
\(248\) | 0 | 0 | ||||||||
\(249\) | 4.00000 | − | 2.82843i | 0.253490 | − | 0.179244i | ||||
\(250\) | 0 | 0 | ||||||||
\(251\) | 8.48528 | 0.535586 | 0.267793 | − | 0.963476i | \(-0.413706\pi\) | ||||
0.267793 | + | 0.963476i | \(0.413706\pi\) | |||||||
\(252\) | 0 | 0 | ||||||||
\(253\) | −16.0000 | −1.00591 | ||||||||
\(254\) | 0 | 0 | ||||||||
\(255\) | 0 | 0 | ||||||||
\(256\) | 0 | 0 | ||||||||
\(257\) | − | 22.6274i | − | 1.41146i | −0.708481 | − | 0.705730i | \(-0.750619\pi\) | ||
0.708481 | − | 0.705730i | \(-0.249381\pi\) | |||||||
\(258\) | 0 | 0 | ||||||||
\(259\) | − | 12.0000i | − | 0.745644i | ||||||
\(260\) | 0 | 0 | ||||||||
\(261\) | 8.00000 | + | 2.82843i | 0.495188 | + | 0.175075i | ||||
\(262\) | 0 | 0 | ||||||||
\(263\) | −5.65685 | −0.348817 | −0.174408 | − | 0.984673i | \(-0.555801\pi\) | ||||
−0.174408 | + | 0.984673i | \(0.555801\pi\) | |||||||
\(264\) | 0 | 0 | ||||||||
\(265\) | 24.0000 | 1.47431 | ||||||||
\(266\) | 0 | 0 | ||||||||
\(267\) | −16.9706 | − | 24.0000i | −1.03858 | − | 1.46878i | ||||
\(268\) | 0 | 0 | ||||||||
\(269\) | − | 8.48528i | − | 0.517357i | −0.965964 | − | 0.258678i | \(-0.916713\pi\) | ||
0.965964 | − | 0.258678i | \(-0.0832870\pi\) | |||||||
\(270\) | 0 | 0 | ||||||||
\(271\) | 18.0000i | 1.09342i | 0.837321 | + | 0.546711i | \(0.184120\pi\) | ||||
−0.837321 | + | 0.546711i | \(0.815880\pi\) | |||||||
\(272\) | 0 | 0 | ||||||||
\(273\) | 4.00000 | + | 5.65685i | 0.242091 | + | 0.342368i | ||||
\(274\) | 0 | 0 | ||||||||
\(275\) | 8.48528 | 0.511682 | ||||||||
\(276\) | 0 | 0 | ||||||||
\(277\) | 10.0000 | 0.600842 | 0.300421 | − | 0.953807i | \(-0.402873\pi\) | ||||
0.300421 | + | 0.953807i | \(0.402873\pi\) | |||||||
\(278\) | 0 | 0 | ||||||||
\(279\) | 5.65685 | + | 2.00000i | 0.338667 | + | 0.119737i | ||||
\(280\) | 0 | 0 | ||||||||
\(281\) | 5.65685i | 0.337460i | 0.985662 | + | 0.168730i | \(0.0539665\pi\) | ||||
−0.985662 | + | 0.168730i | \(0.946033\pi\) | |||||||
\(282\) | 0 | 0 | ||||||||
\(283\) | − | 10.0000i | − | 0.594438i | −0.954809 | − | 0.297219i | \(-0.903941\pi\) | ||
0.954809 | − | 0.297219i | \(-0.0960592\pi\) | |||||||
\(284\) | 0 | 0 | ||||||||
\(285\) | 24.0000 | − | 16.9706i | 1.42164 | − | 1.00525i | ||||
\(286\) | 0 | 0 | ||||||||
\(287\) | −11.3137 | −0.667827 | ||||||||
\(288\) | 0 | 0 | ||||||||
\(289\) | 17.0000 | 1.00000 | ||||||||
\(290\) | 0 | 0 | ||||||||
\(291\) | 14.1421 | − | 10.0000i | 0.829027 | − | 0.586210i | ||||
\(292\) | 0 | 0 | ||||||||
\(293\) | − | 2.82843i | − | 0.165238i | −0.996581 | − | 0.0826192i | \(-0.973671\pi\) | ||
0.996581 | − | 0.0826192i | \(-0.0263285\pi\) | |||||||
\(294\) | 0 | 0 | ||||||||
\(295\) | 8.00000i | 0.465778i | ||||||||
\(296\) | 0 | 0 | ||||||||
\(297\) | 4.00000 | + | 14.1421i | 0.232104 | + | 0.820610i | ||||
\(298\) | 0 | 0 | ||||||||
\(299\) | 11.3137 | 0.654289 | ||||||||
\(300\) | 0 | 0 | ||||||||
\(301\) | 4.00000 | 0.230556 | ||||||||
\(302\) | 0 | 0 | ||||||||
\(303\) | −2.82843 | − | 4.00000i | −0.162489 | − | 0.229794i | ||||
\(304\) | 0 | 0 | ||||||||
\(305\) | − | 5.65685i | − | 0.323911i | ||||||
\(306\) | 0 | 0 | ||||||||
\(307\) | 30.0000i | 1.71219i | 0.516818 | + | 0.856095i | \(0.327116\pi\) | ||||
−0.516818 | + | 0.856095i | \(0.672884\pi\) | |||||||
\(308\) | 0 | 0 | ||||||||
\(309\) | −14.0000 | − | 19.7990i | −0.796432 | − | 1.12633i | ||||
\(310\) | 0 | 0 | ||||||||
\(311\) | 5.65685 | 0.320771 | 0.160385 | − | 0.987054i | \(-0.448726\pi\) | ||||
0.160385 | + | 0.987054i | \(0.448726\pi\) | |||||||
\(312\) | 0 | 0 | ||||||||
\(313\) | 2.00000 | 0.113047 | 0.0565233 | − | 0.998401i | \(-0.481998\pi\) | ||||
0.0565233 | + | 0.998401i | \(0.481998\pi\) | |||||||
\(314\) | 0 | 0 | ||||||||
\(315\) | 5.65685 | − | 16.0000i | 0.318728 | − | 0.901498i | ||||
\(316\) | 0 | 0 | ||||||||
\(317\) | 2.82843i | 0.158860i | 0.996840 | + | 0.0794301i | \(0.0253101\pi\) | ||||
−0.996840 | + | 0.0794301i | \(0.974690\pi\) | |||||||
\(318\) | 0 | 0 | ||||||||
\(319\) | − | 8.00000i | − | 0.447914i | ||||||
\(320\) | 0 | 0 | ||||||||
\(321\) | 12.0000 | − | 8.48528i | 0.669775 | − | 0.473602i | ||||
\(322\) | 0 | 0 | ||||||||
\(323\) | 0 | 0 | ||||||||
\(324\) | 0 | 0 | ||||||||
\(325\) | −6.00000 | −0.332820 | ||||||||
\(326\) | 0 | 0 | ||||||||
\(327\) | 25.4558 | − | 18.0000i | 1.40771 | − | 0.995402i | ||||
\(328\) | 0 | 0 | ||||||||
\(329\) | − | 22.6274i | − | 1.24749i | ||||||
\(330\) | 0 | 0 | ||||||||
\(331\) | − | 10.0000i | − | 0.549650i | −0.961494 | − | 0.274825i | \(-0.911380\pi\) | ||
0.961494 | − | 0.274825i | \(-0.0886199\pi\) | |||||||
\(332\) | 0 | 0 | ||||||||
\(333\) | −6.00000 | + | 16.9706i | −0.328798 | + | 0.929981i | ||||
\(334\) | 0 | 0 | ||||||||
\(335\) | −5.65685 | −0.309067 | ||||||||
\(336\) | 0 | 0 | ||||||||
\(337\) | −22.0000 | −1.19842 | −0.599208 | − | 0.800593i | \(-0.704518\pi\) | ||||
−0.599208 | + | 0.800593i | \(0.704518\pi\) | |||||||
\(338\) | 0 | 0 | ||||||||
\(339\) | 11.3137 | + | 16.0000i | 0.614476 | + | 0.869001i | ||||
\(340\) | 0 | 0 | ||||||||
\(341\) | − | 5.65685i | − | 0.306336i | ||||||
\(342\) | 0 | 0 | ||||||||
\(343\) | 20.0000i | 1.07990i | ||||||||
\(344\) | 0 | 0 | ||||||||
\(345\) | −16.0000 | − | 22.6274i | −0.861411 | − | 1.21822i | ||||
\(346\) | 0 | 0 | ||||||||
\(347\) | −14.1421 | −0.759190 | −0.379595 | − | 0.925153i | \(-0.623937\pi\) | ||||
−0.379595 | + | 0.925153i | \(0.623937\pi\) | |||||||
\(348\) | 0 | 0 | ||||||||
\(349\) | −14.0000 | −0.749403 | −0.374701 | − | 0.927146i | \(-0.622255\pi\) | ||||
−0.374701 | + | 0.927146i | \(0.622255\pi\) | |||||||
\(350\) | 0 | 0 | ||||||||
\(351\) | −2.82843 | − | 10.0000i | −0.150970 | − | 0.533761i | ||||
\(352\) | 0 | 0 | ||||||||
\(353\) | 22.6274i | 1.20434i | 0.798369 | + | 0.602168i | \(0.205696\pi\) | ||||
−0.798369 | + | 0.602168i | \(0.794304\pi\) | |||||||
\(354\) | 0 | 0 | ||||||||
\(355\) | 16.0000i | 0.849192i | ||||||||
\(356\) | 0 | 0 | ||||||||
\(357\) | 0 | 0 | ||||||||
\(358\) | 0 | 0 | ||||||||
\(359\) | 16.9706 | 0.895672 | 0.447836 | − | 0.894116i | \(-0.352195\pi\) | ||||
0.447836 | + | 0.894116i | \(0.352195\pi\) | |||||||
\(360\) | 0 | 0 | ||||||||
\(361\) | −17.0000 | −0.894737 | ||||||||
\(362\) | 0 | 0 | ||||||||
\(363\) | −4.24264 | + | 3.00000i | −0.222681 | + | 0.157459i | ||||
\(364\) | 0 | 0 | ||||||||
\(365\) | 16.9706i | 0.888280i | ||||||||
\(366\) | 0 | 0 | ||||||||
\(367\) | − | 14.0000i | − | 0.730794i | −0.930852 | − | 0.365397i | \(-0.880933\pi\) | ||
0.930852 | − | 0.365397i | \(-0.119067\pi\) | |||||||
\(368\) | 0 | 0 | ||||||||
\(369\) | 16.0000 | + | 5.65685i | 0.832927 | + | 0.294484i | ||||
\(370\) | 0 | 0 | ||||||||
\(371\) | −16.9706 | −0.881068 | ||||||||
\(372\) | 0 | 0 | ||||||||
\(373\) | 26.0000 | 1.34623 | 0.673114 | − | 0.739538i | \(-0.264956\pi\) | ||||
0.673114 | + | 0.739538i | \(0.264956\pi\) | |||||||
\(374\) | 0 | 0 | ||||||||
\(375\) | −5.65685 | − | 8.00000i | −0.292119 | − | 0.413118i | ||||
\(376\) | 0 | 0 | ||||||||
\(377\) | 5.65685i | 0.291343i | ||||||||
\(378\) | 0 | 0 | ||||||||
\(379\) | − | 2.00000i | − | 0.102733i | −0.998680 | − | 0.0513665i | \(-0.983642\pi\) | ||
0.998680 | − | 0.0513665i | \(-0.0163577\pi\) | |||||||
\(380\) | 0 | 0 | ||||||||
\(381\) | 18.0000 | + | 25.4558i | 0.922168 | + | 1.30414i | ||||
\(382\) | 0 | 0 | ||||||||
\(383\) | −22.6274 | −1.15621 | −0.578103 | − | 0.815963i | \(-0.696207\pi\) | ||||
−0.578103 | + | 0.815963i | \(0.696207\pi\) | |||||||
\(384\) | 0 | 0 | ||||||||
\(385\) | −16.0000 | −0.815436 | ||||||||
\(386\) | 0 | 0 | ||||||||
\(387\) | −5.65685 | − | 2.00000i | −0.287554 | − | 0.101666i | ||||
\(388\) | 0 | 0 | ||||||||
\(389\) | − | 2.82843i | − | 0.143407i | −0.997426 | − | 0.0717035i | \(-0.977156\pi\) | ||
0.997426 | − | 0.0717035i | \(-0.0228435\pi\) | |||||||
\(390\) | 0 | 0 | ||||||||
\(391\) | 0 | 0 | ||||||||
\(392\) | 0 | 0 | ||||||||
\(393\) | −28.0000 | + | 19.7990i | −1.41241 | + | 0.998727i | ||||
\(394\) | 0 | 0 | ||||||||
\(395\) | −39.5980 | −1.99239 | ||||||||
\(396\) | 0 | 0 | ||||||||
\(397\) | 18.0000 | 0.903394 | 0.451697 | − | 0.892171i | \(-0.350819\pi\) | ||||
0.451697 | + | 0.892171i | \(0.350819\pi\) | |||||||
\(398\) | 0 | 0 | ||||||||
\(399\) | −16.9706 | + | 12.0000i | −0.849591 | + | 0.600751i | ||||
\(400\) | 0 | 0 | ||||||||
\(401\) | 22.6274i | 1.12996i | 0.825105 | + | 0.564980i | \(0.191116\pi\) | ||||
−0.825105 | + | 0.564980i | \(0.808884\pi\) | |||||||
\(402\) | 0 | 0 | ||||||||
\(403\) | 4.00000i | 0.199254i | ||||||||
\(404\) | 0 | 0 | ||||||||
\(405\) | −16.0000 | + | 19.7990i | −0.795046 | + | 0.983820i | ||||
\(406\) | 0 | 0 | ||||||||
\(407\) | 16.9706 | 0.841200 | ||||||||
\(408\) | 0 | 0 | ||||||||
\(409\) | 26.0000 | 1.28562 | 0.642809 | − | 0.766027i | \(-0.277769\pi\) | ||||
0.642809 | + | 0.766027i | \(0.277769\pi\) | |||||||
\(410\) | 0 | 0 | ||||||||
\(411\) | 5.65685 | + | 8.00000i | 0.279032 | + | 0.394611i | ||||
\(412\) | 0 | 0 | ||||||||
\(413\) | − | 5.65685i | − | 0.278356i | ||||||
\(414\) | 0 | 0 | ||||||||
\(415\) | − | 8.00000i | − | 0.392705i | ||||||
\(416\) | 0 | 0 | ||||||||
\(417\) | −10.0000 | − | 14.1421i | −0.489702 | − | 0.692543i | ||||
\(418\) | 0 | 0 | ||||||||
\(419\) | 36.7696 | 1.79631 | 0.898155 | − | 0.439679i | \(-0.144908\pi\) | ||||
0.898155 | + | 0.439679i | \(0.144908\pi\) | |||||||
\(420\) | 0 | 0 | ||||||||
\(421\) | −22.0000 | −1.07221 | −0.536107 | − | 0.844150i | \(-0.680106\pi\) | ||||
−0.536107 | + | 0.844150i | \(0.680106\pi\) | |||||||
\(422\) | 0 | 0 | ||||||||
\(423\) | −11.3137 | + | 32.0000i | −0.550091 | + | 1.55589i | ||||
\(424\) | 0 | 0 | ||||||||
\(425\) | 0 | 0 | ||||||||
\(426\) | 0 | 0 | ||||||||
\(427\) | 4.00000i | 0.193574i | ||||||||
\(428\) | 0 | 0 | ||||||||
\(429\) | −8.00000 | + | 5.65685i | −0.386244 | + | 0.273115i | ||||
\(430\) | 0 | 0 | ||||||||
\(431\) | 33.9411 | 1.63489 | 0.817443 | − | 0.576009i | \(-0.195391\pi\) | ||||
0.817443 | + | 0.576009i | \(0.195391\pi\) | |||||||
\(432\) | 0 | 0 | ||||||||
\(433\) | −6.00000 | −0.288342 | −0.144171 | − | 0.989553i | \(-0.546051\pi\) | ||||
−0.144171 | + | 0.989553i | \(0.546051\pi\) | |||||||
\(434\) | 0 | 0 | ||||||||
\(435\) | 11.3137 | − | 8.00000i | 0.542451 | − | 0.383571i | ||||
\(436\) | 0 | 0 | ||||||||
\(437\) | 33.9411i | 1.62362i | ||||||||
\(438\) | 0 | 0 | ||||||||
\(439\) | − | 14.0000i | − | 0.668184i | −0.942541 | − | 0.334092i | \(-0.891570\pi\) | ||
0.942541 | − | 0.334092i | \(-0.108430\pi\) | |||||||
\(440\) | 0 | 0 | ||||||||
\(441\) | 3.00000 | − | 8.48528i | 0.142857 | − | 0.404061i | ||||
\(442\) | 0 | 0 | ||||||||
\(443\) | −14.1421 | −0.671913 | −0.335957 | − | 0.941877i | \(-0.609060\pi\) | ||||
−0.335957 | + | 0.941877i | \(0.609060\pi\) | |||||||
\(444\) | 0 | 0 | ||||||||
\(445\) | −48.0000 | −2.27542 | ||||||||
\(446\) | 0 | 0 | ||||||||
\(447\) | −14.1421 | − | 20.0000i | −0.668900 | − | 0.945968i | ||||
\(448\) | 0 | 0 | ||||||||
\(449\) | 33.9411i | 1.60178i | 0.598811 | + | 0.800890i | \(0.295640\pi\) | ||||
−0.598811 | + | 0.800890i | \(0.704360\pi\) | |||||||
\(450\) | 0 | 0 | ||||||||
\(451\) | − | 16.0000i | − | 0.753411i | ||||||
\(452\) | 0 | 0 | ||||||||
\(453\) | −14.0000 | − | 19.7990i | −0.657777 | − | 0.930238i | ||||
\(454\) | 0 | 0 | ||||||||
\(455\) | 11.3137 | 0.530395 | ||||||||
\(456\) | 0 | 0 | ||||||||
\(457\) | 10.0000 | 0.467780 | 0.233890 | − | 0.972263i | \(-0.424854\pi\) | ||||
0.233890 | + | 0.972263i | \(0.424854\pi\) | |||||||
\(458\) | 0 | 0 | ||||||||
\(459\) | 0 | 0 | ||||||||
\(460\) | 0 | 0 | ||||||||
\(461\) | − | 31.1127i | − | 1.44906i | −0.689242 | − | 0.724531i | \(-0.742056\pi\) | ||
0.689242 | − | 0.724531i | \(-0.257944\pi\) | |||||||
\(462\) | 0 | 0 | ||||||||
\(463\) | 2.00000i | 0.0929479i | 0.998920 | + | 0.0464739i | \(0.0147984\pi\) | ||||
−0.998920 | + | 0.0464739i | \(0.985202\pi\) | |||||||
\(464\) | 0 | 0 | ||||||||
\(465\) | 8.00000 | − | 5.65685i | 0.370991 | − | 0.262330i | ||||
\(466\) | 0 | 0 | ||||||||
\(467\) | 25.4558 | 1.17796 | 0.588978 | − | 0.808149i | \(-0.299530\pi\) | ||||
0.588978 | + | 0.808149i | \(0.299530\pi\) | |||||||
\(468\) | 0 | 0 | ||||||||
\(469\) | 4.00000 | 0.184703 | ||||||||
\(470\) | 0 | 0 | ||||||||
\(471\) | −19.7990 | + | 14.0000i | −0.912289 | + | 0.645086i | ||||
\(472\) | 0 | 0 | ||||||||
\(473\) | 5.65685i | 0.260102i | ||||||||
\(474\) | 0 | 0 | ||||||||
\(475\) | − | 18.0000i | − | 0.825897i | ||||||
\(476\) | 0 | 0 | ||||||||
\(477\) | 24.0000 | + | 8.48528i | 1.09888 | + | 0.388514i | ||||
\(478\) | 0 | 0 | ||||||||
\(479\) | −22.6274 | −1.03387 | −0.516937 | − | 0.856024i | \(-0.672928\pi\) | ||||
−0.516937 | + | 0.856024i | \(0.672928\pi\) | |||||||
\(480\) | 0 | 0 | ||||||||
\(481\) | −12.0000 | −0.547153 | ||||||||
\(482\) | 0 | 0 | ||||||||
\(483\) | 11.3137 | + | 16.0000i | 0.514792 | + | 0.728025i | ||||
\(484\) | 0 | 0 | ||||||||
\(485\) | − | 28.2843i | − | 1.28432i | ||||||
\(486\) | 0 | 0 | ||||||||
\(487\) | 18.0000i | 0.815658i | 0.913058 | + | 0.407829i | \(0.133714\pi\) | ||||
−0.913058 | + | 0.407829i | \(0.866286\pi\) | |||||||
\(488\) | 0 | 0 | ||||||||
\(489\) | 6.00000 | + | 8.48528i | 0.271329 | + | 0.383718i | ||||
\(490\) | 0 | 0 | ||||||||
\(491\) | 31.1127 | 1.40410 | 0.702048 | − | 0.712129i | \(-0.252269\pi\) | ||||
0.702048 | + | 0.712129i | \(0.252269\pi\) | |||||||
\(492\) | 0 | 0 | ||||||||
\(493\) | 0 | 0 | ||||||||
\(494\) | 0 | 0 | ||||||||
\(495\) | 22.6274 | + | 8.00000i | 1.01703 | + | 0.359573i | ||||
\(496\) | 0 | 0 | ||||||||
\(497\) | − | 11.3137i | − | 0.507489i | ||||||
\(498\) | 0 | 0 | ||||||||
\(499\) | − | 34.0000i | − | 1.52205i | −0.648723 | − | 0.761025i | \(-0.724697\pi\) | ||
0.648723 | − | 0.761025i | \(-0.275303\pi\) | |||||||
\(500\) | 0 | 0 | ||||||||
\(501\) | −8.00000 | + | 5.65685i | −0.357414 | + | 0.252730i | ||||
\(502\) | 0 | 0 | ||||||||
\(503\) | 5.65685 | 0.252227 | 0.126113 | − | 0.992016i | \(-0.459750\pi\) | ||||
0.126113 | + | 0.992016i | \(0.459750\pi\) | |||||||
\(504\) | 0 | 0 | ||||||||
\(505\) | −8.00000 | −0.355995 | ||||||||
\(506\) | 0 | 0 | ||||||||
\(507\) | −12.7279 | + | 9.00000i | −0.565267 | + | 0.399704i | ||||
\(508\) | 0 | 0 | ||||||||
\(509\) | 2.82843i | 0.125368i | 0.998033 | + | 0.0626839i | \(0.0199660\pi\) | ||||
−0.998033 | + | 0.0626839i | \(0.980034\pi\) | |||||||
\(510\) | 0 | 0 | ||||||||
\(511\) | − | 12.0000i | − | 0.530849i | ||||||
\(512\) | 0 | 0 | ||||||||
\(513\) | 30.0000 | − | 8.48528i | 1.32453 | − | 0.374634i | ||||
\(514\) | 0 | 0 | ||||||||
\(515\) | −39.5980 | −1.74490 | ||||||||
\(516\) | 0 | 0 | ||||||||
\(517\) | 32.0000 | 1.40736 | ||||||||
\(518\) | 0 | 0 | ||||||||
\(519\) | 14.1421 | + | 20.0000i | 0.620771 | + | 0.877903i | ||||
\(520\) | 0 | 0 | ||||||||
\(521\) | 5.65685i | 0.247831i | 0.992293 | + | 0.123916i | \(0.0395452\pi\) | ||||
−0.992293 | + | 0.123916i | \(0.960455\pi\) | |||||||
\(522\) | 0 | 0 | ||||||||
\(523\) | − | 34.0000i | − | 1.48672i | −0.668894 | − | 0.743358i | \(-0.733232\pi\) | ||
0.668894 | − | 0.743358i | \(-0.266768\pi\) | |||||||
\(524\) | 0 | 0 | ||||||||
\(525\) | −6.00000 | − | 8.48528i | −0.261861 | − | 0.370328i | ||||
\(526\) | 0 | 0 | ||||||||
\(527\) | 0 | 0 | ||||||||
\(528\) | 0 | 0 | ||||||||
\(529\) | 9.00000 | 0.391304 | ||||||||
\(530\) | 0 | 0 | ||||||||
\(531\) | −2.82843 | + | 8.00000i | −0.122743 | + | 0.347170i | ||||
\(532\) | 0 | 0 | ||||||||
\(533\) | 11.3137i | 0.490051i | ||||||||
\(534\) | 0 | 0 | ||||||||
\(535\) | − | 24.0000i | − | 1.03761i | ||||||
\(536\) | 0 | 0 | ||||||||
\(537\) | −12.0000 | + | 8.48528i | −0.517838 | + | 0.366167i | ||||
\(538\) | 0 | 0 | ||||||||
\(539\) | −8.48528 | −0.365487 | ||||||||
\(540\) | 0 | 0 | ||||||||
\(541\) | 2.00000 | 0.0859867 | 0.0429934 | − | 0.999075i | \(-0.486311\pi\) | ||||
0.0429934 | + | 0.999075i | \(0.486311\pi\) | |||||||
\(542\) | 0 | 0 | ||||||||
\(543\) | −8.48528 | + | 6.00000i | −0.364138 | + | 0.257485i | ||||
\(544\) | 0 | 0 | ||||||||
\(545\) | − | 50.9117i | − | 2.18082i | ||||||
\(546\) | 0 | 0 | ||||||||
\(547\) | 38.0000i | 1.62476i | 0.583127 | + | 0.812381i | \(0.301829\pi\) | ||||
−0.583127 | + | 0.812381i | \(0.698171\pi\) | |||||||
\(548\) | 0 | 0 | ||||||||
\(549\) | 2.00000 | − | 5.65685i | 0.0853579 | − | 0.241429i | ||||
\(550\) | 0 | 0 | ||||||||
\(551\) | −16.9706 | −0.722970 | ||||||||
\(552\) | 0 | 0 | ||||||||
\(553\) | 28.0000 | 1.19068 | ||||||||
\(554\) | 0 | 0 | ||||||||
\(555\) | 16.9706 | + | 24.0000i | 0.720360 | + | 1.01874i | ||||
\(556\) | 0 | 0 | ||||||||
\(557\) | − | 8.48528i | − | 0.359533i | −0.983709 | − | 0.179766i | \(-0.942466\pi\) | ||
0.983709 | − | 0.179766i | \(-0.0575342\pi\) | |||||||
\(558\) | 0 | 0 | ||||||||
\(559\) | − | 4.00000i | − | 0.169182i | ||||||
\(560\) | 0 | 0 | ||||||||
\(561\) | 0 | 0 | ||||||||
\(562\) | 0 | 0 | ||||||||
\(563\) | 2.82843 | 0.119204 | 0.0596020 | − | 0.998222i | \(-0.481017\pi\) | ||||
0.0596020 | + | 0.998222i | \(0.481017\pi\) | |||||||
\(564\) | 0 | 0 | ||||||||
\(565\) | 32.0000 | 1.34625 | ||||||||
\(566\) | 0 | 0 | ||||||||
\(567\) | 11.3137 | − | 14.0000i | 0.475131 | − | 0.587945i | ||||
\(568\) | 0 | 0 | ||||||||
\(569\) | − | 5.65685i | − | 0.237148i | −0.992945 | − | 0.118574i | \(-0.962168\pi\) | ||
0.992945 | − | 0.118574i | \(-0.0378322\pi\) | |||||||
\(570\) | 0 | 0 | ||||||||
\(571\) | 22.0000i | 0.920671i | 0.887745 | + | 0.460336i | \(0.152271\pi\) | ||||
−0.887745 | + | 0.460336i | \(0.847729\pi\) | |||||||
\(572\) | 0 | 0 | ||||||||
\(573\) | 32.0000 | − | 22.6274i | 1.33682 | − | 0.945274i | ||||
\(574\) | 0 | 0 | ||||||||
\(575\) | −16.9706 | −0.707721 | ||||||||
\(576\) | 0 | 0 | ||||||||
\(577\) | −6.00000 | −0.249783 | −0.124892 | − | 0.992170i | \(-0.539858\pi\) | ||||
−0.124892 | + | 0.992170i | \(0.539858\pi\) | |||||||
\(578\) | 0 | 0 | ||||||||
\(579\) | −19.7990 | + | 14.0000i | −0.822818 | + | 0.581820i | ||||
\(580\) | 0 | 0 | ||||||||
\(581\) | 5.65685i | 0.234686i | ||||||||
\(582\) | 0 | 0 | ||||||||
\(583\) | − | 24.0000i | − | 0.993978i | ||||||
\(584\) | 0 | 0 | ||||||||
\(585\) | −16.0000 | − | 5.65685i | −0.661519 | − | 0.233882i | ||||
\(586\) | 0 | 0 | ||||||||
\(587\) | −14.1421 | −0.583708 | −0.291854 | − | 0.956463i | \(-0.594272\pi\) | ||||
−0.291854 | + | 0.956463i | \(0.594272\pi\) | |||||||
\(588\) | 0 | 0 | ||||||||
\(589\) | −12.0000 | −0.494451 | ||||||||
\(590\) | 0 | 0 | ||||||||
\(591\) | 19.7990 | + | 28.0000i | 0.814422 | + | 1.15177i | ||||
\(592\) | 0 | 0 | ||||||||
\(593\) | − | 33.9411i | − | 1.39379i | −0.717171 | − | 0.696897i | \(-0.754563\pi\) | ||
0.717171 | − | 0.696897i | \(-0.245437\pi\) | |||||||
\(594\) | 0 | 0 | ||||||||
\(595\) | 0 | 0 | ||||||||
\(596\) | 0 | 0 | ||||||||
\(597\) | 2.00000 | + | 2.82843i | 0.0818546 | + | 0.115760i | ||||
\(598\) | 0 | 0 | ||||||||
\(599\) | −39.5980 | −1.61793 | −0.808965 | − | 0.587857i | \(-0.799972\pi\) | ||||
−0.808965 | + | 0.587857i | \(0.799972\pi\) | |||||||
\(600\) | 0 | 0 | ||||||||
\(601\) | 10.0000 | 0.407909 | 0.203954 | − | 0.978980i | \(-0.434621\pi\) | ||||
0.203954 | + | 0.978980i | \(0.434621\pi\) | |||||||
\(602\) | 0 | 0 | ||||||||
\(603\) | −5.65685 | − | 2.00000i | −0.230365 | − | 0.0814463i | ||||
\(604\) | 0 | 0 | ||||||||
\(605\) | 8.48528i | 0.344976i | ||||||||
\(606\) | 0 | 0 | ||||||||
\(607\) | − | 14.0000i | − | 0.568242i | −0.958788 | − | 0.284121i | \(-0.908298\pi\) | ||
0.958788 | − | 0.284121i | \(-0.0917018\pi\) | |||||||
\(608\) | 0 | 0 | ||||||||
\(609\) | −8.00000 | + | 5.65685i | −0.324176 | + | 0.229227i | ||||
\(610\) | 0 | 0 | ||||||||
\(611\) | −22.6274 | −0.915407 | ||||||||
\(612\) | 0 | 0 | ||||||||
\(613\) | −6.00000 | −0.242338 | −0.121169 | − | 0.992632i | \(-0.538664\pi\) | ||||
−0.121169 | + | 0.992632i | \(0.538664\pi\) | |||||||
\(614\) | 0 | 0 | ||||||||
\(615\) | 22.6274 | − | 16.0000i | 0.912426 | − | 0.645182i | ||||
\(616\) | 0 | 0 | ||||||||
\(617\) | − | 28.2843i | − | 1.13868i | −0.822102 | − | 0.569341i | \(-0.807198\pi\) | ||
0.822102 | − | 0.569341i | \(-0.192802\pi\) | |||||||
\(618\) | 0 | 0 | ||||||||
\(619\) | − | 10.0000i | − | 0.401934i | −0.979598 | − | 0.200967i | \(-0.935592\pi\) | ||
0.979598 | − | 0.200967i | \(-0.0644084\pi\) | |||||||
\(620\) | 0 | 0 | ||||||||
\(621\) | −8.00000 | − | 28.2843i | −0.321029 | − | 1.13501i | ||||
\(622\) | 0 | 0 | ||||||||
\(623\) | 33.9411 | 1.35982 | ||||||||
\(624\) | 0 | 0 | ||||||||
\(625\) | −31.0000 | −1.24000 | ||||||||
\(626\) | 0 | 0 | ||||||||
\(627\) | −16.9706 | − | 24.0000i | −0.677739 | − | 0.958468i | ||||
\(628\) | 0 | 0 | ||||||||
\(629\) | 0 | 0 | ||||||||
\(630\) | 0 | 0 | ||||||||
\(631\) | − | 30.0000i | − | 1.19428i | −0.802137 | − | 0.597141i | \(-0.796303\pi\) | ||
0.802137 | − | 0.597141i | \(-0.203697\pi\) | |||||||
\(632\) | 0 | 0 | ||||||||
\(633\) | −2.00000 | − | 2.82843i | −0.0794929 | − | 0.112420i | ||||
\(634\) | 0 | 0 | ||||||||
\(635\) | 50.9117 | 2.02037 | ||||||||
\(636\) | 0 | 0 | ||||||||
\(637\) | 6.00000 | 0.237729 | ||||||||
\(638\) | 0 | 0 | ||||||||
\(639\) | −5.65685 | + | 16.0000i | −0.223782 | + | 0.632950i | ||||
\(640\) | 0 | 0 | ||||||||
\(641\) | 11.3137i | 0.446865i | 0.974719 | + | 0.223432i | \(0.0717262\pi\) | ||||
−0.974719 | + | 0.223432i | \(0.928274\pi\) | |||||||
\(642\) | 0 | 0 | ||||||||
\(643\) | − | 26.0000i | − | 1.02534i | −0.858586 | − | 0.512670i | \(-0.828656\pi\) | ||
0.858586 | − | 0.512670i | \(-0.171344\pi\) | |||||||
\(644\) | 0 | 0 | ||||||||
\(645\) | −8.00000 | + | 5.65685i | −0.315000 | + | 0.222738i | ||||
\(646\) | 0 | 0 | ||||||||
\(647\) | 16.9706 | 0.667182 | 0.333591 | − | 0.942718i | \(-0.391740\pi\) | ||||
0.333591 | + | 0.942718i | \(0.391740\pi\) | |||||||
\(648\) | 0 | 0 | ||||||||
\(649\) | 8.00000 | 0.314027 | ||||||||
\(650\) | 0 | 0 | ||||||||
\(651\) | −5.65685 | + | 4.00000i | −0.221710 | + | 0.156772i | ||||
\(652\) | 0 | 0 | ||||||||
\(653\) | 14.1421i | 0.553425i | 0.960953 | + | 0.276712i | \(0.0892449\pi\) | ||||
−0.960953 | + | 0.276712i | \(0.910755\pi\) | |||||||
\(654\) | 0 | 0 | ||||||||
\(655\) | 56.0000i | 2.18810i | ||||||||
\(656\) | 0 | 0 | ||||||||
\(657\) | −6.00000 | + | 16.9706i | −0.234082 | + | 0.662085i | ||||
\(658\) | 0 | 0 | ||||||||
\(659\) | 14.1421 | 0.550899 | 0.275450 | − | 0.961315i | \(-0.411173\pi\) | ||||
0.275450 | + | 0.961315i | \(0.411173\pi\) | |||||||
\(660\) | 0 | 0 | ||||||||
\(661\) | 10.0000 | 0.388955 | 0.194477 | − | 0.980907i | \(-0.437699\pi\) | ||||
0.194477 | + | 0.980907i | \(0.437699\pi\) | |||||||
\(662\) | 0 | 0 | ||||||||
\(663\) | 0 | 0 | ||||||||
\(664\) | 0 | 0 | ||||||||
\(665\) | 33.9411i | 1.31618i | ||||||||
\(666\) | 0 | 0 | ||||||||
\(667\) | 16.0000i | 0.619522i | ||||||||
\(668\) | 0 | 0 | ||||||||
\(669\) | 2.00000 | + | 2.82843i | 0.0773245 | + | 0.109353i | ||||
\(670\) | 0 | 0 | ||||||||
\(671\) | −5.65685 | −0.218380 | ||||||||
\(672\) | 0 | 0 | ||||||||
\(673\) | 10.0000 | 0.385472 | 0.192736 | − | 0.981251i | \(-0.438264\pi\) | ||||
0.192736 | + | 0.981251i | \(0.438264\pi\) | |||||||
\(674\) | 0 | 0 | ||||||||
\(675\) | 4.24264 | + | 15.0000i | 0.163299 | + | 0.577350i | ||||
\(676\) | 0 | 0 | ||||||||
\(677\) | − | 2.82843i | − | 0.108705i | −0.998522 | − | 0.0543526i | \(-0.982690\pi\) | ||
0.998522 | − | 0.0543526i | \(-0.0173095\pi\) | |||||||
\(678\) | 0 | 0 | ||||||||
\(679\) | 20.0000i | 0.767530i | ||||||||
\(680\) | 0 | 0 | ||||||||
\(681\) | 20.0000 | − | 14.1421i | 0.766402 | − | 0.541928i | ||||
\(682\) | 0 | 0 | ||||||||
\(683\) | 42.4264 | 1.62340 | 0.811701 | − | 0.584074i | \(-0.198542\pi\) | ||||
0.811701 | + | 0.584074i | \(0.198542\pi\) | |||||||
\(684\) | 0 | 0 | ||||||||
\(685\) | 16.0000 | 0.611329 | ||||||||
\(686\) | 0 | 0 | ||||||||
\(687\) | 14.1421 | − | 10.0000i | 0.539556 | − | 0.381524i | ||||
\(688\) | 0 | 0 | ||||||||
\(689\) | 16.9706i | 0.646527i | ||||||||
\(690\) | 0 | 0 | ||||||||
\(691\) | − | 26.0000i | − | 0.989087i | −0.869153 | − | 0.494543i | \(-0.835335\pi\) | ||
0.869153 | − | 0.494543i | \(-0.164665\pi\) | |||||||
\(692\) | 0 | 0 | ||||||||
\(693\) | −16.0000 | − | 5.65685i | −0.607790 | − | 0.214886i | ||||
\(694\) | 0 | 0 | ||||||||
\(695\) | −28.2843 | −1.07288 | ||||||||
\(696\) | 0 | 0 | ||||||||
\(697\) | 0 | 0 | ||||||||
\(698\) | 0 | 0 | ||||||||
\(699\) | −5.65685 | − | 8.00000i | −0.213962 | − | 0.302588i | ||||
\(700\) | 0 | 0 | ||||||||
\(701\) | 25.4558i | 0.961454i | 0.876870 | + | 0.480727i | \(0.159627\pi\) | ||||
−0.876870 | + | 0.480727i | \(0.840373\pi\) | |||||||
\(702\) | 0 | 0 | ||||||||
\(703\) | − | 36.0000i | − | 1.35777i | ||||||
\(704\) | 0 | 0 | ||||||||
\(705\) | 32.0000 | + | 45.2548i | 1.20519 | + | 1.70440i | ||||
\(706\) | 0 | 0 | ||||||||
\(707\) | 5.65685 | 0.212748 | ||||||||
\(708\) | 0 | 0 | ||||||||
\(709\) | −38.0000 | −1.42712 | −0.713560 | − | 0.700594i | \(-0.752918\pi\) | ||||
−0.713560 | + | 0.700594i | \(0.752918\pi\) | |||||||
\(710\) | 0 | 0 | ||||||||
\(711\) | −39.5980 | − | 14.0000i | −1.48504 | − | 0.525041i | ||||
\(712\) | 0 | 0 | ||||||||
\(713\) | 11.3137i | 0.423702i | ||||||||
\(714\) | 0 | 0 | ||||||||
\(715\) | 16.0000i | 0.598366i | ||||||||
\(716\) | 0 | 0 | ||||||||
\(717\) | −16.0000 | + | 11.3137i | −0.597531 | + | 0.422518i | ||||
\(718\) | 0 | 0 | ||||||||
\(719\) | 33.9411 | 1.26579 | 0.632895 | − | 0.774237i | \(-0.281866\pi\) | ||||
0.632895 | + | 0.774237i | \(0.281866\pi\) | |||||||
\(720\) | 0 | 0 | ||||||||
\(721\) | 28.0000 | 1.04277 | ||||||||
\(722\) | 0 | 0 | ||||||||
\(723\) | 2.82843 | − | 2.00000i | 0.105190 | − | 0.0743808i | ||||
\(724\) | 0 | 0 | ||||||||
\(725\) | − | 8.48528i | − | 0.315135i | ||||||
\(726\) | 0 | 0 | ||||||||
\(727\) | 34.0000i | 1.26099i | 0.776193 | + | 0.630495i | \(0.217148\pi\) | ||||
−0.776193 | + | 0.630495i | \(0.782852\pi\) | |||||||
\(728\) | 0 | 0 | ||||||||
\(729\) | −23.0000 | + | 14.1421i | −0.851852 | + | 0.523783i | ||||
\(730\) | 0 | 0 | ||||||||
\(731\) | 0 | 0 | ||||||||
\(732\) | 0 | 0 | ||||||||
\(733\) | −46.0000 | −1.69905 | −0.849524 | − | 0.527549i | \(-0.823111\pi\) | ||||
−0.849524 | + | 0.527549i | \(0.823111\pi\) | |||||||
\(734\) | 0 | 0 | ||||||||
\(735\) | −8.48528 | − | 12.0000i | −0.312984 | − | 0.442627i | ||||
\(736\) | 0 | 0 | ||||||||
\(737\) | 5.65685i | 0.208373i | ||||||||
\(738\) | 0 | 0 | ||||||||
\(739\) | − | 34.0000i | − | 1.25071i | −0.780340 | − | 0.625355i | \(-0.784954\pi\) | ||
0.780340 | − | 0.625355i | \(-0.215046\pi\) | |||||||
\(740\) | 0 | 0 | ||||||||
\(741\) | 12.0000 | + | 16.9706i | 0.440831 | + | 0.623429i | ||||
\(742\) | 0 | 0 | ||||||||
\(743\) | −5.65685 | −0.207530 | −0.103765 | − | 0.994602i | \(-0.533089\pi\) | ||||
−0.103765 | + | 0.994602i | \(0.533089\pi\) | |||||||
\(744\) | 0 | 0 | ||||||||
\(745\) | −40.0000 | −1.46549 | ||||||||
\(746\) | 0 | 0 | ||||||||
\(747\) | 2.82843 | − | 8.00000i | 0.103487 | − | 0.292705i | ||||
\(748\) | 0 | 0 | ||||||||
\(749\) | 16.9706i | 0.620091i | ||||||||
\(750\) | 0 | 0 | ||||||||
\(751\) | 34.0000i | 1.24068i | 0.784334 | + | 0.620339i | \(0.213005\pi\) | ||||
−0.784334 | + | 0.620339i | \(0.786995\pi\) | |||||||
\(752\) | 0 | 0 | ||||||||
\(753\) | 12.0000 | − | 8.48528i | 0.437304 | − | 0.309221i | ||||
\(754\) | 0 | 0 | ||||||||
\(755\) | −39.5980 | −1.44112 | ||||||||
\(756\) | 0 | 0 | ||||||||
\(757\) | −38.0000 | −1.38113 | −0.690567 | − | 0.723269i | \(-0.742639\pi\) | ||||
−0.690567 | + | 0.723269i | \(0.742639\pi\) | |||||||
\(758\) | 0 | 0 | ||||||||
\(759\) | −22.6274 | + | 16.0000i | −0.821323 | + | 0.580763i | ||||
\(760\) | 0 | 0 | ||||||||
\(761\) | − | 28.2843i | − | 1.02530i | −0.858596 | − | 0.512652i | \(-0.828663\pi\) | ||
0.858596 | − | 0.512652i | \(-0.171337\pi\) | |||||||
\(762\) | 0 | 0 | ||||||||
\(763\) | 36.0000i | 1.30329i | ||||||||
\(764\) | 0 | 0 | ||||||||
\(765\) | 0 | 0 | ||||||||
\(766\) | 0 | 0 | ||||||||
\(767\) | −5.65685 | −0.204257 | ||||||||
\(768\) | 0 | 0 | ||||||||
\(769\) | −46.0000 | −1.65880 | −0.829401 | − | 0.558653i | \(-0.811318\pi\) | ||||
−0.829401 | + | 0.558653i | \(0.811318\pi\) | |||||||
\(770\) | 0 | 0 | ||||||||
\(771\) | −22.6274 | − | 32.0000i | −0.814907 | − | 1.15245i | ||||
\(772\) | 0 | 0 | ||||||||
\(773\) | − | 25.4558i | − | 0.915583i | −0.889060 | − | 0.457792i | \(-0.848641\pi\) | ||
0.889060 | − | 0.457792i | \(-0.151359\pi\) | |||||||
\(774\) | 0 | 0 | ||||||||
\(775\) | − | 6.00000i | − | 0.215526i | ||||||
\(776\) | 0 | 0 | ||||||||
\(777\) | −12.0000 | − | 16.9706i | −0.430498 | − | 0.608816i | ||||
\(778\) | 0 | 0 | ||||||||
\(779\) | −33.9411 | −1.21607 | ||||||||
\(780\) | 0 | 0 | ||||||||
\(781\) | 16.0000 | 0.572525 | ||||||||
\(782\) | 0 | 0 | ||||||||
\(783\) | 14.1421 | − | 4.00000i | 0.505399 | − | 0.142948i | ||||
\(784\) | 0 | 0 | ||||||||
\(785\) | 39.5980i | 1.41331i | ||||||||
\(786\) | 0 | 0 | ||||||||
\(787\) | 38.0000i | 1.35455i | 0.735728 | + | 0.677277i | \(0.236840\pi\) | ||||
−0.735728 | + | 0.677277i | \(0.763160\pi\) | |||||||
\(788\) | 0 | 0 | ||||||||
\(789\) | −8.00000 | + | 5.65685i | −0.284808 | + | 0.201389i | ||||
\(790\) | 0 | 0 | ||||||||
\(791\) | −22.6274 | −0.804538 | ||||||||
\(792\) | 0 | 0 | ||||||||
\(793\) | 4.00000 | 0.142044 | ||||||||
\(794\) | 0 | 0 | ||||||||
\(795\) | 33.9411 | − | 24.0000i | 1.20377 | − | 0.851192i | ||||
\(796\) | 0 | 0 | ||||||||
\(797\) | 2.82843i | 0.100188i | 0.998745 | + | 0.0500940i | \(0.0159521\pi\) | ||||
−0.998745 | + | 0.0500940i | \(0.984048\pi\) | |||||||
\(798\) | 0 | 0 | ||||||||
\(799\) | 0 | 0 | ||||||||
\(800\) | 0 | 0 | ||||||||
\(801\) | −48.0000 | − | 16.9706i | −1.69600 | − | 0.599625i | ||||
\(802\) | 0 | 0 | ||||||||
\(803\) | 16.9706 | 0.598878 | ||||||||
\(804\) | 0 | 0 | ||||||||
\(805\) | 32.0000 | 1.12785 | ||||||||
\(806\) | 0 | 0 | ||||||||
\(807\) | −8.48528 | − | 12.0000i | −0.298696 | − | 0.422420i | ||||
\(808\) | 0 | 0 | ||||||||
\(809\) | 50.9117i | 1.78996i | 0.446107 | + | 0.894980i | \(0.352810\pi\) | ||||
−0.446107 | + | 0.894980i | \(0.647190\pi\) | |||||||
\(810\) | 0 | 0 | ||||||||
\(811\) | 30.0000i | 1.05344i | 0.850038 | + | 0.526721i | \(0.176579\pi\) | ||||
−0.850038 | + | 0.526721i | \(0.823421\pi\) | |||||||
\(812\) | 0 | 0 | ||||||||
\(813\) | 18.0000 | + | 25.4558i | 0.631288 | + | 0.892775i | ||||
\(814\) | 0 | 0 | ||||||||
\(815\) | 16.9706 | 0.594453 | ||||||||
\(816\) | 0 | 0 | ||||||||
\(817\) | 12.0000 | 0.419827 | ||||||||
\(818\) | 0 | 0 | ||||||||
\(819\) | 11.3137 | + | 4.00000i | 0.395333 | + | 0.139771i | ||||
\(820\) | 0 | 0 | ||||||||
\(821\) | − | 14.1421i | − | 0.493564i | −0.969071 | − | 0.246782i | \(-0.920627\pi\) | ||
0.969071 | − | 0.246782i | \(-0.0793731\pi\) | |||||||
\(822\) | 0 | 0 | ||||||||
\(823\) | 2.00000i | 0.0697156i | 0.999392 | + | 0.0348578i | \(0.0110978\pi\) | ||||
−0.999392 | + | 0.0348578i | \(0.988902\pi\) | |||||||
\(824\) | 0 | 0 | ||||||||
\(825\) | 12.0000 | − | 8.48528i | 0.417786 | − | 0.295420i | ||||
\(826\) | 0 | 0 | ||||||||
\(827\) | −25.4558 | −0.885186 | −0.442593 | − | 0.896723i | \(-0.645941\pi\) | ||||
−0.442593 | + | 0.896723i | \(0.645941\pi\) | |||||||
\(828\) | 0 | 0 | ||||||||
\(829\) | 18.0000 | 0.625166 | 0.312583 | − | 0.949890i | \(-0.398806\pi\) | ||||
0.312583 | + | 0.949890i | \(0.398806\pi\) | |||||||
\(830\) | 0 | 0 | ||||||||
\(831\) | 14.1421 | − | 10.0000i | 0.490585 | − | 0.346896i | ||||
\(832\) | 0 | 0 | ||||||||
\(833\) | 0 | 0 | ||||||||
\(834\) | 0 | 0 | ||||||||
\(835\) | 16.0000i | 0.553703i | ||||||||
\(836\) | 0 | 0 | ||||||||
\(837\) | 10.0000 | − | 2.82843i | 0.345651 | − | 0.0977647i | ||||
\(838\) | 0 | 0 | ||||||||
\(839\) | 39.5980 | 1.36707 | 0.683537 | − | 0.729916i | \(-0.260441\pi\) | ||||
0.683537 | + | 0.729916i | \(0.260441\pi\) | |||||||
\(840\) | 0 | 0 | ||||||||
\(841\) | 21.0000 | 0.724138 | ||||||||
\(842\) | 0 | 0 | ||||||||
\(843\) | 5.65685 | + | 8.00000i | 0.194832 | + | 0.275535i | ||||
\(844\) | 0 | 0 | ||||||||
\(845\) | 25.4558i | 0.875708i | ||||||||
\(846\) | 0 | 0 | ||||||||
\(847\) | − | 6.00000i | − | 0.206162i | ||||||
\(848\) | 0 | 0 | ||||||||
\(849\) | −10.0000 | − | 14.1421i | −0.343199 | − | 0.485357i | ||||
\(850\) | 0 | 0 | ||||||||
\(851\) | −33.9411 | −1.16349 | ||||||||
\(852\) | 0 | 0 | ||||||||
\(853\) | 26.0000 | 0.890223 | 0.445112 | − | 0.895475i | \(-0.353164\pi\) | ||||
0.445112 | + | 0.895475i | \(0.353164\pi\) | |||||||
\(854\) | 0 | 0 | ||||||||
\(855\) | 16.9706 | − | 48.0000i | 0.580381 | − | 1.64157i | ||||
\(856\) | 0 | 0 | ||||||||
\(857\) | − | 28.2843i | − | 0.966172i | −0.875573 | − | 0.483086i | \(-0.839516\pi\) | ||
0.875573 | − | 0.483086i | \(-0.160484\pi\) | |||||||
\(858\) | 0 | 0 | ||||||||
\(859\) | − | 2.00000i | − | 0.0682391i | −0.999418 | − | 0.0341196i | \(-0.989137\pi\) | ||
0.999418 | − | 0.0341196i | \(-0.0108627\pi\) | |||||||
\(860\) | 0 | 0 | ||||||||
\(861\) | −16.0000 | + | 11.3137i | −0.545279 | + | 0.385570i | ||||
\(862\) | 0 | 0 | ||||||||
\(863\) | 0 | 0 | − | 1.00000i | \(-0.5\pi\) | |||||
1.00000i | \(0.5\pi\) | |||||||||
\(864\) | 0 | 0 | ||||||||
\(865\) | 40.0000 | 1.36004 | ||||||||
\(866\) | 0 | 0 | ||||||||
\(867\) | 24.0416 | − | 17.0000i | 0.816497 | − | 0.577350i | ||||
\(868\) | 0 | 0 | ||||||||
\(869\) | 39.5980i | 1.34327i | ||||||||
\(870\) | 0 | 0 | ||||||||
\(871\) | − | 4.00000i | − | 0.135535i | ||||||
\(872\) | 0 | 0 | ||||||||
\(873\) | 10.0000 | − | 28.2843i | 0.338449 | − | 0.957278i | ||||
\(874\) | 0 | 0 | ||||||||
\(875\) | 11.3137 | 0.382473 | ||||||||
\(876\) | 0 | 0 | ||||||||
\(877\) | 2.00000 | 0.0675352 | 0.0337676 | − | 0.999430i | \(-0.489249\pi\) | ||||
0.0337676 | + | 0.999430i | \(0.489249\pi\) | |||||||
\(878\) | 0 | 0 | ||||||||
\(879\) | −2.82843 | − | 4.00000i | −0.0954005 | − | 0.134917i | ||||
\(880\) | 0 | 0 | ||||||||
\(881\) | − | 33.9411i | − | 1.14351i | −0.820426 | − | 0.571753i | \(-0.806264\pi\) | ||
0.820426 | − | 0.571753i | \(-0.193736\pi\) | |||||||
\(882\) | 0 | 0 | ||||||||
\(883\) | 6.00000i | 0.201916i | 0.994891 | + | 0.100958i | \(0.0321908\pi\) | ||||
−0.994891 | + | 0.100958i | \(0.967809\pi\) | |||||||
\(884\) | 0 | 0 | ||||||||
\(885\) | 8.00000 | + | 11.3137i | 0.268917 | + | 0.380306i | ||||
\(886\) | 0 | 0 | ||||||||
\(887\) | 5.65685 | 0.189939 | 0.0949693 | − | 0.995480i | \(-0.469725\pi\) | ||||
0.0949693 | + | 0.995480i | \(0.469725\pi\) | |||||||
\(888\) | 0 | 0 | ||||||||
\(889\) | −36.0000 | −1.20740 | ||||||||
\(890\) | 0 | 0 | ||||||||
\(891\) | 19.7990 | + | 16.0000i | 0.663291 | + | 0.536020i | ||||
\(892\) | 0 | 0 | ||||||||
\(893\) | − | 67.8823i | − | 2.27159i | ||||||
\(894\) | 0 | 0 | ||||||||
\(895\) | 24.0000i | 0.802232i | ||||||||
\(896\) | 0 | 0 | ||||||||
\(897\) | 16.0000 | − | 11.3137i | 0.534224 | − | 0.377754i | ||||
\(898\) | 0 | 0 | ||||||||
\(899\) | −5.65685 | −0.188667 | ||||||||
\(900\) | 0 | 0 | ||||||||
\(901\) | 0 | 0 | ||||||||
\(902\) | 0 | 0 | ||||||||
\(903\) | 5.65685 | − | 4.00000i | 0.188248 | − | 0.133112i | ||||
\(904\) | 0 | 0 | ||||||||
\(905\) | 16.9706i | 0.564121i | ||||||||
\(906\) | 0 | 0 | ||||||||
\(907\) | − | 2.00000i | − | 0.0664089i | −0.999449 | − | 0.0332045i | \(-0.989429\pi\) | ||
0.999449 | − | 0.0332045i | \(-0.0105712\pi\) | |||||||
\(908\) | 0 | 0 | ||||||||
\(909\) | −8.00000 | − | 2.82843i | −0.265343 | − | 0.0938130i | ||||
\(910\) | 0 | 0 | ||||||||
\(911\) | 11.3137 | 0.374840 | 0.187420 | − | 0.982280i | \(-0.439987\pi\) | ||||
0.187420 | + | 0.982280i | \(0.439987\pi\) | |||||||
\(912\) | 0 | 0 | ||||||||
\(913\) | −8.00000 | −0.264761 | ||||||||
\(914\) | 0 | 0 | ||||||||
\(915\) | −5.65685 | − | 8.00000i | −0.187010 | − | 0.264472i | ||||
\(916\) | 0 | 0 | ||||||||
\(917\) | − | 39.5980i | − | 1.30764i | ||||||
\(918\) | 0 | 0 | ||||||||
\(919\) | − | 30.0000i | − | 0.989609i | −0.869004 | − | 0.494804i | \(-0.835240\pi\) | ||
0.869004 | − | 0.494804i | \(-0.164760\pi\) | |||||||
\(920\) | 0 | 0 | ||||||||
\(921\) | 30.0000 | + | 42.4264i | 0.988534 | + | 1.39800i | ||||
\(922\) | 0 | 0 | ||||||||
\(923\) | −11.3137 | −0.372395 | ||||||||
\(924\) | 0 | 0 | ||||||||
\(925\) | 18.0000 | 0.591836 | ||||||||
\(926\) | 0 | 0 | ||||||||
\(927\) | −39.5980 | − | 14.0000i | −1.30057 | − | 0.459820i | ||||
\(928\) | 0 | 0 | ||||||||
\(929\) | − | 11.3137i | − | 0.371191i | −0.982626 | − | 0.185595i | \(-0.940579\pi\) | ||
0.982626 | − | 0.185595i | \(-0.0594214\pi\) | |||||||
\(930\) | 0 | 0 | ||||||||
\(931\) | 18.0000i | 0.589926i | ||||||||
\(932\) | 0 | 0 | ||||||||
\(933\) | 8.00000 | − | 5.65685i | 0.261908 | − | 0.185197i | ||||
\(934\) | 0 | 0 | ||||||||
\(935\) | 0 | 0 | ||||||||
\(936\) | 0 | 0 | ||||||||
\(937\) | −30.0000 | −0.980057 | −0.490029 | − | 0.871706i | \(-0.663014\pi\) | ||||
−0.490029 | + | 0.871706i | \(0.663014\pi\) | |||||||
\(938\) | 0 | 0 | ||||||||
\(939\) | 2.82843 | − | 2.00000i | 0.0923022 | − | 0.0652675i | ||||
\(940\) | 0 | 0 | ||||||||
\(941\) | − | 53.7401i | − | 1.75188i | −0.482422 | − | 0.875939i | \(-0.660243\pi\) | ||
0.482422 | − | 0.875939i | \(-0.339757\pi\) | |||||||
\(942\) | 0 | 0 | ||||||||
\(943\) | 32.0000i | 1.04206i | ||||||||
\(944\) | 0 | 0 | ||||||||
\(945\) | −8.00000 | − | 28.2843i | −0.260240 | − | 0.920087i | ||||
\(946\) | 0 | 0 | ||||||||
\(947\) | 14.1421 | 0.459558 | 0.229779 | − | 0.973243i | \(-0.426200\pi\) | ||||
0.229779 | + | 0.973243i | \(0.426200\pi\) | |||||||
\(948\) | 0 | 0 | ||||||||
\(949\) | −12.0000 | −0.389536 | ||||||||
\(950\) | 0 | 0 | ||||||||
\(951\) | 2.82843 | + | 4.00000i | 0.0917180 | + | 0.129709i | ||||
\(952\) | 0 | 0 | ||||||||
\(953\) | − | 50.9117i | − | 1.64919i | −0.565723 | − | 0.824596i | \(-0.691403\pi\) | ||
0.565723 | − | 0.824596i | \(-0.308597\pi\) | |||||||
\(954\) | 0 | 0 | ||||||||
\(955\) | − | 64.0000i | − | 2.07099i | ||||||
\(956\) | 0 | 0 | ||||||||
\(957\) | −8.00000 | − | 11.3137i | −0.258603 | − | 0.365720i | ||||
\(958\) | 0 | 0 | ||||||||
\(959\) | −11.3137 | −0.365339 | ||||||||
\(960\) | 0 | 0 | ||||||||
\(961\) | 27.0000 | 0.870968 | ||||||||
\(962\) | 0 | 0 | ||||||||
\(963\) | 8.48528 | − | 24.0000i | 0.273434 | − | 0.773389i | ||||
\(964\) | 0 | 0 | ||||||||
\(965\) | 39.5980i | 1.27470i | ||||||||
\(966\) | 0 | 0 | ||||||||
\(967\) | 50.0000i | 1.60789i | 0.594703 | + | 0.803946i | \(0.297270\pi\) | ||||
−0.594703 | + | 0.803946i | \(0.702730\pi\) | |||||||
\(968\) | 0 | 0 | ||||||||
\(969\) | 0 | 0 | ||||||||
\(970\) | 0 | 0 | ||||||||
\(971\) | 19.7990 | 0.635380 | 0.317690 | − | 0.948195i | \(-0.397093\pi\) | ||||
0.317690 | + | 0.948195i | \(0.397093\pi\) | |||||||
\(972\) | 0 | 0 | ||||||||
\(973\) | 20.0000 | 0.641171 | ||||||||
\(974\) | 0 | 0 | ||||||||
\(975\) | −8.48528 | + | 6.00000i | −0.271746 | + | 0.192154i | ||||
\(976\) | 0 | 0 | ||||||||
\(977\) | 45.2548i | 1.44783i | 0.689889 | + | 0.723915i | \(0.257659\pi\) | ||||
−0.689889 | + | 0.723915i | \(0.742341\pi\) | |||||||
\(978\) | 0 | 0 | ||||||||
\(979\) | 48.0000i | 1.53409i | ||||||||
\(980\) | 0 | 0 | ||||||||
\(981\) | 18.0000 | − | 50.9117i | 0.574696 | − | 1.62549i | ||||
\(982\) | 0 | 0 | ||||||||
\(983\) | 28.2843 | 0.902128 | 0.451064 | − | 0.892492i | \(-0.351045\pi\) | ||||
0.451064 | + | 0.892492i | \(0.351045\pi\) | |||||||
\(984\) | 0 | 0 | ||||||||
\(985\) | 56.0000 | 1.78431 | ||||||||
\(986\) | 0 | 0 | ||||||||
\(987\) | −22.6274 | − | 32.0000i | −0.720239 | − | 1.01857i | ||||
\(988\) | 0 | 0 | ||||||||
\(989\) | − | 11.3137i | − | 0.359755i | ||||||
\(990\) | 0 | 0 | ||||||||
\(991\) | 18.0000i | 0.571789i | 0.958261 | + | 0.285894i | \(0.0922907\pi\) | ||||
−0.958261 | + | 0.285894i | \(0.907709\pi\) | |||||||
\(992\) | 0 | 0 | ||||||||
\(993\) | −10.0000 | − | 14.1421i | −0.317340 | − | 0.448787i | ||||
\(994\) | 0 | 0 | ||||||||
\(995\) | 5.65685 | 0.179334 | ||||||||
\(996\) | 0 | 0 | ||||||||
\(997\) | −38.0000 | −1.20347 | −0.601736 | − | 0.798695i | \(-0.705524\pi\) | ||||
−0.601736 | + | 0.798695i | \(0.705524\pi\) | |||||||
\(998\) | 0 | 0 | ||||||||
\(999\) | 8.48528 | + | 30.0000i | 0.268462 | + | 0.949158i |
(See \(a_n\) instead)
(See \(a_n\) instead)
(See \(a_n\) instead)
(See only \(a_p\))
(See only \(a_p\))
(See only \(a_p\))